Answers
Answer:
The proportion is \(\frac{35}{108}\) = \(\frac{x}{84}\), and the length of the unknown side is \(\frac{245}{9}\) or 27.22 approximately rounded to the nearest hundredth.
Step-by-step explanation:
Since the triangles are similar, the proportion of corresponding sides are equal. The pairs of corresponding sides in these triangles which we'll use to solve it are LK, KE, MK, and KF. LK and KE are corresponding sides, and their proportion is \(\frac{35}{108}\). MK and KF are corresponding sides, and their proportion is \(\frac{x}{84}\) in which x represents the missing side. The proportions are equal, so \(\frac{35}{108}\) = \(\frac{x}{84}\). Multiply both sides by 84 to isolate the variable, and you'll get \(x = \frac{35*84}{108}\), which is \(\frac{2940}{108}\) or \(\frac{245}{9}\).
Related Questions
Please help as soon as possible
Answers
The exact values are:
sin(α + β) = (-6√5 - 8)/25
cos(α + β) = (4√5 - 6)/25
sin(α - β) = (-6√5 + 8)/25
tan(α - β) = (-9√5 + 45)/4
We have,
Recall the trigonometric identities:
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
sin(a - b) = sin(a)cos(b) - cos(a)sin(b)
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
tan(a - b) = (tan(a) - tan(b))/(1 + tan(a)tan(b))
Using these identities, we can find the exact values of the expressions given.
(a) Sin (α + β)
sin(α + β) = sin(α)cos(β) + cos(α)sin(β)
= (√5/5)(-3/5) + (2/5)(-4/5) (using the values given for sin and cos)
= -6√5/25 - 8/25
= (-6√5 - 8)/25
(b) Cos (α + β)
cos(α + β) = cos(α)cos(β) - sin(α)sin(β)
= (2/5)(-3/5) - (√5/5)(-4/5) (using the values given for sin and cos)
= -6/25 + 4√5/25
= (4√5 - 6)/25
(c) Sin (α - β)
sin(α - β) = sin(α)cos(β) - cos(α)sin(β)
= (√5/5)(-3/5) - (2/5)(-4/5) (using the values given for sin and cos)
= -6√5/25 + 8/25
= (-6√5 + 8)/25
(d) tan (α - β)
tan(α - β) = (tan(α) - tan(β))/(1 + tan(α)tan(β))
= ((√5/5) - (-4/5))/(1 + (√5/5)(-4/5)) (using the values given for sin and cos)
= (9√5/5)/(1 - 4/5√5)
= (-9√5 + 45)/4
Therefore,
The exact values are:
sin(α + β) = (-6√5 - 8)/25
cos(α + β) = (4√5 - 6)/25
sin(α - β) = (-6√5 + 8)/25
tan(α - β) = (-9√5 + 45)/4
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What is the volume of the triangular prism?
please help!! quickly its a test a look at the picture
7th grade math
Answers
The area of the triangle is:
A = (base•height) : 2 = (3•2) : 2 = 3 m2
So the volume is:
V = 3 • 8 = 24 m3
(SAT prep) Find the value of x in each case of the following exercises:
Answers
The value of x from the figure is 70°
How to determine the valueIt is important to note that alternate angles are equal and angles in a triangle sum up to 180°
We then have that,
x + 50 + 60 = 180 °
x + 110 = 180°
Make 'x' subject
x = 180 - 110
x = 70 °
Thus, the value of x from the figure is 70°
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Match each expression with A, B, C or D.
A=a^3
B=6a
C=12a
D=3a^2
i)3a x 4
ii)a^2xa
iii) 6 1/2 a^2
Answers
The matching expressions are:
\(i) 3a x 4 = C (12a)\\ii) a^2 x a = A (a^3)\\iii) 6 × 1/2 a^2 = D (3a^2)\)
i) 3a x 4 can be represented as C (12a) since multiplying 3a by 4 gives 12a.
ii) a^2 x a can be represented as A (a^3) since multiplying a^2 by a gives a^3.
iii) \(6 \times 1/2 a^2\) can be represented as D (3a^2) since multiplying 6 by 1/2 and then by a^2 gives 3a^2.
To understand the matching expressions, let's break down each one:
i) 3a x 4:
This expression represents multiplying a variable, 'a', by a constant, 4. The result is 12a, which matches with C (12a).
ii) a^2 x a:
This expression represents multiplying the square of a variable, 'a', by 'a' itself. This results in a^3, which matches with A (a^3).
iii) 6 × 1/2 a^2:
This expression involves multiplying a constant, 6, by a fraction, 1/2, and then multiplying it by the square of 'a', a^2. The final result is 3a^2, which matches with D (3a^2).
Therefore, the matching expressions are:
i) 3a x 4 = C (12a)
ii) a^2 x a = A (a^3)
iii) 6 × 1/2 a^2 = D (3a^2)
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Can someone please help me out!!?
Answers
Answer:
x = 7
Step-by-step explanation:
\(\frac{10}{8} = \frac{3x-6}{12}\) --> Triangle Similarity Theorem
120 = 8(3x - 6) --> Cross Multiplying
120 = 24x - 48 --> Distributing the 8
24x - 48 + 48 = 120 + 48 --> Adding 48 on both sides
24x = 168 --> Simplifying
24x/24 = 168/24 --> Divide 24 on both sides
x = 7 --> Simplifying
Hope this helped! <3
based on the spss output what cna you concllude about the relationship between degree attainment and age dbrn for men
Answers
There is sufficient statistical evidence at 5% level of significance that there is relationship between degree attainment and AGEKDBRN for women.
What is ANOVA model for men?
To ascertain whether there are any statistically significant differences between the means of three or more independent (unrelated) groups, the one-way analysis of variance (ANOVA) is used.
An n-way ANOVA allows a researcher to employ more than two independent variables (with n being the number of independent variables you have). For instance, any disparities in IQ scores can be investigated concurrently by country, gender, age group, ethnicity, etc.
Relationship between degree attainment and AGEKDBRN for women
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Which percent is equivalent to 2 5/6?
Answers
Answer: 283.3333333% (283.3%)
Step-by-step explanation:
First, lets turn 2 5/6 into and improper fraction. It becomes 17/6.
Now, we divide 17/6
17/6 = 2.833333333
Now, to turn it into a percent, we multiply it by 100, or move the decimal point 2 places to the right. That gives us 283.3333333% (283.3%)
Hope this helps!
What is an equation of the line that passes through the points (1,6) and (2, 7)?
Answers
The equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.
We can use the point-slope version of the equation, which is: to determine the equation of a line passing through two specified points.
y - y₁ = m(x - x₁)
where (x₁, y₁) are the coordinates of one of the points, m is the slope of the line, and (x, y) are the coordinates of any other point on the line.
Use the points (1,6) and (2,7) to find the equation of the line:
Using (x₁, y₁) = (1,6):
y - 6 = m(x - 1)
Now, substitute the coordinates (2,7) into the equation:
7 - 6 = m(2 - 1)
1 = m
So, the slope of the line is m = 1.
Substitute this value into the equation:
y - 6 = 1(x - 1)
y - 6 = x - 1
y = x + 5
Therefore, the equation of the line that passes through the points (1,6) and (2,7) is y = x + 5.
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5. Simplify
(7x2+ 8) - (x2 - 2)
Answers
Answer:
\((7 \times 2 + 8) - ( {x}^{2} - 2) \\ (14 + 8) - ( {x}^{2} - 2) \\ 14 + 8 - {x}^{2} + 2 \\ 22 + {x}^{2} + 2 \\ 24 + {x}^{2} \)
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
Find the midpoint: (-1, -5/2) (-2, -3/2) (-5/2, -1) (-1, -3)
Answers
Answer:
\(\left(-\frac{5}{2}, -1 \right)\)
Step-by-step explanation:
\(\left(\frac{-5+0}{2}, \frac{2-4}{2} \right)=\left(-\frac{5}{2}, -1 \right)\)
Need the answers for both questions shown on the image
Answers
Answer:
4. x=2, y=-5
5. x=3, y=4
Step-by-step explanation:
Which expression can be placed on the right side of the equals sign to form an equation. 2+33=
Answers
Answer:
7x.
Step-by-step explanation:
2 + 33 = 7x
35 = 7x
Solution is x = 5.
Answer: 5² + 4
Step-by-step explanation:
7. Write a biconditional for the following conditional. Determine the truth value
of the new statement. If two lines have the same slope, then they are parallel.
Answers
Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.
How do parallel lines work?
Lines in a plane that are regularly spaced apart are known as parallel lines. Parallel lines don't overlap each other. Perpendicular lines are those that cross at a straight angle of 90 degrees.Only if the slopes of two lines are equal can they be said to be parallel. If two lines have different y-intercepts and equal slopes, they are said to be parallel. In a plane, parallel lines are two lines that never cross (meaning they will continue on forever without ever touching). The equal slopes of parallel lines are a distinctive feature. The rise (change in Y coordinates) over the run (change in X coordinates) of a line, or its steepness, is referred to as the slope of a line. The most typical way to depict parallel lines is with two vertical lines (ll). Line AB is parallel to CD, for instance, as indicated by the formula AB ll CD.Learn more about parallel lines
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The size of a television screen is given as the length of diagonal. For example, a 29 inch screen is 29 inches from the lower left corner to the upper right corner. Shaun bought a new 40 inch television screen. One side of the screen is 24 inches long. How long is the other side? 8.7C *
Answers
Answer:
32
i did the test
True OR False a graph must be a straight line and go through the point (0, 0) in order to represent a proportional relationship
Answers
Answer:
TRUE graph must be a straight line and go through the point (0,0)
Step-by-step explanation:
Have a good day :)
Segments RA and NY are best described as which of the following?
A. Parallel segments
B. Perpendicular lines
C. Perpendicular segments
D. Perpendicular rays
Answers
Use these clues to find the dividend.
• The divisor is 7.
• The quotient is 5.
What is the dividend?
Answers
Answer:
Dividend = Divisor * Quotient
Dividend = 7 * 5
Dividend = 35
Which Expression is a factor of 16a2 − 25
Answers
Answer:
should be (4a-5)x(4a+5)
Step-by-step explanation:
A line with a slope of 5 passes through the point (6, 12). Write the equation for this line.
Answers
Step-by-step explanation:
Given
\(slope(m) = 5\)
y-intercept (c) = 12
Now the equation of the line is
y = mx + c
y = 5x + 12
Hope it will help :)❤
-7+(63/9) Evaluate the Following Expression
Answers
Answer:
0
Step-by-step explanation:
\(-7+(\frac{63}{9})=-7+7=0\)
the soccer team manager plans to have 2 gallons of water for every 4 players on the team during practice. determine whether the statements about ratios are true or false.
A. The team manager needs 1 gallon of water for every 1 player
` true or false
B. The ratio of number of players to gallons of water is 2:1
` true or false
C. The team manager ould need 4 gallons of water for 10 players
` true or false
D. For 30 players, the team manager would need 15 gallons of water ` true or false
Answers
Answer:
A.=False
B.=True
C.=False
D.=True
Step-by-step explanation:
The original ration is 2 gallons of water for 4 players.
Each player requires 1/2 gallon of water.
To get the amount of water needed multiply 1/2 by the amount of players.
1*(1/2) does not equal 1
2*(1/2) equals 1
10*(1/2) does not equal 4
30*(1/2) equals 15
B. What is each piece measurement if the angle is cut into 9 equal
lengths? Kerf width is 0.125.
Answers
Each piece Measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.
When a particular angle is cut into nine equal parts, the measure of each piece needs to be calculated.
Therefore, it is essential to first calculate the total angle measure and then divide it by the number of parts into which it is being cut.
What is an Angle?
An angle is a geometrical shape that consists of two rays sharing a common endpoint. The common endpoint is known as the vertex, and the two rays are known as the arms of the angle. An angle can be measured in degrees, radians, or gradians. Degrees are the most commonly used unit of measuring angles.How to Calculate Each Piece Measurement of an Angle if Cut into 9 Equal Lengths
To determine each piece measurement of an angle if cut into nine equal lengths, we will need to carry out the following steps:
Step 1: Calculate the total angle measure Suppose the angle being cut into nine equal lengths is an obtuse angle measuring 120 degrees. In that case, the total angle measure will be 120 degrees.
Step 2: Divide the total angle measure by the number of parts into which it is being cut.120 degrees ÷ 9 = 13.3333 degrees
Step 3: Add the kerf width to the piece measurements.0.125 x 9 = 1.125 degrees13.3333 + 1.125 = 14.4583 degrees
Therefore, each piece measurement of an angle of 120 degrees cut into nine equal lengths with a kerf width of 0.125 would be 14.4583 degrees.
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The boxplot displays the total cost of attendance for all US public and private universities.
Use this graphic to complete the statements.
Both distributions of the total cost of attendance are
. The average cost of attendance is higher for
universities. The costs of more than
% of the public institutions were within the costs of the lowest 25% of private institutions. Both the range and IQR was higher for
universities. Both distributions have
outliers.
Answers
Both distributions of the total cost of attendance are skewed right
The average cost of attendance is higher for private universities.
The costs of more than 75 % of the public institutions were within the costs of the lowest 25% of private institutions.
Both the range and IQR was higher for private universities
Both distributions have outliers.
What is a box plot?A boxplot is a standardized way of displaying the distribution of data based on a five number summary (“minimum”, first quartile [Q1], median, third quartile [Q3] and “maximum”).
It can tell you about your outliers and what their values are
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Answer:
skewed right private 75 private do have outliers
Step-by-step explanation:
A young executive is going to purchase a vacation property for investment purposes. She needs to borrow $127,000.00 for 28 years at 4.3% compounded monthly, and will make monthly payments of $650.71. (Round all answers to 2 decimal places.)
What is the unpaid balance after 15 months? $
During this time period, how much interest did she pay? $
Answers
a.
39. A digital watch set accurately at 8:30 am and then lost 2 second
every minute. What time was indicated on the watch at 6:30 pm
of the same day. If the watch operated in a continuous way until
that time.
Answers
Find the value of x
8,
9,
7,
10
Answers
The value of x in this problem, considering the intersecting chords, is given as follows:
x = 10.
How to obtain the value of x?A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.
When two chords intersect each other, then the products of the measures of the segments of the chords are equal.
Hence the value of x is obtained as follows:
12x = 15 x 8
12x = 120
x = 10.
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whats5666778877 x 81 + 1
Answers
Answer: 459009089038
Step-by-step explanation: I smart for a 3yrs old kid. And I don't even need a diAper but my 17 yrs old sister does so she weirdo...
HEY, I also have good news. I JUST GOT POTY TRANED!! YA Boi.
Find the value of x.
x = ___
Answers
Solving steps In photo wrote down on paper
if gage gets 35 bucks per month how much months will it take him to get 300 bucks
Answers
Answer:
at least 9 months
Step-by-step explanation:
35×9=315
Answer:
It will take Gage 9 months to get $300.
Step-by-step explanation:
Let \(m\) = months.
The expression \(35m\) will represent money per month, and must be greater than or equal to $300.
Set up your inequality:
\(300\leq 35m\)
Divide both sides of the inequality by the coefficient of \(m\):
\(8.6=m\)
Round to the nearest whole number:
\(9=m\)
Therefore, it will take Gage 9 months to get $300.
-
Check your work by substituting the solved value into the initial inequality:
\(300\leq 35(9)\)
\(300\leq 315\)
Since $315 is greater than $300, our solution is correct.
OPTIONAL - Space to calculate your work.
REQUIRED
1
9.
How much water can Portia’s new aquarium hold?
a) 166.28 cubic inches
b) 790.28 cubic inches
c) 956.56 cubic inches
d) 3,120 cubic inches
e) 6,240 cubic inches
REQUIRED
1
10.
Portia's new fish require complete darkness for 12 hours a day. Rather than buying a blackout curtain for her room, she decides to make an aquarium cover out of a tropical print, with a blackout liner. How much tropical print fabric will she need to purchase in order to cover the top and sides of the aquarium?
a) 864 square inches
b) 624 square inches
c) 1,144 square inches
d) 1,104 square inches
e) 480 square inches
Answers
A) The amount of water that Portia’s new aquarium holds is: d) 3,120 cubic inches
B) The amount of tropical print fabric she will need to purchase in order to cover the top and sides of the aquarium is: a) 864 square inches
How to find the volume of the hexagon?The number of sides that a hexagon has is Six sides.
The area of a triangle has the formula:
A = ¹/₂bh.
A hexagon is a total of six triangles.
Thus:'
Area of hexagon here is:
A = 6(¹/₂bh)
B (base) = 8in. The base is usually always at the bottom.
We add as the height into the equation to get:
Area = 6(¹/₂ * 8 * 10) * 13 = 3120.
B) Surface area is the sum of all the faces. There are 2 hexagonal faces and then 6 sides.
Thus:
Surface area = 6(¹/₂ * 8 * 10) + (8 * 13) + 6(104) = 864 square inches
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