As seen in the diagram below, Hawa is building a walkway with a width of a feet to go
around a swimming pool that measures 19 feet by 6 feet. If the total area of the pool
and the walkway will be 770 square feet, how wide should the walkway be?
Answers
Answer:
8 feet
Step-by-step explanation:
you have to calculate :(19+2x)(6+2x)=770
you will get X1=8,X2= negetive some value but measurement cant be negative .if you put X=8 you'll find LHS=RHS
Answer:
[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex] or [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]
Step-by-step explanation:
So first you need to find the area of the swimming pool:
19*6 = 114
Next you add the area of the swimming pool and the area of the walkway:
114 + 770 = 884
After this you solve for x using this equation:
(19 +2x) * (6 + 2x) = 884
This would normally find the area of the whole swimming pool area and the walkway but because we know that we can use it to solve for x.
The step-by-step is this:
[tex]4x^{2} +50x+114=884[/tex]
[tex]4x^2+50x+114-884=884-884[/tex]
[tex]4x^2+50x+114-884=0[/tex]
Now we'll use the quadratic formula to simplify it farther:
[tex]x= \frac{-(50) + \sqrt{(50)^2-4(4)(-770)} }{2(4)}[/tex]
[tex]x=\frac{-50 + or - \sqrt{14820} }{8}[/tex]
[tex]x= \frac{-25}{4}+\frac{1}{4} \sqrt{3705}[/tex] or [tex]x= \frac{-25}{4} + \frac{-1}{4}\sqrt{3705}[/tex]
Related Questions
9x-7=-52
Show all work and justify each step
Answers
Answer:
x = -5
Step-by-step explanation:
9x - 7 = -52
we want to single out x,
add 7 to both sides to be one step closer to getting x alone
9x - 7 + 7 = -52 + 7
9x = -45
divided both sides by 9 to get x alone
9x / 9 = -45 / 9
x = -5
Let me know if you need any clarification!
[tex] 9x - 7 = - 52[/tex]
Firstly rearrange the variable on the left side of the equation...
[tex]9x = - 52 + 7[/tex]
Calculate the sum or differences
[tex]9x = - 45[/tex]
[tex]x = - \frac{45}{9} \\ [/tex]
[tex]x = - 5[/tex]
:)
..
When given
Slope= -6/5
Y-intercept= 2
What is this in Point-Slope form?
Answers
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{Slope = -6/5, Goes through (0, 2)}[/tex]
Find: [tex]\textsf{The equation in point-slope form}[/tex]
Solution: We need to take the values that were given to us and plug them into the point-slope form. It doesn't seem like the problem is asking for anything more than that so we will leave it at that.
Plug in the values
[tex]\textsf{y - y}_1\textsf{ = m(x - x}_1\textsf{)}[/tex][tex]\textsf{y - 2 = -6/5(x - 0)}[/tex]Since the problem is just asking for the equation in point-slope form the final expression would be y - 2 = -6/5(x - 0).
Answer:
[tex]\sf y - 2 = -\dfrac{6}{5}(x - 0)[/tex]
Step-by-step explanation:
[tex]\sf \large \underline{\textsf{Given:}}\ \textsf{a line with a slope of $-\dfrac{6}{5}$, and a y-intercept of $2$}[/tex]
We're given a y-intercept of 2, but using the slope-intercept form, we can immediately determine that x = 0. Hence, the given point is (0, 2).
Then, we substitute these values into the Point-Slope Form to find the equation.
Here are both forms for future reference:
⇒ Slope-Intercept Form: y = mx + b
[ Where: m is the slope, and b is the y-intercept (when x = 0). ]
⇒ Point-Slope Form: y - y₁ = m(x - x₁)
[ Where: m is the slope, and (x₁, y₁) is a given point. ]
Substitute the values into the Point-Slope Form:
[tex]\sf\\\implies y - y_1 = m(x - x_1)\\\\\implies y - 2 = -\dfrac{6}{5}(x - 0)[/tex]
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What is the y-intercept of the function f(x) = 2.3*?
A. (0,6)
B. (2,0)
C. (0,2)
OD. (0,3)
Answers
Analyze the graph of the cube root function shown
on the right to determine the transformations of
the parent function. Then, determine the values of
a, h, and k in the general equation.
y = a√√x-h+k
h =
k =
DONE✔
Answers
The values of a, h, and k in the general equation is h=1, k=4 and a=2
What is parent function?The function which can be transformed into different ways is the parent function.
On a coordinate plane, a cubic function approaches the x-axis in quadrant 2, crosses the y-axis at (0, 2), has an inflection point at (1, 4), and the goes through (2, 6).
The given function is
y =a³ √(x -h) + k
Put the coordinate (0,2) in the equation, we get
2 = a³ √(0 -h) + k..................(1)
Plug (1, 4), we have
4 = a³ √(1 -h) + k..................(2)
Plug (2, 6), we have
6 = a³ √(2 -h) + k..................(3)
On solving these three equations, we have
h=1
k=4
a=2
Thus, value of h is 1, k is 4 and a is 2.
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Answer:
the rest of the answers are:
C
B
C
A
D F
A C D
A
D
H= 1
K=4
A=2
Step-by-step explanation:
The price of a coat is $65. In sale, the price is reduced by 15%. What is the price of the coat in sale?
Answers
Step-by-Step Explanation:
Price of the Coat = $65
Step 1 :- Find 15% of $65.
= 15/100 * 65
= 975/100
=> 9.75
15% of $65 = $9.75
Step. 2 :- Subtract $9.75 from $65.
= 65 - 9.75
=> 55.25
Price of the Coat in Sale = $55.25
A gym has 65 members. If 35 are men and the
rest are women, what is the ratio of the female
members to the total members of the gym?
Answers
Answer:
Step-by-step explanation:
số nữ là 65- 35= 30
vậy tỷ lệ số tv nữ trên tổng số thành viên của phòng tập là 30/65 = 6/13
What is 2*4*6.5*24.5
Answers
Answer:
1274
it is 1274
Step-by-step explanation:
mark as brainlest for the answer thankyou
LK
2(x+2y-x-1⁄2y+3);
When 2(5
4
01x + 2 y +6
Ox+2y+6
07x+8y+6
0176x+4y+3
is simplified, what is the resulting expression?
Answers
You are asked to create a new computer password made up of 4 digits followed
by 3 letters.
Determine how many different computer passwords are possible if digits and
letters cannot be repeated.
Answers
Answer:if we start with 26 letters in the English/Latin alphabet: 26*25*24*23*
and modern Arabic numerals 0–9,
10*9 do the math by multiplying all
Number of dispositions of 4 letters without repetitions of the alphabet (26 letters): 26*25*24*23=358800. 2-digit numbers without repetitions:10*9=90. Number of passwords with 4 letters and 2-digit number without repetitions:
a) if the 2-digit numbers must be in one single position (examples:….XB73DY……..GZ57FE): 358800*90 = 32,292,000.
b) if the 2-digit numbers can be in each of the 5 possible positions (ex.:…73XBDY…X73BDY..XB73DY..XBD73Y..XBDY73…) 5*358800*90=161,460,000.
c) if both digits can be in (C6;2) = 6*5/2= 15 positions (ex.: 7XB3DY…X73BDY…..) 15*358800*90=484,380,000.26*25*24*23*10*9 = 32,292,000
Step-by-step explanation:
4. Write the function of a linear equation that includes the
points (1,3) and (2,9).
Answers
Answer:
y = 6x - 3
Step-by-step explanation:
the equation of a line in slope- intercept form ( linear function ) is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 3 ) and (x₂, y₂ ) = (2, 9 )
m = [tex]\frac{9-3}{2-1}[/tex] = [tex]\frac{6}{1}[/tex] = 6 , then
y = 6x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 3 ) , then
3 = 6 + c ⇒ c = 3 - 6 = - 3
y = 6x - 3 ← equation of linear function
Drag each tile to the correct box. Not all tiles will be used.
Consider function f.
Place the steps for finding in the correct order.
Answers
If the function is f(x) = √(7x – 21). Then the inverse function of the function will be f⁻¹(x) = (1/7) x² + 3.
What is inverse of a function?Let the function will be
f: X → Y
Then the inverse function will be
f⁻¹: Y → X
The function is given below.
f(x) = √(7x – 21)
Then the inverse function will be
x = √[7{f⁻¹(x)} – 21]
x² = 7f⁻¹(x) – 21
7f⁻¹(x) = x² + 21
f⁻¹(x) = (1/7) x² + 3
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When 3 times a number is subtracted from 45 the result is 5 plus the number. what is the number?
Answers
Answer:
n = 10
Step-by-step explanation:
let the number be n , then
45 - 3n = n + 5 ( subtract n from both sides )
45 - 4n = 5 ( subtract 45 from both sides )
- 4n = - 40 ( divide both sides by - 4 )
n = 10
David can you 25/6 meters per hour manually, but using a digging machine he can dig 3 times as fast. how many meters would david be able to dig with the machine in an hour?
Answers
Answer:
12.5 meters
Step-by-step explanation:
1 hour manually = 25/6 meters
1 hour using machine = 25/6 × 3 meters
1 hour using machine = 12.5 meters
Hope this helped and have a good day
What are the more appropriate measures of center and spread for this data
set?
35 40 45
55
90
hi
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
select two choices: one for the center and one for the spread.
a. better measure of spread: the standard deviation
select two choices: one for the center and one for the spread
Answers
The more appropriate measure of center is mean.
The more appropriate measure of spread is standard deviation.
What is mean and standard deviation?Mean is a measure of central tendency that determines the average of a set of numbers. Standard deviation is used to determine the spread of a dataset. It does this by determining the square root of the average of the squared differences of the numbers from the mean of the data set.
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Answer the following questions
A. 10 -4 ×5=?
B. 3+8×4=?
C. (3+8)×4=?
Answers
Answer:
A=30
B=35
C=44
Step-by-step explanation:
I need help answering these questions for geometry :)
1. What happens to the measure of the interior angles as the number of sides of the polygon increases? Explain your answer.
2.What happens to the measure of the exterior angles as the number of sides of the polygon increases? Explain your answer.
4. Explain what happens to the total sum of interior angles as the number of sides in the polygon changes.
5. Explain what happens to the total sum of exterior angles as the number of sides in the polygon changes.
Answers
The answers to the question have been written below
The changes to a polygon1. If the number of sides of the polygon should increase then the measure of the interior angle would increase by 180.
2. A regular polygon has the sum of its external angles as 360. This is solved as 360/n = 0
Hence the value of the exterior would move towards 0 as its sides increases.
4. As the total sum of the of the polygon changes, it would tend towards infinity.
5. The total sum of the exterior angles as the number of sides changes would tends towards 360 degrees.
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can someone help with this
Answers
Step-by-step explanation:
-10-2x = 3x+15
5x = -25
x= -5
The diagonals of a rhombus are: A. are the same length and intersect at different angles B. bisect each other at right angles C. bisect each other and intersect at different angles D. are the same length and intersect at a right angle
Answers
Answer:
Step-by-step explanation:
Comment
Either you know the answer to this or you don't. There is no point in eliminating the wrong answers until you get to the right one. It is better to get to the right one immediately.
A rhombus and its diagonals have many interesting properties. This one is one of those properties. The diagonals are not the same length. The diagonals bisect each other at right angles.
Answer: B
Which value of x would make triangle s u v is-congruent-to triangle t u m by hl? 2 3 4 5
Answers
The question is incomplete. Below you will find the missing content and figure
Which value of x would make triangle ΔSUV is congruent to triangle ΔTUM by HL? Options are 2 3 4 5
The figure is shown below.
The correct option is Option D: the value of x is 5.
Triangles are congruent if the triangles are of the same size and shape. If triangles are congruent the corresponding length of the sides is the same.
Here given that triangle ΔSUV is congruent to triangle ΔTUM.
By the property of the congruent triangle, as triangle ΔSUV and ΔTUM are congruent the corresponding sides are also same.
ΔSUV ≅ΔTUM
⇒ VS≅WT
Given in the question
VS= 2x+9
WT= 4x-1
from above it is clear that
VS=WT
⇒ 2x+9=4x-1
⇒4x-2x=9+1
⇒2x=10
⇒x=10/2
⇒x=5
Therefore the correct option is Option D: the value of x is 5.
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Answer:
It will be 5 on EDG 2022 Your welcome :)
Step-by-step explanation:
The sides of a triangle are 5, 12 and 13 inches long. what is the angle between the 2 shortest sides?
a. 30
b. 45
c. 60
d. 90
e. 120
Answers
Answer: 90 degrees
Step-by-step explanation:
The hypotenuse is opposite the right angle, which is created by the two shortest sides.
A cyclist is stationary when a second cyclist passes travelling at a constant speed of 8 m s−1. The first cyclist then accelerates for 5 s at a constant rate of 2 m s−1 before continuing at constant speed until overtaking the second cyclist. By sketching both graphs, find the equations of the two straight line sections of the graphs and hence find how long it is before the first cyclist overtakes the second.
Answers
Answer:
im not too sure about that sorry!
Step-by-step explanation:
uiwgorihvncjkdnskv
It takes 15 seconds for the first cyclist to overtake the second cyclist.
How can you find how long it took before the first cyclist overtakes the second?First, identify the two phases of the first cyclist's motion.
Phase 1: The cyclist accelerates from rest to a constant speed of 8 m/s.
Phase 2: The cyclist travels at a constant speed of 8 m/s.
Find the equations of the two straight-line sections of the graph.
The equations of the two straight-line sections of the graph are as follows:
Phase 1:
s = [tex]2t^2[/tex]
Phase 2:
s = 8t
where s is the distance traveled by the cyclist and t is the time
Set the two equations equal to each other to find the time it takes the first cyclist to overtake the second cyclist
The first cyclist overtakes the second cyclist when the first cyclist has traveled a distance of 8 m more than the second cyclist.
Let t be the time it takes the first cyclist to overtake the second cyclist.
The distance traveled by the first cyclist is then 8t, and the distance traveled by the second cyclist is 8(t - 5).
Setting these two expressions equal to each other, we get:
8t = 8(t - 5)
Solving for t, we get:
t = 15
Therefore, it takes 15 seconds for the first cyclist to overtake the second cyclist
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What remainder is represented by the synthetic division below?
A vertical line and horizontal line combine to make a L shape. There are two rows of entries within the shape. Row 1 has entries 2, 10, 1, 5. Row 2 has entries blank, negative 10, 0, negative 5. Entry negative 5 is on the outside to the left of the shape, and a third row of entries is outside and below the shape. Row 3 has entries 2, 0, 1, 0.
Answers
The remainder represented by synthetic division is -5.
What is synthetic division?
Synthetic division can be defined as a simplified way of dividing a polynomial with another polynomial equation of degree 1.
Given
A vertical line and a horizontal line combine to make an L shape.
There are two rows of entries within the shape.
Row 1 has entries 2, 10, 1, 5.
Row 2 has entries blank, -10, 0, -5.
Entry -5 is on the outside to the left of the shape. The entry represents the zero of the divisor. This entry to the variable (assume the variable is x) is;
x + 5 = 0
x = -5
Hence, the divisor of the synthetic division is -5.
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Answer:
its a) -5
Step-by-step explanation:
sara scores -4 marks if she got 3 correct answers how many were incorrect
Answers
The number of answers that were incorrect will be 7.
How to depict the information?From the information given, every correct answer will be +1 while and incorrect answer will be -1. The equation to represent the information will be:
3 - x = -4
where x = incorrect answer
3 - x = -4
-x - 4 - 3
-x = -7
x = 7
In conclusion, the number of answers that were incorrect will be 7.
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if f(x)=-x+8 and f(-4), then the result is 12
True or False?
Answers
[tex] \sf \blue{True✅}[/tex]
Step-by-step explanation:Given,
[tex]f(x) = - x + 8 \: and \: f( - 4)[/tex]
Solution:
[tex] f( x) = - ( - 4) + 8 \\ \\ = 4 + 8 \\ \\ = 12[/tex]
Hope it help youWhich is the best estimate to the nearest one percent of startfraction 7 over 15 endfraction?
Answers
The best estimate to the nearest one percent of the fraction; 7/15 is; 47%.
What is the best estimate of the fraction to the nearest percent?From the task content, it follows that the fraction given whose estimate is to be determined is; 7/15.
The fraction expressed as a percentage is;
(7/15) × 100 %
= 46.667%.
Hence, when rounded to the nearest one percent; = 47%.
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A bag contains 4 red, 7 blue and 5 yellow marbles. Event A is defined as drawing a yellow marble on the first draw and event B is defined as drawing a blue marble on the second draw.
If two marbles are drawn from the bag, one after the other and not replaced, what is P(B|A) expressed in simplest form?
A. 7/16
B. 7/15
C. 14/16
D. 14/15
Answers
Answer:
The answer is B. 7/15!!!
i just guessed and got it right, but i knew c. wasnt the answer.
Which expression can be used to convert 22 Australian dollars to US dollars?
Assume 1.2 Australian dollars equals 1 US dollar.
Answers
Answer:
1.2x = 22x = 55/3 ≈ 18.3322 AUD = 18.33 USDStep-by-step explanation:
1 USD - 1.2 AUD
x USD - 22 AUD
cross multiply
1.2 · x = 1 · 22
1.2x = 22multiply both sides by 10
12x = 220
divide both sides by 12
x=55/3 ≈ 18.33USD - United States dollar
AUD - Australian dollar
12. For which of the following quadratic equations are the roots 2 and 57
O A. x²-3x - 10=0
B. x² - 11x 10 = 0
c. x² - 7x + 10 = 0
D. x² + 7x-10=0
O
O
O
Answers
Answer: x²-59x+114=0
explanation:
If the roots are 2 and 57, then:-
sum of roots = 2+57 = 59
and, product of roots = 2×57 = 114
the quadratic equation is given by,
x²-(sum of roots)x+(product of roots)=0
so, x²-59x+114=0 will be the desired quadratic equation.
so, none of the options are correct.
the correct answer is x²-59x+114=0.
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Hi I need help
1) -15+4r=-9
2)5-y/3=-1
3)42=5x-8
That's all, you don't have to show work, but I'd appreciate it:) asap pls
Answers
Equation #1:
-15+4r=-9We move all terms to the left:
-15+4r-(-9)=0
We add all the numbers together, and all the variables
4r-6=0
We move all terms containing r to the left, all other terms to the right
4r=6
r=6/4
r=1+1/2
Equation #2:
5-y/3=-1We move all terms to the left:
5-y/3-(-1)=0
We add all the numbers together, and all the variables
-y/3+6=0
We multiply all the terms by the denominator
-y+6*3=0
We add all the numbers together, and all the variables
-1y+18=0
We move all terms containing y to the left, all other terms to the right
-y=-18
y=-18/-1
y=+18
Equation #3:
Simplifying
42 = 5x + -8
Reorder the terms:
42 = -8 + 5x
Solving
42 = -8 + 5x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-5x' to each side of the equation.
42 + -5x = -8 + 5x + -5x
Combine like terms: 5x + -5x = 0
42 + -5x = -8 + 0
42 + -5x = -8
Add '-42' to each side of the equation.
42 + -42 + -5x = -8 + -42
Combine like terms: 42 + -42 = 0
0 + -5x = -8 + -42
-5x = -8 + -42
Combine like terms: -8 + -42 = -50
-5x = -50
Divide each side by '-5'.
x = 10
Simplifying
x = 10
Step-by-step explanation:
hope it's beneficial.
Draw my attention for further explanations.✨✨
$9,500 is invested in an account earning 9.1% interest (APR), compounded
quarterly. Write a function showing the value of the account after t years, where t
annual growth rate can be found from a constant in the function. Round all
coefficients in the function to four decimal places. Also, determine the percentage
growth per year (APY), to the nearest hundredth of a percent.
Answers
Answer:
$100.5000
Step-by-step explanation:
becuse $9,500 is fived and it got it
