The figure shows a parallelogram inside a rectangle outline:



What is the area of the parallelogram?

A) 1/25 square feet
B) 11/25 square feet
C) 3/25 square feet
D) 4/25 square feet

Answer:

Step-by-step explanation:

plug y into the first equation:

8x+5y=24

8x+5(-4x)=24

8x-20x=24

-12x=24

x=-24/12

x=-2

then plug x to the second equation

y=-4

y=-4(-2)

y=8

x=-2

y=8

8x + 5y = 24

You just told us that  Y = -4x .

If that's true, then

8x + 5(-4x) = 24

8x - 20x = 24

-12x = 24

x = -2

y = -4x

y = -4(-2)

y = 8

Answer:

d. 8

Step-by-step explanation:

The volume of a sphere = 4/3πr³

Let the radius of the smaller sphere be r, then the volume of the large sphere will be 2 r

Finding the volumes of the 2 gives:

volume of large sphere = 4/3π (2r)³

= 32/3πr³

Volume of the smaller sphere = 4/3πr³

Dividing the two volumes we get the ratio of their volumes

32/3πr³÷4/3πr³= 8

Answer: Option d

[tex]\frac{V_2}{V_1}=8[/tex]

Step-by-step explanation:

The volume of a sphere is calculated using the following formula

[tex]V=\frac{4}{3}\pi r^3[/tex]

Where r is the radius of the sphere and V is the volume.

If the radius of the small sphere is r and the volume is [tex]V_1[/tex] then:

[tex]V_1=\frac{4}{3}\pi r^3[/tex]

Let's call [tex]V_2[/tex] the volume of the large sphere. We know that it has a radius of 2r. So:

[tex]V_2=\frac{4}{3}\pi (2r)^3[/tex]

[tex]V_2=\frac{4}{3}*8\pi r^3[/tex]

Now we calculate the quotient of the volumes

[tex]\frac{V_2}{V_1}=\frac{\frac{4}{3}*8\pi r^3}{\frac{4}{3}\pi r^3}\\\\\frac{V_2}{V_1}=\frac{8r^3}{r^3}\\\\\frac{V_2}{V_1}=8[/tex]

The answer is the option d

Answer:

Total length of the x inches long pieces = 4x inches

She has to cut another piece = 7.75 inches

Total length = 4x + 7.75

This is what y represent, so

y = 4x + 7.75

The graph of the equation is continuous

Answer:

The required equation is [tex]y=4x+7.75[/tex] and the graph of the equation is continuous.

Step-by-step explanation:

Consider the provided information.

Julie needs to cut 4 pieces of yarn,

Let x  represent the length of each yarn.

Then the length of 4 pieces will be: 4x

y represents the total length of all of the yarn that Julie decides to cut

Therefore the required equation that can be used to determine the total length of all of the yarn is:

[tex]y=4x+7.75[/tex]

Here, the graph is continuous, because the length of yarn can be any number.

Final answer:

The 9th term of the geometric sequence -1, -5, -25, -125 is found to be -390625, using the formula for a geometric sequence nth term with a common ratio of 5.

Explanation:

To find the 9th term of the geometric sequence -1, -5, -25, -125, we need to determine the common ratio and apply the formula for the nth term of a geometric sequence, which is an = a1 × r(n-1), where a1 is the first term and r is the common ratio.

The common ratio (r) is the factor that each term is multiplied by to get the next term. In this sequence, r is obtained by dividing the second term by the first term: r = -5 / -1 = 5. Therefore, to find the 9th term, we use the formula with a1 = -1, r = 5, and n = 9:

a9 = -1 × 5(9-1) = -1 × 58 = -390625

So, the 9th term of the geometric sequence is -390625.

Answer:

9

Step-by-step explanation:

negative times a negative is a positive. Negative three squared is 9.

The answer is:

The velocity with which the ball can be thrown to have a maximum range of 20 meters is equal to 14 m/s.

[tex]u=14\frac{m}{s}[/tex]

To solve the problem and find the velocity, we need to isolate it from the equation used to calculate the maximum horizontal range.

We have the equation:

[tex]R=\frac{u^{2} }{g}[/tex]

Where,

R is the maximum horizontal range.

u is the initial velocity.

g is the gravity acceleration.

Also, from the statement we know that:

[tex]R=20m\\g=9.8\frac{m}{s^{2} }[/tex]

So, using the given information, and isolating, we have:

[tex]R=\frac{u^{2} }{g}[/tex]

[tex]R*g=u^{2}[/tex]

[tex]u^{2}=R*g=20m*9.8\frac{m}{s^{2} }=196\frac{m^{2} }{s^{2} }\\\\u=\sqrt{196\frac{m^{2} }{s^{2}}}=14\frac{m}{s}[/tex]

Hence, we have that the velocity with which the ball can be thrown to have a maximum range of 20 meters is equal to 14 m/s.

[tex]u=14\frac{m}{s}[/tex]

Have a nice day!

Answer:

The velocity with which a ball must be thrown to have a maximum range of 20 m is 14 m/s.

Note that this problem means to find the magnitude of the velocity and not the direction (it is implicit in the formula that the angle of the launch is 45°).

Explanation:

You just must use the given equation for the maximum horizontal range of a projectile and solve for u which is the unknwon:

Solve for u:

Take square root from both sides:

Answer:

M(t) = 0.1t3 + 5(1.07)t - 5

Step-by-step explanation:

Answer:

[tex]M(t) = 0.1t^{3}[/tex] [tex]+ 5(1.07)^{t}[/tex]- 5

Step-by-step explanation:

(on attachment with step by step explanation)

Answer:

[tex]\large\boxed{(f\cdot g)(x)=2x^3+x^2-14x-7}[/tex]

Step-by-step explanation:

[tex](f\cdot g)(x)=f(x)\cdot g(x)\\\\f(x)=2x+1;\ g(x)=x^2-7\\\\(f\cdot g)(x)=(2x+1)(x^2-7)\qquad\text{use FOIL:}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(2x)(x^2)+(2x)(-7)+(1)(x^2)+(1)(-7)\\\\=2x^3-14x+x^2-7[/tex]

Answer:

There are no solutions to the system because the equation represents parallel lines

Answer:

Step-by-step explanation:

We know by given that the system result is 0 = -12.

This results means that there are no solutions in the system, because the statment 0 = -12 is false, also lines are parallels, that's the real reason why there's no solution.

Remember that parallel lines won't intercept, and a solution of a linear system means that those lines intercept. So, if they don't, then, there's no solution.

Therefore, the right answer is the first choice.

The equation representing the population of the city is P = 50t + 8500. Substituting t=7 in this equation gives the estimated population in year 2017 as 8850 people.

The question is asking for the population of the town in a given year, given it's steadily increasing each year. The original population, in 2010, is 8500 people and each year the number of people increases gradually by 50.

The general equation for a line is y = mx + c, where m is the slope (the rate of change), c is the y-intercept (the initial value), x is the input (in this case, the number of years since 2010), and y is the output (the population).

In this case, m = 50 (because the population increases by 50 people per year), c = 8500 (the population in 2010) and x will be the number of years since 2010. Therefore, the equation for the population of the town is: P = 50t + 8500

To find the population in 2017, you substitute t=7 (because 2017 is 7 years after 2010) into the equation: P = 50*7 + 8500 = 8850

So the estimated population in 2017 would be 8850 people.

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Neither the reflection over the y-axis nor the 270° counterclockwise rotation would map figure ACB onto itself.

To determine whether a reflection over the y-axis and a 270° counterclockwise rotation would map figure ACB onto itself, we need to analyze the effects of these transformations.

Therefore, neither the reflection over the y-axis nor the 270° counterclockwise rotation would map figure ACB onto itself.

Answer:

Step-by-step explanation:

4 square root 5

Final answer:

The dog’s movement 5 seconds after the command, considering different frames of reference for speed, can be described by the distance it would have traveled: either 25 meters on the sidewalk (at 5 m/s) or 10 meters from the student's perspective (at 2 m/s).

Explanation:

The student's question pertains to describing the dog’s movement 5 seconds after the command was given, considering the dog's speed. Since we have learned that the dog has different speeds in different frames of reference—5 m/s on the sidewalk and 2 m/s in the student’s frame—we can describe the dog’s movement based on these speeds. If the dog started moving at the moment the command was given and continued to move for 5 seconds, we can calculate the distance it would have covered in that time.

For the sidewalk's frame, where the dog's speed is 5 m/s, the dog would have covered a distance of:

Distance = Speed × Time

Distance = 5 m/s × 5 s = 25 meters

In the student’s frame, where the dog's speed is 2 m/s, it would have moved:

Distance = 2 m/s × 5 s = 10 meters

The statement that could describe the dog’s movement 5 seconds after the command was given is that the dog could have traveled either 25 meters from its starting point on the sidewalk or 10 meters from the student's perspective, depending on the frame of reference being considered.

Answer:

We need to know angle C which is (180 -123 -34) = 23°

We'll use the Law of Sines

Sine (A) / side a = Sine (B) / side b

Sine (34) / 10 = Sine (123) / side b

0.55919 / 10 = 0.83867 / side b

10 * .83867 / .55919 = side b

side b (or line AC) = 14.998

Step-by-step explanation:

Answer: 26%

Step-by-step explanation:

See attached photo. - my answer got deleted lol

Without additional information, we cannot determine the exact percentage of students age 15 and above who travel to school by bus.

To find the percentage of students age 15 and above who travel to school by bus, we need to compare the number of students who travel by bus to the total number of students in that age group. However, we don't have that information in the given question.

We need more data to calculate the percentage. Without additional information, we cannot determine the exact percentage of students age 15 and above who travel to school by bus.

For this case we can raise a rule of three:

$ 58 ----------> 100%

$ 63 ----------> x

Where "x" represents the percentage equivalent to $ 63.

[tex]x = \frac {63 * 100} {58}\\x = \frac {6300} {58}\\x = 108.62[/tex]

Thus, the percentage increase is 8.62%

Answer:

The percentage of increase is 8.62%

Answer: infinite solutions

Step-by-step explanation:

If the left side equals the right side, then every value you input for the variable will make a TRUE statement --> which means there are infinite solutions.

For example: x + 1 = x + 1

Any value you choose for "x" will result in a true statement.

This is because they are the same line, which is another way of showing that they have infinite solutions.

The linear equation is an identity, which means that it has infinite solutions.

We define an identity as an equation where we have the exact same expression in both sides of the equation.

For example, in:

f(x) = f(x).

Where f(x) is a function.

A easier example can be:

x + 5 = x + 5

Notice that we have the exact same thing in both sides, this is what Jilana gets when solving her linear equation.

This means that for any given value of x, the equation will be true. So, x can be any real value, which means that there are infinite solutions for the equation.

If you want to learn more about linear equations, you can read:

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To find the percentage of the monthly budget that housing represents in a circle graph, divide the housing cost ($175) by the total monthly expenses ($500) and multiply by 100. This calculation shows that housing accounts for 35% of the monthly budget.

When representing a monthly budget on a circle graph, or pie chart, you need to find out what percentage of the total budget each category represents. In this case, a young single person spends $150 on food, $175 on housing, and $175 on other items. To find the percentage that represents housing, we first need to calculate the total amount of monthly expenses which are $150 for food, $175 for housing, and $175 for other items, adding up to a total of $500.

Next, we calculate the percentage that the housing expense represents by dividing the housing cost by the total expenses and then multiplying by 100 to get a percentage:

Therefore, housing represents 35% of the total monthly budget on the circle graph.

Answer:

it is :119.5714

Step-by-step explanation:

15 3/14+24 1/14+12 2/7+12 2/7+10 1/7+10 1/7+35 3/7=

step by step now:

15 3/14+24 1/14+12 4/14+12 4/14+10 2/14+10 2/14+35 6/14=118 22/14=118+1.5714=119.5714

Final answer:

The sum of the given mixed numbers is 119 and 2/7 after adding the whole numbers separately and then the fractions.

Explanation:

To calculate the sum of the given numbers, we start by adding the whole numbers and the fractions separately. All the fractions have a common denominator, which simplifies the process. Let's proceed with the calculation:

Adding the whole numbers: 15 + 24 + 12 + 12 + 10 + 10 + 35 = 118.

Adding the fractions: 3/14 + 1/14 = 4/14, simplifies to 2/7 because 4/14 is dividable by 2. Then, we add 2/7 + 2/7 + 1/7 + 1/7 + 3/7 = 9/7. But 9/7 is more than 1, so we rewrite 9/7 as 1 whole and 2/7.

Now let's combine the sums of whole numbers and fractions: 118 + 1 = 119.

Thus, the total sum is 119 and 2/7.

Answer:

1,715

Step-by-step explanation:

So, we have a product that is sold for $0.85 and costs $0.50 to produce, and we need to find the number is items needed to cover the $600 fixed costs of the company.

We can model this like that, where x is the number of items to make:

0.85x - 0.5x = 600

0.35x = 600

x = 1,714.29

So, to cover the fixed overhead/fixed expenses, they need to make at least 1,715 items, each day.

Answer:

A and B

Step-by-step explanation:

You can tell by just looking. Also because it is a isosceles triangle.

We can see here that the statement that is true regarding ΔEFG are true:

A. EF + FG > EG

B. EF + FG > EF

C. EG - FG < EF

A triangle is a polygon with three sides, three angles, and three vertices. It is one of the fundamental geometric shapes in Euclidean geometry. The sum of the internal angles of a triangle always adds up to 180°.

Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This theorem establishes a fundamental relationship between the lengths of the sides of a triangle.

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Answer:

P(A|B) = 0.30

Step-by-step explanation:

P(A) = 0.30

P(B) = 0.60

To Find:

P(A|B) = ?

P(A|B) means probability of occurring of event A when event B has occurred.

P(A|B) = P(A∩B)/P(B)

We know that for independent events;

P(A∩B) = P(A).P(B)

So, we have:

P(A|B) = P(A).P(B)/P(B)

P(A|B) = P(A)

So, probability of occurrence of an independent event does not depend on the probability of a different event.

The integer that represents the change in temperature is -16°F.

To find the change in temperature, we need to calculate the difference between the final temperature and the initial temperature.

The initial temperature was 6°F, and the final temperature was -10°F. To calculate the change, we subtract the initial temperature from the final temperature:

Change in temperature

= Final temperature - Initial temperature

                             = (-10°F) - (6°F)

                             = -10°F - 6°F

                             = -16°F

Therefore, the integer that represents the change in temperature is -16°F.

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Answer:

B) The scale on the y-axis could be changed to 25–40.

Answer:

B the scale on the y-axis could be changed from 25-40

Step-by-step explanation:

just took test on edg and got a 100

Answer:

B. 14x^3+39x^2+18x+20

Step-by-step explanation:

Given polynomials are:

[tex](7x^2+2x+4)(2x+5)\\For\ product\\(2x+5)(7x^2+2x+4)\\= 2x(7x^2+2x+4)+5(7x^2+2x+4)\\= 14x^3+4x^2+8x+35x^2+10x+20\\Combining\ alike\ terms\\= 14x^3+4x^2+35x^2+8x+10x+20\\=14x^3+39x^2+18x+20[/tex]

The product of given polynomials is:

14x^3+39x^2+18x+20

Hence, Option B is correct ..

Answer:

B.  14x^3 + 39x^2 + 18x + 20.

Step-by-step explanation:

(7x^2 + 2x + 4)(2x + 5)

= 2x(7x^2 + 2x + 4) + 5(7x^2 + 2x + 4)

Distribute over the 2 parentheses:

= 14x^3 + 4x^2 + 8x + 35x^2 + 10x + 20

Add like terms:

= 14x^3 + 39x^2 + 18x + 20.

Final answer:

A system of equations will have the solution (2,0) if, when substituting x=2 and y=0, both equations are satisfied. This can be a linear equation where the y-intercept is set to be the negative double of the slope, or a conic section represented by a quadratic equation that intersects the x-axis at x=2.

Explanation:

Systems of equations that will have a solution of (2,0) must satisfy the condition that when x=2 and y=0, both equations are true. Considering the information provided about quadratic and differential equations, to find a system with the solution (2,0), one can set up a system of any two equations and test if the point (2,0) satisfies them. For instance, any linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept, will have a solution of (2,0) if b is set to -2m. Similarly, a second-order differential equation can be constructed with known solutions, including the point (2,0).

A system with a linear equation y = mx - 2m, where m can be any value.

A homogeneous linear differential equation with boundary conditions that result in the point (2,0) being a solution.

A conic section represented by a quadratic equation that intersects the x-axis at x=2.

For example, the quadratic equation ax² +2hxy+by² = 0, can be factored into two linear factors with no constant term, which means it represents two lines intersecting at the origin. If one of these lines passes through the point (2,0), it would confirm that our solution fits this system as well.

Answer:

.5

Step-by-step explanation:

4/2   -n=3n

2      -n=3n

2          =4n

2/4      =n

.5        =n

Answer:

C

Step-by-step explanation:

-567.45 + 567.45 = 0