Answer:
-1 ± i√3
Step-by-step explanation:
You can rearrange the expression to vertex form:
x^2 +2x +1 +3
(x +1)^2 +3
You want to find the values of x that make this zero:
(x +1)^2 +3 = 0 . . . . . . . set the expression equal to zero
(x +1)^2 = -3 . . . . . . . . . subtract 3 to get the square alone
x +1 = ±√(-3) = ±i√3 . . .take the square root
x = -1 ±i√3 . . . . . . . . . . subtract 1
The zeros are the complex numbers -1+i√3 and -1-i√3.
Sally is solving the linear equation 13+4x-9=7x+7-3x. Her final two steps are 4+4x=4x+7 ,4=7 select the statement that correctly interprets Sally’s solution A: The solution is x=0 B: The solution is ordered pair (4.7). C: There is no solution since 4=7 is a false statement D: There are infinitely many solutions since 4=7 is a false statement
Answer:
C. there is no solution since 4=7 is a false statement
Linear equations are equations with a leading degree of 1. This shows that there is no solution since 4 =7 is a false statement
Solving linear equationLinear equations are equations with a leading degree of 1. Given the linear equation
Given
13+4x-9=7x+7-3x
Simplify
4 + 4x = 4x + 7
Collect the like terms
4x - 4x = 7 - 4
0x = 3
This shows that there is no solution since 4 =7 is a false statement
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team tool bella canoed 15 3/4 miles in 5/4 hours. What was their average rate of speed in mph
Average speed is 12.6 miles per hour
Solution:
Given that team tool bella canoed [tex]15\frac{3}{4}[/tex] miles in [tex]\frac{5}{4}[/tex] hours
To find: average rate of speed in miles per hour
From given information,
[tex]distance = 15\frac{3}{4} \text{ miles } = \frac{15 \times 4+3}{4} = \frac{63}{4} \text{ miles}[/tex]
[tex]time = \frac{5}{4} \text{ hours}[/tex]
To find the speed we use the below formula,
[tex]speed = \frac{distance}{time}[/tex]
Substituting the given values we get,
[tex]speed = \frac{\frac{63}{4}}{\frac{5}{4}}\\\\speed = \frac{63}{4} \times \frac{4}{5} = \frac{63}{5} = 12.6[/tex]
Thus average speed is 12.6 miles per hour
what is the solution to -7/8 ≤ m - 13/8
Solving for m...
-7/8≤m-13/8
6/8≤m
m≥3/4
answer: m≥3/4
Answer: m≥3/4
Step-by-step explanation:
Solving for m:
Step 1: -7/8≤m-13/8
Step 2: 6/8≤m
Step 3: m≥3/4
answer: m≥3/4
Write a two column proof
Answer:
Step-by-step explanation:
Given:
TU ≅ WU
∠T ≅ ∠W
To Prove:
[tex]\overline{TS} \cong \overline{WV}[/tex]
Proof:
In Δ TUS and Δ WUV
STATEMENT REASON
1. TU ≅ WU 1. Given
2. ∠T ≅ ∠W 2. Given
3.∠TUS ≅ ∠WUV 3. Vertically Opposite Angles are equal
4. ΔTUS ≅ ΔWUV 4. Angle-Side-Angle congruence test.
5. ∴ TS ≅ WV 5. Corresponding parts of congruent triangles.
[tex]\overline{TS} \cong \overline{WV}[/tex].......Proved
The sum of Ava’s and Grace’s age is 35. Ava is one year less than three times Grace’s age. How old is Grace?
Grace is 9 years old. We found this by setting up a system of equations with the information given and solving for Grace's age.
Explanation:We are given two pieces of information about Ava and Grace's ages:
The sum of Ava’s and Grace’s age is 35.Ava is one year less than three times Grace’s age.To find Grace’s age, we can set up a system of equations based on the information provided:
Let G represent Grace’s age.Let A represent Ava’s age.The first equation can be written as:
A + G = 35
From the second piece of information, we can write:
A = 3G - 1
Now, we can substitute the expression for A into the first equation:
3G - 1 + G = 35
Combine like terms:
4G - 1 = 35
Add 1 to both sides:
4G = 36
Divide by 4:
G = 9
So, Grace is 9 years old.
What is the product of (-12/14)×(-11/15)?
Answer:
22/35
Step-by-step explanation:
-12/14=-6/7
-6/7*-11/15=66/105=22/35
Brook rode her bike 7 miles in 30 minutes. Joshua rode his bike 25 miles in 2 hours. which one is faster. HEEEEEEELLLLLLLLLLLLLLPPPPPPPPP
Answer:
Brook is faster.
Step-by-step explanation:
1 hour=60 minutes
2 hours=2*60=120 minutes
-------------
7 miles in 30 minutes vs 25 miles in 120 minutes
7/30=0.233...mile per minute
25/120=0.20833...mile per minute
Brook is faster than Joshua.
Explanation:To determine which person is faster, we can compare their average speeds.
Average speed is calculated by dividing the total distance traveled by the total time taken.
For Brook, she traveled 7 miles in 30 minutes, so her average speed is:
7 miles ÷ 30 minutes = 0.2333 miles per minute.
For Joshua, he traveled 25 miles in 2 hours, which is equivalent to 120 minutes. So his average speed is:
25 miles ÷ 120 minutes = 0.2083 miles per minute.
Therefore, Brook is faster than Joshua as her average speed is higher.
Savannah can ride her skateboard 2 miles in 10 minutes. How many miles can she ride her skateboard in 1.5 hours?
Answer:
18 miles in 1.5 hours
Step-by-step explanation:
2 miles = 10 minutes
90 minutes (1.5 hours) / 10 minutes = 9
Multiply
2 miles (9) = 10 minutes (9)
18 miles = 90 minutes
18 miles in 1.5 hours
Hope this helps :)
f(x) = x2 + 3x + 4. Is it quadratic, linear, or neither
Answer:
Linear
Explanation:
The first image attached below is the problem graphed. That is a linear line.
The second image is an example of a quadratic line.
This is how you can tell the line is linear.
In a school of 450 people 110 are in the choir 240 are in a band and 60 are in both
What is the probability
The question doesn't require any specific probabilities, but I'm adding my own calculations to make it easier for you to solve your own problem
Answer:
Questions added and answered below
Step-by-step explanation:
Venn Diagram
When we have different sets, some of them belong only to one set, some belong to more than one, some don't belong to any of them. This situation can be graphically represented by the Venn Diagrams.
Let's analyze the data presented in the problem and fill up the numbers into our Venn Diagram. First, we must use the most relevant data: there are 60 people in both the choir and the band. This number must be in the common space between both sets in the diagram (center zone, purple).
We know there are 110 people in the choir, 60 of which were already placed in the intersection zone, so we must place 110-60=50 people into the blue zone, belonging to C but not to B.
We are also told that 240 people are in a band, 60 of which were already placed in the intersection zone, so we must place 240-60=180 people into the red zone, belonging to B but not to C.
Finally, we add the elements in all three zones to get all the people who are in the choir or in the band, and we get 50+60+180=290. Since we have 450 people in the school, there are 450-290=160 people who are not in the choir nor in the band.
The question doesn't ask for a particular probability, so I'm filling up that gap with some interesting probability calculations like
a) What is the probability of selecting at random one person who is in the band but not in the choir?
The answer is calculated as
[tex]\displaystyle P(A)=\frac{180}{450}=0.4[/tex]
b) What is the probability of randomly selecting one person who belongs only to one group?
We look for people who are in only one of the sets, they are 50+180=230 people, so the probability is
[tex]\displaystyle P(B)=\frac{230}{450}=0.51[/tex]
b) What is the probability of selecting at random one person who doesn't belong to the choir?
We must add the number of people outside of the set C, that is 180+160=340
[tex]\displaystyle P(C)=\frac{340}{450}=0.76[/tex]
solve the equation -t = 9(t-10)−t=9(t−10)
Answer:
Infinitely many solutions.
Step-by-step explanation:
-t=9(t-10)-t=9(t-10)
-t=9t-90-t=9t-90
-t=8t-90=9t-90
8t-(-t)-90=9t-90
8t+t-90=9t-90
9t-90=9t-90
Answer:
If you mean −t=9(t−10), then the answer is 9, if you mean −t=9(t−10)−t=9(t−10) then infinite solutions.
Step-by-step explanation:
Here is the answer if you mean −t=9(t−10):
−t = 9 (t−10)
Simplify the equation.
-t = (9)(t) + (9)(-10)
-t = 9t + -90 (Add the opposite)
-t = 9t - 90
Subtract -9t
-t -9t = 9t - 90 - 9t
-10t = - 90
Divide -10 on both sides to make sure the equation is balanced on both sides. And to isolate t to get the final answer.
-10t = -90
-10t = -10
Therefore,
t = 9Is the final answer.
I Hope this helps! Have a great rest of your morning, afternoon, or evening! :D
Show calculations for each of the ratio table
Answer:
From left to right:
3, 30, 20
Step-by-step explanation:
Start by determining the ratio of yellow to red paint. Use the column where both amounts are given:
yellow to red = 2 to 6 = 1 to 3
2 to 6 the same as 1 to 3 when reduced, by dividing both sides by 2.
This means yellow paint is a third of red paint. Backwards, red paint is three times yellow paint.
To go from yellow to red, do yellow X 3.
To go from red to yellow, do red ÷ 3.
Column 1:
1 X 3 = 3
Column 3:
10 X 3 = 30
Column 4:
60 ÷ 3 = 20
The ratios are:
1 to 3
2 to 6
10 to 30
20 to 60
A trail mix is made by adding pecans that sell for 2.50 per pound to chocolate candies that sell for 1.00 per pound. How much of each should be used to get 60 pounds of trail mix tat sell for 1.70 per pound?
Answer:
Should be used 28 pounds of pecans and 32 pounds of chocolate candies
Let
x -----> pounds of pecans used
y ----> pounds of chocolate candies used
we know that
-----> equation A
-----> -----> equation B
Solve the system of equations by graphing
Remember that the solution is the intersection point both graphs
Using a graphing tool
The solution is the point (28,32)
see the attached figure
therefore
Should be used 28 pounds of pecans and 32 pounds of chocolate candies
Abby bought two slices of pizza and two bottles of water for $7.25 Cameron bought four slices of pizza and one bottle of water for $8.25 what is the solutionm
The solution is price of 1 slice of pizza is $ 1.542 and price of 1 bottle of water is $ 2.083
Solution:
Let "p" be the price of 1 slice of pizza
Let "b" be the price of 1 bottle of water
Given that Abby bought two slices of pizza and two bottles of water for $7.25
So we can frame a equation as:
two slices of pizza x price of 1 slice of pizza + two bottles of water x price of 1 bottle of water = $ 7.25
[tex]2 \times p + 2 \times b = 7.25[/tex]
2p + 2b = 7.25 ---- eqn 1
Also given that Cameron bought four slices of pizza and one bottle of water for $8.25
So we can frame a equation as:
four slices of pizza x price of 1 slice of pizza + one bottles of water x price of 1 bottle of water = $ 8.25
[tex]4 \times p + 1 \times b = 8.25[/tex]
4p + b = 8.25 ---- eqn 2
Let us solve eqn 1 and eqn 2 to find values of "p" and "b"
Multiply eqn 2 by 2
8p + 2b = 16.5 --- eqn 3
Subtract eqn 1 from eqn 3
8p + 2b = 16.5
2p + 2b = 7.25
(-) ----------------------
6p = 9.25
p = 1.542From eqn 1,
2p + 2b = 7.25
2(1.542) + 2b = 7.25
2b = 4.166
b = 2.083Thus price of 1 slice of pizza is $ 1.542 and price of 1 bottle of water is $ 2.083
At the start of the month, Jodie had sold 885 copies of her new book. At the end of the month, she had sold 1,364 copies of her book. If each book profits $13.97, approximately how much did the book profit in the entire month?
Approximately $ 31419 profit is earned from selling books in entire month
Solution:
Given that Jodie had sold 885 copies of her new book
At the end of the month, she had sold 1,364 copies of her book
We have to determine the profit earned in the entire month
From given information,
Start of month sale = 885 copies
End of month sale = 1364 copies
Total copies of books sold = Start of month sold + end of month sold
Total copies of books sold = 885 + 1364 = 2249
Also given that each book profit is $ 13.97
Profit of 1 book = $ 13.97
Therefore for 2249 books, profit earned is given as:
Profit of 2249 books = $ 13.97 x 2249 = 31418.53
Therefore approximately $ 31419 profit is earned from selling books in entire month
While in Europe, if you drive 117 km per day, how much money would you spend on gas in one week if gas costs 1.10 euros per liter and your car's gas mileage is 42.0 mi/gal ? Assume that 1euro=1.26dollars.
Answer:
Total Cost of Week = 81.20 Euros
Total Cost of Week (in dollars) = $102.31
Step-by-step explanation:
117 km per day
You drive 7 days
So,
Total miles driven = 117 * 7 = 819 km
Mileage is 42 miles per gallon. So how many gallons would it require to drive 819 km?
819/42 = 19.5 gallons
We know 1 gallons = 3.78 liters
So,
19.5 gallons would be:
19.5 * 3.78 = 73.82 liters
1.10 Euro PER LITER, so the total cost:
Total Cost of Week = 73.82 * 1.10 = 81.20 Euros
In dollars (1 euro = 1.26 dollars):
Total Cost of Week (in dollars) = 81.20 * 1.26 = $102.31
The cost on gas is approximately 7.2 euros
Data given;
Distance = 117kmrate of consumption = 42.0 mi/galcost of gas = 1.10 eurosConversion of distance from km to milesIf 1mi = 1.609km
And we cover 117km daily, let's convert this into miles
[tex]1mi=1.62km\\ x mi = 117km\\ x = 117/1.62\\ x = 72.2mi[/tex]
This shows that we cover a distance of 72.2 miles daily.
But the car consumes 1 gallon in 42 miles, let's calculate the gas required to cover 72.2 miles
[tex]42mi = 1g\\ 72.2mi =x\\ x = 72.2/42\\ x = 1.719[/tex]
The total gas consumed daily is approximately 1.72 gallons.
Cost of gas dailyThe cost of gas daily can be calculated from the data given but we have to convert the volume from gallon to liter
Gallon - Liter1L = 0.26 gallon
xL = 1.72 gallons
cross multiply this and solve for x
[tex]x = \frac{1*1.72}{0.26}\\ x = 6.6[/tex]
This shows that we consume 6.6L daily.
But we were given that the cost of 1 liter of gas is equal to 1.10 euros
1L = 1.10 euros
6.6L = x euros
[tex]x = \frac{1.1*6.6}{1}\\ x = 7.26[/tex]
The cost of gas daily is 7.26 euros or approximately 7.2 euros.
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Simplify the expression $416.48÷4= $104.12 please
Answer:
Step-by-step explanation:
Just do the long division and you'll find out.
Raise the fraction to the highest term 1/5 to 15ths=
Final answer:
To raise the fraction 1/5 to 15ths, multiply both the numerator and the denominator by 3 to get the equivalent fraction 3/15.
Explanation:
To raise the fraction 1/5 to 15ths, we need to find an equivalent fraction that has a denominator of 15. To do this, we need to find a number that we can multiply both the numerator and the denominator of 1/5 by to get a new fraction with a denominator of 15. Since 5 multiplied by 3 equals 15, we multiply both the numerator and the denominator of 1/5 by 3.
Thus, we have:
1/5 × 3/3 = 3/15
To raise the fraction 1/5 to 15ths, multiply both the numerator and the denominator by 3 to get the equivalent fraction 3/15.
The fraction 1/5 is equivalent to 3/15 when raised to 15ths.
Out of 1,000 tickets in a raffle, one ticket will win a $710 prize. The rest will win nothing. If you have a ticket, what is the expected payoff?
Which ordered pair is a solution of the equation?
-2 – 4y = -10
Choose 1 answer:
@
Only (3,2)
®
Only (–3, 3)
©
Both (3, 2) and (-3,3)
Neither
Answer: Neither
Step-by-step explanation:
I can not figure this question out! Plz help!! A drill team is raising money by holding a car wash. The team earns $6.00 for each car washed. The team's expenses include $50.00 for advertising plus $0.50 in materials for each car washed. Let f(x) represent the team's total earnings for washing x cars and g(x) represents the team's total expenses for washing x cars. Describe how you can use f(x) and g(x) to obtain a function p(x) that gives the team's profit for washing x cars. Then write a rule for p(x).
Answer:
Step-by-step explanation:
Total earnings = f(x) = 6x
Total expenses =g(x) = 0.5x + 50
Profit p(x) = f(x) - g(x)
= 6x - ( 0.5x + 50)
= 6x - 0.5x - 50 = 5.5x - 50
What do the following two equations represent? 4x-2y=-5 and -2x+3y=-3
Choose 1 answer:
A) equal lines
B) parallel lines
C) perpendicular lines
D) none of the above
*40 points*
Answer:
Step-by-step explanation:
4x - 2y = -5
-2y = -4x - 5
y = 2x + 5/2.....slope here is 2
-2x + 3y = -3
3y = 2x - 3
y = 2/3x - 1.....slope here is 2/3
NONE OF THE ABOVE.....they are not the same line....they are not parallel because they dont have the same slope....they are not perpendicular because they do not have negative reciprocal slopes
Answer:
this would be none of the above.
Step-by-step explanation:
its not equal because when solving, x and y isnt the same for both equations.
i cant explain the rest, my apologies but if u use a website called *desmos* you can put up equations and itll graph them for you. :3
A flower shop has 11 red roses seven pink roses nine white roses and three yellow roses in stock one type of roses Ramsey selected for a flower arrangement what Is the probability that the selected rose is red or yellow
Answer:
11/147
Step-by-step explanation:
11 + 7 + 3 = 21
chances of red = 11/21
and chances of yellow = 3/21
3/21 = 1/7
11/21 x 1/7 = 11/147
Answer:
14:30
Step-by-step explanation:
Okay so your looking for the probability of red or yellow roses so you would combine the numbers of red and yellow roses then add all the roses up together, all the red and yellow are 14 and there are 30 roses in the shop so the answer would be 14:30
Ratio as a fraction 12:36
Step-by-step explanation:
[tex]12:36=\dfrac{12}{36}=\dfrac{12:12}{36:12}=\dfrac{1}{3}[/tex]
Answer: 1/3
Step-by-step explanation: The ratio 12:36 can be written as the fraction 12/36. So, we simply put the 12 as the numerator of our fraction and put the 36 as the denominator of our fraction.
12/36 can be simplified by dividing the numerator and the denominator by the greatest common factor of 12 and 36 which is 12 and we get the fraction 1/3.
The fraction 1/3 still represents the ratio 1/3 even though we have written it in the form of a/b or fraction form.
a store sells packages of comic books with a poster.
1 poster + 6 comics = $12.75
Or
1 poster + 13 comics = $19.75
a. write a linear function in the form y=mx+b that represents the cost, y, of a package containing any number of comic books.
b. Construct Arguments. Suppose another store sells a similar package, modeled by a linear function with initial value $7.99 which store has the better deal? Explain.
Answer:
a) [tex]y=m+6.75[/tex] where [tex]m[/tex] is the number of comic books
b) Case B has better deal
Step-by-step explanation:
a)
Let the cost of a poster be [tex]b[/tex] ;Let the cost of a comic book be [tex]x[/tex];Let the number of comic books be [tex]m[/tex];Let the total cost be [tex]y[/tex];Thus, this is in the form of :
[tex]y=m*x+b[/tex]
Given :
[tex]12.75=6*x+b[/tex][tex]19.75=13*x+b[/tex]subtracting both ,
[tex]7=7x\\x=1;[/tex]The cost of one comic book is $1;
substituting in the first equation ,
[tex]12.75=6+b\\b=6.75;[/tex]
The equation is :
[tex]y=m+6.75[/tex]
b)
Since the shop sells poster with a comic book , initial value is the cost of one comic book plus one poster.
[tex]7.99=x+b\\x=1;[/tex] --since its similar.
In case of a. , The cost of one book plus poster = $1+6.75=$7.75
which is lesser than $7.99 .
Thus case B has the best deal.
MAT
8. The development budget, C, for a computer game company is described by the equation
C = $50,000t + $10,000, where t is the number of years since the company's creation.
Which statement is true?
A. Each year development expenses increase by $50,000.
B. Each year development expenses increase by $60,000.
C. Each year development expenses are $50,000.X
D. Each year development expenses are $60,000.
Answer:
B
Step-by-step explanation:
B. Each year development expenses increase by $60,000.
Answer:
B. Each year development expenses increase by $60,000.
Step-by-step explanation:
Find the variable x.
Answer:
x = 5
Step-by-step explanation:
7x is a secant- secant angle and has measure equal to half the difference of the intercepted arcs, that is
7x = 0.5(22x + 10 - 50)
7x = 0.5(22x - 40) ← distribute
7x = 11x - 20 ( subtract 11x from both sides )
- 4x = - 20 ( divide both sides by - 4 )
x = 5
What is the answer???
Answer:
20
-
3
Step-by-step explanation:
A square has an area of 44.89 inches squared. How do I get the length of the diagonal?
Answer:
6.7√2 in ≈ 9.48 in
Step-by-step explanation:
First, use the area of the square to find the side length.
A = s²
44.89 in² = s²
s = 6.7 in
The diagonal of a square divides it into 45-45-90 triangles. You can use Pythagorean theorem to find the length of the diagonal.
c² = a² + b²
c² = (6.7 in)² + (6.7 in)²
c = 6.7√2 in
c ≈ 9.48 in
Answer: 6.7√2
Step-by-step explanation: Let's start this problem by drawing a picture of a square with a diagonal of length x.
Now to find the length of the diagonal, let's first find the length of a side of the square. To find the length of a side, remember that the formula for the area of a square is S² and since we know that the area of the given square is 44.89 inches, we can set up the equation 44.89 = S².
Square rooting both sides, we have 6.7 = S so we can give the side of our square a length of 6.7. Now to find the value of x, it's important to understand that the diagonal of a square creates 45° 45° 90° triangles and in a 45° 45° 90° triangle, the hypotenuse = √2 × leg.
So we have x = 6.7√2.
So the length of the diagonal of the square is 6.7√2 inches.
Image provided.
A truck carries apples, grapes, and blackberries in the ratio of 4:3:4 if the apple weighs 160 pounds how much does the truckload of fruit weigh in total
Answer:
160/x = 4/3
x = (160/4)(3) = 40(3) = 120
Apples: 160 pounds
Grapes: 120 pounds
Blackberries: 160 pounds
The total weight of this truckload of fruit is 160 + 120 + 160 = 440 pounds.
To find the total weight of the truckload of fruit with apples weighing 160 pounds in a ratio of 4:3:4, calculate the total ratio parts and apply it to the weight of apples. The total weight of the fruit is 440 pounds.
Explanation:The truck carries apples, grapes, and blackberries in the ratio of 4:3:4.
To find the total weight, you need to calculate the total ratio parts, which is 4 + 3 + 4 = 11 parts. Then, for apples alone, 4 parts represent 160 pounds, so each part is 160/4 = 40 pounds. The total weight of the truckload of fruit would be 11 parts * 40 pounds = 440 pounds.
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