Final answer:
The center of the given circle is at (13, 1), and the radius of the circle is 2.
Explanation:
The equation of a circle is generally given in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius. Looking at the given equation (x - 13)^2 + (y - 1)^2 = 4, we can see that it is already in this standard form.
To answer the questions:
The center of the circle is (13, 1), which comes from the terms within the parentheses being subtracted from x and y.
The radius of the circle is not simply 4, as one might surmise by a quick glance. Instead, the equation gives us the radius squared, r^2 = 4. Taking the square root of both sides, we find that the radius, r, is 2.
find the exact length of the third side
Answer:
X is 8
Step-by-step explanation:
[tex]100^{2} =6^{2} +x^{2}[/tex]
[tex]x=8[/tex]
Answer:
8
Step-by-step explanation:
This is a right triangle, and we know this because of the little square in the corner. Therefore, we can use the Pythagorean theorem.
a^2+b^2=c^2
a and b are the legs, and c is the hypotenuse.
We know the 6 and the unknown side are the legs, since they form the right angle. We also know that 10 is the hypotenuse, since it is opposite the right angle.
6^2+b^2=10^2
Evaluate the exponents
36+b^2=100
Now, we need to solve for b. To do this, we need to get by itself. First, subtract 36 from both sides
36-36+b^2=100-36
b^2=64
Take the square root of both sides
[tex]\sqrt{b^2}=\sqrt{64}[/tex]
b=8
So, the the unknown side is 8
what is the greatest common factor of the expression below?
22x^5 + 20x
Answer:
the answer is 2x
Step-by-step explanation:
The greatest common factor of the expression 22x^5 + 20x is 2x. Both the numerical values and the variable components are considered to determine this.
Explanation:To find the greatest common factor of the expression, we need to identify the highest number and the highest power of variable that evenly divides both terms. In the case of the expression 22x^5 + 20x, the numerical part of the greatest common factor can be found by examining 22 and 20. The greatest common factor of 22 and 20 is 2. Next we need to look at the variables in each term, in this case 'x'. The highest power of 'x' that will divide both 'x^5' and 'x' is 'x' itself.
So, combining these two elements, the greatest common factor of the expression is 2x.
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Noah scores n points in a basketball game.
a. What does 15 < n mean in the context of the basketball game?
Answer: Noah scores more than 15 points.
Step-by-step explanation:
Hi, to answer this question we have to analyze the inequality:
15 < n
Where n are the scored points on a basketball game.
< means greater than.
So, in the context of the basketball game, it means that Noah scored more than 15 points.
Feel free to ask for more if needed or if you did not understand something.
The correct interpretation of 15 < n in the context of the basketball game is that Noah scores more than 15 points.
The inequality 15 < n indicates that the number of points Noah scores, represented by n, is greater than 15. This means that the actual number of points Noah scores must be any number that is a increment above 15, but cannot be 15 itself. For example, if Noah scores 16 points, 17 points, or any number of points greater than 15, the inequality 15 < n would be satisfied. It is a mathematical way of stating that Noah's score exceeds 15 points.
there are 150 students in the marching band, and 30 of them play the trumpet. Which number line represents the percent of the srudents in the marching band who play the trumpet?
Answer:
30 is 20% of 150 i.e. 20% of total 150 students in the marching bank play the trumpet.
Step-by-step explanation:
Draw two number lines:
One number line to represent number of students from 0 to 150. For convenience, divide the number line into intervals of 15 so that 30 is also present on the line.Second number line to represent percentage and divide it in intervals from 1 to 100.Now, place the other number line just below the other number line and draw a vertical line as shown the attached figure.
We find out that 30 is at 20% of 150.
It means that 20% (30 of total 150) of total 150 students in the marching band, play trumpet.
30 is 20% of 150 i.e. 20% of total 150 students in the marching bank play the trumpet. Step-by-step explanation:
What is -78.6% (-2.4)? A. -188.64 B. -32.75 C. 32.75 D. 188.64
Answer:
D
Step-by-step explanation:
hope this helps
Answer:
188.64
Step-by-step explanation:
-78.6%(-2.4) =
-0.786(-2.4) =
1.8864
1.8864 * 100 = 188.64
So, your answer letter choice D.
Fill in the blank.
A rectangular prism has a length of 11 centimeters, a width of 9 centimeters, and a height of 3 centimeters. Its volume is
a0 cubic centimeters.
Answer:
297 cubic centimeters
Step-by-step explanation:
volume is LWH
11*9*3 = 297
Answer:
297 cubic centimeters
Step-by-step explanation:
mark me brainy plz!
Photo is attached please help ASAP super easy geometry
Answer:
Volume = 280 cm
Step-by-step explanation:
V=(lwh)/3
length: 10
width: 7
height: 12
V= (10*7*12)/3
V= 840/3
V= 280cm
Abby used 10 ounces of dried pineapple, 20 ounces of dried cranberries, and 18 ounces of pecans to make a trail mix. Which statement is a true statement?
Find the interest on $5,200 at 6% for 2 and a half years. Which of the following equations would be used to solve this problem?
i put this before but forgot to put the equations sorry
A: I = (5200)(6)(2.5)
B: 5200 = P(0.06)(2.5)
C: I = (5200)(0.06)(2.5)
D: I = (5200)(0.6)(2.5)
one third of an interger
im dumb as heck so plez halp
You are in charge of the city carnvial committee. You have $8,096.35 to spend. You have already purchased: Decorations $894.60. Tent rental
$1.009.99, new popcorn and cotton candy machines $658.50
How much money do you have left to spend to rent carnival rides for the kids?
Step-by-step explanation:
Total amount to spend = 8096.35
Amount already spent = 894. 60 + 1009.99 + 658.50 = 2563.09
Amount left to spend = 5533.26
emma was given a system of equations to solve by graphing. which statement correctly identifies Emma’s error?
Please help me. i’m struggling a lot on this question and only have a bit of time left
Answer:
A The first line should have an intercept at 2 not at 1
Step-by-step explanation:
The first line should have an intercept at 2 not at 1. The graph is 1 unit too low
The intercept should be at x=3 and y = 1
Answer:
First one
Step-by-step explanation:
Line 1:
When x = 0
y = -(1/3)(0) + 2
y = 2
y-intercept is 2
Estimate the sum by first rounding each
mixed number to the nearest whole number
and then adding:
4 7/12 + 2 1/3
[?]+[] = []
Answer:
7
Step-by-step explanation:
4.583 + 2.333 = 6.916 = 7(to the nearest whole number)
Which represents a perfect cube? 6 times 6 times 6 6 + 6 + 6 3 times 3 times 3 times 3 3 + 3 + 3 + 3 + 3
Answer:
6 times 6 times 6
Step-by-step explanation:
6 x 6 = 6²
Therefore 6 x 6 x 6 = 6³
Answer: 6 times 6 times 6
Step-by-step explanation: I did it on edg :)
Find the value of x in ⊙Q .
Answer:
x= 5
Step-by-step explanation:
both lines are the same length
5x-6=2x+9
-2x -2x
3x-6= +9
+6 +6
3x = 15
÷3 ÷3
x= 5
The value of x is 5.
To find the value of [tex]\(x\)[/tex] in the given circle, we need to use the properties of the circle and the given information about the segments.
1. Given:
PM is a chord of the circle with center [tex]\(Q\)[/tex].
[tex]\(NL\)[/tex] is the perpendicular bisector of [tex]\(PM\)[/tex].
[tex]\(T\)[/tex] is the midpoint of [tex]\(PM\)[/tex], and [tex]\(T\)[/tex] lies on [tex]\(NL\)[/tex].
[tex]\(MT = 5x - 6\)[/tex] and [tex]\(TP = 2x + 9\)[/tex].
2. Key Properties:
Since [tex]\(T\)[/tex] is the midpoint of [tex]\(PM\)[/tex], we have [tex]\(PT = TM\)[/tex].
The perpendicular bisector of a chord passes through the center of the circle, so [tex]\(NL\)[/tex] passes through [tex]\(Q\)[/tex].
3. Equating the Segments:
Since [tex]\(T\)[/tex] is the midpoint of [tex]\(PM\)[/tex], we have:
[tex]\[ PT = TM. \][/tex]
Using the given expressions for [tex]\(MT\)[/tex] and [tex]\(TP\)[/tex]:
[tex]\[ MT = 5x - 6 \quad \text{and} \quad TP = 2x + 9. \][/tex]
Because [tex]\(T\)[/tex] is the midpoint, [tex]\(PT = TM\)[/tex].
Therefore, we have:
[tex]\[ PT = TM = 2x + 9. \][/tex]
Since [tex]\(MT = 5x - 6\)[/tex], and [tex]\(PT = TM\)[/tex], we have:
[tex]\[ 5x - 6 = 2x + 9. \][/tex]
4. Solving for [tex]\(x\)[/tex]:
[tex]\[ 5x - 6 = 2x + 9. \][/tex]
[tex]\[ 3x - 6 = 9. \][/tex]
[tex]\[ 3x = 15. \][/tex]
[tex]\[ x = 5. \][/tex]
- Which of the following is the least?
A).27
B) 1/4
C) 3/8
D) 2/11
E) 11%
Step-by-step explanation:
A) 0.27
B) 1/4 = 0.25
C) 3/8 = 0.375
D) 2/ 11 = 0.1818
E) 11% = 0.11
E is the correct answer
Answer:
E
Step-by-step explanation:
2/11= .18
3/8= .375
1/4= .35
11%= .11
.27= .27
A stadium holds a total of 7,500 people. A random survey of 150 people finds that 17 of them are under 21 years old.
Enter the total number of people predicted to be in the stadium under 21.
Answer: 850 people
Step-by-step explanation:
Stadium capacity = 7,500 people.
A random survey was done for 150 people and it was found out that 17 of them are under 21 years old. This can be expressed as a fraction as:
= 17/150
The total number of people that are predicted to be in the stadium of under 21 will be:
= 17/150 × 7500
= 17 × 50
= 850 people
Samuel and Randi are placemat weavers. Samuel can weave 7 placemats in 8 hours. Randi can weave 5 placemats in 4 hours. How many placemats can they make in 5 days if they worked 8 hours each day?
Answer: 85 placemats
Step-by-step explanation:
Let’s split it into three parts: how much Samuel can weave, how much Randi can weave, and how much they can weave in total
Part 1: Samuel
First, let’s figure out how much Samuel can weave!
First, we know that Samuel can weave 7 placemats in 8 hours (1 day). So, if he weaved placemats for 5 days, then:
= 7 x 5
= 35
Therefore, Samuel weaved 35 placemats in 5 days if he worked 8 hours each day.
Part 2: Randi
We know that Randi makes 5 placemats in 4 hours, which is half, a day. But lets figure out how many placemats he can make it a day.
All we have to do is multiply by two.
= 5 x 2
= 10
So, we now know that he can make 10 placemats in a day. Now, let’s see how many placemats he can make in five days.
= 10 x 5
= 50
Therefore, Randi weaved 50 placemats in 5 days if he worked 8 hours each day.
Part 3: Adding Them
Now, we have 35 placemats from Samuel and 50 placements from Randi. So, we have to add them.
= 35 + 50
= 85
Therefore, Randi and Samuel can make 85 placemats in 5 days together if they work 8 hours each day.
Samuel and Randi can make a total of 85 placemats in 5 days.
Explanation:To find out how many placemats Samuel and Randi can make in 5 days, we need to calculate how many placemats each of them can make in one hour. Samuel can weave 7 placemats in 8 hours, so he can weave 7/8 placemats in one hour. Randi can weave 5 placemats in 4 hours, so she can weave 5/4 placemats in one hour. To find out how many placemats they can make in 5 days, we need to multiply their rates by the number of hours they work in 5 days. Samuel can make (7/8) * (8 * 5) = 35 placemats in 5 days. Randi can make (5/4) * (8 * 5) = 50 placemats in 5 days. Therefore, Samuel and Randi can make a total of 35 + 50 = 85 placemats in 5 days.
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Solve the system using substitution and describe your steps
x = y - 3
2x + y = 12
Answer:
[tex]x=3\\y=6[/tex]
Step-by-step explanation:
[tex]x=y-3\\2x+y=12[/tex]
We have already defined that x = y - 3, replace x for this value.
[tex]2x+y=12\\2(y-3)+y=12[/tex]
Distribute 2.
[tex]2y-6+y=12[/tex]
Add 6.
[tex]2y+y=12+6[/tex]
Combine like terms;
[tex]3y=18[/tex]
Divide by 3.
[tex]y=\frac{18}{3}\\ y=6[/tex]
After having found a variable value, in this case y, replace it in the other equation; x = y - 3, to find x.
[tex]x=y-3\\x=6-3\\x=3[/tex]
A bag contains 20 marbles of the same size that are blue, green, and red. The probability of picking a blue marble is 20%. The probability of picking a green marble is 50%. Determine the probability of picking a red marble from the bag and then classify the probability of picking a red marble as likely or not likely to occur.
What is 2 divided by 3 written as fractions?
1/3 with a line over the answer ( 0.66666666666...)
The fraction form of the expression ''2 divided by 3'' would be 2/3.
Used the concept of the fraction that states,
A fraction is part of a whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.
Given that the statement is,
''2 divided by 3''
Now it can be written in fraction form as,
''2 divided by 3''
= 2 ÷ 3
= 2 / 3
Therefore, the fraction form is 2/3.
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9600 dollars is placed in an account with an annual interest rate of 5%. To the nearest year, how long will it take for the account value to reach 37800 dollars?
Answer: lt will take 28.09 years for the account value to reach $37800
Step-by-step explanation:
Hi, to answer this question we have to apply the compounded interest formula:
A = P (1 + r) t
Where:
A = Future value of investment (principal + interest)
P = Principal Amount
r = Annual Nominal Interest Rate (decimal form)
Replacing with the values given
37800= 9600 (1+0.05)^t
Solving for t (years)
37800/9600 = 1.05^t
3.9375 = 1.05^t
log 3.9375 = log 1.05^t
log 3.9375 = t (log 1.05)
log 3.9375/log 1.05 = t
t = 28.09 years
A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10 units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units. Which expression represents the volume, in cubic units, of the shaded region of the composite figure?
The expression is 1/2(14)* 10*8- π (2.5)² *8.
What is expression?An expression is a sentence with a minimum of two numbers or variables and at least one math operation.
Given:
Prism: side length base= 14 units and 10 units
Cylinder d= 5 units
So, Volume of prism
=1/2(14)* 10*8
and, Volume of cylinder
= π (2.5)² *8
As, the cylinder is cut out then the expression would be
=1/2(14)* 10*8- π (2.5)² *8
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The bases of a 39-foot pole and a 15-foot pole are 45 feet apart, and both poles are perpendicular to the ground. The ground is flat between the two poles. What is the length of the shortest rope that can be used to connect the tops of the two poles?
Answer: 51 feet
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the Pythagorean Theorem:
x^2 = a^2 + b^2
Where x is the hypotenuse of the triangle (in this case length of the rope) and a and b are the other sides.
The difference between the poles' heights is equal to one side of the triangle (39-15=24), the other side of the triangle is the distance between poles (45).
Replacing with the values given:
x^2 = 24^2 + 45^2
x^2 = 576+2,025
x^2 = 2,601
x = √2,601
x = 51 feet
Feel free to ask for more if needed or if you did not understand something.
Factorize completely :
4x² - y² + 4y - 4
Answer:
(2x-y+2)(2x+y-2)
Step-by-step explanation:
4x² - y² + 4y - 4=
=(2x)²-(y²-4y+4)
=(2x)²-(y-2)²
= [2x-(y-2)][2x+(y-2)]
=(2x-y+2)(2x+y-2)
a²-b²=(a-b)(a+b)
Step-by-step explanation:
the answer is (2x-y+2) (2x+y-2)
onsider the system of equations. y = –2x + 4, 3y + x = –3 Which statement is true of this system of equations? Both equations are in slope-intercept form. The first equation converted to slope-intercept form is y + 2x = 4. The second equation converted to slope-intercept form is .y = negative one-third x minus 1 Neither equation is in slope-intercept form.
Answer:
The second equation converted to slope-intercept is y = -1/3 x - 1.
Step-by-step explanation:
take the second equation:
3y + x = -3
3y = -x - 3
y = 1/3 x - 1. <----- Slope-intercept form.
Answer:
its c
Step-by-step explanation:
pls help! will give brainlist!
Answer:
Since this is a transversal, I am using certain rules to figure this out.
For example, angles 1 & 2 should equal 180 when added together, in the same way angles 11 & 12 should do the same thing!
Therefore, since angle 1 is 140°, angle 2 should be 40°, to complete it. This is the same for the other side!
Answer:
Angle2: 40
Angle11: 60
Step-by-step explanation:
ang1+ang2=180 (Linear pair)
140+ang2=180
ang2=40
ang2+ang9+ang11=180 (angle sum property)
40+80+ang11=180
ang11=180-120
ang11=60
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Given AQRS - AXYZ, what is the value of tan(Q)?
A) 3/5
B) 3/4
C) 4/5
D) 4/3
Which describes the cross section of a square prism that passes through vertices A. B. and C?
A. a triangle with three equal sides, all measuring 8 inches
B.a triangle with three equal sides, all longer than 12 inches
C. a triangle with only two equal sides one side measures 8 inches and two sides measure 12 inches
D. a triangle with only two equal sides; one side is longer than 8 inches and two sides of equal length that are longer than 12 inches.
Please answer now, I’m on a timer.
Answer:
c
Step-by-step explanation: