In the diagram, MN is tangent to K at M, NP is tangent to K at P, MN = 128 and NP = 2x + 70. Find x

SHOW YOUR WORK

Answer:

92

Step-by-step explanation:

this figure can be "split" into 3 sub-figures.

one rectangle in the middle, one triangle to the right, and one triangle on top.

these areas we can calculate very easily. and then we simply sum up all 3 of them and we have the answer.

it is clear, the area of a rectangle is length×width.

and the area of triangle is baseline×height/2.

where in a right-angled triangle one of the sides next to the 90 degree angle is the baseline and the other is the height.

the rectangle

R = 10×6 = 60

the triangle to the right

T1 = (14-10)×6/2 = 12

the triangle on the top

T2 = 10×(10-6)/2 = 20

so, the total area is

60+12+20 = 92

The area of the given figure is 92.

This figure contained 3 sub-figures.

One rectangle in the middle, one triangle to the right, and one triangle on top.

The area of these areas we can calculate very easily. and then we ad  all 3 of them and we have the answer.

The area of a rectangle is,

[tex]A=length\times width.[/tex]

The area of triangle is

[tex]A^*= \frac{1}{2} \times base\times height[/tex]

Where in a right-angled triangle one of the sides next to the 90 degree angle is the baseline and the other is the height.

The area of  rectangle

[tex]R =l\times w \\R=10\times 6 \\R= 60[/tex]

The triangle to the right

[tex]T_1 = (14-10)\times 6/2 = 12[/tex]

The triangle on the top

[tex]T_2 = 10\times (10-6)/2 = 20[/tex]

Therefore, the total area is,

60+12+20 = 92

Therefore the area of the given figure is 92.

To learn more about the area visit:

https://brainly.com/question/3948796

Answer:

9/10 x 4/5 = 36/50 simplified = 18/25 is your area

Answer:

8/23. Sana po makatulong

Answer:

22.1

Step-by-step explanation:

33.15/n

33.15/1.5

= 22.1

Answer:

overdraft fees is your answer

Step-by-step explanation:

Oooooooioooooooooooo

Answer:

b

Step-by-step explanation:

Answer:

b) 8

Step-by-step explanation:

6x+(5x+2)=90

11x+2=90

11x=88

x=8

:)

Answer:

See the image below for the answer:)

Step-by-step explanation:

Answer:

(a) (0.9240,  0.956)

(b) (0.6383, 0.7017)

Step-by-step explanation:

The number of internet users involved in the survey, n = 846

The percentage of the respondents that said the internet has been good thing for them personally, [tex]\hat p[/tex] = 94%

(a) The confidence interval of a percentage is given as follows;

[tex]CI=\hat{p}\pm z\times \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]

The z-value for 95% confidence interval = 1.96

We get;

[tex]CI=0.94\pm 1.96\times \sqrt{\dfrac{0.94 \times (1-0.94)}{846}} \approx 0.94 \pm 1.6003 \times 10^{-2}[/tex]

CI = 0.9240 ≤ [tex]\hat p[/tex] ≤ 0.956 = (0.9240,  0.956)

(b) The percentage of the internet users that said the internet has directly strengthened their relationship with their families, [tex]\hat p[/tex] = 67% = 0.67

The 95% confidence interval is therefore;

[tex]CI=0.67\pm 1.96\times \sqrt{\dfrac{0.67 \times (1-0.67)}{846}} \approx 0.67 \pm 3.1686\times 10^{-2}[/tex]

From which we have;

CI = 0.6383 ≤ [tex]\hat p[/tex] ≤ 0.7017 = (0.6383, 0.7017)

Step-by-step explanation:

16x -(3x + 9) + 17

16x -3x -9 +17

13x + 8

Answer:

2*2*2*3

or

2^3   * 3

Step-by-step explanation:

24 = 4*6

But 4 and 6 aren't prime

24 = 4*6 = (2*2)  * (2*3)

All these numbers are prime

24 = 2*2*2*3  or with exponents  = 2^3   * 3

Answer:

¿Cómo comprobar que las razones son proporcionales? ,5

Step-by-step explanation:

Para comprobar si dos o más razones son proporcionales se aplica la propiedad fundamental de las proporciones. 1 * 4 = 1 2 2 4 4 = 4 1 2 3 6 1 * 6 = 6 = 6 = = ? ? 1 2 0,5 1 = Así se concluye que las tres razones son proporcionales. 1 * 1 = 1 = 1 1ra forma. 2 * 2 2 * 3 ? 2 * 0,5

Answer:

Step-by-step explanation:

f/4-5=-9

f-4*5/4=-9

f-20/4=-9

f-20=-9*4

f-20=-36

f=-36+20

f=-16

Answer:

f/4 - 5 = -9

f-20/4=-9

f-20=-9×4

f-20=-36

f=-36+20

f=-16

Answer:

Question 2 = 15 drinks

Question 3 = 7/12

Step-by-step explanation:

Question 2:

For every drink, there are three sizes

Ratio = 1:3

There are 5 flavors

Multiply each side by 5

5:15

15 drinks

Question 3:

5 red, 6 yellow, 8 blue, 3 orange, 2 purple

Possible outcomes = 5 + 6 + 8 + 3 + 2 = 24 possible outcomes

Favourable outcomes = 6 + 8 = 14 favourable outcomes

Fraction = 14/24 = 7/12

If my answer is incorrect, pls correct me!

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-Chetan K

Answer:

The answer is -15

Step-by-step explanation:

(-5)3 is the same as -5 × 3

Answer:

-5 x 3 = -15

Answer:

27 1/3

Step-by-step explanation:

Since both angles form a straight line of 180, you can set your formula up as

180=4x+2x+16

180-16=6x

164=6x

164/6=x

Answer:

1.) Amount of potting soil purchased last week.

2) 2p + 4 = 28

3.) 12 lbs

Step-by-step explanation:

1.) The unknown information is what we intend to find out using the information given, which is the amount of potting soil Emmanuel bought last week.

2.)

Let amount of potting soil bought last week = p

Amount bought this week = 2p + 4

Since amount bought this week = 28

Hence, we have ;

28 = 2p + 4

28 - 4 = 2p

24 = 2p

p = 24 / 2

p = 12

Answer:

a=35

Step-by-step explanation:

5x35=175, and 175 divided by 7 is 25 :)

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: a = 35}}}}}}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]

[tex] \: \frac{5a}{7} = 25[/tex]

➺[tex] \: 5a \: = 25 \times 7[/tex]

➺[tex] \: 5a = 175[/tex]

➺[tex] \: a = \frac{175}{5} [/tex]

➺[tex] \: a = 35[/tex]

[tex]\sf \bf {\boxed {\mathbb {To\:verify:}}}[/tex]

[tex] \: \frac{5a}{7} = 25[/tex]

➺[tex] \: \frac{5 \times 35}{7} = 25[/tex]

➺[tex] \: \frac{175}{7} = 25[/tex]

➺[tex] \: 25 = 25[/tex]

➺[tex] \: L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

9

Step-by-step explanation:

A = B + 2

C = B - 3

A x C = 66

A = Andrew

C = Chris

B = Beatrice

Multiply A and c together

(B + 2) x (b - 3)

b^2 - 3b + 2b - 6

b^2 -b - 6 = 66

b^2 - b - 72 = 0

factors of -72b^2 that add up to - b are -9b + 8b

b^2 + 8b -9b - 72

b (b + 8) -9(b + 8)

b = 9 or - 8

b = 9

Answer:1

Step-by-step explanation:

twice a number minus a second number is -1. Twice the second number added to three times the first number is 9. find the two numbers. System of Equations is how we are supposed to solve this word problem.

Answer:

Since the two angles are complementary, they add up to 90...

If we call the first one x, then the other must be 90-x...

Since they are 35 different, we write

x = (90 - x) + 35

now solve, and get

x = 90 - x + 35

x = -x + 125

2x = 125

x = 62.5 deg

the other must be

90 - 62.5 = 27.5 deg

Answer:

49 square inches

Step-by-step explanation:

area of a square = l * l

a = 7 * 7

a = 49 square inches

Answer:

T=2.25

Step-by-step explanation:

To find the area of a triangle, you do the length times height, times two. Therefor T=2.25 (36/8, then you get 4.5, divide that by 2, get 2.25, 2.25x8x2=36.)

Answer:The system 150x+400y=1950 and x = y+2 could be used to determine the number of small boxes and large boxes ordered where x represents the number of small boxes and y represent the number of large boxes.

Step-by-step explanation:

Answer:

Let s = the number of small boxes purchased

Let l = the number of large boxes purchased

100s + 350l= 2400

s+l= 9

Answer:

A rectangle always has... 4 sides, 4 angles, all right angles, and opposite sides parallel

Answer:

A, B, D, E

Step-by-step explanation:

A   4 sides

В.   4 angles

D.   all right angles

E    opposites sides parallel