[tex](a) {11}^{a} = 1331 \\ = > {11}^{a} = {11}^{3} \\ = > a = 3[/tex]
[tex](b) {2}^{b} = \frac{1}{128} \\ = > {2}^{b} = (\frac{1}{2} ) ^{7} \\ = > {2}^{b} = {2}^{ - 7} \\ = > b = - 7[/tex]
[tex](c) {9}^{c} = 243 \\ = > {3}^{2 \times c} = {3}^{5} \\ = > {3}^{2c} = {3}^{5} \\ = > 2c = 5 \\ = > c = \frac{5}{2} \\ = > c = 2.5[/tex]
[tex](d) {10}^{d} = 0.01 \\ = > {10}^{d} = \frac{1}{100} \\ = > {10}^{d} =( \frac{1}{10} ) ^{2} \\ = > {10}^{d} = {10}^{ - 2} \\ = > d = - 2[/tex]
Answers:a = 3b = -7c = 2.5d = -2Hope it helps.
Do comment if you have any query.
Mr. Ryan is buying a home for $250,000. He is making a 20% down payment and
financing the rest with a 25-year loan at 5% interest. What will his monthly payment
be?
Since 20% down payment, we will find the 20% of that $250,000.
10% is $25,000, now times by 2 would be 20% which is $50,000.
Now $250,000 - $50,000 = $200,000 which would be rest of the non-payed payment.
We will divide $200,000 with the 25 year loan. $200,000/25 = $8,000
There is also the 5% interest.
1% of $8,000 is $80 and times that by 5 would be 5% which is $400.
$8,000 + $400 = $8,400.
Since it is monthly, we will divide $8,400 by 12 months. $8,400/12 = $700.
The monthly payment would be $700.
(I hope this is correct.)
what is the desimal for
Answer:
A decimal is used to identify a unit of measure with precision because not all whole numbers cannot represent a unit of measure in a respective situation.
Answer:
Decimals are used to express the whole number and fraction together.
Step-by-step explanation:
What are the possible values of y if x =4 in the inequality x-2y ≤ 5?
Answer:
y ≥ -0.5
Step-by-step explanation:
First, we can substitute 4 in for x in the inequality.
4 - 2y ≤ 5
Now, to solve for y, we start by subtracting 4 from both sides:
-2y ≤ 1
And divide by -2. When dividing or multiplying by a negative number while solving an inequality, we also have to remember to switch around the inequality sign. This gives us:
y ≥ [tex]\frac{1}{-2}[/tex] or y ≥ -0.5
Therefore, the possible values of y are -0.5 or greater.
what is this matrix called
[2,5,6]
Answer:
The dimension of a matrix is indicated with R × C where R is the number of rows in the matrix and C is the number of columns. When a matrix has the same number of rows as columns, then it's a square matrix. Matrices with just one row are called row matrices, and those with only one column are column matrices.
What is the value of x?
Answer:
x = 21
Step-by-step explanation:
The angles are supplementary
therefor
(3x + 2) + (5x + 10) = 180
Combine like terms
8x + 12 = 180
subtract 12 from both sides
8x = 168
Divide both sides by 8
x = 21
Answer:
x = 21
Step-by-step explanation:
The angle adjacent to 3x + 2 corresponds to 5x + 10 and are congruent.
The 2 adjacent angles then lie on a straight line and sum to 180° , then
5x + 10 + 3x + 2 = 180
8x + 12 = 180 ( subtract 12 from both sides )
8x = 168 ( divide both sides by 8 )
x = 21
$360 is shared among hannah , Ryan and Kelly in ratio 2:3:5 . how much less will hannah receive than kelly?
Answer:
$108 less
Step-by-step explanation:
2 + 3 + 5 = 10 parts
each part is 360/10 = $36
Hanna has 5 - 2 = 3 parts less than Kelly
3 * 36 = 108
$108 less
Help please :)) This is timed as well as mind boggling
Answer: Choice C
==========================================================
Explanation:
Recall that the form
[tex]z = r*\left[\cos\left(\theta\right)+i*\sin\left(\theta\right)\right][/tex]
can be abbreviated to
[tex]z = r*\text{cis}(\theta)[/tex]
The "cis" stands for the first letters of "cosine i sine" in that order.
The original fairly messy quotient can be shortened down to
[tex]\frac{90\text{cis}(\pi/4)}{2\text{cis}(\pi/12)}[/tex]
We have 90cis(pi/4) all over 2cis(pi/12) as one big fraction.
-------------------------------
Now we'll use this rule to divide two complex numbers
[tex]z_1 = r_1*\text{cis}(\theta_1)\\\\z_2 = r_2*\text{cis}(\theta_2)\\\\\frac{z_1}{z_2} = \frac{r_1}{r_2}*\text{cis}(\theta_1-\theta_2)\\\\[/tex]
As you can see, we divide the r1 and r2 values to form the final coefficient out front. The theta angles are subtracted to form the new argument.
-------------------------------
Let's apply that idea to what your teacher gave you
[tex]z_1 = 90*\text{cis}(\pi/4)\\\\z_2 = 2*\text{cis}(\pi/12)\\\\\frac{z_1}{z_2} = \frac{90}{2}*\text{cis}(\pi/4 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(3\pi/12 - \pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(2\pi/12)\\\\\frac{z_1}{z_2} = 45\text{cis}(\pi/6)\\\\[/tex]
That last step then converts directly to the expression shown in choice C.
Question 1 of 10
Using the graph as your guide, complete the following statement.
The discriminant of the function is
101
HA
-10
10
The discriminant of the function is positive
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the discriminant of the function be represented as D
Now , the value of D is
D = ( b² - 4ac )
And , when ( b² - 4ac ) is positive, we get two real solutions
When a quadratic function contacts the x-axis on two different occasions, the function should be positive in this case. When the quadratic function intersects the x-axis precisely on one occasion, the function should be equal to zero.
When the x-axis shouldn't cross the function graph, the function should be smaller than zero.
Hence , the discriminant of the function is positive
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The complete question is attached below :
Using the graph as your guide, complete the following statement.
The discriminant of the function is
The slope of a line is 2. The y-intercept of the line is -6. Which statements accurately describe how to graph the
function?
VX
O Locate the ordered pair (0, -6). From that point on the graph, move up 2. right 1 to locate the next ordered pain
the line. Draw a line through the two points.
O Locate the ordered pair (0.-6). From that point on the graph move up 2. left 1 to locate the next ordered pair
the line. Draw a line through the two points.
Locate the ordered pair (6.0). From that point on the graph, move up 2. right 1 to locate the next ordered pair
the line. Draw a line through the two points
Locate the ordered pair (6.0). From that point on the graph move up 2. left 1 to locate the next ordered pair on
the line. Draw a line through the two points
Save and Exit
Answer:
Locate (0,-6), move up 2, right 1
Step-by-step explanation:
Hi there!
To graph a linear function, we first locate the-intercept, then graph the next point according to the slope.
We're given that the y-intercept is -6. The y-intercept occurs when x=0, so therefore, the point (0,-6) falls on the line.
Locate (0,-6)
Now, to graph the next point, we look at the slope. The slope in this case is 2. This means every time the line travels to the right by 1 unit, it travels up 2 units.
Move up 2, right 1
I hope this helps!
find the surface area of this triangular prism
please help me
108 ft square
Step by step
5x8 is 40
3x4 is 12 x 1/2 is 6.
Again, 3x4 is 12 x 1/2 is 6
8x4 is 32
8x3 is 24
Add that all tigether and its 108
What is a quartic function with only two real zeros of x=0 and x=2?
Answer:
x² - 2x = 0
Step-by-step explanation:
a = 0 ; b = 2
x² - (a +b)x + ab = 0
x² - (0 +2 )x + 0*2 = 0
x² - 2x = 0
Please solve this math problem... I will mark you brainliest
What is the value of x?
Answer:
more ... The letter "x" is often used in algebra to mean a value that is not yet known. It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable, but we can work out its value if we try! A variable doesn't have to be "x", it could be "y", "w" or any letter, name or symbol.
Answer:
[tex]x = 12[/tex]
Step-by-step explanation:
For resolve this problem I use trigonometry identities.
[tex]sin(\theta) = \frac{OP}{H}[/tex]
Where [tex]\theta[/tex] is the angle of the triangle (45), [tex]OP[/tex] is the opposite side of the angle ([tex]6\sqrt{2}[/tex]) and the [tex]H[/tex] is the hypotenuse ([tex]x[/tex]).
Replace the know values in the relation
[tex]sin(45) = \frac{6\sqrt{2}}{x}[/tex]
Isolate [tex]x[/tex] of the equation and solve
[tex]\frac{6\sqrt{2}}{sin(45)} = x\\\frac{6\sqrt{2}}{\frac{\sqrt{2}}{2}} = x\\\frac{12\sqrt{2}}{\sqrt{2} } = x\\12 = x[/tex]
So the final answer is [tex]x = 12[/tex]
3 Write a numerical expression to model the words. Subtract 1 from the product of 4 and 5.
Answer:
Hello!
After reading the question you have provided I have come up with the correct numerical expression:
4x5-1
Step-by-step explanation:
To come up with this solution you need to keep in mind some of the terminoloy being used.
The word "subtract" comes from the action of subtraction
The word "product" comes from the action of multiplication
Thus, using those terminologies correctly, you can then deduce that when the question says "the product of 4 and 5" means "multiplying 4 and 5 together".
So you get the first part being 4x5
Then, you add in the last part of "subract 1" from the "product of 4 and 5":
4x5-1
Remember to keep in mind the rule of "PEMDAS"
You always need to keep the multiplication portion of the equation in front of any subtraction, or addition in any given equation.
Here to form the numerical expression we will first do the product of 4 and 5 and then subtract 1 from their resultant and that is ou required answer.
What is numerical expression ?A numerical expression is written in terms of numbers and their operations numerical expression can of many types for example arithmatic expression , alzebraic expression etc.
some examples of arithmatic operations are -
240+130 = 370
240÷12 = 20
Some examples of alzebraic expressions are
3x + 4y = 7
x² + 3x - 7 = 0
In the given question subtract 1 from the product of 4 and 5 can be expressed as (4x5) - 1 = 20 - 1 = 19
Leran more about numerical expression here :
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Hello, this is my brother's homework. I'm a little bit confused since I studied this lesson a long time ago..Can someone help me? I am not sure about my answer..
Answer:
Length of side of square=25ftLength of three sides=3(25)=75ft
3ft=1m75ft=15mCost per metre=15.00
Total cost:-
[tex]\\ \sf\longmapsto 15(15)=225.00[/tex]
2.1/x+1 4/5=3/10x
what is the Answer?........................................................
Answer:
x=10.03115897…,−0.69782564…x=10.03115897…,-0.69782564…
Step-by-step explanation:
1/4 (-16x +8) distributive property
[tex] - 4x + 2 \\ \\ [/tex]
Round 76.28 to the nearest whole number
Answer:
76
Step-by-step explanation:
Answer:
76
Step-by-step explanation:
.28 is less than .50 therfore it will be rounded down to 76
3x - 1 = 4x - 10 solve for x
Answer:
3x - 1 = 4x - 10
-1 = x - 10
9 = x
Step-by-step explanation:
10-1=4x-3x
9=X
this is the answer with steps
Choose the correct definition of divisor.
A. The answer in a division problem.
B. The number that is divided in a division problem.
C. The number that's left when the divisor doesn't go into the dividend
exactly.
D. The number that divides in a division problem.
Answer:the number that divides a division problem
Step-by-step explanation:the divisor divides the another number for the answer
hope this helps!
f(x)={x+4….
for f(x)
Answer:
x+4 x<5
8 5<_x<7
2x -1 7<_x<_10
Find the value of y.
Answer: y=11 y=5 y=4 y=5 y=7 y=3
Step-by-step explanation:yknow
how to determine if two functions are inverses of each other
Answer:
f(g(x)) = x implies that f and g are inverses; g(f(x)) = x also implies that.
Step-by-step explanation:
Suppose you have two functions f(x) and g(x). If you use g(x) as the input to f(x), and the result is merely x, then we conclude that the two functions are inverses of each other. Similarly with f(x) as argument of g(x).
f(g(x)) = x implies that f and g are inverses; g(f(x)) = x also implies that.
solve pls brainliest
Answer:
$8
Step-by-step explanation:
20% of $40
= [tex]\frac{20}{100}[/tex] × $40
= 0.2 × $40
= $8
$8 is discounted from the regular price
Answer:
$8 off
Step-by-step explanation:
Convert from a percentage to a multiplier by dividing by 100:
[tex]\frac{20}{100}=0.2[/tex]
Then multiply that by the price:
[tex]40*0.2=8[/tex]
meaning the item is $8 off.
You can confirm that like so:
[tex]\frac{8}{40} =0.2\\[/tex]
or 20%
PLEASE SOMEONE EXPLAIN THIS I HAVE NO CLUE WHAT THIS MEANS OR WHAT THE ANSWER IS
What is the domain of this function?
(-3, -7)
(-8, 8)
(10, 1)
(9, 4)
(7,-4)
(-6, -9)
Answer:
-8,-6,-3,7,9,10
Yoo muning1027
( fréé pøints)
Answer:
thx for points ....,..................
For the given central angle, determine the distance traveled along the unit circle from the point (1, 0).
360 degrees
a.
6.28 units clockwise
c.
3.14 units clockwise
b.
6.28 units
d.
3.14 units
9514 1404 393
Answer:
b. 6.28 units
Step-by-step explanation:
The travel through 360° takes you around the full circumference of the circle. That circumference is ...
C = 2πr
Since this is a unit circle, the radius is 1, so the circumference is ...
C = 2π·1 = 2π ≈ 6.28 . . . units (counterclockwise)
Angles are generally considered to be positive in the counterclockwise direction, so the distance traveled is 6.28 units counterclockwise. Answer choice (a) has the correct number of units, but the direction is incorrect.
Find the slope of this line
Answer:
0
Step-by-step explanation:
We can use the two points given, which are (-4, -2) and (3, -2), to solve for the slope and answer the question. We have to subtract the y-values and then subtract the x-values. Those differences, divided, give us our slope, as shown below:
[tex]\frac{-2-(-2)}{-4-3} =\frac{-2+2}{-4-3} =\frac{0}{-7} =0[/tex]
So, the slope is 0. If you have any more questions on finding slope, or found what I just did confusing, let me know so I can help you! :)
The measure of ones angle of a triangle is 40. The measure of the other two angles are in a ratio of 3:4
Answer:
40, 60, 80
Step-by-step explanation:
angles are 40, 3x, 4x
40+ 3x + 4x = 180
40 + 7x = 180
7x = 180 - 40
7x = 140
x = 20
so the angles are 40, 60, 80
PLEASE HELPPPPPPPPPPPPPP
Answer:
The answer is 18
Step-by-step explanation:
4050/225 = 18
Therefore 4050/18 = 225