Answer:
(x + 6)² + (y - 2)² = 75
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 6, 2) and r = 5[tex]\sqrt{3}[/tex], hence
(x - (- 6))² + (y - 2)² = (5[tex]\sqrt{3}[/tex] )², that is
(x + 6)² + (y - 2)² = 75
Which is the graph of g(x) = 2x – 1 + 3?
Answer:
The graph in the attached figure
Step-by-step explanation:
we have
[tex]g(x)=2^{x-1}+3[/tex]
This is a exponential function
The domain is the interval ----> (-∞,∞)
All real numbers
The range is the interval ----> (3,∞)
All real numbers greater than 3
The y-intercept of the function is the value of the function when the value of x is equal to zero
For x=0
[tex]g(0)=2^{0-1}+3[/tex]
[tex]g(0)=2^{-1}+3[/tex]
[tex]g(0)=\frac{1}{2} +3[/tex]
[tex]g(0)=3.5[/tex]
The y-intercept is the point (0,3.5)
using a graphing tool
The graph in the attached figure
Answer:
The first answer
Step-by-step explanation:
I took the test
The degree of the function f(x) = -(x + 1)2(2x - 3)(x + 2)2 is
. and its y-intercept is
Answer:
Degree: 5
Y-intercept: 12
Step-by-step explanation:
The given expression is
[tex]f(x)=-(x+1)^2(2x-3)(x+2)^2[/tex]
Since the factors are multiplying, we can analyse the degree of each factor and add them to find the degree of the polynomial.
The degree of the factor [tex]-(x+1)^2[/tex] is 2.
The degree of [tex](2x-3)[/tex] is 1
The degree of [tex](x+2)^2[/tex] is 2
Therefore the degree of the polynomial is 2+1+2=5
To find the y-intercept, we put x=0.
[tex]f(0)=-(0+1)^2(2(0)-3)(0+2)^2[/tex]
[tex]f(0)=-(-3)(4)=12[/tex]
The y-intercept is 12
Which is equivalent to ?
I do not see an illustration.
Can someone answer this please :)
Answer:
32
Step-by-step explanation:
The face closest to us has 4 by 4 unit cubes which is 16 cubes.
There are 2 faces deep in the cubiod so the total is 32 unit cubes.
Answer:
The size of the cuboid is 32, or approximately 5.66 squared.
Step-by-step explanation:
First, find the dimensions of the cuboid.
(4)(4)(2)
Next, multiply the numerics (the values).
(4x4)x2 = 16x2 = 32
The cuboid's volume is 32, or about 5.66 squared.
in the function y-1=1/2(x-6)^2 what effect does the number 6 have on the graph, as compared to the graph y=x^2
Answer: The graph is shifted 6 units to the right.
Step-by-step explanation:
It is important to remember that:
When [tex]f(x-k)[/tex], then the function is shifted "k" units to the right.
Knowing this and given the quadratic parent function [tex]y=x^2[/tex] and the function [tex]y-1=\frac{1}{2}(x-6)^2[/tex], you can observe that one of the transformations is the following:
[tex]f(x-k)[/tex]
Where:
[tex]k=6[/tex]
Therefore, you can notice that the effect is:
The graph is shifted 6 units to the right.
A square piece of gold has an area of 36 square millimeters. How long is each is each side?
Answer:
9
Step-by-step explanation:
What you're going to do is
-take the area and divide it by the amount of sides (a square has 4)
36/4=9
Please help I’m very confused I will mark brainliest
Divide the total weight of granola by the weight of each bar.
768 ounces / 4 ounces per bar = 192
They can make 192 bars.
Which statement below is ALWAYS TRUE?
(A) Complementary angles are both acute angles.
(B) Any two acute angles are complementary angles.
(C) Supplementary and Complementary angles are always adjacent angles.
(D) Supplementary angles are both obtuse angles
The statement that is always true is that supplementary and complementary angles are always adjacent angles.
Explanation:The statement that is ALWAYS TRUE is (C) Supplementary and Complementary angles are always adjacent angles. Supplementary angles are two angles that add up to 180 degrees, while complementary angles are two angles that add up to 90 degrees. Adjacent angles are two angles that have a common vertex and a common side between them. So, it is always true that supplementary and complementary angles are adjacent angles because they share a common side.
10 Points! Drag the tiles to the correct boxes to complete the pairs.
Match each expression to the correct verbal description.
The answers are:
First box: 7 times the cube of the sum of x and 8
Second box: 8 added to the cube of 7x.
Third box: 8 added to 7 and x cubed.
Fourth box: the cube of the sum of 7x and 8.
Why?We are given the expression and we need to macth to the correct verbal description, so we have:
First box:
[tex]7(x+8)x^{3}[/tex]
It's 7 times the cube of the sum of x and 8
Second box:
[tex](7x)^{3}+8[/tex]
We have that "7x" is cubed and then, added to 8, so, it's 8 added to the cube of 7x.
Third box:
[tex]7x^{3}+8[/tex]
We have "7" times "x" cubed and added to 8, so it's 8 added to 7 and x cubed.
Fourth box:
[tex](7x+8)x^{3}[/tex]
We have "7x" added to 8, and the expression is cubed, so, it's the cube of the sum of 7x and 8.
Have a nice day!
Which of these ordered pairs is a solution to the linear inequality y> 3x + 2? (-2,-7)
(-1,-5)
(2,8)
(2,9)
Answer:
(2, 9)Step-by-step explanation:
Put the coordinates of the points to the inequality and check:
y > 3x + 2
for (-2, -7) → x = -2, y = -7
-7 > 3(-2) + 2
-7 > -6 + 2
-7 > -4 FALSE
==========================
for (-1, -5) → x = -1, y = -5
-5 > 3(-1) + 2
-5 > -3 + 2
-5 > -1 FALSE
==========================
for (2, 8) → x = 2, y = 8
8 > 3(2) + 2
8 > 6 + 2
8 > 8 FALSE
===========================
for (2, 9) → x = 2, y = 9
9 > 3(2) + 2
9 > 6 + 2
9 > 8 TRUE
The average of six numbers is 4. If the of two of those numbers is 2, what is the average of the other four numbers?
Answer:
5
Step-by-step explanation:
total sum of the 6 numbers
= 4 ×6
= 24
sum of numbers without the two 2s
= 24 - 2(2)
= 20
average of other 4 numbers
= 20 ÷ 4
= 5
The average of the other four numbers is 5.
How to find the average?
The average of six numbers is 4. If the of two of those numbers is 2.
The total sum of the 6 numbers
= 4 ×6
= 24
The sum of numbers without the two 2s
= 24 - 2(2)
= 20
The average of other 4 numbers
= 20 ÷ 4
= 5
Hence, The average of the other four numbers is 5.
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You randomly select one card from a 52-card deck. Find the probability of selecting the four of spades or the six of diamonds.
Answer:
1/26
Step-by-step explanation:
There's only 1 four of spades and only 1 six of diamonds. So the probability is:
P = P(4 of spades) + P(six of diamonds)
P = 1/52 + 1/52
P = 1/26
The probability of selecting the four of spades or the six of diamonds from a standard 52-card deck is 1/26. This is determined by adding the probabilities of each individual card being drawn since they are mutually exclusive events.
Explanation:The question asks about the probability of selecting a specific card from a standard 52-card deck. To find the probability of selecting either the four of spades or the six of diamonds, we recognize that these are two distinct events. Since there is one four of spades and one six of diamonds in a deck, and there are 52 cards in total, the probability of drawing the four of spades is 1/52 and similarly the probability of drawing the six of diamonds is also 1/52. These events are mutually exclusive, meaning they cannot happen at the same time, so we can simply add the two probabilities together to find the total probability:
Probability(four of spades or six of diamonds) = Probability(four of spades) + Probability(six of diamonds) = 1/52 + 1/52 = 2/52.
Therefore, the probability is 2/52, which can be simplified to 1/26.
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volume of this prism
The volume is (area of cross-section) x (length) .
-- The cross-section is a triangle. The area of a triangle is
Area = (1/2) (base) (height) .
In this one, the base is 9/4 m and the height is 3-1/3 m .
Area = (1/2) (9/4 m) (3-1/3 m)
Area = (1/2) (9/4) (10/3)
Area = 90/24 m² .
-- Volume = (area of cross-section) x (length)
Volume = (90/24 m²) x (7-1/3 m)
Volume = (90/24) x (22/3) m³
Volume = (1,980 / 72) m³
Volume = 27.5 m³
What can you tell about the mean of each distribution?
Answer:
there is a SMALL DIFFERENCE in the mean number of stray cats placed in homes by a new leash on life animal clinic each week and the mean number of stray cats placed in homes by no ruff stuff animal each week
Step-by-step explanation:
i got it right lol
There is a small difference in the mean number of stray cats placed in homes.
We have given the mean of each distribution
What is the mean?
The mean is the mathematical average of a set of two or more numbers that can be computed with the arithmetic mean method or the geometric mean method.
Therefore we can say that,
There is a small difference in the mean number of stray cats placed in homes by a new leash on life animal clinic each week and the mean number of stray cats placed in homes by no ruff stuff animal each week.
Therefore there is a small difference in the mean of each distribution.
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NEED ANSWER NOW. WILL MARK BRAINLIEST
For which distributions is the median the best measure of center?
Select each correct answer.
A bar graph with most of the values hovering around 25 y.
A bar graph with values that climb up past 18 y then descend down to just above 2 y.
A bar graph with bars that gradually rises up to over 20 y then drops off down below 2 y.
A bar graph with bars that gradually rises up to over 24 y then drops off down below 2 y.
Answer:
it would be c beacuse i did the test so ya
Answer:
b
Step-by-step explanation:
The equation T^2=A^3 shows the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A, in astronomical units, AU. If the orbital period of planet Y is twice the orbital period of planet X, by what factor is the mean distance increased?
2^1/3
2^1/2
2^2/3
2^3/2
Thank you!
Answer:
2^3/2
Step-by-step explanation:
The question is on formulae variation
Given T²=A³.....................the relationship between a planet’s orbital period, T, and the planet’s mean distance from the sun, A
Making T subject of the formulae
T²=A³.............................square root both sides
T= √A³ OR (A³)^1/2
if the orbital period of planet Y is twice the orbital period of planet X then,
Y=2T
Y=2× √A³
Y=2×(A³)^1/2
Applying the laws of indices
Y=2×(A)^(3×1/2)
Y=2×(A)^3/2
Compare
A^3/2 and 2A^3/2
The mean distance increased by 2^3/2
Given: circle k(O), m LM = 164°, m WK = 68°, m∠MLK = 65°. Find: m∠LMW
Answer:
The measure of angle LMW is [tex]m\angle LMW=67\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of arc MW
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK][/tex]
substitute the given values
[tex]65\°=\frac{1}{2}[arc\ MW+68\°][/tex]
[tex]130\°=[arc\ MW+68\°][/tex]
[tex]arc\ MW=130\°-68\°=62\°[/tex]
step 2
Find the measure of arc LK
we know that
[tex]arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\°[/tex] -----> by complete circle
substitute the given values
[tex]164\°+62\°+68\°+arc\ LK=360\°[/tex]
[tex]294\°+arc\ LK=360\°[/tex]
[tex]arc\ LK=360\°-294\°=66\°[/tex]
step 3
Find the measure of angle LMW
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK][/tex]
substitute the given values
[tex]m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°[/tex]
Applying the inscribed angle theorem, the measure of angle LMW is found as: 67°.
What is the Inscribed Angle Theorem?According to the inscribed angle theorem, the measure of an inscribed angle is half the measure of the arc that is intercepted.
Given:
m(LM) = 164°m(WK) = 68°m∠MLK = 65°Find m(MK):
m(MK) = 2(m∠MLK) (inscribed angle theorem)
Substitute
m(MK) = 2(65°)
m(MK) = 130°
Find m(LK):
m(LK) = 360° - m(LM) - m(MK) (full circle)
Substitute
m(LK) = 360° - 164° - 130°
m(LK) = 66°
Therefore:
m∠LMW = 1/2[m(LK) + m(WK) (inscribed angle theorem)
Substitute
m∠LMW = 1/2[66° + 68°]
m∠LMW = 1/2[134°]
m∠LMW = 67°
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PLEASE HELP ME ILL GIVE YOU POINTS
Answer: I think the answer is the second box.
Step-by-step explanation: It says 20 males have watched the show. I hope I helped you. If I am wrong, tell me in a polite way. :D
Hello there! The answer is the second chart, or B.
To find the answer, look at the parts of the question.
Let's start in the beginning. Note how it says "Of the 80 participants, 30 were male and 50 were female". This means that, looking at the options, in the "total" row, there should be a value for "30" by male, "50" by female and 80 at the bottom. This means that it cannot be A since this option says that there were 80 females and 80 males and 160 total, or C since it says there are 80 males and 55 females with a total of 135.
Next, it says that 45 have watched the show and 35 have not. If you look at the options left B and D, the only one the has these numbers for have and have not watched is B, making this the correct answer.
I hope this helps and have a great rest of your day! :)
The sum of x and y is greater than 0. When y is subtracted from x, the difference is less than or equal to 0. Which system of inequalities could you use to solve for x and y?
PLEASE ANSWER ASAP!!!!
Answer:
[tex]x+y>0[/tex]
[tex]x-y\leq 0[/tex]
Step-by-step explanation:
Given that the sum of x and y is greater than 0.
So we can write inequality [tex]x+y>0[/tex].
When y is subtracted from x, the difference is less than or equal to 0.
So the next inequality is [tex]x-y\leq 0[/tex].
Hence required system of inequalities that can be used to solve for x and y is :
[tex]x+y>0[/tex]
[tex]x-y\leq 0[/tex]
Answer:
100% sure its A
Step-by-step explanation:
I took the test
You are standing 16 ft. from the center of a circular swimming pool. The distance from you to a point of tangency is 25 ft. What is the approximate DIAMETER of the pool?
Check the picture below.
recall the diameter is twice as long as the radius, thus d = 2r = 38.42 or rounded up to 38.
Mr. Cooper is building a playset in his backyard for his kids. He has a made a scale drawing of the playset to help him estimate the amounts of building materials he needs to purchase. Part of the playset includes a rectangular sandbox, which has a length of 5 feet and a width of 7 feet. On the scale drawing, the length of the sandbox is 2 A. The scale used in the drawing is = 1 foot. B. On the scale drawing, the width of the sandbox is inches. C. If Mr. Cooper decides to make a new scale drawing of the playset, in which he uses a scale of inch = 1 foot, all of the dimensions in the old drawing will be multiplied by a factor of .
Answer:
If Mr. Cooper decides to make a new scale drawing of the play set, in which he uses a scale of inch = 1 foot, all of the dimensions in the old drawing will be multiplied by a factor of ⇒ the last answer
Step-by-step explanation:
* Lets study what is the meaning of the scale factor
- To find a scale factor between two similar figures
# Find two corresponding sides and write the ratio of the two sides.
# If you begin with the smaller figure, your scale factor will be less
than one.
# If you begin with the larger figure, your scale factor will be greater
than one
* Now lets solve the problem
- The rectangular sandbox, has a length of 5 feet and a width of
7 feet
- On the scale drawing, the length of the sandbox is 2 inches
- The actual sandbox and the drawing sandbox are similar
∵ The length of the actual sandbox is 5 feet
∵ The drawing length is 2 inches
∵ 1 foot = 12 inches
∴ The scale factor is 2/(5 × 12) = 1/30
* That means each actual dimensions will multiply by 1/30 to find
the drawing dimensions
∴ The drawing length of the sandbox = 5 × 12 × 1/30 = 2 inches
∴ The drawing width of the sandbox = 7 × 12 × 1/30 = 2.8 inches
* All of the dimensions in the old drawing will be multiplied by
a factor of 1/30
1/2 inch
3 3/4
2
i know im 2 years late but hopefully this helps someone else
What is the area of the scalene triangle shown (ABC), if AO = 10 cm, CO = 2 cm, BC = 5 cm, and AB = 12.20 cm? (Triangle AOB is a right triangle.)
Answer:
The area of triangle ABC is [tex]25\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of triangle ABC is equal to the area of triangle ABO minus the area of triangle ACO
see the attached figure to better understand the problem
step 1
Find the area of triangle ABO
The area is equal to
[tex]A=\frac{1}{2}(AO)(BO)[/tex]
substitute values
[tex]A=\frac{1}{2}(10)(5+2)=35\ cm^{2}[/tex]
step 2
Find the area of triangle ACO
The area is equal to
[tex]A=\frac{1}{2}(AO)(CO)[/tex]
substitute values
[tex]A=\frac{1}{2}(10)(2)=10\ cm^{2}[/tex]
step 3
Find the area of triangle ABC
[tex]35\ cm^{2}-10\ cm^{2}=25\ cm^{2}[/tex]
The sum of two numbers is 13. Two times the first number minus three times the second number is one. If you let x stand for the first number and y for the second number what are the two numbers?
please and thanks!
Answer: X = 8 And Y = 5 "First Choice Letter A"
Step-by-step explanation: x + y = 13......x = 13 - y
2x - 3y = 1
2(13 - y) - 3y = 1
26 - 2y - 3y = 1
-2y - 3y = 1 - 26
-5y = -25
y = -25/-5
y = 5
x + y = 13
x + 5 = 13
x = 13 - 5
x = 8
so, x = 8 and y = 5
the equation y=-3x^2 describes a parabola what way does the parabola open
Answer:
Downwards.
Step-by-step explanation:
The coefficient of x^2 is negative (-3) so it opens downwards. All values of x will be 0 or negative.
The sequence is recursive. Find the value of the next term in the sequence 7, 1, -5, -11, -17,
Answer:
-23
Step-by-step explanation:
Each term is 6 less than the past term. Hopw this helps!
There is no "standard" way to solve an exercise like this: you just have to eyeball the sequence and try to find/guess the pattern.
The most common (and easy!) examples are arithmetic or geometric sequence, where the difference or ratio between two consecutive terms is constant.
This is one of those cases: this is an arithmetic sequence, because you obtain every next term by subtracting 6 from the previous one:
[tex]a_1 = 7\\a_2 = a_1-6 = 7-6 = 1\\a_3 = a_2-6 = 1-6 = -5\\a_4 = a_3-6 = -5-6 = -11\\a_5 = a_4-6 = -11-6 = -17[/tex]
So, we can deduce
[tex]a_6 = a_5-6 = -17-6 = -23[/tex]
If the ratio of side lengths of similar polygons is 6:11, what is the ratio of perimeters
Answer:
6 : 11
Step-by-step explanation:
the ratio 6 : 11 applies to all linear measure in the similar polygons
Both side lengths and perimeter are linear, hence
ratio of both is 6 : 11
Need a two step equation for number 3
so the bike costs $129, but she already has $24 saved, then she'll be saving $3 per week so let's take a peek at a table of those savings
week 1..................... total amount......... 24 + 3(1)
week 2..................... total amount......... 24 + 3(2)
week 3..................... total amount......... 24 + 3(3)
week 4..................... total amount......... 24 + 3(4)
week 5..................... total amount......... 24 + 3(5)
week w..................... total amount......... 24 + 3(w)
[tex]\bf \stackrel{\textit{total savings}}{s(x)}=\stackrel{\textit{initial amount}}{24}+\stackrel{\textit{weekly savings}}{3w} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{cost of the bike}}{129}=24+3w\implies 105=3w\implies \cfrac{105}{3}=w\implies 35=w[/tex]
Answer:
24 + 3x = 129
35 weeks
Step-by-step explanation:
She already has 24 dollars saved, but will save 3 dollars every week. Use x to represent the number of weeks. In total she will save 129.
Solve for x using the equation:
24-24 + 3x = 129-24
3x = 105
3x/3 = 105/3
x= 35
12 Times 15
My calculator said it was 160
Answer:
False
Step-by-step explanation:
12 × 15 = 180
12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12 = 180
Answer:
180.
Step-by-step explanation:
Something wrong there. Mine says 180.
12 * 15 = 12*10 + 12*5
= 120 + 60
= 180.
Which of the following comparisons is FALSE?
a. 4 liters < 1 gallon b. 1 foot < 1 meter c. 25 grams < 1 ounce d. 10 kilometers < 9 miles
Answer:
A
Step-by-step explanation:
Let's check each one-by-one.
a.
we know 3.79 liters is 1 gallon, so 4 liters IS NOT LESS THAN 1 gallon
THis is false.
b.
We know 1 feet is 0.30 meters, so definitely 1 foot is less than 1 meter.
This is true.
c.
we know around 28.35 grams is 1 ounce, so definitely 25 grams is less than 1 ounce.
THis is true.
d.
We know 1 km is approximately 0.62 miles so 10 km would be around 0.62*10 = 6.2 miles
So definitely 9 miles IS GREATER than 10 km.
THis is true.
So answer choice A is false, only.
Aaron is proving that the slope between any two points on a straight line is the same. He has already proven that triangles 1 and 2 are similar.
Drag statements and reasons to complete the proof.
i think this is the right one sorry if im wrong
Answer: The answers are:
row 1- slope from P to Q = F/E
row 2- definition of slope
row 3- F´/E´ = F/E
I think that this is the correct picture was the correct one for your problem.