in a hurry! have to finish the practice test in 30mins, so I can take the real one!(CHECKING AWNSERS, SO ONLY NEED AWNSERS TO I CAN COMPARE)

We have the next function

We need to calculate some points

x y

0 3

1 2

4 1

9 0

Let's plot the points and then we connect them in order to obtain the graph

SOLUTION

From the right triangle with two interior angles of 45 degrees, the two legs are equal in length, that is AB = BC

And from Pythagoras, the square of the hypotenuse (AC) is equal to the square of the other two legs or sides (AB and AC)

So this means

So from the first option

Hence the 1st option is correct, so its possible

The second option

Hence the 2nd option is wrong, hence not possible

The 3rd option

Hence the 3rd option is wrong, not possible

The 4th option

Hence the 4th option is correct, it is possible

The 5th option

AB = BC

This is correct, and its possible

The last option

This is wrong and not possible because AB should be equal to BC

Hence the correct options are the options bolded, which are

1st, 4th and 5th

First, we need to remember the cosine formula which is: cosine(theta)= adjacent/hypotenuse, now let's apply the formula to the triangle we have:

By using the formula we find that x=3√3 .

The answer is D.

Answer:

disagree

Step-by-step explanation:

product = 2.3 * 10²

             = 2.3 * 100

             = 230

thus, the answer is different from the one acclaimed by Alexa.

Given:

To find:

Coefficient of determination

Explanation:

The coefficient of determination is also known as the R squared value, which is the output of the regression analysis method.

If the value of R square is zero, the dependent variable cannot be predicted from the independent variable.

So, here the required coefficient of determination is:

Final answer:

Hence, the required coefficient of determination is (B) 0.96.

Dave has 17 nickels, 24 dimes and 27 pennies in his piggy bank.

According to the question,

We have the following information:

Dave has 7 more dimes than nickels and 10 more pennies than nickels.

Now, let's take the number of nickels to be x.

So,

Dimes = (x+7)

Pennies = (x+10)

Now, Dave has $3.52 in his piggy bank.

We will convert nickels, dimes and pennies into dollars.

We know that 1 nickel = 0.05 dollars, 1 dime = 0.1 dollars and 1 pennies = 0.01 dollars.

Now, we will convert the given numbers of nickel, dime and pennies into dollars.

x Nickels in dollars = $0.05x

(x+7) dimes in dollars = $0.1(x+7)

(x+10) pennies in dollars = $0.01(x+10)

Now, we will them.

0.05x + 0.1(x+7) + 0.01(x+10) = 3.52

0.05x + 0.1x + 0.7 + 0.01x + 0.1 = 3.52

0.16x + 0.8 = 3.52

0.16x = 3.52-0.8

0.16x = 2.72

x = 2.72/0.16

x = 17

Now, we have:

Number of nickels = 17

Number of dimes = (17+7)

Number of dimes = 24

Number of pennies = (17+10)

Number of pennies = 27

Hence, the number of nickels, dimes and pennies are 17, 24 and 27 respectively.

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Let the first number = n

So second number = n+2

the product of number is 728.

That mean:

Solve the equation:

For positive number is n=26.

scond number is:

So smaller number is 26.

The equation of line perpendicular to 4y = x-8 passing through (4,-1) is:

[tex]y = -4x+15[/tex].

These lines are written in the form y = mx + b, where m is the slope and b is the y-intercept. We know from the question that our slope is 3 and our y-intercept is –5, so plugging these values in we get the equation of our line to be y = 3x – 5.

Given equation of line is:

4y=x-8

We have to convert the given line in slope-intercept form to find the slope of the line

Dividing both sides by 4.

[tex]y = \frac{1}{4}x-2[/tex]

Let [tex]m_{1}[/tex] be the slope of given line

Then,

[tex]m_{1}[/tex] = [tex]\frac{1}{4}[/tex]

Let [tex]m_{2}[/tex] be the slope of line perpendicular to given line

As we know that product of slopes of two perpendicular lines is -1.

[tex]m_{1}*m_{2} = -1\\\frac{1}{4}*m_{2}=-1\\ m_{2} = -4[/tex]

The slope intercept form of line is given by

[tex]y = m_{2}x+c[/tex]

[tex]y = -4x+c[/tex]

to find the value of c, putting (4,-1) in equation

[tex]-1 = -4*4+c\\-1+16 = c\\c = 15[/tex]

Putting the value of c in the equation

  [tex]y=-4x+15[/tex]

Hence, The equation of line perpendicular to 4y = x-8 passing through (4,-1) is  [tex]y = -4x+15[/tex].

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The equation of a line in Slope-Intercept form, is:

Where "m" is the slope of the line and "b" is the y-intercept.

By definition:

- The slopes of parallel lines are equal and the y-intercepts are different.

- The slopes of perpendicular lines are opposite reciprocals.

For this case you need to rewrite the equations given in the exercise in Slope-Intercept form by solving for "y".

- Line #1:

You can identify that:

- Line #2:

You can identify that:

Therefore, since:

You can conclude that: The graphs of the equation are parallel.

Answer:

3*10=30

10^-6=1^-6. (10 raised to the power of-6)

therefore 3*1^-6=3

is equal to

4.86*10=48.6

10^-4=1^-4

therefore 48.6*1^-4=48.6

Explanation:

To find the value od 3-(-2), we will multiply the sign at the outer with the inner

Note : The use of comma as number separator represent point in this solution

Step 1: Let the number be x, thus, 2/7 parts of the number means

Step 2: Subtract 0,4 from 2/7 parts of x

Step 3: Equate the expression above to 3/5

Step 4: Simplify the equation above

Hence, the number is 3,5

Option C is correct

ANSWER

EXPLANATION

To find the area of the rhombus, we have to first find the length of the other diagonal.

We are given half one diagonal and the side length.

They form a right angle triangle with half the other diagonal. That is:

We can find x using Pythagoras theorem:

This means that the length of the two diagonals is:

The area of a rhombus is given as:

where p and q are the lengths of the diagonal.

Therefore, the area of the rhombus is:

The perimeter of a rhombus is given as:

where L = length of side of the rhombus

Therefore, the perimeter of the rhombus is:

we have the functions

Find out f(g(x))

Substitute the variable x in the function f(x) by the function g(x)

so

Answer:

B) 16 ft

Explanation:

The area of a triangle is equal to

We know that the area is 32 ft² and the height is 4 ft, so replacing these values, we get

Now, we can solve for the base. So multiply both sides by 2

Then divide both sides by 4

Therefore, the measure of the base is 16 ft

For this exercise you need to remember that a Cube is a solid whose volume can be calculated using the following formula:

Where "V" is the volume of the cube and "s" is the length of any edge of the cube (because all the edges of a cube have the same length).

For example, if you have a cube and you know that:

You can substitute this value into the formula and then evaluate, in order to find the volume of the cube. This would be:

The answer is:

You can find it using the formula

Where "s" is the length of any edge of the cube

The decimal notation of percentage is the quotient of the percentage divided by 100.

So it follows that :

The answer is 1

The percent error of the house of the pizza would be 2.

The difference between the estimated and actual values in comparison to the actual value is expressed as a percentage. In other words, the relative error multiplied by 100 equals the percent error.

Percent errors indicate the magnitude of our errors when measuring something in an analysis process. Lower percentage errors indicate that we are getting close to the accepted or original value.

Suppose the actual value and the estimated values after the measurement are obtained. Then we have:

Error = Actual value - Estimated value

To determine the percent error, we will measure how much percent of the actual value, the error is, in the estimated value.

We have been given that House of Pizza says that their pizzas are 14 inches wide, but when measured, the pizza was 12 inches.

WE know that Error = Actual value - Estimated value

Then Error = 14 - 12 = 2

Therefore, the percent error would be 2.

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The polar equation of the curve with the given Cartesian equation is r = √7

Given the Cartesian equation: x² + y² = 7

The relationships between polar and cartesian equation :

x = r cosθ

y = r sinθ

Where r is the radius and θ is the angle

Put the values of x and y into the given cartesian equation:

(r cosθ)² + (r sinθ)² = 7

r²cos²θ + r²sin²θ = 7

r²(cos²θ + sin²θ) = 7

Since the trigonometric identity cos²θ + sin²θ = 1

r²(1) = 7

r² = 7

r = √7

Therefore, the polar equation for the represented curve is r = √7

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we have that

between m<3 and m<7 -----> no relationship (because q and p are not parallel)

Part 2

the relationship between m<12 and m<10

is

vertical angles

m<12=m<10 ------> by vertical angles

The width of the box is 12 inches

The formula for calculating the volume of a rectangular box is expressed as:

where:

• l is the ,length ,of the box

• w is the ,width, of the box

• h is the ,height ,of the box

Given the following parameters

• length = 18 inches

• heigh = 9 inches

• volume = 1,944 cubic inches

Substitute the given parameters into the formula to calculate the width of the box as shown:

Divide both sides by 162 to have:

Hence the width of the box is 12 inches

Because x is continuous, we should use interval notation, the domain is:

D: [1, ∞)

For a function y = f(x), we define the domain as the set of possible inputs of the function (possible values of x).

To identify the domain, we need to look at the horizontal axis. The minimum value is the one we can see in the left side, and the maximum is the one we could see on the right side.

There we can see that the domain starts at x = 1 and extends to the left, so the notation we can use for the domain is:

D: x ≥ 1

We know that the value x =1 belongs because there is a closed dot there.

The correct option is A, because the domain is continuous (as we can see in the graph), we should use interval notation. In this case the domain can be written as:

D: [1, ∞)

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The equation that we have to build has the following form:

• The fixed cost of the phone is $88, which will be represented by ,b,.

• The variable cost per month is $116.43, which will be represented by ,m,.

• y ,is the dependent variable that we want to know (, C(t) ,)

• x ,is the independent variable, in our case, ,t,.

Replacing the values given in the problem we get:

The cost for 22 months will be:

Answer:

• Equation

• Cost in 22 months: $2660.46

To find the slope for a line that connects the given points, use the following formula:

where (x1,y1) and (x2,y2) are the given points.

Use:

(x1,y1) = (-1,1)

(x2,y2) = (3,3)

replace the values of the previous parameters in the formula for m:

Hence, the slope is 1/2

5x – 5, -123x – 8,

- 19x – 11, ...

Difference is =

Answer:

16

Explanation:

The angles ∠1 and ∠2 are complementary, meaning

Visually,

Now, ∠1 = 74; therefore,

subtracting 74 from both sides gives

which is our answer!

The number of times that 5.5 points is need to be scored to have a total gain greater than 15 points is A. 1

From the information, it was stated that there were - 3.25 points scored 4 times, -2.75 points scored 5 times, 3 points scored 2 times, and 5.5 points scored 4 times.

In this case, the entire score will be:

= (-3.25 × 4) + (-2.75 × 5) + (3 × 2) + (5.5 ×4)

= -13 - 13.75 + 6 + 22

= 11.25

Therefore, the times that 5.5 points is needed to be scored to have a total gain greater than 15 will be 1 time since 11.25 + 5.5 = 16.75. This is more than 15.

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According to the given data we have the following:

total households in the US=1.2*10^8. hence:

average household uses 400 gallons of water each day

let x=total number of gallons of water used by households in the US each day

Therefore x=total households in the US*average gallons of water households uses each day

x=120,000,000*400

x=48,000,000,000

The total number of gallons of water used by households in the US each day is 48,000,000,000

The given data points from the graph of the exponential function, f, and the, values from the table of the function g, gives the statement that correctly compares the two functions as the option;

The end behaviour of a function is the description of how the function behaves towards the boundaries of the x–axis.

The given points on the exponential function, f, are;

(-0.25, 10), (0, 6), (5, -2) and also the x–intercept (1, 0)

The points on the function g, obtained from the table of the values for g(x), expressed as ordered pairs are;

(-1, 15), (0, 3), (1, 0), (2, -34), (3, -16)

The coordinates of the x–intercept is given by the point where the y–value is zero.

The x–intercept for the exponential function, f, is therefore (1, 0)

Similarly, the x–intercept for the function, g, is (1, 0)

Therefore, both functions have the same x–intercept

However, the end behaviour of the function, f, as the x approaches infinity is that f(x) approaches negative infinity, while the end behaviour of the function, g, as the the value of x approaches infinity is g(x) is increasing towards positive infinity.

The correct option is therefore;

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Given

The data can be modeled using a quadratic regression equation.

Using the general form of a quadratic equation:

We should use a regression calculator to obtain the required coefficients. The graph of the equation is shown below:

The coefficients of the equation is:

Hence, the regression equation is:

We can find the height (y) at a time of 3.8 seconds by substitution:

Hence, the height at time 3.8 seconds is 693 ft