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
Answers
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
Related Questions
33.For a car traveling at a constant speed, the distance driven, d
kilometers, is represented by d(t)=80t, where t is the time in hours. The
cost of gasoline, in dollars, for the drive is represented by C(d)=0.09d.
Evaluate C(d(10))
Answers
Given:
[tex]d(t)=80t[/tex]
[tex]C(d)=0.09d[/tex]
To find:
The value of [tex]C(d(10))[/tex].
Solution:
We have,
[tex]C(d(10))=C(80(10))[/tex] [tex][\because d(t)=80t][/tex]
[tex]C(d(10))=C(800)[/tex]
Now,
[tex]C(d(10))=0.09(800)[/tex] [tex][\because C(d)=0.09d][/tex]
[tex]C(d(10))=72[/tex]
Therefore, the value of [tex]C(d(10))[/tex] is 72.
My remainder is 8. My dividend is 80. I am a 1- digit number. What divisor am I?
Answers
Answer:
9 is the answer..
Step-by-step explanation:
pls mark me the brainliest
Answer:
The divisor is 9.
Step-by-step explanation:
a) Data and Calculations:
Remainder = 8
Dividend = 80
Number divided evenly without remainder 8 = 80 - 8 = 72
72/9 = 8
b)There are four main numbers under the divisional mathematical rule. The first number is the dividend which is the number 80 that is being divided by the divisor. The divisor (9) is the number that divides 80. The quotient (8) is the result obtained by the division, while the remainder 8 is the number left over after the division.
help me l,ll give you brainest
Answers
Answer:
Step-by-step explanation:
he did the question wrong completely, so, check #4, #2, and #3
Answer:
the last three choices
Answer this plz I’ll mark brainliest:)
Answers
Answer:
7.5
Step-by-step explanation:
7.5 is the smallest. 7.51 is bigger by 0.01, 7.501 is bigger by 0.001 and 7.5 with a dot on top means that the number 5 repeats itself indefinately after the comma so it is like if we wrote 7.55555555 and the 5 kept going on forever
3w-5>2w+-7 and 6(c+3) 2+-3
Answers
Answer:
w>−2 and 12c+33
Step-by-step explanation:
Answer:
&&&&
Step-by-step explanation:
Sorry, Don't know buddy
Choose a number that is a factor of 900. 25, 27, 31, 32, 44, 45
Answers
Answer:
25 is a factor of 900
Step-by-step explanation:
900/25= 36
Factor is the number, which is dividing by the number without remainder.
For example for 6, factors are 1,2,3,6
In this case, we have to find the number, that you can divide by, and don’t get a remainder.
900:25= 36
900:27= 33,333..
900:31= 29,03..
900:32= 28,125
900:44= 20,4545..
900:45=20
from this we can see that 25 and 45 are the factors of 900 in this exercise. You also could understand that, because 25 and 45 are ending with 5.
Hope it helps! Please give the brainliest:):)
PLEASE HELP AND SHOW WORK
Answers
you write 2x-6=82, subtract 6 on both sides so ur left with 2x=88, you divide both sides by 2 and you get 44
find the value of the expression n+2×m
for m=6 and n =4
Answers
Answer:n=4
m=6
Step-by-step explanation:
(solve for bracket first the add)
4+2×6
4+12
16
Math proportions..............
Answers
cross multiple to get:
25x = 900
then divide to simply:
x=36
fing the sum of the interior angle measures of the polygon
Answers
(6-2)x180
= 720
Samuel scored a 32.5/40 on his most recent math test what percent did he earn in the test round to the nearest whole percent
Answers
Answer: 81%
Step-by-step explanation:
From the question, we are informed that Samuel scored a 32.5/40 on his most recent math test.
Based on the values given, to convert it to percentage, we have to multiply the score by 100. This will be:
= 32.5/40 × 100
= 3250/40
= 81.25%
= 81% to nearest whole number
i need help i don’t understand what it means or what it is asking for
Answers
Answer:
its D btw
Step-by-step explanation:
I CANT FIGURE THIS OUT!! WHATS 1+1! I WILL GIVE BRAINLIEST IF U KNOW THIS
Answers
Planet X is 1/2 of a light-year away from Earth. Planet Y is 3/10 of a light-year away from Earth. How much farther away is Planet X?
Answers
Answer:
1/2= 5/10
5/10 - 3/10 = 2/10 or 1/5
so planet X is 1/5 of a light-year closer
Step-by-step explanation:
Answer:
5/10
Step-by-step explanation:
Simplified
what is the volume of a regular octahedron inside a cube with the length of its sides measuring 4 centimeters
Answers
Answer:
We conclude that the volume of a regular octahedron will be:
[tex]\:\:V\:\approx \:30.17[/tex] cmStep-by-step explanation:
Given
The length of one of the side or edge of a regular octahedron = a = 4 cm
To determine
The volume of a regular octahedron = V
Using the formula to determine the volume of a regular octahedron
[tex]V\:=\:\frac{\sqrt{2}}{3}a^3[/tex]
substituting a = 4 in the volume equation
[tex]V=\frac{\sqrt{2}\cdot \:4^3}{3}[/tex]
[tex]V=\frac{64\sqrt{2}}{3}[/tex] ∵ 4³ = 64
[tex]\:\:V\:\approx \:30.17[/tex] cm
Therefore, we conclude that the volume of a regular octahedron will be:
[tex]\:\:V\:\approx \:30.17[/tex] cmSolve the equation for y
- 5x + 2y = 1
Answers
Answer:
14x+37=4x
Step-by-step explanation:
Equivalent fractions of 23,479 to 782
Answers
Answer:
93912/391
Step-by-step explanation:
i think its 93912/391
can i have brainiest plssss
The points in the table lie on a line. Find the slope of the line.
Answers
Answer:
-7/6
explanation
if the points correlating to the (x,y) functions are plotted out on a graph, using the rise-over-run method will result in finding a slope of -7/6
Write an equation in slope-intercept form for the line parallel to y=3x-2 that passes through the point (5,-2)
Answers
Answer:
y = 3x - 17
Step-by-step explanation:
Parallel lines have the same slope.
The slope of the given line, y = 3x - 2 is 3.
The equation we are looking for is of the form
y = mx + b
Since we know the slope, m, is 3, we have
y = 3x + b
To find the value of b, we substitute x and y with the values from the given point and solve for b.
-2 = 3(5) + b
b = -17
The equation is
y = 3x - 17
In one game of basketball Henry scored 24 points.
How many points would Henry score if he played 3 games of
basketball?
Answers
Answer:
72
Step-by-step explanation:
24 x 3 = 72 just like the problem.
Dantes Soccer Team Sells T-Shirts To raise money for new equipment. For Each T-shirt sold the team raises $8. Parents Also make a donation of $100 toward the equipment.
What is The equation That the total amount raised y , if x T-shirts are sold?
A. y= 8x
B. Y=12.5x
C. y= 100x + 12.5
D. y= 8x + 100
Answers
Answer:
It would be D
Step-by-step explanation:
100 Points!!!
y(t) = distance of weight from equilibrium position
ω= angular frequency (measured in radians per second)
A = amplitude
Ø= phase (depends on initial conditions)
c1 = A sin
c2 = A cos
Prove that: Asin(ωt+Ø)=c2sinωt+c1cosωt
Note: c1 and c2 are actually with the number slightly below the letter, if that makes sense. It wouldn't let me type it that way. Anyway, if anyone can help I would really appreciate it! Thank you!
Answers
Answer:
An object moving along the x-axis is said to exhibit simple harmonic motion if its position as a function of time varies as
x(t) = x0 + A cos(ωt + φ).
The object oscillates about the equilibrium position x0. If we choose the origin of our coordinate system such that x0 = 0, then the displacement x from the equilibrium position as a function of time is given by
x(t) = A cos(ωt + φ).
A is the amplitude of the oscillation, i.e. the maximum displacement of the object from equilibrium, either in the positive or negative x-direction. Simple harmonic motion is repetitive. The period T is the time it takes the object to complete one oscillation and return to the starting position. The angular frequency ω is given by ω = 2π/T. The angular frequency is measured in radians per second. The inverse of the period is the frequency f = 1/T. The frequency f = 1/T = ω/2π of the motion gives the number of complete oscillations per unit time. It is measured in units of Hertz, (1 Hz = 1/s).
The velocity of the object as a function of time is given by
v(t) = dx(t)/dt = -ω A sin(ωt + φ),
and the acceleration is given by
a(t) = dv(t)/dt = -ω2A cos(ωt + φ) = -ω2x.
The slope of the graphed line is . Which formulas represent the line that is graphed? Check all that apply.
y – 1 = (x – 2)
y – 2 = (x – 1)
y – 4 = (x – 4)
f(x) = x +
f(x) = x +
Answers
Answer:
B, C, E Is the answer on edge :3
Step-by-step explanation:
Have a good day :3
Answer:
B C E
Step-by-step explanation:
Katsuki Bakugou was here you Extras
2 increased by 8 times a number is equal to 5. Write an equation or inequality.
Answers
good luck
hhhhh
Evaluate f(x)=x-5 when x=-5,x=0,and x=5
Answers
Answer:
f(x) = x - 5
f(-5) = -5 - 5
= -10
f(0) = 0 - 5
= -5
f(5) = 5 - 5
= 5
Hope this helps!
Find the value of
[tex] log_{8}^{512} [/tex]
please help friends....
Answers
Answer:
3
Step-by-step explanation:
log 8 512 = 8^ x=512. x=3
Hope this helps :D
you'd like your pendulum to take 20 seconds to complete a cycle how long will the pendulum need to be? is the reasonable in your building which is planned to be 20 feet long?
Answers
Answer:
Concept: Mathematical Analysis
The full rotation of a pendulum is attached, plug in the values and solve.Rate brainlist.this is for the brainlist winner
Answers
!!!!!! ’ ... like Ik there is smart ppl around the world who knows these
Answers
Answer:
into a pyramid i think...
Zach created a blueprint using only similar parallelograms. Which statement about the parallelograms must be true? A) The parallelograms all have congruent sides and angles. B) The parallelograms have corresponding angles that are not congruent. C) The parallelograms have proportional corresponding sides. D) The parallelograms have corresponding sides that are congruent.
Answers
Answer:
A) The parallelograms all have congruent sides and angles.
Step-by-step explanation:
Remember, a parallelogram in simple words is a flat shape (either a square, rectangle, or rhombus) that has four sides of equal length, and whose opposite angles are congruent.
In other words, Zach's blueprint using similar parallelograms would be chosen from either a square, a rectangle, or a rhombus, which all have congruent sides and angles.
Answer:
C
Step-by-step explanation:
I got it wrong because I listened to the other guy :\
Have a great day!
ALSO: PRESS PICTURE TO SEE PROOF, SORRY IT CAME OUT BLURRY, ONCE YOU PRESS IT, IT WILL BE NORMAL.