Answer:
a)89
b)89.45
Step-by-step explanation:
the equation x^2 + y^2 + 21 = 40 + 18y. What is the radius of this cookie?
Answer:
The radius is 10
Step-by-step explanation:
Given
[tex]x^2 + y^2 + 21 = 40 + 18y.[/tex]
Required
The radius
Rewrite as:
[tex]x^2 + y^2 - 18y = 40-21[/tex]
Subtract 81 from both sides
[tex]x^2 + y^2 - 18y +81= 40-21+81[/tex]
Expand
[tex]x^2 + y^2 - 9y - 9y +81= 40-21+81[/tex]
Factorize
[tex]x^2 + y( y- 9) - 9(y -9)= 40-21+81[/tex]
Factor out y - 9
[tex]x^2 + (y- 9) (y -9)= 40-21+81[/tex]
Express as squares
[tex]x^2 + (y- 9)^2= 100[/tex]
[tex]x^2 + (y- 9)= 10^2[/tex]
The equation of a circle is:
[tex](x - a)^2 + (y- b)= r^2[/tex]
By comparison:
[tex]r^2=10^2[/tex]
[tex]r = 10[/tex]
Select the correct answer.
What is the solution to this equation?
log3 (4x) – 2log3x =2
A. 36
B. 9/4
C. 4/9
D. 1/36
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Answer:
C. 4/9
Step-by-step explanation:
There are a couple of ways you can do this.
[tex]\log_3{4x}-2\log_3{x}=2\\\\\log_3{4}+\log_3{x}-2\log_3{x}=2\\\\\log_3{4}-2=\log_3{x}\\\\4\cdot3^{-2}=x\qquad\text{take antilogs}\\\\\boxed{x=\dfrac{4}{9}}\\\\\textsf{or}\\\\\dfrac{4x}{x^2}=3^2\qquad\text{take antilogs}\\\\\dfrac{4}{9}=x\qquad\text{cancel $x$, multiply by $\dfrac{x}{9}$}[/tex]
Help please which option
Answer:
Step-by-step explanation:
-1<x<3. I hope it helpful!
the volume of a cylinder is 44cm3. find the volume of another cylinder of the same height and double the base radius
Answer:
[tex]Volume \ of \ other\ cylinder = 176 \ cm^3[/tex]
Step-by-step explanation:
Let the volume of cylinder Vₐ = 44cm³
Let radius of cylinder " a " be = rₐ
Let height of cylinder " b" be = hₐ
[tex]Volume_a = \pi r_a^2 h_a\\\\44 = \pi r_a^2 h_a[/tex]
Given cylinder " b ", Radius is twice cylinder " a " , that is [tex]r_b = 2 r_a[/tex]
Also Height of cylinder " b " is same as cylinder " a " , that is [tex]h_b = h_a[/tex]
[tex]Volume_b = \pi r_b^2 h_b[/tex]
[tex]= \pi (2r_a)^2 h_a\\\\=4 \times \pi r_a^2 h_a\\\\= 4 \times 44\\\\= 176 \ cm^3[/tex]
Write the equation of the circle with center C(-5,8) and radius = 7
Answer:
( h + 5 )^2 + ( y - 8 ) ^2 = 49
Step-by-step explanation:
Equation of a circle:
( x - h )^2 + ( y - k )^2 = r^2
Where ( h , k ) = center and r = radius
We are given that the circle has a center at ( -5 , 8 ) meaning that h = -5 and k = 8
We are also given that the circle has a radius of 7 meaning that r = 7
Now that we have identified each variable we plug the values into the equation
( h - (-5)^2 + ( y - 8 )^2 = 7^2
Our final step is to simplify
we get that the equation of the circle is
( h + 5 )^2 + ( y - 8 ) ^2 = 49
By the way ^ means exponent
Help me pls this is hard
Answer:
I guess it is the Answer C
Answer:
C
The distance around the edge of the circle
This is a 30-60-90 triangle. What is the measure of x? rationalize the denominator.
Answer:
[tex] x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]
Step-by-step explanation:
Since, given is a 30°-60°-90° triangle.
[tex] \therefore \sqrt 7 = \frac{\sqrt3}{2} \times x[/tex]
[tex] \therefore 2\sqrt 7 = \sqrt3 \times x[/tex]
[tex] \therefore x=\frac{2\sqrt 7}{\sqrt 3}[/tex]
[tex] \therefore x=\frac{2\sqrt 7(\sqrt 3)}{\sqrt 3(\sqrt 3)}[/tex]
[tex] \huge \therefore x=\frac{[2] \sqrt {[21] }}{[3] }[/tex]
Please show work thank you
Answer
No solution
Step-by-step explanation:
4y + 2x = 18
3x + 6y = 26
You need either the x's or the y's to have the same coefficients.
let's line things up first.
4y + 2x = 18 (multiply by 3)
6y + 3x = 26 (multiply by 2)
to keep numbers relatively small we will multiply the top equation by 3 and the bottom equation by 2. Multiply all terms. This will make the coefficients equal.
12y + 6x = 54
12y + 6x = 52
So, if you subtract them from each other you get :
0 = 2
When this happens the solution set is : no solution
Answer:
Impossible
Step-by-step explanation:
Ok, so we first rearrange for convenience:
2x+4y=18
3x+6y=26
We multiply the two equations to eliminate x:
2x+4y=18 * -3
3x+6y=26 * 2
So:
-6x-12y=-54
6x+12y=52
And now we add the two equations:
0+0= -2
Try multiplying the two equations by any other number which will lead to them cancelling, (eg. -9, 6), still the equation will not work.
k+9=7..................................................
Answer:K=-2
Step-by-step explanation:
becuase you do the opposite of +9 which is -9 and you do 7-9 which is -2 so K=-2
PLZ HELPPP I need to pass this!!
Answer:
x=-1
Step-by-step explanation:
the middlepoint is where its symetrical, and so you take the x part of the point. the point is (-1,4), and all we need is x, so you have x=-1
Which of the following represents the graph of f(x) = 4X – 2?
Answer:
The bottom one.
Step-by-step explanation:
To solve the equation, Lorie applies the distributive property, combines like terms, then applies the addition and subtraction properties of equality to isolate the variable term on one side of the equation and the constant term on the other side. What are the possible coefficients of x after Lorie has completed these steps?
10 (one-half x + 2) minus 5 = 3 (x minus 6) + 1
–32 and 2
–2 and 32
–2 and 2
–32 and 32
Answer:
-2 and -2
Step-by-step explanation:
if a loaf of bread coast £1.52 how much change will you get from £10 if you buy 4loaves
Answer:
Balance will be £3.92
Step-by-step explanation:
Cost of 1 loaf = £1.52
Therefore, cost of 4 loaves = 4 x 1 . 52 = £6.08
So if you pay with £10 your balance will be = 10.00 - 6.08 = £3.92
The solution is £ 3.92
The amount of money after the purchase of 4 loaves of bread is given by the equation A = £ 3.92
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
The total amount of money = £ 10
The cost of one loaf of bread = £ 1.52
Now , the number of loaves of bread = 4 loaves
So , the cost of 4 loaves of bread = 4 x cost of one loaf of bread
Substituting the values in the equation , we get
The cost of 4 loaves of bread = 4 x 1.52
The cost of 4 loaves of bread = £ 6.08
The amount of money after the purchase A = total amount of money - cost of 4 loaves of bread
Substituting the values in the equation , we get
The amount of money after the purchase A = £ 10 - £ 6.08
The amount of money after the purchase A = £ 3.92
Therefore , the value of A is £ 3.92
Hence , the amount is £ 3.92
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ2
PLSSSS ASAPPP!!!!!!!!!!
Find the length of the missing side in the right triangle shown below.
A)169
B)7,056
C)None of these answers are correct
D)7,225
E)13
Answer:
D. my answer for your question
A person invests $3,500 in an account that earns 7.5% interest compounded continuously. What is the value of the investment after 4 years?
I think it's: 4,674.14$
Answer:
A = $4724.36
Step-by-step explanation:
P = $3500
r = 7.5% = 0.075
t = 4years
n = 365
[tex]A = P(1 + \frac{r}{n})^{nt}\\\\[/tex]
[tex]=3500(1 + \frac{0.075}{365})^{365 \times 4}\\\\=3500(1.00020547945)^{365\times4}\\\\= 3500 \times 1.34981720868\\\\= 4724.36023037\\\\= \$ 4724.36[/tex]
The strongest winds of Hurricane Isabel extended 50 miles in all directions from the center.
What is the area of the hurricane in square miles? Leave your answer in terms of Pi
Answer:
20
Step-by-step explanation:
your mom
If F(x)= 3x-2 and G(x)= x^2+8, what is G(F(x))?
Answer:
(3x-2)^2+8= 9x^2-12x+12
There are 200 students in a particular graduate program at a state university. Of them, 110 are female and 125 are out-of-state students. Of the 110 females, 70 are out-of-state students. If two of these 200 students are selected at random, what is the probability that both of them are out-of-state students?
Suppose that 48% of high school students would admit to lying at least once to a teacher during the past year and that 25% of students are male and would admit to lying at least once to a teacher during the past year.20 Assume that 50% of the students are male. What is the probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year? Be sure to show your work and indicate all the rules that you use to find your answer.
Answer:
0.73 = 73% probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year.
Step-by-step explanation:
I am going to treat these events as Venn probabilities, considering that:
Event A: Lying to the teacher.
Event B: Male
48% of high school students would admit to lying at least once to a teacher during the past year and that 25% of students are male and would admit to lying at least once to a teacher during the past year
This means that [tex]P(A) = 0.48, P(A \cap B) = 0.25[/tex]
Assume that 50% of the students are male.
This means that [tex]P(B) = 0.5[/tex]
What is the probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year?
This is:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Considering the values we were given:
[tex]P(A \cup B) = 0.48 + 0.5 - 0.25 = 0.73[/tex]
0.73 = 73% probability that a randomly selected student is either male or would admit to lying to a teacher, during the past year.
EXPAND AND SIMPLIFY
Answer:
5⁴a²
Step-by-step explanation:
(5³a³)÷5a-¹×5-²a²
5³a³÷5a-¹×5-²a²
5³a³÷5¹-²×a-¹+²
5³a³÷5-¹a
5³a³/5-¹a
5³-(-¹)a³-¹
5⁴a²
NEED HELP ASAP!!! Giving brainliest!!!!!!!
C.(f-g)(x) = 4x^3 +5x²-7x-1
Step-by-step explanation:
Given information :
[tex]f(x) = 4 {x}^{3} + 5 {x}^{2} - 3x - 6 \\ g(x) = 4x - 5[/tex]
Find :
[tex](f - g)(x) = \\ (4 {x}^{3} + 5 {x}^{2} - 3x - 6) \\ - 4x -5[/tex]
Open bracket and Simplify
[tex]4 {x}^{3} + 5 {x}^{2} - 3x - 6 - 4x + 5 \\ 4 {x}^{3} + 5 {x}^{2} - 7x - 1[/tex]
Tasha needs 75 liters of a 40% solution of alcohol. She has a 20% and a 50% solution available. How many liters of the 20% and how many liters of the 50% solutions should she mix to make the 40% solution?
Answer:
25 liters of 20%
50 liters of 50%
Step-by-step explanation:
x = liters of 50%
75 - x = liters of 20%
50x + 20(75 - x) = 40(75)
50x + 1500 - 20x = 3000
30x = 1500
x = 50
75 - x = 25
Find the missing segment in the image below
Someone help please!!
Answer:
9 (a) [tex]d = \frac{\sqrt{e}}{\sqrt{3}}[/tex]
9 (b) [tex]d = \frac{\sqrt{7k}}{\sqrt{2}}[/tex]
Step-by-step explanation:
Hope this helped!
What number is missing here?
2, 3, 5, 8, 13. ?
Answer:
2, 3, 5, 8, 13 missing number is 18.
Solve the equation.
(X-5)(x + 7) = 0
X=
-D
(Use a comma 6 separate answers as needed.)
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Answer:
x = -7, 5
Step-by-step explanation:
The equation is written as a product equal to zero. The "zero product rule" tells us that a product is zero if and only if one or more factors are zero. Each factor will be zero when x takes on a value equal to the opposite of the constant in that factor.
x -5 = 0 ⇒ x = 5
x +7 = 0 ⇒ x = -7
The solutions to the equation are x = -7, 5.
There are 38 Legs in a group of goat and hens. How many goats and hens are there?
1) 13 Goats , 3 hens
2) 11 goats ,3hens
3) 7 goats,3 hens
4) 8 goats,3 hens
Answer:
4)8 goats, 3 hens.
Step-by-step explanation:
8*4=32
3*2=6
32+6=38
add negative 4 plus negative 6
-10
thats it, thats what i know
4n-6 in as a undistributed expression
Answer:
2( 2n-3)
Step-by-step explanation:
4n-6
2*2 n - 2*3
Factor out the greatest common factor
2( 2n-3)
The table shows a linear relationship between x and y.
х
у
-20
96
-12
60
-6
33
-2
15
What is the rate of change of y with respect to x?
Answer:
[tex] -\frac{9}{2} [/tex]
Step-by-step explanation:
Rate of change of x and y can be calculated using the following formula and using any two given pair of values from the table:
Rate of change = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Using (-12, 60) and (-6, 33).
Where,
[tex] (-12, 60) = (x_1, y_1) [/tex]
[tex] (-6, 33) = (x_2, y_2) [/tex]
Plug is the values
Rate of change = [tex] \frac{33 - 60}{-6 -(-12)} [/tex]
Rate of change = [tex] \frac{-27}{6} [/tex]
Simplify
Rate of change = [tex] \frac{-9}{2} [/tex]
Rate of change = [tex] -\frac{9}{2} [/tex]
