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Find the distance between
the pair of parallel lines.
y = 2x + 4
y = 2x - 4

A) 4.01
B) 3.84
C) 3.58
D) 3.65

Answer:  [tex]\bold{a)\quad \dfrac{BC}{FG}=\dfrac{BE}{FI}}[/tex]

                b) ∠H

                c) ∠E

Step-by-step explanation:

I find it easiest to do these problems if I write one polygon on top of the other.  That way I can easily see the angles and sides that match.

B C D E

F G H  I

a) BC matches to FG and FI matches to BE

   The proportion is:   [tex]\dfrac{BC}{FG}=\dfrac{BE}{FI}}[/tex]

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b) What matches with ∠D? Look at the letter below to see that it is ∠H

******************************************************************************************

c) What matches with ∠I? Look at the letter above to see that it is ∠E

Answer:

x+5

Step-by-step explanation:

subtracting both equations give you x+5

Answer:

$61.18

Step-by-step explanation:

The price last week was an unknown. We will call it x. x is an entire amount, so it is 100% of x.

This week, the price is 15% lower. Since 100% - 15% = 85%, the price this week is 85% of what it was last week. Last week it was x, so this week, the price is 85% of x.

85% of x = $52

0.85x = $52

Divide both sides by 0.85:

0.85x/0.85 = $52/0.85

x = $61.1764...

Answer: $61.18

Final answer:

To determine the original price of the shoes before a 15% discount, divide the discounted price, $52, by 0.85. The original price of the shoes was approximately $61.18.

Explanation:

The question asks to find the original price of the shoes before they were discounted by 15%. To find the original price, you can use the formula for calculating the original price after a discount has been applied. If the current price represents 85% (100% - 15%) of the original price, you can set up the equation as follows: $52 = 85% of the original price.

To find the original price, divide the current price by 85% (or 0.85 in decimal form): Original Price = $52 ÷ 0.85. This calculation gives an original price of approximately $61.18, rounding to the nearest cent.

Answer:  She have to sell 32.5 kg to cover her weekly expenses.

Step-by-step explanation:

Since we have given that

Selling price  of cumin  per kg = $7.20

Quantity of cumin she sells = 90 kg

Net profit she get = $414

Total amount she get after selling 90 kg is given by

[tex]90\times 7.20=\$648[/tex]

So, Weekly expenses would be

[tex]\$648-\$414\\\\=\$234[/tex]

Quantity of cumin she need to sell to cover her weekly expenses is given by

[tex]\dfrac{234}{7.20}\\\\=32.5\ kg[/tex]

Hence, She have to sell 32.5 kg to cover her weekly expenses.

Your answer is 3,147,200 water-filled drinking glasses.

The first thing I would do is change the value of 1,600 water-filled drinking glasses to be equivalent to the total that would result from 281 Americans.

To do this, you just want to multiply 1,600 by 281, as the value of 1,600 is from one person, and for 281 people, the 1,600 would happen 281 times.

1,600 * 281 = 449600

Next, since the value of 449,600 is for 281 Americans in one day's time, multiply by 7 to make it equal to one week's time. This is because one week = 7 days, so the 449,600 total would happen 7 times in one week.

449,600 * 7 = 3,147,200

Therefore, your answer is 3,147,200.

Hope this helps!

In a week 281 Americans will use 3,147,200 water-filled drinking glasses.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, Each day one person uses 1,600 water-filled drinking glasses.

∴ In a week the person will uses (1600×7) = 11200 water-filled drinking glasses.

∴ 281 will use (11200×281) = 3,147,200 water-filled drinking glasses.

learn more about numerical expressions here :

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Explanation:

The point of a reflecting telescope is to reflect the light toward the eyepiece. That's what each reflecting surface does. By arranging the locations of the foci in the manner described, the light path is made to go from one focus to another, and finally to the focus at the eyepiece location.

Each conic surface is a reflecting surface that reflects the light closer to the eyepiece.

Answer:

Inside a telescope, the parabolic mirror reflects parallel light rays entering the telescope to its focus, which is also the focus of the hyperbolic mirror. The hyperbolic mirror then reflects those light rays to its other focus, where the image is observed.

Step-by-step explanation:

Hence, the answer is:

                [tex]\dfrac{1}{4}[/tex]

It is given that:

A correct answer is awarded 4 points, but an incorrect answer costs the student 1 point.

This means that the point +4 is added if the answer is correct.

and -1 will be added if the answer is incorrect.

Also, the probability of getting a correct answer is: 1/4

( since out of 4 choices only one option is correct)

and the probability of getting a incorrect answer is: 3/4

( since out of 4 choices 3 are incorrect)

Hence, the expected point the student should expect to get per question is:

[tex]E(X)=\dfrac{1}{4}\times (+4)+\dfrac{3}{4}\times (-1)\\\\i.e.\\\\E(X)=1-\dfrac{3}{4}\\\\i.e.\\\\E(X)=\dfrac{1\times 4-3}{4}\\\\i.e.\\\\E(X)=\dfrac{4-3}{4}\\\\i.e.\\\\E(X)=\dfrac{1}{4}[/tex]

A student who guesses on a multiple-choice question with four options should expect to earn an average of 0.25 points per question due to the probabilities of correct and incorrect answers and their respective points.

When guessing on a multiple-choice question with four possible answers, the probability of a correct guess is 1/4, while the probability of an incorrect guess is 3/4. The expected points per question is calculated by multiplying the probability of each outcome by the points awarded or deducted for that outcome and summing these products. With 4 points for a correct answer and a loss of 1 point for an incorrect answer, the calculation is as follows:

(1/4) × 4 points + (3/4) × (-1 point) = 1 point - 3/4 points = 1/4 points

Therefore, the student should expect to earn 0.25 points per question on average if they were to guess on each question.

Answer:D

Step-by-step explanation:it’s a supplementary angle which measures 180 degree now subtract side T=79 degrees by the 180 degree= 101

Answer:

C. 93°

Step-by-step explanation:

A rhombus must have 360° in total. You can add all of the numbers you have right in the shape and use to subtract from 360. You will get 93°

You can also see that the angle is nearly 90° Then you would know that it is 93°.

Answer:

First choice.

Step-by-step explanation:

The x-intercepts happen when y=0.

Just like the y-intercepts happen when x=0.

So anyways we are asked to find the x-intercepts.

So set y=0 (set f(x)=0):

0=x^2+6x+5

0=ax^2+bx+c

Since a=1, all we have to do is find two numbers that multiply to be 5 and add up to be 6.

Those numbers are 5 and 1 because 5(1)=5 and 5+1=6.

So the factored form of x^2+6x+5 is (x+5)(x+1).

The equation we have is:

0=(x+5)(x+1).

This means we have x+5=0 or x+1=0.

We need to solve both equations.

x+5=0

Subtract 5 on both sides:

x=-5

x+1=0

Subtract 1 on both sides:

x=-1

So the x-intercepts are at (-5,0) and (-1,0).

OR

Some people just say at -5 and -1.

Answer:

A. -5 and -1

Step-by-step explanation:

Correct on edge 2021! :)

Answer:

  x° = 55°

Step-by-step explanation:

The measure of external angle x° is the sum of the opposite internal angles shown.

  x° = 21° +34° = 55°

Answer:

1

Step-by-step explanation:

Please use parentheses around the coordinates of your points:

(1, 4); (0.5, 3.5), etc.

If we go from (0.5, 3.5) to (1, 4), x increases by 0.5 and y increases by 0.5.  

Thus the slope is m = rise / run = 1/1 = 1.

This is the average rate of change for the sequence shown.

The average rate of change for the sequence shown on the coordinate plane is calculated by finding the ratio of the differences in y-values to differences in x-values. For the given sequence, this average rate of change is 1.

The average rate of change in a sequence given by a series of points on a coordinate plane can be calculated by finding the difference between the y-values divided by the difference in x-values. For the given points 1, 4; 0.5, 3.5; 0, 3; and negative 0.5, 2.5, we have:

So, the average rate of change for the sequence shown is 1.

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Answer:

  4.2 or 15.8 metres

Step-by-step explanation:

We assume your model for the height of the water stream is supposed to be ...

  h(x) = -0.15x^2 +3x

This will have a value of 10 when ...

  -0.15x^2 +3x = 10

  .15x^2 -3x +10 = 0 . . . . . subtract the left side to get standard form

For a quadratic equation of the form ...

  ax² +bx +c = 0

The solutions are given by the "quadratic formula:"

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

The above equation matches the template with a=0.15, b=-3, c=10. Putting these values into the formula gives ...

[tex]x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4\cdot 0.15\cdot 10}}{2\cdot 0.15}=\dfrac{3\pm\sqrt{3}}{0.3}\\\\x=10\pm\dfrac{10}{3}\sqrt{3}[/tex]

  x ≈ 4.2 or 15.8

The firefighter can stand at 4.2 metres or 15.8 metres from the fire to get the water to arrive at the building 10 metres up.

Answer:

neither significantly low nor significantly high.

Step-by-step explanation:

Great question, it is always good to ask away and get rid of any doubts that you may be having.

Since there are a total of 1400 births we can easily calculate that half of that number is 700. Since the total number of girls born are 698 we can see that it is basically half of the total number of births. Therefore I can subjectively state that this number is neither significantly low nor significantly higher. There are almost an equal number of girls being born than there are boys.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Final answer:

Using subjective judgment, the number of girls in 1400 births being 698, as opposed to the expected 682.9 based on the natural ratio, is not significantly high. For the China birth ratio study, the observed 40% girl births in a sample of 150 is lower than the reported 46.7% but requires statistical analysis to determine significance.

Explanation:

When assessing whether a particular set of birth data is significantly high or low, we must compare the observed data to the expected birth ratio. The natural ratio of girls to boys is typically close to 100:105, as mentioned in the Newsweek article. In the case of the 1400 randomly selected births with 698 being girls, we can calculate the expected number of girls using the natural ratio.

Expected number of girls = Total births × Expected ratio of girls = 1400 × (100 / (100+105)) = 1400 × (100 / 205) ≈ 682.9

Comparatively, 698 girls is slightly above what we would expect naturally, but to judge if this is significantly high or not, we would typically perform a statistical test such as a chi-square test. However, using subjective judgment, we may find that the difference of 698 observed minus 682.9 expected is not large enough to be considered significantly high, particularly without calculated statistical significance.

In the example using maternity ward probabilities, the chances of different numbers of boys being born to six women can be calculated using binomial probabilities. For instance, the probability of exactly one boy being born is (6 choose 1) × (0.5)1 × (0.5)5 = 0.09375 or 9.375%.

Regarding the birth ratio in China—using your study showing 60 girls out of 150 births, which gives a percentage of 40%, is lower than the reported 46.7%. Before drawing conclusions from this study, it's important to consider sample size and variability to determine if the study results are statistically significant.

Answer:

The function graphed is y = Ix - 5I - 4 ⇒ answer D

Step-by-step explanation:

* Lets explain how to solve this problem

- From the graph

# The graph intersects the x-axis at x = 1 and x = 9

∴ The x-intercepts are 1 and 9

- We can find x-intercept by equate y by 0

* Lets equate the answers by zero to find the x-intercept

# y = Ix + 5I - 4

∵ Ix + 5I - 4 = 0

- Add 4 to both sides

∴ Ix + 5I = 4

- Remember in Ia + bI = c, then we have two answers :

 a + b = c  OR a + b = -c

∵ Ix + 5I = 4

∴ x + 5 = 4 ⇒ subtract 5 from both sides

∴ x = -1

- OR

∴ x + 5 = -4 ⇒ subtract 5 from both sides

∴ x = -9

∴ The x-intercepts are -1 and -9 not the same with figure

# y = Ix - 5I + 4

∵ Ix - 5I + 4 = 0

- Subtract 4 from both sides

∴ Ix - 5I = -4

- Remember in Ia + bI = c , c can't be negative because the absolute

 value is always positive

∴ We can't solve this equation

# y = Ix + 5I + 4

∵ Ix + 5I + 4 = 0

- Subtract 4 from both sides

∴ Ix + 5I = -4

- Remember in Ia + bI = c , c can't be negative because the absolute

 value is always positive

∴ We can't solve this equation

# y = Ix - 5I - 4

∵ Ix - 5I - 4 = 0

- Add 4 to both sides

∴ Ix - 5I = 4

- Remember in Ia + bI = c, then we have two answers :

 a + b = c  OR a + b = -c

∵ Ix - 5I = 4

∴ x - 5 = 4 ⇒ add 5 to both sides

∴ x = 9

- OR

∴ x - 5 = -4 ⇒ add 5 to both sides

∴ x = 1

∴ The x-intercepts are 1 and 9 the same with figure

* The function graphed is y = Ix - 5I - 4

Answer:

The correct option is B

Step-by-step explanation:

We will consider the following things and figures.

The bank statement of July 31 for Walgreens showed a balance of $6,008.10

There was a deposit in transit made on July 1 for $1,100.10 along with the outstanding checks of $4,580.54.

=$6,008.10-$4,580.54+$1,100.10

=$1,427.56+$1,100.10

=$2,527.66

Thus the correct option is B....

Answer:

$1,890

Step-by-step explanation:

Without including repeated instances of games (for instance, if I said that team 4 plays team 2 twice, then that would just be repeating when I already said that team 2 plays team 4 twice):

Team 1 plays:

teams 2, 3, 4, 5, 6, and 7 twice for a total of 12 games

Team 2 plays:

teams 3, 4, 5, 6, and 7 twice for a total of 10 games

Team 3 plays:

teams 4, 5, 6, and 7 twice for a total of 8 games

Team 4 plays:

teams 5, 6, and 7 twice for a total of 6 games

Team 5 plays:

teams 6 and 7 twice for a total of 4 games

Team 6 plays:

team 7 twice for a total of 2 games

--

Total it up:

[tex]12+10+8+6+4+2\\22+8+6+4+2\\30+6+4+2\\36+4+2\\40+2\\42[/tex]

Multiply by cost per game.

[tex]42*45=1890[/tex]

The quick ratio is a measure of a company's liquidity. It calculates a company's ability to pay off its current liabilities with its most liquid assets. The Golden Braid Bookstore has a quick ratio of 4.75.

The quick ratio, also known as the acid-test ratio, is a measure of a company's liquidity. It calculates a company's ability to pay off its current liabilities with its most liquid assets. The formula for the quick ratio is:

Quick Ratio = (Cash + Accounts Receivable) / Current Liabilities

In this case, the Golden Braid Bookstore has $340,000 in cash and $40,000 in accounts receivable. Its current liabilities include $65,000 in accounts payable and $15,000 in other current liabilities. Plugging these values into the formula:

Quick Ratio = (340,000 + 40,000) / (65,000 + 15,000)

Quick Ratio = 380,000 / 80,000

Quick Ratio = 4.75

Therefore, the Golden Braid Bookstore has a quick ratio of 4.75.

Answer:

  42 feet

Step-by-step explanation:

The vertex of the quadratic function described by the equation is located at ...

  t = -(40)/(2(-10)) = 2

The value of height at t=2 is ...

  h = -10(2²) +40(2) +2 = -40 +80 +2 = 42 . . . . feet

The maximum height is 42 feet.

_____

The equation gives the vertical speed at t=0 as 40 ft/sec, which is in contradiction to the number given in the problem statement as the initial velocity. We have used the given equation to answer the question. Since we don't know the throwing direction, we cannot properly adjust the equation to match the description of the scenario.

Answer:

answer is 7

Step-by-step explanation:

4b squared minus 9,16 is 4b squared because 4 time 4 is 16.thats how you would solve squared.then you want to minus 16 by 9,then your answer should be 7.

Answer:

(2b - 3)(2b + 3)

Step-by-step explanation:

4b² - 9 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

4b² = (2b)² ⇒ a = 2b and 9 = 3² ⇒ b = 3, so

4b² - 9 = (2b)² - 3² = (2b - 3)(2b + 3)

Answer:

0.64 kilometres

Step-by-step explanation:

Step 1: Find the perimeter in metres

Perimeter of square = 4 x (Length)

Perimeter = 4 (160)

Perimeter = 640 metres

Step 2: Convert from metre to kilometre

1 km = 1000 m

x km = 640 m

Cross multiply

1000x = 640

x = 0.64 kilometres

Therefore, the perimeter of the square base is 0.64 kilometres.

!!

here is the solution.

Please let me know if the answer is different and also if you don't understand.  

Answer:

  It is similar to triangle ABC and has coordinates A'(8,-12). B'(4, -16), and C'(-20, 8).

Step-by-step explanation:

Dilation about the origin multiplies each coordinate value by the dilation factor:

  A' = 2A = 2(4, -6) = (8, -12) . . . . A' for example

Dilated figures cannot be congruent if the dilation factor is not 1. They are always similar.

The appropriate description is the one shown above.

The dilated triangle A'B'C' with vertices A'(8, -12), B'(4, -16), and C'(-20, 8) is similar but not congruent to triangle ABC because the triangle's sides are proportional but not identical in length due to the scale factor of 2.

The question concerns the concept of dilation of geometric figures and whether the dilated triangle A'B'C' is similar or congruent to the original triangle ABC. When a figure is dilated by a scale factor, the coordinates of the vertices are multiplied by that factor. Given vertices A(4, -6), B(2, -8), and C(-10, 4) and a scale factor of 2, the coordinates of the dilated triangle A'B'C' should be A'(8, -12), B'(4, -16), and C'(-20, 8).

To determine similarity or congruence, we need to look at the properties of the triangles. Since the lengths of the sides of triangle A'B'C' are twice those of triangle ABC, the triangles are similar because their corresponding angles are equal and their corresponding sides are proportional. However, they are not congruent because their sides are not equal in length.

Answer:

124cm.³

Step-by-step explanation:

V = whl

You will do this: [2][3][8] + [3][4][5]. After finding the volume of both prisms, add them up.

I hope this helps, and as always, I am joyous to assist anyone.

The difference in cost between paying off a $3,200 balance one day later versus 30 days later is the interest accumulated over those 29 days. The daily interest rate is calculated from the annual percentage rate (APR), and then multiplied by the balance and the number of days.

When you have a credit card debt with an Annual Percentage Rate (APR) of 24.31%, interest is accrued daily on the current balance. Therefore, the difference between paying off your $3,200 debt one day later as opposed to 30 days later would essentially be the interest charged over the course of those additional 29 days.

Since APR is annual, the daily interest rate is calculated by dividing the APR by 365. In this case, the daily percentage rate is 0.0666%. Multiply this by the balance ($3,200) to calculate the approximate interest for one day. To find the total for 30 days, simply multiply the one day interest by 30.

However, do note that real-life calculations might be slightly different due to varying bank policies on compounding interest.

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By paying off the balance 1 day later, you would save $62.36 compared to paying it off 30 days later.

To calculate the amount of money saved by paying off the credit card balance 1 day later as opposed to 30 days later, we need to consider the interest charged on the outstanding balance. The credit card has an APR of 24.31% on purchases. We can use the formula:

Interest = (Principal x Rate x Time) / 365

Let's calculate the interest for 1 day and for 30 days and find the difference:

By paying off the balance 1 day later, you would save $62.36 compared to paying it off 30 days later.

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Answer:

The answer is C; F(x) = 5x³ - 2

Step-by-step explanation:

See the attached graph below

Answer:

f(x) = 5x^3 -2

Step-by-step explanation:

We notice two things about the red graph, F(x).  It has been shifted down and it is narrower.

Lets deal with the shifted down first.  Looking at the point where it crosses the y axis on the graph of g(x) is 0

Looking at where it crosses the y axis for f(x) is -2

We have shifted the graph down 2

f(x) = g(x) + C  

C > 0 moves it up

C < 0 moves it down

We will let c = -2

f(x) = g(x) -2

Now lets deal with the compression

f(x) = g(Cx)  

C > 1 compresses it in the x-direction

0 < C < 1 stretches it

Since it got narrower, C > 1

our choices are 5 or negative 5 for the coefficient on x

Remember that the negative sign flips it across the x axis (reflections)

Since we do not have a reflection, we want positive 5

f(x) = 5x^3 -2

Answer:

The equation that represents the new path is y=(1/3)x+4

Step-by-step explanation:

step 1

Find the slope of the give line

we have

y=-3x-6

so

the slope m is equal to

m=-3

step 2

Find the slope of the perpendicular line to the given line

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal of each other

so

we have

m=-3 -----> slope of the given line

therefore

The slope of the perpendicular line is equal to

m=1/3

step 3

With m=1/3 and the point (-3,3) find the equation of the line

y-y1=m(x-x1)

substitute

y-3=(1/3)(x+3)

y=(1/3)x+1+3

y=(1/3)x+4 -----> equation that represent the new path

Answer:

  7π cm² ≈ 22.0 cm²

Step-by-step explanation:

The shaded area is the difference between the area of Circle B and the areas of Circle C and Circle O. That is, those white areas are subtracted from the area of Circle B to get the shaded area.

The formula for the area of a circle is

  A = πr²

Using this, we find ...

  Circle B area = π(3 cm)² = 9π cm²

  Circle C area = Circle O area = π(1 cm)² = π cm²

Then the shaded area is ...

  Shaded Area = Circle B area - Circle C area - Circle O area

  = (9π cm²) - (π cm²) - (π cm²)

  = 7π cm² ≈ 22 cm²

Answer:

The radius of the cone is 21 units

The volume of the cone is 9702 units³

Step-by-step explanation:

* Lets revise the area of the circle and the volume of the cone

- The base if the cone is a circle

- The area of the circle is πr², where r is the radius of the circle

∵ The area of the base of the cone = 1386 units²

∵ The area of the base = πr²

∵ π = 22/7

∴ 1386 = 22/7 (r²) ⇒ multiply each side by 7

∴ 9702 = 22 r² ⇒ divide both sides by 22

∴ 441 = r² ⇒ take √ for both sides

∴ 21 = r

* The radius of the cone is 21 units

- The volume of the cone = 1/3 πr²h , where h is the height of the cone

∵ The cone's height is equal to the radius of its base

∴ h = r

∵ The volume of the cone = 1/3 πr²h

∴ The volume of the cone = 1/3 πr²(r) = 1/3 πr³

∵ r = 21 units

∴ The volume of the cone = 1/3 (22/7) (21)³

∴ The volume of the cone = 9702 unit³

* The volume of the cone is 9702 units³

Answer:

If ABCD is dilated by a factor of 1/2, the coordinate of D' would be (1, -1).

Step-by-step explanation:

When dilating figures, each x-coordinate and y-coordinate is multiplied by the scale factor. In this case, the coordinates of D were being dilated by a factor of 1/2.

D: (2,-2)

D': [(1/2)2, (1/2)-2]

The coordinates of D' are (1,-1).

Answer:

  v = 40 . . . ft/sec

Step-by-step explanation:

Put the value 25 where h is in the formula and do the arithmetic.

  V = √(64·25) = (√64)(√25) = 8·5

  V = 40 . . . . feet per second