Wxyz is a parallelogram in the coordinate plane. the vertices for the parallelogram are w(0,0), (b,c), y (a + b,c), and z(a,0), where a > 0,b > 0, and c> 0 what set of statements prove that the diagonals of the parallelogram bisect each other?

To solve this problem we change the structure from

1/2 + ? = 7/8

to

7/8 - 1/2 = ?

Now we need to subtract the fractions and find the difference. To do this, make the denominators (the bottom numbers on the fractions) the same.

1/2 = 4/8

then subtracts the numerator

7/8 - 4/8 = 3/8

there is your answer... 3/8

The variables we need to use in the question are defined. We will call the price of a knife as [tex]k[/tex] and the price of a spoon as [tex]s[/tex].

The total price of [tex]12[/tex] spoons and [tex]16[/tex] knives is then given. Let's write knives instead of [tex]4[/tex] spoons.

===================================================

Explanation:

k = cost of one knife

s = cost of one spoon

costs are in pounds

12s = cost of 12 spoons

16k = cost of 16 knives

12s+16k = 105.64 pounds is the total cost

We can replace k with 4s because of the phrasing "a knife is 4 times the cost of a spoon". Whatever s might be, quadruple it and it leads us to the value of k.

So,

12s+16k = 105.64

12s+16(4s) = 105.64

12s+64s = 105.64

76s = 105.64

s = 105.64/76

s = 1.39 pounds is the cost of one spoon

k = 4s = 4*1.39 = 5.56 pounds is the cost of one knife

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

Check:

1 spoon = 1.39 pounds

12 spoons = 12*1.39 = 16.68 pounds

1 knife = 5.56 pounds

16 knives = 16*5.56 = 88.96 pounds

12 spoons + 16 knives = 16.68+88.96 =  105.64 pounds total

This fully verifies the answer.

The total number of ways the prizes are awarded is 8855.

The prizes for entrants in a young inventors competition are $100, $50, $25, and $10.

Which are of total 4 types of prizes.

If there are 23 entrants in the competition the prizes can be awarded in the following ways by using Combinations.

Total number of ways =  ²³C₄

                                    = [tex]\frac{23!}{4! * (23 - 4)!}[/tex]

                                    = 8855

The total number of ways the prizes are awarded is 8855.

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Answer: ∠BDG = 50°

Step-by-step explanation:

    We know that a straight line is equal to 180°, meaning that line CDF is 180°.

     Next, we know that angle CDB, angle BDG, and angle GDF should all add up to be 180°, since we know CDF is equal to 180°.

     Lastly, with all this information in mind, we will set up an equation and solve.

130° + BDG = 180°

∠BDG = 50°

Answer:He biked for 3 hours (48 miles)

He ran for 1.5 hours (13.5 miles)

He swam for 1 hour (2.5 miles)

He covered 62 miles in 5.5 hours of activity

Step-by-step explanation:

Answer:

1.5h

Step-by-step explanation:

Answer:

157 cups

Step-by-step explanation:

First, convert in to cm

83.375 in  * 2.54   Cm/in = 211.77 cm

Each cup adds 1.3 cm to the (9.2 - 1.3 cm) base     (Base is 7.9)

211.77  =  7.9  + 1.3  x          X is the number of cups

         X = 156.9 = ~ 157 cups

If the baseball diamond at a playground is a square with sides that measure 80 feet. About how long would a straight line be from home plate to second base is: B.113.1 feet.

Given data

Sides measure in feet = 80 feet.

Since the  diagonal tend to forms the hypotenuse of a right triangle with both sides of 80 feet

Hence,

Using the Pythagoreans theorem to determine the distance

(80)² + (80)² = x²

6400 + 6400 = x²

x² = 12,800

x = √ 12,800

x = 113.1 feet

Therefore the correct option is B.

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Answer:

aproamitly 1.66666666667

Step-by-step explanation: 15/9=1.66666666667 thus

15/1.66666666667=9

Answer: it's 135 the other dude used a calculator probs

Answer:

Step-by-step explanation:

The  area of the triangle when the vertices of the triangle are given can be calculated by the following formula:

Area of triangle = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|  where the vertices are A(Ax, Ay), B(Bx, By), C(Cx, Cy)

Now, we have been given the values of vertices as A(4, -3) B(9,-3) , and C(10, −11)

Therefore,

By applying the formula and substituting the given values, we get

Area = 0.5 * |4 * (-3 + 11) + 9 * (-3 + 11) + 10 * (-3 - 3)|

Area = 0.5 * |44|

Area = 22

Hence, the area of triangle ABC with the given vertices is 22 square units

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Explanation:

The coordinates are given below are

The image is given below as

To calculate the coordinate of A,we will use the formula below

By substituting the values, we will have

Hence,

The coordinate of B will be

Using equations the weight of both Sean and Brad is 156 lbs and 73 lbs.

So, the weight of Sean and Brad.

So, the equation will become:

x + 2x + 10 = 230

Now, solve this equation for 'x' as follows:

Rounding off: 73 lbs

Then,

Therefore, using equations the weight of both Sean and Brad is 156 lbs and 73 lbs.

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Answer:

255 ^t because the amount if toothpicks depend on the number of boxes she/he gets.

Answer: A

Step-by-step explanation:

Answer: n=7

Step-by-step explanation:

First distribute the numbers to get 5n+10=3+6n

Next Subtract 6n from both sides to get -n=10=3

Finally divide both sides my -1 to get rid of the -n to get n=7

Hope this helps :)

The area of a rectangular backyard = 2(4x - 5y)

The algebraic expression has a equivalent expression as = 2 x 4x + 2 x 5y

= 8x + 10y

Im going to answer for the first one.So angles 1 and 2 are corresponding angles and so they are equal because line k and line p and parellel

The average rate of change when x increases from -3 to 5 is given as follows:

r = (f(5) - f(-3))/8.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the average rate of change is given by the fraction presented as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

In the context of this problem, the input x increases by -3 to 5, hence the change in the input is given as follows:

b - a = 5 - (-3) = 5 + 3 = 8.

The change in the output is given as follows:

f(b) - f(a).

(the problem is incomplete hence the answer is given in general terms).

Then the average rate of change of the function when x increases from -3 to 5 is given as follows:

r = (f(5) - f(-3))/8.

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Answer:

=========================

The triangle is isosceles as marked.

The two opposite angles of equal sides are equal, one of them is x and the angle in between them is 28°.

Use angle sum of the triangle:

Same as previous question, we have an isosceles triangle. Equal sides are:

Find the perimeter by substituting the value of x:

Given:

The measure of angle of arrc SQ is 160°.

The measure of angle of arc PR is 102°.

The objective is to find the measure of angle x.

Since, the angle x is away from te center of the circle.

Then, the formula to find the value of angle x is,

Now, substitute the given values in the above formula.

Hence, the value of x is 131°.

A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists  more dispersed.

The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data exists grouped around the mean, whereas a large standard deviation indicates that the data exists  more dispersed.

The standard deviation is a statistic that expresses how much variance or dispersion there is in a group of numbers. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.

Because it aids in comprehending measurements when the data is scattered, standard deviation is significant. The standard deviation of the data will be higher the more evenly dispersed the data is.

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Answer:

18.42

Explanation:

15+3=18

0.4+0.02=0.42

18+0.42=18.42

First, let's find the total cost of all the apples:

Now, we divide this by the total amount of apples bought. In our case, we know that there were 10 Granny Smith apples and 15 Golden Delicious, for a total of 25 apples.

Therfore, we can conclude that the average cost per apple was $0.68

Null hypothesis, [tex]H_{0}[/tex] P.1 = P2 (The proportion of tablets owned by men and women are equal.)

Alternative hypothesis,[tex]H_{0}[/tex]  P1[tex]\neq[/tex]P2 (The proportion of tablets owned by men and women are not equal.)

Sample proportion for men who own tablets  ≈0.433

Sample proportion for women who own tablets ≈0.466

p value of the test  is 0.3320.

Test whether the survey results provide evidence of a difference in the proportion owning a tablet between men and women.

Let p, be the proportion of all men who own tablets and p, be the proportion of all women who own tablets.

Null hypothesis, [tex]H_{0}[/tex] P.1 = P2 (The proportion of tablets owned by men and women are equal.)

Alternative hypothesis,[tex]H_{0}[/tex]  P1[tex]\neq[/tex]P2 (The proportion of tablets owned by men and women are not equal.)

The notations for the sample statistic are  p p1 p2

Pooled proportion p = [tex]\frac{x_{1}+x_{2} }{n_{1}+n_{2} }[/tex]= 197+235/455+504

                                               ≈ 0.45

Sample proportion for men who own tablets,

                               p1 = [tex]\frac{x_{1} }{n_{1} }[/tex]= 197/455

                                           ≈0.433

Sample proportion for women who own tablets,

                              p2 = [tex]\frac{x_{2} }{n_{2} }[/tex] = 235/506

                                          ≈0.466

Since p1<p2  women group has higher tablet ownership.

Sample statistic, p1-p2

                          = 0.433-0.466

p value of the test  is 0.3320.

In mathematics, statistics deals with the study of surveys and reports of numerical data. For questions, we need to define a hypothesis. In general, there are two types of hypotheses. One is the null hypothesis and the other is the alternative hypothesis.

In probability and statistics, the null hypothesis is the general statement or default state that  zero  or nothing will happen. For example, there is no association between groups or no association between two measured events. Here, a hypothesis is generally assumed to be true until  other evidence is presented to disprove the hypothesis.

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Check the picture below.

Answer:

3

Step-by-step explanation:

Considering the sum and the product of the roots of the quadratic equation, it is found that the numeric value of the expression is given as follows:

[tex]\alpha + \beta = -2.5[/tex]

A quadratic equation is defined as follows:

[tex]y = ax^2 + bx + c, a \neq 0[/tex]

The roots of the equation are given as follows:

[tex]\alpha, \beta[/tex]

The sum of the roots is given as follows:

[tex]\alpha + \beta = -\frac{b}{a}[/tex]

The product of the roots is given as follows:

[tex]\alpha\beta = \frac{c}{a}[/tex]

In the context of this problem, the product is of 4, as [tex]\alpha\beta = 4[/tex] hence:

c/a = 4

c = 4a.

The coefficients are in an arithmetic progression, hence:

We have that c = 4a, hence:

4a = a + 2d

2d = 3a

d = 1.5a.

Hence coefficient b is calculated as follows:

b = a + d = a + 1.5a = 2.5a.

Then the sum of the roots is given as follows:

[tex]\alpha + \beta = -\frac{b}{a} = -\frac{2.5a}{a} = -2.5[/tex]

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Answer: m<1 = 146 degrees, m<3 =146 degrees, m<4 = 34 degrees

Step-by-step explanation:

Since m<2 and m<4 are vertical angles, they will be equal to each other.

By using straight lines, we can easily find out that m<1 = 180-34 = 146

Since m<1 and m<3 are vertical angles, they are equal to each other.

Hope this helped :))

Rate of change of x with respect to [tex]\alpha[/tex] when [tex]\alpha =\frac{\pi }{3}[/tex] is 5ft/s.

Since the ladder is 10ft long resting against a vertical wall.

Let the angle between the top of the ladder and the wall is [tex]\alpha[/tex] .

And let the distance from the bottom of the ladder to the wall is x.

Thus we need to find the rate of change of x with respect to [tex]\alpha[/tex]  when [tex]\alpha =\frac{\pi }{3}[/tex]

Consider L to be the length of the ladder.

Then, L = 10ft

Thus, we get the relation between the angle and distance x i.e.

x = L [tex]\sin \alpha[/tex]

On differentiating the above equation,

[tex]\frac{dx}{dt} =L \cos \alpha[/tex]

Now after putting the values [tex]\alpha =\frac{\pi }{3}[/tex] in above equation, we get,

[tex]=(10)\cos(\frac{\pi }{3} )=(10)(\frac{1}{2} )=5[/tex]

Therefore, [tex]\frac{dx}{dt} =5[/tex] ft/s

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