Answer:
The first step is to distribute.
Step-by-step explanation:
2(4x + 2)= 12
8x + 4 = 12
You distribute the 2 to 4x and 2.
Triangle lurlurl, u, r has a uniform thickness of 2.52.52, point, 5, as shown at left. the length of \overline{ud} ud start overline, u, d, end overline, which is the height of the triangle, is 25\sqrt325√ 3 25, square root of, 3, end square root. the triangle has a right angle at vertex uuu and an angle of \dfrac\pi6 6 π start fraction, pi, divided by, 6, end fraction at vertex rrr. given that the width, www, of the shaded triangle is about 50\sqrt{3}50√ 3 50, square root of, 3, end square root, what is the height, hhh, of the shaded triangle to the nearest tenth?
Answer:
37.5
Step-by-step explanation:
The line which marks the height 25\sqrt325
3
25, square root of, 3, end square root of the large triangle is vertical, and the base of the triangle is horizontal, so their intersection is a right angle. The angles in the large triangle add up to \piπpi, so the remaining angle is:
\qquad \begin{aligned} \pi - \dfrac\pi2 - \dfrac\pi6 =& \dfrac\pi3 \end{aligned}
π−
2
π
−
6
π
=
3
π
The original triangle L U R is shown, but now the length of segment U D is shown to be '25 times the square root of 3', and angle U L R is shown to have a measure of ' pi divided by 3' radians.
The original triangle L U R is shown, but now the length of segment U D is shown to be '25 times the square root of 3', and angle U L R is shown to have a measure of ' pi divided by 3' radians.
Hint #2
Looking at the left triangle ULDULDU, L, D, the hypotenuse length LULUL, U is:
\qquad \begin{aligned} \dfrac{25\sqrt3}{\sin\!\left({\Large\frac\pi3}\right)} \end{aligned}
sin(
3
π
)
25
3
Looking at the big triangle LURLURL, U, R, we see that the base length LRLRL, R is:
\qquad \begin{aligned} &\left(LU\right)\dfrac{1}{\sin\!\left({\Large\frac\pi6}\right)} \\ \\ =&\left(\dfrac{25\sqrt3}{\sin\!\left({\Large\frac\pi3}\right)}\right)\dfrac{1}{\sin\!\left({\Large\frac\pi6}\right)} \\ \\ =&\left(\dfrac{25\sqrt3}{ \quad\large\frac{\sqrt{3}}{2}\quad }\right)\dfrac{1}{ \quad\large\frac{1}{2}\quad } \\ \\ =&\left(\dfrac{25}{ \quad\large\frac{1}{2}\quad }\right)\dfrac{1}{ \quad\large\frac{1}{2}\quad } \\ \\ =&100 \\ \end{aligned}
=
=
=
=
(LU)
sin(
6
π
)
1
⎝
⎜
⎛
sin(
3
π
)
25
3
⎠
⎟
⎞
sin(
6
π
)
1
⎝
⎜
⎛
2
3
25
3
⎠
⎟
⎞
2
1
1
(
2
1
25
)
2
1
1
100
Hint #3
The large triangle has uniform thickness, so the inner triangle's sides are parallel to the outer triangle's sides. Therefore, the inner triangle's angles are congruent to the outer triangle's angles. The two triangles are similar.
Hint #4
Similar triangles have proportional lengths, so we can set up the equation:
\qquad \begin{aligned} \dfrac{h}{w} =& \dfrac{H}{W} \\ \\ \dfrac{h}{50\sqrt{3}} \approx& \dfrac{25\sqrt3}{100} \end{aligned}
w
h
=
50
3
h
≈
W
H
100
25
3
Hint #5
\qquad\qquad\, \begin{aligned} \dfrac{h}{50\sqrt{3}} \approx& \dfrac{\sqrt3}{4} \\ \\ {h} \approx& \dfrac{{50\sqrt{3}}\sqrt3}{4} \\ \\ {h} \approx& \dfrac{25\cdot3}{2} \\ \\ h \approx& 37.5 \\ \\ \end{aligned}
50
3
h
≈
h≈
h≈
h≈
4
3
4
50
3
3
2
25⋅3
37.5
Hint #6
To the nearest tenth, the height of the inner triangle is:
\qquad\qquad\, \begin{aligned} h \approx& 37.5 \end{aligned}
h≈
37.5
*note: The answers 37.337.337, point, 3 and 37.437.437, point, 4 may have been obtained by other methods of solving for hhh since this is an approximation. Those answers are also accepted as correct.
Two triangles are similar if the sides of both triangles can be represented as equivalent ratios. The height of the shaded triangle is 37.5 units.
Given that:
[tex]\overline{UD} = 25\sqrt 3[/tex]
[tex]w = 50\sqrt3[/tex]
See attachment
First, we calculate side length [tex]\overline{LD}[/tex].
This calculated using tangent trigonometry ratio
[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]
So, we have:
[tex]\tan(90-\frac{\pi}{3}) = \frac{\overline{UD}}{\overline{LD}}[/tex]
[tex]\tan(90-30) = \frac{\overline{UD}}{\overline{LD}}[/tex]
[tex]\tan(60) = \frac{\overline{UD}}{\overline{LD}}[/tex]
This gives:
[tex]\tan(60^o) = \frac{25\sqrt3}{\overline{LD}}[/tex]
Make LD the subject
[tex]\overline{LD}= \frac{25\sqrt3}{\tan(60^o)}[/tex]
[tex]\overline{LD}= \frac{25\sqrt3}{\sqrt 3}[/tex]
[tex]\overline{LD}= 25[/tex]
Next, we calculate side length [tex]\overline{DR}[/tex].
This calculated using tangent trigonometry ratio
[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]
So, we have:
[tex]\tan(\frac{\pi}{6}) = \frac{\overline{UD}}{\overline{DR}}[/tex]
This gives:
[tex]\tan(30^o) = \frac{25\sqrt3}{\overline{DR}}[/tex]
Make DR the subject
[tex]\overline{DR}= \frac{25\sqrt3}{\tan(30^o)}[/tex]
[tex]\overline{DR}= \frac{25\sqrt3}{1/\sqrt 3}[/tex]
[tex]\overline{DR}= 25\sqrt3 \times \sqrt 3[/tex]
[tex]\overline{DR}= 25 \times 3[/tex]
[tex]\overline{DR}= 75[/tex]
Calculate side length [tex]\overline{LR}[/tex]
[tex]\overline{LR} = \overline{LD}+\overline{DR}[/tex]
[tex]\overline{LR} = 25+75[/tex]
[tex]\overline{LR} = 100[/tex]
Because the triangle has a uniform thickness, the small and the big triangle are similar triangles.
So, the height (h) is calculated using the following equivalent ratios
[tex]h:w =\overline{UD}:\overline{LR}[/tex]
Express as a fraction
[tex]\frac hw =\frac{\overline{UD}}{\overline{LR}}[/tex]
Make h the subject
[tex]h =\frac{\overline{UD}}{\overline{LR}} \times w[/tex]
Substitute known values
[tex]h =\frac{25\sqrt3}{100} \times 50\sqrt 3[/tex]
[tex]h =\frac{3750}{100}[/tex]
[tex]h =37.50[/tex]
Hence, the height of the shaded triangle is 37.5 units.
Read more about similar triangles at:
https://brainly.com/question/16919171
Find the area of the trapezoid?
Answer:
Very simple 6th graders
Step-by-step explanation:
7 X 5 = 35 DIVIDE3D BY 2 = 17.5 THAT IS THE TRIANGLE BUT I CAN NOT SEE THE OTHER.
but i will still help
the number on the top needs to be multiplyed by the number on the side and then add it to the 17.5 and that is your answer
PLEASE HELP ILL GIVE BRAINLIEST
Answer:
The answer is 2
All lines that are parallel have the same slope
Answer:
the slope is (2)
Step-by-step explanation:
Two lines that are parallel to each other have the same slope so,
the equation y=2x+5 is in the form y=mx+c
where m is the slope of the line so if we compare both equations we can see that the slope of the line given will be 2 and therefore, the slope of the line parallel to it will be the same (2)
Paul graphed the equation y = 6 + x. Which point (x, y) does the graph NOT pass through?
Group of answer choices
(12, 20)
(6, 12)
(0, 6)
(9, 15)
Answer:
12,20
Step-by-step explanation:
That's the answer
Help please.
Angle SPR and angle RPQ are complementary. Find the measure of angle RPQ.
Answer:
53 degrees
Step-by-step explanation:
Complimentary angles are angles whose sum equals 90 degrees.
90-37 = 53
Answer:
m∠RPQ = 53°
53 degrees
Step-by-step explanation:
When two angles are complementary angles, it means they add up to 90 degrees (Ex: a 10° angle and 80° angle would be complementary).
Therefore, if ∠SPR and ∠RPQ are complementary, then
m∠SPR + m∠RPQ = 90°
since you are given that m∠SPR = 37°, you can plug that in for m∠SPR to find m∠RPQ:
m∠SPR + m∠RPQ = 90°
37° + m∠RPQ = 90°
m∠RPQ = 90° - 37°
m∠RPQ = 53°
Find the distance between the two points listed below.
(3,7) and (-5, -8)
Answer:
17Step-by-step explanation:
The formula of a distance between two points
[tex]A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}[/tex]
We have
[tex]A(3;\ 7);\ B(-5;\ -8)[/tex]
Substitute
[tex]|AB|=\sqrt{(-5-3)^2+(-8-7)^2}=\sqrt{(-8)^2+(-15)^2}\\\\=\sqrt{64+225}=\sqrt{289}=17[/tex]
10=2x - 4 what is the answer
Answer:
7
Step-by-step explanation:
10=2(7)-4
10=14-4
Solve 5x = 2. How many solutions does the equation have?
Answer:
As we can see, for infinite values of x, there are corresponding infinite values of y. Thus, the given equation has infinite solution.
Step-by-step explanation:
Answer:
one solution
Step-by-step explanation:
you can only multiply 5 by one number (0.4) to get 2
lmk if this doesn't make sense
10. Identify the pronoun in this sentence.
Everything we have done has been by the book.
answers
1: she
2:we
3:everything
4:by
Answer:
The answer is we. Pronouns are I, you, he/she/it, we, you, they.
Answer:
2:we.............
Which one of the following fractions is the largest?
5/6 1/3 3/2 5/2
Answer:
5/2
Step-by-step explanation:
Answer:
5/2 is the largest fraction.
Step-by-step explanation:
To find the largest fraction, we can convert some using the LCD (least common denominator)
Keep 5/6 as is.
1/3 = 2/6
3/2 = 9/6
5/2 = 15/6
So, 5/2 is the largest fraction.
The diagram shows three angles at a point. 168 x 123. Work out the value of x
Answer:
SOMEONE ANSWER THIS PLSSSSSSSSS :D
Step-by-step explanation:
The graph of the rational function f is shown. Which graph is the graph of g(x)=-f(x)?
Using translation concepts, it is found that graph A is equivalent to the graph of g(x)=-f(x).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The transformation g(x)=-f(x) is a reflection over the x-axis of function f(x), which is given by graph A.
More can be learned about translation concepts at https://brainly.com/question/4521517
#SPJ1
which step comes first -b-2<8
Answer:
Step-by-step explanation:
Alright so the step that comes first is adding two to both sides.
Let me show you,
Step 1
-b-2<8 Add 2 to both sides
-b<10
Then you divide the sides by -1
-b<10
b>-10
can sombody please answer this.
Answer:
option (3)is correct, take 180 +180=360
Step-by-step explanation:
I DON'T KNOW IF THIS IS CORRECT IM SORRY IF IT'S WRONG!!!!!!
A geometric figure is dilated by a scale factor of 1.5 with the origin as the center of dilation. Which of the following sentences best describes this dilation?
The x- and y-coordinates of every point of the figure is multiplied by 1.5.
Not here.
The y-coordinate of every point of the figure is multiplied by 1.5.
The x-coordinate of every point of the figure is multiplied by 1.5.
Answer:
Step-by-step explanation:
The x and y points are multiplied by 1.5
See the graph
Notice that if you start with (4,6) and dilate by a scale of 1.5 then the final point is (6,9)
The slope of these two points (if they were on a line should be 1.5
x2 = 6
x1 = 4
y2 = 9
y1 = 6
m = (9 - 6)/(6 - 4)
m = 3 / 2
m = 1.5 which is what it should be.
The x-coordinate of every point of the figure is multiplied by 1.5.
The scale factor is 1.5, and the center of dilation is the origin (0, 0).
When the figure is dilated by a scale factor of 1.5 with the origin as the center, it means that each point's x-coordinate and y-coordinate are separately multiplied by 1.5.
The y-coordinate of every point of the figure is multiplied by 1.5 is not correct the reason is that in this specific dilation scenario, only the x-coordinate is multiplied by 1.5, while the y-coordinate remains the same. The origin as the center of dilation means that the points move away from or towards the origin, maintaining the same vertical distance.
Therefore, the correct description is "The x-coordinate of every point of the figure is multiplied by 1.5."
To learn more on Dilation click:
https://brainly.com/question/29811168
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Please solve the quadratic equation in 4 steps
x^2-14x+49=5
Answer:
=7±5√
Step-by-step explanation:
is easy and no hard
find the slope of the line pictured
At the city museum, child admission is $5.30 and adult admission is $8.60. On Wednesday, 155 tickets were sold for a total of $1049.20. How many adult tickets were sold that day
Answer:
122 adults
Step-by-step explanation:
1049.20(price of tickets sold)÷8.60(ticket price per adult)=122
Angles B and C are called _________ angles.
A. Complimentary
B. Linear
C. Supplementary
D. Vertical
Please help I’ll give brainliest
Answer:
$3.29
Step-by-step explanation:
You need to find the unit price by dividing the cost by the amount.
24.33/7.4 = 3.29
Therefore, one pound of ham is $3.29.
Answer:
1. $3.29
2. $4.60
Step-by-step explanation:
how many pounds are in 8 kilograms?
1kg = 2.2Ibs
8kg = ? Ibs
Answer:
17.6 lbs
1kg=2.2lbs
Multiply each side by 8
8kg=17.6 lbs
Step-by-step explanation:
So heres the short answer: 8kg = 17.637 lbs
Hope it helps!!
The quantity 8 kilograms can be written in pounds as 17.6 pounds.
The given quantity is 8 kilograms.
Metric Conversion refers to the conversion of the given units to desired units for any quantity to be measured.
We know that 1 kg = 2.2 pounds
Here, 8 kg = 8×2.2
= 17.6 pounds
Therefore, the quantity 8 kilograms can be written in pounds as 17.6 pounds.
To learn more about the metric conversion visit:
brainly.com/question/21244256.
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Can yall check if I did this correct plus I will give you brainliest if you answer no joke promise❤
y = 3x do this fast plz
Answer:
Step-by-step explanation:
Given there's 5 red balls and 2 blue balls. What's the probability that after two picks we have a red ball and a blue ball
Answer:
the answer is 58 dear because there he couldn't figure out what he meant
write two mixed so that all rules are applied: one number is larger than the other by 4 2/3, the difference of the numbers is equal to the smaller number, and the sum of the differences is a natural number
Answer:
write 2 mixed whats
Step-by-step explanation:
Can someone help me answer this question
Answer: (C) 25 lawns
Step-by-step explanation: he has 15 cars so his you follow the line from the graph it will end at 25 lawns
sorry this is a bad explanation but C is correct-
A small glass holds about 250 what ?
litros de agua porque nolose pero quiero los pùntos
I can find the common denominator of fractions with unlike denominators.
A.
strongly agree
B.
agree
C.
disagree
D.
strongly disagree
Answer:
C. Disagree
HOPE IT HELPEDStep-by-step explanation:
Expand and simplify 4(2x +7) – 3(x + 5)
Answer:
The answers is 5x + 13
It Equal to 5x + 13
Find the value of r. I have no clue.
Answer:
12
Step-by-step explanation:
18 - 2r and 4r are the same length so the equation would be:
18 - 2r = 4r
Move the 2r to the other side
18 = 6r
Divide it by 6 to get r by itself
r = 3
