does the equation 7x-4y=0 represent a direct variation? what is the constant of variation?

ΔABC and ΔACD are similar. Therefore the sides are in proportion:

[tex]\dfrac{y}{7}=\dfrac{7}{6}[/tex]            multiply both sides by 7

[tex]y=\dfrac{49}{6}\\\\\boxed{y=\dfrac{1}{6}}[/tex]

Question

Anna picked 37 apples . She divided the apples equally among 7 baskets. How many apples are in each basket? How many are leftover?

Answer:

Step-by-step explanation:

37 : 7 = 5 (2 left over)

check

(7 * 5) + 2 = 37

better solution in the picture

Answer:

5 apples in each basket with 2 left over

Step-by-step explanation:

37/7 =5 R 2

brainliest pls

Answer:

4/3 or D

Step-by-step explanation:

Let's get this equation into y=mx+b form.

m=slope b=y-int

Subtract 5 from both sides to isolate y on a side.

4x-6=3y

Divide both sides by 3 to isolate y on one side.

(4/3)x-2=y

y=(4/3)x-2

m=4/3

b=-2

So our slope is 4/3

Answer:

x = -3/7

Step-by-step explanation:

We are given the following equation for which we have to solve for x:

[tex]3(3x - 1) + 2(3 - x) = 0[/tex]

So we will start by expanding the equation by multiplying the common factor with the brackets to get:

[tex]9x-3+6-2x=0[/tex]

Arranging the like terms together (variables on one side of the equation and constants on the other side) to get:

[tex]9x-2x=3-6\\\\7x=-3\\\\x=-\frac{3}{7}[/tex]

Therefore, x = -3/7.

Answer:

Step-by-step explanation:

The first four terms of geometric series is:

[tex]a,ar,ar^2,ar^3[/tex]

Since, we have given information that the third number is greater than 44 that means:

[tex]ar^2=a+44[/tex]

Above equation can be rewritten as:

[tex]a(r^2-1)=44[/tex]

Now, using:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

Here, a=r,b=1

[tex]a(r+1)(r-1)=44[/tex]        (1)

The sum of first four terms is:

[tex]a+ar+ar^2+ar^3=220[/tex]

[tex]a(1+r+r^2+r^3)=220[/tex]

[tex]a(1(1+r)+r^2(1+r))=220[/tex]

[tex]a((1+r)(1+r^2))=220[/tex]      (2)

Divide equation (2) by (1) we get:

[tex]\frac{r^2+1}{r-1}=\frac{220}{44}[/tex]

[tex]r^2+1=5r-5[/tex]

[tex]\Rightarrow r^2-5r+6=0[/tex]

[tex]\Rightarrow r^2-3r-2r+6=0[/tex]

[tex]\Rightarrow r(r-3)-2(r-3)=0[/tex]

[tex]\Rightarrow (r-2)(r-3)=0[/tex]

[tex]\Rightarrow r=2,3[/tex]

CASE1: When r=2 in [tex]ar^2=a+44[/tex]

[tex]a(4)=a+44[/tex]

[tex]3a=44[/tex]

[tex]a=\frac{44}{3}[/tex]

CASE2:When r=3 in [tex]ar^2=a+44[/tex]

[tex]a(3)^2=a+44[/tex]

[tex]\Rightarrow 9a=a+44[/tex]

[tex]\Rightarrow 8a=44[/tex]

[tex]\Rightarrow a=\frac{44}{8}=\frac{11}{2}[/tex]

The series becomes:

From CASE1: [tex]\frac{44}{3},\frac{44\cdot 2}{3},\frac{44\cdot 2^2}{3},\frac{44\cdot 2^3}{3}[/tex]

[tex]\Rightarrow \frac{44}{3},\frac{88}{3},\frac{176}{3},\frac{352}{3}[/tex]

From CASE2: [tex]\frac{11}{2},\frac{11\cdot 3}{2},\frac{11\cdot 3^2}{2},\frac{11\cdot 3^3}{2}[/tex]

[tex]\Rightarrow \frac{11}{2},\frac{33}{2},\frac{99}{2},\frac{297}{2}[/tex]

A geometric progression is characterized by a common ratio.

The terms of the progression are: [tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex] or [tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]

The given parameters are:

[tex]\mathbf{S_4 = 220}[/tex]

[tex]\mathbf{T_3 = T_1 + 44}[/tex]

The third term is represented as:

[tex]\mathbf{T_3 = ar^2}[/tex]

The first term is:

[tex]\mathbf{T_1 = a}[/tex]

So, we have:

[tex]\mathbf{ar^2 = a + 44}[/tex]

Subtract a from both sides

[tex]\mathbf{ar^2 - a = 44}[/tex]

Factor out a

[tex]\mathbf{a(r^2 - 1) = 44}[/tex]

Express as difference of two squares

[tex]\mathbf{a(r + 1)(r - 1) = 44}[/tex]

Make r + 1 the subject

[tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex]

Recall that:

[tex]\mathbf{S_4 = 220}[/tex]

This gives:

[tex]\mathbf{a + ar + ar^2 + ar^3 = 220}[/tex]

Factor out a

[tex]\mathbf{a(1 + r + r^2 + r^3) = 220}[/tex]

Factor out r^2

[tex]\mathbf{a(1 + r + r^2(1 + r)) = 220}[/tex]

Rewrite as:

[tex]\mathbf{a(1(1 + r) + r^2(1 + r)) = 220}[/tex]

Factor out 1 + r

[tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]

Substitute [tex]\mathbf{r +1 = \frac{44}{a(r -1)}}[/tex] in [tex]\mathbf{a((1 + r^2)(1 + r)) = 220}[/tex]

[tex]\mathbf{a((1 + r^2)\times \frac{44}{a(r -1)} = 220}[/tex]

[tex]\mathbf{((1 + r^2)\times \frac{44}{(r -1)} = 220}[/tex]

Divide both sides by 44

[tex]\mathbf{(1 + r^2)\times \frac{1}{(r -1)} = 5}[/tex]

Multiply through by r - 1

[tex]\mathbf{1 + r^2 = 5r - 5}[/tex]

Collect like terms

[tex]\mathbf{r^2 - 5r + 5 +1 = 0}[/tex]

[tex]\mathbf{r^2 - 5r + 6 = 0}[/tex]

Expand

[tex]\mathbf{r^2 - 2r - 3r + 6 = 0}[/tex]

Factorize

[tex]\mathbf{r(r - 2) - 3(r - 2) = 0}[/tex]

Factor out r -2

[tex]\mathbf{(r - 3)(r - 2) = 0}[/tex]

So, we have:

[tex]\mathbf{r = 3\ or\ r = 2}[/tex]

Calculate a using: [tex]\mathbf{a(r^2 - 1) = 44}[/tex]

When r = 3

[tex]\mathbf{a(3^2 -1) = 44}[/tex]

[tex]\mathbf{a(9 -1) = 44}[/tex]

[tex]\mathbf{8a = 44}[/tex]

[tex]\mathbf{a = 5.5}[/tex]

When r = 2

[tex]\mathbf{a(2^2 -1) = 44}[/tex]

[tex]\mathbf{a(4 -1) = 44}[/tex]

[tex]\mathbf{3a = 44}[/tex]

[tex]\mathbf{a = \frac{44}{3}}[/tex]

The nth term of a GP is:

[tex]\mathbf{T_ = ar^{n-1}}[/tex]

So, the terms of the progression are:

[tex]\mathbf{T_n =5.5, 16.5, 49.5,148.5}[/tex]

or

[tex]\mathbf{T_n =\frac{44}{3}, \frac{88}{3}, \frac{176}{3},\frac{352}{3}}[/tex]

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Answer:

The correct answer is (−4, −8)

Step-by-step explanation:

You have to substitute!!! :)

−3x + 4y = −20                y = x − 4

-3(4) + 4(8) = -20             8 = 4 - 4

-12 + 32 = -20                  8 = 0

20 = 20

−3x + 4y = −20                y = x − 4

-3(0) + 4(-5) = -20           -5 = 0 - 4

0 + 20 = -20                    -5 = -4

20 = -20

−3x + 4y = −20                y = x − 4

-3(-2) + 4(-6) = -20          -6 = -2 - 4

6 - 24 = -20                    -6 = -6

-18 = -20      

−3x + 4y = −20                y = x − 4

-3(-4) + 4(-8) = -20         -8 = -4 - 4

12 - 32 = -20                  -8 = -8

-20 = -20

Answer:

(-4,-8)

Step-by-step explanation:

This a system of equation that have two variables x and y and we have two equations that we have to solve simultaneously

−3x+4y=−20 ....(1)

y=x−4 ....(2)

We can substitute equation (2) and (1)

-3x+4y = −20

-3x+4(x−4) = −20

-3x + 4x -16 = -20

x = -4

Now we need to find the value of y

y=x−4 = -4 - 4 = -8

(-4,-8)

Answer:

$1.25

September

$30

Step-by-step explanation:

Let's take this a step a time.

First we need to find how much the price of the flowers were in September.

We know that each flower cost $1.50 on October.

The October price was a 20% increase of the September price.

To calculate for the price of the flowers on September, we can solve it like this:

Let x = Price during September

1.2x = 1.50

We used 1.2 because the price of $1.50 is 120% of the original price.

Now we divide both sides by 1.2 to find x.

[tex]\dfrac{1.2x}{1.2}=\dfrac{1.5}{1.2}[/tex]

x = 1.25

The price of the flowers during September was $1.25 each.

Now the 7th grade class earned 40% of the selling price of each flower.

40% = 0.40

To find how much they made on each month, we simply multiply the percentage to the price and the number of flowers sold.

September = 0.40 x 1.25 x 900

September = 0.5 x 900

September = $450

Now for October.

October = 0.40 x 1.50 x 700

October = 0.6 x 700

October = $420

The 7th Graders earned more on September.

They earned $30 more on September than October.

Hello from MrBillDoesMath!

Answer:

 80,100  (which is NONE of the provided answers)

Discussion:

-225 * -356 =

+ (225 * 356)   =            as the product of two negative numbers is positive

 80,100

Regards,  

MrB

P.S.  I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!

The answer should be D. 9 1/5

Answer:

1,250 drinks

Step-by-step explanation:

Woody spends $0.05 to make a glass of lemonade and makes $0.25 when he sells one, so his net gain is $0.20. 250 / .20 is 1,250.

Final answer:

Woody needs to sell 1,250 glasses of lemonade to earn the $250 required to buy a bicycle. Calculated by dividing the goal ($250) by the profit per glass ($0.20), which is the difference between the selling price ($0.25) and the cost price ($0.05).

Explanation:

Woody is operating a small business of selling lemonade and seeks to achieve a certain amount of total revenues to purchase a bicycle. To solve this, one must determine the profit per glass of lemonade sold, which is the selling price minus the cost to make it. Since Woody sells a glass for $0.25 and it costs $0.05 to make, the profit per glass is $0.25 - $0.05 = $0.20.

To calculate the total number of glasses Woody needs to sell to earn $250, divide his goal by the profit per glass. Thus:

Total number of glasses = ($250 / $0.20 per glass) = 1250 glasses

Hence, Woody must sell 1,250 glasses of lemonade to earn enough money to buy the bicycle.

Answer:

I think it's rotated 90 degrees clockwise

Step-by-step explanation:

The transformation of circle K to circle K' is a translation, specifically a movement of 4 units to the right and 10 units down, represented by T(4, -10).

The transformation that maps circle K to circle K' is a translation. In a translation, every point of the object moves the same distance in the same direction. For circle K to circle K', this would be a shift 4 units to the right and 10 units down. The coordinates of the center of the circle move from (3,7) to (7,-3). We can calculate this movement by subtracting the initial coordinates from the final ones: (7-3, -3-7) = (4, -10). Therefore, the transformation would be written as T(4, -10).

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This is classic Pythagorean solving:

Side^2 + Side^2 = Hypotenuse^2

The hypotenuse is the longest side of a triangle, and it connects the leg and the base usually. In this triangle, 18 is the hypotenuse -- so since we are solving for the unknown side, the equation is:

a^2 + 5.7^2 = 18^2 -- now solve

a^2 = 18^2 - 5.7^2

a^2 = 291.51

a = sqrt(291.51)

a = 17.07 -- because height is the square root of the difference of the squares of 18 and 5.7

The answer is choice B.

The correct answer is b. 17.07 centimeters, because height = Square root of the difference of the squares of 18 and 5.7.

To find the approximate height of the cone-shaped hat, we need to use the Pythagorean theorem. The height of the cone (h) can be found using the formula:

[tex]\[ h = \sqrt{r^2 - a^2} \][/tex]

 where r is the slant height of the cone and a is the radius of the base of the cone.

Given that r = 18 cm and a = 5.7 cm, we substitute these values into the formula:

[tex]\[ h = \sqrt{18^2 - 5.7^2} \][/tex]

[tex]\[ h = \sqrt{324 - 32.49} \][/tex]

[tex]\[ h = \sqrt{291.51} \][/tex]

 Now, we can approximate the square root of 291.51 to find the height:

[tex]\[ h \approx 17.07 \text{ cm} \[/tex]]

 Therefore, the approximate height of the hat is 17.07 centimeters. The other options are incorrect because they do not correctly apply the Pythagorean theorem:

 a. 3.51 centimeters: This is the square root of the difference of 18 and 5.7, which does not use the correct formula for the height of a cone.

c. 18.88 centimeters: This is the square root of the sum of the squares of 18 and 5.7, which would be the length of the slant height, not the height of the cone.

d. 4.87 centimeters: This is the square root of the sum of 18 and 5.7, which is not a correct application of the Pythagorean theorem for finding the height of a cone."

Answer:

The length is 81 feet.

Step-by-step explanation:

If you plot the equations for both length and width on a graph, making them both equal to y of course, you find that they cross each other in two places. The places they cross are (81, 11) and (70, 0). It is impossible for the answer to have the width as 0 feet, so the answer is 81 feet.

Answer:

depends on the how many fee your talking

Step-by-step explanation:

Answer: [tex]\frac{27}{125}[/tex]

Step-by-step explanation:

Here the total numbers are 1,  4,  3,  7,  6

Since the total number of possible arrangement = [tex]5\times 5 \times5 \times 5 \times 5=5^5[/tex]

The total number of the odd numbers in the given numbers = 3

Thus the possible arrangement that the first three digits will be odd numbers = [tex]3\times 3\times 3\times 5\times 5=3^3\times 5^2[/tex]

Thus, the probability that the first three digits of Irvings ID number will be odd numbers = the possible arrangement that the first three digits will be odd numbers / total possible arrangement =  [tex]\frac{3^3\times 5^2}{5^5} = \frac{3^2}{5^{5-2}}[/tex]

= [tex]\frac{3^3}{5^3} = \frac{27}{125}[/tex]

Answer:

The graph shifts 3 units left and 15 down. It narrows by a factor of 2 and is right side up.

Step-by-step explanation:

There are two ways of doing this. You can graph it, or you can put it in the vertex form by completing the square.

A quick way of putting this into the vertex form is write the general equation

y = a(x - h)^2 + k

h= - b/2a = - 12/4 = - 3

So the equation in vertex form is

y = 2(x + 3)^2 - 15

Description

y = 2(x + 3)^2 - 15

shifts 3 units to the left and 15 units down. It also narrows by a factor of 2. Finally, it is right side up.

Graph

Since you have seen the graph before, there is not much more to add. It just shows what has been written above.

Final answer:

To find the value of p when c = 3.2, substitute c = 3.2 into the expression for p. The value of p is 2. To find the value of c when p = 85, substitute p = 85 into the expression for p and solve for c. The value of c is -30.

Explanation:

To find the value of p when c = 3.2, we substitute c = 3.2 into the expression for p.

Substituting c = 3.2 into p = 10 - 2.5c, we get p = 10 - 2.5 * 3.2 = 10 - 8 = 2.

So, p = 2 when c = 3.2.

To find the value of c when p = 85, we substitute p = 85 into the expression for p.

Substituting p = 85 into p = 10 - 2.5c, we get 85 = 10 - 2.5c.

Then, we solve for c: 2.5c = 10 - 85 = -75.

Dividing both sides by 2.5, we get c = -75/2.5 = -30.

So, c = -30 when p = 85.

Answer:

Possible number of outcomes = 24

Number of outcomes have an 'a' and an odd number = 3

Step-by-step explanation:

The total outcomes are as follows:

S = {(a, 1), (a, 2), (a, 3), (a, 4), (a, 5), (a, 6),

      (b, 1), (b, 2), (b, 3), (b, 4), (b, 5), (b, 6),

      (c, 1), (c, 2), (c, 3), (c, 4), (c, 5), (c, 6),

      (d, 1), (d, 2), (d, 3), (d, 4), (d, 5), (d, 6)}

n(S) = 24

Hence, possible number of outcomes = 24

The outcomes have an 'a' and an odd number are:

E = {(a, 1), (a, 3), (a, 5)}

n(E) = 3

Hence, there are 3 outcomes have an 'a' and an odd number.

Answer:

Yes

Step-by-step explanation:

2 x √3 = 3.46410161514 , which is a rational number, because it is a real nomber

The length of Line BC is 10

A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.

Triangles having the same corresponding angles measures and proportional side lengths are called similar triangles.

Considering Δ AXY    and    ΔABC

                      ∠AXY       =      ∠ACB  (corresponding angles are equal)

                       ∠AYX       =      ∠ABC   (corresponding angles are equal)

                       ∠A is common in both the triangles

∴ We can say the triangles are similar .

Now, let H be the height of ΔABC and h be the height of ΔAYX

So, we can say,  [tex]\frac{XY}{BC} = \frac{h}{H}[/tex]

So,   [tex]\frac{AYX}{ABC} = \frac{7.5}{30}[/tex]

⇒    [tex]{\frac{\frac{1}{2} (XY) h }{\frac{1}{2}(BC) H } = \frac{1}{4}[/tex]

Now, substituting XY = 5 and  [tex]\frac{XY}{BC} = \frac{h}{H}[/tex]  in the above equation, we get

[tex]\frac{25}{BC^{2} } = \frac{1}{4}[/tex]

⇒ BC² = 100

⇒ BC = ± 10

Since BC is the length , so it cannot be negative.

So, the negative value is rejected.

∴  BC = 10

Option B is correct.

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Answer:

81

Step-by-step explanation:

45% × 180 = [tex]\frac{45}{100}[/tex] × 180 = 81

Answer:

The answer is  81

Step-by-step explanation:

You can do it following the next steps

1.- Place the the "45" by 100 = 0.45

2.- Multiply 0.45 times 180= 81

Jaimie swims 12 the length of the swimming pool every 14 of a minute. Then in one minute, he will swim = 14/12=1.16  So, he will be able to swim 1.16 length in 1 minute.

The distance of line AB if A(3, 5) and B(-3,-3) is D.10.

[tex]\sqrt[/tex] (5--3)^2 + (3-(-3))^2 = V100 = 10.

To calculate the distance AB between points A (x1, y1) and B (x2, y2), first draw a right triangle with segment ¯AB in the hypothalamus. AC is a horizontal distance, so it's just a difference in x-coordinates: | (x2-x1) |. Similarly, BC is the vertical distance | (y2-y1) |. ..

The vertical distance of the line (Ax + By + c = 0) from point

is equal to | Ax'+ By' + c√A2 + B2 |. Where (x', y') are the coordinates of the point. Since we need the distance of the line from the origin, the coordinates will be (0,0), which is the vertical distance of the line from the origin.

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Answer:

The answer is 1/square root 2

Step-by-step explanation:

30 minutes is half an hour.

so in 30 minutes is 16 commercials, so in 1 hour is twice as many, 32 commercials.

there are 24 hours in a day, so 32 commercials 24 times, 32 * 24.

Answer:

x - 2y = -15

Step-by-step explanation:

Given: m = 1/2 and (-3, 6)

We are given slope and a point.

The equation of the line y - y1 = m (x  - x1)

y - 6 = 1/2 (x -  (-3))

y - 6 = 1/2 (x + 3)

y - 6 = 1/2x + 3/2

1/2x - y = -6 - 3/2

1/2x - y = -15/2

Taking LCD as 2, we get

x - 2y = -15

Thank you.

Answer:

y = 10  PLEASE GIVE BRAINLIEST

Step-by-step explanation:

The angles of this triangle should all add up to 180 degrees.

There are 3 angles so 180 ÷ 3 = 60.  Each angle will = 60 degrees.

To find y:

5y + 10 = 60

5y = 60 - 10

5y = 50

y = 50 ÷ 5

y = 10

Answer: 615= 140 + 19x

Step-by-step explanation:

19x represents the price per guess (x) how many people are coming. Good Luck!

To solve for the number of guests Taryn can invite, set up the inequality 140 + 19x < 615 and then solve for x.

To solve for the number of guests Taryn can invite, we need to set up an inequality. Let x represent the number of guests. The total cost, C, can be calculated by adding the cost to rent the space, $140, to the cost per guest, $19, multiplied by the number of guests. So, the inequality can be written as 140 + 19x < 615.

To solve for x, we need to isolate it by subtracting 140 from both sides: 19x < 475. Finally, divide both sides by 19 to get the solution: x < 25.

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If x and y are proportional, then y : x = constant.

[tex]\dfrac{y}{x}=a\to y=ax[/tex]

We have (4, 3) and (x, 9). Substitute:

[tex]\dfrac{9}{x}=\dfrac{3}{4}[/tex]        cross multiply

[tex]3x=(9)(4)[/tex]

[tex]3x=36[/tex]       divide both sides by 3

[tex]\boxed{x=12}[/tex]

Answer:

The ascending order is [tex]8.11\times 10^{-3},435, 34\times 10^2, 1.2\times 10^7[/tex]

Step-by-step explanation:

First of all find the exact value of each number.

[tex]34\times 10^2=34\times 100=3400[/tex]

[tex]1.2\times 10^7=1.2\times 10000000=12000000[/tex]

[tex]8.11\times 10^{-3}=\frac{8.11}{1000}=0.00811[/tex]

The fourth number is 435.

Using the above calculation we can easily arrange these numbers form least to greatest.

The ascending order is

[tex]0.00811, 435, 3400, 12000000[/tex]

It can be written as

[tex]8.11\times 10^{-3},435, 34\times 10^2, 1.2\times 10^7[/tex].

Answer:

The set of all points on a plane equidistant to a given point

Step-by-step explanation:

"following"?

Answer:

The collection of all points in a plane that are the same distance from a given point.

Step-by-step explanation:

Answer:

€16.40

Step-by-step explanation:

First, we need to divide £12.30 by 3 to find out how many groups of 3 there is:

12.3 ÷ 3 = 4.1

Now we can multiply this by 4 to find the euro equivalent:

4.1 * 4 = 16.4

So £12.30 is €16.40