3. Choose the correct answer.
Which theorem or postulate could be used to prove the congruence of the triangles?

Answer:

x = (1/3)

Step-by-step explanation:

8ˣ = 2

8 = 2³

2³ˣ = 2¹

3x = 1

÷3   ÷3

------------

       1

x = ------

       3

I hope this helps!

Answer:

Step-by-step explanation:

Ok:

Since percent can only add up to 100%, the sum must be no longer over 100%

There is no green on the spinner only red, white, and blue!

This means that 0 out of 100 percent is available for green!

Answer: 0%

The solution is Option C.

The probability of getting a green colored section on the spinner is given by the equation P ( green ) = 33 %

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability of getting a green colored section on the spinner be represented as P ( green )

Now , the equation will be

The number of sections on the spinner = 3 sections

The 3 sections are = { red , white , green }

So , probability of getting a green colored section P ( green ) = 1 /  number of sections on the spinner

Probability of getting a green colored section P ( green ) = 1/3

Probability of getting a green colored section P ( green ) = 0.33

Probability of getting a green colored section P ( green ) = 33 %

Therefore , the value of P ( green ) is 33 %

Hence , the probability is 33 %

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Answer:

===========================

Since absolute value is never negative, this inequality is correct for any value of m.

Correct answer choice is B.

Answer:

All real numbers.

Step-by-step explanation:

The bars either side of an expression or a value are the absolute value symbol. "Absolute value" means how far a value is from zero. Therefore, the absolute value of a number is its positive numerical value.

Given inequality:

[tex]|9m|+40 > 4[/tex]

Subtract 40 from both sides to isolate the absolute value on one side of the equation:

[tex]\implies |9m|+40-40 > 4-40[/tex]

[tex]\implies |9m| > -36[/tex]

As the absolute value of a number or expression is its positive numerical value:

[tex]\implies |9m| \geq 0[/tex]

Therefore, as 9m is always greater than or equal to zero, it will always be greater than -36, regardless of the value of m.

Therefore, the solution of the given inequality is all real numbers.

The answer of resulting box volume = 576[tex]x[/tex] - 100[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]

What are example and volume?

The volume of an object serves as a gauge for its capacity. For instance, if the brim of a cup can hold 100 ml of water, that cup is said to have a 100 ml capacity.. Another way to quantify volume is how much room a three-dimensional object occupies.

Volume = length x breath x height

length = 32-2[tex]x[/tex]
Breath = 18-2[tex]x[/tex]

Height = [tex]x[/tex]

Volume = (32-2[tex]x[/tex]) x (18-2[tex]x[/tex]) x ([tex]x[/tex])

= 576 - 64[tex]x[/tex] - 36[tex]x[/tex] - 4[tex]x^{2}[/tex] x ([tex]x[/tex])

= 576[tex]x[/tex] - 100[tex]x^{2}[/tex] - 4[tex]x^{3}[/tex]
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Answer:

14

Step-by-step explanation:

Check the file

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{5(2)^2 - 6}[/tex]

[tex]\mathsf{= 5(2 \times 2) - 6}[/tex]

[tex]\mathsf{= 5(4) - 6}[/tex]

[tex]\mathsf{= 20 - 6}[/tex]

[tex]\mathsf{= 14}[/tex]

[tex]\huge\text{Therefore, your answer should be: \boxed{\mathsf{14}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Jose will need 40.82 in² of paper to cover the stack of coins

The area in this scenario will be:

A = 2πr² + 2πrh

Where r and h represent the radius of the coins and the height of the coin stack respectively

Given: diameter of coin = 1 inch and thickness = 1/8 inch

radius(r) = diameter/2 = 1/2 inch

Substituting values gives:

A = 2×3.14 × (1/2)² + 2×3.14 ×(1/2)×(100 ×(1/8))

A = 40.82 in²

Note: the correct thickness of the coins should be 1/8 in

Therefore, the area of paper Jose will need to cover the stack of coins is 40.82 in²

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The zeros of the cubic function f(x) = 2x³ - 6x² - 16x - 20 are given as follows:

x = 5, x = -1 + i, x = -1 - i.

The equation is defined by the rule presented as follows:

f(x) = 2x³ - 6x² - 16x - 20.

One solution for the equation is given as follows:

x = 5.

Because f(5) = 0.

Then (x - 5) is a linear factor of the function f(x), which can be written as follows:

2x³ - 6x² - 16x - 20 = (ax² + bx + c)(x - 5).

This is because the product of a linear function and a quadratic function results in a cubic function.

Now we expand the right side to begin finding the coefficients of the quadratic function that we are going to solve to find the remaining zeros:

2x³ - 6x² - 16x - 20 =  = ax³ + (b - 5a)x² + (c - 5b)x - 5c.

Then these coefficients are obtained comparing the left and the right side of the equality as follows:

Hence the equation is:

2x² + 4x + 4.

Using a quadratic equation calculator, the remaining zeros are given as follows:

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the exact value of x, so that the greatest possible amount of light is admitted is 3.92 ft.

let x represents the radius of a semicircle, thus the width of the rectangle = 2x, length be y.

perimeter of the rectangular window = πx + 2y + 2x = x(π +2) + 2y

it is given that the perimeter is 28 ft.,

28 = x(π +2) + 2y

y = 28 - x(π +2) / 2

the area of the window A = 1/2 πx² = 2yx ( area of semicircle + area of rectangle)

A = 1/2 πx² + 2x [(28 - x(π +2) / 2]  (Substituting the value of y)

A = 1/2 πx² + 28x - πx² - 2x²

A = 28x - x² ( 2 + π/2 )

The maximum value of x is when dA/dx = 0

A' = 28- 2x ( 2 + π/2 )

2x ( 2 + π/2 ) = 28

x ( 2 + π/2 ) = 14

x = 3.92 ft

hence the value of x so that the greatest possible amount of light is admitted is 3.92 ft.

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(complete question)

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle. See the figure below.) If the perimeter of the window is 28 ft, find the value of x so that the greatest possible amount of light is admitted.

When r is made the subject of the formula we have; V + πh^3/3πh^2

The term subject of a formula has to do with the variable that we are trying to obtain in the equation. Hence the subject of the formula must be written on the left hand side of the mathematical equation.

We have;

V = πh^2(r - h/3)

We open the bracket;

V = πrh^2 - πh^3/3

Adding πh^3/3 to both sides, we have;

V + πh^3/3 = πrh^2

Then we divide both sides by πh^2

r = V + πh^3/3/πh^2

r =  V + πh^3/3πh^2

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The solutions for the equation (2x+3)² = 10 is:

Given:

the equation is:

(2x+3)² = 10

we need to solve the following equation.

⇒ (2x+3)² = 10

taking square roots on both sides.

⇒ √(2x+3)² = √10

⇒ 2x+3=±√10

Now solving:

2x+3=√10 and 2x+3=-√10

2x=√10-3 and 2x=-√10-3

x=√10-3/2 and x=-√10-3/2

Hence we get the solutions of the given equation.

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Probability of choosing the biased coin if you won a prize is 0.30

Let "B" be the event of selecting biased coin and "H" be the event of getting head.

P(B) = 0.5

P(getting head when coin was biased) = 100% - 78%

= 22% = 0.22

Using conditional Probability that biased coin was selected given that you have won the prize that is getting head

we have to calculate ,

P(B | H ) = P(B∩H)/P(H)

here , P(B∩H) = P(biased coin selected and getting head) = 0.5 × 0.22

and P(H) = P(getting head)

P(getting head when coin was biased) + P(getting head when coin was unbiased) = 0.5 × 0.22 + 0.5 × 0.5

putting all together ,

P(B | H ) = P(B∩H)/P(H) = 0.5 × 0.22 / 0.5 × 0.22 + 0.5 × 0.5

cancelling 0.5 from numerator and denominator

= 0.22 / 0.5+ 0.22

= 0.22 / 0.72 = 22/72

=0.30

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Answer:

Step-by-step explanation:

1. Since the price goes up by whatever number it eventually become 20$ from 16$. SO subtract to get number. 20-16= 4 $

So fitting best...: 20$=p+16;p=4$= TRUE

Answer:20$=p+16;p=4$ or Choice C

PS.Hope you find it helpful!!

The points that represents a viable solution to the system of inequalities include the following:

A. (−10, 170)

B. (80, 90)

C. (250, −50)

In order to determine which points are true and viable with respect to a solution of the given system of inequalities, we would have to test the each of the points by substituting their values into the inequalities as follows;

For points (-10, 170), we have:

x + y ≥ 150

-10 + 170 ≥ 150

160 ≥ 150 (Viable).

1.5x + 3.5y ≤ 600

1.5(-10) + 3.5(170) ≤ 600

-15 + 595 ≤ 600

580 ≤ 600 (Viable).

For points (80, 90), we have:

x + y ≥ 150

80 + 90 ≥ 150

170 ≥ 150 (Viable).

1.5x + 3.5y ≤ 600

1.5(80) + 3.5(90) ≤ 600

120 + 315 ≤ 600

435 ≤ 600 (Viable).

For points (250, -50), we have:

x + y ≥ 150

250 - 50 ≥ 150

200 ≥ 150 (Viable).

1.5x + 3.5y ≤ 600

1.5(250) + 3.5(-50) ≤ 600

375 - 175 ≤ 600

200 ≤ 600 (Viable).

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Answer:

the side a  is equal to 15.

Step-by-step explanation:

I entered it into my calculator.

The Venn diagram is attached below.

We have four sets. The sets are represented by the alphabets "U", "N", "P", and "E". The universal set is represented by U. The sets are defined as given below.

U = {x | - 10 ≤ x ≤ 10, x ∈ l}

N = {x | -10 ≤x≤-1, x ∈ l}

P = {x | 1 ≤ x ≤ 10, x ∈ l}

E = {x | x = 2a, 1 ≤ a ≤ 5, a ∈ l}

The elements in the universal set "U" are -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

The elements in the set "N" are -10, -9, -8, -7, -6, -5, -4, -3, -2, and -1.

The elements in the set "P" are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.

The elements in the set "E" are 2, 4, 6, 8, and 10.

We need to draw the Venn diagram. A Venn diagram is a graphic representation of the contrasts and similarities between two concepts. Venn diagrams are sometimes known as logic diagrams or set diagrams.

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The value to the system of equations is (-10, -4)

In this case, the system of equations is given as

5x -10y = 10

x + 2y = -18

Make x the subject in the second equation

So, we have the following representation

x = -2y - 18

Substitute x = -2y - 18 in the equation 5x -10y = 10

So, we have

5(-2y - 18) -10y = 10

Open the brackets

This gives

-10y - 90 - 10y = 10

Evaluate the like terms

-20y = 80

Divide by -20

y = -4

Recall that x = -2y - 18

So, we have

x = -2 * -4 - 18

Evaluate

x = -10

Hence, the solution is (x, y) = (-10, -4)

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Answer:

(-3,5)

Step-by-step explanation:

we just plug the solutions in the equation to see if it’s true

y<x+12

12<-4+12

12<8

Not true 12 is not less than 8

9<-7+12

9<5
not true 5 is not greater than 9

8<-5+12

8<7

Not true 8 is not less than 7

5<-3+12

5<9
true 5 is less than 9

Hopes this helps please mark brainliest

The vertex form of the equation y = -z² + 12z -4 is y = -(z - 6)² + 32.

A parabola's vertex is the location where the curve turns steepest. If a parabolic function has the shape of a 'U', it has a minimum value; otherwise, it has a maximum value. The parabola's axis of symmetry intersects with the parabola at its vertex.

For any parabola Ax² + Bx + C, the x-coordinate of the vertex is given by -B/(2A).

So, according to our question

A = -1
B = 12
C = -4

So, z = - 12/2(-1)

z = - 12/- 2

z = 6

Plug the value in the equation

y = - (6)² + 12(6) -4

y = -36 +72 -4

y = 32

So, the vertex of the parabola will be at (6, 32) and the vertex form of the equation y = -z² + 12z -4 is y = -(z - 6)² + 32.

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Minimum  number is 33+4*6= 57

Give us two positive numbers, x and y.

196 is the result: x*y = 19

The minimum is the product of the first plus four times the second: x + 4y.

The first equation results in y = 196/x. Put that into the second equation as a replacement:

x + 4y = x + 4(196/x) = x + 784/x

Taking the first derivative now, we can solve for x by setting it to zero.

d(x + 784/x)/dx = 1 - 784/[tex]x^{2}[/tex]

0 = 1 - 784/[tex]x^{2}[/tex]

0 = [tex]x^{2}[/tex]- 784 [[tex]x^{2}[/tex] multiplied on both sides]

784 = [tex]x^{2}[/tex]

[tex]\sqrt{784}[/tex] = [tex]\sqrt{x^{2} }[/tex]

Y = 196/x = 7 since we want a positive integer, hence x = 28

The factors of 196 are 196*1, 99*2, 66*3, 6*33,22*19, and 11*18 as a check.

196 + 4*1 = 200

99 + 4*2 = 107

66 + 4*3 = 78

33+4*6= 57

22 + 4*19 = 98

11 + 4*18=82

In fact, 33+4*6= 57 is minimum.

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By using GCF and distributive Property, it is obtained that

3550 = 5 [tex]\times[/tex] 710 as a product

What is Greatest Common Factor and distributive property?

Greatest Common factor (GCF) of two numbers a and b is the greatest number that divides both a and b.

Distributive property is the property over both addition and multiplication.

If a, b and c are three numbers, then distributive property is given by

[tex]a \times (b + c) = a \times b + a \times c[/tex]

3550 = 3000  + 550

Now,

[tex]3000 = 2\times 2 \times 2\times 3\times 5 \times 5 \times 5\\550 = 2 \times 5 \times 5 \times 11[/tex]

GCF of 3000 and 550 = 5

3550 = 5 [tex]\times[/tex] 600 + 5 [tex]\times[/tex] 110

3550 = 5 [tex]\times[/tex] (600 + 110) [Distributive Property]

3550 = 5 [tex]\times[/tex] 710

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If each  sides of the slab form 90° angles, The number of feet that

each diagonal measure is 34 feet.

Using Pythagoreans theorem formula to find the diagonal feet

D² =L² + W²

Where:

D = Diagonal

L= Length = 16 feet

W = Width = 30

Let plug in the formula

D² = 16² + 30²

D² = 256 + 900

D=√1156

D= 34 feet

Therefore the diagonal measure 34feet

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Answer: 30

Step-by-step explanation:

1. You find the slope by picking 2 points and dividing the change in the y-axis by the change in the x-axis. (Time is ALWAYS x)

(50-40)/40-20

(10)/20)

1/2

SLOPE=1/2

2. You find the y-intercept by picking a point, and plugging them into your equation, and solving for b.

(I will be using the point (20,40) )

40=1/2(20)+b

40=10+b

b=30

Y-INTERCEPT=30

The student council sold $273$ t-shirts were sold at $\$10$ per shirt.

Let $x$ be the number of shirts sold at $\$10$

Let $y$ be the number of shirts sold at $\$12$

$x+y=661$

$10x+12y=3780$

$x=y+101$

$10y+12y=3780$

$22y=3780$

$y=172$

$x=172+101$

$x=273$

Hence $273$ t-shirts were sold at $\$10$ per shirt.

If they sold $661$ t-shirts in total, and they made a mistake when recording the amount of t-shirts sold at each price, then they actually sold more t-shirts at $\$10$ than they thought. This means that they thought they sold fewer t-shirts at $\$10$ than they actually did.

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The values of the variables x in the  equations are;

An equation is a mathematical statement that connects two mathematical expression with an equals sign.

x + 9 = 13

Subtracting 9 from both sides of the equation, we get;

x = 13 - 9 = 4

3•x = 12

Dividing both sides of the equation by 3, we get;

x = 12 ÷ 3

x + 5 - 9 = 0

Subtracting (5 - 9) from both sides of the equation, we get;

x = 9 - 5 = 4

2•x + 5 = 17

Subtracting 5 from both sides of the equation, we get;

2•x  = 17 - 5 = 12

2•x = 12

Dividing both sides of the equation by 2, we get;

x = 12 ÷ 2 = 6

5•x - 3 = 17

Adding 3 to both sides of the equation, we get;

5•x = 17 + 3 = 20

5•x = 20

Dividing both sides of the equation by 5, we get;

x = 20 ÷ 5 = 4

x - 3 = 1

Adding 3 to both sides of the equation, we get;

x = 1 + 3

7•x = 35

Dividing both sides of the equation by 7, we get;

x = 35 ÷ 7 = 5

[tex]\frac{4\cdot x}{4} = 4 [/tex]

Multiplying both sides of the equation by 4 and dividing the result by 4, we get;

x = 4 × 4 ÷ 4 = 4

3•(x + 4) = 15

Dividing both sides of the equation by 3, we get;

x + 4 = 15 ÷ 3 = 5

x + 4 = 5

Subtracting 4 from both sides of the equation, we get;

x = 5 - 4 = 1

8 + x - 5 = 7

Adding 5 and subtracting 8 from both sides of the equation, we get;

x = 7 + 5 - 8 = 4

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There is a probability of 22% that exactly 4 defective parts will be found in a sample of 100.

Probability of a machine producing a defective part is 0.05,

p = 0.05

q  = 1 - p = 1 - 0.05 = 0.95

n = 100

P(x)  = ⁿCₓ pˣqⁿ⁻ˣ

x = 4  

P(4) = ¹⁰⁰C₄(0.05)⁴(0.95)⁹⁶

P(4) = 0.215569

=  0.2156

0.2156 is the probability of finding exactly 4 defective parts from a sample of 100.

The probability of defective parts is the likelihood that a part will be defective. This can be due to a variety of factors, such as poor quality control, incorrect manufacturing process, or use of sub-standard materials. A high probability of defective parts can lead to serious problems, such as faulty products, safety hazards, and financial losses.

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Answer:

Option A

Step-by-step explanation:

We are here given that Mary spent a total of $ 355.58 for a party , $200.93 on food , and an additional charge of $30.93 for each hour of party .

So the total money spent for staying at party , will be ;

[tex]\longrightarrow \$ 355.58 - \$200.93 [/tex]

[tex]\\\longrightarrow \$ 154.65 [/tex]

We can calculate the no. of hours spent at the party by dividing this amount by the rate of staying per hour at party as ;

[tex]\\\longrightarrow \dfrac{ \$ 154.65}{\$ 30.93 / hr } [/tex]

[tex]\\\longrightarrow 5 \ hrs . [/tex]

Hence she spent 5hrs at the party .

Answer:

Option 3 ) 18x - 9 = 72

Step-by-step explanation:

Algebraic equations:

  [tex]\sf \dfrac{3}{5}(30x - 15) = 72\\\\\\[/tex]

Multiply each term of (30x - 15) by 3/5,

    [tex]\sf \dfrac{3}{5}*30x - \dfrac{3}{5}*15=72\\\\\\3*6x - 3*3 = 72\\\\18x - 9 = 72[/tex]

The given equation is same as 18x - 9 = 72

Answer:

n = 3

Step-by-step explanation:

-4n + 7 + 2n = 1

Collect like terms

-2n + 7 = 1

Subtract 7 from both sides

-2n = 1 - 7

Do the math on the right side

-2n = -6

Divide both sides by -2

n = 3