for her cellular service, vera pays $32 a month, plus $0.75 for each minute over the allowed minutes in her plan. vera recieved a bill for $47 last month. write and solve an equation to find how many minutes vera used her phone beyond the allowed minutes.

Answer:

\(x=5,y=4\)

Step-by-step explanation:

\(2x-3y=-2\)

Add 3y to both sides:

\(2x-3y+3y=-2+3y\)

\(2x=-2+3y\)

Divide both sides by 2:

\(\frac{2x}{2}=-\frac{2+3y}{2}\)

\(x=\frac{-2+3y}{2}\)

Substitute this into the second equation:

\(4* \frac{-2+3y}{2}+y=24\)

\(2\left(3y-2\right)+y=24\)

\(7y-4=24\)

Add 4 to both sides:

\(7y-4+4=24+4\)

\(7y=28\)

Divide both sides by 7:

\(\frac{7y}{7}=\frac{28}{7}\)

\(y=4\)

We know that \(x=\frac{-2+3y}{2}\)

Thus, \(x=\frac{-2+3* \:4}{2}\)

\(x=\frac{10}{2}\)

\(x=5\)

Answer:

using elimination rule

multiply equation 2 by 3

we get, 12x+3y=72

now solve both equation

2x-3y= -2

(+)12x+3y=72

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

14x=70

x=70/14=5

put value of x in any of the equation y=4

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Answer:

Your source water comes from the Detroit River, situated within the Lake St. Clair, Clinton River, Detroit River, Rouge River and Ecorse River watersheds in the U.S., and parts of the Thames River, Little River, Turkey Creek and Sydenham watersheds in Canada.

Step-by-step explanation:

please mark this answer as brainliest

Answer:

(3) Both - 3 and 7

Step-by-step explanation:

The zero of a function is x-intercept

Graph intercepts an x-axis at - 3 and 7

Answer:

16/3 in decimal form = 3 ˙ 5.

Step-by-step explanation:

16/3 into decimal form would be 5.3

The value of the square root of 7 is,

⇒ √7 = 2.645

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

WE have to given that;

To find the value of the square root of 7 .

Since, the square root of 7 is,

⇒ √ 7

⇒ 2.645

Thus, The value of the square root of 7 is,

⇒ √7 = 2.645

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Answer:

Step-by-step explanation:

The average rate of change of the function over the interval is -6

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = 2 to x = 4

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(2) = -3

f(4) = -15

Next, we have

Rate = (-15 + 3)/(4 - 2)

Evaluate

Rate = -6

Hence, the rate is -6

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Answer:

35.09 units

Step-by-step explanation:

This is a right-angled triangle where:

Hypotenuse = x units

With respect to angle 20°:

Opposite = 12 units

Use trigonometric function sinФ to solve for x:

sinФ = \(\frac{Opposite}{Hypotenuse}\)

∴sin20° = \(\frac{12}{x}\)

Cross-multiplication is applied:

\((x)(sin20) = 12\)

x has to be isolated and made the subject of the equation:

∴\(x = \frac{12}{sin20}\)

x = 35.09 units (Rounded to 2 decimal places)

Answer:

The length of x is 35.09 units to two decimal places.

Step-by-step explanation:

In the given right triangle, we have been given the length of the side opposite the angle and need to find the length of the hypotenuse.

To find the value of x, use the sine trigonometric ratio.

\(\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

Substitute θ = 20°, O = 12 and H = x into the ratio and solve for x:

\(\implies \sin 20^{\circ}=\dfrac{12}{x}\)

\(\implies x=\dfrac{12}{\sin 20^{\circ}}\)

\(\implies x=35.085652...\)

\(\implies x=35.09\; \sf (2\;d.p.)\)

Therefore, the length of x is 35.09 units to two decimal places.

Answer:

The area of the triangle on left is 9

in², the area of the triangle on the right is 9

in², and the area of the rectangle is 108

in².

The area of the trapezoid is the sum of these areas, which is 126

in².

Answer:

Please attach the picture/figure.

Step-by-step explanation:

Answer:

36 cm

Step-by-step explanation:

Because the plant is growing the same amount each week you would take 12(3) and get 36 cm at the end of the 12 weeks.

Answer:

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m=32

Answer:

200,000

Step-by-step explanation:

The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer:

Step-by-step explanation:

The second one is perimeter, not area. The first one is correct.

Answer:

P(X is less than 348) = 0.2148

Step-by-step explanation:

Given that:

Sample proportion (p) = 0.3

Sample size = 1200

Let X be the random variable that obeys a binomial distribution. Then;

\(X \sim Bin(n = 1200,p =0.3)\)

The Binomial can be approximated to normal with:

\(\mu = np = 1200 \times 0.3 \\ \\ \mu= 360\)

\(\sigma = \sqrt{np(1-p) } \\ \\ \sigma = \sqrt{1200 \times (0.3)(1-0.3) } \\ \\ \sigma = 15.875\)

To find:

P(X< 348)

So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 348 lies between 347.5 and 348.5

Normal distribution:

x = 347.5, \(\mu\) = 360, \(\sigma\) = 15.875

Using the z test statistics;

\(z = \dfrac{x - \mu}{\sigma}\)

\(z = \dfrac{347.5 - 360}{15.875}\)

\(z = \dfrac{-12.50}{15.875}\)

z = -0.7874

z ≅ - 0.79

The p-value for P(X<347.5) = P(Z < -0.79)

From the z tables;

P(X<347.5) = 0.2148

Thus;

P(X is less than 348) = 0.2148

Answer:

$16,525.53.

Step-by-step explanation:

A=Pe^rt

P=$12,000

r=0.04

t=8 years

Answer:

7.5

Step-by-step explanation:

The actual fraction is 15/2, which is equivlent to 7.5

Im pretty sure its infinite solutions

The moment of inertia for rotation about the z axis is  \(I & =\frac{a^2 M}{3}\).

A triangular prism of mass m, whose two ends are equilateral triangles.

Two ends are equal.

The xy plane with side 2a, is centered on the origin with its axis along the z axis.

Find the moment of inertia for rotation the z-axis.

It is divide into 4 triangles with side 'a' k one side is 3cm.

\($$\begin{aligned}& I_{\text {BiG }}=16 I_{\text {small }} . \\& I_{\text {BIG }}=4 I_{\text {small }}+P_{A T}\end{aligned}$$\)

It is fact that the big triangle is made up from four small triangles. connected with parallel axis theorem.

Now, we have to find the distance from the center of mas of small outer triangles to the origin. so, that it is PAT.

\($$\therefore z=2 \sqrt{x^2-\frac{a}{2} ^2}$$\)

\($$\begin{aligned}& =2 \sqrt{\left(\frac{a}{\sqrt{3}}\right)^2-\frac{a^2}{4}} \\& =2 \sqrt{\frac{a^2}{3}-\frac{a^2}{4}} \\I_{\text {Big }} & =\frac{\sqrt{3}}{3} a \cdot \\& \left.=4 I_{\text {small }}+3 m \frac{\sqrt{3}}{3} a\right)^2 \\I_{\text {Big }} & =4 I_{\text {small }}+\frac{3 m}{4} \frac{1}{3} a^2 \\& =\frac{a^2}{4}\end{aligned}$$\)

⇒ Now, by using the \($I_{\text {Big }}=I$\)

⇒\(I & =4\left(\frac{\sqrt{2}}{16}\right)+\frac{a^2 M}{4} \\\)

⇒\(4 I & =I+a^2 m\)

⇒\(4 I-I & =a^2 m \\\)

⇒\(3 I & =a^2 M . \\\)

⇒\(I \quad & =\frac{a^2 M}{3}\)

Therefore, the moment of inertia is \(I & =\frac{a^2 M}{3}\).

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one negative two and then shifted to the rights, that's the translation to the right two units.

What is the sequence of transformation?

its  a 180 Degree Rotation.

And let's see With a 180 degree rotation.

, we can say  coordinates is that  X. Y. Two negative X. Negative Y.

It goes to one negative two and he goes to two negative five And c goes to 5 -2.

So if  one negative two and then shifted to the rights, that's the translation to the right two units.

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Answer:

2 or B

Step-by-step explanation:

Answer:

I believe the minimum value would be 60

With the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

Euclidean geometry states that two objects are comparable if they have the same shape or the same shape as each other's mirror image.

One can be created from the other more precisely by evenly scaling, possibly with the inclusion of further translation, rotation, and reflection.

These three theorems—Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS)—are reliable techniques for figuring out how similar triangles are to one another.

So, in the given situation:

TR and WY are as follows:
TR/WU

24/2

2/1

Similarly,

TS/WV

2/1

7/x

7/3.5

Therefore, with the help of proportions in the given similar triangles we know that the value of x is 3.5 units.

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Answer:

Step-by-step explanation:

Equation of the line is,

y = -x + 2

By comparing this equation with,

y = mx + b

Here, m = slope of the line

b = y-intercept

Therefore, slope of the line given in the graph = (-1)

y-intercept = 2

Now we will find the table for the points lying on the line,

x       -6          -4           0           4            6

y        8           6           2          -2           -4

Now plot these points on the graph and join them to get the line.

Answer:

Asking every 5th person their age

Step-by-step explanation:

I just did the quiz

Answer:

a

\(P(A_1)  =  0.007\)

b

\(P(A_2) = 0.016\)

c

\(P(A_3) =  0.008\)

d

\(P(A_4) =  0.004\)

e

\(P(A_5) =  0.0002\)

Step-by-step explanation:

From the question we are told that

   The number of cards selected is  n = 7

Generally in a standard deck of cards

   The total  number of cards is  N  =  52

    The number of  hearts is  h = 13  

    The  number of diamonds is  d = 13

    The number of  spade is  s  =  13

    The number of  Ace is  a = 4

    The number of kings is  k =  4

Considering question a

   The number of ways to selected 5 hearts out of the  13 hearts is mathematically represented as

      \(G  =  ^{13}C_5\)

Here C means combination so  

The number of cards that is not hearts  is  52 -  13  =  39

Generally the number of ways of selecting the reaming 2 cards is  

    \(H  =  ^{39}C_2\)

Generally the number of ways to select the 7  cards from the 52 deck of cards is  

        \(V  =  ^{52}C_7\)

Generally the probability that exactly 5 of the 7 cards  are hearts is mathematically represented as

     \(P(A_1)  =  \frac{G  *  H}{V}\)

=>  \(P(A_1)  =  \frac{^{13}C_5  *  ^{39}C_2}{^{52}C_7}\)

=>   \(P(A_1)  =  0.007\)

Considering question b

     The number of ways to selected 3 diamonds out of the  13 diamonds is mathematically represented as

      \( B =  ^{13} C_3 \)

The number of ways to selected 3 hearts out of the  13 hearts is mathematically represented as

      \(K  =  ^{13}C_3\)

The number of cards that is not hearts or diamond  is  52 -  (13 +13)  =  26

Generally the number of ways of selecting the reaming 1 cards is  

    \(M  =  ^{26}C_1\)

Generally the probability that there are 3 hearts and 3 diamonds is

    \(P(A_2) =  \frac{B  *  K *  M}{V}\)

=> \(P(A_2) =  \frac{^{13}C_3  *  ^{13}C_3 *  ^{26}C_1}{^{52}C_7}\)

=>  \(P(A_2) = 0.016\)

Considering question c

The number of ways to selected 1 spade out of the  13 spade is mathematically represented as

     \(J = ^{13}C_1\)

Generally the probability that there are 3 hearts, 3 diamonds and 1 spade is

   \(P(A_3) =  \frac{B *  K  *  J}{V}\)

=> \(P(A_3) =  \frac{^{13}C_3 *  ^{13}C_3   *  ^{13}C_1}{^{52}C_7}\)

=>  \(P(A_3) =  0.008\)

Considering question d

The number of ways to selected 2 Aces out of the  4 Aces is mathematically represented a

     \(U = ^{4}C_2\)

The number of ways to selected 2 Kings out of the  4 Kings is mathematically represented a

       \(R = ^{4}C_2\)

The number of cards that is not Aces or Kings  is  52 -  (4 +4)  =  44

Generally the number of ways of selecting the reaming 3 cards is  

     \(S = ^{44}C_3\)

Generally the probability that there are 2 Aces and 2 Kings is

    \(P(A_4) =  \frac{U *  R  *  S}{ V}\)

=>  \(P(A_4) =  \frac{ ^{4}C_2 *  ^{4}C_2  *  ^{44}C_3}{ ^{52}C_7}\)

=>\(P(A_4) =  0.004\)

Considering question e

The number of ways to selected 3 Kings out of the  4 Kings is mathematically represented a

     \(P = ^{4}C_3\)

Generally the number of ways of selecting the reaming 2 cards is  

      \(Q = ^{44}C_2\)

Generally the probability that there are 2 Aces and 3 Kings is

     \(P(A_5) =  \frac{U  *  P  *  Q }{V}\)

=>  \(P(A_5) =  \frac{ ^{4}C_2  *  ^{4}C_3  *  ^{44}C_2 }{^{52}C_7}\)

=>  \(P(A_5) =  0.0002\)

2 terms

Step-by-step explanation:

4[8+2x]

=4*8+4*2x

=32+8x

therefore there are 2 terms

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Answer:

The first factor (4) consists of one (1) term, "4".

The second factor (8 +3x) consists of two (2) terms, "8" and "3x".