Simiplify (3a2+1)−(4+2a2). Write the answer in standard form

Answer:

The dimensions of the three possible boxes are;

Box 1:  2 inches length by 4 inches width by 5 inches height

Box 2:  2 inches length by 2 inches width by 10 inches height

Box 3:  8 inches length by 1 inch width by 5 inches height

Step-by-step explanation:

The dimensions of the required box = 40 in³

Therefore, a box that will hold all the cubes will have a dimension given as follows;

Length, l × Width, w × Height, h = 40 in.³

We therefore, look for possible dimensions of l, w, h, however to make is faster, we note that l × w = base area, BA, hence we look for the factors 40 thus;

BA × h        ≡  l × w × h

8  × 5 = 40 ≡ 2 × 4 × 5 = 40

4 × 10 = 40 ≡ 2 × 2 × 10 = 40

8 × 5 = 40 ≡ 8 × 1 × 5 = 40

Hence we have our three possible boxes as follows;

Box 1: Length = 2 inches, width = 4 inches and height = 5 inches

Box 2: Length = 2 inches, width = 2 inches and height = 10 inches

Box 3: Length = 8 inches, width = 1 inches and height = 5 inches.

Answer:

Step-by-step explanation:

y = atan(10/8) = 51.3 deg

Answer:

125.7 mm

Step-by-step explanation:

Circumference=πd=π·40≈125.66371 mm

Answer:

34 packages

25 packages

Step-by-step explanation:

He needs a pair of buns for each hamburger.

He needs 200 hamburger. That means that he needs 400 buns for his picnic.

If buns come in a package of 12, the number of packages he needs is:

400 / 12 = 33.33 packages

Because packages come in whole numbers, we have to round up.

That means he needs 34 packages.

If buns come in a package of 16, the number of packages he needs is:

400 / 16 = 25 packages

Answer:

The slope of wholesale table is 3/4 times of the slope of the Public table

Step-by-step explanation:

Answer:

The slope of wholesale table is 3/4 times of the slope of the Public table

Step-by-step explanation:

because

Answer:

(−8x+1)(x+2)

Step-by-step explanation:

−8x^2−15x+2

−8x^2−15x+2

=(−8x+1)(x+2)

Answer:

(−8x+1)(x+2) Hope this helps!

Answer:

(-8x-1)(x-2)

Step-by-step explanation:

[tex]-8x^{2} +15x + 2=-8x^{2} +16x - x + 2[/tex]

-8x(x-2)-1(x-2)= (-8x-1)(x-2)

The distance between the ship and the shore is 63.83 meters.

We have,

Distance between the ship and the shore = x

Use tangent trigonometric identites.

tan θ = perpendicular / Base

tan 25 = 30/x

tan 25 = 0.47

0.47 = 30/x

x = 30/0.47

x = 63.83

Thus,

The distance between the ship and the shore is 63.83 meters.

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Answer:

3x^2+4x+2

please see the attached picture for full solution

hope it helps

Good luck on your assignment..

The quotient obtained by dividing the expression (3x³+10x²+10x+4) divided by (x+2) is 3x²+4x+2

A division is a process of splitting a specific amount into equal parts.

We are asked to find the quotient obtained by dividing the expression

(3x³+10x²+10x+4) divided by (x+2)

We can also write this expression as i.e. we are asked to find the value of the expression:

3x³+10x²+10x+4/x+2

We can write the expression on the numerator as:

3x³+10x²+10x+4=(3x²+4x+2)(x+2)

Divide both sides by x+2

3x³+10x²+10x+4/x+2=3x²+4x+2(x+2)/x+2

3x³+10x²+10x+4/(x+2)=3x²+4x+2

Hence, the quotient obtained by dividing the expression (3x³+10x²+10x+4) divided by (x+2) is 3x²+4x+2

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Answer:

54 square feet

Step-by-step explanation:

Area of a triangle is A = 1/2b*h

A = 1/2(9)(12)

A = 1/2(108)

A = 54 square feet

Answer:

4096

Step-by-step explanation:

Lets start by applying a basic exponent rule. (a*b)^n is equal to a^n * b^n

Therefore,

((9(3/16)^-2)^3/2 = 9^3/2 * ((3/16)^-2)^3/2

Now lets focus on ((3/16)^-2)^3/2

(3/16)^-2 = 1/(3/16)^2 = (16^2/3^2)^3/2.

We can quickly eliminate the fractional exponent by plugging it into the numerator and the denominator and we get, 16^3/3^3 = 4096/27

So now we have, 9^3/2 * 4096/27

We can easily compute 9^3/2, which is (sqrt(9))^3, which is equal to 27.

Therefore, you have, 27*4096/27. The 27 cancels to give us a final answer of 4096

Answer: 83

Step-by-step explanation:

225 - 55 -87= 83

You have $83 left on the credit card as your balance.

Answer:24

Step-by-step explanation:

First solve:

800*5 = 4,000

Then:

96 divided by 4,000 = 0.024

0.024 in percent = 24%

Thus, 24% will be your answer

Answer:

B. - 6p - 78

Step-by-step explanation:

-5 (3p+3) + 9 (-7 + p)

Expand.

-15p - 15 - 63 + 9p

Rearrange.

-15p + 9p + -15 + -63

Factor out.

p(-15+9) + -(15+63)

p(-6) + -(78)

-6p + - 78

-6p - 78

Answer:

-6p-78

Step-by-step explanation:

=> -5(3p+3)+9(-7+p)

=> -15p-15-63+9p

=> -15p+9p-78

=> -6p-78

Hope this helps!

Don't hesitate asking anything regarding this!

Give other person the brainliest answer :)

Subtracting [tex]2x[/tex] from both sides gives us the false statement [tex]2=3,[/tex] so this equation can never be true and thus has no solutions.

Answer:

214 ft^3

Step-by-step explanation:

Here, we are asked to calculate the volume of the cylindrical construction pipe.

Mathematically, the volume V

V = pi * r^2 * h

r is radius = diameter/2 = 4/2 = 2 ft

h = 17ft

pi = 3.14

Putting these values, we have;

V = 3.14 * 2^2 * 17 = 213.52 which is 214 ft^3 to the nearest whole number

Answer: shes right

Step-by-step explanation:

Answer:

The answer would be B

Step-by-step explanation:

So you have a totl of 50 rings. You would then add the blue and yellow ones to get 20. Then you divide 20 by 50 and get .4 which is equivalent to 2/5

Answer:

B

Step-by-step explanation:

I agree that the answer is B

Answer:

What is f(x) + f(x) + f(x)? 3f(x)

3f(x) = 3x^2

Evaluate 3f(2) = 12

The required value of the additions of the functios is 3x².

Given that,
f(x) = x2

What is fx) + f(x) + f(x) is to be determined,

A polynomial function is a function that applies only integer dominions or only positive integer powers of a value in an equation such as the quadratic equation, cubic equation, etc. ax + b is a polynomial.

Here,
f( x ) = x²
Now f(x) +f(x) + f(x) = x² + x² + x²
       f(x) +f(x) + f(x) = 3x²

Thus, The required value of the additions of the functions is 3x².

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Answer:

[tex]x = 26.25[/tex] inches

Step-by-step explanation:

Since we know the triangles are similar, we can simply set up ratios to find the length of side length 'x'.

[tex]\frac{15.75}{x} = \frac{9}{15}[/tex]

Cross multiply:

[tex]236.25 = 9x[/tex]

Divide both sides by '9' to solve for 'x':

[tex]\frac{236.25}{9} = \frac{9x}{9}[/tex]

[tex]x = 26.25[/tex]

Therefore, side length 'x' equals 26.25 in.

Answer:

Step-by-step explanation:

Notice that she already painted one face of each cube, that is, 8 faces in total, and she used 24 grams for that.

Now, there remain 3 faces per cube to be painted, which means there are 24 faces.

Then, we use the rule of three, if she used 24 grams of paint for 8 faces, how much grams of paint she would need to paint 24 faces?

[tex]24 \times \frac{24}{8}= 72 \ grams[/tex]

Therefore, Amanda needs 72 grams of paint for the unpainted surfaces.

Answer:

57 degree

Step-by-step explanation:

AB^2 = AC^2+CB^2-2ACCBcosC

AB=25cm

BC^2=AB^2+AC^2-2ABACcosA

A=56.6 degree

Answer:

d =±2sqrt(7) i

Step-by-step explanation:

d^2 = -28

Take the square root of each side

sqrt(d^2) = ±sqrt(-28)

d = ±sqrt(-28)

d = ±sqrt(-1)sqrt(28)

We know that sqrt(-1) = i

d =±i*sqrt(4)sqrt(7)

d =±i 2sqrt(7)

d =±2sqrt(7) i

Answer: f(x)=(x+3)^2-13 = (-3|-13)

Step-by-step explanation:

x^2+6x-4

x^2+6x+3^2-3^2-4

(x+3)^2-3^2-4

(x+3)^2-13

Answer:

(a) Increased by 100%

(b) Increased by 50%

(c) Decreased by 33.33%

(d) Decreased by 50%

(e) Increased by 200%

(f) Decreased by 66.67%

Step-by-step explanation:

To calculate percentage change, we can use the following formula:

[tex]\text{Percentage Change =} \dfrac{\text{New value - Old Value}}{\text{Old Value}} \times 100[/tex]

Positive value of percentage change means increase and

Negative value of percentage change means decrease.

Solution a)

Old Value = 1

New Value = 2

[tex]\text{Percentage Change =} \dfrac{\text{2 - 1}}{\text{1}} \times 100\\\Rightarrow 100\%[/tex]

Increase of 100%

Solution b)

Old Value = 2

New Value = 3

[tex]\text{Percentage Change =} \dfrac{\text{3 - 2}}{\text{2}} \times 100\\\Rightarrow 50\%[/tex]

Increase of 50%.

Solution c)

Old Value = 3

New Value = 2

[tex]\text{Percentage Change =} \dfrac{\text{2 - 3}}{\text{3}} \times 100\\\Rightarrow -33.33\%[/tex]

Decrease of 33.33%.

Solution d)

Old Value = 2

New Value = 1

[tex]\text{Percentage Change =} \dfrac{\text{1 - 2}}{\text{2}} \times 100\\\Rightarrow -50\%[/tex]

Decrease of 50%.

Solution e)

Old Value = 1

New Value = 3

[tex]\text{Percentage Change =} \dfrac{\text{3 - 1}}{\text{1}} \times 100\\\Rightarrow 200\%[/tex]

Increase of 200%.

Solution f)

Old Value = 3

New Value = 1

[tex]\text{Percentage Change =} \dfrac{\text{1 - 3}}{\text{3}} \times 100\\\Rightarrow -66.67\%[/tex]

Decrease of 66.67%.

So, the answer is:

(a) Increased by 100%

(b) Increased by 50%

(c) Decreased by 33.33%

(d) Decreased by 50%

(e) Increased by 200%

(f) Decreased by 66.67%

Answer:

150 miles

Step-by-step explanation:

In this problem, we are only interested in the distance that Lauren drove, this means that her average speed (75 mph to the cost, and 25 mph on the way back) does not matter since the distance remains the same. If one leg of trip is 75 miles long, the total mileage for the round trip is:

[tex]M=75+75\\M=150\ miles[/tex]

Lauren drove 150 miles.

Firstly Bernard = x

A) lets focus on Therese first. Bernard id two years older than her so for Therese’s equation in terms of x it would be x+2. Now for Josephine Bernard is 4 years younger than HER so it would be 4-x.

B) The mother is the PRODUCT of the sisters’ ages so (multiplication)

It would be like this: (x+2)(4-x)= 40 This is all in terms of x.

Solving for the equation (using distributive property) we get:

4x-x+8-2x=40

(Reorganize to group like terms, remember to go in order from the numeral numbers with variables, to variables only then numbers only): 4x-2x-x+8=40 (now combine like terms and simplify): x+8=40 this is his mom’s age in terms of x

C) HERE we can solve for x:

Isolating x to get the answer we move the 8 to the other side of the equation and it becomes a negative 8 so:

x=40-8

x=32

Therefore Bernard is 32 years old.

Hope this helps!

Answer:

3 miles

Step-by-step explanation:

First, we find the rate at which she drives, that is her speed.

Speed is given as:

speed = distance / time

When Cara drives to work, it takes her 30 minutes to drive 15 miles. Her speed is:

s = 15 / 30 = 0.5 miles per minute.

She drives at the same rate to The Dreamy Donut Shop and it takes her 6 minutes.

From the formula of speed, distance is given as:

distance = speed * time

Therefore, the distance of The Dreamy Donut Shop is:

distance = 0.5 * 6 = 3 miles

The Dreamy Donut Shop is 3 miles away.

Answer:

The answer is 3 miles

Step-by-step explanation:

Step-by-step explanation:

a) Let 'm' represents score in a Mathematics test. The variable has a fixed value because the marks Sarah obtained in her test will not change

b) Let 'd' represent the distance between the Zen house and the school. The variable has a fixed value because by using the same route, the distance will always remain constant.

c) Let 't' represent the temperature on the summit of Mount Everest. The variable has a changed value because the temperature may alter depending on the time of day and also climatic conditions which will affect the temperature.

Answer:

[tex]40[/tex] °

Step-by-step explanation:

[tex]tan(x)=\frac{8}{10} \\x=tan^{-1} (\frac{8}{10} )[/tex]

[tex]x=38.65980825[/tex]

Answer:

38.7

Step-by-step explanation:

Answer:

0.2 times

Step-by-step explanation:

Saturn: 8.867 × 108 = 957.636

Uranus: 1.787 × 109 = 194.783

You take (Uranus: 194.783)

& you divide it by (Saturn: 957.636)

You should get a funky number like 0.203399830415732 but since they said approximately you only need to use the first 2 (don't forget to round)

That would make Uranus 0.2 times as far from the sun

Answer:

[tex]x=6\,\,units\,,\,EF=34 \,\,units\,,\,FG=25\,\,units[/tex]

Step-by-step explanation:

Given: [tex]EG =59 \,\,units[/tex]

To find: [tex]x,EF,FG[/tex]

Solution:

From the image, [tex]EG=EF+FG[/tex]

Put [tex]EF=8x-14\,,\,FG=4x+1\,,\,EG=59[/tex]

[tex]8x-14+4x+1=59\\12x-13=59\\12x=59+13\\\\12x=72\\x=\frac{72}{12}=6[/tex]

[tex]EF=8x-14=8(6)-14=48-14=34\\FG=4x+1=4(6)+1=24+1=25[/tex]

Therefore,

[tex]x=6\,\,units\,,\,EF=34 \,\,units\,,\,FG=25\,\,units[/tex]