Can the two triangles be proven congruent? If yes, then by what method?

Answer:

Two solutions:

x = 5 and x = -3

Step-by-step explanation:

Simplify:

x^{2} - 2x = 15

-15              -15

x^{2} - 2x -15 = 0

Find what numbers multiplied by eachother equal -15 and also add to -2:

-5 * 3 = -15

-5 + 3 = -2

Rewrite equation and put each expression equal to 0:

(x - 5)(x + 3) = 0

x - 5 = 0      x + 3 = 0

  +5    +5         -3     -3

x = 5            x = -3

Answer:

Area = 634.21 square metre

Step-by-step explanation:

Area of shaded region = Area of the circle - Area of the sector

[tex]Area \ of \ the \ circle = \pi r^2 = 225 \pi\\\\Area \ of \ the \ sector = \pi r^2 \frac{ \theta}{360} = \pi \times 225 \times \frac{37}{360}[/tex]

[tex]Area \ of \ shaded \ region = 225 \pi - (225 \pi \times \frac{37}{360})[/tex]

                                   [tex]= 225 \pi (1 - \frac{37}{360})\\\\= 225 \pi \times 0.89722\\\\=634.21 m^2[/tex]

Answer:

28+36+y= 180

The value of y is 116

Step-by-step explanation:

Answer:

9 Patients

Step-by-step explanation:

The median is the middle value of all of the selected numbers

4, 5, 7, 9, 11, 12, 17.

Answer:

9 patient

Step-by-step explanation:

Arrange numbers from smallest to largest. Then, Pick the middle one. That's your answer.

Answer:

its 2/7 for the day and 1/12 for the month

Step-by-step explanation:

the probability of picking both of them is 2%

Answer:

53 pushes

Step-by-step explanation:

Total Volume of soap = 474 mL

Volume per push = 8mL

Mimimum volume required = 50mL

The equation which represents the number of push, x that can be made :

Total volume = minimum volume + (volume per push * number of pushes)

Total volume = 50 + (8 * x)

474 ≤ 50 + 8x

474 - 50 ≤ 8x

424 ≤ 8x

53 ≤ x

The number of pushes that can be made = 53

Answer:

188 wrestlers

Step-by-step explanation:

Given

[tex]F =5w + 75[/tex]

[tex]F = 1013[/tex]

Required

Determine the number of wrestlers (w)

We have:

[tex]F =5w + 75[/tex]

Substitute: [tex]F = 1013[/tex]

[tex]1013 = 5w + 75[/tex]

Collect like terms

[tex]5w = 1013 - 75[/tex]

[tex]5w = 938[/tex]

Divide both sides by 5

[tex]w = 187.6[/tex]

Round up to get the number of wrestlers

[tex]w = 188[/tex]

9514 1404 393

Answer:

  15 cm

Step-by-step explanation:

The formula for the surface area of the cone is ...

  A = πr² +πrL =  πr(r +L)

The radius of this cone is half its diameter so is (12 cm)/2 = 6 cm. Then the slant height L can be found from ...

  126π cm² = π(6 cm)(6 cm +L)

  21 cm = 6 cm +L . . . . . . . . . . . . . . divide by 6π cm

  15 cm = L . . . . . . . . . . . . . . . . subtract 6 cm

The slant height is 15 centimeters.

Answer:

Exactly 28million

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Measures of central tendency assist in the discovery of a data set's middle, or average. The statement that is incorrect out of the given statements is option D.

Measures of central tendency assist in the discovery of a data set's middle, or average. The mode, median, and mean are the three most popular metrics of central tendency.

The range is the difference between the largest and smallest value in the set. Therefore, The statement that is incorrect out of the given statements is option D. Standard deviation is the difference between the largest and smallest value in the set.

Learn more about the Central Tendency:

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Answer:

True , null

Step-by-step explanation:

Mostly the true hypothesis is the null hypothesis .

We test the true hypothesis , the null hypothesis  against the claim provided which is named as alternate hypothesis.

When the false hypothesis is the null hypothesis , type II error is made.

Confounded in statistics means when the alternative explanations cannot be eliminated.But we have the alternate hypothesis in hypothesis testing.

So option 1 is correct

Answer:

Hello! answer: 21.4

Hope that helps!

Answer:

(i think)

5q3+25q2

Step-by-step explanation:

To write a polynomial in standard form, simplify and then arrange the terms in descending order.a

x2+bx+c

5⋅1(q2q)+25q2

Simplify each term

answer- 5q3+25q2

Answer: [tex]32.909\ \text{ounce}[/tex]

Step-by-step explanation:

Given

3.25 cm long segment of rope weighs [tex]61.40\ gm[/tex]

Using unitary method

1 cm of a segment measures

[tex]\dfrac{61.40}{3.25}=18.892\ gm[/tex]

[tex]1\ cm\equiv 18.892\ gm[/tex]

converting cm to inch and gm to ounce

[tex]\dfrac{1}{2.54}\ in.\equiv \dfrac{18.892}{28.3495}\ \text{ounce}\\\\1\ in.\equiv \dfrac{18.892}{28.3495}\times 2.54\ \text{ounce}\\\\1\ in.\equiv 1.692\ \text{ounce}[/tex]

for 19.45 in., weight is

[tex]\Rightarrow 19.45\ in.\equiv 1.692\times 19.45\\\\\Rightarrow 19.45\ in\equiv 32.909\ \text{ounce}[/tex]

Answer:

i got it right⬇

Answer:

40/30

Step-by-step explanation:

[tex]tan = opposite/adjacent[/tex]

[tex]tan\ \angle Z = \frac{40}{30}[/tex]

Answer:

take 45 degree as reference angle

use sin rule

sin 45=opposite/hypotenuse

1/[tex]\sqrt{2}[/tex]=b/10(do cross multiplication)

b[tex]\sqrt{2}[/tex]=10

b=10/[tex]\sqrt{2}[/tex]

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Raise 3 to the power of 2.

Answer:

x<16

it's the last one

Step-by-step explanation:

Multiply both sides of the inequality by

then move the constant to the right hand side and

change it's sign and

subtract by four

Answer:

Step-by-step explanation:

No solutions exist because the situation describes two lines that have the same slope and different y-intercepts.

Answer:

12500

Step-by-step explanation:

4.5 × 48=216.

12500 Plus 216= 12,716

The value of the invested money becomes $103393.20 after 4 years if the interest rate is 4.5% and compounded annually.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+r)^t[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          t = How long the money is deposited or borrowed (in years)

We have in the question:

p = $12,500

r = 4.5% ⇒ 0.045

t = 4 years ⇒ 4×12 ⇒ 48 months

Put the above values in the formula, we get;

[tex]\rm A = 12500(1+0.045)^4^8[/tex]

A = 12500×8.27145

A = $103393.20

Thus, the value of the invested money becomes $103393.20 after 4 years if the interest rate is 4.5% and compounded annually.

Learn more about the compound interest here:

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Answer:

12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

((9*6/2)*4)+(6*6)=144

Answer:D

Step-by-step explanation: The answer would be 3b+6 and when you solve 3(b+2) you get 3b +6)

3 times b is 3b and when you add 6 it becomes 3b+6 or 3(b+2)

Answer:

A seems correct

Step-by-step explanation:

so 6 must be multiplied b times and added to 3

Answer:

X=0 or x=8/5

Step-by-step explanation:

Answer:

[tex]a=10[/tex]

Step-by-step explanation:

This problem can be solved in a ridiculous number of ways. However, it is likely introduced as a special-triangle problem in this question, because 4 pieces of information are given opposed to the necessary 3 to solve the triangle.

Special Right Triangles:

In any 30-60-90 triangle, all sides are in the proportion [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse and [tex]x[/tex] is the side opposite to the 30 degree angle. Since we notice that the side we're solving for is directly opposite to the 30 degree angle, we know that the side marked [tex]10\sqrt{3}[/tex] must be [tex]x\sqrt{3}[/tex] and therefore we have [tex]a=\boxed{10}[/tex]

Answer:

0.5 or 1/2

Step-by-step explanation:

each number is half of the bigger triangle. so the answer should be half or 0.5.

EX: 48 x 0.5 = 24

Answer:

equation of a straight line in slope intercept form is x+y-2=0

Step-by-step explanation: