How do you make comparisons between an equation and a table?.

Answer:

16

Step-by-step explanation:

A student earned a grade of 80% on a math test that has 20 problems. Therefore, the student answered 16 problems correctly.

Convert 80 to a decimal: .80

.80 ⋅ 20 = 16

Answer:

He answered 16 questions correctly.

Step-by-step explanation:

=》 80/100 × 20

=》 8/1 × 2

=》16/1

=》16 is the answer

Answer:

Step-by-step explanation:

A refrigerator is a cuboid, so W=3ft, L= 2.5ft, and H=6ft,

the volume of the refrigerator =W x L x H=3x2.5x6=45ft^3

The walls and other parts have 20ft^3 volume, so we have to minus them, so

volume left for food =45-20=25ft^3

Answer:

Step-by-step explanation:

Volume of the fridge = 3 × 2.5 × 6 = 45 ft³

then subtract the 20 ft³

45 - 20 = 25 ft³

Answer:

b can I have

Step-by-step explanation:

Answer:

The proportion that can be used to estimate the height of the tree is option;

A. \(\dfrac{h}{12} = \dfrac{6}{5}\)

Step-by-step explanation:

The given parameters in the question are;

The medium through which the person looks at the top of the tree = A mirror

The angle formed by the person and the tree with the ground = Right angles = 90°

The distance of the person from the mirror, d₁ = 5 ft.

The height of the person, h₁ = 6 ft.

The distance of the tree from the mirror, d₂ = 12 ft.

The angle formed by the incident light from the tree on the mirror, θ₁ = The angle of the reflected light from the mirror to the person, θ₂

Let 'A', 'B', 'M', 'T', and 'R' represent the location of the point at the top of the person's head, the location of the point at the person's feet, the location of the mirror, the location of the top of the tree and the location of the root collar of the tree, we have;

TR in ΔMRT = The height of the tree = h, and right triangles ΔABM and ΔMRT are similar

The corresponding legs are;

The height of the person and the height of the tree, which are AB = 6 ft. and TR = h, respectively

The distances of the person and the tree from the mirror, which are BM = 5 ft. and MR = 12 ft. respectively

∴ The angle formed by the incident light from the tree on the mirror, θ₁ = ∠TMR

The angle of the reflected light from the mirror to the person, θ₂ = ∠AMB

Given that θ₁ = θ₂, we have;

tan(θ₁) = tan(θ₂)

∴ tan(∠TMR) = tan(∠AMB)

\(tan\angle X = \dfrac{Opposite \ leg \ length \ to \ reference \ angle}{Adjacent \ leg \ length \ to \ reference \ angle}\)

\(tan(\angle TMR) = \dfrac{TR}{MR} = \dfrac{h}{12}\)

\(tan(\angle AMB) = \dfrac{AB}{BM} = \dfrac{6}{5}\)

From tan(∠TMR) = tan(∠AMB), we have;

\(\dfrac{h}{12} = \dfrac{6}{5}\)

\(\therefore h = \dfrac{6 \, ft.}{5 \, ft.} \times 12 \, ft. = 14.4 \, ft.\)

The height of the tree, h = 14.4 ft.

Therefore, from the proportion \(\dfrac{h}{12} = \dfrac{6}{5}\) the height of the tree can be estimated.

Answer:

.......................

The value of x in the given system of linear equations, 5x - 8y = 16 and 21x + 12y = 28, rounded to one decimal place, is approximately 0.7.

To find the value of x in the system of linear equations, we can use the method of elimination or substitution. Let's use the method of elimination:

Multiply the first equation by 21 and the second equation by 5 to eliminate the variable y.

105x - 168y = 336

105x + 60y = 140

Subtract the second equation from the first equation to eliminate x:

-228y = 196

Solve for y:

y ≈ -0.8596

Substitute the value of y back into either equation to solve for x. Using the first equation:

5x - 8(-0.8596) = 16

5x + 6.8768 = 16

5x = 9.1232

x ≈ 1.8246

Rounded to one decimal place, the value of x is approximately 0.7.

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Check the picture below.

\(\textit{area of a segment of a circle}\\\\ A=\cfrac{r^2}{2}\left( ~~ \cfrac{\pi \theta }{180}-\sin(\theta ) ~~ \right) \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=8\\ \theta =60 \end{cases} \\\\\\ A=\cfrac{8^2}{2}\left( ~~ \cfrac{\pi (60) }{180}-\sin(60^o ) ~~ \right)\implies A=32\left( ~~ \cfrac{\pi }{3}-\sin(60^o ) ~~ \right) \\\\\\ A=32\left( ~~ \cfrac{\pi }{3}-\cfrac{\sqrt{3}}{2} ~~ \right)\implies A=\cfrac{32\pi }{3}-16\sqrt{3}\implies A\approx 5.8~in^2\)

Answer:

Step-by-step explanation:

Answer is : 2

Answer: A

Step-by-step explanation: I would say A because the angle is greater than 90 degrees

Answer:

We have supplementary angles.

76 + 3x + 2 = 180

3x + 78 = 180

3x = 102

x = 34

The probability of events A and B both occurring is 0.1. The conditional probability of event A occurring given event B is 0.2, and the conditional probability of event B occurring given event A is 0.25.

The probability that events A and B both occur, denoted as P(A and B), is 0.1. This means that out of all possible outcomes, there is a 10% chance that both events A and B will happen simultaneously.

The conditional probability of event A occurring given event B, denoted as P(A|B), is 0.2. This represents the probability of event A happening given that event B has already occurred. It indicates that if event B has happened, there is a 20% chance that event A will also occur.

Similarly, the conditional probability of event B occurring given event A.

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The required graph of the line y = 9x + 1 will be displayed in the as attached file.

A graph can be described as a visual representation or a diagram that represents data or values.

We have been given the equation as:

y = 9x + 1

Rewrite in slope-intercept form.

y = (9)x + 1

To find the slope and y-intercept, use the slope-intercept form.

Here the slope is 9 and  y-intercept = (0, 1)

Using two points, any line may be graphed. Plug two x values into the equation to discover the associated y values.

When substitute the value of x = 0, then the value of y = 1, and When substitute the value of x = 1, then the value of y = 10,

Therefore, the graph represents the line y = 9x + 1

Hence, the required graph of the line y = 9x + 1 will be displayed in the as attached file.

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Answer:

1. Yes it's a function

2. -10, -5, -4, 2, 5, basically anything in the x value slot

3. -5, -10, 5, 8, -7, basically anything in the y value slot.

Step-by-step explanation:

I took the values and interpreted them appropriately to domain or range.

Answer:

The domain of relation is {-10,-5,-4,2,5}

The range of relation is {-5,-10,5,8,-7}

Hopefully it will help you

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False. if you are given a graph with two shif table lines, the correct answer will always require you to move both lines.

In a graph with two shiftable lines, the correct answer may or may not require moving both lines. It depends on the specific scenario and the desired outcome or conditions that need to be met.

When working with shiftable lines, shifting refers to changing the position of the lines on the graph by adjusting their slope or intercept. The purpose of shifting the lines is often to satisfy certain criteria or align them with specific points or patterns on the graph.

In some cases, achieving the desired outcome may only require shifting one of the lines. This can happen when one line already aligns with the desired points or pattern, and the other line can remain fixed. Moving both lines may not be necessary or could result in an undesired configuration.

However, there are also situations where both lines need to be shifted to achieve the desired result. This can occur when the relationship between the lines or the positioning of the lines relative to the graph requires adjustments to both lines.

Ultimately, the key is to carefully analyze the graph, understand the relationship between the lines, and identify the specific criteria or conditions that need to be met. This analysis will guide the decision of whether one or both lines should be shifted to obtain the correct answer.

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With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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Answer:

4th degree polynomial with 4 terms

Step-by-step explanation:

Given:

3n²(n²+ 4n - 5) - (2n² - n⁴ + 3)

Open parenthesis

= 3n⁴ + 12n³ - 15n² - 2n² + n⁴ - 3

Collect like terms

= 3n⁴ + n⁴ + 12n³ - 15n² - 2n² - 3

= 4n⁴ + 12n³ - 17n² - 3

Number 1 term is 4n²

Number 2 term is 12n³

Number 3 term is -17n³

Number 4 term is -3

The highest degree of the polynomial is 4th degree

Therefore,

The difference in 3n²(n²+ 4n - 5) - (2n² - n⁴ + 3) is

4th degree polynomial with 4 terms

Answer:

4th degree polynomial with 4 terms

Step-by-step explanation:

Answer:

\(Pr = \frac{1}{45}\)

Step-by-step explanation:

Given

\(Black =5\)

\(Pink = 2\)

\(Blue = 3\)

Required

\(P(Pink\ and\ Pink)\)

This is calculated as:

\(Pr = P(Pink) * P(Pink)\)

Because it is a selection without replacement, the probability is:

\(Pr = \frac{n(Pink)}{Total} * \frac{n(Pink) - 1}{Total - 1}\)

\(Pr = \frac{2}{10} * \frac{2 - 1}{10 - 1}\)

\(Pr = \frac{2}{10} * \frac{1}{9}\)

\(Pr = \frac{1}{5} * \frac{1}{9}\)

\(Pr = \frac{1}{45}\)

A = ( 4 , 3 ) ..**&**.. B = ( - 1 , 1 )

_____________________________

Slope = [ y(B) - y(A) ] ÷ [ x(B) - x(A) ]

Slope = [ 1 - 3 ] ÷ [ - 1 - 4 ]

Slope = [ - 2 ] ÷ [ - 5 ]

Slope = 2/5

______________________________

y - y(0) = Slope × ( x - x(0) )

y - y(A) = Slope × ( x - x(A) )

y - 3 = 2/5 × ( x - 4 )

y - 3 = 2/5 x - 8/5

y = 2/5 x - 8/5 + 3

y = 2/5 x - 8/5 + 15/5

y = 2/5 x + 7/5

The product of 2 and 1/10 times -7 times 5/12 is -7/12, which is a fraction.

The product of 2 and 1/10 times -7 times 5/12 can be found stepwise by multiplying the numbers together.
1. Convert the mixed fraction 1/10 to an improper fraction: 1/10 = 1 ÷ 10 = 1/10.
2. Multiply the numbers together: 2 × 1/10 × -7 × 5/12 = -70/120.
3. Simplify the fraction: -70/120 = -7/12.
Therefore, the product of 2 and 1/10 times -7 times 5/12 is -7/12.

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Answer:

5,960,000

Step-by-step explanation:

Population in one city= 2,840,000

Population in another city= 3,120,000

Population living in both cities= 2,840,000 + 3,120,000 = 5,960,000

We can simplify \((16x^4)^(-1/2) to 1/(4x^2)\) using the properties of rational exponents.

Certainly! Here's an example:

Simplify the expression: \((16x^4)^(-1/2)\)

We can apply the property of rational exponents which states that \((a^m)^n = a^(m*n)\). Using this property, we get:

\((16x^4)^(-1/2) = 16^(-1/2) * (x^4)^(-1/2)\)

Next, we can simplify \(16^(-1/2)\) using the rule that \(a^(-n) = 1/a^n\):

\(16^(-1/2) = 1/16^(1/2) = 1/4\)

Similarly, we can simplify \((x^4)^(-1/2)\) using the rule that \((a^m)^n = a^(m*n)\):

\((x^4)^(-1/2) = x^(4*(-1/2)) = x^(-2)\)

Substituting these simplifications back into the original expression, we get:

\((16x^4)^(-1/2) = 1/4 * x^(-2) = 1/(4x^2)\)

Therefore, the simplified expression is \(1/(4x^2).\)

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Answer:

.15¢

Step-by-step explanation:

1.20$ total divided by 8 and its .15¢

The work done by the constant force of 6 N in moving an object from x = 0 to x = 4 meters is equal to 24 J.

Work is the dot product of force and displacement, which in this case is the product of the constant force of 6 N and the displacement of 4 meters in the x-direction.

Work is calculated as W = F * d * cos(Θ), where Θ is the angle between the force and displacement vectors, and in this case, it is 0° as the force and displacement are in the same direction.

Therefore, W = 6 N * 4 m * cos(0°) = 6 N * 4 m = 24 Nm = 24 J. The unit of joule (J) can also be expressed as Newton-meter (Nm).

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Answer:

Step-by-step explanation:

Answer: The height of the palm tree is 21 feet.

Step-by-step explanation:

We can use a ratio to solve this:

Actual height to shadow for both objects. The fraction equivalents must be equal.

6/8 = x/28 . Cross multiply

6(28) = 8x

168 = 8x   Divide both sides by 8  (8's "cancel" on the right)

168/8 =8x/8

21 = x . This gives us the tree's height as 21 feet.

Another way to solve this is to use the ratios, but simplify the first fraction

6/8 = 3/4

Then multiply the length of the shadow by 3/4

3/4 × 28 = height

28÷4 = 7    7 × 3 = 21

21  feet= the height of the palm tree.

Answer:

(The image is not provided, so i draw an idea of how i supposed that the problem is, the image is at the bottom)

Ok, we have a rectangle of length x by r.

At the extremes of length r, we add two semicircles.

So the perimeter will be equal to:

Two times x, plus the perimeter of the two semicircles (that can be thought as only one circle).

The radius of the semicircles is r, and the perimeter of a circle is:

C = 2*pi*r

where pi = 3.14

Then the perimeter of the track is:

P = 2*x + 2*pi*r.

b) now we want to solve this for x, this means isolating x in one side of the equation.

P - 2*pi*r = 2*x

P/2 - pi*r = x.

c) now we have:

P = 660ft

r = 50ft

then we can replace the values and find x.

x = 660ft/2 - 3.14*50ft = 173ft

The domain of the function y = log_b(2x – 6), where b > 1, is {x | x > 3}.
The y-intercept of the function f(n) = a^n + b, where a is not equal to 1 and a > 0, is the point (0, b).

The domain of the logarithmic function y = log_b(2x – 6), where b > 1, refers to the set of all valid input values for x. In this case, we need to ensure that the argument of the logarithm, 2x – 6, is greater than zero.

This is because the logarithm function is only defined for positive values.
To determine the domain, we solve the inequality 2x – 6 > 0:
2x – 6 > 0
2x > 6
X > 3

Therefore, the domain is expressed in set-builder notation as {x | x > 3}, meaning all values of x greater than 3.

The y-intercept of the function f(n) = a^n + b, where a is not equal to 1 and a > 0, is the point where the function intersects the y-axis, or when n = 0.

To find the y-intercept, we substitute n = 0 into the function:
F(0) = a^0 + b = 1 + b = b

Therefore, the y-intercept of the graph is (0, b), indicating that the y-coordinate is equal to the constant term b.


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The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

Convert the standard equation into a vertex form, then we have

x² + (b/a)x + (c/a) = 0

x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0

(x + b/2a)² - b²/4a² + c/a = 0

Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be

(x - h)² + k = 0

The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.

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The least amount of extra cash Lilianna requires is $126 and the inequality is \(x+$68\geq 194\)

What justifies an inequality?

The relationship between two values in an imbalanced algebraic statement is represented by an inequality in mathematics. One of the two variables can be larger than, more than or equal to, smaller than, or equal to another value by using a sign of inequality.

Let

The least amount of extra money is x.

The fact that

\(x+$68\geq 194\)

The problem is represented by inequality.

Solve for x.

\(x+$68\geq 194\\x\geq $126\)

The least amount of money Lilianna requires is $126

and inequality is \(x+$68\geq 194\)

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The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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