Pete wants to put a fence around a rectangular section of his backyard.
The space he wants to enclosc measures 30 feet in length, and it is as
wide. How many feet of fencing does he need?
(1) 10
(2) 30
(3) 40
(4) 80
(5) 120

Check the picture below.

well, we can say that since its directrix is a vertical line, the parabola opens horizontally, the focus point is at the left of the directrix thus it opens leftwards, ithas a vertex at (5,-3), recall that the vertex is half-way between the focus point and the directrix.

Anna's total profit was $6000 + $16000 - $4000 = $14000.

How did Anna earn profit

Anna bought $4000 of company stock. The value of the stock doubled when she sold 75% of it, which means she sold 0.75 * $4000 = $3000 worth of stock when its value doubled.

Since the value of the stock doubled, Anna sold the $3000 worth of stock for 2 * $3000 = $6000.

Anna then sold the remainder of the stock (25% of the original amount) for four times the purchase price. Since she originally bought the stock for $4000, the remainder was worth 0.25 * $4000 = $1000.

Selling this remainder for four times the purchase price means that Anna sold it for 4 * $4000 = $16000.

Answer: I Hope some one helps you out

Step-by-step explanation:Y

1 gram of medicine costs 86 nairas, while a 42-hour workweek results in a salary of 27,090 nairas.

Simplifying procedures is one way to achieve uniformity in job efforts, expenses, and time. It reduces diversity and variation that is pointless, harmful, or unneeded. Parenthesis, exponents, multiplication, division, addition, and subtraction are all referred to as PEMDAS. The order of the letters in PEMDAS informs you what to calculate first, second, third, and so on, until the computation is finished, given two or more operations in a single statement.

Given, 12.5g of medicine cost 1,075 nairas.

Since,

Cost of 12.5g medicine = 1075

Cost of 1 g medicine = 1075/12.5

Cost of 1 g medicine = 86 naira

Also given, Someone gets 645 nairas for one hour of work

the total pay for someone who works 42 hours = 645 * 42

the total pay for someone who works 42 hours =  27,090 nairas

therefore, the Cost of 1g of medicine is 86 nairas and the total pay for someone who works 42 hours is 27,090 nairas.

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The positive integer c for the expression to have a rational root is 8

For a quadratic equation to have a rational root, then;

\(b^2-4ac =0\)

From the given equation;

a = 3

b = 20

Substitute into the equation above to have:

20^2-4(3)c = 0

400 - 12c = 0

12c =100

c = 100/12

c= 8.3

Hence the positive integer c for the expression to have a rational root is 8

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By applying the PEMDAS rule, the given expression "1 × (-4) - 8 × - 3/9" is equal to -20/8.

An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.

In order to evaluate this expression, we would apply the PEMDAS rule, where operations within the parenthesis are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the expression to the right. Lastly, the operations of addition or subtraction would be performed from left to right.

Expression = 1 × (-4) - 8 × - 3/9

Expression = -4 - 8 × - 3/9

Expression = -4 - 8 × 1/3

Expression = -4 - 8/3

Expression = -4/1 - 8/3

Expression = (-12 - 8)/3

Expression = -20/8.

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The value of angle a is 48° and angle b is 65°.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Solve for the angle a,

Given that the lines are perpendicular to each other,

Implies that,

a+42=90

a=48

The value of angle a is 48°.

Solve for angle b,

The angle made by a straight line is 180°

therefore,

115+b=180

b=65

The value of angle b is 65°.

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The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

Given the diagram of the hanger which one side has 10 + 5x  and other side has 11.

To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.

Thus, the equation is 10 + 5x = 11.

Consider the equation 10 + 5x = 11

On subtracting 10 from each side gives,

5x = 1

Divide each side by 5 gives,

x = 1/5.

Hence,  the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

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Answer:

y=500

Step-by-step explanation:

y= 250 * 0 + 500

The sentence which show correct verb tense usage is The overall outlook is favorable.

Verbs are a necessary component of communication in every language, including English, without which it would be difficult to convey what the subject is doing. All acts, including those motivated by sentiments and emotions, are included.

Verbs exist in a variety of forms and kinds so they can function in many ways to convey the whole meaning. Let's have a look at how different dictionaries define the word "verb" before we examine the many kinds of verbs and their forms.

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Caludia needs to pay 2917.6128 as a payment of compound interest capital+interest.

What is compound interest?

compound interest is interest on principal + interest and this denotes to the addition of interest to the principal amount of a loan or deposit.

Capital(p) = $6400

Rate of interest(r) = 11%

Years(n) = 3

The general formula of compound interest is \(A= p(1+\frac{r}{100}})^n\).

Now

\(A= 6400(1+\frac{11}{100}})^3\\A=6400 \times \frac{111}{100} \times \frac{111}{100} \times \frac{111}{100}\\A= 8752.8384\)

The entire amount (Capital+interest) is equal to $8752.8384.

If we take 1 year as a period then Claudia needs to pay \(\frac{8752.8384}{3}\\=2917.6128\)

Therefore, Claudia needs to pay 2917.6128 as a payment of compound interest capital+interest.

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As a result, the answer to the given angle problem can be found by comparing the position, measurement, and congruence of two or more angles.

When two lines come together at a common point, an angle is created. They are expressed as a number of degrees, denoted by the symbol °. Acute, right, obtuse, and reflex angles are the other three significant types of angles. 360 degrees make up a circle. A 720° angle indicates that the object has completed two full rotations.

Here,

You can compare angles and take into account their relationships to other angles in addition to calculating degrees or radians.

Since we are comparing the position, measurement, and congruence of two or more angles, we refer to them as having "angle relationships."

For instance, two lines or line segments that cross each other create two pairs of vertical angles.

When a transversal intersects two parallel lines, complex angle relationships, such as alternating interior angles, matching angles, and so forth, result.

As a result, the answer to the given angle problem can be found by comparing the position, measurement, and congruence of two or more angles.

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The Polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

The quotient and remainder when the polynomial x⁵ + x³ - 5 is divided by x - 2, we can use polynomial long division. Here's the step-by-step process:

1. Write the dividend (x⁵ + x³ - 5) and the divisor (x - 2).

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

2. Divide the first term of the dividend (x⁵) by the first term of the divisor (x) to get x⁴. Write x⁴ above the line. x⁴

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

3. Multiply the divisor (x - 2) by the quotient term (x⁴) to get x⁵ - 2x⁴. Write this under the dividend and subtract it.  x⁴

  x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

4. Bring down the next term (-5) from the dividend.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

5. Divide the first term of the new dividend (3x⁴) by the first term of the divisor (x) to get 3x³. Write 3x³ above the line.

 x⁴ + 3x³

   x - 2 | x⁵ + x³ + 0x² + 0x - 5

 - (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

6. Multiply the divisor (x - 2) by the new quotient term (3x³) to get 3x⁴ - 6x³. Write this under the new dividend and subtract it.

x⁴ + 3x³

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

7. Repeat steps 4-6 until you have subtracted all terms.

x⁴ + 3x³ + 6x² + 12x + 24

x - 2 | x⁵ + x³ + 0x² + 0x - 5

- (x⁵ - 2x⁴)

3x⁴ + 0x³ + 0x² + 0x - 5

- (3x⁴ - 6x³)

6x³ + 0x² + 0x - 5

- (6x³ - 12x²)

12x² + 0x + 0

 - (12x² - 24x)

 24x + 0

- (24x - 48)

 48

8. The quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

Therefore, when the polynomial x⁵ + x³ - 5 is divided by x - 2, the quotient is x⁴ + 3x³ + 6x² + 12x + 24, and the remainder is 48.

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Answer:

  TL ≈ 9.90

Step-by-step explanation:

The Pythagorean theorem tells you ...

  TC² +LC² = TL²

In this isosceles triangle, LC = TC, so we have ...

  TL² = TC² +TC² = 2·TC²

Taking the square root gives ...

  TL = TC√2 = 7√2

  TL ≈ 9.90

Based on these considerations, it is necessary to assess the specific layout plan and the surrounding environment to determine whether the copier is suitably placed in room (3) at Hills Secondary.

To determine whether the copier is suitably placed in room (3) at Hills Secondary, we need to consider factors such as accessibility, noise, and convenience.

Firstly, we need to evaluate the accessibility of the copier in room (3). Is it easily accessible for all students and staff who need to use it? If the copier is located in a central position within the school or close to high-traffic areas, it would be considered suitable.

However, if it is tucked away in a corner or not easily visible, it may cause inconvenience and hinder access for users.

Secondly, we should consider noise levels. Copiers can be noisy machines, and if room (3) is located near classrooms or areas where students require a quiet environment, it may not be an ideal placement. Noise disturbances could disrupt learning activities and cause distractions.

Lastly, convenience plays an important role. Room (3) should be spacious enough to accommodate the copier and allow users to operate it comfortably. If the room is cramped or lacks proper ventilation, it may cause inconvenience for users and impact the overall workflow.

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The correct diagram and the equation to find the interior angles of the hexagon is option (C)

The given figure is the regular hexagon

Consider the number of side of the polygon is n

The number of sides of the hexagon = 6

We know interior angle of a regular hexagon = 120 degrees

The interior angle of the hexagon d = 180(n-2) / n

Substitute the value of n = 6 in the equation

The interior angle of the hexagon = 180(6-2) / 6

= 180×4 /6

= 720 / 6

Divide the terms

= 120 degrees

Hence, the correct diagram and the equation to find the interior angles of the hexagon is option (C)

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MNOP is a rhombus then, the length of the segment MP = 49 unit.

One kind of parallelogram is the rhombus, which has four sides and four vertices.

The length of each side is the same as the length of the opposing angle.

Given:

A rhombus is given in the attached image.

In rhombus,

every side is equal in length.

That means,

the parallel sides are equal.

9x - 77 = 3x + 7

6x = 84

x = 14

So,  3(14) + 7 = 42 + 7 unit

That means, the side in rhombus = 49 unit.

Therefore, MP = 49 unit.

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The complete question is given in the attached image.

Answer:

1 2/3

Step-by-step explanation:

8/9 + 7/9

Since the denominators are the same, we can add terms

15/9

This is an improper fraction so we can simplify

9/9 + 6/9

1 + 2/3

1 2/3

the Answer

5/3

or

1 2/3

The outlier of the graph is

An outlier is an isolated data point that significantly differs from the entirety of the points within a dataset. It is an observation that resides an exceptional distance away compared to other values in a random sample from a population.

Outliers can be identified employing various statistical techniques, like graphical methods (for instance, box plots, scatterplots) and numerical procedures (e.g., Z-score, IQR method).

The problem used a scatter plot plot to show that the outlier is (5, 1)

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Answer:

1956 ft

Step-by-step explanation:

To find the area of something you have to multiply length x width. So, you multiply 163 and 12 to get 1956

\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$45700\\ r=rate\to 12\%\to \frac{12}{100}\dotfill &0.12\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years\dotfill &2 \end{cases}\)

\(A = 45700\left(1+\frac{0.12}{4}\right)^{4\cdot 2}\implies A=45700(1.03)^8 \implies A \approx 57891.39 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{earned interest}}{57891.39~~ - ~~45700} ~~ \approx ~~ \text{\LARGE 12191.39}\)

Answer: make me  brainlist

Step-by-step explanation: 13 is A

the one next to it is D so it is D

The equation that best describes the situation is A. 1,500 + 690h = 2,500

Since the plane has already covered 1500 miles, and the plane travelling at 450 knots in still air picks up at tailwind of 150 knots in the same direction, the resultant velocity, V of the plane = speed of plane in still air + speed of wind

= 450 knots + 150 knots

= 600 knots

= 600 × 1 knot

= 600 × 1.15 mph

= 690 mph.

If h is the number of hours after picking up the tail wind, the distance moved by the airplane is thus D = 1500 + 690h

Since D = 2500 miles, we have

1500 + 690h = 2500.

So, the equation that best describes the situation is A. 1,500 + 690h = 2,500

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Answer:

832.5

Step-by-step explanation:

if you multiply the height by the base and then divide by 2 you will get this answer (it's the formula)

Step-by-step explanation:

∫ 9 arctan(1/x) dx

If u = 9 arctan(1/x), then:

du = 9 / (1 + (1/x)²) (-1/x²) dx

du = -9 dx (1/x²) / (1 + (1/x²))

du = -9 dx / (x² + 1)

If dv = dx, then v = x.

∫ u dv = uv − ∫ v du

= 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ∫ 2x dx / (x² + 1)

= 9x arctan(1/x) + 9/2 ln(x² + 1)

Evaluate from x=1 to x=√3.

[9√3 arctan(1/√3) + 9/2 ln(3 + 1)] − [9 arctan(1) + 9/2 ln(1 + 1)]

[9√3 (π/6) + 9/2 ln(4)] − [9 (π/4) + 9/2 ln(2)]

(3π√3)/2 + 9/2 ln(4) − (9π/4) − 9/2 ln(2)

(6π√3)/4 + 9 ln(2) − (9π/4) − 9/2 ln(2)

(6π√3 − 9π)/4 + 9/2 ln(2)

Answer:

\(9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)\)

Step-by-step explanation:

We are given the integral 9 arctan(1/x)dx on the interval x[ from 1 to √3 ].

Now let's say that u = arctan(1/x). The value of 'du' would be as follows:

du = - x / (1 + x²) * dx

If we apply integration by parts, v = 1, and of course u = arctan(1/x):

=> 9x arctan(1/x) − ∫ -9x dx / (x² + 1)

=> 9[x arctan(1/x) - ∫ - x / (1 + x²) * dx] on the interval x[ from 1 to √3 ]

Let's now simplify the expression ' ∫ - x / (1 + x²) * dx':

=> (Take the constant out, in this case constant = - 1), - ∫ x / (1 + x²) * dx

=> (Apply u-substitution, where u = 1 + x²), - ∫ 1/2u * du

=> (Take constant out again, in this case 1/2), - 1/2 ∫ 1/u * du

=> (Remember that 1/u * du = In( |u| )), - 1/2In( |u| )

=> (Substitute back 'u = 1 + x²), - 1/2In| 1 + x² |

So now we have the expression '9[x arctan(1/x) + 1/2In| 1 + x² |]' on the interval x[ from 1 to √3 ]. Let's further simplify this expression;

\(9\left[x\arctan \left(\frac{1}{x}\right)+\frac{1}{2}\ln \left|1+x^2\right|\right]^{\sqrt{3}}_1\\\\=> 9\left[\frac{1}{2}\left(2x\arctan \left(\frac{1}{x}\right)+\ln \left|1+x^2\right|\right)\right]^{\sqrt{3}}_1\)

Now computing the boundaries we have the following answer:

\(9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)\)

A Taxi driver is driving up to the top of the hill with an incline of 27 degrees. The hill has an altitude of 700ft. Assuming they started from the bottom, how far must he drive before reaching the top?

Answer:

700ft

Step-by-step explanation:

Answer:

Step-by-step explanation:

I think the original proce would be  $265

1. Subtract the percentage discount from 100

100 - 20= 80

2. Multiply the final price($245) by 100

245 × 100= 24,500

3. Divide the answer in step 2 by the answer in Step 1

24,500 ÷ 80= $306.25

answer is $306.25

How to check to ensure your answer is correct:

1. Multiply the "answer" by the discount price divided by 100. This will give the discount percentage in dollars.

$306.25 × 0.2( which is 20÷100)= $61.25(discount in dollars)

2. Subtract the discount in dollars from the "answer"

$306.25 - $61.25= $245(final price is the same as in the problem so it is correct)

OR

1. Multiply the original price by the number you get from step 1 in your problem divided by 100

$306.25 × 0.8(80 from the very first step divided by 100)= $245(the final price is the same given in the question)

Answer:

1.The  equation of best fit is ŷ = 2.69152X + 3.45818.

Step-by-step explanation:

Answer:

ΔABC was reflected over both axes.

Step-by-step explanation:

ΔABC was reflected over both axes.