Given that y varies directly as x, write an equation
for the relationship if y=-4 when x=10.
A) y=-4x+10
B) y=-0.4x
C) y=0.4x
D) y=-2.5x

Jason can check his answer isolate the variable, solving the operations and substituting the (x) value in the equation.

The clearance rules to solve the problem are the following:

The sign rules to solve the problem are the following:

Solving the equation we have:

-8. 5x – 3. 5x = –78

Two like signs add the values and keep the common sign.

-12x = -78

What is multiplying goes to the other side of the equality by dividing.

x = -78 / -12

x = 6.5

Substituting the (x) value in the equation we can check the answer and we get:

-8. 5x – 3. 5x = –78

-8.5(6.5) - 3.5(6.5) = -78

-55.25 - 22.75 = -78

- 78 = - 78

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer: The slope is 0

Step-by-step explanation:

Use the slope formula. -5-(-2)/-3-(-3)

-5+2/-3+3=0

The number of possible pair that could be chosen for duet is  1540 .

In the question ,

it is given that ,

total number of females in the choir group = 56 women

for duet the number of females that are required = 2 ,

the number of possible pair that can be chosen for the duet = ⁵⁶C₂ ,

⁵⁶C₂ = (56 × 55 × 54!)/2! × (56 - 2)!

= (56 × 55 × 54!)/2! × 54!

cancelling out the common factor 54! , we get

= (56 × 55)/2          .... because 2!= 2

= 28 × 55

= 1540

Therefore , The number of possible pair that could be chosen for duet is  1540 .

The given question is incomplete , the complete question is

56 women makes up an all female choir in a church. Two women are chosen to sing together for a duet. How many possible pair could be chosen for the duet ?

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Answer:

the answer is-7

Step-by-step explanation:

Answer:

Exact form: -31/4

Decimal form: -7.75

Mixed number form: -7 3/4

The average speed for the whole journey is 95.3km/hour

The average speed is the total distance traveled by the object in a particular time interval. The average speed is a scalar quantity. It is represented by the magnitude and does not have direction.

Average speed = Total distance/total time taken

The distance covered in the first journey is 75km and the time spent is calculated as Distance/speed

= 75/110 = 0.68hour

The time used for the second journey is

= distance/speed

= 7/40 = 0.18 hour

The total time spent = 0.68+0.18 = 0.86 hour

The total distance traveled = 75+7 = 82km

Therefore the average speed = 82/0.86 = 95.3 km/hour.

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The division of 5.375 divided by 0.25 results to 21.5

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components. How many groups will be created,

for instance, if 30 students need to be separated into groups of five for a sporting event?

In this case, we must divide 30 by 5. 30 x 5 = 6 will be the outcome.

Given:

5.375 divided by 0.25

Now, dividing the above decimal

= 5.375/ 0.25

= 5375 x 100 / 25 x 1000

= 215 / 10

= 21.5

Hence, the division results to 21.5

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Answer: Answer is below

Step-by-step explanation:

Angles 1 and 5 and 8 are the same.

Angles 2 and 3 and 6 and 7 are the same.

180-138=42 degrees

So the obtuse are 138 and the acute are 42.

Angle 1 is 138 degrees

Angle 2 is 42 degrees

Angle 3 is 42 degrees

Angle 5 is 138 degrees

Angle 7 is 42 degrees

Angle 8 is 138 degrees

Angle 6 is 42 degrees

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Answer:

Angle 4 is 138 and opposite angles are the same! That makes angle 1, 5, and 8 the same as 4 which is 138!

We need to subtract to find the other 4 angles!

180 - 138 = 42 degrees

Angles 2, 3, 6 and 7 will be 42 degrees!

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Answer:

Step-by-step explanation:

or

Answer:

[tex]\left(\dfrac{12}{5}\right)^2=\left(2\frac{2}{5}\right)^2[/tex]

Step-by-step explanation:

Given mixed number:

[tex]5 \frac{19}{25}[/tex]

Rewrite the given mixed number as an improper fraction:

[tex]\implies 5 \frac{19}{25}=\dfrac{5 \times 25+19}{25}=\dfrac{125+19}{25}=\dfrac{144}{25}[/tex]

Rewrite 144 as 12² and 25 as 5²:

[tex]\implies \dfrac{144}{25}=\dfrac{12^2}{5^2}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^c}{b^c}=\left(\dfrac{a}{b}\right)^c:[/tex]

[tex]\implies \dfrac{12^2}{5^2}=\left(\dfrac{12}{5}\right)^2[/tex]

Convert 12/5 to a mixed number:

[tex]\implies \left(\dfrac{12}{5}\right)^2=\left(\dfrac{10+2}{5}\right)^2=\left(\dfrac{10}{5}+\dfrac{2}{5}\right)^2=\left(2\frac{2}{5}\right)^2[/tex]

Step-by-step explanation:

between the student and the flagpole we create a trapezoid with the line of sight to the top of the flagpole and the ground connection between the student's feet and the flagpole being the other 2 sides.

and between the flagpole and the building we create a similar trapezoid.

the line of sight to the top of the building and the ground connection between the flagpole and the building are the other 2 sides.

since both shapes are created from the same projection (the "projector" is somewhere behind the student on the ground), they are truly and mathematically similar.

that means that the angles of one trapezoid are the same as in the other trapezoid.

and - there must be one constant scale factor between all the sides (or for any other lengths in or on the trapezoids) of one trapezoid to the sides of the other trapezoid.

we know the ground distances and how they relate :

20 ft to 60 ft

that means 20/60 = 1/3

so, any length of the first (smaller) trapezoid is 1/3 of the corresponding length of the second (larger) trapezoid.

so, we know the height of the flagpole (35 ft).

the height of the building must follow the same ratio (scaling factor) as the ground distances.

flagpole height = building height × 1/3

3× flagpole height = building height = 3×35 = 105 ft

the building is 105 ft tall.

The expression below using the MathQuill function is 2x^3+42^3-\sqrt\left(49\right).

Given expression:

= 2x³+42³-√49

Expression:

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

After using MathQuill function:

2x³+42³-√49 = 2x^3+42^3-\sqrt\left(49\right).

Therefore The expression below using the MathQuill function is 2x^3+42^3-\sqrt\left(49\right).

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Answer:

B. $1.52 for 8 oz

Step-by-step explanation:

$1.26/6=$0.21

$1.52/8=$0.19

$2.30/10=$0.23

$2.40/12=$0.2

$0.19<$0.2<$0.21<$0.23

" I hoped I helped you : - ) "

Answer:

The answer to your questions is 96.

Required correct statement is n+ 8 could be positive or negative or zero.

What is a negative number?

A negative number is any number less than zero. For example, -8 is a number that is seven less than 0. It may seem odd to say that a number is less than 0. After all, we often think that zero means nothing.

Option A: n + 8 is always positive is not correct since n is negative and adding a positive number (8) to a negative number will give a negative or zero result.

Option B: n + 8 is always negative is not correct since adding a positive number (8) to a negative number will give a negative or zero result, not always negative.

Option C: n + 8 cannot be zero is a wrong statement, if we put value of n = -8 then we will get zero as answer.

Option D: n + 8 could be positive or negative or zero is correct since it depends on the value of n.

If n is a large negative number, n + 8 could still be negative. If n is a small negative number or zero, n + 8 could be positive or zero.

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Correct question is "n is a negative number.

Which statement is correct?

Choose only one answer.

A) n +8 is always positive

B) n +8 is always negative

C) n + 8 cannot be zero

D) n+ 8 could be positive or negative or zero"

The equation in vertex form would be y = [tex]2(x+5)^{2}[/tex] -6

The vertex of a parabola is the point where the parabola crosses its axis of symmetry.  If the coefficient of the x2 term is positive, the vertex will be the lowest point on the graph, the point at the bottom of the “ U ”-shape.  If the coefficient of the x2 term is negative, the vertex will be the highest point on the graph, the point at the top of the “ U ”-shape.

The standard equation of a parabola is

y=a[tex]x^{2}[/tex]+bx+c .

But the equation for a parabola can also be written in "vertex form":

y= a(x-h)² +k

if the curve passes through (-3, 2) and the coordinates of vertex h = -5, K= -6, then we can find a by simple substitution

2 = a[tex](-3 + 5)^{2}[/tex] - 6

2 = a([tex]2^{2}[/tex]) - 6

2 = 4a - 6

collecting like terms

4a = 2 + 6

4a = 8

dividing both sides by 4

a = 8/4

a = 2.

So the equation of parabola in vertex form is y = 2[tex](x+5)^{2}[/tex] - 6

In conclusion, the equation of parabola in vertex form is 2[tex](x+5)^{2}[/tex] - 6

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The value of 20,304 using exponents will be 2.0304 × 10⁴.

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.

For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

In this case, the value of 20,304 will be:

= 2.0304 × 10000

= 2.0304 × 10⁴.

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Answer: n = 31.66666667

Step-by-step explanation:

Add '-12n' to each side of the equation.

500 + -12n = 120 + 12n + -12n

Combine like terms: 12n + -12n = 0

500 + -12n = 120 + 0

500 + -12n = 120

Add '-500' to each side of the equation.

500 + -500 + -12n = 120 + -500

Combine like terms: 500 + -500 = 0

0 + -12n = 120 + -500

-12n = 120 + -500

Combine like terms: 120 + -500 = -380

-12n = -380

Divide each side by '-12'.

n = 31.66666667

Simplifying

n = 31.66666667

Answer:

d) [tex]4x+23=10x-1[/tex]

Step-by-step explanation:

This is an isosceles triangle, which is defined as having two equal sides, and two equal angles corresponding to those sides.

Given this definition, it can be said that [tex]4x+23[/tex] is equal to [tex]10x-1[/tex]. Therefore,

[tex]4x+23=10x-1[/tex]

The probable percentage of complete and usable observation is 18.87%

Probable percentage is probability of a certain event which can be written as percentage

Total number of variables in data set = 20 variables

percentage of randomly spread missing observation in data set = 8%

percentage of non missing observation in data set = 100% - 8%

= 92%

changing percentage into number = 92 / 100

= 0.92

Probable percentage of complete and usable observation =

(0.92)²⁰ × 100

solving the power

0.18869 × 100

= 18.87

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Answer:

Step-by-step explanation: the distance is 6 but if you're talking decimal then the distance is 1.4142

The distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is [tex]3\sqrt{13}[/tex].

First, let us understand the distance formula:

The distance formula is the measurement of the distance between 2 points. It calculates the straight line distance between the given points.

The distance formula is given by:

Distance = [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]

Where A(a, b) and B(c, d) are the coordinates.

We are given;

The park entrance is located at (-3, 7).

Another point at (3, -2).

We need to find the distance from the entrance to the garden at another given point.

Substitute the given values in the distance formula, we will get;

Distance = [tex]\sqrt{(a-c)^2+(b-d)^2}[/tex]

Distance = [tex]\sqrt{(-3-3)^2+(7-(-2))^2}[/tex]

Distance = [tex]\sqrt{(6)^2+(9)^2}[/tex]

Distance = [tex]\sqrt{36+81}[/tex]

Distance = [tex]\sqrt{117}[/tex]

Distance = [tex]3\sqrt{13}[/tex]

So, the distance between the given points is [tex]3\sqrt{13}[/tex].

Thus, the distance from the entrance which is located at (-3,7) to the garden at points (3,-2) is [tex]3\sqrt{13}[/tex].

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Answer:

6.481.

Square Root of 42 in Decimal Form: 6.481.

Answer:the last option

Step-by-step explanation:

The inequality that represents the number of songs and albums that Jorge could download is:

$2*s + $12*a ≤ $50

Here we have the variables:

s = number of songs.

a = number of albums.

Then the total cost can be written as:

$2*s + $12*a

And we know that Jorge has a maximum of $50 to spend, so the total cost can be equal to or smaller than $50, so the inequality is:

$2*s + $12*a ≤ $50

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The solution for y and x in the expressions given as 2/5(10y-5) =2y + -10 and x − 3.28 = −5.34 are y = 6 and x = -2.06, respectively

Variable y

From the question, the algebraic expression is given as

2/5(10y-5) =2y + -10

Open the brackets

This gives

4y - 2 = 2y + -10

Collect the like terms in the above equation

So, we have the following representation

4y - 2y = 10 + 2

Evaluate the like terms

2y = 12

Divide by 2

y = 6

Variable x

Here, we have

x − 3.28 = −5.34

There is a constant to add to or subtract from the expression

So, we add 3.28 to both sides

x = 3.28 − 5.34

Evaluate the like terms

x = -2.06

Hence, the solution is x = -2.06

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Answer:

5

Step-by-step explanation:

Answer:

The answer for the question is five!

The evaluation of the inverse of the function, f(x) = -0.086·x + 2.92 are;

a. The inverse of the function is f⁻¹(x)  = -11.63·x + 33.95

B. The inverse function gives the number of year after 2000 when the percentage of children taking antidepressants is equal to x

b. The percentage of children taking antidepressant is 2.3% in 2007

The inverse of a function is a function that gives the input from the output such that it undoes the function's effect.

The function that indicates the percentage of children taking that take antidepressants from from the year 2004 to the year 2009 is presented as follows;

f(x) = -0.086·x + 2.92

x = The number of years after the year 2000

The inverse of the function can be obtained by making x the subject of the function formula as follows;

f(x) = -0.086·x + 2.92

f(x) - 2.92 = -0.086·x

x = (f(x) - 2.92)/(-0.086) ≈ -11.63·f(x) + 33.95

x  ≈ -11.63·f(x) + 33.95

Which through plugging in f⁻¹(x) = x, and f(x) = x,

Indicates;

f⁻¹(x) = -11.63·x + 33.95

In the inverse function, the argument is the percentage, while the output is the number of years, f⁻¹(x)

When x = 2.3,

f⁻¹(2.3) = -11.63×2.3 + 33.95 ≈ 7.2

The inverse when the percentage is 2.3% is 7.2 years

a. The inverse function is f⁻¹(x) = -11.63·x + 33.95

The output of the inverse function represents the number of years since 2000 when the percentage of the children taking antidepressants is x. The correct option is option B

b. The year in which the number of children taking antidepressant equals 2.3% is 2,000 + 7 = 2007

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The 95% confidence interval for the mean weight per apple is calculated and the p value foe that particular interval is 0.1447

There is not sufficient evidence to reject the company's claim.

Z Test of Hypothesis for the Mean

Data

Null Hypothesis m =120

Level of Significance 0.05

Population Standard Deviation 12

Sample Size 49

Sample Mean 122.5

Intermediate Calculations

Standard Error of the Mean 1.7143

Z Test Statistic 1.4583

Two-Tail Test  

Lower Critical Value -1.9600

Upper Critical Value 1.9600

p-Value 0.1447

Do not reject the null hypothesis

Hence, the p value foe that particular interval is 0.1447

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Answer:

1/2 teaspoon of salt per 1 teaspoon of baking soda.

Step-by-step explanation:

If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.

:)