Answers
Answer:
x = 3
Step-by-step explanation:
Angle S and Angle T are consecutive interior angles. Therefore, we know that T + S = 180°.
First, we need to solve for T, and since angles S and T are consecutive interior angles, we know that T + S = 180°. If we reorganize the equation to include the things we know (S = 105°), then we get 180° - 105° = 75°. So T is 75°.
Now, we use T = 75° and the information given to us in the picture to set up an equation. 75 = 24x + 3. Now, we can find x by isolating it. Do this by:
1) Subtracting 3 from both sides to give you 72 = 24x. We do this to get rid of the 3 from the "x side", but we must also do it to the other to keep the equation true. This moves the 3 from the "x side" to the other since we're trying to isolate x.
2) Divide 24 by both sides to get 3 = x. We use the same logic as we did for 3, except this time we divide since that's the opposite of multiplying.
In conclusion, x = 3.
Related Questions
find the sum of 1+2-3+4+5-6+7+8-9+...+97+98-99
Answers
Answer:
Hi,
Step-by-step explanation:
Let's make group of 3 numbers
1+2-3=0
4+5-6=3
7+8-9=6
...
97+98-99=96
s=1+2-3+....+97+98-99=0+3+6+..+96=3*(0+1+2+3+...+32)
=3*(32+0)*33/2
=1584
the number 2.525252.... can be written as a fraction, when reduced to its lowest term, the sum of numerator and denominator is:
Answers
Answer:
Here's your answer.
Let the number be x.
Here we have to multiply with 100 on both sides.
[tex] \implies \: 100x = 252.5252 \\ \\ \implies \: 100x = 250 \ + 2.5252... \\ \\ \implies \: 100x = 250 + x \\ \\ \implies \: 99x = 250 \\ \\ \implies \: x = \frac{250}{99} [/tex]
Therefore, sum of numerator and denominator = 25099 = 349
Hope it helps you from my sideAnswer:
349
Step-by-step explanation:
2.525252.... is a non-terminating and recurring number.2.525252.... can be expressed as [tex]2.\overline {52}[/tex]Now, we convert [tex]2.\overline {52}[/tex] as a fractional number. Lets start.[tex]Let \: x =2.\overline {52}[/tex]........(1)Multiply both sides of eq (1) by 100, we find:[tex]100x =252.\overline {52}[/tex]........(2)Subtracting (2) from (1)[tex]100x -x=252.\overline {52}-2.\overline {52}[/tex][tex]\implies 99x=250[/tex][tex]\implies x=\frac{250}{99}[/tex]Numerator = 250Denominator = 99 Sum of numerator and denominator = 250 + 99 = 349The mean age of a group of students is 16. John joins the group and the mean age changes to 18. How old is john ?
Answers
Answer:
John is 20 years old.
Step-by-step explanation:
Given the second mean is 18, it is equal to the first mean age plus John's unknown age. The sum is also divided by 2 because there are 2 values in the sum (1. John's age and 2. the mean, 16 yrs old).
Set up an equation: [tex]\frac{x+16}{2}=18[/tex]
multiply both sides by 2: [tex]x+16=36[/tex]
simplify: [tex]x=20[/tex]
Faelyn grouped the terms and factored the GCF out of the groups of the polynomial 6x4 – 8x2 + 3x2 + 4. Her work is shown.
Step 1: (6x4 – 8x2) + (3x2 + 4)
Step 2: 2x2(3x2 – 4) + 1(3x2 + 4)
Faelyn noticed that she does not have a common factor. Which accurately describes what Faelyn should do next?
Faelyn should realize that her work shows that the polynomial is prime.
Faelyn should go back and regroup the terms in Step 1 as (6x4 + 3x2) – (8x2 + 4).
In Step 2, Faelyn should factor only 2x out of the first expression.
Faelyn should factor out a negative from one of the groups so the binomials will be the same.
Answers
An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.
What are prime polynomials?Those polynomials with integer coefficients that cannot be factored further, with factors of lower degree and integer coefficients are called a prime polynomials.
The polynomial 6x⁴ – 8x² + 3x² + 4 needs to be factored and the steps are:
Step 1: (6x⁴ – 8x²) + (3x² + 4)
Step 2: 2x²(3x² – 4) + 1(3x² + 4)
Since they do not have any common factor.
Faelyn should realize that her work indicates that the polynomial is prime.
Prime polynomials have integer coefficients.
An accurately describes what Faelyn should do next is option B. Faelyn should realize that her work shows that the polynomial is prime.
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guys pls help me i will give brain list pls help me out
if someone could please help me i will be sending more so plsss i need help
Answers
Answer:
200
Step-by-step explanation:
Please help on the area for 7 8 9 please all i need help is
Answers
The area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.
What is the area of the equilateral, isosceles and right angle triangle?Note that:
The area of an Equilateral triangle is expressed as A = ((√3)/4)a²
Where a is the dimension of the side.
The area of an Isosceles triangle is expressed as A = (ah)/2
Where a is the dimension of the base and h is the height.
The area of a Right angled triangle is expressed as A = (ab)/2
Where a and b is the dimension of the two sides other than the hypotenuse.
For the Equilateral triangle.
Given that;
a = 5.4mmArea A = ?A = ((√3)/4)(5.4mm)²
A = ((√3)/4)( 29.16mm² )
A = 12.6mm²
Area of the Equilateral triangle is 12.6mm²
For the Isosceles triangle.
Given that;
Base a = 3.4inSlant height b = 5.9inheight h = ?Area A = ?The height h is the imaginary line drawn upward from the center of a.
First, we calculate the height using Pythagorean theorem
x² = y² + z²
Where x = b = 5.9in, y = a/2 = 3.4in/2 = 1.7in, and z = h
(5.9in)² = (1.7in)² + h²
34.81in² = 2.89in² + h²
h² = 34.81in² - 2.89in²
h² = 31.92in²
h = √31.92in²
h = 5.65in
Now, the area will be;
A = (ah)/2
A = (3.4in × 5.65in )/2
A = 19.21in²/2
A = 9.61in²
Area of the Isosceles triangle is 9.61in².
For the Right angled triangle
Given that;
a = 8.2ydsb = 4.1ydsc = 9.17ydsArea A = ?A = (ab)/2
A = ( 8.2yds × 4.1yds)/2
A = ( 33.62yds²)/2
A = 16.81yds²
Area of the Right angled triangle is 16.81yds²
Therefore, the area of the equilateral, isosceles and right angled triangle are 12.6mm², 9.61in² and 16.81yds² respectively.
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Which equation shows an example of the associative property of addition?
Answers
Answer:
(2+3)+4 = 2+(3+4) this is an example of associative property
use a number line to find the product.
5 x (-5)
a. -25
b. 25
c. 10
d. 0
Answers
Answer: a. -25
Step-by-step explanation:
1. Multiply the numbers
5x(−5)
Solution
−25x
Work out the circumference of this circle.
Give your answer in terms of pi and state its units
Answers
Answer:
14π cm
Step-by-step explanation:
Circumference of a circle given the diameter is :
πd
We simply substitute the value given in the image into our formula to find our answer:
πd = π×14 = 14π
Units will be cm as circumference is a length
This is our final answer as the question states to leave it in pi form .
Hope this helped and brainliest please
Answer:
14π cm
Step-by-step explanation:
Circumference of a circle with radius r = 2πr or 2rπ
The diameter d is twice the radius so circumference = dπ
Here d= 14 so the answer is 14π cm
Diberi 1 ½s = ⅗t² + ⅓u², hitung (ii) nilai t apabila u = -6 dan s = 28
Answers
Answer:
√2' = t
Step-by-step explanation:
1 1/2s = 3/5t^2 + 1/3u^2; substitute known values
1 1/2 • 28 = 3/5 • t^2 + 1/3 • -6^2; simplify
42 = 3 • t^2 ÷ 5 + 1/3 • 36
42 = 3 • t^2 ÷ 5 + 12; apply property of subtraction of equality
42 – 12 = 3t^2 ÷ 5 + 12 – 12; simplify
30 = 3t^2 ÷ 5; apply property of multiplication of equality
30 • 5 = 3t^2 ÷ 5 • 5; simplify
6 = 3t^2; apply property of division of equality
6 ÷ 3 = 3t^2 ÷ 3; simplify
2 = t^2
√2' = t
An account earns annual simple interest. Find the balance of
the account.
$250 at 4% for 1 year
HELP FAST
Answers
The balance of the account which earns annual simple interest of $250 at 4% for 1 year is $260
How to find simple interest?Principal, P = $250Interest rate, r = 4%Time, t = 1 yearSimple interest = principal × rate × time
= 250 × 4% × 1
= 250 × 0.04 × 1
= $10
Balance = Principal + Simple interest
= $250 + $10
= $260
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What is the greatest common factor of
15x^7y^5+5x^5y^4-20x^6y
Answers
Answer:
5x^5y
Step-by-step explanation:
Find the equation of the line in slope-intercept form containing the two points: (−1,5) and )(4,−3) Leave equation in fractional form.
Answers
Answer:
y = 1.6x + 3.4
Step-by-step explanation:
We have to use the equation y = m x + c to find the equation of the line.
Here,
m ⇒ slope
c ⇒ y-intercept
First, let us find the slope.
For that, we can use the given two coordinates.
( -1 , 5 ) ⇒ ( x₁ , y₁ )
( 4 , -3 ) ⇒ ( x₂ , y₂ )
The formula to find the slope of a line is :
m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )
Let us solve now.
m = ( y₁ - y₂ ) ÷ ( x₁ - x₂ )
m = ( 5 - ( -3 ) ) ÷ ( -1 - 4 )
m = ( 5 + 3 ) ÷ -5
m = 8 ÷ -5
m = -1.6
Now let us find the y-intercept (c ) of the line.
For that, let us get one of the coordinates which are given in the question.
I'll get ( -1 , 5 ) from that.
( -1 , 5 ) ⇒ ( x , y )
Let us solve now.
y = mx + c
5 = -1.6 × -1 + c
5 = 1.6 + c
5 - 1.6 = c
3.4 = c
Therefore,
m ⇒ -1.6
c ⇒ 3.4
So, the equation of the line is :
y = mx + c
y = 1.6x + 3.4
Jane had $5.00, then spent $2.00. How much does she have now?
Answers
Answer:
$3.00
Step-by-step explanation:
$5.00 = 5
$2.00 = 2
5
-2
_
3
3 = $3.00
Answer:
$3.00
Step-by-step explanation:
In the expression 67.8046 8.264 - 243.5, all of the numbers are measured quantities and have the same units. Evaluate this expression to the correct number of significant figures.
Answers
The result of evaluating 67.8046 + 8.264 - 243.5 is -167.431
How to evaluate the expression?The expression is given as:
67.8046 + 8.264 - 243.5
The highest number of significant figures in the expression is 6 (i.e. 67.8046)
This means that the result must be in 6 significant figures.
Next, we evaluate the expression as follows:
67.8046 + 8.264 - 243.5 = -167.4314
Approximate to 6 significant figures.
67.8046 + 8.264 - 243.5 = -167.431
Hence, the result of evaluating 67.8046 + 8.264 - 243.5 is -167.431
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please helb it is very hadr
Answers
Answer:
a=15.7mm2,31.4
b=18.84in2,37.68
Considering the results from part a, it follows that the volume of a cylinder can be found in the same way as the volume of a rectangular prism. use your results and what you know about volume to explain how to find the volume of a cylinder with a base radius of r units and a height of h units.
Answers
To find the volume of a cylinder we must perform a mathematical operation that is expressed in the following formula V = Π h r².
How to find the volume of a cylinder?To find the volume of a cylinder we must solve the following mathematical formula:
V = Πhr²let's do an exampleOur example cylinder is 10 centimeters high and 6 centimeters in diameter. What is its volume?
To find the volume we substitute the values as follows:
V = 3.1415 × 10cm × 3cm²V = 307.35 cm³Learn more about volume in: https://brainly.com/question/1578538
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A major arc will have a measure that is
O A. greater than 180°
OB. less than 180°
O C. equal to 180°
Answers
Think Major greater than 180°, Minor less than 180°. If arc equals 180° than it is a semi circle.
A.
These graphs depict the price and output levels of apples under perfect competition and monopoly market structures. what is the extra amount that mary would pay for apples under a monopoly instead of a perfect competition? a. $2 b. $3 c. $4 d. $5 e. $6
Answers
The extra amount that Mary would pay for apples under a monopoly instead of perfect competition is B. $3
Calculations and Parameters:From the complete information,
There are images of the prices that can be gotten under a monopoly and the ones that can be gotten in a perfect competition by Mary.
The marginal cost which is graphed against the pound of apples and the price shows Mary would pay $15 and the marginal revenue shows that Mary would pay $12.
Hence, the difference between them, which is the extra amount to be paid would be $15-$12
=$3
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Answer:
B. 3$
Hope this helps!
Step-by-step explanation:
2 cups is equivalent to___ pint.
Answers
Answer:
1 pint is equal to 2 cups
Step-by-step explanation:
2 cups is equivalent to__1_ pint.
Hope This Helped
Answer:
answer is 1
Step-by-step explanation:
A jar has 9 pennies.
3 nickels, 8 dimes, and
5 quarters. A coin is chosen
at random, not replaced
then another is chosen.
Find the probability that
a quarter was chosen
followed by a penny,
Answers
Answer:
the answer to this question is 3/40
Step-by-step explanation:
if you want my explanation you ca
There is 1/2 of a pizza left for 4 friends to share. What fraction of a pizza will each friend get to eat?
Answers
Answer:
12.5% is the answer.
Step-by-step explanation:
the graph f(x) is shown below. Which function could represent the graph of f(x)?
(1) f(x)=(x+2)(x^2+3x-4)
(2) f(x)=(x-2)(x^2+3x-4)
(3) f(x)=(x+2)(x^2+3x+4)
(4) f(x)=(x-2)(x^2+3x+4)
Answers
The function which represents the graph is f(x) = (x + 2)(x² + 3x - 4). Then the correct option is 1.
What is a function?A function is a statement, rule, or law that establishes the connection between two variables. In mathematics, functions are everywhere and are necessary for constructing physical connections.
The graph is given below.
The value of the function is zero for the values of x are -4, -2, and 1.
Let's check which function gets satisfied.
f(x) = (x + 2)(x² + 3x - 4)
The function can be written as
f(x) = (x + 2)(x + 4)(x - 1)
Then the values of x for which the value of the function is zero.
f(x) = 0
(x + 2)(x + 4)(x - 1) = 0
x = 1, -2, -4
Then the function will be f(x) = (x + 2)(x² + 3x - 4). Then the correct option is 1.
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Leah's family took a road trip to Mount Rushmore. Leah fell asleep 44% of the way through the trip. If Leah fell asleep after they had travelled 132 miles, what was the total length of the trip?
Answers
The total length of the trip 190.08 miles
How you do it is to add the 44% of 132 to 132
= (132 + (132×44%))
What is the length?Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived.
First, you have to find out how much 44% is. Change it into decimal form (0.44) and then multiply the two together.
132 × 0.44 is 58.08 miles.
Then you add that to the rest of the trip, 132 miles.
= (132 + 58/08
=190.08
The total length of the trip was 190.08 miles.
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The interior angles of a pentagon are 126°, 114°, y°, and 83°. Find the value of y°?
please can someone help me with the answer to this question pls
am preparing for my WASSCE(west Africa senior school certificate examination) which is going to be held tomorrow
pls can someone help me
Answers
Answer:
217
Step-by-step explanation:
angles in a pentagon =540°
y°+126°+114°+83°=540°
y°+323°=540°
y°=540°-323°
y°=217°
If 2^2^x = 2^3 what is the value of x
Answers
Answer:
[tex]\dfrac 32[/tex]
Step-by-step explanation:
[tex]~~~~~~~2^{2x} = 2^3\\\\\implies \ln\left(2^{2x} \right) = \ln (2^3)\\\\\implies 2x \ln(2) = 3 \ln(2) \\\\\implies 2x = 3\\\\\implies x = \dfrac 32[/tex]
Answer:
B
Step-by-step explanation:
evaluate for f(6), show all work
Answers
Answer:
32
Step-by-step explanation:
f(6)=6^2-4
f(6)=36-4
f(6)=32
Answer:
f(6)=32
Step-by-step explanation:f(6)=6^2 -4
f(6)=36-4
f(6)=32
Look at the set of quadrilaterals in the coordinate plane shown below.
Which statement is TRUE?
Because quadrilateral ABCD can be reflected across the x-axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .
Because quadrilateral ABCD can be reflected across the y-axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
Because quadrilateral ABCD can be reflected across the y -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .
Because quadrilateral ABCD can be reflected across the x-axis, then rotated 90° clockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° clockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .
Because quadrilateral ABCD can be reflected across the line y = x, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.Look at the set of quadrilaterals in the coordinate plane shown below.
Which statement is TRUE?
Because quadrilateral ABCD can be reflected across the x-axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .
Because quadrilateral ABCD can be reflected across the y-axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
Because quadrilateral ABCD can be reflected across the y -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .
Because quadrilateral ABCD can be reflected across the x-axis, then rotated 90° clockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° clockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D' .
Because quadrilateral ABCD can be reflected across the line y = x, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 1.5 to obtain quadrilateral A'B'C'D', then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
Answers
The true statement about the set of quadrilaterals in the coordinate plane is B. Because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
What is a quadrilateral?A quadrilateral is a polygon having four sides, four angles, and four vertices.
In this case, because quadrilateral ABCD can be reflected across the x -axis, then rotated 90° counterclockwise about the origin, and then dilated about the origin by a scale factor of 2 to obtain quadrilateral A'B'C'D' , then quadrilateral ABCD is similar to quadrilateral A'B'C'D'.
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Question 7 of 25
All else being equal, a study with which margin of error would give you the
most confidence in the results?
O A. 13 percentage points
OB. +12 percentage points
OC. 19 percentage points
OD. 16 percentage points
SUBMIT
Answers
Answer:
+12 percentage points
Step-by-step explanation:
All options have positive percentage in themselves
So lesser marginal error should be more applicable as lower the marginal errors lower the probability of doing mistakes so higher marks .
Option B
You deposit $4000 in an account earning 7% interest compounded continuously. How much will you have in the account in 10 years?
Answers
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$4000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years\dotfill &10 \end{cases} \\\\\\ A=4000e^{0.07\cdot 10}\implies A=4000e^{0.7}\implies A\approx 8055.01[/tex]