Harrison has a rectangular plank of wood that is 29 inches long. He creates a ramp by resting the plank against a wall with a height of 14 inches, as shown. Using Pythagoras' theorem, work out the horizontal distance between the wallI and the bottom of the ramp. Give your answer in inches to 1 d.p.​

The theorem holds for all real numbers x and the other case is that x < 5.

option C.

A real number is a value that represents a quantity along a continuous number line. Real numbers can be either rational or irrational. Rational numbers are numbers that can be expressed as a ratio of two integers, such as 1/2, 3/4, or -7/8.

For the given question, if one of the cases is that x > 5, we can determine the other case by considering the definition of absolute value:

If x > 5, then ∣x-5∣ = x-5 (since x-5 is positive),

so x + ∣x-5∣ = x + (x-5) = 2x - 5

which is clearly greater than or equal to 5.

If x < 5, then ∣x-5∣ = -(x-5) (since x-5 is negative),

so x + ∣x-5∣ = x - (x-5) = 5,

which is also greater than or equal to 5.

Therefore, the theorem holds for all real numbers x.

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The complete question is below:

Theorem: For any real number x, x+∣x−5∣≥5. In a proof by cases of the theorem, there are two cases. One of the cases is that x > 5.

What is the other case?

A. x≤0

B. x≤5

C. x<5

D. x<0

The numerical value of x is 3.

The Midsegment Theorem states that the segment joining the midpoints of two sides of a triangle is parallel to and half the length of the third side.

This simply means that:

The middle segment = half the third side

From the image:

Using the Midsegment Theorem

x + 10 = 1/2 × (x + 23)

Solve for x

Multiply both sides by 2

2( x + 10 ) = 1/2 ×2 (x + 23)

2( x + 10 ) = x + 23

2x + 20 = x + 23

2x - x = 23 - 20

x = 3

Therefore, the value of x is 3.

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answer: 23

explanation - 143 - 5 = 138

(total time - the intro)

138 / 6 = 23

(remaining time divided by skit time)

Answer:

Step-by-step explanation:

As per question, point B is the midpoint of AC.

According to definition of midpoint, AB = BC:

The length of AB is:

Answer:

AB = 18

Step-by-step explanation:

To find:-

Answer:-

We are here given that points A , B and C are collinear and B is the midpoint of AC . From the data provided in the question we have;

Since B is the midpoint of AC, it will divide AC into two equal parts namely AB and BC. And these parts will be equal to one another. ( By Euclid's first axiom, Things which are half of the same thing are equal to one another.)

So we have;

[tex]\sf:\implies AB = BC \\[/tex]

[tex]\sf:\implies 3x = 4x - 6 \\[/tex]

[tex]\sf:\implies 3x -4x = -6 \\[/tex]

[tex]\sf:\implies -x = -6 \\[/tex]

[tex]\sf:\implies\red{ x = 6} \\[/tex]

Finally plug in the value of x, in the given expression of AB as ,

[tex]\sf:\implies AB = 3(x) \\[/tex]

[tex]\sf:\implies AB = 3(6) \\[/tex]

[tex]\sf:\implies \red{AB = 18} \\[/tex]

Hence the value of AB is 18 .

The probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.

What is the formula to calculate standard deviation?

The formula to calculate standard deviation is:

SD = sqrt [(Σ(xi - μ)²) / N]

Where, SD = standard deviation

x = individual data points

μ = mean of the sample

N = sample size

What is the formula for z-score?

The formula for z-score is:

z = (x - μ) / σ

Where,

z = z-score

x = raw score

μ = mean of the population

σ = standard deviation of the population

Given that, The average BMI (body mass index) value of children 9 years old is 18.4 with a standard deviation of 4.5.

To find the probability that a randomly selected 9-year-old has a BMI greater than 26.8, we have to find the z-score.

z = (x - μ) / σz = (26.8 - 18.4) / 4.5z = 1.86

Now, we have to find the probability from the z-table, which is 0.9686. But we have to find the probability greater than 26.8, so we have to subtract it from 1.1 - 0.9686 = 0.0314 ≈ 0.031

Therefore, the probability that a randomly selected 9-year-old has a BMI greater than 26.8 is 0.031. Hence, the answer is 0.031.

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Answer:

144 feet²

Step-by-step explanation:

12 x 12 = 144

When calculating the price of an order that has been paid in advance, the school supplier will use the following formula:

4n - 2

The ordering cost formula is useful for calculating the economic order quantity and gives businesses insight into how

much of an item is necessary to meet customer demand and fulfill sales goals.

These ordering costs can include shipping fees, unexpected transportation costs, inspection fees and other expenses

necessary to acquire inventory products. Essentially, any money your company spends to place and receive inventory

orders accounts for the purchasing and ordering costs.

Where n represents the number of boxes purchased.

The school supplier sells boxes of A4 paper for £4, and a £2 discount is given on any order paid for in advance.

Formula for calculating what to charge for any order paid in advance:

To calculate the price for an order paid in advance, the formula 4n - 2 should be used.

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Answer:

Step-by-step explanation:

8:2 doubled is 16:4

One way to approach this problem without using a calculator is to group the numbers by their place value (i.e., thousands, hundreds, tens, and ones), and then add them together.

For example,

For thousands:

User A has 3 thousands,

User B has 4 thousands,

User C has 2 thousands,

User E has 7 thousands.

There are no thousands for User D.

So the total number of thousands is 3+4+2+7 = 16 thousands.

For hundreds:

User A has 550 hundreds (since 3550 = 3 x 1000 + 550),

User B has 0 hundreds (since 4000 is a multiple of 1000),

User C has 450 hundreds (since 2450 = 2 x 1000 + 450),

User D has 10 hundreds,

User E has 0 hundreds (since 7000 is a multiple of 1000).

So the total number of hundreds is 550+0+450+10+0 = 1010 hundreds.

For tens and ones:

Since all the numbers are in thousands or hundreds, there are no tens or ones to add.

Therefore, the total amount of data stored on the server is:

16 thousands + 1010 hundreds = 16,100 GB

Answer:

Already in simplest form. -37/76

Step-by-step explanation:

Nothing changes, it's the most simplified it can be.

answer #

you can't simplify the answer

(a) The simplest interest is $12.

(b) The simplest interest is 5 cents.

(c) The simplest interest is $360.

(d) The simplest interest is $15.

What is the interest rate?

In relation to the amount lent, deposited, or borrowed, the amount of interest due each period is expressed as an interest rate. The total interest on a sum lent or borrowed is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time over which it is lent deposited, or borrowed.

The formula of simple interest is I = P × R × T

(a) Given that P = $500, R = 8% = 0.08, T = 3 months = (3/12) years = 1/4 years

The simple interest is

500 × 0.08 × (1/4)

= $12

(b) Given that P = $50, R = 12% = 0.12, T = 1 months = (1/12) years

The simple interest is

50 × 0.12 × (1/12)

=$0.5

= 5 cents

(c) Given that P = $1,000, R = 18% = 0.18, T = 24 months = (24/12) years = 2 years

The simple interest is

1000 × 0.18 × 2

=$360

(d) Given that P = $600, R = 15% = 0.15, T = 60 days = (60/360) years

The simple interest is

600 × 0.15 × (60/360)

=$15

P is principal, R is known as rate of interest.

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Answer:

Height*width*depth= volume

60 ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce

Let x be the amount of herb that costs $1.00/oz and y be the total amount of the mixture that costs $2.20/oz.

The total weight of the mixture is:

= y=x+40

The total cost of the mixture is:

4(40) + 1x = 2.20y

160 + x = 2.20 (x + 40) .......Substitute y using the expression from the first equation

160 + x = 2.20x + 88 .........Subtract 160 and x from both sides

1.20x = 72 .........Divide both sides by 1.20

x = 60

The herbalist must mix 60 oz of the herb that costs $1.00/oz to the mixture, therefore we can say that:

60 ounces of herbs costing $1 per ounce should be mixed with these 40 oz of herbs to produce a mixture costing $2. 20 per ounce

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Answer:

$2.90

Step-by-step explanation:

We know

Philip's meal costs $14.50 at a local restaurant. Philip would like to a 20% tip

20% = 0.2

14.50 x 0.2 = $2.90

So, he should leave $2.90 as a tip.

Mariya made a mistake in the third step of her work by multiplying both sides of the inequality by -13 instead of dividing.

An inequality is a mathematical statement that compares two values or expressions using a symbol such as <, >, ≤, or ≥. It indicates that one value is not equal to another, and may be greater than or less than it.

This resulted in a change of the direction of the inequality from less than or equal to (≤) to greater than or equal to (≥). Therefore, the correct inequality would be a ≥ -13 × -16. The solution of this inequality is a ≥ 208.

When graphing the solution, the solution set will include all values of a greater than or equal to 208, which can be represented by a shaded line to the right of the point 208 on a number line.

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Answer:

The answer would be -5x^5 + 2x^4 - 5x^3 - 5x^2 + 9x + 10.

[tex]\mathcal{A} = \pi r^{2} = \pi (11^{2}) = 121 \pi \ ft^{2}[/tex]

Answer:

121 pi divide to 4

Step-by-step explanation:

the answer is 121 pi divide to 4. please see it on the picture.

Answer: y = -12x + 63

Step-by-step explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope of the line, which is -12, and a point that the line passes through, which is (6,-9).

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

y - (-9) = -12(x - 6)

Simplifying this equation, we get:

y + 9 = -12x + 72

Subtracting 9 from both sides, we get:

y = -12x + 63

Therefore, the equation of the line in slope-intercept form is y = -12x + 63.

the first institution has 441 and the second institution has 189.

We can use algebra to solve the problem. We can start by assigning variables to represent the two institutions:

Let x be the multiplier of the ratio.

Then, we have:

7x is the first institution.

3x is the second institution.

From the problem, we know that the sum of the two institutions is 630:

7x + 3x = 630

Simplifying the left side, we get:

10x = 630

Dividing both sides by 10, we get:

x = 63

Now that we know the value of x, we can find the number of each institution:

First institution = 7x = 7(63) = 441

Second institution = 3x = 3(63) = 189

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Answer:

I think it has an area of 4 and a perimeter of 8, i'm not totally sure but I thought I'd try to help

Answer:

area:4

perimeter:8ft

Step-by-step explanation:

when doing the area, you have to MULTIPLY the length by the width. For example, length:5ft width:7ft so to find the area you have to multiply both and get the answer of 35. so for the sum you have is 2 × 2 = 4

for perimeter, you have to ADD all the sides so if you have a square with all sides of 4 you add them all up which = 16. so for your sum, add them all up = 8ft

Hope it helps I'm not that good at explaining :)

The diameter of each round pizza should be approximately d ≈ 2r ≈ 39.6

Rounding to the nearest tenth, we get a diameter of 39.6 cm.

The rectangular pizza has an area of:

35 cm x 70 cm = 2450 [tex]cm^2[/tex]

Dividing the area by 24 gives us the area of each square piece:

[tex]2450 cm^2 / 24 = 102.08 cm^2[/tex]

For the round pizzas, each slice is a sector of the circle, and the area of each sector is given by:

[tex]A = (θ/360)\pi r^2[/tex]

where θ is the angle of the sector in degrees, and r is the radius (half the diameter) of the circle.

Since each round pizza is cut into 12 slices, each slice covers an angle of:

θ = 360/12 = 30 degrees

We want the area of each slice to be equal to the area of each square piece from the rectangular pizza, which is 102.08 [tex]cm^2[/tex]. Therefore, we can set up the equation:

[tex](30/360)\pi r^2 = 102.08[/tex]

Simplifying, we get:

[tex]\pi r^2/12 = 102.08[/tex]

[tex]\pi r^2 = 1224.96[/tex]

[tex]r^2[/tex] ≈ 391.2

r ≈ 19.8

Therefore, the diameter of each round pizza should be approximately:

d ≈ 2r ≈ 39.6

Rounding to the nearest tenth, we get a diameter of 39.6 cm.

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Answer: 4.1

Step-by-step explanation: To find a missing leg you must square both numbers, then subtract the leg you do have from the hypotenuse ( 33.64 -  16.81) to get the squared number for the missing leg ( 16.83). You then have to find the square root of that number and round to the nearest tenth (4.1).

Answer:

520.37 cm

Step-by-step explanation:

apply equation:

x = 736.97(0.7061) = 520.374517
Notice 70.61% is the same as 0.7061 (just divide by 100)

now you need to round to 2 DP

x ≈ 520.37

so the 70.61% of 736.97cm is  520.37 cm

Answer:

37.03 sq. mm.

Step-by-step explanation:

got it right on usa test prep

The length οf the secοnd lane is apprοximately 160 meters, and the width is apprοximately 74 meters. Sο the cοrrect οptiοn is D.

We can start by nοticing that the given equatiοn [tex]x^2/6241 + y^2/1296 = 1[/tex]is the equatiοn οf an ellipse cantered at the οrigin, with a majοr axis οf length 2a = 279 = 158 and a minοr axis οf length 2b = 236 = 72. This is the equatiοn οf the innermοst lane.

Tο find the equatiοn οf the secοnd lane, we need tο add 1 meter tο bοth sides οf the equatiοn, since each lane is apprοximately 1 meter apart. This gives:

[tex]x^2/6241 + y^2/1296 = 2^2[/tex]

Simplifying, we get:

[tex]x^2/6241 + y^2/1296 = 4[/tex]

This is the equatiοn οf an ellipse with the same center as the first ellipse, but with a majοr axis οf length 2(a+1) = 280 = 160 and a minοr axis οf length 2(b+1) = 237 = 74.

Therefοre, the length οf the secοnd lane is apprοximately 160 meters, and the width is apprοximately 74 meters. Sο the cοrrect οptiοn is D.

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Therefore , the solution of the given problem of variable comes out to be John worked for four hours and Max worked for nine.

A variable is a quality that can be evaluated expression and have various values. Height, age, salary, province of birth, academic status, and style of residence range are a few examples of variables.

Here,

Let's use the variables "J" and "M" to denote the respective number of hours done by John and Max. Next, we can formulate the formulae in the following system:

=> J + 5 = M (Max put in five hours more than John did.)

=> 15J + 10M = 150 (They prepared a total of 150 sandwiches) (They made a total of 150 sandwiches)

This system can be resolved using replacement. By deducting 5 from both sides of the first equation, we can find "J" in terms of "M":

=> J = M - 5

Now, we can enter the following formula in place of "J" in the second equation:

=> 15J + 10M = 150

Using J = M - 5 as a substitute, 15(M - 5) Plus 10M = 150.

=> 15M - 75 + 10M Equals 150 (distributing the 15) (distributing the 15)

=> 25M = 225 (adding 75 to both ends) (adding 75 to both sides)

=> M = 9

Max thus put in nine hours of labour. John worked a total of __ hours, so we can re-enter ___ into the first calculation as follows:

=> J + 5 = M

=> J + 5 Equals 9 (M replaced with 9)

=> J = 4

John spent 4 hours at work.

The answer is that John worked for four hours and Max worked for nine.

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Step-by-step explanation:

To determine whether 360 is prime, composite, or neither, we need to check if it has any factors other than 1 and itself.

We can start by finding the prime factorization of 360:

First, we can divide 360 by 2 to get 180:

360 ÷ 2 = 180

Next, we can divide 180 by 2 to get 90:

180 ÷ 2 = 90

We can continue dividing by 2 until we can no longer divide evenly:

90 ÷ 2 = 45

45 ÷ 3 = 15

15 ÷ 3 = 5

5 is a prime number, so we have found the prime factorization of 360:

360 = 2 × 2 × 2 × 3 × 3 × 5

Therefore, we can see that 360 is composite because it has more than two factors. We can write it as the product of its prime factors as shown above.

In summary, the number 360 is composite and its prime factorization is:

360 = 2 × 2 × 2 × 3 × 3 × 5

The diameter οf the cup is 6 centimeters.

A circle's diameter is defined as a line thrοugh the centre that jοins the circumference at bοth ends. It is twice as lοng as the circle's radius. In οther wοrds, the line that splits a circle in half evenly at its centre is the diameter οf the circle.

The diameter οf a circle is equal tο twice its radius.

Therefοre, tο find the diameter οf the cup, we need tο multiply the radius by 2:

Diameter = 2 x Radius

Diameter = 2 x 3 cm = 6 cm

Hence, the diameter οf the cup is 6 centimetres.

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Answer: Acute

Step-by-step explanation:

Acute - Less than 90 degress

Straight - Exactly 180 degrees

Obtuse - More than 90 degrees

Right - Exactly 90 degrees

However, the response would be (x - 2 + 2i2)(x - 2 - 2i2) if you are searching for factors with real coefficients.

A polynomial is a mathematical expression made up of variables, factors, one or more terms, and non-negative integer exponents used in addition, subtraction, multiplication, and multiplication. Any mathematical object, including numbers, variables, and even functions, can be represented by the variables in a polynomial. In the polynomial equation 3x2 + 2x - 5 as an illustration, the coefficients are 3, 2, and -5, the variable is x, and the exponent is 2. This polynomial has the terms 3x2, 2x, and -5, each of which is denoted by a plus or negative sign. Monomials have one term, binomials have two terms, trinomials have three terms, and so on. Polynomials can be categorized based on how many terms they contain.

given

The solution to the first question is "none of the above," as the signs of the terms in a polynomial are not what determine the signs of the factors.

(x - 2i)(x + 2i) is one of the prime factors of x2 - 4x + 12, where I is the imaginary number.

However, the response would be (x - 2 + 2i2)(x - 2 - 2i2) if you are searching for factors with real coefficients.

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