Answer:
center at (6, -4) r = √7
Step-by-step explanation:
(x – 6)^2 + (y + 4)^2 = 7
This is 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 of the circle
Rearranging the equation to match this form
(x – 6)^2 + (y -- 4)^2 = sqrt(7) ^2
The center is at (6, -4) and the radius is the sqrt(7)
Answer:
center at (6, -4) r = √7
Step-by-step explanation:
(x – 6)^2 + (y + 4)^2 = 7 This is 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 of the circle Rearranging the equation to match this form (x – 6)^2 + (y -- 4)^2 = sqrt(7) ^2 The center is at (6, -4) and the radius is the sqrt(7)
A party store has 54 packs of plates in stock. The packs are either sets of 8 or sets of 12. If the store has 496 total plates in stock, how many plates would the customer buy if he or she buys all of the 12 that the store has in stock?
A) 16
B) 38
C) 192
D) 304
Answer:
a 16
Step-by-step explanation:
16 x 12 = 192 plates
496 total plates - 192 = 304
304 packages of 8 plates
304 / 8 = 38 sets of 8 plates
38 + 16 = 54 packs of plates
Which set of numbers can represent the side lengths, in millimeters, of an obtuse triangle?A. 8, 10, 14B. 9, 12, 15C. 10, 14, 17D. 12, 15, 19
Answer:
A. 8, 10, 14
Step-by-step explanation:
As a rough cut, a triangle will be obtuse if the longest side is about 1.4 or more times the length of the second-longest side. This derives from the relationship in an isosceles right triangle, where the hypotenuse is √2 ≈ 1.414 times the length of the two equal-length sides. If one side is shorter than the other, and the hypotenuse is still 1.414 times the length of the second-longest side, then the triangle is no longer a right triangle, but is an obtuse triangle.
Here, the first selection has a middle-length side of 10 and a longest side of 14, about 1.4 times 10. It is an obtuse triangle.
_____
More rigorously, you can see if the sum of the squares of the short sides is less than the square of the longest side. If so, the triangle is obtuse. (The Law of Cosines will tell you the angle opposite the longest side must have a negative cosine, so must be greater than 90°.)
Our answer choices are ...
A. 8^2 + 10^2 = 164 < 14^2 = 196 . . . . . obtuse
B. 9^2 + 12^2 = 225 = 15^2 . . . . . . . . . . right
C. 10^2 +14^2 = 296 > 17^2 = 289 . . . . . acute
D. 12^2 +15^2 = 369 > 19^2 = 361 . . . . . acute
Answer:
A) 8, 10 and 14
correct on edg2020 :)
the values in the table represent an exponential function.what is the common ratio of the associated geometric sequence
x y
1 8
2 32
3 128
4 512
5 2048
A.4 B.24 C.40 D.8
Answer:
A. 4
Step-by-step explanation:
The common ratio will be the ratio of any adjacent pair of y-values:
32/8 = 128/32 = 512/128 = 2048/512 = 4
Find the mean of the data summarized in the given frequency distribution. compare the computed mean to the actual mean of 51.8 degrees. low temperature (circlef) 40minus44 45minus49 50minus54 55minus59 60minus64 frequency 3 4 10 6 2
Answer:
Mean = 47.52 degrees
Step-by-step explanation:
We will use the following method to find the mean
Class interval Frequency(f) Class Mark(X) fx
40-44 3 42 126
45-49 4 47 188
50-54 10 52 520
55-59 6 57 342
60-64 2 62 124
.........................................................................................................
25 1188
.........................................
The formula for mean is:
Mean = ∑fx / ∑f
= 1188/25
= 47.52 degrees
The computed mean is less than the actual mean of 51.8 degrees ..
simplify. -x/17 = -0.9
a. -15.3
b. 15.3
c. 153
d. -153
Answer:
[tex]\large\boxed{b.\ 15.3}[/tex]
Step-by-step explanation:
[tex]-\dfrac{x}{17}=-0.9\qquad\text{multiply both sides by (-17)}\\\\(-17\!\!\!\!\!\diagup^1)\left(-\dfrac{x}{17\!\!\!\!\!\diagup_1}\right)=(-17)(-0.9)\qquad{/(-)(-)=(+)/}\\\\x=15.3[/tex]
A deposit of $10,000.00 was made to an account the year you were born. After 12 years, the account had earned $6,600.00 in interest. What simple interest rate did the account earn?
Answer:
5.5% per year
Step-by-step explanation:
Using Formula A = P (1 + rt)
Where
A = Final amount = $10,000 + $6,600 = $16,600
P = Principal = Beginning Amount = $10,000
t = time = 12 years
r = rate in $/year (which we need to find)
Assembling the formula
A = P (1 + rt)
16,600 = 10,000 (1 + 12r)
[tex]\frac{16,600}{10,000}[/tex] = 1 + 12r
1.66 = 1 + 12r
1.66 - 1 = 12r
0.66 = 12 r
r = 0.055 = 5.5%
Use Cavalieri's Principle to calculate the exact volume of an oblique cylinder with a height of 20 centimeters and a circular base with a radius of 10 centimeters.
Answer:
The exact volume of an oblique cylinder is [tex]V=2,000\pi\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The Cavalieri's principle states that if two or more figures have the same cross-sectional area at every level and the same height, then the figures have the same volume
so
The volume of the oblique cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]h=20\ cm[/tex]
[tex]r=10\ cm[/tex]
substitute
[tex]V=\pi (10)^{2} (20)[/tex]
[tex]V=2,000\pi\ cm^{3}[/tex]
Answer:
the volume of an oblique cylinder is V=2,000\pi\ cm^{3}
please help asap will mark brainliest
Answer:
10x
Step-by-step explanation:
Note the place values of the value 3 in both of the decimals.
The value of the 3 in 46.132 is in the hundredths place.
The value of the 3 in 8.553 is in the thousandths place.
Divide thousands with hundreds: 1000/100 = 10
The value of the 3 in 46.132 is 10x larger than the value of 3 in 8.553
~
please help asap reward
Hello There!
-The Numbers Ordered From Least To Greatest-
-59 -41 -23 -11
The closer the number is to zero, it is going to be a bigger number than a number far away from zero.
A triangle has vertices of (1, 5), (2, 2), and (6, 3). What are the vertices of the image created by applying the translation (x,y) --> (x+6,y-4)?
Answer:
Step-by-step explanation:
the translation (x,y) --> (x+6,y-4):
(1, 5)--> (1+6,5-4)=(7,1)
(2, 2)--> (2+6,2-4)=(8,- 2)
(6, 3)--> (6+6,3-4)=(12,- 1)
the image of A triangle has vertices of (1, 5), (2, 2), and (6, 3) is :
the triangle has vertices of (7, 1), (8,- 2), and (12, -1)
What is the vertex of the parabola defined by the equation
(x − 2)2 = -12(y − 2)?
A.
(-12, 2)
B.
(2, 2)
C.
(6, 2)
D.
(2, -2)
Answer:
The vertex of the parabola is (2 , 2) ⇒ answer B
Step-by-step explanation:
* Lets revise the equation of a parabola
- The equation is in the form (x − h)² = 4p (y − k), where h and k are the
vertex of the parabola
- If p > 0, the parabola opens up
- If p < 0, the parabola opens down
* Lets solve the problem
∵ The equation of the parabola is (x - h)² = 4p (y - k)
∵ The equation of the parabola is (x - 2)² = -12 (y - 2)
- By comparing the two equations
∴ 4p = -12 ⇒ divide both sides by 4
∴ p = -3 ⇒ -3 < 0
∵ p < 0
∴ The parabola opens down
- From the two equations
∴ h = 2 ⇒ the x-coordinate of the vertex
∴ k = 2 ⇒ the y-coordinate of the vertex
∴ The vertex of the parabola is (2 , 2)
The vertex of the given parabola (x - 2)^2 = -12(y - 2) is at the point (2, 2), which corresponds to Option B.
The vertex of the parabola defined by the equation (x - 2)^2 = -12(y - 2) can be found by identifying the point (h, k), where the equation fits the general form (x \\- h)^2 = 4p(y \\- k). Here, h and k represent the coordinates of the vertex, and p indicates the distance from the vertex to the focus or directrix. The given equation can be rearranged to match the general form with h = 2 and k = 2, making the vertex (2, 2). Hence, the correct answer is Option B.
A mixture of 30 liters of paint is 25% red tint, 30% yellow tint and 45% water. 8 liters of yellow tint are added to the original mixture.
Answer:
Yellow Paint: 0.44736842105%
Red Paint: 0.19736842105%
Water: 0.35526315789%
Step-by-step explanation:
Yelow:
30 x 0.3 = 9
8 + 9 = 17
30 + 8 = 38
17/38 = 0.44736842105%
Red:
30 x 0.25 = 7.5
7.5/38 = 0.19736842105%
Water:
30 x 0.45 = 13.5
13.5/38 = 0.35526315789%
Simplify the following expression by combining like terms.
2 x plus 8 x squared minus 4 x plus 5 x squared2x+8x2−4x+5x2
Answer:
8x^2+3x
Step-by-step explanation:
What I read is 2x+8x^2-4x+5x
combining like terms means putting the terms that have the same variable part together
8x^2 is the only one that doesn't have any terms like it as far as the variable part
so 8x^2+2x-4x+5x
We just need to figure out 2-4+5 which is -2+5=3
So the answer is 8x^2+3x
GEOMETRY PLS HELPPPPPP
ANSWER
(0,2)
EXPLANATION
The mapping point A has coordinate (0,2).
We want to find the coordinates of this point after a rotation of -90° about the origin.
In other words, we want to find the image of this point after a rotation of 90° anticlockwise.
The rule is
[tex](x,y) \to( - y,x)[/tex]
This implies that
[tex](2,0) \to(0,2)[/tex]
Ordered 145 packs of printer paper based on average daily use she knows that the paper will last about 65 days how many packs of printer paper should the manager expect to have after 5 days
Answer:
11.15 packs of paper are used in 5 days; therefore, 133.85 are left
Step-by-step explanation:
Set this up as ratio with days on top and packs of paper on the bottom. Filling in the ratio with the info we have, keeping in mind we are looking for packs of paper left after 5 days:
[tex]\frac{days}{packs}:\frac{65}{145}=\frac{5}{x}[/tex]
Cross multiply to get 65x = 725 and x = 11.15. This represents the number of packs used. To get the number of packs remaining, subtract 11.15 from 145 to get 133.85 remaining after 5 days.
Nathan is flipping a coin three times.
What is the probability that it will land on tails twice and heads once?
Answer:
There is a 1 and 6 chance (16.666...%)
Mary wants to fill in a cylinder vase. At the flower store they told her that the vase should be filled 3/4 for the flowers to last yhe longest. Her cylinder vase has a radius of 2 in and a height of 9 in how much water should mary pour into the vase?
Answer:
84.8 in³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h
The volume Mary will be filling will be 3/4 of the 9-inch height of the vase, so is ...
V = π(2 in)²(3/4·9 in) = 27π in³ ≈ 84.8 in³
_____
Comment on the answer
In more conventional units of measure, that is very nearly 3 pints of water.
A prong horn runs 59 miles per hour, what is the speed in feet per second,to the nearest whole number
Step-by-step explanation:
59 mi/hr × (5280 ft/mi) × (1 hr / 3600 s) = 86.53 ft/s
Rounded to the nearest whole number, the speed is approximately 87 ft/s.
A merchant has coffee worth $60 a pound that she wishes to mix with 50 pounds of coffee worth $90 a pound to get a mixture that she will sell for $70 a pound. How many pounds of the &60 coffee should be used?
Answer:
100 lbs
Step-by-step explanation:
Let x represent the number pounds of $60 coffee that should be used to create the mix. The total cost of the mix will be ...
60x + 90·50 = 70(x+50)
60x +4500 = 70x +3500 . . . . simplify
1000 = 10x . . . . . . . . . . . . . . . . subtract 3500+60x
100 = x . . . . . . . . . . . . . . . . . . . divide by 10
The merchant should use 100 pounds of the $60 coffee.
_____
The cost of the mix parts and the total mix is figured from ...
(dollars/lb)×(lbs) = dollars
Tamie uses 3/4 of a cup of water with 1/8 of a pound of flour to make a paste for a sculpture she is creating. How many cups of water does she need to mix with 1 pound of flour to create the same paste?
For this case we can raise a rule of three:
[tex]\frac {3} {4}[/tex]cup of water ---------> [tex]\frac {1} {8}[/tex] pound of flour
x --------------------------------- > 1 pound of flour
Where:
x: Represents the amount of water that Tamie must use with 1 pound of flour.
[tex]x = \frac {1 * \frac {3} {4}} {\frac {1} {8}}\\x = \frac {\frac {3} {4}} {\frac {1} {8}}\\x = \frac {3 * 8} {4 * 1}\\x = \frac {24} {4}\\x = 6[/tex]
So, Tamie should use 6 cups of water
Answer:
6 cups of water
Write the contrapositive of the conditional statement. Determine whether the contrapositive is true or false. If it is false, find a counterexample.
A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.
A) a non-converse statement is not formed by exchanging the hypothesis and conclusion of the conditional. True
B) A statement not formed by exchanging the hypothesis and conclusion of the conditional is a converse statement. False; an inverse statement is not formed by exchanging the hypothesis and conclusion of the conditional.
C) A non-converse statement is formed by exchanging the hypothesis and conclusion of the conditional. False; an inverse statement is formed by negating both the hypothesis and conclusion of the conditional.
D) A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement. True
Answer:
D is the contrapositive.
Step-by-step explanation:
Contrapositive of if A then B is if not B then not A
Answer:
Option D is correct here.
Step-by-step explanation:
A conditional statement is in the form of if p then q.
A contrapositive statement is when we interchange the hypothesis and conclusion of the sentence and negate both of them. It is in the form of - if not q then not p.
Given statement here is - A converse statement is formed by exchanging the hypothesis and conclusion of the conditional.
This is a true statement. It is the definition of converse statement.
Its contrapositive will be : A statement not formed by exchanging the hypothesis and conclusion of the conditional is not a converse statement.
So, here option D is the contrapositive that is also true.
A rectangle has a length of 9 centimeters and a width of x centimeters. The perimeter of the rectangle is 28 centimeters. What is the value of x?
NEED HELP!!
Answer:
x=5
Knowing that the length of the rectangle is 9, we can simply multiply this by 2 since there are two sides that will equal the same. This gets us 18. If we subtract that from 28, we get 10. There are four sides in a rectangle, meaning we have two sides left. This leaves us to divide 10 by two to get a final answer of the width of the retangle being 5 centimeters.
The value of x, which represents the width of the rectangle, can be found by inserting the given length and perimeter into the perimeter formula of a rectangle, P = 2L + 2W. Then, solve for W to get the value of x.
Explanation:The first step to solve this problem is to understand the formula for the perimeter of a rectangle. This formula is P = 2L + 2W, where P is the perimeter, L is the length and W is the width. We know that the length (L) is 9 cm and the perimeter (P) is 28 cm based on the problem given. We are looking to find the value for x which represents the width (W).
Let's substitute the given values into the formula:
28 = 2(9) + 2W.
This simplifies to:
28 = 18 + 2W.
Now, let's solve for W by subtracting 18 from both sides of the equation:
10 = 2W.
To isolate W, divide both sides of the equation by 2:
W = 5
So, the value of x, which represents the width of the rectangle, is 5 cm.
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If the graphs of the lines in the system of equations above the intersect at (-3,1), what is the value of K/H?
A) 3/2
B) 2
C) 3
D) 6
Answer:
h = 2 and k = 6
Step-by-step explanation:
Since the lines intersect at (- 3, 1) then this is the solution to the system of equations.
That is x = - 3 and y = 1
Substitute these values into the equations and solve for h and k
hx - 4y = - 10
- 3h - 4 = - 10 ( add 4 to both sides )
- 3h = - 6 ( divide both sides by - 3 )
h = 2
Similarly
kx + 3y = - 15
- 3k + 3 = - 15 ( subtract 3 from both sides )
- 3k = - 18 ( divide both sides by - 3 )
k = 6
(01.03)
Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.
square root of the quantity x minus 3 end quantity plus 5 equals x
Answer:
x=7 satisfy the equation, so it is the solution.
x=4 doesn't satisfy the equation so it is extraneous solution.
Step-by-step explanation:
The equation given is:
[tex]\sqrt{x-3}+5=x[/tex]
Adding -5 on both sides
[tex]\sqrt{x-3}=x-5[/tex]
Taking square on both sides
[tex](\sqrt{x-3})^2=(x-5)^2[/tex]
Now solving
[tex]x-3 = x^2 -10x+25\\Arranging\\x^2-10x-x+3+25=0\\x^2-11x+28=0\\Factorizingx^2-7x-4x+28=0\\\\x(x-7)-4(x-7)=0\\(x-4)(x-7)=0\\x-4=0 \,\,and\,\, x-7=0\\x=4 \,\,and\,\, x=7[/tex]
Verifying solutions:
Putting x=4 in the equation
[tex]\sqrt{x-3}+5=x[/tex]
[tex]\sqrt{4-3}+5=4[/tex]
[tex]\sqrt{1}+5=4[/tex]
[tex]1+5=4[/tex]
[tex]6\neq 4[/tex]
So, x=4 doesn't satisfy the equation so it is extraneous solution.
Now Putting x=7 and verifying
[tex]\sqrt{x-3}+5=x[/tex]
[tex]\sqrt{7-3}+5=7[/tex]
[tex]\sqrt{4}+5=7[/tex]
[tex]2+5=7[/tex]
[tex]7=7[/tex]
x=7 satisfy the equation, so it is the solution.
Answer:
= 7
Step-by-step explanation:
4. The cosine function can be made to have the same values as the sine function for each angle by including a shifted _______ in the calculation.
A. amplitude
B. wavelength
C. period
D. phase
Answer: Option D
phase
Step-by-step explanation:
By definition, the cosine function has the following form
[tex]y = cos (x - \phi)[/tex]
Where [tex]\phi[/tex] is known as the phase angle
By definition the sinx function is equal to the cosx function with a phase shift of [tex]\frac{\pi}{2}[/tex]
So if we have the function
[tex]y = cos (x - \phi)[/tex] and we want to transform it into the function [tex]y=sin(x)[/tex] then [tex]\phi = \frac{\pi}{2}[/tex]
Finally
[tex]y = cos(x - \frac{\pi}{2})=sin(x)[/tex]
the answer is the option D
Final answer:
The cosine function aligns with the sine function by introducing a phase shift, typically represented by phi (φ), indicating that D. phase is the correct answer.
Explanation:
The cosine function can be made to have the same values as the sine function for each angle by including a shifted phase in the calculation. This shift is referred to as a phase shift and is typically represented by the Greek letter phi (φ).
In the context of trigonometric functions, a phase shift will slide one function over to match that of another.
Specifically, when the sine function is shifted left by 90 degrees (π/2 radians), it aligns perfectly with the cosine function, indicating that the sine and cosine are out of phase by 90 degrees.
Thus, the correct answer is D. phase.
A pizza shop offers the toppings shown below how many different three topping pizzas can you make ?
Pepperoni
Mushrooms
Sausage
Onion
Ham
A. 6
B. 10
C. 4
D. 5
Answer:
B. 10.
Step-by-step explanation:
This is the number of combinations of 3 from 5.
5C3 = 5! / 3! (5-3)!
= 5*4*3*2*1 / 3*2*1 * 2*1
= 5*4/2*1
= 10.
Answer: 10 i think
Step-by-step explanation:
Given the exponential function f(x) = 54(0.45)x, classify the function as exponential growth or decay and determine the percent rate of growth or decay.
A.Exponential decay, 55% decrease
B.Exponential growth, 45% increase
C.Exponential decay, 45% decrease
D.Exponential growth, 55% increase
Answer:
Option A.Exponential decay, 55% decrease
Step-by-step explanation:
we have
[tex]f(x)=54(0.45)^{x}[/tex]
This is a exponential function of the form
[tex]f(x)=a(b)^{x}[/tex]
where
a is the initial value
b is the base
b=(1+r)
r is the rate of change
In this problem
a=54
b=0.45
so
0.45=1+r
r=0.45-1
r=-0.55
Convert to percentage
r=-55% ------> is negative because is a exponential decay
Answer:
Exponential decay, 55% decrease
Step-by-step explanation:
[tex]f(x) = 54(0.45)^x[/tex]
General exponential growth function is [tex]y=a(1+r)^x[/tex]
exponential growth function is [tex]y=a(1-r)^x[/tex]
The value of 1-r is less than 1 then it is exponential decay
In the given f(x) , the 1-r is 0.45 that is less than 1
So it is exponential decay.
[tex]1-r= 0.45[/tex]
Subtract 1 on both sides
[tex]r=0.55[/tex]
Multiply by 100 to get %
r= 55%
Exponential decay, 55% decrease
Help with vectors! Write each vector in terms of a, b or a and b. Please explain how to do this! I don't know!
Answer:
see explanation
Step-by-step explanation:
Find equivalent routes for the directed lines, that is
(a)
FE = FA + AB + BE = b + a - 3b = a - 2b
(b)
BC = BE + ED + DC = - 3b + a + 2b = a - b
(c)
FC = FA + AB + BE + ED + DC
= b + a - 3b + a + 2b = 2a
suppose that y varies inversely with x, and y=0.2 when x=8. what is the equation for the inverse variation
Answer:
xy = 1.6
Step-by-step explanation:
The equation for inverse variation is
xy = k where k is the constant of variation
8 * .2 = k
1.6 = k
xy = 1.6
1. Use the correct order of operation to solve the following problem: 3 × (50 – 62) ÷ 2 A. 69 B. 18 C. 21 D. 57
Answer:
The correct answer is option B. -18
Step-by-step explanation:
It is given an expression : 3 × (50 – 62) ÷ 2
To find the answer we have to use BODMAS principle
BODMAS means that the order of operations
B- Bracket, O - of , D - Division, M - Multiplication, A - Addition and
S - Subtraction
To find the correct option
Step 1: Do the bracket first
3 × (50 – 62) ÷ 2 = 3 × (-12) ÷ 2
(Multiplication and division are in the order of appearance)
Step 2: Multiplication
3 × (-12) ÷ 2 = -36 ÷ 2
Step 3 : Division
-36 ÷ 2 = -18
The correct option is option B. -18
Answer:
=-18
Step-by-step explanation:
3×(50-62)÷2
Using PEMDAS, we first evaluate the parentheses. 50-62=-12
The new expression becomes
3×⁻12÷2
We now perform the multiplication in the order in which they occur.
3×-12=-36 and -36÷2= -18
=-18