The base of a box is a rectangle. The width of the box is half its length. The height of the box is 0.5 m. Find the volume of the box if the area of the base is 1.08m² less than the combined area of the sides.

The equation of the line in the slope-intercept form is: y = -2.00 x + 10.

The slope and provided point are both in the equation for the straight line.

The generic point (x, y) must satisfy the equation if we have a non-vertical land in a that passes through any point(x1, y1) has gradient m.

y-y₁ = m(x-x₁)

It is the necessary equation for a line in the form of a point-slope.

That gift card to the Coffee Café has been provided. = $10

Medium coffee = $2.00

customers

The quantity of coffees a consumer can purchase can be represented using a linear equation.

Slope formula

m = (8 - 10)/(1 - 0)

m = -2

Now consider the line's point-slope shape.

y-y₁ = m(x-x₁)

( y - 10) = -2.00 ( x - 0)

y = -2.00 x + 10

The slope: m = - 2.00

The equation of the line: y = -2.00 x + 10

The y-intercept is 10

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Answer:

-14

Step-by-step explanation:

Rewrite the equation:

-3m = 42

Next, divide both sides by -3:

-3m = 42 ---> m = -14

Last, let's make sure this is correct:

-3(-14) = 42

42 = 42 <--- This tells us it's correct

Hope this helps :)

The equation does not hold true, the ordered pair (3, 10) is not a solution of the equation y = 2x + 6.In this way, we can determine whether an ordered pair is a solution of the given equation or not.

Given the equation y = 2x + 6To determine if an ordered pair is a solution of this equation or not, substitute the values of x and y in the equation. If the equation holds true, then the ordered pair is a solution.

If it is not true, then the ordered pair is not a solution.For example, let's consider the ordered pair (1, 8).

Here, x = 1 and y = 8.Substituting these values in the given equation,

we get: y = 2x + 6 => 8 = 2(1) + 6 => 8 = 8 Since the equation holds true,

the ordered pair (1, 8) is a solution of the equation y = 2x + 6.

Now, let's consider another ordered pair, say (3, 10). Here, x = 3 and y = 10.Substituting these values in the given equation, we get: y = 2x + 6 => 10 = 2(3) + 6 => 10 = 12

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(a). The graph of y = -f(x) is shown in the image below.

(b). The graph of y = g(-x) is shown in the image below.

By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;

y = -f(x)

y = -|x + 2| - 4

Part b.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of this line;

Slope (m) = rise/run

Slope (m) = -2/4

Slope (m) = -1/2

At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 5 = -1/2(x - 0)

g(x) = -x/2 + 5, -4 ≤ x ≤ 4.

y = g(-x)

y = x/2 + 5, -4 ≤ x ≤ 4.

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Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

Answer:

exterior angles add up to 369

12p=360

p=30

ii) 180-3p = 90

Answer:

A normal good is a good that experiences an increase in its demand due to a rise in consumers' income. Normal goods has a positive correlation between income and demand. Examples of normal goods include food staples, clothing, and household appliances.

Step-by-step explanation:

Answer: Height = 20 inches, Width = 36 inches

Step-by-step explanation:

Let the height be \(h\) and the width be \(h+16\).

Using the formula for the perimeter of a triangle,

\(2(h+h+16)=112\\\\2(2h+16)=112\\\\2h+16=56\\\\2h=40\\\\h=20 \implies h+16=36\)

Answer:

90

Step-by-step explanation:

90

The correct statement is: g(x) is translated up 5 units compared to f(x).

The correct answer is A.

The correct answer is A.

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x=6

d=12

7x+12 or 7x+d

7(6) + 12 or (7x6) + 12 = 54

78-12 = 66

66/6 = 11

11x + 12 =78.

Answer:

$15,842

Step-by-step explanation:

We use the Present value formula

Present Value = Future value/(1 + r)ⁿ

r = 6% = 0.06

n = 4 years

Future value = $20,000

Present value = 20,000/(1 + 0.06)⁴

= $15841.873265

≈ $15,842

Answer:

\(\mathrm{Factor}\:x^2+5x+6:\quad \left(x+2\right)\left(x+3\right)\)

Step-by-step explanation:

Let us assume the trinomial of the form \(x^2+bx+c\)

\(x^2+5x+6\)

Break the expression into the groups

\(=\left(x^2+2x\right)+\left(3x+6\right)\)

Factor out 'x' from \(x^2+2x\)

i.e.

\(\:x^2+2x=x\left(x+2\right)\)

Factor out '3' from 3x+6

i.e.

3x+6 = 3(x+2)

so the expression becomes

\(\:x^2+2x=x\left(x+2\right)\)

\(\mathrm{Factor\:out\:common\:term\:}x+2\)

\(=\left(x+2\right)\left(x+3\right)\)

Hence,

\(\mathrm{Factor}\:x^2+5x+6:\quad \left(x+2\right)\left(x+3\right)\)

In probability function, the value of b = \(\frac{\pi}{2}\).

What is Probability?

Probability is the measure of the likelihood of a given event occurring. It is usually expressed as a number between 0 and 1, where 0 indicates an impossibility of the event occurring and 1 indicates a certainty that the event will occur. Probability theory is an important part of mathematics, and is used in a variety of applications, from predicting weather patterns to assessing the risk of a financial investment.

For f(x) to be a probability density function, the total area under the graph of the function should be equal to 1. This implies that the integral of f(x) from 1 to 3 should be equal to 1. This gives us the equation

\(\int1^3 (x^2 - b) dx = 1\)

Solving the integral, we get b = 4.

For h(x) to be a probability density function, the total area under the graph of the function should be equal to 1. This implies that the integral of h(x) from -b to b should be equal to 1. This gives us the equation

\(\int-b^b cos x dx = 1\)

Solving the integral, we get b = \(\frac{\pi}{2}\).

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Answer:

(2x + 5)(2x + 1)

Step-by-step explanation:

 4x^2 + 12x + 5

=4x^2 + 2x  + 10x + 5

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

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

Hope this helps!

Answer:

she did not get at least 2100 and definitely not 85% of the worth

Step-by-step explanation:

3000*0.85=2550

3000*0.7=2100

Answer:

Gia hoped to sell it for $2,550, but wanted at least $2,100. Because it sold for $1,800, she did not get what she hoped and/or wanted.

Step-by-step explanation:

85% of $3,000 can be solved by moving the decimal two places to the left and multiplying: 85.0% becomes 0.85. So, we multiply 0.85x3,000=$2,550.

We do the same thing to figure out 70% of $3,000. Again, solving it by moving the decimal two places to the left and multiplying: 70.0% becomes 0.70. So, we multiply 0.70x3,000=$2,100.

Answer:

5/8

Step-by-step explanation:

Answer:

6.

Step-by-step explanation:

1) OA=d/2=20/2=10;

2) AB=AC/2=16/2=8;

\(3) \ OB=\sqrt{OA^2-AB^2} =6.\)

Answer:

Step-by-step explanation:

Let x be the number of miles you and your friend travel.We know that the cost of the bus ride is 60 cents per mile, so the total cost of the trip is 60 * x.This can be written as an equation as follows:Cost = 60 * xOr, more simply:Cost = 60xThis equation represents the relationship between the number of miles you and your friend travel and the cost of the trip. As the number of miles increases, the cost of the trip also increases at a rate of 60 cents per mile.

Answer:

The critical value that should be used in constructing the confidence interval is T = 1.316.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 26 - 1 = 25

80% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 25 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.8}{2} = 0.9\). So we have T = 1.316

The critical value that should be used in constructing the confidence interval is T = 1.316.

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 1.316\frac{0.23}{\sqrt{26}} = 0.059\)

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 2.8 - 0.059 = 2.741 pounds

The upper end of the interval is the sample mean added to M. So it is 2.8 + 0.059 = 2.859 pounds.

The 80% confidence interval for the mean waste recycled per person per day for the population of Montana is between 2.741 pounds and 2.859 pounds.

Answer:

Volume V = 18.735 m3

Step-by-step explanation:

hope this helps

The angles that we have in the image here are:

When two angles are measured, they sum up to 180. They are said to be supplementary angles.

On the question, we have two angles that are 90 degrees on a straight line. Hence they are supplementary.

This is an angle that is at 90 degrees. We have to two right angles on the diagram that we have here.

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Answer:

Well, the smallest successive composites with gap 17, 73, 2, and 19 would have to be:

1. $341 = 11 \times 31$

2. $458 = 2 \times 299$

3. $460 = 2^2 \times 5 \times 23$

4. $479 = 13 \times 37$

Answer:  5

Step-by-step explanation:

Answer:

2(1/2)

Step-by-step explanation:

1(2/3) = 5/3

5/3 divided into 2/3

is the same as

5/3 multiplied by 3/2

        5/3 x 3/2 = 15/6  

15/6 = 5/2

5/2 = 2(1/2)

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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Answer:

\(21.7 x 10^5\)

Step-by-step explanation:

(6.2 x 10²) x (3.5 x 10³)

First, multiply the coefficients: 6.2 x 3.5 = 21.7.

Then, add the exponents: 10² x 10³ = 10^(2+3) = 10^5.

Therefore, the result is 21.7 x 10^5.

Answer:

3286000

Step-by-step explanation:

That since exact value of sin(A-β) depends on the cos(-β) value, which we miss, we are not able to determine the value.

To determine (A-β), we can use trigonometric identities.

Tan(A) = 3/4 and sin() = 4/5 in Quadrant III.

The identification can be used for:

tan(A) = cos/sin(A) (A)

Sin(A) in this instance equals 3/4. * cos(A) (A)

We can adopt a different guise.

(A-sin) = sin (A)

(cos) - (cos (A)

Sin(β), so sin(A-) = (3/4 * cos(A)) (sin()) - cos()) (cos(A))

sin(A-β) = (3/4) - (4/5) * (sin(A) * (cos(A) * cos())

We can now apply the double angle formula.

cos(2A) = sin2 + cos2(A) (A)

Therefore, cos(A) = (1 - sin(A)2), and sin(A-) = (3/4) * (± √(1 - (3/4)^2) * cos(β)) - (4/5) * (3/4)

sin(A-β) = (3/4) * (± √(1 - (9/16)) * cos(β)) - (3/5)

The formula for sin(A-) is (3/4) * ((7/16) * cos()) - (3/5)

That since exact value of sin(A-) depends on the cos(-) value, which we miss, we are not able to determine the value.

Therefore, using the equation given, it is impossible to figure out the precise value of (A-β).

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Answer:

\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)\( \boxed{75 : 100 }$$$$ \)

\((\stackrel{x_1}{40}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{20}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{20}-\underset{x_1}{40}}} \implies \cfrac{ -2 }{ -20 } \implies \cfrac{ 1 }{ 10 }\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{ 1 }{ 10 }}(x-\stackrel{x_1}{40})\implies {\Large \begin{array}{llll} y=\cfrac{1}{10}x+4 \end{array}}\)