Question 1 (9 points)
Combine like terms.
10 - 3 - 2 + 4
After combing like terms, the simplified expression is
Blank 1:

Answer:

14. H. 110°

15. D. <8

Step-by-step explanation:

14. Given that line AD and line EG are parallel as shown above, m<3 and m<4 are linear pairs and are supplementary. That is, m<3 + m<4 = 180°.

If m<3 = 70°, therefore, m<4 = 180° - 70°

m<4 = 110°

15. <3 corresponds with <8. Corresponding angles are congruent. Therefore, <3 = <8.

Answer: volume is 9 cubic units

===================================================

Explanation:

Each cross section is a square with side length x, so the area of this cross section is x^2

We're integrating from x = 0 to x = 3

So we have

[tex]\displaystyle f(x) = x^2\\\\\\\displaystyle g(x) = \int x^2 dx = \frac{1}{3}x^3+C\\\\\\\displaystyle \int_{a}^{b} f(x) dx = g(b) - g(a)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = g(3) - g(0)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = \left(\frac{1}{3}(3)^3+C\right) - \left(\frac{1}{3}(0)^3+C\right)\\\\\\\displaystyle \int_{0}^{3} x^2 dx = 9\\\\\\[/tex]

Answer:

False

Step-by-step explanation:

|x+y| = |x| + |y|

To show this is false, all we have to do is find one example where it is false

Let x = -1 and y = 4

|-1+4| = |-1| + |4|

|3| = |1| + |4|

3 = 5

This is false so we have a set of integers where the statement is not true

Answer:

none

Step-by-step explanation:

110 + 60 = 170

but 170 is obviously not 180 sooo none will be 60 degrees

Answer:

C

Step-by-step explanation:

So we have:

[tex]\frac{6^{\frac{3}{10}}}{6^\frac{1}{5}}[/tex]

To simplify, we can use the quotient rule of exponents, which says that if we have:

[tex]\frac{x^a}{x^b}[/tex]

Then this equals:

[tex]=x^{a-b}[/tex]

So, our equation will be:

[tex]\frac{6^{\frac{3}{10}}}{6^\frac{1}{5}}\\=6^{\frac{3}{10}-\frac{1}{5}}[/tex]

Subtract the exponents. Turn 1/5 into 2/10 by multiplying both layers be 2. Thus:

[tex]6^{\frac{3}{10}-\frac{1}{5}}\\=6^{\frac{3}{10}-\frac{2}{10}}[/tex]

Subtract in the exponent:

[tex]=6^{\frac{1}{10}}[/tex]

So, our answer is C :)

Step-by-step explanation:

The answer is not in the option.

The answer is 29/24.

Answer:

14 + 3x  + 46 = 90

3x + 60 =90

3x = 30

x = 10

Answer:

Step-by-step explanation:

If u see it is right angle so 90 - 14 u will get an or bc 76

3x+46=76

3x=76-46

3x=30

X=30/3

10

Answer:

[tex]Probability = \frac{845}{5832}[/tex]

Step-by-step explanation:

Given

Two standard dice

Required

Probability that the outcome will be greater than 8 for the first time on the third roll

First, we need to list out the sample space of both dice

[tex]S_1 = \{1,2,3,4,5,6\}[/tex]

[tex]S_2 = \{1,2,3,4,5,6\}[/tex]

Next, is to list out the sample when outcome of both dice are added together[tex]S = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}[/tex]

Next, is to get the probability that an outcome will be greater than 8

Represent this with P(E)

[tex]P(E) = \frac{Number\ of\ outcomes\ greater\ than\ 8}{Total}[/tex]

[tex]P(E) = \frac{10}{36}[/tex]

[tex]P(E) = \frac{5}{18}[/tex]

Next, is to get the probability that an outcome will noy be greater than 8

Represent this with P(E')

[tex]P(E) + P(E') = 1[/tex]

[tex]P(E') = 1 - P(E)[/tex]

[tex]P(E') = 1 - \frac{5}{18}[/tex]

[tex]P(E') = \frac{18 - 5}{18}[/tex]

[tex]P(E') = \frac{13}{18}[/tex]

Now, we can calculate the required probability;

Probability of a number greater than 8 first on the third attempt is:

Probability of outcome not greater than 8 on the first attempt * Probability of outcome not greater than 8 on the second attempt * Probability of outcome greater than 8 on the third attempt

Mathematically;

[tex]Probability = P(E') * P(E') * P(E)[/tex]

Substitute values for P(E) and P(E')

[tex]Probability = \frac{13}{18} * \frac{13}{18} * \frac{5}{18}[/tex]

[tex]Probability = \frac{13 * 13 * 5}{18 * 18 * 18}[/tex]

[tex]Probability = \frac{845}{5832}[/tex]

Answer:

4, 15, 6, 18.

Step-by-step explanation:

Try the others by yourself and if you have any questions ask me in the comments

Answer:

d = ±7i

Step-by-step explanation:

d^2 -1 = -50

Add 1 to each side

d^2 -1 = -50

d^2 = -49

Take the square root of each side

sqrt(d^2) = sqrt(-49)

d = sqrt(-1) sqrt(49)

d = i( ±7)

d = ±7i

Answer:

A.

Step-by-step explanation:

d^2-1= -50

First, add 1 to both sides.

d^2= -49

Take the square root of both sides:

d=√-49

Since i^2=-1

d=i√49

d= ±7i

Hope this helps!

Answer:

5/6

Step-by-step explanation:

To simplify this fraction, we need to find the GCF (greatest common factor) of the numerator and denominator. In this case, the GCF of 55 and 66 is 11. Now, all we have to do is divide both the numerator and denominator by the GCF. The numerator will become 55 / 11 = 5 and the denominator will become 66 / 11 = 6 so the simplified fraction is 5 / 6.

Answer:

f (x) = { 19 + 0.39(x - 300), x > 300

Step-by-step explanation:

Andrew has a cell phone plan that provides 300 free minutes each month for a flat rate of $19. For any minutes over 300, Andrew is charged $0.39 per minute. Let x be the number of minutes Andrew uses per month and f(x) be the charges based on Andrew's cell phone plan. If  then If  then first 300 minutes are free and each minute of next (x-300) minutes costs $0.39, therefore Hence, { 19 + 0.39(x - 300), x > 300

Hoped I helped

Answer:

12<4 (12 to the power of 4)

Step-by-step explanation:

an exponet is used when a number is repeated multiplied against itself. sinec 12 is being multiplied against itself 4 times, we can use the exponent of 4

Answer: [tex]12^4[/tex]

Step-by-step explanation:

Concept to know: for exponents, the amount of same number that is multiplied together will be the number of exponents

--------------------------------------

12×12×12×12

There are in total 4 [12]'s multiplied together, so we will get [tex]12^4[/tex]

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

This means in the first week the number sells of digital copies is 308, paperback sells was 385 copies and hardback sell was 77 copies

Step-by-step explanation:

Let the number of digital copies be x, the number of paperback copies be y and the number of hardback copies be z.

4 digital sales is equal to 5 paperback sales and 1 hardback sale.

5x = 4y, x = 4z, y = 5z

The company sells 308 more paperback copies of the book than hardback copies

y = 308 + z

But y = 5z

5z = 308 + z

4z = 308

z = 77

y = 5z = 5(77) = 385

x = 4z = 4(77) = 308

This means in the first week the number sells of digital copies is 308, paperback sells was 385 copies and hardback sell was 77 copies

Answer:

0.49926

Step-by-step explanation:

We solve for this using z score formula

z-score is

z = (x-μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation

The probability that defect length is at most 20 mm is calculated as:

x = 20mm, μ = 33 mm, σ = 7.9mm

z = 20 - 33/7.9

= -13/7.9

= -1.64557

Obtaining the Probability value from Z-Table:

Probability (At most 20mm) = P(x ≤ 20mm) P(z = -1.64557)

P(x ≤ 20) = 0.049926

Therefore, the probability that defect length is at most 20 mm is 0.049926

Answer:

The probability that defect length is at most 20 mm is 0.0495.

Step-by-step explanation:

We are given that the defect length of a corrosion defect in a pressurized steel pipe is normally distributed with a mean value of 33 mm and a standard deviation of 7.9 mm.

Let X = the defect length of a corrosion defect in a pressurized steel pipe

The z-score probability distribution for the normal distribution is given by;

                             Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean defect length = 33 mm

           [tex]\sigma[/tex] = standard deviation = 7.9 mm

So, X ~ Normal([tex]\mu=33 \text{ mm}, \sigma^{2} = 7.9^{2} \text{ mm}[/tex])

Now, the probability that defect length is at most 20 mm is given by = P(X [tex]\leq[/tex] 20 mm)

        P(X [tex]\leq[/tex] 20 mm) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{20-33}{7.9}[/tex] ) = P(Z [tex]\leq[/tex] -1.65) = 1 - P(Z < 1.65)

                                                             = 1 - 0.9505 = 0.0495              

The above probability is calculated by looking at the value of x = 1.65 in the z table which has an area of 0.9505.

Answer: x = -2

x + 9 = 7, Move the constant to the right.

x =7 -9 now calculate that.

then you get x = -2

Hope that helps ya out :D

Answer:

x+9=7

So x= 7-9

( 9 became -9 because we brought it back to the other side to have the x alone and the digits alone )

So x= -2

Answer:

the sum of the this series is Sn = [n(n+1)] / 2

Answer:

The equation for constant of proportionality is:

y = kx

K = Constant of proportionality

An example:

4y = 8x

=> 4y/4 = 8x/4

=> y = 2x

In the answer, y = 2x;   2 is the constant of proportionality

Answer:

it is ratio of the amount s y and x:k = y/x. put another way: y = Kx.

Example:- you are paid 20 rupaye an hour the constant of proportionality is 20

because pay = 20 hours worked

Answer:

table 2

Step-by-step explanation:

see attached

Answer:

table no. 2

Step-by-step explanation:

Answer:-6x^2+10x-5.

Step-by-step explanation: -6x^2-1−6x 2−1+x+9x+9                                                          -6x^2-1−6x 2−1+10x+9                                                                                                -6x^2-1-12−1+10x+9                                                                                                         -6x^2+10x-1-12-1+9                                                                                                                 6x^2+10x-5

The sum of the two expressions are -6x²+22x+9

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions.

Given here the expressions here as -6x²+1+6x ×2-1, x+9x+9

The sum is -6x²+1+6x ×2-1 +x+9x+9=-6x²+22x+9

Hence, The sum of the two expressions are -6x²+22x+9

Learn more about like and unlike terms here:

https://brainly.com/question/29078851

#SPJ2

Answer:

∠ B = 54°

Step-by-step explanation:

Supplementary angles sum to 180°.

Sum A and B  and equate to 180, that is

7x + 14 + 5x - 26 = 180, that is

12x - 12 = 180 ( add 12 to both sides )

12x = 192 ( divide both sides by 12 )

x = 16

Thus

∠ B = 5x - 26 = 5(16) - 26 = 80 - 26 = 54°

Answer: [x/2 , 1]

Step-by-step explanation: Convert the inequality to interval notation.

The union consists of all of the elements that are contained in each interval. There is No Solution.

I hope this helps you out. If not, my apologizes.

-Leif Jonsi-

Answer:

Answer: so the answer is 80 miles per 0.8 Step-by-step explanation: consistence

Answer:

80,617

Step-by-step explanation:

the 1 in the tens place puts the number back down to 600

Answer:

the answer is b

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

We can first expand 5(x-10), getting 5x - 50.

Thus, 5x - 50 = 30 - 15x

We can then isolate x, getting (5+15) x = 30 + 50

20 x = 80

x = 4.

Answer:

5(x - 10) = 30 - 15x

We distribute 5 (x-10)

So 5x-50 = 30 -15x

5x+15x=50+30

(-15x became 15x because we brought it back to the other side and -50 became 50 because we brought it back to the other side to put the x's with the x's and the digits with the digits.)

So 20x=80

x= 50/20

We simplify 80/20

So x=4

Answer:

the area of the triangle is 20 units, and the answer to the expression is also 20, so its equal to each other. 20=20

the area of the trapezoid is 38.5 units

Step-by-step explanation:

Answer:

[tex]10^{11}[/tex]

Step-by-step explanation:

A statement is given i.e. "ten to the eighth divided by ten to the negative third."

It means that 10 to power 8 divided by 10 to the power -3.

Mathematically,

[tex]\dfrac{10^8}{10^{-3}}[/tex]

We know that, [tex]\dfrac{x^a}{x^b}=x^{a-b}[/tex]

Here, x = 10, a = 8 and b = -3

So,

[tex]\dfrac{10^8}{10^{-3}}=10^{8-(-3)}\\\\=10^{8+3}\\\\=10^{11}[/tex]

So, the answer is [tex]10^{11}[/tex]

Answer:

x =0

Step-by-step explanation:

[tex]\left(6^2\right)^x=1\\\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}\\\left(6^2\right)^x=6^{2x}\\\\6^{2x}=1\\\mathrm{If\:}f\left(x\right)=g\left(x\right)\mathrm{,\:then\:}\ln \left(f\left(x\right)\right)=\ln \left(g\left(x\right)\right)\\\ln \left(6^{2x}\right)=\ln \left(1\right)\\\\\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\\\ln \left(6^{2x}\right)=2x\ln \left(6\right)\\2x\ln \left(6\right)=\ln \left(1\right)\\[/tex]

[tex]\mathrm{Solve\:}\:2x\ln \left(6\right)=\ln \left(1\right):\\\quad x=0[/tex]

Hello,

a) We know the binomial coefficients are all integers, so

[tex]\dfrac{p!}{k!(p-k)!}[/tex]

is an integer.

And we can notice that the numerator p! is divisible by p.

If we take [tex]1\leq k\leq (p-1)[/tex]

It means that k! does not contain p, and we can say the same for (p-k)!

So, we have no p at the denominator so the binomial coefficient is divisible by p, meaning this is 0 modulo p.

b) We can write that

[tex]\displaystyle (x+y)^p=\sum_{i=0}^{p} \ {\dfrac{p!}{i!(p-i)!}x^{p-i}y^i[/tex]

We use the result from question a) and the binomial coefficients are 0 modulo p for i=1,2 , ... p-1 so there are only two terms left and then,

[tex](x+y)^p=x^p+y^p \text{ modulo p}[/tex]

c) Let's prove it by induction.

step 1 - for x = 0

This is trivial to notice that

[tex]0^p=0 \text{ modulo p}[/tex]

Step 2 - we assume that this is true for k

meaning [tex]k^p=k \text{ modulo p}[/tex]

and we need to prove that this is true for the k+1

We use the results of b)

[tex](k+1)^p=k^p+1^p=k^p+1 \text{ modulo p}[/tex]

and we use the induction hypothesis to say

[tex](k+1)^p=k^p+1^p=k^p+1=k+1 \text{ modulo p}[/tex]

And it means that this is true for k+1

Step 3 - conclusion

We have just proved by induction the Fermat's little theorem.

p a prime number, for for all x integers

[tex]\Large \boxed{\sf \bf x^p=x \textbf{ modulo p}}[/tex]

Thank you