The equation of a circle is given below. Identify the center and the radius.
4x² + 32x + 4y2 – 20y = – 53
Answers
Answer:
Step-by-step explanation:
Related Questions
Can someone please help me! Big ideas number 22 8.4
Answers
Answer:
26
Step-by-step explanation:
the whole area is the sum of the area of the rectangle in the middle and the 2 triangles on either side of the rectangle.
sBC = distance between (0,3) and (4,-1)
and that is the Pythagoras calculation with the coordinate differences
sBC² = (4-0)² + (-1 - 3)² = 16 + 16 = 32
sBC = sqrt(32) = sFE
to get the area of the rectangle we need also FB (or CE).
sFB² = (0 - -2)² + (3-1)² = 4 + 4 = 8
sFB = sqrt(8) = sCE
area of rectangle is
sBC×sFB = sqrt(32)×sqrt(8) = sqrt(32×8) = sqrt(256) = 16
the area of a right-angled triangle is
a×b/2
we have sFB and need sAF
sAF² = (-5 - -2)² + (4-1)² = 9 + 9 = 18
sAF = sqrt(18)
the area of the left triangle is
sFB×sAF/2 = sqrt(8)×sqrt(18)/2 = sqrt(8×18)/2 = sqrt(144)/2 = 12/2 = 6
for the right triangle we have sCE and need sED.
sED² = (2 - 4)² + (-3 - -5)² = 4 + 4 = 8
sED = sqrt(8)
the area of the right triangle is
sCE×sED/2 = sqrt(8)×sqrt(8)/2 = 8/2 = 4
so in total we have for the area
16 + 6 + 4 = 26
Explain what you would do first to simplify the expression below. Justify why, and then state the result of performing this step.
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How is mathematical thinking established? How can we have mathematical thinking?
修改翻译结果
Answers
Translate How is mathematical thinking established? How can we have mathematical thinking? in to Chinese.
数学思维是如何建立的？ 怎样才能有数学思维？
Question 1: Use the image and your knowledge of the isosceles triangle to find the value of x
Answers
Answer:
35 degrees
Step-by-step explanation:
since both sides are equal, so are the angles involved.
I need help please!!!
Answers
Answer:
40 degrees
Step-by-step explanation:
Ross resides in an apartment where houses are arranged horizontally.
She resides at door number 3. If she wants to visit her friend Martha at
door number 7, how many houses should she cross?
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Answer:
4
Explanation:
f(x)=2^x by a factor of five
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Given P(A) = 0.36, P(B) = 0.2 and P(ANB) = 0.122, find the value of P(AUB), rounding to the nearest thousandth, if necessary.
Answers
Answer:
The value of P(AUB) = 0.438
Step-by-step explanation:
Given:
P(A) = 0.36
P(B) = 0.2
P(A∩B) = 0.122
Find:
The value of P(AUB)
Computation:
P(AUB) = P(A) + P(B) - P(A∩B)
The value of P(AUB) = 0.36 + 0.2 - 0.122
The value of P(AUB) = 0.56 - 0.122
The value of P(AUB) = 0.438
Flying against the wind, a jet travels miles in hours. Flying with the wind, the same jet travels miles in hours. What is the rate of the jet in still air and what is the rate of the wind
Answers
Answer:
Velocity in still air: 760 mi/ hr
Velocity against the wind: 210 mi/ hr
Step-by-step explanation:
Given
See attachment for complete question
Required
The rate in still air
The rate of the wind
From the question, the velocity (v) against the wind is:
[tex]v =\frac{distance}{time}[/tex]
[tex]v =\frac{3040}{4}[/tex]
[tex]v_1 =760mi/hr[/tex]
The velocity with the wind is:
[tex]v_2 = \frac{8260}{7}[/tex]
[tex]v_2 = 1180mi/hr[/tex]
Let:
[tex]x \to[/tex] velocity in still air
[tex]y \to[/tex] velocity of the wind
So, we have:
[tex]x - y = 760[/tex]
[tex]x + y = 1180[/tex]
Add both equations
[tex]x + x -y + y = 760 + 1180[/tex]
[tex]2x = 1940[/tex]
Divide by 2
[tex]x = 970[/tex]
Substitute [tex]x = 970[/tex] in [tex]x - y = 760[/tex]
[tex]970 - y= 760[/tex]
Make y the subject
[tex]y = 970 - 760[/tex]
[tex]y = 210[/tex]
John is 20 years old than Steve. In 10 years, Steve's age will be half that of John's. What is the Steve age??
Answers
Answer:Steve age will be 15 y.o
Step-by-step explanation:
in a two digit number the tens digit is 6 more than the units digit. if the digits are interchanged, the sum of the new and the original number is 132. Determine the original number.
Answers
Given:
In a two digit number the tens digit is 6 more than the units digit.
If the digits are interchanged, the sum of the new and the original number is 132.
To find:
The original number.
Solution:
Let the unit digit of the original number be x. So, the tens digit is (x+6) and the value of the number is:
[tex]m=(x+6)\times 10+x\times 1[/tex]
[tex]m=10x+60+x[/tex]
[tex]m=11x+60[/tex]
If we interchange the digits, then the value of new number is:
[tex]n=x\times 10+(x+6)\times 1[/tex]
[tex]n=10x+x+6[/tex]
[tex]n=11x+6[/tex]
The sum of the new and the original number is 132.
[tex]m+n=132[/tex]
[tex]11x+60+11x+6=132[/tex]
[tex]22x+66=132[/tex]
[tex]22x=132-66[/tex]
[tex]22x=66[/tex]
Divide both sides by 22.
[tex]x=\dfrac{66}{22}[/tex]
[tex]x=3[/tex]
So, the unit digit of the original number is 3 and the tens digit is:
[tex]x+6=3+6[/tex]
[tex]x+6=9[/tex]
Therefore, the original number is 39.
Find the area of the parallelogram
Answers
Answer:
The answer is 32.
Step-by-step explanation:
Just multiply the height by the base length. 4*8=32
the area of a rectangular bathroom mirror is 20 square feet. it is 2 feet tall. how wide is it?
Answers
Area = length x width
Fill in the given information
20 = 2 x width
Solve for width by dividing both sides by 2
Width =20/2
Width = 10 feet
Answer:
It is 10 feet wide
Step-by-step explanation:
The area of a rectangle is:
A = Length x width
So if we have the area, finding the width means diving the area by the given length.
In this case, the area of the rectangle is 20 square feet and the length is 2 feet:
20/2 = 10
Therefore the missing width is 10 feet
m-2n = 8
n = m - 2
The value of m in the system of equations is:
Answers
Step 1: Substitute information
To solve this we will use the substitution method. This means that we will use the information provided to us in the second equation, and substitute it into the first equation. We are told what n equals, so let’s substitute this now.
m-2n=8
m-2(m-2)=8
Step 2: Distribute
Now that we have substituted the information, let’s distribute. This means that we will multiply the numbers on the outside of the parentheses with the numbers on the inside of the parentheses. Let’s do this now.
m-2(m-2)=8
m-2m+4=8
Step 3: Combine like terms
Now that we have distributed, we can continue solving the problem. The next step is to combine like terms. This means to combine terms with the same variable, or lack of. In this case, that is m and -2m.
m-2m+4=8
-m+4=8
Step 4: Get variable alone on the left side
We can now work to get the variable alone on the left side. We can do this by moving the number on the right side, in this case by adding 4 on both sides.
-m+4=8
-m=4
Step 5: Make m positive
In this final step, we must work to make m positive. We can do this by multiplying each term by -1. This will make m positive, and 4 negative. Let’s do this now.
-m=4
-1(-m)= -1(4)
m= -4
This is your answer! M is equal to -4. Hope this helps! Comment below for more questions.
HELP MEEE QUICK THIS MY LAST QUESTION!!!
Question 10 of 10
Is APQR- AXYZ? If so, name which similarity postulate or theorem applies.
80
Q
180°
P
5
R
х
10
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
Ο Ο
D. Cannot be determined
SUBMIT
Answers
Answer:
A. Similar - AA
Step-by-step explanation:
The given parameters of ΔPQR and ΔXYZ are;
In ΔPQR, we have; PQ = 3, PR = 5, and ∠PQR = 80°
In ΔXYZ, we have; XY = 6, XZ = 10, and ∠XYZ = 80°
In ΔPQR, by sine rule, we have;
3/(sin(∠PRQ)) = 5/(sin(80°))
sin(∠PRQ) = (3/5) × sin(80°)
∴ ∠PRQ = arc sin((3/5) × sin(80°))
In ΔXYZ, by sine rule, we have;
6/(sin(∠XZY)) = 10/(sin(80°))
sin(∠XZY) = (6/10) × sin(80°) = (3/5) × sin(80°)
∴ ∠XZY = arc sin((3/5) × sin(80°))
∠PRQ = ∠XZY by transitive property of equality
Therefore in ΔPQR and ΔXYZ, we have;
∠PRQ = ∠XZY and ∠PQR = ∠XYZ
Therefore, ΔPQR is similar to ΔXYZ by Angle Angle, AA, similarity postulate.
Solve 3 - x/2 > 15..
Answers
Answer:
x ≥-24
Step-by-step explanation:
3 - x/2 ≥ 15
Subtract 3 from each side
3-3 - x/2 ≥ 15-3
-x/2 ≥12
Multiply by -2
-x/2 * -2 ≥12 *-2
x ≥-24
Answer:
A. x ≤ 24
Step-by-step explanation:
[tex] \small \sf \: 3 - \frac{x}{2} ≥ 15 \\ [/tex]multiply both side by 2 . Since 2 is the positive the inequality direction remains the same.
6 - x ≥ 30subtract 6 from both sides
6 - 6 - x ≥ 30 - 6 -x ≥ 24Divide both side by - 1. Since -1 is negative, the inequality direction remains the change.
x ≤ -24Which property would allow you to use mental computation to simplify the problem 27 + 15 + 3 + 5?
Answers
Answer:
commutative property of addition.
a sequence of additions can be done in any order and the total remains the same.
Step-by-step explanation:
so, we can actually do
27 + 3 + 15 + 5
and now it is easy to combine 27+3 to 30 and 15+5 to 20, and to make the final calculation of 30 + 20 = 50 in our minds.
Multiplicar:
a. (– 6) (– 7) =
b. – 12 x – 5 =
c. (+ 10) (– 6) =
d. (– 15) (+ 5) =
e. (+ 11) (+6) =
f. (– 3) (– 5) (– 6) =
g. (– 8) (+6) (-3) =
h. (- 5) (+ 3) (+9) =
Answers
Answer:
a. 42
b. -12x-5
c. -60
d. -75
e. 66
f. -90
g. 144
h. -135
HELP ASAP!!!
The circle graph shows the percentage of visitors at a
convention who ordered various flavors of juice. There were 700
visitors at the convention.
About how many visitors ordered grape juice or apple juice?
Enter your answer in the box.
Answers
Step-by-step explanation:
40+24+11+8+17= 100
100 - 700
24 - ?
24×700/100
= 168 visitors ordered apple juice
100-700
11-?
11×700/100
=77 people ordered grape juice
Can someone help me with this math homework please!
Answers
Answer:
-1
Step-by-step explanation:
we match the input to the output to find that f(3) points towards -1
The distance traveled (in meters) by a frog is modeled by the equation d=2t where d is the distance traveled in meters and t is the time in minutes. Find the distance traveled in 25 minutes.
Answers
Given,
d = 2t
here, t = 25
Therefore,
d = 2*25
= 50m
The sides of a triangle have lengths 2, 3, and 3. What kind of triangle is it?
Answers
This is because the triangle has exactly two sides that are the same length.
If all three sides were the same length, then it would be equilateral.
If neither of those cases, then we consider the triangle scalene.
Explanation: An isosceles triangle is a type of triangle in which two sides share the same length, and two angles share the same degree. Using the lengths of the triangle provided to us, we can tell that this shape is an isosceles triangle because two of the sides are equal.
The Marked price, inclusive of GST, of a notebook computer is $1679.90.it is sold at a discount of 10%.
a) find its marked price before GST
b)Find the GST before discount.
c)What is the selling price of the computer
d) find the GST after the discount
e)what is the percentage decrease in the GST
Answers
Answer:i don’t know
Step-by-step explanation:i don’t know
What is the word form of 0.604
Answers
Answer:
zero point six hundred and four
Step-by-step explanation:
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.
Ice Cubes 4 2 3 5 5 3 1
Juice (milliliters) 177 234 202 140 155 210 265
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice cubes?
A.
10
B.
89
C.
118
D.
208
Answers
Answer:
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.
Ice Cubes 4 2 3 5 5 3 1
Juice (milliliters) 177 234 202 140 155 210 265
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice
Step-by-step explanation:
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.
Maya collected data about the number of ice cubes and milliliters of juice in several glasses of juice and organized the data into this table.
Ice Cubes 4 2 3 5 5 3 1
Juice (milliliters) 177 234 202 140 155 210 265
She used a graphing tool to display the data in a scatter plot, with x representing the number of ice cubes and y representing the milliliters of juice. Then she used the graphing tool to find the equation of the line of best fit:
y = -29.202x + 293.5.
What is the line of best fit?
A line of best fit refers to a line through a scatter plot of data points that best expresses the relationship between those points. Statisticians typically use the least-squares method to arrive at the geometric equation for the line, either through manual calculations or regression analysis software.
Based on the line of best fit, approximately how many milliliters of juice will be in a glass with 7 ice.
To learn more about the data visit:
https://brainly.com/question/19243813
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A car with a passenger of mass 56 kg can travel a distance of 120 km using 10 l of petrol. If the number of passengers increases to 4 people with a total mass of 224 kg, the distance travelled decreases by 10%.
What is the total distance that the car carrying 4 passengers can travel using 10 l of petrol?
Answers
Answer:
120 * 0.90 = 108 km
Step-by-step explanation:
Answer:
108km
Step-by-step explanation:
D=22/7×d-90 Solve the equation
Find D
Fast!
Answers
Answer:
D=22-90+22d/7
Step-by-step explanation:
D=22/7×d-90
D=-90+22d/7
Tamisha's shampoo bottle holds 1/2 bottle of shampoo.She used 5/6 of the bottle.How many gallons of shampoo has Tamisha used?
Answers
Answer:
5/12
Step-by-step explanation:
1/2 x 5/6 = 5/12
Need help on this!! 10 points!!!
Answers
Answer:
The answer is B
Abraham set the table for a picnic using round plates. Each plate has a diameter of 8 inches. What is the area of each plate?
Answers
Answer:
50.265
Step-by-step explanation:
Area is radius square times pi. Radius is half of diameter .Diameter is 8 inches. Radius is 4 inches. 4 squared is 16. 16 times pi is 50.265