Answer:
The ramp must be placed 13.08 feet from the base of the house.
The angle the ramp will make with the ground is 20.92°.
Step-by-step explanation:
An illustrative diagram for the scenario is shown below.
In the diagram, d represents the distance of the door from the ground, r represents the length of the ramp and x represent the distance of the ramp from the base of the house.
To determine how far away from the base of the house the ramp must be placed, that is to determine x in the diagram.
The diagram is a right angle triangle and x can be determine using the Pythagorean theorem which states " the square of the hypotenuse equals sum of the squares of the other two sides"
In the diagram, the hypotenuse is r
∴ r² = d² + x²
r = 14 ft
d = 5 ft
∴ 14² = 5² + x²
196 = 25 + x²
Then, x² = 196 - 25
x² = 171
x = √171
x = 13.08
Hence, the ramp must be placed 13.08 feet from the base of the house.
Now, to determine what angle the ramp will make with the ground, that is θ in the diagram.
From the formula
Sinθ = Opposite / Hypotenuse
In the diagram, opposite = d = 5ft
and Hypotenuse = r = 14ft
∴ Sinθ = 5ft / 14ft
Sinθ = 0.3571
∴ θ = Sin⁻¹(0.3571)
θ = 20.92°
Hence, the angle the ramp will make with the ground is 20.92°.
.Factor the expression using the GCF.
8y - 6x
Answer:
2(4y - 3x)
Step-by-step explanation:
The amount of money that Jacob earns based on the number of hours he works is shown in the table. Find the constant of proportionality.
Answer:
Y=7.5x
Step-by-step explanation:
8-5=3 and 60-37.5 is 22.5 divide 22.5 by 3 and you get 7.5 which is the rate that he earns an hour
Pls answer soon lol.
................................................
(95)×(3×10^4 )
Answer:
2.85 × 10^6
Step-by-step explanation:
Answer:
2850000
Step-by-step explanation:
What is the value of x?
X=
Step-by-step explanation:
[tex]{:}\longrightarrow[/tex][tex]\sf 13x-12=7x-6 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 13x-7x=-6+12 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 6x=6 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac{6}{6}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=1 [/tex]
Solve.
4 - 2x = 10
A)-7
B)-3
C)0
D)3
Answer: The answer should be B) -3. To solve the equation you have to rewrite the equation.
Susan makes a purchase of $175 and is charged 7.75% for sales tax. What is the total cost of the purchase if Susan charges it on a credit card with a daily interest rate of 0.039% and pays the balance off at the end of 30 days? a. $176.17 b. $186.70 c. $190.77 d. $200.26
Answer:
C. 190.77
Step-by-step explanation: edge 2022
The required, total cost of the purchase is $190.77. Option C is correct.
What is the percentage?The percentage is the ratio of the composition of value to the overall composition of value multiplied by 100.
Here,
To calculate the total cost of the purchase, we first need to calculate the amount of sales tax and add it to the original price.
Sales tax = 7.75% of $175 = 0.0775 x $175 = $13.56
Total cost of purchase = $175 + $13.56 = $188.56
If Susan charges the purchase to her credit card and pays it off after 30 days, she will be charged interest on the outstanding balance for those 30 days. The interest rate is 0.039% per day, which is equivalent to 1.17% per month (0.039% x 30).
The interest charged on the outstanding balance after 30 days will be:
Interest = $188.56 x 1.17% = $2.20
Therefore, the total cost of the purchase, including sales tax and credit card interest, will be,
Total cost = $188.56 + $2.20 = $190.76
Therefore, the total cost of the purchase is $190.77.
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Problem 1
Select all of the ordered pairs (x, y) that are solutions to
the linear equation 2x + 3y = 6.
(Select all that apply.)
(0,2)
(0,6)
(2,3)
(3,-2)
(3,0)
(6, -2)
After substituting the given values of x and y in the equation, all that can apply are (0, 2), (3, 0), and (6, -2).
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given information in the question,
The given equation is,
2x + 3y = 6
Now, substitute the corresponding points and check,
1. For points (0, 2)
2(0) + 3(2) = 6
6 = 6, this is correct.
2. For points (0, 6)
2(0) + 3(6) = 18
6 ≠ 18, this is incorrect.
3. For points (2, 3)
2(2) + 3(3) = 6
13 ≠ 6, this is incorrect.
4. For point (3, -2)
2(3) + 3(-2) = 6
0 ≠ 6, this is incorrect.
5. For point (3, 0)
2(3) + 3(0) = 6
6 = 6, this is correct.
6. For point (6, -2)
2(6) + 3(-2) = 6
6 = 6, this is correct.
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write an explicit rule for the sequence
Expand and simplify 6(2x - 3) – 2(2x + 1)
Answer 8x - 20
Step-by-step explanation:
6(2x - 3) - 2(2x + 1)
Distribute
6(2x) -6( 3) - 2(2x) -2( 1)
12x -18 -4x -2
Combine like terms
12x -4x -18 -2
8x-20
5.
For each equation, determine if x = 2 is a solution. Explain or show your reasoning.
a.
-2(x – 4) = 4
b.
26
= 13
C.
-3.8x = -7.4
4(x - 1) – 3(x - 2) = -8
d.
x=2 is a solution of equations -2(x – 4) = 4 and 26/x=13
What is Equation?Two or more expressions with an Equal sign is called as Equation.
-2(x-4)=4
-2(2-4)=4
4=4
Hence, x=2 is the solution
26/x=13
Now x=2
26/2=13
13=13
Hence, x=2 is the solution
-3.8x=-7.4
Now x=2
-3.8×2=-7.4
-7.6=-7.4
x=2 is not a solution of -3.8×2=-7.4
4(x - 1) – 3(x - 2) = -8
4(2-1)-3(2-2)=-8
4=-8
x=2 is not a solution of -3.8×2=-7.4
Hence, x=2 is a solution of equations -2(x – 4) = 4 and 26/x=13
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every 5 days alma rides her skateboard in the park every 4 days she bikes to her best friends house how often does alma do both
Answer:
In what time frame. It asks how often she does both but does that mean in a week or another span of time?
Step-by-step explanation:
7th grade math, I will give brainliest to right answer!
t/4 = 1
what is the value of t?
Answer:
t = 4
Step-by-step explanation:
Anything divided by itself is 1
Jennifer solved 27 problems, which is 3 11 of all the problems in her homework. How many problems are in her homework? find the number
Answer:
99 problems
Step-by-step explanation:
27 problems solved, x problems unsolved
27/x to 3/11
27/3 = 9
3/11(9/9)
27/99
There are 99 problems in Jennifer's homework.
I will give brailiest to whoever needs it!
Answer:
me please
Step-by-step explanation:
Answer:
idc if i get it
Step-by-step explanation:
Michael spends a half hour adding water to his pool part of the time at a rate of 15 gallons per minute and the rest of the time at a rate of 9 gallons per minute. Let t be the time in minutes that he adds water at the faster rate write an algebraic expression to represent the total number of water added to the pool
Answer:
24t + 270 gallons
Step-by-step explanation:
Given that :
Addition rate 1 = 15 gallons per minute
Addition rate 2 = 9 gallons per minute
Total time spent adding water = half an hour = 30 minutes = 0.5 hour
Time spent adding water at faster rate = t
Time spent addition water at slower rate = (30 - t)
Total number of water added to the pool :
Amount of water added = addition rate * time
Hence,
Amount of water added at faster rate :
(15 gal / min) * t = 15t gallons
Amount added at slower rate :
(9 gal / min) * (30 - t) = (270 - 9t) gallons
Total amount of water added to the pool:
15t gallons + (270 - 9t)gallons
15t + 270 + 9t
24t + 270 gallons
H shows the ratio of pencils to pens sold at the school bookstore. If the bookstore sells 15 pencils, what is the ratio of pencils to pens sold written as a fraction?
Answer:
[tex]Ratio = \frac{3}{2}[/tex]
Step-by-step explanation:
See attachment for complete question.
We start by solving for the equation of the graph (The graph shows a linear equation)
Represent pencils with x and pen with y
From the graph, we have that:
[tex](x_1,y_1) = (6,4)[/tex]
[tex](x_2,y_2) = (12,8)[/tex]
Solve for slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{8 - 4}{12- 6}[/tex]
[tex]m = \frac{4}{6}[/tex]
[tex]m = \frac{2}{3}[/tex]
The equation is calculated using:
[tex]y - y_1 = m(x - x_1)[/tex]
Where
[tex]m = \frac{2}{3}[/tex]
[tex](x_1,y_1) = (6,4)[/tex]
[tex]y - 4 = \frac{2}{3}(x - 6)[/tex]
[tex]y - 4 = \frac{2}{3}x - \frac{2}{3} * 6[/tex]
[tex]y - 4 = \frac{2}{3}x - \frac{2 * 6}{3}[/tex]
[tex]y - 4 = \frac{2}{3}x - \frac{12}{3}[/tex]
[tex]y - 4 = \frac{2}{3}x - 4[/tex]
Add 4 to both sides
[tex]y - 4 +4= \frac{2}{3}x - 4 + 4[/tex]
[tex]y= \frac{2}{3}x[/tex]
Now, to the question.
When pencils is 15 implies that
[tex]x = 15[/tex]
Solving for x, we have:
[tex]y= \frac{2}{3}x[/tex]
[tex]y= \frac{2}{3} * 15[/tex]
[tex]y= \frac{2* 15}{3}[/tex]
[tex]y= \frac{30}{3}[/tex]
[tex]y= 10[/tex]
i.e. Pen = 10
Ratio = x ; y
[tex]x : y = 15 : 10[/tex]
Convert to fraction
[tex]\frac{x}{y} = \frac{15}{10}[/tex]
Simplify
[tex]\frac{x}{y} = \frac{3}{2}[/tex]
Hence,
[tex]Ratio = \frac{3}{2}[/tex]
Answer:
3/2 :)
Step-by-step explanation:
Find the 12th term of the geometric sequence 2, 10,50,...
The first term of the geometric sequence is 2 and the common ratio is 5. So, the 12th term of the geometric sequence is 97656250.
Geometric sequence:Important information:
Given geometric sequence is 2, 10,50,...We need to find the 12 th term.
In the given geometric sequence, the first term is [tex]a=2[/tex] and the common ratio is [tex]d=\dfrac{10}{2}=5[/tex].
The nth term is:
[tex]a_n=ar^{n-1}[/tex]
Where [tex]a[/tex] is first term, [tex]r[/tex] is common ratio.
The 12th term is:
[tex]a_{12}=2(5)^{12-1}[/tex]
[tex]a_{12}=2(5)^{11}[/tex]
[tex]a_{12}=97656250[/tex]
Therefore, the 12th term of the geometric sequence is 97656250.
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Answer: 97656250.
Step-by-step explanation:
dm
A line passes through the points (-5, 2) and (10,-1). Which is the equation of the line?
o y=-3x+1
O y-zx=3
O y = -5x – 23
O y = 5x + 27
HURRY
solve: -3 |x-3| = -6
how do i solve absoulute value ?
Answer:
x=5,1
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
-4/7 + 2/7 x –14x + 4/7
Choose the graph below that represents the following system of inequalities:
y ≥ −3x + 1
y ≤ 1/2 x + 3
Answer:
the following system of inequalities:
y ≥ −3x + 1
y ≤ (1/2)x + 3
using a graph tool
see the attached figure
the answer is the option
B)Graph of two lines that intersect at one point. Both lines are solid. One line passes through points negative 2, 2 and 0, 3 and is shaded below the line. The other line passes through points 0, 1 and 1, negative 2 and is shaded above the line
Step-by-step explanation:
Rectangle A measures 10 inches by 8 inches. Rectangle B is an enlarged copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B.
Answer:
See Explanation
Step-by-step explanation:
Given
Rectangle A:
[tex]Length: 10\ in[/tex]
[tex]Width: 8\ in[/tex]
Required
Determine the possible dimensions of Rectangle B
The question has missing options; however, the question can still be solved.
Rectangle B being an enlarged copy of A implies that the dimension of A A is enlarged in equal proportion to form B
Take for instance, the measurements of Rectangle B are
[tex]Length: 15 in[/tex]
[tex]Width: 12 in[/tex]
Divide the corresponding lengths of B by A to get the enlargement ratio
[tex]Ratio = \frac{B}{A}[/tex]
For length:
[tex]Ratio = \frac{15}{10}[/tex]
[tex]Ratio = 1.5[/tex]
For width
[tex]Ratio = \frac{12}{8}[/tex]
[tex]Ratio = 1.5[/tex]
Notice that both ratios are the same.
For this measurement of B, we can conclude that B is an enlargement of A
Assume another measurements for B
[tex]Length: 20\ in[/tex]
[tex]Width: 10\ in[/tex]
Calculate Ratios
[tex]Ratio = \frac{B}{A}[/tex]
For length:
[tex]Ratio = \frac{20}{10}[/tex]
[tex]Ratio = 2[/tex]
For width
[tex]Ratio = \frac{10}{8}[/tex]
[tex]Ratio = 1.25[/tex]
Notice that, both ratios are not equal.
For this measurement of B, we can conclude that B is not an enlargement of A
Conclusively, all you have to do is: determine the ratios of the dimensions of B to A, if the result are equal then B is an enlarged copy of A; if otherwise, then B is not an enlarged copy
What system of equations can be used to ring s, the cost in dollars of each standard photo and w, the cost in dollars of each wallet photo ?
Answer:
A
Step-by-step explanation:
can someone please help me with these two
Answer:
1)
x=8 degrees
<B=70 degrees
2)
<MON=57 degrees
Step-by-step explanation:
Detailed ans is in attachment
hope it helps :)
plz mark as brainliest
Find the value of the missing angle
Answer:
130 degrees.... I am pretty sure
Cus angles of a triangle add to 180 and so the inside angle is 130 and they are vertical angles so they are the same right? right?
Step-by-step explanation:
Answer:
130 degrees
Step-by-step explanation:
I first came up with the equation 30+20+?=180 (I got 180 because every angle in a triangle added up is 180), then added the 30 and 20 to get 50+?=180. I subtracted 50 from both sides and got ?=130. I know that the angle on the inside and the outside are equal because it seems like a reflection, so if the inside angle is 130 the outside angle is 130 degrees too.
Hope this helps you :)
A bee flies at 9 feet per second directly to a flower bed from its hive. The bee stays at the flowerbed for 15 minutes, and then flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 18 minutes
Complete question is;
A bee flies at 9 feet per second directly to a flower bed from its hive. The bee stays at the flowerbed for 15 minutes, and then flies directly back to the hive at 6 feet per second. It is away from the hive for a total of 18 minutes.
a. What equation can you use to find the distance of the flowerbed from the hive?
b. How far is the flowerbed from the hive?
Answer:
A) (d/9) + 900 + (d/6) = 1080
B) d = 648 ft
Step-by-step explanation:
A) We are told that A bee flies at 9 feet per second directly to a flower bed from its hive.
Time taken is given as;
t = distance/speed
If distance is d from the hive to the flower bird.
Then, t1 = d/9
The bee stays at the flowerbed for 15 minutes. Thus, time spent at the flowerbird in seconds is; t2 = 15 × 60 = 900 seconds.
We are told that the bee flew directly back to the hive at 6 feet per second.
Thus,time is;
t3 = d/6
Since total time spent away from hive is 18 minutes, then converting to seconds, we have; t = 18 × 60 = 1080 s
Thus;
(d/9) + 900 + (d/6) = 1080
B) Since we have derived;
(d/9) + 900 + (d/6) = 1080
Then we can find d.
Multiply through by 18 to get;
2d + (900 × 18) + 3d = 1080 × 18
2d + 16200 + 3d = 19440
5d = 19440 - 16200
5d = 3240
d = 3240/5
d = 648 ft
What is the slope of у= 3х — 9
Answer:
3?
Step-by-step explanation:
3 is the slope intercept I believe
Anyone in 10th grade geometry I could really use a partner to help me with it please?! :)
Answer:
I can help
Step-by-step explanation:
I'm in honors classes
Suponga que le piden averiguar cuán alto es un poste de luz, su mejor
momento es durante la tarde en un día soleado, si la única herramienta
que tiene es una cinta métrica de 5m ¿cómo haría para saber con la
mayor exactitud posible el tamaño del poste?
Answer:
gtdnuf fjgdyj gudchu hfvhd gjsjck
grixbedfb hvdb kgtd kggyan samera hhgv bcc
Brian bought a jacket that cost d dollars. He paid the clerk $60,00 He received $7.39
in change. How much did Brian pay for the jacket?
Answer:
52.61 is what Brian payed for the Jacket.
Step-by-step explanation:
52.61 + 7.39 = 60$ in total.
Answer:
ok so a jacket would never cost 60,00 i think you meant 60.00 so it would be $52.61 for the jacket
Step-by-step explanation:
Subtract 7.39 from 60
if you really did mean 60000 the answer would be 5992.61