A circle has a diameter with endpoints (-7, 1) and (-3, 7).
What is the equation of the circle?
r2 = ( x - 3) 2 + ( y + 4) 2
r2 = ( x + 3) 2 + ( y - 4) 2
r2 = ( x + 5) 2 + ( y - 4) 2
r2 = ( x - 5) 2 + ( y + 4) 2
Answer: (C) r² = (x+5)²+(y-4)²
Solution:-
The given endpoints are (-7,1) and (-3,7)
so the center will be at the mid point of the line connecting these two points.
hence, center ={ (-7+-3)/2, (1+7)/2 }
hence, C= (-5,4)
so, the equation of the circle is:-
⇒ (x-(-5))²+(y-4)²=r²
or, (x+5)²+(y-4)²=r²
Help!! Please and thank you!
It is clear that T lies on the perpendicular bisector of NP. See the explanation below.
Given that M (X,Y) is the midpoint of NP
X thus = (5+1)/2
= 3
Y = (7+1)/2
= 4
Hence, we have M (3,4)
Consequent on the above:
Slope TM (m') = (4-2) / (3-6) = - 2/3
Slope of NP (m) = (7-1) / (5-1) = 6/4 = 3/2
M' = -1/m
Hence
TM ⊥ NP; and NP ⊥ TM
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helen rolls a dice and flips a coin.
calculate the probability
Answer:
1/12
Step-by-step explanation:
dice rolling=1/6
coin flipping=1/2
Hence probability=1/6×1/2
Answer:
Dice roll = 1/6
Coin flip = 1/2
Which of the following are solutions to the equation below?
4x^2 + 4x + 1 = 9
Check all that apply
Answer:
Option B and D
Step-by-step explanation:
Subtract 9 from both sides :
4x² + 4x - 8 = 0
Divide both sides by 4 :
x² + x - 2 = 0
Factorise using factorisation method :
x² - x + 2x -2 = 0
x(x - 1) +2(x-1) = 0
(x+2)(x-1) = 0
Solve for x
x +2 = 0 OR x - 1 = 0
x = -2 OR x = 1
Answer will be Option B and D
Hope this helped and have a good day
Answer:
option b. –2 and d. 1 are correct.
*For detailed explanation refer to the attachment
A rectangular prism has a square base with a width of 6 and a volume of 360 cm3. If a square pyramid has a base with the same width and height, what is the volume of the pyramid? Round to the nearest tenth.
The volume of the square pyramid is the one-third of the square prism with same height and base area. Then the volume of the pyramid will be 120 cubic cm.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (L × B × H) / 3
The volume of the square prism will be
V = (L × B × H)
Then the volume of the square pyramid is the one-third of the square prism with same height and base area.
[tex]\rm V_{pyramid} = \dfrac{V_{prism} }{3}[/tex]
A rectangular prism has a square base with a width of 6 and a volume of 360 cm³.
If a square pyramid has a base with the same width and height.
Then the volume of the pyramid will be
V = 360 / 3
V = 120 cubic cm
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its math help me out
Answer:
60 minutes
Step-by-step explanation:
we can see that the number of minutes increases by 8 each day
(12 + 8 = 20, 20 + 8 = 28, 28 + 8 = 36...)
So, because we have the value for the previous day (day 6) we know that we can simply add 8
52 + 8 = 60
So, the predicted number of minutes for day 7 is 60
hope this helps!!
Need help and a better understanding
The market value of a home is $180,000. The assessment rate is 55%. What is the assessed value of the home?
Answer:
$99 000
Step-by-step explanation:
[tex](180000)(\frac{55}{100} )=99000[/tex]
Hope this helps
Find the value of z
[tex]\textsf {Finding y :}[/tex]
[tex]\implies \mathsf {1^{2} + y^{2} = 3^{2}}[/tex]
[tex]\implies \mathsf {y^{2} = 8}[/tex]
[tex]\implies \mathsf {y = 2\sqrt{2}}[/tex]
[tex]\textsf {Finding z :}[/tex]
[tex]\implies \mathsf {(2\sqrt{2})^{2}+8^{2}=z^{2}}[/tex]
[tex]\implies \mathsf {z^{2} = 72}[/tex]
[tex]\implies \mathsf {z = 6\sqrt{2}}[/tex]
Answer:
z =8.49 or 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Do the Pythagorean theorem = [tex]a^{2} +b^{2} =c^{2}[/tex]
Length of hypotenuse = 8+1=9
length of one side = 3
so, a²+3²=9²
a²+3²=9²
a²=81-9
a²=72
a=√72=8.49 or 6[tex]\sqrt{2}[/tex]
On a biased dice the probably of getting a 6 is 4/5 the dice is rolled 500 times estimate how many 6s would be riled
Answer:
400
Step-by-step explanation:
4/5×500
=400 6s would be riled
Function h is a transformation of the parent exponential function. Which statement is true about this function?
As x approaches positive infinity, approaches 0.
As x approaches negative infinity, approaches positive infinity.
As x approaches positive infinity, approaches positive infinity.
As x approaches negative infinity, approaches negative infinity.
The statement that is true about this function is C. As x approaches positive infinity, h(t) approaches positive infinity
Calculations and Parameters
Given that we have:
The domainThe rangeThe functionTherefore, when x approaches to negative infinity,
[tex]\lim_{x \to \infty} h(x)[/tex]
= 2^(-∞-5)
= 2^(-∞)
= 1/2^∞
=0
Also, as x approaches negative infinity, function h(x) approaches 0.
Then when x approaches to positive infinity,
[tex]\lim_{x \to \infty} h(x)[/tex]
2^(∞-5)
= 2^(∞)
= ∞
Therefore, As x approaches positive Infinity, h(x) approaches positive infinity.
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An investment group compares returns on an account against the function represented in the table, where x is the time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the table?
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
an increasing exponential function
The function over the interval is an increasing exponential function.
What is quadratic function?A quadratic function is" a polynomial function with one or more variables in which highest exponent of variable is 2".
The complete question is
An investment group compares returns on an account
against the function represented in the table, where x is the
time in years and f(x) is the total return on investment.
Which describes the function over the interval given in the
table?
х
a decreasing quadratic function
an increasing quadratic function
a decreasing exponential function
an increasing exponential function
0
5
f(x)
10,000
12,201.90
14,888.64
22,167.15
10
20
A decreasing quadratic function is the vertex of the parabola lies on the axis parabola. So, time in years change does not give maximum total return on investment.
For increasing quadratic equation, the graph increasing at one side of the axis and decreases at other side.
For, Exponential function
When the exponential function then it shows total return on investment is not maximum.
When the exponential function is increasing it shows time goes, total return on investment is maximum.
Hence, the exponential function is increasing.
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The graph shows two lines, A and B:
Based on the graph, which statement is correct about the solution to the tC system of equations for lines A and B?
O (3, 4) is the solution to both lines A and B.
© (3, 4) is the solution to line A but not to line B.
O (0, 2) is the solution to both lines A and B.
O (0, 2) is the solution to line A but not to line B.
Answer:
the answer is (3,4) is the solution to line A but not to line b
A girl travels from garage a for 59km ti garage b on a bearing of 037degree and then turn right through 90degree and travels for 119km to garage c what is the bearing frim c from a if ac is 138km
The bearing from C to A of the given travel path is gotten as; 100.63°
How to calculate the bearing?From the bearing image attached, we can use trigonometric ratios to get;
tanx = opp/adj
x = 53 + θ ---------- eqn(1)
opp = 119
adj = 59
Thus;
tan x = 119/59
tan x = 2.0169
x = tan⁻¹(2.0169)
x = 63.63°
From eqn (1), we have;
θ = x - 53
θ = 63.63 - 53
θ = 10.63°
Thus, the bearing from C to A = 90 + 10.63 = 100.63°
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This probability distribution shows
the
typical grade distribution for a Geometry
course with 35 students.
Grade
B
F
Frequency
5
10
15
3
2
Find the probability that a student earns
a
grade of B or C.
p=[?]
Answer:
The probability that a student earns a grade of A is 1/7.
Let E be an event and S be the sample space. The probability of E, denoted by P(E) could be computed as:
P(E) = n(E) / n(S)
As the total number of students = n(S) = 35
Students getting the grade A = n(E) = 5
So, the probability that a student earns a grade of A:
P(E) = n(E) / n(S)
= 5/35
= 1/7
Hence, the probability that a student earns a grade of A is 1/7.
Keywords: probability, sample space, event
The equation y = 180 + 5x represents the amount a school club will pay a T-shirt company for custom T-shirts, where x represents the number of T-shirts purchased and y represents the total cost in dollars. The equation y = 10x represents the club’s income from selling the T-shirts, where y represents the money earned in dollars and x represents the number of T-shirts sold. Assuming that the club members sell all the T-shirts they purchase, when will the club make a profit? The following graph represents this situation:
Answer:
36 TSHIRTS is the number for minimum profit
Step-by-step explanation:
Y = Y
180 + 5X = 10X
180 = 10X - 5X
180 = 5X
X = 180/5
X = 36
Describe the transformations of the graph of y=5 times 2^x-2+3 as compared to the graph of y=2^x
the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.Which transformations are used?
We start with the function:
[tex]f(x) = 2^x[/tex]
And we have the transformed function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Bow, let's start with the original function f(x). If first we apply a vertical dilation of scale factor 5, then we have:
g(x) = 5*f(x).
Then we apply a shift of 2 units to the right, so we have:
g(x) = 5*f(x - 2)
Then we apply a shift of 3 units up, so we have:
g(x) = 5*f(x - 2) + 3
Replacing f(x) by the actual function:
[tex]g(x) = 5*2^{x-2} + 3[/tex]
Then the transformations used are:
Dilation of scale factor 5.Shift of 2 units to the right.Shift of 3 units up.If you want to learn more about transformations:
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slope of (0,1) and (4,3)
Answer:
1/2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(3-1)/(4-0)
m=2/4
m=1/2
The slope of the given points (0,1) and (4,3) will be ( 1 / 2 ).
What is the slope of the line?
The increase divided by the run, or the ratio of the rise to the run is known as the line's slope. In the coordinate plane, it describes how steep a line is.
The slope of the line is calculated by the formula given below:-
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\dfrac{3-1}{4-0}=\dfrac{2}{4}=\dfrac{1}{2}[/tex]
Therefore the slope of the given points (0,1) and (4,3) will be ( 1 / 2 ).
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The table lists the average monthly cost to workers for family health insurance for various years.
a) Use a graphing calculator to fit a regression line to the data.
b) Predict the average monthly cost to workers for family health insurance in 2021, and compare the value with $510.37, which
is obtained using the points (1,338) and (4,385).
c) Find the correlation coefficient for the regression line, and determine whether the line fits the data closely.
Answer:
5 dollars :)
Step-by-step explanation:
ig
A group of 328 people consists of men ,women, and children. There are five times as many men than children and twice as many women then children. How many women are there
Step-by-step explanation:
Ultimately we know:
Men = * 5
Women = * 2
Children =
We can already make the estimation that the amount of children will be below 50. So by trial and error you will get to your answer by substituting with 41.
Children - 41
Women - 41 x 2 = 82
Men - 41 x 5 = 205
205 + 41 + 82 = 328
So your answer is 41
There is a basketball court. A basketball, who never misses takes a random shot at the basket. What is the probability that the ball will go into the basket
Answer:
100% probability or 1/1
Step-by-step explanation:
This is because since the basketball NEVER misses, there is no chance the the ball will not go inside the basket, leaving room for only the ball to GO inside the basket. Hope this helps!! :D
Which statement describes the graph?
<-10
10-
-10+
10
OA. The graph crosses the y-axis at (0, -5), decreasing from x = -10 to
x= -2 and increasing from x= -2 to x = 10.
B. The graph crosses the y-axis at (0, -5), decreasing from x = -10 to
x = 0 and remaining constant from x = 0 to x = 10.
C. The graph crosses the y-axis at (-6, 0), decreasing from x= -10 to
x = -2 and remaining constant from x=-2 to x = 10.
OD. The graph crosses the y-axis at (0, -5), decreasing from x = -10 to
x= -2 and remaining constant from x=-2 to x= 10.
Correct answer is option D.
The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.
What is Increasing Function?A function f(x) is said to be increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) ≤ f(y).
For this case, the first thing you should observe is that you have a different function in two distinct intervals.
We have then:
For [-10, 2]:
The linear function has a positive slope, therefore it grows and cuts the y-axis at the point (0, 5)
For [2, 10]:
We have a constant function whose equation is:
y = 5
Thus, the correct Answer is:
D. The graph crosses the y-axis at (0, 5), increasing from x = -10 to x = 2 and remaining constant from x = 2 to x = 10.
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The average hourly salary of workers in a warehouse is $14.50 with a standard deviation of $1.75. the shaded area of which curve represents the probability of the hourly salary being between $11 and $16.25?
Answer:
where is the question Skidoo
this is just a statement
Rsm question please explain
The question is in the picture
A triangle is a three-edged polygon with three vertices. ΔAKE and ΔCKP are congruent.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angle of a triangle is always equal to 180°.
In ΔABC, since AB≅BC, therefore, the triangle will be an isosceles triangle, and the measure of ∠A ≅ ∠C, using the base angle theorem.
Now In ΔAKE and ΔCKP,
∠A ≅ ∠C {Proved above}
∠AKE ≅ ∠CKP {Given}
AK ≅ KC {Given }
Since two angles and a side of the triangle are equal, therefore, we can write the two triangle are congruent using the Side-angle-side or Angle-Side-Angle congruence.
Hence, ΔAKE and ΔCKP are congruent.
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Which of the following best describes how the y values are changing over each interval?
X
1
23
3
4
5
y
2
4
8
16
32
O They are increasing by 2 each time.
O They are increasing by 4 each time.
They are being multiplied by 2 each time.
O They are being multiplied by 4 each time.
Answer:
They are being multiplied by 2 each time.
Step-by-step explanation:
The X values are going up by 1 and every time X goes up by 1, Y doubles. So (1,2) goes to (2,4) and then (3,8) etc.
$10,000 is invested at 7% annual interest which is compounded continuously what is the balance after eight years with no deposits or withdrawals are made
Answer:
$17,506.73
Step-by-step explanation:
Continuous Compounding Formula
[tex]\large \text{$ \sf A=Pe^{rt} $}[/tex]
where:
A = Final amountP = Principal amounte = Euler's number (constant)r = annual interest rate (in decimal form)t = time (in years)Given:
P = $10,000r = 7% = 0.07t = 8 yearsSubstitute the given values into the formula and solve for A:
[tex]\sf \implies A=10000e^{(0.07 \times 8)}[/tex]
[tex]\sf \implies A=10000e^{0.56}[/tex]
[tex]\implies \sf A=17506.725...[/tex]
Therefore, the value of the account after 8 years is $17,506.73 to the nearest cent.
Create three probability problem, Solve the problems.
Question:
A fair die is tossed.
Find the probability of obtaining an even number
Answer:
sample space=(1,2,3,4,5,6)
number of favourable outcomes=3
Event A= (outcome is even)
= (2,4,6)
Total number of outcomes=6
Thus, P(even number)=3/6
=1/2
Question 2:
A drawer contains 10 identical handkerchiefs of which 2 are white, 5 are blue, and 3 are pink. A handkerchief is drawn at random. what is the probability that it is white or pink?
Answer:
total number of outcomes=10
P(the handkerchief is white or pink)=2+3/10
=5/10
=1/2
79=11x+13
Solve each equation by using the properties of equality and justify each step
Solution: X=6
Detailed explanation:
In this problem we're asked to find "x" or the unknown.
The first step is to subtract 11x from both sides.
[tex]---\mapsto\boldsymbol{-11x+79=13}[/tex]
Next, subtract 79 from both sides.
[tex]---\mapsto\boldsymbol{-11x=-66}[/tex]
To finish this off, divide both sides by -11.
[tex]---\mapsto\boldsymbol{x=6}[/tex]
Voila! There's our answer!
Cheers!! ^-^___________________
Hope I helped. Best wishes.
Reach far. Aim high. Dream big.
___________________
[tex]\large\green\longrightarrow \tt \large \:79 \: = \: 11x \: + \: 13[/tex]
[tex]\large\green\longrightarrow \tt \large \:79 \: - \: 13 \: = \: 11x[/tex]
[tex]\large\green\longrightarrow \tt \large \:66 \: = \: 11x[/tex]
[tex]\large\green\longrightarrow \tt \large \: \frac{ \cancel{66} \: \: ^{ \pink6} }{ \cancel{11}} \: = \: x \\ [/tex]
[tex]\large\green\longrightarrow \tt \large \:6 \: = \: x[/tex]
Hence , the value of x is 6
What should be added to (-10) to get (+10)
Answer:
20
Step-by-step explanation:
-10 + 20 = +10
Answer:
[tex]\fbox {20}[/tex]
Step-by-step explanation:
Let the required term be x
Then :
x + (-10) = 10x - 10 = 10x = 10 + 10x = 20Millie needs a total of 7.8 feet of ribbon for a school project. She needs 0.7 more feet of ribbon. How much ribbon, in feet, did Millie already have? Write and solve an equation to find the answer.
6.9
7.1
7.5
8.5
Subtraction is a mathematical operation that reflects the removal of things from a collection. The ribbon that Millie already had is 7.1 feet.
What is subtraction?Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.
Given Millie needs a total of 7.8 feet of ribbon for a school project. Also, She needs 0.7 more feet of ribbon. Therefore, the ribbon that Millie needs is,
Ribbon Millie had = Total Ribbon - ribbon that is needed
= 7.8 feet - 0.7feet
= 7.1 feet
Hence, the ribbon that Millie already had is 7.1 feet.
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