(5ytohte power 2+2y+7)-(3yto the power two +y+5) find the product with steps

Answer:

w = 120

x = 60

y = 120

z = 60

Step-by-step explanation:

w = 120 (vertically opposite angles)

sum of co interior angles is 180

⇒ w + x = 180 and x + y = 180

w + x = 180

⇒ 120 + x = 180

⇒ x = 180 - 120

⇒  x = 60

x + y = 180

⇒  60 + y = 180

⇒   y = 180 - 60

⇒   y = 120

z = x (corresponding angles)

z = 60

Answer:

y=  1/4(2+3x)

Step-by-step explanation:

The solution of the expression for the value of y is y = 8 + 12x.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The given expression is 3x-1/4y=-2. The value of y will be calculated as below:-

3x-1/4y=-2

-(1/4)y = -2 - 3x

y = 4 ( 2 + 3x)

y = 8 + 12x

Therefore, the solution of the expression for the value of y is y = 8 + 12x.

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The independent variable in this data is the speed of the car. This is because the congressman is trying to determine whether or not the gas mileage improves at lower speeds.

The dependent variable is the gas mileage, because it is the variable that is being measured and that is affected by the independent variable.

The other variables in this data are the weight of the car, the type of engine, and the year of the car. However, these variables are not being changed in this experiment, so they are not considered to be independent variables.

The data shows that the gas mileage of the Toyota Camry improves as the speed of the car decreases. This supports the claim of the supporters of the bill to reduce the speed limit.

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The following are the solutions for the student data:

a. 25 students like exactly two of the composers

b. 31 students like exactly one these composers

c. 10 students like only Mozart

d. 19 students like haydn and exactly one of the other two composers

e. Only one student like none of these composers.

Venn diagrams are commonly used in mathematics, statistics, and logic to illustrate relationships between sets of data. It consists of circles that overlap to show the similarities and differences between the sets like in the case of students data.

Students who like:

All three composers = 8

Only Mozart and Beethoven = 14 - 8 = 6

Only Mozart and Haydn = 20 - 8 = 12

Only Beethoven and Haydn = 15 - 8 = 7

Only Mozart = 36 - (6 + 12 + 8) = 10

Only Beethoven = 37 - (6 + 7 + 8) = 16

Only Haydn = 32 - (12 + 7 + 8) = 5

Students who like none of the composers:

65 - (10 + 16 + 5 + 12 + 6 + 7 + 8)

65 - 64 = 1

Therefore, students who like:

exactly two of the composers = 12 + 6 7 = 25 students

exactly one these composers = 10 + 16 + 5 = 31 students

only Mozart = 10 students

Haydn and exactly one of the other two composers = 12 + 7 = 19 students

none of the composers = 1 student

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Answer:

Here we can take advantage of exactly the property suggested by Xisca... that is, sqrt(44)=2sqrt(11), which reduces the calculation to more accuracy with a lesser knowledge of the squares of numbers.

As a first approximation, we know that 33*33=1089, or 3.3*3.3=10.89, which is already very close to 11.  

Thus a first approximation to sqrt(44)=2sqrt(11)=2*3.3=6.6 (approximately).

To refine the calculation of sqrt(11), we use Newton's approximation, namely

a better approximation is given by 3.3 + (11 - 3.3^2) / (2*3.3) = 3.3+0.11/6.6 = 3.3+1/60

which gives

sqrt(44) = 2(3.3+1/60) = 6.6+1/30 = 6.6333,

actually accurate almost to the nearest 1/10000.

All of the above can be done mentally

For those who need help with rounding to the nearest hundredth (0.01), we drop digits AFTER the 2nd decimal, namely *.**33.  If the first digit dropped is 5 or more, add one to the last digit retained, otherwise, retain only the two digits after the decimal.  In this case, the first digit dropped is 3, so it will simply be dropped.  The final answer is then 6.63, to the nearest hundredth.

Step-by-step explanation:

the first one is -6

and the last one is 11x

Answer:

Step-by-step explanation:

Point estimate is also referred to as sample proportion, p. It is used to estimate the population proportion. The formula for determining point estimate is expressed as

p = x/n

Where

x = number of success

n = number of trials or samples

a) x = 454

n = 478

p = 454/478 = 0.9498

b) x = 741

n = 833

p = 741/833 = 0.8896

c) x = 1058

n = 1644

p = 1058/1644 = 0.6436

The proportion of people that used the internet decreased as the age group increased. Therefore, they are inversely proportional

The monthly income of the first person is $600.

Given that, the average monthly income of three persons is RS 3,600.

The income of the first is 1/5 of the combined income of the other two.

Here, Let income of the first be A, let income of the second be B and let Income of the third be C.

A+B+C=3600 -----(i)

Income for the first person = 1/5(B+C) -----(ii)

Substitute equation (ii) in equation (i), we get

(B+C)/5 +B+C =3600

B+C+5B+5C=3600×5

6B+6C=18000

6(B+C)=18000

B+C=3000 ------(iii)

Substitute (iii) in equation (i), we get

A=$600

Therefore, the monthly income of the first person is $600.

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Answer:

196 gallon/minute

Step-by-step explanation:

Peter is filling a swimming pool with water

After a period of 7 minutes the pool is filled up with 1372 gallons

After 12 minutes the pool is filled up with 2352 gallons

Therefore the rate in gallon per minutes at which the pool is being filled can be calculated as follows

=( 2352-1372)/(12-7)

= 980/5

= 196 gallon/minute

Hence the pool is filled up at 196 gallon/minute

Given a normal distribution with m = 100 and s = 10, the probabilities are;

a) X > 75 = 0.0062

b) X < 70 = 0.00135

c) X < 80 or X > 110 = 0.053954

We are given;

Population mean; m = 100

standard deviation; s = 10

The z-score is gotten from the formula;

z = (X - m)/s

Thus;

1) Probability that X > 75 is;

z = (75 - 100)/10

z = -2.5

From online p-value from z-score calculator, we have;

probability = 0.0062

2) Probability that X < 70 is;

z = (70 - 100)/10

z = -3

From online p-value from z-score calculator, we have;

probability = 0.00135

3) Probability that X < 80 is;

z = (80 - 100)/10

z = -2

From online p-value from z-score calculator, we have;

probability = 0.02275.

Probability that X > 110 is;

z = (110 - 100)/10

z = -1

From online p-value from z-score calculator, we have;

probability = 0.158655

Thus, P(0.02275 < x < 0.158655) = 0.053954

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Answer:

d . candle burns down 1 cm per hour .

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Got it correct

Answer: y= 3x+22

70=3x+22

70-22=3x

58=3x

58/3=x

19.33

He needs to buy at least 19 GB

Step-by-step explanation:

The inequality represented by the graph is given as follows:

y > 3x - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:

b = -4.

When x increases by 1, y increases by 3, hence the slope m is given as follows:

m = 3.

Hence the equation of the line is:

y = 3x - 4.

The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:

y > 3x - 4.

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The points on a parabola with the focal axis parallel to the abscissa axis, of parameter p and A, B is -12.

Since A and B are points on the parabola, write two equations using the general form of the parabolic equation:

(x - h)² = 4p(y - 1)

The focal axis is parallel to the x-axis, so the distance from the vertex to the focus is equal to p. Therefore, use the distance formula to write an equation for the distance between the vertex and point A:

√((13 - h)² + (a - 1)²) = p

Similarly, write an equation for the distance between the vertex and point B:

√((4 - h)² + (b - 1)²) = p

A and B lie on the line 2x - y - 13 = 0, so substitute the x and y coordinates of A and B into this equation and solve for a and b:

2(13) - a - 13 = 0

2(4) - b - 13 = 0

Solving these equations gives us a = 3 and b = -5.

Now three equations and three unknowns (a, b, and h):

√((13 - h)² + 4) = p + 1

√((4 - h)² + 36) = p + 1

2h - 3 - 13 = 0

The third equation simplifies to 2h = 16, or h = 8.

Substituting this value of h into the first two equations and squaring both sides:

(13 - 8)² + 4 = (p + 1)²

(4 - 8)² + 36 = (p + 1)²

Simplifying these equations and solving for p gives us p = 3.

Finally, find a" + bP by substituting the values found for a, b, and p:

a" + bP = 3 + (-5)(3) = -12

Therefore, the solution is a" + bP = -12.

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Answer:

slope (m) = 2/3

Step-by-step explanation:

slope = change in x /change in y

Also, slope is y2 - y1 / x2 -x1. That is what I apply for this activity, hence:

slope = 3 - (-1) / 0 - (-6)

         = 3 + 1 / 0 + 6

         = 4 / 6

         = 2/3

∴ slope(m) = 2/3

Answer:

Step-by-step explanation:

It can be determined that the function is:

So missing x is:

Missing y is:

Missing numbers are:

Correct choice is d.

                                           FIRST METHOD

Answer:

Step-by-step explanation:

Given the table

x                                         y

7                                        16

9                                        17

Missing x                          18

13                                        Missing y

From the table, it is clear that y-values are incremented by 1 unit and the x-values are incremented by 2 units.

i.e.

y = 17-16 = 1

y = 18-17 = 1

as 19-18 = 1

Thus,

Thus, the value of Missing y = 19

also the x-values increment by 2.

i.e.

x  = 9-7 = 2

as x = 11 - 9 = 2

Thus, Missing x = 11

Therefore,

                                                2ND METHOD

Given that the table represents a  linear function, so the function is a straight line.

Taking two points

Finding the slope between (7, 16) and (9, 17)

\(\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(7,\:16\right),\:\left(x_2,\:y_2\right)=\left(9,\:17\right)\)

\(m=\frac{17-16}{9-7}\)

\(m=\frac{1}{2}\)

Using the point-slope form to determine the linear equation

\(y-y_1=m\left(x-x_1\right)\)

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = 1/2 and the point (7, 16)

\(y-y_1=m\left(x-x_1\right)\)

\(y-16=\frac{1}{2}\left(x-7\right)\)

Add 16 to both sides

\(y-16+16=\frac{1}{2}\left(x-7\right)+16\)

\(y=\frac{1}{2}x+\frac{25}{2}\)

Thus, the equation of the linear equation is:

\(y=\frac{1}{2}x+\frac{25}{2}\)

Now substituting y = 18 in the equation

\(18=\frac{1}{2}x+\frac{25}{2}\)

Switch sides

\(\frac{1}{2}x+\frac{25}{2}=18\)

subtract 25/2 from both sides

\(\frac{1}{2}x+\frac{25}{2}-\frac{25}{2}=18-\frac{25}{2}\)

\(\frac{1}{2}x=\frac{11}{2}\)

\(x=11\)

Thus, the value of missing x = 11 when y = 18

Now substituting x = 13 in the equation

\(y=\frac{1}{2}\left(13\right)+\frac{25}{2}\)

\(y=\frac{13}{2}+\frac{25}{2}\)

\(y=\frac{13+25}{2}\)

\(y=\frac{38}{2}\)

\(y = 19\)

Thus, the value of missing y = 19 when x = 13

Hence, we conclude that:

Hence, option D is true.

In the provided text is a questionnaire or form related to a research tool for assessing a campaign in the community.

The first question asks whether the campaign pursues its aims, with the options of answering "YES" or "NO." The respondent is then instructed to elaborate on their answer.

A questionnaire is a research tool   used to collect data by presenting a series of questions to respondents,typically in a written format.

Questionnaires are an important research tool as they allow researchers to gather   large amounts of data from a large number of participants in   a standardized and efficient manner.

They provide a structured approach to collecting information,allowing for easy analysis and comparison   of responses.

Questionnaires can be used in various   research settings and are particularly useful for collecting quantitative data,measuring attitudes, opinions, behaviors, and gathering demographic information.

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Answer:

The scale of the drawing is 1 cm to 90 m. This means that every 1 cm on the drawing represents 90 m in real life. The length of the field is 450 m, so the length of the drawing will be 450 m / 90 m = 5 cm.

Therefore, the length of the dam drawing is 5 cm.

Step-by-step explanation:

Answer:

The change in volume of the cylinder is 9600π cubic centimeters.

Step-by-step explanation:

Statement is incomplete. Complete statement is:

A right circular cylinder has a radius of 40 cm and a height of 100 cm. Use differentials to estimate the change in volume of the cylinder if its height and radius are both increased by 1 cm.

From Geometry we know that volume of right circular cylinder, measured in cubic centimeters, is represented by the following expression:

\(V = \pi\cdot r^{2}\cdot h\) (Eq. 1)

Where:

\(r\) - Radius of the right circular cylinder, measured in centimeters.

\(h\) - Height of the right circular cylinder, measured in centimeters.

The change in volume of the cylinder, measured in cubic centimeters, is obtained by total differentials:

\(\Delta V = \frac{\partial V}{\partial r}\cdot \Delta r + \frac{\partial V}{\partial h}\cdot \Delta h\) (Eq. 2)

Where:

\(\Delta r\) - Change in radius, measured in centimeters.

\(\Delta h\) - Change in height, measured in centimeters.

\(\frac{\partial V}{\partial r}\) - Partial derivative of volume in radius, measured in square centimeters.

\(\frac{\partial V}{\partial h}\) - Partial derivative of volume in height, measured in square centimeters.

All partial derivatives are obtained, respectively:

\(\frac{\partial V}{\partial r} = 2\pi\cdot r\cdot h\) (Eq. 3)

\(\frac{\partial V}{\partial h} = \pi\cdot r^{2}\) (Eq. 4)

By applying (Eqs. 3, 4) in (Eq. 2), we obtain the resulting expression:

\(\Delta V = 2\pi\cdot r\cdot h \cdot \Delta r+\pi\cdot r^{2}\cdot \Delta h\)

\(\Delta V =\pi\cdot r \cdot (2\cdot h\cdot \Delta r +r\cdot \Delta h)\) (Eq. 5)

If we know that \(r = 40\,cm\), \(h = 100\,cm\) and \(\Delta r = \Delta h = 1\,cm\), the change in volume of the cylinder is approximately:

\(\Delta V = \pi\cdot (40\,cm)\cdot [2\cdot (100\,cm)\cdot (1\,cm)+(40\,cm)\cdot (1\,cm)]\)

\(\Delta V = 9600\pi\,cm^{3}\)

The change in volume of the cylinder is 9600π cubic centimeters.

Answer:

32 cm²

Step-by-step explanation:

Area of rectangle

= length × breadth

= 8 cm × 4 cm

= 32 cm²

Answer:

\(\frac{29}{6}\)

Step-by-step explanation:

Multiply the denominator by the whole number.

6 × 4 = 24

Add the answer from step 1 to the numerator.

24 + 5 = 29

Write answer from step 2 over the denominator

\(\frac{29}{6}\)

Answer:

whole circle on the 5, arrow facing the left

Answer:

Step-by-step explanation:

x+9

Let x, be 4

4+9=13

given condition,

x+9<4x

4+9<4(4)

13<16

The answer is:

Work/explanation:

Our inequality is:

\(\sf{x+9 < 4x}\)

Flip it

\(\sf{4x > x+9}\)

Solve

\(\sf{4x-x > 9}\)

Combine like terms

\(\sf{3x > 9}\)

Divide each side by 3

\(\sf{x > 3}\)

Answer:

A

Step-by-step explanation:

I am not 100% certain but it seems the best.

Rolling a die and flipping a coin re out of the top, obvious reasons. Using a spinner 75% 25% seems less logical as it doesnt tell us the exact numbers of novels vs. biographies. However, choosing out of 3 white marbles (exact number of novels) or 2 black marbles (exact number of biographies) fits better.

The intervals of each behavior of the function are given as follows:

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Answer:

your answer should be 49.7097

Step-by-step explanation:

Answer:

slope = \(\frac{5}{4}\)

Step-by-step explanation:

calculate the slope m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (0, 5 ) ← coordinates of y- intercept

and (x₂, y₂ ) = (- 4, 0 ) ← coordinates of x- intercept

m = \(\frac{0-5}{-4-0}\) = \(\frac{-5}{-4}\) = \(\frac{5}{4}\)

Answer:

\(y=-\frac{1}{4}x+5\)

Step-by-step explanation:

Given the point (8,3) and slope of 4, we can write an equation in point-slope form.

We know that any line perpendicular to another line has a opposite reciprocal. The opposite reciprocal of 4 is \(-\frac{1}{4}\).

Now, to write this in point slope form.

Point slope formula:

\(y-y_1=m(x-x_1)\)

New equation:

\(y-3=-\frac{1}{4}(x-8)\)

Simplify:

\(y=-\frac{1}{4}x+5\)

Here is the equation :)