The rhombus QRST is made of two congruent isosceles triangles. Given angle QRS = 34, what is the measure of angle S?
Answers
Answer:
146
Step-by-step explanation:
Since we know that this is a rhombus, we know that opposite angles must be equal to each other. This means that angle QTS is equal to angle QRS. Therefore angle QTS also equals 34.
Now, we also know that all the interior angles in a quadrilateral add up to 360. We can subtract 360-34-34=292.
Now we know that the remaining two angles S and Q need to add up to 292. We also know that they are equal because they are opposite angles. Therefore, we can solve the equation 292÷2=146. Each of these angles is 146. So the measure of angle S is 146.
The measure angle of S is 146 .
A rhombus is a special case of the parallelogram and is a quadrilateral with four equal sides. In a rhombus, the opposite sides are parallel and the opposite angles are equal. Also, all the sides of the rhombus are equal in length and the diagonals bisect each other at right angles. The rhombus is also known as a diamond.
By symmetry ;
This means that m∠QTS is equal to m∠QRS. Therefore ∠QTS is also equals 34.
We also know that The common property for all the above four-sided shapes is the sum of interior angles is always equal to 360 degrees. For a regular quadrilateral such as square, each interior angle will be equal to: 360/4 = 90 degrees.
Now we know that the remaining two angles S and Q need to add up to 292.
= 360 -34 -34= 292
We also know that they are equal because they are opposite angles.
Therefore, we can solve the equation,
[tex]\frac{sum of two opposite angle}{2}[/tex] = [tex]\frac{292}{2}[/tex] = 146
Each of these angles is 146.
So the measure of angle S is 146.
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Related Questions
the Venn diagram is shown below
Answers
n(A), n(B) and n(AnB) are given and n(AUB)'s complement is asked.
One car rental agency charges $0.29 per mile plus a $10 weekly fee. Another rental agency charges $.0.35 per mile with no fee. You need to rent the car for 3 weeks. Write and solve an equation to find the number of miles for which both agencies will charge the same.
Answers
Answer:
166.67 miles.
Step-by-step explanation:
let the number of mile for which the cost for both car rental be same is x mile
For first car rental
weekly fees charged = $10
cost of 1 mile = $0.29
cost of x miles = x*cost of 1 mile = $0.29x
total money charged by first car rental = $10 + $0.29x
For other car rental
weekly fees charged = 0
cost of 1 mile = $0.35
cost of x miles = x*cost of 1 mile = $0.35x
total money charged by other car rental = $0.29x
_______________________________________
since we have to find miles for which charges are same
thus
total money charged by first car rental = total money charged by other car rental
10 + 0.29x = 0.35x --------------------equation required
=> 10 = 0.35x - 0.29x
=> 10 = 0.06x
=> x = 10/0.06 = 166.67
Thus, the number of miles for which both agencies will charge the same is 166.67 miles.
C. The King football team ordered 50 hats. The cost of shipping was
$6.50. If King spent $256, how much was each hat?
Answers
if 1/4 of the pie was eaten what fraction of the original whole pie remains
Answers
Answer:3/4
Step-by-step explanation:
Paul's mom sent him to the grocery store with $10 to buy bread and cheese for sandwiches. Paul picked out a loaf of bread that costs $3.25, and a deli cheese that costs $5.99 a pound. He would like to buy as much cheese as possible, so he asks the deli worker to see how much each slice weighs. Each slice weighs 0.04 pounds. Which inequality can be solved to find x, the number of slices that Paul can afford to buy?
Answers
Given:
Total amount = $10
Cost of loaf of bread = $3.25
Cost of cheese = $5.99 per pound
Each slice weights = 0.04 pounds.
To find:
The inequality for the number of slices that Paul can afford to buy.
Solution:
Let x be the number of slices that Paul can afford to buy.
Weight of on slice is 0.04 pounds. So, weight of x slices is 0.04x pound.
Cost of cheese = $5.99 per pound
So, total cost of cheese for x slices = $5.99 × 0.04x
Now, Paul has $10 to buy bread and cheese for sandwiches. Cost of loaf of bread is $3.25.
[tex]3.25+(5.99\times 0.04x)\leq 10[/tex]
[tex]0.2396x\leq 10-3.25[/tex]
[tex]0.2396x\leq 6.75[/tex]
Divide both sides by 0.2396.
[tex]x\leq \dfrac{6.75}{0.2396}[/tex]
[tex]x\leq 28.172[/tex]
The maximum integer value of x is 28.
Therefore, the required inequity is [tex]3.25+(5.99\times 0.04x)\leq 10[/tex] and 28 number of slices Paul can afford to buy.
In a certain fraction, the denominator is 4 larger than the numerator. If 2 is added to both the numerator and the denominator,the result is 3\5. Find the original fraction. PLS ANSWER
Answers
Step-by-step explanation:
Here you go, I tried my best
cheers
The original fraction is [tex]\frac{4}{8}[/tex]
Let the numerator = a
Let the denominator = b
Denominator is 4 larger than the numerator: b = a + 4
2 is added to both the numerator and the denominator: (a + 4 +2) and a + 2
The algebraic equation from the given statement is formed as follows;
[tex]\frac{a+ 2}{a+4+2 } = \frac{3}{5} \\\\\frac{a+ 2}{a + 6} =\frac{3}{5} \\\\5(a + 2) = 3(a + 6)\\\\5a + 10 = 3a + 18\\\\5a - 3a = 18 -10\\\\2a = 8\\\\a =4[/tex]
The original fraction is calculated as follows;
[tex]\frac{a }{a +4} = \frac{4}{4+ 4} = \frac{4}{8}[/tex]
Thus, the original fraction is [tex]\frac{4}{8}[/tex]
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There are 32 marbles in a bag 14 were red, what is the ratio of blue to red?
Please help
Answers
Answer: 9:7
Subtract 32 by 14, because there are 14 red marbles.
32 - 14 = 18.
Now, get the numbers 14 and 18. Reduce them to the lowest.
18 ÷ 2 = 9
14 ÷ 2 = 7
Make 9 & 7 to a ration.
Ration- 9:7
================================================
Explanation
There are 32 marbles and 14 are red. If there are only two colors, then we have 32-14 = 18 blue marbles.
The ratio of blue to red is 18:14. We write the two values separated by a colon. The order matters (blue comes first, then red).
The last step is to reduce the ratio 18:14 to 9:7. Note how I divided both parts by the GCF 2.
Find the value of w in the pentagon below if the perimeter is 105 meters.
(3 + 2w) m
(3 + 2w) m
(3 + 2w) m
(3 + 2w) m
(3 + 2w) m
Answers
Answer: 9 (with a margin of: 0)
Step-by-step explanation:
Times everything by 5
That gives you 15 + 10w = 105.
Subtract 15 from both sides
Divide by 10 to get w by itself
Then you solve
2x-3y=6 How do you get y by itself
Answers
Answer:
[tex]y=\frac{2x-6}{3}[/tex]
Step-by-step explanation:
3y=2x-6
[tex]y=\frac{2x-6}{3}[/tex]
First, you have to move the x, along with the coefficient(2).
To move the 2x, you have to subtract it from both sides.
So you have -3y= 6-2x
Now you have to divide by -3.
DON’T FORGET THE NEGATIVE.
So you have y = -2 +2/3
In slope intercept form
If this helped please mark branliest
Sarah is planning to download music and has purchased a monthly package for $12.00 plus $0.60 for each song that she downloads. If Sarah’s bill this month totaled $39.00 how many songs did she download?
Answers
Answer:
Sarah downloaded 65 songs.
What is an equation of the line that passes through the points (6,4) and (4,1)
Answers
First, you find the slope.
This is done by plugging in to the equation y2 - y1 / x2 - x1
Let 6 and 4 by x2 and y2 and 4 and 1 be x1 and y1.
4-1 / 6-4 = 3/2
The slope is 3/2.
Now, y = 3/2 x +b
To solve for b, plug in a point.
I plugged in (6, 4)
4 = 3/2(6) + b
4 = 9 + b
-5 = b
So, the equation is y = 3/2 x - 5
Hope this helps
[tex]y = \frac{3}{2} x - 5[/tex]
What’s the volume to this shape?
Answers
Answer:
30x^6
Step-by-step explanation:
5×2×3=30
x+x+x+x+x+x=6x
Indices gets added when they are multiplied
Answer:
[tex]540x^{3}[/tex]
Step-by-step explanation:
First, we need to simplify all over the cubes and squares.
2x^2 = 4x
3x^3 = 27x
5x=5x
Then , we need to multiply them together.
27x*4x= 108x
108x*5x = 540x
Now, we have our answer
1. The first step to solving a 2-Step Equation, like in the problem below, is
to: *
2 points
-3x + 5 = 12
Division: Divide both sides by -3 to isolate the variable.
Addition: Add 3 to both sides to isolate the variable.
Subtraction: Subtract 5 from both sides to isolate the variable term.
Multiplication: Multiply by the common denominator 60.
Answers
Answer:
addition add 3 to both sides to isolate the variable term
From 24 grams to 96 grams ( percent change )
Answers
Answer:
i think it is 300%
Step-by-step explanation:
The rent of a bowling lane is $25 for 5 minutes.
How much per minute?
Answers
Answer:
5 dollars
Step-by-step explanation:
Earth is 148.61 million km from the sun in scientific notation it is
Answers
Answer:
1.48x10^2 ten to the second
Step-by-step explanation:
mike bought an item for $14,000 after a discount of 30% what was the original price of the item mike brought? please show work.
Answers
Answer:
It should be $20,000
Step-by-step explanation:
From $20,000 to $14,000 = -30%
Which the -30% is the discount basically
So your final answer should be $20,000
$20,000 was the original price.
What the equation of the line that is perpendicular to the line y = −3x + 5 that goes through point D (9, 2)?
Answers
Answer:
y=1/3-1 ...............
NEED HELP ASAP PLEASE.
Answers
Step-by-step explanation:
true i think i think its true
Find the quotient.
(Idk what it means I’m kinda confused)
Answers
Answer:
1 1/3
Step-by-step explanation:
-4/9 ÷ -1/3
Copy dot flip
-4/9 * -3/1
Rewriting
-4/1 * -3/9
simplify
-4/1 * -1/3
Multiply
4/3
Change to a mixed number
1 1/3
Answer:
So the quotient is when you divide so it would be the last one 1 and 1/3
Step-by-step explanation:
-4/9x3/-1(flip the reciprocal)
-12/-9
remove both negatives
simplify and divide both by three and you should get 4/3 which is 1 1/3
0.375, 75% , 5/8, 1/2
From least to greatest pls
Answers
cghmfhjvghvjvhjvhjvgnmvgvhvgmvgnmvg i need answer
Answers
2.)22(mode is the number that is repeated the most in a data set)
Carl drives to the beach at 50 mph. When he returns home he is able to travel at 55
mph. Assuming the trip home takes him a half hour less, find the distance to the beach.
Answers
Answer:
the distance to the beach is 27.5 miles (multiple choice is under rated)
What is the DOMAIN of the given relationship?
(-2, 4), (1, 0), (3, -1), (4, 4)
Someone answer ASAP plsss
Answers
Answer:
(-2,4)
Step-by-step explanation:
Because -2 is the x minimum and 4 is the x maximum :)
A rock garden is in the shape of a triangle as shown. Which equation could be used to find the area of the rock garden
Answers
Answer1/2(8x15)=60ft2
Step-by-step explanation: hope this helps you
The area of the rock garden will be represented by the equation 1/2 x 15 x 8 = 60. The correct option is D.
What is the area of a triangle?The entire area filled by a triangle's three sides in a two-dimensional plane is referred to as the triangle's area. The fundamental equation for a triangle's area is A = 1/2 x b x h, where b and h are the product of the triangle's base and height.
The area of the triangle will be calculated as,
Area = 1/2 x 15 x 8
Area = 15 x 4
Area = 60 square feet
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If f(x) = ln(x+4+e^-3x) then f'(0) is what?
Answers
Answer: f(0) = 0
Step-by-step explanation: anything multiplied by 0 is 0.
The value of [tex]f'(0)=\frac{-2}{5}[/tex]
What is Derivative of a function?
The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument
It is denoted by f ' ( x ) = dy / dx
Given data ,
Let the function be f ( x ) = [tex]ln(x + 4 + e^{-3x} )[/tex]
To differentiate f ( x ) ,
Let [tex]y=ln(a)[/tex] , where [tex]a=x+4+e^{-3x}[/tex]
So ,
[tex]e^{y} =a[/tex]
Using this function , we can write
[tex]e^{y} = x + 4 + e^{-3x}[/tex]
On differentiating , we get
[tex]e^{y}\frac{dy}{dx} = 1 + 0 -3e^{-3x}[/tex]
Dividing by [tex]e^{y}[/tex] on both sides , we get
[tex]\frac{dy}{dx} = \frac{ 1-3e^{-3x}}{e^{y} }[/tex]
We know , [tex]e^{y} =a[/tex]
And [tex]e^{y}=x+4+e^{-3x}[/tex]
So , [tex]\frac{dy}{dx} = \frac{ 1-3e^{-3x}}{x+4+e^{-3x} }[/tex]
Therefore [tex]f'(x)=\frac{dy}{dx} = \frac{ 1-3e^{-3x}}{x+4+e^{-3x} }[/tex]
Now , [tex]f'(0)=\frac{1-3e^{0}}{0+4+e^{0} }[/tex]
[tex]f'(0)=\frac{-2}{5}[/tex]
Hence , the value of [tex]f'(0)=\frac{-2}{5}[/tex]
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Match the side and angle measures of each triangle to its correct classification.
Answers
Answer: 38° obtuse isosceles 26° obtuse scalene 60° acute equilateral 22° right scalene
Step-by-step explanation:
Trust me
We can match like this
Angle measures : 38 degrees, 38 degrees and 104 degrees
Side lengths : 8 inches, 8 inches, 11 inches
Obtuse Isosceles Triangle
Angle measures : 22 degrees, 68 degrees, 90 degrees
Side lengths : 5 inches, 12 inches, 13 inches
Right scalene triangle
Angle measure : 26 degrees, 36 degrees, 118 degrees
Side lengths : 1.5 inches, 2 inches, 3 inches
Obtuse scalene triangle
Angle measure : 60 degrees, 60 degrees, 60 degrees
Side length : 4 inches, 4 inches, 4 inches
Acute equilateral triangle
What is an obtuse scalene triangle?"An obtuse scalene triangle is a scalene triangle that has an obtuse internal angle. These triangles are scalene and obtuse at the same time. An obtuse angle is an angle that is greater than 90 degrees and a scalene triangle is a triangle that has all its sides with different lengths and all of its angles with different measures."
What is a right scalene triangle?"A right scalene triangle is a scalene triangle that has exactly one right angle. A triangle is scalene if none of its sides are equal."
What is an obtuse isosceles triangle?"The Obtuse Isosceles Triangle may be defined as the triangle in which one angle is greater than 90 degrees and two sides that forms the Obtuse Angle are equal in length."
What is acute equilateral triangle?"In a equilateral triangle, all the angles are equal. All the angles in a triangle sum up to 180 degrees. In the acute equilateral triangle, all angles are less than 90 degrees that are acute."
In the first option
Angle measures : 38 degrees, 38 degrees and 104 degrees
Side lengths : 8 inches, 8 inches, 11 inches
We can observe that one of the angle is greater than 90 degrees and two sides of the triangle are equal in length.
The Obtuse Isosceles Triangle may be defined as the triangle in which one angle is greater than 90 degrees and two sides that forms the Obtuse Angle are equal in length.
In the second option
Angle measures : 22 degrees, 68 degrees, 90 degrees
Side lengths : 5 inches, 12 inches, 13 inches
We can observe that one of the angle is right angle and all sides are different.
A right scalene triangle is a scalene triangle that has exactly one right angle. A triangle is scalene if none of its sides are equal.
In the third option
Angle measure : 26 degrees, 36 degrees, 118 degrees
Side lengths : 1.5 inches, 2 inches, 3 inches
We can observe that an angle is greater than 90 degrees and all the sides with different lengths.
An obtuse scalene triangle is a scalene triangle that has an obtuse internal angle. An obtuse angle is an angle that is greater than 90 degrees and a scalene triangle is a triangle that has all its sides with different lengths and all of its angles with different measures.
In the fourth option
Angle measure : 60 degrees, 60 degrees, 60 degrees
Side length : 4 inches, 4 inches, 4 inches
We can observe that all the angles are equal and angles are less than 90 degrees. All the sides are equal.
In a equilateral triangle, all the angles are equal. All the angles in a triangle sum up to 180 degrees. In the acute equilateral triangle, all angles are less than 90 degrees that are acute.
We can match like this
Angle measures : 38 degrees, 38 degrees and 104 degrees
Side lengths : 8 inches, 8 inches, 11 inches
Obtuse Isosceles Triangle
Angle measures : 22 degrees, 68 degrees, 90 degrees
Side lengths : 5 inches, 12 inches, 13 inches
Right scalene triangle
Angle measure : 26 degrees, 36 degrees, 118 degrees
Side lengths : 1.5 inches, 2 inches, 3 inches
Obtuse scalene triangle
Angle measure : 60 degrees, 60 degrees, 60 degrees
Side length : 4 inches, 4 inches, 4 inches
Acute equilateral triangle
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For three consecutive plays, the Patriots gained
12 yards per play. On the next play, they lost 5
yards. What is the change in field position for
these four plays?
Answers
Answer:
The overall change in field position is 7yds, 0 - 5 + 12 = 7, if that isn't a "sum of integers" I apologize.
Step-by-step explanation:
f(x) = -2x+3
find f(-3)
Answers
Answer:
3
Step-by-step explanation:
this is because 3 would be the answer
0=-2x+3
2x=3
Divide both sides
x=3/2
27. Which ordered pair fits the function h(x) = x2 + 3 ?
A) (3,9)
B) (2,4)
C) (-3,12)
D) (-2,-1)
B
С
D