Four more than twenty-six time a number is equivalent to 12 times the same number less 15.
What is the number?

Answer:

2. Eunju is right

3. [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].

Step-by-step explanation:

Polynomial Remainder Theorem

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

As a consequence, if a polynomial is divisible by x-a, f(a)=0.

Part 1:

Let's make:

[tex]f(x)=(x+b)^3+(x+c)^2-(b-c)[/tex]

To find out if x+b is a factor of f(x), we find f(-b):

[tex]f(-b)=(-b+b)^3+(-b+c)^2-(b-c)[/tex]

Operating:

[tex]f(-b)=(-b+c)^2-(b-c)[/tex]

The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).

Part 2:

We must find out if [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex] without using long division or synthetic division.

We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:

[tex]x^2+5x+6 =(x+2)(x+3)[/tex]

Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.

Let's make:

[tex]f(x)=x^4+5x^3+2x^2-20x-24[/tex]

Find f(-2):

[tex]f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24[/tex]

[tex]f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0[/tex]

Find f(-3):

[tex]f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24[/tex]

[tex]f(-3)=81-5*27+2*9+60-24[/tex]

[tex]f(-3)=81-135+18+60-24 =0[/tex]

Since both f(-2) and f(-3) are zero, [tex]x^2+5x+6[/tex] is a factor of [tex]x^4+5x^3+2x^2-20x-24[/tex].

Answer:

2688

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

From the total 1000 students, 450 are male, so 1000 - 450 = 550 students are female.

117 students are both [enrolled in extracurriculars] and [female].

The total number of [female] students is equal to the total number of [female AND enrolled] students plus the total number of [female AND not enrolled] students. The events of being enrolled in extracurriculars and not being enrolled are mutually exclusive. So if x is the number of female students not enrolled in extracurriculars, then

550 = x + 117

x = 550 - 117

x = 433

and the answer is B.

Answer:

0.92

Step-by-step explanation:

Answer:

We can't set up a proportion to solve for x in a percent equation. For example,   34/100=5/x

Step-by-step explanation:

Answer:

0.001 (one thousandth)

Step-by-step explanation:

hope this helps

Answer:

1 thousandth

Step-by-step explanation:

2 is in the ones place, 3 is in the tenths place, 9 is in the hundredths place, 1 is in the thousandths place.

Hope it helps!

Answer:

The slope of UV = 4

Step-by-step explanation:

Given the points

Finding the slope of UV

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(-1,\:1\right),\:\left(x_2,\:y_2\right)=\left(-2,\:-3\right)[/tex]

[tex]m=\frac{-3-1}{-2-\left(-1\right)}[/tex]

[tex]m=4[/tex]

Thus, the slope of UV = 4

Answer:

the answer ur looking for

81 −11.7 ≈ 70

Answer:

We have 92 % confidence that the true mean time a student sleeps per night is between (-0.25, 1.61).

Step-by-step explanation:

Compute the sample mean and sample standard deviation as follows:

[tex]\bar x=\frac{1}{n}\sum X=\frac{54.3 }{8}=6.788\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{8-1}\times 11.8288}=1.299[/tex]

Since, the sample standard deviation is computed the t-statistics will be used for the confidence interval.

The critical value of t for (n - 1) degrees of freedom and 92% confidence level is:

[tex]t_{\alpha/2, (n-1)}=t_{0.04, 7}=2.046[/tex]

*Use a t-table.

Compute the 92% confidence interval for the true mean time a student sleeps per night as follows:

[tex]CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\frac{s}{\sqrt{n}}[/tex]

     [tex]=6.788\pm 2.046\times\frac{1.299}{\sqrt{8}}\\\\=6.788\pm 0.9392\\\\=(-0.2504, 1.6080)\\\\\approx (-0.25, 1.61)[/tex]

We have 92 % confidence that the true mean time a student sleeps per night is between (-0.25, 1.61).

Answer:

270

Step-by-step explanation:

First, to find how far the car will go in one hour, you do 180 divided by 4. We already know that the car drives at a constant rate. If you do 180 divided by 4, you get 45. Then you multiply 45 by the amount of hours (6) to get 270

Answer:

undefined

Step-by-step explanation:

The formula for slope is [ y2-y1/x2-x1 ].

4-5/2-2

-1/0

When the denominator is 0, the slope is undefined.

Best of Luck!

Answer: There is no slope so 0

Step-by-step explanation:

Answer:

So before I answer this question may I ask a doubt, is this data handling?

Answer:

6/8

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

move x to the 3x side and move 5 to 9 side.

you get 2x=4

then you divide 2 from both sides and get 2

Answer:

x=2

Step-by-step explanation:

•Original Expression;

3x+5=x+9

•Group like terms;

3x-x=9-5

•Simplify

3x-x

=2x

Then

9-5

=4

Which is going to be;

2x=4

•Divide both sides by 2 to find x

4 can be divided by 2 two times so;

x=2

Answer:

Commutative property of multiplication is shown above. This is because no matter how you put them, the answer will still be 140  

Answer:

7/40

Step-by-step explanation:

12-5=7

54-14=40

7/40

Answer:

5x=3+7

5x=10

X=10/5

=2

Answer:

A

Step-by-step explanation:

The mode describes the most frequently occurring score or observation in a distribution. The tallest bar would describe the most frequently occurring score. Hence, the mode can be inferred directly from a histogram.

Hence, the frequency distribution or histogram could be used to directly deduce the mode of a distribution.

Learn more : https://brainly.com/question/16785562

Answer:

Step-by-step explanation:

[tex]f(x) = 2 {x}^{2} - 5x - 20[/tex]

To find f(-9) , substitute the value of x that's - 9 into f (x). That is for every x in f(x) replace it with - 9

We have

[tex]f( - 9) = 2 ({ - 9})^{2} - 5( - 9) - 20 \\ = 2(81) + 45 - 20 \\ = 162 + 25 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ = 187 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

We have the final answer as

Hope this helps you

Answer:

∠1 = 36°

∠2 = 122°

∠3 = 122°

∠4 = 38°

Step-by-step explanation:

∠2 = 180°-58° (Supplementary angles add up to 180°)

    = 122°

∠2 = ∠3 (Vertically opposite angles are equal)

    = 122°

∠1 = 180°-122°-22° (Sum of angles in a triangle is 180°)

   = 36°

∠4 = 180°-122°-20° (Sum of angles in a triangle is 180°)

     = 38°

Answer:

The answer to this question is C. 40.274.

Answer:

thanks bro

Step-by-step explanation:

Step-by-step explanation:

ggggggddfhhhjhhhjjjkkklllll

Answer:

345 divided by 5, answer in standard form

69 ....

Answer:

69

Step-by-step explanation:

Standard: 69

word : sixty nine

awnser

12;8

Step-by-step explanation:

i belive its that if its not then its prolly 12;20 if you get it wrong i will give you points-

Answer:

Step-by-step explanation:

147 x 23 = 3381

=>

Answer:

B: 3381

Step-by-step explanation:

147 X 23 = 3,381. if she drove 147 miles for 23 days that's 3381 miles in one month

Step-by-step explanation:

true

hope it helps!

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