Equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k) is the center of the circle
r is the radius
For the given circle:
Use the center and the given point to find the radius: the radius is the distance from the center to any point in the circumference.
Distance between two points:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} (0,0) \\ (-5,4) \\ \\ r=\sqrt[]{(-5-0)^2+(4-0)^2} \\ r=\sqrt[]{(-5)^2+4^2} \\ r=\sqrt[]{25+16} \\ r=\sqrt[]{41} \end{gathered}[/tex]Use the center (0,0) (the origin) and the rafius to write the equation of the circle:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=(\sqrt[]{41})^2 \\ \\ x^2+y^2=41 \end{gathered}[/tex]Then, the equation of the given circle in standard form is:[tex]x^2+y^2=41[/tex]PROBLEM: Equivalent Expressions Create three different expressions that are each equal to 20. Each expression should include only these three numbers: 4. -2. and 10.
Given the numbers: 4, -2, and 10.
We want to create three different expressions that are each equal to 20.
First Expression
[tex](4-2)\times10=20[/tex]Second Expression
[tex]\begin{gathered} (4\times10)+(-2\times10) \\ =40+(-20) \\ =40-20 \\ =20 \end{gathered}[/tex]Third Expression
[tex]\begin{gathered} 10\lbrack4+(-2)\rbrack \\ =10\lbrack4-2\rbrack \\ =10\times2 \\ =20 \end{gathered}[/tex]The population of the city of Woodville is growing in a constant rate the expression 35,000+2400 X model would real population which three statements are correct
The expression is,
38000+2400x.
The x represents the number of year.
38,000 represents the current population.
2400 represents the yearly growth.
Thus, option (a), (c) and (d) are the correct solution.
One afternoon you picked 6/8 of a pound of strawberries that night you ate 3/6 of what you picked
Given :
the amount of picked strawberries = 6/8 pounds
you ate 3/6 of what you picked.
so, the amount is eaten =
[tex]\frac{6}{8}\times\frac{3}{6}[/tex]cross out the number 6
so, the answer will be = 3/8 pounds
A linear function f(x) contains the coordinates (-9,4) and (6,4). Joy says f(x) is a horizontal line, and Lu says f(x) is a vertical line. Which student correctly described the function? Explain.
The student whose name is Joy has described the function correctly as the line is horizontal line.
What are the coordinates ?
Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
The given coordinates of the linear function f(x) are (-9, 4) and (6,4).
The y-coordinates for both of these points will be the same if we plot them on the graph.
Additionally, if the y-coordinates on the graph are the same, then the line connecting these points is horizontal in nature.
So , we can conclude that , Joy is saying correct by saying it is a horizontal line.
Therefore , the student whose name is Joy has described the function correctly as the line is horizontal line.
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Find the x-intercept and y-intercept of the graph of − 2 x + 3 y = − 6 . Then graph.
The x and y intercepts of the graph - 2x + 3y = - 6 are (3, 0) and (0, -2).
What are the x and y intercepts?We know to find the x-intercept of a graph we have to substitute y = 0 in the given equation and to find the y-intercept we have to substitute x = 0 in the given equation.
The graph of the equation is - 2x + 3y = - 6.
Now at y = 0, the equation becomes
- 2x + 3(0) = -6.
- 2x = - 6.
2x = 6.
x = 3.
Now at x = 0, the equation becomes
- 2(0) + 3y = - 6.
3y = - 6.
y = - 2.
∴ The x and y intercepts of the graph are (3, 0) and (0, -2).
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For her 9th birthday, Cindy
wanted to buy her class
number nine donuts. If each
number donut costs $1.09 and
she has 22 students in
her class, how much will
she spend on donuts?
Answer:
23.98 dollars
Step-by-step explanation
Multiply 22 x 1.09
Answer:
$23.98
Step-by-step explanation:
If there's 22 students to serve, Cindy needs to take the price of one donut ($1.09) and multiply that by 22.
22 x 1.09 = 23.98
A student entering a doctoral program in educational psychology is required to select three courses from the list of courses provided as part of his or herprogram(a) List all possible three-course selections.(6) Comment on the likelihood that EPR 669, EPR 634, and EPR 679 will be selectedClick the icon to view the course list(a) Select all the possible three-course selections below.A. 669,644, 679C. 669,634, 644DE 669.669, 634G. 669, 679, 6561669,634, 656K. 669, 669M. 634, 644,679(b) There is a chance that these courses will be selected.(Simplify your answer)B. 634, 644, 656D. 669. 644, 656OF 634, 679,656DH. 669,634, 679J. 656, 612, 656OL. 644,679, 656N. 644, 656, 644
(a) We need to find the number of combinations of selecting 3 courses of a group of 5 courses.
The number of combinations of n things chosen r at a time is found using:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]Substituting with n = 5 and r = 3, we get:
[tex]_nC_r=\frac{n!}{r!(n-r)!}=\frac{5!}{3!(5-3)!}=\frac{5\cdot4\cdot3!}{3!2!}=\frac{5\cdot4}{2\cdot1}=10[/tex]The 10 possible combinations are:
• 669, 644, 679
,• 669, 634, 644
,• 669, 679, 656
,• 669, 634, 656
,• 634, 644, 679
,• 634, 644, 656
,• 669, 644, 656
,• 634, 679, 656
,• 669, 634, 679
,• 644, 679, 656
(b) There is a 1 in 10 chance that these courses will be selected
Can somebody answer on 2 and 4 I’m lost
The measure of the angles are given below.
What is an angle?
An angle is a symbol in Euclidean space made up of two arcs that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located. The meeting of 2 dimensions ultimately creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius. The arc is centered when there is a geometric angle.
Answer 2
angle 1 = angle 6 = angle 9 = angle 14 = 97°
angle 4 = angle 7 = angle 12 = angle 15 = 114°
angle 2 = angle 5 = angle 10 = angle 13 = 180° - 97° = 83°
angle 3 = angle 8 = angle 11 = angle 16 = 180° - 114° = 66°
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A 22-foot-tall structure standing next to a 5-foot shed casts a shadow. If the shed's shadow is 40 feet
long, how long is the structure's shadow?
Answer:
176 feet of shadow
Step-by-step explanation:
Since 5 feet cast 40 feet, that means that 1 foot casts 8 feet. 22*8 = 176.
Solve: 82 ÷ 3 Follow the steps for long division. Write the number that should appear in the letter blank to solve the problem. Write the remainder in the box represented as "R:" in the image. And i need it now please
Answer:27 R1
Step-by-step explanation:2 7
3 8 2
- 6
2 2
- 2 1
1
do these pairs of values (x and y) represent two quantities that are proportional? x. y3. 125. 206. 249. 36
Info given
We have the following info given
x. y
3. 12
5. 20
6. 24
9. 36
Solution
In order to see if the two quantites are prportional we can check the following:
k=y/x
If we analyze the first pair of values we have:
k= 12/3=4
And for the next pairs we have:
k= 20/5=4
k= 24/6=4
k=36/9=4
So then as we can see the value of k is the same so then we can say that x and y are proportional since for each unit that x increase y increase 4 units
Urgent!! Math work in image!! Urgent help!!
The TV would not fit as the TV is too tall option (C) is correct after applying the concept of the ratio.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The aspect ratio is:
= 4:3
Multiply by 16 to the above ratio:
= 64: 48
The height in the area = 47"
But from the aspect ratio the height of the TV = 48"
Thus, the TV would not fit as the TV is a too tall option (C) is correct after applying the concept of the ratio.
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Rewrite the given standard form linear equation using function notation. Identify the slope, y-intercept, and z
-intercept. Sketch the graph of the linear equation.
-5x +9y = 45
Writing f as a function of z, the equivalent function notation form of the equation is:
Part 1
[tex]-5x+9y=45 \\ \\ 9y=5x+45 \\ \\ y=\frac{5}{9}x+5 \\ \\ \therefore f(x)=\frac{5}{9}x+5[/tex]
Part 2
Correct.
Part 3
Correct.
Part 4
Correct.
x^2+16x+64 factor polynomial completely if polynomial is prime state this
(x + 8)(x + 8)
Explanation:[tex]x^2\text{ + 16x + 64}[/tex]factors of 64 whose sum gives 16: +8 and +8
[tex]\begin{gathered} 8\text{ + 8 = 16} \\ 8(8)\text{ = 64} \\ x^2\text{ + 8x + 8x + 64} \end{gathered}[/tex]factorise:
[tex]\begin{gathered} x(x\text{ + 8) + 8(x + 8)} \\ (x\text{ + 8)(x + 8)} \\ \\ A\text{ polynomial is only prime if it not factorisable with an whole number.} \\ \text{This is a reducible polynomial (factorisable). Hence, not a prime} \end{gathered}[/tex]Hence, the factorised form:
(x + 8)(x + 8)
helpppppppppppppppppppppppppp
Answer:
yes
Step-by-step explanation:
The final answer would be -126<-105
simplify the product using a table [tex]( - 3h - 4)(4h - 3)[/tex]
1) Simplifying this product, using the distributive property
(-3h -4)(4h-3)
-12h²+9h-16h+12
-12h²-7h +12
2) Inserting the table, or better making a similar one, multiplying the row by the column number:
_____|4h | -3 |
-3h | -12h² | 9h |
------------------------------
-4 | -16h | 12
------------------------------
-12h² +9h -16h +12
-12h² -7h +12
3) So the answer is -12h²-7h +12
Use the figure to find the measures of the numbered angles. Explain your reasoning
The measures of the numbered angles are as follows:
3.
m∠1 139°m∠2 = 41°m∠3 = 139° m∠4 = 139° m∠5 = 41°m∠6 = 139°m∠7 = 41°4.
m∠1 = 117° m∠2 = 63°m∠3 = 117°m∠4 = 63° m∠5 = 117° m∠6 = 63° m∠7 = 63° How to find measures of angles?When parallel lines are cut by a transversal line, angle relationships are formed such as alternate angles, corresponding angles, linear angles, vertically opposite angles etc.
Therefore, line a and b are parallel to each other. The transversal line t cut the parallel lines.
Hence,
3.
m∠1 = 180 - 41 = 139° (angles on a straight line)
m∠2 = 41° (vertically opposite angles)
Vertically opposite angles are congruent.
m∠3 = 139° (vertically opposite angles)
m∠4 = 180 - 41 = 139° (same interior angles)
Same interior angles are supplementary.
m∠5 = 41° (same interior angles)
m∠6 = 139° (vertically opposite angles)
m∠7 = 41° (vertically opposite angles)
4.
m∠1 = 117° (alternate exterior angles)
Alternate exterior angles are congruent
m∠2 = 180 - 117 = 63° (sum of angles on a straight line)
m∠3 = 117° (vertically opposite angles)
m∠4 = 63° (vertically opposite angles)
m∠5 = 117° (vertically opposite angles)
m∠6 = 180 - 117 = 63° (sum of angles on a straight line)
m∠7 = 63° (vertically opposite angles)
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Using factoring, what are the solutions to the polynomial below? 2x ^ 3 + 4x ^ 2 - 30x = 0
We can start solving the solution to the polynomial given by factoring out 2x, getting:
[tex]2x(x^2+2x-15)=0[/tex]The expression inside the parenthesis is a quadratic equation. By methods of factoring, we can rewrite this as:
[tex]\begin{gathered} 2x((x+5)(x-3))=0 \\ 2x(x+5)(x-3)=0 \end{gathered}[/tex]Solving for the value of x that satisfies the polynomial given, we have:
[tex]\begin{gathered} 2x=0,x+5=0,x-3=0 \\ x=0,x=-5,x=3 \end{gathered}[/tex]Hence, the solutions to the polynomial given are x = -5, 0, 3.
Answer: x = -5, 0, 3
The Empire State building in New York City is approximately 1250 ft tall. How many U.S. dimes would be in a stack of the same height? Each dime is 1.35 mm thick.
Answer:
It is necessary to stack 277778 dimes.
Step-by-step explanation:
The height of the Empire State building in meters is 1250 * 0,30 = 375 meters.
A washer and a dryer cost $905 combined. The washer costs $55 more than the dryer. What is the cost of the dryer?sXХ5?
Solution:
Given:
Let the washer be represented by w.
Let the dryer be represented by d.
Hence,
[tex]\begin{gathered} A\text{ w}asher\text{ and a dryer cost \$}905 \\ This\text{ means;} \\ w+d=905.........................(1) \\ \\ \\ The\text{ washer costs \$55 more than the dryer} \\ w=d+55..........................(2) \end{gathered}[/tex]Substituting the equation (2) into equation (1);
[tex]\begin{gathered} d+55+d=905 \\ 2d+55=905 \\ 2d=905-55 \\ 2d=850 \\ d=\frac{850}{2} \\ d=425 \\ \\ \\ Hence,\text{ } \\ w=d+55 \\ w=425+55 \\ w=480 \end{gathered}[/tex]Hence, the cost of the dryer is $425 and the cost of the washer is $480.
Therefore, the cost of the dryer is $425.
As she climbs a hill, a cyclist slows down from 40 km/h to 10 km/h in 10 seconds. What is her deceleration?
Deceleration is the term used to describe a decrease in speed as the body moves away from the beginning place. The opposite of acceleration is deceleration. It is written as. Negative acceleration is another name for deceleration.
As she climbs a slope, a bicycle slows from 40 km/h to 10 km/h in 10 seconds. How quickly does she brake?
When motion changes, the term acceleration is used to describe it. It is customary to refer to accelerating as going faster and decelerating as going slower.
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Is 8 a solution of the equation x+6=−2?
I need help answering this please ! The calculator has to be In degree mode and the second picture is used to help you find the answer
A) AB is a side and not an angle. A side is a length, an angle is a junction of two lines.
B) You are given a side, AC and two angles, Angles B and C
C) Angles and lines are named according to their oppositeness. Angle A is opposite to side a.
[tex]\frac{\sin A}{BC}=\frac{\sin B}{AC}=\frac{\sin C}{AB}=\frac{\sin A}{BC}=\frac{\sin50}{12}=\frac{\sin 62}{AB}[/tex]D) To find AB, we crossmultiply with the expression in the middle of the equation. This gives:
[tex]AB\text{ = }\frac{\text{12 sin 62}}{\sin 50}=13.8313[/tex]Line AB is 13.83 to the nearest hundredth
Ay help a guy out, won’t you? I’m very lost I only got until November 12th.
The quadratic equations solved using the square root property is;
a. x = -3 and 7
b. x = 3 and -11
How to solve the quadratic equationsGiven the quadratic equation as;
(x -2)² - 11 = 14
To determine the roots, we have to take the following steps;
expand the bracket
(x-2)(x-2) - 11 = 14
x² -2x -2x + 4 - 11 =1 4
collect like terms
x² - 2x - 2x + 4 -11 - 14 = 0
Add or subtract like terms
x² - 4x - 21 = 0
Factorize the equation
x² - 7x + 3x - 21 = 0
factorize further
x(x - 7) + 3(x - 7) = 0
Then. x = - 3, x = 7
x² + 8x + 16 = 49
collect like terms
x² + 8x + 16 - 49 = 0
x² + 8x - 33 = 0
Factorize further
x² + 11x - 3x - 33 = 0
x( x + 11) - 3(x + 11) = 0
Then, x = 3 and x = -11
Hence, the values are -3 and 7 and 3 and -11 respectively.
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Eleni's landscaping company placed two orders. The first order was for 13 bushes and 4 trees and totaled $487. The second order was for 6 bushes and 2 trees and totaled $232. What is the price of one tree?
The required cost of the bushes is $23 and the cost of the tree is $45.
What is arithmetic?
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
Let the prices of bushes are x and prices of tress are y,
According to the question,
13x + 4y = 487 - - - - - -(1)
6x +2y = 232 - - - - - - -(2)
From equation 2
y = 116 - 3x - - - - -(3)
Put this y in equation 1
13x + 4(116 - 3x) = 487
13x + 464 - 12x = 487
x = 487 - 464
x = 23
Now put this x in equation 3
y = 116 - 3(23)
y = 116 - 69
y = 45
Thus, the required cost of the bushes is $23 and the cost of the tree is $45.
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Yesterday, Charmaine went on a bike ride. Her average speed was 10 miles per hour. Today, she went on another ride, this time averaging 13 miles per hour. In
the two days, she biked for a combined total time of 12 hours.
Let x be the number of hours she biked yesterday. Write an expression for the combined total number of miles she biked in the two days.
total number of miles biked
What is the effect on the graph of f(x) = x2 when it is transformed toh(x) = 12 – 13?
downloading about 35%
a groundskeeper needs grass seed to cover a circular field 290 ft in diameter. a store sell 50 lb bags of grass seed. 1 lb of grass seed covers about 400 square feet of field. what is the smallest number of bags the groundskeeper must buy to cover the circular field?
The diameter of circular field is 290ft .
The area of circular field is
[tex]A=\Pi(r^2)^{}[/tex][tex]A=\Pi(145)^2=66018.5ft^2[/tex]It is given that 1 lb of grass seed covers about 400 square feet of field.
The smallest number of bags he should buy is
[tex]\frac{66018.5}{400}=165\text{ bags}[/tex]Percent decrease of $16 to $4
Answer:
75% decrease
Step-by-step explanation:
x/100*12/16
x = percent decrease
subtract what you got in the end (4) from the original number (16) to get 12
(12*100) ÷ 16
1200 ÷ 16 = 75% decrease
x = 75%
6. A poll was taken of 14,502 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results are shown below. Education Level Male Female Total High School or Less 3618 3117 6735 Bachelor's Degree 2860 3762 6622 Master's Degree 574 476 1050 Ph.D. 41 54 95 Total 7093 7409 14,502 A person is selected at random. Compute the following probabilities. (a) What is the probability that the selected person does not have a Ph.D.? (b) What is the probability that the selected person does not have a Master's degree? (c) What is the probability that the selected person is female or has a Master's degree? (d) What is the probability that the selected person is male or has a Ph.D.?
Okay, here we have this:
We need to calculate the probability that the selected person is female or has a Master's degree, so according with this we obtain the following information:
The number of female is 7409, and the number of male with a master's degree is 574, so finally we obtain the following probability:
[tex]\begin{gathered} p=\frac{7409+574}{14502} \\ p=\frac{7983}{14502} \\ p\approx0.5505 \\ p=55.05\text{ percent} \end{gathered}[/tex]Finally we obtain that the percentage is %55.05.
