Help please, and explain.

Answer:

5y^3

Step-by-step explanation:

Find what is common to all the terms

5y^5 = 5 * y*y*y*y*y

35y^4 = 5*7*y*y*y*y

15y^3 = 3*5*y*y*y

The all have 5*y*y*y

So the  GCF is 5 y*y*y or 5y^3

Since we are given that ABC is congruent to JKL, then AB has to be equal to JK

therefore --- [tex]14x+7=5x+34[/tex]

Subtract 7 from both sides

[tex]14x=5x+27[/tex]

Subtract 5x from each side

[tex]9x=27[/tex]

Divide 9 on each side

[tex]x=3[/tex]

Since, We are asked to find the length of AB and JK

plug in 3 for x

[tex]5(3)+34=15+34=49[/tex]

f(x) = 2x^2 - 4x - 3; opens up; vertex: (1, -5); y-intercept: (0, -3)

g(x) = -x^2 + x + 1; opens down; vertex: (0.5, 1.25); y-intercept: (0, 1)

h(x) = -2x^2 + 3x - 1; opens down; vertex: (0.75, 0.125); y-intercept: (0, -1)

m(x) = x^2 - 9; opens up; vertex: (0, -9); y-intercept: (0, -9)

n(x) = -3x^2 + 7; opens down; vertex: (0, 7); y-intercept: (0, 7)

I have attached an image of the functions and their graphs.

Hope this helps!

Answer:

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

Step-by-step explanation:

Quadratic equation is in the form of

[tex]f(x)= ax^2+bx+c[/tex]

When the value of 'a' is positive then the graph opens up

When the value of 'a' is negative  then the graph opens down

When the graph opens up then the vertex is minimum.

When the graph opens down then the vertex is maximum.

y intercept is the value of 'c'

[tex]f(x) = 2x^2 - 4x - 3[/tex], a=2 the graph opens up

[tex]f(x) = -x^2 +x +1[/tex], a=-1 the graph opens down. So the vertex is maximum. Y intercept is +1. y intercept is positive.

[tex]f(x) = -2x^2 +3x - 1[/tex], a=-2 the graph opens down. So the vertex is maximum. Y intercept is -1. y intercept is negative.

[tex]f(x) = 2x^2 - 4x - 3[/tex], a=2 the graph opens up

Answer:

The budget in 2010 is $4453.10915 billion

Step-by-step explanation:

We are given exponential function as

[tex]f(t)=39.4e^{0.0787932t}[/tex]

where t is the time in years since 1950

now, we can find time in 2010

t=2010-1950=60

now, we can plug t=60

and we get

[tex]f(60)=39.4e^{0.0787932\times 60}[/tex]

we get

[tex]f(60)=4453.10915[/tex]

So, the budget in 2010 is $4453.10915 billion

Answer:

B

Step-by-step explanation:

Let [tex]r[/tex] be the radius of one sphere.

Since radius is r,  the height of the cylinder will be [tex]4r[/tex]

Also, the cylinder has the same radius as the sphere: [tex]r[/tex]

Plugging in the values we get: [tex]V=\pi (r)^{2}(4r)=4\pi r^3[/tex]

Ratio of volume of 1 sphere to volume of cylinder is:

[tex]\frac{\frac{4}{3}\pi r^3}{4\pi r^3}=\frac{\frac{4}{3}}{4}=\frac{4}{3}*\frac{1}{4}=\frac{1}{3}[/tex]

The ratio is 1:3

Answer choice B is right.

The correct answer for dividing [tex](a^{2n} - a^n - 6) by (a^n + 8)[/tex] is indeed:

[tex](a^n - 9) + (-78)/(a^n + 8).[/tex]

Let's divide the given polynomials:

[tex]\frac{a^{2n -a^n -6}}{a^n +8}[/tex]

Here's the breakdown of the solution:

Factoring: We can factor the numerator [tex](a^{2n} - a^n - 6)[/tex] using difference of squares:

[tex](a^{2n} - a^n - 6) = (a^n)^2 - (a^n) - 6 = (a^n + 2)(a^n - 3)[/tex]

Division: Now, we can divide the factored numerator by the denominator:

[tex][(a^n + 2)(a^n - 3)] / (a^n + 8) = (a^n + 2) - [(a^n + 8) * (a^n - 3)] / (a^n + 8) = (a^n + 2) - (a^n - 3) = a^n - 9[/tex]

Remainder: Since the degree of the numerator is less than the degree of the denominator, we get a non-zero remainder.

This remainder is obtained by dividing the constant term (-6) in the numerator by the constant term (8) in the denominator, resulting in [tex]-78/(a^n + 8).[/tex]

Therefore, the final answer is [tex](a^n - 9) + (-78)/(a^n + 8)[/tex], with a quotient of [tex](a^n - 9)[/tex] and a non-zero remainder of [tex](-78)/(a^n + 8).[/tex]

Answer:

( 85 x 6 ) - 69 would equal 441

Step-by-step explanation:

You do 85 x 6 then - 69 (:

Answer:

441

Step-by-step explanation:

first do the

(85x6) you get 510

510-69

441

The correct equation is 14 + n = 8n, option A is correct.

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let the number is n,

8 times of the number = 8n

According to the condition, The sum of 14 and number n is 8 times the number,

Implies that,

14 + n = 8n

The correct equation is 14 + n = 8n.

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Answer:

b

Step-by-step explanation:

B// 8pi x-24pi

Since it's 48 out of 160 and you're trying to find the percentage out of 100, this particular formula would look like this: 48/160=x/100.

Then you cross multiply: 48x100=4800

Then you take the result of that and divide it by the total number of houses. 4800/160=30

30% of the houses are brick.

Answer:

B

(x-2) is a factor since remainder is 0.

Step-by-step explanation:

We divide (x-2) into the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] through long division or synthetic. We choose long division and look for what will multiply with (x-2) to make the polynomial [tex]-4x^4+6x^3+8x^2-6x-4[/tex] .

[tex](x-2)(-4x^3)=-4x^4+8x^3[/tex]

We subtract this from the original [tex]-4x^4-(-4x^4)+6x^3-(8x^3)+8x^2-6x-4[/tex].

This leaves [tex]-2x^3+8x^2-6x-4[/tex]. We repeat the step above.

[tex](x-2)(-2x^2)=-2x^3+4x^2[/tex].

We subtract this from [tex]-2x^3-(-2x^3)+8x^2-(4x^2)-6x-4=4x^2-6x-4[/tex]. We repeat the step above.

[tex](x-2)(4x)=4x^2-8x[/tex].

We subtract this from [tex]4x^2-(4x^2)-6x-(-8x)-4=2x-4[/tex]. We repeat the step above.

[tex](x-2)(2)=2x-4[/tex].

We subtract this from [tex]2x-(2x)-4-(4)=0[/tex]. There is no remainder. This means (x-2) is a factor.

The remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2) is 0, indicating that (x - 2) is indeed a factor of p(x).

To find the remainder R when the polynomial p(x) = -4x4 + 6x3 + 8x2 - 6x - 4 is divided by (x - 2), we can use the Remainder Theorem. The Remainder Theorem states that the remainder of the division of a polynomial p(x) by a linear term (x - a) is equal to p(a). Therefore, to find R, simply calculate p(2).

p(2) = -4(2)4 + 6(2)3 + 8(2)2 - 6(2) - 4

p(2) = -4(16) + 6(8) + 8(4) - 12 - 4

p(2) = -64 + 48 + 32 - 12 - 4

p(2) = 0

Since the remainder is 0, this means that (x - 2) is a factor of p(x).

The correct answer is therefore R = 0, and yes, (x - 2) is a factor of p(x).

Answer:

P ( blue ) =  1/4

P ( white ) =  5/12

P ( red ) = 1/3

P ( not red ) =  2/3

Step-by-step explanation:

To find the probability of a marble being chosen,  it is the number of that color over the total

We need to find the total number of marbles

4 red+ 5 white+3 blue = 12 marbles

P ( blue ) = 3 blue / 12 total = 3/12 = 1/4

P ( white ) = 5 white / 12 total = 5/12

P ( red ) = 4 red/ 12 total = 4/12 = 1/3

How man marbles are not red

total marbles - red marbles = 12-4 = 8

8 marbles are not red

P ( not red ) = 8 not red / 12 total = 8/12 = 2/3

Answer:

[tex]x \leq 14.05[/tex]

Step-by-step explanation:

First, to find the boundary we need to find the amount of money left, simply subtract the spent amount from the total:

60 - 45.95 = 14.05

Seeing as this is the amount, she can spend any amount up to and including 14.05, so we need an equal to or smaller than sign:

Let x be the value of the object:

[tex]x \leq 14.05[/tex]

Which is the inequality!

Answer:

0.1071

Step-by-step explanation:

Given

Total number of students=8

Boys=2

Girls=6

When we are picking a group from population we use combinations to calculate sample space and for event

So if a group of 5 has to be picked from 8 students

ⁿC_k=  n!/(k!)(n-k)!

C_(n,k)=  n!/(k!)(n-k)!

Here n=8 and k=5

C_8,5=  8!/(5!)(8-5)!

This will give us:  

C_8,5=56

And if we have to pick only girls:

C_6,5=  6!/(5!)(6-5)!

=6

The probability of picking all girls:

=6/56

=0.1071

The correct answer to this question would be 3/28

Answer:

The bowling alley should rent 150 pairs of shoes and should about 75 games per day in order to reach a goal of 300 dollars.

Step-by-step explanation:

Slope-intercept form:

y = mx + b

"m" is the slope, "b" is the y-intercept (the y value when x = 0 or (0,y))

You know m = 2, so you can plug it into the equation

y = 2x + b

To find "b", plug in the point (3, -2) into the equation

y = 2x + b

-2 = 2(3) + b

-2 = 6 + b

-8 = b

y = 2x - 8

The slope-intercept form:

[tex]y=mx+b[/tex]

m - slope

b - y-intercept

We have the slope m = 2 and the point (3, -2) → x = 3 and y = -2.

Substitute:

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

[tex]-2=6+b[/tex]      subtract 6 from both sides

[tex]-8=b\to b=-8[/tex]

Substitute to the equation y = mx + b:

Answer:

12

Step-by-step explanation:

There are 6 for tails. Each is 2. 6 x 2 =12

The point-slope form of line:

[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-5, -6) and (2, 8). Substitute:

[tex]m=\dfrac{8-(-6)}{2-(-5)}=\dfrac{8+6}{2+5}=\dfrac{14}{7}=2\\\\y-(-6)=2(x-(-5))\\\\\boxed{y+6=2(x+5)}[/tex]

After drinking 24 gallons out of the required 40 gallons, the elephant needs at least 4 more tanks of water as each tank holds 4 gallons. The inequality representing this is x ≥ 4.

The student needs to calculate how many more tanks of water an elephant needs to drink to reach its daily requirement of at least 40 gallons if each tank contains 4 gallons of water. To start, we determine how much water the elephant still needs after drinking 24 gallons:

Required daily water - Water already consumed = Remaining water needed

40 gallons - 24 gallons = 16 gallons

Next, we find out how many tanks are needed for the remaining 16 gallons, knowing that each tank holds 4 gallons:

Number of tanks needed = Remaining water needed / Water per tank

Number of tanks needed = 16 gallons / 4 gallons per tank

Number of tanks needed = 4 tanks

Since the elephant needs at least 40 gallons, it will need at least 4 more tanks of water. However, since we're writing this as an inequality, we want to express that the elephant may drink more. Hence, the inequality will be:

x ≥ 4

Answer:

Kyle can jump rope the most times per minute.  

Step by step explanation:

We have been given that Daren can jump rope 116 times in 2 minutes.

So number of rope jumps done by Daren in 1 minute will be:

[tex]\text{Unit rate of Jump rope done by Daren}=\frac{116\text{ times}}{2\text{ minute}}[/tex]

[tex]\text{Unit rate of Jump rope done by Daren}=58\frac{\text{ times}}{\text{ minute}}[/tex]

Therefore, Daren jumps rope 58 times per minute.

We have been given that Kyle can jump rope 240 times in 4 minutes.

So number of rope jumps done by Kyle in 1 minute will be:

[tex]\text{Unit rate of Jump rope done by Kyle}=\frac{240\text{ times}}{4\text{ minute}}[/tex]

[tex]\text{Unit rate of Jump rope done by Kyle}=60\frac{\text{ times}}{\text{ minute}}[/tex]

Therefore, Kyle jumps rope 60 times per minute.

We have been given that Marissa can jump rope 225 times in 5 minutes.

So number of rope jumps done by Marissa in 1 minute will be:

[tex]\text{Unit rate of Jump rope done by Marissa}=\frac{225\text{ times}}{5\text{ minute}}[/tex]

[tex]\text{Unit rate of Jump rope done by Marissa}=45\frac{\text{ times}}{\text{ minute}}[/tex]

Therefore, Marissa jumps rope 45 times per minute.

As Kyle jumps rope 60 times per minute, which is greater than jumps rope done by Daren and Marissa, therefore, Kyle can jump rope the most times per minute.

It's an arithmetic sequence:

[tex]a_1=4;\ a_2=10;\ a_3=16;\ a_4=22;\ ...[/tex]

The explicit rule:

[tex]a_n=a_1+(n-1)d[/tex]

[tex]d=a_{n+1}-a_n\to d=a_2-a_1=a_3-a_2=a_4-a_3=...[/tex]

[tex]d=10-4=16-10=22-16=6[/tex]

Substitute:

[tex]f(n)=4+(n-1)(6)=4+6n-6=6n-2[/tex]

The explicit rule for the arithmetic sequence 4, 10, 16, 22, ... is aₙ = 4 + (n - 1) x 6, where aₙ is the nth term of the sequence.

The given sequence is arithmetic, which means that it increases by the same amount each time. To find an explicit rule for the sequence, we should determine the common difference and use the formula for an arithmetic sequence, which is aₙ = a₁ + (n - 1)d, where an is the nth term, a1 is the first term, n is the number of the term in the sequence, and d is the common difference between terms.

In the sequence 4, 10, 16, 22, ..., the first term a1 is 4, and the common difference is 6 (since 10 - 4 = 16 - 10 = 22 - 16 = 6). Therefore, the explicit rule for the nth term of the sequence is aₙ = 4 + (n - 1) x 6.

Answer: 13 units

The x value goes from x = 21 to x = 9, which is an x distance of 12 units (21-9 = 12)

The y distance is 5 units (16-11 = 5)

We have a right triangle with legs of 12 and 5. The hypotenuse is x

Use the pythagorean theorem to find x

a^2 + b^2 = c^2

5^2 + 12^2 = x^2

25 + 144 = x^2

169 = x^2

x^2 = 169

x = sqrt(169)

x = 13

The hypotenuse of this right triangle is 13 units, so this is the distance between the two points.

Answer:

He will make 16.50 per hour after his raise.

Step-by-step explanation:

15 x .10 = 1.50

15.00 + 1.50 = 16.50

Answer:

∠A=40°

Step-by-step explanation:

Equation 1: ∠A+∠B+∠C=180°

Equation 2: ∠B/2+∠C/2+110°=180°

2(Equation 2): ∠B+∠C+220°=360°

                                 ∠B+∠C=140°

Equation 1 - 2(Equation 2): ∠A=40°

Therefore, ∠A=40°

Question:

line x + 2y = 0 is end side of angle θ

and cos θ < 0

Answer: sin θ = √5/5

Step-by-step explanation:

cos θ < 0 means x < 0

Line is y = -x/2, slope -1/2

Line intersects unit circle when x^2+y^2=1

x^2 + (-x/2)^2 = 1

x^2 + x^2/4 = 1

5x^2/4 = 1

x = -√(4/5) = -2√(1/5) = -2√5/5

y = √5/5

x^2 = 4/5, y^2 = 1/5

sin θ is y value at intersection of line and unit circle, √5/5

In this exercise we have to use the given equation and thus calculate the intersection value:

[tex]sin (\theta) = \sqrt{5/5}[/tex]

So knowing that you were informed:

Line x + 2y = 0 is end side of angle θ and  cos θ < 0 means x < 0.  Line is y = -x/2, slope -1/2 and the  Line intersects unit circle when :

[tex]x^2+y^2=1\\x^2 + (-x/2)^2 = 1\\x^2 + x^2/4 = 1\\5x^2/4 = 1\\x = -\sqrt{4/5} = -2\sqrt{1/5} = -2\sqrt{5/5}\\y = \sqrt{5/5}\\x^2 = 4/5, y^2 = 1/5[/tex]

[tex]sin(\theta)[/tex]  is y value at intersection of line and unit circle, [tex]\sqrt{5/5}[/tex]

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Answer:

x > 5

Step-by-step explanation:

isolate x by subtracting 7 from both sides

x > 12 - 7

x > 5

Answer:

[tex]t\leq 70[/tex]

Step-by-step explanation:

The team spends 20 minutes running laps

At least 15 minutes discussing plays.

Practice lasts one hour and 45 minutes.

We know that 1 hour = 60 minutes, so the practice lasts,

60+45= 105 minutes.

The team spends a total of [tex]20+15=35[/tex] minutes  in running and discussion.

So the time remaining to work on other drills is,

[tex]t\leq 105-35[/tex]

[tex]t\leq 70[/tex]