The two triangles are similar. What is the value of x? Enter your answer in the box. x = Two right triangles, one smaller than the other, back to back, so that their right angles form a straight angle. The two acute angles along the straight angle are congruent to each other. The overlapping part of the legs is labeled 12. The part of the overlapping side that extends above the smaller triangle is labeled 3. The leg of the smaller triangle that is a ray of the straight angle is labeled 3 x plus 1. The leg of the larger angle that is a ray of the straight angle is labeled 4 x.
Answer:
The two triangles are similar.
What is the value of x?
Enter your answer in the box.
x=
The value of x is 7 units.
What is Similarity of Triangles?Two triangles are said to be comparable if their two sides are in the same ratio as the two sides of another triangle and their two sides' angles inscribed in both triangles are equal.
Given :
AD = 6 units , BD = 8 units, m∠ABC = m∠DBE = 90° and
∠DEB ≅ ∠ACB
Now, AB = AD + BD
= 8 + 6 = 14 units
Now, In ΔABC and ΔDBE,
∠DBE = ∠ABC ( Each of 90° )
∠DEB = ∠ACB ( given )
So, By using AA postulate of similarity of triangles , ΔABC ~ ΔDBE
Now, proportion of the corresponding sides will be equal.
AD/ DB= BC/ BE
14/8 = 3x/ 2x-2
4x= 28
x= 7
Hence, the value of x is 7 units.
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James inherited 19.5hectares of land from his father. The area of the land he inherited is 65% of the total land his father owned. Calculate the total area of the land that his father owned
Answer:
30 hectares
Step-by-step explanation:
Answer:
Step-by-step explanation:
Land area James inherited = 19.5 hectares
The area of the land he inherited is 65% of the total land his father owned.
Let
x = Total land his father owned
Land area James inherited = 65% of the total land his father owned
19.5 = 65% of x
19.5 = 65/100 * x
19.5 = 0.65 * x
19.5 = 0.65x
x = 19.5 / 0.65
x = 30
x = Total land his father owned = 30 hectares
Find the missing length indicated
Answer:
x = 240
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
( leg of big Δ )² = ( part of hypotenuse below it ) × ( whole hypotenuse )
x² = 144 × 400 = 57600 ( take the square root of both sides )
x = [tex]\sqrt{57600}[/tex] = 240
The area of the given shape above is?
A.20ft2
B.84ft2
C.400ft2
D.40ft2
E.10ft2
Answer:
B. 84 ft²
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Area of a Rectangle Formula: A = lw
l is lengthw is widthStep-by-step explanation:
Step 1: Define
Identify variables
l = 14 ft
w = 6 ft
Step 2: Find Area
Substitute in variables [Area of a Rectangle Formula]: A = (14 ft)(6 ft)Multiply: A = 84 ft²Determine if the function f is an exponential function. If so, identify the base. If not, why not? f(x) = x^e
Answer:
It is not exponential because it is f(x)= x-3.141.
Step-by-step explanation:It is a slope-intercept formula. An exponential formula is y=a^x
What are the solutions of X^2-8+16=11
Answer:
x = ±√3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsSolving quadraticsStep-by-step explanation:
Step 1: Define
Identify
x² - 8 + 16 = 11
Step 2: Solve for x
Combine like terms: x² + 8 = 11[Subtraction Property of Equality] Subtract 8 on both sides: x² = 3[Equality Property] Square root both sides: x = ±√3A PE teacher has to organise two year groups into netball teams, each separately. Year 7 has 70 students and Year 8 has 98 students. If each year group must be split up equally into teams all of the same size, what is the largest team size she can use?
Answer:
14
Step-by-step explanation:
Find HCF
Year 7: 70 students
7x5x2=70
Year 8: 98 students
7x7x2=98
HCF: 14
The largest team size she can use is 14 students.
Grade 7: 5 teams
Grade 8: 7 teams
Brainliest please, thanks!
two angles ina triangle have measures of 20 degrees and 50 degrees. whats the measure of the third angle?
70, 30, 120, or 110 dggrees?
Answer:
Step-by-step explanation:
All the triangle's angles measure adds up to a total of 180º
Jada bought a bag
for its 75 and
sold for 85.did she Profit or lose
❀ [tex]\huge\underline{ \underline{ \tt {ANSWER :-}}}[/tex]
⁺˚*･༓☾✧.* ☽༓･*˚⁺‧
⟹ Jada will have a profit because she sold the bag for money than she had bought it for.
[tex]85 - 75 \\ = 10[/tex]
⟹ She'll have about 10 (currency name) as the profit.
⁺˚*･༓☾✧.* ☽༓･*˚⁺‧
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ ツ
[tex]\underbrace{ \overbrace{ \tt{Carry \: On \: Learning}}}[/tex]
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
which expression gives the volume of a sphere with radius 4
Answer:
Expression would be (4/3) (π) (4^3)
Equation would be V = (4/3) (π) (4^3)
Step-by-step explanation:
Just plug in the radius into the volume formula!
Jerry lives in a city where all the roads are organized into square blocks and the roads either run North/South or East/West (forming a big square grid). Jerry goes out walking one day. He starts by walking 3 blocks North and then 4 blocks East. Jerry next walks 2 blocks South and 1 block West, when he realizes it is getting late and he must get home quickly. If Jerry walks on the roads home using as few blocks as possible, how many blocks will it take?
Answer:
it will take Jerry 4 blocks to get home. 3 blocks West and 1 block South
Step-by-step explanation:
We use our vector notation to describe the problem. Since Jerry walks 3 blocks North, he moves in the direction 3j. He then walks 4 blocks East in the direction 4i. He walks 2 blocks South in the direction -2j and 1 block West in the direction -i.
So, his position vector r = 3j + 4i - 2j - i = 4i - i + 3j - 2j = 3i + j.
Now if we assume his home was at the origin, then his initial position r₀ = 0i + 0j
Since he is supposed to return home from his current position, his displacement is final position - initial position = r₀ - r = 0i + 0j -(3i + j) = 0i - 3i + 0i - i = -3i - j
Since -i means movement in the West direction, -3i means movement 3 blocks West.
Since -j means movement in the Southern direction, -j means movement 1 blocks South.
So, it will take Jerry 1 + 3 blocks = 4 blocks to get home. 3 blocks West and 1 block South
what is advertising used for? check all that apply
Plz help me!!!!!!!!! Whoever solves correct will mark brainlist
Answer:
in picture
Step-by-step explanation:
Brainliest please~
Need help!! Plz show work
Answer:
19,000
Step-by-step explanation:
because for 1 year its 19,000 just for that year so it would be 19,000
Atividade 12 Observe o sistema de equações abaixo. {m−3n=16m+5n=−8 Quais são os valores de "m" e "n" que satisfazem esse sistema de equações? m=1en=3. m=7en=–3. m=52en=–12. m=–20en=–12.
Responder:
m = 7; n = - 3
Explicação passo a passo:
Dada a equação:
m − 3n = 16m + 5n = −8
Resolvendo a equação:
m − 3n = 16 - - - (1)
m + 5n = - 8 - - - (2)
Subtraia 1 de 2
m - m - 3n - 5n = 16 - - 8
-3n - 5n = 16 + 8
-8n = 24
n = 24 / - 8
n = - 3
Coloque n = - 3 em (1)
m − 3n = 16
m - 3 (-3) = 16
m + 9 = 16
m = 16 - 9
m = 7
A passenger traveling by air is allowed a maximum of 20kg luggage. A man has 4 bags weighing 3.5kg , 15kg, 2kg, 1.5kg. Find the excess weight of the luggage. Express the excess weight as a percentage of the maximum weight
Answer:
The passenger's luggage has an excess weight of 2 kg, which is 10% of the maximum weight.
Step-by-step explanation:
First, we need to find the weight (W) of the 4 bags:
[tex] W = 3.5 kg + 15 kg + 2 kg + 1.5 kg = 22 kg [/tex]
Now, knowing that the maximum allowed (M) is 20 kg the excess weight of the luggage is:
[tex] W_{e} = W - M = 22 kg - 20 kg = 2 kg [/tex]
We can express the excess weight in percentage as follows:
[tex] \% W_{e} = \frac{W_{e}}{M} \times 100 = \frac{2 kg}{20 kg}\times 100 = 10 \% [/tex]
Therefore, the passenger's luggage has an excess weight of 2 kg, which is 10% of the maximum weight.
I hope it helps you!
2. suppose the ping pong balls in shoe box a are larger than those in shoes box b would be easy to tell which one has the greater volume? why?
Answer:
Box A have greater volume because it will be having more mass than Box B
can someone help please? i don’t know the answer.
Answer:
C) 119.75 + 2.25p <= 500; p <= 169
Step-by-step explanation:
My friend, for this problem you must realize that there is a fixed cost of 119.75 that we add always. Then $2.25 per pastry manufactured is also part of the total costs. Thus, we add both of them where p represents pastry to get 119.75 + 2.25p.
But, the question says the shopkeeper would like to stay under or be exactly at $500 for total costs. Thus, for this inequality, we set this equation as being less than equal to 500.
Solve for p by adding 119.75 on both side and dividing both sides by 2.25 afterwards and you get 169.
find the slope of the line
Answer:
Slope = 4
Step-by-step explanation:
Consider two set of point through which the line passes.
Let it be ( 0, 4 ) and ( -1 , 0)
Find slope .
[tex]Slope = \frac{rise}{run } = \frac{y_2 - y_ 1 }{x_2 - x_1} , \ where \ \ (x_1 , y_1) = (0, 4 ) \ and \ (x_2, y _ 2) = ( -1 , 0 )[/tex]
[tex]Slope = \frac{0-4}{-1-0} = \frac{-4}{-1} = 4[/tex]
I’m a failed in math lol
Help me I have more pls
Answer:
y= 2/3x +4
Step-by-step explanation:
choose 2 points to find slope
I chose points of intersection
(-6,0) (0,4)
m=y2-y1/x2-x1
[tex]m = \frac{4 - 0}{0 - ( - 6)} = \frac{2}{3} [/tex]
then use slope point form rule
y-y1=m(x-x1)
[tex]y - 4 = \frac{2}{3} (x - 0) \\ \\ y = \frac{2}{3} x + 4[/tex]
Answer:
y = [tex]\frac{2}{3}[/tex] x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-6)}[/tex] = [tex]\frac{4}{0+6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
The line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = [tex]\frac{2}{3}[/tex] x + 4 ← equation of line
Find f ′(x) for f(x) = cos (5x2).
Answer:
I think its No Solution
Step-by-step explanation:
Hope it helps
Find two integers whose sum is -23 and product is 132
Step-by-step explanation:
Let x and y be two integers
x * y = 132
x + y = -23
x= -23 - y
y(-23 - y) = 132
-23y - y^2 = 132
y^2 +23y + 132 = 0
(y + 11) (y + 12) = 0
y = -11 or - 12
If y = -11 then x + (-11) = -23 -> x = -12
If y = -12 then x + (-12) = -23 -> x = -11
So the two integers are -11 and -12
A monkey is trying to scale a tree That is 6O feet tall. Each minute, the monkey... -Goes up three feet -But, slips down two feet How long will it take the monkey to get to the top of the tree?
Answer:
58 Minute
Step-by-step explanation:
According to the Question,
Given, A monkey is trying to scale a tree That is 6O feet tall. Each minute, the monkey Goes up three feet But, slips down two feet.Therefore, he climbs (3-2)1 Foot in 1 minute. Now at 57minute, he scales 57feet.
Now, at the 58th minute, he climbs 3 feet MoreThus 57 feet + 3 feet = 60feet( Reached the Top of the tree Now he Never Fall again)
the monkey will take total 58 minutes to get to the top of the tree.What is the product of 4xy and y^2 + 2x
Answer:
C
Step-by-step explanation:
4xy(y^2 + 2x) Remove the brackets (distributive law)
4xy^3 + 8x^2y
You have to turn the two terms around to see the correct answer. That's perfectly alright when dealing with addition of pluses.
8x^2y + 4xy^3
chadwick contributes 17% of his 68,000 annual salary to his 401(k)plan.What is his pre-tax income?
Which equation represents g(x)? The graph of g(x) is a translation of y = x. Ту O g(x) = 3-4 5 O g(x) = 3/x+4 4 3 O g(x) = 5x + 1.5 2 000). 1 O g(x) = 3x - 1.5
Hi there!
Before we get into translation or transformation of a graph. Let's understand how the graph of cube root of x looks like.
1. How does an original graph, or a graph without any translations look like?
They just look like in attachment as only in a shape of graph. The only difference is how the graph shifts. As you see in the attachment that the graph shifts to 4 units from 0. That means the graph of cube root of x intersects at (0,0) or origin point instead of (4,0). Since the shown graph shifts to right 4 units and intersect at (4,0). What do you think the equation for the graph would be? Let's find out below!2. Translations/Transformation of the graph.
Have you got an equation or the answer in your mind yet? Let's say... when you shift the graph to right 4 units which equal to x = 4, the graph finally intersects the x-axis plane or y = 0. Thus making the relation for x and y (4,0). What we have to do is to substithte x = 4 and see which equation result in pure 0.3. Conclusion and Answer
If you have already gotten the answer before reading this then congratulations! If you are confident that it is correct though. So the equation that makes x = 4 and y = 0 would be the first equation because when we substitute x = 4, it becomes cube root of 4-4 which becomes 0. Hence, the equation for the graph is cube root of x-4 or the first choice!I hope this helps! Let me know if you have any doubts regarding your question or my answer.
Solve the inequality: 3x - 3 < 9
Answer:
[tex]x<4[/tex]
Step-by-step explanation:
Given:
[tex]3x-3<9[/tex]
Add 3 to both sides
[tex]3x<12[/tex]
Divide both sides by 3 to get x alone
[tex]x<4[/tex]
Hope this is helpful
Write an equation of a line that is perpendicular to
the line y = 2/3x+5 and that passes through the
point (0,4).
Answer:
y = (-3/2)x + 4
Step-by-step explanation:
The slope of the given line is 2/3. The slope of any line perpendicular to the given line is the negative reciprocal of 2/3, which comes out to -3/2.
Now we have the slope of the new line and know that it passes through (0, 4). (0, 4) happens to be the y-intercept, b, in y = mx + b:
Substituting -3/2 for m and 4 for b, we get y = (-3/2)x + 4.
Determinar el valor de las siguientes progresiones:
1)4, 12, 36, 108,…
2)4, 20, 100, 500,…
3)5, 10, 20, 40,…
Answer:
Step-by-step explanation:
1) . .324, 972, 2916
2) ...2500, 12500, 62500
3). . 80, 160, 320