Given cos=
a.
b.
sin 8
4
and csc <0, find sine and tan
9
-4
9
A
B
tan =
csc0= 4√√9, tane=
9
4
65
9
C.
d.
sin = 4, tan 9 =
sin =
Please select the best answer from the choices provided
65
19
-4√65
9
tan 9 =
The best answer that matches the calculated values is C. sin θ = -1/3, tan θ = -3/(2√2)
Let's break down the given values and find the values of sine and tangent.
We are given:
cos θ = √(8/9)
csc θ < 0
Using the Pythagorean identity, sin^2θ + cos^2θ = 1, we can find the value of sin θ.
sin^2θ + (√(8/9))^2 = 1
sin^2θ + 8/9 = 1
sin^2θ = 1 - 8/9
sin^2θ = 1/9
Taking the square root of both sides, we get:
sin θ = ±1/3
Since csc θ is negative (csc θ < 0), we can conclude that sin θ is negative. Therefore, sin θ = -1/3.
Next, let's find the value of tan θ.
tan θ = sin θ / cos θ
tan θ = (-1/3) / (√(8/9))
tan θ = -√9/√8
tan θ = -√9/√(4*2)
tan θ = -√9/(2√2)
tan θ = -3/(2√2)
So, the values are:
sin θ = -1/3
tan θ = -3/(2√2)
The best selection from the available options that matches the calculated values is:
C. sin θ = -1/3, tan θ = -3/(2√2)
for such more question on tangent
https://brainly.com/question/19132778
#SPJ8
Answer if the following statement is true of false. *
1.X=X?
True
O False
The statement is:
O True
Work/explanation:
The following statement is true, because 1x is indeed the same thing as x. So when combining like terms, 2x + x is the same thing as 2x + 1x, which evaluates to 3x.
Therefore this is the answer.determine the surface area and volume
Answer:
surface area=214cm2, volume=183 cm3
Step-by-step explanation:
slanted height=√5^2+7^2 (Pythagoras theorem)
= √74
area of bottom part=π(5)^2
=25π
area of top cone part=π(5)(√74)
surface area of cone=25π+π(5)(√74)
=214 cm2(to 3 s.f.)
volume of cone=1/3π(5)^2×7
=183 cm3(to 3 s.f.)
what is the value of [3]\[n]{x}[/64}
Answer:
all go d Alaska causticC field lap cc feels it works happy claps dockside all letter or quip all L do all app all app all app all do all app all app all app all app 10 10 all do all app all app so we rip so do all
Step-by-step explanation:
w usually app all app all do all app so all rip so we rip do all do all app all do all do all do all do all rip trip we rip all app so all do all do all app all do all app all yep all app all app all app all app all app all app all app to
Antiderivative with the equation
The antiderivative of the function is f(x) = 2x + 5x³ + 2x⁶ - 9.
Find an antiderivative of f(x)To find an antiderivative of f(x), we can integrate each term of f'(x) individually.
Given:
f'(x) = 2 + 15x² + 12x⁵
To integrate 2, we get:
∫2 dx = 2x + C₁, where C₁ is the constant of integration.
To integrate 15x², we get:
∫15x² dx = 5x³ + C₂, where C₂ is another constant of integration.
To integrate 12x⁵, we get:
∫12x⁵ dx = 2x⁶ + C₃, where C₃ is another constant of integration.
Putting it all together, the antiderivative of f(x) is:
f(x) = 2x + 5x³ + 2x⁶ + C,
where C = C₁ + C₂ + C₃ represents the constant of integration.
To find the specific value of C, we are given that f(1) = 0. Substituting x = 1 into the antiderivative equation:
0 = 2(1) + 5(1)³ + 2(1)⁶ + C,
0 = 2 + 5 + 2 + C,
0 = 9 + C.
Therefore, C = -9.
The final expression for f(x) is:
f(x) = 2x + 5x³ + 2x⁶ - 9.
Learn more on antiderivative of function here;
https://brainly.com/question/12956882
#SPJ1
A 18-foot ladder leaning against a building forms an 22angle with the side of the building How far is the base of the ladder from the base of the building?
Answer:
Using the sine function, we have:
sin(angle) = opposite / hypotenuse
sin(22 degrees) = opposite / 18 feet
We can rearrange this equation to solve for the opposite side (height of the building):
opposite = sin(22 degrees) * 18 feet
Calculating this:
opposite ≈ 6.24 feet
Therefore, the base of the ladder from the base of the building is approximately 6.24 feet.
What is the most likely reason that Sora lists the
activities of customers going through self-checkout?
to prove the claim that customers are trained
enough to get paid for self-checkout
2
O to prove the claim that self-checkout is difficult
O to prove the claim that cashiers' duties are as simple
as self-checkout routines
O to prove the claim that self-checkout is eliminating
jobs
The most likely reason that Sora lists the activities of customers going through self-checkout is to prove the claim that self-checkout is eliminating jobs.
By observing and documenting the activities of customers using self-checkout, Sora may be gathering evidence to support the argument that self-checkout systems are replacing the need for human cashiers and leading to job loss in the retail industry.
By highlighting the tasks that customers can now perform independently, Sora may be emphasizing the efficiency and convenience of self-checkout systems, which can potentially lead to the reduction of cashier positions.
It's important to note that without more context, we cannot definitively determine Sora's exact intentions or motivations. However, based on the given options and the mention of activities related to self-checkout, the claim that self-checkout is eliminating jobs appears to be the most plausible reason for listing the activities of customers going through self-checkout.
For such more question on customers:
https://brainly.com/question/14651262
#SPJ8
Cameron sorts 56 books into groups of 5, but has some books left over
How many books are left over?
Cameron has 1 book left over after sorting it into group of 5
To determine the number of book left,
we need to first divide 56 by 5 [56 ÷ 5]
Quotient = 11
then find the remainder which is 1
therefore there os only 1 book left over
To know more about Word Problems refer to this link
https://brainly.com/question/28128441
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.
To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.
The loan amount can be calculated by subtracting the down payment from the property value:
Loan amount = Property value - Down payment
= $170,000 - $20,000
= $150,000
Now we can calculate the LTV ratio:
LTV ratio = Loan amount / Property value * 100
= $150,000 / $170,000 * 100
= 88.24%
Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.
To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:
PMI payment = (Loan amount * PMI rate) / 12
= ($150,000 * 0.30%) / 12
= $450 / 12
= $37.50
For more such questions on Payment,click on
https://brainly.com/question/25793394
#SPJ8
The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.
Use the table to find her monthly PMI payment
Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.
30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%
15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.
A. $51.25
B. $37.50
C. $23.75
D. $42.50
What is the probability that you will be in district 12 with Katniss & Peeta?
Answer:
0
Step-by-step explanation:
theres only 2 people each district
For two invertible n by n matrices A, B,
where rank(A)=rank(B)=n,
is the following always true?
"rank(AB) = n"
If so,
I wonder how we can prove it.
If not,
I'd appreciate you if you show me a counterexample.
Thank you in advance.
The statement "rank(AB) = n" is not always true for invertible n by n matrices A and B with rank(A) = rank(B) = n.
Counterexample:
Consider the following counterexample:
[tex]A = \begin{bmatrix} 1 & 0 \ 0 & 1 \end{bmatrix}\\B = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]
Both matrices A and B are invertible, as they are both identity matrices. However, when we multiply them together, we get:
[tex]AB = \begin{bmatrix} 1 & 0 \ 0 & 0 \end{bmatrix}[/tex]
The rank of AB is 1, not n. In this case, n = 2, but rank(AB) = 1. Therefore, the statement "rank(AB) = n" is not always true for all invertible n by n matrices A and B with rank(A) = rank(B) = n.
In general, the rank of the product AB is less than or equal to the minimum of the ranks of A and B. So, in order for rank(AB) to be equal to n, both A and B need to have rank n individually, but that does not guarantee the rank of their product to be n as well.
For more such questions on matrices
https://brainly.com/question/29223307
#SPJ8
WILL GIVE 100 points A deli wraps its cylindrical containers of hot food items with plastic wrap. The containers have a diameter of 3.5 inches and a height of 4 inches. What is the minimum amount of plastic wrap needed to completely wrap 6 containers? Round your answer to the nearest tenth and approximate using π = 3.14.
44.0 in2
63.2 in2
379.2 in2
505.5 in2
Answer:
379.2 in^2
Step-by-step explanation:
Each cylinder's side area is pi *d * h = 43.98 in^2
you need six : =263.89 in^2
each ned of the cylinder area = pi r^2 = 9.621 in^2
and you have 12 ends for 115.45 in^2
For total : 379.3 in^2 (slight difference due to the value of pi used and rounding)
NO LINKS!! URGENT HELP PLEASE!!
21. Determine whether CD || AB. Explain your reasoning.
Reason:
If CD was parallel to AB, then triangles CDE and ABE would be similar. In turn it would mean that EA/EC = EB/ED is a true proportion.
Let's calculate each side separately.
EA/EC = 28/(28+20) = 0.5833EB/ED = 16/(16+10) = 0.6154Both decimal values are approximate.
The two values don't match up which makes EA/EC = EB/ED to be false.
Since EA/EC = EB/ED is false, we know that triangles CDE and ABE are not similar. Therefore, CD is not parallel to AB.
Answer:
CD is not parallel to AB
Step-by-step explanation:
According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.
Therefore, if CD is parallel to AB, then EA : AC = EB : BD.
Substitute the values of the line segments into the equation:
[tex]\begin{aligned}EA : AC &= EB : BD\\\\28:20&=16:10\\\\\dfrac{28}{20}&=\dfrac{16}{10}\\\\1.4 &\neq 1.6\end{aligned}[/tex]
As 1.4 does not equal 1.6, then CD is not parallel to AB.
how to distribute 3(2+3x)
Answer: 6+9x or 9x + 6
Step-by-step explanation:
Multiply 3 by each of the numbers inside the parentheses
The answer is:
6 + 9xWork/explanation:
To simplify this expression, we will use the distributive property:
[tex]\sf{3(2+3x)}[/tex]
Distribute the 3:
[tex]\sf{3\cdot2+3\cdot3x}[/tex]
Simplify
[tex]\sf{6+9x}[/tex]
Therefore, the answer is 6 + 9x.PLEASEEEE HELP I GIVE YOU 100 POINTS
The missing dimensions from the given expression should be completed with the following:
(81.) A) 2
(82.) AD) x
(83.) E) 12
The expression as a product should be written as: DE) 2(x + 12).
What is a factored form?In Mathematics and Geometry, a factored form simply refers to a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.
In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;
x 12
2 2x 24
Note: 2x/2 = x.
24/2 = 12.
Next, we would write the expression 2x + 24 as a product as follows;
(2x + 24) = 2(x + 12).
Read more on factored form here: brainly.com/question/30285637
#SPJ1
Please help!!
The graph of function is shown
Function g is represented by the table
-1
X
9(x)
24
0
4
1
0
2
3
-#
Which statement correctly compares the two functions?
OA They have the same x-intercept and the same end behavior as x approaches
OB. They have the same
and y-intercepts
OC. They have different
and y intercepts but the same end behavior as x approaches
OD. They have the same y-intercept and the same end behavior as x approaches
Best
The x- and y-intercept values in the graph for the function f and in the table for the function g(x), indicates that the correct option is option C
C. The have different x- and y-intercepts but the same end behavior as x approaches ∞What are the x- and y-intercept of a graph of a function?The x-intercept is the point at which the y-value is 0, and the coordinates of the point is specified as the x-intercept.
The x-intercept is the point at which the x-value is 0, and the coordinates of the point is specified as the y-intercept
The question compares the x- and y-intercepts of the graph and the function in the table
The x-intercept of the function f in the graph are; (0, 3)
The y-intercept of the function f in the graph are; (4, 0)
The function g(x) in the table indicates that the x- and y-intercepts are;
The value of g(x) is 0 at the ordered pair (1, 0), therefore, the x-intercept of g(x) is (1, 0)
The value of x is 0 at the ordered pair (0, 4), therefore, the function, g(x) has a y-intercept at the point (0, 4)
Therefore, the function f and g have different intercepts, but the value in the table and the graph indicates that as x approaches infinity, the y-value, approaches -1, the correct option is therefore, option C
Learn more on the x- and y-intercept of a graph here: https://brainly.com/question/29252186
#SPJ1
100 POINTS Use the drawing tool(s) to form the correct answer on the provided graph.
Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry for the function below.
The x-intercepts, y-intercept, vertex, and axis of symmetry for the given function g(x) = x² + 4x + 3 have been plotted on the graph below.
What is the graph of a quadratic function?In Mathematics and Geometry, the graph of a quadratic function would always form a parabolic curve because it is a u-shaped. Based on the given quadratic function, we can logically deduce that the graph would be a upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero (0).
Since the leading coefficient (value of a) in the given quadratic function g(x) = x² + 4x + 3 is positive 1, we can logically deduce that the parabola would open upward and the x-intercept (roots) is given by the ordered pair (-3, 0) and (-1, 0).
In conclusion, the vertex is given by the ordered pair (-2, -1) and the minimum value is -1.
Read more on quadratic functions here: brainly.com/question/29499209
#SPJ1
Answer:
x-intercepts = (-3, 0) and (-1, 0)
y-intercept = (0, 3)
Vertex = (-2, -1)
Axis of symmetry: x = -2
Step-by-step explanation:
Given quadratic function:
[tex]g(x) = x^2 + 4x + 3[/tex]
[tex]\hrulefill[/tex]
x-interceptsTo find the x-intercepts of the given function g(x), set g(x) equal to zero and solve for x.
Set g(x) = 0:
[tex]x^2 + 4x + 3 = 0[/tex]
Factor the quadratic equation:
[tex]x^2+x+3x+3=0[/tex]
[tex]x(x+1)+3(x+1)=0[/tex]
[tex](x + 3)(x + 1) = 0[/tex]
Set each factor equal to zero and solve for x:
[tex]x + 3 = 0 \implies x = -3[/tex]
[tex]x + 1 = 0 \implies x = -1[/tex]
Therefore, the x-intercepts are at (-3, 0) and (-1, 0).
[tex]\hrulefill[/tex]
y-interceptTo find the y-intercept of g(x), substitute x = 0 and solve for y.
[tex]\begin{aligned}x=0 \implies y&= (0)^2 + 4(0) + 3\\y& = 0 + 0 + 3 \\y&= 3\end{aligned}[/tex]
Therefore, the y-intercept is at (0, 3).
[tex]\hrulefill[/tex]
VertexThe x-value of the vertex of a parabola in the form y = ax² + bx + c is x = -b/2a.
For the function g(x), a = 1, and b = 4.
Therefore, the x-coordinate of the vertex is:
[tex]\textsf{$x$-coordinate of vertex} = \dfrac{-b}{2a} = \dfrac{-4}{2(1)} = -2[/tex]
To find the y-coordinate of the vertex, substitute x = -2 into function g(x):
[tex]\begin{aligned}x=-2 \implies y &= (-2)^2 + 4(-2) + 3\\y& = 4-8 + 3 \\y&= -1\end{aligned}[/tex]
Therefore, the vertex is at (-2, -1).
[tex]\hrulefill[/tex]
Axis of symmetryThe axis of symmetry of a vertical parabola is the x-coordinate of its vertex.
As the x-coordinate of the vertex is -2, the axis of symmetry is x = -2.
[tex]\hrulefill[/tex]
SummaryThe x-intercepts are at (-3, 0) and (-1, 0).The y-intercept is at (0, 3).The vertex is at (-2, -1).The axis of symmetry is x = -2.I need help with 36 please I don’t understand
Answer:
36)
[tex]f(x) = \frac{1}{x + 3} - 1[/tex]
The equation of the function is y = 1/(x + 3) - 1
How to determine the equation of the transformationFrom the question, we have the following parameters that can be used in our computation:
The reciprocal function shifted down one unit and left three units
The equation of the reciprocal function is represented as
y = 1/x
When shifted down one unit, we have
y = (1/x) - 1
When shifted left three units, we have
y = 1/(x + 3) - 1
Hence, the equation of the function is y = 1/(x + 3) - 1
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
Maria wrote the equation of a line that has a slope of Four-thirds and passes through point (3, 5). Which statement is true?
The y-intercept is 4.
The slope-intercept equation is y = four-thirds x + 1.
The point-slope equation is y minus 3 = four-thirds (x minus 5).
The line also passes through the point (0, –2)
Answer:
The slope-intercept equation is y = four-thirds x + 1
Step-by-step explanation:
slope: [tex]\frac{4}{3}[/tex]
point: (3, 5)
y = mx + b
[tex]y=\frac{4}{3}x+b[/tex]
[tex]5=\frac{4}{3}(3)+b[/tex]
[tex]5=4+b[/tex]
[tex]b=5-4[/tex]
[tex]b=1[/tex]
Equation: [tex]y=\frac{4}{3}x+1[/tex]
[tex]-2=\frac{4}{3}(0)+1[/tex]
[tex]-2=0+1[/tex]
[tex]-2\neq 1[/tex]
Thus, the second statement is true!
Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-
axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C?
4
3
1
3-2-11
99 +4
1 234
4
A
$65
A B and B C
A A, B B, C C
Fach trianola ie a rinht triannla
The reason why Figure A is congruent to Figure C is that they undergo the same sequence of transformations: a translation followed by a reflection.
The statement "Figure A is translated 3 units right and 2 units up. The translated figure is labeled Figure B. Figure B is reflected over the x-axis. The reflected figure is labeled Figure C" describes a sequence of transformations applied to Figure A to obtain Figure C.
When Figure A is translated 3 units right and 2 units up, it undergoes a rigid transformation known as a translation. This transformation preserves the shape and size of the figure. The translated figure, Figure B, will have the same dimensions and orientation as Figure A but will be shifted to the right and up.
When Figure B is reflected over the x-axis, it undergoes a reflection. This transformation flips the figure vertically, changing the sign of the y-coordinates of its vertices while keeping the x-coordinates the same. The reflected figure, Figure C, will have the same shape and size as Figure B, but it will be oriented in the opposite direction.
Since translations and reflections are both rigid transformations, they preserve congruence. Therefore, Figure A and Figure C are congruent because they undergo the same sequence of transformations (translation followed by reflection) from Figure A.
In conclusion, Figures A and C go through the same set of transformations, a translation and a reflection, which explains why they are congruent.
for such more question on congruent
https://brainly.com/question/26085366
#SPJ8
Select the correct answer. Which fraction converts to a terminating decimal number? A. 1\6 B. 2\9 C. 3\8 D. 4\7
The fraction that converts to a terminating decimal number is C. 3/8.
To determine which fraction converts to a terminating decimal number, we need to analyze the denominator of each fraction. A fraction will result in a terminating decimal if its denominator has only prime factors of 2 and/or 5.
Let's examine each option:
A. 1/6: The denominator is 6, which can be factored into 2 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
B. 2/9: The denominator is 9, which can be factored into 3 * 3. Since 3 is not a factor of 2 or 5, this fraction does not convert to a terminating decimal.
C. 3/8: The denominator is 8, which can be factored into 2 * 2 * 2. Since all the factors are 2, this fraction does convert to a terminating decimal.
D. 4/7: The denominator is 7, which cannot be factored into 2 or 5. Therefore, this fraction does not convert to a terminating decimal.
Based on our analysis, the fraction that converts to a terminating decimal number is C. 3/8.
For more questions on fraction, click on:
https://brainly.com/question/30154928
#SPJ8
Jessica and Barry squeezed oranges for juice. Jessica squeezed 23
5
cups of juice. Barry made 1
4
cup less than Jessica. Barry estimated that Jessica squeezed about 21
2
cups of juice.
Which is the best estimate for the amount of juice Barry made?
The best estimate for the amount of juice Barry made is 235 cups.
In this question, Jessica and Barry squeezed oranges for juice. Jessica squeezed 235 cups of juice. Barry made 14 cups less than Jessica. Barry estimated that Jessica squeezed about 212 cups of juice. We need to find the best estimate for the amount of juice Barry made.
Let's begin by finding the amount of juice Barry actually made. Barry made 14 cups less than Jessica, which means he made: 235 - 14 = 221 cups of juice.
Now, let's compare this to Barry's estimate. Barry estimated that Jessica squeezed about 212 cups of juice. Since Jessica actually squeezed 235 cups of juice, her estimate was too low by:235 - 212 = 23 cups.
So, we can apply this error to Barry's estimate to get a better estimate for the amount of juice he made. If Barry's estimate was 212 cups, and he underestimated by 23 cups, then he actually made:212 + 23 = 235 cups of juice. Therefore, the best estimate for the amount of juice Barry made is 235 cups.
For more such questions on juice Barry, click on:
https://brainly.com/question/33239700
#SPJ8
Landon finds some dimes and quarters under the couch cushions. How many coins does he have if he has 5 dimes and 10 quarters? How many coins does he have if he has d dimes and q quarters?
Answer:
15 coins, d + q coins
Step-by-step explanation:
If asking for the amount (in $)
5(.10) + 10(.25) = 2.5+.5 = $3
He would have 0.1d + 0.25q for d dimes and q quarters.
You pick a card at random. Without putting the first card back, you pick a second card at random.
6,7,8,9
What is the probability of picking a 6 and then picking a 9?
(Write you answer as a fraction or whole number)
NEED ASAP PLS!!!!!
Answer:
1/12 is the correct answer
6.) Find the area of the circle shown.
a.
16 m²
b.
25 m²
c.
d.
50 m²
101 m²
7.) Find the perimeter of the circle shown in the previous question.
a. 12.5 m
b.
25 m
C. 50 m
d. 101 m
8.) Find the area of the figure. Assume right angles
a. 122u²
b. 126u²
c. 114u²
d. 156u²
9.) Find the geometric mean between 8 and 25.
a. 33
b. 17
c. 10√2
d. 20
13
10.) The perimeter of an equilateral triangle is 18. Find the measure of the altitude.
a. 3
b. 6
с 3V2
d. 3√3
Solution
verified
Verified by Toppr
The circumference of circle is 2πr=176
2×
7
22
×r=176
r=176×
22
7
2
1
r=7×4=28cm
Area of circle is πr
2
=
7
22
×28×28=88×28=2464cm
2
Please answer ASAP I will brainlist
Answer:
(a) The graph is an exponential growth curve.
(b) f(0) = 2, f(1) = 10
(c) The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.
Step-by-step explanation:
Given function:
[tex]k(x)=2(5)^x[/tex]
[tex]\hrulefill[/tex]
Part (a)The graph is an exponential growth curve.
The curve begins in quadrant II, crosses the y-axis at (0, 2) into quadrant I, and increases rapidly as x increases.
In general, an exponential growth function is in the form:
[tex]\boxed{y = ab^x}[/tex]
where:
a is the y-intercept.b is the base.In this case, the y-intercept is 2 and the base is 5.
As the value of a is positive, and the value of b is greater than 1, it indicates exponential growth.
[tex]\hrulefill[/tex]
Part (b)The term "second coordinates" refers to the y-values of the points on a graph.
To find the second coordinates of the points with first coordinates 0 and 1, substitute x = 0 and x = 1 into the function and solve.
[tex]\begin{aligned}k(0)&=2(5)^{0}\\&=2(1)\\&=2\end{aligned}[/tex]
[tex]\begin{aligned}k(1)&=2(5)^{1}\\&=2(5)\\&=10\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Part (c)The graph is entirely above the x-axis and increases from left to right, more steeply than the graph of y=5ˣ.
As 2(5)ˣ > 0, the graph is entirely above the x-axis.
The end behaviour of the function is:
As x → -∞, k(x) → 0.As x → ∞, k(x) → ∞.Therefore, the graph increases from left to right.
In y = 2(5)ˣ, the base is 5, but it is multiplied by 2. This means that for every unit increase in x, the corresponding y-value is doubled compared to the graph of y = 5ˣ. Therefore, the multiplication by 2 makes the graph of y = 2(5)ˣ steeper than the graph of y = 5ˣ.
The graph is completely on the x-axis; It then increases from left to right. it is less steep that y = 5ˣ
The values are (0, 2) and (1, 10)
How to determine the shape of the functionFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2(5ˣ)
The above function is an exponential growth curve
This means that
The graph is completely on the x-axisIt then increases from left to rightit is less steep that y = 5ˣCalculating the values of the functionHere, we have
f(x) = 2(5ˣ)
This gives
f(0) = 2(5⁰)
f(0) = 2
f(1) = 2(5¹)
f(1) = 10
So, the values are (0, 2) and (1, 10)
Read more about exponential functions at
https://brainly.com/question/2456547
#SPJ1
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping shown does not represents a function
Determining if the mapping is a functionFrom the question, we have the following parameters that can be used in our computation:
The mapping
From the mapping, we have
(1, 7), (8, 3), (8, -1) and (3, 0)
The above ordered pair is not a function
This is so because the input value 8 have different output values 3 and -1
i.e. it would not pass the vertical line test when represented on a graph
Read more about functions at
brainly.com/question/22340031
#SPJ1
What is (-,-) quadrant
In the context of a Cartesian coordinate system, the term "(-,-) quadrant" refers to the third quadrant, also known as Quadrant III.
The Cartesian coordinate system consists of four quadrants, numbered from I to IV in a counterclockwise direction. Each quadrant is defined by the signs of the x and y coordinates.
In Quadrant III, the x-coordinates are negative (represented by the "-") and the y-coordinates are also negative. This means that any point located in this quadrant will have both x and y values that are less than zero.
Visually, Quadrant III is situated below the x-axis and to the left of the y-axis. It is characterized by its lower left position in the coordinate plane.
Points in Quadrant III can be thought of as having a negative horizontal position (to the left of the origin) and a negative vertical position (below the origin).
for such more question on Cartesian coordinate system
https://brainly.com/question/15378553
#SPJ8
When x increases from a to a + 2, y increases by a difference of 6. For which function is this statement true? Responses A y = 2(9)x y = 2 ( 9 ) x B y = 3x + 2y = 3x + 2 C y = 2(3)x y = 2 ( 3 ) x D y = 9x + 2
The function that satisfies the given condition is y = 3x + 2.
The correct answer to the given question is option B.
We are to find the function that satisfies the condition: When x increases from a to a + 2, y increases by a difference of 6.
A statement such as this represents a linear function, where y increases at a constant rate with respect to the increase in x.Let y = mx + b, be a linear function.
We know that when x increases from a to a + 2, y increases by a difference of 6. In other words, we can express this relationship using the following equation:
2m + b − m − b = 6 ⇒ m = 3
The function has been found to be y = 3x + b.
To find the value of b, we need to use the fact that when x increases from a to a + 2, y increases by a difference of 6: y(a + 2) − y(a) = 6 ⇒ 3(a + 2) + b − 3a − b = 6 ⇒ 6 = 6
Therefore, the function that satisfies the given condition is y = 3x + 2. The correct option is B) y = 3x + 2.
For more such questions on function, click on:
https://brainly.com/question/29631554
#SPJ8
ANSWER ASAP question in image
The values in the boxes that correctly complete the division model and quotient are presented as follows;
[tex]{}[/tex] 10 2 4
6 [tex]{}[/tex] 60 16
76 ÷ 6 = 12 R 4
What is a division area model?A division area model comprises of the number being divided, representing the area of a rectangle, and a factor or the divisor, being a side length of the rectangle.
The number 76 divided by 6 using the division model can be evaluated by setting the area of the rectangle as 76 and the length of side of the rectangle as 6, asw follows;
The division model
The model for the division of 76 ÷ 6 can be presented as follows;
[tex]{}[/tex] 10 2 4
6 [tex]{}[/tex] 60 16
Therefore; 76 ÷ 6 = 10 + 2 = 12 Remainder 4
Learn more on representing division using division area models here: https://brainly.com/question/27954894
#SPJ1