Answer:
missing side lengths are
leg 1 is 4√2
leg 2 is 4√2
hypotenuse is 8
Step-by-step explanation:
leg 1 is y
leg 2 is 4√2
45-45-90 right triangle means
legs are equal
the longest side is the hypotenuse which is
x
pythagorean theorem =
a² + b² = c²
a and b are the legs
c is hypotenuse
(4√2)² + (4√2)² = c²
4√2 = √16*2 = √32
(√32)² + (√32)² = c²
32 + 32 = c²
64 = c²
take the square root of both sides
√64 = √c²
8 = c
c = 8
Use trigonometric identities to verify each expression is equal.
c) csc^2(x)-2csc(x)cot(x)+cot^2(x) = tan^2(x/2)
d) [cos(x)cos(y)][tan(x)+tan(y)] = sin(x+y)
Part (c)
[tex]\text{LHS}=\csc^{2} x-2\csc x\cot x+\cot^{2} x\\\\=(\csc x-\cot x)^{2}\\\\=\left(\frac{1}{\sin x}-\frac{\cos x}{\sin x} \right)^{2}\\\\=\left(\frac{1-\cos x}{\sin x})^{2}\\\\=\tan^{2} \left(\frac{x}{2} \right)\\\\=\text{RHS}[/tex]
Part (d)
[tex]\text{LHS}=[\cos x \cos y][\tan x+\tan y]\\\\=[\cos x\cos y]\left[\frac{\sin x}{\cos x}+\frac{\sin y}{\cos y} \right]\\\\=\sin x \cos y+\sin y \cos x\\\\=\sin(x+y)\\\\=\text{RHS}[/tex]
Please find the area of the given picture. Please as fast as possible........
Answer:
Area = 168 cm²
Step-by-step explanation:
**Please note that there is an error in the drawing of the given parallelogram. In order for the parallelogram to have the given shape, the diagonal AC is actually 22.5 cm in length, whereas diagonal DB is 15 cm in length (see attached diagram). Therefore, I shall be using the attached diagram for my calculations. However, please note that due of the properties of a parallelogram, the final answer will be the same, regardless of which diagonal is used.**
To calculate the area of a parallelogram, we would usually multiply the base by the perpendicular height. As the perpendicular height is unknown in the given parallelogram, use the following formula:
[tex]\textsf{Area of parallelogram} = ab \sin (x)[/tex]
where:
a and b are the lengths of parallel sidesx is the included angleAs the diagonal of the parallelogram is given, use the cosine rule to calculate the measure of the included angle ∠DCB.
Cosine Rule (for finding angles)
[tex]\sf \cos(C)=\dfrac{a^2+b^2-c^2}{2ab}[/tex]
where:
C is the anglea and b are the sides adjacent the anglec is the side opposite the angleFrom inspection of the given diagram:
C = ∠DCBa = DC = 13 cmb = CD = 14 cmc = DB = 15 cmSubstitute the given values into the cosine rule formula and solve for ∠ABC:
[tex]\implies \sf \cos(DCB)=\dfrac{13^2+14^2-15^2}{2(13)(14)}[/tex]
[tex]\implies \sf \cos(DCB)=\dfrac{140}{364}[/tex]
[tex]\implies \sf \cos(DCB)=\dfrac{5}{13}[/tex]
[tex]\implies \sf \angle DCB=67.38013505...^{\circ}[/tex]
Substitute the found angle and the length of the parallel sides into the area formula:
[tex]\begin{aligned}\textsf{Area of parallelogram} & = ab \sin (x)\\\\\implies \textsf{Area} & = \sf (13)(14) \sin (DCB)\\& = \sf (13)(14) \left(\dfrac{12}{13}\right)\\& = \sf 168\:\:cm^2\end{aligned}[/tex]
Therefore, the area of the given parallelogram is 168 cm².
For year y, the population of massachusetts was approximately what percent of the population of vermont?
Answer: 50%
Step-by-step explanation: 50%
In an instant lottery, your chances of winning are 0.1. if you play the lottery five times and outcomes are independent, the probability that you lose all five times is
The probability that you lose all five times will be 0.59.
How to calculate the probability?From the information given, the chances of winning are 0.1. Therefore, the chance of losing will be:
= 1 - 0.1 = 0.9
Therefore, the probability that you lose all five times will be:
= 0.9 × 0.9 × 0.9 × 0.9 × 0.9
= 0.59
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PLEASE HELP ME, I BEG OF YOU TO HAVE MERCY ON MY POOR SOUL
1. Calculate the slope of the trend line. (Choose two points on the line and find vertical change over horizontal change.)
2. Using the slope and y-intercept, write the equation of the trend line (y = mx + b).
3. Choose a "calories from fat" value that is not in your collected data set and that is at least 10 fat calories away from any collected value. Use the equation calculated in step to predict the number of fat grams in an item having that number of fat calories. Be sure to show your work.
4. Search for an item in a fast food menu having the same number of fat calories as the one you chose above. (If you cannot find the exact value, get as close as you can.) Compare the calculated value from step VI to this actual value. Explain why (or why not) you would have expected your prediction (calculated value) to be close to the actual value.
The answer for the following question is
1. m= 10
2. y- intercept = 300
3. y = 10x + 300
What is Regression line?A regression line is a graphic representation of the regression equation expressing the hypothesized relationship between an outcome or dependent variable and one or more predictors or independent variables
1.slope= rise/ run
m= 10
2. y- intercept = 300
3. Now, the regression line:
y = 10x + 300
At, x = 1
y = 10(1) + 300
y = 310 calories
and x = 14
y = 10(14) + 300
y = 440
We know the actual value is 330.
Hence, the value of calories is 90 and when x = 14 the value of y = 440 from the regression line, but the actual value is 330.
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Determine the intervals on which the function is (a) increasing; (b) decreasing: (c) constant.
(a) The function is increasing on the interval(s)
(Use a comma to separate answers as needed. Type your answer in interval notation.)
The intervals of the function in which it is increasing, decreasing and constant are given as follows:
a) Increasing: [tex]x \in \left[-4.5, 2\right][/tex].
b) Decreasing: [tex]x \in \left[4,6\right][/tex].
c) Constant: [tex]x \in \left[2,4\right][/tex].
When a function is increasing?A function is increasing when the graph of the function is pointing upwards, hence this function is increasing on the interval [tex]x \in \left[-4.5, 2\right][/tex].
When a function is decreasing?A function is increasing when the graph of the function is pointing downwards, hence this function is decreasing on the interval [tex]x \in \left[4, 6\right][/tex].
When a function is constant?A function is constant when it is graph is a line without inclination, hence this function is constant n the interval [tex]x \in \left[2, 4\right][/tex].
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Which best describes the function on the graph?
O direct variation; k =1/4
O direct variation; k = 4
O inverse variation; k =1/4
O inverse variation; k = 4
The option that best describes the graphed function is: D. inverse variation; k = 4
What is an Inverse Variation?Given two variables x and y has an inverse variation, the equation that models the relationship of the inverse variation is: y = k/x, where k = xy.
This means that as x increases, y decreases. This is the same for the graph given. So, it is an inverse variation.
When x = 2, y = 2. Therefore:
k = (2)(2)
k = 4
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If the 6th term of an arithmetic progres- sion is 11 and the first term is 1, find the common difference.
Answer:
2
Step-by-step explanation:
An arithmetic progression with first term a and common difference d has the following first 6 terms:
a, a + d, a + 2d, a + 3d, a + 4d, a + 5d
We are given a = 1 and a + 5d = 11.
1 + 5d = 11
5d = 10
d = 2
Answer: The common difference is 2.
HELP WITH THIS PLSSS ITS CYLINDERRR
Answer:
6) B
7) D
Step-by-step explanation:
6)
The surface area of a cylinder is 2 * pi * r * (r + h)
SA = 2 * 3.14 * 3.6 * (3.6 + 8.5) = 2 * 3.14 * 3.6 * 12.1 = 273.6 cm^2
7)
The volume of a cylinder is pi * r^2 * h
V = 3.14 * (3.6)^2 * 8.5 = 345.9 cm^3
Answer:
6. surface area= 2πrh
where r=radius of the base
h=height of the cylinder
π=pie
π=22/7, r=3.6, h=8.5
2×22/7×3.6×8.5= 192.3cm²
square root of 192.3 is 13.9, the one whose square root is closest to that of 192.3 in the options is 178 whose square root is 13.3. A
7. volume=product of the height and its base area
volume=πr²h
22/7×3.6²×8.5 = 346.2. D
help please
what is the answer?
Answer:
y = 25°
Step-by-step explanation:
115° and x are a linear pair and sum to 180° , so
x + 115° = 180° ( subtract 115° from both sides )
x = 65°
the sum of the 3 angles in the triangle = 180° , then
x + x + 2y = 180°
65° + 65° + 2y = 180°
130° + 2y = 180° ( subtract 150° from both sides )
2y = 50° ( divide both sides by 2 )
y = 25°
The two-way table shows the estimated number of students who will enroll in three area high schools next year. a 5-column table has 4 rows. the first column has entries mount woodson high school, valley high school, riverside high school, total. the second column is labeled tenth grade with entries 110, 180, 160, 450. the third column is labeled eleventh grade with entries 120, 150, 140, 410. the fourth column is labeled twelfth grade with entries 80, 120, 200, 400. the fifth column is labeled total with entries 310, 450, 500, 1,260. in decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade? 0.2 0.3 0.4 0.5
Answer:
A. 0.2
Step-by-step explanation:
First make the table.
10-grade 11-grade 12-grade Total
Woodson high school | 110 | 120 | 80 | 310 |
Valley high school | 180 | 150 | 120 | 450 |
Riverside high school | 160 | 140 | 200 | 500 |
Total | 450 | 410 | 400 | 1260 |
Question: In decimal form, to the nearest tenth, what is the probability that a randomly selected riverside high school student is in twelfth grade?
First, find 12-grade and riverside high school number. 200. Take the total lined up with total number, which is 1260, and divide 200 divided by 1260.
200/1260=0.2
The answer is 0.2.
Hope this helps!
If not, I am sorry.
Answer:
its .4
Step-by-step explanation:
i got it wrong when i tried it says it is .4 or the third option c
A cyclist is stationary when a second cyclist passes travelling at a constant speed of 8 m s−1. The first cyclist then accelerates for 5 s at a constant rate of 2 m s−1 before continuing at constant speed until overtaking the second cyclist. By sketching both graphs, find the equations of the two straight line sections of the graphs and hence find how long it is before the first cyclist overtakes the second.
Answer:
im not too sure about that sorry!
Step-by-step explanation:
uiwgorihvncjkdnskv
It takes 15 seconds for the first cyclist to overtake the second cyclist.
How can you find how long it took before the first cyclist overtakes the second?First, identify the two phases of the first cyclist's motion.
Phase 1: The cyclist accelerates from rest to a constant speed of 8 m/s.
Phase 2: The cyclist travels at a constant speed of 8 m/s.
Find the equations of the two straight-line sections of the graph.
The equations of the two straight-line sections of the graph are as follows:
Phase 1:
s = [tex]2t^2[/tex]
Phase 2:
s = 8t
where s is the distance traveled by the cyclist and t is the time
Set the two equations equal to each other to find the time it takes the first cyclist to overtake the second cyclist
The first cyclist overtakes the second cyclist when the first cyclist has traveled a distance of 8 m more than the second cyclist.
Let t be the time it takes the first cyclist to overtake the second cyclist.
The distance traveled by the first cyclist is then 8t, and the distance traveled by the second cyclist is 8(t - 5).
Setting these two expressions equal to each other, we get:
8t = 8(t - 5)
Solving for t, we get:
t = 15
Therefore, it takes 15 seconds for the first cyclist to overtake the second cyclist
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What type of triangle is this triangle?
acute scalene
right isosceles
right scalene
acute isosceles
A triangle with two acute angles and one angle that has a small square. Two sides each have one tick mark.
what is the answer for this question pls
Answer:
12
Step-by-step explanation:
1 hour = 60 minutes
2 people paint a fence in 1 hour = 60 minutes
10 people are 5 times 2 people, so they need 5 times less time than 2 people.
10 people paint a fence in 60/5 minutes
10 people paint a fence in 12 minutes.
The value of a car decreases as shown in the table below.
A 2-column table with 6 rows. The first column is labeled years after purchase with entries 0, 1, 2, 3, 4, 5. The second column is labeled value (dollar sign) with entries 25,000; 18,000; 14,000; 10,500; 8,000; 6,000.
Which statements are true? Check all that apply.
The statements which are true from the given table are:
The function that best represents the data is f(x) = 24,512(0.755)x.
The function decreases indefinitely.
It is reasonable to interpolate the value of the car at 4.5 years.
What is Depreciation?Depreciation refers to the accounting method where the value of a tangible asset reduces over a period of time.
The value of the car is shown with the purchase with entries that shows its value over time,
The function that best represents the data is f(x) = 24,512(0.755)x and that this function decreases indefinitely.
The statements which are true from the given table are:
The function that best represents the data is f(x) = 24,512(0.755)x.
The function decreases indefinitely.
It is reasonable to interpolate the value of the car at 4.5 years.
The complete question is
"The value of a car decreases as shown in the table below.
A 2-column table with 6 rows.
The first column is labeled years after purchase with entries 0, 1, 2, 3, 4, 5.
The second column is labeled value (dollar sign) with entries 25,000; 18,000; 14,000; 10,500; 8,000; 6,000.
Which statements are true? Check all that apply.
The function that best represents the data is f(x) = 24,512(0.755)x.
The function that best represents the data is f(x) = 554x2 – 5,439x + 24,600.
The function decreases indefinitely.
It is reasonable to interpolate to the value of the car at 4.5 years.
It is reasonable to extrapolate to 40 years"
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If $a$ and $b$ are positive integers for which $ab - 6a + 5b = 373$, what is the minimal possible value of $|a - b|$?
Answer:
31
Step-by-step explanation:
We can solve the given equation for 'b', then find the integer values of 'a' that make 'b' a positive integer. There are 3 such values. One of these minimizes the objective function.
__
solve for bab +5b = 373 +6a . . . . . . isolate b terms by adding 6a
b = (6a +373)/(a +5) . . . . . divide by the coefficient of b
b = 6 +343/(a +5) . . . . . . . find quotient and remainder
integer solutionsThe value of 'b' will only be an integer when (a+5) is a factor of 343. The divisors of 343 = 7³ are {1, 7, 49, 343}. so these are the possible values of a+5. Since a > 0, we must eliminate a+5=1. That leaves ...
a = {7, 49, 343} -5 = {2, 44, 338}.
Possible values of b are ...
b = 6 +343/{7, 49, 343} = 6 +{49, 7, 1} = {55, 13, 7}
Then possible (a, b) pairs are ...
(a, b) = {(2, 55), (44, 13), (338, 7)}
objective functionThe values of the objective function for these pairs are ...
|a -b| = |2 -55| = 53
|a -b| = |44 -13| = 31 . . . . . the minimum value of the objective function
|a -b| = |338 -7| = 331
The cost of the fruit is given by the function y=3x+1, where x is the number of fruits and y is the total cost. Find the range of the function.
Please help
15 points bc I’m new and only have like 50. I’ll also give branliest
Let a population consist of the values cigarettes, cigarettes, and cigarettes smoked in a day. Show that when samples of size 2 are randomly selected with replacement, the samples have mean absolute deviations that do not center about the value of the mean absolute deviation of the population. What does this indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?.
The "sample" with "mean absolute deviation" indicate about a sample mean absolute deviation is being used as an estimator of the mean absolute deviation of a population
Mean of the sample MAD=3.3Population MAD =6.4What does this indicate about a sample mean absolute deviation used as an estimator of the mean absolute deviation of a population?Generally, The MAD measures the average dispersion around the mean of a given data collection.
[tex]1/n \sum_i-1^{n} |x_i -m(X)|[/tex]
In conclusion, for the corresponding same to mean
the sample mean absolute deviation
7,7 ↔ 0
7,21 ↔ 7
7,22 ↔ 7.5
21,7 ↔ 7
21,21 ↔ 0
21,22 ↔ 0.5
22,7 ↔ 7.5
Therefore
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which expresion is equivalent to the given expresion
(3m-4)³(3m³)
The equivalent expression of [tex](3m^{-4})^3 * (3m^3)[/tex] is [tex]729m^{-9}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex](3m^{-4})^3 * (3m^3)[/tex]
Expand the brackets
[tex]27m^{-12} * 27m^3[/tex]
Apply the law of indices
[tex]729m^{-12+3}[/tex]
Evaluate the sum
[tex]729m^{-9}[/tex]
Hence, the equivalent expression of [tex](3m^{-4})^3 * (3m^3)[/tex] is [tex]729m^{-9}[/tex]
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what is the length of EF if DE=17 and DF=13 in DEF
By the fact that the sum of internal angles in a triangle and the law of the cosines, the possible lengths of the side EF are represented by 16 ≤ EF ≤ 900.
How to determine the possible lengths of a missing side in a triangle
In this question we have a triangle with two known lengths and there many possible solutions for the length of the segment EF. By geometry we know that the sum of the internal angles in a triangle equals 180° and by the law of cosines we have the following expression for the missing length:
EF² = 17² + 13² - 2 · (13) · (17) · cos D
EF² = 458 - 442 · cos D, 0 ≤ θ ≤ 180°
As the cosine is a function bounded between - 1 and 1, then the possible lengths of the side EF are:
16 ≤ EF ≤ 900
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The length of a rectangle is 8 cm more than four times the width. If the perimeter of the rectangle is 46 cm, what are the dimensions?
Answer:
length = 20 cm
width = 3 cm
Step-by-step explanation:
Hey, any help would be very needed thanks so much!!
Let's take this problem step by step:
To find the ordered pair of the system:
⇒ must set both equations equal to each other
⇒ must solve for 'x'
Let's solve:
[tex]x^2-2x+3=-2x+28\\x^2-2x+3+2x-28=0\\x^2-25=0\\(x-5)(x+5)=0[/tex]
Let's find the x-values:
[tex](x-5)=0\\x=5\\\\(x+5)=0\\x=-5[/tex]
Let's find f(x)'s value for each of the 'x':
[tex]x=5\\f(5)=-2(5)+28=18\\\\x=-5\\f(-5)=-2(-5)+28=38[/tex]
Answer: (5, 18), (-5,38)
Hope that helps!
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1.1 divided by 1.54 simplified
Answer:
1•4
Step-by-step explanation:
1•54÷1•1
1•54
1•1
divide by 10 both side with can move decimal
15•4
11
=my answer is 1•4.
Answer:
The correct answer for algebraic expression 1.54÷1.1 is = 1.4.
Step-by-step explanation:
this is question based on simple algebra -
Simple Algebraic equations - An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. we can apply many operations on algebraic equations like addition, subtraction, multiplication, division and raising to a power, and extraction of a root.
these equations are two algebraic expressions that are joined together using an equal to ( = ) sign. An algebraic equation is also known as a polynomial equation because both sides of the equal sign contain polynomials
so in the question algebraic operation used to solve is simple division.
therefore here in question we have to divide 1.54 with 1.1,
using the concept written above,
let the value of division be 'x'
we can write 1.54/1.1 = x
by dividing and multiplying the equation by 100 to remove the decimals.
(1•54/ 1•1)×100/100 = x
154/110 = x
now by simple division,
1.4 = x answer
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct statements are options C and option D.
- 6x + 15 < 10 - 5x ⇒ 3rd answerAn open circle is at 5 and a bold line starts at 5 and is pointing to the right.What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
The inequality is -3(2x - 5) < 5(2 - x)
At first, simplify each side
-3(2x - 5) = -3(2x) + -3(-5)
Remember (-)(-) = (+)
-3(2x - 5) = - 6x + 15
5(2 - x) = 5(2) + 5(-x)
Remember (+)(-) = (-)
5(2 - x) = 10 - 5x
- 6x + 15 < 10 - 5x
Subtract 15 from both sides
- 6x < -5 - 5x
Add 5x to both sides
- x < - 5
Remember the coefficient of x is negative, then when you divide both sides by it you must reverse the sign of inequality
The coefficient of x is -1
Divide both sides by -1
x > 5
Therefore the correct statements are options C and option D.
- 6x + 15 < 10 - 5x ⇒ 3rd answerAn open circle is at 5 and a bold line starts at 5 and is pointing to the right.To know more about inequality follow
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Identify the Property of Equality that is used in each statement.
If x=2, then 2x = 4.
5= 3a; therefore, 3a = 5.
If T=4, then 5T + 7 equals 27.
If 9 = 4x and 4x = m, then 9 = m.
Step-by-step explanation:
x = 2. 2(x) = 2(2). 2x= 4. Multiplication Property of Equality (if you have two equals sides and then multiply them by the same quantity both sides will remain equal)
5=3a therefore 3a = 5. Symmetric Property if a=b then b=a
T = 4 => 5T = 20 (Multiplication Property of Equality) => 5T + 7 = 27 (Addition Property of Equality. basically if two sides are equal and you add the same quantity they will remain equal)
Last one is transitive property which states. if a=b and b=c then a=c so in this case a would be 9, b would be 4x and c would be m
Estimate the solution to the following system of equations by graphing.
OA (-1,-1)
OB. (1,-1)
oc (1)
D.
3x + 5y = 14
61 - 4y = 9
An equation is formed of two equal expressions. The estimated solution of the two system of equations is at (5/2,4/3). Thus, the correct option is D.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the system of equation is the point at which the two lines will intersect as shown below. Therefore, the solution will be,
Solution = (5/2, 4/3)
Hence, the estimated solution of the two system of equations is at (5/2,4/3). Thus, the correct option is D.
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Mandy used the input and output in this table to write ratios. She concluded that because they are not all equivalent, this is not a proportional relationship. Is she correct? Explain.
A 2-column table with 4 rows. Column 1 is labeled x with entries 1, 2, 5, 10. Column 2 is labeled y with entries 5, 10, 25, 50.
Answer:
No, she is not correct. Because this is a proportional relationship.
Step-by-step explanation:
Proportional relationships are relationships having equal ratios.
here, Mandy's conclusion is incorrect because the relationship is proportional, and it has a uniform ratio of 5.
column 1 column 2 column 2/column1
'x' 'y'
1 5 5
2 10 5
5 25 5
10 50 5
As we clearly see that ratio of column 2 and column 1 is same for every row, therefore we can conclude that the given relation in the relation is proportional.
Thus, the given relation is proportional.
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Which of the numbers below is greater than −7/3? Select all that apply. A) −3 B) −5.5 C) −2 D) −3/2 E) 1.25
Answer:
C, D and E
Step-by-step explanation:
The numbers which are greater than given number are : -2, -1.5, and 1.25.
What is Fraction?
A fraction represents a part of a whole or, more generally, any number of equal parts.
Here, given number: -7/3
or we can write this as -2.33
Now, Converting option fraction value into decimal
A). -3
B) -5.5
C). -2
D). -1.5
E). 1.25
On comparing options from the given value we get
the number which are greater than -2.33; -2, -1.5, and 1.25
Thus, the numbers which are greater than given number are : -2, -1.5, and 1.25.
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help please i dont know this
Answer:
150 yd
Step-by-step explanation:
the angle bisector divides the opposite sides into segments that are proportional to the other 2 sides .
let x be the distance from the oak tree to the hole, then
[tex]\frac{225}{x}[/tex] = [tex]\frac{375}{250}[/tex] ( cross- multiply )
375x = 56250 ( divide both sides by 375 )
x = 150 yd