On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, negative 2), and point K is at (negative 2, negative 3). HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other

[tex]a. $ x = 23^{\circ}\\b. $ m \angle ECH =28^{\circ}\\c. $ m\angle HCD = 62^{\circ}\\d. $ m \angle GCF = 28^{\circ}\\e. $ m \angle ECG = 152^{\circ}\\f. $ m \angle GCD = 118^{\circ}[/tex]

Given:

[tex]m \angle ECH = x + 5\\m \angle HCD = 3x - 7[/tex]

Note the following:

Since CD is perpendicular to EF, therefore:

[tex]m \angle ECD = 90^{\circ}\\m \angle FCD = 90^{\circ}[/tex]

Thus:

a. Find x

[tex]m \angle ECH + m \angle HCD = m \angle ECD[/tex]

Substitute

[tex](x + 5) + (3x - 7) = 90[/tex]

Add like terms

[tex]x + 5 +3x - 7 = 90\\4x -2 = 90\\4x = 90 + 2\\4x = 92[/tex]

Divide both sides by 4

[tex]x = 23[/tex]

b. Find [tex]m \angle ECH[/tex]

[tex]m \angle ECH = x + 5[/tex]

Plug in the value of x

[tex]m \angle ECH = 23+ 5\\m \angle ECH =28^{\circ}[/tex]

c. Find [tex]m \angle HCD[/tex]

[tex]m \angle HCD = 3x - 7\\m \angle HCD = 3(23) - 7\\m \angle HCD = 62^{\circ}[/tex]

d. Find [tex]m \angle GCF[/tex]

[tex]m \angle GCF = m \angle ECH[/tex] (vertical angles are congruent)

Substitute

[tex]m \angle GCF = 28^{\circ}[/tex]

e. Find [tex]m \angle ECG[/tex]

[tex]m \angle ECG = 180 - m \angle GCF[/tex] (angles on a straight line)

Substitute

[tex]m \angle ECG = 180 - 28\\m \angle ECG = 152^{\circ}[/tex]

f. Find [tex]m \angle GCD[/tex]

[tex]m \angle GCD = m\angle FCD + m \angle GCF[/tex]

Substitute

[tex]m \angle GCD = 90 + 28\\m \angle GCD = 118^{\circ}[/tex]

Therefore:

[tex]a. $ x = 23^{\circ}\\b. $ m \angle ECH =28^{\circ}\\c. $ m\angle HCD = 62^{\circ}\\d. $ m \angle GCF = 28^{\circ}\\e. $ m \angle ECG = 152^{\circ}\\f. $ m \angle GCD = 118^{\circ}[/tex]

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Answer:

Step-by-step explanation:

I hope it helps :)

[tex]\sqrt{x+4} -7=1\\\mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\\sqrt{x+4}-7+7=1+7\\\sqrt{x+4}=8\\\mathrm{Square\:both\:sides}\\\left(\sqrt{x+4}\right)^2=8^2\\x+4=64\\x = 64-4\\x = 60[/tex]

Step-by-step explanation:

A student divided the given number by 100 that resulted to 28.003 in his chart. So what we are looking for in the given situation is that the value of the number before it was divided by 100.

To get the desired value, we can simply multiply the obtained result by 100

=> 28.003 x 100

=> 2800.3

So, by dividing 100 to the given number, we simply move the value to the right in a value of hundreds.

Answer:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 ...

Step-by-step explanation:

Answer:

Step-by-step explanation:

9x^3,15x^5= 3x^3

The GCF is constructed by multiplying all the factors that are common to all the given expressions, exponentiated to the smallest power.

In our example, the following factors are common to all the given expressions: 3, x^3

Therefore, the GCF is equal to 3x^3.

Answer:

Thursday=80%

Saturday=82 %

Step-by-step explanation:

Thursday trains not late=40-8=32

% trains not late=32/40×100=80

Saturday trains not late=50-9=41

% trains not late on Saturday=41/50×100=82

Answer:

Sector

Step-by-step explanation:

A sector of a circle is the portion of circle enclosed by two radii and arc

Answer:

hope this help

Step-by-step explanation:

here is the answer

Answer:

10x -24 ft^2

Step-by-step explanation:

The area of the square is x^2

The area of the flower garden is lw

( x-4) ( x-6)

x^2 -6x-4x +24

x^2 -10x +24

Subtract the flower garden from the square to find the area of the patio

x^2 - ( x^2 -10x +24)

Distribute the minus sign

x^2 -x^2 +10x -24

10x -24

Answer:

c. 10x -24 sq. ft

Step-by-step explanation:

area of lot = x * x

area of garden = (x-4)(x-6) = x^2-10x+24

Area of patio

= area of lot - area of patio

= x^2 -(x^2-10x+24)

= 10x-24 sq.ft

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▹ Answer

2 5/6

▹ Step-by-Step Explanation

[tex]\frac{17}{6} \\\\6 * 2 = 12\\12 + 5 = 17\\\\2\frac{5}{6}[/tex]

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

2 5/6

Step-by-step explanation:

17/6

6 goes into 17 2 times  

2*6 = 12

17-12 = 5  

There is a remainder of 5  this goes over the denominator

2 5/6

Answer:

The median of the data in the table is 19.

Step-by-step explanation:

We are given the following data that shows the number of cars Jing sold each month last year below;

Number of cars Jing sold: 13, 16, 19, 20.5, 23.5

For calculating the median, firstly we have to observe that the number of observations (n) in our data is even or odd because;

                           Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]

                           Median = [tex]\frac{(\frac{n}{2} )^{th} \text{ obs.} + (\frac{n}{2}+1 )^{th} \text{ obs.} }{2}[/tex]

Here, the number of observations in our data is odd, i.e. n = 5.

So, Median = [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]

                   = [tex](\frac{5+1}{2} )^{th} \text{ obs.}[/tex]

                   = [tex](\frac{6}{2} )^{th} \text{ obs.}[/tex]

                   = 3rd obs. = 19

Hence, the median of the data in the table is 19.

Answer:

k=0

Step-by-step explanation:

8(4k-4)=5k-32

32k-32=-5k-32

32k-32+32=-5k-32+32

32k=-5k

32k+5k=-5k+5k

37k=0

37k/37=0/37

k=0

Answer:

k=0

Step-by-step explanation:

To solve for k, we need to first distribute the 8 through the parenthesis.

32k-32=-5k-32

Lets add 5k to both sides.

37k-32=-32

add 32 to both sides

37k=0

divide 37 from both sides

k=0

Answer:

I believe it's A) 302.94

Step-by-step explanation:

There are 360 degrees in a circle. So I enetered 360/112 in a calculator and got 3.214.

Then I multiplied 3.214 by 30pi and got 302.939 AKA 302.94. I did this because I looked at it like a ratio problem but idk if thats correct.

Answer:

60 ounces.

Step-by-step explanation:

Given:

A mixture contains 5 parts of white paint for every 4 parts of blue paint.

i.e. Ratio of white paint : blue paint = 5 : 4

Quantity of White paint = 75 ounces

To find:

How many ounces of blue paint = ?

Solution:

Here, we are given the ratio of white and blue paint in the mixture.

Also, we are given the quantity of white paint in the paint can.

And we have to find the quantity of other paint in the can.

Let us use all the given statements to find the unknown quantity of blue paint.

Ratio of white paint : blue paint= Ratio of quantity of white paint: blue paint

[tex]\dfrac{5}{4} = \dfrac{75}{\text{Quantity of blue paint}}\\\Rightarrow \text{Quantity of blue paint} = 15 \times 4\\\Rightarrow \text{Quantity of blue paint} = 60\ ounces[/tex]

So, the quantity of blue paint in the can is 60 ounces.

Answer:

[tex]\huge \boxed{729}[/tex]

Step-by-step explanation:

9 raised to 3 is the base 9 with an exponent of 3.

[tex]9^3[/tex]

9 is being multiplied by itself 3 times.

[tex]9^3 =9 \times 9 \times 9 = 729[/tex]

Answer:

-5X+2Y-2

Step-by-step explanation:

-5X-7-2+2Y+7

-5X-2+2Y

HOPE I HELPED

PLS MARK BRAINLIEST

DESPERATELY TRYING TO LEVEL UP

✌ -ZYLYNN JADE ARDENNE

JUST A RANDOM GIRL WANTING TO HELP PEOPLE!

                               PEACE!

Answer/Step-by-step explanation:

Recall: [tex] x^{-a} = \frac{1}{x^a} [/tex]

a. [tex] 4^{-3} = \frac{1}{4^3} = \frac{1}{64} [/tex]

b. [tex] 13^{-2} = \frac{1}{13^2} = \frac{1}{169} [/tex]

c. [tex] (-3)^{-2} = \frac{1}{-3^2} = \frac{1}{9} [/tex]

Answer

[tex] \boxed{10 \: \: units}[/tex]

Step by step explanation

Let the points be A and B

A ( 5 , 1 ) ⇒ ( x₁ , y₁ )

B ( -3 , -5 )⇒ ( x₂ , y₂ )

Now, let's find the distance between theses two points:

Distance = [tex] \mathsf{ \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } }[/tex]

Plug the values

[tex] \mathsf{ \sqrt{ {( - 3 - 5)}^{2} + {( - 5 - 1)}^{2} } }[/tex]

Calculate

[tex] \mathsf{ \sqrt{ { ( - 8)}^{2} + {( - 6)}^{2} } }[/tex]

Evaluate the power

[tex] \mathsf{ \sqrt{64 + 36} }[/tex]

Add the numbers

[tex] \mathsf{ \sqrt{100} }[/tex]

Write the number in exponential form with a base of 10

[tex] \mathsf {\sqrt{ {10}^{2} } }[/tex]

Reduce the index of the radical and exponent with 2

[tex] \mathsf{10 \: units}[/tex]

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The distance formula is used to determine the distance ( d ) between two points. If the co-ordinates of the two points are ( x₁ , y₁) and ( x₂ , y₂ ) , the distance equals the square root of x₂ - x₁ squared + y₂ - y₁ squared.

Hope I helped!

Best regards!

Answer:

Hope this helps you.

Step-by-step explanation:

I plugged in x for t, but it is the same graph.

Answer:

a. [tex]\mathtt{P(X \geq 25) =0.0170}[/tex]     ( to four decimal places)

b. [tex]P(22.5<X<25) = 0.9043[/tex]   ( to four decimal places )

c. The limits will be between the interval of   ( 22.33,24.67 )

Step-by-step explanation:

Given that :

mean = 23.50

standard deviation = 5.00

sample size = 50

The objective is to calculate the following:

(a)  What is the likelihood the sample mean is at least $25.00?

Let X be the random variable, the probability that the sample mean is at least 25.00 is:

[tex]P(X \geq 25) = 1 - P(\dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}} < \dfrac{25- 23.50}{ \dfrac{5}{\sqrt{ 50}} })[/tex]

[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5}{ \dfrac{5}{7.07107}} })[/tex]

[tex]P(X \geq 25) = 1 - P(Z< \dfrac{1.5 \times 7.071}{ {5}})[/tex]

[tex]P(X \geq 25) = 1 - P(Z< 2.1213)[/tex]

[tex]P(X \geq 25) = 1 - P(Z< 2.12)[/tex]   to two decimal places

From the normal tables :

[tex]P(X \geq 25) = 1 - 0.9830[/tex]

[tex]\mathtt{P(X \geq 25) =0.0170}[/tex]     ( to four decimal places)

(b) What is the likelihood the sample mean is greater than $22.50 but less than $25.00?

[tex]P(22.5<X<25) = P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{25-23.5}{\dfrac{5}{\sqrt{50}}} ) - P(\dfrac{X-\mu}{\dfrac{\sigma}{\sqrt{n}}} <\dfrac{22.5-23.5}{\dfrac{5}{\sqrt{50}}} )[/tex]

[tex]P(22.5<X<25) = P(Z<\dfrac{1.5}{\dfrac{5}{7.071}} ) - P(Z<\dfrac{-1}{\dfrac{5}{7.071}} )[/tex]

[tex]P(22.5<X<25) = P(Z<2.12) - (Z<-1.41 )[/tex]

[tex]P(22.5<X<25) = (0.9830 ) - (0.0787)[/tex]

[tex]P(22.5<X<25) = 0.9043[/tex]  to four decimal places

(c) Within what limits will 90 percent of the sample means occur?

At 90 % confidence interval, level of significance = 1 - 0.90 = 0.10

The critical value for the [tex]z_{\alpha/2} = 0.05[/tex] = 1.65

Standard Error = [tex]\dfrac{\sigma}{\sqrt{n}}[/tex]

Standard Error =  [tex]\dfrac{5}{\sqrt{50}}[/tex]

Standard Error = 0.7071

Therefore, at 90 percent of the sample means, the limits will be between the intervals of : [tex](\mu \pm z_{\alpha/2} \times S.E)[/tex]

Lower limit =  ( 23.5 - (1.65×0.707) )

Lower limit =  ( 23.5 - 1.16655 )

Lower limit = 22.33345

Lower limit = 22.33    (to two decimal places).

Upper Limit = ( 23.5 + (1.65*0.707) )

Upper Limit = ( 23.5 + 1.16655 )

Upper Limit = 24.66655

Upper Limit = 24.67

The limits will be between the interval of   ( 22.33,24.67 )

Answer:

Step-by-step explanation:

the odds of choosing a ginger ale is 1/21

Answer:

3 terms

Step-by-step explanation:

A term in mathematics, especially in Algebra, could be a number, a variable, variable together with a number or variables multiplied together as a single whole. Terms are usually separated with either negative or positive sign in an expression.

In the expression, [tex] 1 + 2k - j [/tex] , there are 3 terms here spared by either the negative sign or the positive.

The 3 terms are: [tex] 1, 2k, j [/tex].

Answer:

(I) 17.25 miles

(ii) 1hr56mins20seconds

(III) 4hrs47mins38seconds

Step-by-step explanation:

(I) read from the lowest distance given

(ii) read from the longest time given

(III) added all times together to get total cycling time

Step-by-step explanation:

here,

shortest distance is 17.25 miles

the longest time is 1:56:20 hrs:mins:secs

total time is 4:47:38

Answer:

1.18 dollar.

Step-by-step explanation:

E = 17/20D

E => The amount in euros.

D => The amount in dollars.

From the question given,

E = 1

D =?

E = 17/20D

1 = 17/20D

Cross multiply

20 x 1 = 17D

20 = 17D

Divide both side by 17

D = 20/17

D = 1.18

Therefore, 1.18 dollar is equivalent to 1 euro.

Answer:

How many Euros have the same value as 1 U.S. dollar?

17/20 euros

How many U.S. dollars have the same value as 1 euro?

59/50 dollars

(or 0.85 either one is correct)

Step-by-step explanation:

Khan Academy

Hope this helps! ;)

1 mile = 5,280 feet

1 hour = 3600 seconds

3600/5280 = 0.681818 feet per second

25 ft per second x 0.681818 = 17.045 miles per hour

Round the answer as needed.

Answer:

The correct answer is 17.045 miles per hour.

Answer:

y * ( 6*5)

Step-by-step explanation:

(y x 6) x 5

We can change the order of multiplication by changing where the parentheses are placed using the associative property

y * ( 6*5)

Answer:

The answer will be Y*(6*5)

Step-by-step explanation:

this is the answer because while doing the associative property you switch the parenthesis to the different numbers or the other side in this case were 6 and 5

Answer:

Step-by-step explanation:

3(m-12)+8

x=m-12

Answer:

theta  = 180 -(A +B)

Step-by-step explanation:

The sum of the angles of a triangle is 180

theta + A + B = 180

solve for theta

Subtract ( A + B) from each side

theta +A+B -(A +B) = 180 -(A +B)

theta  = 180 -(A +B)

Answer:

A)

Step-by-step explanation:

[tex](a^{m})^{n} = a^{mn}\\\\x^{3}*(x^{3}*y^{2})^{2}=x^{3}*(x^{3})^{2}*(y)^{2}\\\\\\=x^{3}*x^{3*2}*y^{2}\\\\\\=x^{3}*x^{6}*y{2}\\\\\\=x^{3+6}*y^{2}\\=x^{9}y^{2}[/tex]