Answer:
[tex](x+10)^2+(y+6)^2=121[/tex]
Step-by-step explanation:
The standard form of a circle's equation is
[tex](x-h)^2 + (y-k)^2 = r^2[/tex]
Where (h,k) is the center and r is the radius of the circle.
The equation is given in general form, we need to convert it to the standard form. This can be done by completing squares.
The equation is:
[tex]x^2+y^2+20x+12y+15=0[/tex]
Rearrange x's and y's separate:
[tex]x^2+20x+y^2+12y=-15[/tex]
We have also subtracted 15. Now to complete squares, recall the formula:
[tex](a+b)^2=a^2+2ab+b^2[/tex]
The first two terms are equivalent to the first two terms of the above formula. It's clear that the second term is 2ab=20x. Solving for b:
b=10. Thus, to complete the square, we add 100 to the equation.
The third and fourth terms can also be used to complete the squares for y, knowing that 2ab=12y. In this case:
b=6. To complete this square, we add 36. The equation is now:
[tex](x^2+20x+100)+(y^2+12y+36)=-15+100+36=121[/tex]
Operating and simplifying, knowing that 121=11^2:
[tex]\boxed{\mathbf{(x+10)^2+(y+6)^2=121}}[/tex]
This corresponds to the first choice
Which value is solution to be the inequality 2x-3 < -9
Answer: x < -3
Step-by-step explanation:
noww
need help asap now
Answer:
what's the question
Step-by-step explanation:
there is no question written
(3/8 + 1/3) + 5/8 find the sum
Answer:
1 1/3
Step-by-step explanation:
Find the LCD of all of the fractions.
(9/24 + 8/24) + 15/24
Start by adding the parenthesis.
17/24 + 15/24
Add the remaining fractions.
32/24
Simplify the improper fraction.
1 8/24
Make the fraction into simplest form.
1 1/3
slope = - 3/2; passes through (-4, 7)
Answer:
[tex]y=-\frac{3}{2}x+1[/tex]
Step-by-step explanation:
The equation of a line in slope-intercept form is:
[tex]y=mx+b[/tex]
Each variable represents:
"y" - y coordinate for any point on the line
"m" - slope of the line
"x" - x coordinate for any point on the line
"b" - y-intercept of the line (where the line intercepts the y-axis)
Given:
Slope = -3/2
Passes through (-4, 7) --> x = -4, y=7
Find:
y-intercept
Let's substitute the given information into the equation:
[tex]y=mx+b\\7=-\frac{3}{2}(-4)+b\\7=-\frac{-12}{2}+b\\7=-(-6)+b\\7=6+b\\$Subtract 6 from both sides\\$b=1[/tex]
Therefore the final equation is:
[tex]y=-\frac{3}{2}x+1[/tex]
Suppose y varies directly as x, and y = 10 when x = 25. Find y when x = 18.
Answer:
y = 7.2
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 10 when x = 25, then
10 = 25k ( divide both sides by 25 )
[tex]\frac{10}{25}[/tex] = 0.4 = k
y = 0.4x ← equation of variation
When x = 18, then
y = 0.4 × 18 = 7.2
1. Find the surface area of the sphere below.
od
2 ft
store
Answer:
50.24ftt²
Step-by-step explanation:
surface area of sphere=4πr²
solution
4*3.14*2*2
=50.24ftt²
A high school choir had a car wash to raise money. The number of trucks washed was 2 fewer than half the total number of cars and SUVs washed. They washed twice as many cars as trucks. They washed a total of 28 trucks and cars and SUVs. Let T = the number of trucks, C = the number of cars, and S = the number of SUVs washed. Which ordered triple, (T, C, S) represents the solution to the system below? Verify your answer fully in the box provided.
Answer:
Number of trucks = 28
Number of cars = 14
Number of SUVs = 46
Total number of vehicles = 88
Step-by-step explanation:
Let T = the number of trucks, C = the number of cars, and S = the number of SUVs washed.
We are told :
They washed twice as many cars as trucks.
Hence: T = 2C
They washed a total of 28 trucks and cars and SUVs
Number of trucks = 28
Number of Cars =
T= 2 C
C = T/2
C = 28/2
C = 14
The number of trucks washed was 2 fewer than half the total number of cars and SUVs washed.
T = 1/2(C + S) - 2
T = 28
C = 14
Hence:
28 = 1/2(14 + S) - 2
28 = 1/2(14) + 1/2(S) - 2
28 = 7 - 2 +S/2
28 - 7 + 2 = S/2
30 - 7 = S/2
23 = S/2
S = 23 × 2
S = 46
Hence, number of SUVs = 46
Total number of vehicles = 28 + 14 + 46
= 88
*
Which expression means the same as the quotient of 10 and 5?
*please help*
Answer:
10 divided by 5
i need answer please
Answer:
60°
Step-by-step explanation:
Given:
QP and QR are tangent segments
∠PCR = 120°
Find:
∠PQR
Tangent lines always intersect a circle at one point. This means that the line from the center of the circle to the point of intersection would be the radius. This also means that the tangent line is perpendicular to the radius of the circle.
Therefore...
∠CPQ=90°
∠CRQ=90°
Using the diagram, we can conclude that Figure CPQR is a quadrilateral. We need to find the sum of the interior angles of the Figure CPQR.
The formula to find the sum of the interior angles of a figure is...
[tex](n-2)\times180[/tex]
Note that n represents the amount of sides the figure has.
In this case Figure CPQR has 4 sides therefore...
[tex](4-2)\times180=2\times180=360^{\circ}[/tex]
Now let's set up an equation to find ∠PQR...
∠PCR + ∠CPQ + ∠CRQ + ∠PQR = 360°
Substitute the measures of the known angles into the equation:
120° + 90° + 90° + ∠PQR = 360°
120° + 180° + ∠PQR = 360°
300° + ∠PQR = 360°
Subtract 300° from both sides
∠PQR = 60°
You surveyed 82 students in your grade and found that twenty-three have 2 brothers and twenty-eight have 1 brother. Nine students are only children, ten have only 1 sister, seven have only 1 brother, six have 2 sisters and i brother, twenty-two have 2 sisters, twenty-seven have no sisters, and eight have 1 sister and 2 brothers. Make a two-way frequency table of the given information.
A two-way frequency table for these 82 students is shown in the table attached below.
What is a two-way frequency table?A two-way frequency table can be defined as a table that is used for the graphical representation of frequencies or relative frequencies that are associated with two (2) categorical variables.
This ultimately implies that, a two-way frequency table is mainly used to show, analyze, and examine the relationships between two (2) categorical variables.
Generally, one of the two (2) categorical variables is represented by rows while the other is represented by columns.
Read more on two-way frequency here: https://brainly.com/question/20744563
2
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000
pencils are being divided into packages of 15. How many pencils will be left over?
Answer: 5 pencils left over
Step-by-step explanation:so 133 times 15 is 1995 and you can’t add 15 more to that so you’ll have 5 left over
Answer:
133
Step-by-step explanation:
Cube of -1 Who ever gets it will mark Brainlist
Answer:
-1
Step-by-step explanation:
(-1) ^3
-1*-1*-1
1 * -1
-1
Answer:
-1
Step-by-step explanation:
Cube of -1:
-1 × -1× -1= -1
What is LN equal to?
Since triangle LKJ is similar to triangle LNM,
we know that JK / MN = LK / LN.
JK = 40
MN = 25
LK = LN + KN = LN + 12
LN = ?
Sub these values in and solve for LN...
40 / 25 = (LN + 12) / LN
Simplifying and distributing...
1.6 = 1 + 12 / LN
Subtracting 1 from on both sides...
0.6 = 12 / LN
Multiplying both sides by LN...
0.6 * LN = 12
Dividing both sides by 0.6...
LN = 20
Dilate the figure below with a scale factor of 1.5 centered at the origin and then rotate the figure 90° clockwise about the origin.
Answer:
Step-by-step explanation:
Vertices of the quadrilateral are (-4, 1), (-3, 2), (-1, 2) and (-2, 1).
If the given quadrilateral is dilated by ta scale factor of 1.5 about the origin.
Rule for the dilation,
(x, y) → (kx, ky) [k = scale factor]
New vertices of the quadrilateral after the transformation will be,
(-4, 1) → (1.5×4, 1.5×1)
→ (-6, 1.5)
(-3, 2) → (-4.5, 3)
(-1, 2) → (-1.5, 3)
(-2, 1) → (-3, 1.5)
Now the new points are rotated by 90° clockwise about the origin,
Rule for the rotation of the points,
(x, y) → (y, -x)
So the new vertices will be,
(-6, 1.5) → (1.5, 6)
(-4.5, 3) → (3, 4.5)
(-1.5, 3) → (3, 1.5)
(-3, 1.5) → (1.5, 3)
We can plot these points on the graph to form a new (image) quadrilateral.
SOME PLEASE HELP PLEASE LOTS OF POINTS
The graph shows the relationship between the number of months different students practiced tennis and the number of matches they won: The title of the graph is Tennis Matches. On x axis, the label is Number of Months of Practice. On y axis, the label is Number of Matches Won. The scale on the y axis is from 0 to 22 at increments of 2, and the scale on the x axis is from 0 to 12 at increments of 2. The points plotted on the graph are the ordered pairs 0, 2 and 1, 5 and 2, 8 and 3, 9 and 4, 10 and 5, 12 and 6, 13 and 7, 16 and 8,17 and 9, 18 and 10,20. A straight line is drawn joining the ordered pairs 0, 3.3 and 2, 6.8 and 4, 10 and 6, 13.5 and 8, 17 and 10, 20.5.
Part A: What is the approximate y-intercept of the line of best fit and what does it represent? (5 points)
Part B: Write the equation for the line of best fit in the slope-intercept form and use it to predict the number of matches that could be won after 13 months of practice Show your work and include the points used to calculate the slope. (5 points)
Answer:
Part A; Y - intercept = 4 matches,
Part B; y = 2x + 4
Part C; 30 Matches Won
Step-by-step explanation:
13 months is represented by the x - axis, so let us
plug it into the equation that we formulated and
solve for y, the number of matches one;
Which expression has the same meaning as n 3/8?
Answer:
I think its the one on the bottom right
Step-by-step explanation:
Answer:
bottom right is the answer i think
This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information. If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base? This isosceles triangle has two sides of equal length, a, that are longer than the length of the base, b. The perimeter of the triangle is 15.7 centimeters. The equation 2a + b = 15.7 models this information. If one of the longer sides is 6.3 centimeters, which equation can be used to find the length of the base?
Answer:
[tex]12.6 + b = 15.7[/tex]
[tex]b = 3.1[/tex]
Step-by-step explanation:
Given
[tex]Perimeter: 2a + b = 15.7[/tex]
[tex]a = 6.3[/tex]
Required
Which equation models b
Substitute 6.3 for a
[tex]2a + b = 15.7[/tex] becomes
[tex]2 * 6.3 + b = 15.7[/tex]
[tex]12.6 + b = 15.7[/tex]
Solve for b
[tex]b = 15.7 - 12.6[/tex]
[tex]b = 3.1[/tex]
Answer:
12.6 + b = 15.7
Step-by-step explanation:
I need help A circle has a radius of 4. 6 centimeters. What is the approximate
area of the circle. Use 3. 14 for pi
Answer:
66.4424
Step-by-step explanation:
This is because r^2*3.14
Find the area of a square with sides of length 1/3 yard. please help fast!
A. 1/3 sq yd
B. 14 sq yd
C. 1/9 sq yd
D. 2/9 sq yd
Answer:
The answer is 1/9 square yard. I hope this helps!
Answer: C. 1/9 sq yd
Step-by-step explanation:
To find the area of a square, you do the side length squared. (1/3)^2 is the same as (1/3) * (1/3). Multiply the numerators together to get 1 * 1 = 1 and the denominators to get 3 * 3 = 9. This gives you 1/9.
help i need an answrrrrrrr please asap
Answer:
y=[tex]\frac{5}{6}[/tex]x-2
Step-by-step explanation:
Using the formula rise/run I calculated the slope. Then I saw the line passes through the point in the y axis -2. So the equation would be y=5/6x-2
The prism shown has a volume of 35cm³
Work out h, the height of the triangular cross section.
Answer:
h = 2.5 cm
Step-by-step explanation:
the volume (V) of a prism is calculated as
V = Al ( A is the area of triangular base and l the length )
A = [tex]\frac{1}{2}[/tex] bh = [tex]\frac{1}{2}[/tex] × 4 × h = 2h and l = 7
given V = 35 , then
2h × 7 = 35
14h = 35 ( divide both sides by 14 )
h = 2.5 cm
What is the equation of this line?
y=1/2x
y= -1/2x
y=-2x
y=2x
Answer:
d
Step-by-step explanation:
up 2 right 1
Answer:
y=1/2x
Step-by-step explanation:
4. Xavier has a rectangular piece of card. He cuts off the four corners.
What do the angles of the remaining shape add up to?
Answer:
1080°
Step-by-step explanation:
the rectangle has 4 sides and 4 angles of 90° angles; when the corners are cut, there are now 8 sides and 8 angles, aka an octogon, which has the total angles of 1080°
15% discount off of $35.
Original:
Discount:
New price
Plz help
Answer:
It $29.75
Step-by-step explanation:
Answer:
Orignal Price: $35
Discount Price: $29.75
Step-by-step explanation:
The original price is $35 since it says 15% off of $35. To get the discount price you would use the equation 35-15%, which would give you $29.75. Your new price is $29.75.
Hope this is what you were looking for. :D
Guys I need help and like super fast, I don’t know what to dooooooooo
Answer:
translation
i just got done learning about this a couple of weeks ago
please help for a cookie
Answer:
C) (0, 2)
Step-by-step explanation:
The y-intercept is the y value when x = 0.
Another way to reword that is when the graph crosses the y-axis.
We see from the graph that it crosses the y-axis at 2. Therefore, our y-intercept is (0, 2).
Line m passes through points (-20, 5) and (-4,7). Line n passes through points (-5,5) and (7,4). Are lines m and n perpendicular? Explain.
A. No, the lines are not perpendicular because the product of their slopes does not equal -1.
B. No, the lines are not perpendicular because the product of their slopes equals -1.
C. Yes, the lines are perpendicular because the product of their slopes equals -1.
D. Yes, the lines are perpendicular because the product of their slopes does not equal -1.
Answer:b
Step-by-step explanation: it’s right because it is
A car dealership paid $9,000 for a car. The sticker price is $10,395 for a customer to buy the car. a. What’s the markup in dollars? b. By what percent is the markup?
Answer:
1) To determine how much the change of $9,000 to $10,395, we must subtract 9,000 from 10,395;
10,395 - 9,000 = $1,395 is the change in price (an increase).
Formula to find percentage of change;
Change in price/original amount x 100% (100/100)
Replace those values:
1,935 (change in price/increase) 100
_____ x _____ = %0.215
9,000(original amount) 100
Decrease £16855.21 by 13.5%
Give your answer rounded to 2 DP.
Answer:
14,579.76
Step-by-step explanation:
New value =
16,855.21 - Percentage decrease =
16,855.21 - (13.5% × 16,855.21) =
16,855.21 - 13.5% × 16,855.21 =
(1 - 13.5%) × 16,855.21 =
(100% - 13.5%) × 16,855.21 =
86.5% × 16,855.21 =
86.5 ÷ 100 × 16,855.21 =
86.5 × 16,855.21 ÷ 100 =
1,457,975.665 ÷ 100 =
14,579.75665 ≈
14,579.76
Danielle sold a certain number of tickets to the school play, d. Sara sold 4 more tickets to the school play than the number Danielle sold. Brett sold 3 times as many as Danielle sold. The number of tickets that the 3 students sold altogether can be represented by the expression below. d+d+4+3d
Answer:
5d+4
Step-by-step explanation:
Number of ticket sold by Daniel = d .... 1
If Sara sold 4 more tickets to the school play than the number Danielle sold, the total number sold by Sarah is expressed as d+4 .... 2
If Brett sold 3 times as many as Danielle sold, the amount sold by Brett is 3×d = 3d ..... 3
The number of tickets that the 3 students sold altogether can be gotten by adding equation 1, 2 and 3 together as shown;
d+(d+4)+3d
Collect like terms
= d+d+3d+4
= 2d+3d+4
= 5d+4
Hence the number of tickets that the 3 students sold altogether is represented as 5d+4
Answer:
5d+4
Step-by-step explanation:
Have a good day