The phone company NextFell has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone.

Answer:

A. AB = AC because of the definition of an isosceles triangle

B. ∠B = ∠C because corresponding parts of congruent triangles are congruent.

D. BM = CM because of the definition of a midpoint

Step-by-step explanation:

A. An isosceles triangle is a triangle with two equal sides, hence:

AB = AC because of the definition of an isosceles triangle. option A is correct.

D. Since Point M is drawn as the midpoint of BC, hence:

BM = CM because of the definition of a midpoint. Option D is correct.

E. Reflexive property of congruence states that an angle, line segment, or shape is always congruent to itself. hence AM ≈ AM because of reflexive property.

AM ≈ AM because of the Symmetric Property is wrong. Option E is wrong.

C) The side - side - side (SSS) triangle congruence theorem states that if all the sides of two triangles are equal, then they are congruent triangles.

Since BM = CM, AM = AM and AB = AC, hence ΔABM = ΔACM because of the SSS triangle congruence criterion

ΔABM = ΔACM because of the SAS triangle congruence criterion is wrong. Option C is wrong.

D. Corresponding parts of congruent triangles are congruent. hence:

∠B = ∠C because corresponding parts of congruent triangles are congruent. Option B is correct

Answer:

B

Step-by-step explanation:

They can buy 120 vans, 60 small trucks, and 80 large trucks.

The truck company plans to spend 10 million on 260 vehicles. Each commercial van cost 25,000 dollars. Each small truck 50,000 dollars and each large truck 50,000 dollars. They needed twice as many van as small truck

Therefore,

let

s = number of small truck

number of van = v

let

l = number of large truck

v + s + l = 260

25,000(v) + 50,000(s) + 50,000(l) = 10,000, 000

v + 2s + 2l = 400

Hence,

v = 2s

So,

2s + 2s + 2l = 400

4s + 2l = 400

2s + s + l = 260

3s + l = 260

2s + l = 200

s = 60

l = 200 - 2(60)

l = 200 - 120

l = 80

v = 2(600 = 120

Therefore, they can buy the following:

number of small truck = 60

number of van = 120

number of large truck = 80

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Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

\(\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

\(\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}\)

The formulas for the area of a regular polygon and the area of a circle given their radii are:

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}\)

Therefore, the area of the regular pentagon is:

\(\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}\)

The area of the circumcircle is:

\(\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}\)

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

\(\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}\)

                                                 \(\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}\)

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

Answer:

W=23.13

Step-by-step explanation:

2(−6.4 + w) = 33.46 

divide both sides

-6.4+w=16.73

move the constant to the right

w=16.73+6.4

end result-

w=23.13

Answer:

answer is 23.13

Answer:

\(x = -\frac{7 + 2z}{(y + 1)}\)

Step-by-step explanation:

-2z - xy = x + 7

Add 2z to both sides:

-2z + 2z - xy = x + 7 + 2z

-xy = x + 7 + 2z

Next, subtract x from both sides:

-xy - x  = x - x + 7 + 2z

- xy - x = 7 + 2z

Factor out -x from the left-hand side of the equation:

- x(y + 1) = 7 + 2z

Divide both sides by - (y + 1) to isolate x:

\(\frac{x(y + 1)}{- (y + 1)} = \frac{7 + 2z}{-(y + 1)}\)

\(x = -\frac{7 + 2z}{(y + 1)}\)

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9514 1404 393

Answer:

  A.  2,144.66 in³

Step-by-step explanation:

The formula for the volume of a sphere is ...

  V = (4/3)πr³

The radius is half the diameter, so this can be written in terms of diameter as ...

  V = (4/3)π(d/2)² = (π/6)d³

For a diameter of 16 inches, the volume is ...

  V = (π/6)(16 in)³ ≈ 2,144.66 in³

Answer:

a. y = 265 + 5x

b. 500 = 265 + 5x

   5x = 500 - 265

   5x = 235

   x = 235/5

   x = 47

She took 47 aerobic classes.    

Step-by-step explanation:

Total Cost is yearly cost + 5 into however many aerobic classes you take.

Find the number of classes by substituting values in the equation.

The value of the determinants are

D=13

Dx =26

Dy =52

Dz =26

The determinant of a matrix is ​​a scalar value calculated for a given square matrix. Linear algebra deals with the determinant, it is calculated using the elements of a square matrix. It can be thought of as a scaling factor for the matrix transformation. Useful for solving a system of linear equations, calculating the inverse of a matrix, and numerical operations.

Given system is

x+ y-z= 4

3x+4y-3z=16

9x- 3y+4z=14

from the system the determinants become,

D=  1   1  -1

      3  4  -3

      9   -3  4

D= 1(16-9)-1(12+27)-1(-9-36)

   =7-39+45

   13

Dx=4   1  -1

      16  4  -3

      14   -3  4

   =26

Dy=1  4  -1

      3  16  -3

      9   14  4

   =52

Dz=1  1  4

      3  4  16

      9   -3  14

 =26

Hence, D=13, Dx=26, Dy=52, Dz=26

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Given rational expression is

Factor the numerator and denominator first.

Factor the denominator 6t-12:

So,

Therefore, the given expression in lowest form is

The Solution:

Given the functions below:

We are required to find the value of f(-1)g(2)

So,

Similarly,

g(2) means we should substitute 2 for x in g(x).

Now, we shall multiply f(-1) and g(2) together.

Therefore, the correct answer is [option C]

Answer:

\(\textsf{1.(a)} \quad x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

\(\textsf{1.(b)} \quad 9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\begin{aligned}\textsf{2.(a)}\quad3x^2-24x+48&=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\\&=3\left(x-\boxed{4}\right)^2\end{aligned}\)

\(\begin{aligned}\textsf{2.(b)}\quad \dfrac{1}{2}x^2+8x+32&=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\\&=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\end{aligned}\)

Step-by-step explanation:

(a) When completing the square for a quadratic equation in the form ax² + bx + c where the leading coefficient is one, we need to add the square of half the coefficient of the x-term:

\(x^2-14x+\left(\dfrac{-14}{2}\right)^2\)

\(x^2-14x+\left(-7\right)^2\)

\(x^2-14x+49\)

We have now created a perfect square trinomial in the form a² - 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Therefore:

\(a^2=x^2 \implies a=1\)

\(b^2=49=7^2\implies b = 7\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(x^2-14x+\boxed{49}=\left(x-\boxed{7}\right)^2\)

(b) When completing the square for a quadratic equation where the leading coefficient is not one, we need to add the square of the coefficient of the x-term once it is halved and divided by the leading coefficient, and then multiply it by the leading coefficient:

\(9x^2 + 30x +9\left(\dfrac{30}{2 \cdot 9}\right)^2\)

\(9x^2 + 30x +9\left(\dfrac{5}{3}\right)^2\)

\(9x^2 + 30x +9 \cdot \dfrac{25}{9}\)

\(9x^2 + 30x +25\)

We have now created a perfect square trinomial in the form a² + 2ab + b². To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 +2ab + b^2 = (a +b)^2}\)

Therefore:

\(a^2=9x^2 = (3x)^2 \implies a = 3x\)

\(b^2=25 = 5^2 \implies b = 5\)

Therefore, the perfect square trinomial rewritten as a binomial squared is:

\(9x^2 + 30x +\boxed{25}= \left(3x +\boxed{5}\right)^2\)

\(\hrulefill\)

(a) Factor out the leading coefficient 3 from the given expression:

\(3x^2-24x+48=3\left(x^2-\boxed{8}\:x+\boxed{16}\right)\)

We have now created a perfect square trinomial in the form a² - 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2 -2ab + b^2 = (a -b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=3\left(x-\boxed{4}\right)^2\)

(a) Factor out the leading coefficient 1/2 from the given expression:

\(\dfrac{1}{2}x^2+8x+32=\dfrac{1}{2}\left(x^2+\boxed{16}\:x+\boxed{64}\right)\)

We have now created a perfect square trinomial in the form a² + 2ab + b² inside the parentheses. To factor a perfect square trinomial, use the following formula:

\(\boxed{a^2+2ab + b^2 = (a +b)^2}\)

Factor the perfect square trinomial inside the parentheses:

                        \(=\dfrac{1}{2}\left(x+\boxed{8}\right)^2\)

Step-by-step explanation:

Since ABCD is a rectangle

⇒ AB = CD and BC = AD

x + y = 30 …………….. (i)

x – y = 14 ……………. (ii)

(i) + (ii) ⇒ 2x = 44

⇒ x = 22

Plug in x = 22 in (i)

⇒ 22 + y = 30

⇒ y = 8

\(9 (4\sqrt{5x {}^{} } ) - 2(4 \sqrt{5x}) = 5(4 \sqrt{5x} )\)

Answer:

x = 7deg

Step-by-step explanation:

7x + 10 + 15x + 16 = 180 (angles adjacent to each other in a //polygon are supplementary)

22x = 154

x = 7deg

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Answer:

y=5/6x+8/3

Step-by-step explanation:

Let's use the slope-intercept form:

y=mx+b

m: slope

b: y-intercept

x and y: x and y coordinate pair

We start by finding the slope.

Slope = (y₂-y₁)/(x₂-x₁)

Slope = (6-1)/(4-(-2)) These are the two points on the line given to us

Slope = 5/6

Now we find the y-intercept:

y=5/6x+b

We can plug in one of the x and y coordinate pairs into the equation:

6=5/6(4)+b

6=10/3+b

b=8/3

Since we have the y-intercept and the slope, we can write the equation:

y=5/6x+8/3

Answer:

Step-by-step explanation:

( - 2 , 1 )

( 4 , 6 )

m = \(\frac{1-6}{-2-4}\) = \(\frac{5}{6}\)

y - 6 = \(\frac{5}{6}\) ( x - 4 )

y = \(\frac{5}{6}\) x - \(\frac{10}{3}\) + 6

y = \(\frac{5}{6}\) x + \(\frac{8}{3}\)

Answer:

The calculated value of z = - 0.197  falls in the critical region therefore we reject the null hypothesis and conclude that  at  the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays

Step-by-step explanation:

We formulate the null and alternative hypotheses as

H0: p1= p2 there is no difference in population proportions of households that decorate their houses with lights for the holidays

against Ha : p1≠ p2  (claim)  ( two sided)

The significance level is set at ∝= 0.05

The critical value for two tailed test at alpha=0.05 is ± 1.96

or Z∝= 0.05/2= ± 1.96

The test statistic is

Z = p1-p2/√pq(1/n1 +1/n2)

p1= proportions of households  decorating in city 1  = 45/60=0.75

p2= proportions of households  decorating in city 2 = 40/50= 0.8

p = the common proportion on the assumption that the two proportion are same.

p =   \(\frac{n_1p_1 +n_2p_2}{n_1+n_2}\)

Calculating

p =60 (0.75) + 50 (0.8) / 110

p=  45+ 40/110= 85/110 = 0.772

so  q = 1-p= 1- 0.772= 0.227

Putting the values in the test statistic and calculating

z= 0.75- 0.8/ √0.772*0.227( 1/60 + 1/50)

z= -0.05/√ 0.175244 ( 110/300)

z= -0.05/0.25348

z= -0.197

The calculated value of z = - 0.197  falls in the critical region therefore we reject the null hypothesis and conclude that  at  the 5% significance level there is significant difference in population proportions of households that decorate their houses with lights for the holidays

Answer:

t+8+3t

8+4t

Step-by-step explanation:

I guess the question is incomplete

The total distance covered is 15000 m. The total time taken is 5220 seconds and the speed is 2.87 m/s.

We know that speed has to do with the ratio of the distance that has been covered to the time taken. The speed is a scalar quantity and as such we do not consider the direction hence we would not consider that going back in the opposite direction. The total distance can be obtained algebraically.

The total distance that the student travelled can be obtained from;

5000 m + 5000 m + 5000 m

= 15000 m

The total time taken in seconds = 1800 seconds + 1800 seconds + 1620 seconds

= 5220 second

Speed = Distance/ Time

= 15000 m/5220 second

= 2.87 m/s

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Answer:

B is the linear relationship

Answer:

second option where y = 8, 16 and 24

Step-by-step explanation:

second option where y = 8, 16 and 24

This table shows a linear relationship because the y-values increase by the same amount each time (i.e. the difference between the y-values is the same).

Answer:

\(\huge\boxed{\bf\:19}\)

Step-by-step explanation:

Given,

Now, the expression is: \(20 - (3y - 4x)\).

To solve this question we just need to substitute the values of x & y in the given expression. Then,

\(20 - (3y - 4x)\\= 20 - (3(7) - 4(5))\\= 20 - (21 - 20)\\= 20 - 1\\= \boxed{\bf\:19}\)

\(\rule{150pt}{2pt}\)

Answer:

3/10

Step-by-step explanation:

Answer:

\(\frac{3}{10}\)

Step-by-step explanation:

\(\frac{8}{10}\) - \(\frac{5}{10}\) = \(\frac{3}{10}\)

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Answer:

9

Step-by-step explanation:

a² +b²=c²

a²+40²=41²

a²=41²-40²

a²= 81

\( \sqrt{ {a}^{2} } = \sqrt{81} \)

a=9

Answer:

D=1

Step-by-step explanation:

1. Combine multiplied terms into a single fraction
2. Cancel terms that are in both numerator and denominator
3. Divide by 1

Answer:

I honestly don't know but I think its all real numbers but not zero

Step-by-step explanation:

A line of two points (4, 2) and (-1, k) is perpendicular to the line y=2x+1, then k = 9/2.

Given a line with equation y = mx + c, the slope is denoted by m.

Given 2 points with slopes m₁ and m₂, those two lines are perpendicular if:

m₁ x m₂ = -1

The given line equation is:  y = 2x+1

Hence,

m₁ = 2

Compute the slope from 2 points: (4, 2) and (-1, k)

m₂ = (k - 2) / (-1 - 4)

m₂ = (-1/5) (k - 2)

Use the condition for perpendicular lines:

m₁ x m₂ = -1

2 x (-1/5) (k - 2) = -1

2k - 4 = 5

2k = 9

k = 9/2

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Answer:

height of the candle after 6 hours= 18.6 centimeters

Step-by-step explanation:

the function gives a line with a slope of −0.4.

the height of the candle after 11 hours is 16.6 centimeters.

after 6 hours, the height will be

But slope= y2-y1/x2-x1

Y2 is the unknown

Y1 = 16.6

X1= 11 hours

X2= 6 hours

y2-y1/x2-x1= -0.4

(Y2-16.6)/(6-11)= -0.4

(Y2-16.6)/(-5)= -0.4

(Y2-16.6)= -5( -0.4)

(Y2-16.6)= 2

Y2 = 2+16.6

Y2 = 18.6 centimeters

height of the candle after 6 hours= 18.6 centimeters

Answer: 160

Step-by-step explanation:

I divided 144/9 to see how many students are their per 10% of the 90% of students and got the answer 16. I then added 16 as the other missing 10% to 144 and got the answer 160.

Answer:

B

Step-by-step explanation:

12 long 9 wide = 12*9 =108 sqft

$5/sqft

so she'll need 108*5 =540

but she rounded to 100 sqft

It is non-linear but it is proportional

Therefore, the correct option is:

A. Non-linear and proportional