AB is parallel to DE
.
.
CO
Alicia noticed that:
ZwLx
Ly La
.
B
.
A
w
I
F
E
D
Note: Alicia used the following theorems:
When a transversal crosses parallel lines, alternate interior angles are congruent.
Vertical angles are congruent
Choose 1 answer
A.Angles that form a linear pair are complementary
B. when a transversal crosses parallel lines same side interior angles are congruent
C. when a transversal crosses parallel lines alternate exterior angles are supplementary
D. when a transversal crosses parallel lines corresponding angles are congruent to.

Answer: Eiko

Step-by-step explanation:

Eiko has the shortest time.

Base on the given ratio of quantity of sugar to number of cakes, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar

Ratio refers to a number representing a comparison between two named things or quantities. The ratio of sugar and cake is the comparison between the quantity of sugar used to make cake.

Find the ratio of quantity of sugar to number of cakes

Quantity of sugar : Number of cakes

71.1 g : 9 cakes = x : 4 cakes

71.1 / 9 = x / 4

71.1 × 4 = 9 × x

284.4 = 9x

x = 284.4 / 9

x = 31.6g of sugar

In conclusion, the quantity of sugar needed to bake 4 cakes is 31.6g of sugar

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THE SUM OF THE INNER ANGLES IS 180°

[tex](x - 7) + (2x - 8) + 90 = 180 \\ x - 7 + 2x - 8 + 90 = 180 \\ x + 2x = 180 + 7 + 8 - 90 \\ 3x = 105 \\ \frac{3x}{3} = \frac{105}{3} \\ x = 35[/tex]

OPTION C IS THE RIGHT ANSWER.

Answer:

y = (3/2)x + 3

Step-by-step explanation:

Point 1: (0, 3) Point: (2, 6)

            (x₁, y₁)          (x₂, y₂)

        y₂ - y₁        6 - 3            3

m = ------------ = ------------ = --------

        x₂ - x₁         2 - 0           2

y - y₁ = m(x - x₁)

y - 3 = (3/2)(x - 0)

y - 3 = (3/2)x

  +3               +3

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

y = (3/2)x + 3

I hope this helps!

when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.  Check the picture below.

[tex]\cfrac{x}{13}~~ = ~~\cfrac{11}{x}\implies x^2=(13)(11)\implies x^2=143\implies x=\sqrt{143}[/tex]

The amount which Mr. Jonas will have to repay after 4 years is $13,888 when the interest rate is 3% per year on a loan of $12,400.

According to the question,

We have the following details:

The amount of the loan or the principal amount = $12,400

Interest rate = 3% per year

Time = 4 years

Now, it is given that the interest is not a compound interest. So, the total interest can be found using the formula of simple interest.

Simple Interest (S.I.) = (Principal*rate*time)/100

S.I. = (12400*3*4)/100

S.I. = (12400*12)/100

S.I. = 148800/100

S.I. = $1,488

Now, the total amount Mr. Jonas have to repay will be the sum of the loan he has taken out and the simple interest after 4 years.

Total amount = Principal + S.I.

Total amount = 12400+1488

Total amount = $13,888

Hence, the total amount of loan Mr. Jonas has to repay is $13,888.

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Answer:

x= -11

It only has one solution.

Step-by-step explanation:

The variables a and b have a possible value of 7 and 11

The given parameters are

GCF(a, b)• LCM (a, b) = 77

As a general rule, the product of two numbers equals the product of the greatest common factor and the least common multiple of the numbers

This implies that

a * b = GCF(a, b)• LCM (a, b)

So, we have

a * b = 77

Express 77 as 7 * 11

a * b = 7 * 11

By comparison, we have

a = 7 and b = 11

Hence, the possible values are a = 7 and b = 11

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[tex]5x - 2y = 4 \\ 5x = 4 + 2y \\ \frac{5x}{5} = \frac{4 + 2y}{5} \\ x = \frac{4 + 2y}{5} ......(3)equation[/tex]

NOTE I AM SOLVING BY SUBSTITUTION

[tex]8( \frac{4 + 2y}{5} ) + 5y = - 10 \\ \frac{32 + 16y}{5 } + 5 y = - 10 \\ \frac{32 + 16y}{5} (5) + 5y(5) = - 10(5) \\ 32 + 16y + 25y = - 50 \\ 41y = - 50 - 32 \\ \\ \\ \\ 41y = - 82 \\ \frac{ - 41y}{41} = \frac{ - 82}{41} \\ y = - 2[/tex]

[tex]x = \frac{4 + 2( - 2)}{5} \\ x = \frac{4 - 4}{5} \\ x = \frac{0}{5} \\ x = 0[/tex]

ATTACHED IS THE SOLUTION

Answer: (0,-2)

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{5x-2y=4\ \ \ \ \ (1)} \atop {8x+5y=-10\ \ (2)}} \right.[/tex]

Multiply equation (1) by 5, and equation (2) by 2:

[tex]\displaystyle\\\left \{ {{25x-10y=20\ \ \ \ (3)} \atop {16x+10y=-20\ \ (4)}} \right.[/tex]

Add equations (3) and (4):

[tex]41x=0[/tex]

Divide both parts of the equation by 41:

[tex]x=0[/tex]

Let's substitute the value of x into equation (2):

[tex]8(0)+5y=-10\\0+5y=-10\\5y=-10[/tex]

Divide both parts of the equation by 5:

[tex]y=-2[/tex]

Thus, (0,-2)

Answer:

3/8 barrels / minute.

Step-by-step explanation:

Rate = fraction of barrel filled / time

        = 1/4 / 2/3

        = 1/4 * 3/2

        = 3/8.

the answer is T becouse T is the time which is what you get when distance is divided by 80 mph

By taking the 20 percent of £85 and adding that to the base salary, we can see that last week Brett earned £95

Here we need to work with percentages. We know that Brett wins a commission of 20% of sales.

So, if he sells a total amount of A (A is in dollars). Then what he gets is:

0.2*A

Where 0.2 is the decimal form of 20%.

Here we know that Brett wins £78 as a base, and last week he sell a total of £85, then the amount he gets by the commission is:

0.2* £85 =  £17

Adding that to the base he already earns each week, we get:

£78 +  £17 =  £95

In this way, we conclude that last week Brett earned £95

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We must know the following exponent rules to help us solve this question:

[tex]3^p=\dfrac{\sqrt[3]{9}}{3}[/tex]

⇒ Rewrite [tex]\sqrt[3]{9}[/tex] as [tex]9^\frac{1}{3}[/tex]:

[tex]3^p=\dfrac{(3^2)^\frac{1}{3}}{3}[/tex]

⇒ Multiply:

[tex]3^p=\dfrac{3^\frac{2}{3}}{3}[/tex]

⇒ Subtract:

[tex]3^p=3^{\frac{2}{3}-1}[/tex]

[tex]p=\dfrac{2}{3}-1\\\\p=-\dfrac{1}{3}[/tex]

[tex]p=-\dfrac{1}{3}[/tex]

The probability of picking an odd number ball in fraction form is; 6/11

We are told that a bag contains eleven balls labelled 1 through 11. These numbers are;

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. This is a total of 11 numbers.

The even numbers are a total of 5 while the odd numbers are a total of 6.

Now, the probability of selecting an odd number will be;

P(selecting odd number) = Number of possible odd numbers/Number of Total Numbers

Plugging in the relevant numbers gives;

P(selecting odd number) =  6/11

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The probability that none of these vehicles requires warranty service is 0.2824

The probability exactly one of these vehicles requires warranty service is

0.3766

The probability that exactly two of these vehicles require warranty service is 0.2301

The mean of this probability distribution is 1.2

Given, n=12, and the probability is 0.1, we use the binomial distribution formula to solve the probabilities:

[tex]P(X=0)=C^{n}_{x} } P^{x} Q^{n-x}[/tex]

The probability that none of these vehicles requires warranty service

[tex]P(X=0)=C^{12}_{0} } (0.1)^{0} (0.9)^{(12-0)}[/tex]

               =0.2824

The probability exactly one of these vehicles requires warranty service

[tex]P(X=1)=C^{12}_{1} } (0.1)^{1} (0.9)^{(12-1)}[/tex]

                =0.3766

The probability that exactly two of these vehicles require warranty service.

[tex]P(X=2)=C^{12}_{2} } (0.1)^{2} (0.9)^{(12-2)}[/tex]

               =0.2301

Compute the mean of this probability distribution

Mean = n*P, where n = 12, P=0.1

          =12*0.1

          =1.2

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Answer:

He will only afford to rent the car for 4 days, he will spend 160 dolars to just have the car for 4 days. Since he plan to drive 125 miles, the cost for the miles will be 10 dolars. So if we add 160 (4 days with the car) plus 10 (for the miles) it would give 170.

Step-by-step explanation:

Answer:

A) 2nd graph

Explanation:

The 1st graph shows a radical expression, where:

to find the inverse, replace f(x) with y, switch the x and the y, then solve for y. The only graph showing exponential growth is the 2nd graph (note how at 1 it's 1, at 2 it's 4, at 3 it will be 9, etc.)

We found the length of the other leg by using Pythagoras’ theorem y is equal to 21.0 centimeters when the length of one of its legs is 20.0 centimeters.

In this question we have to make an equation by using the right triangle's value which is given in the question,

by putting these values in the Pythagoras’ theorem.

As given, the hypotenuse of a right triangle = 29.0 centimeters.

The length of one of its leg = 20.0 centimeters

Now, by using Pythagoras’ theorem we will find the length of the other leg:

hypotenuse^2 = base^2 + perpendicular^2,

We put the value according as given in question:

29^2 = 20^2 + y^2

After finding the square of number of both side:

841 = 400 + y^2

Now we will rearrange this equation:

y^2 = 841 - 400  

y = 21 centimeters is the length of the other leg.

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Answer:

27x+50

Step-by-step explanation:

How to solve your problem

50 + 108x/4

Simplify

Cancel terms that are in both the numerator and denominator

50+ 108x/4

50+ 27x

Rearrange terms

50 + 27x

27x +50

=27x+50

Answer:the answer is b

Step-by-step explanation:

Answer:

gradient is 1/2  =  0.5

Step-by-step explanation:

y= 1/2 x−3

Swap sides so that all variable terms are on the left hand side.

1/2 x−3=y

Add 3 to both sides.

1/2 x=y+3

Multiply both sides by 2.

1/2 x = 1/2 y+3

​

Dividing by  1/2 undoes the multiplication by  1/2

x= 1/2 y+3

​

Divide y+3 by  1/2  by multiplying y+3 by the reciprocal of  1/2

​

.

x=2y+6

Answer: (6, -5)

Step-by-step explanation:

       The slope 2/3 means that there is a positive change of 2 in the y-value ( + 2) and a positive change in the x-value of 3 (+ 3) for every new point. To find another point on the line, we can add 2 to the y-value and 3 to the x-value.

    ➜ Slope is written as y over x

    ➜ Coordinate points are written as (x, y)

       (3, -7)

       (3 + 3, -7 + 2)

       (6, -5)

       We can also find a point on the line by graphing. See attached.

Answer:

y = 4x + - 9

Step-by-step explanation:

(3, 3), (4, 7)

(x₁, y₁)  (x₂, y₂)

        y₂ - y₁        7 - 3           4

m = ------------ = ------------ = ------- = 4

        x₂ - x₁         4 - 3           1

y - y₁ = m(x - x₁)

y - 3 = 4(x - 3)

y - 3 = 4x - 12

  +3          +3

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

y = 4x - 9

I hope this helps!

Notice that the slope of the line is equal to the speed

hence, the speed = 5 miles / hour

Rewrite 50% as 1/2

We need a fraction that is equal to 1/2 of 1/6.
-> That fraction equals to 1/2 x 1/6 = 1/12 (or 1/6 : 2)

Answer:

1/12

Step-by-step explanation:

1/6*100/50=1/12.

Answer:

1

Step-by-step explanation:

Anything to the power of 0 is 1 except for 0.  If the base is o, the answer is undefined.  It is will dividing by 0.  That is also undefined.

Answer:

-10degree

Step-by-step explanation:

because the 0 is the degree

∠K , ∠1 and ∠JKL  are the three names of the angle 1 indicated by red color in the figure given in the question.

We need to select three names of the angle 1 indicated by red color in the figure given in the question . We are provided with the following options ∠JLK , ∠K , ∠LJK , ∠1 , ∠JKL and ∠J .  

∠JLK is not similar to ∠1 .  ∠K and  ∠1  are same angle. ∠LJK is not similar to ∠1 . ∠JKL and  ∠1  are same angle.  ∠J and ∠1 are different angles. So, we can finally conclude that the three names of the angle 1 indicated by red color in the figure given in the question are ∠K , ∠1 and ∠JKL .

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