Given: ABCD is a parallelogram and FBED is a parallelogram.
Prove: FAB is congruent to ECD.

Answer:-59

Step-by-step explanation:

-2*36 + -2*-8

-72+16-3

-56-3

-59

The number of nickels and dimes Latanys have is 10 and 14.

An equation is a mathematical statement of two expressions connected by an equal sign.

We have,

Total coins = 24

$1 = 20 nickels

$1 = 10 dimes

Now,

Number of nickels = N

Number of dimes = D

Now,

N + D = 24 ____(1)

N = 24 - D _____(2)

0.05N + 0.1D = 1.90 ____(3)

Putting (2) in (3) we get,

0.05(24 - D) + 0.1D = 1.90

1.2 - 0.05D + 0.1D = 1.90

0.05D = 1.90 - 1.2

0.05D = 0.7

D = 0.7 / 0.05

D = 14

Now,

N = 24 - D

N = 24 - 14

N = 10

Thus,

The number of nickels is 10.

The number of dimes is 14.

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When both riders have stopped, the person that is further away from the parking lot is; The second rider.

Let the required distance be represented by x.

Using Pythagoras theorem, we have:

hypotenuse² =  opposite² + adjacent²

x = √(8² + 15²)

x = √289

x = 17 km

This means that the first biker is 17.0 km from the starting point.

Using the law of cosine which is given by the expression;

c² = a² + b² - 2ab cos C

x² = 8² + 15² - 2(8*15) cos (160)

x = 20.22 km

This means that the second biker is 20.22 km from the starting point.

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The least amount possible is $25 and the number of miles is 25 miles

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

Yellow Taxi service charges a $15 flat fee plus $2.50

This means that

Yellow Taxi: y = 15 + 2.5x

For the graph, we have

y-intercept = 10

(x, y) = (0, 10) and (2, 16)

So, the slope is

slope = (y₂ - y₁)/(x₂ - x₁) = (16 - 10)/(2 - 0) = 3

So, we have

Black and White Taxi service: y = 10 + 3x

Yellow Taxi: y = 15 + 2.5x

When he travels for 5 miles, we have

Black and White Taxi service: y = 10 + 3 * 5 = 25

Yellow Taxi: y = 15 + 2.5 * 5 = 27.5

Hence, the least amount possible is $25

This means that we equate the above equations

So, we have

15 + 2.5x = 10 + 3x

Evaluate the like terms

0.5x = 5

Divide

x = 25

Hence, the distance is 25 miles

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Answer:

The cellular plan allows you to use 4 gigabytes and charges you a flat $90. After 4 gigabytes have been used then, every gigabyte after that is an extra $20.

The values of x that provide meaningful predictions for the output value y are given as follows:

c. Prediction values are meaningful only for X-values in (or close to the range of the original data.

Regression equations are built from a sample of a data-set, and are used to model the entire data.

Depending on the behavior of the data, the regression equation can be linear, quadratic, logistic, exponential, and so on...

These regression equations are not valid for all values of the input x, some conditions are given as follows:

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Center point of dilation is a fixed point in a plane about which all the points of the figure expanded or contract. And scale factor of a dilation is the ratio of new formed image to the old given image.

Explanation:

Therefore, the center of the dilation can be find using the translation and scale factor can be calculated using the ratio of the new to the old images.

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Answer: 60

6 x 10 is 60 and a negative times a negative is positive.

Answer: 60 hope this helps

The time taken to reach $1000000 with an interest rate in a mutual fund of 8% compounded monthly is about 64 years and 2 months.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

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

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

P = $6000

r = 8%

n = 12

A = $1000000

Now,

1000000 = 6000 [tex](1 + 0.08/12)^{12t}[/tex]

1000/6 = [tex]1.0067^{12t}[/tex]

log on both sides.

log 166.67 = 12t log 1.0067

2.22 = 12t x 0.0029

12t = 2.22 / 0.0029

12t = 765.52

t = 765.52/12

t = 64.163 years

This means,

About 64 years and 2 months.

Thus,

The time taken to reach $1000000 is 64 years and 2 months.

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The lines or angles with measure must be true for the lines and angles.

To predict the truthfulness of the statements, we must understand the concept of congruency. Any two entities will be congruent if they measure the same. In the question, the line AN will be congruent to line segment LB and line NC will be congruent to line BZ.

Similarly, the angle measurements should also be same to the angles to be congruent. In case of same angles, the Angle BMZ will be congruent to Angle CMZ and Angle ZBM will be congruent to Angle ZCM.

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Answer: D

Step-by-step explanation:

In order to dilate something on a coordinate plane, multiply the coordinate with the scale factor. This process is known as mapping.

What is a dilation?

Dilation is a process of altering a thing. It is a process of renewal that to make the objects smaller or larger, with the use of specific scale factor.

The new figure that is the result of dilation is known as the image. Initial figure is referred to as the pre-image.

What is a center of dilation?  

Center of dilation is the resizing that happens from a point. The objects/figures are expanded or contracted from the center of dilation.

Scale factor is a figure by which the size of any geometrical figure can be resized, with respect to its original size. The scale factor is multiplied to get image.

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The dilation will change the size of the figure, so it can be getting bigger or smaller

The dilation is the process of changing the size of the figure, but the shape of the figure will be same. Therefore we can say that the dilation is one form of the transformation of the figure

The dilation can be increase the size or decrease the size

If you consider the case of dilation with scale factor, when the scale factor is greater than 1  the size will be bigger and if the scale factor is between 0 and 1 the size will be smaller than original size

Therefore, the dilation can be getting bigger or smaller

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Integers are closed under addition by all the properties. Hence, the answer is True.

Integers are set of zero, positive, and negative numbers. The set of integers is represented by the symbol ‘Z’.

Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}

To check if the integers are closed under addition or not we will check out the four properties namely, the closure property, the commutative property, the associative property, and the distributive property.

Let us consider each property one by one -

1. The closure property-

let's take two integers say 5 and 2.

now 5+2=7, but -2+5= -3 which is an integer.

Thus, integers are closed under addition by closure property.

2. The commutative property-

let's take two integers say 5 and 2.

now 5+2=7 and 2+5=-7

hence, we get 2+5 = 5+2.

Thus, integers are closed under addition by commutative property.

3. The associative property-

let's take three integers say 5, 3, and 2.

now (5+3)+2 = 10 and 5+(3+2)= 10

hence, we get (5+3)+2 = 5+(3+2).

Thus, integers are closed under addition by associative property.

4. The distributive property-

let's take three integers say -2, 6, and 5.

now, -2 × ( 6 + 5 ) =  -2 × 6 + (-2) × 5  = -12 - 10 = -22

        and -2 × ( 6 + 5 ) = -2 × 11 = -22

Hence, -22 = -22

Thus, integers are closed under addition by distributive property.

Hence, we can conclude that integers are closed under addition by all the properties.

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The complete question is-

Are Integers closed under addition. True or false?

x=-9/2 and y=17/4 are the solution to the system of linear equations.

Two or more expressions with an Equal sign is called as Equation.

The system of linear equations are:

y=-5/2x-7..(1)

x+2y=4...(2)

x=4-2y

Subtract x value in equation 1.

y=-5/2(4-2y)-7

y=-20/2+5y-7

y=-10+5y-7

y=5y-17

Subtract both sides by 5y

y-5y=-17

-4y=-17

Divide both sides by 4

y=17/4

Now add y value in equation 2.

x+2(17/4)=4

x+17/2-4=0

x+9/2=0

x=-9/2

Hence, x=-9/2 and y=17/4 are the solution to the system of linear equations.

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The student that is correct is George as the ratio of pools open on weekends to the total number of pools is 6:16.

Ratio is the relationship between two or more numbers. It is the number of times that one value is contained within other value(s). The sign that is used to represent ratio is :.

In order to determine the ratio between the number of pools open on the weekend to the total number of pools express the numbers that represent each value as ratios.

This will be:

= number of pools open on weekends: total number of pools

= 6 : 16

George is correct.

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a) The scatter plot and the line of fit are given on the second image shown at the end of the answer.

b) The linear function is defined as follows: y = 1.75x + 168.

The linear function is defined in the slope-intercept format, as follows:

y = mx + b.

In which:

Considering the data for 2009 and for 2017 from the table, taking x as the number of years since 2005, two points are given as follows:

(4,175) and (12, 189).

The slope, given two points, is calculated as the division of the change in y divided by the change in x, hence:

m = (189 - 175)/(12 - 4) = 14/8 = 1.75.

Hence:

y = 1.75x + b.

When x = 4, y = 175, hence the intercept b is calculated as follows:

175 = 1.75(4) + b

b = 168.

Then the line of fit is:

y = 1.75x + 168.

The scatter plot is composed by all the points of the data-set, considering x as the number of years since 2005, hence:

(0, 169), (2, 175), ... (12, 189).

The table is given by the first image at the end of the answer.

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We need to use 7 terms to estimate the value of ln(1.4) to within 0.0001.

A Maclaurin series is a function that is used to estimate the values functions, evaluate the sum, or determine the value of the anti-derivative of a function.

We have:

f(x)=ln(1+x)

Expansion of In(1+x) up to seven terms is:

In(1+x) = x - x^2/2 + x^3/3 - x^4/4 + x^5/5 - x^6/6+ x^7/7

Where it is known that -1 <= x <= 1

Put x=0.4 in the above series:

ln(1.4) = 0.4 - 0.4^2/2 + 0.4^3/3 - 0.4^4/4 + 0.4^5/5 - 0.4^6/6+ 0.4^7/7

We get:

ln(1+4) = 0.3365333

Therefore,  we need 7 terms to estimate the value of ln 1.4 to within 0.0001.

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The length of the perimeter is 44cm if the area of a rectangle is 105sq in and length of one of the side is 7 in.

A perimeter is a closed path that encompasses, surrounds, or delineates something, whether it be a two-dimensional shape or a one-dimensional length. The outermost border of an ellipse or circle is its circumference.

Knowing the perimeter is helpful in a variety of circumstances. Calculated perimeter refers to the length of fence required to entirely enclose a yard or garden.

Given,

Area of a rectangle=105cm²

And also given that,

Width w=7cm

Area= Length× Width

Length=Area/Width

Length-105/7

Length=15cm

Here, Now we have to calculate the perimeter of a rectangle

Perimeter=2(Width+ Length)

Perimeter=2(7cm+15cm)

Perimeter=44cm.

Hence, the length of the perimeter is 44cm.

Therefore, the length of the perimeter is 44cm if the area of a rectangle is 105sq in and length of one of the side is 7 in.

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Let the number of pens be p and number of pencil cases be c.

Use given information and set inequality:

Simplify it by dividing all terms by 20:

If number of pens is more than 100, we get:

Substitute this into inequality:

If Dona sells more than 100 pens then she will exceed php 2000 regardless the number of pencil cases sold.

The rectangular horse pasture's largest area, in square feet, can be enclosed in [tex]80000m^{2}[/tex]

Let the sides of the rectangle-shaped fence be a and b.

We have to use wire for the three sides of the fence.

[tex]a+b*2=800[/tex]

Area A is given by

[tex]A=a*b[/tex]

Also, we can write A as a function of b

[tex]A=A(b)\\=(800-2*b)b=800b-2b^{2}[/tex]

Taking the derivative of A

[tex]A'=800-4b\\A'=0\\b=200m[/tex]

Then the length of the other side

[tex]a=800-2*200\\=400m[/tex]

The largest area

[tex]A=400*200\\=80000m^{2}[/tex]

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The final scores will be dependent on the prior ones.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

raw scores for as long as possible before assigning a letter grade to a student.

Because the final scores will be dependent on the prior ones.

Hence The final scores will be dependent on the prior ones.

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Answer:

Leopard: 60 lb

Lion: 420 lb

Step-by-step explanation:

Let x = weight of leopard.

Weight of lion = 7x.

Sum of the weights = x + 7x = 8x

Total weight = 480 lb

8x = 480

x = 60

7x = 7 × 60 = 420

Answer:

Leopard: 60 lb

Lion: 420 lb

Answer: shown below

Step-by-step explanation:
x = 7y

x+y+ 480

7y+y = 480

8y = 480

y = 480/8 = 60 pounds for the leopard

x = 7(60) = 420 pounds for the lion

Answer: D

Step-by-step explanation:

The line is positive and not very steep. For slope, 13 is too steep, -13 and -3 are negative. It must be y-5=3(x-1), which has an accurate slope of 3.

The value of the inequality will be;

⇒ x ≤ 2 1/2

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ 3 1/2 ≥ 1.4x

Now,

Since, The inequality is,

⇒ 3 1/2 ≥ 1.4x

Hence, Solve for x as;

⇒ 7/2 ≥ 1.4x

⇒ 3.5 ≥ 1.4x

⇒ 3.5/1.4 ≥ x

⇒ 35/14 ≥ x

⇒ 5/2 ≥ x

⇒ x ≤ 2 1/2

Thus, The value of the inequality for x is;

⇒ x ≤ 2 1/2

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Answer:

-g+12

Step-by-step explanation:

Answer:

A: The system of linear inequalities that fits the situation is:

15x + 13y >= 300

60x + 20y <= 1200

Where x is the number of dozen cookies and y is the number of dozen cupcakes.

B: The new inequalities that need to be added to the problem are:

x <= 12

y <= 40

C: The maximum amount of baked goods that she could make is:

x = 12

y = 40

D: The amount she will earn if she made the maximum amount of baked goods is:

15x + 13y = 15 * 12 + 13 * 40 = $660

E: The time it will take her to make the maximum amount of baked goods is:

60x + 20y = 60 * 12 + 20 * 40 = 960 minutes = 16 hours

F: The least amount of time she could work and still earn $300 is:

15x + 13y = 300

x + y = 20

Solving this system of equations, we get:

x = 8

y = 12

In this case, she would make 8 dozen cookies and 12 dozen cupcakes in a minimum of 8 hours.

Step-by-step explanation:

Answer:

the volume of the space left in the larger box for packing materials is 1000 - 512 = 488 cubic inches.

Step-by-step explanation:

To find the volume of the space left in the larger box for packing materials, we first need to calculate the volume of the smaller cube and then subtract it from the volume of the larger box. The volume of a cube with side length s is given by s^3, so the volume of the smaller cube with side lengths of 8 inches is 8^3 = 512 cubic inches. The volume of the larger box with side lengths of 10 inches is 10^3 = 1000 cubic inches