Sofia cuts a piece of felt in the shape of a kite for an art project. The top two sides measure 20 cm each and the bottom two sides measure 13 cm each. One diagonal, EG, measures 24 cm. What is the length of the other diagonal, DF? 5 cm 16 cm 21 cm 32 cm
The length of the other diagonal, DF is 44 cm.
What is the Pythagorean theorem?Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
We can apply this theorem only in a right triangle.
Example:
The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.
Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm
We have,
Since the kite has two pairs of congruent adjacent sides, we know that the diagonals of the kite are perpendicular bisectors of each other.
Therefore, we can use the Pythagorean theorem to find the length of the other diagonal DF.
Let x be the length of the other diagonal, DF.
We know that one diagonal EG has a length of 24 cm, so we can use the Pythagorean theorem to find the length of the perpendicular bisector of EG, which is half of DF.
By the Pythagorean theorem, we have:
[tex](20/2)^2 + (x/2)^2 = 24^2\\100 + (x/2)^2 = 576\\(x/2)^2 = 476\\x/2 = \sqrt(476)\\x = 2 \times 21.86\\x = 43.72\\x = 44[/tex]
Therefore,
The length of the other diagonal DF is 44 cm
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Isaac and his sister plan to surprise their parents by buying them each a pair of shoes. They agree that Isaac will pay 68% of the price since he receives a greater allowance. Use an estimation strategy to determine how much Isaac will pay if the total bill is $97.65. Show the step-by-step process you used to solve the problem.
What is the benefit of using statistical sampling versus nonstatistical sampling?
What happens when you multiply 2 negative numbers?
What is the measurement of angle R?
Is the following relation a function? {(0.3,0.6),(0.4,0.8),(0.3,0.7),(0.5,0.5)}
Answer:
No, the given relation is not a function.
Step-by-step explanation:
Consider the given relation
[tex]\{(0.3,0.6),(0.4,0.8),(0.3,0.7),(0.5,0.5)\}[/tex]
We need to check whether the given relation is function or not.
A relation is a function if there exist a unique value of y for each value of x.
In the given relation, for x=0.3 there exist more than one value of y.
y=0.6 at x=0.3
y=0.7 at x=0.3
For one input there exist more than one output. Therefore, the given relation is not a function.
Find three consecutive odd integers whose sum is 117.
What is the length of each side of the right isosceles triangle with a hypotenuse that measure 2.5√2 units.
a^2 +b^2 = (2.5sqrt(2))^2
2a^2 = 6.25 *2
a^2 = 6.25
a = sqrt(6.25)
a = 2.5
length of each side = 2.5 units
Help plz
What is the approximate distance between points A and B?
A 3.61
B 9.22
C 10.35
D 12.62
Answer:
B 9.22
Step-by-step explanation:
Hello
to find the distance, you can use the distance between two points equation
Given
[tex]P1(x_{1},y_{1})\\P2(x_{2},y_{2})\\\\the\ distance(d)\\\\D=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\[/tex]
Step 1
define
[tex]P1=A=(4,3)\\P2=B=(-2,-4)\\[/tex]
Step 2
put the values into the equation
[tex]D=\sqrt{(x_{2}-x_{1})^{2} +(y_{2}-y_{1})^{2} } \\D=\sqrt{(-2-4)^{2} +(-4-3)^{2} }\\ D=\sqrt{(-6)^{2}+(-7)^{2} }\\ D=\sqrt{36+49} \\D=\sqrt{85} \\D=9.22[/tex]
the distance between the points is 9.22 ⇒B
Have a great day
the answer you are looking for is....
B 9.22PLEASE HELP FOR BRAINIEST ASAP!!
Draw two isosceles triangles, ∆ABC and ∆ADC with common base AC. Vertexes B and D are in the opposite semi-planes determined by AC. Draw the line segment BD. Prove: AC ⊥ BD.
During a certain day, a worker did 77 parts. He usually does 55 parts per day. What was the percent by which he increased the usual number of parts?
Which of the following is equivalent to 34 · 3-2?
Use < , > , or = to compare the numbers. 54 68 70 70 55 930 778 703
Mrs. hensen cataloged a group of incoming library books in 8 hours. mr. taylor can catalog the same number of books in 4 hours. mrs. phillips can catalog them in 6 hours. how long would it take if they all worked together?
Which best describes the relationship between the 125° angle and angle A? They are same side interior angles. Angle A measures 55°. They are alternate interior angles. Angle A measures 125°. They are vertical angles. Angle A measures 125°. They are corresponding angles. Angle A measures 55°.
Answer:
a. They are same side interior angles. Angle A measures 55°.
They are same side interior angles. Angle A measures 55° which is correct option(A).
What are Interior angles?Interior angles is defined as those that lie inside a shape, or those that are located in the region enclosed by two parallel lines that cross each other at a horizontal angle.
What are Alternate Interior Angles?Alternate Interior Angles is defined as these angles are created when a transversal intersects two parallel lines. The opposing sides of the transversal produce this non-adjacent pair of angles.
What are Vertical angles?Vertical angles is defined as when two lines meet each other at a point. They are always equal to each other, In other words, four angles are created anytime two lines cross or intersect.
What are corresponding angles?Corresponding angles is defined as any pair of angles that are both on the same side of the transversal and of one of the two lines that it intersects.
Given angle measure as 125°
Therefore, they are same side interior angles. Angle A measures 55°.
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Find the tangent of the angle in standard position in which the terminal side passes through the point (3,4)
Byron earns $11.00 per hour. How many hours will Byron have to work to earn $143.00?
1. 7.7 hours
2. 13.0 hours
3. 14.3 hours
4. 15.7 hours
divide 143.00 by 11.00
143/11 = 13
Answer is 2. 13.0 hours
Answer:
Step-by-step explanation:
Byron earns $11.00 per hour.
Lets say he works for x hours
for x hour Byron earn =11x
It is given that
Byron have to work to earn= $143.00
so
11x= 143
x=143/11
x=13
so He must work for 13.0 hours .
An angle measures 150° less than the measure of a supplementary angle. what is the measure of each angle?
The measure of the angle is 30 degrees
What is a supplementary angle?A supplementary angle can be defined as an angle that sum up t0 180 degrees.
The two angles must add up to 180 degrees, that is, angles on a straight line.
The properties of supplementary angles are;
The two angles are supplementary angles when they add up to 180°The two angles together make a straight line, but the angles need not in a place“S” of supplementary angles represents a “Straight” line. This means they form 180°From the information given, we have that;
The angle measures 150 degrees less of supplementary angles
Then,
180 - 150
30 degrees
Hence, the value is 30 degrees
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The two supplementary angles in question measure 15° and 165° respectively, with one angle being 150° less than the other.
We are given that one angle measures 150° less than its supplementary angle. By definition, supplementary angles add up to 180°. Let's call the angle in question 'A', and its supplementary angle 'B'.
We thus have the following relationship:
A = B - 150°
and
A + B = 180°
Substituting the first equation into the second, we get:
(B - 150°) + B = 180°
This simplifies to:
2B - 150° = 180°
2B = 330°
B = 165°
Now that we know the measurement of B, we can find A:
A = 165° - 150°
A = 15°
So, the two angles are 15° and 165° respectively.
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What is the value of p in the equation 4p + 3(p + 4) = 12p + 12?
12, 1, 0, -1.
Which of these is a simplified form of the equation 7x + 4 = 5 + 3x + 1x?
3x = 9, 3x = 1 , 11x = 9, 11x = 1
What is the value of z in the equation 3z + 5 = 4z − 8?
13, 1, -13, -1
The work of a student trying to solve the equation 3(4x − 2) = 9 + 2x + 5 is shown below:
Step 1: 3(4x − 2) = 9 + 2x + 5
Step 2: 12x − 2 = 14 + 2x
Step 3: 12x − 2x = 14 + 2
Step 4: 10x = 16
Step 5: x = 1.6
In which step did the student first make an error and what is the correct step?
Step 2: 12x − 2 = 4 + 2x
Step 2: 12x − 6 = 14 + 2x
Step 3: 12x + 2x = 14 + 2
Step 3: 12x − 2x = 14 − 2
Newton uses a credit card with a 18.6% APR, compounded monthly, to pay for a cruise totaling $1,920.96. He can pay $720 per month on the card. What will the total cost of this purchase be?
Which equation could be used to solve the given problem: if three times a number is increased by 24, the result is 4 less than seven times the number?
The equation of the given problem would be 3x + 24 = 7x - 4 and the solution is 7.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We have given that "if three times a number is increased by 24, the result is 4 less than seven times the number"
Let the number be x then we have;
three times a number means 3x
seven times the number means 7x
Therefore, the equation will be;
3x + 24 = 7x - 4
Now solving for x unknown number;
3x + 24 = 7x - 4
24 + 4 = 7x -3x
28 = 4x
x = 7
Hence, the equation of the given problem would be 3x + 24 = 7x - 4, and the solution is 7.
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∠DAC and ∠CAB are adjacent. m∠DAC = 53°, m∠DAB = 64°. What is the measure of ∠CAB?
A) 11°
B) 117°
C) 53°
D) 64°
What is the equation in point-slope form for the line parallel to y = -2x + 10 that contains J(6, 8)?
a. y - 8 = -2(x - 6)
b. x - 8 = 2(y - 6)
c. y - 8 = 2(x - 6)
d. y + 8 = -2(x - 6)
Answer: Hello mate!
A linear equation has the form y = ax + b
where x is the variable, a is the slope and b is the x-intercept.
We want to find the pararel line to y = -2x + 10
A paralel line of this, will be another line with the same slope ( -2 in this case) and a different x-intercept; then our line has the shape of:
y = -2x + b
and we know that this line pases through the point (6,8), and with this info we could find the value of b:
8 = -2*6 + b
b = 8 + 12 = 20
then y = -2x + 20 is the pararel line that passes through the point (6.8)
Then the correct answer is the option a:
a) y - 8 = -2(x - 6) = -2x + 12
y = -2x + 12 + 8 = -2x + 20
How would I solve
-1+2i / -1-3i
A gas station sells regular gas for $2.30 per gallon and premium gas for $3.00 a gallon. at the end of a business day 250 gallons of gas had been sold, and receipts totaled $631. how many gallons of each type of gas had been sold?
Mario baked cookies for the class party. the students ate 3/4 of what mario bought. the students on his bus ate 1/3 of what was left. mario had 6 left when he got home. how many cookies did mario bake?
Carly is making 3 and 1/2 batches of biscuits. If one batch calls for 2and 1/3 cups of flour, how much flour will she need?
Patty is inviting her friends to a party. She has 30 snack bars and 45 juice boxes, and she wants to give the same number of each item to each friend. Use the drop-down menus to describe how many friends Patty can invite. At most, Patty can invite friends to the party. If she invites that many friends, each will receive snack bars and juice boxes.
Given m∠P = 38° and m∠O = 70°, find m∠1.
38
72
108
142
pls
Answer:
The answer is m∠1 = 72°
Step-by-step explanation:
One of the properties of a triangle is that all the angles of the triangle must add up to 180°.
Therefore:
m∠P + m∠O + m∠1 = 180°
Given that:
m∠P = 38° and m∠O = 70°
We can conclude that:
38° + 70° + m∠1 = 180°
m∠1 = 180° - 38° - 70°
m∠1 = 72°
Somebody help me on this real quic plz