Rick has a piece of lumber that is 12 feet long. He cuts it into pieces that are each 3/4 of a foot long. How many pieces of 3/4 foot lumber will he be able to make?
Answer:
He will be able to make 16 pieces of lumber
Step-by-step explanation:
Exercise 21
Let x represents a length in cm where x > 1.5.
AB = 2x - 3, BC = 4x – 6,
AD = 2x + 3 and BE = 4x +1
• ABC is right triangle of area Si.
. CBFG is a rectangle of area S2.
. ADEB is a right trapezoid of area S3.
1) Express S1 and S2 and S3 in terms of x
Plzzz I need help
Answer:
see explanation
Step-by-step explanation:
area of Δ ABC is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 4x - 6 and h = 2x - 3 , then
A = [tex]\frac{1}{2}[/tex] (4x - 6)(2x - 3) ← expand using FOIL
= [tex]\frac{1}{2}[/tex](8x² - 24x + 18) ← distribute
= 4x² - 12x + 9
----------------------------------------------------------
Area of rectangle CBFG is calculated as
A = lb ( l is length, b is breadth )
Here l = 4x - 6 and b = 3x - 2, then
A = (4x - 6)(3x - 2) ← expand using FOIL
= 12x² - 26x + 12
----------------------------------------------------------
Area of trapezoid is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂)
where h is the height and b₁, b₂ the parallel bases
Here h = 2x - 3, b₁ = 4x + 1, b₂ = 2x + 3 , then
A = [tex]\frac{1}{2}[/tex] (2x - 3)(4x + 1 + 2x + 3)
= [tex]\frac{1}{2}[/tex] (2x - 3)(6x + 4) ← expand using FOIL
= [tex]\frac{1}{2}[/tex] (12x² - 10x - 12) ← distribute
= 6x² - 5x - 6
please i need this done in an hour
Which equation is represented by the graph below?
On Monday and Tuesday the lake received 18.45 inches of water. If it received 7.85 inches on Monday, how much did it receive on Tuesday?
Answer:
10.60 inches
Step-by-step explanation:
18.45
-7.85
_____
10.60 inches
17. Write a rational function in expanded form that satisfies the
following criteria:
• V.A. x=2
• SI.A y =5x-1
• Zero of function (-1,0)
pls help thank you<3
Answer:
[tex]f(x) = \frac{5x^2 + 4x - 1}{x - 2}[/tex]
Step-by-step explanation:
Given
VA; [tex]x = 2[/tex]
SLA: [tex]y = 5x - 1[/tex]
Zero of function: [tex](-1,0)[/tex]
Required
Determine the rational function in expanded form
Analyzing the vertical asymptote
The vertical asymptote is given as:
[tex]x = 2[/tex]
Subtract 2 from both sides
[tex]x - 2 = 2 - 2[/tex]
[tex]x - 2 = 0[/tex]
This means that the denominator must be [tex]x - 2[/tex]
Analyzing the zero of the function
The zero of the function is given as: [tex](-1,0)[/tex]
This means that [tex]x = -1[/tex], when [tex]y = 0[/tex]
Equate [tex]x = -1[/tex] to 0 by add 1 to both sides
[tex]x + 1 =- 1 + 1[/tex]
[tex]x + 1 =0[/tex]
This means that one of the numerators must be [tex]x + 1[/tex]
Analyzing the slant asymptote:
[tex]y = 5x - 1[/tex]
This means that one of the numerators must be [tex]5x - 1[/tex]
Hence, the function is:
[tex]f(x) = \frac{(5x - 1)(x+1)}{x - 2}[/tex]
Expand the numerator
[tex]f(x) = \frac{5x^2 + 5x - x - 1}{x - 2}[/tex]
[tex]f(x) = \frac{5x^2 + 4x - 1}{x - 2}[/tex]
What equation is equal to 8-2x=12?
A)2x-8=-12
B)2x-8=12
C)x-4=6
D)2x=20
Joseph is weaving a ceremonial Native American sash. The sash will be 8 feet long when it is completed. Joseph wants to add a diamond shape every 0.4 feet along the sash. How many diamonds will the sash have when it is completed? A. 20 B. 19 C. 18 D. 17 pls give answer
Answer:
20 diamonds
Step-by-step explanation:
It is given that,
Length of the sash when it is completed = 8 feet
Joseph wants to add a diamond shape every 0.4 feet along the sash.
We need to find no of diamonds the sash have when it is completed. It can be calculated by dividing total length by 0.4 feet. As a result,
n = 8/0.4
n = 20
Hence, 20 diamonds the sash will have when it is completed
What is the interest you will pay if you borrowed $550 at 8% interest for 3 years?
Answer:
132
Step-by-step explanation:
it is
Simple interest is the interest calculated on the principal at a given rate for a time period.
The formula for simple interest is given as,
SI = (P x R x T) / 100
P = Principal
R = rate
T = time in years
The interest that will be paid after 3 years with 8% interest is $132.
What is simple interest?It is the interest calculated on the principal at a given rate for a time period.
The formula for simple interest is given as,
SI = (P x R x T) / 100
P = Principal
R = rate
T = time in years
We have,
P = $550
R = 8%
T = 3 years
SI = (P x R x T) / 100
SI = (550 x 8 x 3) / 100
SI = $132
Thus,
The interest that will be paid after 3 years with 8% interest is $132.
Learn more about simple interests here:
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HELP ME PLSS,, I need help
Answer:
$100 per deposit
Step-by-step explanation:
Answer:
It is very simple all you have to do is take the first two points and figure how far they are apart from each other. Well from 250 to 150 is 100 so every deposit they put 100 dollars in so the answer is.
$100 dollars deposit
Graph the equation y=2x+1
Answer:
hope it helps
Step-by-step explanation:
Split 36 into the ratio 1:2
Answer:
12 : 24
Step-by-step explanation:
sum the parts of the ratio, 1 + 2 = 3 parts
Divide 36 by 3 to find the value of one part of the ratio.
36 ÷ 3 = 12 ← value of 1 part of the ratio , thus
2 parts = 2 × 12 = 24
Thus
36 in the ratio 1 : 2 is 12 : 24
Richard and Linda enjoy visiting Hilton Head Island, South
Carolina. The distance from their home to Hilton Head is
975 mi, so the drive takes them 2 days. Richard and Linda
travel twice as far the first day as they do the second day.
How many miles do they travel each day?
Answer:
first day: 650, second day: 325
Step-by-step explanation:
Let x be the number of miles travelled on the second day and 2x the number of miles travelled on the first day. They add up to 975.
2x+x=975
3x=975
x=325
x represents the number of miles travelled on the second day so they travelled 650 miles on the first day and 325 miles on the second day.
Answer:
650 miles the first day, 325 miles the second day
Step-by-step explanation:
We can call the distance they traveled on the first day as 2x and the distance they traveled on the second day as x. The former is 2x because they traveled twice as far the first day compared to the second day. Since the total distance traveled is 975 miles, we can write the following equation to solve for x:
[tex]2x + x = 975[/tex]
[tex]3x = 975[/tex] (Simplify LHS; 2x + x = 3x)
[tex]\frac{3x}{3}=\frac{975}{3}[/tex] (Divide both sides of the equation by 3 to get rid of the coefficient on x)
[tex]x = 325[/tex] (Simplify)
Therefore, [tex]2x = 2 * x = 2 * 325 = 650[/tex] so the final answer is they traveled 650 miles the first day and 325 miles the second day. Hope this helps!
how do you work out the percentage increase
Please answer correctly !!!!!!!!!!!!!! Will mark Brianliestttt !!!!!!!!!!!!!!!!!!!!!!!!
Answer:
D {36,47,60}
Step-by-step explanation:
it would have to be {37,48,60} for it to be a right triangle
hope this helps you out
Kiesha and her classmates wrote proportions for the reduction of a triangle.
A larger and smaller triangle have corresponding heights and bases.
Which proportions are set up correctly? Select three options.
StartFraction original height over original base EndFraction = StartFraction reduction height over reduction base EndFraction
StartFraction original height over reduction height EndFraction = StartFraction original base over reduction base EndFraction
StartFraction original height over reduction base EndFraction = StartFraction reduction height over original base EndFraction
StartFraction reduction height over reduction base EndFraction = StartFraction original height over original base EndFraction
StartFraction original height over original base EndFraction = StartFraction reduction base over reduction height EndFraction
Answer: A, B, and D are correct!
Step-by-step explanation:
Hope this helps! :)
The three proportions that are set up correctly for the reduction of a triangle are:
original height / original base = reduction height / reduction base
original height / reduction height = original base / reduction base
original height / reduction base = reduction height / original base
Options 1, 2, and 3 are correct.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The three proportions that are set up correctly for the reduction of a triangle are:
1)
original height / original base = reduction height / reduction base
This proportion represents that the ratio of the original height to the original base is equal to the ratio of the reduction height to the reduction base.
2)
original height / reduction height = original base / reduction base
This proportion represents that the ratio of the original height to the reduction height is equal to the ratio of the original base to the reduction base.
3)
original height / reduction base = reduction height / original base
This proportion represents that the ratio of the original height to the reduction base is equal to the ratio of the reduction height to the original base.
Thus,
original height / original base = reduction height / reduction base
original height / reduction height = original base / reduction base
original height / reduction base = reduction height / original base
Learn more about triangles here:
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can anyone help and explain why this is either proportional or not? urgent!! (it needs an explanation too)
Answer:
Yes
Step-by-step explanation:
I would say yes, x is multiplied by itself to get an answer for y.
2 2/9 +1 4/9 please help
Answer:
3 2/3
Step-by-step explanation:
In addition, the denominator has to be the same and it doesn't change when 2 fractions are added together, unless ur trying to simplify the equation, anyways:
2 2/9 +1 4/9
3 6/9
simplify
3 2/3
What is the value of x^2 - 3y + 5x + 2 whenx = 7 and y = 4?
Answer:
74
Step-by-step explanation:
[tex]x^2 - 3y + 5x + 2 \\ \\ = {7}^{2} - 3(4) + 5(7) + 2 \\ \\ = 49 - 12 + 35 + 2 \\ \\ = 74[/tex]
Given parallel lines, which pair of angles are congruent?
transversal angles
Step-by-step explanation:
When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles . When the lines are parallel, the corresponding angles are congruent .
8 t-shirts and a hat costs £42.00
3 t-shirts and a hat costs £17.00.
How much does a t-shirt cost?
How much does a hat cost
Answer:
a T-shirt costs £5
a hat costs £2
Step-by-step explanation:
Suppose
A T-shirt=x
A Hat=y
So the equation is
8x+y=42
3x+y=17
So
8x+y=42
3x+y=17
------------
5x=25
x=5
So a T-shirt costs £5
3.5+y=17
15+y=17
y=2
So a hat costs £2
Answer:
t-shirt: £5
hat: £2
Step-by-step explanation:
Please see the attached picture for the full solution.
two boats leave a ramp traveling in opposite directions. The second boat is 10 miles per hour faster than the first. After 3 hours they are 150 miles apart. Find the speeds of the boats.
Answer:
220 mph ; 230 mph
Step-by-step explanation:
Given that :
Speed of First boat = x
Speed of Second boat = y
y = (10 + x) mph
Distance apart after 3 hours = 150 miles
Speed of the boats :
Speed / time = distance
First boat distance = x / 3
Second boat distance = (10+x) /3
x/3 + (10+x)/3 = 150
x + 10 + x = 150 * 3
2x + 10 = 450
2x = 450 - 10
2x = 440
x = 220 mph
Speed of second boat = 220 + 10 = 230 mph
The surface area of a sphere is 196 π . Its radius is
Answer:
The radius of the sphere is 7 units
Step-by-step explanation:
Surface Area
Given a sphere of a radius (r), the surface area is given by the formula:
[tex]\displaystyle A=4\pi r^2[/tex]
If the surface area is given, we can solve for r:
[tex]\displaystyle r=\sqrt{\frac{A }{4\pi }}[/tex]
The surface area of a sphere is given A=196π.
Calculating the radius:
[tex]\displaystyle r=\sqrt{\frac{196\pi}{4\pi }}[/tex]
[tex]\displaystyle r=\sqrt{49}[/tex]
r = 7 units
The radius of the sphere is 7 units
Solve: -1/2x +2=-x+7
Answer:
x = 10
Step-by-step explanation:
-1/2x + 2 = -x + 7
multiply by 2 so that -1/2x becomes -x
(-1/2x + 2 = -x + 7)2
-x + 4 = -2x + 14
subtract 4 from both sides
-x = -2x + 10
add -2x to both sides
x = 10
Find the midpoint. Help pleaseeee
Answer:
0.5
Step-by-step explanation:
Co-ordinate of the mid point of the segment whose co-ordinates are -6 & 7 is =
[tex] \frac{7 + ( - 6)}{2} = \frac{1}{2} = 0.5[/tex]
What is the area of a rectangle with vertices
(-1,-4), (-1,6), (3, 6), and (3,-4)?
16 square units
24 square units
36 square units
40 square units
Answer:
40squared units!
I hope it will be useful.
Answer: 40 square units
Step-by-step explanation:
I took the assignment
the lamp is $10 and the sales tax is 5% whats the total cost of the lamp
Answer:
10.50
Step-by-step explanation:
Answer:
10.50
Step-by-step explanation:
multiply 10 by .5 and you get 50cents so add that to 10 and you get 10.50
What is the percent of change of 25 when decreased to 18?
Answer:
your answer is that it decreases to 7%
Answer:
28% decrease
Step-by-step explanation:
(18−25)|25|×100
=−725×100
=−0.28×100
=−28%change
=28%decrease
Order the set of integers from greatest to least. {8, 43, -25, 12, -14, 3}
Step-by-step explanation:
{43, 12, 8, 3, -14, -25}
What is the relationship between cos(90degrees) and cos(-90°)?
Answer:
The relationship between the two is that they are equal.
Step-by-step explanation:
Since y = cosx is a even function, that means that cosx = cos(-x). Therefore, cos 90 degrees = cos -90 degrees.
We can also test this out:
cos 90 = 0
cos -90 = cos 270 = 0
Therefore, this came to the same conclusion as our first solution.
I hope this helps! :)