Answer:
[tex] x = -2 [/tex] or [tex] x = -5 [/tex]
Step-by-step explanation:
You need to complete the square before you can take the square root of both sides.
[tex] x^2 + 7x + 10 = 0 [/tex]
Subtract 10 from both sides.
[tex] x^2 + 7x = -10 [/tex]
To complete the square, you need to add the square of half of the x-term coefficient to both sides.
The x-term coefficient is 7. Half of that is 7/2. Square it to get 49/4. Now we add 49/4 to both sides of the equation.
[tex] x^2 + 7x + \dfrac{49}{4} = -10 + \dfrac{49}{4} [/tex]
[tex] (x + \dfrac{7}{2})^2 = -\dfrac{40}{4} + \dfrac{49}{4} [/tex]
[tex] (x + \dfrac{7}{2})^2 = \dfrac{9}{4} [/tex]
Now we use the square root property, if
[tex] x^2 = k [/tex], then
[tex] x = \pm \sqrt{k} [/tex]
[tex] x + \dfrac{7}{2} = \pm \sqrt{\dfrac{9}{4}} [/tex]
[tex] x + \dfrac{7}{2} = \pm \dfrac{3}{2} [/tex]
[tex] x + \dfrac{7}{2} = \dfrac{3}{2} [/tex] or [tex] x + \dfrac{7}{2} = -\dfrac{3}{2} [/tex]
[tex] x = -\dfrac{4}{2} [/tex] or [tex] x = -\dfrac{10}{2} [/tex]
[tex] x = -2 [/tex] or [tex] x = -5 [/tex]
the expression 7(-2x+2)
simplifies to Ax + B, where
A=
B=
Answer:
A = 14
B = 14
Step-by-step explanation:
7(-2x+2)
-14x + 14
A = 14
B = 14
4 [-2a - 6b + 5a - 1]
Answer:
4(3a-6b-1)Step-by-step explanation:
[tex]4 [-2a - 6b + 5a - 1]\\\\Simplify\:\\-2a - 6b + 5a - 1 : 3a-6b-1\\\\=4\left(3a-6b-1\right)[/tex]
Write an equation in slope-intercept form for the line that passes through (8,1) and (4,3)
.
y=−2x+5
y=−1/2x+5
y=1/2x+5
y=−1/2x+1/5
Solve the inequality and graph the solution on the line provided.
3x + 12 > 3
Answer:
x>-3
Step-by-step explanation:
3x+12>3
3x>-9
x>-3
please please please Help!!!
Answer:
The Answer Is B
Step-by-step explanation:
Given f(x) and g(x) below, find the value of f(2) and g(1). *
1 point
If f(x) = 4x + 1 and g(x) = x2 – 4, find the value of f(2) and g(1).
Answer:
f(2) = 9
g(1) = -3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Function NotationStep-by-step explanation:
Step 1: Define
f(x) = 4x + 1
g(x) = x² - 4
f(2) is x= 2
g(1) is x = 1
Step 2: Evaluate
f(2)
Substitute: f(2) = 4(2) + 1Multiply: f(2) = 8 + 1Add: f(2) = 9g(1)
Substitute: g(1) = 1² - 4Exponents: g(1) = 1 - 4Subtract: g(1) = -3Mr. Cantu is selling snow cones. He used 26.72 ounces of ice to make 4.7 snow cones. If he used an equal amount of ice in each one, how many ounces of ice are in each snow cone?
What is the solution to the inequality x + 4 + 2x ≤ 20 + 5x – 32
Answer:
x+4+2x = 20+5x-32
Step-by-step explanation:
x+4+2x
= 3x + 4
20+5x-32
= 20-32+5x
= 5x-12
Finding the value of X
3x+4 = 5x-12
= 4+12 = 5x-3x
= 16 = 2x
= 16/2 = X
= 8 = X
By putting the value of X in the equation
(3×8)+4
= 24 +4
= 28
(5×8)-12
= 40-12
28
28 = 28
so the X+4+2x < 20+5x-32 is wrong
find the total to the nearest cent $24 lunch 15% tip# show work
Answer:
$27.60
Step-by-step explanation:
First, we need to find how much the tip is:
we can convert 15% directly to a decimal:
15% = 0.15
Then we find :
15% of 24 = 0.15 x 24 = 3.59999999999999
3.599999999999999 to the nearest cent is 3.60
Then we add the tip to the original bill:
3.60 + 24 = 27.60
So the total cost of the lunch is $27.60
In pedros town 42% of the houses have both internet service and a home phone. If 82% of all the houses in his town have internet service, what is the probability that a house has a home phone if it has internet service?
Answer: 0.51
Step-by-step explanation:
We know that:
For a random selection, we have a probability of 0.42 where the house has both services and a probability of 0.82 that the house has only internet service.
Let's suppose that the percentage of houses the houses with internet service (the 82% of the total) that also have a home phone is X
Then we must have that, (X/100%) times the 0.82, must be equal to 0.42
(X/100%)*0.82 = 0.42
X = (0.42/0.82)*100% = 51%
This means that 51% of the houses with internet service, also have a home phone.
Then the probability that a house has a home phone given that it has internet service, is equal to:
51%/100% = 0.51
The probability is 0.51
PLEASE HELP MEEEE!!!
Answer:
the constabt or proportinaity is 2 because
2/1=2
4/2=2
8/4=2
10/5=2
Step-by-step explanation:
2) 50 apples cost $25. How much would 75 apples cost?
Answer:
50 : 25 = 75 : 37.50
Step-by-step explanation:
If 50 apples cost $25, that means 2 apples cost $1.
75 apples cost 37.5, or $37.50
Which statement describes a unit rate? Group of answer choices Sara is reading 97 words in 1 minute. Sara ate 3 crackers and 1 apple. Sara ate 1 cookie. Sara is driving 16 miles.
Answer:
97 words in 1 minute
Step-by-step explanation:
A unit measure is so many somethings done usually per unit time. Examples
1 orange in 1 minute.10 tomatoes per tomato plant50 miles in one hour10 cookies per week3 crackers and 1 apple is not. For ever apple, she ate 3 crackers would be
1 cookie is not. It is not per anything.
Driving 16 miles is not. Again, it is not per anything.
The answer is 97 words in 1 minute.
What is the ratio of 24 players to 3 teams in simplest form?
24:3
1:8
8:1
3:24
What is 16-12x=4y when you are solving the equation for x ?
Answer:
x = [tex]\frac{-1}{3}y[/tex] + [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
16 - 12x = 4y
Add -16 to both sides.
-12x + 16 + (-16) = 4y + (-16)
-12x = 4y - 16
Then divide both sides by -12
-12x / (-12) = [tex]\frac{4y-16}{-12}[/tex]
x = [tex]\frac{-1}{3}y[/tex] + [tex]\frac{4}{3}[/tex]
what is -4/-3 simplified
Answer:
[tex]\frac{4}{3}[/tex]
Step-by-step explanation:
The negative cancels out each other
At the baseball statuim, four hot dogs and three bags of candy cost $22.75. Ten hot dogs and nine bags of candy cost 63.25. What does a hot dog cost?
Answer:
Ayooo why u eating a glizzy ;-;
Step-by-step explanation:
Ty worked 4 hours and earned $28. At this rate, how much would he earn in 9 hours?
Answer:
63
Step-by-step explanation:
Ty worked 4 hours ad earned $28. This means that he earned $7 per hour. So, 7 times 9 is equal to 63. Which means that Ty will earns $63 in 9 hours.
Pat earns $30.00 for traveling to the homes plus $10.50 for each hour of tutoring. Write a linear equation that models their total earnings for traveling and tutoring for a given number of hours.
Answer: 30 + 10.50h
Step-by-step explanation:
From the question, we are informed that Pat earns $30.00 for traveling to the homes plus $10.50 for each hour of tutoring.
The linear equation that models their total earnings for traveling and tutoring for a given number of hours would be written as:
= $30 + $10.50h
where h represents the number of hours for tutoring used.
For example, if 2 hours if tutoring was used, the total amount earned would be:
= 30 + 10.50h
= 30 + 10.50(2)
= 30 + 21
= $51
Can someone please show me the working out because I really don’t know how to find the area of this.
Step-by-step explanation:
Base of smaller pink triangle
= (3m + 6m) - 7m = 2m.
Area of smaller pink triangle
= 0.5(2m)(5m) = 5m².
Area of bigger pink triangle
= 0.5(6m)(5m) = 15m².
Hence total area shaded = 5m² + 15m² = 20m².
Are shape I and shape Il similar? If so, give the dilation that proves they are similar. If not, explain why the shapes are not similar
Answer:
They are similar.
Step-by-step explanation:
They are similar because, the top triangle has one more square to the height as well as the width. If you take one square away from the height and width the top triangle is the same size as the bottom triangle.
four different ' four 4's problems ( where they all equal a different #) and four different four 4's that equal the same #
please help!!
Answer:
1=(4/4)*(4/4)
2=(4/4)+(4/4)
3 = (4+4+4)/4
4 = 4 + (4-4)*4
20=4 × (4/4 + 4)
20=4 × (4/4 - (-4))
[tex]20 = \sqrt{4} +\sqrt{4} + (4x4)[/tex]
[tex]20 = \sqrt{4} +\sqrt{4} + (-4 x -4)[/tex]
Step-by-step explanation:
The x is a multiplication sign not a variable, I hope this right. Good luck, I am so tired.
how maby solutions does this have
8 + 2 (x - 6 ) = -2 +2x - 2
Answer:
This has infinite solutions.
Step-by-step explanation:
Key skills needed are: One variable equations, Algebra, Adding/Subtracting Like Terms
1) We first start with the equation: 8 + 2 (x - 6 ) = -2 +2x - 2
2) We first need to use distribution property for the parentheses.
We need to distribute the 2 to the x and the -6.
3) This would be 8 + 2x - 12 = -2 +2x - 2
4) The next thing to do is combine like terms.
Like terms are terms with the same variable, or no variable at all. 8 and 6 would be like terms, and 2x and 4x would be like terms. 2x^2 and 4x would not be like terms as one has x^2 and the other has only x.
3) Now you know what like terms are, you can implement this into the problem --> Combine the 8 and 12 on the left side + Combine the -2 and -2 on the right side ----> 2x-4 = 2x-4
4) Since both sides have the same exact thing (both sides have 2x-4) this equation has infinite solutions.
Hope you understood and have a nice day!! :D
What is the total cost of a $75.00 item with a sales tax of 4%?
$78.00
$72.00
$79.45
$81.00
Answer: The answer is A, $78.00
Step-by-step explanation: Hope it helps
The required cost of the item after 4% of sales tax is given as $78.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
Let the total cost of the item be x,
According to the question,
x = cost + sales tax
X = 75 + 4% of 75
x = 75 + 3
x = $78
Thus, the required cost of the item after 4% of sales tax is given as $78.
Learn more about percentages here:
brainly.com/question/13450942
#SPJ6
A lake near the Arctic Circle is covered by a 222-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 333 weeks, the sheet is only 1.251.251, point, 25 meters thick. Let yyy represent the ice sheet's thickness (in meters) after xxx weeks. Complete the equation for the relationship between the thickness and number of weeks.
A lake near the Arctic Circle is covered by a 2-meter-thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a constant rate. After 3 weeks, the sheet is only 1.25 meters thick. Let y represent the ice sheet's thickness ( in meters) after x weeks. Complete the equation for the relationship between the thickness and number of weeks.
Answer:
y = 2 - 0.25x
Step-by-step explanation:
From the question, the initial thickness of the ice sheet = 2 meters,
After 3 weeks, the thickness of ice sheet reduced to 1.25 meters
Hence, the difference in the thickness in 3 weeks is calculated as:
2m - 1.25m = 0.75m
The amount of changes that occurred in 3 weeks is given as:
= 0.75/3 = 0.25 meters,
We are told that, the ice is melting with the constant rate.
Therefore, the equation for the relationship between the thickness and number of weeks is given as:
y = 2 - 0.25x
Answer: the answer above is correct
Step-by-step explanation:
What is tally marks?
Answer:
tally mark also called hash marks and they are a unary numeral system
1.221 x 1/100 =
answer with the product. Correct answer will be awarded with branliest
Answer:
0.1221
Step-by-step explanation:
HURRY! A student works at a bicycle shop. When he sells a bicycle, he earns 6% of the sale price as a commission. If he sells 1 bicycle for $450 and 2 bicycles for $250 each, what is the total amount of commission he earns?
A $69.00
B $57.00
C $6.90
D $5.70
Answer:
B.
Step-by-step explanation:
First your going to need to find 6% of 450 which is 27
then you need to find 6% of 250 which is 15 and you have two 250's so you have two 15's
next add them all up and you got yourself 57
btw sorry my explanation sucks
Answer:
57$
Step-by-step explanation:
450 + 500 = 950 and 6% of 950 is 57
Please help me with this homework
Step-by-step explanation:
Negative slope
Its going from left to right.
The lines graphed below are perpendicular. The slope of the red line is
What is the slope of the green line?
Answer:
Is there a picture for this one and also you didn't mention the slope of the red line is?
Step-by-step explanation:
Answer:
The slope of the Green line should be the same as the red line- but a negative number instead of a positive.
Step-by-step explanation:
This is the inverse of the line
So by reflecting it over the y-axis, the slope remains the same but will change from positive to negative and vise versa