ANSWER
The radius is 4
EXPLANATION
The given equation is:
[tex] {x}^{2} + {y}^{2} - 10y + 6x + 18 = 0[/tex]
We complete the square to get the expression in standard form:
[tex]{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0[/tex]
[tex]{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25[/tex]
We factor using perfect squares to get:
[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = 16[/tex]
This implies that,
[tex]{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2} [/tex]
Comparing to
[tex]{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
The radius is r=4
When asked his age, Michael said, "If you square
my age, then subtract 12 times my age, the result
is 85." How old is he?
Answer:
(x + 5)=0 or (x - 17)=0
x=-5 or x=17
Discard the negative value
x=17 is considered.
Michael is 17yrs old
Answer:
[tex]\boxed{\textbf{He is 17 years old}}[/tex]Step-by-step explanation:
Let x = Michael's age.
Then x² = the square of his age
and x² - 12x = the square of his age – 12 times his age
and x² - 12x = 85
We must solve the quadratic for x.
1. Subtract 85 from each side.
x² - 12x - 85 = 0
2. Multiply the leading coefficient and the constant
1 × 85 = 85
3. Find two numbers that multiply to give -85 and add to give -12.
Possible pairs are 1, 85; 5, 17
Start with the numbers near the end of the list.
By trial and error, you will find that 5 and -17 work:
5 ×(-17) = -85
and 5 - 17 = -12
4. Rewrite -12x as 5x -17x
x² + 5x – 17x - 85 =0
5. Factor by grouping the first two and the last two terms
x(x + 5) - 17(x + 5) =0
(x + 5)(x - 17) = 0
6. Find the zeroe
[tex](x + 5)(x - 17) = 0\\\\\begin{array}{rlrl}x + 5 & = 0 & x - 17 & =0\\x & = -5 & x & = 17\\\end{array}\\\text{Michael can't have a negative age, so } \boxed{\textbf{he is 17 years old.}}[/tex]
Check:
[tex]\begin{array}{rcl}(-17)^{2} + 12(-17) & = & 85\\289 - 204 & = & 85\\85 & = & 85\\\end{array}[/tex]
OK.
What is the solution to the equation 6x+2=9x-1
Answer:
X=1
Step-by-step explanation:
Subtract by 2 from both sides of equation.
6x+2-2=9x-1-2
Simplify.
1-2=-3
6x=9x-3
Then subtract by 9x from both sides of equation.
6x-9x=9x-3-9x
Simplify.
-3x=-3
Divide by -3 from both sides of equation.
-3x/3=-3/-3
Simplify, to find the answer.
-3/-3=1
X=1 is the correct answer.
Answer:
x=1
Step-by-step explanation:
A plot of land has an area 33.75 square feet. Jackson wants to put a 4-foot by 4 foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the length of the f the trapezoid
Answer:
The height of the trapezoid is [tex]4.5\ ft[/tex]
Step-by-step explanation:
we know that
The area of a trapezoid is equal to
[tex]A=\frac{1}{2}(b1+b2)h[/tex]
In this problem we have
[tex]A=33.75\ ft^{2}[/tex]
[tex]b1=5\ ft[/tex]
[tex]b2=10\ ft[/tex]
substitute in the formula and solve for h
[tex]33.75=\frac{1}{2}(5+10)h[/tex]
[tex]67.5=15h[/tex]
[tex]h=67.5/15=4.5\ ft[/tex]
Answer:
[tex]h=4.5\text{ feet}[/tex]
Step-by-step explanation:
We have been given that a plot of land has an area 33.75 square feet. Jackson wants to put a 4-foot by 4 foot shed on the land. Jackson wants to put a 4-foot by 4 foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet.
We will use area of trapezoid to find the height of trapezoid.
[tex]\text{Area of trapezoid}=\frac{1}{2}(a_1+a_2)\times h[/tex], where,
[tex]a_1\text{ and }a_2=\text{ Parallel sides or bases of trapezoid}[/tex],
[tex]h=\text{Height}[/tex].
We can see that parallel sides are 5 feet and 10 feet. We have been given that area of trapezoid is 33.75 square feet.
[tex]33.75\text{ feet}^2=\frac{1}{2}(\text{ 5 feet + 10 feet})\times h[/tex]
[tex]33.75\text{ feet}^2=\frac{1}{2}(\text{ 15 feet})\times h[/tex]
Switch sides:
[tex]2\times\frac{1}{2}(\text{ 15 feet})\times h=2\times 33.75\text{ feet}^2[/tex]
[tex]\text{ 15 feet}\times h=67.50\text{ feet}^2[/tex]
[tex]\frac{\text{ 15 feet}\times h}{\text{ 15 feet}}=\frac{67.50\text{ feet}^2}{\text{ 15 feet}}[/tex]
[tex]h=4.5\text{ feet}[/tex]
Since the height of trapezoid is 4.5 feet, therefore, Jackson can put a 4 foot by 4 foot shed on the land.
Please help me I need it fast
Answer:
b and c
Step-by-step explanation:
i think its b and c
Answer:
A, D, and E
Step-by-step explanation:
They all have ten 0.1 square which equals 1.
Find the median.
12, 8, 5, 6, 1, 10, 13, 11
A. 8.25
B. 9
C. 12
D. 66
Your answer asks to find the median of the given numbers.
Answer: B). 9To find the median, you would need to sort of the numbers from least to greaters.
The given numbers we have:
12, 8, 5, 6, 1, 10, 13, 11
Now, just sort them from least to greatest.
1, 5, 6, 8, 10, 11, 12 ,13
What you would do next is eliminate the numbers on the side, one by one, in order to get your median.
[tex]1, 5, 6, 8, 10, 11, 12 ,13\\\\5, 6, 8, 10, 11, 12\\\\6, 8, 10, 11\\\\8, 10[/tex]
We ended up with two numbers, 8 and 10. Since we didn't end up with one number, we're going to have to add those numbers, and then divide it by two.
[tex]8+10=18\\\\18\div2=9[/tex]
You should get 9.
Therefore, the median would be 9.
B). 9 should be your FINAL answer
I hope this helps!Best regards, MasterInvestorAnswer:
The correct answer is option B. 9
Step-by-step explanation:
Median:
Median of a data set means that, the central data when arrange all the in ascending or descending order
It is given a data set ,
12, 8, 5, 6, 1, 10, 13, 11
To find the median of data set
Here there are 8 items, median is average of 4th and 5th terms
Ascending order,
1, 5, 6, 8, 10, 11, 12, 13
Median = (8 + 10)/2 = 18/2 = 9
The correct answer is option B. 9
What conclusion can be drawn from the following statements?
P(EF) = 0.3
P(E)= 0.3
A Events E and F are mutually exclusive.
B. Event F is a subset of event E.
C Events E and Fare equal.
D. Events E and Fare independent.
Answer:
D.
Step-by-step explanation:
The conclusion that can be drawn from the given statements is that " events E and F are independent".
When are independent events?Two events such as A and B are said to be independent if the occurrence of event A does not affect the occurrence of event B. I.e.,
P(A ∩ B) = P(A)×P(B)
What is conditional probability?If A and B are two events in a sample space S, then the probability of event B after event A has occurred is called the conditional probability and it is denoted by P(B|A) = [P(A ∩ B)]/P(A).
Verifying how the given events are related:Given that E and F are two events.
P(E|F) = 0.3
P(E) = 0.3
So, the conditional probability is written as,
P(E|F) = P(E ∩ F)/P(F)
If E and F are independent events, then the probability P(E ∩ F) = P(E) × P(F).
On substituting,
P(E|F) = P(E) × P(F)/P(F)
= P(E)
Therefore, P(E|F) = P(E) = 0.3
Hence, events E and F are independent.
Learn more about independent events here:
https://brainly.com/question/1374659
#SPJ2
Angle EOF and angle EOG are supplementary angles. What's the measure of angle EOF if the measure of angle EOG is 71°?
Answer:
supplementary angle sum = 180°
EOG + EOF = 180°
71° +EOF = 180°
EOF = 180° -71°
EOF = 109°
Step-by-step explanation:
Answer:
m<EOF = 109 deg
Step-by-step explanation:
Definition of supplementary angles:
Two angles are supplementary if the sum of their measures is 180 degrees.
Angles EOF and EOG are supplementary, so the sum of their measures is 180 degrees.
m<EOF + m<EOG = 180
We are given the measure of <EOG: m<EOG = 71 deg.
We substitute that measure in our equation and solve the equation for m<EOF.
m<EOF + 71 deg = 180 deg
Subtract 71 deg from both sides.
m<EOF = 109 deg
Find the x-intercepts of the parabola with
vertex (1,1) and y-intercept (0,-3).
Write your answer in this form: (X1,y,),(X2,).
If necessary, round to the nearest hundredth.
To find the x-intercepts of a parabola with given vertex and y-intercept, we can use the vertex form of the equation. Substituting the given values, we find the value of a, and then substitute the values again to find the x-intercepts. The x-intercepts of this parabola are approximately (0.55, 0) and (1.45, 0).
Explanation:To find the x-intercepts of a parabola, we need to find the values of x when y is equal to zero. Starting with the equation of the parabola in vertex form, y = a(x-h)^2 + k, where (h,k) is the vertex, we can substitute the given values for the vertex (1,1) into the equation. This gives us y = a(x-1)^2 + 1. Next, we substitute the y-intercept (-3) into the equation, so we have -3 = a(0-1)^2 + 1. Solving for a, we get a = -2.
Now we can substitute a and the given values into the equation again to find the x-intercepts. Plugging in a = -2, we have 0 = -2(x-1)^2 + 1. Simplifying this equation and solving for x, we get x = 1 ± √(3/2). Rounding to the nearest hundredth, the x-intercepts are approximately (0.55, 0) and (1.45, 0).
Learn more about Finding x-intercepts of a parabola here:https://brainly.com/question/29158613
#SPJ12
The figure shown is a rhombus.
Which equation is true regarding the angles formed by the
diagonals and sides of the rhombus?
x + y = Z
2x = y + z
OZ + x = 2y
2x + 2y =4z
Answer:
Answer: A (first option)
Step-by-step explanation:
E2020
The angles formed by the diagonals and sides of the rhombus are
x + y = z.
Option A is correct.
As, When the diagonals of a rhombus are perpendicular, the angle z must be exactly 90 degrees (z=90).
Any triangle's interior angles must add up to 180 degrees.
Using Angle Sum Property
x + y + z = 180°
(x+y+z)=180°
x+y+z=180
As, z=90
x + y + 90 = 180
x + y = 90
So, the angles formed by diagonals is x + y = z.
Learn more about Rhombus here:
https://brainly.com/question/4910909
#SPJ7
What is the answer to 6w=w+20
Answer: w = 4
Step-by-step explanation:
Subtract 1w from each side of the equation to get 5w = 20.
Divide both sides of the equation by 5 to get w = 4.
Hello!
Answer:
[tex]\boxed{w=4}\checkmark[/tex]
Answer should be positive sign.
Step-by-step explanation:
First, you subtract by w both sides of an equation.
[tex]6w-w=w+20-w[/tex]
Simplify.
[tex]5w=20[/tex]
Then, you divide by 5 both sides of an equation.
[tex]\frac{5w}{5}=\frac{20}{5}[/tex]
Finally, simplify and then solve.
[tex]20\div 5 = 4[/tex]
[tex]\boxed{w=4}[/tex], which is our final answer.
Hope this helps!
Thanks!
Have a nice day! :)
PLEASE HELP!!! I don’t understand
Answer:
Step-by-step explanation:
Use the half angle identity for cosine:
cos(x/2)=+ or - sqrt(1+cos(x))/sqrt(2)
I'm going to figure out the sign part first for cos(x/2)...
so x is in third quadrant which puts x between 180 and 270
if we half x, x/2 this puts us between 90 and 135 (that's the second quadrant)
cosine is negative in the second quadrant
so we know that
cos(x/2)=-sqrt(1+cos(x))/sqrt(2)
Now we need cos(x)... since we are in the third quadrant cos(x) is negative...
If you draw a reference triangle sin(x)=3/5 you should see that cos(x)=4/5 ... but again cos(x)=-4/5 since we are in the third quadrant.
So let's plug it in:
cos(x/2)=-sqrt(1+4/5)/sqrt(2)
No one likes compound fractions (mini-fractions inside bigger fractions)
Multiply top and bottom inside the square roots by 5.
cos(x/2)=-sqrt(5+4)/sqrt(10)
cos(x/2)=-sqrt(9)/sqrt(10)
cos(x/2)=-3/sqrt(10)
Rationalize the denominator
cos(x/2)=-3sqrt(10)/10
which of the binomials below is a factor of this exression?
16x^2+40xy+25y^2
A.4x-5y
B. 2x-5y
C.4x+5y
D.2x+5y
Answer:
C. 4x+5y
Step-by-step explanation:
Lets start by factorizing the expression 16x²+40xy+25y²
Consider the expression ax²+bx+c
During factorization, two numbers picked should add up to b while the product should be=ac
We find two numbers that when added give 40 and when multiplied = 16×25=400
These numbers are 20 and 20
Therefore the expression will be broken into:
16x²+20xy+20xy+25y²
4x(4x+5y)+5y(4x+5y)
(4x+5y)(4x+5y)
The expression is a perfect square.
Answer:
c
Step-by-step explanation:
a p e x
If f(x) = 3x - 2 and g(x) = 2x + 1, find (f + g)(x).
Step-by-step explanation:
The answer to the question
what is the equation of a line with endpoints (0,0) and (2,-8)
Answer:
y=-4x
Step-by-step explanation:
You can graph it.. It might be easier for you to count than to use the formula for slope. We are counting from (0,0) to (2,-8)... I'm doing rise/run... I have to go down from (0,0) 8 units so the rise is -8 and the run is 2. So the slope is -8/2=-4.
We know the y-intercept is (0,0)... so the equation is y=-4x+0 or just y=-4x
Maybe you seen that this was proportional because it was a straight diagonal line going through the origin which we knew then that the line was already in the form of y=kx
Then you can look at the point (2,-8) and see what you need to do 2 to get -8 multiplication-wise.
2(-4)=-8
so
x(-4)=y
or
y=-4x
Which of the following is an equation of a line parallel to the equation y=4x+1?
Answer:
y = 4x + b, where b is any number
Step-by-step explanation:
Adrian, you need to share the possible answer choices.
Every line parallel to y = 4x + 1 has the slope 4.
This is true for any y-intercept, that is, for any b in y = mx + b.
Final answer:
An equation of a line parallel to y=4x+1 would have the same slope of 4 and can be expressed as y=4x+b, where b is any y-intercept not equal to 1.
Explanation:
An equation of a line parallel to the line represented by y=4x+1 would have the same slope as the given equation. This is because parallel lines have identical slopes. In the equation y=4x+1, the slope is 4, as this is the coefficient of x. Therefore, any line that has a slope of 4 will be parallel to y=4x+1. The general form for such a parallel line would be y=4x+b, where b is the y-intercept, which can be any number different than 1 to ensure the lines are not the same.
if the price of gas went from $3.45 a gallon to $4 a gallon what was the percent change in the price of the gas was there an increase or decrease
Answer:
there was an increase and it increased by 6.9%
How can you solve linear inequalities in one variable?
Answer:
There can be three solution sets of linear equalities. They can have one solution, or they can have no solutions or they can have infinitely many solutions. System of linear inequalities that have many or infinite solutions are called ” dependent”.
Step-by-step explanation:
What is the solution to the system of equations? 2x – y = 7 y = 2x + 3
Answer:
the answer is no solutions
Step-by-step explanation:
the solution is found at the point in which the two lines intersect.
in this case they do not intersect because the lines are parallel. if you rearrange 2x – y = 7 you will get y = 2x - 7. the slope is 2x
the slope of the second equation is 2x as well. when slopes are the same they are parallel and therefore never cross.
For this case we have the following system of equations:
[tex]2x-y = 7\\y = 2x + 3[/tex]
To solve, we substitute the second equation in the first:
[tex]2x- (2x + 3) = 7\\2x-2x-3 = 7\\-3 = 7[/tex]
As noted, equality is not fulfilled. Thus, the system has no solution.
It can also be observed that the equations are:
[tex]y = 2x + 3\\y = 2x-7[/tex]
That is, they have the same slope, [tex]m = 2[/tex], so the lines are parallel. If the lines are parallel, they never intersect.
Answer:
The system has no solution
For which pairs of functions is (f•g)(x)=12x? f(x)=3-4x and g(x)=16x-3
F(x)=6x2 and g(x)= 2/x
F(x)= and g(x) = 144x
F(x)=4x and g(x) =3x
Answer:
F(x)=4x and g(x) =3x
Step-by-step explanation:
We will have to check each pair of functions one by one
So,
For f(x)=3-4x and g(x)=16x-3
For composition we have to put g(x) in place of x in f(x)
(fog)(x)=3-4(g(x))
= 3-4(16x-3)
=3-64x+12
=-64x+15
So first pair doesn't give 12x.
Now for,
F(x)=6x2 and g(x)= 2/x
(fog)(x)= 6(g(x))^2
=6(2/x)^2
=6*(4/x^2)
=24/x^2
For the last pair:
F(x)=4x and g(x) =3x
(fog)(x)=4(g(x))
=4(3x)=12x
So for the last pair of functions (fog)(x) is 12x ..
Answer:
d
Step-by-step explanation:
on edge
Need help ASAP!!!!! Will give brainliest!!!!
Answer:
You multiply
Step-by-step explanation:
The base: 12 in times 12 in
Each side (There are four, so multiply by 4!): 10 in times 12 in divided by 2
65% of what number is 78
To solve this you must use a proportion like so...
[tex]\frac{part}{whole} = \frac{part}{whole}[/tex]
65 is a percent and percents are always taken out of the 100. This means that one proportion will have 65 as the part and 100 as the whole
We want to know out of what number is 78 65%. This means 78 is the part and the unknown (let's make this x) is the whole
[tex]\frac{78}{x} =\frac{65}{100}[/tex]
Now you must cross multiply
78*100 = 65*x
7800 = 65x
To isolate x divide 65 to both sides
7800/65 = 65x/65
120 = x
This means that 65% of 120 is 78
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer: 120
It is because google said so
what is the product [-1,2,4] •[3,6,1,2,4,0,0,6,2]
Answer:
[tex]\large\boxed{\left[\begin{array}{ccc}1&26&7\end{array}\right] }[/tex]
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}-1&2&4\end{array}\right] \times\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right]\\\\=\left[\begin{array}{ccc}(-1)(3)+(2)(2)+(4)(0)&(-1)(6)+(2)(4)+(4)(6)&(-1)(1)+(2)(0)+(4)(2)\end{array}\right]\\\\=\left[\begin{array}{ccc}-3+4+0&-6+8+24&-1+0+8\end{array}\right] \\\\=\left[\begin{array}{ccc}1&26&7\end{array}\right][/tex]
Option B [1 26 7] is the product of given matrix.
What is matrix multiplication formula?
Consider matrix A which is a × b matrix and matrix B, which is a b ×c matrix.
Then, matrix C = AB is defined as the A × B matrix.
An element in matrix C, Cxy is defined as Cxy = Ax1By1 +….. + AxbBby =
AxkBky for x = 1…… a and y= 1…….c
How to multiply given matrix?
[tex]\left[\begin{array}{ccc}-1&2&4\end{array}\right][/tex]×[tex]\left[\begin{array}{ccc}3&6&1\\2&4&0\\0&6&2\end{array}\right][/tex]
=[ -1×3+2×2+4×0 -1×6+2×4+4×6 -1×1+2×0+4×2 ]
=[-3+4+0 -6+8+24 -1+0+8]
=[1 26 7 ]
Learn more about matrix : https://brainly.com/question/14490203
#SPJ2
What is the answer to this question
[tex]2x+7x=747\\9x=747\\x=83\\\\2x=166\\7x=581[/tex]
Tom - [tex]\pounds166[/tex]
Ben - [tex]\pounds581[/tex]
I will mark brainliest ,thank, and rate to to the best answer!Please help! ASAP
At Westside Middle School, 10 percent, or 140 students, participate in soccer. How many students are in the school? Check all that apply.
Answer:
1st, 3rd, and 6th
Step-by-step explanation:
Let's look at each statment...
1.) Correct
Explanation: 10 percent of the students at the school participate in soccer. If 140 is 10% of the number of students at the school, there is more than 140 students at this school.
2.) Incorrect
Explanation: We've already established that the # of students at the school is more than 140.
3.) Correct
Explanation: 10% as a decimal is 0.1 Divide 140 by 0.1 and you get 1,400. So, the total number of students is 1,400.
4.) Incorrect
Explanation: We've already established that the number of students is 1,400, not 290.
5.) Incorrect
Explanation: We've already established that the number of students is 1,400, not 150.
6.) Incorrect
Explanation: If the percent was a ratio, it would be 10:100 or 10/100. This is because a whole percent is 100% and the percent of students who play soccer is 10%.
7.) Correct
Explanation: We've already established that the ratio would be 10:100 or 10/100. Thus, this is correct.
I hope this helps! :)
what is x plus 2-5= 1/2
What term best describes a line and a point that lie in the same plane?
A. Congruent
B. Coplanar
C. Collinear
D. Equal
Answer:
B AND C
Step-by-step explanation:
Collinear Points: points that lie on the same line.
Coplanar Points: points that lie in the same plane.
What is 0.580 =. Rewrite as a simplified fraction
Answer:
29/50 is the same as 0.580
Step-by-step explanation:
0.580 is the same as 0.58
.58=58/100
I knew to put 58 over 100
because the decimal terminates in the hundredths spot
58/100 can be reduced
58 and 100 are both even so they are both divisible by 2
58/2=29
while
100/2=50
so 58/100 is the same as saying 29/50
Answer:
29/50
Step-by-step explanation:
0.58 = 58/100 = 29/50
What is the y-intercept of the quadratic function f(x) = (x – 6)(x – 2)?
Answer:
x=6
x=2
Step-by-step explanation:
Fortunately for us, the function is written in factorized terms, so it is easier to find its roots.
The roots are the values for the 'x' variables that makes the functions goes to zero.
They are x=6 and x=2, any of those value make the function equals zero, or in other words, they are the points of interception with the 'y' axis.
To obtain these value
lets study the following condition
(x-6) * (x-2)=0
The above is accomplish when (x-6)=0 or (x-2)=0
We have two independent equations from where we obtain that x=6 and x=2
Please help with this question
Answer:
Segment JK is a chord in circle H
Line LM is a secant to circle H
Step-by-step explanation:
* Lets revise some definition in the circle
- The radius of the circle is a line segment drawn from the center of
the circle to a point on the circumference of the circle
- The chord of a circle is a line segment whose endpoints lie on the
circumference of the circle
- The secant is a line intersect the circle in two points
- The tangent is a line touch or intersect the circle in one point
* Now lets solve the problem
- In circle H
∵ JK is a segment in circle H
∵ Point J lies on the circumference of circle H
∵ Point K lies on the circumference of circle H
∴ Segment JK is a chord in circle H
∵ LM is a line
∵ LM intersect circle H in two points L and M
∴ Line LM is a secant to circle H
If you shift the quadratic parent function, f(x)=x^2, right 12 units, what is the equation of the new function?
Answer:
f(x)=(x-12)^2
Step-by-step explanation:
We know that the function f(x+m) equals to the function f(x) translated 'm' times to the left. Therefore, to translate the function f(x) = x^2 twelve units to the right, we have to:
f(x-12) = (x-12)^2
Therefore, the new function is: f(x)=(x-12)^2