Answer:
[tex](x-7)^2+(y-4)^2=25[/tex]
Step-by-step explanation:
The circle has diameter endpoints of ( 4, 8 ) and (10, 16 ).
The midpoint of the diameter is the center
[tex](\frac{4+10}{2},\frac{8+16}{2})[/tex]
[tex](\frac{14}{2},\frac{24}{2})[/tex]
[tex](7,12)[/tex]
The radius is the distance from the center to any point on the circumference.
[tex]r=\sqrt{(7-4)^2+(12-8)^2}[/tex]
[tex]r=\sqrt{(3)^2+(4)^2}[/tex]
[tex]r=\sqrt{9+16}[/tex]
[tex]r=\sqrt{25}=5[/tex]
The equation of the circle with center (h,k) and radius r is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
We plug in the values to get:
[tex](x-7)^2+(y-4)^2=5^2[/tex]
[tex](x-7)^2+(y-4)^2=25[/tex]
Answer:
The equation of the circle is (x - 7)² + (y - 12)² = 25
Step-by-step explanation:
* Lets revise the equation of the circle
- The equation of the circle which has center (h , k) is:
(x - h)² + (y - k)² = r²
- The endpoints of a diameter re (4 , 8) and (10 , 16)
- The center of the circle is the mid-point of the diameter
* Lets revise the rule of the mid point to get the center of the circle
and revise the rule of the distance to get the length of the diameter
- The mid point (x , y) of segment has endpoints (x1 , y1) and (x2 , y2) is
x = (x1 + x2)/2 and y = (y1 + y2)/2
- The distance between the two point (x1 , y1) and (x2 , y2) is:
d = √[(x2 - x1)² + (y2 - y1)²]
* Now lets find the center of the circle
∵ (h , k) is the mid-point of the diameter
∵ (4 , 8) is (x1 , y1) and (10 , 16) is (x2 , y2)
∴ h = (4 + 10)/2 = 14/2 = 7
∴ k = (8 + 16)/2 = 24/2 = 12
∴ The center of the circle is (7 , 12)
∵ The length of the diameter = √[(10 - 4)² + (16 - 8)²
∴ d = √[6² + 8²] = √[36 + 64] = √100 = 10
∵ The radius = 1/2 the diameter
∴ r = 1/2 (10) = 5
* Lets write the equation of the circle
∵ The equation of the circle is (x - h)² + (y - k)² = r²
∵ h = 7 , k = 12 , r = 5
∴ The equation of the circle is (x - 7)² + (y - 12)² = 5²
∴ The equation of the circle is (x - 7)² + (y - 12)² = 25
the value of n is a distance of 3 units from 1 1/2 on a number line
Answer:
What is your question?
Is " n " to the left or the right?
How many units are on the number line?
It may be the number 3.
The values of n is a distance of 3 units from 1 1/2 on a number line are 4.5 units and -1.5units
The number line consists of positive values to the right of zero and negative values to the left.
Given the value 1 1/2 units, it is 1.5 units to the right of zero.
If the value of n is a distance of 3 units from 1 1/2 on a number line, the value of n can be 3 units to the right or to the left.
Valuee to the right = 3 + 1.5 = 4.5units
Value to the left = 1.5 - 3 = -1.5 units
Hence the values of n is a distance of 3 units from 1 1/2 on a number line are 4.5 units and -1.5units
Learn more here: https://brainly.com/question/23379455
Find the values of a and b so that the polynomial x^3 -10x^2 +ax +b is exactly divisible by x-1 as well as x-2
Answer:
a = 23, b = - 14
Step-by-step explanation:
If the polynomial is divisible by (x - 1) then f(1) = 0
f(x) = x³ - 10x² + ax + b
f(1) = 1³ - 10(1)² + a + b = 0, that is
1 - 10 + a + b = 0, hence
a + b = 9 → (1)
Similarly if (x - 2) is a factor then f(2) = 0
f(2) = 2³ - 10(2)² + 2a + b = 0, that is
8 - 40 + 2a + b = 0, hence
2a + b = 32 → (2)
Subtract (1) from (2)
a = 23
Substitute a = 23 into (1)
23 + b = 9 ⇒ b = 9 - 23 = - 14
Colin and Jezebel are employees at Game Zone. They recorded the number of computer games they sold each week for the past 9 weeks.
Colin 15 20 21 9 3 16 9 14 17 Jezebel 10 14 20 11 4 26 5 8 20 (a) All of the games sold of which person had the greatest spread? Explain how you know. (b) The middle 50% of the games sold of which person had the least spread? Explain how you know. (c) What do the answers to Parts 2(a) and 2(b) tell you about Colin’s and Jezebel’s sold games?
Answer:
a) The sold games of Jezebel had the greatest spread.
b) The middle 50% of the games sold by Colin has the least spread.
c) Jezebel sold more games than colin.
Step-by-step explanation:
Range is sued to calculate the spread of the given data.
Range is given by:
Range=Max Value-Min Value
So,
Part a)
For Collin:
Range=21-3=18
For Jezebel:
Range=26-5=21
Part b)
Middle 50% of the values will be the values between 1st quartile and 3rd quartile
So, to find quartiles:
For Colin:
=3,9,9,14,15,16,17,20,21
The median is 15.
The lower half is 3,9,9,14
Q1 = (9+9)/2= 18/2 = 9
The upper half is 16,17,20,21
Q3 = (17+20)/2= 37/2= 18.5
The middle 50% is first quartile subtracted from third quartile
So, the spread is:
18.5-9=9.5
For Jezebel:
4,5,8,10,11,14,20,20,26
The median is 11.
The lower half is 4,5,8,10
Q1 = (5+8)/2=13/2=6.5
The upper half is 14,20,20,26
Q3 = (20+20)/2=40/2=20
The middle 50% values' spread is:
20-6.5=13.5
Part c) The answer to part a tells us that Jezebels sold games have more spread than Colin's sold games. Similarly the answer of part b tells us that the spread of middle 50% values of Jezebel's sold games was more than the spread of middle 50% values of Colin's sold games ..
I need help please????
Answer:
x = - 1
Step-by-step explanation:
Given
3x + 2 = y and y = - 1
Substitute y = - 1 into the equation and solve for x, that is
3x + 2 = - 1 ( subtract 2 from both sides )
3x = - 3 ( divide both sides by 3 )
x = - 1
This is verified by the point on the graph with coordinates (- 1, - 1)
Method 1: By substitution
Step 1: In the equation 3x + 2 = y when you see a y replace it with -1
3x + 2 = -1
Step 2: Combine like terms by subtracting 2 to both sides
3x + (2-2) = -1 - 2
3x = -3
Step 3: Isolate x by dividing 3 to both sides
[tex]\frac{3x}{3} = \frac{-3}{3}[/tex]
x = -1
Method 2: By looking at the graph
To solve this way you see where the line on the graph has y = -1 and look for its complimentary x
If you look at the graph attached below you can see that at y = -1 the x also equals -1
x = -1
Hope this helped!
HURRY ILL GIVE BRAINLIEST!!!
Suppose a line has slope m and passes through the point (a, b). Which other point MUST also be on the graph?
A) (a + m, b + 1)
B) (a + m, b - 1)
C) (a + 1, b - m)
D) (a + 1, b + m)
ANSWER
D) (a + 1, b + m)
EXPLANATION
The given line passes through (a,b) and has slope m.
The equation is:
[tex]y - b = m(x - a)[/tex]
When x=a+1, we obtain
[tex]y - b = m(a + 1 - a)[/tex]
This
[tex]y = m( 1 ) + b[/tex]
[tex]y = m + b[/tex]
Therefore,(a + 1, b + m) must also lie on this line.
The correct answer is D.
Answer:
d
Step-by-step explanation:
I got it correct
What is the simplified expression for the expression below?
Answer:
3x+5
Step-by-step explanation:
i took test
Find m
Answers choices
53
44
65
35
For this case we have to define trigonometric relations of rectangular triangles that:
The cosine of an angle is given by the leg adjacent to the angle on the hypotenuse of the triangle.The sine of an angle is given by the leg opposite the angle on the hypotenuse of the triangle.Then, according to the figure we have:
[tex]Sin (M) = \frac {3} {5}\\M = ArcSine (\frac {3} {5})[/tex]
[tex]M = 36.87[/tex] degrees
Answer:
36.87 degrees
Find the value of the expression.
y3 + x
for x = 6 and y = 1
Given the expression y^3 + x, upon substituting y = 1 and x = 6 into the equation, the resultant value of the expression is 7.
Explanation:The question requires finding the value of the expression y3 + x when x = 6 and y=1. Since y is equal to 1, y3 (1 cubed) is also 1. So the expression becomes 1 + 6, which equals 7. Therefore, the value of the expression y3 + x for y = 1 and x = 6 is 7.
Learn more about Expression evaluation here:https://brainly.com/question/35471134
#SPJ2
Final answer:
The value of the expression [tex]y^3 + x[/tex] for x = 6 and y = 1 is 7, which is found by substituting the values into the expression and performing the arithmetic operations.
Explanation:
To find the value of the expression [tex]y^3 + x[/tex]for x = 6 and y = 1, you simply substitute the given values into the expression and perform the arithmetic operations.
Here's the step-by-step calculation:
Replace y with 1: (1)3 + 6.
Calculate 1 cubed, which is 13 = 1.
Add the result to x, where x is 6: 1 + 6.
The final answer is 7.
This means that the value of the expression [tex]y^3 + x[/tex]when x = 6 and y = 1 is 7.
(2x^2+2x+3)-(x^2+2x+1 find each difference
[tex]
(2x^2+2x+3)-(x^2+2x+1) \\
2x^2+2x+3-x^2-2x-1 \\
\boxed{x^2+2}
[/tex]
A recent study on the relationship between children's weight and their achievement test scores determined the correlation coefficient to be .9734. Which is the most reasonable conclusion based on the correlation coefficient?
A) Children who weigh more score lower on achievement tests.
B) As age increases, so do body weight and achievement test scores.
C) Children who weigh more spend more time on studying for achievement tests.
D) Children should increase their food intake to increase their achievement test scores.
Answer:
C. Children who weigh more spend more time on studying for achievement test .
Step-by-step explanation:
Correlation is a measure of relationship , mutual co-interdependence (fluctuation) between two quantitative variables .
Direct / Positive (+) correlation means the variables are directly related - one increase , other increase & one increase , other decrease . Inverse / Negative (-) correlation means the variables are inversely related - one increase , other decrease & one decrease, other increase . It lies between -1 to +1 . Correlation more than + 0.5 implies Strong correlation, less than that implies Weak correlation.
The correlation between above variables - weight and achievement test score is 0.9734 i.e there is Strong Positive relationship . So , increase in one strongly leads to increasing trend in other
Answer:
B) As age increases, so do body weight and achievement test scores.
Step-by-step explanation:
Cade made A table to relate two units of time. The number pairs in his Table are One and 24, two and 48, three and 72, four and 96. What are the best labels for Cades table
Answer:
Days, Hours
Step-by-step explanation:
1 day = 24 hours
2 days = 48 hours
3 days = 72 hours
4 days = 96 hours
(its increasing by 24)
State your variables and what they represent. Write a linear function describing the situation. Use the function to solve the problem.
A phone costs $8 per month, plus 10 cents per message unit. How much is the monthly bill if 40 message units are used?
Answer:
y = 0.10x + 8, $12
Step-by-step explanation:
y = monthly bill
x = number of message units
Each message unit costs $0.10, so the cost of x message units is 0.10x. The phone adds $8 to the monthly bill. Therefore:
y = 0.10x + 8
If x = 40, then:
y = 0.10 (40) + 8
y = 4 + 8
y = 12
The monthly bill is $12.
Bethany added a decorative border across the top of each wall of her kitchen. A diagram of her kitchen is shown below.
She used a total of 62 feet of border. What is the length in feet of the unlabeled wall?
Choices:
a.) 5
b.) 10
c.) 8
d.) 13
The answer is your mom. Nah it’s B)10
For this case we have that the perimeter of the figure is given by the sum of its sides, they tell us that the perimeter is 62 feet.
So:
Let "x" be the variable that represents the length of the unlabeled wall, so the perimeter is:
[tex]x + 8 + 5 + 13 + 18 + 8 = 62[/tex]
We find the value of "x":
[tex]x = 62-8-5-13-18-8\\x = 10[/tex]
Thus, the length of the unlabeled wall is 10 feet.
Answer:
Option B
Complete the function table.
Function: y = 4x + 1
Answer:
2=9
4=17
Step-by-step explanation:
4(2)+1
8+1=9
4(4)+1
16+1=17
hampton has an 8 foot tall oak tree in his backyard.if the tree will grow n feet in height each year,which of the following represents the height of the tree,in feet,4 years from now?
Answer:
8+4n=height of tree in 4 years
Step-by-step explanation:
start of with 8
then every year add N feet
4 years times n feet + what we started with(8)
and you get 8+4n
The height of the tree, in feet, 4 years from now can be calculated as 8 + 4n, where n is the number of feet the tree grows each year.
Explanation:The subject of this question is a mathematical problem involving height growth over time, specifically about a tree that grows at a constant rate each year. In this case, the height of a tree in the future can be represented by a simple equation which considers the current height of the tree (8 feet), the rate of growth each year (n feet per year), and the number of years in the future we want to calculate for (4 years). The formula to calculate the height of the tree 4 years from now is:
Future Height = Current Height + Growth Rate * Time
Plug in the values we know:
Future Height = 8 feet + n feet/year * 4 years
So, the height of the tree, in feet, 4 years from now is 8 + 4n.
Learn more about Tree Height over Time here:https://brainly.com/question/2479960
#SPJ3
A standard deck has 52 cards, and contains 13 cards of each of the four suites: diamonds, spades, hearts, and clubs. What is the probability that you choose a diamond, given that you have already chosen a diamond and have not replaced it?
a) 1/4
b) 13/51
c) 3/13
d) 4/17
Answer:
Option d) [tex]P=\frac{4}{17}[/tex]
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
In this problem we have
[tex]x=13-1=12[/tex]
[tex]y=52-1=51[/tex]
substitute
[tex]P=\frac{12}{51}[/tex]
Simplify
[tex]P=\frac{4}{17}[/tex]
PLEASE HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
Step-by-step explanation:
2nd one
What are the solutions to the system of equations? Y=x^2-7x+12 and y=-x+7
[tex]\bf \begin{cases} y=x^2-7x+12\\ y=-x+7 \end{cases}\implies \stackrel{y}{x^2-7x+12}=\stackrel{y}{-x+7} \\\\\\ x^2-6x+12=7\implies x^2-6x+5=0 \\\\\\ (x-5)(x-1)=0 \implies \blacktriangleright x= \begin{cases} 5\\ 1 \end{cases} \blacktriangleleft \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf y=-x+7\implies \stackrel{x=5}{y=-(5)+7}\implies \blacktriangleright y=2\blacktriangleleft \\\\\\ y=-x+7\implies \stackrel{x=1}{y=-(1)+7}\implies \blacktriangleright y=6 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (5,2)\qquad (1,6)~\hfill[/tex]
Answer:
[tex](5, 2)[/tex], [tex](1, 6)[/tex]
Step-by-step explanation:
We have a system composed of two equations
The first is a quadratic equation and the second is a linear equation.
[tex]y=x^2-7x+12[/tex]
[tex]y=-x+7[/tex]
To solve the system, equate both equations and solve for x
[tex]x^2-7x+12 = -x+7\\\\x^2 -6x +5=0[/tex]
To solve the quadratic equation we must factor it.
You should look for two numbers a and c that when multiplying them obtain as result 5 and when adding both numbers obtain as result -6.
This is:
[tex]a * c = 5\\a + c = -6[/tex]
The numbers searched are -5 and -1
So
[tex]x^2 -6x +5 = (x-5)(x-1) = 0[/tex]
Finally the solutions to the system of equations are:
[tex]x= 5[/tex], [tex]x=1[/tex]
6x + 4(3x-7) = 116 x=
Answer:
x = 8
Step-by-step explanation:
Given
6x + 4(3x - 7) = 116 ← distribute the parenthesis on the left side
6x + 12x - 28 = 116 ← collect like terms on left side
18x - 28 = 116 ( add 28 to both sides )
18x = 144 ( divide both sides by 18 )
x = 8
Find the slope of (1, 2), (-1, -2). Reduce all fractional answers to lowest terms
Answer:
The slope is 2
Step-by-step explanation:
The slope is equal to
m = (y2-y1)/(x2-x1)
= (-2-2)/(-1-1)
= -4/-2
= 2
How can you express 1/1000 as a decimal
Answer:
0.001
Step-by-step explanation:
1/1000 is one-thousandths. As a decimal, the first place is the tenth, the second is the hundredths, and the third place is the thousandths. That is three steps away from the decimal point. That's where we put our 1, which gives us 0.001.
1/1000 can be expressed as one-thousandths and in decimal form as 0.001
How to convert from decimal to fraction?For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point, then we write 10 raised to that many power as the denominator and the considered number without any decimal point as the numerator.
As a decimal, the first place is the tenth, the second is the hundredths, and the third place is the thousandths.
1/1000
Which is three steps away from the decimal point 1, gives us 0.001.
Learn more about place value here:
https://brainly.com/question/17983725
#SPJ5
Right triangle ABC is shown . Which equation can be used to solve for c
Answer:
A^2+B^2=C^2
-/(A^2+B^2)=C
Step-by-step explanation:
-/ means squareroot whats in the parenthese
Answer:
sin(50°) = 3/c
Step-by-step explanation:
Ice cream beans are selling for $10 per pound and durians are selling for $9 per pound. If the market sold a total of $196 worth of durians and ice cream beans yesterday, and it sold 11 pounds of durian, which of the following is a good estimation of the total pounds of ice cream beans sold?
.
Durain beans cost $9 per pound and they sold 11 pounds.
Multiply the cost by the amount sold: 9 x 11 = $99
Subtract that from the total sold:
196 - 99 = $97
Now divide the amount left by the cost per pound for Ice cream beans:
97 / 10 = 9.7 pounds.
Round the answer as needed to match one of your choices.
someone help plzzzzz
Answer:
B
Step-by-step explanation:
rsu is equal to vst, so you can solve 5x+17=9x-11, which yields x=7.
So vst=52 and wsv=90-52=38.
help me with this please
Answer:
m∠8 = 124°
Step-by-step explanation:
1. Find m∠1
m∠1 and m∠2 are supplementary, since they are on the same line.
That means m∠1 + m∠2 = 180.
Plug in: 4x + 2x - 6 = 180
Simplify + subtract: 6x = 186
Divide: x = 31
Plug in: m∠1 = 4(31) --> m∠1 = 124°
2. Since ∠1 and ∠4 are vertical, they are congruent. Since ∠4 and ∠8 are corresponding on parallel lines, they are also congruent. Therefore, ∠1 and ∠8 are congruent, which means m∠1 = m∠8
Plug in: m∠8 = 124°
What is (1-7x)(1+9x)
ANSWER
[tex](1-7x)(1+9x) =- 63 {x}^{2} + 2x + 1[/tex]
EXPLANATION
The given product is (1-7x)(1+9x).
Expand using the distributive property.
[tex](1-7x)(1+9x) = 1(1 + 9x) - 7x(1 + 9x)[/tex]
[tex](1-7x)(1+9x) = 1 + 9x - 7x - 63 {x}^{2}[/tex]
Simplify to obtain:
[tex](1-7x)(1+9x) = 1 + 2x - 63 {x}^{2}[/tex]
You can rewrite in standard form to get,
[tex](1-7x)(1+9x) =- 63 {x}^{2} + 2x + 1[/tex]
Answer:
1+2x-63x^2
Step-by-step explanation:
factor 1(1+9x)=1+9X
-7x(1+9x)=-7x-63x^2
add 1+9x-7x-63x2
What will be the simple interest earned when you invest $1,000 for 3 years at 10 percent and the compound interest earned when you invest the same sum for 2 years at 5 percent ? The simple interest earned when you invest $1,000 for 3 years at 10 % is $ . The interest compounded when you invest the same sum for 2 years at 5 % is $ .
Answer:
Simple interest = $1,000(.10)(3) = $300
Compound interest =
$1,000(1.05)² - $1,000 = $102.50
A car has a length of 193.2 inches. A scale drawing is made using a ratio of 20:1 . What is the length of the scale drawing?
The ratio of 20:1 means for every 20 inches the car is in real life, the drawing will be 1 inch.
To find the length of the drawing, divide the length of the real car by 20.
193.2 / 20 = 9.66 inches.
2. A bag contains six red marbles, eight yellow
marbles, and nine blue marbles.
a. What is the probability that you pick a yellow
marble or a red marble?
Answer:
14/23
Step-by-step explanation:
The total number of marbles is 6 + 8 + 9 = 23.
The probability of yellow or red is:
P(yellow or red) = P(yellow) + P(red)
P(yellow or red) = 8/23 + 6/23
P(yellow or red) = 14/23
Answer:
8 in 23 chance of picking a yellow marble
6 in 23 chance of picking a red marble
Explanation:
Firstly, we must determine the total number of marbles. To do this, we add all the marbles together:
6+8+9 = 23
Since the question says we have 8 yellow marbles, that means 8/23 marbles are yellow. Therefor, you would have a 8 in 23 chance (8/23) of picking a yellow marble. Similarly, the question states that we have 6 red marbles. Meaning 6/23 marbles are red. So, one would have a 6 in 23 or 6/23 chance of picking a red marble.
I NEED HELP PLEASE !
A big ship drops its anchor.
E(t) models the anchor's elevation relative to the water's surface (in meters) as a function of time t (in seconds)
E (t) = -2.4t + 75
How far does the anchor drop every 5 seconds?
Answer:
The answer is 75
Step-by-step explanation: