Answer:
radius: 9
center: (-6, -8)
Step-by-step explanation:
First, you may wan to rearrange the equation so it is easier to sole, like:
x^2 + 12x + y^2 + 16y + 19 =0
Next, we need to complete the square. x^2 + 12x is the start of the square of x + 6, which ends in 36, and y^2 + 16y is the start of the square of x + 8, which ends in 64. We can start to write in the squares like:
x^2 + 12x + 36 - 36 + y^2 + 16y + 64 - 64 + 19 = 0
(36 & 64 are subtracted so the equation stays the same)
You can factor getting:
(x + 6)^2 - 36 + (y + 8)^2 - 64 + 19 = 0
You can combine the constants to get -36 - 64 + 19 = -81 and we can add 81 to both sides to get:
(x + 6)^2 + (y + 8)^2 = 81
The standard form of a circle equation is:
(x - h)^2 + (y - k)^2 = r^2
where (h, k) is the center and r is the radius.
In this case, by substituting, we get the center is (-6, -8) and the radius is 9.
Does the table below represent a proportional relationship?
A. Yes, because all the ratios of y to x are equal to 2.
B. Yes, because all the ratios of y to x are equal to 3.
C. No, because all the ratios of y to x are not equal.
D. No, because all the numbers are positive.
The table represents a proportional relationship because all the ratios of y to x are equal to 3. (option B)
What is a proportional relationship?Two variables exhibit a proportional relationship if the constant of proportionality remains constant for all the given values in the table.
The equation that is used to represent a proportional relationship is:
y = kx
Where:
k = constant of proportionality
Value of k when x is 1:
3 = k
Value of k when x is 2:
6 = 2k
k = 6 / 2
k = 3
Value of k when x is 3:
9 = 3k
k = 9 / 3
k = 3
Value of k when x is 4:
12 = 4k
k = 12 / 4
k = 3
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A study selected independent random samples of 50 dogs and 60 cats and found that 38 of the dogs and 15 of the cats could be trained to fetch a ball.
Do these data provide convincing evidence that the proportion of all dogs that can be trained to fetch a ball is greater than the proportion of all cats that can be trained to fetch a ball?
Use Alpha = 0.05.
Select all statements that are correct.
We have two independent random samples.
We have two groups in a randomized comparative experiment.
The 10% condition is met.
The 10% condition does not apply.
The expected number of successes and failures for both samples are 38, 12, 15, 45.
The expected number of successes and failures for both samples are 24, 26, 29, 31.
Answer:
Sorry for answering this late, only just found this.
Answers are
a. We have two independent random samples.
c. The 10% condition is met.
f. The expected number of successes and failures for both samples are 24, 26, 29, 31.
Step-by-step explanation:
EDGE 2021
Once I finish the assignment I'll be making a quizlet with the answers.
Constant of Variation
Find the y-intercepts of the graph y = 10/x² ?
a. There are no y-intercepts
b. y-intercept is (0,1)
c. y-intercept is (0,2)
d. y-intercept is (0,3)
Please select the best answer from the choices provided
Answer:
A. There are no y-intercepts
Step-by-step explanation:
I calculated it logically
How many ways can someone purchase at least one CD from a group of 5
rock, 3 metal, and 7 punk CDs?
Answer:
Step-by-step explanation:
Heavy metal (or simply metal) is a genre of rock music that developed in the late 1960s and early 1970s, largely in the United Kingdom and the United States.
I will give branliest! My problem is NUHUHH
Step-by-step explanation:
Ok so basically you have to do
julio has 13 red marbles 4 blue mables and 8 yellow marbles julio draws a marble out of the bag 100 times how many time out of 100 can julio expect a blue marble
Answer:
16 times
Step-by-step explanation:
13 + 4 +8 = 25 total marbles
(4 is total number of blue marbles, 25 is complete total of marbles)
4/25 times = ?/100 times
Because 25 times 4 is equal to 100, you then multiply 4 by 4 to get 16
16/100 times
Jonah bought 36-ounce Big Mouth soda. After he drinks 27 ounces what percent of his soda is left?
Joe is using the function E= 1.89x + 2.89y to minimize his expenses when selling
markers and erasers. He has the following
constraints.
2x + y > 10
x + 2y > 8
X>0
y >
What is the minimum value of E?
$28.90
$9.45
$15.12
$13.34
Answer:
[tex](d)\ \$13.34[/tex]
Step-by-step explanation:
Given
[tex]E = 1.89x + 2.89y[/tex] -- Objective function
Constraints:
[tex]2x + y > 10[/tex]
[tex]x + 2y > 8[/tex]
[tex]x,y>0[/tex]
Required
Minimum value of E
To do this, we apply graphical method
See attachment for plots of [tex]2x + y > 10[/tex] and [tex]x + 2y > 8[/tex]
From the attached plot, the point that satisfy [tex]x,y>0[/tex] is:
[tex](x,y) = (4,2)[/tex]
So, we have:
[tex]E = 1.89x + 2.89y[/tex]
This gives:
[tex]E =1.89 * 4 + 2.89 * 2[/tex]
[tex]E =7.56 + 5.78[/tex]
[tex]E =13.34[/tex]
Find the slope of the line passing through each of the following pairs of points. (–7, 1) (7, 8)
Answer:
1/2
Step-by-step explanation:
Slope(m)
= (y2 - y1)/(x2 - x1)
= (8 - 1)/(7+7)
= 7/14
= 1/2
་་བ་ཆེ། འོན་ཏེ་ ས་གནས་ཀྱི འན
རས་ན། ན་ནས། ན་བ་ བས་ ཆུ་
Answer:
???
Step-by-step explanation:
how many solutions are on this graph
Answer:
3
Step-by-step explanation:
a A' (1, 1), B' (3, 9), C' (9, 3)
b A' (-1, -1), B' (-1, -3), C' (-3, -3)
c A' (3, 3), B' (9, 3), C' (3, 9)
d A' (3, 3), B' (3, 9), C' (9, 3)
Answer:
c is incorrect
Step-by-step explanation:
Can someone pls help answer this asap!! I’d really appreciate it!
Answer:
124 degrees
Step-by-step explanation:
Since they are congruent the corresponding angles will be equal. There is only one obtuse in each triangle, Angles Y and N. N is measured to be 124 degrees so Y is also 124 degrees.
the mass liquid having a density of 1.40 g and a
volume of 3090 ml
The mass of the liquid is 4326 grams.
How to find the mass of a liquid?The liquid has a density of 1.40 g/ml and the volume of the liquid is 3090 ml. Therefore, the mass of the liquid can be calculated as follows:
The density of a liquid is a measure of how heavy it is for the amount measured. The liquid density is defined as its mass per unit volume.
Therefore,]
density = mass / volume
cross multiply
mass = density × volume
density = 1.40 g/ml
volume = 3090
Therefore,
mass of the liquid = 1.40 × 3090
mass of the liquid = 4326 grams.
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a movie theater has 24 screens. ration of action to other films is 1:2. How many action films are currently showing
Answer: 12
Step-by-step explanation: Because of the ratio we know that half of the screens will be showing action films. Half of 24 is 12, so 12 screens will be playing action.
There is 42,000 litres of water in the lake this year. Find the water in the lake, a year ago if the
water of the lake is decreased by 30% every year.
Answer:
60,000 liters
Step-by-step explanation:
30% of 60000 = 18000
60000 - 18000 = 42000
I know it says college level, but it isn't lol.
the ratio of students to adults at the open house is 9:7 suppose there are 832 students and adults at the open house. how many students are there
Answer:
To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:
students/adults = 9/7
You can then cross-multiply to find the value of "students":
7 * students = 9 * adults
7 * students = 9 * (832/(9+7))
7 * students = 832
students = 832 / 7
students = approximately 118.85714285714 students
To determine the number of students at the open house, you can use the fact that the ratio of students to adults is 9:7 and set up the following proportion:
Copy code
students/adults = 9/7
You can then cross-multiply to find the value of "students":
Copy code
7 * students = 9 * adults
7 * students = 9 * (832/(9+7))
7 * students = 832
students = 832 / 7
students = approximately 118.85714285714 students
Since the number of students must be an integer, the number of students at the open house is approximately 118 students.
Step-by-step explanation:
Which is 70% of 2,000?
A.14
B.70
C.140
D.700
E.1400
Answer:
Option E) 1400
Step-by-step explanation:
Based on the given conditions, formulate: 70‰ x 2000
Convert the percentage to decimals: 0.7 x 2000
Calculate the product or quotient: 1400
Hence , the answer is 1400
Six different students went to a used book sale. They recorded the prices of the books that they bought and created the dot plots below. Each X represents 1 book. Which of the following dot plots report a purchase of 8 books? Select all that apply.
Answer:
Options 3, 4, and 5
Step-by-step explanation:
just count the x's.
If it equals 8, then its correct
Jimmy bought one seedless watermelon
for $2. How many watermelons can
DeShawn buy if he has $6?
Answer:
3 watermelons
Step-by-step explanation:
So this is a basic unit rate problem, so you're going to divide:
6 ÷ 2 = 3
So DeShawn can buy 3 watermelons with $6
hope this helps:)
Every time an insect jump forward the distance covered is half of previous jump. if the insect initially jumped 8.4cm calculate to the nearest two decimal places distance of sixth jump
The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.
What is a geometric sequence?Let a₁ be the first term and r be the common ratio.
Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
Every time an insect jump forward, the distance covered is half of the previous jump. If the insect initially jumped 8.4 cm.
The equation is given as,
aₙ = 8.4 · (1/2)ⁿ⁻¹
The distance that he jumped in the sixth jump will be given as,
a₆ = 8.4 · (1/2)⁶⁻¹
a₆ = 8.4 / 64
a₆ = 0.13125
a₆ ≈ 0.13
The distance that he jumped in the sixth jump nearest to two decimal places will be 0.13.
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Find the volume of a cube that has a taotal surface area of 96 squares feet.
A.) 84.0ft³
B.) 84.06ft
C.) 84.06ft³
D.) 84.06ft^2
Allen needs to prepare a compound for the patient to pick up tomorrow. He needs to mix 2/5 of drug A, with 5/3 of drug B and 9/3 of drug C. What is the total amount of the drugs mixed together?
Answer:
76/15 or 5 1/15
Step-by-step explanation:
2/5=6/15
5/3=25/15
9/3=45/15
6/15+25/15+45/15=76/15 or 5 1/15
y= 2x + 7 (List 4 Ordered Pairs for the equation) 1 points each
Answer:
(1,9), (2,11), (3,13) (4,15)
Step-by-step explanation:
When u plug in those numbers for your x values, you get those numbers for the y values.
The O'Neil family is taking a road trip. Their final destination is more than 243 miles from their house, and so far they have traveled 157 miles. Their
car can travel 21.5 miles on a gallon of gas. Which number line shows the solution set for the number of gallons of gas the O'Neil family needs to
reach their destination?
Answer:
The solution you are looking for is D.)
Step-by-step explanation:
To determine this, we need to find the amount of miles left they need to travel (243 - 157 = 86). Then we can divide that by the amount of miles per gallon (86 / 21.5 = 4). Because a possible solution to the answer is 4, we know that the dot needs to be solid (filled in), and because the solution can be greater than four, the arrow would be directed to the right / positive side of the line.
A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
Complete the table to show the relationship between the amounts of salt and water in the stew recipe. Enter a number in each box.
Can someone please help me quickly!! And also let me know if I got the first 2 correct
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
What is the amount of salt?A stew recipe uses 3 teaspoons of salt for every 4 cups of water.
There is a ratio issue here.
As X is to three, 3 is to 4.
3 : 4 :: X : 3
To eliminate the fractions, multiply each integer in the ratio by 12.
9 : 12 :: 9X : 12
This is a portion of what is
9 / 12 = 9X / 12
to obtain, cross-multiply.
9 / 12 = 3 teaspoons of salt,
Check: 3 cup of flour yields 3 cups, which is a 4x increase.
The amount of salt in 9/12 tablespoons is four times that of 3 tablespoons.
The amount of salt in 3/4 tablespoons is four times that of 3 tablespoons.
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Which of the following is the correct equation for the trend line in the scatter plot?
The equation of the trend line will be : Y = (1/4)x - 1.
What is trend line in scatter plots?A trend line is a straight line that best represents the points on a scatterplot. The trend line may go through some points but need not go through them all.Given is a scatter plot a shown in the image.
The general equation of a straight line is -
y = mx + c
{m} - slope
{c} - intercept along the y - axis
We can find the slope as follows. The line passes through the points -
(4, 0) and (0, - 1). We can write -
m = (- 1 - 0)/(0 - 4)
m = - 1/-4
m = 1/4
and
[c] = - 1
So the equation of the trend line will be -
Y = (1/4)x - 1
Therefore, the equation of the trend line will be : Y = (1/4)x - 1.
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If 2^2x=2^3, what is the value of x?
Answer:
B) 3/2
Step-by-step explanation:
Determine which solution is correct for solving StartFraction 5 over 7 EndFraction y = 6using reciprocals.
Given:
The equation is:
[tex]\dfrac{5}{7}y=6[/tex]
To find:
The solution of the given equation by using the reciprocals.
Solution:
We have,
[tex]\dfrac{5}{7}y=6[/tex]
We need to multiply both sides by the reciprocal of [tex]\dfrac{5}{7}[/tex] to isolate the variable x.
The reciprocal of [tex]\dfrac{5}{7}[/tex] is [tex]\dfrac{7}{5}[/tex]. So, multiplying both sides by [tex]\dfrac{7}{5}[/tex], we get
[tex]\dfrac{5}{7}y\times \dfrac{7}{5}=6\times \dfrac{7}{5}[/tex]
[tex]y=\dfrac{42}{5}[/tex]
[tex]y=8.4[/tex]
Therefore, the value of y is 8.4.
Answer:
42/5
Step-by-step explanation: