How many solutions does this system of equations have?

y=-2x+2
2y+4x=4

Answer: Noelle's age is 20 years

Noelle's father is 54 years

Step-by-step explanation: First of all, let Noelle's age be represented by x. Given that her father's age is 6 less than three times her age, her father's age would be expressed as

3n - 6

Note also that their ages sum up to 74.

Therefore,

n + (3n - 6) = 74

n + 3n - 6 = 74

4n - 6 = 74

Add 6 to both sides of the equation

4n = 80

Divide both sides of the equation by 4

n = 20

Hence, Noelle's father's age is 54 (that is 3n - 6)

While Noelle's age is 20

Noelle’s age is 20

her dads age is 54

Answer:

The mid point of the line segment is [tex]$ \bigg(- \frac{3}{2}, -\frac{3}{2} \bigg ) $[/tex].

Step-by-step explanation:

From the graph we can find the end points of the line segment. The end points are: [tex]$ (- 1, - 4) $[/tex] and [tex]$ (4, 1) $[/tex].

When the end points of a line segment are known, the mid point of the line segment is given by:

                                   [tex]$ \bigg ( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg ) $[/tex]

where [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are the end points.

Here: [tex]$ (x_1, y_1) = (- 1, - 4) $[/tex] and [tex]$ (x_2, y_2) = (4, 1) $[/tex]

Therefore, the mid point of the line segment would be:

[tex]$ \bigg ( \frac{- 1 + 4}{2}, \frac{- 4 + 1}{2} \bigg) $[/tex]

[tex]$ \bigg(- \frac{3}{2}, -\frac{3}{2} \bigg ) $[/tex] is the required answer.

A compound is a unique substance that forms when two or more elements combine chemically. It always has the same elements in the same proportions.

Answer:

y=-x+7

Step-by-step explanation:

every year she goes down how many times she is younger than him by 1 so -x is actually -1x, and it starts at 7 years so we put that as our y intercept

Step-by-step explanation:

[tex] \triangle \: ABC \cong \triangle \: FED[/tex]

Here, all the sides or angles of triangle ABC are congruent to the corresponding sides or angles of triangle FED. As both triangles are reflections of each other.

Answer:9.4 miles

Hope this helps

Answer:

(2,  5 )

Step-by-step explanation:

Given a quadratic in standard form : y = ax² + bx + c : a ≠ 0

Then the x- coordinate of the vertex is

[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]

y = 3x² - 12x + 17 ← is in standard form

with a = 3 and b = - 12, thus

[tex]x_{vertex}[/tex] = - [tex]\frac{-12}{6}[/tex] = 2

Substitute x = 2 into the function for corresponding value of y

y = 3(2)² - 12(2) + 17 = 12 - 24 + 17 = 5

vertex = (2, 5 )

Answer:

0.097

move your decimal to the left twice

Answer:

[tex]c=5.1\ units[/tex]

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Find the measure of angle B

we know that

In the right triangle ABC

[tex]m\angle A+m\angle B=90^o[/tex] ---> by complementary angles in a right triangle

we have

[tex]m\angle A=35^o[/tex]

substitute

[tex]35^o+m\angle B=90^o[/tex]

[tex]m\angle B=90^o-35^o=55^o[/tex]

step 2

Find the length side c

Applying the law of sines

[tex]\frac{c}{sin(C)}=\frac{b}{sin(B)}[/tex]

substitute the given values

[tex]\frac{c}{sin(90^o)}=\frac{4.2}{sin(55^o)}[/tex]

[tex]c=\frac{4.2}{sin(55^o)}=5.1\ units[/tex]

Answer:

112

Step-by-step explanation:

Given: Joe gave 1/4 of his total candies to his classmate.

            Then, he gave 4/6 of when he had left to his brother.

             He gave 25% of the remaining candies to his sister.

             Finally, he only had 21 candies left.

Lets assume the total number of candies at the beginning be "x".

First, finding the number candies left after giving candies to classmate.

∴ Remaining candies=  [tex]x- x\times \frac{1}{4}[/tex]

Solving it to find remaining candies after giving candies to clasmate.

⇒ Remaining candies= [tex]x-\frac{x}{4}[/tex]

Taking LCD as 4

⇒ Remaining candies= [tex]\frac{4x-x}{4} = \frac{3x}{4}[/tex]

∴ Remaining candies after giving candies to clasmate= [tex]\frac{3x}{4}[/tex]

now, finding the candies left after giving candies to his brother.

∴ Remaining candies= [tex]\frac{3x}{4} - \frac{3x}{4} \times \frac{4}{6}[/tex]

Solving it to find the remaining candies after giving candies to his brother.

⇒ Remaining candies= [tex]\frac{3x}{4} - \frac{x}{2}[/tex]

Taking LCD 4

⇒ Remaining candies= [tex]\frac{3x-2x}{4} = \frac{x}{4}[/tex]

∴ Remaining candies after giving candies to his brother= [tex]\frac{x}{4}[/tex]

We know, Joe was left with only 21 candies after giving candies to his sister.

Therefore, putting an equation for remaining candies to find the number of candies at the beginning.

⇒[tex]\frac{x}{4} - 25\% \times \frac{x}{4} = 21[/tex]

⇒[tex]\frac{x}{4} - \frac{0.25x}{4} = 21[/tex]

Taking LCD 4

⇒ [tex]\frac{x-0.25x}{4} = 21[/tex]

⇒ [tex]\frac{0.75x}{4} = 21[/tex]

Multiplying both side by 4

⇒[tex]0.75x= 21\times 4[/tex]

dividing both side by 0.75

⇒[tex]x= \frac{21\times 4}{0.75}[/tex]

∴[tex]x= 112[/tex]

Hence, Joe had 112 candies at the beginning.

x = 14 and y = 10

Two shapes are similar if they have the same form but not necessarily the same size. In other words, when shapes are similar they are in proportion. Since you haven't provided any diagram, I'll choose two irregular polygon that are similar as indicated in the figure below. So we can calculate both x and y with proportions as follows:

[tex]For \ x: \\ \\ \frac{x}{7}=\frac{16}{8} \\ \\ x=\frac{7\times 16}{8} \\ \\ x=14 \\ \\ \\ For \ y: \\ \\ \frac{y}{20}=\frac{8}{16} \\ \\ y=\frac{8\times 20}{16} \\ \\ y=10[/tex]

Translation: https://brainly.com/question/11131466

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Answer:

The solution to the system of equations given is (3, 2)

Step-by-step explanation:

Let's solve the system of equations given:

2y = 4  

-x = -3

****************

2y = 4

y = 4/2

y = 2

____________________

-x = - 3

x = 3

The solution to the system of equations given is (3, 2)

The solution to the system of equations is x = 3 and y = 2.

To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the substitution method.

From the first equation, we can solve for y:

2y = 4

y = 4/2

y = 2

Now, substitute this value of y into the second equation:

-x = -3

x = 3

So the solution to this system of equations is x = 3 and y = 2.

Answer:

k = 6.

Step-by-step explanation:

k = 6

2k = 12

12 - 6 - 3 = 3

k = 1

2k = 2

2 - 6 - 3 = -7

So, the answer is k = 6 because it makes more sense.

Answer- You can get 10 Small rafts

12 x 100+ 1200

1600-1200=400

400/40 =10 Rafts

A linear equation representing the given situation and the number of small rafts is required.

The required equation is [tex]100x+40y=1600[/tex]

The number of small rafts will be [tex]10[/tex]

Cost of one large raft = $100

Cost of one small raft = $40

Total amount to spend = $1600

Let the number of large rafts be [tex]x[/tex]

and small rafts be [tex]y[/tex]

The equation will be

[tex]100x+40y=1600[/tex]

The number of large rafts [tex]x=12[/tex]

[tex]100\times 12+40y=1600\\\Rightarrow y=\dfrac{1600-100\times 12}{40}\\\Rightarrow y=10[/tex]

Learn more:

https://brainly.com/question/8449665

https://brainly.com/question/16135223

Amil's unit rate is calculated by dividing the distance traveled (15 miles) by the time in hours (0.917 hours), resulting in approximately 16.36 mph. Abe's unit rate is faster but cannot be precisely determined without more information about his distance or time.

Amil rode 15 miles in 55 minutes. To find Amil's unit rate, we divide the total distance by the total time. The unit rate is a measure of speed, indicating how many miles are traveled in one minute. To find this unit rate, we perform the following calculation:

Convert the time from minutes to hours to find the unit rate in miles per hour (mph), since speed is often expressed this way: ​55 minutes × (1 hour/60 minutes) = 0.917 hours

Divide the distance by the time: 15 miles ÷ 0.917 hours = 16.36 mph (rounded to two decimal places).

Amil's unit rate is approximately 16.36 mph. This information can be used to estimate Abe's unit rate, knowing that Abe rode at a faster rate. If we knew how far Abe rode or his unit rate in miles per minute, we could compare the two directly. Without additional information about Abe's distance or time, we can only say that Abe's unit rate exceeds 16.36 mph.

Answer:

Yes 60 is the answer

Step-by-step explanation:

Multiply the numbers in the bracket

Then multiply by 5

Answer:

Step-by-step explanation: 5×(3×4) =60

5×(12) =60

5×12 =60

Answer:

10  20 40

Step-by-step explanation:

Step-by-step explanation:

Given, Total number of students is 80.

and 30% of the total students take a car to school

30% of 80

[tex]=\frac{30}{100}\times 80[/tex]

=24

Therefore 24 students take a car to school.

Answer:

24 students take a car to school

Answer:loss 20

Step-by-step explanation:

She lost 20

Step-by-step explanation:

60 take away 40 is 20

Answer: No

Step-by-step explanation:

5 + 1/2 = 5 1/2

Answer:

1) x = -4

2) x = 21

Step-by-step explanation:

6x = -24

6/6x=-24/6

x=-4

and

x/7 = 3

x/7*7=3*7

x=21

Answer:

Here, the coordinates aren't telling special characteristic of any shape, so it would be Paralleogram

In short, Your Answer would be Option B

Step-by-step explanation:

Hey there! I'm happy to help!

We have a room that is 22 by 17 feet. We know that for every foot, we draw a 1/2 inch. This means that we need multiply our dimensions by 1/2 to find the dimensions of the drawing.

22×1/2=11

17×1/2=8.5

Therefore, the dimensions of the room are 11 feet by 8.5 inches. These are the dimensions of a normal white paper!

Have a wonderful day! :D

To convert the actual room dimensions of 22 feet by 17 feet to a scale drawing with a scale of 1/2 inch equals 1 foot, the length becomes 11 inches, and the width becomes 8.5 inches in the drawing.

When creating a scale drawing, the dimensions of the actual room need to be converted into scale dimensions. According to the scale given, which is 1/2 inch equals 1 foot, the actual room dimensions of 22 feet by 17 feet should be converted using this scale ratio.

To do this conversion, each actual dimension must be divided by the scale factor. The scale factor is determined by the number of feet that are represented by 1/2 inch. Since 1/2 inch is equivalent to 1 foot, the scale factor is 1 foot per 1/2 inch. Therefore, we calculate the dimensions as follows:

Length: 22 feet / 1 foot per 1/2 inch = 22 x 1/2 inches = 11 inches

Width: 17 feet / 1 foot per 1/2 inch = 17 x 1/2 inches = 8.5 inches

Thus, the dimensions on the scale drawing for a room that is 22 feet by 17 feet would be 11 inches by 8.5 inches.

Answer:

4

Step-by-step explanation:

U will add 5 plus 3 and then divide 8 by 2

Answer:4

Step-by-step explanation:

I think it might be D

The size of the sample space is the total number of possible outcomes. For example, when you roll 1 die, the sample space is 1, 2, 3, 4, 5, or 6. So the size of the sample space is 6. Then you need to determine the size of the event space.

Answer:

I think it's the last one

Step-by-step explanation:

To solve the equation 4r + 8 + 5 = -15 - 3r, combine like terms and isolate the variable r leading to the solution r = -4.

The student is asking how to solve the algebraic equation 4r + 8 + 5 = -15 - 3r. To solve for r, we must first simplify and combine like terms. This means we need to get all the terms with r on one side of the equation and the constant numbers on the other side.

Therefore, the solution to the equation is r = -4.

Final answer:

The solution to the equation 4r + 8 + 5 = -15 - 3r is r = -4.

Explanation:

The algebraic equation provided by the student is 4r + 8 + 5 = -15 - 3r.

To solve for r, we must first simplify and rearrange the equation by combining like terms and moving the variables to one side and the constants to the other.

By subtracting 3r from both sides and also subtracting 8 + 5 from both sides, we end up with 4r + 3r = -15 - 8 - 5. Simplifying further, we get 7r = -28.

Finally, dividing both sides by 7 yields r = -4.

Answer:

12%

Step-by-step explanation:

There are a total of 175 units in an apartment complex.

Out of which, 154 units are occupied.

Now, we have to find the percentage of the apartment which are unoccupied.

So, the number of units that are not occupied is (175 - 154) = 21.

Hence, the percentage of the number of unoccupied units of the apartment complex will be [tex]\frac{21}{175}\times 100 \% = 12 \%[/tex] (Answer)