Lydia buy 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. This system of equations represents the situation, where x is the cost per pound of apples, and y is the cost per pound of bananas.

Kevin needs to read 57 novels in 19 months.

Given,

The number of novels Kevin needs to read in a month = 3

N = Number of novels Kevin needs to read in M months.

Write an equation with M and N.

That is,

Kevin needs to read 3 novels in one month.

So, number of novels, N Kevin reads in M months,  3M = N

The equation is;

3M = N

Now,

The number of months Kevin needs to read the novels = 19

Then,

The number of novels Kevin reads in 19 months;

3M = N

3 × 19 = 57

That is,

Kevin needs to read 57 novels in 19 months.

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For the given points S(2,-9), 7(6, -6), U(9,-7), and V (6, y), the value of y such that ST is perpendicular to UV is -3.

What is the slope of a line?

A line's slope, also known as its gradient, is defined as the value of a line's steepness or direction in a coordinate plane. Slope can be calculated using various methods given a line equation or the coordinates of points on a straight line.

If P(a, b) and Q(c, d) are two given points on a coordinate plane, then the slope of line PQ can be computed using the formula

                        [tex]Slope(m) = \frac{d-b}{c-a}[/tex]

The slope of two perpendicular lines:

If two perpendicular lines are given then the product of their slopes will be equal to -1.

The given points are S(2,-9), 7(6, -6), U(9,-7), and V (6, y).

The slope of line ST   [tex]=\frac{-6-(-9)}{6-2}[/tex]

                                    [tex]= \frac{-6+9}{4}\\ = \frac{3}{4}[/tex]----------------(I)

Now, finding the slope of line UV,

The slope of line UV [tex]=\frac{y-(-7)}{6-9}[/tex]

                                  [tex]=\frac{y+7}{-3}[/tex]  ---------------(II)

Now, by using the property of slopes of two perpendicular lines, we can write

    Slope of line ST × Slope of line UV = -1

                                [tex]\frac{3}{4} *\frac{y+7}{-3}=-1 \\y+7=4\\y=4-7\\y=-3[/tex]

Hence, For the given points S(2,-9), 7(6, -6), U(9,-7), and V (6, y), the value of y such that ST is perpendicular to UV is -3.

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The solution is

1) Angles 7 and 6 are Vertical angles

2) Angles 1 and 8 are Alternate exterior angles

3) Angles 4 and 5 are Alternate interior angles

4) Angles 2 and 6 are Corresponding angles

5) Angles 6 and 8 are Complementary angles

What are angles in parallel lines?

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Given data ,

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.

Each pair of alternate angles around the transversal are equal to each other.

The pairs of angles formed on the same side of the transversal that are either both obtuse or both acute and are called corresponding angles and are equal in size.

Each pair of corresponding angles on the same side of the intersecting transversal are equal to each other.

Co-interior angles on the same side of an intersecting transversal add to 180°

Hence , the angles are

1) Angles 7 and 6 are Vertical angles

2) Angles 1 and 8 are Alternate exterior angles

3) Angles 4 and 5 are Alternate interior angles

4) Angles 2 and 6 are Corresponding angles

5) Angles 6 and 8 are Complementary angles

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Answer: First, I substituted x for 11. -2 times 11 = -22. -22 + 5 equals -17. Therefore, f(11) or y, is equal to -17.

Step-by-step explanation:

Answer:

[tex]x + 3y = -30:[/tex] Perpendicular to line a

[tex]y = \frac{1}{3} x + 1 :[/tex] Neither Parallel nor Perpendicular to line a

[tex]-3x + y = -2 :[/tex] Parallel to line a

Explanation:

[tex]-3x + y = -4\\y = 3x - 4[/tex]

[tex]x + 3y = -30\\3y = x - 30\\y = \frac{1}{3} x - 10[/tex]

[tex]y = \frac{1}{3} x + 1[/tex]

[tex]-3x + y = -2\\y = 3x - 2[/tex]

Answer: Table A

Step-by-step explanation:

The table must have a constant rate of change on both sides. Table B goes up by 2, then 2, then 3, which breaks the pattern (this is in the y-axis).

Table C goes up by 3, then 4, then 4, which is ALSO an inconsistent pattern (in the x-axis). Table D goes up by 2, then 1, then 2, which is also inconsistent (y-axis).

This leaves Table A, which has a consistent pattern on both sides.

Answer: [tex]x=-3z+4, y=-2z+1, z=z[/tex]

Step-by-step explanation:

We have the system:

[tex]x-2y-z=2\\\\-x+3y+3z=-1\\\\-x+4y+5z=0[/tex]

Adding the first and second equations yields [tex]y+2z=1[/tex].

Adding the first and third equations yields [tex]2y+4z=2[/tex].

We know that there are infinitely many solutions, so [tex]y=1-2z[/tex].

Substituting this result back into the first equation,

[tex]x-2(1-2z)-z=2\\\\x-2+4z-z=2\\\\x+3z-2=2\\\\x=-3z+4[/tex]

The solution in term of z variable is; x = 4 - 3z

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

We have the linear system:

x - 2y - z = 2

-x + 3y + 3z = -1

-x + 4y + 5z = 0

Adding the first and second equations;

y + 2z = 1

Now Adding the first and third equations yield;

2y + 4z = 2

We know that there are infinitely many solutions, so;.

y = 1-2z

Then Substituting this result back into the first equation;

x - 2y - z = 2

x - 2( 1-2z) - z = 2

x - 2 + 4z - z = 2

x -4 + 3z = 0

x = 4 - 3z

The solution in term of z variable is; x = 4 - 3z

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The number of degrees does it move in 2 1/5 hours is -66°.

From the information given, it was illustrated that the hour hand of a clock moves −30° every hour.

Therefore, to calculate the degree for a number of hours, we simply have to multiply.

In this case, to get the degree for 2 1/5 hours will be:

= Degree every hour × Number of hours

= -30° × 2 1/5

= -30° × 2.2

= -66°

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Answer:

the answer is that there is 8 percent that they all will spend an hour on the internet.

Step-by-step explanation:

The radius is the distance from the center to a point on a circle.

The diameter is twice the radius.

1. 3 yd, 6 yd

2. 46 in, 92 in

3. 23 ft, 46 ft

Answer:

it is £16490.36

Step-by-step explanation:

since £156.78 is 100%, £16470.45 by 3.5 is £16490.36

Answer:

it's 17,046.92

Step-by-step explanation:

that's what my calculations said

Answer:

86

Step-by-step explanation: 89+92+81+x=total score=262+x

avg score = 87= (262+x)/4

262+x=348

.

x=86

.

Check,,,(89,92,81,86)/4 = 87

Answer: 86

Step-by-step explanation:

Answer:

233 is a Fibonacci number

Step-by-step explanation:

(D) The range is the output.

The domain of a function is the set of values that we are allowed to enter into our function. The x values for a function like f make up this set (x).

The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set. They are the y values.

The sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. The domain and range of a function are the components of a function.

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Answer:

1.23457

Step-by-step explanation:

You count 5 places from the decimal point. Then since 6 is greater than 5 you round up

Let W=width of wing

The ratio (Length/Width) is given and is constant, so you can set ratios equal (this is a proportion):

      Length / Width = 8/1 = 32.3/W

 (1) cross-multiply, (2) invert both sides, multiply both sides by one of the denominators ... any legal operation of algebra in order to isolate W.

multiply both sides by (W/8):

                      W = 32.3/8 = 4.04

Answer:

v = 7

Step-by-step explanation:

42 = v + 35

-35        -35

7 = v

The answer is D. 7

I took the quiz and got it right

Step-by-step explanation:

girls:boys

3:1

total=400

1/3 × 400

400/3

=133.33

to whole number

=133 boys

Answer:

The correct answer is 100

The equation represents the relationship between the x and y values is y = 2.75x

The first point = (0,0)

The second point = (4,11)

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The slope of the line m = (11-0) / (4-0)

= 11 / 4

= 2.75

The slope intercept form is

y = mx + b

m is the slope of the line

b is the y intercept

The equation will be

y = 2.75x

Hence, the equation represents the relationship between the x and y values is y = 2.75x

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The grid has 100 squares and each exercise will be represented by the following percentages:

Percentages refer to the ratio or proportion of a value when compared to the whole.

Percentages are fractional values, computed as a quotient of the part with respect to the whole, and usually expressed over 100.

The percentage sign (%) is used to depict values in percentages.

Exercise          Minutes   Percentage

Endurance:          8                 20% (8/40 x 100)

Strength:            16                 40% (16/40 x 100)

Balance:              4                  10% (4/40 x 100)

Flexibility:          12                 20% (12/40 x 100)

Total                 40                100% (40/40 x 100)

Thus, the percentage representation of the exercises on the grid shows that Endurance occupies 20%, Strength 40%, Balance 10%, and Flexibility 30%.

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In the grid below, represent the percentage of each exercise.

Considering the function C = 5 + 4e, it is found that:

a. The situation represents a linear function, as the increase in the price is constant for each kwh hour used.

b. The continuous domain of the function is: e ≥ 0.

c. The graph of the function is given by the image shown at the end of the answer.

A linear equation is a special function that has the format of the equation given as follows:

y = mx + b.

The coefficients of the equation y = mx + b are given as follows:

For this problem, the function is:

C(e) = 5 + 4e.

Which is a linear function, as it follows the same format of the general linear function, with a constant cost of 4 per each kwh used.

The domain of the function contains the set of all possible input values of the function. Hence, in this problem, it is composed by the amounts of kwh used, which:

Hence the domain is:

e ≥ 0.

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Answer:

  B by a factor of about 5.208

Step-by-step explanation:

Given two right square pyramids (A and B) with perimeters 396 m and 496 m, and corresponding heights of 72 m and 239 m, you want to which has the greater volume and by what factor.

The volume of a right square pyramid is proportional to its height and to the square of its perimeter.

Pyramid B has both a longer perimeter and a greater height, so Pyramid B has the greater volume.

The constant of proportionality between the dimensions and the volume is the same for both pyramids, so the ratio of their volumes is ...

  Vb/Va = ((Pb)²Hb)/((Pa)²Ha) = (496²·239)/(396²·72) ≈ 5.208

Pyramid B has about 5.2 times the volume of Pyramid A.

__

Additional comment

The volume of a right square pyramid is given by ...

  V = 1/3s²h . . . . . where s is the side length and h is the height

  V = 1/3(P/4)²h = (1/48)P²h . . . . where P is the perimeter of the base

The age of  Mark and Lynne’s house right now, given the number of years left till the mortgage is paid off is 4 years.

Mark and Lynne’s house is currently aged such that in 20 years when the mortgage is paid off, it will be five times as old as it is now.

Assuming the age of the house right now is x, the age of the house can be shown in an equation as:

20 years = 5x

The age of the house now is therefore:

x = 20 / 5

x = 4 years

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Answer:

p = 1

Step-by-step explanation:

Given equation,

→ -8(1 + 4p) + 7p = -25 - 8p

Let's solve for the value of p,

→ -8(1 + 4p) + 7p = -25 - 8p

→ -8 - 32p + 7p = -25 - 8p

→ -32p + 7p + 8p = -25 + 8

→ -17p = -17

→ p = (-17)/(-17)

→ [ p = 1 ]

Hence, the value of p is 1.

The total pay change for each issue of Math is Fun sold by Carlos is $110. If he doesn't sell copies of Math is Fun, Carlos's gross wages are $2500 for him.

Given that:

x represents the number of copies of Math is Fun he sells. Suppose that x and y are related by the equation 2500 + 110x = y.

Equation: The equation is the values of two expressions that are equal.

Here,

For equation,

y = 2500 + 110x

The change in Carlos's total pay for each copy of Math is Fun he sells,

Differentiate the equation,

dy/dx = 110

The total pay for each copy of Math is Fun he sells is $110.

Carlos's total pay if he doesn't sell any copies of Math is Fun,

x = 0

y = 2500

Carlos's total pay if he doesn't sell any copies of Math is Fun is $2500.

Thus, the change in Carlos's total pay for each copy of Math is Fun he sells is $110. Carlos's total pay if he doesn't sell any copies of Math is Fun is  $2500.

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Answer:

---------------------

Initial number of pairs of shoes is 20.

To achieve 50 pairs Mindy needs 30 more pairs.

Each week 2 pairs added but 1 removed. It makes total of 1 pairs addition.

After 28 weeks Mindy will have 20 + 28 = 48 pairs of shoes.

The next week he will purchase 2 more pairs and get 50 pairs in total.

The number of weeks it will take for her closet to have 50 pairs of shoes would be = 30 weeks.

A purchase price is the amount of money that was use to obtain a valuable.

The number of shoes owned by Mindy = 20 pairs

The number of shoes Mindy purchases per week = 2 pairs

The number of shoes Mindy destroys = 1 pair.

Therefore, in a week Mindy has an additional 1 pair of shoe.

The number of pairs she needs extra = 50-20 = 30

Since 1 pair of shoe = 1 week, she will require 30 weeks to purchase additional 30 pairs making it up to 50 pairs of shoes she owns.

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Answer:

9.995%

Step-by-step explanation:

principal-10760

n(time)-17

rate-?

amount-54343

[tex]a = p(1 + \frac{r}{100} ) {}^{n} [/tex]

54343=10760(1+(r/100))^17

5.05=(1+(r/100))^17

1.09995=1+(r/100)

0.09995=r/100

r=9.995%

If the length of HJ is 7 unit then the length of EI is 14 unit.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

We are given a circle with center H.

Therefore, the radius of the circle is found as; HJ

Then the Diameter is the line from one point in the circle to the other point through the center of the circle.

Diameter of the circle = EI

Since we know that One of the theorems of a circle states that the angles in the same segments or on the same chord are equal.

Then the name of the chord is FG.

If the length of HJ is 7 unit then the length of EI is;

EI = 2 HJ

EI = 14 unit.

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Answer:

when x = 3

8(3)

8*3=24

all you have to do is to substitute x into the expression

The fraction which shows what part of packages they have eaten is 3/5.

What is fraction?

A fraction is characterized as a portion of something larger. Fractions make calculations quicker and easier by making it easier to distribute and judge numbers.

Main Body:

Total no. of boxes of cereals in a package = 10

Total no. of boxes eaten by family = 6

Fraction  can be calculated by directly by diving the values.

Fraction ⇒ 6/10

dividing by 2 on both denominator and numerator

hence, Simple fraction is 3/5.

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