4. A class read 3,452 pages the first week and 4,090 more pages in the second week than in the first week. How many pages had they read by the end of the second week?

h(3z) = 2(3z)^2 + 3 = 18z^2 + 3

h(3z) is equal to 18z² + 3

To find h(3z), we substitute 3z into the function h(x). This means we replace x with 3z in the expression for h(x).

h(3z) = 2(3z)² + 3

Simplifying this expression, we have:

h(3z) = 2(9z²) + 3

h(3z) = 18z² + 3

So, h(3z) is equal to 18z² + 3. This means that if we input any value of z into the expression, the function h will output the corresponding value by evaluating 18z² + 3.

The function h(3z) represents a quadratic expression in terms of z, where the coefficient of z² is 18 and there is a constant term of 3 added to the result.

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The property illustrated in equation 4(-8+5) = -32 + 20 is the Distributive Property.

The Distributive Property states that when a number is multiplied by a sum or difference in parentheses, it can be distributed or multiplied by each term inside the parentheses separately, and then the results can be added or subtracted.

In this case, the number 4 is multiplied by the sum (-8 + 5). By applying the Distributive Property, we distribute the 4 to each term inside the parentheses:

4(-8 + 5) = (4 * -8) + (4 * 5)

This simplifies to:

4(-8 + 5) = -32 + 20

Finally, we can perform the addition:

-32 + 20 = -12

Therefore, the equation demonstrates the application of the Distributive Property.

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There are 120 different combinations of 3 programmers that can be chosen to transfer to the new department

From the question, we have

Total number of programmers, n = 10

Numbers to programmers to select, r = 3

The number of ways of selection could be drawn is calculated using the following combination formula

Total = ⁿCᵣ

Where

n = 10 and r = 3

Substitute the known values in the above equation

Total = ¹⁰C₃

Apply the combination formula

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10!/(7! * 3!)

Evaluate

Total = 120

Hence, the number of ways is 120

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Solution:

The only term that has a x-variable is "-95x".

The coefficient of x is -95.

\(\qquad \qquad\huge \underline{\boxed{\sf Answer}}\)

let's evaluate ~

\(\qquad \sf  \dashrightarrow \: ( {x}^{2} + x - 12)( {x}^{2} + 10x + 25)\)

\(\qquad \sf  \dashrightarrow \: {x}^{4} + 10 {x}^{3} + 25 {x}^{2} + {x}^{3} + 10 {x}^{2} + 25x - 12 {x}^{2} - 120x - 300\)

\(\qquad \sf  \dashrightarrow \: {x}^{4} + 11 {x}^{3} + 23 {x}^{2} - 95x - 300\)

In the given expression we can clearly observe that the Coefficient of x is " -95 "

Step 1. The information that we are given is:

• The height of the cylinder:

• The radius of the cylinder:

• The value that we need to use for pi is:

Step 2. To find the volume of a cylinder we use this formula:

Substituting the known values:

Step 3. Solving the operations:

The result is already rounded to the nearest hundredth.

Answer:

Answer:

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x:

2x² - x - 10 = 0

To factor this quadratic equation, we look for two numbers that multiply to give -20 and add up to -1 (the coefficient of the x-term). The numbers -5 and 4 satisfy these conditions:

2x² - 5x + 4x - 10 = 0

x(2x - 5) + 2(2x - 5) = 0

(x + 2)(2x - 5) = 0

Setting each factor equal to zero gives us:

x + 2 = 0 or 2x - 5 = 0

Solving these equations, we find:

x = -2 or x = 5/2

Therefore, the x-intercepts of the graph of f(x) are -2 and 5/2.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or minimum, we can look at the coefficient of the x² term. Since the coefficient is positive (2), the parabola opens upwards, and the vertex represents a minimum point.

To find the coordinates of the vertex, we can use the formula x = -b / (2a), where a and b are the coefficients of the x² and x terms, respectively.

In this case, a = 2 and b = -1:

x = -(-1) / (2 * 2) = 1/4

To find the corresponding y-coordinate, we substitute this x-value back into the equation:

f(1/4) = 2(1/4)² - 1/4 - 10

f(1/4) = 1/8 - 1/4 - 10

f(1/4) = -81/8

Therefore, the vertex of the graph of f(x) is a minimum and has coordinates (1/4, -81/8).

Part C: To graph f(x), we can use the information obtained in Part A and Part B.

1. Plot the x-intercepts: Mark -2 and 5/2 on the x-axis.

2. Plot the vertex: Mark (1/4, -81/8) as the lowest point on the graph.

3. Determine additional points: Choose a few more x-values, calculate the corresponding y-values using the equation f(x) = 2x² - x - 10, and plot these points.

4. Draw a smooth curve: Connect the plotted points with a smooth curve, keeping in mind that the parabola opens upward.

Using these steps, you can graph f(x) and accurately represent the x-intercepts, vertex, and overall shape of the parabolic curve.

Answer:

the bigger angle is 119

the smaller one is 61

Answer:

6

Step-by-step explanation:

becuase 6^2 equals 36

Answer:

d=6

Step-by-step explanation:

Use the inverse operation of square roots

Answer:

6mx^4-7x^4

Step-by-step explanation:

Answer:

16.25 mL

Step-by-step explanation:

Since we are mixing from the syrup in the inventory, we can say that the syrup in the inventory must be equal to that in the final solution. Thus, we will use the dilution equation to solve for the Initial volume;

Dilution equation is;

V₁C₁ = V₂C₂

Where;

V₁ is initial volume

C₁ is initial concentration or initial molarity

V₂ is final volume

C₂ is final concentration of final molarity

We are given;

C₁ = 80% = 0.8

C₂ = 60% = 0.6

V₂ = 65 mL

Making V₁ the subject in the dilution equation, we have;

V₁ = (V₂C₂)/C₁

V₁ = (65 × 0.6)/0.8

V₁ = 48.75 mL of inventory syrup

Since we have 48.75 mL of inventory syrup and the dilute solution is 65 ml, then the volume of soda solution required = 65mL - 48.75 mL = 16.25 mL

Answer:

Step-by-step explanation:

The segment sum theorem tells you the whole is the sum of the parts. That can be used to write an equation for y.

  RS +ST = RT

  (5y +5) +(4y +8) = 67

Simplifying, we get ...

  9y +13 = 67

  9y = 54 . . . . . . . . subtract 13

  y = 6 . . . . . . . . . divide by 9

RS = 5y +5 = 5·6 +5 = 35

ST = 4y +8 = 4·6 +8 = 32

The values of interest are ...

Answer:

Step-by-step explanation:

So the temperature when both the Celsius and Fahrenheit scales are the same is -40 degrees.

Answer:

- 40

Step-by-step explanation:

Answer:3

Step-by-step explanation:

Given points           Reflected points             Dilated points              

D ( 6, 3 )                ⇒ D' ( -6, 3 )                  ⇒ D'' ( 2, -1 )

E ( 9, 3 )                ⇒ E' ( -9, 3 )                   ⇒ E'' ( 3, -1 )

F ( 9, 12 )              ⇒ F' ( -9, 12 )                  ⇒ F'' ( 3, -4 )

G ( 6, 12 )               ⇒ G' ( -6, 12 )                ⇒ G' ( 2, -4 )

Given data

The dimensions of the rectangle DEFG is

D ( 6, 3 )

E ( 9, 3 )

F ( 9, 12 )

G ( 6, 12 )

Reflecting across y axis

Reflecting across y axis is done for example A ( x, y ) to AA

AA will be ( -x, y ).

Using this procedure we get points D'E'F'G' as follows

D ( 6, 3 ) ⇒ D' ( -6, 3 )

E ( 9, 3 ) ⇒ E' ( -9, 3 )

F ( 9, 12 )  ⇒ F' ( -9, 12 )

G ( 6, 12 ) ⇒ G' ( -6, 12 )

To dilate by factor n with the center of dilation at the origin. for example B ( x, y ) to BB

BB will be ( -nx, -ny )

using the procedure we get the points D''E''F''G" as follows

D ( 6, 3 ) ⇒ D' ( -6, 3 ) ⇒ D'' ( 2, -1 )

E ( 9, 3 ) ⇒ E' ( -9, 3 )   ⇒ E'' ( 3, -1 )

F ( 9, 12 )  ⇒ F' ( -9, 12 )  ⇒ F'' ( 3, -4 )

G ( 6, 12 ) ⇒ G' ( -6, 12 ) ⇒ G' ( 2, -4 )

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complete question

The complete question is attached

Answer:687.09 dollars

Step-by-step explanation:

Answer:

Mean = sum of all observed values / sum of frequency

Mean= (1*2 +2*2 + 3*2 + 4*1 + 5*2 + 6*1) / (2+2+2+1+2+1)

Mean = 32 / 10

Mean = 3.2

A.  {(–1, 2), (0, 3), (1, 4), (2, 5)} → Non-linear function.

B. {(–3, 9), (–2, 4), (3, 9), (4, 16)} → Non-linear function.

C. y = –14x + 9 → Linear function

D.  y = x  → Linear function

A linear function has a straight line as its graph. A linear function has the form shown below.

a + bx = y = f (x).

A linear function consists of one independent variable and one dependent variable. The independent and dependent variables are x and y, respectively.

When the absolute value of the input value of the function is connected to more than 1 output value, then the function is linear else it is a non-linear function.

From the given choices;

A.  {(–1, 2), (0, 3), (1, 4), (2, 5)}

Here, the absolute value of 1 is connected to more than one point, so non-linear function.

B. {(–3, 9), (–2, 4), (3, 9), (4, 16)}

Here, the absolute value of 3 is connected to more than one point, so non-linear function.

C. y = –14x + 9 is equivalent to the slope-intercept form of linear function y = ax + b.

D.  y = x is a linear function.

Therefore, B and D are linear functions.

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The statistics class was where the data were gathered. The variable is indicated by the column headers, along with each row's Eye Shoe Height 9.

5 different variables are present. Category-specific characteristics include gender, handedness, and field side. Quantitative factors include height and the distance covered when walking. Numbers are used to express variables like the number of siblings and student height. It is discrete since it is a count of siblings. As a continuous numerical variable, height varies throughout time.

There are three primary types of variables: controllable, dependent, and independent. His realization that shoe size is an interval variable came later. Eureka! There is no zero point in an interval variable, but there is a defined range between values. If we take shoe sizes into consideration,

we can conclude that the difference between

a size 2 and a size 3 = size 8 - a size 7

Two major categories—categorical and numeric—can be used to group variables.

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Full question:

Answer:

The forth option

It forms a right angle with the segment.

The reason that the point (3, 5) is not a solution to the given inequality is given below.

We are given that;

y > 2x + 1

Now,

The inequality y > 2x + 1 can be graphed by first graphing the boundary line y = 2x + 1. Since the inequality is strict (y >), we draw a dashed line to indicate that points on the line are not solutions to the inequality. Then, we shade the region above the line to indicate all points that satisfy the inequality.

If we have (3,5) as a point, we can see that it lies on the boundary line

y = 2x + 1.

Since the inequality is strict (y >), points on this line are not solutions to the inequality

Therefore, by the inequality the answer will be given above.

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We are agree with the statement that is Calvin selected a card, his egg carton was already filled. He promises to fill up his egg carton.

Given that,

4 Drawing fraction cards from a deck to add up to totals that fill a 12-egg carton is the object of the game Calvin and Leah are playing. When Calvin selected a card, his egg carton was already filled. He promises to fill up his egg carton.

We have to find whether we agree or disagree if yes why.

We know that,

In the picture we can see

1/3×12=12/3=4

Calvin has 4 egg cartons full.

Then he close a card with 8/12

8/12×12=8

Then 8+4=12

Calvin will fill the cartons with eggs full.

Therefore, We are agree with the statement that is Calvin selected a card, his egg carton was already filled. He promises to fill up his egg carton.

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Answer:

i think 3/4

Step-by-step explanation:

Answer:

3/4

Step-by-step explanation:

An equation of the line that passes through the points (6,-1) and (8,-4)

y = (-3/2)x + 8.

First consider the equation for the slope.    

m = (y2 - y1)/(x2 - x1)

   = (-4+1)/(8 - 6) = -3/2.

Next consider the linear point-slope formula

y = mx + b. Choose a point and plug it in (either will do, the result will be the same).

-1 = (-3/2)(6) + b

-1 = -9 + b

b = -1+9 = 8

Hence the answer will be y = (-3/2)x + 8,  is the equation you desire.

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Answer:

\(\displaystyle \frac{75}{2}\) or \(37.5\)

Step-by-step explanation:

We can answer this problem geometrically:

\(\displaystyle \int^6_{-4}f(x)\,dx=\int^1_{-4}f(x)\,dx+\int^3_1f(x)\,dx+\int^6_3f(x)\,dx\\\\\int^6_{-4}f(x)\,dx=(5*5)+\frac{1}{2}(2*5)+\frac{1}{2}(3*5)\\\\\int^6_{-4}f(x)\,dx=25+5+7.5\\\\\int^6_{-4}f(x)\,dx=37.5=\frac{75}{2}\)

Notice that we found the area of the rectangular region between -4 and 1, and then the two triangular areas from 1 to 3 and 3 to 6. We then found the sum of these areas to get the total area under the curve of f(x) from -4 to 6.

Answer:

\(\dfrac{75}{2}\)

Step-by-step explanation:

The value of a definite integral represents the area between the x-axis and the graph of the function you’re integrating between two limits.

\(\boxed{\begin{minipage}{8.5 cm}\underline{De\:\!finite integration}\\\\$\displaystyle \int^b_a f(x)\:\:\text{d}x$\\\\\\where $a$ is the lower limit and $b$ is the upper limit.\\\end{minipage}}\)

The given definite integral is:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x\)

This means we need to find the area between the x-axis and the function between the limits x = -4 and x = 6.

Notice that the function touches the x-axis at x = 3.

Therefore, we can separate the integral into two areas and add them together:

\(\displaystyle \int^6_{-4} f(x)\; \;\text{d}x=\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\)

The area between the x-axis and the function between the limits x = -4 and x = 3 is a trapezoid with bases of 5 and 7 units, and a height of 5 units.

The area between the x-axis and the function between the limits x = 3 and x = 6 is a triangle with base of 3 units and height of 5 units.

Using the formulas for the area of a trapezoid and the area of a triangle, the definite integral can be calculated as follows:

\(\begin{aligned}\displaystyle \int^6_{-4} f(x)\; \;\text{d}x & =\int^3_{-4} f(x)\; \;\text{d}x+\int^6_{3} f(x)\; \;\text{d}x\\\\& =\dfrac{1}{2}(5+7)(5)+\dfrac{1}{2}(3)(5)\\\\& =30+\dfrac{15}{2}\\\\& =\dfrac{75}{2}\end{aligned}\)

Answer:

(e) x−y>(−23)

x+7>(−2) and y−5<9  

First isolate x and y  

x+7>(−2)→ x > -9  

y−5<9→ y < 14  

Transform the second inequality to make the < to a > (multiply by -1):  

y < 14  → -y > -14    

add both inequalities:  

x > -9 and -y > -14  

x-y > -9 - 14  

x - y > -23

Step-by-step explanation:

The required solution is x - y > -23.

It is required to find the solution.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

We have to find the fill in the blanks.

By applying the inequality we have,

According to given question we have,

x+7>(−2) and y−5<9

First isolate x and y  

x+7>(−2)→ x > -9  

y−5<9→ y < 14  

Transform the second inequality to make the < to a > (multiply by -1):  

y < 14  → -y > -14    

add both inequalities:  

x > -9 and -y > -14  

x-y > -9 - 14  

x - y > -23

Therefore, the required solution is x - y > -23.

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option is missing

x - y > -23.

The value of the cosine of the angle of (a - b) will be 0.80.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

It is a function that repeats itself in a particular time interval.

Suppose that sin(a) = 4/6 and cos(b) = 1/5.

Then the value of 'a' is given as,

sin(a) = 4/6

sin(a) = 2/3

a = 41.81°

Then the value of 'b' is given as,

cos(b) = 1/5

b = 78.46°

Then the value of the cosine of the angle of (a - b) will be given as,

⇒ cos(41.81° - 78.46°)

⇒ cos(-36.65°)

⇒ cos 36.65°

⇒ 0.80

The value of the cosine of the angle of (a - b) will be 0.80.

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Both the coordinate points are plotted on the graph. The cartesian graph is attached with the answer.

Given are the two coordinates to be plotted on a Cartesian plan -

(5, 4) , (3, 4).

The two given coordinate points are (5, 4) , (3, 4).

Refer to the graph attached. It shows both the points plotted.

Therefore, both the coordinate points are plotted on the cartesian graph.

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