Stephen and Bridget are marking exam papers. Each set takes Stephen 71 minutes and Bridget 2 hours. Express the times Stephen and Bridget take as a ratio in its simplest form.

Answer:

y = 1/2x+5

Step-by-step explanation:

You have two points so you can find the slope

m = (y2-y1)/(x2-x1)

m = (8-3)/(6 - -4)

   (8-3)/(6+4)

    5/10

 1/2

The slope intercept form is y = mx+b where m is the slope and b is the y intercept

y = 1/2 x+b

Substitute a point into the equation

8 = 1/2(6)+b

8 = 3+b

b=8-3 = 5

y = 1/2x+5

Answer:t=8

Step-by-step explanation:

solve for t by simplifying both sides of the equation,then isolating the variable

Answer:

[tex]t = 8[/tex]

Step-by-step explanation:

→You need to get "t," by itself, and to do this, you must multiply both sides by the reciprocal of [tex]\frac{1}{4}[/tex], which is 4. You are multiplying because you can't divide by a fraction.

[tex]\frac{1}{4} t=2[/tex]

[tex]4*\frac{1}{4} t=2*4[/tex]

[tex]t = 8[/tex]

Answer:

72 + 2y = 180

2y = 108

y = 108/2

y = 54

C. 54

Answer:

C

Step-by-step explanation:

Sum of three angles of triangle = 180

72 + y + y = 180  {add like terms}

72 +2y = 180    {Subtract 72 from both sides}

2y = 180 - 72

2y = 108    {divide both sides by 2}

y = 108 / 2

y = 54°

Answer:

21+12i i hope this will help you

Step-by-step explanation:

(3-4i)(1+5i)-(2-i)

=[3(1+5i)-4i(1+5i)]-(2-i)

=[3+15i-4i-20i²]-(2-i)

=(3+11i-20i²)-(2-i)

opening brackeys

=3+11i-20i²-2+i

=3+11i+1i-20i²-2

as we know that i²=-1

=3-20(-1)-2+12i

=3+20-2+12i

=21+12i

The expression (3 - 4i)(1 + 5i) - (2 - i) is simplified as 21 + 12i

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the expression be A = (3 - 4i)(1 + 5i) - (2 - i)

Now , we know i² = -1

And , on simplifying the expression , we get

A = (3 - 4i)(1 + 5i) - (2 - i)

A = 3 + 15i - 4i - 20i² - 2 + i

A = -20i² + ( 3 - 2 ) + ( 15i - 4i + i )

A = -20 ( -1 ) + 1 + ( 11i + i )

A = 20 + 1 + 12i

A = 21 + 12i

Hence , the value of the expression (3 - 4i)(1 + 5i) - (2 - i) is ( 21 + 12i )

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Answer:

I would say B.

Step-by-step explanation:

I used synthetic division for this, so I'm unsure if this is right. I have yet to learn exponents with it. Here's how I wrote it : 3] 2 -3 -5 -12. I bring down the 2 and multiply it by three to get six. After that, I multiply the sum of it (3) and got 9. I do the same, get -4 and multiply it another time, getting positive 12. I add the twelves together, get zero, and put it together as 2x^2+3x+4.

Hope this helps!

Answer:

A (-2, 10)

Step-by-step explanation:

If you plug in the point into x and y you should get "false" on a calculator, or the answer won't make sense, meaning that it's not a part of the set

(-2,10) is not the solution set of the given equation [tex]3y+2 =x^{2} -5x+17[/tex].

The solution, or root, of an equation is any value or set of values that can be substituted into the equation to make it a true statement.

According to the given question

We have an equation

[tex]3y + 2 =x^{2} -5x+17[/tex]

The above equation can be written as

[tex]x^{2} -5x +17-3y-2=0...(i)[/tex]

For finding the point which is not the solution set of the equation, first we will substitute the given points in the above equation and check whether it making the equation true or not.

For point (-2, 10)

Substitute, x = -2 and y = 10 in the equation (i)

[tex](-2)^{2} -5(-2) + 17 - 3(10) -2\\=4+10+17-30-2\\= -1\neq 0[/tex]

Hence, (-2, 10) is not the solution of the given equation.

For point (5, 5)

Substitute, x = 5, and y = 5 in equation (i)

[tex](5)^{2} -5(5)+17-3(5)-2\\=25-25+17-15-2\\=0[/tex]

Hence, (5, 5) is the solution of the given equation.

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Answer:

The answer is 72

Step-by-step explanation:

You'll do 42 divided by 7 times 2

42/7x2

Hope it helps.

A car travels 72 km on 12 liters of petrol.

What is Division method?

Division method is used to distributing a group of things into equal parts.

Given that;

A Car travels 42 km on 7 liters of petrol.

Now,

Since, On 7 liters of petrol a car travel 42 km

Hence, On 1 liter of petrol distance cover by a car = 42 ÷ 7

                                                                             = 6 km

So, On 12 liters of petrol distance cover by a car = 6 × 12

                                                                           = 72 km

Thus, A car travels 72 km on 12 liters of petrol.

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Answer:

169.7

Step-by-step explanation:

first lets find the other side of the small triangle

cos(30 degrees)=(7*sqrt (3))/x

x*cos(30 degrees)=7*sqrt (3)

x=(7*sqrt (3))/cos(30 degrees)

x=14

14/14=1

so proportion is 1/1

thus the bottom the outer part of the triangle is also 7*sqrt(3)

now, for the area

lets find the 2 side length of the triangle we need

DE: 14+14=28

DF: 7*sqrt(3)+7*sqrt(3)=14*sqrt(3)

let's find EF,

sin(30 degrees)=x/28

x/28=sin( 30 degrees)

x=28*sin( 30 degrees)

x=14

A=(14*sqrt(3))*14*0.5

A=(14*sqrt(3))*7

A= around 169.7

Answer:

≈169.7

Step-by-step explanation:

cos30 = (7[tex]\sqrt{3}[/tex])/x

x= (7[tex]\sqrt{3}[/tex])/cos30 = 14

h = 14+14 = 28

sin30 = EF/28

EF = sin30 * 28 = 14

tan30 = 14/DF

DF = 14/tan30 ≈ 24.248

Area = 24.248*14/2 ≈ 169.74 ≈ 169.7

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:

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:

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:

D. both lines

Step-by-step explanation:

I am 100% sure! Please give brainiest!!!

Answer:

B

Step-by-step explanation:

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:

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 & Step-by-step explanation:

4(8 - 6)52 - 6 ÷ (-3)

First, subtract 6 from 8

4(2)52 - 6 ÷ (-3)

4(2)(52) - 6 ÷ (-3)

Multiply 2 by 52

416 - 6 ÷ (-3)

Divide -6 by -3.

416 + 2

Add 2 to 416

418

So, your evaluated answer would be 418.

Answer:

its 200+2

So addition is the last calculation to be done.

Step-by-step explanation:

Answer:

The correct answer is B!

Step-by-step explanation:

Answer:

its b

Step-by-step explanation:

Answer:

this is false because 5/18 is equivalent to 10/36

Answer:

√24

Step-by-step explanation:

4.89897948 will be the answer. Which is a number in between 4 and 5. Hope this helps :)

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:

Angle measure two is equal to 75º and Angle measure one is equal to 105º

Step-by-step explanation:

I know this because angle one is alternate exterior angle with angle 7 and angle seven forms a staight line with angle 75 so to find angle 7 you have to do 180-75 and that would equal 105.

for angle two it is interior angles with angle 75 so this means that are congruent angles which means they both have the same measure

Answer: <2 is 75 degrees & <1 is 105 degrees

Step-by-step explanation:

Answer:

A and B. increasing heart rate and positive correlation

Step-by-step explanation:

The heart rate increases as they drink more cups of coffee and because the both sets of data are increasing in the same direction, it's positive correlation.

Hope my answer helps and isn't too short <3

Answer: B AND D

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

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Answer:

R=6

Step-by-step explanation:

T+R+A=100

T=88 A=6 R=?

88+R+6=100

Move known numbers to other side

R=6

Answer:RT is congruent to WX

Step-by-step explanation:

Answer: RT

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

plug in 0 for x

0 * anything = 0 (cancels out the -2/9) and you're left with 1/3

Answer:

1. Triangular prism

2. Trapezoidal prism

3. Pentagonal prism

4. Hexagonal prism

Answer:

95

Step-by-step explanation:

Let x be the number of children

10x+35 = money

15x+5 = money

Set  the equations equal

10x+35 = 15x+5

Subtract 10x from each side

35 = 5x+5

Subtract 5 from each side

30 =5x

Divide by 5

30/5 =5x/5

6 =x

There are 6 children

10x+35 = money

10(6) +35

60+35

95

The amount of money is 95

Answer:

96

Step-by-step explanation:

Because math