8 Solve: 2 3= 4x + 2 - O- O 1 2 AP 4 ( ) 1 4. O 1 2

Solution

- The solution is given below:

- Thus, we have:

- Thus, the plot is:

Answer:

1/4

Step-by-step explanation:

it can be simplified by dividing both the numerator and denominator with 9.

[tex] \displaystyle \large{ \sf{ \frac{9}{36}}} [/tex]

[tex]\displaystyle \large{ \sf{ \frac{9}{36} = \frac{ \cancel9}{ \cancel3 \cancel6} }}[/tex]

[tex]\displaystyle \large{ \bf{ = \frac{1}{4} }}[/tex]

simplest form is 1/4

The slope of the line that passes through points (x1, y1) and (x2, y2) is computed as follows:

Replacing with the points (-8, 3) and (0,1) we get:

We simplify by combining like terms

therefore

Answer:

It is the diameter of the circle

it is 7 cm

it is a chord

Explanation:

First, we notice that the line segment CB passes through the centre of the circle and its endpoints touch the circumference - this tells us that CB is the diameter.

Furthermore, any line segment whose endpoints lie on the circumference of the circle is a chord (meaning that the diameter is the longest chord), and so we deduce that CB is also a chord.

Since CB is the diamter, its length is 2 times the radius. The raduis of the circle we know is DA = 3.5 cm; therefore, the dimater is CB = 2 DA = 2 * 3.5 = 7 cm.

Hence, the correct choices are:

It is the diameter of the circle

it is 7 cm

it is a chord

1) In this problem, we can see that this is an isosceles right triangle.

2) So, one way of solving it is to make use of the Pythagorean theorem. Note that an isosceles triangle has two congruent sides, so we can write out:

Usually, we rationalize it. But since the question requests the denominator to be a rational one, so this is the answer.

First, we graph the trapezoid and the line

If we reflect the figure across the line y = 1, then we get the following figure

As you can observe in the graph, the vertices would be J'(-4,-1), K'(-2,-5), L'(2,-5), and M'(3,-1).

Answer:

The distance from the edge of the fountain to the centre is approximately 23.87 inches.

The water fountain forms a circle. The distance around the water fountain is the circumference of the circle formed.

Therefore,

circumference = 2πr

150 = 2πr

The distance from the edge of the fountain to the centre is the radius of the circle formed. Therefore,

75 = πr

r = 75 / 3.14159

r = 23.8732616287

r = 23.87 inches

The distance from the edge of the fountain to the centre is approximately 23.87 inches.

Lines are parallel and on the same plane. The final answer, "No, because the lines are in the same plane," is the proper response.

What is a line that is perpendicular?

Perpendicular lines are those that cross at a perfect right angle. Parallel lines are those that are always the same distance apart from one another.

The question is incomplete.

Please see the accompanying image for a comprehensive explanation of the question.

Line l and line m are the two lines that are depicted in the image.

The skew lines are in different planes and do not overlap, as far as we are aware.

Therefore,

Lines are parallel and on the same plane. The final answer, "No, because the lines are in the same plane," is the proper response.

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64 ounces of cherries are displayed in all in the farm stand.

According to the question,

We have the following information:

Farm stand has cherries on 2 shelves.

Number of boxes in each shelf = 4 boxes

So, the number of boxes in 2 shelves will be (2*4) or 8.

Ounces of cherries in each box = 8 ounces

Now, the ounces of cherries in 8 boxes can be easily found by multiplying the ounces of cherries in 1 box by the number of total boxes.

Ounces of cherries in 8 boxes = (8*8) ounces

Ounces of cherries in 8 boxes = 64 ounces

Now, the expression that represents the amount is (number of shelves*number of boxes*ounces of cherries in each box).

Hence, the ounces of cherries displayed in all is 64 ounces.

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On July 31, Oscar Jacobs checked out of the Sandy Beach hotel after spending four nights. The cost of the room was $76.90 per night. He wrote a check to pay for his four-night stay. What is the total amount of his check, expressed in words?

step 1

Multiply $76.90 by 4

76.90*4=$307.6

so

expressed in words is

The answer of the given expression is 80.

Exponents

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

For example:-

[tex]5^4[/tex] can be written as 5*5*5*5.

Here 4 is the exponent or power and 5 is the base.

There are some laws of exponents which we use while calculating the answer to such expressions.

Given expression:-

[tex]\frac{12^7*30^5}{25^2*8^5*27^4}[/tex]

We have to simplify the given solution using the laws of exponents.

First we will divide them in their prime factors.

We know that,

[tex](x^a)^b=x^{ab}[/tex]

We can write,

[tex]12^7 = (2^2)^7*3^7=2^{14}*3^7[/tex]

[tex]30^5=2^5*3^5*5^5[/tex]

[tex]25^2=(5^2)^2=5^4[/tex]

[tex]8^5=(2^3)^5=2^{15}[/tex]

[tex]27^4=(3^3)^4=3^{12}[/tex]

Hence, we can write the given expression as follows,

[tex]\frac{2^{14}*3^7*2^5*3^5*5^5}{5^4*2^{15}*3^{12}}[/tex]

Also, we know that,

[tex]x^a*x^b=x^{a+b}\\x^a/x^b=x^{a-b}[/tex]

We can write,

[tex]{2^{(14+5-15)}*3^{(7+5-12)}*5^{(5-4)}}[/tex]

[tex]2^4*3^0*5^1[/tex] = 16*1*5 = 80

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ANSWER

y = -x - 3

STEP BY STEP EXPLANATION

Step 1: The given points are:

(-6, 3) and (5, -8)

Step 2: The slope-intercept form is

where m is the slope and c is the intercept

Step 3: Find the slope m

Step 4: Solve for intercept c using either of the points

Step 5: Re-writing the slope-intercept form to include the values of m and c

Hence, the equation of the line in slope-intercept form is y = -x - 3

Solution

- Linear:

The general form of a linear function is

- Quadratic:

The general form of a quadratic function is:

- Exponential:

The general form of an exponential function is:

- Now that we know the general forms of these functions, we can proceed to solve the question.

- The amount a person is paid per hour in wages is the amount that the person collects for every hour that he works

- Let us imagine that a person receives $a for every hour worked.

- This means that:

After 1 hour, the person makes $a

After 2 hours, the person makes $a + $a = $2a

After 3 hours, the person makes $a + $a +$a = $3a

- We can therefore generalize as follows:

Thus, after x hours, the person makes:

- Thus, the function representing the amount a person makes per hour of work is given by:

- Comparing this result with the 3 function definitions above, we can see that this corresponds to a Linear function

Final Answer

The answer is Linear

ANSWER

There are 37 tens in the cash register

EXPLANATION

Given that;

The total amount in the cash register is $740

The cash register contain five dollar and ten dollar

Follow the steps below to find the number of ten dollar in the cash register.

Let x represents the number of $5 and $10 in the cash register.

Recall, that the register contain twice as many $5 as ten dollars and this can be expressed mathematically as

Evaluate x in the above expression

Therefore, we have 37 tens in the cash register

The 30-60-90 triangle is given by

AS we can note , the hypotenuse is twice as long as the shorter leg. Additionally, the longer leg is square root of 3 tines as long as the shorter leg. Therefore, the answer is option C and F

Arc XY = 2π • (PX)/ 4

. = 2π • 5/4

. = 6.28 • 5/4= 31.40/4 = 7.85

Then answer is

Option G) 7.854

Proportional relationships are relationships between two variables where their ratios are equivalent.

From the table given;

g:h are respectively;

Since the ratios above are not equivalent, their relationship is not proportional.

Hence, the correct option is B

Given:

Numbers from 1 - 40

Let's find the probability of:

Pleven | at least 12)

Where:

Even numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 20 numbers

Even numbers that are at least 12 = 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 15 numbers.

Numbers that are at least 12 = 29 numbers

Therefore, to find the probability, we have:

Where:

Therefore, we have:

Therefore, the probability that a number chosen at random is even given that it is at least 12 is 0.52

ANSWER:

0.52

The velocity is v= 30.6 ft/ sec.

Velocity defines the direction of the movement of the body or the object. Speed is primarily a scalar quantity. Velocity is essentially a vector quantity. It is the rate of change of distance. It is the rate of change of displacement.

Given that,

We have given the height

s(t) = 0.2[tex]t^{3}[/tex] + 21t, where 0 ≤ [tex]x[/tex] ≤ 17.

To find the velocity we have to differentiate s(t) wrt to t.

s(t) = 0.2[tex]t^{3}[/tex] + 21t

    = 0.6[tex]t^{2}[/tex]+21

velocity of the particle at t = 4

s(4) = 0.6*[tex]4^{2}[/tex]+21

     = 9.6+21

     = 30.6

v= 30.6 ft/ sec

Hence, The velocity is v= 30.6 ft/ sec.

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The single trig function that simplifies the function is sec(t)

Trigonometry deals with the functions of angles and how they're applied.

Given cot(t)/csc(t)-sin(t)

since csc(t) =  1/sin(t) , we have:

[tex]\frac{ cot(t)}{csc(t)-sin(t)} = \frac{cot(t)}{\frac{1}{sin(t)} - sin(t) }[/tex]

[tex]\frac{ cot(t)}{csc(t)-sin(t)} = \frac{cot(t)}{\frac{1-sin^{2}(t) }{sin(t)} }[/tex]

since:

cos²(t) = 1 - sin²(t)

Therefore we have:

cot(t) / csc(t)-sin(t) = cot(t)/ cos²(t)/sin(t)

cot(t) / csc(t)-sin(t) = cot(t) / cos(t).cos(t)/sin(t)

Since  cos(t) / sin(t) = 1/tan(t) = cot(t)

Therefore:

cot(t) / csc(t)-sin(t) = cot(t)/ cot(t)×cos(t)

cot(t) / csc(t)-sin(t) = 1/cos(t)

Since   1/cost = sec(t)

Finally, cot(t) / csc(t)-sin(t) is sec(t).

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The limit of a function is the value that a function approaches as that function's inputs get closer and closer to some number.

The question asks us to estimate from the table:

To find the limit of g(x) as x tends to -2, we need to check the trend of the function as we head towards -2 from both negative and positive infinity.

From negative infinity, the closest value we can get to before -2 is -2.001 according to the values given in the table. The value of g(x) from the table is:

From positive infinity, the closest value we can get to before -2 is -1.999 according to the values given in the table. The value of g(x) from the table is:

From the options, the closest estimate for the limit is 8.03.

The correct option is the SECOND OPTION.

done

Let's use the variable x to represent the amount of pure acid and y to represent the amount of 10% acid.

Since the total amount wanted is 90 L, we can write the equation:

Also, the final solution is 81%, so we can write our second equation:

From the first equation, we can solve for y and we will have y = 90 - x.

Using this value in the second equation, we have:

Solving for x, we have:

Therefore the amount of pure acid to be used is 71 L and the amount of 10% acid is 19 L.

The substitution u = (2x - 2) to the integral x³e(^2x^4-2) dx is (2x – 2)/4 +c

Therefore,

Use the substitution

U = (2x -2)

to evaluate integral x³e(^2x^4-2) dx

let u = 2x -2

du = x dx or dx =du/2

u = 2x-2

du = d(2x – 2)

du = 2dx

dx = du/2

∫ (2x -2)dx = ∫u du/2

=1/2 ∫u du

= ½ u square /2 +c

= u square /4 +c

= (2x – 2)/4 +c

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The equation of the line follows the following general structure:

Where m is the slope of the line and b is the y intercept.

Find the corresponding values in the given formula, this way:

In the given equation, m has a value of -1/2, it means the slope is -1/2.

Answer:

I may be wrong but I think it's D.

Step-by-step explanation:

I made an educated guess.

Explanation

The area of a portion of a circle with radius 'r' and central angle 'a' in radians is:

In this problem, the radius is r = 4cm, and the angle a = 30º.

First we have to express the angle in radians:

And now we can find the area of the shaded region:

Answer

The area of the shaded region is:

The expression given is,

Subtract 3 from both sides

Divide both sides by 5

Apply absolute rule:

Add 3 to both sides

Therefore, the answer has the form:

Hence, the solution using interval notation is