In triangle abc, ac=10, bc=8, angle b =90 degrees and angle bda = 90. how long is line bd
Answers
we know that
applying the Pythagorean theorem in triangle ABC
AC²=AB²+BC²----------> AB²=AC²-BC²---------> 10²-8²-------> AB²=36-----> AB=6
in the triangle ABC
tan a=BC/AB--------> 8/6--------> tan a=4/3
tan c=AB/BC--------> 6/8--------> tan c=3/4
in the triangle ABD
tan a=BD/AD---------> tan a=BD/x-------> BD=x*tan a
BD=x*(4/3)-----------> equation 1
in the triangle BDC
tan c=BD/DC------------------> BD=(10-x)*tan c------> BD=(10-x)*(3/4)
BD=(10-x)*(3/4)-------------> equation 2
equal 1 and 2
x*(4/3)=(10-x)*(3/4)------> 16x=9*(10-x)--------> 16x=90-9x----> 25x=90
x=90/25-----------> x=3.6
BD=x*(4/3)--------> BD=3.6*(4/3)----------> BD=4.8 units
the answer is BD=4.8 units
Related Questions
when should you use graphing to solve a system?
Answers
the volume of a prism is:
A. The area of the base times the area of the side.
B. The area of the base times the perimeter of the base.
C. The perimeter of the base times the height.
D. The area of the base times the height of the prism
Please help!
Answers
The volume of a prism is calculated by multiplying the area of the base with the height of the prism. The correct answer is D. The area of the base times the height of the prism.
Explanation:The volume of a prism is calculated by multiplying the area of the base with the height of the prism. This means that out of the four options provided, the correct choice would be: D. The area of the base times the height of the prism.
For instance, if the area of the base of a rectangular prism is 30 square units and the height of that prism is 10 units, then the volume would be calculated as 30 (area of the base) * 10 (height of the prism) = 300 cubic units. Always remember that the volume of a 3D solid is expressed in cubic units.
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A car salesman earns 2% commission on all of his sales. If he needs to make $3,000 a month for his living expenses, what total dollar amount must he sell to make that in commission each month?
Answers
I hope this helps!
The total dollar amount he must sell to make that in commission each month is $150000.
What is percentage?In mathematics →
a percentage is a number or ratio expressed as a fraction of 100.it is often denoted using the percent sign "%".Given is that a car salesman earns 2% commission on all of his sales. He needs to make $3,000 a month for his living expenses,
Assume that the total dollar amount he must sell to make that in commission each month is ${x}. Then, we can write -
3000 = 2% of {x}
3000 = (2/100) × {x}
{x} = (3000 x 100)/2
{x] = 300000/2
{x} = 150000
Therefore, the total dollar amount he must sell to make that in commission each month is $150000.
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Alani uses 3/4 cup of pineapple juice to make one bread how much juice will she use to make 5 breads
Answers
5 breads = 3/4 x 5
5 breads = 15/4
5 breads = 3 3/4cups
--------------------------------------------------------------------
Answer: Alani will use 3 3/4 cups to make 5 bread.
--------------------------------------------------------------------
To make five loaves of bread, Alani will use 3 3/4 cups of pineapple juice, calculated by multiplying the amount required for one loaf, which is 3/4 cup, by five.
To solve this, you multiply the amount of pineapple juice needed for one bread by the total number of breads.
Multiply the amount of juice for one bread by the number of breads: 3/4 cup × 5 = 15/4 cups.
Convert the improper fraction to a mixed number: 15/4 cups is equal to 3 3/4 cups.
Therefore, Alani will use 3 3/4 cups of pineapple juice to make five loaves of bread.
The perimeter of to similar polygon is 20 and 28. On side of the smaller polygon is 4. Find the corresponding side of the larger polygon
Answers
Use proportions to figure out the similarity and the missing side.
The smaller polygon has a side of 4.
[tex] \frac{4}{20} = \frac{x}{28} [/tex]
[tex]20*x= 4*28 [/tex]
[tex]20x=112[/tex]
[tex]x= 5.6 [/tex]
The corresponding side of the larger polygon is 5.6.
I hope this helps!
~kaikers
Final answer:
The corresponding side of the larger polygon is 5.6 units, found by setting up a proportion between the sides and the perimeters of the similar polygons. Scaling a square's side length by 2 makes its area 4 times larger, reflecting the square of the scale factor.
Explanation:
To solve the problem of finding the corresponding side of the larger polygon, we must use the property that the perimeters of similar polygons are proportional to their corresponding sides. Given that the perimeters are 20 for the smaller polygon and 28 for the larger one, we can set up a proportion to find the length of the corresponding side.
Let x be the length of the corresponding side in the larger polygon. The ratio of the perimeters is the same as the ratio of any pair of corresponding sides. Since we have a side of the smaller polygon being 4, we would set up the proportion as follows:
4 / x = 20 / 28
Cross-multiplying to solve for x, we have:
4 x 28 = 20 x x
112 = 20x
x = 112 / 20
x = 5.6
Therefore, the corresponding side of the larger polygon is 5.6 units. In the context of squares, when scaling a square by a factor of 2, the area increases by the square of the scale factor. If the smaller square has a side of 4 inches, the larger square will have a side length of 8 inches. Hence, the area of the larger square is 64 square inches (8x8), which is 4 times larger than the area of the smaller square which is 16 square inches (4x4).
Kevin is 2 times as old as Gabriela. 12 years, Kevin was 6 times as old as Gabriela.How old is Gabriela now
Answers
Final answer:
Gabriela's current age is found by setting up algebraic equations based on the information that Kevin is twice as old as Gabriela now, and was six times as old 12 years ago. Solving the equations, we find that Gabriela is 15 years old.
Explanation:
Finding Gabriela's Current Age:
The problem statement tells us that Kevin is currently 2 times as old as Gabriela and that 12 years ago, Kevin was 6 times as old as Gabriela. To solve for Gabriela's current age, let us use algebra. Let's denote Gabriela's current age as G and Kevin's current age as K. The given information can be translated into the following two equations:
K = 2G (Kevin is 2 times as old as Gabriela now)K - 12 = 6(G - 12) (12 years ago, Kevin was 6 times as old as Gabriela)Substituting the first equation into the second, we get:
2G - 12 = 6(G - 12)
Expanding both sides:
2G - 12 = 6G - 72
Moving all terms involving G to one side and constant terms to the other side, we get:
2G - 6G = -72 + 12
-4G = -60
Dividing both sides by -4 to solve for G:
G = 15
So, Gabriela is currently 15 years old.
When solving the equation 10x + 2 = 22, what is the first thing you're going to do?
Answers
[tex]10x \: = \: 20[/tex]
A box contains 24 light bulbs of which 4 are defective
Answers
Paul is going to buy a collectible vintage painting from the local art gallery. The painting is priced at $600 in the gallery. The gallery owner does accept credit cards but pefers cash. In fact, he offers to give Paul a 5% discount if he can pay in cash. Paul doesn’t have any cash but can get a cash advance on his credit card. His credit card has and APR f 16% in credit purchases and a 32% APR on cash advances. Assuming Paul wants to pay the painting off over 12 months, which of the following is true?
Answers
If paid using credit card and in installment basis.$600 x 16% = $96 interest on credit card balance$600 + $96 = $696 total debt$696 ÷ 12 months = $58 monthly payments
If paid using cash from cash advance.$600 x 5% discount = $30$600 - $30 = $570$570 x 32% = $182.40 interest on cash advance$570 + $182.40 = $752.40$752.40 ÷ 12 months = $62.70 monthly payment
It is cheaper for Paul to buy the painting using his credit card. He will only pay $58 per month on his credit card provider compared to the $62.70 monthly bill if he used cash advance.
Hope this helped☺☺
Answer:
Answer ended up being "B" just finished the test and this is one i got wrong, however it lets you see the correct answer, which again was option "B"
Step-by-step explanation:
i gotta write some words here my guy. good luck tho
Express the given integral as the limit of a riemann sum but do not evaluate: the integral from 0 to 3 of the quantity x cubed minus 6 times x, dx.
Answers
[tex]\int_{0}^{3} (x^3-6x) dx=\int_{0}^{3} x^3 dx-6\int_{0}^{3} x dx[/tex]
We take the interval and we divide it n times:
[tex]\Delta x=\frac{b-a}{n}=\frac{3}{n}[/tex]
The area of the i-th rectangle in the right Riemann sum is:
[tex]A_i=\Delta xf(a+i\Delta x)=\Delta x f(i\Delta x)[/tex]
For the first part of our integral we have:
[tex]A_i=\Delta x(i\Delta x)^3=(\Delta x)^4 i^3[/tex]
For the second part we have:
[tex]A_i=-6\Delta x(i\Delta x)=-6(\Delta x)^2i[/tex]
We can now put it all together:
[tex]\sum_{i=1}^{i=n} [(\Delta x)^4 i^3-6(\Delta x)^2i]\\\sum_{i=1}^{i=n}[ (\frac{3}{n})^4 i^3-6(\frac{3}{n})^2i]\\ \sum_{i=1}^{i=n}(\frac{3}{n})^2i[(\frac{3}{n})^2 i^2-6][/tex]
We can also write n-th partial sum:
[tex]S_n=(\frac{3}{n})^4\cdot \frac{(n^2+n)^2}{4}
-6(\frac{3}{n})^2\cdot \frac{n^2+n}{2}[/tex]
To express the integral from 0 to 3 of the function as the limit of a Riemann sum, divide the interval into [tex]f(x) = x^3 - 6x[/tex] subintervals of equal width, find a Riemann sum, and then take the limit as n approaches infinity.
Explanation:To express the given integral as the limit of a Riemann sum without evaluating, we represent the integral of the function [tex]f(x) = x^3 - 6x[/tex]split the interval [0,3] into n equal subintervals, each of width Δx = 3/n. Then we choose sample points x_i in each subinterval [x_{i-1}, x_i]. The Riemann sum is thus [tex]R = Σ(x_i^3 - 6x_i)Δx[/tex]en from i=1 to n and x_i is any point in the ith subinterval.
As n approaches infinity, which is equivalent to Δx approaching zero, the Riemann sums converge to the integral. The limit of the Riemann sum is then represented as lim_{n to ∞} R, which gives the exact area under the curve f(x) between 0 and 3, but we are not evaluating this limit.
2. Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
Answer:
m < C =
m < B =
m < A =
m < D =
Answers
1. m ∠C = 88°
2. m ∠B = 100°
3. m ∠A = 92°
4. m ∠D = 80°
Explanation:
∠A and ∠C are supplementary angles; therefore:
∠A + ∠C = 180° --- (A)
Since,
∠A = (x+2)°
and
∠C = (x-2)°
Plug-in the values in equation (A):
(A) => (x+2)° + (x-2)° = 180°
=> x° + 2° + x° - 2° = 180°
=> 2x° = 180°
=> x = 90°
Since x = 90°, therefore,
∠A = (x+2)° = 92°,
and
∠C = (x-2)° = 88°
Since ∠B and ∠D are supplementary angles; therefore,
∠B + ∠D = 180°
∠B + (x-10)° = 180°
Since,
x = 90°; therefore,
∠B + 80° = 180°
∠B = 100°
And since,
∠B + ∠D = 180°
and
∠B = 100°
Therefore,
∠D = 180° - 100°
∠D= 80°
-i
The Campbell family has a disposable income of $60,000 annually. Assume that their marginal propensity to consume is 0.8 (the Campbell family spends 80% of new disposable income on consumption) and that their autonomous consumption spending is equal to $10,000. What is the amount of the Campbell family\'s annual consumer spending?,
Answers
The annual consumer spending of the Campbell family is $58,000.
Explanation:To calculate the amount of the Campbell family's annual consumer spending, you need to consider their autonomous consumption spending and their marginal propensity to consume. The autonomous consumption spending is $10,000, which means that even if their disposable income is zero, they will still spend $10,000. The marginal propensity to consume is 0.8, so for every additional dollar of disposable income, they will spend 80 cents. To find the annual consumer spending, you can use the formula: Consumer Spending = Autonomous Consumption Spending + (Marginal Propensity to Consume * Disposable Income). In this case, the disposable income is $60,000, so the annual consumer spending would be $10,000 + (0.8 * $60,000) = $58,000.
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Angle 1 and angle 3 are complementary and angle 1 =~ angle 2 which one of these statements will always be true
Answers
Also since the options aren't there I'll just help set up.
So angle 1 and angle 3 add up to 90 degrees. Angle 1 and Angle 2 are equal so whatever option has something around those lines is correct.
Modern Appliances offers a one-year monthly installment plan for a refrigerator. The payment for the first month is $75, and then it increases by 6% each month for the rest of the year. Which expression can be used to find the total paid in the first 12 months?
Answers
Expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].
What is expression?" Expression is defined as the equation representing the relation between the numbers or the variables using mathematical operation."
Formula used
Geometric progression,
[tex]S_{n} = \frac{a(1-r^{n}) }{1-r}[/tex]
[tex]a=[/tex] first term
[tex]r=[/tex] common ratio
[tex]n=[/tex] number of terms
According to the question,
Given,
Amount to be paid first month [tex]'a' = \$75[/tex]
Increases by [tex]6\%[/tex] each month
Therefore,
Common ratio [tex]'r' = 1 + \frac{6}{100}[/tex]
[tex]= 1.06[/tex]
Number of months [tex]'n'= 12[/tex]
Substitute the value in the formula to get the expression for the given condition,
Required expression,
[tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex]
Hence, expression used represents the given paid installment for [tex]12[/tex] months is equal to [tex]S_{12} =\frac{ 75(1-1.06^{12}) }{1-1.06}[/tex].
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(PLEASE HELP! WILL VOTE BRAINLIEST) The table below shows four systems of equations: System 1 System 2 System 3 System 4 4x − 5y = 2 3x − y = 4 4x − 5y = 2 10x − 21y = 10 4x − 5y = 2 24x − 47y = 22 4x − 5y = 2 10x + 3y = 15 Which pair of systems will have the same solution?
Answers
Answer:
system 2 and system 3 have the same solution.
Step-by-step explanation:
system 1:
[tex]4x-5y=2[/tex]
[tex]3x-y=4[/tex]
we'll solve the two equation by the method of elimintaion to get the value of x and y.
on solving we get [tex]x=\frac{18}{11} ,y=\frac{10}{11}[/tex].
system 2:
[tex]4x-5y=2\\10x-21y=10[/tex]
on solving the above two equation by the method of elimination we get the value of x and y.
on solving we get [tex]x=\frac{-4}{17},y=\frac{-10}{17}[/tex].
system 3:
[tex]4x-5y=2\\24x-47y=22[/tex]
on solving the above two equation by the method of elimination we get the value of x and y.
on solving we get [tex]x=\frac{-4}{17} ,y=\frac{-10}{17}[/tex].
system 4:
[tex]4x-5y=2\\10x+3y=15[/tex]
on solving the above two equation by the method of elimination we get the value of x and y.
on solving we get [tex]x=\frac{81}{62} ,y=\frac{20}{31}[/tex].
on looking for the solution of all the four system we see that system 2 and system 3 have the same value for x and y.
Hence, system 2 and system 3 have the same solution.
The square of the sum of 7 times x and 3 divided by 4 times the difference of x and 1
Answers
Squaring the sum on the top, rules out 1 and 2 (not squaring the 7 only)
then 4 times the difference. so I believe 4 (x-1) on the bottom.
Answer: Third option is correct.
Step-by-step explanation:
Since we have given that
The square of the sum of 7 times x and 3 divided by 4 times the difference of x and 1.
The square of the sum of 7 times x and 3 would be written as
[tex](7x+3)^2[/tex]
and 4 times the difference of x and 1 is written as
[tex]4(x-1)[/tex]
Mathematically, it is expressed as
[tex]\dfrac{(7x+3)^2}{4(x-1)}[/tex]
Hence, Third option is correct.
The International Space Station orbits Earth at an altitude of 240 miles. If a camera were set up on the Space Station, how far along Earth's horizon will the camera be able to "see?" Use 4,000 miles as the average radius of the Earth and round your answer to the nearest hundredth of a mile. (Hint: Sketch and label the problem first, drawing the right angle in the correct place.)
A. 480.31 miles
B. 240.00 miles
C. 4240.00 miles
D. 1406.27 miles,
Answers
Simplify.
2x5 - 6x2 + 4x4y
-------------------------
2x
Answers
Notice that in the denominator all the numbers are divisible by two, so 2 is part of our common factor; also, all the terms have the variable [tex]x[/tex], and the least exponent of that variable is 1, so [tex]x[/tex] will be the other part of our common factor. Lets put the two parts of our common factor together to get [tex]2x[/tex].
Now that we have our common factor, we can rewrite our numerator as follows:
[tex] \frac{2x(x^{5}-6x+2(2y)}{2x} [/tex]
We are luckily, we have [tex]2x[/tex] in both numerator and denominator, so we can cancel those out:
[tex]x^{5}-6x+2(2y)[/tex]
[tex]x^5-6x+4y[/tex]
We can conclude that the simplified version of our rational function is [tex]x^{5}-6x+4y[/tex].
How many different 5 digit street addresses can have the digits 4 7 3 4 and 8
Answers
Colin was thinking of a number. Colin adds 18 to it, then doubles it and gets an answer of 65.5. What was the original number?
Answers
65.5 ÷ 2 = 32.75.
32.75 - 18 = 14.75.
Answer:
14.75
Step-by-step explanation:
65.5/2 = 32.75.
32.75 - 18 = 14.75
thats your answer. hope it helps
Nick’s parents purchased their first home in the 1980’s with a 30-year mortgage at 19.5%.
Answers
$ 2037.40
Interesting that there was no down payment..........The staggering monthly payment above would be enough to pay off the total mortgage in just over 5 years. Nick's parents would be much better off to save their money for a few years.
Final answer:
Using the formula for a fixed-rate mortgage payment, the monthly mortgage payment for Nick's parents, who bought a home for $125,000 with a 30-year mortgage at 19.5%, is calculated to be $2,037.40, making the answer A. $2,037.40.
Explanation:
To calculate the monthly mortgage payment for Nick's parents, who purchased their first home with a 30-year mortgage at 19.5% interest, we need to use the formula for a fixed-rate mortgage payment. The formula is:
M = P[r(1+r)ⁿ]/[(1+r)ⁿ⁻¹]
Where:
M is the total monthly mortgage payment.P is the principal loan amount.r is the monthly interest rate (annual rate divided by 12 months).n is the number of payments (loan term in years multiplied by 12 months).For this calculation:
P = $125,000r = 19.5% annual interest rate, which is 0.195/12 per month.n = 30 years x 12 months = 360 payments.We insert these numbers into our formula:
M = $125,000[0.195/12(1+0.195/12)³⁶⁰]/[(1+0.195/12)³⁶⁰⁻¹]
After calculating, we find that the monthly mortgage payment (rounded to two decimal places) would be $2,037.40.
Therefore, the answer is A. $2,037.40.
I need help with math help me?
Cindy bought 5 dresses for $20 each and 3 pairs of shoes for $20 each. She used this expression to calculate the total amount she spent.
(5 × 20) + (3 × 20)
What is another expression to calculate the total amount spent?
A) (5 + 3) × 20
B) 5 × (20 + 3)
C) 5 × 20 × 3
D) (5 + 20) × (3 + 20)
Answers
Answer:
A) (5+3) x 20
Step-by-step explanation:
5 and 3 both go into 20. So therefore the answer is A because 20 goes into both 5 and 3.
PLEASE HELP QUICK! Thank you!
Answers
so
x = (50 / 8) = (25 / 4) = $ 6.25 per wand
Checking Prices
a) 4 x = 20
x = $ 5, Does not have the same price per wand as glitter wands
b) 6 x = 37.50
x = (37.50 / 6) = $ 6.25, Has the same price per wand as glitter wands
c) 10 x = 65
x = 6.5, Does not have the same price per wand as glitter wands
1. What is the value of x? Show all of your work.
Answers
We know A and C, let's find B by doing it backwards
C^2 - A^2 = B^2
4^2 - 7 (square root of 7 squared is just 7) = B^2
16 - 7 = B^2
9 = B^2
1.01 an rational number
Answers
What is the definition of a circle? A circle is a plane figure with no straight sides. A circle is a point and all the points in a plane that are the same distance from it. A circle is the set of all points in a plane that are a given distance from a given line segment. A circle is the set of all points in a plane that are the same distance from a fixed point called the center.
Answers
The first one you mentioned, a circle is a plane figure with no straight sides... I can name another shape with no straight sides... an oval.
The second one you mentioned, is a true statement
The third one you mentioned, a circle is from a point, not a line segment.
The last one mentioned is also a true statement.
Answer:
I believe the answer is "A circle is a set of all points in a plane that are the same distance from a fixed point called the center." I am 95% sure but please correct me if I am wrong. Hope this possibly helps someone!
Step-by-step explanation:
Write the standard equation for the circle.
center (-6 9) r=3
A. (X-9)^2+(y+6)^2=9
B. (X+6)^2+(Y-9)^2=3
C. (X-6)^2+(Y+9)^2=3
D. (X+6)^2+(Y-9)^2=9
Find the center and radius of the circle with equation (x+2)^2+(y+10)2=4
A. Center (-2, -10); r=2
B. Center (2, 10); r=4
C. Center (-2, -10); r=4
D. Center (10, 2); r=2
What is the equation of the fircle with center 3,5 that passes through the point (-4, 10)?
A. (x-3)^2 + (y-5)^2 = 226
B. (x+4)^2 + (y-10)^2 = 74
C. (x+4)^2 + (y-10)^2 = 226
D. (x+3)^2 + (y-5)^2 = 74
What is the equation of the circle with center (0,0) that passes through the point (5,-4)?
A. x^2 + y^2 = 41
B. (x+4)^2 + (y+4)^2 = 41
C. (x-5)^2 + (y+4)^2 = 9
D. x^2 + y^2 = 9
Answers
.. (x -h)^2 +(y -k)^2 = r^2
1. selection D matches the specification of the circle
2. selection A matches the given equation
3. None of the offered selections matches
.. (x -3)^2 +(y -5)^2 = 74
4. selection A matches the requirements
Factor. 25m^100−121n^16
(5m10−11n4)(5m10+11n4)(5m50−11n8)2(5m50−11n8)(5m50+11n8)(5m10−11n4)2
Answers
this question is a difference of squares. the basic equations is when you get 2 square numbers and you have to find their difference ;
x²-y² = (x+ y)(x-y)
you have to then find the product of these factors.
the question given can be rewritten to write the numbers in their square forms
25m¹⁰⁰ - 5²m⁵⁰ˣ² - square root - 5m⁵⁰
121n¹⁶ - 11²n⁸ˣ² - square root - 11n⁸
we have to then factorise them
the answer for 25m¹⁰⁰-121n¹⁶ = (5m⁵⁰ - 11n⁸) (5m⁵⁰ + 11n⁸)
please help asap!!!!!! lots of points
Answers
The correct answer is B.
what is the GCF of the terms of the polynomial.
44x5 + 16x3
Answers
the greatest common factor of x^5 and x^3 is x^3 (always take the smallest exponent)
so the answer is 4x³