Answer:
Length=8 Width=5
Step-by-step explanation:
Set this up as a system of equations with l standing for length and w standing for width.
w+3=l
l×w=40
Substitute rhe first equation into the 2nd one.
w(w+3)=40 --------> w^2+3w=40
Move all the terms to the left side
w^2+3w-40=0
Factor
(w+8) (w-5)
Set both factors equal to 0.
w+8=0 -----> w=-8
w-5=0 ------> w=5
Since distance cannot be negative we can eliminate -8. So w=5
Plug it back into any one of the equations and solve for l.
5+3=l -----> 8=l
So the answer is the length is 8 and the width is 5.
The dimensions of the rectangle are:
Length = 8 meters.
width = 5meters.
We are given that the length of a rectangle is 3 meters longer than its width and the area of a rectangle is 40 square meters.
We need to find the length and width of the rectangle.
What is a rectangle?A rectangle is a closed 2-dimensional shape that has two dimensions, the length, and the width. Length is the longer side and width is the shorter side of the rectangle.
The area of a rectangle is given by :
A = Length x Width.
Let the area, length, and width of the rectangle be A, L, and W.
The length of a rectangle is 3 meters longer than its width.
We can write it as,
L = 3 + W
The area of a rectangle is 40 square meters.
We can write it as,
A = 40 square meters
We can write it as,
L x W = 40
Substituting L = 3 + W.
(3 + W) W = 40
[tex]3W + W^2 = 40\\W^2 + 3W = 40 \\W^2 + 3W - 40 = 0[/tex]
This is a quadratic equation and we will apply middle-term factorization.
[tex]W^2 + 3W - 40=0\\W^2 + (8-5)W - 40=0\\W^2 + 8W - 5W - 40=0\\W(W + 8) - 5 ( W + 8)=0\\(W+8)(W - 5)=0\\W+8 = 0~~and~~W-5=0\\W = -8~~and~~W=5[/tex]
The distance can not be negative so W = -8 is eliminated.
We have, W = 5
Substituting W = 5 in L = 3 + W.
We get,
L = 3 + 5 = 8
L = 8.
The dimensions of the given rectangle are:
Length = L = 8 meters.
Width = W = 5 meters.
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Find the slope: (7,4) (5, 6)
Answer:
Slope = - 1
Step-by-step explanation:
(x₁ , y₁) = (7,4) & (x₂, y₂) = (5, 6)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]= \frac{6-4}{5-7}\\\\= \frac{2}{-2}\\\\= - 1[/tex]
Write an equation of the line containing the given point and parallel to the given line.
(6,-2); 4x - 3y = 8
Answer:
y = (4/3)x − 10
Step-by-step explanation:
Rewrite in slope-intercept form.
The slope-intercept form is y = mx + b, where m is the slope and b is they-intercept.
y = mx + b
Subtract 4x from both sides of the equation.
−3y = 8 − 4x
Divide each term by −3 and simplify.
Divide each term in −3y = 8 − 4x by −3.
(−3y/−3)= (8/−3) + (−4x/−3)
Cancel the common factor of −3.
y= (8/−3) + (−4x/−3)
Simplify (8/−3) + (−4x/−3)
y= (4x/3 - 8/3)
Reorder terms.
y= 4x/3 - 8/3
Using the slope-intercept form, the slope is 4/3
m = 4/3
To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.
Use the slope 4/3 and a given point (6, −2) to substitute for [tex]x_{1}[/tex]and [tex]y_{1}[/tex]in the point-slope form. [tex]y[/tex] − [tex]y_{1}[/tex] = [tex]m[/tex] ([tex]x[/tex] − [tex]x_{1}[/tex]) which is derived from the slope equation[tex]m=[/tex] ([tex]y_{2}[/tex]− [tex]y_{1}[/tex])/([tex]x_{2}[/tex] - [tex]x_{1}[/tex])
y − (−2) = (4/3) ⋅ (x − (6))
Simplify the equation and keep it in point-slope form.
y − (−2) = (4/3) ⋅ (x − (6))
solve for y
y = (4/3)x − 10
Jada traveled 135 miles in 3 hours. Andre traveled 228 miles in 6 hours. Both Jada and Andre traveled at a constant speed. who traveled faster? explain or show your reasoning
Answer:
Jada
Step-by-step explanation:
Jada traveled faster (45mph) and Andre traveled a longer distance (228 miles) but went 38mph, concluding that Jada traveled faster.
45x3=135 (Jada)
38x6=228 (Andre)
*
Simplify the expression:
(-6p+7). -4
Answer:
I'm assuming you need to distribute. When simplified the expression is 42p-28
Step-by-step explanation:
Answer:
24p-28
Step-by-step explanation:
Daniel's store sold 75% fewer pairs of shorts this month than last month. If the store sold 5 pairs of shorts this month, then _________ pairs of shorts were sold last month.
Answer:
EXACT ANSWER: 6.666666666667
ANSWER ROUNDED: 7
Step-by-step explanation:
lol, I can't explain well, but it's correct.
Please answer the following question below
Answer:
65°
Step-by-step explanation:
The tangent is perpendicular to the diameter BD therefore m‹CBR=90°-25°=65°
whats 3(x + 2) = 21?
show work please !!
Answer:
x=5
Step-by-step explanation:
[tex]3(x+2)=21[/tex]
[tex]3x+6=21[/tex]
[tex]3x+6-6=21-6\\\\3x=15\\\\\frac{3x}{3} = \frac{15}{3} \\\\x=5[/tex]
Answer:
x = 5
Step-by-step explanation:
You first have to multiply 3 by x and 2, and you would get 3x and 6. 3(x + 2)=3x +6
Then you have to move the 6 to the other side and it will become negative. 3x= -6 +21
Then you subtract 21-6 to get 15. 3x = 15
Then you are left with 3x = 15.
Divide 3 from both sides and you get x =5.
In the figure below, determine the perimeter of triangle EFG
Answer:
82 units
Step-by-step explanation:
From the image, we can see that the 2 triangles are similar triangles.
Thus:
BC = EF
BD = EG
CD = FG
Now, BD = 4x - 9 and EG = 2x + 15
Thus;
4x - 9 = 2x + 15
4x - 2x = 15 + 9
2x = 24
x = 24/2
x = 12
Thus, in triangle EFG where EG = 2x + 15, then EG = 2(12) + 15 = 39
Also, EF = BC = 17
FG = 26
Thus, perimeter of triangle EFG is;
P = 26 + 17 + 39
P = 82 units
seven less than the quotient of a number and five is two
The value of the number for the expression seven is less than the quotient of a number and five is two is 45.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a number is seven less than the quotient of a number and five is two.
The value of the unknown number will be calculated as,
x/5 - 7 = 2
x/5 = 9
x = 45
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A small business has 15 full-time employees. How many people does the small business employ if the full-time workers make up 30% of the employees the company has?
Answer:
50 employees
Step-by-step explanation:
The total number of employees the business has will have to be made up the full-time employees and part-time employees.
The number of full-time employees = 15
Let the total number of employees = x
[tex]15 = 30 percent of x[/tex]
[tex]15 = 30/100 \times x\\x=1500/30 = 50[/tex]
The company has a total of 50 employees
If f(x)=2x+1, then f(3)= ?
(2 to the power of x)
(not 2 times x)
Please show work :)
Answer:
9
Step-by-step explanation:
Input 3 for x
f(x)=2^3+1
f(3)=2^3+1
f(3)=8+1
f(3)=9
Solve the equation. Check your solution. a/4 - 5/6= -1/2
Answer:
a= 4/3
Step-by-step explanation:
1.) Simplify both sides of the given equation:
1/4a + -5/6 = -1/2
2.) Add the 5/6 to both sides (cancels the -5/6)
1/4a + -5/6 (+5/6) = -1/2 (+5/6)
1/4a = 1/3
3.) Multiply both sides by 4 (the denominator)
4 * 1/4a = 1/3 * 4
a = 4/3
To check the solution, plug in 4/3 into a:
4/3/4 - 5/6 = -1/2
2.) Dividing fractions is also multiplication:
(4/3 * 1/4) - 5/6 = -1/2
3.) Get the difference of 1/3 and 5/6
1/3 - 5/6 = -1/2
4.) Simplify -3/6 (3 goes into 3 ONCE and into 6 TWO times)
-3/6 = -1/2
5.) Check to see if both sides match
-1/2 = -1/2
I need help ASAP with questions 3-7 plz show steps I will also mark brainliest
Answer:
.
Step-by-step explanation:
.
3-⁶x (3^4 ÷ 3⁰)²
simplify
Answer:
Step-by-step explanation:
– 634302
Please help, needed fast
Answer:
46
Step-by-step explanation:
6*5
-2*-8
30+16=46
Answer:
It would be 46
Step-by-step explanation:
6. (03.02) Factor completely 3x4 + 4x3 + 6x + 8. (1 point)
Answer:
(3x+4)(x³+2)
Step-by-step explanation:
Follow me Please
Answer:
Hope it can help you and mark me as brainlist.
HELP! Is (0,-5) a solution to 3x - 2y < 10 ?
Answer:
false
Step-by-step explanation:
3(0) - 2(-5) = 10
the < says it cannot be equal
4/5 divided by 3/7 :))
Answer:
1.86666666667
Step-by-step explanation:
Answer:
1 13/15
Step-by-step explanation:
Judy is baking 5 cheesecakes. A recipe for one of the cheesecakes requires 1 1 2teaspoons of vanilla. Judy's bottle of vanilla contains 12 teaspoons of vanilla. After Judy bakes the 5 cheesecakes, how many teaspoons of vanilla will be left in the bottle?
Answer:4 1/2 Teaspoons of vanilla will be left in the bottle
Step-by-step explanation:
Step 1
Recipe for 1 cheesecake = 1 1/2 teaspoons of vanilla
Since she s making 5 cheesecakes, she will requite = 5 x 1 1/2 teaspoons
= 5 x 3/2= 15/2 = 7 1/2 teaspoons of vanilla.
Step 2
If a bottle of vanilla contains = 12 teaspoons of vanilla
After baking 5 cheesecakes which consumed = 7 1/2 teaspoons of vanilla
Teaspoons left of vanilla = Total teaspoons of vanilla-teaspoons of vanilla used for 5 cheesecakes= 12 - 7 1/2 =4 1/2
Therefore 4 1/2 Teaspoons of vanilla will be left in the bottle
Which part is the y-intercept in this equation? y=3x+9
Answer:9+3x=12x
Step-by-step explanation: first you do 9+3 then that would equal 12 and y=12 so then after that you do 12x bc you didnt use the 9+3 with x so you add the x with the 12 and that makes it 12x
-5x+3y>9 help me plesese so i can grids
Answer:[tex]x<−95+3y5[/tex]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
What is the y-intercept when a line has a slope of 1/2 and passes
through the point (2, -1)?
Answer:
2
Step-by-step explanation:
You called this question to the right person. To find the y-intercept, you must do the formula of Point Slope (y-y1 = m (x-x1)) Since 2, is x1 and the -1 is y1, we must lay the equation out like this: y - -1 = m (x-2). Next, we must distribute the slope to the x and the 2, which would allow the x, to fit in with the slope, and the 2 to become 1 since 1/2 x 2 is 1. Now what we need to do is get rid of the -1, so what we do here is add 1. And algebra golden rule, whatever you do to one side, you must do to the other side. This would leave y = 1/2x + 2 And therefore 2 is your y-intercept, since it's at the last part of the equation.
You deposit $500 in an account that earns 4% simple annual interest entrance and each year is added to the principal to create a new principal find the total amount in your account after each year for three years
Answer:
first year $20 second year $20.80 Third year $21.63
Step-by-step explanation: This is for an extra money per year so after the first year that is how much extra money he gets every year.
Which set of values could be the side length of a 30-60-90 Triangle!
What is the value of this expression? 1.25 + 8.25 × 4 ÷ (4.75 + 0.75) Group of answer choices 6.91 7.25 8.75 8.95
Answer:
b
Step-by-step explanation:
Answer:
the answer is 7.25
Step-by-step explanation:
Hope this helps :)
What is the value of the function f(x) = 7x when x = 0.75? *
Answer:it is -1
Step-by-step explanation:
Answer:
5.25
Step-by-step explanation:
As per the question, we have
f(x)=7x
at x=0.75
f(0.75)=&(0.75)
f(0.75) = 7 x 75/100 (this is a fraction)
f(0.75)= 525/100 (this is a fraction)
f(0.75)=5.25
Hence, the value of f(x)=7x at x=0.75 is 5.25
3x + 5x - 1 expression
Answer:
8x - 1
Step-by-step explanation:
Combine like terms. 3x and 5x are like terms.
3x + 5x -1 = 8x - 1
What is the domain of the square root function graphed below?
Answer:
X is greater than or equal to 3
Step-by-step explanation:
As you Can See the graph Starts at (3, 1) and the point is filled in which mean it includes 3 the graph continues going there for the domain= x-axis is greater than or equal to 3
Answer:
i think its A or B but im not really sure,most likely A =w=
Meg is a veterinarian. She found that 25% of the 24 dogs she saw this week were boxers. Steve is also a veterinarian. He found that 8, or 50%, of the dogs he saw this week were boxers. Does each person need to find the part, the whole, or the percent?
Answer:
Percent
Step-by-step explanation:
lol I just got it right
how do i solve this problem?
Answer:
You can use a^2+b^2=c^2;
Step-by-step explanation:
42^2+78^2=(6x-1+10x+5)^2
Answer:
3.5
Step-by-step explanation:
Triangles always equal to 180
42 + 78 + 16x + 4 = 180
124 + 16x = 180
56 = 16x
3.5 = x