Answer:
Expression
An algebraic expression is a combination of variables, numbers, arithmetic operations, powers, roots, and more. Within algebra, there are many forms of expressions that may have specific names, such as polynomials. Below are a few examples of algebraic expressions:
x + 7
x2 + 3x + 4
Evaluating expressions
Expressions can be part of equations, or they can also be evaluated for a given value. This means to substitute the given value into the expression then perform the operations in the expression.
Examples
1. Evaluate the following expression given that x = 5
(2x + 7) × x
(2(5) + 7) × 5 = (17) × 5 = 85
Another way that this problem could have been posed is using the following notation:
[(2x + 7) × x] | x = 5
The vertical bar means to evaluate the expression given what comes after the bar.
2. (2x2 + 7x) | x = 5
2(5)2 + 7(5) = 50 + 35 = 85
From the above examples we can see that:
(2x + 7) × x = 2x2 + 7x
They are equivalent expressions.
Equivalent expressions
Equivalent expressions are expressions in which for some given variable (or variables), such as x, the values of the expressions are equal.
2x + 2 = 2(x + 1)
For any value of x, the expressions above have the same value; they are just in different forms. We can test this by plugging a few values in for x.
If x = 1: 2(1) + 2 = 2(1 + 1)
4 = 4
If x = -5: 2(-5) + 2 = 2(-5 + 1)
-8 = -8
We can do this for many more numbers, but the result will be the same.
Writing expressions in different but equivalent forms can be helpful in certain mathematical contexts, including solving equations in algebra. Having a factored, equivalent form of an expression is one commonly used method for solving algebraic equations involving variables raised to a power.
Example
Solve 2x + 2 = (x + 1)(x + 7)
Expand the right side of the equation, then group the like terms:
2x + 2 = x2 + 8x + 7
x2 + 6x + 5 = 0
Factor the left side of the equation to find an equivalent expression:
x2 + 6x + 5 = (x + 1)(x + 5) = 0
Now that the equation is factored, we can solve for x by dividing each term and setting the remainding term equal to 0. Note that we must do this for each term or we would lose one of the solutions to the problem.
x + 1 = 0
x = -1
and
x + 5 = 0
x = -5
Therefore, the solutions to the above equation are x = -1 and x = -5
Answer:
18 is the answer ...
Step-by-step explanation:
8-2+12
5kg of compost cost £7.50. Find the cost of 3kg of compost
Answer:
£4.5
Step-by-step explanation:
5kg= £7.50
£7.50/5 = £1.5
£1.50 =1 kg
£1.50 times 3 equals £4.5
£4.5
Lisa has a garden with the dimensions of 10x5ft. She can plant an eggplant every 1.5 foot. How many eggplants can she grow to stick them up her a$hole?
HELP PLEASEEEE
Tammy has a rectangular rug with an area of 21 square feet. The rug is 4 feet longer than it is wide. Which equation can be used to determine the length and the width of the rug?
A.
21 = 4w^2
B.
21 = w^2 + 4w
C.
21 = w^2 – 4w
D.
21 = w^2 + 4
Answer:
D
Step-by-step explanation:
The equation to determine the length and width of the rug is 21 = w² + 4w.
What is Rectangle?A rectangle is a four sided figure with opposite sides are equal .
Area of a rectangle = Length x width
Given that A rectangular rug with an area of 21 square feet.
The rug is 4 feet longer than it is wide.
Let 'l " be the length of the rug and 'w' be the width of the rug
Length is 4 feet longer than its width
l = w + 4
Area is 21 square feet.
Area = l x w
21 = (w + 4)w
21 = w² + 4w
The equation to determine the length and width of the rug is 21 = w² + 4w.
So width is 3 ft
Length = w +4
length = 3+4= 7 feet
Thus Length of the rug is 7 feet
Length of rug = 7 feet
width of the rug = 4 feet
Learn more information about ' Area of rectangle ' here;
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Someone help my sister out, cause I’m not helping her I’m to lazy. Lolz.
Answer:
72 sq. cm.
Step-by-step explanation:
V = b * h
4 * 6 = 24 which is the base of this object
24 * 3 = 72 which is the volume of this object
A fair-sided coin is tossed 18 times.
Which of the experimental outcomes is most consistent with theoretical outcomes?
A. 4 heads and 14 tails
B. 6 heads and 12 tails
C. 9 heads and 9 tails
D. 10 heads and 8 tails
Steve puts an 18-foot ladder against his house. The ladder reaches a height of 15 feet on the house. How far is the bottom of the ladder from the base of the house? Leave the answer as a simplified square root.
Answer:
[tex]3 \sqrt{11} [/tex]
Step-by-step explanation:
Since we are given the hypotenuse which is 18 since it slanted, and leans on the house. And we are given one of the legs which is 15 since it is vertical. We can use the pythagorean theorem to solve for this problem.
[tex] {a}^{2} + {b}^{2} = c {}^{2} [/tex]
where a and b are the legs and c is the hypotenuse l.
Let plug it in
[tex] {a}^{2} + 15 {}^{2} = {18}^{2} [/tex]
[tex] {a }^{2} + 225 = 324[/tex]
[tex] {a}^{2} = 99[/tex]
[tex]a = \sqrt{99} [/tex]
[tex]a = \sqrt{9 \times 11} [/tex]
[tex]a = 3 \sqrt{11} [/tex]
A student was estimating 9% of 38. Would 4 be a
reasonable answer?
4 wont be the answer. answer is 3.42
Here is a funny thing
Someone does math with out using a calculator
WITCHCRAFT
need help with my math homework
Write the equation of the line that goes through the point (6, O) and has a slope of -1/2
Answer:
y = -1/2x + 3
Step-by-step explanation:
y - y₁ = m(x - x₁)
⇒ y - 0 = -1/2(x - 6)
⇒ y = -1/2x + 3
In VWX, ZW XV, XV = 13 and VW = 8. Find the length of WX. .
Answer:
It is an isosceles triangle with angle V at the vertex
The measures of the other 2 angles are
angle W and angle X = (180 -50) / 2
angle W and angle X = 65 degrees each
Step-by-step explanation:
6²•8² = [?]
Enter the value
Answer:
2,304
Step-by-step explanation:
6² = 36
8² = 64
36 • 64 = 2,304
Answer:
100 I believe
Step-by-step explanation:
Ok calculator time.. 6 to the power of 2 = 36 and 8 to the power of 2 is 64 so 36 + 64 = 100. Hope that helps...
A group of 4 friends bought movie tickets. Each person also bought a large popcorn for $7.50. If they spent a total of $72, how much was each movie ticket (t)?
Answer:
$16.125 but i don't know if you have to round
Step-by-step explanation:
please please help me it's due today! (slopes) (brainliest)
Step-by-step explanation:
is there any pictures? or something cause if there is i would love to help you
Which side lengths form a right triangle?
y-intercept of y=-1.33x+72.6
Answer:
the y-intercept is (0,72.6)
Step-by-step explanation:
Answer:
y- intercerpt (0,72.6) Step-by-step explanation:
I think but I hope that helps
What is the solution?
2
WHATS THE ANSWER!!! hurry
Answer:
(1, -1)
Step-by-step explanation:
Hope this helps. Pls give brainliest.
Answer:
(-1,-1)
Step-by-step explanation:
this is where the point cross
How do you dilate a shape by 3 and 5?
Answer:
To dilate a shape by 3 and 5, I believe you simply multiply them with the original numbers given.
Can you please help me on this??
Answer:
Step-by-step explanation:
y = 8
272/34 = 8
y =8
Answer:
hhhhjjjjjiiiiuuuuuuiuu
1. A cab company charges its customers a flat rate of
$10 plus $0.75 per mile. Find a rule for the linear
function that describes the cab company's basic fees.
Answer:
0.75x + 10 = y
Which value of k makes the equation k2=10k2=10 true?20
20
12
8
5
Answer:
5
Step-by-step explanation:
Directions: Solve for X. Round to the nearest tenth. . 12 54
A company is going to make a water tank in the shape of a cylinder. As shown below, the tank will have a height of 2ft and a radius of 5ft. The tank will be made from metal (including its top and bottom). Suppose the total cost of the metal will be 8572.20. How much will the metal cost per square foot? Use 3.14 for pi, and do not round your answer.
Please give an understandable step-by-step explanation. Thank you !!
Answer:
$39 per square foot.
Step-by-step explanation:
The cylinder has a height of 2 feet and a radius of 5 feet.
The total cost of the metal will be (assuming US dollars) $8572.20.
And we want to determine the cost per square foot.
First, we can find the surface area of the cylinder. The surface area for a cylinder is given by the formula:
[tex]SA=2\pi r^2+2\pi rh[/tex]
Where r is the radius and h is the height.
Since the radius is 5 feet and the height is 2 feet and using 3.14 for π, the surface area is:
[tex]SA=2(3.14)(5)^2+2(3.14)(5)(2) =219.8\text{ feet}^2[/tex]
Therefore, to find the cost of metal per square foot, we can divide the total cost over the amount of surface area. Hence:
[tex]8572.20 / 219.8= \$ 39 \text{ per square foot}[/tex]
So, the metal costs $39 per square foot.
x - 2 = Y
Y = -2/3x + 3
Answer: (3,1) in point form x=3,y=1
Step-by-step explanation:
Find the value of X.
X= 30
X= 32
X= 25
X=27
Step-by-step explanation:
x+25+3x+27=180
4x=128
x=32
so option b
Question 7: Timani bought a video game console and some games for $350. The video game
console cost $200. Each game cost $25. Using Linear Equation y = mx + b, explain each letter represent what value.
y=350, m=200, b=25, x is the # of games he purchased.
y=350, m=25, b=250, x is the # of games he purchased.
y=200, m=350, b=25, x is the # of games he purchased.
y=200, m=25, b=200, x is the # of games he purchased.
None of these are right
y=$350 because that is her total.
m=$25 because each game cost that.
B=$200 because that's how much the console cost.
$350=$25x+$200
Find the geometric mean of each pair of numbers 12 and 50
pls help with question 25 50 points brainslest if right
Answer:
25,26,27
Step-by-step explanation:
n +(n+1)=(n+2)+24
2n+1=n+26
n=26-1=25
3 integers=25, 26, 27
what is the length of AB
Answer:
the length of side AB is 6 units
what is 5/4 divided by 10 pls be right if u were right ill give u brainliest!!!!!!!!!!!!!!
Answer:
0.004.
Step-by-step explanation:
First, I'll change [tex]\frac{5}{4}[/tex] to a decimal.
[tex]\frac{5}{4} = 1.25.[/tex]
Then, we divide.
[tex]\frac{1.25}{10} = 0.004.[/tex]
The answer is 0.004.
How many meters are the clouds above the ground? Round your answer to the nearest tenth.
Answer:
6,000 meters
Clouds are classified by their shape or appearance and their height above the ground. High clouds start above around 20,000 feet (6,000 meters). They often look thin and patchy or feathery.
Step-by-step explanation:
Answer:
20,000
Step-by-step explanation: