Given: Triangle ACD is isosceles; <1 is congruent to <3 Prove: Segment AB || Segment CD

The value of x after completing the steps is -16

Given the equation solved by Lorie expressed as":

[tex]10(0.5x+2) - 5=3(x-6)+1[/tex]

Expand the bracket using the distributive law as shown:

5x + 20 - 5 = 3x - 18 + 1

Collect the like terms:

5x - 3x = -18 + 1 - 20 + 5

Simplify by adding and subtracting

2x = -32

Divide both sides by 2:

2x/2 = -32/2

x = -16

Hence the value of x after completing the steps is -16

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Answer:

$15,000,000

Step-by-step explanation:

Fórmula de intereses = P × R × T

P = $15,000,000

R = 30% anual = 0.3

T = 8 meses = 8/12 = 0.6667

Intereses = $15,000,000 × 0.3 × 0.6667

Intereses = $3,000,000

Después de 8 meses, el monto a pagar = $15,000,000.00+ $3,000,000

= $18,000,000

Si hace un pago de $3,000,000 dentro de 2 meses, cuánto deberá pagar al cabo de los 8 meses si se considera una tasa de 30% anual

= $18,000,000 - $3,000,000

= $15,000,000

Answer:

Hey there!

We want to change the equation for each line into slope intercept form, or y=mx+b form.

Luckily, the first one is already in slope intercept form.

The second line can be converted to: y=-3/4x-7/4.

The third line can be converted to: -8y=-6x+4, or y=3/4x-1/2

Line one and line two are neither perpendicular or parallel.

Line one and line three are perpendicular.

Lines two and three are neither perpendicular or parallel.

This is because parallel lines have same slope, and perpendicular lines have opposite reciprocal slopes.

Hope this helps :)

Answer:

Line 1 and Line 2: Neither

Line 1 and Line 3: Perpendicular

Line 2 and Line 3: Neither

Step-by-step explanation:

To make the answering process easier, begin by converting each formula into the format y = mx +b:

Line 1: y = -4/3x + 1 (already in format)

Line 2:

-4y = 3x + 7

Divide all terms by -4:

y = -3/4x - 7/4

Line 3:

6x - 8y = 4

Subtract both sides by 6x:

-8y = -6x + 4

Divide all terms by -8:

y = 3/4x - 1/2

We can determine the relationships of the lines:

Line 1 and Line 2: Neither. They do not have the same slope, and they are not opposite reciprocals of each other.

Line 1 and Line 3: Perpendicular. The slopes of each line are opposite reciprocals: (-4/3 and 3/4)

Line 2 and Line 3: Neither. The slopes are the same but one is negative.

Answer:

None

Step-by-step explanation:

If one angle is 95 degrees and other is an obtuse angle (greater than 90 degrees) Say 91 (Just 1 degree greater than 90). So, no triangle would be made because a triangle can never be made from 2 obtuse angles.

Answer:

78/4=19.5, 68/7=9.71, 98/6=16.3

Step-by-step explanation:

Step-by-step explanation:

The least number is 11

N = 11

99 x n = 99 x 11 = 1089

Which is a perfect square

Answer: 1035 cm^2

Step-by-step explanation:

Given that the shape s is exactly one quarter of solid sphere.

Where the volume of the shape s is 1994πcm^3.

The formula for volume of a sphere is

V = 4/3πr^3

The volume will be divided by 4 since the given solid is exactly quarter of solid sphere. Then equate it to the given value

1994π = 4/3πr^3 × 1/4

The π will cancel out

1994 = r^3/3

Cross multiply

5982 = r^3

r = cube root of 5982

r = 18.2 cm

The surface area of a sphere is

A = 4πr^2

Substitute r in the formula

A = 4× π × 18.2^2

A = 4141

Since the shape is exactly one quarter of solid sphere. Divide the answer by 4

A = 4141/4

A = 1035.3 cm^2

The surface area of s is therefore 1035.3 cm^2

The surface area of the shape s is approximately 329.53 cm².

Important information:

Volume of a sphere is:

[tex]V=\dfrac{4}{3}\pi r^3[/tex]

The volume of one-quarter of a solid sphere is 1994π cm².

[tex]1994\pi=\dfrac{1}{4}\times \dfrac{4}{3}\pi r^3[/tex]

[tex]1994\pi=\dfrac{1}{3}\pi r^3[/tex]

[tex]\dfrac{1994\pi\times 3}{\pi}=r^3[/tex]

[tex]5982=r^3[/tex]

Taking cube root on both sides, we get

[tex]\sqrt[3]{5982}=r[/tex]

[tex]r\approx 18.153[/tex]

Surface area of a sphere is:

[tex]S=4\pi r^2[/tex]

Surface area of one quarter of solid sphere is:

[tex]S=\pi r^2[/tex]

[tex]S=\pi (18.153)^2[/tex]

[tex]S=329.5314\pi[/tex]

[tex]S\approx 329.53\pi[/tex]

Therefore, the surface area of the shape s is 329.53 cm².

Find out more about 'Sphere' here:

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Answer:

y=0.6x

(a)$43.20

(b)$1416.67

Step-by-step explanation:

Let:

The club donates 60% to the foundation.

Therefore, the amount of money the foundation will receive

n=60% of m

n=0.6m

(a) If the club raised $72

m=$72

n=0.6*72

The amount of money the foundation will receive, n=$43.20

(b)If the foundation received a cheque of $850

n=$850

Therefore:

850=0.6m

m=850/0.6

m=$1416.67

The club raised $1416.67 in total for the year

Answer: 1

Step-by-step explanation:

If you get a 10/10 on something, it’s 100%. If you get a 9/10, it’s 90%. If you get a 9/9, it’s 100%. So, if you get 8/9, it’s roughly 90% but not exact. It’s actually 88.8%

Answer:

7 questions

Step-by-step explanation:

if 9 = 100%

? = 80%

if less more divides

80/100 ×9

4/5×9

36/5

7.2 which is approximately 7 questions

Area of the circle = π * (35 yd)^2

Let A be the area of the sector subtended by a central angle measuring 80º. Then

A / (π * (35 yd)^2) = 80º / 360º  ==>  A = 2450π/9 yd^2 ≈ 854.78 yd^2

Subtract from A the area of the triangle, whose base has length 45 yd and with height 25 yd:

A - 1/2 * (45 yd) * (25 yd)  ≈ 292.28 yd^2

This is the area of the missing circular segment.

Then the area of the playground is equal to the area of the circle minus this area,

π * (35 yd)^2 - 292.28 yd^2 ≈ 3554 yd^2

Answer:

1) 10

2) 16

Step-by-step explanation:

1) 2x+15=37-2

2x+15=35

2x=35-15

2x=20

2 2

x=10

2)10x-8=9x+8

10x-9x=8+8

x=16

Hope this helps ❤

Answer:

The answer is given below

Step-by-step explanation:

The slope of a line is the gradient of the line and is the ratio of the vertical change (change in y) to horizontal change (change in x) between two points. The slope of a line determines its steepness and direction.

A positive slope means the line slants from the right downward while a negative slope means the line slant upwards to the left. The greater the slope of for a positive slope the greater the steepness while for a negative slope the lesser the slope the greater the steepness.

Line f has a slope of −63, and line g has a slope of −84. Since both lines have negative slope, the line slant upwards to the left. The slope of line g is smaller than that of line f, therefore line g is more steeper than line f.

Answer: 3/4 cups per cake.

Step-by-step explanation:

He needs 3 cups for 4 cakes.

Then, if you want to know the amount that he needs for each cake, you need to see the quotient between the number of cups and the number of cakes:

S = 3cups/4 cakes = (3/4) cups per cake.

In the number line, 3/4 will be:

0--I--I--(here)--1--I--I--I--2

Answer:  A. (10, 5)

Step-by-step explanation:

Inverse variation means xy = k

Given: x = 5, y = 10 --> k = 5(10) = 50

A. 10(5) = 50    This works!

B. -5(10) = -50  

C. -10(5) = -50

D. 5(-10) = -50

The only option that results in k = 50 is option A.

Answer:

Average rate of change in dollars per year between years 15 to 20 is:

$5300 per year.

Step-by-step explanation:

Given that:

Initial Investment, P  = $5000

Formula:

[tex]A(t) = P(1.06)t[/tex]

To find: If James invests $5000,

average rate of change in dollars per year (rounded to the nearest dollar) between years 15 and 20=?

Solution:

First of all, let us find out A(15) and A(20):

Putting t = 15 first,

[tex]A(15) = 5000(1.06)\times 15 ....... (1)[/tex]

Putting t = 20,

[tex]A(20) = 5000(1.06)\times 20 ....... (2)[/tex]

Average rate of change / year is defined as:

[tex]\dfrac{\text{Change in value of A}}{\text{Number of years}}[/tex]

So, required rate of change:

[tex]\dfrac{A(20)-A(15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 20-5000 \times 1.06 \times 15}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times (20-15)}{5}\\\Rightarrow \dfrac{5000 \times 1.06 \times 5}{5}\\\Rightarrow 5000 \times 1.06\\\Rightarrow \$5300\ per \ year[/tex]

So, the answer is:

Average rate of change in dollars per year between years 15 to 20 is:

$5300 per year.

Answer:

[tex]\huge\boxed{j=38}[/tex]

Step-by-step explanation:

[tex]\dfrac{j}{-2}+7=-12\qquad\text{subtract 7 from both sides}\\\\\dfrac{j}{-2}+7-7=-12-7\\\\\dfrac{j}{-2}=-19\qquad\text{multiply both sides by (-2)}\\\\(-2)\!\!\!\!\!\!\!\diagup\cdot\dfrac{j}{-2\!\!\!\!\!\diagup}=(-2)(-19)\\\\j=38[/tex]

Answer: j = 38

Step-by-step explanation: First isolate j/-2 by subtracting

7 from both sides of the equation.

That gives you j/-2 = -19.

From here, since j is being divided by -2, multiply

both sides of the equation by -2 so j = 38.

Answer:

[tex]x^7y^2+x^5z^3+y^3z^4+xyz[/tex]

Step-by-step explanation:

It is required that the algebraic expression has exactly 3 different variables

Since it must have a degree of 7, the highest power in the expression will be 7.

Therefore, an example of such an algebraic expression will be:

[tex]x^7y^2+x^5z^3+y^3z^4+xyz[/tex]

Answer:

C. 15/16

Step-by-step explanation:

A. Divide by 3

B. Divide by 5

C. Can't divide by anything.

D. Divide by 4

Answer:

C

Step-by-step explanation:

21/24 = 7/8

35/40 = 7/8

7/8 ≠ 15/16

14/16 ≠ 15/16

28/32 = 7/8

Answer:

(A)[tex](-\infty, 2)(2, \infty)[/tex]

(−[infinity], 2) (2, [infinity])

Step-by-step explanation:

Given the rational function, f(x) such that:

[tex]f(x)=\dfrac{x+1}{x-2}[/tex]

The domain of the function are the values of x for which f(x) is defined.

A rational function is undefined when its denominator equals zero.

Denominator of f(x)=x-2

x-2=0

x=2

Therefore, f(x) is undefined at x=2.

The domain of f(x) is all therefore all real numbers excluding 2.

This is written in set notation as:

[tex](-\infty, 2)(2, \infty)[/tex]

The correct option is A.

Answer: A (-infinity,2) (2,infinity)

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

This is false because a population represents all and not some. A population is the collection of all outcomes, responses, measurements, or counts that are of interest. It is not a collection of 'some' outcomes. It is a collection of 'all' outcomes.

A population data set is a set which contains all the items or elements of a specified group or data set. It is a complete list of all the possible data values.

The sample of a population are drawn out of a population. They are A subset of a population.

Answer:

[tex]245[/tex] [tex]cm^{2}[/tex]

Step-by-step explanation:

If Every side is 7cm, that means that every side is congruent to the other.

So,

[tex]7[/tex]×

There are basically 5 squares, counting the one in the middle.

So, we will multiply 49 by 5.

[tex]5[/tex]×[tex]49[/tex]=[tex]245[/tex] [tex]cm^{2}[/tex]

Hence, your answer will be [tex]245[/tex] [tex]cm^{2}[/tex]

Answer:

to the nearest hundreths or any one

Step-by-step explanation:

Answer:

Option (B)

Step-by-step explanation:

Let the five distinct positive integers are a, b, c, d, e.

Average of these five integers is 20.

[tex]\frac{a+b+c+d+e}{5}=20[/tex]

a + b + c + d + e = 100

If these integers are in the increasing order,

Median of these integers 'c' = 12

If the sum of d and e is the largest then the sum of a and b will be the smallest.

Therefore, the smallest positive integers a and b will be,

a = 1 and b = 2

1 + 2 + 12 + d + e = 100

15 + d + e = 100

d + e = 100 - 15

d + e = 85

Since d will be greater than the median c,

d > c

d > 12

For the largest value of integer 'e', value of 'd' will be minimum.

The least value of d will be = 13

Then, 13 + e = 85

e = 85 - 13

e = 72

{a, b, c, d, e} = {1, 2, 12, 13, 72}

Therefore, the largest possible number is this set will be 72.

Option (B) will be the answer.

Answer: x=6, y=20

Step-by-step explanation:

Since ΔBCD and ΔTUS are congruent triangles, we can set the sides equal to each other.

y=2y-20                           [subtract both sides by 2y]

-y=-20                              [divide both sides by -1]

y=20

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

3x+32=9x-4                    [add both sides by 4, and subtract both sides by 3x]

36=6x                              [divide both sides by 6]

x=6

Answer:

Angle B =  75 degrees

AC =  35.7

BC =  9.6

Step-by-step explanation:

Angle A = 15 degrees (given)

Angle C = 90 degrees (given)

c = 37 (given)

Angle B = 90-15 = 75 degrees

AC = AB cos(A) = 37 cos(15) = 35.7

BC = AB sin(A) = 37 sin(15) = 9.6

Answer:

x= 48

Step-by-step explanation:

x∝ y

x= ky

24= 8k

k= 3

Now solve for x

x= ky

x= 3x 26

x= 48

I hope it helped

Responda:

P (verde) = 8/15

P (vermelho) = 1/3

P (azul)). 2/15

P (verde ou azul) = 2/3

P (não verde) = 7/15

Explicação passo a passo:

Dado o seguinte:

Número de bolas verdes = 8

Número de bolas vermelhas = 5

Número de bolas azuis = 2

N (verde) = 8

N (vermelho) = 5

N (azul) = 2

Portanto, número total de bolas;

N (total) = 8 + 5 + 2 = 15

Probabilidade = número de resultados requeridos / Total de resultados possíveis

1.) Probabilidade de escolher uma bola verde:

P (verde) = número de bolas verdes / número total de bolas

P (verde) = 8/15

2.) Probabilidade de pegar uma bola vermelha: P (vermelho) = número de bolas vermelhas / número total de bolas

P (vermelho) = 5/15 = 1/3

3) Probabilidade de pegar uma bola azul:

P (azul) = número de bolas azuis / número total de bolas

P (azul) = 2/15

4) probabilidade de verde ou azul:

P (verde ou azul) = P (verde) + p (azul)

P (verde ou azul) = 15/8 + 2/15 = 10/15 = 2/3

P (não verde) = 1 - P (verde)

P (não verde) = 1-8/15

P (não verde) = 7/15

Answer: 1 3/4

Step-by-step explanation:

Step 1: Subtraction

1/4+1 1/2

Step 2: Addition

1 3/4

Hope it helps <3

Answer:

1 3/4

Step-by-step explanation:

Simplify 1/2 -1/4+1 1/2​

1/2 - 1/4 + 1 1/2 =

= 2/4 - 1/4 + 1 2/4

= 1/4 + 1 2/4

= 1 3/4

Answer:

58>13>-35>-51, so A is correct.

Step-by-step explanation:

Altitude of Snowvale: 13

Altitude of Highbridge: 58

Altitude of Westsilver: -51

Altitude of Springmoor: -35

Decreasing order means from greatest to least.

Obviously, positive numbers are greater than negative numbers, so we put the positive numbers first. 58>13>-35>-51.

(Note that with negatives, a greater number is a number closer to zero!)

Answer:

A

Step-by-step explanation:

The altitudes have to be arranged in decreasing order.

58 > 13 > -35 > -51