Answer:
The width of the walkway is of 12.86 feet.
Step-by-step explanation:
Area of a rectangle:
The area of a rectangle of length l and width w is given by:
A = lw
A rectangular garden has a width of 10 feet and a length of 14 feet.
So the area of the rectangular garden is of 10*14 = 140 square feet.
The area of the garden and the walkway together are 320 square feet.
So the area of the walkaway is of 320 - 140 = 180 square feet.
What is the width of the walkway
It has the same length of the garden, of 14. So
[tex]14w = 180[/tex]
[tex]w = \frac{180}{14}[/tex]
[tex]w = 12.86[/tex]
The width of the walkway is of 12.86 feet.
1. 2x-y=0
X+3y=-14
2. Write the equation of the line in slope intercept form that goes through the point (7,2) and has a slope of 4.
3. 4-5x+3=4x-2
Show steps, thx:)
Answer:
(1) [tex](x,y) = (-2,-4)[/tex]
(2) [tex]y = 4x -26[/tex]
(3) [tex]x = 1[/tex]
Step-by-step explanation:
(1):
[tex]2x - y = 0[/tex]
[tex]x + 3y = -14[/tex]
Required: Solve for x and y
Make x the subject in [tex]x + 3y = -14[/tex]
[tex]x = -3y - 14[/tex]
Substitute -3y - 14 for x in the first equation
[tex]2x - y = 0[/tex]
[tex]2(-3y-14) - y = 0[/tex]
Open bracket
[tex]-6y - 28 - y = 0[/tex]
Collect Like Terms
[tex]- y-6y = 28[/tex]
[tex]-7y = 28[/tex]
Divide both sides by -7
[tex]y = -4[/tex]
Substitute -4 for y in [tex]2x - y = 0[/tex]
[tex]2x - (-4) = 0[/tex]
[tex]2x + 4 = 0[/tex]
Collect Like Terms
[tex]2x = -4[/tex]
Divide by 2
[tex]x = -2[/tex]
Hence, the solution is:
[tex](x,y) = (-2,-4)[/tex]
(2):
[tex](x_1,y_1) = (7,2)[/tex] -- points
[tex]m = 4[/tex] --- slope
Required: Determine the line equation
This is calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives:
[tex]y = 4(x - 7) + 2[/tex]
Open bracket
[tex]y = 4x - 28 + 2[/tex]
[tex]y = 4x -26[/tex]
(3)
[tex]4 - 5x + 3 = 4x - 2[/tex]
Required: Solve for x
Collect Like Terms
[tex]- 5x -4x = - 2-3-4[/tex]
[tex]-9x = -9[/tex]
Divide both sides by -9
[tex]x = 1[/tex]
Elaine drives her car 180 miles and has an average of a certain speed. If the average speed had been 5mph more, she could have traveled 200 miles in the same length of time. What was her average speed?
Answer:
45 mph
Step-by-step explanation:
Using the equation d = rt, we can rearrange the equation to be t = d/r
Since the amount of time was the same, we can set d/r equal to each other for both speeds.
Let x represent the average speed.
[tex]\frac{d}{r}[/tex] = [tex]\frac{d}{r}[/tex]
[tex]\frac{180}{x}[/tex] = [tex]\frac{200}{x+5}[/tex]
Cross multiply and solve for x:
200x = 180x + 900
20x = 900
x = 45
So, the average speed was 45 mph
: 3a2 + 2b2 when a = -3 and b = 6
Answer: 63
Step-by-step explanation:
3(-3)^2 + 2(6)^2 (multiply 3 times -3) & (multiply 2 times 6)
-9^2+12^2 (-9 to the 2nd power and 12 to the 2nd power)
-81+144 (add them up)
=63
The value of the expression is 3a² + 2b² is 69.
What is Expression?A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:
An absolute numerical number is referred to as a constant.Variable: A symbol without a set value is referred to as a variable.Term: A term can be made up of a single constant, a single variable, or a mix of variables and constants multiplied or divided.Coefficient: In an expression, a coefficient is a number that is multiplied by a variable.Given:
Expression: 3a² + 2b²
Not, put the value of a= -3 and b=6 we get
= 3a² + 2b²
= 3(-3)² + 2(4)²
= 3 x 9 + 2 x 16
= 37 + 32
= 69
Hence, the value of expression is 69.
Learn more about Expression here:
https://brainly.com/question/14083225
#SPJ2
How can you isolate the variable in x-3 = 7
Answer:
x = 10
Step-by-step explanation:
To isolate the variable (x) you would first write out x - 3 = 7. Now to make x on its own we have to get rid of the -3 so to do that we would add the reciprocal of -3 (or the opposite) which is +3. x - 3 + 3 = 7 + 3 or x = 10.
The graph show how the amount of fuel in the gas tank changes over time. Choose the graph that correctly combines the graphs of Car A and Car B to show when Car B has more fuel in its tank than Car A.
Answer:
its b
Step-by-step explanation:
Suppose a loaded die has the following probability model: If this die is thrown and the top face shows an odd number, what is the probability that the die shows a 1
Answer:
the probability is 0.6
Step-by-step explanation:
The computation is shown below:
Let us assume the X would be the number appear on the top face
Now
= P(X = 1) ÷ P(X = 0)
= 0.3 ÷ 0.3 + 0.1 + 0.1
= 0.3 ÷ 0.5
= 0.6
hence, the probability is 0.6
b) 2(x-3) + X = 5x-2(x+5)
Answer:
X=x−4
Step-by-step explanation:
2(x−3)+X=5x−2(x+5)
Use the distributive property to multiply 2 by x−3.
2x−6+X=5x−2(x+5)
Use the distributive property to multiply −2 by x+5.
2x−6+X=5x−2x−10
Combine 5x and −2x to get 3x.
2x−6+X=3x−10
Subtract 2x from both sides.
−6+X=3x−10−2x
Combine 3x and −2x to get x.
−6+X=x−10
Add 6 to both sides.
X=x−10+6
Add −10 and 6 to get −4.
X=x−4
The perimeter of a square garden is 128m. Find the area of the garden in hectares?five star
five star rating brainliest and thanks will be given for the right answer plss help asap!!
Answer:
1024m
Step-by-step explanation:
128÷4=32
32×32=1024
2.)---------------------------------------------------------------------------
A.) A paint store sells exterior for $35.75 a gallon and paint rollers for $6.00 each. Write an equation in standard form for the number of gallons p of paint rollers r that a customer could buy with $190.
B.) Use your equation to determine the number of gallons of paint needed if a customer bought 6 rollers
The total price for the gallons of paint will be 35.75p
The total price for the rollers will be 6r
So the equation if the customer have 190 will be
price for gallons of paint + price for rollers = 190
35.75p + 6r = 190
(This is the equation)
I do not understand what I'm supposed to do
What simplified ratio correctly compares 10,000 centimeters to 1000 meters? Drag and drop the appropriate numbers into the boxes. A.1 B.10 C.100 1000 D10.000 E.100.000
Answer:
C.
Step-by-step explanation:
william runs 40 yards in 4.5 seconds. at the same pace how long will he take to run 100yards?
Answer:
11.25 seconds
Step-by-step explanation:
first, we need to figure how how far william can run per second
we can find this by 40 ÷ 4.5
= 8.889 per second
so we know that 8.889 • s (seconds) = 100
8.889s = 100 divide both sides by 8.889
s = 11.25 seconds
Answer:
William will take 11.25 seconds to run 100 yards
Step-by-step explanation:
Constant Rate
William runs 40 yards in 4.5 seconds. The rate of change of the distance is
[tex]\frac{40}{4.5}[/tex]
To run 100 yards, we divide by the rate obtained above:
[tex]\displaytstyle \frac{100}{\frac{40}{4.5}} =100*\frac{4.5}{40} =11.25[/tex]
William will take 11.25 seconds to run 100 yards
find the slope of the line passing through the points (-9,5) and (-1,5)
Slope = change in Y / change in x:
Slope = (5- 5) / (-1 - -9)
Slope = 0/8
Because the change in Y = 0, the slope = 0
Slope = 0
Answer:
0
Step-by-step explanation:
(-9,5) and (-1,5)
To find the slope of the line, we use the slope formula: (y₂ - y₁) / (x₂ - x₁)
Plug in these values:
(5 - 5) / (-1 - 9)
Simplify the parentheses.
= (0 ) / (-10)
Simplify the fraction.
0/-10
= 0
This is your slope.
This is also a horizontal line, which will have a slope of 0.
a cubical house can hold 4096 cm3 of air find the height of the house
Answer:
The height is 16
Step-by-step explanation:
Given
Shape: Cube
[tex]Volume = 4096cm^3[/tex]
Required:
Determine the height of the house.
Volume is represented as:
[tex]Volume = L^3[/tex]
Make L the subject
[tex]L = \sqrt[3]{Volume}[/tex]
This gives:
[tex]L = \sqrt[3]{4096}[/tex]
[tex]L= 16[/tex]
The height is 16
Factor completely 4x^2 + 3x - 10.
A) (4x - 2)(x + 5)
B) (4x + 2)(x - 5)
C) (4x - 5)(x + 2)
D) (4x + 5)(x - 2)
Answer:
(4x-5)(x+2)
Step-by-step explanation:
please help with my homework
Answer:
It will be 16pie =50 andpie4^2
Step-by-step explanation:
Hope this Helped
SOMEONE JUSt please HELP ME HELP ME PLEASE ITS URGENT
Answer:pretty sure it’s both 35°
Step-by-step explanation:
a gumball machine gives you no gum if you insert 5c, 5 gumballs if you insert 10c , 10 gumballs if you insert 15c and 15 gumballs if you insert 20c. how many gumballs could you expect to receive if you insert 35c?
Answer:
30
Step-by-step explanation:
create a function where x is the money you insert in cents and y is the amount of gumballs you get.
y = x - 5 (meaning you get five less gumballs than the amount of cents you insert)
Therefore, when x = 35:
y = 35 - 5 = 30.
You will get 30 gumballs.
With a coupon, you can get a pair of shoes that normally cost $84 for only $72. What percentage was the discount. Please give the step by step explanation!
Answer:
14.28%
Step-by-step explanation:
Given that,
You can get a pair of shoes that normally cost $84 for only $72.
We need to find the discount percentage. So, it can be calculated as follows :
[tex]\%=\dfrac{84-72}{84}\times 100\\\\\%=14.28\%[/tex]
So, the required percentage is 14.28%.
2.2 + 2x > -5.8 A. -3.88 B. -4.12 C. -4.18 D. -4.22
math algebra HELP!!!!
Answer:
y = 32
Step-by-step explanation:
[tex]\frac{1}{2} y + 22 = 38[/tex]
Subtract 22 from both sides to isolate the y variable.
[tex]\frac{1}{2} y = 16[/tex]
Divide both sides by [tex]\frac{1}{2}[/tex], which is the same as multiplying by 2.
y = 32
1/2y + 22 = 38
-22 -22
1/2y = 16
x2 x2 ---> This is because if 1/2y = 26, that means y times 1/2 is 26, but we want to know what y times 1 is because y times 1 is equal to y so we multiply by 2 because 1/2 times 2 equals 1.
y = 32
A number is _____ by another number if the quotient is a counting number and the remainder is zero.
Answer:
56888
Step-by-step explanation:
guy is unavailable right now because this video is not available
Tuesday’s attendance was 70% of Monday’s attendance, 50. What was Tuesday’s attendance?
Answer:
35
Step-by-step explanation:
100 / 50 = 2
70 / 2 = 35
(X-2)(x^2+2x+4) what is the answer to this equation?
Answer:
x^3 - 8
Step-by-step explanation:
How many ways can the teacher choose a group of 5 students to present on the first day if Marjorie must present on the first day?
Answer:
126
Step-by-step explanation:
2 Fill in the boxes to find the resulting equation when 25 is subtracted from
each side. Simplify both sides of the equation,
25 +2=
25
31
25
Solve it
Given:
The equation is
[tex]25+x=31[/tex]
25 is subtracted from both sides.
To find:
The missing values for the given blanks.
Solution:
We have,
[tex]25+x=31[/tex]
If 25 is subtracted from both sides, we get
[tex]25+x-25=31-25[/tex]
[tex](25-25)+x=6[/tex]
[tex]0+x=6[/tex]
So, the missing values for the blanks are 0 and 6 respectively.
It is also written as
25 + x = 31
-25 -25
-----------------------------
0 + x = 6
------------------------------
Therefore, the missing values for the blanks are 0 and 6 respectively.
Find the perimeter of lsosceles triangle ABC (below) if mAD = 3 and m < BAC = 55 degrees. Round to the nearest hundredth.
Answer:
r
Step-by-step explanation:
The shorter leg of a right triangle is 9 ft shorter than the longer leg. The hypotenuse is 9 ft longer than the long leg. Find the sides of the triangle
Answer and Step-by-step explanation:
|\
| \
| \
| \
| \
| \ 9 + x
x - 9 | \
| \
| \
| \
| \
|_____________\
x
That is your triangle.
Now, since its a right triangle, we can use the Pythagorean theorem to solve for x.
The equation for the Pythagorean theorem is this: [tex]A^{2} + B^{2} = C^{2}[/tex]
So we plug in the values.
[tex](x^{2} ) + (x-9)^{2} = (x + 9)^{2}[/tex]
We solve for x.
[tex]x^{2} + x^{2} -18x + 81 = x^{2} + 18x + 81[/tex]
Get everything to the left side of the equation. (x^2 + x^2 = 2x^2, - x^2 = x^2;
-18x - 18x = -36x; 81 - 81 = 0)
[tex]x^{2} -36x = 0[/tex]
Add 36x to both sides, then divide by x.
[tex]x^{2} = 36x\\\\x = 36[/tex]
Shortest Leg = 36 - 9 = 27
Longest Leg = 36
Hypotenuse = 45
#teamtrees #WAP (Water And Plant)
Suppose you plan to sell five trading cards. Three of the cards
will be shipped domestically, and two will be shipped
internationally. The cost of international shipping is $2.50
greater than the cost of domestic shipping.
Write About It!
If you spent $22.50 on shipping, how much is the cost of
domestic shipping? Define a variable, write an equation,
and solve the problem.
Answer: $3.50
Step-by-step explanation:
Let the cost of domestic shipping be x.
Since the cost of international shipping is $2.50 greater than the cost of domestic shipping. This will be:
= x + 2.50
Since we are further told that three of the cards will be shipped domestically, and two will be shipped internationally and that $22.50 will be spent on shipping, this will be express in an equation as:
3x + 2(x + 2.50) = 22.50
3x + 2x + 5.00 = 22.50
5x = 22.50 - 5.00
5x = 17.50
x = 17.50/5
x = $3.50
The cost if domestic shipping is $3.50
Find the exact value of sec795°
Answer:
I believe the answer would be [tex]\sqrt{6}+\sqrt{2}[/tex] or 3.8637
Step-by-step explanation:
Answer:
c
Step-by-step explanation: