Hello!
[tex]\large\boxed{a = 0, -3, 7}[/tex]
a³ = 4a² + 21a
Move all "a" to one side:
0 = -a³ + 4a² + 21a
Factor out "-a" from the equation:
0 = -a(a² - 4a - 21)
Solve for a by factoring:
0 = -a(a - 7)(a + 3)
Solve for the roots by setting each factor equal to 0:
-a = 0
a = 0
a - 7 = 0
a = 7
a + 3 = 0
a = -3
Solutions: a = 0, -3, 7
One factor of x^2 + 5x - 24 is?
Answer:
(x-3)(x+8)
Step-by-step explanation:
Answer:
(x-3)(x+8) take your pick
In the figure below, lines p and s are parallel.
Answer:
c
Step-by-step explanation:
i used a calculator (they never lie)
Answer:
22
Step-by-step explanation:
60+6x-12= 180
6x = 180 -48
x= 132/6= 22
3x-8y=-2 and 14x+8y=36
Answer:
X=2
Y=1
Step-by-step explanation:
........... Solution on the photo above
At the local bookstore, Jim bought 2 paperback books for $13.00. Maria bought 5 paperback books for $32.50. Tanya bought 7 paperback books for $45.50. Graph the situation.
Answer:
Hi
Step-by-step explanation:
In a scale drawing 1/2 inch represents 3 feet. If the same scale is used, how many inches will be needed to represent 24 feet?
2 inches
4 inches
8 inches
12 inches
Carys calculates The total amount E, in dollars, that she earns for working h hours using the equation E=10h.
How many dollars does carys earn per hour?
Write 3 expressions that are equivalent to 9x(78)
Example:9(80-2)
Answer:
3*3(156/2)9(95-17)10-1(80-2)t is -40°F on a cold night in the North Pole. When the sun is out the next day, it is -5°F. What is the difference in temperatures?
Answer:
because at 40 its still warm but really cold but in -5 its cold wherever you go even in the warmest blanket
Step-by-step explanation:
khloe and her children went into a movie theater where they sell bags of popcorn for $7 each and candies for $4 each. khope has $60 and must buy no less than 11 bags of popcorn and candies altogether. if x represents the number of bags of popcorn purchased and y represents the number of candies pruchased, write and solve a system of inequalities and determine one possible solution
both inequalities must start with y
Answer: Khloe could buy 3 bags of popcorn and 9 candies.
Step-by-step explanation:
\underline{\text{Variable Definitions:}}
Variable Definitions:
x=
x=
\,\,\text{the number of bags of popcorn}
the number of bags of popcorn
y=
y=
\,\,\text{the number of candies}
the number of candies
\text{\textquotedblleft no less than 11 items"}\rightarrow \text{11 or more items}
“no less than 11 items"→11 or more items
Use a \ge≥ symbol
Therefore the total number of bags of popcorn and candies, x+yx+y, must be greater than or equal to 11:11:
x+y\ge 11
x+y≥11
\text{\textquotedblleft \$60 to spend"}\rightarrow \text{can spend \$60 or less}
“$60 to spend"→can spend $60 or less
Use a \le≤ symbol
One bag of popcorn costs $7, so xx bags of popcorn cost 7x.7x. One candy costs $4, so yy candies cost 4y.4y. The total 7x+4y7x+4y must be less than or equal to \$60:$60:
7x+4y\le 60
7x+4y≤60
\text{Solve each inequality for }y\text{:}
Solve each inequality for y:
\begin{aligned}x+y\ge 11\hspace{30px}& 7x+4y\le 60 \\[0.8em] y\ge 11-x \hspace{30px}& 4y\le 60-7x \\[0.8em] \hspace{30px}& y\le \frac{60-7x}{4} \\[0.8em] & y\le 15-\frac{7}{4}x\end{aligned}
x+y≥11
y≥11−x
7x+4y≤60
4y≤60−7x
y≤
4
60−7x
y≤15−
4
7
x
Graph y\ge 11-xy≥11−x by shading up and graph y\le 15-\frac{7}{4}xy≤15−
4
7
x by shading down:
0
the number of bags of popcorn
the number of candies
x
y
0
the number of bags of popcorn
the number of candies
(3, 9)
Since the point (3, 9(3,9) is inside the double shaded region, one possible solution to the system of inequalities would be:
Khloe could buy 3 bags of popcorn and 9 candies.
The system of inequalities are x + y ≥ 11 and 7x + 4y ≤ 60 and the solution is given by the point P ( 3 , 9 ) where x represents the number of bags of popcorn purchased and y represents the number of candies purchased
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the inequality equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let x represents the number of bags of popcorn purchased and y represents the number of candies purchased
Now , the total number of bags should be no less than 11
And , the inequality is
x + y ≥ 11 be equation (1)
And , cost of each popcorn bag = $ 7
So , the cost of x bags = 7x
And , cost of each candy bag = $ 4
So , the cost of y bags = 4y
The total amount with Khloe = $ 60
And , the inequality is
7x + 4y ≤ 60 be equation (2)
On graphing the inequalities , we can see that the point P ( 3 , 9 ) lies inside the solution
So , 7 ( 3 ) + 4 ( 9 ) ≤ 60
21 + 36 ≤ 60
57 ≤ 60
And , 3 + 9 ≥ 11
12 ≥ 11
Hence , the system of inequalities are solved and the graph is plotted
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write the ratio as a fraction in simplest form.
56 days to 5 weeks
Answer: 8 weeks
Step-by-step explanation:
Which of the following is equivalent to 17g2 – 2g2?
Answer:
whichever equation equals =15g2
Step-by-step explanation:
Answer:
(17 – 2)g ^2
Step-by-step explanation:
The graphs below have the same shapes what is the equation of the blue graph
I do not understand how you can do this without more information.
Answer:
Step-by-step explanation:
I think you are correct. The bottom of the drawing has to have a width or someway of finding it. Also the breakup of the height needs some sort of clue where that breakup occurs. I think you likely have to ask your instructor.
2q-r=p, r=q-s, p=q+2r prove s=2r
Answer:
s=2r
Step-by-step explanation:
Solution:
Given;
2q-r=p
r=q-s
or,q=r+s
p=q+2r
To prove: s=2r
Now,
2q-r=p
or,2(r+s)-r=q+2r
or,2r+2s-r=r+s+2r
or,r+2s=3r+s
or,s=2r
PROVED
If you want any other solutions follow me
THANK YOU
By using the substitution method we can prove s = 2r.
Given,
2p - r = p
r = q - s
p = q + 2r
We need to prove s = 2r.
What is a substitution method?It is a method where we substitute the value of one variable in one equation for the same variable in the other equation.
Example:
x + 4 = y _____(1)
x = y - 4
x + 5 = 2y ______(2)
Putting x = y - 4 in (2)
y - 4 + 5 = 2y
-4 + 5 = 2y - y
1 = y
y = 1
Prove s = 2r.
We have,
2q - r = p ____(1)
r = q - s _____(2)
p = q + 2r ______(3)
From (1) and (2)
Substituting (2) in (1)
2q - (q - s) = p
2q - q + s = p
q + s = p _____(4)
Putting (4) in (3)
q + s = q + 2r
q - q + s = 2r
s = 2r
Hence proved.
Thus we can prove s = 2r.
Learn more about how to prove a given expression here:
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The image above is a parallelogram because both pairs of opposite sides are parallel by the converse of the
Alternate (Interior Exterior) Angle Theorem.
Write which word should go in the underlined space after the word Alternate?
Directions for answering:
Choose the correct word in the parenthesis in the sentence above and type it exactly as shown into the answer
space.
Answer:
msnsjakzooapaozoziznzn zjzkzkamamz xnejiqpwkx
Lots a Loot Bank charges a monthly service fee and a fee per check, and the chart below shows your total monthly fees in relation to the number of checks issued per month.
Answer:
Monthly service fee is like the fixed cost which is basically the y-value where graph crosses the y-axis.
From graph we see that graph crosses at 1 on y-axis so monthly service fee according to sample graph = $1
Now the per check fee works like slope of the line.
To find the slope we need two points so find any two points on the graph of line. I'm using points (1,0) and (4,3)
now slope can be found using formula
Hence per check fee will be $0.5 as per attached sample graph.
You can use same technique for the original graph given with this question.
Step-by-step explanation:
Answer:
A monthly service fee of 0.50 and a per-check fee of 0.50
Step-by-step explanation:
The last 40 boat rentals at a boat rental company were 22 sunfish, 10 kayaks, and 8 rowboats.
The diagram shown can be used to prove the Pythagorean theorem. Which statement is TRUE about the diagram?
es »
A)
The areas of the two rectangles are not equal.
B)
The diagonal of each rectangle is the hypotenuse of a triangle.
0
The area of the red square is represented by ab.
D)
The area of the blue square is represented by a² + b2
Answer:
Step-by-step explanation:
the answer is c
Solve the equation -3=6x-3y for y
Answer:
y = 2x + 1
Step-by-step explanation:
-3 = 6x - 3y
Add 3y to both sides.
3y - 3 = 6x
Add 3 to both sides.
3y = 6x + 3
Divide both sides by 3.
y = 2x + 1
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Luke has a savings account with an initial balance of $380. He makes two transactions.
After the two transactions, the balance of Luke's savings account is the same as the
initial balance.
Which of the following could be the two transactions that Luke made?
a. A withdrawal of $200 and a deposit pf $180
b. A withdrawal of $215 and a deposit of $215
C. A withdrawal of $200 and a withdrawal of $180
d. A deposit of $400 and a withdrawal of $20
Answer:
If Luke ends up with the same as the start $380 that means he withdrew and deposited the same amount. Answer will be b.
Step-by-step explanation:
$380 - $215 = $ 165
$165 + $215 = $ 380
Answer:
10
Step-by-step explanation: r+6+5
Solve the inequality for x.
–3x + 6 –3
D) x > –7
The radius of a circle can be found by dividing the circumference of the circle by 6.28. What is the radius of a circle that has a circumference of 17.27 feet?
0.36 ft
2.75 ft
10.99 ft
2.58 ft
Answer:
2.75 ft
Step-by-step explanation:
Answer:
2.75
Step-by-step explanation:
What is the slope of the line represented by the equation Y=4/5x-3?
what is the domain and range
Answer:
domain = x value
range = y value
Step-by-step explanation:
domain = x value
range = y value
You bought a house in 1963 for $56,000. Since then, you have increased the value 6% per year. What is the value of your house in 2017?
Answer:
244,160
Step-by-step explanation:
How much acetic acid is in a 15-liter container of acetic acid and water that is marked 40% acetic acid?
The solution is 40% acetic acid.
Multiply the amount of the solution by 40%:
15 liters x 0.40 = 6 liters
There is 6 liters of acetic acid
4/3 in a mixed numbers
Answer:
the answer is
[tex]1 \frac{1}{3} [/tex]
PLS HELPPP!!!!!
its due soon, and mainly its asking for verbal
(60) POINTS AND 5 STAR AND THANKS AND BRIAN-LIST!!!!!
The chart below describes the speed of four desktop printers.
Which printer is the fastest?
A Roboprint
B Voltronn
C Vantek Plus
D DLS Pro
6 A store sells bags of 12 apples for $3.60. What is the unit cost per apple?
A $0.30
B $0.33
C $3.33
D $3.60
Answer:
1. Send me the chart and ill get you the answer.
2. unit cost is $0.30
Step-by-step explanation:
Mr. Smith marked up the price of his sofa by 15%. If the sofa originally cost $399, what is the new sale price?
Answer:
457.8
Step-by-step explanation: