x + y = 3, 4y = -4x - 4
System of Equations

The number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.

For the given situation,

Peter sold a cup of lemon juice = $1.25

Peter sold a cup of apple juice =  $2.50

Total number of cups sold = 155 cups

Total amount = $256

Let number of cup of lemon juice be x and

let number of cup of apple juice be y

The equations for the above statements are

[tex]x + y = 155 ------- (1)\\1.25x +2.50y = 256 ------- (2)[/tex]

From equation 1,

⇒ [tex]x=155-y[/tex]

Now substitute x in equation 2,

⇒ [tex]1.25(155-y)+2.50y=256[/tex]

⇒ [tex]193.75-1.25y+2.50y=256[/tex]

⇒ [tex]1.25y=256-193.75[/tex]

⇒ [tex]1.25y=62.25\\[/tex]

⇒ [tex]y=\frac{62.25}{1.25}[/tex]

⇒ [tex]y=49.8[/tex] ≈ [tex]50[/tex]

Now substitute y in equation 1,

⇒ [tex]x=155-50[/tex]

⇒ [tex]x=105[/tex]

Hence we can conclude that the number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.

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Answer:

x = (4,0)

y = (0,-4)

Step-by-step explanation:

x - y = 4

(0) - y = 4

-(-y) = -(4)

y = -4

x - (0) = 4

x = 4

x = (4,0)

y = (0,-4)

Answer:

x = 4 . 0

y = 0 . -4)

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

because is a ok yo12222122221112w

Answer:

Option C is correct

Step-by-step explanation:

[tex]3 + 11 + 13 = 27[/tex]

[tex]5 + 11 + 13 = 29[/tex]

[tex]2 + 7 + 19 = 28[/tex]

[tex] 2 + 5 + 13 = 20[/tex]

Answer:

(B)

Step-by-step explanation:

Can't explain lol, but that's the answer

Given:

30-hour review course average a score of 620 on that exam.

70-hour review course average a score of 749.

To find:

The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.

Solution:

Let x be the number of hours of review course and y be the average score on that exam.

30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).

70-hour review course average a score of 749. So, the linear function passes through the point (70,749).

The linear function passes through the points (30,620) and (70,749). So, the linear equation is:

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

[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x-30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]

[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]

Adding 620 on both sides, we get

[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]

[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]

We need to find the y-value for [tex]x=57[/tex].

[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]

[tex]y=183.825+523.25[/tex]

[tex]y=707.075[/tex]

[tex]y\approx 707.1[/tex]

Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.

Answer:

54°

Step-by-step explanation:

Here :-

Measure of 6 :-

Answer:

m<6 = m<2 = 54º

Step-by-step explanation:

13x + 9 + 5x + 9 = 180

18x + 18 = 180

18x = 180 - 18

18x = 162

x = 162 / 18

x = 9

13x + 9

13(9) + 9

126

180 - 126

54

m<6 = m<2 = 54º

Answer:

{0,-3,-9,5,7}

Step-by-step explanation:

range = all y values

function =(x,y)

so all the second values are ranges

Answer:

5:15 simplified as 1:3

Step-by-step explanation:

Answer:

p = 0

Step-by-step explanation:

1 - 4p - 2p = 1 - 5p

-6p + 1 = -5p + 1

-p + 1 = 1

-p = 0

p = 0

Answer:

C is the answer

Step-by-step explanation:

I'm sure it is

Answer:

see explanation

Step-by-step explanation:

To verify cos²A + sin²A = 1 with A = 90° , then

cos²90° + sin²90°

= (0)² + (1)²

= 0 + 1

= 1

Answer:

Step-by-step explanation:

Average rate of change is the same thing as the slope. This is a quadratic so the slope is not something that is constant like it is in a line. Here you have the x coordinates of 1 and 5; each one of these x coordinates has a y coordinate that goes with it. If we draw a line from one of these coordinates to another,  that line will have a slope. That is the slope we are trying to find. Thus, we need the y coordinates that go with each of these x coordinates. To do that, plug x into the equation and do the math to find y:

Let's start with x = 1.

f(1) = [tex]17-(1)^2[/tex] so

f(1) = 16 and the coordinate is (1, 16).

f(5) = [tex]17-(5)^2[/tex] so

f(5) = -8 and the coordinate is (5, -8). Now we apply the slope formula:

[tex]m=\frac{-8-16}{5-1}=\frac{-24}{4}=-6[/tex] So the answer is -6.

Answer:

9

Step-by-step explanation:

x = 1

y = 4

x + 2y = 1 + 8 = 9

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

9

Step-by-step explanation:

x + 2y

subtitute:

1 + 2(4)

simplify:

1 + 8 = 9

Answer:

The lengths of the other sides would be 10, as well.

Step-by-step explanation:

Since we already know two of the three angles, we can subtract to find the other angle. The interior angles of a triangle will always add up to 180°. We have 60° and 60°, giving us 120°. 180 - 120 is equal to 60°, so that's the missing angle. Because all of the angles are the same, this is an equilateral triangle, which means the sides also have to be the same length. If one of the sides is 10, all of the sides are 10.

The triangle with sides 10 , 10 and 10 and all angles at 60° is an equilateral triangle

An equilateral triangle is a triangle in which all three sides have the same length.

Let the triangle be ΔABC , and

∠A = ∠B = ∠C = 60° and AB = BC = CA

Given data ,

Let the triangle be represented as ΔABC

Let the side length of the triangle be AB = 10

Now , the measure of ∠ABC = 60°

And , the measure of ∠BAC = 60°

So , the total sum of all the angles in a triangle = 180°

And , the measure of ∠ACB = 180° - ( 60° + 60° ) = 60°

Therefore , all the angles of the triangle are 60°

So , it is an equilateral triangle

And , the measure of side lengths of the triangle is 10

Therefore , AB = BC = CA = 10

Hence , it is an equilateral triangle

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[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { f(-9)= 0.48}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]f(x) = \frac{2x + 3}{4x + 5} \\[/tex]

For [tex]f(-9)[/tex], put "[tex]-9[/tex]" for every value of "[tex]x[/tex]".

[tex]↬f( - 9) = \frac{2( - 9) + 3}{4( - 9) + 5}\\ [/tex]

[tex]↬ f(-9) = \frac{ - 18 + 3}{ - 36 + 5} \\[/tex]

[tex]↬ f(-9) = \frac{ - 15}{ - 31}\\ [/tex]

[tex]↬ f(-9)= \frac{15}{31}\\ [/tex]

[tex] ↬f(-9)= 0.48\\ [/tex]

[tex]\bold{ \green{ \star{ \red{Mystique35}}}}⋆[/tex]

[tex]\huge\textsf{Hey there!}[/tex]

[tex]\mathsf{f(x) = \dfrac{2x + 3}{4x + 5}}[/tex]

[tex]\mathsf{y = \dfrac{ 2x + 3}{4x + 5}}[/tex]

[tex]\mathsf{y = \dfrac{2(-9) + 3}{4(-9) + 5}}[/tex]

[tex]\mathsf{2(-9)}[/tex]

[tex]\mathsf{\bf = -18}[/tex]

[tex]\mathsf{y = \dfrac{-18 + 3} {4(-9) + 5}}[/tex]

[tex]\mathsf{-18 + 3}\\\mathsf{= \bf -15}[/tex]

[tex]\mathsf{y = \dfrac{ -15} {4(-9) + 5}}[/tex]

[tex]\mathsf{4(-9)}\\\mathsf{\bf = -36}[/tex]

[tex]\mathsf{y = \dfrac{-15}{-36 + 5}}[/tex]

[tex]\mathsf{-36 + 5}\\\mathsf{= \bf-31}[/tex]

[tex]\mathsf{y = \dfrac{-15}{ -31}\rightarrow\boxed{\bf \dfrac{15}{31}}}[/tex]

[tex]\boxed{\boxed{\huge\text{Answer: } \boxed{\bf f(-9) = \dfrac{15}{31}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

1452628383763637£838

Answer:

B

Step-by-step explanation:

Answer:

2 ( Option A )

Step-by-step explanation:

The given integral to us is ,

[tex]\longrightarrow \displaystyle \int_0^1 5x \sqrt{x}\ dx [/tex]

Here 5 is a constant so it can come out . So that,

[tex]\longrightarrow \displaystyle I = 5 \int_0^1 x \sqrt{x}\ dx [/tex]

Now we can write √x as ,

[tex]\longrightarrow I = \displaystyle 5 \int_0^1 x . x^{\frac{1}{2}} \ dx [/tex]

Simplify ,

[tex]\longrightarrow I = 5 \displaystyle \int_0^1 x^{\frac{3}{2}}\ dx [/tex]

By Power rule , the integral of x^3/2 wrt x is , 2/5x^5/2 . Therefore ,

[tex]\longrightarrow I = 5 \bigg( \dfrac{2}{5} x^{\frac{5}{2}} \bigg] ^1_0 \bigg) [/tex]

On simplifying we will get ,

[tex]\longrightarrow \underline{\underline{ I = 2 }}[/tex]

Answer:

A.

Step-by-step explanation:

A.-6r+6

Answer:

A: The y-intercept of f(x) is equal to the x-intercept of g(x)

Step-by-step explanation:

From the equation of f(x) given, we have;

f(x) = -4(1.09)^(x)

Now,the y-Intercept will be the point where x = 0.

Thus;

f(0) = -4(1.09)^(0)

f(0) = -4

Now,from the table given for g(x), we can see that at x = 0,g(x) = -4.

Thus,it means that the y-intercept of f(x) is equal to the x-intercept of g(x)

Answer:

1/2×d1×d2

=1/2× (4+4)(6+3)

=36

Answer:

4/9 of an hour (26.666 minutes)

Step-by-step explanation:

4 * x * 40/60 = 1

x * 160/60 = 1

x=60/160 = 6/16 = 3/8 (this is the rate for one worker)

~~~~~~~~~~~~~~~~

6 * (3/8) * x = 1

x = 4/9

Answer:

[tex]f(n) = \frac{32}{3}(\frac{3}{2})^n[/tex]

Step-by-step explanation:

Given

[tex]r = \frac{3}{2}[/tex]

[tex]f(5) = 81[/tex]

Required

The geometric sequence

A geometric sequence is represented as:

[tex]f(n) = ar^{n-1}[/tex]

Replace n with 5

[tex]f(5) = ar^{5-1}[/tex]

[tex]f(5) = ar^4[/tex]

Substitute values for f(5) and r

[tex]81 = a* (\frac{3}{2})^4[/tex]

Open bracket

[tex]81 = a* \frac{81}{16}[/tex]

Make a the subject

[tex]a = \frac{81 * 16}{81}[/tex]

[tex]a = 16[/tex]

So, the explicit function is:

[tex]f(n) = ar^{n-1}[/tex]

[tex]f(n) = 16 * (\frac{3}{2})^{n-1}[/tex]

Split

[tex]f(n) = 16 * (\frac{3}{2})^n \div (\frac{3}{2})[/tex]

Convert to multiplication

[tex]f(n) = 16 * (\frac{3}{2})^n * \frac{2}{3}[/tex]

[tex]f(n) = \frac{32}{3}(\frac{3}{2})^n[/tex]

Answer:

f(x) = 16*(3/2)^(x-1)

Step-by-step explanation:

right on edge

Answer:

C

Step-by-step explanation:

The scale factor is the ratio of corresponding sides, image to original, so

scale factor = [tex]\frac{XY}{AB}[/tex] = [tex]\frac{9}{45}[/tex] = [tex]\frac{1}{5}[/tex] → C

The scale factor will be equal to 1 / 5. the correct option is C.

The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.

In the given image all the angles are the same and the sides are dilated so the scale factor will be calculated as below,

Scale factor = Original size / dilated size

Scale factor = XY / AB

Scale factor = 9 / 45

Scale factor = 1 / 5

Therefore, the scale factor will be equal to 1 / 5. the correct option is C.

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five I think I am not sure

Step-by-step explanation:

???????? what is easy??

Answer:

72

Step-by-step explanation:

6*6 = 36

3*12 = 36

36 + 36 = 72