Which of the following expressions is equivalent to 3x2 + 6x – 24?A. 3(x+2)(x–4) B. 3(x–2)(x+4) C. (x+6)(x–12) D. (x–6)(x+12)

Answer:

Step-by-step explanation:

Given function:

Answer choices:

If x represents the number of bracelets and y represents the number of rings, there were 24 more bracelets sold than rings. The total sales were $520.

If x represents the number of bracelets and y represents the number of rings, there were 38 more bracelets sold than rings. The total sales were $520.

If x represents the number of bracelets sold at $24 each and y represents the number of rings sold at $38 each, the total sales were $520.

If x represents the number of bracelets and y represents the number of rings, there were 520 bracelets and rings sold. Bracelets were $24, and rings were $38.

Answer:

Step-by-step explanation:

C

The percent of fat calories an American consumes each day is normally distributed with a mean of 36 and a standard deviation of about 10.

Standard deviation is a measure of the spread of a data set. It is calculated by taking the square root of the variance of the data set. It is a measure of how much the individual values in a data set are spread out from the mean. It is used to quantify the amount of variation or dispersion of a set of data values.

According to the Central Limit Theorem, the mean of the sample X will be normally distributed with a mean of 36 and a standard deviation of 10/sqrt(20). This means that the mean percent of fat calories in the sample will be normally distributed with a mean of 36 and a standard deviation of about 3.16. This means that 68% of the time, the mean percent of fat calories in the sample will be between 32.84 (36-3.16) and 39.16 (36+3.16), 95% of the time it will be between 29.68 (36-6.32) and 42.32 (36+6.32), and 99% of the time it will be between 26.52 (36-9.48) and 45.48 (36+9.48).

In other words, this is happening because the Central Limit Theorem states that the sample mean will be normally distributed, and that the standard deviation of the sample mean will be the standard deviation of the population divided by the square root of the sample size. By understanding this theorem, we can calculate the probability that the mean of the sample will fall within certain ranges.

In conclusion, the percent of fat calories an American consumes each day is normally distributed with a mean of 36 and a standard deviation of about 10. By understanding the Central Limit Theorem, we can calculate the probability that the mean of the sample will fall within certain ranges. This allows us to make predictions about the sample mean and helps us understand why this is happening.

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Answer:

any number

Step-by-step explanation:

Call the amount of apples Fatima bought as x.

She gave half of the apple to Salma -> x : 2

Then she gave Maha 5 apples -> x : 2 - 5

She is left with 3 apples, so we have the equation x : 2 - 5 = 3

Solve for x :
x = (3+5) x 2 = 16.

Fatima bought 16 number of apples from the grocery store.

Two or more expressions with an Equal sign is called as Equation.

Let  the number of apples Fatima bought will be "x".

Fatima gave half of the apples to Salma, which is (1/2)x apples.

So, she had (1/2)x apples left.

Then she gave 5 apples to Maha, which means she had (1/2)x - 5 apples left.

Finally, she kept 3 apples for herself, which means she had (1/2)x - 5 - 3 apples left.

We know that the number of apples she had left is equal to the number of apples she gave away

(1/2)x - 5 - 3 = (1/2)x

Solve for x

-8 = -x/2

Multiplying both sides by -2, we get:

x = 16

Hence, Fatima bought 16 apples.

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Answer:

In order to prove that RQ = RS, we need to consider the properties of a circle. Firstly, we know that the radius (RQ) of a circle is equal to its circumference (RS), and the circumference of a circle is related to its diameter by the formula 2πr = C, where r is the radius and C is the circumference.

Therefore, since QS is a diameter of the larger circle and RO is the radius of the smaller one, we can use the formula to calculate the circumference of the larger circle using the radius of the smaller one. If we substitute r with RO and C with QS, we get: 2πRO = QS. We can then simplify this to get RQ = RS.

Green points: (0,0) and (3,4)

Transformated points:

(-1, -1) and (2, 0.34)

Answer:

B (-3,3)

Step-by-step explanation:

coordinates are x,y and h has -3x and 3y

Answer:

4

Step-by-step explanation:

we're basically solving for x. I've always been taught to make the equation from the words and solve from there. if we do that we get 10 - (3 x W). So we need to figure out what W is. 4 and 2 equal 8. let's put that in. 4 times 3 is 12 and 12 - 10 equals 2. the width is 4 wile the length is 2

Answer:

A. Congruent and D. Discs

Step-by-step explanation:

You won't see a cylinder that doesn't have congruent bases

Look at the shape of the bases and look at a disc compare their shape

We can describe the bases of a cylinder as congruent.

The volume of cylinder is given by -

V = πR²h

Given is to describe the bases of a cylinder.

The cylinders are uniform in cross - section. Therefore, the bases of the cylinder will have the same area. So, we can conclude that the given bases are congruent.

Therefore, we can describe the bases of a cylinder as congruent.

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Answer: 3.5 cm.

Step-by-step explanation:

1/280 is your scale in this scenerio, and since your cities are 80 miles away, you divide 280 by 80. If you do this, you get the answer 3.5, and since the map isn't miles long, the answer is 3.5 cm.

Answer:

79.5 feet

Step-by-step explanation:

5.3 per minute can also be written as the ratio 5.3:1. so if we have x:15, we can see that we've multiplied the right side by 15 so we have to do the same to the other side. 15 times 5.3 is 79.5. so thats your answer.

i hope this helps :))

The integer that explained the depth of the hole after 15 minutes is 79.5 feet.

Given that,

So, the integer that explained the depth of the hole after 15 minutes is

\(= Rate \times time \\\\= 5.3 \times 15\\= 79.5\ feet\)

Therefore we can conclude that the integer that explained the depth of the hole after 15 minutes is 79.5 feet.

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Answer:

Step-by-step explanation:

1.25 km × 0.75 km = 0.9375 km²

1 km = 100 hectares

0.9375 km² = 93.75 hectares²

part a.

There is  a 49.1% chance that HRC finds a sample mean between $477 and $527.

part b.

There is a 20.9% chance that the sample mean falls between $492 and $512.

The standard error (SE) of the sample mean.

SE = σ / √(n)

σ = $80 and n = 68.

SE = 80 / √(68)

z1 = (X1 - μ) / SE

z2 = (X2 - μ) / SE

for first scenario:

X1 = $477, X2 = $527, and μ = $499.

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

For the range $477 to $527:

z1 = (477 - 499) / SE

z2 = (527 - 499) / SE

z1 = -0.275

z2 = 0.35

Probability 1 =  0.4909 = 49.1%

We have a 49.1% chance that HRC finds a sample mean between $477 and $527.

For the second scenario

X1 = $492, X2 = $512, and μ = $499.

z1 = (492 - 499) / Standard Error

z2 = (512 - 499) / SE

We have a 20.9% chance that the sample mean falls between $492 and $512.

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Answer:

wwwuhwhwuiwhwhwhshss

Answer:

Length

We are already knowing that

A = lw

A = Area

L = Length

W = width

Let the length be l

70 = 7 × l

70/7 = l

10 = l

Length = 10 ft

\( \\ \)

Answer:

8 : 1

Step-by-step explanation:

Consider the points on the line relating raspberry juice to lemon- lime soda

That is

raspberry juice    lemon- lime sode

         8                             1

        16                             2

        24                            3

         32                           4

These values are all in the ratio of 8 : 1

Answer:

8:1

Step-by-step explanation:

i just know

Answer:

Option A. Intersecting lines that have different slopes and different y-intercepts.

Step-by-step explanation:

we know that

A system of two linear equations can have one solution, an infinite number of solutions, or no solution.

If a system has at least one solution, it is said to be consistent

If a consistent system has exactly one solution, it is independent

If we have intersecting lines that have different slopes and different y-intercepts

then

will have one solution

therefore

The system will be consistent independent

Answer:

hope this helps

Step-by-step explanation:

intersecting lines that have the same slope and the same y-intercept

For the  trigonometric identity

11. If cos 27° = x, then the value of tan 63° interims of "x" is  x/√1 - x²

12. If Θ be an acute angle and 7sin²Θ + 3 cos²Θ= 4, then tan Θ is  1/√3

13. The value of tan 80° × tan 10° + sin² 70° + sin² 20° is 2

14. The value of (sin 47°/cos 43°)² + (cos 43°/sin 47°) -  4 cos²45° is 0

15. If 2 (cos²Θ - sin²Θ) = 1, Θ is a positive acute angle them the value of Θ is  30°

16. If 5 tan Θ = 4, then (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ) is equal to 1/6

17. If sin(x + 20)° = cos (x + 10)° then the value of "x" is  30°

18. The value of (sin 65°)/ (cos 25°) is 1

To solve the various   trigonometric identity;

11. Given: cos 27° = x

We know that cos (90 - θ) = sin θ

So, cos 63° = sin 27°

And sin 63° = √1 - cos²27°

Substituting cos 27° = x, we get

sin 63° = √1 - x²

Therefore, Therefore, tan 63° = sin 63° / cos 63° = cos 27° / cos 63° = x / cos 63°.

= x/√1 - x²

12. Given: Θ is an acute angle and 7sin²Θ + 3 cos²Θ= 4

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation 7sin²Θ + 3 cos²Θ= 4, we get

7 (sin²Θ/ cos²Θ) + 3 = 4/cos²Θ - 4 sec²Θ

⇒ 7tan²Θ + 3 = 4(1 + tan²Θ)

⇒ 7tan²Θ + 3 = 4 + 4 tan²Θ

⇒3 tan²Θ = 1

⇒ tan²Θ = 1/3

⇒ tanΘ = 1/√3

13. For tan 80° × tan 10° + sin² 70° + sin² 20°

⇒ tan 80° = cot (90 - 80)° = cot 10°

⇒  sin 70° = cos (90 - 70) = cos 20°

⇒ cot 10° × tan 10° +  cos 20° + sin² 20°

= 1 + 1 = 2

14. (sin 47°/cos 43°)² + (cos 43°/sin 47°) - 4 cos²45°

= (sin 47°/cos43°)² + (cos 43°/sin 47°)² - 4(1/√2)²

= (sin (90° - 43°)/cos43°)² +  (cos (90° - 47°)/sin)²  = 4(1/2)

= (cos 43°/cos 43°)² + (sin 47°/ sin   47°)² - 2

= 1 + 1 - 2 = 0

15. 2 (cos²Θ - sin²Θ) = 1

cos²Θ - sin²Θ = 1/2

Since Θ is an acute angle, sin²Θ + cos²Θ = 1

Substituting sin²Θ + cos²Θ = 1 into the equation cos²Θ - sin²Θ = 1/2, we get

cos²Θ - (1 - cos²Θ) = 1/2

2cos²Θ = 3/2

cos Θ = √3/2(cos 30° = (√3)/2

= 30°

16. Given: 5 tan Θ = 4

We know that tan Θ = sin Θ / cos Θ

So, 5 sin Θ / cos Θ = 4

5 sin Θ = 4 cos Θ

Dividing both sides of the equation by 5, we get

sin Θ / cos Θ = 4/5

∴ sin Θ = 4/5 cos Θ

given that the expression is (5 sin Θ - 3 cos Θ)/(5 sin Θ + 2 cos Θ)

we substitute sin Θ = 4/5 cos Θ  into the equation

⇒(5 × 4/5 cos Θ  - 3 cos Θ)/(5 × 4/5 cos Θ  + 2 cos Θ)

= (4-3)/(4 + 2) = 1/6

17. Given: sin(x + 20)° = cos (x + 10)°

We know that sin(90 - θ) = cos θ

So, sin(x - 20)° = sin(90 - (3x + 10))°

⇒ (x - 20)° = (90 - (3x + 10))°

⇒ x - 20° = 90° - 3x + 10

⇒ 4 x = 120°

⇒ x = 120°/4

⇒ x = 30°

18. To find the value of (sin 65°) / (cos 25°), we can use the trigonometric identity:

To solve this, we can use the following trigonometric identities:

sin(90 - θ) = cos θ

cos(90 - θ) = sin θ

We can also use the fact that sin²θ + cos²θ = 1.

Rewrite sin (65°) / cos (25°)

⇒ sin (65°) = cos (25°)

∴ cos (25°)/ cos (25°) = 1

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Answer:

simple look at y intercept then look at slope or you can solve two points by using the formula y2-y1/x2-x1

but your formula is

y =1/2 +5 so b would be your answer

Answer:

4

Step-by-step explanation:

multiply 3 by 4 to get 12 and add 12 to 2 and you get 14

Answer: 39.13 for 18 plants

Step-by-step explanation:

120/55.20= 2.17 dollars per plant

18*2.17=39.13

Answer: In that picture the slope is increasing

Step-by-step explanation: positive rise and positive run (uphill from left to right)

Answer:

x-2=-3

Step-by-step explanation:

x ^2 + 9 = 73

| 3 y | + 3 = 3

x − 2 = − 3

2x-5(x-3)=2(x-10)

First multiply the parentheses.

2x-5x+15=2x-20

Then combine like terms.

-3x+15=2x-20

Then add 20 to both sides.

-3x+35=2x

Then add 3x to both sides.

35=5x

Finally, divide 5 from both sides.

7=x

hope it helps!

The friends from the first one who is predicted to finish her book to the third one who is predicted to finish her book is given by the order Nancy > Barbara > Judy

Given data ,

The total number of pages in each friend's book as follows:

Barbara's book: 320 pages

Judy's book: 260 pages

Nancy's book: 480 pages

Now, we can calculate their reading rates as pages read per day:

Barbara's reading rate: 100 pages / 4 days = 25 pages/day

Judy's reading rate: 54 pages / 3 days = 18 pages/day

Nancy's reading rate: 160 pages / 5 days = 32 pages/day

Hence , the descending order is Nancy > Barbara > Judy

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The solution of the integration is:

∫ 1/(x ln (5x + 1)) dx = (1/5) ln(ln(5x + 1)) - (1/5) [(ln(5x + 1)) ln(ln(5x + 1)) - (5x + 1)] + C

Now, For integrate the function f(x) = 1/ (x ln (5x + 1)) dx, we can use substitution.

Let u = 5x + 1,

So, du/dx = 5

dx = du/5.

Substituting u and dx in terms of u in the original integral, we get:

= ∫ 1/(x ln (5x + 1)) dx

= ∫ 1/(ln u) (1/5) du

Now, integrate with respect to u:

= ∫ 1/(ln u)  (1/5) du

= (1/5) ∫ (ln u)^(-1) du

Using integration by parts,

dv = (ln u)⁻¹ du

v = ln(ln u)

u = ln u

du = (1/u) du

Now, we can substitute u and v in terms of u:

= (1/5) ln(ln u) - (1/5) ∫ (1/(u ln u)) ln(ln u) du

= (1/5) ln(ln u) - (1/5) ∫ (ln u)' ln(ln u) du

= (1/5) ln(ln u) - (1/5) [(ln u) ln(ln u) - ∫ (ln u) (1/ln u) du]

= (1/5) ln(ln u) - (1/5) [(ln u) ln(ln u) - u + C]

Substituting back u = 5x + 1, we obtain:

∫ 1/(x ln (5x + 1)) dx

= (1/5) ln(ln(5x + 1)) - (1/5) [(ln(5x + 1)) ln(ln(5x + 1)) - (5x + 1) + C]

Therefore, the solution is:

∫ 1/(x ln (5x + 1)) dx = (1/5) ln(ln(5x + 1)) - (1/5) [(ln(5x + 1)) ln(ln(5x + 1)) - (5x + 1)] + C

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Answer:

Step-by-step explanation: Twice means x2

Difference means subtract

A number is a unknown value so you put a variable

(Z - 4) x 2= 7

3.5 x 2= 7

(7.5 - 4) x 2= 7

Answer: The answer to your question is C. Brainliest?

Step-by-step explanation:

For the first square, we can multiply both the numerator and denominator by 5 to get an equivalent fraction with a denominator of 60:

2/12 = (2 x 5) / (12 x 5) = 10/60

For the second square, we can multiply both the numerator and denominator by 4 to get an equivalent fraction with a denominator of 60:

2/15 = (2 x 4) / (15 x 4) = 8/60

Now, we can add the two fractions:

10/60 + 8/60 = 18/60

Simplifying this fraction by dividing both numerator and denominator by 6, we get:

18/60 = 3/10

Therefore, the total shaded area in the diagram is 3/10 or 0.3 in decimal form.

The answer is C. 0.3.