.
Writing the Equation of
a
What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (-5, 1)? Check all
that apply.
y=-2x-1
2x + 5y = -5
y=-2x-3
2x + 5y = -15
1= -2.(x + 5)

Answer: x = 5

Step-by-step explanation:

multiply the outside number to both numbers in parenthesis

3x-15  divide

find out how many time 3 goes into 15 and divide  

three divided by fifteen equals five

Final answer:

The equivalent expression to 3(x-5) is 3x - 15, which is found by applying the distributive property of multiplication over subtraction.

Explanation:

The question asks for an expression equivalent to 3(x-5). To find an equivalent expression, we need to apply the distributive property of multiplication over subtraction. This means we will multiply the number 3 by each term inside the parentheses.

Here's the step-by-step process:

Multiply 3 by x to get 3x.

Multiply 3 by -5 to get -15.

Combine these two products to get the equivalent expression, which is 3x - 15.

Therefore, the equivalent expression to 3(x-5) is 3x - 15.

Answer: a = 22

Step-by-step explanation: First isolate a/3 by adding 7 to both sides of the equation. That gives you a/3 = 22.

From here since a is being divided by 3, multiply both sides of the equation by 3 so a = 66. We can check our answer by substituting a 66 back in for a in the original equation and we have [tex]\frac{66}{3} - 7 =15[/tex] or 22 - 7 = 15 or 15 = 15. Since this is a true statement, our answer checks.

Answer:

The greatest possible number of boxes that is needed to pack the items with no leftovers is 24.

Step-by-step explanation:

Given:

Number of rice bags = 72

Number of blankets =48

Number of water cases = 24

To Find :

The greatest possible number of boxes that the items can be packed into so that there are no leftover = ?

Solution:

we can find the greatest possible number of boxes that is required by finding the HCF(Highest common factor) of(24,48,72)

Finding the HCF (Highest common factor):

The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24

The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The factors of 72 are: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

24 is the greatest common factor

Hence 24 will the number boxes required

Answer:

y = -x -5

Step-by-step explanation:

The -x (i.e., multiplication of x by -1) gives the line a slope of -1. The -5 translates the line down to cross the y-axis at -5.

The required simplified expression for 0.2(5x – 0.3) – 0.5(–1.1x + 4.2) is 1.55x - 2.16.

What is simplification ?

Simplification means reducing the expression in a simpler form using various operations. It eliminates unnecessary diversiry and variety.

The given expression is

0.2(5x – 0.3) – 0.5(–1.1x + 4.2)

or, 0.2 [5x + (–0.3)] + (–0.5)(–1.1x + 4.2) x – 2.16

Now,Let us expand the bracket-

0.2*5x - 0.2*0.3 - 0.5(-1.1x) - 0.5*4.2

Further,

x - 0.06 + 0.55x - 2.1

therefore,

x + 0.55x - 0.06 - 2.1

⇒ 1.55x - 2.16

Hence,the required simplified expression for 0.2(5x – 0.3) – 0.5(–1.1x + 4.2) is 1.55x - 2.16.

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Answer:

1.55 is the answer on edge

Answer:

width: 7 cm

length: 56 cm

Step-by-step explanation:

Let:

x=width

8x=length

P=2l+2w

126=2x + 2(8x)

126=2x+16x

18x=126

x=7

width: 7 cm

length: 56 cm

hope this helps!!

Answer:

see the explanation

The solution's table in the attached figure

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]

Let

y ----> the price

x ----> the weight

Find the value of the proportionality constant for each ordered pair in each table

[tex]k=\frac{y}{x}[/tex]

If all the values of k are equal, then the table represents a proportional relationship between the variable x and the variable y

Table 1

For x=1.5 lb, y=$4.50 ---->  [tex]k=\frac{4.5}{1.50}=3[/tex]

For x=2 lb, y=$9.00 ---->  [tex]k=\frac{9.00}{2}=4.5[/tex]

The values of k are different

therefore

The table not represent a proportional relationship

Table 2

For x=10 g, y=$0.50 ---->  [tex]k=\frac{0.50}{10}=0.05[/tex]

For x=15 g, y=$0.55 ---->  [tex]k=\frac{0.55}{15}=0.04[/tex]

The values of k are different

therefore

The table not represent a proportional relationship

Table 3

For x=0.5 Kg, y=$0.75 ---->  [tex]k=\frac{0.75}{0.5}=1.5[/tex]

For x=5 g, y=$7.50 ---->  [tex]k=\frac{7.50}{5}=1.5[/tex]

The values of k are equal

therefore

The table represent a proportional relationship

Table 4

For x=1 oz, y=$2.00 ---->  [tex]k=\frac{2}{1}=2[/tex]

For x=2 lb, y=$4.00

Convert lb to oz

Remember that

1 lb=16 oz

so

2 lb=2(16)=32 oz

For x=32 lb, y=$4.00 ---->  [tex]k=\frac{4}{32}=0.125[/tex]

The values of k are different

therefore

The table not represent a proportional relationship

The horse traveled 439.6 feet after walking around the track 5 times

Solution:

Given that, horse walks around a circular track while its trainer stands in the center

The trainer is 14 feet from the horse at all times

Therefore, radius of circular track = 14 feet

The circumference of circle is the distance traveled by horse for 1 lap

The circumference of circle is given as:

[tex]C = 2 \pi r[/tex]

Where, "r" is the radius and [tex]\pi[/tex] is a constant equal to 3.14

[tex]C = 2 \times 3.14 \times 14\\\\C = 87.92[/tex]

Thus the distance traveled by horse for one time in circular track is 87.92 feet

About how far had the horse traveled after walking around the track 5 times?

Multiply the circumference by 5

[tex]distance = 5 \times 87.92\\\\distance = 439.6[/tex]

Thus the horse traveled 439.6 feet after walking around the track 5 times

Answer:

The correct answer is D. 30°, 60°, 90°; 1,  √3, 2

Step-by-step explanation:

Let's find out the solution to this question:

Arc cos (β) = √3/2 = 1.732/2 = 0.866

β = 30°

Let's recall that the ratio of the sides of a triangle 90 - 60 - 30 is:

1 : 2 : √3

β = 30°, α = 60°, r = 2, h = 1, k = √3

The correct answer is D. 30°, 60°, 90°; 1,  √3, 2

Since M and N are independent events, [tex]P(M)=P(M|N)=0.71[/tex]

Step-by-step explanation:

Two events A and B are said to be independent when the probability of A happening does not depend on whether B has happened or not.

In other word, this condition can be rewrite as follows:

[tex]P(A|B)=P(A)[/tex]

where

[tex]P(A|B)[/tex] is the probability of A happening  given that B has happened

[tex]P(A)[/tex] is the probability of A happening

In this problem, we have:

- M and N are independent events: so M does not depend on whether N occurs or not

Therefore,

[tex]P(M)=P(M|N)[/tex]

- Also, we know that

[tex]P(M|N)=0.71[/tex]

Therefore, it follows that

[tex]P(M)=0.71[/tex]

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Answer: try this hi i am in four

Answer:

  tan(F) = z/(2y)

Step-by-step explanation:

Make use of the similarity relationship to find the side necessary to compute the tangent. Then make use of the tangent definition.*

__

The two triangles are given as being similar. That means corresponding sides have the same ratios:

  EF/AC = ED/AB

  ED = AB·(EF/AC) = 4z(x/(8x)) = (4/8)z = z/2

The mnemonic SOH CAH TOA reminds you that the tangent relationship is ...

  Tan = Opposite/Adjacent

  tan(F) = ED/DF = (z/2)/y

  tan(F) = z/(2y)

_____

* Actually, you need to do this in reverse order: first you need to determine if you have all the necessary information to answer the question. You don't.

You need to know the length of side ED in terms of z. You notice that the corresponding side in similar triangle ABC has its length marked as a function of z, so all you need to find ED is the scale factor between the two triangles.

Since both hypotenuses are marked in terms of x, the scale factor is easily found.

Answer:

Answer:Let's solve your equation step-by-step.

Step 1:

13x+8−5x=5x−5x

8x+8=0

Step 2: Subtract 8 from both sides.

8x+8−8=0−8

8x=−8

Step 3: Divide both sides by 8.

8x

8

=

−8

8

x=−1

Answer:

x=−1

Answer:

the solution of given problem is x= -1

Step-by-step explanation:

step:-1

given equation is 13 x+8=5 x

subtracting 5 x on both sides we get

[tex]13 x +8-5 x = 5 x -5 x[/tex]

simplify [tex]8x +8 =0[/tex]

subtracting  8 on both sides , we get solution is

[tex]8 x = -8[/tex]

[tex]x=-1[/tex]

Answer:

1/13

Step-by-step explanation:

since there are four 6 in a deck ( 1 for each suite )

probability of picking up a 6 is 4/52 = 1/13

A: 1/13

Divide 52 by 4 because there are 4 copies of each card in the deck (Not counting joker) You should get 13 and if you are drawing only ONE card, then you will have a 1/13 chance to draw a 6

[tex]\dotfill[/tex]

To find the value of the given function, substitute x = 12 instead of x and evaluate.

Given function:

[tex]\sf f(x)=\cfrac{2}{3} x+14[/tex]

Substitute 12 for x:

[tex]\sf f(12)=\cfrac{2}{3}\times12+14[/tex]

Convert 12 to a fraction to make multiplying easier:

[tex]\sf f(12)=\cfrac{2}{3}\times\cfrac{12}{1}+14[/tex]

[tex]\sf f(12)=\cfrac{2\times12}{3\times1}+14[/tex]

[tex]\sf f(12)=\cfrac{24}{3}[/tex]

[tex]\sf f(12)=8[/tex]

>>> Therefore, the value of the function is 8.

The value of  [tex]\( f(x) = \frac{2}{3}x + 14 \)[/tex] is 22.

To find the value of f(12), you simply need to substitute (x = 12) into the function f(x) and evaluate it:

Given: [tex]\( f(x) = \frac{2}{3}x + 14 \)[/tex]

Substituting x = 12:

[tex]\[ f(12) = \frac{2}{3} \times 12 + 14 \][/tex]

Now, let's calculate:

[tex]\[ f(12) = \frac{2}{3} \times 12 + 14 \]\[ = \frac{2}{3} \times 12 + 14 \]\[ = 8 + 14 \]\[ = 22 \][/tex]

So, [tex]\( f(12) = 22 \)[/tex].

Answer:

A, B, D

Step-by-step explanation:

25% of 37

= 25/100 × 37

= 1/4 × 37

= 0.25 × 37

= 9.25

To find 25% of 37, you can use the equations: 'x/37 = 25/100', 'p = (0.25)37', and '25/100 x 37'. Option '37/0.25 = w' is not appropriate for finding 25% of 37.

To find 25% of 37, you can use the following methods: a), b), and d).

These three options essentially represent how percentages can be calculated:

Option c) is not suitable here because by dividing 37 by 0.25, you are finding out how many times 25% can fit into 37, not 25% of 37.

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Answer:

The answer to the factor expression is [tex]\frac{20}{3}[/tex]

Therefore [tex]12\frac{1}{3}-5\frac{2}{3}=\frac{20}{3}[/tex]

Step-by-step explanation:

Given that the factor expression is  [tex]12\frac{1}{3}-5\frac{2}{3}[/tex]

Now convert the mixed fraction into improper fraction as below :

[tex]12\frac{1}{3}-5\frac{2}{3}=\frac{37}{3}-\frac{17}{3}[/tex]

[tex]=\frac{37-17}{3}[/tex]

[tex]=\frac{20}{3}[/tex]

Therefore [tex]12\frac{1}{3}-5\frac{2}{3}=\frac{20}{3}[/tex]

The answer to the factor expression is [tex]\frac{20}{3}[/tex]

Answer:

The value of the annuity in 10 years will be US$ 15,552.90

Step-by-step explanation:

Let's use the ordinary simple annuity formula to calculate the value of the annuity in 10 years, this way:

FV = Future value of an annuity stream

PMT = Dollar amount of each annuity payment  = US% 50

r = Interest rate = 3.5% compounded biweekly = 0.035/26

n = Number of periods in which payments will be made  = 26 * 10 = 260

FV = PMT * [(1 + r)ⁿ  − 1]/r

Now, replacing with the real values, we have:

FV = 50 *  [(1 + 0.035/26)²⁶⁰  − 1]/(0.035/26)

FV = 50 *  [(1.001346154)²⁶⁰  − 1]/0.001346154

FV = 50 * 0.41873217/0.001346154

FV = 50 * 311.058148

FV = 15,552.90

We only rounded the last product to the next cent, in all the other cases we used all the decimals for the calculations.

The volume of the solid is 540 mm

Step-by-step explanation:

The volume a rectangular prism is calculated as the product of its length, width and height.

Mathematically, V=l*w*h where l is length of the prism, w is width and h is the height

Given that the dimensions of the rectangular prism as;

Length=15 mm

Width= 6 mm

Height = 6 mm

V=15*6*6= 540 mm

Answer:

28) 120 x 20y

30) 3w x 36

Step-by-step explanation:

28) 20 x (6 x y)

20 x 6 = 120

y x 20 = 20 y

120 x 20y

30) (w x 12) x 3

3 x w = 3w

12 x 3 = 36

3w x 36

Answer:

120 x 20y               3w x 36

Step-by-step explanation:

Distributive Property

Answer:

The graph is attached.

Step-by-step explanation:

The graph of the line with the slope [tex]m[/tex] and the y-intercept [tex]b[/tex], has the form

[tex]y=mx+b[/tex]

In our case the rate of change [tex]m[/tex] is [tex]0.4[/tex]; therefore we have the equation

[tex]y=0.4x[/tex]

The graph of which is attached.

P.S: we have set [tex]b=0[/tex]  by default, because we are not given any information for it.

The line that represents a proportional relationship between y and x where the unit rate of change (or slope) is 0.4 can be plotted on a graph. Start from the origin and for each increase of 1 in x, y increases by 0.4. Plot these points and draw a straight line which represents this proportional relationship.

To graph the line that represents a proportional relationship between y and x where the unit rate of change of y with respect to x is 0.4, you can start by creating a plot with an x- and y-axis. The y-axis represents the dependent variable and the x-axis represents the independent variable.

In this case, we're looking at a linear relationship, which means the line produced on the graph will be straight. This kind of straight-line graph typically uses the equation y = mx, where m is the slope (or unit rate of change) and x is the independent variable.

For this graph, the slope or unit rate of change is 0.4. This means that with every increase of 1 in x, y increases by 0.4. Plot some points on the graph starting from the origin (0,0). If x is 1, y will be 0.4 (1*0.4). If x is 2, y will be 0.8 (2*0.4). Keep plotting these points and connect them to draw the line. This line demonstrates the proportional relationship between x and y.

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The expression D=23g shows the distance that Kurt can drive on a tank of gasoline.

Step-by-step explanation:

Given,

Distance covered by Kurt's car = 23 miles per gallon of gasoline

Kurt fills up tank of his car with g gallons.

Number of gallons in car's tank = g gallons

Distance covered by g gallons = D = Distance covered by one gallon * Number of gallons

D = 23*g

D = 23g

The expression D=23g shows the distance that Kurt can drive on a tank of gasoline.

Keywords: distance, multiplication

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Answer:

The maximum amount that the company X can borrow is $ 145,000

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Current ratio of assets/liabilities = 2.9

Current assets = $ 377,000

Current liabilities = Currents assets/Ratio = 377,000/2.9 = $ 130,000

2. The board of directors determines that the current ratio must never be below 2.6. What is the maximum amount that the company can borrow?

Desired ratio of assets/liabilities = 2.6

Current assets = $ 377,000

Desired liabilities = $ Current assets/Ratio = 377,000/2.6 = $ 145,000

The maximum amount that the company X can borrow is $ 145,000

Answer:

This is a lengthy answer

Step-by-step explanation:

So contact me. Message me and I can explain to the fill extent

Final answer:

To find the total length of the wall, calculate the length built in 40 minutes (1200 cm) and divide by 3/4 to get the full length of 1600 cm, which is equivalent to 16 meters.

Explanation:

The question is asking us to determine the total length of the wall that a construction company is building, given that 3/4 of the wall is built in 40 minutes at a rate of 30 cm per minute. First, let's calculate the length of the wall built in 40 minutes:

The total length of the wall is 16 meters.

Answer:

47 stamps

Step-by-step explanation:

You just have to subtract 15 from 62 so it looks like this: 62-15=47

Answer:

C & D

Step-by-step explanation:

Social Science and Math/CS do represent 1/4 of the total majors.

Furthermore, Science and Social Sciences represent half of the majors.

Therefore, C & D are true.

Combining Science and Social Science represent half the intend majors. Therefore, option D is the correct answer.

Given that, a dean polled the sophomore class about their intended majors, then created this graph based on the data.

A pie chart is a type of a chart that visually displays data in a circular graph. It is one of the most commonly used graphs to represent data using the attributes of circles, spheres, and angular data to represent real-world information.

From the given pie chart,

More students intend to majors in science

Less students intend to majors in Maths/CS

1/4 of students intend to major in other subjects.

Combining Science and Social Science represent half the intend majors. Therefore, option D is the correct answer.

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Answer:2/16 4/32 8/64 16/4,096

Step-by-step explanation:what you do is multiply 2and4

Answer:

Step-by-step explanation:

Horizontal

Answer:

slope = 0

Step-by-step explanation:

A horizontal line is parallel to the x- axis.

Since the x- axis has a slope of zero then the slope of a horizontal line is 0

Answer:

-6.2y-4.5

Step-by-step explanation:

Answer:

The correct answer is A

Step-by-step explanation: