Step-by-step explanation:
minimum.
since the term with x² has a positive factor, this will grow exponentially in the positive direction compared to the other terms, so y (the functional value) will grow and grow with growing distance of x to the vertex.
and that makes the vertex the minimum of the parabola (which opens upwards).
if the factor would be negative (like -x² - 2x + 10), the vertex would be a maximum, and the parabola would open downwards.
Corin measures the apparent height of a tower 800 feet away by holding a ruler in front
of her eye and observing that the tower appears to be 9 inches tall. The apparent height h
(in inches) varies inversely with Corin's distance d (in feet) from the tower. Write an
equation that gives d as a function of h. How tall would the apparent height of the tower
be if she was standing 2000 feet away from the tower? Show your work.
Answer:
Since the apparent height h of the tower varies inversely with Corin's distance d from the tower, we know that h and d are inversely proportional. This means that the product of h and d is constant. We can write this relationship as:
hd = k
where k is a constant.
We can find the value of k by substituting the known values of h and d:
9 inches * 800 feet = k
Solving for k, we find that k = 7200 inches * feet.
Since h and d are inversely proportional, we can write the inverse relationship as:
d = k / h
Substituting the value of k that we found earlier, we have:
d = 7200 inches * feet / h
To find the apparent height of the tower if Corin is standing 2000 feet away, we can substitute 2000 for d in the equation above:
h = 7200 inches * feet / 2000 feet = 3.6 inches
Therefore, the apparent height of the tower would be 3.6 inches if Corin is standing 2000 feet away.
Step-by-step explanation:
consider the trinomial 15x² - 34x - 16.
List all the factor pairs for -240.
Answer: To find the factor pairs for -240, we can use the following steps:
Find the prime factorization of -240: -240 = (-2) * (-2) * (-2) * (-3) * (-5)
For each prime factor, there are two possible factor pairs: (-1) and (1), and (-n) and (n). For example, for the factor -2, the possible factor pairs are (-1) and (1), and (-2) and (2).
The factor pairs for -240 are: (-1) and (1), (-2) and (2), (-3) and (3), (-5) and (5), (-6) and (6), (-10) and (10), (-15) and (15), (-30) and (30).
Thus, the factor pairs for -240 are: (-1, 1), (-2, 2), (-3, 3), (-5, 5), (-6, 6), (-10, 10), (-15, 15), and (-30, 30).
Step-by-step explanation:
The value of a second-hand car is £8,000.
Each year it loses 20% of its value.
Work out the value of the car after 5 years.
The value of the car will be £2,621 after 5 years.
What is exponential decay?Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.
Given that, The value of a second-hand car is £8,000. Each year it loses 20% of its value, we are asked to find its value after 5 years.
This is a situation of exponential decay.
Hence, using the exponential decay formula =
A = P(1-r)ⁿ
Where A is final value, P is principal value, r is rate of decrease and n is the number of years.
Here, we will find A, and we have,
P = £8,000.
r = 20% = 0.20
t = 5
Therefore,
A = 8000(1-0.20)⁵
A = 8000(0.80)⁵
A = 8000(0.32768)
A ≈ 2,621
Hence, the value of the car will be £2,621 after 5 years.
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find the order pairs for y=-5x-4
Answer:
(0,-4),(1,1)(2,6)
Step-by-step explanation:
— 12 – 6р – (-2)
help pls
Answer: -6P - 10
Step-by-step explanation:
STEP 1. -12 - 6P + 2
STEP 2. -6P + ( -12 + 2 )
STEP 3. -6P - 10
Anna and Sharon both construct a triangle. Anna begins by drawing a segment with a length of 3 inches. Starting from one vertex, she draws another segment with a length of 5 inches so that the two segments have an included angle of 35°. Sharon constructs her triangle by drawing a segment with a length of 5 inches, measuring a 35° angle, and drawing a ray from one vertex. Then she measures and terminates the ray at 3 inches. Do Anna and Sharon create congruent triangles? Explain.
Answer:
Yes, Anna and Sharon both created triangles that are congruent. Their triangles are congruent because they have 2 corresponding, congruent side-lengths and an included angle that is congruent. Therefore, their triangles are congruent by SAS (Side-Angle-Side).
Estthe product silve using an area model and the standard algorithm 1.7x55=
The expression 1.7 x 5.5 can be an area model of the rectangle where the length is 1.7 and the width is 5.5
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The expression 1.7 x 55 is an area model.
Area of rectangle = length x width
Now,
Length = 1.7
Width = 55
Area = 1.7 x 5.5
Thus,
The expression 1.7 x 5.5 can be an area model.
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How much did the population change between 1970 and 1980? population change between 1990 and 1995? What was the average annual change for that period?
Hint: Calculate the changes, then calculate the mean, or average, by dividing by the number of years. State the units clearly. The units are listed on the chart.
The population change for each period is given as follows:
1970 to 1980: 0.748 billion.1990 to 1995: 0.407 billion.Hence the average annual change for the period between 1970 and 1995 is given as follows:
7,932,000 people a year.
How to obtain the population change?The population change over a period is given by the subtraction of the population at the end of the period by the population at the beginning of the period.
The population data for each year is given by the table on the image presented at the end of the answer.
Hence the changes are obtained as follows:
1970 to 1980: 4.456 - 3.708 = 0.748 billion.1990 to 1995: 5.691 - 5.284 = 0.407 billion.The change between 1970 and 1995 is of:
5.691 - 3.708 = 1.983 billion.
This period is composed by 25 years, hence the average annual change is of:
1.983/25 = 0.07932 billion people a year = 7,932,000 people a year.
Missing InformationThe chart is given by the image presented at the end of the answer.
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A 94-ft tree casts a shadow that is 110 ft long. What is the angle of elevation of the sun?
Answer:
Step-by-step explanation:
Setting up a diagram would be helpful here, so we should have the vertical leg representing the 84-ft. tree and the horizontal leg representing the 120 ft. shadow. With the two measurements we are given, we should use the tangent ratio, opp/adj, to set up an equation to solve for the angle of elevation. So the equation will be:
tan θ = 84/120. Using the tan inverse function on the calculator, we have tan-1( 84/120) = θ and, rounding our decimal value to the nearest 10th, we have θ =35°.
Need help on these problems
Answer:
1.) x = 50 2.) x = 70
Step-by-step explanation:
These angles are complementary angles meaning the angles add up to 90°. Therefore, we can set up equations to solve for the variables.
1.)
x + 40 = 90
x = 50
2.)
x + 20 = 90
x = 70
Answer:
x = 50°
x = 70°
Step-by-step explanation:
90° - 40° = 50°
x = 50°
90° - 20° = 70°
x = 70°
John needs to print 36 copies of his colored poster. His HP printer can print 16 copies in 5 minutes. His Epson printer can print 4 copies in 1 minute.
9a) Enter an equation that can be used to find the number of minutes, t, John would take to make 36 copies if he used both printers. Enter your response in the first response box. (DO NOT PUT SPACE IN YOUR ANSWER. USE t AS YOUR VARIABLE. Write fractions using the correct order of operations.)Plz help
Answer:
It would probably be 36t
Step-by-step explanation:
because if you think about It.
It is mainly asking you how long it is going to take, so you need a a equation to find the answer.
-John needs 36 copies
- Hp printers out 16 in 5 minutes
- Epson printer out 4 in 1 minutes
so 36 x t or 36t
Supplementary solving for x
Answer:
M<1 is 43 degrees and M<2 is 137
Step-by-step explanation:
This is a case of supplementary angles. M<1 and M<2 are supplementary, which means that their angle degrees added together will be equal to 180. The same is for M<2 and M<3, and M<3 and M<4, and M<1 and M<4. Basically, two angles are supplementary when they form a straight line, or 180 degrees
First, we know that M<1 and M<2 added together is 180. We know M<1 is 7x+1, so then, we have:
(7x+1) + (M<2) = 180
Therefore, we have 180-(7x+1) = M<2. We can't solve the equation further on from there, so we move on.
Next, we know that M<2 and M<3 added together is 180. We know that M<3 is 12x-29, so then, we have:
(12x-29) + (M<2) = 180
Therefore, we have 180-(12x-29) = M<2. Now, we have two equations to solve x:
180-(7x+1) = M<2 and 180-(12x-29) = M<2. As both equations equal M<2, they equal each other. Thus, we have:
180-(7x+1) = 180-(12x-29)
We can cancel out 180, so:
-(7x+1) = -(12x-29)
-7x-1 = -12x+29
-30 = -5x
x = 6.
Now that we have x, we can find M<1, M<3, and M<2. M<1 is (7x+1), so we use substitution, putting 6 for x, and M<1 is evaluated to 43 degrees.
Now that we have M<1, we can find M<2 easily. M<1 + M<2 = 180, so 43 + M<2 must be 180. Therefore, M<2 is 137 degrees.
We can do the same for M<3, but the problem does not require it.
Please help quick (timed)
What isometric transformation was Applied to triangle XYZ ?
Translation ?
Reflection ?
Dilation ?
Rotation ?
Answer:
Rotation
Step-by-step explanation:
19) Write in Ascending Order
7613 m , 7.6 km , 7.59km ____________________
7.6 km,7.59 km, 7613 m
O 7613 m , 7.59 km , 7.6 km
O 7.59 km , 7.6 km, 7613 m
kjs is a right triangle formed by the placement of 3 squares. what is the area of the shaded square?
area of small square = 87 in
side of big square = 18 in
The area of the square having the same length of the base of the triangle is 7245 square inches.
What is Pythagoras's theorem?In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.
From the given figure as the base of the triangle is an equal length of the side of a square we can obtain the area of the square by first applying Pythagoras on the right angle triangle having a height of 87 inches and a hypotenuse of 18 inches.
So,
Base = {√(87² - 18²)}.
Base = √(7245) inches.
Base = 85.11 inches.
Now, We also know that the area of a square is (side)².
Therefore it is (87.11)² which is the same as 7245 sq inches.
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Please help triangle similarity
9514 1404 393
Answer:
(C) SAS
Step-by-step explanation:
The obtuse angles in each triangle are "corresponding" with respect to the segments marked parallel and the horizontal transversal.
Those angles are between pairs of proportional sides:
60/42 = 40/28 = 10/7
so, the applicable theorem is SAS. The triangles can be proven similar using the SAS theorem.
Angle α intersects the unit circle at point (-0.2538, 0.9673). What is the value of tan(α)?
The value of the tan(α) is -0.2624.
What is the tangent of an angle?In trigonometry, the tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.
In other words, it is the ratio of sine and cosine function of an acute angle such that the value of cosine function should not equal to zero.
Given that, the angle α intersects the unit circle at point (-0.2538, 0.9673). We need to find the value of tan(α),
We know that, the tangent of the angle is the ratio of the perpendicular and the base,
So,
tan(α) = -0.2538 / 0.9673
= -0.2624
Hence, the value of the tan(α) is -0.2624.
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12 feet below the surface of the water. What is the pool's depth in feet?
Answer:
Step-by-step explanation:
-12
Which of the following lists all prime numbers between 6 and 18?
Ramon invested a total $9,700 into two accounts, account 1 earns 6% simple interest and account 2 earns 4% simple interest. After one year, the total interest earned from both accounts was $466. Let X be the amount you invested in account 1 and y be the amount invested in account 2
Answer:
In the account that paid 3% Ramon put $800
In the account that paid 6% Ramon put $1,600
Step-by-step explanation:
Answer:
x+y= 9700 & 0.06x + 0.04y=466
Step-by-step explanation:
let X & Y be each account. Together, they are $9,700.
So, x+y=9700
thus, account 1 (x) earns 6 %. which converted to decimal is 0.06
account 2 (y) earns 4 % which converted is 0.04
It also said that both accounts were $466, after 1 year.
0.06x+0.04y=466
Do the following set of points describe a function, a relation, both or neither?
(3, 6), (3, 3). (9. -3). (-5. -9)
Select all answers that apply.
A. Relation
B. Function
Answer:
It's Both
Step-by-step explanation:
for the first two co-ordinates, there are many y-value for a single x-value, then for the last two co-ordinates theres a single y-value for one x-value
Find the value of x.
30°
105°
xo
Exterior angle of triangle x has a value of 135 in this sentence.
What is the simplest technique to measure angles?A protractor can be used to measure angles precisely. Angles are measured in degrees, hence the term "degree measure." Since one full revolution is equivalent to 360 degrees, it is divided into 360 segments.
What exactly is the triangle rule?According to the "sides of a triangle rule," any two sides of a triangle must add up to be longer than the third side.
By extending one side of the triangle, an external angle is formed. An exterior angle is the angle formed by the stretched side and the side that is immediately adjacent.
Practice. Triangle Angle Measurement
via the triangle's external angle characteristic, x = 105 + 30 = 135.
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An initial amount of $1300 is invested in an account at an interest rate of 1% per year, compounded continuously. Find the amount in the account after five years. Round your answer to the nearest cent.
Answer:
65, given the amount of $1300 times 0.01 percent times 5 years would equal $65 over 5 years, to break it down, multiply 1300 times 0.01 times 5.
Step-by-step explanation:
A sample of radioactive element follows the law of exponential decay. if there are 50g of the element at noon 30g at 3:00 pm that same day then how many grams will there be at 9:00 pm that same day?
Answer:
10.8 g
Step-by-step explanation:
Exponential decay equation: [tex]A=A_0e^{-rt}[/tex]
[tex]A_0[/tex] is the initial amount (at time t = 0, "noon")
r is the decay rate
You have two pieces of information:
Noon t = 0 [tex]A_0=50[/tex]
3:00 pm t = 3 [tex]A=30[/tex]
Plug those in to get [tex]30=50e^{-r(3)}[/tex]
Divide by 50.
[tex]0.6=e^{-3r}[/tex]
Take the natural log of both sides.
[tex]\ln(0.6)=-3r[/tex]
Divide by -3.
[tex]\frac{\ln{(0.6)}}{-3}=r\\\\r \approx .17027[/tex]
Now, for 9:00 pm, use this value of r and t = 9.
[tex]A=50e^{-.17027(9)} \approx 10.8[/tex]
Select all of the following that are quadratic equations.
3x ^2 + 5x - 7 = 0
x ^3 - 2x ^2 + 1 = 0
2x - 1 = 0
5x ^2+ 15x = 0
6x - 1 = 4x + 7
x ^2 - 4x = 4x + 7
Answer:
3x ^2 + 5x - 7 = 0
5x ^2+ 15x = 0
x ^2 - 4x = 4x + 7
Step-by-step explanation:
Just find a equation with a degree of 2 and boosh
What is the area of the kite?
A)
45 in2
B)
64 in 2
C)
80 in 2
D)
128 in2
Answer:
c
Step-by-step explanation:
Answer:
I believe it would be 64 in 2 correct me if I am wrong.
If I ate 300 apples and there were 29 left how many were there in the start. Or before I ate the apples.
Cones A and B both have volume 48pi cubic units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B.
The possible radius and height for Cone B are 3 units and 16 units respectively
How to determine the radius and height of the cone
The formula for calculating the volume of a cone is expressed mathematically;
Volume = 1/3 πr²h
Given that;
π takes the value 3.1 4r is the radius of the coneh is the height of the coneFrom the information given, we have that;
Both cone A and B have volume of 48πCone A has 6 units and height of 4 unitsNow, let the height of cone B be 16 units
Substitute the value into the formula, we have;
48π = 1/ 3 × π × r² × 16
multiply the values, we have
48 = 16r²/3
cross multiply
16r² = 144
Divide both sides by 16
r² = 144/16
r² =9
Find the square root of both sides
r = 3units
Hence, the values are 3 units and 16 units
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Identify the local maximum for the function shown.
A)
(4,1)
B)
(1,4)
(-1,0)
D)
(0, -1)
What is the slope of the line with the equation of y = =*
Ex that passes through the point (2, 1)?
A.) - 2/3
B.) - 3/2
C.) 2/3
D.) 3/2