ZA and ZB are supplementary angles. If m/A= (7x - 20)° and
m/B = (2x - 7)°, then find the measure of ZB.

To find the x-intercepts of the function g(x), we must set it equal to 0 and solve for x.

We have the following:

we can use the quadratic formula to get the roots of the polynomial:

therefore, the x-intercepts of the function g(x) are the points (3/4,0) and (-1/4,0)

[tex](5x - 23) + (7x - 1) = 180 \\ 5x + 7x - 23 - 1 = 180 \\ 12x - 24 = 180 \\ 12x = 180 + 24 \\ 12x = 204 \\ \frac{12x}{12} = \frac{204}{12} \\ x = 17[/tex]

x=17°

[tex] = x \times 2 + 15 \\ = 2x + 15[/tex]

DOUBLING IT MEANS MULTIPLYING IT BY 2

THEN ADD 15 AS SHOWN ABOVE.

HOPE THIS HELPS

Answer:1,600

Step-by-step explanation:C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

you already have the answer :)

Given the information, we have the following:

Now, since AC=15, we have the following expression:

Solving for x we get:

Therefore, x=-6

The parabolic equation that passes through the points is y = 29/7x^2 + -27/7x - 342/7

Parabolic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The given parameters are

x-intercepts (-3,0) and (4,0)

Point = (2,-40)

From the definition above, we have the form to be

y = ax^2 + bx + c

Substitute (-3,0) and (4,0)  in the above equation

So, we have

0 = a(-3)^2 + b(-3) + c

0 = a(4)^2 + b(4) + c

This gives

9a -3b + c = 0

16a + 4b + c = 0

Substitute (2,-40) in the above equation y = ax^2 + bx + c

a(2)^2 + b(2) + c = -40

So, we have

4a + 2b + c = -40

The equations become

9a -3b + c = 0

16a + 4b + c = 0

4a + 2b + c = -40

Using a graphing tool, we have

a = 29/7, b = -27/7 and c = -342/7

So, we have

y = ax^2 + bx + c

This gives

y = 29/7x^2 + -27/7x - 342/7

Hence, the equation is y = 29/7x^2 + -27/7x - 342/7

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The speed from City A to City B is 352 miles/hour.

Given:

Distance for trip = 1600 miles

Distance for return trip = 1600 miles

The round-trip took 8 h 20 min.

Total time taken for both trips = 8 hours 20 minutes = 8 + (1/3) hours = 25/3 hours

It is mentioned that on the return trip, the average speed was 20% faster than the outbound speed.

Let's assume x is the speed for an outbound trip.

So, x + 20% of x is the average speed of the return trip

x + 20% of x = x + 0.2x = 1.2x

Speed for the return trip = 1.2x

Total time = (distance/speed of outbound trip) + (distance/speed of return trip)

⇒ [tex]\frac{25}{3} =\frac{1600}{x} +\frac{1600}{1.2x}[/tex]

⇒ [tex]\frac{25x}{3} =\frac{1600*1.2 +1600}{1.2}[/tex]

⇒ [tex]10x = 3520[/tex]

⇒ [tex]x = 352[/tex]

Therefore, the speed from City A to City B is 352 miles/hour.

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Step-by-step explanation:

a)

[tex]f(x+h) = 4(x+h)+4[/tex]

[tex]f(x+h)=4x+4h+4[/tex]

b)

[tex]f(x+h)-f(x)=4x+4h+4-(4x+4)[/tex]

[tex]f(x+h)-f(x)=4x+4h+4-4x-4[/tex]

[tex]f(x+h)-f(x)=4h[/tex]

c)

[tex]f(x+h)-f(x)h=4x+4h+4-h(4x+4)[/tex]

[tex]f(x+h)-f(x)h=4x+4h+4-4hx+4h[/tex]

[tex]f(x+h)-f(x)h=-4hx+8h+4x+4[/tex]

(a) The percentage of discounts for manufacturers A and B is 32.92% and 31%, respectively.

(b) The Home Depot should buy from manufacturer A.

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The required quotient is 6.5625 when -5 2/8 is divided by (-4)/5.

A quotient is defined as the outcome of dividing an integer by any divisor that can be said to be a quotient. The dividend contains the divisor a specific number of times.

The quotient is given in the question:

-5 2/8 ÷ (-4)/5

-(42/8) / (-4)/5

Reciprocal the term in the denominator

-(42/8) × -(5)/4

210/32

6.5625

Therefore, the required quotient is -5 2/8 ÷ (-4)/5 = 6.5625.

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Using the probability concept, we have that:

a) The probability is of 0.244.

b) The probability is of 0.756.

c) A student given a $1 bill is more likely to have kept the money.

A probability is calculated as the number of desired outcomes in the experiment divided by the number of total outcomes in the experiment.

For item a, we have that out of 11 + 34 = 45 students who were given a $1 bill, 11 spent the money, hence the probability is given as follows:

p = 11/45 = 0.244.

For item b, we have that out of 11 + 34 = 45 students who were given a $1 bill, 34 kept the money, hence the probability is given as follows:

p = 34/45 = 0.756.

For item c, we have that a student given a $1 bill is more likely to have kept the money, as 0.756(kept) > 0.244(spent), which are the two probabilities we found in the previous items.

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The slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.

Slope, also called as gradient of a line is a value or number that describes both of the directions x and y. It basically tells the steepness of the line.

To find the slope of line, formula given below is used

[tex]\frac{y_{2} - y_{1} }{x_{2} -x_{1} }[/tex] = slope

Here, y2 = 9

          y1 = 7

          x2 = 6

          x1 = 3

Thus, 9 - 7/6 - 3

= 2/3

Therefore, we can conclude that the  slope of a line containing P1(3, 7) and P2(6, 9) is 2/3.

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The group of restrictions used to simulate the issue includes

The issue includes the following information.

The following are the restrictions for modeling the issue: There is a maximum of a five-fold difference between the number of hours Savanah has booked and that John has.

Savanah will provide childcare for at least 40 hours, with no more than meaning it is not larger than that which suggests it is less than, Hence, y<5x

Meaning "at least 40 hours" is "at least 40 hours." 40 hours or more may be expressed as

y ≥ 40 hours

The two necessary restrictions are represented as y< 5x and y=> 40 hours in an inequality model.

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Using proportions, it is found that due to the higher proportion of successful trials, Treatment A had the better success rate

A proportion is a fraction of a total amount, and hence it is represented by the sum of the desired amounts divided by the sum of the total amounts.

For Treatment A, we have that:

Hence the proportion of successful trials for Treatment A is given by:

315/357 = 0.8824.

For Treatment B, we have that:

Hence the proportion of successful trials for Treatment B is given by:

289/350 = 0.8257.

The proportion for Treatment A is higher, as 0.8824 > 0.8257, hence it had the better success rate.

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Minh can use unitary method to determine how many cans he will need in all to paint the 12 rooms, which will give a total of 8 cans as requirement. The tools he'll need for the same are : counters, pencil and paper.

In its simplest form, the unitary procedure is used to determine the value of a single unit from a given multiple.

How to calculate the value of one pen, for example, if 40 cost Rs. 400. To finish it, using the unitary method. Additionally, after the value of a single unit has been established, we can multiply that value by the quantity of additional units required to establish the value of the additional units.

This is typically how the concepts of ratio and proportion are used. The unitary method entails calculating the value of a single unit before calculating the value of the required number of units.

Given, He requires 2 paint cans to paint 3 rooms.

Once more, he will require 2/3 of a can of paint to paint 1 room.

He will thus require cans of paint to paint 12 rooms, which equals (2/3)*23 = 8.

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Answer:

6 and 2

Step-by-step explanation:

Let the first and second numbers be x and y respectively.

x = 4 + y..... (1)

2x = 4 + 4y...... (2)

Using the substitution method from Eqn(1) into (2)

Anywhere we see x in Eqn(2) we substitute it with 4 + y

I. E. 2(4 + y) = 4 + 4y

8 + 2y = 4 + 4y

Collect like terms.

8 - 4 = 4y - 2y

4 = 2y

.: y = 2

Put y = 2 in Eqn(1), and we have;

x = 4 + 2

x = 6.

.: the first number is 6 and the second number is 2.

Option C is correct.

Answer:

d) division property of =

Step-by-step explanation:

by step 3, the variable x is still being multiplied by 3. In order to isolate x, you must divide by 3 on both sides.

We are asked to find the simple interest associated with a principal of 5480 , an annual rate of 0.04 (4%) and at the end of 7 years:

We use the simple interest formula:

I = P r t

in our case: I = (5480) (0.04) (7) = 1534.4

So the interest is: 1534.40

We answer using two decimal places because this is refering to cents of a dollar.

Answer:

3:7

Step-by-step explanation:

Given:

To Find:

Formula used:

Using the formula, we have

No. of boys = 28 - 16 = 12

Proportion of boys = 12/28 = 3/7

So, proportion of boys = 3:7.

The distance between MO is 9.

From the question MP is straight line and O & N is points between M & P.

so the total length of line is 15

Need to find MO , To find  MO = MP - (NP - NO)

                                                   = 15 - (8 -2)

                                                  = 15 - 6 = 9

The MO is 9.

To find points in graph :

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In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

angle = 26 degress

complement angle = ?

Step 02:

26 + x = 90

x = 90 - 26

x = 64

The answer is:

The complement angle is 64 degrees

The result of the multiplication operation yields 7 7/12

From the question, we are to multiply the given fractions. The given fractions are

1 3/4 and 4 2/6

First, we will convert the fractions to improper fractions

Converting 1 3/4 to an improper fraction

1 3/4 = 7/4

Converting 4 2/6 to an improper fraction

4 2/6 = 26/6

Thus,

The multiplication operation becomes

7/4 × 26/6

= 7/4 × 13/3

= 91/12

= 7 7/12

Hence, the product of the given numbers is 7 1/12

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The values are as follows:

center:  y²/25-x²/25 = 1

transverse axis : b = 5

Vertices:  (0,5) and (0,-5)

Foci: (0,5√2) and (0,-5√2)

Asymptotes: y = x and y = -x

An asymptote is a line being approached by a curve but never touching the curve. i.e., an asymptote is a line to which the graph of a function converges. We usually do not need to draw asymptotes while graphing functions.

Types of Asymptotes:

1) Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k.

2) Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k.

3) Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b.

y² -x² =25 up down hyperbola with (h,k) = (0,0) a = 5 and b = 5

(y-k)²/a²-(x-h)²/b² = 1 is the standard equation of up-down hyperbola.

With semi-axis is a and semi-conjugate axis is b.

and centre (h,k).

Center = (y-0)²/5²-(y-0)²/5² = 1

= y²/25-x²/25 = 1

The axes are a = 5 and b = 5

transverse axis is b = 5

The foci are given by (h, k+c) and (h, k-c), where c = √a²+b²

c = √5²+5² = 5√2

therefore, the foci are (0,5√2) and (0,-5√2).

The vertices are (h, k+a) and (h, k-a)

(h,k) = (0,0) and a = 5 and b = 5

vertices are (0,5) and (0,-5)

Asymptotes are y = x and y = -x.

Therefore, the summary is as follows:

center:  y²/25-x²/25 = 1

transverse axis : b = 5

Vertices:  (0,5) and (0,-5)

Foci: (0,5√2) and (0,-5√2)

Asymptotes: y = x and y = -x

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Answer:

  see attached

Step-by-step explanation:

You want to finish filling the given 2-way table.

Any single missing value in a row or column will be the value that makes the total correct for that row or column. Filling the single missing values will fill enough of a row or column with two or more missing values so that the remaining missing values can be filled the same way.

It is basically a series of subtraction problems.

For example, the upper left cell is filled with 20 -4 = 16, so the total on that row is 16+4=20.

Answer:

t > -2/3

Step-by-step explanation:

−8>−3t−10

Step 1: Flip the equation.

−3t−10<−8

Step 2: Add 10 to both sides.

−3t−10+10<−8+10

−3t<2

Step 3: Divide both sides by -3.

−3t/−3 < 2/−3

t > −2/3

The definition of the slope can be interpreted by the following formula.

selcect two points from the graph

(0,-2)

(0,-4)

replace the points into the formula

Since any number divided by 0 is indetermined, the slope of the line is undefined.

The value of x coordinate be 0 or -2.

Given,

Vertex of the graph, f(x) = x² + 2x + 2

We have to find the x coordinate.

Here,

f(x) = x² + 2x + 2 is in the form of quadratic equation.

So, we can find x coordinate by using quadratic formula.

Quadratic formula: [tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

Here,

a = 1, b = 2 and c = 2

So,

[tex]\frac{-b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex]

= [tex]\frac{-2(+-)\sqrt{2^{2}-4(1)(2) } }{2(1)}[/tex]

= [tex]\frac{-2(+-)\sqrt{4-8} }{2}[/tex]

= (-2±(-√4)) ÷ 2

= (-2±(-2)) ÷ 2

Solve for.

-2 + (-2) / 2 = -2 -2 / 2 = -4/2 = -2

Solve for,

-2 - (-2) / 2 = -2 + 2 / 2 = 0

That is,

The value of x coordinate be 0 or -2.

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