Answer:
Center: (3, - 4)
Step-by-step explanation:
We can start to solve this problem by converting this equation into standard form. In other words, by completing the square --- (1)
Subtract " 10 " from either side of the equation x² + y² - 6x + 8y + 10 = 0
x² + y² - 6x + 8y = - 10
Step 1: Complete the square for the expression " x² - 6x "
Using the quadratic equation ax² + bx + c we know that a = 1, b = - 6, c = 0. Assume that d = b / 2a. We have...
d = - 6 / 2(1) = - 6 / 2 = - 3
Now let's assume that e = c - (b²) / 4a...
e = 0 - (-6)² / 4(1) = 0 - 36 / 4 = 0 - 9 = 9 (Substitute values d and e)
(x - 3)² - 9
Step 2: Respectively we can complete the square for the remaining expression " y² + 8y "
Here a = 1, b = 8, c = 0
d = 8 / 2(1) = 8 / 2 = 4
e = 0 - (8)² / 4(1) = 0 - 64 / 4 = 0 - 16 = - 16 (Substitute values)
(y + 4)² - 16
This leaves us with the expression " (x - 3)² - 9 + (y + 4)² - 16 = - 10. " If we simplify this a bit further it leaves us with the following circle equation. Using this we can identify the center of the circle as well --- (2)
[tex]\mathrm{Standard}\:\mathrm{Circle}\:\mathrm{Equation} : (x - 3)^2 + (y +4)^2 = 15,\\\mathrm{General}\:\mathrm{Form} : (x - h)^2 + (y +k)^2 = r^2,\\\mathrm{Properties} : \mathrm{Center} = (3, - 4), \mathrm{Radius} = \sqrt{15}[/tex]
As you can see our center here is (3, - 4)
A coach for a little league baseball team is ordering trophies for the team. Players on the team are allowed to choose between 2 types of trophies. The gold baseball trophies cost $5.99 each and the uniform baseball trophies cost $6.49 each. The team orders g gold baseball trophies and u uniform baseball trophies. Write an expression that could represent the total cost of all of the trophies.
Answer:
y= 5.99(g) + 6.49(u)
Step-by-step explanation:
1) First you determine the variable in the equation $5.99, $6.49, g, and u.
2) Then analyze the equation and identify that each gold baseball trophy (g) is worth $5.99, and each uniform baseball trophy (u) is worth $6.49 each.
3) Since you are finding the total you insert a plus sign.
The expression that could represent the total cost of all of the trophies will be C = 5.99g + 6.49u
Cost of gold baseball trophies = $5.99
Cost of uniform baseball trophies = $6.49
Number of gold baseball trophies ordered = g
Number of uniform baseball trophies ordered = u
Therefore, the total cost will be:
= (5.99 × g) + (6.49 × u)
C = 5.99g + 6.49u
Therefore, the expression that could represent the total cost of all of the trophies is C = 5.99g + 6.49u
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Find the value of ab when a=5/12 and b=1/3
Step-by-step explanation:
When two letters are right next to each other, you multiply them. Since a and b are next to each other, we multiply them together.
[tex]A=\frac{5}{12}[/tex]
[tex]B=\frac{1}{3}[/tex]
To multiply fractions, you place them next to each other and multiply across.
[tex]\frac{5}{12}*\frac{1}{3} \\5*1=5\\12*3=36[/tex]
Our final answer: [tex]\frac{5}{36}[/tex] (we cannot simplify it any further)
Clarissa has taken 4 tests (100 points each) and has an average of 82.5 What score does she have to get on the next test in order to bring her average up to 85?
Answer:
Clarissa needs a 95
Step-by-step explanation:
4 x 82.5 = 330
Keep trying numbers to see if they work
330 + 95 = 425
425 / 5 = 85
Qual o resultado da subtração dos dois polinômios abaixo? (2x2 + 4x) (–2x2 + x – 6)
Answer:
-4x^4-6x^3-8x^2-24x
Step-by-step explanation:
[tex]\left(2x^2+4x\right)\left(-2x^2+x-6\right)\\[/tex]
distribuir parênteses
[tex]=2x^2\left(-2x^2\right)+2x^2x+2x^2\left(-6\right)+4x\left(-2x^2\right)+4xx+4x\left(-6\right)[/tex]
Aplicar regras de menos mais ;[tex]+\left(-a\right)=-a[/tex]
[tex]=-2\times\:2x^2x^2+2x^2x-2\times\:6x^2-4\times\:2x^2x+4xx-4\times\:6x[/tex]
simplificar
[tex]-2\times\:2x^2x^2+2x^2x-2\times\:6x^2-4\times\:2x^2x+4xx-4\times\:6x:\\\quad -4x^4-6x^3-8x^2-24x[/tex]
Evaluate the expression below.
6+15•(5 – 3) + (9-4) - 7
A. 5
B. o
C. 70
D. 19
Answer:
34
Step-by-step explanation:
[tex]6 + 15(5 - 3) + (9 - 4) - 7\\6 + 15(2) + 5 - 7\\6 + 30 + 5 - 7\\36 + 5 - 7\\41 - 7\\34[/tex]
Use PEMDAS, order of operations.
First work out the Parenthesis, then any Exponents, then Multiplication, then Division, then Addition and finally, Subtraction, from left to right.
Find the indicated angle measures. ok last one i promise y’all pls help-
Answer:
bfc = 64, afb = 126
Step-by-step explanation:
I solved in the picture
Hope this helps ^-^
As a quality control manager for her distributing company, Zoe has 875.23 pounds of apples where she found 143.875 pounds of apples were rotten. How many pounds of fresh apples does she have? show your work.
Answer:
731.355
Step-by-step explanation:
875.230 - 143.875 = 731.355
apples rotten fresh
How does -2x + x equal -x ?
Answer:
See below.
Step-by-step explanation:
[tex]-2x+x=-x[/tex]
because we combine like terms. You will essentially ignore the x and just do -2 + 1, which is -1. So, the answer would be -1x which is simply just -x.
To see why we can combine like terms, use the distributive property. So we have:
[tex]-2x+x[/tex]
This is the same thing as saying:
[tex]=(-2)x+(1)x[/tex]
Factor out the x:
[tex]=x(-2+1)[/tex]
Add:
[tex]=x(-1)[/tex]
And simplify:
[tex]=-1x\\=-x[/tex]
Answer:
Step-by-step explanation:
-2x + x could also be written as x - 2x, which is x(1 - 2), or -x. Here we can rearrange the terms as we wish (commutative property).
write 18/31 in simplest form. Use / for fraction line.
witch of the following is equivalent to -8-9(55+2x)
Answer:
-8-495-18x
Step-by-step explanation:
-8-9(55)-9(2x)
-8-495-18x
There are three consecutive integers such that twice the sum of the smallest and the largest is eight more than twice the largest. Find the smallest integer in the sequence.
Answer: 4
Step-by-step explanation:
Let the consecutive integers be x, x+1 and x+2.
There are three consecutive integers such that twice the sum of the smallest and the largest is eight more than twice the largest. This means that:
2(x + x+2) = 2(x+2) + 8
2(2x + 2) = 2x + 4 + 8
4x + 4 = 2x + 12
Collect like terms
4x - 2x = 12 - 4
2x = 8
x = 8/2
x = 4
The smallest integer in the sequence is 4
0.000000000009256 scientific method
Answer:
9.256×10^−12
Step-by-step explanation:
to get standard notation we have a number less ten.
since it is a very small number it has a negative exponent
2 x 2
3
Write in its simplest form
Answer:
[tex] \frac{2}{3} \times 2 \\ = \frac{4}{3} [/tex]
omitir
Step-by-step explanation:
_________________
A construction uses a protactor and a ruler true or false
Answer:
True
Step-by-step explanation:
I just did a whole essay about thin in Geometry and I got an A.
Hope this helps! （づ￣3￣）づ╭❤～
Water flows through a pipe at a rate of 7 liters every 9.5 hours. Express this rate of flow in pints per week. Round your answer to the nearest whole number
Answer:
Water flow per week = 124 liters
Step-by-step explanation:
Given:
Water flow in 9.5 hours = 7 liters
Find:
Water flow per week
Computation:
Water flow per hour = 7 / 9.5
Hours in a week = 7 × 24 = 168 hours
Water flow per week = Hours in a week × Water flow per hour
Water flow per week = 168 × [7 / 9.5]
Water flow per week = 123.7894
Water flow per week = 124 liters
If A and B are independent events with P( A) = 0.60 and P( A| B) = 0.60, then P( B) is: a. 0.60 b. cannot be determined with the information given c. 0.36 d. 1.2
Answer:
B. cannot be determinedStep-by-step explanation:
For two events A and B to be independent, it means they can occur at the same time i.e the occurrence of one does not affect the other occurring. It is represented as P(A∩B) = P(A)P(B)
Given P( A) = 0.60 and P( A| B) = 0.60, to find P(B), we will use the formula for the conditional probability P( A| B) = P(A∩B) /P(B)
P( A| B) = P(A)P(B) /P(B)
P( A| B) = P(A)
Since P( A| B) = 0.60, therefore P(A) is also equal to 0.60 and P(B) cannot be determined since they cancelled out already
The pizza has an area of 78.5 in². What is the minimum width of a placemat that can be placed underneath it so that the pizza does not touch the table? Use 3.14 for pi. someone pls help me
Answer:
The minimum width of the placemat is 10 inches.
Step-by-step explanation:
Let suppose that placemat has a square form, whose width must be at least equal to the diameter of the pizza, so that pizza does not touch the table. Hence, the following relationship is obtained:
[tex]w = D[/tex]
Where:
[tex]w[/tex] - Width of the placemat, measured in inches.
[tex]D[/tex] - Diameter of pizza, measured in inches.
The area of the pizza, measured in square inches, is determined by this formula:
[tex]A = \frac{\pi}{4} \cdot D^{2}[/tex]
The diameter is cleared afterwards:
[tex]D = \sqrt{\frac{4\cdot A}{\pi} }[/tex]
If [tex]A = 78.5\,in^{2}[/tex] and [tex]\pi = 3.14[/tex], then:
[tex]D = \sqrt{\frac{4\cdot (78.5\,in^{2})}{3.14} }[/tex]
[tex]D = 10\,in[/tex]
The minimum width of the placemat is 10 inches.
The minimum width of a placemat that can be placed underneath the pizza so that the pizza wouldn't touch the table is; 10 inches
We are told that the pizza has an area of 78.5 in². Thus;
A = 78.5 in²
Now, the pizza is circular in shape and the minimum width of a placemat that can be placed underneath the pizza so that the pizza wouldn't touch the table will be the diameter of the pizza
Thus, area of a circle with diameter d is;
A = πd²/4
Plugging in the relevant values, we have;
78.5 = 3.14d²/4
d² = 78.5 × 4/3.14
d² = 100
d = √100
d = 10 inches.
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How many turning points does this graph have? *
Answer:
5
Step-by-step explanation:
A turning point is the point where a graph changes from increasing to decreasing or decreasing to increasing.
Count up the points and there are 5!
A sample of 36 observations is selected from a normal population. The sample mean is 49, and the population standard deviation is 5. Conduct the following test of hypothesis using the .05 significance level.
H0: ? = 50
H1: ? = 50
What is the value of the test statistic?
What is the p-value?
A recent national survey found that high school students watched an average (mean) of 6.5 DVDs per month with a population standard deviation of 0.60 hour. The distribution of DVDs watched per month follows the normal distribution. A random sample of 33 college students revealed that the mean number of DVDs watched last month was 5.80. At the 0.05 significance level, can we conclude that college students watch fewer DVDs a month than high school students?
What is the p-value?
Answer:
A) p = 0.230139
B) p = 0 .00001
There is not enough evidence to show that fewer DVDs a month than high school students
Step-by-step explanation:
A) The correct hypothesis are;
Null hypothesis;H0: μ = 50
Alternative hypothesis;H1: μ ≠ 50
We are given;
Sample mean; x' = 49
Standard deviation; σ = 5
Sample size;n = 36
Formula for the test statistic is given by;
z = (x' - μ)/(σ/√n)
z = (49 - 50)/(5/√36)
z = -1.2
So, from online p-value calculator from z-values as attached, using z-score of -1.2, significance level of 0.05, two tailed, we have;
p = 0.230139
B) we are given ;
x = 5.80
μ = 6.5
n = 33
Standard deviation;σ = 0.6
Significance level = 0.05
Hypotheses are;
Null hypothesis;H0: μ = 6.5
Alternative hypothesis; μ < 6.5
So, formula for the test statistic again;
z = (x' - μ)/(σ/√n)
z = (5.8 - 6.5)/(0.6/√33)
z = -6.7
from online p-value calculator z-values as attached, using z-score of -6.7, significance level of 0.05, one tailed tailed, we have;
p = 0 .00001
This is less than the significance level of 0.05, thus we will reject the null hypothesis and conclude that there is no evidence to show that fewer DVDs a month than high school students
Please help:((((((((((
Answer:
7. 3x + 6 = 3x + 10
8. 3x + 6 = x + 2(x + 3)
Step-by-step explanation:
7.
To write an equation with no solutions, we write an equation in which the x terms are eliminated, and we end up with a false statement when we try to solve the equation.
Start with
3x + 6 =
This means: take a number, x, multiply it by 3, then add 6 to it.
To make it into an impossible equation, take the same number x, multiply it by 3, and now add 10 instead of 6. The same number x, multiplied by 3 just like above, and now with 10 added to it cannot equal 3x + 6.
Let's write the equation and try to solve it.
3x + 6 = 3x + 10
Subtract 3x from both sides.
6 = 10
Since 6 = 10 is a false statement, there is no solution.
8.
Now we need an equation that is true for every value of x.
We start with 3x + 6 on the left side.
3x + 6 =
To make it true for every value of x, which means it has an infinite number of solutions, we write an expression on the right side that is the same as 3x + 6, just written in a different form.
For example, start with
3x + 6
Separate 3x into x + 2x, now you have
x + 2x + 6
Now factor 2 out of 2x + 6, so you get
x + 2(x + 3)
The expression x + 2(x + 3) is equal to the expression 3x + 6. Now we use x + 2(x + 3) on the right side of the equation we are writing. We get:
3x + 6 = x + 2(x + 3)
Let's solve this equation.
Distribute on the right side.
3x + 6 = x + 2x + 3
Combine like terms on the right side.
3x + 6 = 3x + 6
Subtract 6 from both sides.
3x = 3x
Subtract 3x from both sides.
0 = 0
0 = 0 is a true equation. Therefore, the equation 3x + 6 = x + 2(x + 3) has infinitely many solutions. in other words, every real number is a solution of the equation.
For 5 days Lydia studied math for a certain amount of time and read for 15 minutes each day Represent the total amount of time Lydia studied and read over the 5-day period.
Since Lydia studied for 5 days
Then it will be 5*15=75 minutes in 5 days
2+49 divided by 7 i need help
subtract 6 from me then multiply by 2 if you subtract 40 and then divide by 4 you get 8 what number am I
Answer:
42
Step-by-step
do it backward starting from 8
Answer:
42
Step-by-step explanation:
How many solutions are there to the equation below?
12x + 32 = 12x - 7
O A. O
B. 1
O C. Infinitely many
Answer:
A
Step-by-step explanation:
12x + 32 = 12x - 7
12x - 12x + 32 = 12x - 12x - 7
32 = -7
This is a false statement so the answer is A) 0.
Additionally, you can see that we have the quantity 12x on both sides but on one side, it's being added by 32 and on the other, it's being subtracted by 7. How can a quantity added by 32 be equal to the same quantity subtracted by 7? It is impossible for a real number to do so, therefore, the answer is 0.
Answer:
Hey there!
Original Equation: 12x+32=12x-7
Subtract 12x: 32=-7
32 does not equal -7, so there is no solution.
Hope this helps :)
Write an expression to determine (represent) the ratio of the circle's circumference to its radius.
Answer:
C/r
Step-by-step explanation:
The ratio of the circle's circumference to its radius is 2π
Please find attached a diagram of a circle and its radius
A circle is a two dimensional figure bounded by one curved line. All the straight lines that are drawn from a certain point within it to the bounding line, are equal.
The radius of a circle is the distance from the center of a circle to its circumference.
The radius of a circle is represented by r
The circumference of a circle is the perimeter of a circle. It is the distance round a circle.
The formula for the circumference of a circle is 2πr
π = pi = 22/7
r = radius
A ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The ratio of a circle's circumference to its radius is
2πr : r
Divide both sides of the equation by r
= 2π : 1
= 2π
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Its chapter LCM .
After traveling every 84 km, a motorbike needs to fill petrol and after 120 km it needs to change Mobil. If these works are done together, after traveling what distance will both the works repeat again?
Answer:
Both works will be repeated at 840km
Step-by-step explanation:
Given
Fills Petrol = Every 84km
Change Mobil = Every 120km
Required
Determine the distance where both works are done at the same time
This solution to this question is to solve for the LCM of 84 and 120
Start by factoring 84
[tex]84 = 2 * 2 * 3 * 7[/tex]
Then, 120
[tex]120 = 2 * 2 * 2 * 3 * 5[/tex]
Then the LCM is as follows;
[tex]LCM = 2 * 2 * 2 * 3 * 5 * 7[/tex]
[tex]LCM = 840[/tex]
Hence, both works will be repeated at 840km
What is 3.30 divided by -2.00? Show work.
Answer:
1.65Step-by-step explanation:
[tex]\frac{3.3}{-2}\\\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}\\=-\frac{3.3}{2}\\\\\mathrm{Divide\:the\:numbers:}\:\\\frac{3.3}{2}=1.65[/tex]
Thomas’s gross salary in 2017 was $68,000. If he qualifies for an $8,350 exemption when filing his taxes, how much does he owe for the year in federal income taxes? (Section 4.6 and 4.7) (1 point)
Answer: $14,912.5
Step-by-step explanation:
given data:
thomas salary in 2017 = $68,000
exemption = $8,350
solution:
thomas taxable income
= salary in 2017 - tax exemptions
= $68,000 - $8350
= $59,560
federal income tax = 25%
= 0.25 * $59,560
= $14,912.5
thomas Owe’s $14,912.5 in federal Income tax at the end of the year.
A Women making $29 an hour gets a 15% raise. How much money will she make after 4 hours of working with the increased hourly pay?
Answer:
$133.40
Step-by-step explanation:
First you have to find 15% of 29 which is 4.35. The way I figured this out was 10% of 29 is 2.9 and 5% of 29 is 1.45 and 2.9 + 1.45 = 4.35.
Then you want to add 4.35 to 29 which equals 33.35, her new hourly pay. Multiply 33.35 by the 4 hours she is working and you end up with $133.40.
You’ve seen how a polygon can reflect onto itself during a transformation. use what you know about symmetry to describe the line of reflection required for such a transformation. be sure to use the word symmetry in your answer.
When the line of reflection occurs simultaneously with a line of symmetry for a polygon or shape, the shape will be able to reflect onto itself
Hope this helps
When the line of reflection occurs simultaneously with a line of symmetry for a polygon or shape, the shape will be able to reflect onto itself.
What is reflection symmetry?Reflective symmetry is a type of symmetry where one-half of the object reflects the other half of the object. It is also known as mirror symmetry. For example, in general, human faces are identical on the left and right sides. The wings of most butterflies are identical on both sides, the left and right sides.
Which figure has a reflection symmetry?Triangles with reflection symmetry are isosceles. Quadrilaterals with reflection symmetry are kites, (concave) deltoids, rhombi, and isosceles trapezoids. All even-sided polygons have two simple reflective forms, one with lines of reflections through vertices, and one through edges.
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