Find the missing length indicated. need help
The missing length of given right triangle is equal to 25.
RIGHT TRIANGLE
A triangle is classified as a right triangle when it presents one of your angles equal to 90º. The greatest side of a right triangle is called hypotenuse. And, the other two sides are called cathetus or legs.
The math tools applied for finding angles or sides in a right triangle are the trigonometric ratios or the Pythagorean Theorem.
The Pythagorean Theorem says: (hypotenuse)²=(leg1)²+(leg2)² . And the main trigonometric ratios are: sin (x), cos (x) and tan (x) , where:
[tex]sin(x)=\frac{opposite\ leg}{hypotenuse} \\ \\ cos(x)=\frac{adjacent\ leg}{hypotenuse} \\ \\ tan(x)=\frac{opposite\ leg}{adjacent\ leg}[/tex]
There is another important property, where h²=m*n. See the attached image.
From the previous informations presented, you can solve the given question.
From Pythagorean Theorem you can find h (heigth). Thus,
15²=9²+h²
h²=225-81
h²=144
h=12
If h=12 and m=9, from h²=m*n you can find n.
h²=m*n
12²=9*n
144=9n
n=144/9
n=16
Therefore, x= m+ n= 9+16=25.
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When the absolute value of slope gets bigger the graph of the line gets ???
Simplify the expression using the proper order of operations
5[6 ÷ 2^2 ∙ 3 - 1]
The simplification of the expression 5(6 ÷ 2² × 3 - 1) using the proper order of operation is 3.75
Simplification5(6 ÷ 2² × 3 - 1)
Bodmas
B - BracketO - ofD - divisionM - MultiplicationA - AdditionS - Subtraction= 5(6 ÷ 4 × 3 - 1)
= 5(6 ÷ 4 × 2)
= 5(6 ÷ 8)
= 5(0.75)
= 3.75
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Solving for the area.
Area
1/2(sum of parallel sides)height1/2(50+65)(30)1/2(115)(30)15(115)1150+5751725ft²Answer:
1725 ft²
Step-by-step explanation:
The formula to find the area of a trapezoid is :
Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height
Let us solve it now.
Area = [tex]\frac{1}{2}[/tex] × ( sum of the parallel sides ) × height
Area = [tex]\frac{1}{2}[/tex] × ( 65 + 50 ) × 30
Area = [tex]\frac{1}{2}[/tex] × ( 115 ) × 30
Area = [tex]\frac{1}{2}[/tex] × 3450
Area = 1725 ft²
What is the difference of the fractions below? 10x/3-2x/3 2x 13 3 A. 8 B. 8x C. 8x/3 D. 8/3x
The difference of the fractions is 8x/3. Option C is correct.
Given the fraction is 10x/3-2x/3.
When subtracting fractions with the same denominator, just subtract the numerators of the fractions. To find the difference between equal fractions, we subtract the smaller numerator from the larger numerator.
The given expression is 10x/3-2x/3.
Here the denominator in both the fractions are same so, we will take the LCM, we get
10x/3-2x/3=(10x-2x)/3
Now, we will simplify the numerator by subtracting the smaller term from larger, we get
10x/3-2x/3=8x/3
Hence, the difference of the fractions 10x/3-2x/3 is 8x/3 and the correct option is C.
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Jason’s utility and telephone bills for the month totaled $180. The utility bill was 3 times as much as the telephone bill. How much was each bill?
Answer:
telephone was $45, utility was $135
Step-by-step explanation:
Let the telephone bill be x, then the utility bill is 3x
3x+x = 180
4x = 180
x = 45
3x = 135
Complete the left-hand column of the table below following the steps indicated in the right-hand column to show that "sin a sin b = 1/2[cos(a-b)-cos(a+b)]" is an identity. Use the definitions of sum and difference formulas for cosine.
The equations which completes the left-hand column of the table are;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Which equations and identities complete the left-hand column of the table?The given expression on the right is written as follows;
First row;
[tex] \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
The definition of the sum and difference of cosine are;
cos(a - b) = cos(a)•cos(b) + sin(a)•sin(b)
cos(a + b) = cos(a)•cos(b) - sin(a)•sin(b)
Therefore;
Second row;
cos(a - b) - cos(a + b) = (cos(a)•cos(b) + sin(a)•sin(b)) - (cos(a)•cos(b) - sin(a)•sin(b))cos(a - b) - cos(a + b) = 2•sin(a)•sin(b)
Which gives;
[tex] sin(a) \cdot sin(b) = \frac{1}{2} \cdot \left(cos(a - b) - cos(a + b) \right)[/tex]
Third row;
sin(a)•sin(b) = (1/2)•(cos(a - b) - cos(a + b))Learn more about trigonometric functions here:
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A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a function of time, in seconds, is given by
h(t) = −4.9t(squared) + 20t + 12.
How long does it take to reach maximum height? (Round your answer to three decimal places.)
The ball takes approximately a time of 2.041 seconds to reach its maximum height.
What time does the ball take to reach maximum height?
The height of the ball as a function of time is modelled by a quadratic equation, the required information can be found by transforming the expression into vertex form:
h = - 4.9 · t² + 20 · t + 12
h = - 4.9 · (t² - 4.082 · t - 2.449)
h + (- 4.9) · (6.615) = - 4.9 · (t² - 4.082 · t + 4.166)
h - 32.414 = - 4.9 · (t - 2.041)²
The ball takes approximately a time of 2.041 seconds to reach its maximum height.
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Fill in the missing term in the pair of equivalent ratios. *
5:30 15:
Your answer
The state low temperatures for five states are as follows: -42
The inside dimensions of a box are 12 inches long, 5 inches wide, and 2 inches deep.
How many cubic inches does it contain?
60
110
120
240
none of these
To find the quotient of two fractions, you first need to rewrite the division problem as an equivalent multiplication problem. Find this quotient using multiplication.
The divisor of the expression 2/3 ÷ 6/5 is 9.
We have,
Expression:
2/3 ÷ 6/5
The concept used.
a/b ÷ c/d = ad / bc
Now,
2/3 ÷ 6/5
This can be written as,
= 2/3 x 5/6
= (2 x 5) / (3 x 6)
= 10 / 18
= 2 x 5 / 2 x 9
Cancel the common factor.
= 5 / 9
This can be read as,
Dividend = 5
Divisor = 9
Thus,
The divisor of the expression is 9.
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what’s 5x times 2-7 min
Answer:33
Step-by-step explanation: The expressions have equivalent values when x + 6
The expressions have equivalent values for any value of x.
When x=10 , both expressions have a value of 33.
A rectangle is 6 meters long and 4 meters wide. What is the area of the rectangle?
24 cm 2
10 cm 2
48 cm 2
20 cm 2
Select all the correct answers.
Exponential function fis represented by the table.
2
X
0
0
-12
B
-4
Function gis represented by the equation.
9 (2) = -12 (3)
Which statements are true about the two functions?
0
3
2
4
3
Both functions are increasing on all intervals of x.
Both functions approach the same value as x approaches ...
The functions have the same x-intercept.
Both functions approach - as x approaches -...
The functions have the same y-intercept.
The true statements are
(d) they have the same y-intercept(e) they approach negative infinity as x approaches negative infinityHow to determine true statements?The function g(x) is given as:
[tex]g(x) = -12(\frac 13)^x[/tex]
Set x = 0, to determine the y-intercept
[tex]g(0) = -12(\frac 13)^0[/tex]
g(0) = -12
From the table, we y-intercept of f(x) is
f(0) = -12
This means that they have the same y-intercept
Because the functions have negative initial values, they would approach negative infinity as x approaches negative infinity
Hence, the true statements are (d) and (e)
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Which equation is represented by the graph below?
A y=In x-3
B y=In x-4
C y=e^3 -3
D y=e^3 -4
Answer:
D
Step-by-step explanation:
I assume that for C and D, you meant e^x.
Since the function is defined at 0, eliminate A and B (since ln 0 is undefined)
Between C and D, we know that when x=0, e^x = 1. Since the y intercept of the graph is -3, this means the equation is y = e^x - 4.
What is 13 2/3 subtracted from 49 1/3
Answer:
35 2/3
Step-by-step explanation:
49 1/3 - 13 2/3
First convert both into improper fractions, which is
148/3 - 41/3
Then subtract!
107/3
Next simplify the fraction.
35 2/3
Graph the solution of the system of linear inequalities.
y + 2x ≥0
3x-2y≤6
Step-by-step explanation:
all the details are in the attachment; the solution are is filled with purple color.
write the equivalent of the fraction using a denominator of 52. 2/13
Answer: 8/52
2/13=x/52
(2×52)/13=x
104/13=x
8=x
x=8
8 is the equivalent of the fraction using a denominator of 52. 2/13
Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both are equal to 3/4 when simplified.
All equivalent fractions get reduced to the same fraction in their simplest form as seen in the example given above. Explore the given lesson to get a better idea of how to find equivalent fractions and how to check if the given fractions are equivalent.
⇒[tex]\frac{2}{13} =\frac{x}{52}[/tex]
⇒[tex]\frac{2(52)}{13} = x[/tex]
⇒[tex]x = 8[/tex]
therefore, 8 is the equivalent of the fraction using a denominator of 52. 2/13
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Given f of x is equal to 1 over the quantity x minus 3 end quantity and g of x is equal to the square root of the quantity x plus 3 end quantity comma what is the domain of f (g(x))?
[–3, ∞)
[–3, 6) ∪ (6, ∞)
(–∞, 3) ∪ (3, ∞)
ℝ
The domain of the composite function is given as follows:
[–3, 6) ∪ (6, ∞)
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given as follows:
[tex](f \circ g)(x) = f(g(x))[/tex]
In this problem, the functions are:
[tex]f(x) = \frac{1}{x - 3}[/tex].[tex]g(x) = \sqrt{x + 3}[/tex]The composite function is of the given functions f(x) and g(x) is:
[tex]f(g(x)) = f(\sqrt{x + 3}) = \frac{1}{\sqrt{x + 3} - 3}[/tex]
The square root has to be non-negative, hence the restriction relative to the square root is found as follows:
[tex]x + 3 \geq 0[/tex]
[tex]x \geq -3[/tex]
The denominator cannot be zero, hence the restriction relative to the denominator is found as follows:
[tex]\sqrt{x + 3} - 3 \neq 0[/tex]
[tex]\sqrt{x + 3} \neq 3[/tex]
[tex](\sqrt{x + 3})^2 \neq 3^2[/tex]
[tex]x + 3 \neq 9[/tex]
[tex]x \neq 6[/tex]
Hence, from the restrictions above, of functions f(x), g(x) and the composite function, the domain is:
[–3, 6) ∪ (6, ∞)
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a coffee shop, the first 100 customers' orders were as follows. Small Medium Large Hot 5 48 22 Cold 8 12 5 What is the probability that a customer ordered a large given that he or she ordered a cold drink? Rounded to the nearest percent, [? ]% Enter
Using it's concept, there is a 20% probability that a customer ordered a large given that he or she ordered a cold drink.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, 8 + 12 + 5 = 25 people ordered a cold drink, and of them, 5 were large, hence the probability is:
p = 5/25 = 0.2 = 20%.
20% probability that a customer ordered a large given that he or she ordered a cold drink.
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1/2x + 1/4y = 3 solve for y
Answer:
y=-2x+12
Step-by-step explanation:
First, subtract 1/2 from each side
1/4y = -1/2x + 3 --> multiply each side by 4
y = -2x + 12 is your final answer
22. Chris bought a new car for $12,500. He made a $3,000 down payment and financed the rest at an annual interest rate of 14.5% for 36 months (3 years). How much less would his total interest be for the same loan for 24 months (2 years)? A. $1,387.50 B. $1,377.50 C. $1,367.50 D. $1,357.50
Answer:
Step-by-step explanation:
Purchase price (A) : $12,500
Down Payment (B): $3,000
Loan Taken (C = A - B): $9500
D : Interest calculation for $9,500 for 3 years P(1 + rt)
= 9500(1 + (14.5/100) * 3)
= 9500(1 + 0.145 * 3)
= 9500 * 1.435
= $13632.5
E : Interest calculation for $9,500 for 2 years P(1 + rt)
= 9500(1 + (14.5/100) * 2)
= 9500(1 + 0.145 * 2)
= 9500 * 1.29
= $12,255
Difference between D - E
= $13632.5 - $12,255
= $1377.5
Hence the answer is B i.e. $1377.5 less interest for same amount of load for 2 years vs 3 years
I need help with my homework please!!
Extremely confused!
I need all the equations imputations and how to solve for everything!
Answer:
what do you need person jjff
5
364,860
0/1 point
Camila has finally found a house she adores! The cost of the home is $210,000, which she intends to purchase on a 30-year fixed mortgage. Blinded by her adoration for the
property, she has agreed to a 5.5% interest rate. Round all answers to the nearest cent.
How much will Camila pay in interest over the lifetime of the mortgage?
The total interest on the mortgage loan is $219,249.60
What is a mortgage loan?
It is a loan taken in order to purchase a property that requires periodic repayments such as monthly repayment since most mortgages are repaid monthly.
Our first task is to determine the monthly repayment using the present value formula of an ordinary annuity because the monthly payment becomes due at the end of each month.
PV=monthly repayment*(1-(1+r)^-N/r
PV=loan amount=$210,000
monthly repayment=unknown(assume it is X)
r=monthly interest rate=5.5%/12=0.00458333333333333
N=number of monthly payments in 30 years=30*12=360
$210,000=X*(1-(1+0.00458333333333333)^-360/0.00458333333333333
$210,000=X*(1-(1.00458333333333333)^-360/0.00458333333333333
$210,000=X*(1-0.19277525234572900)/0.00458333333333333
$210,000=X*0.80722474765427100/0.00458333333333333
$210,000=X*176.12176312456800000
X=$210,000/176.12176312456800000
X=monthly payment=$1,192.36
total repayments(360 months)=$1,192.36*360
total repayments(360 months)=$429,249.60
Total interest=total repayments(360 months)-loan amount
Total interest=$429,249.60-$210,000
Total interest=$219,249.60
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What is the Pythagorean theorem
Answer:
The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.
Pythagoras Theorem Equation
The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.
Answer:
The Pythagoras theorem states that:The sum of the squares on the edges of a right triangle angle is equal to the squareon the hypotenuse.Mathematically stated as: a² +b² = c²Hope this helps.Good luck ✅.Consider the diagram shown and answer the following questions; the radius of this circle is 6 inches.
a. Define how lines a, b, c, and d relate to circle P. (What special names do these lines have in relation to the circle?)
b. If the measure of angle OPS is 139°, what extra information would we need to calculate the measure of angle ORS using intersecting chords? Explain how we can use this information to calculate the angle.
c. Segment NS is 14 the length of segment TO. Explain how theorem 65 would allow us to calculate the length of segments RO, RS, RV, and RT.
The additional information needed to calculate ORS are the measures of SPR and PSR
The special names of the linesThe lines are given as:
Lines a, b, c and d
The special names of the lines are as follows:
Line a: A secant. This is because the line divides the circle into unequal segmentsLine b: A tangent: This is because the line touches the circle at a point on the circumferenceLine c: A diameter. This is because the line divides the circle into equal segmentsLine d: A secant. This is because the line divides the circle into unequal segmentsThe additional information neededThe angle is given as:
OPS= 139 degrees
Start by calculating SPR using
SPR = 180- 139
SPR = 41 degrees
So, the additional information needed to calculate ORS are the measures of SPR and PSR
How to calculate the lengths RO, RS, RV, and RTThe theorem 65 is not stated.
So, the question cannot be answered
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Numbers from 1 to 50 Find the probability of choosing
numbers with 4 in tens places.
Answer: 1/5
Step-by-step explanation:
There are 10 numbers, out of 50, which have a 4 in their tens place: 40, 41, 42, 43, 44, 45, 46, 47, 48, and 49.
Therefore our desired probability is 10/50 or 1/5.
On average, an American hummingbird flaps its wings about 3,180 times per minute.
About how many times per second does it flap its wings?
Enter your answer in the box.
times
Answer:
53 times per second
Step-by-step explanation:
There are 60 seconds in 1 minute, so divide the 3180 flaps per minute into 60 equal parts.
3180 / 60 = 53
Carlos spent 1\dfrac141
4
1
1, start fraction, 1, divided by, 4, end fraction hours doing his math homework. He spent 1\dfrac141
4
1
1, start fraction, 1, divided by, 4, end fraction as much time practicing piano.
How many hours did Carlos spend practicing piano?
write as a fraction
The time Carlos spend practicing his multiplication facts in fraction is 5/16 hours.
FractionA fraction is a value which has a numerator (upper or top value) divided by a denominator (lower or bottom value).
Time Carlos spent doing his math homework = 1 1/4 hoursTime spent practicing his multiplication facts = 1/4 of 1 1/4 hours
= 1/4 × 1 1/4
= 1/4 × 5/4
= (1 × 5) / (4 × 4)
= 5/16 hours
Therefore, the time Carlos spend practicing his multiplication facts is 5/16 hours.
Complete question:
Carlos spent 1 1/4 hours doing his math home work. He spent 1/4 of this time practicing his multiplication facts.
How many hours did Carlos spend practicing his multiplication facts?
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How much, including taxes of 12%, would you pay for an item with a retail price of $194.95?
Answer:
$217.88
Step-by-step explanation:
12% of 194.95 plus the original cost of 194.94 equals the total
1.12*194.54 = $217.8848
Rounded: $217.88