In the diagram below of triangle
F
G
H
FGH,
I
I is the midpoint of
F
H
‾
FH
and
J
J is the midpoint of
G
H
‾
GH
. If m
∠
H
F
G
=
57
−
6
x
∠HFG=57−6x, and m
∠
H
I
J
=
−
4
x
+
49
∠HIJ=−4x+49, what is the measure of
∠
H
I
J
∠HIJ
Answers
Applying the corresponding angles theorem, the measure of ∠HIJ = 33°.
What is the Corresponding Angles Theorem?If two triangles are similar to each other, their corresponding angles would be equal. Also, based on the corresponding angles theorem, corresponding angles are equal to each other.
Triangles IHJ and FGH are similar to each other, therefore, angles HFG and HIJ are corresponding angles.
Therefore:
The measure of angle HFG = the measure of angle HIJ
m∠HFG = 57 − 6x
m∠HIJ = −4x + 49
Thus:
57 − 6x = -4x + 49
Combine like terms
4x - 6x = -57 + 49
-2x = -8
Divide both sides by -2
-2x/-2 = -8/-2
x = 4
m∠HIJ = −4x + 49 = -4(4) + 49
m∠HIJ = 33°
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Complete Question:
In the diagram below of triangle FGH, I is the midpoint of FH and J is the midpoint of GH. If m∠HFG = 57 − 6x, and m∠HIJ = −4x + 49, what is the measure of ∠HIJ?
Related Questions
The tens digit of a two-digit number is five more than the units digit. The number itself is equal to the sum of its digits multiplied by 8. Find the number
Answers
Answer:
72
Step-by-step explanation:
- reason why it's 72
tens ones
(2+5)=7 2
A/Q:
7+2=99*8=724x+y=104, x, plus, y, equals, 10
Complete the missing value in the solution to the equation.
Answers
Answer:36,37,38,39 one of the those or between
Step-by-step explanation:
it would be great if someone could help me with these please?
Answers
Answer:
Find the angle measurement like a 90 degree angle or something for both of them and then find the solution following it. If you need further help post the question with the name where these questions are posted!
PLEASE GIVE BRAINLIEST THANK YOU!!!
5[tex]\sqrt{8}[/tex]simplified
Answers
Answer:
[tex]10\sqrt{2}[/tex]
Step-by-step explanation:
To simplify a square root you have to find any perfect square numbers.
(ex. 4, 9, 16, 25 ...)
[tex]\sqrt{8} = \sqrt{2*4} = \sqrt{2} * \sqrt{4}[/tex]
Simplify:
[tex]\sqrt{4} = 2[/tex]
[tex]2 \times \sqrt{2}\\ = 2\sqrt{2}[/tex]
Don't forget to multiply the 5, so:
[tex]5 \times 2\sqrt{2}\\ = 10\sqrt{2}[/tex]
A basketball has a volume of about 452.1 cubic inches. Fine the radius of the basketball in inches
Answers
The radius of the basket ball having volume 452.1 cubic inches is 4.76 inches.
What is the volume?
Volume is the 3 dimentional occupied space by any object. It is measured in SI units [tex]\textnormal{m}^3[/tex] and other derived units like [tex]\textnormal{in}^3[/tex].
All properties of a spherical shape is defined by its radius. The shape of a basketball is spherical hence, the formula of the volume is given by the followin expression:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Here, V is the volume of the basket ball and r is the radius of the basket ball.
Rearrange the above equation for [tex]r[/tex].
[tex]3V=4\pi r^3\\\frac{3V}{4\pi}= r^3[/tex]
[tex]r=[\frac{3V}{4\pi}]^{1/3}[/tex]
Substitute values.
[tex]V=[\frac{3(452.1 \ \textnormal{cubic inches})}{4\pi}]^{1/3}\\=4.76 \ \text{inches}[/tex]
Hence, the radius of the basket ball is 4.76 inches.
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explain why the exterior angle of a regular polygon could be 20* 30* or 40* but not 50*
Answers
Answer:a polygon cannot have 7.2 sides
Step-by-step explanation:
each exterior angle of a regular polygon with n sides is equal and these angles add up to 360∘ . a polygon cannot have 7.2 sides. since , the exterior angle of a regular polygon cannot be 50∘
Find the fourth degree polynomial that contains the origin and to which the line x+2y=14 is tangent at both x=4 and x=-2.
Answers
Answer: 60,30,180, and 37
Step-by-step explanation:
Look at this graph:
10
9
8
7
5
4
3
2
1
0 1 2 3 4 5 6 7 8
What is the slope?
Answers
The slope of the line is -1
First we have to choose two points
The coordinates of the first point = (9, 1)
The coordinates of the second point = (8, 2)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line.
The slope of the line m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line = (2-1) / (8-9)
= 1 / -1
= -1
Hence, the slope of the line is -1
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3/4x - 3 = 5/6 Rewrite the equation below so that it does not have fractions.
Do not use decimals in your answer.
Answers
Answer:
18x - 72 = 20
Step-by-step explanation:
[tex] \rm \implies \dfrac{3}{4} x - 3 = \dfrac{5}{6} \\ \\ \rm \implies \dfrac{3}{4} x - 3 \times \frac{4}{4} = \dfrac{5}{6} \\ \\ \rm \implies\dfrac{3}{4} x - \frac{12}{4} = \dfrac{5}{6} \\ \\ \rm \implies \frac{3x - 12}{4} = \frac{5}{6} \\ \\ \rm \implies \frac{3x - 12}{ \cancel{4}} \times \cancel{4} = \frac{5}{6} \times 4 \\ \\ \rm \implies 3x - 12 = \frac{20}{6} \\ \\ \rm \implies (3x - 12) \times 6 = \frac{20}{ \cancel{6}} \times \cancel{6} \\ \\ \rm \implies 18x - 72 = 20 [/tex]
Suppose we are given the following.
Line 1 passes through (-3, 8) and (0,4).
Line 2 passes through (4, 4) and (-4,-2).
Line 3 passes through (4, 1) and (8,4).
(a) Find the slope of each line.
Slope of Line 1-
Slope of Line 2-
Slope of Line 3-0
(b) For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2: OParallel
Line 1 and Line 3:
OParallel
Line 2 and Line 3:
OParallel
Operpendicular ONeither
Operpendicular
ONeither
OPerpendicular
Neither
Answers
Slope of line 1 is -4/3, slope of line 2 is 3/4, slope of line 3 is 3/4, and Line 1 and Line 2 are perpendicular, Line 1 and Line 3 are also perpendicular, Line 2 and Line 3 are parallel.
What is slope of a line?
The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate points and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates on a line in order to determine its slope.
Slope of a line can be calculated using the formula:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here, m = slope and (x1, y1), (x2, y2) are two points on the line,
Calculating the slope of line 1 whose points are (-3, 8), (0, 4)
[tex]m = \frac{4 - 8}{0 - (-3)}[/tex]
m = -4/3
Calculating the slope of line 2 whose points are (4, 4), (-4, -2)
[tex]m = \frac{-2 - 4}{ -4 - 4}[/tex]
m = 3/4
Calculating the slope of line 2 whose points are (4, 1), (8, 4)
[tex]m = \frac{4 - 1}{ 8 - 4}[/tex]
m = 3/4
Now we know that if lines are parallel that their slope is equal and when lines are perpendicular the product of their slope is -1,
Therefore, Line 1 and Line 2 are perpendicular, Line 1 and Line 3 are also perpendicular, Line 2 and Line 3 are parallel.
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Four friend go out to eat and their meal cot $86. 50. The ale tax i 6. 75% and they hould tip the waiter 20%. How much do they have to pay?Round to the nearet cent
Answers
Four friends go out to eat and their meal cost $86. 50. The sales tax 6. 75% and they should tip the waiter 20%.each person must pay $27.7 for their meal
Four friends go out to eat and $86.50 for their meals.
The sales tax is 6.75%, and the waiter is tipped 20%.
M = 86.5 * 10675 / 10000 = 92.34
92.34$, and the total amount of money that four friends will give, including waiter tip, is
T=92.35 * 120 / 100 = 110.80
and each person must give
110.8/4= $27.7
each person must pay $27.7
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an experiment may have: a. only one outcome b. only two outcomes c. two or more outcomes d. several events
Answers
Using the concepts of probability, we got that an experiment may have d) several events
Event is called one or more outcomes of an experiment. Example of this is -rolling a dice, we get a possible outcomes as {1,2,3,4,5,6}.
In an experiment there can be one outcome, two outcomes, more than two outcomes or several outcomes.
An event is the collection of one or more of the outcomes of an experiment. An event that actually includes one and only one of the (final) outcomes for an experiment is called the simple event and is denoted by Ei.
Hence, an experiment may have d)several events
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a car dealer buys a car for $500, gives it a clean new, is sold for $100. what is the percentage of loss
Answers
Answer:
Step-by-step explanation:
1. Find decrease.
If the car dealer bought the car for 100$ and only received 100$ for selling the car, he had 400$ in disadvantage!
2. Caculate Percent Loss:
400/ 500*100=
400/5=
80
There was a 80% decrease from the starting value!
Answer: 80% decrease!
What effect do you think the sample size have on the mean of the sampling distribution of the mean?.
Answers
The effect that sample size on the mean of the sampling distribution has is that it effects the variations .
In the question ,
If the sample size is increased ,
which means if the number of sample is increased then the errors in the sampling distribution becomes very less .
and if the sample size is decreased then it leads to the increase in the error of the distribution .
The formula for the relationship between variation and sample size is given by ,
σx = σ / sqrt (n)
we can see that the variation and sample size are inversely proportional .
Which means that increase in the sample size results in a reduction of variation.
Therefore , The effect that sample size on the mean of the sampling distribution has is that it effects the variations .
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Find the inverse of the function y=2x+8
Answers
The inverse function of the given is [tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4 .
What is inverse function?
The domain of the original function becomes the range of the inverse function, and the range of the given function becomes the domain of the inverse function. The inverse function is denoted by the notation f-1 in relation to the original function f. Swapping (x, y) with (y, x) with reference to the line y = x yields the graph of the inverse function. Only when f is both a one-one and an onto function does it have an inverse, indicated by the symbol f-1. Keep in mind that f-1 is NOT f's inverse. The domain value of x is given by combining the function f and the reciprocal function f-1.
Here the given function is,
=> y = 2x+8
Now interchange x and y then
=> x=2y+8
Now simplify the expression with respect to y then,
=> x-8=2y
=> y = [tex]\frac{x}{2}[/tex]-4
=>[tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4
Hence inverse function is [tex]y^-1[/tex]= [tex]\frac{x}{2}[/tex]-4 .
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[tex]\sf 10+2x=4[/tex]
Answers
-10
2x = -6
/2
x = -3
Answer: x = -3
Answer:
10+2x=4first, by using inverse operations subtract 10 on both sides.
10-10+2x=4-104-10 is -6. whys the 6 negative? because the number takes the sign of the bigge number.
2x=-6Divide by 2 to isolate x
2x÷2=-6÷2In multiplication and division one negative sign stays and 2 negative signs cancel eachother but here theres only one negative sign so;
~~~~~~~~~~~~~~~~
X=-3Offering points for who can help me with this
Answers
Answer:
204 feet^2
Step-by-step explanation:
rectangle area = 18 * 10 = 180 feet^2
triangle width = 18 - 10 = 8 feet
triangle area = 6 * 8 /2 = 24 feet^2
total area = 180 + 24 = 204 feet^2
[tex]\sf x+ (-9) =-18[/tex]
what's the value x ?
Answers
Answer:
x = -9
Step-by-step explanation:
Below:-
Answer:
x = -9
Step-by-step explanation:
Given equation,
→ x + (-9) = -18
Now the value of x will be,
→ x + (-9) = -18
→ x - 9 = -18
→ x = -18 + 9
→ [ x = -9 ]
Hence, the value of x is -9.
what is f(-3) for the function f(x) = 2x^2 + 5? need answer ASAP please!
Answers
Answer:
F(-3)= 23
Step-by-step explanation:
F(-3)= 2(-3)^2 + 5
Hope this helps!
IF LINE TV IS PARALLEL TO LINE ZX AND LINE ZX IS PARALLEL TO LINE QS, THEN IS LINE TV PARALLEL TO LINE QS BY TRANSITIVE PROPERTY?
Answers
Yes line TV is also parallel to line QS according to transverse property
What is transverse property?According to the transitive property, all the quantities are equal to each other if two quantities are equal to the third quantity.
When the term equal is replace by parallel it suits the case at hand hence transitive property of parallel lines is introduced
When attempting to demonstrate that several parallel lines have congruent properties, the transitive property of parallel lines can be used to create a link between numerous equal quantities.
Therefore, it can be interpreted as: if line TV || line ZX and line ZX || line QS then line TV || line ZX
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Simplify:
[tex]\frac{4-i\sqrt{2}}{4+i\sqrt{2}}[/tex]
Answers
(7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)
What is complex number?a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit
The given expression is
(4-i√2)/(4+i√2)
Now we have to rationalize the above expression
((4-i√2)/(4+i√2))×((4-i√2)/(4-i√2))
(4-i√2)(4-i√2)/(4+i√2)(4-i√2)
16-4i√2-4i√2-2/16-2
16-8i√2-2/14
14-8i√2/14
2(7-4i√2)/2(7)
(7-4i)√2/7
Hence (7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)
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A board 65 inches long is sawed into two pieces. One of the pieces in 7 inches shorter than twice the length of the other piece. Find the length of the two pieces.
Answers
Answer:
24 and 41 inches.
Step-by-step explanation:
Let the lengths of the two pieces be a and b.
The total length of the two-piece should be the length of the original board.
Therefore:
a + b = 65
One piece, say b, is 7 inches shorter than twice the length of the other, a.
Therefore, we can write the following equation:
b = 2a - 7
The “2a” represents the twice, and the “-7” represents the 7 shorter inches.
We now have a system of equations:
a + b = 65
b = 2a - 7
We can solve using substitution. Substitute the second equation with the first. Hence:
a + (2a - 7) = 65
Combine like terms:
3a - 7 = 65
Add 7 to both sides:
3a = 72
Divide both sides by 3:
a = 24
So, the shorter piece is 24 inches.
Then, we can use our second equation again:
b = 2a - 7
Since we now know a substitute 24 for a and evaluate. Hence:
b = 2(24) - 7
= 48 - 7
= 41
Therefore, the length of the other two pieces is 24 and 41 inches.
The area of a circle is 25pieft2. What is the circumference, in feet? Express your answer in terms of pie
Answers
The circumference of the circle in feet is 10π feet.
According to the question,
We have the following information:
Area of the circle = 25π square feet
We know that the following formula is used to find the area of circle:
π[tex]r^{2}[/tex] where r is the radius of the circle
π[tex]r^{2}[/tex] = 25π
Dividing by π on both the sides:
[tex]r^{2}[/tex] = 25
r = 5 feet ...(1)
We know that the following formula is used to find the circumference of circle:
2πr
Putting the value of r from equation 1:
2π*5
10π feet
Hence, the circumference of the circle in feet is 10π feet.
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Two angles of a quadrilateral measure 260° and 15º. The other two angles are in a ratio of 7:10. What are the measures of those two angles?
Answers
The measures of those two angles are 35° and 50°.
How to calculate the angle?It's important to note that the sum of angles on a quadrilateral is 360°. In this case, two angles of a quadrilateral measure 260° and 15º.
The remaining angles will be:
= 360° - (260° + 15°)
= 85°
Since the other two angles are in a ratio of 7:10, the measure will be:
= 7 / (7 + 10) × 85°
= 7/15 × 85°
= 35°
Also, 10/17 × 85°
= 50°
The angles are 35° and 50°.
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Which decimal is equivalent to \
{31}{9}
9
31
start fraction, 31, divided by, 9, end fraction?
Answers
3.4
Step-by-step explanation:
When they are saying equivalent it means
they are NOT looking for something the
same but something that's equal to the
solution.
Why is the following no solution?
|x| = -5
Answers
The absolute value is the distance of a number from 0 without considering direction, and distance can’t be negative
What did I do wrong?
Answers
Step-by-step explanation:
I gone through your work and I don't see anything wrong.
Try reaching out to your teacher.
Answer:
You answered every question correctly. All ten of them. The program you are using has some issues. lol
Step-by-step explanation:
Could I get help with this?
Answers
Answer: convergencnt
Step-by-step explanation:
Question
Forty-five people are going on a road trip. Each car seats 5 people.
How many cars are needed for 45 people?
Answers
9 cars are needed
1. Fill in the missing Terms for the sequence
2. Find the number the sequence is going by
3. Write the explicit formula
Answers
The answer r = 7, and the missing terms are -2, -14, -98, -686, -4802. in the Geometric progression.
What is Geometric progression?
A geometric progression, sometimes termed a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio. A geometric progression with the common ratio 3 is, for instance, the sequence 2, 6, 18, 54,... A geometric series having a common ratio of 1/2 is also 10, 5, 2.5, 1.25, etc.
By calculating the product of the values of a set of numbers, the Geometric Mean (GM) is the average value or mean that denotes the central tendency of the data. The average of the data set's numbers is defined by the mean. There are several distinct forms of means, including arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM).
Here 1st term a = -2
4th term given is ar³= -686
r³= -686/-2
r=∛343
a) r=7
2nd term will be -14
3rd term will be -98
5th term will be -4802
b) -2, -14, -98, -686, -4802.
Hence, r = 7, and the missing terms are -2, -14, -98, -686, -4802.
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