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Divide
(x^2+5x+4)÷(x+2)
^= to the second

Answer:

[tex]2^{2} \times a \times b^{2}=4ab^{2}[/tex]

Step-by-step explanation:

Greatest common factor of two or more terms is the largest(greatest) possible term which exactly divides all the given term. For example the greatest common factor of 20 and 30 is 10 as 10 is the largest possible number that can exactly divide 20 and 30 without leaving any remainder. GCF is found as the product of all the common factors

Given terms are:

[tex]8a^{3} b^{2} =2^{3}\times a^{3}\times b^{2}[/tex]

[tex]12ab^{4}=4 \times 3 ab^{4} =2^{2} \times 3 \times a \times b^{4}[/tex]

From the above factors we can see that the common factors are:

[tex]2^{2} , a , b^{2}[/tex]

Therefore, the greatest common factor will be:

[tex]GCF=2^{2} \times a \times b^{2}=4ab^{2}[/tex]

The greatest common factor of 8a³b² and 12ab⁴ is 4ab², found by identifying the smallest powers of the common factors in each term.

To find the greatest common factor (GCF) of the given terms, we need to identify the highest power of each variable that appears in both terms.

The prime factorization of 8 is [tex]\(2^3\)[/tex], and the prime factorization of 12 is [tex]\(2^2 \times 3\)[/tex]. Thus, the greatest common factor of the coefficients is [tex]2^2 = 4.[/tex]

For the variables a and b:

- [tex]\(a^3\)[/tex] appears in the first term.

- a appears in the second term.

- [tex]\(b^2\)[/tex] appears in both terms.

So, the greatest common factor of [tex]\(a^3 b^2\) and \(ab^4\) is \(ab^2\).[/tex]

Therefore, the greatest common factor of [tex]\(8a^3 b^2\) and \(12ab^4\) is \(4ab^2\).[/tex]

Answer:

79%

Step-by-step explanation:

The probability that the percent of 18 to 34-year-olds who check social media before getting out of bed in the morning is, at most, 32 is 0.7881 = 78.81%

When the distribution is normal, we use the z-score formula.

In a set with mean  [tex]\mu[/tex]and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean.

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score.

This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

In this question:

[tex]\mu=28,\sigma=5[/tex]

Find the probability that the percent of 18 to 34-year-olds who check social media before getting out of bed in the morning is, at most, 32.

This is the p-value of Z when X = 32. So

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

[tex]Z=\frac{32-28}{5}[/tex]

[tex]Z=0.8[/tex]

Z=0.8 has a p-value of 0.7881

0.7881 = 78.81% probability that the percent of 18 to 34-year-olds who check social media before getting out of bed in the morning is, at most, 32.

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Answer:

B

Step-by-step explanation:

An equation that represents the graph of g(x) include the following: B. [tex]g(x)=\sqrt[3]{x+2}[/tex].

In Mathematics, a translation is a type of transformation that shifts every point of a geometric object in the same direction on the cartesian coordinate, and for the same distance.

Based on the information provided in the diagram, we have the following:

(x, y)       →    (x + h, y + k)

(0, 0)     →    (-2, 0).

-2 = x + h

-2 = 0 + h

h = 0 - 2

h = -2 (2 units left)

0 = y + k

0 = 0 + k

k = 0.

In conclusion, a horizontal translation of 2 units to the left would map the parent cubic function f(x) to the transformed cubic function g(x);

g(x) = f(x + 2)

[tex]g(x)=\sqrt[3]{x+2}[/tex]

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Complete Question:

The graph of [tex]f(x) =\sqrt[3]{x}[/tex] is shown with g(x). Which equation represents the graph of g(x)?

[tex]g(x)=\sqrt[3]{x-2} \\\\g(x)=\sqrt[3]{x+2} \\\\g(x)=\sqrt[3]{x} +1\\\\g(x)=\sqrt[3]{x} -1[/tex]

Answer:

Step-by-step explanation:

graph y = 1/3x + 1/2  

the slope is 1/3

y intercept is 1/2 ( that would be on the y axis)

slope would be 1/3 . ..up one over three

plot points starting with 1/2 . . and then move the points up one over three

with Y less than that line . . .it would have to move to the right on the number line . . .so you shade the right hand side of the line on the graph

Answer:

10y + 2

Step-by-step explanation:

The formula for the perimeter of a rectangle or square is [length + length + width + width = perimeter  or  2(length) + 2(width) = perimeter]

Our length here is y + 2. Either formula you use, [(y+2) + (y+2) or 2(y+2)] you should get the answer 2y + 4.

Next our width. The width is 4y-1. Either formula you use, [(4y-1) + (4y-1) or 2(4y-1)] you should get 8y - 2.

Then, simply add (2y+4) and (8y-2) to get 10y + 2. So, the perimeter of the garden is 10y + 2.

I hope this helps!

$9.95 - 30% = $6.97

Answer:

Is this a question?

Step-by-step explanation:

You're correct, but this isn't a question...

Answer:

72 sq. inch.

Step-by-step explanation:

9 inches in feet is 9/12 = 0.75 feet.

We can set up a ratio to figure out the width of the scale drawing.

[tex]\frac{36}{0.75}=\frac{32}{x}[/tex]

This means "if 36 feet is 0.75 feet in drawing, how much (let that be x) is 32 feet?"

let's cross multiply and solve for x:

[tex]\frac{36}{0.75}=\frac{32}{x}\\36x=32*0.75\\36x=24\\x=\frac{24}{36}=\frac{2}{3}[/tex]

So width is 2/3 feet and length is 0.75 feet.

Converting back to inches (since we need the area in sq. inches):

2/3 feet = 2/3 * 12 = 8 inches, and

0.75 feet = 0.75 * 12 = 9 inches

Hence, area is 8 * 9 = 72 sq. inches.

Step-by-step explanation:

[tex]\begin{array}{ccc}1&-&d\\2&-&c\\3&-&a\\4&-&b\\5&-&f\\6&-&e\end{array}[/tex]

Value 1:

r = 5ft, h = 10ft. Substitute:

[tex]SA=2\pi(5)(10)+2\pi(5^2)=100\pi+50\pi=150\pi\ ft^2[/tex]

Value 2:

r = 2in, h = 4in. Substitute:

[tex]V=\dfrac{1}{3}\pi(2^2)(4)=\dfrac{1}{3}\pi(4)(4)=\dfrac{16\pi}{3}\\\\\pi\approzx3.14\to V\approx\dfrac{(16)(3.14)}{3}\approx16.75\ in^3[/tex]

Value 3:

r = 6m. Substitute:

[tex]V=\dfrac{4}{3}\pi(6^3)=\dfrac{4}{3}\pi(216)=4\pi(72)=288\pi\ m^3\\\\\pi\approx3.14\to V\approx288(3.14)=904.32\ m^3[/tex]

Answer:

a

Step-by-step explanation:

Answer:

m(ARC)EHL: 108°

m(ARC)LVE: 252°

Step-by-step explanation:

Hey, so initially, we should start off with some stuff:

The sum of the arcs add up to 360°

m∠EYL=72°

We can create a system and use substitution to find the measure of an arc we don't know.

Step 1: We can use the 'Secants exterior angle theorem' to help us find the measure of (ARC)EHL.

<EYL=1/2((ARC)EVL-[ARC]EHL) (the theorem)

Step 2: By using substitution, we can say that (ARC)EVL=360°-(ARC)EHL

Thus, when we substitute it back into the theorem, the answer will be <EYL=1/2((360°-(ARC)EHL)-(ARC)EHL)=72°

Step 3: When we solve this out (and you can replace (ARC)EHL with x when solving), you will get an answer of x=108° or (ARC)EHL=108°.

Step 4: (ARC)LVE will be equal to 360°-m(ARC)EHL, which, when we substitute, will be 360°-108°, which will come out to be 252°.

Therefore, by algebra, substitution, and part-whole-postulate, (ARC) LVE=252°.

This is right, this was one of my problems for my 8th grade RSM online homework :)

Answer:

Small box weighs 13.75 kg & large box weighs 15.75 kg

Step-by-step explanation:

We can write 2 simultaneous equation and solve for weight of each box.

Let weight of large box be l and small box be s.

"3 large boxes and  5 small boxes has a total weight of  116 kilograms":

[tex]3l+5s=116[/tex]

and

"9 large boxes and  7 small boxes has a total weight of  238 kilograms":

[tex]9l+7s=238[/tex]

Now we can solve for l in the 1st equation and put it into 2nd equation and get s:

[tex]3l+5s=116\\3l=116-5s\\l=\frac{116-5s}{3}[/tex]

now,

[tex]9l+7s=238\\9(\frac{116-5s}{3})+7s=238\\3(116-5s)+7s=238\\348-15s+7s=238\\348-238=15s-7s\\110=8s\\s=\frac{110}{8}=13.75[/tex]

now we plug in 13.75 into s into equation of l to find s:

[tex]l=\frac{116-5s}{3}\\l=\frac{116-5(13.75)}{3}\\l=15.75[/tex]

Answer:

137.5 miles

Step-by-step explanation:

1. Do 55/2 to account for the half hour.(should equal 27.5)

2. Do 55 x 2 to account for the 2 hour drive.(should equal 110)

3. Add everything up. 110 + 27.5 = 137.5 miles

ANSWER

137.5kmi

EXPLANATION

The relation between speed , time and distance is given by the relation:

[tex]speed = \frac{distance}{time} [/tex]

Therefore

Distance= speed × time

John was traveling at a speed of 55mph

for 2 ½ hours.

The distance covered will be:

=55×2.5mi

=137.5mi

Answer:

SPED

Step-by-step explanation:

STEP 1. YOU GOT THAT COVERED

STEP 2. GOOGLE SPED CAUSE YOU PROLLY DONT EVEN KNOW WHAT THAT IS

[tex]

5(6\times2y+y)+3y(-2\times2-5) \\

5(12y+y)+3y(-4-5) \\

60y+5y+3y(-9) \\

60y+5y-27y \\

60y-22y \\

\boxed{38y}

[/tex]

The answer to this problem is 0.80

The square root of 7/11 is 0.240522846.

Answer:

2(x + 4)(x − 3)

Step-by-step explanation:

Hope it helped you

Answer:

2(x + 4)(x - 3)

Step-by-step explanation:

Given

2x² + 2x - 24 ← factor out 2 from each term

= 2(x² + x - 12)

To factor the quadratic

Consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (+ 1)

The factors are + 4 and - 3, since

4 × - 3 = - 12 and 4 - 3 = + 1, thus

x² + x - 12 = (x + 4)(x - 3) and

2x² + 2x - 24 = 2(x + 4)(x - 3)

8950.1 / 10000 = 0.89501...

1000 x 10 = 10000, so you’ll need to divide 8950.1 1000 times!

29 out of 40 as a percentage is simply 29 divided by 40 (29/40): 0.725 = 72.5%

126 out of 200 as a percentage is the same process = 63%

Hope this helps!! :)

29 out of 40 as a percentage

126 out of 200 as a percentage is 63%

A percentage is defined as the ratio that can be expressed as a fraction of 100.

To express 29 out of 40 as a percentage:

(29/40) * 100 = 72.5%

Thus, 29 out of 40 as a percentage is 72.5%.

To express 126 out of 200 as a percentage:

(126/200) * 100 = 63%

Thus, 126 out of 200 as a percentage is 63%.

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Answer:

42 apples altogether; $70

Step-by-step explanation:

If 3/7 of the apples in a box are red, that means 4/7 of the apples in the box are green. This means that (4/7)x=24 (x=number of apples altogether), since 24 of the apples are green. The equation can then be solved by dividing 24 by 4/7, giving us 42.

x=42

If Josh spent 2/5 of his money and had $42 dollars, $42 would be 3/5 of his money. This means that (3/5)x=42 (x= amount of money he started with). The equation can be solved by dividing 42 by 3/5, which gives us 70.

x=70

there were 42 apples in total and josh initially had $70.

Let the total number of apples be x. Therefore, [tex]\frac{4}{7}[/tex] of x are green apples, and this equals 24:

[tex]\frac{4}{7} \times x = 24[/tex]

We can solve for x as follows:

[tex]x = 24 \times \frac{7}{4}\\\\x = 42[/tex]

So, there are 42 apples in total.

Let y represent the total amount of money Josh had initially. According to the problem, after spending [tex]\frac{2}{5}[/tex] of his money, he had [tex]\frac{3}{5}[/tex] remaining, which equals $42:

[tex]\frac{3}{5} \times y = 42[/tex]

Now we can solve for y as follows:

[tex]y = 42 \times \frac{5}{3}\\\\y = 70[/tex]

Josh initially had $70.

So, there were 42 apples in total and josh initially had $70.

Answer: All of them besides 2/9

Step-by-step explanation:

2/3 equels 6/9 and 8/12. That first explanation is for the last to answers.

The first 2 have numerators greater than the denominator.

Answer:

5) 140.8m^2   6) 360in^2

Step-by-step explanation:

5.

6.4 x 6.4 = 40.96

(7.8 x 6.4) ÷ 2 = 24.96

24.96 x 4 = 99.84

99.84 + 40.96 = 140.8m^2

6.

12 x 10 = 120in

13 x 10 = 130in

5 x 10 = 50in

(12 x 5) ÷ 2 = 30in

30 x 2 = 60in

60 + 50 + 130 + 120 = 360in^2

Answer:

2x³ + x² - 14x - 7

Step-by-step explanation:

The product of f(x) and g(x) is

(2x + 1)(x² - 7)

Each term in the second factor is multiplied by each term in the first factor

2x(x² - 7) + 1 (x² - 7) ← distribute both parenthesis

= 2x³ - 14x + x² - 7

= 2x³ + x² - 14x - 7 ← in standard form

Answer:

Estimated cost; $9

Exact amount; $9.69

Step-by-step explanation:

We are told that ​Annie bought 3/4 kg of cocoa powder, which cost $12.92 per kg.

a.

We are required to estimate the cost of the 3/4 kg of cocoa powder given that 1 kg costs 12.92

We can round down the cost of a kg to obtain $12 per kg. Therefore, 3/4 of a kg will cost approximately;

(3/4) of 12

= (3/4)*12 = $9

Thus the estimated cost is $9

b.

We are required to determine the the exact amount she had to pay for the 3/4 kg of cocoa powder;

1 kg cost 12.92

3/4 of a kg will cost;

(3/4) of 12.92

= (3/4) * 12.92

Using a calculator we have;

9.69

Therefore, the exact amount paid was $9.69

Answer:

Part a) The estimate cost is about $9

Part b) The exact cost is $9.69

Step-by-step explanation:

we know that

Annie bought 3/4 kg of cocoa powder, which cost $12.92 per kg

Part a

To find the estimate cost round the numbers and multiply

we have

[tex]\$12.92=\$12[/tex] -----> round down

so

[tex]\frac{3}{4}(12)=\$9[/tex]

Part b

To find the exact amount she had to pay, multiply 3/4 by $12.92

so

[tex]\frac{3}{4}(12.92)=\$9.69[/tex] ----> exact value

Answer:

381.051178

Step-by-step explanation:

222 (tan) 60=381.051178

The height of the tree is 381.05 ft.

Given distance of man from the bottom of the tree is 220 ft.

Let height of the tree be x ft.

Now we have to look up at a 60 degree angle to see the top of the tree.

So we can write in trigonometric ratio form, [tex]tan60= \frac{perpendicular}{base}[/tex]

[tex]\sqrt{3} =\frac{x}{220}[/tex]   ( tan 60=[tex]\sqrt{3}[/tex])

[tex]x= 220\times\sqrt{3}[/tex]

[tex]x= 381.05 ft[/tex]

The height of the tree is 381.05 ft.

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Answer:

(a) [tex]x ^ 2 + y ^ 2 = 6 ^ 2[/tex]

(b) [tex](x-1) ^ 2 + y ^ 2 = 1[/tex]

Step-by-step explanation:

Remember that to convert from polar to rectangular coordinates you must use the relationship:

[tex]x = rcos(\theta)[/tex]

[tex]y = rsin(\theta)[/tex]

[tex]x ^ 2 + y ^ 2 = r ^ 2[/tex]

In this case we have the following equations in polar coordinates.

(a) [tex]r = 6[/tex].

Note that in this equation the radius is constant, it does not  depend on [tex]\theta[/tex].

As [tex]r ^ 2 = x ^ 2 + y ^ 2[/tex]

Then we replace the value of the radius in the equation and we have to::

[tex]x ^ 2 + y ^ 2 = 6 ^ 2[/tex]

Then [tex]r = 6[/tex] in rectangular coordinates is a circle centered on the point (0,0) and with a constant radius [tex]r = 6[/tex].

(b) [tex]r = 2cos(\theta)[/tex]

The radius is not constant, the radius depends on [tex]\theta[/tex].

To convert this equation to rectangular coordinates we write

[tex]r = 2cos(\theta)[/tex]     Multiply both sides of the equality by r.

[tex]r ^ 2 = 2 *rcos(\theta)[/tex]    remember that [tex]x = rcos(\theta)[/tex], then:

[tex]r ^ 2 = 2x[/tex]        remember that [tex]x ^ 2 + y ^ 2 = r ^ 2[/tex], then:

[tex]x ^ 2 + y ^ 2 = 2x[/tex]         Simplify the expression.

[tex]x ^ 2 -2x + y ^ 2 = 0[/tex]     Complete the square.

[tex]x ^ 2 -2x + 1 + y ^ 2 = 1[/tex]

[tex](x-1) ^ 2 + y ^ 2 = 1[/tex]  It is a circle centered on the point (1, 0) and with radio [tex]r=1[/tex]

Answer:

A

Step-by-step explanation:

?? That a tuff one.hope u find the answer soon

The red triangles that show a 90° counterclockwise rotation of the blue triangle are in options 1, 2, and 5.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. ΔABC denotes a triangle with vertices A, B, and C.

The red triangles that show a 90° counterclockwise rotation of the blue triangle are in options 1, 2, and 5.

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Answer:

320 cubic cm

Step-by-step explanation:

To answer a prism volume question, also see it as a shape (in this case a triangle) that is very thick.

First step is to calculate the area of the shape.  We all know the formula to calculate the area of a triangle: (b x h)/2.  And we those two measures.  The height of the triangle is b (8 cm), the base of the triangle is a (10 cm).

A = (b * h)/2 = (10 * 8) / 2 = 80 / 2 = 40 sq cm

Then we multiply the base area of the prism by its height to get the total volume. In this case, the height is also known, h = 8 cm.

V = b * h = 40 * 8 = 320 cubic cm

Answer:

320

Step-by-step explanation:

The volume of a prism is the height times the area of the base.

V = hA

The base is a triangle.  The volume of a triangle is half the base times height.

V = h (½ ab)

Given a = 10, b = 8, and h = 8:

V = ½ (8) (10) (8)

V = 320

Answer:

2. 6j^2 + 3

Step-by-step explanation:

Answer:

1/6, 1/3, 2/3

Step-by-step explanation:

Given data:

The sum of the first three terms of a finite geometric series is7/6 and their product 1/27 is .

Let a/r , a and ar be the three terms of a finite geometric series then:

a/r + a + ar = 7/6

and

(a/r) x (a) x (ar) = 1/27

Now first solving for a:

solving second equation

a^3r/r = 1/27

a^3= 1/27

a = 1/[tex]\sqrt[3]{27}[/tex]

a=1/3

Now solving for r:

Solving first equation

 a/r + a + ar = 7/6

Putting value of a= 3 in above equation

1/3r + 1/3 + r/3 = 7/6

(1+r+r^2)/3r= 7/6

6(1+r+r^2)= 7(3r)

6+ 6r+ 6r^2= 21r

6r^2 - 15r +6=0

r=2

Hence the first three terms of a finite geometric series are

a/r= (1/3)/(2)

    = 1/6

a= 1/3

ar= 1/3 (2)

   =2/3 !