Write the equation of the line in fully simplified slope-intercept form.

Answer:

[tex]\frac{1}{27}((13)^{\frac{3}{2}}-(6)^ {\frac{3}{2}})[/tex]

Step-by-step explanation:

The slope of the line T will be 1 and the y-intercept will be (0,4) in the given coordinate plane.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope-intercept form of an equation is used whenever the equation of a line is expressed in the form y = mx + b. M represents the line's slope. In the case of the equation y = 3x - 7, the slope is 3 and the y-intercept is (0, 7). And b is the value of b in the point that is the y-intercept (0, b). By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them. The letter "m" is frequently used to denote slope.

Here,

The slope of line D=1

y-intercept=(0,0)

factor=2

coordinate=(3,4)

The slope will not change that will be 1.

y-intercept=0+4

=4

y-intercept=(0,4)

In the given coordinate plane, the y-intercept of line T will be (0,4) and its slope will be 1.

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By using the concept of mathematical expression, it is obtained that

(62−42)×3 is represented by  3 times the difference between 62 and 42

First option is correct

What is mathematical expression?

A mathematical expression consist of numbers connected with addition, subtraction, multiplication and division.

Here the given  mathematical expression is (62−42)×3

Here, the signs shown are subtraction and multiplication. So the concept of difference and times will be used here

(62−42)×3  means whole of (62 - 42) is multiplied with 3

So, this is 3 times the difference between 62 and 42

First option is correct

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Correct Question

Which phrase represents this expression?

(62−42)×3

a) 3 times the difference of 62 and 42

b) 3 times the difference of 42 and 62

c) The difference of 62 and the product of 3 times 42

d) The difference of the product of 3 times 42 and 62

Answer:

2

Step-by-step explanation:

i gotchu my boy

1.  The rewritten form of the equation is (x + 2)² = -6

2. The solutions to the equation are 0.45 and -4.45

Given,

The equation;  

0=x^2+4x+10

1. We have to rewrite the equation;

x² + 4x + 10 = 0

x² + 4x = -10

Add the square of the half of coefficient of x to both sides

4/2 = 2

x² + 4x  + 2² = -10 + 2²

x² + 4x + 4 = -6

(x + 2)² = -6

Therefore,

The rewritten form of the equation is (x + 2)² = -6

2. Calculate the value of x

(x + 2)² = -6

Square root both sides

√(x + 2)² = ±√6

x + 2 = ±2.45

x= ±2.45 - 2

x = 2.45 - 2 and -2.45 - 2

x = 0.45 and -4.45

Hence the solutions to the equation are 0.45 and -4.45

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Answer:

0=x²+4x+1

3=(x+2)²

x=−2± [tex]\sqrt{3}[/tex]

Step-by-step explanation:

The equivalent function of the exponential function is (a) f(x) = (7/4)ˣ

From the question, we have the following function that can be used in our computation:

f(x) = (4/7)^-x

This function can be properly expressed as

f(x) = (4/7)⁻ˣ

Solving further, we need to apply the exponent law of indices

This is represented as

a⁻ˣ = 1/aˣ

When the above rule is applied, we have

f(x) = 1/(4/7)ˣ

Evaluate the quotient

f(x) = (7/4)ˣ

Hence, the equivalent is (a) f(x) = (7/4)ˣ

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Answer:

36 minutes

Step-by-step explanation:

The total distance covered by the two vehicles per hour: 70 + 50 = 120 miles.

Time is distance over velocity.

[tex]t=\frac{72}{120}[/tex]  hours

Which simplifies to

[tex]\frac{3}{5}[/tex]  hours.

Convert hours to minutes.

There is 60 minutes in 1 hour.

[tex]\frac{1}{60}=\frac{\frac{3}{5} }{x}[/tex]

[tex]x=36[/tex]

The answer will be 13 km that is displacement of the car.

What is displacement?

When a body shifts from one position to another, displacement is the smallest (straight line) distance between the starting position and the ending position of the body, which is symbolized by an arrow pointing from the starting position to the ending position. Displacement is a vector quantity that describes "how far out of place an object is"; it represents the overall change in the position of the object.

A car travels 12 km north and turns left to travel 5km.

So the final position of car from the initial position is :

So the placement of the car is √(12²+5²) = √169 =13km

Hence the Displacement of the car is 13 km

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The required derivatives of the given hyperbolic functions are

d/dx(sinh3x) = 3cosh3x, d/dx(cosh7x) = 7sinh7x, d/dx(tanh6x) = 6sech²6x, d/dx(coth5x) = −5csch²5x, d/dx(sech3x) = −3sech3xtanh3x, and d/dx(csch7x) = −7csch7xcoth7x.

The differentiation formulas for the hyperbolic functions are below as

d/dx(sinhx) = coshx

d/dx(coshx) = sinhx

d/dx(tanhx) = sech²x

d/dx(cothx) = −csch²x

d/dx(sechx) = −sechxtanhx

d/dx(cschx) = −cschxcothx

As per the given question,

⇒ d/dx(sinh3x)

Using formula d/dx(sinhx) = coshx,

⇒ cosh3x × (d/dx(3x))

⇒ cosh3x (3)

⇒ 3cosh3x

⇒ d/dx(tanh6x) = 6sech²6x

⇒ d/dx(coth5x) = −5csch²5x

⇒ d/dx(sech3x) = −3sech3xtanh3x

⇒ d/dx(csch7x) = −7csch7xcoth7x

Thus, the required derivatives of the given hyperbolic functions are

d/dx(sinh3x) = 3cosh3x, d/dx(cosh7x) = 7sinh7x, d/dx(tanh6x) = 6sech²6x, d/dx(coth5x) = −5csch²5x, d/dx(sech3x) = −3sech3xtanh3x, and d/dx(csch7x) = −7csch7xcoth7x.

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The $28,000 investment will earn $696 more than the $16,000 investment if both make a 5.8% (APY) annual percentage yield for a year.

APY means annual percental yield.

Annual Percentage Yield describes the real interest rate earned on an investment in a year.

The Annual Percentage Yield refers to the interest an investment, saving, and loan attracts for the time value of money and inflationary effects.

The Annual Percentage Yield is applied to the investment amount for a year to calculate the interest earned.

                                 Plan A         Plan B

Investments            $28,000     $16,000

Interest earned         $1,624           $928 ($16,000 x 5.8%)

The difference in interest earned = $696 ($1,624 - $928)

Thus, when an investor puts $28,000 in a savings account at 5.8%, they earn $696 more than investing $16,000 at the same APY.

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Step-by-step explanation:

Solving -8 + x > -9 for x is: x > -1.

-8 + x > -9

add 8 to both sides:

-8 + x + 8 > -9 + 8

x > -1

True

Solving a system of equations we will see that the speed of the wind is 60mi/h.

When the plane flies with the wind, the two speeds adds up, while if the plane flies against the wind, the speeds need to be subtracted.

We know that the speed of the plane is 300 mi/h.

If the speed of the wind is W, then we can write the two equations:

(300 mi/h + W)*t = 600mi

(300mi/h - W)*t = 400mi

So we have a little system of equations, if we take the quotient between them we get:

[(300 mi/h + W)*t]/[(300mi/h - W)*t ] = 600mi/400mi

(300 mi/h + W)/(300mi/h - W) = 6/4

Now we can solve this for W.

(300 mi/h + W) = (6/4)*(300 mi/h - W)

W + (6/4)*W = (6/4)*300mi/h - 300 mi/h

W*(10/4) = 150 mi/h

W = (4/10)*150 mi/h

W = 60 mi/h

That is the speed of the wind.

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Answer:

7x-5=86

Step-by-step explanation:

By using the formula for compound interest, it can be calculated that

He must pay back $81095 after 9 years

What is Compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially, rather than linearly, then the interest earned is called compound interest

If p is the principal, r is the rate and t is the time, then the amount is calculated by the formula

[tex]A = p(1 + \frac{r}{100})^n[/tex]

The difference between the amount and the principal gives the compound interest.

Principal = $48000

Rate = 6%

Time = 9 years

Amount = [tex]48000(1+ \frac{6}{100})^9\\[/tex]

             = $81095

He must pay back $81095 after 9 years

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The value of the house when it was purchased is 260,000 units

The house has increased in value by 15 percent since it was purchased. The current value is 299,000.

The value of the house when it was purchased can be calculated as follows:

let the amount purchased = x

Hence,

15% of x + x  = 299000

0.15x + x  = 299000

1.15x = 299000

divide both sides by 1.15

Hence,

x = 299000 / 1.15

x = 260000

Therefore, the value of the purchase is 260,000 units

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Answer:

∴ [tex]x = 9[/tex]

Step-by-step explanation:

         [tex]\frac{8}{6} = \frac{12}{x}[/tex]

[tex](\frac{8}{6})(6x) = (\frac{12}{x})(6x)[/tex]

       [tex]8x = 72[/tex]

     ∴ [tex]x = 9[/tex]

The value of x for the given question 8/6 = 12/x is 9.

In the given problem, we know that we need to perform fraction multiplication and algebra to find the value of x.

Here, on the left hand side, we have ⇒ 8/6 (i)

On the right hand side, we have ⇒ 12/x (ii)

To find the value of x, we perform cross multiplication between both sides (LHS and RHS). After performing this function, we get

⇒ 8x = 72

Solving this problem even further, we get  

⇒ x = 9

Therefore, the value of x is 9 for the given problem.

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The expression -9z - 21y - 2.4 ​when -3 is factored out is -3(3z + 7y + 0.8)

From the question, we have the following expression that can be used in our computation:

-9z - 21y - 2.4 ​

The common factor is given as

-3

So, we divide -9z - 21y - 2.4 ​ by 3

The results of these divisions are

-9z/3 = -3z

- 21y/3 = -7y

- 2.4 /3 = -0.8

So, we have the following results

-9z - 21y - 2.4 ​ = -3(3z + 7y + 0.8)

Hence, the factored expression is -3(3z + 7y + 0.8)

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A savings account with a set term and interest rate is known as a certificate of deposit (CD). While CDs often provide greater rates than traditional savings accounts, you can't get to your money right away until the term is over.

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Answer:

-0.6, -0.2, 0, 0.5, 0.7

Step-by-step explanation:

To find out this answer, we know first that negatives are the least. And -0.6 is farther away from 0 than -0.2, so we can have -0.6, -0.2 as our last numbers.

Then, 0.5 and 0.7 are greater than 0, so, then we have -0.6, -0.2, 0.

Then, 0.7 is greater than 0.5, so we can arrange the final numbers:

-0.6, -0.2, 0, 0.5, 0.7

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Answer: -0.6,-0.2, 0, 0.5, 0.7

Step-by-step explanation: Use a number line

The both fractional parts of an English ton are each of these fish.

The English ton, also known as the long ton, is equivalent to 2,240 pounds. Therefore, the fractional parts, of each of the two fish, of the English ton are:

Fish caught in region A weights = 279 lb

Therefore, fish caught in region A

A = 279 ÷ 2240

Fish caught in region B weights = 619 lb

Therefore, fish caught in region B

B = 619 ÷ 2240

Both fractions are irreducible.

So, both fractional parts of an English ton are each of these fish.

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Answer: would be -120 + 78, or -42 feet.

Step-by-step explanation:

The person needs to sell a minimum amount of $550000 to earn $22000.

The percentage is a ratio that can be expressed as a fraction of 100.

Given that, the income of the person is 4% of the total selling value.

Let the person sells $x to earn $22000, therefore,

4% of x is $22000

Or, 4x/100 = 22000

     4x = 2200000

       x = 550000

Hence, the person needs to sell a minimum amount of $550000 to earn $22000.

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Answer:

Step-by-step explanation: xxxdadyxxx12 snap

y

Answer:

Step-by-step explanation:

c

Answer:

It's A

Step-by-step explanation:

I=Prt

I=$660(3.5%)5

I=23.1(5)

I=$115.50

The distance of the line segment from ( -5,5 ) to ( 3,-1 ) is 10 units

What is the distance of a line between 2 points?

The distance of a line between 2 points is always positive and given by the formula

[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Given data ,

Let the two points be A and B

A ( x₁ , y₁ ) = A ( -5 , 5 )

B ( x₂ , y₂ ) = B ( 3 , -1 )

So , the distance between 2 points is given by the formula

[tex]D = \sqrt{(x_{2}-x_{1})^{2} + (y_{2}-y_{1})^{2} }[/tex]

Substituting the values of x₁ , y₁ , x₂ , y₂ in the formula , we get

[tex]D = \sqrt{(-5-3)^{2} + (5-(-1))^{2} }[/tex]

[tex]D = \sqrt{(8)^{2} + (6)^{2} }[/tex]

[tex]D=\sqrt{(64+36)}[/tex]

[tex]D = \sqrt{100}[/tex]

[tex]D= 10 units[/tex]

Hence , the distance of the line is 10 units

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The rocket's maximum height is therefore 2704 feet, its maximum height is reached in 3 seconds, and the rocket reaches the ground at time t=16 seconds.

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

Given,

A rocket is fired upward from some initial distance above the ground. Its height (in feet), h, above the ground t seconds after it is fired is given by h ( t ) = − 16 t 2 + 80 t + 384

Following is our relationship between height and time:

h ( t ) = − 16 t 2 + 80 t + 384

The vertex of the equation above is as follows because it is a parabola equation.

In this case, a = -16, b = 96, and c = 2560.

The highest point at:

= -96/(2×(-16)

= 96/32

= 3 sec.

Maximum height at three seconds later:

h = -16 ×3² + 96 × 3 + 2560

h = 2704 feet

The rocket reaches the ground at y = 0, adding the following value to the parabolic equation:

0 = 16t² + 96t + 2560

Once we've solved it, we'll get:

t = 16 or

t = -10

Time cannot be negative, so we will choose t = 16 seconds.

The rocket's maximum height is therefore 2704 feet, its maximum height is reached in 3 seconds, and the rocket reaches the ground at time t=16 seconds.

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Answer: 5x³

Step-by-step explanation:

The solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. the region of overlap called the intersection.        

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

For the inequality, we have to apply the arithmetic operation in which we do the multiplication of x and apply the inequality for the given data.

Thus, the solutions to a system of linear inequalities are located in the region where all the shaded regions of the inequalities overlap. the region of overlap called the intersection.        

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The procedure to calculate the p-value from z-score depends on one of two choices: one-tailed (which may be Left-tailed or Right-tailed) or two-tailed tests.

A z-table, otherwise termed the standard normal table, provides the area under the curve to the left of a z-score.

The technique for using z-tables to find p-values depends on the test being carried out; which may be; one- or two-tailed test.

For one-tailed tests, the directionality is also a factor.

It therefore follows that;

For a Left-tailed z-test: the p-value = Φ(Zscore)

For a Right-tailed z-test: the p-value = 1 - Φ(z-score).

For a Two-tailed z-test: the p-value = 2 * Φ(−|z-score|).

The procedure described above represents how to calculate p-value from z-score.

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The following formulas can be used to determine the p-value from its corresponding z-score

From the question, the parameters are given as

Also, from the question, we understand that:

The p value depends on the z-score for its own value

There are three types of test for z-score; these test are:

The p-value would assume different value for a z-score when the type of test is different

This means that the p value for z = 0.2 at right tail test is different at a left tailed test.

This means that there are three formulas for calculating the p-value from the z-score, and these formulas are

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A 95​% confidence interval for the population proportion is ( 0.297, 0.335 ).

What is confidence interval?

A confidence interval (CI) for an unknown parameter in frequentist statistics is a range of estimations. The most popular confidence level is 95%, but other levels, such 90% or 99%, are occasionally used for computing confidence intervals. The fraction of related CIs over the long run that actually contain the parameter's true value is what is meant by the confidence level. The parameter's true value, for instance, should be present in 95% of all intervals computed at the 95% level.

Given that,

Point estimate = sample proportion = p' = x / n = 738 / 2336 = 0.316

 1 - p' = 1 - 0.316 = 0.684  

 Z(α/2) = Z(0.025)  = 1.96

A 95% confidence interval for population proportion p is ,

p' ±  E

= 0.316  ± 0.019

= ( 0.297, 0.335 )

With 95% confidence, it can be said that the population proportion of adults who believe in UFO's is between the endpoints of the given confidence interval  

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