Solve [tex]2 cosx=4cosx sin^2x[/tex]

Answer:

Jiri is 25 years old.

Step-by-step explanation:

1)Pamela =Jiri-9 ( Pamela is 9 years younger than Jiri)

2)Pamela +Jiri=41

Substitute equation 1 into equation 2

(J-9)+J= 41

2J-9=41

Add 9 to both sides:

2J=41+9

Divide by 2:

2J=50

J=25

the required Jiri's age is 25 years.

Pamela is 9 years younger than Jiri and the sum of their ages is 41. What is Jiri's age is to be determined.

In mathematics, it deals with numbers of operations according to the statements.

Let the age of Pamela and Jiri is x and y respectively
Pamela is 9 years younger than Jiri. so,
y = x + 9   - - - - (1)
the sum of their ages is 41
x +  y = 41  - - - - (2)

From equation 1 put y in equation 2
x + x + 9 = 41
2x + 9 = 41
2x = 41 - 9
2x = 32
x = 32/2
x = 16
Now put this x =16 in equation 1
y = 16 + 9
y = 25

Thus, the required Jiri age is 25 years

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The probability of selecting two prime numbers is 1/6.

Probability determines the odds that a random event would happen. The odds that the random event would happen lie between 0 and 1.

The probability of selecting two prime numbers  = (number of prime numbers between 1 and 9 / total numbers between 1 and 9) x [(number of prime numbers between 1 and 9 / total numbers between 1 and 9) - 1]

Prime numbers between 1 and 9 = 2, 3, 5, 7

4/9 x 3/8 = 1/6

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Step-by-step explanation:

++++5

+++++++_2

1=false

true

false

false

The computation of the equations is illustrated below.

a. x - y = 1 .... i

x + y = -9 ..... ii

Subtract the equations

-2y = 10

y = 10/-2 = -5

Since x - y = 1

x - (-5) = 1

x + 5 = 1

x = 1 - 5 = -4

b. 3x + 2y = -9

x - y = -13

Multiply equation i by 1

Multiply equation ii by 3

3x + 2y = -9

- 3x - 3y = -39

5y = 30

y = 6

Since x - y = 13

x - 6 = 13

x = 13 + 6 = 19

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1598 cm square is the area of the container.

According to the statement

we have given that the container is rectangular prism

And Length of rectangular prism is 34cm

Width of rectangular prism is 17 cm

Height of rectangular prism is 20 cm

we use the below written formula to find the surface area

Surface area formula A=(wl+hl+hw)

To find the surface area of the container.

Substitute the values of Length, width and height in the formula then

A=(wl+hl+hw)

A=((17)(34)+(20)(34)+(20)(17))

After solving the values

A=(578+680+340)

A= 1598

So, 1598 cm square is the area of the container.

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Answer:

C. (2;9)

Step-by-step explanation:

for more details see the attachment.

Factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)

For us to determine if a set of inequality  function has a solution, we will equate the functions and determine the point of intersection if there are any,

Given the inequalities

y ≤ x^2 - 3

y > -x^2 + 2

Equate

x^2 - x = -x^2 + 2

Collect like terms

2x^2 - x - 2 = 0

In order to determine the value of x, we will factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)

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The rate if he went three years without an accident based on the information about the insurance is $552.15.

From the information given, his basic insurance cost is $613.50 per year and his insurance company offers a typical "safe-driver discount.

The amount will be:

= 613.50 - (20.45 × 3)

= 552.15

In conclusion, the rate is $552.15.

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Answer:

203681

203,681

Two hundred and three thousand, six hundred eighty-one

Step-by-step explanation:

The number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.

In the question, we are asked to write the number 203681 in words.

In the given number, we have:

Keeping the thousands as different section, we have 203 in thousands section, and 681 in the remaining.

203 can be named as two hundred and three.

681 can be named as six hundred and eighty-one.

Since, 203 is in the thousands section, we add thousand in its name.

Thus, the name we get is two hundred and three thousands, six hundred and eighty-one.

Thus, the number 203681 in words can be written as two hundred and three thousands, six hundred and eighty-one.

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Answer:

10

Step-by-step explanation:

g(x) = 3(10-x^2)-8=>30-3x^2-8=>-3x^2+22

then substitute -2 in x

-3(-2)^2+22

-3(4)+22=-12+22=10

Answer:

d=27

Step-by-step explanation:

d+13=40

  -13  -13    Subtract 13 from both sides to leave by itself

d=27

Hope it helps:)

The value of y at x =15 is 9.

Two variables are said to be in Direct Variation when increasing one variable the other also increases.

The direct variation is represented by

y ∝ x

y = kx

where k is the proportionality constant

the value of y =12 , x = 20

12 = k * 20

12/20 = k

k = 0.6

The equation becomes

y = 0.6 x

The value of y at x = 15 is

y = 0.6 * 15

y =9

Therefore, the value of y at x =15 is 9.

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Answer:

2.4536 years

Step-by-step explanation:

compound formula:

A=P*(1+r/n)^nt

A = 6000

P = 5000

r = rate

n = 4 times per year compounded

t = time in years

6000 = 5000(1 + .075/4)^4t

divide both sides by 5000

1.2 = (1.01875)^4t

log both sides

log(1.2) = 4t * log(1.01875)

solve for t

t = 2.4537 years

The total amount of Chandra's investments after 8 years exists at $110.03 Compound interest.

The formula for calculating the compound interest exists described as;

[tex]A = P(1+r/n)^{nt[/tex]

where, P is the amount invested = $75

r be the rate. = 0.048

t be the time = 8 years

n = 12 (monthly)

Substitute, the values in the above equation, then we get

[tex]$A = 75(1+0.048/12)^{96[/tex]

A = 75(1.467)

A = 110.03

Hence the total amount of Chandra's investments after 8 years is $110.03 Compound interest.

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Answer:

Step-by-step explanation:

Since diameter x pi=3.14,this should be easy.

4x3=12

4x14/100=.56

12+.56=12.56

12.56 is the answer

Applying the triangle sum theorem, we have:

First angle measure = 35°

Second angle = 70°

Third angle = 75°

According to the triangle sum theorem, all angles in a triangle will give a sum of 180 degrees.

First angle measure = x

Second angle = 2x

Third angle = (2x + x) - 30 = 3x - 30

x + 2x + 3x - 30 = 180 [triangle sum theorem]

6x - 30 = 180

6x = 180 + 30

6x = 210

x = 210/6

x = 35

First angle measure = x = 35°

Second angle = 2x = 2(35) = 70°

Third angle = 3x - 30 = 3(35) - 30 = 75°

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See below for the complete table and graph of y = x + 4

The function is given as:

y = x +4

Where x = -2, 0, 2, 6 and 8

So, we have

y = -2 +4 = 2

y = 0 +4 = 4

y = 2 +4 = 6

y = 6 +4 = 10

y = 8 +4 = 12

The above computation implies that the complete table is

Input x        x + 4        Output, y        (x, y)

-2               -2  + 4          2                  (-2,2)

0                 0  + 4          4                  (0,4)

2                 2  + 4          6                  (2,6)

6                 6  + 4          10                 (6,10)

8                 8  + 4          12                  (8,12)

See attachment for the graph of y = -x + 4

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The number of mice that didn't get a tumor is 9 mice out of the 25 mice.

Identify the total mice who did not have any effects or the effects did not include a tumor.

Repiratory failure: 9 mice

Based on this, it can be concluded 9 mice did not have a tumor, while 21 mice hat at least a tumor and some of them had a tumor and respiratory failure.

Note: This question is incomplete; here is the missing section:

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Answer:

14

Step-by-step explanation:

[tex] {x}^{2} = {4}^{2} \\ = 16\\ 4y = 4 \times - 3 \\ 4 \times - 3 = - 12 \\ 16 - - 12 =16 + 12 \\ - \times - = + \\ 16 + 12 = 28 \\ 28 \div 2 = 14[/tex]

$13,000 was invested at 6% whereas $7,000 was invested at 10% using simple interest approach

What is simple interest?

Simple interest is determined as the amount invested multiplied by the interest rate and the number of years that investment lasts.

I=PRT

I=interest

P=principal

R=rate of return

T=time

Let X be the amount invested at 6%

I at 6%=6%*X*1

I=0.06X

The amount invested at 10% is 20,000-X

total interest=0.06X+0.10*(20000-X)

total interest=1,480

1480=0.06X+0.10*(20000-X)

1480=0.06X+2000-0.10X

1480-2000=0.06X-0.10X

-520=-0.04X

X=-520/-0.04

X=13,000

13,000 was invested at 6%

amount invested at 10%=20,000-X

amount invested at 10%=20,000-13,000

amount invested at 10%=7,000

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Answer: 97350

Step-by-step explanation:

The numbers (3251)(30) are separated by using parentheses by multiplying the numbers we get 97350.

When we notice two or more numbers together that exist divided by parentheses, then the parentheses exist pointing us to multiply.  In math, multiplying indicates adding equivalent groups. When we multiply, the number of things in the group rises. The two elements and the product exist as regions of a multiplication problem.

Given: (3251)(30)

Here, the numbers are separated by using parentheses, then the parentheses exist pointing us to multiply.

Therefore, by multiplying the numbers we get

(3,251)(30) = 97350

Therefore, the correct answer is 97350.

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The mathematical mistake that Riley made is that: "She used the wrong common denominator." (Option A)

A common denominator is a factor that is similar to all the fractions in the sequence of equations.

Hence the correct answer is:

(2(2x² - 6x + 9))/((x-3) (x-2) (x+3))

See the correct sequence of steps below:

Step One - the Expression is given as:

(x/(x-3)(x-2)) + (3/(x+3))

Step 2 - Find the common denominator and rewrite the expression so that the numerators are above the common denominators.

Hence we have:  (x (x+3) + 3(x-3) (x-2))/(x-3)(x-2)(x+3)

Step 3  Apply the Law of Multiplicative Distribution:

Hence we have  (x² +3x+3x²-9x-6x+16)/(x-3)(x-2)(x+3)

Step 4 -  Collect Like Items

This gives us: (x²+3x²)+(3x-9x-6x)+18/(x-3)(x-2)(x+3)

Step 5 Sort for like coefficients

This gives us:  ((1+3)x² +(3-9-6) * x + 18)/(x-3)(x-2)(x+3)

Step 6 -  check for the sum or difference

This gives us: (4x²+(3-9-6) * x+ 18)/(x-3)(x-2)(x+3)

We simplify and factor the expression to get

(2(2x²-6x+6)/(x-3)(x-2)(x+3).

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Answer:

11  units

Step-by-step explanation:

We first need to solve for x

3x -28 +3x -30 + x = 33  Combine the x's

7x - 28 -30 = 33  Combine -28 and -30

7x - 58 = 33  Add 58 to both sides

7x = 91  Divide both sides by 7

x = 13  Now plug 13 into the expression for DE

3x - 28

3(13) - 28

39 -28

11

Answer: B

Step-by-step explanation:

1: 5 × 1.25 = 6.25

 2 × 1.25 = 2.5

 1.7 × 1.25 = 2.125

2: L × W × H = 6.25 × 2.5 × 2.125 = 33.20 cubic

The dimensions of the rectangle as described in the task is; 12.4 by 5.7 yd.

Since the area, length and breadth of the rectangle are as described, it follows that;

66 = x(2x+1)

66 = 2x² + 1

x² = 32.5

x = 5.7

Therefore, the dimensions are 5.7 and 12.4.

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Answer:

9

Step-by-step explanation:

it should be that should be the answer it should be 9 bcuz he bout gum for 1 he got 5 peaces so dets 5$ then someone else got sumthing for 1$ and they got 4 peicea so thats 4$ 5+4 is 9