Janice wants to create a test containing 20 questions worth 50 points. If Janice creates questions worth either two points or four points, she can include (blank)
two-point questions and (blank) four-point questions.

Answer:

[tex]\boxed{\text{\$10; \$20}}[/tex]

Step-by-step explanation:

Let t = the price of  a T-shirt

and j = the price of a pair of jeans

You have a system of two equations:

[tex]\begin{cases}(1)& 2t + j = 40\\(2) & 2(0.5t) + 5(0.5j) = 60\end{cases}\\[/tex]

[tex]\begin{array}{lrcll}(3) & t+ 2.5j & = & 60 &\text{Removed parentheses in (2)}\\(4)& 2t + 5j & = & 120 &\text{Multiplied (3) by 2}\\& 4j & = & 80 &\text{Subtracted (4) from (1)}\\(5)& j & = & 20 &\text{Divided each side by 4} \\& 2t + 20& = & 40 & \text{Substituted (5) into (1)} \\&2t & = & 20 & \text{Subtracted 20 from each side}\\& t & = & 20 & \text{Divided each side by 2}\\\end{array}[/tex]

[tex]\text{The price of a T-shirt is \boxed{\textbf{\$10}}}\\\\\text{and the price of a pair of jeans is \boxed{\textbf{\$20}}}\\[/tex]

Check:

[tex]\begin{array}{rclcrcl}2\times10\ + 20 & = & 40 & \qquad &2(0.5\times10) + 5(0.5\times20)&=&60\\20 + 20 & = & 40 & \qquad &2\times5 + 5\times 10& = &60\\40& = & 40 &\qquad &10 + 50 & = & 60\\& & &\qquad &60 & = & 60\\\end{array}[/tex]

OK.

Answer:

f(x) = 3x(x-1)(x-3)

Step-by-step explanation:

f(x) = 3x³-12x²+9x = 3x(x²-4x+3) =

= 3x(x²-x-3x+3) = 3x[x(x-1)-3(x-1)] =

= 3x[(x-1)(x-3)] = 3x(x-1)(x-3)

Answer:

3x(x - 1)(x - 3)

Step-by-step explanation:

the sum of the coefficients = 3 - 12 + 9 = 0

hence x = 1 is a root of f(x) and (x - 1) is a factor

dividing 3x³ - 12x² + 9x gives

f(x) = (x - 1)(3x² - 9x)

    = (x - 1)3x(x - 3) = 3x(x - 1)(x - 3) ← in factored form

Answer:

D is false

Step-by-step explanation:

f(x) = -2x2 + 4x + 6 should be written with a " ^ " to indicate exponentiation:

f(x) = -2x^2 + 4x + 6.

Because of the - sign, we know that the graph of this function opens down, so there is a maximum at the vertex.  We can determine the x-value at the vertex by using the formula x = -b/(2a), which here is x = -4/(2*-2), or 1.

Evaluating f(x) = -2x^2 + 4x + 6 at x = 1, we get -2 + 4 + 6, or 8.  So statement A is true:  there's a max at (1, 8).  This is also the vertex of the graph.

Let's now look at C and D.  We evaluate f(x) at x = 3 and x - 2.  If the output (y) value is 0, we know we have an x - intercept:

f(3) = -2(9) + 4(3) + 6 = 0.  Yes, C is true, (3, 0) is an x-intercept.

f(-2) = -2(4) - 8 + 6 is not 0.  Therefore D is false; (-2, 0) is not an x-intercept.

Look at B:  Let x = 0 and find y:  it's 6.  Thus, (0, 6) is the y-intercept.  B is true.

Answer:

B) x + 12 < 8 − 3x

Step-by-step explanation:

Answer:its c

Step-by-step explanation:

becuase you cant have a overdrawn bank becuase if you do you have to pay that and the fine.

The true statement about credit cards is that interest is charged if the balance is not paid each month (Option B). Credit cards provide a short-term loan, unlike debit cards, which draw directly from your bank account.

Credit cards work by providing a short-term loan from the credit card company to the user. If the balance is not paid each month, interest is charged on the remaining amount. This is different from debit cards, where money is immediately withdrawn from the user's bank account when making a purchase.

Therefore, option B is correct

Answer:

A circle.

Step-by-step explanation:

This is it the correct answer to this question.

Hope this helps!!!

Kyle.

Answer:

Option 4: 0.554

Step-by-step explanation:

As we can see that the intervals and their frequencies are given.

We have to calculate the probability of students' score falling between 70 and 89. It will use the frequency of both intervals 70-79 and 80-89.

So, combined scores of both intervals are:

172+105 = 277

Now to find the probability

= 277/500

=0.554

So option no 4 is the correct answer ..

Answer:

Correct choice is D. [tex]y=-x+3[/tex].

Step-by-step explanation:

pick any two points from the table say (0,3) and (1,2)

Now we we can use both points to find the equation of line.

slope [tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{2-3}{1-0}=\frac{-1}{1}=-1[/tex]

now plug slope m=-1 and any point say (0,3) into point slope formula

[tex]y-y_1=m\left(x-x_1\right)[/tex]

[tex]y-3=-1\left(x-0\right)[/tex]

[tex]y-3=-1\left(x\right)[/tex]

[tex]y-3=-x[/tex]

[tex]y=-x+3[/tex]

Hence correct choice is D. [tex]y=-x+3[/tex].

For this case we must factor the following expression:

[tex]x ^ 2 + 3x-4 = 0[/tex]

We must find two numbers that when multiplied give as result -4 and when summed give as result +3. These numbers are +4 and -1:

[tex]+ 4-1 = + 3\\4 (-1) = - 4[/tex]

Then, the factorization is given by:

[tex](x + 4) (x-1) = 0[/tex]

Answer:

[tex](x + 4) (x-1) = 0[/tex]

Answer:

3847 ft³

Step-by-step explanation:

The volume of a cylinder of radius r and height h is V = πr²h.

Here, the volume is V = π(7 ft)²(25 ft) = 1225π ft³, or approximately 3847 ft³.

Answer:

using the foil

Step-by-step explanation:

you always have to get rid of the x for example if it is +3x you add it on to get rid of it and you carry on until you have solved x.

Answer:

getting the correct answer

Step-by-step explanation:

Answer:

[tex]\large\boxed{x=\pm\sqrt{13}}[/tex]

Step-by-step explanation:

[tex]10x^2-6=144\qquad\text{add 6 to both sides}\\\\10x^2=130\qquad\text{divide both sides by 10}\\\\x^2=13\to x=\pm\sqrt{13}[/tex]

Answer:

2

Step-by-step explanation:

f(x)=2x^2+9x-5

When we are find how many times it intersects the x axis, we are finding the zero's. Set the equation equal to zero

0=2x^2+9x-5

Factor the equation

0 = (2x+1) (x-5)

2*1

1*-5 = -5

2*-5 +1*1 = -9

This checks for the first last and middle terms so we factored correctly

Then using the zero product property

2x+1 = 0 and x-5 =0

2x = -1    x=5

x = -1/2  and x=5

This function crosses the x axis 2 times

Answer:

131.3312

Step-by-step explanation:

Answer:

131.3312

Step-by-step explanation:

        63.14

      x 2.08  

      50512

     0000

   12628    

   131.3312

Answer: 1 term

Reason:Polynomials are classified according to their number of terms. 4x3 +3y + 3x2 has three terms, -12zy has 1 term, and 15 - x2 has two terms. As already mentioned, apolynomial with 1 term is a monomial. A polynomial with twoterms is a binomial, and apolynomial with three terms is a trinomial.

Answer:

One Term

Step-by-step explanation:

The answer is one term, because there are no "+" or "-" happening. A term is only separated by the addition/subtraction sign, and since there are neither plus or minus, there is only one term.

The answer to your question is "A line with 4 tick marks labeled Cat, Dog, Rabbit, and Guinea Pig. Cat has 2 crosses, Dog has 3 crosses, Rabbit has 1 cross, and Guinea Pig has 3 crosses. The line is labeled Number of Pets, and title of graph is Pet Owners."  Because this is the only plot described that fits with the data from the table with the information on how many cats, dogs, rabbits, and guinea pigs there are.

Answer:

A line with 4 tick marks labeled Cat, Dog, Rabbit, and Guinea Pig. Cat has 2 crosses, Dog has 3 crosses, Rabbit has 1 cross, and Guinea Pig has 3 crosses. The line is labeled Number of Pets, and title of graph is Pet Owners.

Step-by-step explanation:

Given,

Number of cats = 2,

Dogs = 3,

Rabbits = 1,

Guinea pigs = 3,

Thus, for making the data plot,

We will draw a line,

In which 4 ticks will mentioned, first is for cat, second is for dog, third is for rabbit and fourth is for guinea pigs,

Now, we draw crosses above the each mark that will shows their number.

( shown below )

Hence, second option is correct.

Answer:

5/6

Step-by-step explanation:

Step 1: Find Alicia's share of the gift. To do this, all you have to do is multiply 120 by 2/5, which is 40%. 120 * 40% (0.4) is 48. Alicia's share is $48.

Step 2: Find Jason's share of the gift. In this case, divide 120 by 3. 120/3 is 40. Jason's share is $40.

Step 3: Express the numbers as a fraction and simplify it. 40/48 is the common fraction. Find the GCF of 40 and 48. When you solve for it, the GCF is 8. Divide both the numerator and the denominator by 8. 40/8 is 5/ 48/8 is 6. There. 5/6 is our simplified fraction, which is the ratio.

For this case we substitute the value of "[tex]x = 2[/tex]" in each of the inequalities and evaluate:

Option A:

[tex]6x + 20 <29\\6 (2) +20 <29\\12 + 20 <29\\32 <29[/tex]

It is not fulfilled!

Option B:

[tex]7x-10 <11\\7 (2) -10 <11\\14-10 <11\\4 <11[/tex]

Is fulfilled!

Option C:

[tex]14x + 10 <37\\14 (2) +10 <37\\28 + 10 <37\\38 <37[/tex]

It is not fulfilled!

Option D:

[tex]15x-18 <12\\15 (2) -18 <12\\30-18 <12\\12 <12[/tex]

It is not fulfilled!

ANswer:

Option B

S_n = n(first term + a_n)/2

n = 15

S_15 = 15(2 + a_n)/2

We need a_n.

a_n = first term + d(n - 1)

a_n = 2 + d(15 - 1)

1. Find d.

2. Plug d into expression to find a_n.

3. After finding a_n, plug back into

S_15 = 15(2 + a_n)/2 to find the sum of the first 15 terms.

Take it from here.

ANSWER

[tex]x = 4[/tex]

and

[tex]y = - 1[/tex]

EXPLANATION

Line s has equation:

y=x-5

And line t has equation:

[tex]y = - \frac{3}{4}x + 2[/tex]

We equate the two equations to get:

[tex]x - 5 = - \frac{3}{4} x + 2[/tex]

Multiply through by 4

[tex]4x - 20 = - \frac{3}{4} x \times 4 + 2 \times 4[/tex]

[tex]4x - 20 = - 3 x + 8[/tex]

[tex]4x + 3x = 8 + 20[/tex]

7x=28

[tex]x = \frac{28}{7} = 4[/tex]

[tex]y = 4 - 5 = - 1[/tex]

Answer:

(4, -1) is the solution of the system of equations.

Step-by-step explanation:

A system of equations consists of a line y = x - 5 and a line passing through two points (0, 2) and (8, -4)

And the equation of that passes through these points will be [tex]y=-\frac{3}{4}x+2[/tex]

Now we have to find the solution of the system of linear equations.

By equating both the equations

x - 5 = [tex]-\frac{3}{4}x+2[/tex]

Now we multiply this equation by 4

4(x - 5) = -3x + 4×2

4x - 20 = -3x + 8

4x + 3x = 8 + 20

7x = 28

x = 4

Now we put x = 4 in the equation y = x - 5

y = 4 -5

y = -1

Therefore, (4, -1) is the solution of the system of equations.

Answer:

[tex]\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{x}=\dfrac{1}{6}[/tex]

60 hours

Step-by-step explanation:

John - 12 hours

Rick - 15 hours

Molli - x hours

Together - 6 hours

Each of them can paint:

John - [tex]\frac{1}{12}[/tex] of a room per hour

Rick - [tex]\frac{1}{15}[/tex] of a room per hour

Molli - [tex]\frac{1}{x}[/tex] of a room per hour

Together - [tex]\frac{1}{6}[/tex] of a room per hour

So the equation is

[tex]\dfrac{1}{12}+\dfrac{1}{15}+\dfrac{1}{x}=\dfrac{1}{6}[/tex]

Solve this equation:

[tex]\dfrac{1}{x}=\dfrac{1}{6}-\dfrac{1}{12}-\dfrac{1}{15}\\ \\\dfrac{1}{x}=\dfrac{10-5-4}{60}=\dfrac{1}{60}\\ \\x=60[/tex]

Molli can paint the room in 60 hours.

Answer:

15 hours and 10 min

Step-by-step explanation:

6 1/2 hours on Monday

8 2/3 hours on Tuesday

You have to make the fractions equal to each other so you would have

1/2 x 3 = 3/6

2/3 x 2 = 4/6

Then add them together to get

7/6 or 1 1/6

6+8 = 14

Then add the 1 to 14 to get 15

1/6 of an hour is 10 minutes

Therefore your answer would be 15 hours and 10 minutes

The correct answer is B.

Distance = speed x 90

Answer:

It’s b

Step-by-step explanation:

Answer:

-5/6

Step-by-step explanation:

in order for a line to be parallel to the other it must have the same slope (angle)

The slope of a line parallel to a line with a slope of -[tex]\frac{5}{6}[/tex] is also −[tex]\frac{5}{6}[/tex], as parallel lines have identical slopes to demonstrate a consistent rate of change.

The question concerns the concept of parallel lines in coordinate geometry. When two lines are parallel, they have the same slope. Therefore, a line parallel to another line with a slope of −[tex]\frac{5}{6}[/tex] will also have a slope of −[tex]\frac{5}{6}[/tex]. This value reflects the consistent rate of change in the y-value per unit of change in the x-value along the line.

It's important to remember that this slope is unchanging for a given straight line, as it represents the regression line: a summary of the average relationship between two variables in a scatter diagram.

Answer:

b = 2 or b = 7

Step-by-step explanation:

b/(b-7) - 2/b = 7/ (b-7)

b * b - 2(b - 7) = 7 * b

b^2 - 2b + 14 = 7b

b^2 - 9b + 14 = 0

(b - 2)(b - 7) = 0

b - 2 = 0; b = 2

b - 7 = 0; b = 7

Answer

b = 2 or b = 7

Answer:

[tex]b=5[/tex]

Step-by-step explanation:

The given equation is:

[tex]y=3x+5[/tex]

To find the point where this line intersect the y-axis, we put x=0 into the given equation.

When x=0, we have [tex]y=3(0)+5[/tex].

This implies that; y=5.

The y-intercept is (0,5).

Comparing (0,5) to (0,b), we can conclude that; b=5

The given equation is not in the correct form. Once corrected to y = -3x - 5, it's clear the y-intercept (b) is -5, so the line intersects the y-axis at the point (0, -5).

The equation of a line in the xy-plane is typically written in the form y = mx + b, where m represents the slope and b represents the y-intercept.

The y-intercept is the value of y when x is zero, which means it is the point at which the line crosses the y-axis.

In the case of the equation provided, y + 3x + 5, this equation is not yet in the standard form for the equation of a line. To find the value of b, we need to isolate y. The correct form of the equation should be y = -3x - 5. Here, the y-intercept b is -5. This means that the line intersects the y-axis at the point (0, -5).

Inconsistent if you look very close it doesn’t match

The value of x in the expression (5x-15)°, which is the measure of an interior angle of a regular triangle, is 15.

The expression (5x-15)° is given as the measure of one interior angle of a regular triangle. This is a bit complex, as regular triangles, also known as equilateral triangles, only have angles that measure 60° each. Thus, we can set up the equation 5x - 15 = 60.

Solving for x, we get:

So, the value of x that would result in each angle of an regular triangle measuring (5x-15)° is 15.

https://brainly.com/question/31223205

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Answer:

The interior volume of the work box is 70 inches³

Step-by-step explanation:

* Lets talk about the volume of the regular solid

- The volume of the solid = area of the base × its height

- If the base of the solid shaped rectangle

∵ The area of the rectangle = Length × width

∴ The volume = Length × width × Height

* Now lets solve the problem

- The work box has three dimensions

# Length = 5 inches

# Width = 3.5 inches

# Height = 4 inches

∴ The work box is shaped a rectangular solid

∴ Its volume = Length × width × height

∵ Length = 5 inches

∵ Width = 3.5 inches

∵ Height = 4 inches

∴ The volume = 5 × 3.5 × 4 = 70 inches³

* The interior volume of the work box is 70 inches³

Answer: 180 ft2

Step-by-step explanation:

The formula for the area of a rectangle is Area = length X width. Since the length is 20 feet and the width is 9 feet , you multiply 20 X 9, which gives you 180 square feet. Hope this helps!

Answer:

Andrew's height is [tex]1\frac{5}{8}[/tex] meters

Explanation:

We know that John's height is [tex]1\frac{3}{4}[/tex] meters

We are given that:

John is [tex]\frac{1}{8}[/tex] meters shorter than Paul

This means that:

Paul's height = John's height + [tex]\frac{1}{8}[/tex]

Paul's height = [tex]1\frac{3}{4} + \frac{1}{8} = 1\frac{7}{8}[/tex] meter

We are given that:

Paul is 0.25 meters taller than Andrew

This means that:

Andrew's height = Paul's height - 0.25

Andrew's height = [tex]1\frac{7}{8} - 0.25 = 1\frac{5}{8}[/tex] meters

Hope this helps :)

Answer:

1 5/8 meters....

Step-by-step explanation: