In the figure ABCD is a parallelogram. P, Q, R and S are the midpoint of the sides of the parallelogram. Prove that PQ = RS and QR = PS.

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Explanation:

Any triangle prism is composed of 2 parallel triangular faces (base faces), along with 3 rectangular lateral faces.

The bottom triangle face has a base of 10 cm and a height of 4 cm. The area is 0.5*base*height = 0.5*10*4 = 20 square cm. Two of these triangles combine to an area of 2*20 = 40 square cm. We'll use this later.

The lateral surface area of any prism can be found by multiplying the perimeter of the base by the height of the prism. The base triangle has side lengths 5, 8 and 10. The perimeter is 5+8+10 = 23. So the lateral surface area is (perimeter)*(height) = 23*9 = 207

Add this to the total base area we got earlier and the answer is 40+207 = 247. The units are in square cm, which we can write as cm^2.

Answer:

2

Step-by-step explanation:

In order to make the equation undefined, you should make the denominator 0. Remember that dividing anything by 0 will become undefined.

[tex]2x-4=0\\\frac{2x=4}{2} \\x=2[/tex]

Answer:

[tex]\boxed{x = 2}[/tex]

Step-by-step explanation:

A rational expression is undefined when Denominator = 0

Here Denominator = 2x-4

So,

=> 2x - 4 = 0

Adding 4 to both sides

=> 2x = 4

Dividing both sides by 2

=> x = 2

Answer:

Step-by-step explanation:

Hello!

X: content of sugar of a sample of cereal.

Data set:

0.03, 0.24, 0.30, 0.47, 0.43, 0.07, 0.47, 0.13, 0.44, 0.39, 0.48, 0.17, 0.13, 0.09, 0.45, 0.43

n= 16

[tex]\frac{}{X}[/tex]= 0.295g

S= 0.17g

You have to test if the mean sugar content is less than 0.3g

H₀: μ ≥ 0.3

H₁: μ < 0.3

α: 0.05

Assuming that the variable has a normal distribution, you have to conduct a t test:

[tex]t= \frac{\frac{}{X}-Mu }{\frac{S}{\sqrt{n} } } ~~t_{n-1}[/tex]

[tex]t_{H_0}= \frac{0.295-0.30}{\frac{0.17}{\sqrt{16} } } = -0.12[/tex]

p-value: 0.4533

The p-value is greater than α, the decision is to not reject the null hypothesis.

At a 5% significance level the decision is to not reject the null hypothesis. You can conclude that the average sugar content of the cereal is equal or greater than 0.3g of sugar per gram of cereal.

I hope this helps!

Answer:

17 cans

Step-by-step explanation:

18 cans

7 are taken away

18-7 =11

Then we put 6 back on

11+6 = 17

There are now 17 cans

Answer:

They are not perpendicular because their slopes are not negative reciprocals.

Step-by-step explanation:

Well first we need to find slope.

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

Line HJ)

(-4,-2) , (0,4)

y2 is 4 y1 is -2, so 4 - -2 = 6

0 - -4 = 4

6/4 -> 3/2

Due to the point (0,4) having no x value 4 is the y intercept.

Hence, y = 3/2x + 4 is the slope of line HJ

Line FG)

(-4,1) , (0,-2)

y2 is -2 y1 is 1, so -2 - 1 = -3

0- -4 = 4

Because (0,-2) is missing an x value -2 is the y intercept,

Equation: y = -3/4x - 2

They are not perpendicular because their slopes are not negative reciprocals.

The slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).

Recall:

Given that lines HJ (blue line) and FG (red line) are on a coordinate plane as shown in the diagram attached below, let's find their slope:

Slope of line HJ:

[tex]Slope (m) = \frac{-2 - 4}{-4 -0} = \frac{-6}{-4} = \frac{3}{2}[/tex]

Slope of line FG:

[tex]Slope (m) = \frac{-2 - 1}{0-(-4)} = \frac{-3}{4} = -\frac{3}{4}[/tex]

Therefore, the slope of HJ (3/2) and the slope of FG (-3/4) are not negative reciprocal, so, they are not perpendicular. (Option D).

Learn more here:

https://brainly.com/question/18975049

Answer:

[tex]\boxed{\mathrm{False}}[/tex]

Step-by-step explanation:

[tex](p-q)^2[/tex]

[tex](p-q)(p-q)[/tex]

Use FOIL method.

[tex]p^2-pq-pq +q^2[/tex]

[tex]p^2-2pq +q^2[/tex]

I believe it is C, as the graphs do look the same.

Answer:

p(x) = (x + 1) (x - 3) (x + 2)

Step-by-step explanation:

x³ - 7x - 6

(x+1) (x² - x - 6) found by doing long division

(x+1) ( x - 3) (x + 2) are the factors

The polynomial p(x) as a product of linear factors is; p(x) = (x + 1) (x - 3) (x + 2)

They are mathematical expressions involving variables raised with non negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non negative exponentiation of variables involved.

We are given the polynomial as;

x³ - 7x - 6

Then we found by doing long division;

(x+1) (x² - x - 6)

(x+1) ( x - 3) (x + 2)

These are the factors.

Hence, The polynomial p(x) as a product of linear factors is; p(x) = (x + 1) (x - 3) (x + 2)

Learn more about polynomials here:

https://brainly.com/question/27343162

#SPJ2

Answer:

Average speed

= 5 5/6 mph , or

= 5.83 mph (to 2 decimals)

Step-by-step explanation:

Average speed is total distance divided by the total time it takes to cover the given distance.

Since uphill = 5 mph, and downhill = 7 mph, we know the average speed is between 5 and 7 mph.

Let

x = distance uphill, and also distance downhill.

Total distance = 2x miles

Total time = x/5 + x/7 hours  = 12x/35 hours

Average speed

= total distance/total time

= 2x / (12x/35) mph

= 70x / 12x

= 5 5/6 mph

= 5.83 mph (to 2 decimals)

Answer: The probability that she will visit them in the exact order ABCD or DCBA =  [tex]\dfrac{1}{12}[/tex]

Step-by-step explanation:

Given: Jennifer wants to visit 4 different cities A,B,C and D on her vacation.

If she visits in an order , total such orders will be [tex]4![/tex] = 4 x 2 x 3 x 1 =24.

Since probability = [tex]\dfrac{\text{Favourable outcomes}}{\text{total outcomes}}[/tex]

In this case favorable outcomes ( ABCD ,  DCBA)=  2

Total outcomes = 24

Required probability = [tex]\dfrac{2}{24}=\dfrac{1}{12}[/tex]

Hence, the probability that she will visit them in the exact order ABCD or DCBA =  [tex]\dfrac{1}{12}[/tex]

ok                                                         its 11 sqrt 6                                    

because if sqrt 6 is x, and 5x +6x=11x

so its 11 sqrt 6              

Answer:

[tex]x=20[/tex]

[tex]y=10\,\sqrt{3}[/tex]

Step-by-step explanation:

In the triangle we have the following trigonometric equations:

[tex]tan(60^o)=\frac{opposite}{adjacent} \\\sqrt{3} =\frac{y}{10} \\y=10\,\sqrt{3}[/tex]

and also:

[tex]cos(60^o)=\frac{adjacent}{hypotenuse}\\\frac{1}{2} =\frac{10}{x}\\x=20[/tex]

Answer:

Step-by-step explanation:

each term has h^1

each term's coefficient is divisible by 12

12h( 3, h^5, 4h^4)

Answer:

80 in²

Step-by-step explanation:

8/10 = x/100

x = 80

Answer:

k=5

a= -5

Step-by-step explanation:

if the polynomial x^4-6x^3+16x^2-25x+10 is divided by x^2-2x+k the remainder comes out to be x+a,find k and a

Solution

x^4-6x^3+16x^2-25x+10 / x^2-2x+k = x-a

We have,

(4k-25+16-2k)x+[10-k(8-k)] = x+a

(2k+9)x + (10-8k+k^2)=x+a

2k-9=1

2k=1+9

2k=10

Divide both sides by 2

2k/2=10/2

k=5

And

10-8k+k^2=a

10-8(5)+(5^2)=a

10-40+25=a

-5=a

Therefore, a=-5

x^4-6x^3+16x^2-25x+10 divided by x^2-2x+5 = x-5

Answer:

y = 10

Step-by-step explanation:

y = 2x + 6

Let x  =2

y = 2*2 +6

y = 4+6

y = 10

Answer:

Step-by-step explanation:

[tex]y = 2x + 6 \\ x = 2 \\ y = 2(2) + 6 \\ y = 4 + 6[/tex]

[tex]y = 10[/tex]

Answer:

2

Step-by-step explanation:

|a+x|/2-|a-x|/2

Plug in the values.

|-2+-6|/2-|-2- -6|/2

Evaluate.

|-8|/2-|4|/2

Apply rule : |-a| = a

8/2 - 4/2

4 - 2

Subtract.

= 2

Answer:

Onyango is 48, his daughter is 16 and his son is 12

Step-by-step explanation:

Let's call Onyango's age x, therefore his daughter and son's ages are 1/3 x and 1/4 x respectively. We can write:

x + 8 = 12 + (1/3x + 8 + 1/4x + 8)

x + 8 = 7/12x + 28

5/12x = 20

x = 48 → 1/3x = 48 / 3 = 16, 1/4x = 48 / 4 = 12

Answer:

Option B

Step-by-step explanation:

When we compare the number of shirt with it's cost, we find out that 8 shirts cost $120.

For more understanding, see the attached file.

Answer:

Step-by-step explanation:

what do u see!????????

You are correct. The higher the standard deviation is, the more spread out the data set will be. Nice work.

Answer:

Hey there! The correct answer is A. Data set C.

---

Standard deviation is simply defined as the spread of a data set in relation to the mean of the data set. The standard deviation can be calculated with a formula as shown below.

[tex]\displaystyle \sigma = \sqrt{\frac{\Sigma(x_i-\mu)^2}{N}[/tex]

Each variable has a significant meaning for this formula.

With this information, we can find the standard deviation of a data set.

Generally speaking, statisticians want a standard deviation that is on the lower end so that conclusions can be drawn about the data that was observed.

If a standard deviation is large, that means that most of the data is quite far from the mean and the data usually disproves a hypothesis. This is undesirable since the original hypothesis cannot be proven with this experiment.

When the standard deviation is quite low, this points to data that can be relied upon since it fulfills the initial requirement to prove the hypothesis.

Therefore, since the highest standard deviation correlates with the most spread out data, A. Data set C is the answer.

Answer:

Ok, a system of equations means that we have a given number of equations with the same solutions.

If we only have tables, this means that we need to have one table for each equation:

For example, if we are working only with two variables, x and y, in those tables we can see the pints (x, y) that belong to each equation.

Now, a point (x, y) will be a solution of the system of equations only if it belongs to the data table for each equation

This would mean that if we graph those data sets, the graphs will intersect at the point (x, y) that belongs to all the tables of data.

Other way may be using the data in the tables to construct the equations, but you said that you only want to use the tables, so this method can be discarded.

Answer:

Step-by-step explanation:

[tex]\frac{27}{45} \times 100/1\\= \frac{2700}{45}\\ \\=60\%[/tex]

Answer:

60 %

Step-by-step explanation:

To find the percentage spent on fruit, take the amount spent on fruit over the total amount

27/45

.6

Change to a percent by multiplying by 100

60%

Answer:

did you already try A???

Answer:

Probability : [tex]\frac{5}{33}[/tex]

Step-by-step explanation:

The probability of drawing an orange on the first attempt would be 5 / 12, considering that in this first attempt their are 5 oranges present out of a total of 12 fruits. Now after that fruit is chosen their are 4 out of 11 oranges present, such that the probability of drawing an orange on the second attempt would be 4 / 11.

Probability of choosing an orange on the first try : [tex]5 / 12[/tex]

Probability of choosing an orange on the second try : [tex]4 / 11[/tex]

Probability of selecting two oranges in a row ( blindfolded ) : [tex]5 / 12 * 4 / 11[/tex]

[tex]\frac{5}{12}\cdot \frac{4}{11}[/tex] ( cross cancel common factor 4 )

[tex]\frac{5}{3}\cdot \frac{1}{11}[/tex] ( multiply fractions )

[tex]\frac{5\cdot \:1}{3\cdot \:11}[/tex] = [tex]\frac{5}{3\cdot \:11}[/tex] = [tex]\frac{5}{33}[/tex] - the probability of selecting two oranges in a row blindfolded, is [tex]\frac{5}{33}[/tex].

Answer:

10

Step-by-step explanation:

let n represent the number

sum means to add

product means multiply

n + 9 < n • 4

if you fill in 10 for your variable n you will get:

19 < 40

10 plus 9 is 19

10 by 4 is 40

and

because 19 is less than 40 that statement is true

Answer:

x= -19

Step-by-step explanation:

3-(x-3)=25

Distributive property to cancel out the paranthesis

3-x+3=25

Add the number

6-x=25

Subtract 6 on both sides

-x=19

Divide by -1 on both sides so the x to eliminate the negative sign

x=-19

Answer:

Let x be the original number.  Also, please note that a percentage can be written as a decimal(54%=0.54), and that a percentage increase is the percent +1(A 54% increase is x*1.54), and that a percentage decrease is 1- the percent(A 54% decrease is 0.46)

1)1.8*0.6x= 1.08x (greater than the original)

2).6666*1.5x=0.9999x (same as original)(.999999 is essentially 1, because .3333 is not equal to 1/3)

3)x+25-30 = x-5 (less than original)

4)0.5*2x=x (same as original)

5)1.2*.75x=.9x (less than original)

Hope it helps <3

Greater than the original.

Same as the original.

Less than the original.

Same as the original.

Less than the original.

To check all the scenarios, let's say that the original value is 100.

An 80% increase followed by a 40% decrease:

100 * (1 + 0.8) = 100 * 1.8 = 180.

180 * (1 - 0.4) = 180 * 0.6 = 108.

It is greater than the original.

A 33 1/3% decrease followed by a 50% increase:

100 * (1 - 0.33333333) = 100 * 0.6666666667 = 66.666666667.

66.6666666667 * (1 + 0.5) = 66.666666667 * (3/2) = 100.

It is the same as the original.

A $25 increase followed by a $30 decrease:

100 + 25 = 125.

125 - 30 = 95.

It is less than the original.

A 50% decrease followed by a 100% increase:

100 * (1 - 0.5) = 100 * 0.5 = 50.

50 * (1 + 1) = 50 * 2 = 100.

It is the same as the original.

A 20% increase followed by a 25% decrease:

100 * (1 + 0.2) = 100 * 1.2 = 120.

120 * (1 - 0.25) = 120 * 0.75 = 90.

It is less than the original.

Answer:

X = 5

Y = 7

Step-by-step explanation:

First we will find x

4x + 2 = 3x + 7

x + 2 = + 7

x = 5

Next we will find y

2y + 9 = 4y - 5

-2y + 9 = -5

-2y = -14

y = 7

Answer:

Step-by-step explanation:

first term = a = 3

common ratio = 2nd term ÷ first term

                       = 12 ÷ 3

                      r = 4

[tex]a_{n} = ar^{n-1}\\\\a_{10}=3*4^{9}\\\\\\ = 3 * 262144\\\\= 786432[/tex]

Answer:

at s = 10m, v(t_1) =  7.663 m/s

at s = 15m, v(t_2) = 10.041 m/s

Step-by-step explanation:

for the interval 0-10 seconds,

a(t) = t m/s^2

v(0) = 0

v(t) = v(0) + integral(a(t)dt)

= 0 +  [t^2/2]  

= (1/2) t^2

s(0) = 0      .................. arbitrary

s(t) = s(0) + integral(v(t)dt)

= 0 + integral ((1/2)t^2)

= (1/6)t^3

When s(t) = 10 m,

(1/6)t^3 = 10

t^3 = 60

t_1 = 60 ^(1/3) = 3.9149 s approx.

v(t_1) = (1/2) t_1^2 = (1/2)3.9149^2 = 7.663 m/s

When s = 15 m

(1/6)t^3 = 15

t^3 = 90

t_2 = 4.4814 s approx.

v(t_2) = (1/2)t_2^2 = (1/2)4.4814^2 = 10.041 m/s

Answer:

at s = 10m, v(t_1) =  7.663 m/s

at s = 15m, v(t_2) = 10.041 m/s

Step-by-step explanation:

I took the test and got it right