a rectangle has a height of 4x4x4, x and a width of 3x 13x 13, x, plus, 1. express the area of the entire rectangle.

Answer:

x = 8 because of the explanation given in the image above hopefully it helps :) let me know if you have any questions!

The value of a is -16

If α and β are zeroes of the quadratic equation x²-6x+a, then we know that:

α + β = 6

α * β = a

We are also given that 3α + 2β = 20.

3α + 2β = 20

3(α + β) - α = 20

3(6) - α = 20

18 -α = 20

18 - 20 = α

α = -2

Substituting α = -2 into the equation α + β = 6, we get:

- 2 + β = 6

beta = 8

Therefore, α = -2 and β = 8, and we can find a using the equation α * β = a:

a = α * β

= - 2 * 8

= 16

Therefore, the value of a is -16

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Answer:

Volume of cylinder = 3,617.28 cm³ (Approx.)

Step-by-step explanation:

Given:

Height of cylinder = 18 centimeter

Length of base diameter of cylinder = 8 centimeter

Find:

Volume of cylinder

Computation:

Volume of cylinder = πr²h

Volume of cylinder = (22/7)(8)²(18)

Volume of cylinder = (22/7)(64)(18)

Volume of cylinder = (3.14)(64)(18)

Volume of cylinder = (22/7)(64)(18)

Volume of cylinder = (200.96)(18)

Volume of cylinder = 3,617.28

Volume of cylinder = 3,617.28 cm³ (Approx.)

Answer:

V=904.8  centimeters^3

Step-by-step explanation:

Answer:

A and B

Step-by-step explanation:

simplify both sides of the equation

add 4x to both sides subtract 3 from both sides. Divide both sides by 9 and that's it

If the equation given a unique and single value of variable after solving then the equation is said one solution equation.

The equation which has only one solution are,

\(5x+3=-2(2x+3)\)

Thus, the option C is the correct option.

How to find one solution of equation?

If the equation given a unique and single value of variable after solving then the equation is said one solution equation.

Such equation gives exactly one solution.

Given information-

To find the equation we have to solve each equation one by one.

\(-7x+2&=-3(x-3)-4x-7\\\)

Solve it further,

\(-7x+2&=-3x+9-4x-7\\-7x+2&=-7x+2\\.\;\;\;\;\;\;\;\;\;\;\;0=0\)

Thus this equation has no solution. Hence the option A is the incorrect option.

\(14x&=7(2x+2)\)

Solve it further,

\(14x&=14x+14\\.\;\;\;0=14\)

Thus this equation has no solution. Hence the option B is the incorrect option.

\(5x+3=-2(2x+3)\)

Solve it further,

\(5x+3=-(4x+6)\\5x+3=-4x-6\)

Bring the same variable terms one side.

\(5x+4x=-6-3\\9x=-9\\x=-1\)

As the expression of equation gives the value of variable which is -1.Thus this equation has one solution.

Hence the option C is the correct option.

\(3(4x+2)-9=12x-3\)

Solve it further,

\(12x+6-9=12x-3\\2x-3=12x-3\\.\;\;\;\;\;\;\;0=0\)

Thus, this equation does not has one solution.

Hence the option D is the incorrect option.

Hence the equation which has only one solution are,

\(5x+3=-2(2x+3)\)

Thus, the option C is the correct option.

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The equations of the lines that pass through the point (4, -3) and have the given slopes are:

y = -x + 1

y = x - 7

y = -x + 1

y = -x + 1

To find the equation of a line, we need the slope and a point on the line.

The given point is (4, -3), and we have four options for the slope: -1, 1, -1, and -1.

Let's go through each option and determine the equation of the line for each case:

Slope = -1 (from Oy = -x - 2):

Using the point-slope form of a line, we have:

y - y1 = m(x - x1)

y - (-3) = -1(x - 4)

y + 3 = -x + 4

y = -x + 4 - 3

y = -x + 1

Slope = 1 (from Oy = x + 2):

Using the point-slope form:

y - y1 = m(x - x1)

y - (-3) = 1(x - 4)

y + 3 = x - 4

y = x - 4 - 3

y = x - 7

Slope = -1 (from Oy = -x - 3):

Using the point-slope form:

y - y1 = m(x - x1)

y - (-3) = -1(x - 4)

y + 3 = -x + 4

y = -x + 4 - 3

y = -x + 1

Slope = -1 (from Oy = -x + 3):

Using the point-slope form:

y - y1 = m(x - x1)

y - (-3) = -1(x - 4)

y + 3 = -x + 4

y = -x + 4 - 3

y = -x + 1

So, the equations of the lines that pass through the point (4, -3) and have the given slopes are:

y = -x + 1

y = x - 7

y = -x + 1

y = -x + 1

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Answer:

Step-by-step explanation:

6--6 = 12

4-1 = 3

12/3 = 4

y=4x

-6-4 = -10

y=4x-10

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

The line passes through (1, -6) and (4, 6).

The formula of slope:

Slope = (d - b) / (c - a)

where (a, b) and (c, d) are the two points.

Now,

(1, -6) = (a, b) and (4, 6) = (c, d)

Slope = (6 + 6) / (4 - 1) = 12 / 3 = 4

m = 4

The equation of a line is given as y = mx + c.

(1, -6) = (x, y)

-6 = 4 x 1 + c

-6 = 4 + c

-6 - 4 = c

c = -10

Now,

The equation of the line that passes through (1, -6) and (4, 6) is

y = 4x - 10

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You must identify the equation that defines the graph in order to assess the graph's expression. This equation will be a mathematical expression that explains the connection between the graph's variables.

A graph is a visual representation of the relationship between two or more variables. It is a way of showing how the variables change in relation to each other. A graph typically consists of a set of points plotted on a coordinate plane, with each point representing a specific set of values for the variables. The shape of the graph can reveal patterns and trends in the data, and it can be used to make predictions and draw conclusions about the relationship between the variables.

You can use the coordinates of points on a graph, the slope and y-intercept of the graph (if it's a linear function), or the properties of the graph to get its equation (such as the shape of the curve or the presence of asymptotes).

Once you have the equation for the graph, you may simplify it and substitute the variable values there to evaluate the expression.

Take the graph of the function y = x2 - 2x + 1, for instance. You can substitute the value of x into the equation and simplify to determine the value of this function for a specific value of x. For instance, the function's value in the case of an x of 3 is y = 32 - 2(3) + 1 = 9 - 6 + 1 = 4.

A graph itself can be used to assess the expression of a graph. To determine the equation of the graph, you may, for instance, read the coordinates of the graph's points or examine the curve's shape and any asymptotes' locations.

Keep in mind that you need a mechanism to represent both the graph and the equation that describes it in order to evaluate the expression of a graph. This could entail manually creating the graph, using software or a graphing calculator, or representing the graph as a table of values.

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Answer

The second day she produced 14 more dollars adding a child ticket.

so now i know that a child ticket costs 14 dollars. from the first question i subtract 38 from 14 which equals 24. I then divide 38 from 3 (the amount of senior people that came) which equals 12.66 dollars for a senior.

maybe round 12.66 which can equal to 12.70 if needed

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

Given that the sum of the digits is seventeen, we have the equation:

x + y = 17 (equation 1)

The number with the digits reversed is thirty more than 5 times the tens' digit of the original number. The number with the digits reversed would be 10y + x.

According to the given information, we have the equation:

10y + x = 5x + 30 (equation 2)

To solve the system of equations, we can substitute equation 1 into equation 2:

10(17 - x) + x = 5x + 30

Expanding and simplifying:

170 - 10x + x = 5x + 30

170 - 30 = 5x + 10x - x

140 = 14x

x = 10

Substituting the value of x back into equation 1:

10 + y = 17

y = 7

Therefore, the original number is 10x + y = 10(10) + 7 = 107.

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Answer:

x>2

That is the answer do you want the work?

The statement 3 more than 7 means, a number is 3 more than a given number. Since here the number is 7 so the required number will be 7+3= 10

In numerical more than simply refers to adding and less than refers to subtracting. If it is given that a number let's say Z is Y more than X then the value will be Z= X+Y

If a given number let's say Z is Y less than X then the value of Z will be

Z=X-Y

More than means add which gives us a bigger value. Less than means subtract which gives us a smaller value

So, 3 more than 7 means 7+3 = 10

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Answer:

100 points cool the answer is 30

Answer:

t=5

Step-by-step explanation:

∵ (t,17) lies on (x,y) plane y=x²-3x+7,t>0

∴ 17=t²-3t+7

t²-3t+7-17=0

t²-3t-10=0

t²-5t+2t-10=0

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

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

t=5,-2

t>0

so t=5

Answer:

The correct answers are:

A) 60 miles; and B) 3.375 hours.

Explanation:

We will use the equation d = rt for this.

For the first leg of the trip, the bird travels 20 miles per hour for x hours.  This gives us the equation

d = 20x

For the return trip, the bird travels 4 miles per hour slower, so 20-4 = 16 miles per hour.  He also travels 6 miles less than the return distance, for x hours:

d-6 = 16x

To isolate d, we will add 6 to each side:

d-6+6 = 16x+6

d = 16x+6

We will set the two equations equal to one another, since they both equal d:

20x = 16x+6

Subtract 16x from each side:

20x-16x = 16x+6-16x

4x = 6

Divide both sides by 4:

4x/4 = 6/4

x = 1.5

He travels for 1.5 hours both times.

The first time, 1.5 hours at 20 miles per hour is:

d = 1.5(20) = 30 miles

The original trip is 30 miles.  This makes the entire trip 30(2) = 60 miles.

On the return trip, he travels 30-6 = 24 miles at 16 miles per hour:

24 = 16x

Divide both sides by 16:

24/16 = 16x/16

1.5 = x

If he goes 24 miles in 1.5 hours at 16 miles per hour, we can use a proportion to find the time it takes for the entire return trip:

24/1.5 = 30/x

Cross multiplying,

24*x = 1.5(30)

24x = 45

24x/24 = 45/24

x = 1.875

This gives him a total time of 1.5+1.875 = 3.375 hours

Step-by-step explanation:

Answer: 99%

Step-by-step explanation:

The complete question is

"Substitute the values for a, b, and c into b2 – 4ac to determine the discriminant. Which quadratic equations will have two real number solutions? (The related quadratic function will have two x-intercepts.) Check all that apply.

0 = 2x^2 – 7x – 9

0 = 4x^ 2 – 3x – 1

The quadratic equations that have real number solutions are; 4x^2 – 3x – 1, and 2x^2 – 7x – 9.

The formula for finding the discriminant is

\(b^2 - 4ac\)

The solution contains the term \(\sqrt{b^2 - 4ac}\) which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

For the quadratic equation \(2x^2 - 7x - 9\)

\(b^2 - 4ac\)

\(= (-7) ^2 - 4( 2) ( -9)\\\\= 49 + 72 = 121\)

This equation has two real number solutions.

For the quadratic equation \(4x^ 2 - 3x- 1\)

\(b^2 - 4ac\)

\(= (-3) ^2 - 4( 4) ( -1)\\\\= 9 + 16 = 25\)

This equation will have two real number solutions.

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Answer: A, C, D

Step-by-step explanation:

Answer:

the axis of symmetry is X = 1

Step-by-step explanation:

make sure to ask if you need any further guidance.

Answer:

A. 54.09

Step-by-step explanation:

cos (angle) = Adjacent/Hypotenuse

cos (75) = 14/x

x= 14/cos (75)

x=54.09

Answer:

its A

Step-by-step explanation:

Answer:

What I do for these is do the shapes separately and use the appropriate formulas! Then add them Up! So the easiest is the rectangle that would be 5 × 4 = 20 then the triangles would be 5 x 1 = 5 then ÷ by 2 = 2.5 but since there are two of those triangles we just multiply by 2 again so 2.5 × 2 = 5 for the last two triangles at the top it would be 4 × 4 = 16 then ÷ by 2 = 8 but since theres 2 triangles multiply by 2 so 8 × 2 = 16 now we add all of these numbers up so 20 + 5 + 16 = 41 Hope that helps!

The Pythagorean Theorem is a mathematical theorem that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In other words, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides. This theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. The Pythagorean Theorem is one of the most well-known and widely used theorems in mathematics and has numerous applications in fields such as architecture, engineering, and physics.

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Answer:

The flag pole is 12.8 feet tall.

Step-by-step explanation:

doing the second one hold up

Answer:

Step-by-step explanation:

36 x 9 = 324

324^6

=324*324*324*324*324*324

=324^6

=1156831381426176

The general solution to the given differential equation is:

y = 7x³+ C

To solve the given differential equation \(\(\frac{dy}{dx} = 21x^2\)\), we can integrate both sides with respect to their respective variables.

\(\[\int dy = \int 21x^2 dx\]\)

Integrating the left side with respect to y yields y, and integrating the right side with respect to x gives us:

\(\[y = \int 21x^2 dx\]\)

To integrate \(\(x^2\)\), we can use the power rule of integration. For any constant n, the integral of \(\(x^n\)\) with respect to\(\(x\) is \(\frac{x^{n+1}}{n+1}\)\). Applying this rule, we have:

\(\[y = \frac{21}{3}x^3 + C\]\)

where C is the constant of integration. Thus, the general solution to the given differential equation is:

y = 7x³+ C

where C can be any constant.

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The given statement that "unpaid volunteer selling or serving alcohol at an event does not hold the volunteer to be civilly or criminally liable for selling/serving alcohol to an intoxicated person as far as the volunteer is TABC certified" is false because, under the TABC program, alcohol is prohibited to be served or sold to the intoxicated person.

The Texas Alcoholic Beverage Commission (TABC) does not prohibit alcohol to be served at private, invitation-only events in private residences, where there is no direct or indirect charge for that alcohol. However, TABC certification disallows to serve of alcohol to already dru-nk persons.

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The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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