An old house has a basement stairway that has steps with 7.25 inch vertical risers and 7 inch horizontal treads. What is the slope of the stairway? Round to two decimal places.

Answer:

x = 1 , y = 2

Step-by-step explanation:

Solve the following system:

{5 x + 2 = 7 | (equation 1)

y = x + 1 | (equation 2)

Express the system in standard form:

{5 x+0 y = 5 | (equation 1)

-x + y = 1 | (equation 2)

Add 1/5 × (equation 1) to equation 2:

{5 x+0 y = 5 | (equation 1)

0 x+y = 2 | (equation 2)

Divide equation 1 by 5:

{x+0 y = 1 | (equation 1)

0 x+y = 2 | (equation 2)

Collect results:

Answer: {x = 1 , y = 2

The number of unripe apples in a sack, given that there are N total apples and 3 are ripe, is calculated by subtracting 3 from N (N - 3).

The question posed is asking for a basic subtraction calculation within the context of ripe and unripe apples.

Given that there are N apples in total and 3 of them are ripe, we need to find out how many are not ripe.

The number of not ripe apples is N - 3, where N is the total number of apples in the sack.

To solve this, we subtract the number of ripe apples from the total number of apples:

For example, if a sack has 10 apples and 3 are ripe, then there would be 10 - 3 = 7 unripe apples.

Answer:

  (-2, 3)

Step-by-step explanation:

f(x) +5 means 5 is added to the y-value that is output from the function. The given point indicates the function output is -2, so when 5 is added, the result is +3. The point (-2, 3) is on the graph of f(x)+5.

George shovels at a rate of 8.33 square yards per hour. In 5 1/2 hours, he will shovel approximately 45.815 square yards of his driveway.

The student asked about how many square yards of driveway George would shovel in 5 1/2 hours after shoveling 12 2/4 square yards in 1 1/2 hours. To find this, we first need to calculate the rate at which George is shoveling.

George shovels 12 2/4 square yards in 1 1/2 hours. Simplifying these fractions, we have 12.5 square yards in 1.5 hours. The rate is therefore 12.5 ÷ 1.5 yards per hour = 8.33 square yards per hour.

Next, we multiply this rate by the total time George will be shoveling to find how much he would shovel in 5 1/2 hours:

8.33 yards/hour × 5.5 hours = 45.815 square yards

So, George will shovel approximately 45.815 square yards of his driveway in 5 1/2 hours.

Final answer:

To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information and multiply the rate by the time.

Explanation:

To find out how many square yards of driveway George would shovel in 5 1/2 hours, we can set up a ratio using the given information. In 1 1/2 hours, he shovels 12 2/4 square yards of snow. We can write this as a fraction: 12 2/4 / 1 1/2. To simplify this fraction, we can convert the mixed numbers to improper fractions: 50/4 / 3/2.

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction: (50/4) × (2/3). Multiplying the numerators and denominators, we get (50 × 2) / (4 × 3) = 100/12.

So, in 1 1/2 hours, George shovels 100/12 square yards of snow. To find out how many square yards he would shovel in 5 1/2 hours, we can multiply this rate by 5 1/2: (100/12) × (5 1/2). Multiplying the numerators and denominators, we get (100 × 11) / (12 × 2) = 1100/24. Simplifying this fraction, we get 275/6.

Therefore, George would shovel approximately 275/6 square yards of driveway in 5 1/2 hours.

Answer:

Step-by-step explanation:

substitute x = - y - 2 in 0.5x + y = 1

0.5(- y - 2) + y = 1

-0.5y-1+y=1

0.5y=2

y=4

x=- y - 2

x=-4-2

x=-6

Answer:

x=4; x=-6

Step-by-step explanation:

Answer:

see below

Step-by-step explanation:

Answer: 50%

Step-by-step explanation:

12x1.5=18

Answer:

50% increase

Step-by-step explanation:

Percentage change = increase/original × 100

[tex]change = \frac{(18 - 12)}{12} \times 100[/tex]

[tex]change = \frac{6}{12} \times 100[/tex]

[tex]change = 0.5 \times 100[/tex]

[tex]change = 50\%[/tex]

Answer:

Yes, both equations should be true.

The given statement written in symbolic language is x = 3y + 4 and x + y = 72 where "x" is the cost of one book and "y" is the cost of another book

Solution:

Given that Bruce bought two books

One book costs $ 4.00 more than three times the other

Let the two books be denoted as Book A and book B

Let "x" be the cost of book A

Let "y" be the cost of Book B

From given,

One book costs $ 4.00 more than three times the other

Let Cost of book A = $ 4.00 more than three times the other book B

x = 4 + 3 times cost of Book B

x = 4 + 3y

x = 3y + 4 --- (i)

Also given that Together, the two books cost him $72

cost of book A + cost of Book B = 72

x + y = 72 ------- (ii)

Therefore the given statement written in symbolic language is:

x = 3y + 4 and x + y = 72

Answer: They are skew and will never instersect.

Step-by-step explanation: First of all, they will never instersect because they are in the parallel planes. They are also skew because in the 3 dimensional geometry, they are also not parallel because they can be different directions.

Answer:

Step-by-step explanation:

WE know that lines are in different planes which are parallel, this means that those planes have the same angle of direction.

If planes are parallel, then all lines inside them are skew, that is,  line a and line b will never intersect and they aren't necessarily has to be parallel.

For example, imagine you are in a apartment, parallel planes are the roof and the floor, they are parallel, that is, the will never intersect each other. So, if you have a ruler attached to the roof and another ruler on the floor, you will see that those rulers are not necessarily parallels, and they won't intersect each other because, they have the same angle of direction.

Therefore, the right answer is "They are skew and will never intersect"

Answer:

x=-3, y=-6. (-3, -6).

Step-by-step explanation:

-4x+y=6

-5x-y=21

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

-9x=27

x=27/-9

x=-3

-5(-3)-y=21

15-y=21

y=15-21

y=-6

Answer:

B

Step-by-step explanation:

x² - 10x -24 = (x + 2) (x - 12)  ....(1)

x² - 3x - 108 = (x + 9) ( x - 12) ....(2)

(1) / (2)     formula (2) can't be 0 ∴ x ≠ -9 and x ≠ 12

(1) / (2) = (x + 2) / (x + 9)

answer is (B)

Number of adult tickets sold is 100 and number of children tickets sold is 150

Solution:

Let "c" be the number of childrens ticket sold

Let "a" be the number of adult tickets sold

Cost of 1 children's musical ticket = $ 2.00

Cost of 1 adult musical ticket = $ 3.50

Given that 250 tickets were sold

number of childrens ticket sold + number of adult tickets sold = 250

c + a = 250 ---- eqn 1

250 tickets were sold for a total of 650

So we can frame a equation as:

number of childrens ticket sold x Cost of 1 children's musical ticket + number of adult tickets sold x Cost of 1 adult musical ticket = 650

[tex]c \times 2.00 + a \times 3.50 = 650[/tex]

2c + 3.50a = 650 ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "a" and "c"

From eqn 1,

c = 250 - a ----- eqn 3

Substitute eqn 3 in eqn 2

2(250 - a) + 3.50a = 650

500 - 2a + 3.50a = 650

1.5a = 150

From eqn 1,

c = 250 - 100

Thus number of adult tickets sold is 100 and number of children tickets sold is 150

Final answer:

The area of Triangle B is two times greater than the area of Triangle A, due to the height of Triangle B being twice that of Triangle A with the base remaining constant.

Explanation:

The question pertains to the comparison of the areas of two triangles that share the same base. The height of Triangle B is twice the height of Triangle A. To find the area of a triangle, we use the formula 1/2 × base × height. Given that both triangles have the same base, if we call the height of Triangle A 'h', then the height of Triangle B is '2h'.

So, the area of Triangle A is (1/2 × base × h), and the area of Triangle B is (1/2 × base × 2h). Simplifying the expression for the area of Triangle B, we find it is equal to 2 × (1/2 × base × h), which means it's exactly twice the area of Triangle A. Thus, the area of Triangle B is two times greater than the area of Triangle A.

If one triangle's height is double the other's, its area is four times greater, with same base.

let's break it down step by step.

1. Area of a Triangle Formula: The area of a triangle is calculated using the formula:

[tex]\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \][/tex]

2. Given Information:

  - Both Triangle A and Triangle B have the same base.

  - The height of Triangle B is twice the height of Triangle A.

3. Comparing the Areas:

  - Let's denote the base of both triangles as [tex]\( b \).[/tex]

  - Let the height of Triangle A be [tex]\( h_A \)[/tex] and the height of Triangle B be [tex]\( h_B \).[/tex]

4. Area of Triangle A [tex](A_A)[/tex]:

  - Using the area formula, the area of Triangle A is:

   [tex]\[ A_A = \frac{1}{2} \times b \times h_A \][/tex]

5. Area of Triangle B [tex](A_B)[/tex]:

  - Triangle B has double the height of Triangle A, so the height of Triangle B is [tex]\( 2h_A \).[/tex]

  - Using the area formula, the area of Triangle B is:

   [tex]\[ A_B = \frac{1}{2} \times b \times (2h_A) = b \times h_A \][/tex]

6. Comparing the Areas:

  - Since both triangles have the same base [tex](\( b \)),[/tex] and the height of Triangle B [tex](\( 2h_A \))[/tex] is twice the height of Triangle A [tex](\( h_A \)),[/tex] the area of Triangle B is [tex]\( b \times h_A \)[/tex] which is exactly the same as Triangle A.

7. Conclusion:

  - The area of Triangle B is not just greater, it's exactly the same as Triangle A.

So, if the base and one of the heights are doubled, the area of the triangle also doubles. This is because the area of a triangle is directly proportional to its height when the base is constant.

Answer:

Answer to #1: -44.21

Answer to #2: 1.2

:)

8.27 - 52.48 = -44.21

7.38 - 6.18 = 1.2

Answer:

Hence after solving the given equation we get x = 13/20.

Step-by-step explanation:

Given:

-3 x + 0.1 + 10 x = x + 4

-3 x + 10 x - x = 4 - 0.1

6 x = 3.9

x = [tex]\frac{3.9}{6}[/tex]

x = [tex]\frac{1.3}{2}[/tex]

x = [tex]\frac{13}{20}[/tex]

The slope of the line that passes through the pair of point (5, 7), (2, 1) is 2

Solution:

Given that line that passes through the pair of point (5, 7), (2, 1)

To find: slope of the line

The slope of line is given as:

For a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] slope is given as:

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

Here in this problem,

[tex]\left(x_{1}, y_{1}\right)=(5,7) \text { and }\left(x_{2}, y_{2}\right)=(2,1)[/tex]

Substituting the values in above formula,

[tex]m=\frac{1-7}{2-5}=\frac{-6}{-3}=2[/tex]

Thus the slope of given line is 2

Answer:

  9 loaves

Step-by-step explanation:

Judy get 3/4 of the bread, so ...

  (3/4) · 12 loaves = 9 loaves

Final answer:

In order to find out how much bread Kendra gives Judy, we can set up a system of equations.

Explanation:

In order to find out how much bread Kendra gives Judy, we can set up a system of equations based on the information given. Let's say Kendra gives Lynn x loaves of bread. According to the problem, Kendra gives Judy 3 times the amount she gives Lynn, so Judy receives 3x loaves of bread. Together, they receive 12 loaves of bread, so x + 3x = 12. Simplifying the equation, we get 4x = 12. Dividing both sides by 4, we find x = 3. Therefore, Kendra gives Judy 3x = 3(3) = 9 loaves of bread.

*I'm not sure what you mean when to add and subtract but I hope this helps!

Answer:

Triangle1: 13

Triangle2: 25

Triangle3: 17

Step-by-step explanation:

*Pythagorean Theorem Formula: a²+b²=c² where c is the hypotenuse (the side opposite of the right angle)

Triangle1:

1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.

  5²+12²=c²

  25+144=c²

  169=c²

  c=√169

  c=13

Triangle2:

1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.

  15²+20²=c²

  225+400=c²

  625=c²

  c=√625

  c=25

Triangle3:

1. Plug in the values into the Pythagorean Theorem Formula and simplify as shown below.

  8²+15²=c²

  64+225=c²

  289=c²

  c=√289

  c=17

Answer:

The only correct statement is the first one

because the product of a number greater than 1 and another positive number always makes the second number greater than its original value

:)

Answer:

$240

Step-by-step explanation:

i = prt

i = $2,000 x 0.03 x 4

i = $240

The amount of interest Antonia will earn in 4 years is $240.

Answer:

The solution is the ordered pair (3,2)

The graph in the attached figure

Step-by-step explanation:

we have

[tex]y=\frac{1}{3}x+1[/tex] -----> equation A

[tex]x+y=5[/tex] ----> equation B

Solve by graphing

Remember that

The solution of the system of equations is the intersection point both lines

using a graphing tool

The intersection point is (3,2)

see the attached figure

therefore

The solution is the ordered pair (3,2)

A system of equation can be solved in several ways, which includes the use of graphs

The solution to the system of linear equations is (3,2)

The system of equations is given as:

[tex]y=\frac 13x+1[/tex]

[tex]x+y=5[/tex]

See attachment for the graphs of  [tex]y=\frac 13x+1[/tex]  and [tex]x+y=5[/tex].

From the attachment, the point of intersection of the lines of both equations is (3,2)

Hence, the solution to the system of linear equations is (3,2)

Read more about system of equations at:

https://brainly.com/question/14323743

Answer:

$2.80 (rounded from 2.796)

Step-by-step explanation:

13.98*0.2

Answer:

$2.80

Step-by-step explanation:

Multiply $13.98 by 0.2 (0.2 = 20%):

[tex]13.98*0.2=2.796[/tex]

Since you can't tip less than a cent, round to the nearest cent (hundredth of a dollar):

[tex]2.80[/tex]

20% tip on a bill of $13.98 is $2.80.

Answer:

The first answer is the correct choice.

Step-by-step explanation:

For this, there are two initial options. A cake or a shake. This means that there are two different trees that need to exist. One for Cakes and one for shakes.

Each of these trees needs to have the options of having vanilla and strawberry.

The first answer is the only one that follows this criteria

Answer:

1st one is correct.

Step-by-step explanation:

Answer:

I DONT KNOW

Step-by-step explanation:

I DO NOT KNOW

Answer:

23 points

Step-by-step explanation:

If he shane scored 3 fewer points, then that means double of Jason's score is 56. divide 56 by two to get Jason's real score, which is 23.

Answer:

The smaller one measures 80 degrees.

Step-by-step explanation:

We are given:

[tex]a+b=180[/tex]

[tex]\frac{a}{b}=\frac{5}{4}[/tex]

So we have a system to solve.

I'm going to solve the bottom equation for [tex]a[/tex] by multiplying [tex]b[/tex] on both sides:

[tex]a=\frac{5}{4}b[/tex].

Let's plug this into the first equation: [tex]a+b=180[/tex]:

[tex]\frac{5}{4}b+b=180[/tex]

[tex]\frac{5}{4}b+\frac{4}{4}b=180[/tex]

[tex]\frac{9}{4}b=180[/tex]

Multiply both sides by 4/9:

[tex]b=\frac{4}{9} \cdot 180[/tex]

[tex]b=\4 \cdot \frac{180}{9}[/tex]

[tex]b=4 \cdot 20[/tex]

[texb=80[/tex].

This means [tex]a=\frac{5}{4} \cdot 80=5 \cdot \frac{80}{4}=5 \cdot 20=100[/tex].

We do have [tex]100+80=180 \text{ and } \frac{100}{80}=\frac{5}{4}[/tex].

So the smallest of the two angles is the one that measures 80 degrees.

The one that is the larger of the two is the one that measures 100 degrees.

Final answer:

The measure of the smaller angle, which is part of a pair of supplementary angles in a 5:4 ratio, is 80 degrees.

Explanation:

Supplementary angles are two angles that add up to 180 degrees. When two angles are in the ratio of 5:4, we can find the measure of the smaller angle by first adding the parts of the ratio together, which gives us 5+4=9 parts. Since the total is 180 degrees, each part is equal to 180 ÷ 9 = 20 degrees. Therefore, the smaller angle, which is 4 parts of the ratio, is 4 x 20 degrees = 80 degrees.

Answer:

The required equation models the total profit, y, based on the number of hot dogs sold, x  is   y = 3 x - 30.

Step-by-step explanation:

Let x = total number of hot dogs sold

y = total profit from total sales of hot dogs

The given situation can be written as: y = m x +  C  ......[A]

Now, Profit for 40 hot dogs = $90 profit

So, here this can be written as:

90 = 40 m + C ......[1]

Profit for 80 hot dogs = $210 profit

So, here this can be written as:

210 = 80 m + C ......[2]

Now, solving both the equations, we get:

Subtracting  [1] and [2], we get

210  - 90  = 80 m + C  - (40 m + C)

or, 120 = 40 m

or, m = 120/40 = 3

or, m = 3

Solving for the value of C , we get: C = - 30

Putting the value of m back in the equation : y   = m x + C

y = 3 x -30

Hence, the required equation models the total profit, y, based on the number of hot dogs sold, x  is   y = 3 x - 30.

The right answer is: g(x)  is translated 2 units up from  f(x)

Step-by-step explanation:

Given functions are:

[tex]f(x) = 4x\\g(x) = 4x+2[/tex]

In order to shift the functions upward or downward, an integer is added or subtracted from the original function's output.

We can see by comparing both functions that 2 can be added to f(x) to make function g.

As 2 is added to the function, not the input, it is a vertical shifting.

As the integer is positive, the shift is upward.

So,

The right answer is: g(x)  is translated 2 units up from  f(x)

Keywords: Functions, shifting

Learn more about functions at:

#LearnwithBrainly