Jessica qent for a drive in a new car. She drove 204.8 miles in 4 hours. What was her speed

Answer:

The number of school flags sold are 135 and the number of t-shirts sold are 85.

Step-by-step explanation:

It is given that at a recent school event the booster club was selling school flags and t-shirts as a fundraiser each school flag was sold for $2 and each t-shirt sold for $5 they sold a total of 220 items and made a total of $695.

Now, let us analyze these statements one by one;

Each school flag for the fundraiser was sold for dollar = $2

Each t-shirt for the fundraiser was sold for dollar = $5

Further, they sold a total of 220 items including the school flags and t-shirts and made a total of $695.

Now, let us assume that;

The number of school flag for the fundraiser sold are 'x' and

The number of t-shirts for the fundraiser sold are 'y'

So, we can formulate an equation from the given conditions;

=> 2x + 5y = 695

and

=> x + y = 220

Now, on solving both the equations and putting the value of x in another equation we get;

=> x + y = 220

=> x = 220 - y

Furthermore,

=> 2x + 5y = 695

=> 2 (220 - y) + 5y = 695

=> 440 - 2y + 5y = 695

=> 440 + 3y = 695

=> 3y = 695 - 440

=>  3y = 255

=> y = 255/3

=> y = 85

Now, let us put the value of y in one of the equations formed on the given conditions;

=> x = 220 - y

=> x = 220 - 85

=> x = 135

Therefore, the number of school flags sold are 135 and the number of t-shirts sold are 85.

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The total money was shared = $3304

What are proportion and ratio?

Two quantities are compared to form a ratio. An equality of two ratios is a proportion. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

Aaron, Ben, and Charles split a sum of money in the following proportions: 2: 5: 7. What was the initial amount of money shared if Charles' part was 1180 higher than Aaron's portion?

——-

Ben:::: 5x

Charles:7x

Aaron:2x

———-

7x = 2x + 1180 in the equation

5x = 1180

x = 236

————-

2x + 5x + 7x = 14x

14x = 14*236 = $3304

—————————————

Hence the total money was shared = $3304

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Answer:

0.000348 (rounded)

Step-by-step explanation:

Please tell me if this is wrong.

Answer:

-10

Step-by-step explanation:

22-12=10

CHECK:

-12+(-10)=-22 (correct, and proven)

Answer:

x=2

Step-by-step explanation:

To find the axis of the simmetry of parabola ( the curve of the quadratic function) we have to find the x of the top point of the parabola.

The x= -12/-(2*3)= 2

So the axis of the symmetry is the line x=2

The graph of f(x) is the second one, so the correct option is B.

Here we have f(x), a piecewise function, and we want to see which one of the four graphs is the correct one.

You can see that the first domain of the function is:

x ≤ -4

So we must have a closed circle at x = -4, when the parabola ends.

The second domain is:

-4 < x < 1

So x here is not equal to -4 nor 1, so this part starts and ends with open circles.

finally, the linear part starts with a closed circle.

Also, notice that the line has a negative slope, so it goes down, then we can discard the first option.

Then we can see that the correct option is the second graph.

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Answer:

\(y = 26 - 2 \\ y = 24\)

Answer: 24.45 miles apart

Step-by-step explanation:

because if its 1.5 inches apart so we already know 1 inch is 16.3 then half and inch is 8.15 so 16.3+8.15 is 24.45

Answer:

Area of a sphere

Radius

15 m

Diameter

30 m

Volume

14,137 m³

Surface to volume ratio

0.2 1/m

Surface area

2,827.4 m²

Step-by-step explanation:

The equation for the cross section exists x = z , -z.

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used.

When two expressions in a variable (or variables) have the same value, the condition is said to be an equation. The equation's solution, or root, is the value of the variable for which the equation holds true. Even if the RHS and LHS are switched, an equation still holds true.

In the question it is given that

Equation of curve => x² = 49y² + z²

(a) Write an equation for the cross section at z = -7

Putting z = -7 in the equation,

⇒ x² = 49y² + (-7)²

⇒ x² - 49y² = 49

(b) Write an equation for the cross section at z = 0

Putting z=0

⇒ x² - 49y² = 0

(c) Write an equation for the cross section at z = 7

Putting z = 7 ,

⇒  x² - 49y² = 49

(d) Write an equation for the cross section at y = -7

Putting y = -7 in equation this time,

⇒  x² = 49( -7)² + z²

⇒ x² - z² = 2401

(e) Write an equation for the cross section at y = 0

Putting y = 0,

⇒ x² = z²

⇒ x = z , -z

Therefore, the equation for the cross section exists x = z , -z.

The compete question is:

Use traces to sketch the surface. (If an answer does not exist, enter DNE. Select Update Graph to see your response plotted on the screen. Select the Submit button to grade your response.) x2 = 49y2 + z2 = (Write an equation for the cross section at z = -7 using x and y.) (Write an equation for the cross section at z = 0 using x and y.) (Write an equation for the cross section at z = 7 using x and y.) (Write an equation for the cross section at y = -7 using x and z.) IIIIIIII (Write an equation for the cross section at y = 0 using x and z.) (Write an equation for the cross section at y = 7 using x and z.) (Write an equation for the cross section at x = -7 using y and z.) (Write an equation for the cross section at x = 7 using y and z.)

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What your friend needs to do is substitute that equation into the other one, and then solve it.

The solution of the system is x = 7 and y = -1.

Here we have the following system of equations:

x + 7y = 0

2x - 8y = 22

Your friend starts by isolating x on the first equation to get:

x = -7y

The next step is to substitute that equation into the other one, we will get:

2*(-7y) - 8y = 22

Now you can solve that equation for y.

-14y - 8y = 22

-22y = 22

y = 22/-22

y = -1

Now that we know the value of y, we can find the value of x:

x = -7y

x = -7*(-1)

x = 7

The solution is (7, -1)

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The standard form is 6\(x^4\) + 10x³ - 4x² - 15x + 5.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

(3x−1) (2x³ +4x² −5)

Simplifying

3x (2x³ +4x² −5) - 1 (2x³ +4x² −5)

6\(x^4\) + 12x³ - 15x - 2x³ - 4x² + 5

Adding the like terms.

6\(x^4\) + 10x³ - 4x² - 15x + 5

Thus,

6\(x^4\) + 10x³ - 4x² - 15x + 5

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Step-by-step explanation:

Factor out two from the expression. The answer should be 2(2*(-2, 3)-(6, -7))

Question

Combine like terms to create an equivalent expression.

-3.6-1.9t+1.2+5.1t

Answer:

3.2t - 2.4

Step-by-step explanation:

Given;

-3.6 - 1.9t + 1.2 + 5.1t

Combining like terms means bringing terms that have "t" together and separately, those that don't have "t" together. i.e

=> − 1.9t + 5.1t - 3.6 + 1.2

=> 3.2t - 2.4

Therefore, the equivalent expression is;

3.2t - 2.4

Answer:

3.2t - 2.4

Step-by-step explanation:

right on khan

Answer:

It will look like this

Step-by-step explanation:

The equation of line y = 4 / 5x + 8 / 5 can be represented on the basis of coordinates (0, 8/5), (1, 12/5), and (10, 48/5) in the graph attached below.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given:

-4x + 5y = 8

Write the line in slope intercept form as shown below,

5y = 4x + 8

y = 4 / 5x + 8 / 5

Put the random values of x and find y,

y = 4 / 5 × 0 + 8 / 5   (when x = 0)

y = 8 / 5

y = 4 / 5 × 1 + 8 / 5  (When x = 1)

y = 12 / 5

y = 4 / 5 × 10 + 8 / 5  (When x = 10)

y = 48 / 5

Plot the coordinates (0, 8/5), (1, 12/5), and (10, 48/5) in the graph and mark the points, joining all the points to get the line.

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It would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

To calculate the time it would take to drive from Statesville, NC to Washington, DC, we can divide the distance of 389 miles by the average speed of 65 mph.

Time = Distance / Speed

Time = 389 miles / 65 mph

Time ≈ 5.98 hours

Therefore, it would take approximately 5.98 hours to drive from Statesville, NC to Washington, DC on interstates with an average speed of 65 mph.

To calculate the cost of driving to Washington, DC, we need to know the number of gallons of gas required for the trip. We can find this by dividing the distance by the car's mileage, which is 29 miles per gallon.

Number of gallons = Distance / Mileage

Number of gallons = 389 miles / 29 miles per gallon

Number of gallons ≈ 13.41 gallons

The cost of gas can be calculated by multiplying the number of gallons by the cost per gallon, which is $3.89.

Cost = Number of gallons * Cost per gallon

Cost ≈ 13.41 gallons * $3.89/gallon

Cost ≈ $52.18

Therefore, it would cost approximately $52.18 to drive from Statesville, NC to Washington, DC with a car that gets 29 miles per gallon on the interstate, considering a gas cost of $3.89 per gallon.

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a) The radius of the sphere is given as follows: 27.13 ft.

b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.

The surface area for a sphere of radius r is given by the equation presented as follows:

S = 4πr².

The surface area for this problem is given as follows:

9244 ft².

Hence the radius is given as follows:

\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)

r = 27.13 ft.

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The coordinates of W after the rotation are:

W' = (7, -2)

For any point (x, y), a rotation of 180° maps the point into another with coordinates (-x, -y)

In this case, we can see that the coordinates of point W are (-7, 2), then we apply a rotation of 180° clockwise, and using the above rule, the coordinates of W after the transformation are:

W' = (- (-7), -2)

W' = (7, -2)

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Answer:

Solution

\(x = - 3,\: y = -3\)

Step-by-step explanation:

If the objective is to solve for the system of equations
- 7x - 5y = 36    [1]

x = 2y + 3    [2]

Then the process is as follows

Work Shown:

21/35 = (7*3)/(7*5) = 3/5

The equation of the line is y = -11x + 232

The given parameters are:

Slope (m)= -11

Point (x1, y1) = (31, -109)

The linear equation is then calculated as:

y = m(x - x1) + y1

This gives

y = -11(x - 31) - 109

Evaluate the product

y = -11x + 341 - 109

Evaluate the like terms

y = -11x + 232

Hence, the equation of the line is y = -11x + 232

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Answer:

A. 40°

Step-by-step explanation:

Given:

m<BEF =25°

m<B = 50°

m<ACB = 65°

Required:

m<D

SOLUTION:

m<CED = m<BEF (vertical angles theorem)

m<CED = 25° (Substitution)

m<ACB + m<DCE = 180° (linear pair theorem)

65° + m<DCE = 180° (substitution)

Subtract 65 from both sides

m<DCE = 180° - 65°

m<DCE = 115°

m<DCE + m<CED + m<D = 180° (sum of triangle)

115° + 25° + m<D = 180° (substitution)

140° + m<D = 180°

Subtract 140° from both sides

m<D = 180° - 140°

m<D = 40°

Carey's graph will be a straight line with a slope of -1 and a y-intercept of 3.

Carey correctly graphs a linear function with a slope of -1 and a y-intercept of 3. A linear function is represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

In this case, the slope is -1, which means that for every unit increase in the x-coordinate, the y-coordinate decreases by 1 unit. The y-intercept is 3, indicating that the graph intersects the y-axis at the point (0, 3).

To plot the graph, Carey starts by marking the point (0, 3) on the graph. Then, for every unit increase in the x-coordinate, Carey moves one unit downward. Similarly, for every unit decrease in the x-coordinate, Carey moves one unit upward. These steps ensure the correct slope of -1.

After connecting the points, Carey will obtain a line that starts at the y-intercept (0, 3) and slants downward, with a slope of -1. The resulting graph will be a straight line extending to both sides of the coordinate plane.

In conclusion, it is represented by the equation y = -x + 3.

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The equivalent expressions \($\frac{21^x}{7^x}\) is \($3^{x}$$\).

Equivalent expressions exist as expressions that work exactly even though they look different. If two algebraic expressions exist as equivalent, then the two expressions contain the exact value when we plug in the same values for the variables.

Given: \($\frac{21^x}{7^x}\)

Factor \($21^{x} = 7^{x} \cdot 3^{x}$\)

\($=\frac{7^{x} \cdot 3^{x}}{7^{x}}$$\)

Cancel the common factor: \($7^{x}$\)

\($=3^{x}$$\)

Therefore, the correct answer is option B. \($3^{x}$$\).

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The value of the fraction -6 3/5 -(-7 4/15) + 2 1/5 will be 2 13/15.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

The value of the fraction -6 3/5 -(-7 4/15) + 2 1/5 will be:

= -6 3/5 -(-7 4/15) + 2 1/5

= 7 4/15 + 2 1/5 - 6 4/5

= 7 4/15 + 2 3/15 - 6 9/15

= 9 7/15 - 6 9/15

= 2 13/15

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Answer:

C

Step-by-step explanation:

20+22+24=66

22+24+26=72

24+26+28=78

26+28+30=84