By two column proof, we get:
∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° and ∠8 = 60
Two column Proof:
A two-column geometric proof consists of a list of statements and the reasons why we know these statements are true. The complaints are listed in the left column and the reasons for the complaint are listed in the right column.
According to the Question:
l II m and p is their transversal and 1 = 120°
∠1 + ∠2 = 180 °(Straight line)
120° + ∠2 = 180° > ∠2 = 180° - 120° = 60°
∠2 = 60°
But ∠1 = ∠3 (Vertically opposite angles)
∠3 = ∠1 = 120°
Similarly ∠4 = ∠2
By Vertically opposite angles,
∠4 = 60°
∠5 = ∠1 (Corresponding angles)
∠5 = 120°
Similarly, by corresponding angles:
∠6 = ∠2
∠6 = 60°
∠7 = ∠5 (Vertically opposite angles)
∠7 = 120°
And,
∠8 = ∠6 (Vertically opposite angles)
∠8 = 60°
Hence ∠2 = 60°, ∠3 = 120°, ∠4 = 60°, ∠5 = 120°, ∠6 = 60°, ∠7 = 120° and ∠8 = 60°
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A softball team has 20 players. How many 9 player batting orders are possible?
There are 184,756 possible 9 player batting orders for a softball team with 20 players.
The formula to calculate the combination number of possible batting orders for a team with n players is n!/(n-r)! where n = the total number of players, and r = the number of players in the batting order. Therefore, for a softball team with 20 players, the number of possible 9 player batting orders is 20!/(20-9)! = 184,756.
20! = 20 × 19 × 18 × 17 × 16 × 15 × 14 × 13 × 12 × 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1
(20-9)! = (20 - 9) × (19 - 9) × (18 - 9) × (17 - 9) × (16 - 9) × (15 - 9) × (14 - 9) × (13 - 9) × (12 - 9) × (11 - 9) × (10 - 9) × (9 - 9)
20!/(20-9)! = 184,756
Therefore, there are 184,756 possible 9 player batting orders for a softball team with 20 players.
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The average cost of a pizza in 2022 is $18. Inflation has been averaging 3.25% for many years. In what year was the average cost of a pizza 9$ (half)? Approximate using rule of 72.
Therefore , the solution of the given problem of average comes out to be the average price of a pizza in 2000 was about $9 (or half of $18).
Explain average.An organised collection's median value is the precise value that makes up the collection's mean. In this case, the ratio between the lowest and highest 50% of the data is a normal but rather probability measure. When finding the middle and mode, a variety of algorithms can be applied in order to identify any unusual or even amounts of values.
Here,
By dividing 72 by the interest rate, we can calculate how many years it will take an investment to double in value at a specific interest rate. This is known as the law of 72. In this instance
With an inflation rate of 3.25 percent, it takes roughly how many years for the price of a pizza to double as a result of inflation:
72 / 3.25 = 22.15 years
In light of this, we can calculate that a pizza cost $9 (half of $18) roughly 22 years ago, which corresponds to the following year:
2022 - 22 ≈ 2000
As a result of inflation running at an average of 3.25% for many years, the average price of a pizza in 2000 was about $9 (or half of $18).
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Find the TOTAL surface area of each figure. Round answers to the nearest hundredth, if necessary
The total surface area of this figure is 94, rounded to the nearest hundredth.
The figure in question is a rectangular prism. To calculate the total surface area of a rectangular prism, we must use the following formula: Total Surface Area = 2(lw + wh + lh), where l is the length, w is the width, and h is the height.
For this figure, the length is 5, the width is 4, and the height is 3. Thus, we can calculate the total surface area of the figure as follows: 2(5*4 + 4*3 + 5*3) = 2(20 + 12 + 15) = 2(47) = 94. Therefore, the total surface area of this figure is 94, rounded to the nearest hundredth.
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A classroom has 23 grade twelves (13 females and 10 males) and 11 grade elevens (7 females and 4 males). If the teacher randomly chooses a student at random, what is the probability that it is a female or a grade eleven?
P(female or grade 11) = 31/34
Given that a classroom has 23 grade twelves (13 females and 10 males) and 11 grade elevens (7 females and 4 males). The teacher randomly chooses a student at random, what is the probability that it is a female or a grade eleven?The sample space is the total number of students which is given by23 + 11 = 34.There are 13 females in the grade 12 and 7 females in the grade 11. So the total number of female students is 13 + 7 = 20.There are 11 grade 11 students. So the total number of grade 11 students is 11.The total number of students that are female or in grade 11 is obtained by adding the two:20 + 11 = 31.So the probability of choosing a female or grade 11 student is:P(female or grade 11) = 31/34
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a) Show that sin(BAC) = in both drawings. 5 b) Work out angle BAC in the drawing where it is acute. c) Work out angle BAC in the drawing where it is obtuse. Give each angle to 1 d.p. 15 mm B 24 mm 30° B. 15 mm A 24 mm 30° Not drawn accurately
Answer:
Step-by-step explanation:
Which statement best compares and contrasts the two formats?
The infographic shows the movement of water visually, while the text describes it.
The infographic would be less appealing to visual learners than the text.
It is impossible to understand the infographic without the text.
The text is more accurate than the infographic.
Given: ABCD is a rectangle
AE≅CF
Prove: DE≅BF
(written in a two-column proof please)
Therefore , the solution of the given problem of rectangle comes out to be DE ≅ BF | Corresponding parts of congruent triangles are congruent
What is a rectangle?A rectangle is a cube with four perpendicular sides in the Euclidean plane. It is also known as an equal-sided rectangle or an equiangular trapezoid. Additionally, the trapezoid may have a straight border. A square has four edges that are the same length. Quadrilaterals that are rectangular have four identical sides but instead four 90° edges. As a result, it is sometimes referred to as a "rectangular trapezoid".
Here,
ABCD is a rectangle | Given
=> AE ≅ CF | Given
AEFC is a parallelogram | Definition of parallelogram
=> AC ≅ EF | Opposite sides of a parallelogram are congruent
=> ∠EAF ≅ ∠ACF | Opposite angles of a parallelogram are congruent
=> ∠EAF ≅ ∠CAD | Diagonals of a rectangle bisect each other
=> ∠ACF ≅ ∠CAD | Transitive property of congruence
=> ∆ACF ≅ ∆CAD | ASA (angle-side-angle) congruence
=> DF ≅ DF | Reflexive property of congruence
=> ∆DFC ≅ ∆DFE | SSS (side-side-side) congruence
=> ∠BCF ≅ ∠ADE | Corresponding angles of congruent triangles are congruent
=> ∠BCF ≅ ∠BDF | Diagonals of a rectangle bisect each other
=> ∠ADE ≅ ∠BDF | Transitive property of congruence
=>∆ADE ≅ ∆BDF | ASA congruence
=> DE ≅ BF | Corresponding parts of congruent triangles are congruent
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Sebastian is supposed to walk his dog 25 minutes every day. He was running late for school, and was only able to walk his dog 20 minutes today. Choose the division expression that shows what fraction of time Sebastian walked the dog today.
Therefore , the solution of the given problem of expressions comes out to be Sebastian strolled his dog for 4/5 of the allotted time today.
What does a expression actually mean?Calculations like arbitrary division, joining, multiplication variable , and removal are required. If they were merged, they would produce the following: A mathematical formula, some data, and an equation. A declaration of veracity is made up of values, elements, formulae, and mathematical operations like additions, subtractions, errors, and segments. It is possible to assess and analyse words and sentences.
Here,
You can calculate how much of the allotted time Sebastian spent walking his dog today by dividing the time he spent walking him (20 minutes) by the time he was meant to walk him (25 minutes).
Therefore, the division formula that represents this portion is:
=> 20 ÷ 25
The short form of this phrase is:
=> 4/5
As a result, Sebastian strolled his dog for 4/5 of the allotted time today.
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(a-b)x2-(a+b)x+2b ssolve this quadratic equation plsss
The two solutions to the given quadratic equation are x = (a+b + √(a2 - 6ab + 8b2))/(2(a-b)) and x = (a+b - √(a2 - 6ab + 8b2))/(2(a-b)).
The general form of a quadratic equation is ax2 + bx + c = 0. To solve this equation, we need to use the Quadratic Formula. The Quadratic Formula is [tex]x = [-b ± √(b2 - 4ac)]/ 2a[/tex].
We can plug the values for a, b, and c into this equation. For this equation, a = (a-b), b = -(a+b), and c = 2b.
Therefore, using the Quadratic Formula, we get [tex]x = [-(-(a+b)) ± √((-(a+b))2 - 4(a-b)(2b))]/ 2(a-b)[/tex].
Simplifying this, we get [tex]x = [a+b ± √(a2 + 2ab - 4ab - 8b2)]/(2(a-b))[/tex].
Finally, we can solve for the two values of x by computing the two cases. In the first case, we add the square root, and in the second case, we subtract the square root. This gives us the two solutions [tex]x = [(a+b + √(a2 - 6ab + 8b2))/(2(a-b))][/tex] and [tex]x = [(a+b - √(a2 - 6ab + 8b2))/(2(a-b))][/tex].
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Merisa spent 3/4 of her money on a dictionary. She spent 1/2 of the remainder on a calculator. The dictionary cost $30 more than the calculator. How much did the dictionary cost?
Step-by-step explanation:
she has x money at the beginning.
(3/4)x = dictionary
the remainder is (1/4)x.
1/2 of that (1/4 × 1/2 = 1/8) is the calculator.
that means she has (1/4)x - (1/8)x = (1/8)x left.
the dictionary is $30 more than the calculator.
so,
(3/4)x = (1/8)x + 30
(6/8)x = (1/8)x + 30
(5/8)x = 30
5x = 240
x = 240/5 = $48
so, the dictionary cost
(3/4)x = (3/4)×48 = 3×12 = $36
find the area of a circle with a circumference of 11 pi feet 
Answer:
95ft²
Step-by-step explanation:
2πr = 11π
πr = 11π/2
r = 11/2 = 5.5ft
area = πr²
area = π(5.5)² = 95.0331... ≈ 95ft²
when ball hits the sweet spot, it will travel. a greater distance if it hits any other part of the bat. a shot for distance than if it hits any other part of the bat .the same distance as if it hits any other part of the bat . no distance at all
A greater distance if it hits any other part of the bat.
When a ball hits the sweet spot of a bat, it will travel a greater distance than if it hits any other part of the bat. This is because the sweet spot is part of the bat where the energy transfer from the bat to the ball is most efficient, resulting in a more powerful hit and greater distance travelled by the ball.
This is because the sweet spot is part of the bat where the energy transfer from the bat to the ball is most efficient, resulting in a more powerful hit and greater distance travelled by the ball.
If the ball hits any other part of the bat, the energy transfer is less efficient, resulting in a less powerful hit and a shorter distance travelled by the ball.
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I need help on quiz 4-1 classifying and solving for sides/ angles
According the given question the side οf the WY is 25.
What is cοngruent by ASA?Angle-Side-Angle cοngruence rule is referred tο as ASA. Twο triangles are said tο be cοngruent accοrding tο this rule if any twο angles and the side included between them οf οne triangle are equal tο the cοrrespοnding angles and the included side οf the οther triangle.
See if the twο triangles given, ABC and XYZ, are cοngruent accοrding tο the ASA rule by lοοking at the image prοvided belοw. Accοrding tο the ASA cοngruence rule, twο triangles are said tο be cοngruent if twο οf their respective sides and angles are equal tο thοse οf twο οther triangles and their respective sides and angles, respectively.
BC = BD
m< B=13x-35
m < C = 5x-19
m < D = 2x + 14
m< B=13*11 - 35
m< B=143-35
m< B = 108
m<C=5x-19
m<C=511 - 19
m < C = 55-19
m < C = 36
This is sο because the theοrem οf SAS (Side-Angle-Side)
Sο, we have:
9x117x - 3
WY = 7x-3
WY = 7*4-3
WY = 28-3
WY = 25
Hence the side οf the WY is 25.
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Helpppppppppppppppppppp
Answer:
SAS proves that these triangles are congruent.
What is the value of x.
Answer:
19.8
Step-by-step explanation:
Let X be the number of successes observed in a sample of n = 4 items selected from a population of N = 8. suppose that of the N=8 items, 5 are considered ''successes''.
a) Find the probability of observing all successes.
b) Find the probability of observing one success.
c) Find the probability of at most two successes.
a)0.1071
b)0.2857
c) 0.3571`.
a) The probability of observing all successes is `(5/8) × (4/7) × (3/6) × (2/5) = 0.1071`b) The probability of observing one success is `(5/8) × (3/7) × (4/6) × (4/5) = 0.2857`c) The probability of at most two successes is equal to `P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)`.The probability of observing zero successes is `(3/8) × (2/7) × (1/6) × (0/5) = 0`.The probability of observing one success is `(5/8) × (3/7) × (4/6) × (4/5) = 0.2857`The probability of observing two successes is `(5/8) × (3/7) × (4/6) × (1/5) = 0.0714`.Therefore, `P(X ≤ 2) = 0 + 0.2857 + 0.0714 = 0.3571`.
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Fatal Accidents The American Automobile Association (AAA) reports that of car accidents, 56% are caused by aggressive driving. If 3 accidents are chosen at random, find the probability for the following. Please round the final answers to 2 or 3 decimal places. Part 1 of 3 (a) None are caused by aggressive driving. P (none are caused by aggressive driving) = _____
Answer : The probability that none of the 3 accidents are caused by aggressive driving is 0.085, according to the American Automobile Association (AAA).
The probability of an accident being caused by aggressive driving is 56%, or 0.56. Therefore, the probability of an accident NOT being caused by aggressive driving is 1 - 0.56 = 0.44. Since the accidents are chosen at random, we can assume that they are independent events. Therefore, we can multiply the probabilities together to find the overall probability.
For part 1, we want to find the probability that none of the 3 accidents are caused by aggressive driving. This means we want the probability of an accident not being caused by aggressive driving (0.44) to happen 3 times in a row:
P(none are caused by aggressive driving) = 0.44 * 0.44 * 0.44 = 0.085184
Round to 3 decimal places:
P(none are caused by aggressive driving) = 0.085
Therefore, the probability that none of the 3 accidents are caused by aggressive driving is 0.085, according to the American Automobile Association (AAA).
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Estimate 12% of 77.
10
8
6
12
Answer:
Step-by-step explanation:
12% of 77 is 10.24 or 10.
Step-by-step explanation:
12/100 * 77
12*77=824
824/100
divide by 2
206/25
use long division method
8.24
Keshawn has � x nickels and � y dimes, having a maximum of 14 coins worth a minimum of $1 combined. A maximum of 4 of the coins are nickels. Solve this system of inequalities graphically and determine one possible solution. Number\
One possible solution is Keshawn has 2 nickels and 12 dimes.
What is inequality equation?
An inequality equation is a mathematical expression that compares two values or expressions using inequality symbols such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to)
To solve the system of inequalities graphically, we can plot the two inequalities on the coordinate plane and shade the region that satisfies both inequalities. Let x be the number of nickels and y be the number of dimes.
The first inequality represents the maximum number of coins:
x + y ≤ 14
The second inequality represents the minimum value of the coins:
0.05x + 0.1y ≥ 1
We can rewrite this inequality as:
x + 2y ≥ 20
Now we can plot these two inequalities on the coordinate plane:
Draw a horizontal line for x + y = 14.
Draw a diagonal line with negative slope for x + 2y = 20.
Shade the region below the diagonal line and to the left of the horizontal line.
The shaded region represents the feasible region that satisfies both inequalities. We also know that x ≤ 4 since a maximum of 4 coins are nickels.
One possible solution that lies in the shaded region and satisfies the constraint x ≤ 4 is (x, y) = (2, 12). This means Keshawn has 2 nickels and 12 dimes. We can check that this solution satisfies both inequalities:
2 + 12 = 14 (maximum number of coins)
0.05(2) + 0.1(12) = 1.2 ≥ 1 (minimum value of the coins)
Therefore, one possible solution is Keshawn has 2 nickels and 12 dimes.
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The ratio of the student government budget for dances to its budget for charity events is 5 to 7. If $532.00 is budgeted for charity events, how much is budgeted for dances?
The amount budgeted for dances is approximately $380.00.
Assume that "x" is the budgeted sum for dances. The problem states that there is a 5:7 ratio between the budget for dances and the budget for charitable activities. Hence, we can write:
x/532 = 5/7
We can cross-multiply and simplify to find the answer for "x"
7x = 532 × 5
7x = 2660
x = 2660/7
x ≈ 380.00
The estimated $380.00 planned money for dances is the result.
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Pls help help Algebra1
The expanded form that can be used to factor the function is 12x² - 18x + 10x - 15.
option C,
What is the factorization of the equation?
To factor 12x² - 8x - 15 by grouping, we need to split the middle term -8x into two terms whose sum is -8x and whose product is -180 (the product of 12 and -15).
We can do this by splitting -8x into -18x and +10x:
12x² - 18x + 10x - 15
Now, we can group the first two terms together and the last two terms together, and factor out the greatest common factor from each group:
6x(2x - 3) + 5(2x - 3)
Notice that we have a common factor of (2x - 3) in both groups, so we can factor it out:
(2x - 3)(6x + 5)
Therefore, the factored form of 12x² - 8x - 15 by grouping is (2x - 3)(6x + 5).
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Determine whether the equation is true or false.
By answering the presented question, we may conclude that When x equals 7, the equation holds true. As a result, "True" is the correct response.
What is equation?A math equation is a technique that links two assertions and denotes equivalence using the equals sign (=). In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For example, in the equation 3x + 5 = 14, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on either side of a letter. The logo and the programmed are usually interchangeable. As an example, 2x - 4 equals 2.
The image's equation is:
2x + 4 = 18
We must solve for x to discover if the equation is true or untrue.
When we subtract 4 from both sides, we get:
2x = 14
When we divide both sides by 2, we get:
x = 7
When x equals 7, the equation holds true. As a result, "True" is the correct response.
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the only question i need help is number 48 pleaseee
Therefore, the measure of angle 1 is 40°.
What does a mathematical angle mean?Two rays (half-lines) that share a terminal are combined to form an angle. In contrast, the rays are variously referred to as the angle's legs and its arms, with the latter serving as the angle's vertex.
The measure of an inscribed angle is half the measure of its intercepted arc. Therefore, we can use this property to find the measure of angle 1.
If mAB = 80°, then arc AB is also 80° because an inscribed angle intercepts an arc with the same measure as the angle. Therefore, the measure of arc AB is 80°.
Since angle 1 is an inscribed angle that intercepts arc AB, its measure is half the measure of arc AB. Therefore, we can find the measure of angle 1 as follows:
m∠1 = (1/2) x m arc AB
m∠1 = (1/2) x 80°
m∠1 = 40°
Therefore, the measure of angle 1 is 40°.
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1). Solve this 11-11x11+11=?
After solving the given numbers with (PEMDAS) 11 - 11 x 11 + 11 = we get the answer of -88.
To solve 11-11x11+11, we need to use the order of operations, which is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is:
Parentheses
Exponents
Multiplication and Division (from left to right)
Addition and Subtraction (from left to right)
Using this order of operations, we can simplify the expression as follows:
11 - 11 x 11 + 11
= 11 - 121 + 11 (since multiplication should be done before addition and subtraction)
= -99 + 11
= -88
Therefore, the value of 11-11x11+11 is -88.
In general, when simplifying expressions, it is important to follow the order of operations to ensure that you get the correct answer. Additionally, it is always a good idea to check your work by plugging the answer back into the original expression and making sure that it is correct.
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Lupe measured the height of three rectangular prisms she was using to pack up some clothing. The large box was 7/8 of a meter tall. The medium box was 2/6 shorter than the large box. The small box was 1/4 of a meter shorter than the medium box. If the boxes are all stacked on top of each other, what is their combined weight
If the boxes are all stacked on top of each other, what is their combined height is 11/8
Height of large box = 7/8m
Height of medium box = 2/6m shorter than large box
Height of small box = 1/4m shorter than the medium box
Calculating the height of the medium and small boxes.
Medium box height x large box height
= 2/6 × 7/8
= 7/24
Since, the small box is 1/4 of a meter shorter than the medium box, therefore its height -
= 7/24 - 1/4
= 5/24
Calculating the height of three boxes -
7/8 + 7/24 + 5/24
= 21/24 + 7/24 + 5/24
= 33/24
= 11/8
Correct Question:
Lupe measured the height of three rectangular prisms she was using to pack up some clothing. The large box was 7/8 of a meter tall. The medium box was 2/6 shorter than the large box. The small box was 1/4 of a meter shorter than the medium box. If the boxes are all stacked on top of each other, what is their combined height?
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What is the volume of the prism, in cubic centimeters?
Answer:
Vol = 120 cm^3
Step-by-step explanation:
The volume of a prism is:
Vol = BaseArea×height
Here, the base is the triangle.
Area_triangle
= 1/2bh
= 1/2•6•4
= 12 cm^2
The height is 10cm (and we don't even need the 5cm measurement given)
Volume
= BaseArea × height
= 12 × 10
= 120 cm^3
It’s a solve for why problem pls help me
The exponential function in the given table is:
y = 0.02*(1/2)^x
How to get the function in the table?This seems to be an exponential function of the form:
y = a*b^x
Using the points in the table we can try to find the values of a and b.
for the first point we can write:
0.02 = a*b^0
0.02 = a
Then the function is:
y = 0.02*b^x
Now the second point, (1, 0.01), replacing that we will get:
0.01 = 0.02*b^1
0.01 = 0.02*b
0.01/0.02 = b
1/2 = b
The function is:
y = 0.02*(1/2)^x
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A bottle of apple juice has 25 ounces. Find the number of quarts of apple juice in a case of 24 bottles
There are 18.75 quarts of apple juice in a case of 24 bottles.
To calculate the number of quarts of apple juice in a case of 24 bottles, we must first calculate the number of ounces in the case. To do this, we can use the formula:
Total Ounces = Number of Bottles x Ounces per Bottle
Total Ounces = 24 x 25
Total Ounces = 600
Now that we have the total ounces of apple juice in the case, we can convert this to quarts using the formula:
Quarts = Ounces ÷ 32
Quarts = 600 ÷ 32
Quarts = 18.75
Therefore, there are 18.75 quarts of apple juice in a case of 24 bottles.
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10. Kendall drew a right triangle. The tangent value for one angle in her triangle is 1.8750. Which set of side lengths could belong to a right triangle similar to the triangle Kendall drew? A. 16, 30, 35 B. C. 6, 8, 10 D. 1.875, 8, 8.2 8, 15, 17
The sets of side lengths that are similar to the triangle that Kendall drew are; A. 16, 30, 35, and D. 8, 15, 17.
How to obtain the sidesThe tangent of a right triangle is given as the opposite side divided by the adjacent side. Now, we are given the value of the tangent to be 1.8750.
To obtain the tangents, we are going to divide the opposite by the adjacent as follows:
30/16 = 1.875
8/6 = 1.333
8/1.875 = 4.266
15/8 = 1.875.
So, the set of side lengths that are similar to the triangle that Kendall drew are 16, 30, 35, and 8, 15, 17.
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A cabinet maker can build a kitchen island in 11 hours. If the cabinet maker's apprentice helps, they can construct the kitchen island in 8 hours. How long would it take apprentice to complete a kitchen island alone?
It would take the apprentice alone 11 hours to complete a kitchen island, the same amount of time it took the cabinet maker and apprentice together.
When the cabinet maker and apprentice work together, they are able to complete the kitchen island in 8 hours. This implies that the apprentice is able to do their portion of the work in 3 hours, while the cabinet maker does their portion in 8 hours. Therefore, if the apprentice were to work on the kitchen island alone, it would take them 11 hours to complete it, the same amount of time it took the cabinet maker and apprentice together. This is because the apprentice does not have the same level of experience and expertise as the cabinet maker, so they are not able to complete the same amount of work in the same amount of time as the cabinet maker. The cabinet maker is able to work faster and more efficiently, which is why they are able to complete the kitchen island in 8 hours, while the apprentice would need 11 hours to complete the same task.
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What do I put (please do not put a complicated answer) and this is 7th grade math
Answer:
x = 17
Step-by-step explanation:
We Know
(6x + 3) + (7x - 44) = 180°
Let's solve
6x + 3 + 7x - 44 = 180
13x - 41 = 180
13x = 221
x = 17°
So, x = 17°