Answer:
[tex]\large\boxed{\large\boxed{5ft}}[/tex]
Explanation:
A ramp is modeled by a right triangle with hypotenuse equal to the length of the ramp, horizontal leg equal to the ground length(horizontal run), and vertical leg equal to the rise.
Hence, you can use Pythagora's theorem:
[tex](13ft)^2=(12ft)^2+y^2[/tex]
Solve of the y, which represents the rise:
[tex]y^2=(13ft)^2-(12ft)^2=169ft^2-144ft^2=25ft^2\\\\y=5ft[/tex]
Final answer:
Using the Pythagorean theorem with the length of the ramp as the hypotenuse (13 feet) and the horizontal distance covered (12 feet), it is determined that the ramp rises 5 feet high.
Explanation:
To determine how high the ramp rises, we can use the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (adjacent and opposite).
Let's denote:
The length of the ramp (hypotenuse) as c = 13 feetThe horizontal distance covered (adjacent side) as a = 12 feetThe height of the ramp (opposite side) as b, which we want to findUsing the Pythagorean theorem:
a² + b² = c²
Substituting the known values:
12² + b² = 13²
144 + b² = 169
To find b, we subtract 144 from both sides of the equation:
b² = 169 - 144
b² = 25
Taking the square root of both sides gives us the height:
b = √25 = 5 feet
Therefore, the ramp rises 5 feet high.
Find each function value f(7) if f(x) =5x
The value of f(7) is 35
Solution:
Given function is:
f(x) = 5x
We have to find the value of f(7)
The value of f(7) can be found by substituting x = 7 in given function
Plug in x = 7 in function
[tex]f(x) = 5x\\\\f(7) = 5(7)\\\\f(7) = 5 \times 7\\\\f(7) = 35[/tex]
Thus the value of f(7) is 35
To find f(7), substitute x = 7 into the function f(x) = 5x. The value of f(7) is 35.
Explanation:To find the value of f(7) if f(x) = 5x, substitute x = 7 into the function. We get:
f(7) = 5(7)f(7) = 35Therefore, the value of f(7) is 35.
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a car travels 2 5/8 miles in 3 1/2 minutes at a constant speed. write an equation to represent the distant d that the car travels in m minutes
Find how far the car traveled in one minute by dividing distance traveled by total time:
2 5/8 miles / 3 1/2 minutes = 3/4 mile per minute.
Now for distance (D) multiply miles per minute by number of minutes (m)
D = 3/4m
a jet travels 520 miles in 5 hours at this rate how far could the jet fly in 11 hours what is the rate of speed of the jet
The rate of speed of jet is 104 miles per hour
The jet could cover 1144 miles in 11 hours
Solution:Given that,
A jet travels 520 miles in 5 hours
Find the miles traveled in 1 hour ( speed in miles per hour)[tex]speed = \frac{distance}{time}[/tex]
[tex]Speed = \frac{520}{5}\\\\Speed = 104\ miles\ per\ hour[/tex]
How far could the jet fly in 11 hoursTime = 11 hours
Speed = 104 miles per hour
[tex]Distance = speed \times time\\\\Distance = 104 \times 11\\\\Distance = 1144[/tex]
Thus the jet could cover 1144 miles in 11 hours
Match the expression with corresponding x- and y- values so that all three expressions are equivalent to one another.
Answer:
x = 4, y = 1---->7(4)(1) - 3 = 28 - 3 = 25
x = 1, y = 6---->1 + 4(6) = 25
x = 1, y = 3---->(1 + 3 + 1)² = 5² = 25
The length of a rectangle is 6 inches more than the width. The perimeter is 40 inches. Find the length and the width of the rectangle
Answer:
lenght = 13 inches
width = 7 inches
Step-by-step explanation:
p= 2(l+b)
let lenght be x
width be y
so x=y+6
40 = 2(y+6 + y)
40= 2( 2y+6 )
20= 2y +6
2y = 20-6
2y=14
y=7
x=7+6=13
so lenght is 13 inches
width is 7 inches
The problem is about finding the length and width of a rectangle given its perimeter and their relationship. Solve it by forming an equation from the given information and solving for 'x'. The resulting dimensions are a width of 7 inches and length of 13 inches.
Explanation:The question given is a problem in algebra and pertains to the dimension of a rectangle. To solve it, let's assume the width of the rectangle to be 'x'. As per the information given, the length can be written as 'x+6'. The formula for the perimeter of a rectangle is 2*(Length + Width).
In this problem, we have perimeter = 40 inches. By substituting the values of length and width into the formula, we get: 2*(x + (x+6)) = 40.
By simplifying, you find that 2*(2x+6) = 40, which reduces to 4x+12 = 40. If you subtract 12 from each side, you get: 4x = 28. Finally, dividing each side by 4 you find the width 'x' equals 7.
Substituting x=7 in length equation: length = 7+6 = 13. So, the dimensions of the rectangle are width = 7 inches, and length = 13 inches.
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suppose you borrowed $112,500 at 5 1/2 % interest on June 10 for 72 days. your bank uses the exact interest method. Determine the amount of interest on the loan?
Answer:
used an interest calculator
What is the equation of the line passing through the point (-3,1) that is perpendicular to the line 2x+y=0
Answer:
look at the picture shown
GIVING BRAINLIEST Green Middle School has 270 boys, 250 girls, 26 teachers, and a supporting staff of 5 employees. The school uses an average of 126,776 gallons of water per week. Assuming that the water usage is proportional to the number of people in the school, about how much water do the students consume per month? a. 28,704 gal c. 478,400 gal b. 119,600 gal d. 507,104 gal
Answer:
b 119,600
Step-by-step explanation:
250+270+26+5=551 250+270 = 520 520/551 ~94%
94% of 126,776~ 119,600
Find slope-intercept of a line going through (-5,-5) with the slope 2/5
Answer:
y=2/5x-3
Step-by-step explanation:
y-y1=m(x-x1)
y-(-5)=2/5(x-(-5))
y+5=2/5(x+5)
y=2/5x+2-5
y=2/5x-3
Dave drove 55 mph for part of the trip and 60mph for the rest. The 245 mile trip took him 4 hours 12 minutes. How long did the 2nd part of the trip take? How far did he drive during the 2nd part of his trip?
Answer:
Dave drove 168 miles during the 2nd part of the trip
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Speed of Dave for part of the trip = 55 mph
Speed of Dave the rest of the trip = 60 mph
Total time of the round trip = 4 hours 12 minutes
Total distance of the trip = 245 miles
2. How far did Dave drive during the 2nd part of his trip?
Let's recall that the formula of speed is:
Speed = Distance/Time, therefore Distance = Speed * Time
x = Time of part of the trip
4 hours 12 minutes - x = Time of the rest of the trip
4.2 hours - x = Time of the rest of the trip
Now, we can write solve for x, this way:
55 * x + 60 (4.2 - x) = 245
55x + 252 - 60x = 245
-5x = 245 - 252
-5x = -7
x = -7/-5 = 7/5 = 1.4 ⇒ 4.2 - x = 2.8
1st part of the trip = 55 * 1.4 = 77 miles
2nd part of the trip = 2.8 * 60 = 168 miles
Dave drove 168 miles during the 2nd part of the trip and 77 miles during the 1st part
Kroger has 12 ounces of orange juice for $1.95 and Food Lion has 18 ounces for $2.10. Which store has the better but. Round to nearest hundredth place.
Answer: the one that sells 12 ounces for 1.95
Step-by-step explanation:
A: 1.95÷12=0.1625
B: 2.10÷18=0.1166666667
A gets more money.
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Suppose θ is an angle in the standard position whose terminal side is in Quadrant IV and cotθ= -2/17 . Find the exact values of the five remaining trigonometric functions of θ.
Final answer:
Given an angle θ in Quadrant IV with cotθ = -2/17, a right triangle is formed. Using the Pythagorean theorem, the hypotenuse is calculated, and the five additional trigonometric functions of θ are determined with appropriate signs for Quadrant IV.
Explanation:
If θ is an angle in the standard position whose terminal side is in Quadrant IV and cotθ = -2/17, we can find the five remaining trigonometric functions.
The cotangent of an angle θ, which is the reciprocal of the tangent, tells us that the tangent of θ is -17/2. Since the angle is in Quadrant IV, where cosine and secant are positive but sine and cosecant are negative, we can form a right triangle within the coordinate plane to represent this scenario. In this triangle, the adjacent side (x) to the angle θ will be positive, and the opposite side (y) will be negative.
Using the Pythagorean theorem, if we assume the adjacent side to be 17 (because cotθ = adjacent/opposite), and the opposite side to be -2 (to make cotθ = 17/(-2) = -2/17), the hypotenuse (r) can be calculated as:
√(17² + (-2)²) = √(289 + 4) = √293
Now we can find the other five trigonometric functions:
Sinθ = opposite/hypotenuse = -2/√293Cosθ = adjacent/hypotenuse = 17/√293Tanθ = opposite/adjacent = -2/17 (which was given)Cscθ = hypotenuse/opposite = -√293/2Secθ = hypotenuse/adjacent = √293/17The signs of these values are consistent with the properties of trigonometric functions in the fourth quadrant.
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What is the vertex of the function: f(x) = x² + 12x ? Please explain.
(–6, 0)
(-6, -36)
(6, 0)
(6, –36)
The vertex of the function is (-6,-36).
Step-by-step explanation:
f(x) = x²+ 12x
From the above function, we can find the x- coordinate of the vertex as,
x = -b/2a
Here a = 1, b = 12
Plugin the values as,
x = -12 /(2×1) = -6
Now plug in the x value in the above function, we will get y as,
f(x) = y = x² + 12x = (-6)² + 12(-6)
= 36-72 = -36
So the vertex is (-6, -36).
A car traveled 360 km in 6 h. A train traveled 400 km in 8 h. A boat traveled 375 km in 5 h. Which had the fastest average speed?
Answer:
boat 75
Step-by-step explanation:
Car--360/6=60
Train--400/8=50
Boat--375/5=75
Answer:
boat traveled the fastest by 35km/h
Step-by-step explanation:
car traveled= 360
6
train traveled= 400
5
boat traveled= 375
5
traveled:
Car= 60km/h
train= 50km/h
boat= 75km/h
Therefore BOAT WITH 75km/h has the FASTEST average speed
Hope it is a proper explanation & correct answer
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f(x)=x^2. What is g(x)?
Answer:
The answer is A
Step-by-step explanation:
B (1/4x)^2 will widen the parabola
C 4x^2 is too wide to be g(x)
D (16x)^2 is too narrow to be g(x)
A is the correct answer. When graphed on desmos . com / calculator it shows this is the correct answer. I hope this helped!
If it is 8:50 a.m., what will the time be 4 hours and 20 minutes later?
Answer:
1:10 pm
Step-by-step explanation:
60 minutes in an hour, so
8:50am + 4 hours = 12:50pm
12:50pm + 20 minutes = 1:10pm
I’ve been stuck on this question for a while someone please help me
A) Equation: f = 2.75p
B) 38.5 cups of flour are needed to make 14 pound cakes
Step-by-step explanation:
A)
The table shows the following data:
Pound cakes, p 3 6 9
Cups of flour, f 8.25 16.5 24.75
From the table, we notice that the increase in cups of flour needed per increase in pound cakes is:
[tex]m=\frac{16.5-8.25}{6-3}=\frac{8.25}{3}=2.75[/tex]
This means that for each additional pound cake, we need 8.25 more cups of flour.
This is a direct relationship between the two variables, therefore we can write their relationship using the equation:
[tex]f=2.75 p[/tex]
B)
Now we can complete the table.
We have to found how many cups of flour are needed when the number of pound cakes is
p = 14
In order to do that, we use the equation found in part A):
f = 2.75p
And substituting p = 14 into the equation, we find
f = (2.75)(14)= 38.5
Which means that 38.5 cups of flour are needed to make 14 pound cakes.
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Find the LCM of 91, 143 and 169
Answer:
13013
Step-by-step explanation:
Express each number in terms of the product of prime numbers.
91 = 7 × 13
143 = 11 × 13
169 = 13 × 13
Now consider the maximum number of times each factor occurs for each number.
The factor 7 occurs once
The factor 11 occurs once
The factor 13 is repeated twice ( maximum number of times for 1 number )
Thus LCM = 7 × 11 × 13 × 13 = 13013
91 = 7×13
143 = 11×13
169 = 13²
LCM = 7×11×13² = 77×169 = 13013
Which of the following expressions have a quotient of −17?
Question 6 options:
A)
(−)7
B)
17
C)
1(−7)
D)
−(17)
E)
(−1)(−7)
Answer:
C = -6
Step-by-step explanation:
1 +-7 =-6:::::::::::::::::::
KRISTIN SPENT 40$ on diapers. 8$ / package , how many packages did she buy
Answer:
5 packages . .
Step-by-step explanation:
Answer:
5 packages of diapers
Find the area of the shape shown
Answer:
The area is 18un^2
Step-by-step explanation:
The trapezoid area formula is (b1+b2)*h/2
so the two bases are 9 and 3. add them 9+3 = 12
the height is 3 multiply 12*3 = 36
then divide by two 36/2 = 18
A function is defined as {(0, 1), (2, 3), (5, 8), (7, 2)}. Isaac is asked to create one more ordered pair for the function. Which ordered pair can he add to the set to keep it a function? (1) (0, 2) (4) (1, 3) (3) (7, 0) (2) (5, 3)
Answer:
2
Step-by-step explanation:
Claire is buying a new bicycle for $295. If the
sales tax is 4.75%, what will she pay in total?
Answer:
$309.01
Step-by-step explanation:
To calculate tax, you need to turn the percent to a decimal. This is done by moving the decimal point two spaces to the left, adding zeros and needed.
4.75% = 0.0475
Now take the price of the bike, 295, and multiply it by 0.0475.
295 x 0.0475 = 14.0125
All you need are the first two numbers after the decimal point since you are dealing with money.
Add the product, 14.01, to the price of the bike, 295, and you have your answer.
$309.01
Hope this helps.
Answer:
309.01
Step-by-step explanation:
let h represent Mark’s height in inches. Suzanne is 7 inches shorter than mark. Write an algebraic expression that represents Suzanne’s height in inches.
Answer
h-7
Step-by-step explanation:
Brian drank 4.4 gallons of water today. There are approximately 3.8 liters in 1 gallon. How many liters did her drink? Round to the nearest hundredth.
Question 4 options:
0.6 L
7.33 L
0.86 L
1.16 L
Answer:
Step-by-step explanation:
16.72 or 17
Answer:
16.72
Step-by-step explanation:
Ⓗⓘ ⓣⓗⓔⓡⓔ
Well, all you would have to do is multiply 3.8*4.4
3.8*4.4=16.72
However, I'm not sure why {maybe a typo?}, but 16.72--nor any other numbers similar are listed.
(っ◔◡◔)っ ♥ Hope this helped! Have a great day! :) ♥
Solve for x.
6.5 cm
8 cm
7.5 cm
7.2 cm
Answer:
7.2 cm
Step-by-step explanation:
For the similar triangles, the ratio of the length of the bottom side to the right side is the same:
bottom/right = (x cm)/(6 cm) = (12 cm)/(10 cm)
x cm = (6 cm)(12/10) = 7.2 cm
_____
Technically, x = 7.2, not 7.2 cm.
Given a function described as equation y=3x+4, what is y when x is 1,2 and 3?
Answer:
x=1 y= 7
x=2 y= 10
x=3 y= 13
Step-by-step explanation:
y=3x+4
y=3(1)+4
=7
y=3(2)+4
=-10
y=3(3)+4
=13
For this case we have the following equation:
[tex]y = 3x + 4[/tex]
We must find the value of the variable y when the variable x takes certain values.
For [tex]x = 1:[/tex]
[tex]y = 3 (1) +4\\y = 3 + 4\\y = 7[/tex]
For [tex]x = 2:[/tex]
[tex]y = 3 (2) +4\\y = 6 + 4\\y = 10[/tex]
For [tex]x = 3:[/tex]
[tex]y = 3 (3) +4\\y = 9 + 4\\y = 13[/tex]
Thus, the values of y are 7,10,13 respectively.
Answer:
[tex]y = 7\\y = 10\\y = 13[/tex]
the length of a rectangle is 3 yards more than twice the width x the area is 629 yd.²
Answer:
The length is 37yd
The width is 17yd
Step-by-step explanation: please see attachment for explanation
What is the inequality x+5<2
Answer:
x < - 3
Step-by-step explanation:
Given
x + 5 < 2 ( subtract 5 from both sides )
x < - 3
Yo sup??
x+5<2
adding -5 on both the sides
x+5-5<2-5
x<-3
Therefore x can take any value from -3 (-3 not included) to negative infinity.
Hope this helps.
y=3/4 x-4
Any help?
(y=3
- x-4
4
Soo confused. What am I supposed to do?
Answer:
see graph of y=3/4 x-4
Step-by-step explanation:
Assuming you mean
[tex]y = \frac34x - 4[/tex]
Below is a graph of that one. The slope is 3/4 and the interception with the y axis is at y=-4. The equation is in its normal form y=ax+b with a=3/4 (slope) and b=-4 (y intercept), so no conversion needed.
You have to be careful on how you write these equations down. It might very well be that you meant:
[tex]y = \frac{3}{4x-4}[/tex] or [tex]y = \frac{3}{4x} - 4[/tex]
However, those are more complex so I'm hoping for the first one... ;-)