Which of the following reasons can be used to justify statement #4 in the proof?
A Given
B the vertical angle theorem
C the alternative interior angle theorem
D SSS​

Answer:

 [tex]2. m\angle H+m\angle J +m\angle K =180^{\circ}[/tex]

Reason: the sum of all interior angles of any triangle is equal to 180º.

Step-by-step explanation:

1) Organizing

Statement  1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100° 1. Reason: given

2) Since the sum of all internal angles of any triangle is equal to 180º, just like the formula. N the number of sides of a triangle:

[tex]S_{i}=180^{\circ}(n-2)\rightarrow 180(3-2) \therefore S_{i}=180^{\circ}[/tex]

3) We can also say

[tex]m\angle K=180^{\circ}-(m\angle H+m\angle J)\\m\angle K=180^{\circ}-\left ( 30^{\circ}+50^{\circ} \right )\\m\angle K=100^{\circ}[/tex]

Similarly to the other triangle:

[tex]m\angle L=180^{\circ}-(m\angle N+m\angle P)\\m\angle L=180^{\circ}-\left ( 100^{\circ}+50^{\circ} \right )\\m\angle L=30^{\circ}[/tex]

4) Hence,

[tex]2. m\angle H+m\angle J +m\angle K =180[/tex]

Reason: The sum of interior angles is equal to 180º.

Answer:

B

Step-by-step explanation:

Answer:

10,000 nickles

Step-by-step explanation:

Since there are 40 nickles in a roll and you have 250, think that you have 250 sets of 40. This means that this question is a multiplication problem.

Multiply 40 x 250. This would give you 10,000.

Don't forget units.

The number of nickels in 250 rolls is 10000

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here, There are 40 nickels in a roll. If I have 250 rolls of nickels, then the number of nickels in total is = 250×40

                                                     = 10000

Hence, The number of nickels in 250 rolls is 10000

Learn more about the unitary method here:

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Answer:

Because they are in the ratio 2:3 we'll call red and blue paint 2x and 3x respectively. We know that there are 15 liters of blue paint which means that 3x = 15. Solving for x we get x = 5. Since red paint is denoted by 2x it would be 2 * x = 2 * 5 = 10.

Answer:

10 liters

Step-by-step explanation:

Red : Blue

2          3

We want 15 blue liters

15/3 = 5

Multiply each term by 5

Red : Blue

2*5      3*5

10 :    15

Answer:

8

Step-by-step explanation:

(100 - 20) / 10 = 8

Answer: He has to take a class per month from the both pros

Step-by-step explanation:

Answer:

3x(3x+5)(x-2)

Step-by-step explanation:

[tex]9x^3-3x^2-30x= \\\\3x(3x^2-x-10)= \\\\3x(3x^2+5x-6x-10)= \\\\3x(x(3x+5)-2(3x+5))= \\\\3x(3x+5)(x-2)[/tex]

Hope this helps!

Answer:

D. Yes, because the amount of money on her gift card should decrease each week.

Step-by-step explanation:

The amount of money on the gift card decreases every Friday as it states in the problem.

Yes Kate's graph represent the situation, because the amount of money on her gift card should decrease each week. so option D is correct.

A graph contains data of which input maps to which output.

Analysis of this leads to the relations which were used to make it.

For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.

We can see that the graph shows that the slope is decreasing, if you got $75 and spend $5.00 each Friday, wouldn't that be  decrease and Lastly, of course, they should not start at the origin as they started at $75.00.

The amount of money on the gift card decreases every Friday as it states in the given situation.

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Answer:

The answer is A.

Step-by-step explanation:

You have to add up both polynomials together :

A = 7x² + 3xy

B = -3xy

A + B = 7x² + 3xy + (-3xy)

= 7x² + 3xy - 3xy

= 7x²

Answer:

This does not factor

Step-by-step explanation:

2x^2-17x-35=0

Since the x^2 has a coefficient of 2

(2x    ) ( x     )

Looking at the factors of -35

-1 35       1, -35

-5   7       5, -7

We need to  get to -17

You cannot factor this

-

Answer:

18.2%

Step-by-step explanation:

The total number of trees in the wood = 420 + 160 + 300

                                                                = 880 trees

∴ The percentage of the oak trees = [tex]\frac{160}{880} * \frac{100}{1}[/tex]

                                                            = [tex]\frac{2 * 100}{11}[/tex]%

                                                            = [tex]\frac{200}{11}[/tex]%

                                                            = 18.181818...%

In 1 decimal place = 18.2%

Hope this helps!!

Answer:

The major categories of financial institutions include central banks, retail and commercial banks, internet banks, credit unions, savings, and loans associations, investment banks, investment companies, brokerage firms, insurance companies, and mortgage companies

Step-by-step explanation:

sorry i did not put 2 examples, i put too many examples lollll

Answer:

There are two primary types of financial institutions non-depository and depository.

Step-by-step explanation:

an insurance company would fall under the non-depository group, and a credit union would be defined as a depository institution.

Answer:

Step-by-step explanation:

[tex](-14+\frac{3}{2}b)-(1+\frac{8}{2}b)=-14-1+\frac{3}{2}b-4b[/tex]

                                   = ([tex]-15-\frac{5}{2}b[/tex])

[tex](5+2b)+(2b+\frac{3}{2})=(5+\frac{3}{2})+(2b+2b)[/tex]

                             = [tex](4b+\frac{13}{2})[/tex]

[tex](\frac{7}{2}b-3)-(8+6b)[/tex] = [tex](\frac{7}{2}b-6b)-(3+8)[/tex]

                             = ([tex]-\frac{5}{2}b-11[/tex])

[tex](-10+b)+(7b-5)=(-10-5)+(b+7b)[/tex]

                               = [tex](8b-15)[/tex]

Answer:

B

Step-by-step explanation:

Answer:

35/70*100 = 50 miles

Step-by-step explanation:

Answer: a=2

Step-by-step explanation:

-14a=-28

divide both sides by -14

a=2

Answer:

The answer to this problem would be :

-2y^2-y-5

Answer:

85

Step-by-step explanation:

The sum of the angles of a triangle are 180 degrees

A + B+ C = 180

A +72+ 23 = 180

Combine like terms

A + 95  = 180

Subtract  95  from each side

A +95-95 = 180-95

A =85

Answer:

[tex]4y+ y"x^2-4y'x = 0[/tex]

    ↓

[tex]F(x, y, y', y'') = 0[/tex]

Step-by-step explanation:

From the information given:

[tex]y = c_1x + c_2x^4 \\ \\ y^1'= c_1 + 4c_2x^3 \\ \\ c_1 =y' - 4c_2x^3 \\ \\[/tex]

So;

[tex]y = y'x -4c_2x^4+c_2x^4 \\ \\ y - y'x - 3c_2x^4 \\ \\ y'= y"x+y'- 12c_2x^3 \\ \\ c_2= \dfrac{y"x}{12x^3} \\ \\ c_2= \dfrac{y"}{12x^2}[/tex]

∴

[tex]y = y'x- \dfrac{3x^4*y'' }{12x^2} \\ \\ \\ y = y'x - \dfrac{y" x^2}{4} \\ \\ \\ 4y+ y"x^2-4y'x = 0[/tex]

  ↓

[tex]F(x, y, y', y'') = 0[/tex]

Answer:

Decreased 24 degrees

Step-by-step explanation:

subtract the 17 from Saturday which gets you to 0 but it ends up being -7 on Sunday so i did 17+7 and it gives 24 so that's how much it went down

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.24

For the alternative hypothesis,

p ≠ 0.24

This is a two tailed test

Considering the population proportion, probability of success, p = 0.24

q = probability of failure = 1 - p

q = 1 - 0.24 = 0.76

Considering the sample,

Sample proportion, P = r/n

Where

r = 12

n = 52

P = 12/52 = 0.23

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.23 - 0.24)/√(0.24 × 0.76)/52 = - 0.17

Recall, population proportion, P = 0.24

The difference between sample proportion and population proportion(p - P) is 0.24 - 0.23 = 0.01

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.24 - 0.01 = 0.23

the p for the right tail is 0.24 + 0.01 = 0.25

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail 0.43

We would double this area to include the area in the right tail of z = 0.17 Thus

p = 0.43 × 2 = 0.86

The level of significance is 5%

Since alpha, 0.05 < than the p value, 0.86, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, this information does not imply that the color preference of all college students is different (either way) from that of the general population.

Answer:

   possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25

   p(x) = (x +1)^2(2x -5)(x^2 -4x +5)

   complex roots: 2±i

   see the last attachment for a graph

Step-by-step explanation:

2. The leading coefficient of p(x) is 2, and the constant term is 25. The Rational Root Theorem tells you possible rational roots will be of the form ...

  ±(divisor of 25)/(divisor of 2)

That is, they are ...

  ±1/2, ±1, ±5/2, ±5, ±25/2, ±25

__

3. Before we get into synthetic division, we choose to see if we can reduce this list any. We note that p(0) = -25. The value of p(1) is the sum of the coefficients:

  p(1) = 2 -9 +6 +22 -20 -25 = 30 -54 = -24

Similarly, the value of p(-1) is the same sum with odd-degree coefficients negated:

  p(-1) = -2 -9 -6 +22 +20 -25 = 42 -42 = 0

So, we found our first root: -1. Using synthetic division, we can reduce the polynomial and start over. See the first attachment for this division.

__

The reduced polynomial is ...

  p1(x) = 2x^4 -11x^3 +17x^2 +5x -25

We already know that +1 is not a of it. Checking -1, we have ...

  p1(-1) = 2 +11 +17 -5 -25 = 0

So, we found our second root: -1. Using synthetic division, we can reduce the polynomial and start over. See the second attachment for this division.

__

The reduced polynomial is ...

  p2(x) = 2x^3 -13x^2 +30x -25

The alternating signs tell us there are no more negative real roots. They also tell us there are 1 or 3 positive real roots. We know p2(0) = -25. Then ...

  p2(1) = 2 -13 +30 -25 = 32 -38 = -6

The average rate of change between these points is (-6 -(-25))/(1 -0) = 19. At this rate, we expect a root between x=1 and x=2. Testing x=2 using synthetic division, we get a remainder of -1. (See the 3rd attachment.) Then the rate of change between x=1 and x=2 is (-1 -(-6))/(2-1) = 5, suggesting x=5/2 might be a worthwhile test value.

The synthetic division is shown in the 4th attachment. You will note that we divide the polynomial p2(x) by its leading coefficient, so the coefficients used for p2(x) in the synthetic division are 1, -13/2, 15, -25/2. The remainder of 0 tells us that (x -5/2) is a factor of p2(x)/2, or (2x -5) is a factor of p2(x).

__

The reduced polynomial is ...

  p3(x) = x^2 -4x +5

This can be written in vertex form as ...

  p3(x) = (x -2)^2 +1

The positive leading coefficient means the graph opens upward, and the vertex at (2, 1) means there are no real solutions.

The real solutions to p(x) are x = -1, -1, and 5/2.

__

4. The complex solutions will be the solutions to ...

  (x -2)^2 +1 = 0

  (x -2)^2 = -1

  x -2 = ±√(-1) = ±i

  x = 2 ±i . . . . complex roots of p(x)

__

5. The graph is shown in the last attachment. The odd degree and positive leading coefficient of p(x) means the overall shape will be from lower left to upper right (/). That is, the sign of the end value of p(x) will match the sign of x.

The graph will touch the x-axis from below at x = -1, and will cross at x = 2.5. There is no particular symmetry.

The final quadratic factor is graphed and its vertex shown. The vertex matches that of the vertex-form equation for p3(x), above.

Answer:

possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25

real solutions to p(x) are x = -1, -1, and 5/2.

(x -2)^2 +1 = 0

(x -2)^2 = -1

x -2 = ±√(-1) = ±i

x = 2 ±i complex roots

Answer:

I'd need to see the lines but basically, parallel lines have to be directly across from each other and they have to be the same size, I put a pic so you can see what I mean

Hope this helps you

Answer:

C) yes, because both lines have a slope of 2/3

Step-by-step explanation:

edg2020

Answer:

Probability ≈ 0.0833

Step-by-step explanation:

Consider steps below;

[tex]Total Possible Outcomes - 9C6,\\\\9! / 6! ( 9 - 6 )!,\\1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 / ( 1 * 2 * 3 * 4 * 5 * 6)( 1 * 2 * 3 ),\\\\362,880 / 720 * 6 = Combinations - 84,\\\\[/tex]

[tex]Number Of Outcomes - 7C6,\\\\7! / 6! ( 7 - 6 )!,\\1 * 2 * 3 * 4 * 5 * 6 *7/ ( 1 * 2 * 3 * 4 * 5 * 6 ) ( 1 ),\\\\Outcomes - 7[/tex]

[tex]Conclusion ; Solution - 7 / 84 = ( About ) 0.0833\\Hope That Helps![/tex]

Solution; Probability ≈ 0.0833

Answer:

9

Step-by-step explanation:

[tex]p(y)=y^3+3y^2-5y-6 \\\\p(-3)=(-3)^3+3(-3)^2-5(-3)-6= \\\\-27+27+15-6= \\\\9[/tex]

Hope this helps!

Answer:

p(-3)=9

Step-by-step explanation:

This question ask us to find p(-3), or what p(y) is when y is equal to -3.

We know that:

p(y)= y^3+3 y^2-5y-6

We want to find p(-3), so substitute -3 in for every y.

p(-3)= (-3^3)+3(-3^2)-5(-3)-6

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Solve the exponents first (-3^3 and -3^2)

-3^3=-3*-3*-3= -27

-3^2= -3* -3= 9

p(-3)= -27+ 3(9) -5(-3) -6

Next, multiply 3 and 9

p(-3)= -27+27-5(-3)-6

Then, multiply -5 and -3

p(-3)= -27+27+15-6

-27 and 27 equal 0, so they cancel each other out.

p(-3)=15-6

p(-3)= 9

Answer:

4

Step-by-step example

Slop is the

Answer:

Step-by-step explanation:

Since the grass on the field erodes by -1 1/2% every year, it means that the rate of erosion is exponential. It is therefore eroding in geometric progression. We would apply the formula for determining the sum of n terms of a geometric sequence which is expressed as

Sn = a(1 - r^n)/(1 - r)

Where

n represents the number of terms(number of years) in the sequence.

a represents the first term in the sequence(the length 3 years ago)

r represents the common ratio(rate of erosion)

From the information given,

a = 220 feet

r = - 1.5/100 = - 0.015

n = 3

Therefore, the length of the field after 3 years, S3(length of the field now) would be

Sn = a(1 - r^n)/(1 - r)

S3 = 220(1 - (- 0.015^3)/(1 - - 0.015)

S3 = 220.0007425/1.015

S3 = 216.7495 feet

Answer:

complementary angle: 63

supplementary angle: 153

Step-by-step explanation:

Complementary angles mean angles that add up to 90.  Therefore 90-27=63

Supplementary angles are angles that add up to 180. Therefore 180-27=153

Answer: $ 10,988.25

Step-by-step explanation:

Hi, to answer this question, first we have to multiply the original number of students scheduled to go to the trip (420) by the added students’ percentage (15%) in decimal form (divided by 100)

420 x (15/100) = 420 x 0.15 = 63 students added

Adding the number of extra students to the original number:

420+63 = 483 students (total number of students)

Finally, we have to multiply the result by the cost of each admission ticket (22.75)

483 x 22.75 = $ 10,988.25  

Answer:

Volume of prism = 3,240 cm³

Step-by-step explanation:

GIven.

Hexagonal prism.

Side of base(b) = 12cm

Height of prism = 9cm

Height of base (h)= 10cm

Find:

The volume of the prism.

Computation:

Area of base of hexagonal prism = n/2[bh]

Area of base of hexagonal prism = 6/2[(12)(10)]

Area of base of hexagonal prism = 360 cm²

The volume of prism = Area of base of hexagonal prism × Height of prism

The volume of prism = 360 × 9

Volume of prism = 3,240 cm³

Answer:

$1,592.74

Martha will need to pay $1,592.74 more

Step-by-step explanation:

Using the compound interest/inflation formula;

A = P(1+r)^(t)

Where;

A = final value

P = initial value = $10,000

r = inflation rate = 3% = 0.03

t = time = 5 years

Substituting the values;

A = $10,000(1+0.03)^(5)

A = $11592.740743

A = $11,592.74

How much more will Martha need to save;

C = final value - initial value = A - P

C = $11,592.74 - $10,000

C = $1,592.74

Martha will need to pay $1,592.74 more

Answer:

1,590.00

Step-by-step explanation: I took the test