The form of the equation of the circle is
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) are the coordinates of the center
r is the radius
Since the endpoints of the diameter are (11, 2) and (-7, -4), then
The center of the circle is the midpoint of the diameter
[tex]\begin{gathered} M=(\frac{11+(-7)}{2},\frac{2+(-4)}{2}) \\ M=(\frac{4}{2},\frac{-2}{2}) \\ M=(2,-1) \end{gathered}[/tex]The center of the circle is (2, -1), then
h = 2 and k = -1
Now we need to find the length of the radius, then
We will use the rule of the distance between the center (2, -1) and one of the endpoints of the diameter we will take (11, 2)
[tex]\begin{gathered} r=\sqrt[]{(11-2)^2+(2--1)^2} \\ r=\sqrt[]{9^2+3}^2 \\ r=\sqrt[]{81+9} \\ r=\sqrt[]{90} \\ r^2=90 \end{gathered}[/tex]Now substitute them in the rule above
[tex]undefined[/tex]26 is 50% of what number?
What’s the correct answer answer asap for brainlist
Please help with 7-9 they are related to the same circle
40º
7) In this problem, we can see that both tangent lines to that circle come from the same point O.
So, we can write out the following considering that there is one secant line DO and one tangent line to the circle AO
[tex]\begin{gathered} m\angle1=\frac{1}{2}(160-80) \\ m\angle1=\frac{1}{2}(80) \\ m\angle1=40^{\circ} \end{gathered}[/tex]
Hi, can you help me answer this question please, thank you!
SOLUTION
3To calculate the test statistics, we use the following steps:
Step 1: We write out the parameters
[tex]\begin{gathered} sample\text{ mean (}\bar{\text{x}}\text{)}=0.9 \\ \text{standard deviation(s)=}0.58 \\ \operatorname{mean}(\mu)=0.8 \\ n=32 \end{gathered}[/tex]Step 2: Write out the formula for the test statistics (t)
[tex]t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt[]{n}}}[/tex]step 3: Find t
[tex]\begin{gathered} t=\frac{0.9-0.8}{\frac{0.58}{\sqrt[]{32}}} \\ t=\frac{0.1}{0.1025} \\ t=0.97532 \\ t\approx0.98 \end{gathered}[/tex]Hence, the test statistic is approximately 0.98 to two decimal places.
Select the correct answer. What is the solution to the equation? (x - 2)^1/2 + 4 = x A. -3 and -6 B. 3 and 6 C. -3 D. 6
Answer:
D. x = 6
Step-by-step explanation:
Given equation:
[tex](x-2)^{\frac{1}{2}}+4=x[/tex]
Subtract 4 from both sides:
[tex]\implies (x-2)^{\frac{1}{2}}+4-4=x-4[/tex]
[tex]\implies (x-2)^{\frac{1}{2}}=x-4[/tex]
Square both sides:
[tex]\implies \left( (x-2)^{\frac{1}{2}}\right)^2=(x-4)^2[/tex]
[tex]\implies x-2=(x-4)^2[/tex]
Expand the brackets on the right side:
[tex]\implies x-2=(x-4)(x-4)[/tex]
[tex]\implies x-2=x^2-8x+16[/tex]
Subtract x from both sides:
[tex]\implies x-2-x=x^2-8x+16-x[/tex]
[tex]\implies -2=x^2-9x+16[/tex]
Add 2 to both sides:
[tex]\implies -2+2=x^2-9x+16+2[/tex]
[tex]\implies 0=x^2-9x+18[/tex]
[tex]\implies x^2-9x+18=0[/tex]
Factor the left side of the equation:
[tex]\implies x^2-6x-3x+18=0[/tex]
[tex]\implies x(x-6)-3(x-6)=0[/tex]
[tex]\implies (x-3)(x-6)=0[/tex]
Apply the zero-product property:
[tex]\implies x-3=0 \implies x=3[/tex]
[tex]\implies x-6=0\implies x=6[/tex]
Therefore, the solutions of the quadratic equation are:
[tex]x=3, \quad x=6[/tex]
Input both solutions into the original equation to check their validity:
[tex]\begin{aligned}x=3 \implies (3-2)^{\frac{1}{2}}+4&=3\\(1)^{\frac{1}{2}}+4&=3\\1+4&=3\\5&=3\end{aligned}[/tex]
[tex]\begin{aligned}x=6 \implies (6-2)^{\frac{1}{2}}+4&=6\\(4)^{\frac{1}{2}}+4&=6\\2+4&=6\\6&=6\end{aligned}[/tex]
Therefore, the only valid solution to the given equation is x = 6.
Answer:
The answer is D. 6
Step-by-step explanation:
Add both sides:
(x - 2)^1/2 + 4 + (-4) = x + (-4)
(x - 2)^1/2 = -4
Solve exponent:
(x - 2)^1/2 = x - 4
((x - 2)^1/2)^2 = (x - 4)^2
x − 2 = x^2 − 8x + 16
x − 2 − (x^2 − 8x + 16) = x^2 − 8x + 16 − (x^2 − 8x + 16)
−x^2 + 9x − 18 = 0
(−x + 3)(x − 6) = 0
−x + 3 = 0 or x − 6 = 0
x = 3 or x = 6
Check the answers: (Plug them in to see what will work.)
x = 3 (won't work)
x = 6 (does work)
Therefore,
x = 6
PLEASE HELP ME I'M OFFERING ALL OF MY POINTS AND I WILL GIVE BRAINLIEST
Answer:
m∠1 = 80°
m∠2 = 80°
m∠3 = 100°
Step-by-step explanation:
Same-side Exterior Angles Theorem
When two parallel lines are intersected by a transversal, the angles that are exterior to the parallel lines and on the same side of the transversal line are supplementary (sum to 180°).
Therefore:
⇒ m∠1 + 100° = 180°
⇒ m∠1 + 100° - 100° = 180° - 100°
⇒ m∠1 = 80°
Corresponding Angles Postulate
When a straight line intersects two parallel straight lines, the resulting corresponding angles are congruent.
Therefore:
⇒ m∠2 = m∠1 = 80°
Vertical Angles Theorem
When two straight lines intersect, the opposite vertical angles are congruent.
Therefore:
⇒ m∠3 = 100°
Find the x- and y-intercepts for the following equation. Then use the intercepts to graph the equation.y = −2x +1x-intercept: ( ?,0)y-intercept: (0,?)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given function
[tex]y=-2x+1[/tex]STEP 2: Determine the x-intercept for the given function.
To determine the x intercept, we set y equals zero and solve for x. Therefore, we have:
[tex]\begin{gathered} y=-2x+1 \\ y=0 \\ \therefore\Rightarrow0=-2x+1 \\ Collect\text{ like terms,} \\ 0-1=-2x \\ -1=-2x \\ Divide\text{ both sides by -2} \\ -\frac{1}{-2}=\frac{-2x}{-2} \\ \frac{1}{2}=x \\ x=0.5 \\ \\ \therefore x-intercepts\Rightarrow(0.5,0) \end{gathered}[/tex]STEP 3: Get the y-intercept
We can get the y-intercept by setting x towards zero and solve for y
[tex]\begin{gathered} y=-2x+1 \\ x=0 \\ y=-2(0)+1 \\ y=0+1 \\ y=1 \\ \\ \therefore y-intercept\Rightarrow(0,1) \end{gathered}[/tex]STEP 4: Plot the graph of the given function
A shop repairs 4 types of electronic devices. The number of repairs of each device last week is shown in the bar graph below. Use this bar graph to answer the questions.
Answer:
a) Telephone; 2 repairs
b) 3 more repairs
c) computer, radio , and television = 3 types
Explanation:
From the bar graph we see that the least amount of repairs done to the telephones. How many r
can somebody please help me with this question
Answer:
I don't really understand this but I think will be a great way to solve this so 123.00
Step-by-step explanation:
.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the following scenarios with the correct inequality.
A phone company charges $15 per
month, and $2.50 for each gigabyte
of data used. Jaime cannot spend
more than $30 a month.
arrowBoth
A chess club has only $50 to make
t-shirts. It costs $15 for the design
and $3 per t-shirt.
arrowBoth
Sarah has $40 in a piggy bank. She
wants to keep at least $20 in the
piggy bank, and takes out half of
a dollar each week for a soda.
arrowBoth
The linear inequalities in this problem are given as follows:
Jaime/phone company: 15 + 2.5x ≤ 30.Chess club/t-shirt: 15 + 3x ≤ 50.Sarah/bank: 40 - 0.5x ≥ 20. What is a linear function?A linear function, in slope-intercept format, is modeled according to the rule presented as follows:
y = mx + b
In which the parameters of the function are described as follows:
The coefficient m is the slope of the function, representing the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the value of y when the function crosses the y-axis(x = 0).For cost/monetary functions, the slope and the intercept are given as follows:
Slope: variable amount, such as cost per item.Intercept: fixed amount = one-time amount, such as flat fees.Then the inequalities are given as follows:
Jaime/phone company: 15 + 2.5x ≤ 30. (slope of 2.5 and intercept of 15).Chess club/t-shirt: 15 + 3x ≤ 50. (slope of 3 and intercept of 15).Sarah/bank: 40 - 0.5x ≥ 20. (slope of -0.5, negative as the amount is removed from the bank account, and intercept of 40).More can be learned about linear functions at https://brainly.com/question/24808124
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Cuantas veses cabe el 13 en 47
Hay 3 veces 13 en 47.
La respuesta la divides 47 por 13 lo que te daría 3.6153846153846.
i need help with this problem
Answer:
whats the problme?
Step-by-step explanation:
A bag contains 4 black and 3 pink balls. A ball is picked from the bag and is not replaced. A second ball is then picked from the bag.
The tree diagram below can be used to calculate various probabilities.
What is the probability of picking one
ball of each colour?
A
4/49
B
24/42
C
1/2
D
12/42
Answer:
1/2
Step-by-step explanation:
There are 4 possibilities:
First ball Second ball
1. Black Pink
2. Black Black
3. Pink Pink
4. Pink Black
The first and the forth options are the the probabilities that there is picked one ball for each color. (2 possibilities )
The second and the third options are the probabilities that there ate picked 2 balls of same colour.
(2 possibilities)
There are 4 possibilities in total. So the probability is 2/4=1/2
Please help step by step
The set of values for y={-3, 0, 5} for given values of x={0, 3, 8} and the equation is 3x-3y=9 and the domain D={0≤x≤8}.
What is Domain?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f(x). A function's range is the set of values it can take as input. After we enter an x value, the function outputs this set of values.
What is equation?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
The given equation,
3x-3y=9
When x=0, 3*0-3y=9
-3y=9
y=-3
When x=3, 3*3-3y=9
-3y=0
y=0
When x=8, 3*8-3y=9
3y=15
y=5
The set of values for the equation 3x-3y=9 and the domain D=0≤x≤8 is given as x={0, 3, 8} and y={-3, 0, 5}.
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find the endpoint S given R(5,1) and midpoint M(1,4)
Given:
Point R: (5, 1)
Midpoint M: (1, 4)
Since it's been mentioned that point M is a midpoint. Finding S, the graph should look like this:
Let's determine the translation from point M to R, because the opposite of it will be the translation to get point S.
From Point M to R:
[tex]\text{ }\Delta x\text{ = 5 - 1 = 4 (4 units to the right)}[/tex][tex]\Delta y\text{ = 1 - 4 = -3 (3 units downward)}[/tex]Therefore, getting to the endpoint S, it will have 4 units to the left and 3 units upward.
We get,
[tex]x_S\text{ = 1 - 4 = -3}[/tex][tex]y_S\text{ = 4 + 3 = 7}[/tex]Therefore, the missing endpoint is: -3, 7
Six friends went out for dinner. The total cost of their dinner was $92,82. If they divide the bill equally, how much should
each friend pay?
Provide your answer below:
Answer:$15.47 per person
Step-by-step explanation:
The total cost of the bill, divided into 6 groups:
92.82/6=15.47
For each relation, decide whether or not it is a function.
Relation 1: Yes, each input corresponds to only one output.
Relation 2: No, the input of -1 corresponds to two outputs: sun and moon.
Relation 3: Yes, each input corresponds to only one output.
Relation 4: Yes, each input corresponds to only one output.
4x-7 (2-x)=3x+2/ need help
First, apply distributive property to solve the parenthesis:
[tex]4x-7(2)-7(-x)=3x+2[/tex][tex]4x-14+7x=3x+2[/tex]Combine like terms:
[tex]-14+11x=3x+2[/tex][tex]11x-3x=2+14[/tex][tex]8x=16[/tex]Divide both sides by 8:
[tex]\frac{8x}{8}=\frac{16}{8}[/tex][tex]x=\text{ 2}[/tex]pls help??
A.24
B.50
C.84
D.75
A
I got it right on the test and i got the answer on another app
4592 round to the nearest ten
Answer:
4590
Step-by-step explanation:
less the 5 round down
Answer:
4590
Step-by-step explanation:
When rounding to the nearest ten we use these following rules.
We round the number up to the nearest ten if the last digit in the number is 5,6,7,8 or 9.
We round the number down to the nearest ten if the last digit in the number is 1,2,3, or 4.
If the last digit is 0, then we do not have to do any rounding, because it is already to the ten.
Can anyone answer this
Answer:
(d) The triangles are similar, because each has angles that measure 36°, 62°, and 82°.
Step-by-step explanation:
Given triangle A has angles 36° and 82°, and a figure showing angles related to triangle B, you want to know if the triangles are similar.
SimilarityThe triangles will be similar if the angles of one are congruent to the angles of the other. Between the two triangles, we are given 3 different angle values, so we need to find at least two additional angle values in order to determine if the triangles are similar.
Angle sum theoremThe sum of angles in a triangle is 180°, so the third angle of triangle A will be ...
angle = 180° -36° -82° = 62°
Exterior angleThe exterior angle of triangle B, given as 144°, is the sum of the remote interior angles:
144° = 62° +angle
82° = angle
ComparisonNow, we have the angles of triangle A as 36°, 62°, and 82°. Two of the angles of triangle B are known to be 62° and 82°, matching those of triangle A.
The triangles are similar, because each has angles that measure 36°, 62°, and 82°.
Evaluate. 5[83–(8-1)²]
5 [ 83- (8-1)²]
we will first work on the inner parenthesis
5 [ 83 - (7)²]
5[ 83 - 49]
5[34]
=170
Graph the line that has an z-intercept of (-3,0) and a y-intercept of (0, - 5). What is the slope of this line?
Answer:
the slope is -5/3
Step-by-step explanation:
it is that because to find slope u do y2-y1/x2-x1
Pre calculus 6a. Consider the equation x^5 - 3x^4 + mx^3 + nx^2+ ox + q = 0, where m, n, P, q € R.The equation has three distinct real roots which can be written as log2a, log2b and log2C.The equation also has two imaginary roots, one of which is di where dE R.Show that abc = 8.6b. The values a, b, and C are consecutive terms in a geometric sequence. Show that one of the real roots is equal to 1.6c. Given that q = 8d^2, find the other two real roots.
We have a fifth degree polynomial:
[tex]x^5-3x^4+mx^3+nx^2+px+q=0[/tex]This polinomial has 3 real roots, that can be expressed as: log2(a), log2(b) and log2(c).
Also, it has two imaginary roots, one of which is di (they have to be conjugate, so the other imginary root is -di).
We have to show that abc = 8.
If we consider the information given, we have some information about all the roots.
We can rewrite the polynomial in factorized form as:
[tex]\begin{gathered} (x-\log _2a)(x-\log _2b)(x-\log _2c)(x-di)(x+di)=0 \\ (x-\log _2a)(x-\log _2b)(x-\log _2c)(x^2+d^2)=0 \end{gathered}[/tex]As the polynomial is defined for real numbers, we can write a polynomial with only the real roots as:
[tex](x-\log _2a)(x-\log _2b)(x-\log _2c)=0[/tex]Then, we can relate the roots as:
[tex]\begin{gathered} 2^{(x-\log _2a)(x-\log _2b)(x-\log _2c)}=2^0 \\ 2^{(x-\log _2a)}\cdot2^{(x-\log _2b)}\cdot2^{(x-\log _2c)}=1 \\ \frac{2^x}{2^{\log_2a}}\cdot\frac{2^x}{2^{\log_2a}}\cdot\frac{2^x}{2^{\log_2a}}=1 \\ \frac{2^{3x}}{a\cdot b\cdot c}^{}=1 \\ abc=2^{3x} \\ abc=2^3\cdot2^x \\ abc=8\cdot2^x \end{gathered}[/tex]What is the value of (–3 + 3i) + (–2 + 3i)?
Answer: -5+6i
Step-by-step explanation:
8. Find the slope between (-5, 4) & (0,3). * O m = 1/5 O O m = -5 m = 5 O m = -1/5
We can determine the slope using the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Now, using the two points given, we have:
[tex]m=\frac{3-4}{0-(-5)}\Rightarrow m=-\frac{1}{5}[/tex]From this, we have that the slope(m) equals -1/5.
What is the scale factor of Figure B to Figure A?48.6B2510A1021.5A. O 6.25B.O 2.5C.0.16D. 0.4
As per given by the question,
There are given that two traingle, figure A and figure B.
Now,
The ratio of a dimension on figure B to the corresponding dimension on figure A is,
[tex]4\colon10=8.6\colon21.5=10\colon25[/tex]So,
The scale factor is,
[tex]\begin{gathered} k=\frac{10}{4}=\frac{25}{10}=\frac{21.5}{8.6}=2.5 \\ \end{gathered}[/tex]The scale factor of figure B on the figure A is 2.5.
Hence, the option B is correct.
The tables of ordered pairs represent some points on the graphs of lines q and v. Line 9 Line v Х -9 -3 2. Х 0 10 у 0 18 33 у 10 8 3 Which system of equations is represented by lines q and v? F 21x - y = 9 5x + 6y = 40 G 3x - y = -27 x + 2y = 16 H 21x - y = 9 5x - 6y = 20 3 9x - y = -27 x + 2y = 8
One of the forms we can write the equation of a line is like this:
y - y1 = m(x - x1)
Where (x1, y1) is a point where the line passes through, and the value of m, the slope of a line is given by the following formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]Then, for the first line (line q), we can take the points (-9, 0) and (-3, 18), then we get:
[tex]mq=\frac{18-0}{-3-(-9)}=\frac{18}{-3+9}=\frac{18}{6}=3[/tex]By replacing the value of the slope and the coordinates of the point (-9, 0), we get:
y - 0 = 3(x - (-9))
y = 3(x + 9)
y = 3x + 27
y - y = 3x + 27 - y
0 = 3x + 27 - y
-27 = 3x + 27 - 27 - y
-27 = 3x - y
For line v, we can take the points (-4, 10) and (0, 8), then we get:
[tex]mv=\frac{8-10}{0-(-4)}=\frac{-2}{4}=-\frac{1}{2}[/tex]By taking -1/2 for the slope and the coordinates of the point (0,8), we gat:
y - 0 = -1/2(x - 8)
y = -1/2x + 4, multiplying both sides by 2:
2y = -x + 16
2y + x = -x + x + 16
2y + x = 16
Then, the system represented by the lines q and v is option G
An influencer is planning a lunch banquet. The equation C 410 + 22g models the relation between the
cost in dollars, C, of the lunch banquet and the number of
guests, g.
Find the cost if the number of guests is 50.
The cost is blank
dollars
The cost, if the number of guests is 50, will be $22500.
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. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation.So, the relationship between the dollar cost of the dinner, C, and the number of guests, g, is represented by the equation C = 410 + 22g.
We can see that the equation we have been given is in the form of a slope-intercept equation, y = MX + b, where m denotes the slope of the line and b denotes the y-intercept or beginning value.We can observe that the slope and C-intercept of the following equation are 22 and 410, respectively.The C-intercept tells us that when there are 0 guests in the banquet, the cost would be $450.When we have 50 guests at the banquet the cost would be:
50 x 450= $22500Hence, the cost, if the number of guests is 50, will be $22500.
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after how many hours will the two trucks be 558 miles apart?
Given:
a.) A truck travels due west at an average speed of 48 miles per hour.
b.) The other truck travels due east at an average speed of 45 miles per hour.
Let's determine how many hours will the two trucks be 558 miles apart.
We will be using the following equation:
Let the two trucks be named Truck A and Truck B.
Let x = the time the two trucks will be 558 miles apart
[tex]\text{ (Speed of Truck A)(x) + (Speed of Truck B)(x) = 558 miles}[/tex]We get,
[tex]\text{ 48x + 45x = 558}[/tex]Let's find x,
[tex]\text{ 48x + 45x = 558}[/tex][tex]\text{ 93x = 558}[/tex][tex]\text{ }\frac{\text{93x}}{93}\text{ = }\frac{\text{558}}{93}[/tex][tex]\text{ x = }6[/tex]Therefore, the two trucks will be 558 miles apart after 6 hours.