Complete question :
A 12-foot by 15-foot patio is increased by placing a stone border around the patio. The width of the border is the same all around the patio.The perimeter of the patio after it is expanded is 74 feet. The equation which represents x, the width of the border is 2[(12+2x)+15+2x)]=74. What is the width of the border?
1) 2 1/2 feet
2) 3 feet
4) 5 feet
5) 8 1/2 feet
Answer:
2.5
Step-by-step explanation:
Solving for X in the perimeter equation :
2[(12+2x)+15+2x)]=74
Open the bracket
2[(12 + 2x + 15 + 2x)] = 74
2(27 + 4x) = 74
54 + 8x = 74
8x = 74 - 54
8x = 20
x = 20/8
x = 2.5
Hence, width fo border = 2.5
Geometric sequence
Answer options:
A) an=54(-3)n-1
B) an=-2(-3)n-1
C) an=25(-2)n-1
D) an=4(-5)n-1
PLEASE ANSWER, NO LINKS
Answer:
D P/B=T
Step-by-step explanation:
\dfrac{x^2}{46}+\dfrac{(y+8)^2}{26}=1 46 x 2 + 26 (y+8) 2 =1start fraction, x, squared, divided by, 46, end fraction, plus, start fraction, left parenthesis, y, plus, 8, right parenthesis, squared, divided by, 26, end fraction, equals, 1 What are the foci of this ellipse? Choose 1 answer:
Answer:
The focus of the ellipse are;
(-12·√(10), -8) and (12·√(10), -8)
Step-by-step explanation:
The given equation for the ellipse is presented as follows;
[tex]\dfrac{x^2}{46} + \dfrac{(y + 8)^2}{26} = 1[/tex]
From the general equation of the ellipse, we have;
[tex]\dfrac{(x - h)^2}{a^2} + \dfrac{(y - k)^2}{b^2} = 1[/tex]
The focus of the ellipse are, (h - c₁, k) and (h + c₁, k)
By comparison, we get;
h = 0, k = -8, a = 46, b = 26
We have;
c² = a² - b²
c² = 46² - 26² = 1440
c = 12·√(10)
The focus of the ellipse are therefore;
(0 - 12·√(10), -8) = (-12·√(10), -8), and (0 + 12·√(10), -8) = (12·√(10), -8).
Write a function for the line that includes the points (4,−5) and (8,−7).
Answer:imma try to help you
Step-by-step explanation:
The function for the line can be written as F(x) = -(1/2)x - 3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that line that includes the points (4,−5) and (8,−7).
The slope will be calculated as,
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -7 +5 ) / ( 8 - 4)
Slope = -2 / 4= -1/2
The y-intercept will be calculated as,
y = mx + c
-7 = -1/2 x 8 + c
-7 = -4 + c
c = -3
The equation can be written as,
y = mx + c
y= -1/2(x) - 3
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if the polygon is a decagon, then it has ____sides?
Answer:
10 sides
Step-by-step explanation:
Deca means 10 (decameter/decahedron/decagon)
Answer: 10 sides
Step-by-step explanation:
There are a list of suffixes for a "-gon"
- Pentagon=5 sides
- Hexagon=6 sides
- Heptagon=7 sides
- Octagon=8 sides
- Nonagon=9 sides
- Decagon=10 sides
- Hendecagon=11 sides
- Dodecagon=12 sides
Therefore, if the polygon is a decagon, then it has 10 sides
Hope this helps!! :)
Please let me know if you have any questions
What is the image of (-4,-4) after a dilation by a scale factor of 3 centered at the
origin?
Answer:
(-12, -12)
Step-by-step explanation:
Since the scale factor is 3, you would multiply the x-coordinate and y-coordinate by it.
-4×3=-12
Hope this helps!!
Witch fraction is equivalent to 33/200
Answer:
16.5/100
Step-by-step explanation:
An equivalent fraction to 33/200 could be 66/400.
Please help!!
Find the radius
Answer:
The radius is 20 units.
Step-by-step explanation:
(r)^2 + 21^2 = (r+9)^2
r^2 + 441 = r^2 + 18r + 81
360 - 18r = 0
360 = 18r
20 = r
image below answer correcctly and u will have brainliest no links i or i wiil report u
Answer:
40.32
Step-by-step explanation:
lengthxwidthxheight
540g and 2 kg
ok solve this question
Answer: Step-by-step explanation:
540g and 2 kg=2540g
POSSIBLE POINTS: 1.43
Cell phone Plan A costs $70 per month and comes with a free $500 phone. Cell phone Plan B costs $50 per month but does not
come with a phone. If you buy the $500 phone and choose Plan B, how many months is it until your cost is the same as Plan A's?
Answer:
it will take 25 months until the cost is the same.
500 / 20 = 25
Step-by-step explanation:
Find the fourth-degree polynomial function with zeros 4, -4, 4i , and -4i . Write the function in factored form.
Given:
A fourth-degree polynomial function has zeros 4, -4, 4i , and -4i .
To find:
The fourth-degree polynomial function in factored form.
Solution:
The factor for of nth degree polynomial is:
[tex]P(x)=(x-a_1)(x-a_2)...(x-a_n)[/tex]
Where, [tex]a_1,a_2,...,a_n[/tex] are n zeros of the polynomial.
It is given that a fourth-degree polynomial function has zeros 4, -4, 4i , and -4i. So, the factor form of given polynomial is:
[tex]P(x)=(x-4)(x-(-4))(x-4i)(x-(-4i))[/tex]
[tex]P(x)=(x-4)(x+4)(x-4i)(x+4i)[/tex]
[tex]P(x)=(x-4)(x+4)(x^2-(4i)^2)[/tex] [tex][\because a^2-b^2=(a-b)(a+b)][/tex]
On further simplification, we get
[tex]P(x)=(x-4)(x+4)(x^2-4^2i^2)[/tex]
[tex]P(x)=(x-4)(x+4)(x^2+16)[/tex] [tex][\because i^2=-1][/tex]
Therefore, the required fourth degree polynomial is [tex]P(x)=(x-4)(x+4)(x^2+16)[/tex].
The fourth degree polynomial is given by f(x) = (x - 4)(x + 4)(x + 4i)(x - 4i)
Polynomial
Polynomial is an expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.
Polynomials can be classified based on degree as linear, quadratic, cubic, fourth degree.
Let f(x) represent the function with zeros 4, -4, 4i , and -4i. Hence:
x = 4; x = -4; x = 4i; x = -4i
x - 4 = 0; x + 4 = 0; x - 4i = 0; x + 4i = 0
f(x) = (x - 4)(x + 4)(x + 4i)(x - 4i)
The fourth degree polynomial is given by f(x) = (x - 4)(x + 4)(x + 4i)(x - 4i)
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If mAD
-
(17x + 2); mAC = (7x – 10), and m_ABC = (4x + 15), find m_ABC.
A
B
G
C С
D
Answer:
36
Step-by-step explanation:
you add the first two the order of operations then you do big and little
Applying the angle of intersecting tangents theorem, m∠ABC = 99°
What is the Angle of Intersecting Tangents Theorem?If two tangents intersect and form an angle outside a circle, based on the angle of intersecting tangents theorem, the angle formed equals half the positive difference of the intercepted arcs.
Given the following:
m(AD) = (17x + 2)m(AC) = (7x – 10)m∠ABC = (4x + 15),Apply the angle of intersecting tangents theorem:
m∠ABC = 1/2[m(AD) - m(AC)]
Substitute
4x + 15 = 1/2[(17x + 2) - (7x - 10)]
2(4x + 15) = 17x + 2 - 7x + 10
8x + 30 = 10x - 12
8x - 10x = -30 - 12
-2x = -42
x = -42/-2
x = 21
m∠ABC = (4x + 15)
Plug in the value of x
m∠ABC = 4(21) + 15 = 99°
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What is the slope of the line passing through the points (-5, -4) and (-1, 6)?
A.2/5
B.-5/2
C.-2/5
D.5/2
Answer:
5/2
Step-by-step explanation:
Prove or disprove that the point (51−−√, 7) lies on the circle centered at the origin and containing the point (6, 8).
Answer:
Yes, it lies on the circle.
Step-by-step explanation:
The actual question is:
"Prove or disprove that the point (√51, 7) lies on the circle centered at the origin and containing the point (6, 8)."
The equation of a circle of radius R and centered at the point (a, b) is:
(x - a)^2 + (y - b)^2 = R^2
In this case we have a circle centered at the origin, then: (a, b) = (0, 0)
And the equation becomes:
(x - 0)^2 + (y - 0)^2 = R^2
x^2 + y^2 = R^2
We also know that this circle contains the point (6, 8), then we can find the radius of our circle if we replace x by 6 and y by 8.
6^2 + 8^2 = R^2
100 = R^2
√100 = 10 = R
Then the circle equation is:
x^2 + y^2 = 10^2
Now let's see if the point (√51, 7) is a solution of the above equation:
(√51)^2 + ( 7)^2 = 10^2 = 100
51 + 49 = 100
100 = 100
This is true, so we can conclude that (√51, 7) is a solution of the circle equation, so the point lies on the defined circle.
find the area of each figure. Round your answers to the nearest hundredth 7-10
Answer:
7.
area of parallelogram=base×height=19×7.8=148.2yd²
8.
area of semi circle=1/2[π(d/2)²]=
π×44²/8=760.265in²
9.
area of rectangle =length ×breadth
=16.4×11.8=193.52ft²
10.
area of triangle =1/2 ×base×height=1/2×20.4×14.6=148.92in²
Area of the given shapes are:
parallelogram: 148.2yd²Rectangle: 193.52 ft²Semicircle: 760.265 in²triangle: 148.92 in²What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Given, Four shapes and we need to calculate the area.
For parallelogram:
area of parallelogram = base×height
area of parallelogram = 19×7.8 = 148.2yd²
For, Semicircle:
area of semi circle= 1/2 [π(d/2)²]
area of semi circle= π×44²/8 = 760.265 in²
For Rectangle:
area of rectangle = length ×breadth
area of rectangle = 16.4×11.8 = 193.52 ft²
For triangle:
area of triangle = 1/2 ×base×height
area of triangle = 1/2×20.4×14.6 = 148.92in²
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Determine o valor da expressão: -1 + 6 x (7 – 4 ÷ 2)
Answer:
29 is the correct answer. Hope you like my answer.
What is the volume of the rectangular prism?
I need a lot of help bro
1. A lab has two bacteria cultures. Culture A
contains 8 × 104 bacteria, and Culture B
contains 4 × 106 bacteria. How do the two
cultures compare in size?
A. Culture A contains twice as many
bacteria as Culture B.
B. Culture A contains 1
2
as many bacteria as
Culture B.
C. Culture A contains 1
25
as many bacteria as
Culture B.
D. Culture A contains 1
50
as many bacteria as culture B.
Answer:
A.
Step-by-step explanation:
To get the answer, you will need to divide the number of bacterias that Culture A has by the number of bacterias that Culture B has.
Size=(8*104)/(4*104)
=2
So, A will be the correct answer. (I have corrected your answer's no. of bacterias that Culture B contains as 104.)
An elevator goes down 3 floors, up 5 floors, and finally down 7 floors, Write an expression that represents the total number of floors the elevator traveled
Answer: -5
Step-by-step explanation:so the elwvator goes down 3 floors so -3+5-7=-5 because 3-5=2 and 2-7=-5 hope this helps
Find the volume of the figure
HELP ME PLEASE IM STRUGGLING!!
Answer:
I got great news for you! I have a wonderful grade in math...
Anyway the answer is 6,318
Step-by-step explanation:
Ok so 18x13 is 234. 234x21 is 4,914. Now we have the volume of the box (4,914).
as we know 18x13 is 234. So if we multiply 234x12 we get 2,808. So now all we have to do is divide 2,808 by 2. That gives us 1,404.
1,404+4,914=6,318
So now WALLA we have our answer.
what is a non example substitution method?
Answer:
The substitution method consists of solving for in one of the equations, basically the one that is easiest, and substituting the resulting expression in the other. With this, the second equation is converted into a linear equation with one unknown, which is solved by simply solving for.
Step-by-step explanation:
l hope and this can help you
Can someone help pls
Answer:
F
Step-by-step explanation:
I'm guessing wjdhksdjene
Answer:
J
Step-by-step explanation:
The answer is option J
BRAINILIEST PLEASEI need help plz will give brainliest alos need how u got the answer
Answer: B. x = 16/3
3/5x + 1/2 = 3/4x -3/10
minus 3/4x on both sides
-3/20x + 1/2 = -3/10
minus 1/2 on both sides
-3/20x = -3/10
multiply both sides by 20/-3
x = 16/3
Answer:
B) [tex]x=\frac{16}{3}[/tex]
Step-by-step explanation:
[tex]\frac{3}{5}x+\frac{1}{2}=\frac{3}{4}x-\frac{3}{10}[/tex]
[tex]\frac{12}{20}x+\frac{10}{20}=\frac{15}{20}x-\frac{6}{20}[/tex]
[tex]\frac{10}{20}=\frac{3}{20}x-\frac{6}{20}[/tex]
[tex]\frac{16}{20}=\frac{3}{20}x[/tex]
[tex]16=3x[/tex]
[tex]\frac{16}{3}=x[/tex]
Therefore, your answer is B) [tex]x=\frac{16}{3}[/tex]
Which of the following is an arithmetic sequence?
© 0, 2, 4, 6, ...
O 1, 2, 4, 8, ...
O 1, 4, 8, 13, ...
Place these numbers in order from least to greatest: -4.5, 6, 5.7, 0, -2, -14
Answer:
-14, -4.5, -2, 0, 5.7, 6
Step-by-step explanation:
5(y + 2/5) = -13
Solve for y
Show or explain your method
Answer:
I attached both the work and explanation down below. Hope it helps!
Ray invested $300 in Stock A
and $750 in Stock B. Since then,
the value of Stock A has increased
by 15% each year and the value of
Stock B has decreased by 12% each
year. After 4 years, which statement
is true regarding the value of
his investments?
The claim that Stock A is worth $74.93 more than Stock B is accurate regarding the value of his investments after 4 years is
What is meant by value?Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Location value plus face value equals value. For illustration: If we take 45 into account. Here, the fourth digit is in the tens column. The value a digit in a number represents based on where it is in the number is known as place value. For instance, 700 is the place value of 7 in 3,743. Nevertheless, 7,000 or 7,000 is the place value of 7 in 7,432.To learn more about value, refer to:
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Shannon participated in a national math contest by taking a math test. The test results followed a normal distribution with a mean score of 72.6 points out of 100 and a standard deviation of 8.7. Shannon received a score of 81 points. Shannon thinks she performed better than 68% of the students in the contest
Answer:
.
Step-by-step explanation:
What is the slope of the line?
Answer:
3/1
Step-by-step explanation:
is the slop of this graph