The two triangles are similar.
What is the value of x?
Enter your answer in the box.
X=
Answer:
x = 5
Step-by-step explanation:
Looking at the ratios of height to base:
Smaller triangle 3x + 1 : 12
Larger triangle 4x : 3 + 12 = 4x : 15
Therefore as triangles are similar:
3x + 1 : 12 = 4x : 15
Write as fractions:
⇒ [tex]\dfrac{3x+1}{12}=\dfrac{4x}{15}[/tex]
Cross multiply and solve for x:
⇒ 15(3x + 1) = 12 · 4x
⇒ 45x + 15 = 48x
⇒ 15 = 3x
⇒ x = 5
Ratio remains same
[tex]\\ \tt\Rrightarrow \dfrac{3+12}{4x}=\dfrac{12}{3x+1}[/tex]
[tex]\\ \tt\Rrightarrow \dfrac{15}{4x}=\dfrac{12}{3x+1}[/tex]
[tex]\\ \tt\Rrightarrow 15(3x+1)=12(4x)[/tex]
[tex]\\ \tt\Rrightarrow 45x+15=48x[/tex]
[tex]\\ \tt\Rrightarrow 3x=15[/tex]
[tex]\\ \tt\Rrightarrow x=5[/tex]
I need to find out the leng of XZ
Answer:
16.84?
Step-by-step explanation:
12.6/cos(29)=16.84
Graph -9x+6y=18−9x+6y=18minus, 9, x, plus, 6, y, equals, 18.
please help fast! I have no idea what I'm supposed 2 do
Answer:
Constant of proportionality: [tex]\frac{1}{3}[/tex]
Equation: [tex]y=\frac{1}{3}x[/tex]
Step-by-step explanation:
The constant of proportionality is the ratio between y and x, according to the following formula
constant of proportionality = k = y/x
Take the given pairs and replace the data.
1.
[tex]k=\frac{\frac{2}{3}}{2}[/tex]
[tex]k = \frac{1}{3}[/tex]
2.
[tex]k = \frac{1}{3}[/tex]
3.
[tex]k=\frac{\frac{10}{3}}{10}[/tex]
[tex]k = \frac{1}{3}[/tex]
4.
[tex]k = \frac{4}{12}[/tex]
[tex]k = \frac{1}{3}[/tex]
As you can see, the constant is the same for all the pairs.
constant of proportionality = [tex]\frac{1}{3}[/tex]
Now, in order to know the equation make a graph of the given data.
The graph is in the picture
Since it is a line, use the equation of the line in point slope form
[tex]y- { y }_{ 1 } = m \left( x- { x }_{ 1 } \right)[/tex]
where (x1, y1) = any pair of the data
m = slope = constant of proportionality
Replace the data in the equation
[tex]y-1 = \dfrac{ 1 }{ 3 } \left( x-3 \right)[/tex]
Use the distributive property to multiply [tex]\frac{1}{3}[/tex] by x - 3
[tex]y-1=\frac{1}{3}x-1[/tex]
Add 1 to both sides
[tex]y = \dfrac{ 1 }{ 3 } x-1+1[/tex]
Add −1 and 1 to get 0
[tex]y=\frac{1}{3}x[/tex]
or
[tex]y=\frac{x}{3}[/tex]
need help with simplify root square
Answer:
Step-by-step explanation:
[tex](\sqrt{24b^{3} } )(\sqrt{40b^{2} } )(\sqrt{b^{2} } )=(2b\sqrt{6b})(2b\sqrt{10} )(b)[/tex]
[tex]=4b^{3} (\sqrt{6b})(\sqrt{10} )[/tex]
Hope this helps
12. Tina hanged 20 lanterns at an equal distance apart on a string as shown below. The distance between the 1st lantern and the 5th lantern is 80 cm. Find the distance between the 1st and the last lantern.
an equal distance = arithmetic sequence
xn= a+d(n-1)⇒ x₁ = a
x₅ - x₁ = 80
x₁ + 4d - x₁ = 80
4d = 80
d = 20 cm
x₂₀ - x₁ = x
x₁ + 19d - x₁ = x
19d = x
19.20 = 380
You load boxes onto an empty truck at a constant rate. After 3 hours, there are 100 boxes on the truck. How much longer do you work it you load a total of 120 boxes? You work hour(s) longer Justify your answer
Answer:
36 minutes
Step-by-step explanation:
100 boxes in 3 hours is a rate. It is how fast you are working in boxes per hour 100/3 boxesperhour.
But 3 doesn't go into 100 very neatly and its going to make all kinds of ugly fractions or decimals. But lets look at minutes. 3 hours is 3 × 60 minutes (bc there's 60 minutes in an hour) So you loaded 100 boxes in 180 minutes. That's 100/180 boxes per minute.
100/180 = 10/18
10/18 means 10 boxes in 18 minutes.
So times 2 on the top and the bottom gives you 20/36.
20/36 means 20 boxes in 36 minutes.
This is your answer. It will take 36 minutes to load 20 more boxes.
Here are 10 numbers 3,7,2,4,7,5,7,1,8,8,
A) write down the mode
B) work out the median
C) calculate the mean
D) what is the range
Can you please help me???
Question:
If x =
[tex] \frac{ \sqrt[3]{m + 1{ }} + \sqrt[3]{m - 1} }{ \sqrt[3]{m + 1} - \sqrt[3]{m - 1} } [/tex]
Then the value of x³-3mx²+3x is:
No link please, Tq
[tex] \text{Given Equation is } \frac{x}{1} = \frac{ \sqrt[3]{m + 1{ }} + \sqrt[3]{m - 1} }{ \sqrt[3]{m + 1} + \sqrt[3]{m - 1} }[/tex]
[tex]\text{On Applying componendo and dividendo, we get:-}[/tex]
[tex] \frac{x + 1}{x - 1} = \frac{( \sqrt[3]{m + 1} + \sqrt[3]{m - 1} )+ ( \sqrt[3]{m + 1}) - \sqrt[3]{m - 1} }{ (\sqrt[3]{m + 1} + \sqrt[3]{m - 1}) - ( \sqrt[3]{m + 1}) - \sqrt[3]{m - 1} } [/tex]
[tex] \implies \: \frac{x + 1}{x - 1} = \frac{2( \sqrt[3]{m + 1)} }{2( \sqrt[3]{m - 1)} } \\ \\ \implies \frac{ x + 1}{x - 1} = \frac{ \sqrt[3]{m + 1} }{ \sqrt[3]{m - 1} } [/tex]
[tex] \text{On Cubing both sides, we get} \\ \frac{(x + 1) {}^{3} }{(x - 1) {}^{3} } = \frac{m + 1}{m - 1} [/tex]
[tex]\text{Again, Applying componendo and dividendo, we get:-}[/tex]
[tex] \frac{(x + 1) {}^{3} + (x - 1) {}^{3} }{(x + 1) {}^{3} - (x - 1) {}^{3} } = \frac{m + 1 + m - 1}{m + 1 - (m - 1)} [/tex]
[tex] \implies \frac{ {x}^{3} + 1 {}^{3} + 3 {x}^{2} \times 1 + 3x \times {1}^{2} + ( {x}^{3} - 1 {}^{3} - 3x {}^{2} \times 1 + 3x \times 1 {}^{2} ) }{x {}^{3} + 1 {}^{3} + 3 {x}^{2} \times 1 + 3x \times {1}^{2} - (x {}^{3} - 1 {}^{3} - 3 {x}^{2} \times 1 + 3x \times {1}^{2}) } = \frac{2m}{2} [/tex]
[tex] \implies \frac{2x {}^{3} + 6x}{ {6x}^{2} + 2 } = \frac{m}{1} [/tex]
[tex] \implies \frac{2(x {}^{3 } + 3x) }{2(3 {x}^{2} + 1) } = \frac{m}{1} [/tex]
[tex] \implies \: x {}^{3} + 3x = 3m {x}^{2} + m \\ \\ \implies {x}^{3} - 3mx {}^{2} + 3x \\ = m[/tex]
Hope This Helps!!
Based on the calculations, the value of [tex]x^3-3mx^2+3x[/tex] is equal to m.
Given the following data:
[tex]x=\frac{\sqrt[3]{m+1} +\sqrt[3]{m-1}}{\sqrt[3]{m+1} +\sqrt[3]{m-1}}[/tex]
How to evaluate the fraction.In order to simplify the given mathematical expression, we would apply the componendo and dividendo rule because it would the number of expansions as follows:
[tex]\frac{x}{1} =\frac{\sqrt[3]{m+1} +\sqrt[3]{m-1}}{\sqrt[3]{m+1} -\sqrt[3]{m-1}}\\\\\frac{x+1}{x-1} =\frac{(\sqrt[3]{m+1} +\sqrt[3]{m-1})+(\sqrt[3]{m+1} -\sqrt[3]{m-1})}{(\sqrt[3]{m+1} +\sqrt[3]{m-1})-(\sqrt[3]{m+1} -\sqrt[3]{m-1})}\\\\\frac{x+1}{x-1} =\frac{\sqrt[3]{m+1} +\sqrt[3]{m-1}+\sqrt[3]{m+1} -\sqrt[3]{m-1}}{\sqrt[3]{m+1} +\sqrt[3]{m-1}-\sqrt[3]{m+1} +\sqrt[3]{m-1}}\\\\\frac{x+1}{x-1} =\frac{2(\sqrt[3]{m+1})}{2(\sqrt[3]{m-1})} \\\\\frac{x+1}{x-1} =\frac{\sqrt[3]{m+1}}{\sqrt[3]{m-1}}[/tex]
Taking the cube of both sides, we have:
[tex](\frac{x+1}{x-1})^3 =(\frac{\sqrt[3]{m+1}}{\sqrt[3]{m-1}})^3\\\\\frac{(x+1)^3}{(x-1)^3}=\frac{m+1}{m-1}[/tex]
Applying the componendo and dividendo rule, we have:
[tex]\frac{(x+1)^3+(x-1)^3}{(x-1)^3-(x-1)^3}=\frac{m+1+(m-1)}{m-1-(m-1)}\\\\\frac{(x+1)^3+(x-1)^3}{(x-1)^3-(x-1)^3}=\frac{2m}{2} \\\\\frac{(x+1)^3+(x-1)^3}{(x-1)^3-(x-1)^3}=m\\\\\frac{2x^3+6x}{6x^2+2} =m\\\\\frac{2(x^3+3x)}{2(3x^2+1)} =m\\\\\frac{x^3+3x}{3x^2+1} =m\\\\x^3+3x=m(3x^2+1)\\\\x^3+3x=3mx^2+m\\\\x^3-3mx^2+3x=m[/tex]
Read more on componendo and dividendo here: https://brainly.com/question/134857
someone please help me! i will mark brainliest if i can
Answer: 19.8x - 11.1y
Step-by-step explanation: you’re welcome:)
Again lol
Help pls!
The sum of -9 and a number
A) -9-x
B)-9/x
C) 9 + x
D) -9x
Answer:
C) 9 + x is the answer
Step-by-step explanation:
sum means to add
Hey there!
Guide:
• Sum means add/addition
• Difference means subtract/subtraction
• Product means multiply/multiplication
• Quotient means divide/Division
So, let’s answer your given question.
Key terms in your word problem
“The SUM of -9 and a NUMBER”
Sum is to add and Number is to unknown so we can label it as “x”
Your equation/answer should be:
-9 + x
Because you’re adding -9 to your unknown number (x)
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
CORRECT ANSWER GETS BRAINLIEST
Answer:
x=30 degrees
If you replace the x with 30, it will all equal 180 which is the total you should get when making the triangle in a straight line. (not good english)
a student writes an innocent step while checking if the sum of the measures of the two remote (50 POINTS) HURYYY PLS
Answer:
Step 3 is right answer.
Step-by-step explanation:
He is substituting the values wrong. His 2nd step is right but as he moved to the 3rd step he put measure of angle n instead if measure if angle o
So Step 3 is right answer.
The figure shows a rectangle ABCD where the diagonals AC and BD intersect at E.
Given that BEC = 52°, find
(I) ADB
(ii) ACD
Answer:
(i) 64°
(ii) 26°
Step-by-step explanation:
Answer:
(i) m<ADB = 64°
(ii) m<ACD = 26°
Step-by-step explanation:
I use this to mean the measure of angle ADC: m<ADC
(i)
m<BEC = 52°
<DEA and <BEC are vertical angles, so they are congruent.
m<DEA = m<BEC = 52°
Polygon ABCD is a rectangle. When the diagonals, AC and BD, of a rectangle are drawn, 4 triangles are formed. Each two opposite triangles are congruent, and all 4 triangles are isosceles.
Triangle ADE is an isosceles triangle with congruent sides ED and EA. That makes opposite angles ADB and DAC congruent. Also the sum of the measures of the angles of a triangle is 180°.
m<ADB + m<DAC + m<DEA = 180°
m<ADB = m<DAC; m<DEA = 52°
2m<ADB + 52° = 180°
2m<ADB = 128°
m<ADB = 64°
(ii)
Angles DEC and BEC form a linear pair. That means the angles are supplementary, and the sum of their measures is 180°.
m<DEC + m<BEC = 180°
m<DEC + 52° = 180°
m<DEC = 128°
Triangle DEC is an isosceles triangle with congruent sides ED and EC. That makes opposite angles ACD and BDC congruent.
m<ACD + m<BDC + m<DEC = 180°
2m<ACD + 128° = 180°
2m<ACD = 52°
m<ACD = 26°
JOSHUA ORDERED A NEW PAIR OF NIKES ONLINE FOE $168 AND 2 HATS FOR $39 EACH HIS SHIPPING FEE IS 10% OF HIS TOTAL PURCHASE RICE HOW MUCH WILL JOSHUA PAY ALTOGETHER
Answer:
Joshua is paying a total of $270.60.
Step-by-step explanation:
Info that we have:
Pair of Nikes is $168.
2 hats for $78. (Not 39 because the question said $39 for each).
Shipping fee is 10% of total purchase.
We need to add up the cost.
168 + 78 = $246
Find how much is 10%.
10% of 246 = 24.6
Add the shipping fee to the total.
246 + 24.60 = 270.60
Answer:
Joshua is paying a total of $270.60.
Info that we have:
Pair of Nikes is $168.
2 hats for $78.
Shipping fee is 10% of total purchase.
The length of a rectangular table is represented by the function L(x) = 3x The width of the table is represented by the function (x) = 4x2 - 6x +5. What is the area of the table in terms of 2
O LOW)(x) = 7x2-3x+8x
O (LOW)(x) = 122-18x+15
O (LW) = 122-182? +15x
O LOW)(x) = 122 +182 +15x
from the conclusion that I'm of and dont I feel like the answer is letter C I'm not sure
Trisha had the following seven distances (in feet) in the triple jump.
29, 30, 28, 32, 28, 31, 27
What was the interquartile range of her distances?
1
2
5
3
Answer:
5 is your answer sweetheart
Step-by-step explanation:
We know that the range to a data set is the difference between the maximum data value and the minimum data value .
The given data set : 29, 30, 28, 32, 28, 31, 27
Maximum value = 32
Minimum value = 27
Then , the range the given data set would be :-
\begin{gathered}\text{Range = Maximum-Minimum}\\\\\Rightarrow\text{Range}=32-27=5\end{gathered}Range = Maximum-Minimum⇒Range=32−27=5
Hence, the range of her distances = 5
Answer:
5
Step-by-step explanation:
Miguel paid a total of $12,000 for stock that was $8 per share. If he sold all his shares for $15,000, how much profit on each share did he make? a. $2 b. $8 c. $10 d. $12 Please select the best answer from the choices provided A B C D.
Answer: 10
Step-by-step explanation:
Miguel paid a total of $12,000 stock that was $8 per share. That's $1,500 you make. 15,000 that was $8 per share. That's $1,875. I dont know if the answer is right, but I wish you well
please educated people solve my question i have reposted for the 4th time now...
Answer: i think that picture 2 is b
Step-by-step explanation:
Type the integer that makes the following addition sentence true:
- 6 + = −8
Answer:
-2
-Step-by-step explanation:
As, -6+(-2)= -6-2=-8
Thus, solved.
Hope it helps...
WILL CHOOSE BRAINLIEST
Without solving, identify whether this equation has a solution that is positive, negative, or zero:
3 x − 5 = - 3
Solve the equation.
x − 5 ( x − 1 ) = x − ( 2 x − 3 )
Fiona enlarges a parallelogram that has a perimeter of 17 meters. A small parallelogram has a left side length of 3. 5 meters. A larger parallelogram has a left side length of 21 meters. Not drawn to scale What is the perimeter of the enlarged parallelogram? 30 meters 73. 5 meters 102 meters 105 meters.
Answer:D
Step-by-step explanation:got it right on my test
Answer:
The answer is C i got a 100 on the test
Step-by-step explanation:
find the measure of angle A of the following triangle
Answer:
θ ≈ 48.2°
Step-by-step explanation:
The trig function that relates the angle, adjacent side, and hypotenuse is ...
Cos = Adjacent/Hypotenuse
This tells you ...
cos(θ) = 6/9
The angle is found from the cosine value using the inverse cosine function.
θ = arccos(6/9) ≈ 48.2°
Angle A is about 48.2°.
Help please, will give brainliest!!
Answer:
[tex]{2}^{3} = 2 \times 2 \times 2 = 8[/tex]
Step-by-step explanation:
*We're focusing on 2 to the power of 3.
2^3 is represented as 2 x 2 x 2, 2 is being multiplied by itself 2 times.
When we multiply, we find the product of 8.
Therefore,
[tex] {2}^{3} = 2 \times 2 \times 2 = 8[/tex]
Ratio of girls to boys is 2:3. How many boys if there are 56 girls?
Answer:
78 boys
Step-by-step explanation:
If the ratio is 2:3 that means there are 5 equal parts
56/2= 28
3 x 28 = 78
Therefore there are 78 Boys
56:78
[RevyBreeze]
A customer bought a soda and 2 hot dogs for 7$. Another customer bought a soda and 4 hot dogs for $12.
What is the rate of change?
What is the initial value
s + 2h = 7
s + 4h = 12
s = 12 - 4h
12 - 4h + 2h = 7
- 2h = -5
2h = 5
hotdog = $2.50
s = 12 - 10
soda = $2
The midpoint of AB is M(2, 0) If the coordinates of A are (-3, 3) what are the coordinates of B
Answer:
(7, -3)
Step-by-step explanation:
If M is the midpoint you can use the same translation from A to M as M to B.
The movement from A to M is 5 units up and 3 units left, or (x+5, y-3). If we do the same movement to point M (Which is (2) +5, (0) -3) we will get (7, -3).
Answer:
the coordinates of B is B(7,-3)
Step-by-step explanation:
Solution,
Here, M(2,0) is the midpoint of a line segment joining the points A(-3,3)
and B(a,b)
Let,
(x,y)=(2,0)
(x1,y1)=(-3,3)
(x2,y2)=(a,b)
Now,
Using midpoint formula
[tex]x=\frac{x_1+x_2}{2} ,y=\frac{y_1+y_2}{2} \\\\2=\frac{-3+a}{2} ,0=\frac{3+b}{2} \\\\[/tex][Cross multiply]
[tex]4=-3+a,0=3+b\\\\4+3=a,0-3=b\\\\a=7,b=-3[/tex]
Riley has 300 stamps. 20% are from Russia 18% are for Europe 38% are from Australia the rest are from North America. How many of his stamps are from North America
Answer: 135%
Step-by-step explanation: Given
Europe = 35%
Asia = 10%
Australia* = 20%
North America = ?
To find
Europe + Asia + Australia =
35% + 10% + 20% = 65%
Then the total subtracted from the given
200 - 65 = 135
Therefore,
North America = 135%
Confirm
To make sure that is the correct answer, add it all together.
35 + 10 + 20 + 135 = 200
Which means it is correct.
Need help solving this equation
Answer:
no solution
Step-by-step explanation:
this statement states y=y
-x+3 is not equal to -x+5
I’ll give points to correct answer !!!!!
Answer:
i think the answer is 12
Step-by-step explanation: