8. Which ordered pair is a solution of the equation y = 2x + 5?

A (3, 11)

B (2, 7)

C (1, 6)

Answer:

C. Negative three-fourths

Step-by-step explanation:

Step-by-step explanation:

Given two fractions -1 1/4 and 1/2, the sum of the fractions is expressed as shown below:

-1 1/4 + 1/2

Converting the improper fraction -1 1/4 to mixed fraction will give -5/4. The expression will now become:

-5/4 + 1/2

Taking the LCM of the expression

= (-5+2)/4

= -3/4

Hence the sum of fraction Negative 1 and one-fourth and one-half is negative three-fourths

Final answer:

To add negative three-fourths and one-half, we first convert 1/2 to 2/4 to have the same denominator as -3/4. Adding the numerators gives us -1/4 as the sum, which can be visualized on the number line.

Explanation:

The student has asked how to find the sum of the fractions negative three-fourths (-3/4) and one-half (1/2) using a number line and equivalent fractions. To solve this problem intuitively, we can use our understanding of fractions as parts of a whole. First, we need to find a common denominator which is the least common multiple of 4 and 2, which is 4 in this case. So, we convert 1/2 to 2/4 since one half of one-half is one quarter, and then add it to -3/4.

Now, we have -3/4 + 2/4, which simplifies to -1/4 when we add the numerators, -3 and +2. This result can be visually confirmed on a number line. If we start at -3/4 on the number line and move 2/4 (which is half) to the right, we'll end up at -1/4, between -1 and 0.

Through this intuition and number line visualization, we have determined that -3/4 plus 1/2 equals -1/4. This highlights how our intuition about everyday things like parts of a pie or quarters in a dollar can help us with fraction operations like addition and finding common denominators.

Answer:

x=14.7

Step-by-step explanation:

use the law of sines

sinA = sinB= sinC

------ ------ ------

a b c

Answer:

[tex]4.53 \times 10^{- 1}[/tex]

Step-by-step explanation:

We have to divide [tex]1.6 \times 10^{- 10}[/tex] by [tex]3.53 \times 10^{- 10}[/tex] and we have to write the answer in scientific notation.

Now, [tex](1.6 \times 10^{- 10}) \div (3.53 \times 10^{- 10})[/tex]

= [tex](\frac{1.6}{10^{- 10}})\div (\frac{3.53}{10^{- 10}})[/tex] {Since using the property of exponent [tex]x^{- a} = \frac{1}{x^{a} }[/tex] }

= [tex](\frac{1.6}{10^{- 10}}) \times (\frac{10^{- 10}}{3.53} )[/tex]

{Since we know the mathematical operation [tex]\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}[/tex] }

= [tex]\frac{1.6}{3.53}[/tex]

= 0.45325

= [tex]4.53 \times 10^{- 1}[/tex] (Answer) {Rounded the coefficient to two decimal places}

Answer: 2y−8

Step-by-step explanation:

1) Simplify step-by-step.

−2y−8+4y

=−2y+−8+4y

2) Combine Like Terms:

=−2y+−8+4y

=(−2y+4y)+(−8)

=2y+−8

Answer:

both A and B

Step-by-step explanation:

The cost to rent the canoe for 7 hours is $ 104

Solution:

At eagle bay it cost $12 per hour to rent a Canoe

Nate and his friends rented a canoe for 4 hours and paid $68

Let "x" be the number of hours rented

We can solve use the point slope equation

[tex]y-y_1 = m(x-x_1)[/tex]

Where, "m" is the rate of change

[tex](x_1, y_1)[/tex] is the sample point

From given,

m = 12

[tex](x_1, y_1) = (4, 68)[/tex]

Therefore,

[tex]y - 68 = 12(x-4)[/tex]

[tex]y - 68 = 12x -48\\\\y = 12x -48+68\\\\y = 12x + 20[/tex]

Thus the linear equation is found

Here, "y" represents the amount paid for "x" hours

Find the cost to rent the canoe for 7 hours

Substitute x = 7 in linear equation

y = 12(7) + 20

y = 84 + 20

y = 104

Thus cost to rent the canoe for 7 hours is $ 104

To find the cost to rent the canoe for 7 hours, we can use the equation: Cost = Rate x Time. Given that the rate is $12 per hour and the time is 4 hours, the cost can be calculated as $68. Therefore, the cost to rent the canoe for 7 hours would be $119.

To find the cost to rent the canoe for 7 hours, we can use the equation:

Cost = Rate x Time

Given that the rate is $12 per hour and the time is 4 hours, we can substitute these values into the equation:

68 = 12 x 4

Solving for the rate, we get:

Rate = 68 ÷ 4

Therefore, the rate is $17 per hour. To find the cost to rent the canoe for 7 hours, we can multiply the rate by the time:

Cost = Rate x Time = 17 x 7 = $119

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The type of land form that Caleb most likely draws is a hill. The answer is option C- a hill.

Step-by-step explanation:

The correct answer is option C. He most likely drawing a hill.

Contour maps are used to represent the topography or elevation of an area using contour lines. Contour lines connect points of equal elevation above a reference level (usually sea level).

A hill is typically represented on a contour map by concentric closed contour lines, with higher elevations towards the center and lower elevations towards the periphery.

Answer:

Temperature in Maine = 20

Step-by-step explanation:

22-82 =

60

60/3 =

20

Answer:

Step-by-step explanation:

ok...so she leaves Orlando at 11:05 am.....the flight takes 5 hr and 17 minutes..

11:05 am + 5 hrs = 4:05 pm.....4:05 + 17 minutes = 4:22 pm.

so she arrives at 4:22 pm eastern time....(orlando time)...but Las Vegas is pacific time

so if 12 pm eastern = 9 am pacific.....a difference of 3 hrs

so the local time in Las Vegas when her plane lands is :

4:22 pm - 3 hrs = 1:22 pm <===

Answer:1:22 p.m.

Step-by-step explanation:

Answers:

a. The domain of f is ]-∞ , ∞[

b. The range of f is [-4 , ∞[

c. f(1) = 5

d. The vales of x for which f(x) is -3 are 7 and 9

e. The points at which the graph crosses the x-axis are (6,0) and (10,0)

f. The point where the graph of f crosses the y-axis is (0,5)

g. The values of x for which f(x) < 0 are ]6 , 10[

h. f(-7) is positive

Explanation:

Part a:

The domain of the function refers to all the possible x-values that can be used as an input for this function.

Taking a look at the graph, we can see that the graph extends endlessly from both ends of the x-axis. This means that all x-values can be used as a domain for the function. In other words, the domain of the function is all the real numbers.

In interval notation, this is written as:

Domain = ]-∞ , ∞[

Part b:

The range of the function refers to all the possible y-values that can be used as an output for the function.

From the graph, we can note that the function extends endlessly in the direction of the positive y-axis while it stops at a value of -4 in the direction of the negative y-axis.

This means that the range of the function starts from -4 (included) and extends to positive infinity.

In interval notation, this is written as:

R = [-4 , ∞[

Part c:

f(1) means that we are looking for the output (the value of y) for which the input (the value of x) is 1.

From the graph, we start by searching for x=1 (first square edge after the origin) and then move vertically till we intersect the graph.

Doing this, we will find that the value of y at x=1 is 5

Therefore:

f(1) = 5

Part d:

f(x) = -3 means that the output value (the value of the y) for the certain input (value of x) is -3

To get the value of x, we go y=-3 and move horizontally till we intersect the graph.

Doing this, we will find that the value of y is -3 at x = 7 and x = 9

Part e:

The points where the graph crosses the x-axis are the points that have y-value equal to 0

Checking the graph, we can note that the function crosses the x-axis at two points which are (6,0) and (10,0)

Part f:

The point where the graph crosses the y-axis is the point that has x-value equal to 0

Checking the graph, we can note that the function crosses the y-axis at only one point which is (0,5)

Part g:

f(x) < 0 means that the output of the function (the y-value) is less than 0 (0 is not included)

Taking a look at the graph, we can note that the function has negative output on the interval from 6 (excluded) to 10 (excluded)

In interval notation, this is written as ]6 , 10[

Part h:

f(-7) means the output of the function (the y-value) at input (x-vale) equal to -7

From the graph, we can note that the function has a constant value of 5 starting from x=5 till -∞

This means that, at x=-7, the value of y is 5 which is a positive value

Hope this helps :)

The solution to the inequality 2x<8 is x<4.

Step-by-step explanation:

Given inequality is;

2x < 8

For solving this inequality, we will divide both sides by 2 to find the value of x, therefore;

Dividing both sides by 2

[tex]\frac{2x}{2}<\frac{8}{2}\\x<4[/tex]

It means that x is less than four.

Thus,

The solution to the inequality 2x<8 is x<4.

Keywords: inequality, division

Learn more about division at:

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Answer:

11x+1+80=180

11x+81=180

11x=99

x=9

11(9)+1= 99+1=100°

Answer:

Step-by-step explanation:

5/y + 7/x =24.........(1)

12/y + 2/x =24........(2)

Let 1/y = a and 1/x = b

5a + 7b = 24 ...........(3)

12a + 2b = 24...........(4)

Multiply (3) by 2 and (4) by 7

10a + 14b = 48..........(5)

84a + 14b = 168.........(6)

Substracting (5) from (6)

84a - 10a = 168 - 48

74a = 120

a = 120/74

a = 60/37

Putting a = 60/37 in (3)

5a + 7b = 24

5(60/37) + 7b = 24

300/37 + 7b = 24

Multiply each term 37

300 + 259b = 888

259b = 888 - 300

259b = 588

b = 588/259

And a = 1/y

60/37 = 1/y

Cross multiply

60y = 37

y = 37/60

Also

b = 1/x

588/259 = 1/x

Cross multiply

588x = 259

x = 259/588

The ratio of the variables 'x' and 'y' will be 5/7.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The system of equations is given below.

5/y + 7/x =24

12/y + 2/x =24

Let 1/x = X and 1/y = Y. Then the equation is given as

5Y + 7X = 24            ...1

12Y + 2X = 24          ...2

From equations 1 and 2, then we have

12[(24 - 7X) / 5] + 2X = 24

288 - 84X + 10X = 120

74X = 168

X = 168 / 74

1/x = 168/74

x = 74/168

The value of the variable Y is given as,

12Y + 2(168 / 74) = 24

12Y = 720 / 37

Y = 60/37

1/y = 60/37

y = 37/60

The ratio of the variable 'x' and 'y' will be given as,

Ratio = x / y

Ratio = (74 / 168) / (37 / 60)

Ratio = (74 / 168) x (60 / 37)

Ratio = 5/7

The ratio of the variables 'x' and 'y' will be 5/7.

More about the solution of the equation link is given below.

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Maria needs to purchase three gallons of paint to cover her room walls with two coats, as calculations show she needs slightly more than two gallons.

To calculate how many gallons of paint Maria needs, first determine the total area of the walls. Each rectangular wall is 14 feet by 7 feet, with an area of 98 square feet, and each of the longer walls is 25 feet by 7 feet, with an area of 175 square feet. Thus, there are two of each, resulting in a total area of 2(98) + 2(175) = 546 square feet. Since Maria wants to apply two coats of paint, the total area to be painted doubles to 1,092 square feet. Given that one gallon covers 500 square feet, Maria needs 1,092 / 500 = 2.184 gallons. Therefore, Maria should purchase three gallons of paint to have enough for two coats, since paint is only sold by the gallon.

Answer: [tex]SA=189\ mm^2[/tex]

Step-by-step explanation:

You need to use the following formula for calculate the Surface area of a Right triangular prism:

[tex]SA=ph+2B[/tex]

Where "p" is the perimeter of the base, "h" is the height of the prism and "B" is the area of the base.

You can identify that the height is:

[tex]h=9\ mm[/tex]

The area of a triangle can be found with this formula:

[tex]A=\frac{bH}{2}[/tex]

Where "b" is the height of the triangle and "H" is its height.

Knowing this formula, you can find the area of the base of the prism. This is:

[tex]B=\frac{6\ mm*4.5\ mm}{2}\\\\B=13.5\ mm^2[/tex]

Since the perimeter of a figure is the sum of the lenghts of its sides, "p" is:

[tex]p=4.5\ mm+6\ mm+7.5\ mm=18\ mm[/tex]

Therefore, substituting values into the formula, you get:

[tex]SA=(18 mm)(9} mm)+2(13.5} mm^2)\\\\SA=189\ mm^2[/tex]

Answer:

z = 1.75

Step-by-step explanation:

2z + 3/8 = 3 7/8

2z = 3 7/8 - 3/8

2z = 3 4/8 or 2z = 3 1/2

z = 3 1/2 / 2 or 3.5 / 2

z = 1.75

2x + 5y = -15 is the standard form of equation

Solution:

Given that,

The point slope form of the equation of the line that passes through (-5, -1) and (10, -7) is given by:

[tex]y + 7 = \frac{-2}{5}(x-10)[/tex]

We have to write the standard form of the equation

The standard form of an equation is Ax + By = C

In this kind of equation, x and y are variables and A, B, and C are integers

Let us convert the given equation into standard form

[tex]y + 7 = \frac{-2}{5}(x-10)\\\\\text{Simplify the right hand side of equation }\\\\y + 7 = \frac{-2x}{5}+\frac{20}{5}\\\\y + 7 = \frac{-2x +20}{5}\\\\5(y+7) = -2x + 20\\\\\text{Simplify the left hand side of equation }\\\\5y + 35 = -2x + 20\\\\\text{Move the variables to left side of equation and constants to right side }\\\\2x + 5y = 20 - 35\\\\2x + 5y = -15[/tex]

Thus the standard form of equation is found

Answer:

B) 36 + 9 = 3(12 + 3)

Step-by-step explanation:

The distributive property of multiplication over addition is:

a(b + c) = ab + ac

This is demonstrated by switching the sides of option B) 36 + 9 = 3(12 + 3)

Answer:

B

Step-by-step explanation:

B  Because 12*3 = 36 and 3*3 =9

Answer:

16

Step-by-step explanation:

x² + 8x = 4 ⇔ x² + 8x + 16 = 4 + 16 ⇔ x² + 2×4x + 4² = 20 ⇔ (x + 4)² = (2√5)²

Remark : (2√5)² = 20

Answer:

A. O liters

Step-by-step explanation

.5 x 3L = 0 liters left

Answer:A

Step-by-step explanation:

3*2=6 6-6=0

Each multiplication problem was evaluated individually, revealing that two products are greater than 1 and one is less than 1.

When evaluating whether each product is less than 1, equal to 1, or greater than 1, it's important to consider the values being multiplied. Let's examine each multiplication problem provided:

2 x 1/3: Multiplying 2 by one-third gives us 2/3, which is less than 1.

5 x 1/3: Multiplying 5 by one-third gives us 5/3, which simplifies to 1 and 2/3, meaning it is greater than 1.

1/2 x 3: Multiplying one-half by 3 gives us 3/2, which simplifies to 1 and 1/2, so this is also greater than 1.

Answer:

The coordinate  to the given equations is (3,1)

Step-by-step explanation:

Given equation is [tex]2x+6y=12\hfill (1)[/tex]

and [tex]4x-3y=9\hfill (2)[/tex]

To find the coordinate of the given equations :

Multiply the equation (2) into 2 we get

[tex]8x-6y=18\hfill (3)[/tex]

Now adding the equations (1) and (3) we get

[tex]2x+6y=12[/tex]

[tex]8x-6y=18[/tex]

_______________

[tex]10x=30[/tex]

[tex]x=\frac{30}{10}[/tex]

Therefore x=3

Substitute x=3 in (1)

2(3)+6y=12

6y=12-6

[tex]y=\frac{6}{6}[/tex]

Therefore y=1

The coordinate  to the given equations is (3,1)

To find the coordinates of the intersection point of the equations 2x+6y=12 and 4x-3y=9, we can solve the system of equations using the method of substitution. The coordinates of the intersection point are (3, 1).

To find the coordinates of the intersection point of the equations 2x+6y=12 and 4x-3y=9, we can solve the system of equations by using the method of substitution or elimination. Let's use the method of substitution:

The coordinates of the intersection point are (3, 1).

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Answer:

G

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The given number is 1.15. Here, the digits after the decimal are terminating, so the given number is rational, NOT irrational. Thus, 1.15 is NOT an irrational number.

Answer:

Step-by-step explanation:

#1 the answer is 32lb

first you want to make an equation. My equation looks like this

x+4x=40

the x is the weight of the cat.

then solve for x  = 8

8*4 = 32

#2 the answer is 3:20 PM

Since it took 15 min to get home, we take 15 min away from 4:25 leaving us with 4:10

then we take away the length of practice 30min

4:10 - 30 min = 3:40

then we take away the 20 min of break time before the practice.

3:40 - 20 min = 3:20

Answer:

1.) the dog is 10

2.) 3:55

Step-by-step explanation:

1.)its just u dived by 4

2.) 15 + 20=35 35-4:25=3:55

Step-by-step explanation:

X=ky

2=8k

K=4

X=4y

6=4y

Y=1. 5

Answer:

Step-by-step explanation:

y varies directly as x

y ∞ x

y = kx

and y=8 when x=2

8 = 2(k)

8 = 2k

k = 8/2

k = 4

y = 4x

find y when x=6

y = 4(6)

y = 24

Answer:

The length of the side of an equilateral traingle [tex]s=2\sqrt{2}[/tex] inches

Step-by-step explanation:

Given that the area of an equilateral triangle is given by

[tex]A=3^\frac{1}{2}s^2[/tex]

It can be written as

[tex]a=\frac{\sqrt{3}}{4} s^2[/tex] Square inches        (1)

To find the length of the side s os an equilateral triangle

Given that area of an equilateral triangle is [tex]12^\frac{1}{2}[/tex] square inches

It can be written as

[tex]A=12^\frac{1}{2}[/tex]

[tex]A=\sqrt{12}[/tex] square inches

It can be written as

[tex]A=12^\frac{1}{2}[/tex]

[tex]A=\sqrt{12}[/tex] square inches           (2)

Now comparing equations (1) and (2) we get

[tex]\frac{\sqrt{3}}{4}s^2=\sqrt{12}[/tex]

[tex]\frac{\sqrt{3}}{4}s^2=\sqrt{4\times 3}[/tex]

Dividing by [tex]\frac{\sqrt{3}}{4}[/tex] on both sides we get

[tex]\frac{\frac{\sqrt{3}}{4}s^2}{\frac{\sqrt{3}}{4}}=\frac{2\sqrt{3}}{\frac{\sqrt{3}}{4}}[/tex]

[tex]\frac{\sqrt{3}}{4}s^2\times\frac{4}{\sqrt{3}}=2\sqrt{3}\times\frac{4}{\sqrt{3}}[/tex]

[tex]s^2=8[/tex]

[tex]s=\sqrt{8}[/tex]

Therefore [tex]s=2\sqrt{2}[/tex] inches

Therefore the length of the side of an equilateral traingle [tex]s=2\sqrt{2}[/tex] inches

Answer:

C(F) = 5/9 F-160/9

Step-by-step explanation:

Answer:

C(F) =  

5/9

F −  

-16/9

⇒ 160/9

Step-by-step explanation:

Your Welcome :D

Answer:

y= 2(2x-1) -4

Step-by-step explanation:

you subtract 4 from both sides and it cancel outs at the y side(because 4-4 is 0) leaving just y.