Answers
So ΔOAP≅ΔOBQ(by AAS) so OA ≅ OB(CPCTC) and PO ≅ OQ(CPCTC)
What do you mean by AAS Theorem ?The AAS theorem, also known as the angle-angle-side theorem, is a theorem in Euclidean geometry that states: "If two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then the two triangles are congruent."
Given that,
AP ≅ BQ
AP ⊥ AB and BQ ⊥ AB
so ∠A = 90° and ∠B = 90°
To prove that
AO ≅ BO and PO ≅ OQ
In ΔOAP AND ΔOBQ
AB ≅ BQ (given)
∠A = ∠B = 90°
∠AOP = ∠BOQ (vertically opposite angle theorem)
Therefore,Δ OAP ≅ Δ OBQ
∴ OA ≅ OB (CPCT)
PO ≅ OQ (CPCT)
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Related Questions
The width of a rectangle measures (5v2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
Answers
Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P = 2(11v + 5w) cm.
Explain about the perimeter of the rectangle?The perimeter of a rectangle is the length measured around the edge of the rectangle. Although a rectangle has two dimensions, its perimeter only has one and is expressed in linear distances like feet or meters.
The perimeter calculation can be used, for instance, to calculate that many ft of brick border are required overall if somehow the rectangle depicts a garden which needs a brick border.
The sum of the lengths of a rectangle's four sides is known as its perimeter.
Rectangle perimeter = 2L + 2W.
Length = (6v+7w)
width = (5v - 2w)
P = 2 (length + width)
P = 2(6v+7w + 5v - 2w)
On simplifying:
P = 2(11v + 5w)
Thus, the obtained expression for the perimeter of the rectangle in centimeters is found as: P = 2(11v + 5w) cm.
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Compete question:
The width of a rectangle measures (5v - 2w) centimeters, and its length measures (6v+7w) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answers
Answer:
Step-by-step explanation:
[tex]y=\frac{1}{2} x+2[/tex]
[tex]y=(x-h)^2+k[/tex]
[tex]y=(x+3)^2-2=x^2+6x+7[/tex]
The temperature in Chicago was 7 degrees Celsius. It was dropping at a steady rate of 3 degrees per hour. How many hours did it take for the temperature to drop below -5 degrees Celsius?
Write an inequality that represents the situation.
Answers
Answer:
-3x+7 < -5
Step-by-step explanation:
Lets set x as the number of hours since the time it was 7 degrees.
This means that the expression 7-3x would represent the temperature after x hours.
To find the inequality that represents when it would be below -5 degrees, we just set this less than -5:
-5 > 7-3x.
If you want, you can also rearrange this to -3x+7 < -5.
Answer:
4 hours
Step-by-step explanation:
Inequality:
[tex]7-3x < -5[/tex]
[tex]7-7-3x < -5-7[/tex]
[tex]-3x < -12[/tex]
[tex]\frac{-3x}{-3} < \frac{-12}{-3}[/tex]
[tex]x > 4[/tex]
Hope this helps
Tammy must run more than 63 miles total to reach your fitness goals. She has already ran 31 miles and runs for miles per day which of the following inequalities could be used to solve for X the number of days Tammy still needs to run to reach your fitness goals.
Answers
Answer:
[tex]31+4x > 63[/tex]
To reach her fitness goal, she needs to run for more than 8 days.
Step-by-step explanation:
She has already run 31 miles and runs 4 miles per day:
This means that after x days, the distance she will have run is:
[tex]D(x)=31+4x[/tex]
Tammy must run more than 63 miles total to reach her fitness goals.
This means that:
[tex]D(x) > 63[/tex]
[tex]31+4x > 63[/tex]
The inequality is:
[tex]31+4x > 63[/tex]
Solution:
[tex]4x > 32[/tex]
[tex]x > \dfrac{32}{4}[/tex]
[tex]x > 8[/tex]
To reach her fitness goal, she needs to run for more than 8 days.
82. Write an expression that represents the number that
(a) is 7 more than X;
(d) exceeds X by 7;
(b) is 7 less than X;
(e) is X less than 7;
(c) is X more than 7
(f) exceeds 7 by X
Answers
Answer:
dont understand 14+14=π
1. Given the function f(x)=x^2+1, copy and complete the following table
Answers
Eric has 4 pounds of blueberries to make into pies. How many pies can Eric make if each pie needs the given amount of blueberries?
Answers
Rajan baut a book for Rs 180 and sold it to sajan at a profit of 20%. Sajan sold that book to nirajan at a lost 20%. At what price nirajan should sell the book to receive 5% profit ?
Answers
Solution,
CP for rajan=180 rs
Sp for rajan=(20%+1)×180
=216
Cp for niranjan=216
And, Sp=.8×216
=172.8
Cp for niranjan=172.8
For 5% profit,
Sp for Niranjan=(5%+1)×172.8
=181.44
Hence, for Niranjan to gain 5% profit, he must sell it for 181.44 rs
Answer - 181.44
Explanation - For Rajan,
Cost Price = Rs 180
Profit Percent = 20%
Profit Percent = (S.P - C.P/C.P)*100
20 = (S.P - 180/180) *100
S.P = Rs 216
For Sajan,
C.P = Rs 216
Loss Percent= 20%
Loss = (C.P - S.P/C.P)*100
20 = (216-S.P/216)*100
S.P = Rs 172.8
For Niranjan to Sell Book and get 5% profit,
C.P = Rs 172.8
Profit Percent = (S.P - C.P/C.P)*100
5 = (S.P-172.8/172.8)*100
S.P = 181.44
Name the minor arc and find it’s measure. Then name the major arc and find it’s measure.
Answers
The minor arc in the given diagram as required to be determined is; arc TU and it's measure is; 116°.
The major arc in the given diagram as required to be determined is; arc TVU and it's measure is; 244°.
What are the measures of the minor and major arcs in the diagram?It follows from the task content that the minor and major arcs are to be named and their measures determined as required.
The minor arc in a circle is usually subtended by an angle less than 180° while the major arc is subtended by an angle greater than 180°.
Ultimately, the minor arc is; arc TU and it's measure is; 116° while the major arc is; arc TVU and it's measure is; 244°.
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The height after t seconds of a projectile that is launched upward with a velocity of 64 feet per second from the top of a 45 foot building is given by. When will the projectile attain a height of 85 feet?
Answers
The projectile will attain a height of 85 feet at approximately 0.775 seconds or 3.225 seconds.
Calculating the Time to reach a certain heightGiven that
Velocity = 64 feet per second --- v
Initial height = 45 feet --- h
The height function can be represented as
h(t) = -16t² + vt + h
So, we have
h(t) = -16t² + 64t + 45
where h is the height in feet and t is the time in seconds.
To find when the projectile will attain a height of 85 feet, we need to solve the equation for t
So, we have
-16t² + 64t + 45 = 85
-16t² + 64t - 40 = 0
Using a graphing tool, we have
t = 0.775 and t = 3.225
Therefore, the projectile will attain a height of 85 feet at approximately t = 0.775 seconds or t = 3.225 seconds.
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Write an equation for a linear function whose graph has the given characteristics. Horizontal, passes through (9, −45)
Answers
Answer:
y = -45
Step-by-step explanation:
y=mx+b
because the graph is horizontal m = 0
y=0x+b --> y=b
next sub in points
y=b (9,-45)
-45=b
therefore equation is y=-45
A salesman gets paid an annual salary of $35,000 plus he makes $75 for each sale. If this salesman made $46,700, how many sales did he make?
Answers
Answer: 156
Step-by-step explanation:
Annual Salary = $35, 000
Subtract anual salary from 46, 700. ---> 46,700-35,000= 11,700
One sale = $75
To find out how many sales, divide the remaining 11,700 by 75.
11,700/75= 156
156 sales.
What is the area, in square inches, of the shaded part of the rectangle below?
72 points <3
Answers
Answer:
Step-by-step explanation:
16 × 19 = 304
1/2(19×9)=85.5
304-85.5= 218.5
. Sam is 8 ft man and the length of his shadow is 10 feet. Find the height of the building casting a shadow of 200 feet. (Draw a diagram , and label, set up a proportions and solve)
Answers
The height of the building is 160 ft
Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios.
Types of proportion :
Direct Proportion
Inverse Proportion
Continued Proportion
Comparing the heights and shadows using ratio proportions
Sam Height = 8 ft
Sam Shadow = 10 ft
Building Height = x ft
Building Shadow = 200 ft
Sam Height/Sam Shadow = Building Height/Building Shadow
AB/BC = PQ/QR
8/10 = x/200
8*200 = 10*x
1600/10 = x
x = 160 ft
The height of the building is 160 ft
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A point R (-5, 6) is reflected across X axis to obtain point S, write the coordinates of S.
Answers
This is because a reflection across the x axis retains the same x value and the why value flips
What’s the value of a?
Answers
a= n/(b^2 - 4)
A circle is shown. 2 radii with length 8 inches are drawn. A line connects the radii points on the circle to form a triangle. The angle between the 2 radii is 90 degrees. The area between the triangle and the outline of the circle is shaded.
What is the area of the shaded portion of the circle?
(16π – 32) in2
(16π – 8) in2
(64π – 32) in2
(64π – 8) in
Answers
The Area οf the shaded pοrtiοn is given by (16 π -32) inch², the cοrrect οptiοn is A.
What is a CircIe?A circIe is a rοund shaped figure whοse aII pοints Iie in οne pIane and the distance between the center οf the circIe and aII the pοints οn the circIe is cοnstant.
The area οf the shaded pοrtiοn is equaI tο the difference οf the area οf the arc and Area οf the TriangIe.
Area οf an Arc =(θ /360) × π r²
Area = (90/360) × π × (8)²
Area οf the arc = 16 π in²
Area οf the triangIe = (1/2) × base × height
Area οf the triangIe = (1/2) × 8 × 8 = 32 in²
Area οf the shaded pοrtiοn = (16 π -32) inch²
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An airline can sell no more than 155 tickets for a flight. So far 97 tickets
have been sold. Denzel made this number line to show the number of
tickets the airline is still able to sell.
Answers
Answer:
Step-by-step explanation:
I need to find the maximum revenue!
Answers
The revenue is maximized for a value p = 100, and the maximum revenue is:
R = 23,500
How to maximize the revenue?We know that the number of items sold for a prize p is:
-2.35p + 470
Then the revenue will be:
R = (-2.35p + 470)*p
So we need to find the value of p that maximizes that quadratic equation, we can see that the maximum will be at the vertex, then let's write:
R = -2.35p² + 470p
The vertex is at:
p = -470/(2*2.35)
p = 100
Finally, the maximum revenue is:
R = -2.35*100² + 470*100
R = 23,500
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In the circle below, suppose and . Find the following.
Answers
The missing values in the figure are solved to be
angle KLI = 111
angle LIJ = 129 degrees
How to find the missing anglesThe missing angles are solved using the inscribed angle theorem and the knowledge of cyclic quadrilateral
arc KLI = 138 degrees = 2 * angle KJI (inscribed angle theorem)
angle KJI = 138 / 2
angle KJI = 69 degrees
angle KLI + angle KJI = 180 degrees (cyclic quadrilateral property)
where angle KJI = 69
angle KLI = 180 - 69
angle KLI = 111 degrees
angle LIJ + angle LKJ = 180 degrees (cyclic quadrilateral property)
angle LKJ = 51 degrees (given)
angle LIJ = 180 - 51
angle LIJ = 129 degrees
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I need help with these 3 questions.
Answers
a. The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.
What is the statistics
b.the pressure to build to its highest point (75/264).
c. Sample statistic's value is 0.2835.
d. Estimate's standard error is 0.0255.
e. Its highest level, the 95% confidence interval, is (0.2326, 0.3344).
A subfield of mathematics called statistics is concerned with the gathering, examination, interpretation, presentation, and arrangement of data.
Several disciplines, including business, economics, sociology, psychology, epidemiology, and public health, employ it. Statistic uses a variety of techniques to gather and analyse data to better understand.
(A) The percentage of persons (p) who would permit the pressure to increase to its highest point is what we are predicting.
(b) The sample statistic, given as p, is the percentage of subjects that allowed the pressure to build to its highest point (75/264).
(c) The sample statistic's value is 0.2835.
(d) The estimate's standard error is 0.0255.
(e) For the percentage of people who would permit the pressure to reach its highest level, the 95% confidence interval is (0.2326, 0.3344).
Therefore, Overall, the findings of this study indicate that a significant majority of high school pupils will tolerate pressures up to 300 mmHg without ever complaining about the discomfort. The range of values inside the 95% confidence.
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Find the extract value of x
Answers
Answer:
25 + 5√29
Step-by-step explanation:
(I added a photo below)
First, let's find BC using the Pythagorean theorem (from ∆BCD):
[tex] {bc}^{2} = {25}^{2} + {10}^{2} = 625 + 100 = 725[/tex]
[tex]725 > 0[/tex]
[tex]bc = \sqrt{725} =5 \sqrt{29} [/tex]
Then we see, that AB = 25 + x
So, now we can find AC:
[tex] {ac}^{2} = ({25 - x})^{2} - ({5 \sqrt{29} })^{2} = 625 - 50x + {x}^{2} - 25 \times 29 = 625 - 50x + {x}^{2} - 725 [/tex]
Now we have a quadratic equation:
[tex] {x}^{2} - 50x - 100 = 0[/tex]
[tex]d = {b}^{2} - 4 \times a \times c = ({ - 50})^{2} - 4 \times 1 \times ( - 100) = 2500 + 400 = 2900 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{50 - 10 \sqrt{29} }{2} = 25 - 5 \sqrt{29} [/tex]
This is a negative number and we cannot use it, since x has to be a natural number
[tex]x2 = \frac{ - b + \sqrt{d} }{2 a} = \frac{50 + 5 \sqrt{29} }{2} = 25 + 5 \sqrt{29} [/tex]
can you solve this question?
f'(7)=?
instantaneous rate of change=?
Answers
(a) f'(7) = 9. The derivative of the function f(x) evaluated at x=7, is 9.
(b) The instantaneous rate of change of y with respect to x at x = 7 is 9.
What is the derivative of the function?
Given that the tangent line to the graph of y = f(x) at point (7, 56) has the equation y = 9x - 7, we can use the slope-intercept form of the equation of a line to find the slope of the tangent line.
The slope of the tangent line is 9. This is also equal to the derivative of the function f(x) evaluated at x=7, which gives us the answer to part (a).
The instantaneous rate of change of y with respect to x at x = 7 is also given by the derivative of the function at x=7. Therefore, the answer to part (b) is also f'(7) = 9.
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Determine the length of side AB and BC in triangle ABC.
AB=9.68,BC=7.04
AB=8.8,BC=6.4
AB=9.152,BC=6.656
AB=7.92,BC=5.76
Answers
In triangle ABC, the values of AB and BC are 9.68 and 7.04 respectively i.e. A.
What is a triangle's definition?
A triangle is a geometric form that has three straight sides and three angles. It is a fundamental geometric form that is frequently utilised in mathematics, science, and everyday life.
Triangles are distinguished by three sides and three angles. The sum of each triangle's three angles is always 180 degrees. Triangles are classified according to the length of their sides and the measurement of their angles.
Now,
As given ΔDEF ≈ΔABC
that means ratio of all sides will be equal
i.e. AB/DE=BC/EF=AC/DF
then AB/8.8=6.71/6.1
AB=1.1*8.8
AB=9.68
and BC/6.4=6.71/6.1
BC=1.1*6.4
BC=7.04
Hence,
the values of AB and BC are 9.68 and 7.04 respectively.
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Eight times a number, x, is one-third the sum of the number and two. Which answer represents this situation? Responses 8x=13x+2 8 x equals 1 third x plus 2 8x=13(x+2) 8 x equals 1 third open parentheses x plus 2 close parentheses 8x+13(x+2) 8 x plus 1 third open parentheses x plus 2 close parentheses 8x+13x+2
Answers
The problem can be translated into an equation as follows: 8x = (1/3)(x+2)
the answer that represents this situation is: 8x = (1/3)(x+2)
Simplifying the right side of the equation:
8x = (1/3)x + (2/3)
Multiplying both sides of the equation by 3 to eliminate the fraction:
24x = x + 2
Subtracting x from both sides of the equation:
23x = 2
Dividing both sides of the equation by 23:
x = 2/23
Therefore, the answer that represents this situation is:
8x = (1/3)(x+2)
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Peyton drew a right triangle with sides 5
cm, 12
cm, and 13
cm long. Carter drew a similar triangle to Peyton’s. Which of the following can be the measurements of Carter’s triangle?
Answers
Option B. The length of the hypotenuse of Carter's triangle is 13cm.
Since Carter's triangle is similar to Peyton's triangle, the ratio of corresponding side lengths will be the same. Let's use x to represent the length of the hypotenuse of Carter's triangle.
We know that the ratio of the lengths of the hypotenuse and the shorter leg of Peyton's triangle is 13:5. So, the ratio of the lengths of the hypotenuse and the shorter leg of Carter's triangle must also be 13:5.
Thus, we have x/5 = 13/5, which simplifies to x = 13.
Therefore, the length of the hypotenuse of Carter's triangle is 13cm.
Therefore, the only possible length for Carter's hypotenuse is 13cm, and the correct answer is A.
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Peyton drew a right triangle with sides 5cm, 12cm, and 13cm long. Carter drew a similar triangle to Peyton’s. Which of the following can be the measurements of Carter’s triangle?
A. 15cm
B. 13cm
C. 11cm
D. 10cm
the recipe for ellie fruit drink included 1 1/4 quarts of cranberry juice 2 2/3 quarts of apple juice and 5/8 of a quart of lemonade. The recipe makes enough for 4 people. Ellie needs to make enough fruit drink for 20 people . How much of each ingredient does she need?
Answers
Answer:
25/4 quarts of cranberry juice
40/3 quarts of apple juice
25/8 quarts of lemonade
Step-by-step explanation:
just multiply everything by 5
:)
If f(x) = -4x + 4, what is f(x) when x = 3?
f(3) = what is it
Answers
Answer:
-8
Step-by-step explanation:
f(3) = -4(3) + 4 = -12 + 4 = -8
Answer:
f(x) = -8Step-by-step explanation:
[tex]\boxed{\sf f(x) = -4x + 4 \;\: when \;\; x=3}[/tex]
For f(x) -4x+4 substitute x with 3:-
[tex]\sf f\left(3\right)\:=\:-4(3)\:+\:4[/tex]
[tex]\sf f\left(3\right)\:=\:-4\times 3\:+\:4[/tex]
[tex]\sf f(3)=-12+4[/tex]
[tex]\sf f(3)=-8[/tex]
Therefore, f(x) = -8.
______________________
Hope this helps!
Find the shaded area
Answers
Answer:
21.5 m^2
Step-by-step explanation:
Area of circle A = πr^2 = 3.14(10/2)^2 = 78.5
Area of square A = 10^2 = 100
Area of shaded area: 100 - 78.5 = 21.5 m^2
determine whether the proportion is true or false 16miles/18quarts=24miles/27quarts
Answers
To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:
16 miles / 18 quarts = 24 miles / 27 quarts
Cross-multiplying, we get:
16 miles * 27 quarts = 18 quarts * 24 miles
432 milesquarts = 432 milesquarts
The equation holds, so the proportion is true.
The proportion is true .
To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:
16 miles / 18 quarts = 24 miles / 27 quarts
Cross-multiplying, we get:
16 miles * 27 quarts = 18 quarts * 24 miles
432 milesquarts = 432 milesquarts
Proportion can be checked by simplifying the ratios given,
16miles/18quarts=24miles/27quarts
Simplifying further,
8miles/9squarts = 8miles / 9squarts .
The equation holds, so the proportion is true.
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