Answers
10
The length of line BC is 10.
EXPLANATION:
Triangle ABC is four times the area of triangle AYX.
Area of triangle ABC = 4 × Area of triangle AYZ
This is as:
30 = 4 × 7.5
THEREFORE:
The length of line BC must be twice of the length of line XY.
BC = 2 × XY
BC = 2 × 5
BC = 10
The length of Line BC is 10
What is a triangle?A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.
What are similar triangles?Triangles having the same corresponding angles measures and proportional side lengths are called similar triangles.
How to find the length of the line BC?Considering Δ AXY and ΔABC
∠AXY = ∠ACB (corresponding angles are equal)
∠AYX = ∠ABC (corresponding angles are equal)
∠A is common in both the triangles
∴ We can say the triangles are similar .
Now, let H be the height of ΔABC and h be the height of ΔAYX
So, we can say, [tex]\frac{XY}{BC} = \frac{h}{H}[/tex]
Now, we know that area of the triangle can be found with the help of the formula (1/2)x(base)x(height)So, [tex]\frac{AYX}{ABC} = \frac{7.5}{30}[/tex]
⇒ [tex]{\frac{\frac{1}{2} (XY) h }{\frac{1}{2}(BC) H } = \frac{1}{4}[/tex]
Now, substituting XY = 5 and [tex]\frac{XY}{BC} = \frac{h}{H}[/tex] in the above equation, we get
[tex]\frac{25}{BC^{2} } = \frac{1}{4}[/tex]
⇒ BC² = 100
⇒ BC = ± 10
Since BC is the length , so it cannot be negative.
So, the negative value is rejected.
∴ BC = 10
Option B is correct.
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Related Questions
I need help figuring this out (#9)
Answers
there are 60 minutes in 1 hr.
every 10 minutes the factory makes 15 bears.
so 10+10+10+10+10+10 is 1 hr, and is really 15+15+15+15+15+15 bears, namely 90 per hour.
every day, the factory does that for 8 hours straight, so namely they make 90 * 8 teddy bears, or 720 per day.
let's make a table of bears per day
1 day............................... 720(1)
2 days............................ 720(2)
3 days............................ 720(3)
4 days............................ 720(4)
x days............................ 720(x)
so the amount of bears they make say "A" is per day is A = 720x.
what would be the fewest days to make 5000?
well, whatever 720x is, it has to be either 5000 exactly OR more, not less, then
5000 ⩽ 720x.
and dividing both sides by 720 we get about 6.94 ⩽ x.
so we can conclude that whole days, it'll be 7, since 6.94 is about 7 days, but rounded up to whole days it'll be 7 days.
Which is an equation in point-slope form for the lines that passes though the points (-1,4) and (3,-4)
Answers
I don't know if this is the equation you need. But here it is.
Y - 4 = -2 (x + 1)
A college has a student to teacher ratio of 30 to 2. If there are 182 teachers at the college, how many students attend the college?
A.
3,822
B.
1,092
C.
2,184
D.
2,730
Answers
30/2 =15. So 182 times 15 is 2730, or D.
Which relation is a function?
Answers
Answer:
B
Step-by-step explanation:
For a relationship to be a function
Each value of x in the domain can only have 1 unique value of y in the range. That is, one-to-one correspondence.
The only relation which meets this criteria is B
Answer:
The answer is option B: {(1,3);(-1,5);(2,7);(-2,7);(3,5);(-3,3)}
Step-by-step explanation:
Each element is composed of a first and second point, or by an 'x' and 'y' coordinates, respectively. In this way, all x coordinate from the set of elements constitute the 'domain', and all y coordinates of the set of elements constitute the 'image'.
So, for a set of elements be a function, each point of the domain have to have one an only one image. In other words, two elements with the same image have to have a distinct x's coordinate.
If we take a look at the set of elements in the different options, we find different elements which repeat image:
1) The pairs (1,0) and (1,-1) in the set of point of option A
2) The pairs (-2,-1) and (-2,-2) in the set of point of option C
3) The pairs (1,3) and (1,3) in the set of point of option
In the set of elements of B option, all the elements with the same y coordinate have different x's coordinates.
You take out a cash advance of $2,790.00 on a credit card with a 3.5% cash advance fee and a 13.5% APR. What is the amount due by the end of the month? $2,920.14 $3,277.48 $2,821.39 $2,887.65
Answers
Answer:
The answer is $3277.48
Step-by-step explanation:
An Annual Percentage Rate or APR is calculated by taking into account the interest rate on a credit card (or another borrowed sum) and any other charges such as an annual fee or arrangement fee.
So the first step here is to calculate the 3.5% cash advance fee on cash advance of $2790.00.
$2790.00 × 3.5%
2790 × (3.5 ÷ 100)
2790 × 0.035
$97.65
Now APR is calculated on the sum of cash advance and cash advance fee, i.e.,
13.5% × (2790 + 97.65)
13.5% × 2887.65
( 13.5 ÷ 100 ) × 2887.65
0.135 × 2887.65
$389.83
The total amount due at the end of the month is sum of Cash advance, Cash advance fee and APR
$2790 + $97.65 +$389.83 = $3277.48
3.277.48
this a a short answear
A jacket costs $35 and has an 8 percent tax rate. Which expression will find the cost of the tax on the jacket
Answers
Answer:
Step-by-step explanation:
35 x .08 = $2.80
35 + 2.80 = 37.80
Answer:
T = 0.08 × 35
Step-by-step explanation:
The cost of a jacket = $35
The tax rate on the jacket = 8% = [tex]\frac{8}{100}[/tex]
= 0.08
The expression to find the cost of the tax on the jacket would be
T = 0.08 × 35
Arithmetic, Geometric, or Neither Classify each sequence as arithmetic, geometric, or neither. (matching) 4/9, 4/3, 4, 12, 36. 0, 1, 2, 3, 4, 5, 6. -10, -6, -2, 2, 6, 10.
Answers
Answer:
The given sequence is neither arithmetic not geometric.
Step-by-step explanation:
A sequence is in arithmetic if it has a common difference.
i.e., a sequence a, b, c is in arithmetic if
b - a = c - b
Let's check if the given sequence is in arithmetic.
[tex]\frac{4}{3} -\frac{4}{9} =\frac{12}{9} -\frac{4}{9}[/tex]
[tex]= \frac{8}{9}[/tex]
[tex]4-\frac{4}{3} =\frac{12-4}{3}[/tex]
[tex]=\frac{8}{3}[/tex]
So, [tex]\frac{4}{3} -\frac{4}{9} \neq 4-\frac{4}{3}[/tex]
Hence, the given sequence is not arithmetic.
Let's check if the given sequence is in geometric.
A sequence is in geometric if it has a common ratio.
i.e., a sequence a, b, c is in geometric if
[tex]\frac{b}{a} =\frac{c}{b}[/tex]
[tex]\frac{4/3}{4/9} =\frac{4}{3} (\frac{9}{4} )[/tex]
= 3
[tex]\frac{4}{4/3} =4(\frac{3}{4} )[/tex]
= 3
Clearly, [tex]\frac{12}{4} =\frac{36}{12} =3[/tex]
But, [tex]\frac{0}{36} =0[/tex]
Therefore, the given sequence is not in geometric.
Hence, the given sequence is neither arithmetic not geometric.
What are the solutions of -1/2x + 4 = x+1
Answers
[tex]-\dfrac{1}{2}x+4=x+1\qquad\text{multiply both sides by 2}\\\\-x+8=2x+2\qquad\text{subtract 8 from both sides}\\\\-x=2x-6\qquad\text{subtract 2x from both sides}\\\\-3x=-6\qquad\text{divide both sides by (-3)}\\\\\boxed{x=2}[/tex]
How many radians is -135°?
Answers
Answer:
[tex]-135\degree=-\frac{3}{4}\pi\: radians.[/tex]
Step-by-step explanation:
This question demands that we convert from a degree measure to a radian measure.
To convert from a degree measure to radians, multiply by [tex]\frac{\pi}{180\degree}[/tex].
That is [tex]-135\degree=-135\degree \times \frac{\pi}{180\degree}[/tex].
This can be simplified by canceling out the common factors to get,
[tex]-135\degree=-3\times45\degree \times \frac{\pi}{4\times 45\degree}[/tex].
This will give us,
[tex]-135\degree=-\frac{3}{4}\pi\: radians.[/tex]
Answer:
- 3pi over 4
Step-by-step explanation:
How do I show that x5-y5=(x-y)(x4+x3y+x2y2+xy3+y4)
Answers
The equation[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4)[/tex] is a representation of the Difference of Powers formula in algebra. This formula can be proven accurate by expanding the expression on the right hand side and simplifying.
Explanation:Your question essentially asks about the proof of a formula in algebra known as the Difference of Powers. This formula is applied when you have a difference of two terms, each raised to the same power.
Let us prove[tex]x^5 - y^5 = (x - y)(x^4 + x^3y + x^2y^2 + xy^3 + y^4):[/tex]
Expand the expression on the right-hand side: [tex](x - y)(x^4 + x^3y + x2y^2 + xy^3 + y^4).[/tex]You do this by distributing x to all the terms in the parenthesis and then y to all the terms in the parenthesis.When you simplify this expression, you will find that it equals to x5 - y5.
This demonstrates that the original formula you asked about is accurate.
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u need question problem 2 to solve problem 3
Answers
Answer:
You are correct
Step-by-step explanation:
Start with 1 1/2. This can be made into an improper fraction which is 3/2
Now multiply both top and bottom of 3/2 by 5
(3*5)/(2 * 5) = 15 / 10
16/10 is just slightly bigger than 15/10
The fraction is grather than 1 if the numerator is greater than denominator.
The fraction is less than 1 if the numerator is less than denominator.
The fraction is equal 1 if the numerator is equal the denominator.
----------------------------------------------------------------------------------
[tex]a.\ \text{greater than 1:}\ \dfrac{4}{3},\ \dfrac{7}{5};\ \dfrac{16}{10}\\\\b.\ \text{less than 1:}\ \dfrac{1}{3};\ \dfrac{12}{15};\ \dfrac{3}{10};\ \dfrac{3}{5}\\\\c.\ \text{equal to 1:}\ \dfrac{3}{3}[/tex]
[tex]\dfrac{16}{10}=\dfrac{10+6}{10}=\dfrac{10}{10}+\dfrac{6}{10}=1+\dfrac{6}{10}=1\dfrac{6}{10}=1\dfrac{6:2}{10:2}=1\dfrac{3}{5}\\\\3\text{ is greater than half of 5.}\ \text{Therefore}\ \dfrac{3}{5}>\dfrac{1}{2}.\\\\\text{Therefore}\ \dfrac{16}{10}>1\dfrac{1}{2}.\\\\OTHER:\\\\\dfrac{16}{10}=1\dfrac{6}{10}\\\\1\dfrac{1}{2}=1\dfrac{1\cdot5}{2\cdot5}=1\dfrac{5}{10}<1\dfrac{6}{10}\\\\OTHER\\\\\dfrac{16}{10}=1\dfrac{6}{10}=1.6\\\\1\dfrac{1}{2}=1.5\\\\1.6>1.5\Rightarrow\dfrac{16}{10}>1\dfrac{1}{2}[/tex]
Which equation correctly applies the distributive property?
a) −2.5⋅(4⋅3.67)=(−2.5⋅4)⋅3.67
b) (42⋅3.5)+(42⋅1.3)+(42⋅5.2)=42+(3.5+1.3+5.2)
c) −3⋅(6.48)=(−3⋅6)+(−3⋅0.4)+(−3⋅0.08)
d) 2.4⋅(−3.4)⋅(−1.25)=−3.4⋅2.4⋅(−1.25)
Answers
The distributive property: a(b + c) = ab + ac
Answer:c) -3 · (6.48) = -3 · (6 + 0.4 + 0.08) = (-3 · 6) + (-3 · 0.4) + (-3 · 0.08)Answer:
c) -3 · (6.48) = -3 · (6 + 0.4 + 0.08) = (-3 · 6) + (-3 · 0.4) + (-3 · 0.08)
Step-by-step explanation:
Question:
1. What is the value of x? Show your work to justify your answer. (2 points)
2. What is the value of the exterior angle? Show your work to justify your answer. (2 points)
Answers
Answer:
x=56 and the exterior angle is 116
Step-by-step explanation:
We will call the unknown angle in the triangle y. Angle y and the angle (2x +4) form a straight line so they make 180 degrees.
y + 2x+4 =180
Solve for y by subtracting 2x+4 from each side.
y + 2x+4 - (2x+4) =180 - (2x+4)
y = 180-2x-4
y = 176-2x
The three angles of a triangle add to 180 degrees
x+ y+ 60 = 180
x+ (176-2x)+60 = 180
Combine like terms
-x +236=180
Subtract 236 from each side
-x+236-236 = 180-236
-x = -56
Multiply each side by -1
-1*-x = -56*-1
x=56
The exterior angle is 2x+4. Substitute x=56 into the equation.
2(56)+4
112+4
116
leah has a collection of 36 baseball cards. She..
Answers
Answer:
She gave away 24 cards
Step-by-step explanation:
(36)*([tex]\frac{2}{3}[/tex])=24
if 4x+41=3x+45, what is the value for x
Answers
Answer:
x = 4
Step-by-step explanation:
4x+41=3x+45
Subtract 3x from both sides
x + 41 = 45
Subtract 41 from both sides
x = 4
the expression 1.2p represents the total bill given to a pizza delivery man if he is given a tip of 20% and p represents the cost of the pizza. is this true expression?
Answers
Answer: The statement is false because 1.2 is calculating 120% of the cost of pizza. The expression should be .2p.
Step-by-step explanation:
The expression 1.2p correctly represents the total bill for a pizza including a 20% tip, with p representing the price of the pizza. To determine the total cost, you multiply the price by 1.20.
The expression 1.2p does indeed represent the total bill including a 20% tip for the delivery of a pizza where p is the cost of the pizza. When you give a tip of 20%, you are adding 20% of the cost of the pizza to the original price. This is calculated by multiplying the price by 1.20 (which is equivalent to 100% + 20%).
Example Calculation:
If the cost of the pizza is $10 (p = $10), then the total bill with a tip would be 1.2 × $10 = $12. The 20% tip on $10 is $2, so the total bill equals $10 + $2 = $12.
Can someone help please
Answers
I would say B. The mean is a good measure of central tendency.
I hope this helps!
what is the cost of renting a car for 4 days at $17.59 per day and driving 237 miles at 19¢ per mile
Answers
Answer: $58.40 Multiply 4 times 17.59 and add 237 times 0.19
Final answer:
The total cost of renting a car for 4 days at $17.59 per day and driving 237 miles at 19¢ per mile would be $115.39.
Explanation:
To calculate the cost of renting a car for 4 days:
For the rental cost, we multiply the daily rental rate by the number of days:
Rental cost=Number of days × Daily rental rate
Cost of renting the car for 4 days = 4 days x $17.59 per day = $70.36
Next, to find the cost of driving 237 miles, we multiply the distance driven by the cost per mile:
Cost of driving=Distance driven × Cost per mile
Cost of driving 237 miles at 19¢ per mile = 237 miles x $0.19 = $45.03
Total cost = Cost of renting + Cost of driving = $70.36 + $45.03 = $115.39
0.7(3x−0.2)=0.3(0.8−2x)
URGENT
20 Points!
Please Help!!!
Answers
Answer:
x = .140741
Step-by-step explanation:
0.7(3x−0.2)=0.3(0.8−2x)
Distribute
.7 * 3x - .7*.2 = .3*.8 - .3 * 2x
2.1x - .14 = .24 - .6x
Add .6x to each side
2.1x +.6x -.14 = .24 -.6x+.6x
2.7x -.14 = .24
Add .14 to each side
2.7x -.14+.14 = .24+.14
2.7x = .38
Divide by 2.7 on each side
2.7x/2.7 = .38/2.7
x = .140741
Which inequality matches the graph?
A) x > -2
B) x < -2
C) x = -2
D) x ≤ -2
Answers
Answer:
D) x ≤ -2
Step-by-step explanation:
The dot is at -2 = -2
the dot is filled in = ≤ or ≥ because its means equal too
think of ≤ or ≥ like arrows = it points left.
so its x ≤ -2
Note on using the ≤ or ≥ like pointing arrows
this only works if its written:
variable < constant form,
which is the way they are usually seen, like x < 5
but it could be 5 > x which means the > points the opposite way
Hello! :)
Answer:
D. x≤-2
*The answer must have a negative sign and less than or equal to.*
Step-by-step explanation:
Lesson: It's about the graphing inequalities
An inequality is a statement that compares mathematical expressions that are not equal. The expressions are separated by an inequality symbol (<,>, ≤, ≥, or ≠).
The arrow points to the left. The circle is closed.
Hope this helps!
Have a nice day! :)
:D
-Charlie
Thanks!
James completed 4 math problems in 6 minutes. At that rate, how many would he be able to complete in 1 hour?
Answers
60÷6 is 10
10×4 is 40
I will give a thanks and a 5star is you answer ASAP
Answers
Answer: -2,0,2,4,6
The solution of the inequality is x<1
Step-by-step explanation:
Answer:
x < 1
Step-by-step explanation:
2x < 2
Divide 2 on both sides
x < 1
------------------------------------------------------------------------
Table: (I think)
-2 , 0 , 2 , 4 , 6
how do i determine ordered pairs from a word problem?
Answers
On a trip, a family drove an average of 250 mi each day. If the family drove a total of 3,000 mi on their trip, how many days were they gone?
Answers
Answer: The answer is 12 days
Step-by-step explanation: miles total=miles per day times number of days
3000=250 times days
divide both sides by 250
12=days
Two boats sail away from a buoy making a 90 degree angle. The first boat is 165 meters away and is traveling at 25 m/s. The second boat has been traveling at 35 m/s for pi mINUTES. What is the rate of change in distance between the two boats?
Answers
Answer:
Step-by-step explanation:
lets say in the shown triangle x=165
so speed [tex]\frac{dx}{dt} =25[/tex]
and [tex]\frac{dy}{dt} =35[/tex]
Also since distance = speed* time
time = pi minutes = pi/60 seconds
y = [tex]\frac{35\pi \pi }{60}[/tex]
y = [tex]\frac{7\pi }{12}[/tex]
Now using the pythagorean :
[tex]x^2+y^2=z^2\\so \\165^2+(\frac{7\pi }{12} )^2 =z^2[/tex]
derivate the equation so we get :
[tex]x\frac{dx}{dt} +y\frac{dy}{dt} =z\frac{dz}{dt} \\[/tex][tex]165*25+35*\frac{7\pi }{12}=\sqrt{165^2+(\frac{7\pi }{12})^2} *\frac{dz}{dt}[/tex]
[tex]\frac{dz}{dt} =25.387[/tex] m/s
So Rate of change = 25.387 m/s
a man pays 20% of his salary as tax and has 24,000$ left. How much did he pay as tax
Answers
Answer:
He paid $6,000 in taxes.
Step-by-step explanation:
His final amount after taxes is $24000. In order to obtain this number we had to tax 20% of the total (Note that 100%-20%=80%). In other words if he was taxed 20% he took home 80% of what he was paid. Therefore mathematically we have:
[tex]0.8A_{pre-tax}=A_{taxed}[/tex]
Since we know he was left with $24000 after taxes then:
[tex]0.8A_{pre-tax}=24000\\\\\frac{0.8A_{pre-tax}}{0.8}=\frac{24000}{0.8}\\\\A_{pre-tax}=\frac{24000}{0.8}\\\\A_{pre-tax}=30000[/tex]
So originally he had $30,000. So how much did he pay in taxes? We can calculate the difference of both pretax and after tax and we get:
$30,000 - $24,000= $6,000 taxed
I need help with this question show steps! Quickly please!
Answers
use both points to find the slope
[tex]\frac{y2-y1}{x2-x1}[/tex]
[tex]\frac{-13-3}{9-(-3)}[/tex]
[tex]\frac{-16}{12} =\frac{-4}{3} =slope[/tex]
Now, to find b, plug in one of the points in y=mx+b
3=[tex]\frac{-4}{3}[/tex](-3)+b
3=4+b
b= -1
therefore, your final equation should be,
y=[tex]\frac{-4}{3}[/tex]x-1
How many zero will be in product (6x5)x the power of 10 3
Answers
To solve for the number of zeros in the product of (6x5) x 10³, one should first multiply the whole numbers (6x5) to get 30. Then, append as many zeros as the power of 10, which in this case is 3. So, we append three 0's to 30 which yields 30000. This gives us four zeros in total.
Explanation:The problem (6x5) x 10³ refers to a multiplication involving whole numbers and a power of ten. Our task is to find out how many zeros will be in the resulting product.
Step 1: Multiply the whole numbers. 6x5 equals 30.
Step 2: When multiplying by a power of ten, you add as many zeros to the end of the number as there are in the exponent of ten. So, in this case, as it is power of ten to the power of 3 (10³), we would add three 0's.
Final result: 30000.
So, the product (6x5) x 10³ will have four zeros.
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the ratio of width to length of the united states flag is 10:19. If the width of the flag of Emerson's School is 4 ft , what is the length?
Answers
Answer: The length of the united states flag is [tex]2\frac{2}{19}\ feet[/tex]
Step-by-step explanation:
Since we have given that
Ratio of width to length of the united states flag is 10:19
So, Let the length of the united states flag be 10x
Let the width of the united states flag is 19x
As we have the width of the flag of Emerson's school = 4 feet.
According to question,
[tex]19x=4\\\\x=\frac{4}{19}[/tex]
So, our length of the united states flag will be
[tex]10x=10\times \frac{4}{19}\\\\=\frac{40}{19}\\\\=2\frac{2}{19}\ feet[/tex]
Hence, the length of the united states flag is [tex]2\frac{2}{19}\ feet[/tex]
Final answer:
To find the length of the flag, you can set up a proportion using the given ratio of width to length. Solve for the unknown length by cross-multiplying and dividing. The length in feet is found by multiplying the width of Emerson's School flag by the ratio and dividing by 10.
Explanation:
To find the length of the United States flag, you can set up a proportion using the given ratio of width to length. The ratio is 10:19, and the width of Emerson's School flag is 4 ft. First, write the proportion using the length as the unknown value: 10/19 = 4/L. To solve for L, cross-multiply and divide: 10L = 4 * 19. Divide both sides by 10 to find the length:
L = (4 * 19) / 10.
Multiply 4 and 19, then divide by 10 to get the length in feet.
L= 7.6
PLEASE HURRY!
There is a geometric theorem that says "If twp lines in a plane are perpendicular to the same line, they are parallel to each other." Explain why this is true by writing and comparing equations for two different lines that are perpendicular to y= -1/3x.
Answers
Two lines perpendicular to a third line are parallel to each other because they both inherit the slope from their perpendicularity. The resulting lines only differ in their y-intercepts, indicating they run parallel.
Explanation:The theorem you're referring to essentially relates to the slope of the lines. If two lines are each perpendicular to the same line, this means the slope of all three lines are related. This occurs because the slope of any line perpendicular to y=-1/3x is 3, the negative reciprocal of -1/3. For example, if we have two lines L1: y = 3x + b1 and L2: y = 3x + b2 which are both perpendicular to y= -1/3x (and thus parallel to each other), their formulas would only differ by their y-intercepts (b1 and b2). Since the coefficient of x (the slope) remains the same (3), we can conclude that these two lines are indeed parallel to each other which confirms the mentioned geometric theorem.
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