Which function passes through the points (2, 15) and (3, 26)? A. y = 11x + 7 B. y = 11x − 7 C. y = 7x + 11 D. y = -11x − 7 E. y = 7x − 11

The given condition is- A bottle contains 20% milk and the rest water. The bottle has 1 liter of water.

Part A:

Let the amount of mixture in the bottle be = x ; mixture will be amount of water plus milk

Given is- the bottle has 1 liter of water and 20% is milk. 20% is 0.2

Hence equation will be:

[tex]0.2x+1 =x[/tex]

Part B:

Solving the equation

[tex]x-0.2x=1[/tex]

[tex]0.8x=1[/tex]

[tex]x=\frac{1}{0.8}[/tex] = 1.25

Hence, total mixture is 1.25 liters.

Water is 1 liter so milk will be = [tex]1.25-1=0.25[/tex]

Or it can also be solved using milk percentage of 0.2%

[tex]0.2*1.25=0.25[/tex]

Hence, milk is 0.25 liter

The expression for the cost of the ABC Book Club is 2x + 40.  The expression for the cost of the Easy Book Club is 3x + 35.  To find when the total charge for both book clubs is equal, the two expressions must equal each other. (x = the number of books read)

2x + 40 = 3x + 35

Subtract 35 from both sides.

2x + 5 = 3x

Subtract 2x from both sides.

5 = x

So, the total charge for each club is equal when 5 books are read.

The number of books read from both ABC and Easy book clubs must be 5 in other to have a equal monthly charge.

Let the number of books read = b

ABC Book club :

Monthly charge = $40

Fee per book read = $2

Total monthly charge = 40 + 2b - - - - (1)

Easy Book Club :

Monthly charge = $35

Fee per book read = $3

Total monthly charge = 35 + 3b - - - (2)

To obtain an equal monthly charge ;

Equation(1) = Equation(2) and solve for b

40 + 2b = 35 + 3b

40 - 35 = 3b - 2b

5 = b

Hence, to have an equal monthly charge, the number of books read from each club must be 5.

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To determine how many bottles of soda are needed for 12 bowls of punch, we use the given ratio of 7 bowls to 5 bottles and set up a proportion. We find that 9 bottles of soda are needed for 12 bowls of punch.

The question asks us to figure out how many bottles of soda we need to make a larger amount of punch based on a known ratio. Since it is given that 7 bowls of punch require 5 bottles of soda, we can set up a proportion to find out how many bottles of soda we need for 12 bowls of punch. To do this, we use the initial ratio (7 bowls/5 bottles) and set it equal to the desired ratio (12 bowls/x bottles), where x represents the unknown number of bottles needed for 12 bowls.

We can solve for x by cross-multiplying and dividing:

Set up the proportion: (7 bowls / 5 bottles) = (12 bowls / x bottles)

Cross-multiply: 7 * x = 5 * 12

Simplify: 7x = 60

Divide both sides by 7: x = 60 / 7

Since 60 divided by 7 is not a whole number, we round up, because you can't have a fraction of a bottle in this context. Therefore, x
= 9 bottles (rounded up from 8.57)

So, we would need 9 bottles of soda to make 12 bowls of punch.

Answer:

Your answer choice is appropriate

Step-by-step explanation:

The orientation is vertical, so the parent function is

... y² - x² = 1

The vertical offset is -3 and the horizontal offset is positive, so the variables will be of the form (y+3)² and (x-something)². At this point, you're able to choose the correct answer.

The distance center to vertex is 13, so we know the y-term denominator is 13². We cannot tell from this graph what the x-term denominator should be, but all the answer choices are in agreement that it should be 81.

The appropriate choice is ...

... (y+3)²/169 - (x-2)²/81 = 1

Answer:

If you are looking for the answer to a graph that looks similar but slightly different, the answer is C.

This graph looks like the one above, but it is inverted, the top hyperbola reaches 15, and the bottom reaches 10. This is correct for A.P.E.X

Hope this helps I couldn't find it anywhere else on brainly.

For the graph of given function ,

At x=2, the graph crosses x axis

At x=-6, the graph touches x axis

At x=-12, the graph crosses x axis

Given :

Equation of a function  [tex]f\left(x\right)\:=\:\left(x\:-\:2\right)^3\left(x\:+\:6\right)^2\left(x\:+\:12\right)\:[/tex]

Lets find out the roots and analyze

lets set each factor =0 and solve for x

Exponent in each factor tell us the multiplicity . Using multiplicity we check whether crosses or touches x axis

When multiplicity is odd then graph crosses x axis .

when multiplicity is even then graph touches x axis.

[tex]f\left(x\right)\:=\:\left(x\:-\:2\right)^3\left(x\:+\:6\right)^2\left(x\:+\:12\right)\:\\(x-2)^3= 0\\x-2=0\\x=2[/tex]

Root is x=2  with multiplicity 3. 3 is odd

At x=2, the graph crosses x axis

[tex](x+6)^2=0\\x+6=0\\x=-6[/tex]

At x=-6, multiplicity is 2 that is even .

At x=-6, the graph touches x axis

[tex]x+12=0\\x=-12[/tex]

x=-12  with multiplicity 1. 1 is odd

At x=-12, the graph crosses x axis

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One

Slope

The general slope intercept equation for a line is

y = mx + b

If you are told outright what the slope is then you can write m = slope in this case - 3

So you have so far is y = -3x + b. Now you use the point to get the y intercept.

(2,5) means that when x = 2, y = 5. that allows you to solve for b

Y intercept

When x = 2, y = 5. Substitute that into the general equation with the slope.

5 = -3x + b            Put 2 in for x

5 = -3 * 2 + b         Multiply -3 * 2

5 = - 6 + b             Add 6 to both sides

5 + 6 = b

11 = b

Answer

y = -3x + 11

Two

This question is a little harder. You have to find the slope.

Slope Formula

[tex]\text{m = } \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

Givens

Points (2, -1), (-6, - 5)

y2 = -1 ; y1 = -5; x2 = 2;  x1 = -6

Solve

m = (-1 - - 5)/(2 - - 6) = (-1 + 5)(2 + 6) = 4/8 = 1/2

Now find the y intercept. Use either one of the given points

(2,-1) when x = 2, y = - 1

y = 1/2 x + b      Show what you have so far. Put in x = 2 for x and y = - 1 for y

-1 = 1/2(2) + b    Multiply 2*1/2

-1 = 1 + b            Subtract 1 from both sides.

-1 -1 = b

- 2 = b

Answer

y = (1/2)x - 2 which is D

Lea spends $134 on model cars and paint.

To find out how much Lea spends on model cars and paint, we need to calculate the total cost of each item and then add them together. The cost of 6 model cars is 6 x $15 = $90. The cost of 4 bottles of paint is 4 x $11 = $44. Adding these two amounts together, Lea spends $90 + $44 = $134 on model cars and paint.

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1. If the intersection of two lines is a point, then they intersect. = Converse

2. If two lines do not intersect, then their intersection is not one point. = Inverse

3. If the intersection of two lines is not one point, then the two lines do not intersect. = Contrapositive

I did the assignment already, it's correct.

The conditional statement 'If two lines intersect, then their intersection is one point' is matched with three possible related statements.

The conditional statement 'If two lines intersect, then their intersection is one point' can be matched with the following:

If the intersection of two lines is a point, then they intersect

If two lines do not intersect, then their intersection is not one point

If the intersection of two lines is not one point, then the two lines do not intersect

Explanation:

This question is about conditional statements related to the geometric properties of lines. The given statement is that if two lines intersect, their intersection is exactly one point. Statement 1 is the converse, meaning if their intersection is a point, then the lines must intersect. Statement 2 is the contrapositive, asserting that if two lines do not intersect, they can't have a single intersection point. Statement 3 reason that if the intersection is not exactly one point, then they do not intersect at all.

Imma guess the middle one

Answer:

B

Step-by-step explanation:

A 7th grade student will be absent approximately 0.4 times during the month.

To find out how many times a 7th grade student will be absent during the month, we first need to determine the average number of absent students per day for each grade. The total number of absent students across all grades is 5 + 8 + 9 = 22. Since there are 20 school days in a month, the average number of absent students per day is 22 / 20 = 1.1.

Next, we need to determine the proportion of absent students that are 7th graders. The 7th graders had 8 absent students, so their proportion of absent students is 8 / 22 = 0.3636 (rounded to four decimal places).

Finally, to find out how many times a 7th grade student will be absent during the month, we multiply the average number of absent students per day (1.1) by the proportion of absent students that are 7th graders (0.3636). This gives us the final answer of approximately 0.39996 (rounded to five decimal places) or about 0.4 times.

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The slope is [tex]m=\dfrac{\Delta y}{\Delta x}[/tex]

We have slope m = 3.

[tex]m=3=\dfrac{3}{1}[/tex]

3 > 0 - up 3 units

1 > 0 - right 1 unit

Answer in attachment.

What's the equation?

Without knowing the specific equation, it's difficult to definitively judge the student's conclusion. Assuming the equation is correctly simplified, if both sides of the equation are identical, then it has infinitely many solutions.

The student's claim about the equation having infinitely many solutions is valid only if, upon reducing the equation to its simplest form, both sides are completely identical. Unfortunately, without knowing the specific equation in question, it's impossible to precisely identify whether the conclusion is correct or not.  However, if we assume the student has correctly simplified the equation and found that both sides match exactly, then we can say that statement C: 'The conclusion is correct because when simplified, both sides of the equation are equivalent' is valid.

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There are multiple ways that you could graph this quadratic equation. I would start by finding the vertex. The x-value in the vertex is found with -b/2a. The take you value and input back into the equation to find the y-value of your vertex. Then, you could make a list of points on both sides of the vertex to create a table with which to create the parabola.

Answer:

Step-by-step explanation:

is equal 45

Final answer:

The area of the flour tortilla with a 14-centimeter radius is approximately 615.75 square centimeters.

Explanation:

The area of a circle is given by the formula A = πr², where r is the radius. Given a 14-centimeter radius, the area of the flour tortilla would be:

A = π(14 cm)² = 196π cm² ≈ 615.75 cm²

Thus, the area of the flour tortilla is approximately 615.75 square centimeters.

The total interest accrued on two credit cards in the first month is $28.44, with $19.51 coming from the first card with a balance of $3,745 at 6.25% APR and $8.93 from the second card with a balance of $1,045 at 10.25% APR based on a credit score of 500.

The question involves calculating the total interest accrued on two credit cards in the first month. The first credit card has a balance of $3,745.00 at an annual percentage rate (APR) of 6.25%, and the second credit card has a balance of $1,045.00 with an APR that depends on the credit score. Given a credit score of 500, the APR for the second card is 10.25% (per the provided table).

First, to find the monthly interest for each card, we can use the formula: Monthly Interest = (Balance) x (APR) / 12 months.

For the first card: Monthly Interest for $3,745.00 at 6.25% APR is ($3,745.00) x (0.0625) / 12 = $19.51.

For the second card: Monthly Interest for $1,045.00 at 10.25% APR is ($1,045.00) x (0.1025) / 12 = $8.93.

To find the total interest accrued from both credit cards in the first month, simply add the monthly interest amounts from each card: $19.51 + $8.93 = $28.44.

ANSWER

[tex]x=-6y-\frac{21}{2} [/tex]

EXPLANATION

We have

[tex]\frac{2}{3}x +4y=-7[/tex].

Expressing  [tex]x[/tex]  in terms of  [tex]y[/tex] means we should rewrite the relation such that  [tex]x[/tex]  will remain on one side of the equation while  [tex]y[/tex]  and any other constant will be at the other side.

To make [tex]x[/tex] the subject, we add [tex]-4y[/tex] to both sides of the equation.

[tex]\frac{2}{3}x =-4y-7[/tex].

we now multiply the whole equation by the reciprocal of the coefficient of [tex]x[/tex], which is [tex]\frac{3}{2}[/tex].

This implies that;

[tex]\frac{3}{2} \times \frac{2}{3} x=\frac{3}{2} \times (-4y)-\frac{3}{2} \times 7[/tex]

This simplifies to;

[tex]x=-6y-\frac{21}{2} [/tex]

Here we will use the formula of compound interest which is as follows:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

Where,

A=amount

P=principal

r=rate of interest

n=number of times interest is compounded in a year

t=time

We are given,

r=2% or 0.02

t= 5 years

n =4( compounded quarterly)

A= $300

Let us plug these in the formula to find Principal

[tex]300=P(1+\frac{0.02}{4})^{4*5}[/tex]

[tex]300=P(\frac{4.02}{4})^{4*5}[/tex]

[tex]300=P(1.005)^{20}[/tex]

[tex]300=P(1.105)[/tex]

Principal = $271.49

Answer: Mark earned $271.49 during odd jobs.

To calculate the original amount Mark earned, the compound interest formula is used with the given interest rate, compounding frequency, future amount, and time period. After solving for the principal amount, it's determined that Mark originally earned approximately $271.73.

In order to determine how much Mark originally earned, we need to use the formula for compound interest which is A = P(1 + r/n)^(nt), where:

Given that the final amount A is $300.00, the annual interest rate r is 2%, the interest is compounded quarterly (so n is 4), and the time t is 5 years, we can plug these values into the formula and solve for P:

300 = P(1 + 0.02/4)⁴*⁵

300 = P(1 + 0.005)²⁰

300 = P(1.005)²⁰

To find P, we divide both sides by (1.005)²⁰:

P = 300 / (1.005)²⁰

Using a calculator, we can find that:

P ≈ 300 / 1.10408

P ≈ 271.73

Therefore, Mark originally earned approximately $271.73 doing odd jobs last summer.

-2x + 6y = -38   ⇒   3(-2x + 6y = -38)   ⇒   -6x + 18y = -114

3x  - 4y  = 32   ⇒    2(3x  - 4y  = 32)   ⇒    6x - 18y =   64

                                                                              0   =   50

                                                                                 FALSE

False statement means there are no solutions.

Answer: No Solution

We will solve this system with method of opposing coefficients - Gaussian algorithm

-2x+6y= -38

3x-4y= 32

We will divide first equation with number 2 and get

-x+3y = - 19

then we will multiply the same equation with number 3 and get

-3x+9y = - 57

We will overwrite the second equation below the last one and get next equivalent system

-3x+9y = - 57

 3x-4y = 32

We add first equation to the second and get

5y = -25 => y= -25/5 => y= -5

Now we will replace variable y= -5 in the equation -x+3y = - 19 and get

-x+3(-5) = -19 => -x-15 = -19 => x- 19-15=4 => x=4

The correct answer is (x,y) = (4,-5)

We can check in the first equation and get

-2*4+6*(-5) = -38

-8-30 = -38

-38 = -38  We get equality, the solutions are correct.

This system have one real solution.

Good luck!!!

Answer:

Ac and ad

Step-by-step explanation:

The following are opposite rays; AC and AD. so option B is correct answer.

For points to be collinear means they lie on the same line. A rays to be opposite, they should be in the same line making a 180° or a straight line with each other.

A Coplanar means the points lie in the same plane. For these rays to be opposite and collinear the points should lie in the same plane.

Given; Points c, a and b are collinear.

A, B, C are coplanar and also A, B, C are collinear.

The following are opposite rays; AC and AD. so option B is correct answer.

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Elizabeth had to save $280 each month.

The correct option is (2).

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics.

As per the given data:

The annual tuition at a public two-year college last year was $3,200.

Expected growth in the tuition fee = 5%

We have to find the amount Elizabeth should have saved monthly during the previous year to pay her tuition fees.

For finding the increase in tuition fee:

= 5% of 3200

= (5/100) × 3200

= $160

Tuition fees after growth = 3200 + 160 = $3360

Amount Elizabeth had to save each month = Tuition fees after growth/12

= 3360/12

= $280

Elizabeth had to save $280 each month.

Hence, Elizabeth had to save $280 each month.

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C . Find a point that lies in the shaded region, or plug the points in and determine which point makes the inequality true.

If Jill pays with a credit card, her payment will be recorded immediately. This means that the item could be shipped almost as soon as she pays for it. On the other hand, if she uses a check or money order, then her payment will take a while to be received, as she would have to send the physical item over the mail. Therefore, she would receive her package earlier if she paid with a credit card.

The equation of the line that passes through the point (–1, 1) and has a slope of –2 is y = -2x - 1.

The question is asking for the equation of the line that passes through the point (–1, 1) and has a slope of –2. The formula for a line is y = mx + b, where m is the slope and b is the y-intercept. Since we know the slope (m) is -2, and we have the coordinates of a point on the line (-1,1), we can substitute these values into the formula to solve for 'b', the y-intercept.

So, 1 = -2*(-1) + b, which simplifies to 1 = 2 + b. Solving this for b gives us a y-intercept (b) of -1.

Therefore, the equation of the line that contains the given point and has the given slope is y = -2x - 1.

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14|x| - 14 = 41      |add 14 to both sides

14|x| = 55      |divide both sides by 14

|x| = 55/14 ↔ x = - 55/14 or x = 55/14

First day temperature is 0 degree.

Second day temperature is 3 degree higher than first day's temperature.

In order to find the higher temperature we need to add increased temperature in previous day's temperature.

First day given temperature is 0 degree .

Three degree higher than 0 would be 0+3.

On adding 0 and 3 we would get 3.