Answer: The equation for the translation of x2 + y2 = 64 three units to the left and two units down is:
(x − 3)2 + (y − 2)2 = 64
Step-by-step explanation:
This is known as the standard equation of a circle centered at (3, 2) with a radius of 8.
When translating a shape, we need to change the center point of the shape. If we want to translate 3 units to the left and 2 units down, it means that we need to change the center point of the shape from the origin to (3, 2). This can be achieved by subtracting 3 from x and subtracting 2 from y in the equation of the circle. This results in (x - 3)2 + (y - 2)2 = 64, which is the equation for the translated circle.
Answer: (x - 3)^2 + (y - 2)^2 = 64.
Step-by-step explanation:
This is because to translate a point or a function in the x-axis by a certain value we need to add or subtract the value from the x variable. To translate in the y-axis we need to add or subtract the value from the y variable. In this case, we are translating it three units to the left, so we subtract 3 from x, and two units down so we subtract 2 from y.
Which of the following graphs has a slope of negative three halves and a y-intercept of 2?
graph of a line passing through the points 0 comma 2 and 3 comma 0
graph of a line passing through the points 0 comma 2 and 2 comma negative 1
graph of a line passing through the points 0 comma 3 and 2 comma 0
graph of a line passing through the points 0 comma 3 and 3 comma 1 pls hurry I will give brainlist
The graph that has a slope of negative three halves and a y-intercept of 2 is the graph of a line passing through the points (0,2) and (3,0).
What is the slope?
One of the most important things to understand about lines is the definition of slope. The slope is the 'steepness' of the line, also commonly known as rise over run. We can calculate the slope by dividing the change in the y-value between two points over the change in the x-value.
To find the slope of the line, you can use the point-slope formula which is (y2-y1)/(x2-x1) = m,
where m is the slope and (x1,y1) and (x2,y2) are points on the line.
So using the given points in the question, we get (0-2)/(3-0) = -2/3 = -0.66 = -3/2.
And the y-intercept is the point where the line crosses the y-axis, which is 2 in this case.
Hence, the graph that has a slope of negative three halves and a y-intercept of 2 is the graph of a line passing through the points (0,2) and (3,0).
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Jackie wants to buy a new van for work.
She wants to borrow £7,500 to buy the van and looks at two bank loans for this amount.
an image
Formula for simple interest is: I=PRT100
I
=
P
R
T
100
Formula for compound interest is: A=P(1+r100
A
=
P
(
1
+
r
100
)n
n
What is the difference in the interest charged between the two banks?
Answer: The interest rates charged in both formulas are different.
Step-by-step explanation:
To begin with, the simple interest = PRT/100
In this, the interest is the same as the number of years.
For example, P=10,000 R=10% T=2yrs
SI = PRT/100
= 10,000*10*2/100
= 2000
This rupee 2000 is the same interest for two years.
compound interest = A= P(1+r/100)^n
In this, the interest changes every year up to the period of time.
For example, P= 10,000 R=10% N=2yrs
A= 10,000(1+10/100)^2
= 10,000*11/10*11/10
= 12100
I= A-P
=12100-10000
= 2100
This interest varies for 2 years.
Jada told Noah that she has $4.20 worth of quarters and nickels in her pocket and 20 coins all together. Figure out how many of each type of coin she has.
Answer: We can set up a system of equations to solve this problem. Let x be the number of quarters and y be the number of nickels. We know that:
x + y = 20 (the total number of coins)
0.25x + 0.05y = 4.20 (the total value of the coins in dollars)
We can use the first equation to solve for one variable in terms of the other, and then substitute that into the second equation to get a single equation with one variable.
For example:
x = 20 - y
0.25(20-y) + 0.05y = 4.20
5-0.25y + 0.05y = 4.20
5= 4.20
y = 20 - 5
y = 15
x = 20 - 15
x = 5
So Jada has 5 quarters and 15 nickels in her pocket.
Step-by-step explanation:
From the triangle below, if AD = 8 and CD = 18, find the length of side BD.
Answer:
19.7
Step-by-step explanation:
A^2 + B^2 = C^2
8^2 + 18^2 = sqrt(388)
Find the measure of the given angle
Answer:
A= 110 degrees AND B= 140 degrees.
Y= 112 degrees and X= 157 degrees.
Step-by-step explanation:
Triangle XYZ is an isocoles triangle, because it has two congruent sides. 70 degrees is a measurement of an angle opposite of one of those congruent sides, so angle YXZ is also 70 degrees. By the triangle angle sum theorem, we can say that the measurement of angle YZX is 40 degrees. So, for the first triangle, by the linear pairs theorem, we can find the two missing angles.
A= 110 degrees AND B=140 degrees.
For the triangle on the right, we can use the triangle angle sum theorem to say that angle BDC is 68 degrees. Then, we can say that by the by the linear pairs theorem that angle ADE is 112 degrees. From there, we need to look at the 23 degree measurement on the lower right triangle. We can see that the angle steadily rises on that line and then we can take 180-23 by the linear pairs theorem to conclude than angle BEA is 157 degrees. This can be confirmed by looking at the two innermost angles in the top right triangle. If you take 180-23-112, you will get 45. If you add 45 to 112, you will get 157.
Y= 112 degrees and X= 157 degrees.
Audrey deposited $10,000 into a 3-year certificate of deposit that earned 10% annual interest, compounded annually. Audrey made no additional deposits to or withdrawals from the certificate of deposit. What was the value of the certificate of deposit at the end of the 3-year period?
A. $13,000
B. $13,300
C. $13,310
D. $13,401
Answer: C
Step-by-step explanation:
10000(1+0.10)³
=10000(1.10)³
=10000*1.331
=13310
Melissa has a student dictionary on her jasper dictionary connect 76 pages and the dictionary more word start with the letter S. then any other letter I'll keep on 13 full pages she opens up the dictionary random what is the proper ability that the page can contain words starting with the word s
What is the equation of the line in slope-intercept form that passes through point (0, −2) and is parallel to the line y = -1/2 + 6? Show all necessary steps.
Answer:
y = - [tex]\frac{1}{2}[/tex] x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mc + c ( m is the slope and c the y- intercept )
y = - [tex]\frac{1}{2}[/tex] x + 6 ← is in slope- intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
• Parallel lines have equal slopes , then
slope of parallel line = - [tex]\frac{1}{2}[/tex]
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = - [tex]\frac{1}{2}[/tex] x - 2 ← equation of parallel line
- Grace is trying to read as many books
over the summer as she can. Grace
has already read 15 books. She plans
to read 2 additional books per week.
Define a variable for the number of
weeks she reads additional books. Use
the variable to write an expression
for the total number of books Grace
reads over the summer.
Step-by-step explanation:
let the number of weeks be w
the total number of books Grace reads will always be 15 + something because we start with 15 and cannot unread a book
for each week, she reads 2 books. this can be represented as 2 * w
books Grace already read + books Grace reads each week = total books
15 + 2 * w = total books
At a college, the ratio of teachers to students is 1 to 11. The ratio of female students to the total number of students is 4 to 9. If there are 264 female students, then how many teachers are there
Answer:
We know that the ratio of female students to the total number of students is 4 to 9.
That means that for every 4 female students, there are 9 students in total.
So, we can set up the proportion:
4/9 = x/264
where x is the total number of students.
Solving for x, we get:
x = (4/9)*264 = 96
Since the ratio of teachers to students is 1 to 11, then for every 11 students there is 1 teacher, we can set up the proportion:
1/11 = y/96
where y is the total number of teachers.
Solving for y, we get:
y = (1/11)*96 = 8.72 ≈ 8
So, there are 8 teachers in the college.
Step-by-step explanation:
help me with this one
Answer:
Angle A is 66°
Step-by-step explanation:
< b is equal to 57 because the opposite side lengths are equal.
The sum of the interior angles of a triangle is 180
180 - 57 - 57 = 66
find the total number of relations on the set s={1,2,3}
The total number of relations in the set s = {1,2,3} is given as follows:
9.
How to obtain the total number of relations in a set?
The total number of relations in a set is given by the cardinality of the square of the set.
The square of a set is composed by all the possible pairs that can be formed with the elements in the set.
The set for this problem is defined as follows:
s = {1, 2, 3}.
The set has a cardinality of 3, as it has 3 elements, hence the cardinality of the square of the set is given as follows:
3² = 9.
Which is the total number of relations in the set.
These relations are all the ordered pairs with elements of s, hence:
Relations = {(1,1), (1,2), (1,3), (2,1), (2,2), (2,3), (3,1), (3,2), (3,3)}
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In trapezoid PQRS, PQ is parallel to SR, and diagonal PR is drawn.
SP=SR, SRP=50°, and PRQ=85°
Find the measures of RQP, SPR, and PSR.
Justify your answers.
The measure of ∠RQP is, 45°
The measure of ∠SPR is, 50°
The measure of ∠PSR is, 50°
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
In trapezoid PQRS,
PQ is parallel to SR, and diagonal PR is drawn.
And, SP = SR, SRP = 50°, and PRQ = 85°
Here, SP = SR
So, We get;
In Δ PSR; ∠PRS = ∠SPR = 50°
And, PQ is parallel to SR.
Hence, We get;
⇒ ∠SRP = ∠RPQ = 50°
Now, In Δ PQR;
⇒ ∠PRQ + ∠QPR + ∠PQR = 180°
⇒ 85° + 50° + ∠PQR = 180°
⇒ 135° + ∠PQR = 180°
⇒ ∠PQR = 180° - 135°
⇒ ∠PQR = 45°
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construct a right-angled isosceles triangle whose equal side measure 2 cm
A construction of a right-angled isosceles triangle whose equal side measure 2 cm is shown in the image attached below.
What is an isosceles right triangle?In Mathematics, an isosceles right triangle can be defined as a type of right-angled triangle in which two (2) of its side lengths are equal and one of its angle is a right angle.
What are the steps for the construction of a right-angled isosceles triangle?Generally speaking, the steps that are required for the construction of a right-angled isosceles triangle include the following:
You should draw a line segment, with line AB equal to 2 cm (AB = 2cm).At point A, draw an angle with a measure of 90 degrees (90°).You should draw an arc of radius from point A in order to intersect the perpendicular drawn at point A at the point C.You should join point A and point B.In conclusion, triangle ABC (ΔABC) is the required right-angled isosceles triangle as shown in the image attached below.
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Help please will give brainliest!
Answer:24.353333333
Step-by-step explanation:
graph the equation.
H
-2
-1
0
2
4y + 16x = 28
Y
Ordered Pair
10
-5
10+
5
-S
-10-
Clear All
y
5
५
IC
The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)
What is the solution to a linear equation?The solution of a linear equation is defined as the points, in which the lines represent the intersection of two linear equations. In other words, the solution set of the system of linear equations is the set of all possible values to the variables that satisfies the given linear equation.
Given here: The equation as 4y+16x=28 or y+4x=7
putting (1,3) in the equation we get 3+4×1=7
Similarly we can find the ordered pair as (2, -1) , (3,-5) , (4,-9)
Hence, The ordered pairs are (1,3) , (2, -1) , (3,-5) , (4,-9)
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Find the sides of the triangle if two of it's sides are equal, the third side is 1 1/3 cm longer than the others and it's prerimeter is 2 2/5 cm.
let's firstly convert the mixed fractions to improper fractions and then sum them up.
[tex]\stackrel{mixed}{1\frac{1}{3}}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} ~\hfill \stackrel{mixed}{2\frac{2}{5}} \implies \cfrac{2\cdot 5+2}{5} \implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{equal sides}}{x+x}~~ + ~~\stackrel{\textit{third side}}{\left( x+\cfrac{4}{3} \right)} ~~ = ~~\stackrel{perimeter}{\cfrac{12}{5}}\implies 3x+\cfrac{4}{3}=\cfrac{12}{5}[/tex]
[tex]\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15\left( 3x+\cfrac{4}{3} \right)=15\left( \cfrac{12}{5} \right)}\implies 45x+20=36\implies 45x=16 \\\\\\ \stackrel{\textit{equal sides}}{\boxed{x=\cfrac{16}{45}}}\hspace{10em}x+\cfrac{4}{3}\implies \cfrac{16}{45}+\cfrac{4}{3}\implies \stackrel{\textit{third side}}{\boxed{\cfrac{76}{45}}}[/tex]
PLEASE HELP 20 POINTS!
A new cruise ship line has just launched 3 new ships: the Pacific Paradise, the Caribbean Paradise, and the Mediterranean ParadiseThe Caribbean Paradise has 16 more deluxe staterooms than the Pacific Paradise. The Mediterranean Paradise has 28 fewer deluxe staterooms than four times the number of deluxe staterooms on the Pacific Paradise Find the number of deluxe staterooms for each of the ships if the total number of deluxe staterooms for the three ships is 1176
ANSWERS MUST ADD UP TO 1176
Step-by-step explanation:
x = number of deluxe staterooms on Pacific.
deluxe staterooms on Caribbean = x + 16
deluxe staterooms on Mediterranean = 4x - 28
1176 = x + (x + 16) + (4x - 28) = 6x - 12
1188 = 6x
x = 1188/6 = 198
so,
Pacific has 198 luxury staterooms.
Caribbean has 198 + 16 = 214 luxury staterooms.
Mediterranean has 4×198 - 28 = 792 - 28 = 764 luxury staterooms.
Find the solutions of the equation on the indicated interval. List the smaller answer first. Round to 3 decimal places. 3 cos ( x ) + 4 = 5 with − π ≤ x ≤ π .
Answer:
Step-by-step explanation:
The solutions to this equation are x = 1.273 and x = -0.273.
When x = 1.273, 3 cos (x) + 4 = 5.
When x = -0.273, 3 cos (x) + 4 = 5.
Rounding to 3 decimal places, the solutions to the equation on the indicated interval are x = 1.273 and x = -0.273.
Rationalize the denominator and simplify the following expression:
fraction numerator 4 plus square root of 2 over denominator 2 space minus square root of 2 end fraction
5 plus 3 square root of 2
10 plus 6 square root of 2
2 plus 6 square root of 2
2 plus 3 square root of 2
Answer:
[tex]\textsf{A)} \quad 5+3\sqrt{2}[/tex]
Step-by-step explanation:
Given rational expression:
[tex]\dfrac{4+\sqrt{2}}{2 -\sqrt{2}}[/tex]
To rationalise the denominator, multiply both the numerator and denominator by the conjugate of the denominator.
The conjugate of an expression is where we change the sign in the middle of the two terms. Therefore, the conjugate of the denominator of the given expression is:
[tex]2 + \sqrt{2}[/tex]Multiply the numerator and denominator by the conjugate of the denominator:
[tex]\implies \dfrac{4+\sqrt{2}}{2 -\sqrt{2}} \cdot \dfrac{2 +\sqrt{2}}{2 +\sqrt{2}}[/tex]
Simplify:
[tex]\implies \dfrac{(4+\sqrt{2})(2 +\sqrt{2})}{(2 -\sqrt{2})(2 +\sqrt{2})}[/tex]
[tex]\implies \dfrac{8+4\sqrt{2}+2\sqrt{2}+\sqrt{2}\sqrt{2}}{4+2\sqrt{2}-2\sqrt{2}-\sqrt{2}\sqrt{2}}[/tex]
[tex]\implies \dfrac{8+6\sqrt{2}+2}{4-2}[/tex]
[tex]\implies \dfrac{10+6\sqrt{2}}{2}[/tex]
Reduce to its simplest form by dividing the numerator and the denominator by 2:
[tex]\implies 5+3\sqrt{2}[/tex]
2 How much would you need to invest in a money market account if you would like to have $20,000 in the account at the end of 10 years? The account provides an APR of 2% compounded monthly.
Answer:
$16377.34---------------------------------
Use the compound interest formula:
A = P(1 + r/n)^(nt),Where A - future amount, P - invested amount, r- annual interest rate, n - number of compounds a year, t - number of years
Given:
A = $20000,r = 2% = 0.02n = 12,t = 10.Substitute known values and solve for P:
20000 = P(1 + 0.02/12)^(12*10)P = 20000/(1 + 0.01/6)^120P = 16377.34what is the slope of y= 4x-5
Answer:
it is 4
Step-by-step explanation:
the slope is always the number before x and so since 4 is before x then 4 is the answer
Here you can see the problem in the picture
Answer:
[tex]\sqrt{6}[/tex]
Step-by-step explanation:
In a 45-45-90 triangle to find the two shorter sides (a and b) are represented as the number n in this case n is [tex]\sqrt{3\\[/tex] . The hypotenuse on the other hand is can be found by doing n[tex]\sqrt{2\\}[/tex] so you multiply [tex]\sqrt{3}(\sqrt{2} )[/tex] to get [tex]\sqrt{6}[/tex]
a 12 foot ladder is leaning aginst a building. if the base of the ladder is 5 feet from the base of the house how high up the house will the ladder reach
The height of the house with the ladder is 10.9 feet
What is Pythagoras theorem?Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
The hypotenuse = 12
adjascent = 5
opp = x
hyp² = opp² + adj²
12² = 5² + x²
x² = 12² - 5²
x² = 144 - 25
x² =119
x² = √119
x= 10.9 feet
therefore the height of the house from the ladder is 10.9 feet
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Show each inequality on a number line and then write all the one-digit integers that satisfy it. k ≥0
The one-digit integers that satisfy the inequality k>0 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
What is a number line?A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R."
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
A number is a line that is made up of positive and negative numbers with the distance between the preceding and succeeding unit to be 1.
The negative values on the number line are -1, -2, -3...-9 while the value greater than zero are 1, 2, 3, 4,...9
Hence the one-digit integers that satisfy the inequality k>0 are 1, 2, 3, 4, 5, 6, 7, 8, and 9.
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please help asap
• it would mean sm and make my day
Answer:
I know it
Step-by-step explanation: Btw did somone already answer this?
The graph of a quadratic function with vertex (-1,-4) is shown in the figure below.
Find the domain and the range.
Based on the graph of this quadratic function with vertex (-1, -4), the domain and the range are as follows;
Domain = {-3, 0.5}.
Range = {-4, ∞}.
How to identify the domain and range of a function?In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
Additionally, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.
Note: The vertex of any quadratic function represents the minimum of the given function.
By critically observing the graph shown in the image attached below, we can reasonably and logically deduce the following:
Domain = -3 < x < 0.5 or [-3, 0.5].
Range = -4 < y < ∞ or [-4, ∞].
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Use elimination to solve
-3x+12y = 9
x-4y=-3
Answer:
Step-by-step explanation:
Elimination is a method of solving a system of equations by adding or subtracting the equations from each other to eliminate one of the variables.
In this case, we will be using elimination to solve the system of equations:
-3x + 12y = 9
x - 4y = -3
Step 1: Multiply the first equation by -1.
(Multiplying by -1 switches the sign of every number in the equation)
3x - 12y = -9
Step 2: Add the two equations together.
3x - 12y = -9
+x - 4y = -3
______________
4x - 16y = -12
Step 3: Isolate the y-variable by adding 16y to both sides of the equation.
4x - 16y = -12
+16y +16y
______________
4x = -12 + 16y
Step 4: Divide both sides of the equation by 4 to isolate the y-variable.
4x = -12 + 16y
4/4 4/4
______________
x = -3 + 4y
Therefore, the solution to the system of equations is x = -3 + 4y.
Please help with this question
Answer:
c.
Step-by-step explanation:
that is easy.
a matrix multiplied by a constant is multiplying every element in the matrix by that constant.
and subtracting a matrix from another is subtracting the elements on each position.
it is a simile as that.
for that reason I only need to look at the first, top left element to determine the correct answer :
-1×2 - 4×7 = -2 - 28 = -30
so, c. is the right answer.
the calculation in full :
2A =
-2 18 4
20 -20 4
-10 12 -10
4B =
28 -4 -4
24 -16 -12
-40 40 -28
so, 2A - 4B =
-30 22 8
-4 -4 16
30 -28 18
Thhe study of choices people make to fulfill their unlimited needs and wants even though there are limited resources.
Group of answer choices
Economics
Scarcity
Choices
Opportunity Cost
The study of choices people make to fulfill their unlimited needs and want even though there are limited resources is called Economics. Thus option A is correct.
What are resources?Resources can be defined as the means through which the material is provided to people. This will be to know that the resources are properly allocated.
An economy is a region where products and services are produced, distributed, traded, and consumed. a social domain that places an emphasis on production-related practices, discourses, and material expressions. The factors that affect production, such as land, cash, labor, and natural facilities, are governed by economic structures.
Therefore, option A is the correct option.
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