Which of the following statements is true for ∠a and ∠b in the diagram?

Answer:

option A : 25

Step-by-step explanation:

Given :

P = (- 6, 7) , Q = ( 2 , 1 ) , R = ( -1 , -3)

Find the length of PQ ,QR , PR.

Using distance formula to find the lengths.

[tex]distance = \sqrt{(x_2 - x_1 )^2 + (y_ 2- y_1)^2[/tex]

[tex]PQ = \sqrt{(2 -- 6)^2 + (1-7)^2} = \sqrt{8^2 + 6^2 } = \sqrt{64 + 36 } =\sqrt{100} = 10\\\\QR = \sqrt{(2 --1)^2 + (-3-1)^2}= \sqrt{3^2 + 4^2} =\sqrt{9+ 16} =\sqrt{25} = 5\\\\PR = \sqrt{(-1--6)^2 + (-3 -7)^2} = \sqrt{5^2 + 10^2} = \sqrt{25 + 100} = \sqrt{125}[/tex]

Clearly , the triangle satisfies Pythagoras theorem :

Square of larger side = Sum of squares of other sides.

Therefore , PQR is a right triangle,

with base = 5, height 10 and slant height(hypotenuse) = [tex]\sqrt{125}[/tex] .

[tex]Area = \frac{1}{2} \times base \times height[/tex]

       [tex]=\frac{1}{2} \times 5\times 10\\\\= 5 \times 5 \\\\= 25 \ square\ units[/tex]

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

Explanation:

Each square has a side length of 5 inches, so each square has area 5*5 = 25 square inches. We have 6 such squares to give a total surface area of 6*25 = 150 square inches.

Effectively, this is the same as using the formula below

S = 6x^2

S = 6*5^2

S = 6*5*5

S = 150

x = 5 refers to the side length and S is the surface area. It might help to cut the figure from the paper, and fold it up and you should find that a 3D box will form. There are 6 faces with area of 5*5 each, hence the 6*5*5

Answer:

City A and city B will have equal population 25years after 1990

Step-by-step explanation:

Given

Let

[tex]t \to[/tex] years after 1990

[tex]A_t \to[/tex] population function of city A

[tex]B_t \to[/tex] population function of city B

City A

[tex]A_0 = 10000[/tex] ---- initial population (1990)

[tex]r_A =3\%[/tex] --- rate

City B

[tex]B_{10} = \frac{1}{2} * A_{10}[/tex] ----- t = 10 in 2000

[tex]A_{20} = B_{20} * (1 + 20\%)[/tex] ---- t = 20 in 2010

Required

When they will have the same population

Both functions follow exponential function.

So, we have:

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]B_t = B_0 * (1 + r_B)^t[/tex]

Calculate the population of city A in 2000 (t = 10)

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]A_{10} = 10000 * (1 + 3\%)^{10}[/tex]

[tex]A_{10} = 10000 * (1 + 0.03)^{10}[/tex]

[tex]A_{10} = 10000 * (1.03)^{10}[/tex]

[tex]A_{10} = 13439.16[/tex]

Calculate the population of city A in 2010 (t = 20)

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]A_{20} = 10000 * (1 + 3\%)^{20}[/tex]

[tex]A_{20} = 10000 * (1 + 0.03)^{20}[/tex]

[tex]A_{20} = 10000 * (1.03)^{20}[/tex]

[tex]A_{20} = 18061.11[/tex]

From the question, we have:

[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]  and  [tex]A_{20} = B_{20} * (1 + 20\%)[/tex]

[tex]B_{10} = \frac{1}{2} * A_{10}[/tex]

[tex]B_{10} = \frac{1}{2} * 13439.16[/tex]

[tex]B_{10} = 6719.58[/tex]

[tex]A_{20} = B_{20} * (1 + 20\%)[/tex]

[tex]18061.11 = B_{20} * (1 + 20\%)[/tex]

[tex]18061.11 = B_{20} * (1 + 0.20)[/tex]

[tex]18061.11 = B_{20} * (1.20)[/tex]

Solve for B20

[tex]B_{20} = \frac{18061.11}{1.20}[/tex]

[tex]B_{20} = 15050.93[/tex]

[tex]B_{10} = 6719.58[/tex] and [tex]B_{20} = 15050.93[/tex] can be used to determine the function of city B

[tex]B_t = B_0 * (1 + r_B)^t[/tex]

For: [tex]B_{10} = 6719.58[/tex]

We have:

[tex]B_{10} = B_0 * (1 + r_B)^{10}[/tex]

[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]

For: [tex]B_{20} = 15050.93[/tex]

We have:

[tex]B_{20} = B_0 * (1 + r_B)^{20}[/tex]

[tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex]

Divide [tex]B_0 * (1 + r_B)^{20} = 15050.93[/tex] by [tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]

[tex]\frac{B_0 * (1 + r_B)^{20}}{B_0 * (1 + r_B)^{10}} = \frac{15050.93}{6719.58}[/tex]

[tex]\frac{(1 + r_B)^{20}}{(1 + r_B)^{10}} = 2.2399[/tex]

Apply law of indices

[tex](1 + r_B)^{20-10} = 2.2399[/tex]

[tex](1 + r_B)^{10} = 2.2399[/tex] --- (1)

Take 10th root of both sides

[tex]1 + r_B = \sqrt[10]{2.2399}[/tex]

[tex]1 + r_B = 1.08[/tex]

Subtract 1 from both sides

[tex]r_B = 0.08[/tex]

To calculate [tex]B_0[/tex], we have:

[tex]B_0 * (1 + r_B)^{10} = 6719.58[/tex]

Recall that: [tex](1 + r_B)^{10} = 2.2399[/tex]

So:

[tex]B_0 * 2.2399 = 6719.58[/tex]

[tex]B_0 = \frac{6719.58}{2.2399}[/tex]

[tex]B_0 = 3000[/tex]

Hence:

[tex]B_t = B_0 * (1 + r_B)^t[/tex]

[tex]B_t = 3000 * (1 + 0.08)^t[/tex]

[tex]B_t = 3000 * (1.08)^t[/tex]

The question requires that we solve for t when:

[tex]A_t = B_t[/tex]

Where:

[tex]A_t = A_0 * (1 + r_A)^t[/tex]

[tex]A_t = 10000 * (1 + 3\%)^t[/tex]

[tex]A_t = 10000 * (1 + 0.03)^t[/tex]

[tex]A_t = 10000 * (1.03)^t[/tex]

and

[tex]B_t = 3000 * (1.08)^t[/tex]

[tex]A_t = B_t[/tex] becomes

[tex]10000 * (1.03)^t = 3000 * (1.08)^t[/tex]

Divide both sides by 10000

[tex](1.03)^t = 0.3 * (1.08)^t[/tex]

Divide both sides by [tex](1.08)^t[/tex]

[tex](\frac{1.03}{1.08})^t = 0.3[/tex]

[tex](0.9537)^t = 0.3[/tex]

Take natural logarithm of both sides

[tex]\ln(0.9537)^t = \ln(0.3)[/tex]

Rewrite as:

[tex]t\cdot\ln(0.9537) = \ln(0.3)[/tex]

Solve for t

[tex]t = \frac{\ln(0.3)}{ln(0.9537)}[/tex]

[tex]t = 25.397[/tex]

Approximate

[tex]t = 25[/tex]

Answer:

ur mom

Step-by-step explanation:

doin doin

Answer:1380

Step-by-step explanation: 12x115

Answer:

1,380

Step-by-step explanation: 12 times 115 gives you the product of 1,380. :)

Hope this is helpful

Answer:

18

Step-by-step explanation:

f(x) = 2x^2

Let x = -3

f(-3) = 2 * (-3)^2

Exponents first

f(-3)=2 *9

f(3) = 18

Answer:

f ( - 3 ) = 18

Step-by-step explanation:

f ( x ) = 2x²

Find f ( - 3)

let , x = - 3

lf ( - 3 ) = 2 ( -3 )²

f ( - 3 ) = 2 × ( - 3 )²

Evaluate the power

f ( -3) = 2 × 9

multiply the numbers

f ( - 3 ) = 18

Answer:

The answer is "The second choice".

Step-by-step explanation:

[tex]r=6\\\\h=13 \\\\[/tex]

Formula:

[tex]A=2\pi rh[/tex]

[tex]=2\times 3.14 \times 6 \times 13\\\\=2\times 3.14 \times 78\\\\=3.14 \times 156\\\\=3.14 \times 156\\\\=489.84 \approx 489.8 ft^2[/tex]

Answer:

20 degree

Step-by-step explanation:

x + x + 70 = 110 degree (sum of two opposite interior angle equal to the exterior angle formed)

2x = 110 - 70

x = 40/2

x = 20 degree

9514 1404 393

Answer:

  4/10 and 10/25

Step-by-step explanation:

If each of the ratios reduces to the same lowest terms, then they are a proportion. All are in lowest terms except the first pair. Reducing those gives ...

  4/10 = 10/25 = 2/5

4/10 and 10/25 form a proportion

__

All of the other pairs are pairs of different ratios, so do not form a proportion.

Answer:

(6290.678 ; 7790.742)

Step-by-step explanation:

Given the data :

5640, 5090, 6590, 6380, 7165, 8440, 9980

The sample mean, xbar = Σx / n = 49285 / 7 = 7040.71

The 90% confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * σ/√n

Since the σ is known, we use the z- distribution

Zcritical at 90% confidence = 1.64

Hence,

Margin of Error = 1.64 * 1210/√7

Margin of Error = 750.032

90% confidence interval is :

7040.71 ± 750.032

Lower boundary = 7040.71 - 750.032 = 6290.678

Upper boundary = 7040.71 + 750.032 = 7790.742

(6290.678 ; 7790.742)

Answer:

Area of the bookmark = 52.56 cm²

Step-by-step explanation:

The two semicircles attached at both end of the rectangle will give us a full circle.

Therefore,

Area of the bookmark = area of rectangle + Area of a circle

Area of the bookmark = L × W + πr²

Length (L) = 10 cm

Width (W) = 4 cm

radius (r) = ½(4) = 2 cm

π = 3.14

Plug in the values into the equation

Area of bookmark = 10 × 4 + 3.14 × 2²

= 40 + 12.56

= 52.56 cm²

Answer:

1 gallon

Step-by-step explanation:

gallons of paint needed; 4

gallons used: (3/4)*4

= 1 gallon was used

Answer:

Answer is 3 gallons

Step-by-step explanation:

1 gallon= 25%

2 gallons=50%

3 gallons=75%

3/4 is equivalent to 75%

Hope this helped!

Answer:

4/9

Step-by-step explanation:

2+16 = 18 total marbles

16 ÷ 2= 8 plastic marbles

Since there are 18 total marbles and 8 plastic red marbles we can say that there is a probability of 8/18.

8/18 in simplest form is 4/9.

Hope this helps! Brainliest?

Answer: 6 hours and 10 minutes

Step-by-step explanation:

Answer:

VPQ = 83°

Step-by-step explanation:

You can draw a circle around the point P, and a circle have 360°, so it means that the sum off all the angles have ro be 360°. Some of these angles have the same measure, because they're formed by the same lines segments, they are:

SPR = UPV; TPU = RPQ; TPS = VPQ

360 - SPR - UPV - RPQ - TPU = VPQ + TPS

As some of they are equal, we can just multiply they by 2:

360 - 2×SPR - 2×RPQ = 2× VPQ

360 - 2×35 - 2×62 = 2×VPQ

360 - 70 - 124 = 2×VPQ

2 VPQ = 166

VPQ = 166/2

VPQ = 83°

Step-by-step explanation:

kayo na po bahala mag calculate

Answer:

below

Step-by-step explanation:

p = 2( a + b)

p = 2(24 +16)

p =80 in

p semicircle

=πr

= 3.142 *8

= 25.136

p of figure

p =80 +25.136

p=105.136 in

[tex]3 {x}^{2} + 11x - 4[/tex]

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

[tex](3x - 1)(x + 4) \\ \\ = 3x(x + 4) - 1(x + 4) \\ \\ = 3 {x}^{2} + 12x - x - 4 \\ \\ = 3 {x}^{2} + 11x - 4[/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

they just go straight what does it mean?

Answer:

the answer is the alphabet A at the picture

The circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A

Given the inequality expression

-4(x+3) <= -2-2x

Expand the inequality

-4x - 12 <= -2-2x

Collect the like terms

-4x + 2x <= -2+12

-2x <= 10

Divide both sides by -2

-2x/-2 >= 10/-2

x >= -5

For the number line, the circle must be on -5 and arrow drawn to the right. Hence the correct answer is number line A.

Learn more on inequality expression: https://brainly.com/question/24372553

Answer:

f(x) = (x+5)^2 +12

The minimum value is 12

Step-by-step explanation:

f(x)=x^2+10x+37

The vertex will be the minimum value since this is an upwards opening parabola

Completing the square by taking the coefficient of x and squaring it adding it and subtracting it

f(x) = x^2+10x  + (10/2) ^2 - (10/2) ^2+37

f(x) = ( x^2 +10x +25) -25+37

    = ( x+5) ^2+12

Th is in vertex form y = ( x-h)^2 +k  where (h,k) is the vertex

The vertex is (-5,12)

The minimum is the y value or 12

Answer:

Below:

Step-by-step explanation:

A) 0.15 (0.35 + 0.40 + 0.10 + 0.15 = 1)

B) 0.45

C) 0.40

A) the total probability has to equal 1.

To find the probability of rat subtract the other animals from1:

Rat = 1 - 0.35-0.4-0.1 = 0.15

Rat = 0.15

B) probability of cat or hamster equals the sum of their probabilities:

Cat = 0.35 + hamster = 0.1 = 0.45

Answer = 0.45

C) the probability of them both picking the same = dog x dog = 0.4 x 0.4 = 0.16

Answer = 0.16

Answer:

60

Step-by-step explanation:

135-75 = 60

HOPE IT HELPS

Answer:

m∠ACD = 130

Step-by-step explanation:

If ABC is an isosceles, AB = AC and m∠A = 80°, then m∠B and m∠C is equal to 50°.

This is because angles in a triangle adds up to 180°.

180° - 80° = 100°/2 = 50°

∴ m∠ACD = 130°, this is because the interior opposite angles in a triangle is supplementary to the opposite exterior angle:

50° + 80° = 130°

Or

Angles on a straight line adds up to 180°.

180° - 50° = 130°

Answer:

[tex]\left[\begin{array}{ccc}3\\3.8\end{array}\right][/tex]

Step-by-step explanation:

Here we want to compute the product of two matrices, one 2x2, and other 2x1.

[tex]\left[\begin{array}{ccc}0.3&0.3\\0.35&0.4\end{array}\right]*\left[\begin{array}{ccc}4\\6\end{array}\right][/tex]

Remember that in the product, we multiply the rows of the first one by the columns of the second one, then the product is just:

[tex]\left[\begin{array}{ccc}0.3&0.3\\0.35&0.4\end{array}\right]*\left[\begin{array}{ccc}4\\6\end{array}\right] = \left[\begin{array}{ccc}0.3*4 + 0.3*6\\0.35*4 + 0.4*6\end{array}\right] = \left[\begin{array}{ccc}3\\3.8\end{array}\right][/tex]

Answer:

the next three terms, 0.075,0.0375,0.01875 (common ratio 0.5)

the formula is 0.3*0.5^n-1

the formula for finding the nth term of a geometric sequence preset would be

a*r^n-1

a is first term

r is common ratio

Step-by-step explanation:

The value of function f (- 2) would be,

⇒ f (- 2) = 3 / 4

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

The value of function is,

⇒ f (x) = 3 × 2ˣ

Now,

At x = - 2;

The value of function f (- 2) would be,

⇒ f (x) = 3 × 2ˣ

⇒ f (- 2) = 3 × 2⁻²

⇒ f (- 2) = 3 × 1 / 4

⇒ f (- 2) = 3 / 4

Thus, The value of function f (- 2) would be,

⇒ f (- 2) = 3 / 4

Learn more about the function visit:

https://brainly.com/question/11624077

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