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Answer:

(x+y+5)(x-y+1)

Step-by-step explanation:

factor by grouping

x^2+6x+5-4y-y^2

x^2+6x+9 - (y^2+4t+4) + 5-9+4

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

(x+3+(y+2))(x+3-(y+2))

(x+y+5)(x-y+1)

Answer:

The remainder is 11.

Step-by-step explanation:

We are given the polynomial:

[tex]f(x) = x^3 + x^2 - 9x + 23[/tex]

And we want to find its remainder when the polynomial is divided by:

[tex]x + 4[/tex]

We can use the Polynomial Remainder Theorem. According to the PRT, if we divide a polynomial P(x) by a binomial in the form (x - a), the remainder will be given by P(a).

In this case, our binomial is (x + 4) or (x - (-4)). Hence, a = -4.

Then the remainder will be f(-4):

[tex]\displaystyle \begin{aligned}f(-4) &= (-4)^3 + (-4)^2 - 9(-4) + 23 \\ &= 11 \end{aligned}[/tex]

In conclusion, the remainder of the operation is 11.

Answer: a. 0.13% b. 2.28%

Step-by-step explanation:

Let x denotes the useful life of batteries.

Given: months,

Since X is normally distributed.

The probability that batteries with a useful life of less than 38 months

The percent of batteries with a useful life of less than 38 months =0.13%

The probability that batteries will last longer than 68 months

The percent of batteries that will last longer than 68 months =2.28%

Step-by-step explanation:

Answer:

f(-2) = 35

Step-by-step explanation:

Let x = -2.

[tex]3(-2)^2-8(-2)+7\\\\12+16+7\\\\35[/tex]

Answer:

1

Step-by-step explanation:

By order of operations, we first evaluate the parentheses, which is 2 * 1 = 2.  We then evaluate the brackets, which are 3 / 2 = [tex]\frac{3}{2}[/tex].  Finally, [tex]\frac{3}{2}[/tex] * [tex]\frac{2}{3}[/tex] = [tex]\frac{6}{6}[/tex] or 1.

The relationship between the heights of the fence, the lengths, the distance below the ground level is an illustration of addition and subtraction.

Plan A

[tex]Length = 4\frac 14[/tex]

[tex]Ground\ Level = \frac 78[/tex]

Plan B

[tex]Length = 6\frac 34[/tex]

[tex]Ground\ Level = 1\frac 12[/tex]

The height of the fence is calculated by subtracting the length below ground level from the length of the fence. So, we have:

[tex]Plan\ A = 4\frac 14 - \frac 78[/tex]                                   [tex]Plan\ B = 6\frac 34 - 1\frac 12[/tex]

[tex]Plan\ A = \frac{17}{4} - \frac 78[/tex]                                   [tex]Plan\ B = \frac{25}{4} - \frac 32[/tex]

                                         Take LCM

[tex]Plan\ A = \frac{17\times 2 - 7}{8}[/tex]                                   [tex]Plan\ B = \frac{25 - 3\times 2}{4}[/tex]

[tex]Plan\ A = \frac{34 - 7}{8}[/tex]                                       [tex]Plan\ B = \frac{25-6}{4}[/tex]

[tex]Plan\ A = \frac{27}{8}[/tex]                                           [tex]Plan\ B = \frac{19}{4}[/tex]

[tex]Plan\ A = 3\frac{3}{8}[/tex]                                           [tex]Plan\ B = 4\frac{3}{4}[/tex]

Hence, the height of fence is [tex]3\frac 38[/tex] in plan A  and [tex]4\frac 34[/tex] in plan B

The fence in plan B is taller because [tex]4\frac 34[/tex] is greater than [tex]3\frac 38[/tex]

The difference (d) in the heights is:

[tex]d = 4\frac 34 - 3\frac 38[/tex]

[tex]d = \frac{19}{4} - \frac{27}{8}[/tex]

Take LCM

[tex]d = \frac{19 \times 2 - 27}{4}[/tex]

[tex]d = \frac{38 - 27}{4}[/tex]

[tex]d = \frac{11}{4}[/tex]

[tex]d = 2\frac{3}{4}[/tex]

Fence in plan B is taller by [tex]2\frac{3}{4}[/tex] feet.

I will recommend the fence in plan B because:

For (5), we have:

[tex]Total = \$356.88[/tex]

[tex]Cash = \$220[/tex]

The remainder is the difference in the total amount and the amount they paid:

[tex]Charge = Total - Cash[/tex]

[tex]Charge = \$356.88 - \$220[/tex]

[tex]Charge = \$136.88[/tex]

Hence, they charge $136.88

Read more about addition and subtraction at:

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Answer:

x < -5

Step-by-step explanation:

-2(5x+1) >48

-10x-2 > 48

-10x-2+2 > 48+2

-10x > 50

p.s : when dividing by a negative number with inequalities, change the sign, i.e. < would then be >....

therefore:

x < -5

Hey there!

The formula for feet to inches is to simply multiply the length value by 12.

So, multiply 140 by 12.

I believe your answer would be 1680 inches.

Hope this helps!

Have a great day!

Answer:

140 feet is 1680 inches. Don't forget to put your units in; your teacher may dock off points for forgetting to put in the unit.

Step-by-step explanation:

A foot is 12 inches, so you must multiply 140 by 12.

[tex]140\times12=1680[/tex]

Answer: 3/2= 1.5

Step-by-step explanation: To double check just multiply 1.5 by 2, hope this helped :))

Answer:

x = 4

Step-by-step explanation:

Start by setting the two expressions equal to each other, since they're the same height.

6 + 15x = 6x + 42

Subtract 6x from both sides

6 + 9x = 42

Subtract 6 from both sides

9x = 36

Divide both sides by 9

x = 4

An equation is formed of two equal expressions. The value of x is 4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that the height of Ashton and James are the same height. Also, Ashton's height is represented by (6 + 15x) and James's height is represented by (6x + 42). Therefore, we can write,

Ashton's height = James' height

6 + 15x = 6x + 42

6 + 15x = 6x + 42

15x - 6x = 42 - 6

9x = 36

x = 36/9

x = 4

Hence, the value of x is 4.

Learn more about Equation here:

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Answer:

10-(3×4)-2+1=5

10-12-3=5

10-15=5

10=5+15

10=20

20-10

10

Answer:

[10 - 3 × (4-2)] +1= 5

.......

Answer:

Bro it is simple the answer is 23415

Step-by-step explanation:

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Answer:

z-score=7.5-6        1.5

___________=______=0.5

3                                   3

Step-by-step explanation:

Look up -0.1 on a z-table. The result is 0.4602. The means there is a 0.4602 probability the random variable will be below 5.7.

The find the probability the random variable will be between 7.5 and 5.7, simply subtract the two probabilities we found (above) from one another:

0.6915+-+0.4602+=+0.2313

So, there is a 0.2313 probability the random variable will fall between 7.5+and 5.7.

Answer:

3 cups of sugar should be used if 5 cups of floue is included

Answer:

these statements are not logically equivalent.

Step-by-step explanation:

steps are in picture.

If you have any question about it you can ask freely.

(23) 7×10¹ + 3×1 = 70 + 3 = 73

(25) 3×10² + 8×10¹ + 5×1 = 300 + 80 + 5 = 385

(27) 5×10⁵ + 2×10⁴ + 8×10³ + 7×10² + 4×10¹ + 3×1 = 500000 + 20000 + 8000 + 700 + 40 + 3 = 528743

It should be quite clear what you have to do from here, I think.

(29) 7002

(31) 600002007

Answer:

b. Add 4, 2, 6, 10

Step-by-step explanation:

(a)

Given:

72 to be split into 1:3:5

Solution:

First divide the amount with the sum of the ratio given

72 / 1 + 3 + 5 = 72 / 9 = 8

Now multiply the answer with each value:-

8 × 1 = 8

8 × 3 = 24

8 × 5 = 40

∴ The ratio will be 8:24:40

{To check your answer add to get the exact value: 8 + 24 + 40 = 72}

(b)

Given:

150 to be split into 2:3

Solution:

First divide the amount with the sum of the ratio given

150 / 2 + 3 = 150 / 5 = 30

Now multiply the answer with each value:-

30 × 2 = 60

30 × 3 = 90

∴ The ratio will be 60:90

{Now check your answer in the same way above: 60 + 90 = 150}

We have that  the distance in meters of the object is

[tex]d=687.55m[/tex]

From the Question we are told that

Angular diameter [tex]d_a= 30 arcseconds[/tex]

Linear diameter [tex]d_l= 10 cm=0.10m[/tex]

Generally the equation for Linear diameter  is mathematically given as

[tex]d_l=\frac{d_a*d}{206265}[/tex]

Therefore

[tex]d=\frac{0.10m*206265}{30}[/tex]

[tex]d=687.55m[/tex]

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[tex]\\ \rm\longmapsto 5x-y[/tex]

[tex]\\ \rm\longmapsto 5(7)-12[/tex]

[tex]\\ \rm\longmapsto 35-12[/tex]

[tex]\\ \rm\longmapsto 23[/tex]

Answer:

[tex]5x - y \\ x = 7 \\ y = 12 \\ then \: 5x - y = 5 \times 7 - 12 \\ = 35 - 12 \\ = 23 \\ thank \: you[/tex]

Answer: 13. is c, 14. is yes and 15 is no

Step-by-step explanation: Try your best and you might succeed

Answer:

1,000,000.

Step-by-step explanation:

You are rounding to the nearest hundred thousand place value, which will be underlined and bolded:

982,510

Note that when you round, you look at the digit directly next to the place value you are solving for. Note:

If the value of the digit is 5 or greater, round up.

If the value of the digit is 4 or less, round down.

In this case, the value directly next to the place value is the ten thousands place, which has the value of 8. Because 8 is greater than 5, you will round up.

982510 rounded to the nearest hundred thousand is 1,000,000.

~

For the numberline, simply plot the points on both end of the spectrum, with 0 being on the left and x value on the right. Plot 1,000,000 corresponding to the value given on the right.

~

Answer: m∠ABF = 120°

Concept:

Here, we need to know the idea of the corresponding angle theorem and linear pair postulate.

The corresponding angle theorem states that if a transversal cuts two parallel lines, their corresponding angles are congruent.

The linear pair postulate states that two angles that form a linear pair are supplementary.

Solve:

Given information

m∠ABF = m∠ABF = 2x + 3x

m∠BCH = 3x

Total angle = 180°

Given equation

m∠ABF + m∠BCH = Total Angle

Substitute values into the equation

2x + 4x + 3x = 180

Combine like terms

9x = 180

Divide 9 on both sides

9x / 9 = 180 / 9

x = 20

m∠ABF = 2x + 4x = 2 (20) + 4 (20) = 40 + 80 = 120°

Hope this helps!! :)

Please let me know if you have any questions

Answer:

It is 3 : 27

Step-by-step explanation:

Ratio of blue to yellow = 3:24

[tex]{ \sf{total \: ratio = 24 + 3 = 27}}[/tex]

ratio of blue to all triangles:

[tex] = 3 : 27[/tex]

Answer:

(3.5,4)

Step-by-step explanation:

add and divide by 2

(7,8)

(3.5,4)

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Answer:175 degrees

Step-by-step explanation: The shape isn't properly drawn.But,I assumed it is a five sided polygon because of the fifth ange

Answer:

Walking speeds vary depending on age, and health of walkers. However, an average comfortable walking speed is about 5 km per hour and 9km per hour can be achieved by many people. This means that in 30 minutes it should be possible to easily walk 2.5km and in 2 hours it should be possible to walk 10km.

Answer:

0.07929 km/min

Step-by-step explanation:

1 miles is 1.903 km

5 miles is 9.515 km in 2 hours

9.515 /2 = 4.7575 km/h

Then divide th speed value by 60

4.7575 / 60 = 0.07929

Answer:

It's geometric sequence where a_1=12, q=-\dfrac{1}{2}a

1

=12,q=−

2

1

So a_n=12\cdot\left(-\dfrac{1}{2}\right)^{n-1}a

n

=12⋅(−

2

1

)

n−1

Answer:

[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex]

Step-by-step explanation:

The nth term of a geometric sequence is

[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Here a₁ = 12 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-6}{12}[/tex] = - [tex]\frac{1}{2}[/tex] , then

[tex]a_{n}[/tex] = 12 [tex](-\frac{1}{2}) ^{n-1}[/tex] ← explicit formula