How many gallons of 70% antifreeze should be mixed with 30% antifreeze to make 100 gallons of 45% antifreeze?

The distance from P to l of the given coordinates is 13.34

The slope of Line I is calculated as;

m = (4 + 9)/(-2 - 1)

m = 13/-3 = -13/3

Thus, the equation using the first coordinate of point I is;

y =  (-13/3)x + b

4 = (-13/3 * -2) + b

4 = 26/3 + b

Thus;

b = 4 - 26/3

b = (12 - 26)/3

b = -14/3

Thus, the equation of the line I passing through the given two points is;

y = -13x/3 - 14/3

Let us now find the line perpendicular to I and passing through (14, -6). Plug in x = 14 and y = -6 into the first line equation to get b;

y =  (-13/3)x + b

-6 = 3(14)/13 + b

b = -6 - 42/13

b = -78/13 - 42/13

b = -120/3

Thus, the equation is;

y = (3/13)x - 120/13

Let us now find the intersection point of the two lines by equating them;

3x/13 - 120/13 = -13x/3 - 14/3

multiply through by 39 to get;

9x - 360 = -169x - 182

178x = 360 - 182

178x = 178

x = 1

Thus;

y = -27/3

y =-9

The point is (1,-9) and as such the distance from (1,-9) to (14,-6) is;

d² = 9 + 169

d² = 178

d = √178

d = 13.34

Thus, the distance from P to l of the given coordinates is 13.34

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Complete Question is;

Line l contains points (-2,4) and (1,-9). Point P has coordinates (14,-6). Find the distance from P to l

The calculated value of k on the line is 9

From the question, we have the following parameters that can be used in our computation:

XZ is the perpendicular bisector of segment WY

This means that

WX = XY

substitute the known values in the above equation, so, we have the following representation

3k - 4 = 2k + 5

So, we have

3k - 2k = 4 + 5

Evaluate

k = 9

Hence, the value of k is 9

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What is the maximum height of the ball 182.25 feet

How many seconds does it take until the ball hits the ground 6 seconds

The maximum height will occur at the vertex v(h', k)

h' = -b/2a

From the equation h = − 16 t^2 + 84 t + 72

a = -16

b = 84

h' = -84/(2 * -16)

h' = t = 2.625

k = h = − 16 t^2 + 84 t + 72 at t = 2.625

= − 16 * 2.625^2 + 84 * 2.625 + 72

= 182.25 feet

The ball hits the ground when h = 0

0 = − 16 t^2 + 84 t + 72

solving the quadratic equation gives

t = 6 OR -3/4

Use the positive value

t = 6 seconds

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Answer:

Amount of jelly beans=50

Amount of blue or green jelly beans=17+10

probability that the jelly bean will be a blue or green one=27/50

The expression for the identity is given as;

cos(∠ABC-60°) = 3/10 - 2/5√3

Option D

From the information given, we have that the expression is given as;

cos(∠ABC-60°)

This is simplified as;

cos (B - 60)

Now, let us expand the bracket, we get;

(1/2)cos(B) + (sqrt(3)/2)sin(B).

We have that the identities are expressed as;

cos B = 3/5

sin B = 4/5

Substitute the values, we get;

cos(∠ABC-60°) = 1/2 × 3/5 - √3/2 × 4/5

divide the values, we have;

cos(∠ABC-60°) = 3/10 - 2/5√3

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According to the information provided, 4.5 litres of red paint and 1400 ml of blue paint are required to manufacture the paint mixture.

Red paint requires 3/4 x 6 = 9/2 = 4.5 litres.

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Answer:

3600

Step-by-step explanation:

4.8x10^3-1200=3600

Each letter should be matched to its correct term as follows;

1. A ⇔ Efficiency.

2. B ⇔ Impossible.

3. C ⇔ Inefficiency.

In Economics and Mathematics, a production possibilities curve (PPC) can be defined as a type of graph that is typically used for illustrating the maximum and best combinations of two (2) products that can be produced by a producer (manufacturer) in an economy, if they both depend on the following two (2) factors;

Based on the production possibilities curve shown in the image attached above, we can reasonably infer and logically deduce that each of the letters represent the following terminologies;

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It is proved that m = √n.

To prove that given a nonnegative integer n, there is a unique nonnegative integer m, we just need to take the square root of the given equation:

m^2 ≤ n < (m + 1)^2.

So, after taking the square root, it will be:

m ≤ √n < m + 1

From that we can see m = √n is the unique m.

A nonnegative integer is an integer which is either positive or zero. It is the union of the natural numbers and the number zero. Occasionally, it is referred to as Z*, and it can be described as the set {0, 1, 2, 3, 4, 5, …}. In other words, nonnegative integers are integers that are not negative.

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Although part of your question is missing, you might be referring to this full question: Prove that given a nonnegative integer n, there is a unique nonnegative integer m such that m^2 ≤ n < (m+1)^2.

Answer:

c. 2640

Step-by-step explanation:

20 x 12 x 11 = 2640

Answer: C. 2,640

Step-by-step explanation:

Answer:

i think its 700 hope it help

Step-by-step explanation:

the answer would be

70 times

Answer:

x-25y-50

Step-by-step explanation:

simplifying an expression means getting rid of the parantheses and writing it in the simplest form

5(\(\frac{1}{5} x-5y-10)\)=

\(5*\frac{1}{5} x-5*5y-10*5\\x-25y-50\)

Answer:

\(x-25y-50\)

Step-by-step explanation:

\(5\left(\frac{1}{5}x-5y-10\right)\)

\(5\cdot \frac{1}{5}x-5\cdot \:5y-5\cdot \:10\) .......multiply 5 with everything inside the bracket

\(x-25y-50\)     ...........final answer.

The graph of the feasible region is attached

From the question, we have the following parameters that can be used in our computation:

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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We want to see which would be the correct graph of a given inequality.

We will see that the correct option is the third one:

"number line with a closed dot on 2 and an open dot on 8 and shading in between"

Here the inequality is:

-8 ≥ −5x + 2 > −38

Let's simplify this, first we can subtract 2 in the 3 parts of the inequality:

-8 - 2 ≥ −5x + 2 - 2 > −38 - 2

-10 ≥ −5x  > −40

Now we can divide the 3 parts by -5, notice that as it has a negative sign, the direction of the symbols must change:

-10/-5 ≤ −5x/-5 < −40/-5

2 ≤ x < 8

Then the graph will be a solid dot at x = 2 (because x = 2 is a valid solution) that extends to the right unitl it hits an open dot at x = 8 (because x = 8 is not a solution).

Thus the correct option is the third one:

"number line with a closed dot on 2 and an open dot on 8 and shading in between"

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Answer:

TWO CRACKERS

Step-by-step explanation:

I'm assuming they want to find x. Here we see that these two are similar triangles, so the sides are reflective. 5x/5 should be equal to 4/x, so 5x/5 = 4/x. If we use cross multiplying we get 5x^2 = 20. divide both sides by 5 and we get x^2 = 4 or x = 2.

Hope this helped

With the help of probability we can say that, DUM={GG,BB,GB,BG).

Probability is the concept that describes the likelihood of an event occurring.

In real life, we frequently have to make predictions about how things will turn out.

We may be aware of the result of an occurrence or not.

When this occurs, we state that there is a possibility that the event will occur.

In general, probability has many excellent applications in games, commerce, and this newly growing area of artificial intelligence

The chance of an event can be calculated using the probability formula by only dividing the favourable number of possibilities by the total number of potential outcomes.

hence, DUM={GG,BB,GB,BG)

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Answer:

EF = 36

Step-by-step explanation:

FE and GD are congruent

2u - 36 = u

subtract 2u from both sides (-36 = -u)

divide each side by -1 ( u = 36)

now that you know the value of u plug it into the equation 2u -36

the equation is now 2(36)-36

2 times 36 equals 72

now do 72 - 36 and you get 36

that is the value of line segment EF

Answer:

36

Step-by-step explanation:

Ef is equal to gd

so 2u－36＝u

＋36 ＋36

so 2u＝u＋36

－u －u

so u＝36

hope this helps

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

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The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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The required probability of selecting the black marble is given as 0.40. Option C is correct.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Total number of marbles in the bag = 15
Number of black marble = 6 [from the table]

Now,
The experimental probability of selecting a black marble,
= Number of black marble/Total number of marbles
= 6/15 = 0.40

Thus, the required probability of selecting the black marble is given as 0.40. Option C is correct.

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Answer:

A

Step-by-step explanation: yes

Answer: C

Step-by-step explanation:

The area of the triangle, when a = 2 and c = 3, is 1512 square centimeters.

We must apply the formula for the area of a triangle, which is provided by: to determine the triangle's area.

(1/2) * Base * Height = Area

We can enter the values of a = 2 and c = 3 into the formula given that the base length is 3ac2 and the height is 2 centimetres greater than the base length.

Base length =\(3ac^2 = 3 * 2 * (3^2) = 3 * 2 * 9 = 54\) centimeters

Height is calculated as Base Length + 2 (54 + 2 = 56 centimetres).

Using these values as a substitute in the formula, we obtain:

Area =\((1/2) * 54 * 56 = 1512\) square centimeters

centimetres square

It's crucial to understand that the calculation assumes the triangle is a right triangle with the specified base and height and that the given values of a and c are accurately used in the formula.

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Answer:

  5x +3y = -14

Step-by-step explanation:

The equation of the given line is in standard form. This makes it easy to write the equation for a perpendicular line.

__

The perpendicular line will have a slope that is the negative reciprocal of the slope of the given line. This can be made to happen by ...

So, the line perpendicular to 3x -5y = 2 will have an equation of the form ...

  5x +3y = c . . . . . for some constant c

The constant will be what is needed to make the line go through the given point. That is, for (x, y) = (-1, -3), the equation is satisfied.

  5(-1) +3(-3) = c = -5 -9 = -14 . . . . . substitute values for x and y

Then the equation for the perpendicular line through (-1, -3) is ...

  5x +3y = -14

The dimensions of the smaller rectangle are 13 centimeters by 52 centimeters.

Let's assume the dimensions of the smaller rectangle are length L and width W (in centimeters).

We know that the area of the smaller rectangle is 676 square centimeters:

L * W = 676    ----(1)

We also know that the larger rectangle has a shorter side of 41 centimeters. Let's say the corresponding longer side of the larger rectangle is H centimeters.

The area of the larger rectangle is 3457 square centimeters:

41 * H = 3457    ----(2)

Our current set of equations contains two unknowns. In order to get the smaller rectangle's dimensions, we can simultaneously solve these equations.

In order to find H, we can use equation (2):

H = 3457 / 41

H ≈ 84.22

Now we can substitute this value of H into equation (1):

L * W = 676

We need to find the dimensions (L and W) that multiply to give 676. We can start by looking for factors of 676.

Factors of 676: 1, 2, 4, 13, 26, 52, 169, 338, 676

By trial and error, we can see that the factors that give a close match to the dimensions of the larger rectangle (41 and 84.22) are 13 and 52:

L = 13

W = 52

Therefore, the smaller rectangle has measurements of 13 by 52 centimetres.

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When the former image is rotated, the dots will be located at section 2 and 7.

When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.

From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.

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Answer:

C. Points

Step-by-step explanation:

Got it right on my quiz :)

Answer:

-19.9y-5.3

Step-by-step explanation:

The variables 8 observations have x2 values of 2 or greater.

Two variables, x1 and x2, are present in the supplementary data set. There are a total of 20 observations in this data set. The x2 values for 8 of these 20 observations are equal to 2. Thus, x2 values of two were present in eight out of twenty observations, or 40%. The following 12 observations' x2 values do not add up to 2. Thus, 8 of the 20 observations in the data set have x2 values of 2 or higher.8 of these 20 observations have x2 values that are equal to 2. Thus, eight out of twenty observations, or 40 percent, had x2 values equal to two. The x2 values for the next 12 observations are not equal to 2. Consequently, 8 of the data set's 20 observations have x2 values of 2 or above.

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Given,

David buys candy that costs $7 per pound.

He will buy at most 10 pounds of candy.

Reuired

The possible amounts he will spend on candy.

Consider,

c is the amount (in dollars) David will spend on candy.

The expression of inequality is,

Hence, the possible amounts he will spend on candy is less

Answer:

The answer is c! 7,36,60,30

Step-by-step explanation:

To answer this equation you have   to find  a number that fits the description of what is required. It may seem difficult but it's not  first off it's trial and error  you have to find the right equation for every given number. For example,  what makes 15  equal 5  true? To make the equation true you have to do 15 divided by 3 equals 5  now we take the / 3 and apply them to all the other numbers  so 21 / 3 is  7 ,  36  divided by 3 is 12  hi, 60 / 3 is 20 ,  90 /3 is 30. If you have any other question like this all you have to do is trial and error with a number to make the equation true hopefully that helps! (B.t.w / symbol means divided by)