5) Can you give some real world examples (at least two for each) of positive and negative slope?

Step-by-step explanation:

70.31

hope it's helpful

Answer:

Step-by-step explanation:

no

The given formula can be written as 5F = 9C + 160.

A measurement unit is a unit to measure certain quantities. To find the measurement of a new quantity knows units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

Given that,

The conversion formula for °C into °F is 9C  = 5(F - 32)

The given formula can be written in the form of cF = aC + b as,

9C = 5(F - 32)

⇒ 5F = 9C + 160

Hence, the given formula can be written by making F as the subject as 5F = 9C + 160.

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Answer:

d+12/3

Step-by-step explanation:

*= multiply /= fraction ALL OVER= fraction over fraction

find the common denominator-

d/3+4

d/3+3*4/3

combine fractions with the common denominator

d/3+3*4/3 ALL OVER d+3*4/3

multiply

d+3*4/3 ALL OVER d+12/3

The domain of the given function is -∞ < x < ∞.

So, the function is:

Now, the domain of the given function is:

The domain will therefore be -∞ < x < ∞.

Therefore, the domain of the given function is -∞ < x < ∞.

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Answer: 15 !

Step-by-step explanation:

Change the division sign to a multiplication sign and reverse the fraction.

5 x 3/1 = 15

Answer:

[tex]g(x) + h(x) = x^3 + 6x + 5[/tex]

Step-by-step explanation:

We are told that:

[tex]g(x) = x^3 + 5x[/tex]

[tex]h(x) = x + 5[/tex],

and we are asked to find an expression for [tex]g(x) + h(x)[/tex].

In order to find the expression for  [tex]g(x) + h(x)[/tex], we have to simply add the expressions of [tex]g(x)[/tex] and [tex]h(x)[/tex] together:

[tex]g(x) + h(x)[/tex]

= [tex]x^3 + 5x + x + 5[/tex]

= [tex]x^3 + 6x + 5[/tex]

The sentence which represents the equation [tex]8\frac{3}{4} = 17-x[/tex] is  First Option (i.e.  [tex]8\frac{3}{4}[/tex] is the same as the 17 decreased by a number).

What is a number sentence?

A mathematical statement made up of numbers and symbols is called a number sentence. The sentences illustrate many mathematical operations, including addition, subtraction, multiplication, and division.

Given, [tex]8\frac{3}{4} = 17-x[/tex]

where, [tex]x[/tex] is a number and ([tex]17-x[/tex]) represents [tex]17[/tex] is decreased by a number [tex]x[/tex]

And, [tex]8\frac{3}{4}[/tex]  will be equal to the [tex]17[/tex] is decreased by a number [tex]x[/tex].

Therefore, the required answer choice will be the first option i.e. [tex]8\frac{3}{4}[/tex] is the same as [tex]17[/tex] decreased by a number.

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The amounts are given as follows, using proportions:

i) Amount spent on entertainment: $240.

c) Monthly salary: $840.

A proportion is a fraction of an amount, and this fraction is combined with the unit rates in the context of a problem along with basic arithmetic operations such as multiplication or division to find the desired amounts.

The ratio of food : travelling : entertainment = 4 : 2 : 3 means that:

The amount spent on food $160 more than travelling, the total amount is obtained as follows:

(4/9 - 2/9)x = 160

2/9x = 160

2x = 160 x 9

x = 80 x 9

x = 720.

Then the amount invested in entertainment was of:

3/9 x 720 = 1/3 x 720 = $240.

He invests 6/7 of his monthly salary, as 1/7 is deposited, hence:

6x/7 = 720

6x = 720 x 7

x = 120 x 7 (simplifying both sides of the equality by 6)

x = $840.

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Answer:

-6

Step-by-step explanation:

The value of [tex]b[/tex] is the same as the value of [tex]y[/tex] when [tex]x=0[/tex].

The coordinates of the point that is one-half the distance between A(-1,-2) and B(6,12) is (2.5,5)

What is the midpoint?

The mid-point lies midway between the two ends. Its x value lies in the middle of the other two x values. Its y value lies in the middle of the other two y values.

Given, [tex]A(6,12) = (x_{1}, y_{1} )[/tex]

           [tex]B(6,12) = (x_{2}, y_{2} )[/tex]

Let M is a midpoint of AB, then

[tex]M(x,y)=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1} +y_{2}}{2} )= (\frac{-1+6}{2} ,\frac{-2+12}{2} )=(2.5,5)[/tex]

The midpoint of point AB is M(2.5,5)

Therefore, the coordinates of the point which is one-half the distance between A(-1,-2) and B(6,12) is M(2.5,5).

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A midwife delivers 10 babies, with 50% chance of delivering a boy and 50% of delivering a girl. The probability that 6 out of 10 babies will be boys is 20.5%

The problem can be solved using binomial distribution, that is the probability of 2 possible outcomes in a number of trials.

The formula is given by:

P(x) = ⁿCx . P^x . (1 - P)^(n-x)

x = total number of event A

n = number of trials

P = probability of A in a single trial

Parameters given in the problem:

n = 10

x = 6

P = 50% = 0.5

Plug these parameters into the formula:

P(6 boys) = ¹⁰C₆ . (0.5)⁶ .  (0.5)⁴

                = 0.205 = 20.5%

Hence, the probability that 6 out of 10 babies will be boys is 20.5%

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Answer:

-4/5

Step-by-step explanation:

do -3/2to get your answer

Step-by-step explanation:

You find the image of triangle by translation

The solution of x when solving x/2 + 1 = √3 is :

x is 2√3 - 2 .

Here in the question given equation ,

x/2 + 1 = √3

To find solution,

we have to subtract 1 from LHS and RHS of equation,

⇒ x/2 + 1 - 1 = √3 - 1

⇒ x/2 = √3 - 1

Next multiply both sides  by 2

2( x/2) = 2(√3 -1)

By simplifying both sides we get,

x = 2√3 - 2

So the value of x = 2√3 -2.

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Answer: 0.04536

Step-by-step explanation:

Answer:

0.2c-c

Step-by-step explanation:

The solution of the linear equation:

(2x + 6)/5 = 4x - 3

is x = 7/6

Here we have the following equation:

(2x + 6)/5 = 4x - 3

To solve this, we need to isolate x in one of the sides of the equation, we can start by multiplying both sides by 5.

2x + 6 = 5*(4x - 3)

Expanding the right side we get:

2x + 6 = 20x - 15

Now you can see that this is a simple linear equation, now we need to group like terms:

6 + 15 = 20x - 2x

21 = 18x

Now we can divide both sides by 18 to get:

21/18 = x

Finally, if we divide both numerator and denominator of the fraction by 3, we get:

21/3 = 7

18/3 = 6

Then 21/18 = 7/6

Finally, we conclude that the solution is:

x = 7/6

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Answer:

y = - 2x + 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 11) and (x₂, y₂ ) = (6, - 11) ← 2 points on the line

m = [tex]\frac{-11-11}{6-(-5)}[/tex] = [tex]\frac{-22}{6+5}[/tex] = [tex]\frac{-22}{11}[/tex] = - 2

the line crosses the y- axis at (0, 1 ) ⇒ c = 1

y = - 2x + 1 ← equation of line

Answer: 31%

Step-by-step explanation:

Out of the students that receive financial aid, 1879 out of the 6101 total students are graduates.

So, the probability is [tex]\frac{1879}{6101} \approx 31\%[/tex]

Since Point G is the centroid of right triangle ABC with hypotenuse AB=18in. Then  CG is 6 in.

The area of the square whose side is the hypotenuse (the side across from the right angle) in any right triangle equals the sum of the areas of the squares whose sides are the two legs, according to the Pythagorean theorem.

Note that from the question, A triangle's centroid, G, is located 2/3 of the way down one of its medians. We tend must determine the median C's length in order to find CG.

We require the use of Thale's Theorem to get the median length at C. According to this, a right triangle ABC can be encircled by a semicircle with the hypotenuse acting as the diameter.

Therefore, the median C is a point on the semicircle that connects to the diameter of the hypotenuse AB. Since it is connected to the center, median C is a radius. Half of its length, or 18/2, or 9 inches, makes it.

So:

CG is 2/3 down the median, which is:

9 x 2/3 = 6 inches.

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According to the vertical angles theorem, m∠1 = 117°.

Based on the corresponding angles theorem, m∠2 = 117°.

The set of angle pairs formed that are directly opposite each other when two straight lines intersect or when two parallel lines are crossed by a transversal are said to be vertical angles, and therefore congruent to each other based on the vertical angles theorem.

When two lines are intersected by a transversal, the angles that are on the same transversal and lie in relative position or corner in the two parallel lines are said to be corresponding angles which are congruent based on the corresponding angles theorem.

Using the information given in the diagram attached below, angles 1 and 117° are vertical angles.

Therefore:

m∠1 = 117° [vertical angles theorem]

Angles 1 and 2 are corresponding angles. Therefore:

m∠2 = m∠1

Substitute

m∠2 = 117° [corresponding angles theorem]

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The values satisfies the linear equation y = −47x−2 is (0, -2).

For the given question.

The linear equation is given as;

y = −47x −2

Check the result by putting the values from option.

For : −7 −6

Put x = -7

y = −47(-7) −2

y = 799 -2

y = 498 (incorrect)

For: 0 −2

Put x = 0

y = −47x −2

y = −47(0) −2

y = -2 (correct)

Thus, the values satisfies the linear equation y = −47x−2 is (0, -2).

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Answer:

1 = 88

2 = 92

3 = 88

4 = 92

5 = 92

6 = 88

7 = 92

8 = 88

Step-by-step explanation:

10x + 2 = 14x - 50

52 = 4x

18 = x

Answer:

       7 [tex]\frac{7}{8}[/tex]

Step-by-step explanation:

Multiply 3 1/2 by 2 1/4

Convert to improper fraction to make it simpler:

7/2 times 9/4 = 7 7/8 square millimeters.

Hope this helps :)

Answer:

Step-by-step explanation:

3.5 x 2.25 = 7.875 or 7 and 7/8

Answer: Hence the answer is 27 square feet.

Please look at the images for more details.

Answer:

27 square feet

Step-by-step explanation:

Define the variables:

To increase a number by a certain percent, divide the percent by 100, add it to 1, then multiply the original number by this number.

If the length of the new flag is 20% greater than the length of the old flag:

[tex]\implies \textsf{Length}=\left(1+\dfrac{20}{100}\right) \timesl \times l=1.2l[/tex]

To decrease a number by a certain percent, divide the percent by 100, subtract it from 1, then multiply the original number by this number.

If the width of the new flag is 10% less than the width of the old flag:

[tex]\implies \textsf{Width}=\left(1-\dfrac{10}{100}\right) \times w =0.9w[/tex]

[tex]\boxed{\textsf{Area of a rectangle}=\sf width \times length}[/tex]

Therefore, given the area of the old flag is 25 ft²:

[tex]\implies wl=25[/tex]

To find the area of the new flag, substitute the expressions for width, length and wl into the formula for area of a rectangle:

[tex]\begin{aligned}\textsf{Area of new flag}&=\sf width \times length\\&=0.9w \times 1.2l\\&=0.9 \times 1.2 \times wl\\&=1.08 \times 25\\&=27\sf \;\; ft^2\end{aligned}[/tex]

Therefore, the area of the new flag is 27 square feet.

The value needs to be added to x²+10x+6 to complete the square is 19.

Perfect square trinomials come in the form a² + 2ab + b², which is equal to (a + b)².

In the presented trinomial, we can immediately find that a = x, and b² = c,

We know that a = x, and , 2ab = 2bx.

Now, 2bx and 30x are corresponding terms, 2bx = 30x.

Take the coefficient of x = 10

Divide by 2

10/2 =5

Then Square it

5 x 5=25

Add this to make a perfect square trinomial;

x² + 10x + 25

In the given equation we need to add 19 to make the perfect square trinomial; x² + 10x + 25.

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The principal square root of √64 is 8, √100 is 10,√169 is 13, √196 is 14 and √256 is 16.

According to the question,

We have the following information:

1. √64

2. √100

3. √169

4. √196

5. √256

Now, in order to find the principal square root of these numbers, we will express these numbers in the form of the product of numbers then we will find the square root.

1) [tex]\sqrt{64}[/tex]

We have the following expression:

[tex]\sqrt{2*2*2*2*2*2}[/tex]

2*2*2

8

2) [tex]\sqrt{100}[/tex]

[tex]\sqrt{2*2*5*5}[/tex]

2*5

10

3) [tex]\sqrt{169}[/tex]

[tex]\sqrt{13*13}[/tex]

13

4) [tex]\sqrt{196}[/tex]

[tex]\sqrt{2*2*7*7}[/tex]

2*7

14

5) [tex]\sqrt{256}[/tex]

[tex]\sqrt{2*2*8*8}[/tex]

2*8

16

Hence, the principal square root of √64 is 8, √100 is 10,√169 is 13, √196 is 14 and √256 is 16.

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Answer:

use absolute value

Step-by-step explanation:

absolute of x +5