A student correctly evaluated an expression with P = -2 and a = 3 and got 3 as the result. Which of the following expressions could she have been evaluating
Answers
Answer:
B
Step-by-step explanation:
A student correctly evaluated an expression where p = -2 and q = 3 and acquired 3 as the result.
And we want to determine which expression could the student have been evaluating.
Thus, we simply need to check each expression by letting p = -2 and q = 3 and see which one equals 3.
Checking the first one:
[tex]\displaystyle \begin{aligned} 3p^2 +2pq - 6q +2 &= 3(-2)^2+2(-2)(3)-6(3) + 2\\ &= (12)+(-12) +(-18) + 2 \\ &=-16\end{aligned}[/tex]
The result is not 3. Hence, A is not correct.
The second expression:
[tex]\displaystyle \begin{aligned} p^3 + 2p^2q-p^2+2pq+q &= (-2)^3+2(-2)^2(3)-(-2)^2+2(-2)(3)+(3)\\ &= (-8)+(24)-(4)+(-12)+(3) \\ &= 3\stackrel{\checkmark}{=}3\end{aligned}[/tex]
Therefore, we can conclude that our answer is B.
We can check the other two regardless.
The third expression:
[tex]\begin{aligned} p^2+q-4q^2 &= (-2)^2 + (3) - 4(3)^2 \\ &= (4) + (3) -(36) \\ &= -29\end{aligned}[/tex]
And the fourth:
[tex]\displaystyle \begin{aligned} p^2+3q^2-q^2+p &= (-2)^2+3(3)^2-(3)^2+(-2) \\ &= (4) + (27) - (9) + (-2) \\ &= 20\end{aligned}[/tex]
Thus, neither the third expression nor the fourth is also correct.
In conclusion, our answer is B.
Related Questions
At 5:00 a.m., the temperature outside was 6°F below zero. By noon, it rose by 15°F.
At 7:00 p.m., the temperature dropped by 5°F. What was the evening temperature?
Answers
Answer:
The evening temperature is 4° F
Step-by-step explanation:
6° F below 0 = -6.
15° F. -6 + 15 is 9.
9° F. 5° F. 9 - 5 = 4
Mrs. Vacarro sliced a banana into 5 pieces. After eating one slice, she gave ⅘ of the original total to her toddler. After her child was finished, there were ⅖ of the banana slices left. What expression would you use to find out what fractional amount of banana Mrs. Vacarro's toddler ate?
Answers
Explanation: there were 5 existing pieces, mrs. Vacarro had 1 and gave the rest to her toddler which were 4 pieces. The remaining pieces were 2 which means the toddler ate 2/5 pieces
The fractional amount of banana Mrs. Vacarro's toddler ate is 2/5.
What is a word problem?
A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Mrs. Vacarro sliced a banana into 5 pieces.
Number of slices she gave to her toddler = 4/5
Number of slices left after her toddler had finished eating = 2/5
Thus number of slices toddler ate,
⇒ [tex]\frac{4}{5} -\frac{2}{5}[/tex]
⇒ [tex]\frac{4-2}{5}[/tex]
⇒ [tex]\frac{2}{5}[/tex]
Hence we can conclude that the fractional amount of banana Mrs. Vacarro's toddler ate is 2/5.
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Last year 160 new candidates submitted applications to work for an agency. This year, that number is on target to increase by 25%. There are 6 months left in the year. How many new applications has the agency received so far this year?
Answers
Answer:100
Step-by-step explanation:
Given
Last year 160 new candidates submitted to work for agency
It is expected to increase by 25% that is , increase in one year should be
[tex]\Rightarrow 160+160\times 25\%\\\Rightarrow 160(1+0.25)\\\Rightarrow 160\times 1.25\\\Rightarrow 200[/tex]
200 application in the upcoming year. So, in 6 months, agency must have accepted 100 applications.
lf y 1/4 · when x=5, find y when x=7. given that y varies directly with x.
y=
Answers
Answer:
y= 0.35
Step-by-step explanation:
y 1/4
when x=5,
find y=? when x=7.
given that y varies directly with x.
y = kx
Where k is the constant of proportionality
k= y/x
k= (1/4)÷ 5
k= 0.05
y= kx
y= (0.05)(7)
y= 0.35
I Hope this will helpful...
15. The perimeter of the triangular field is 540m and its sides are in the ratio 25:12:5 find the area of the field.
Answers
Answer:
let the sides be 25x,12x and 5x ......then
25x+12x+5x=540
45x=540
x=25
sides are 25×12=300
12×12=144
5×12=60
we can find area by herons formula
Use the substitution method to find the solution for the system of equations. Write the answer as an ordered pair. 3x+2y=23 (1/2)-y=4
Answers
Answer:
x = 7.75 y = -0.125
Step-by-step explanation:
3x + 2y = 23 1/2x - y = 4
2(1/2x - y) = (4)2 1x - 2y = 8
3x + 2y = 23
+ 1x - 2y = 8
4x = 31
x = 7.75
3(7.75) + 2y = 23
23.25 + 2y = 23
2y = -0.25
y = -0.125
The cost,c(x), for a taxi ride is given by c(x)=3x+2.00, where x is the number of minutes. What does the slope mean for this situation
Answers
Answer:
for every minute it will cost 3 dollars
Step-by-step explanation:
c(x)=3x+2.00
The cost to get in the taxi is 2 dollars
The slope is 3
3x means that for every minute it will cost 3 dollars
Solve for a.
a
2
8
a =
✓ [?]
Pythagorean Theorem: a2 + b2 = c2
Enter
Answers
Answer: [tex]a=\sqrt{60}[/tex]
Step-by-step explanation:
To solve for a, we want to use Pythagorean Theorem as provided int eh problem. a and 2 are the legs while 8 is the hypotenuse.
[tex]a^2+2^2=8^2[/tex] [exponent]
[tex]a^2+4=64[/tex] [subtract both sides by 4]
[tex]a^2=60[/tex] [square root both sides]
[tex]a=\sqrt{60}[/tex]
Now we know that [tex]a=\sqrt{60}[/tex].
please help me !! :)
Answers
Answer: c
Step-by-step explanation:
c is the same and it is the correct answer
Simplify 7t · s · 3rt.
Answers
Answer:
21 s t^2
Step-by-step explanation:
7t · s · 3rt
Multiply the coefficients
7*3 =21
t*t = t^2
s
Multiply back together
21 s t^2
Check all that apply.
4x2 + 4x + 1 = 0
O A. X=
1
2
1
B. X= -2
c. x=-1
O D. x = 2
O E. x=
=
3
2
O F. X = 3
Answers
Answer:
x = -1/2
Step-by-step explanation:
4x^2 + 4x + 1 = 0
Factor
(2x+1)(2x+1) =0
Using the zero product property
2x+1 = 0 2x+1 =0
2x = -1 2x=-1
x = -1/2 x = -1/2
The diagram below represents which percent?
An area model with 4 shaded sections and 1 unshaded section.
Answers
Answer:
25%
Step-by-step explanation:
1 ÷ 4 = 0.25
0.25 x 100 = 25 = 25%
Giải phương trình
2x+6=0
Answers
Answer: x = -3
[tex]2x+6=0\\\\2x=-6\\\\x=\frac{-6}{2} =-3[/tex]
Answer:
x= -3
Step-by-step explanation:
Solve the equation:
2x +6 = 0
We have isolate 'x'.
First subtract 6 from both sides
2x = 0-6
2x = -6
Divide each side by 2
x = -6/2
x = -3
Type the correct answer in the box. Use numerals instead of words.
Betty sets up a lemonade stand and charges $1 per glass. It cost her $50 to set up the stand. Which function gives the profit, p, she makes by selling g glasses of lemonade?
The number of glasses of lemonade, g, that Betty needs to sell to make a profit, p, if the setup cost her $50 is given by the function p(g) =
.
Answers
Answer:
1g - 50 = p(g)
Step-by-step explanation:
The profit function is,
⇒ p(g) = g - 50
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Betty sets up a lemonade stand and charges $1 per glass.
It cost her $50 to set up the stand.
And, We have to find the function gives the profit, p, she makes by selling g glasses of lemonade.
Now, The number of glasses of lemonade sold = g,
And, A profit, p by function p(g)
Setup cost = $50
Since, Charges for 1 glass = 1 $
Hence, Charges for g glasses = 1.g = $g
Here, The cost = $50
Hence, Profit = $g - 50
⇒ p(g) = g - 50
Therefore, The profit function is,
⇒ p(g) = g - 50
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A number is raised to the 4 th power, then divided by half the of the original number, and finally increased by 141/2. If the result is 100, what was the orginal number
Answers
Answer:
the number is 2.45
Step-by-step explanation:
let the original number = n
[tex]\frac{n^4}{n/2} = \frac{2n^4}{n} = 2n^3\\\\2n^3 + \frac{141}{2} = 100\\\\4n^3 + 141= 200\\\\4n^3 = 200 - 141\\\\4n^3 = 59\\\\n^3 = \frac{59}{4} \\\\n^3 = 14.75\\\\n = \sqrt[3]{14.75} \\\\n = 2.45[/tex]
Therefore, the number is 2.45
what is x increased by 10 divided by 4 as an expression?
please help need answer, I ask you don't answer if you don't know the answer, thank you!
Answers
Answer:
[tex]\displaystyle \frac{x+10}{4}[/tex]
Step-by-step explanation:
We want to write an expression for the phrase: "x increased by 10 divided by 4."
If x is being increased by 10, the expression is:
[tex]x+10[/tex]
And if it is then divided by 4, we can place the entire expression over four. Hence:
[tex]\displaystyle \frac{x+10}{4}[/tex]
Our expression is:
[tex]\displaystyle \frac{x+10}{4}[/tex]
[tex]x^2-x-6=0[/tex]
Answers
Answer:
x = 3 or x = -2
Step-by-step explanation:
x² - x - 6 = 0
(x - 3)(x + 2) = 0
x - 3 = 0 or x + 2 = 0
x = 3 or x = -2
Which equation is equivalent to -2(2 − 2x) = 4 − 8(1 − x)?
Answers
Answer:
x = 0
Step-by-step explanation:
-2(2 − 2x) = 4 − 8(1 − x)
Apply the distributive property:
−2(2 − 2x) = 4 − 8(1 − x)
(−2)(2) + (−2)(−2x) = 4 + (−8)(1) + (−8)(−x)
−4 + 4x = 4 + (−8) + 8x
Combine like terms:
4x − 4 = (8x) + (4+−8)
4x − 4 = 8x + (−4)
4x − 4 = 8x − 4
Subtract 8x from both sides:
4x − 4 − 8x = 8x − 4 − 8x
−4x − 4 = −4
Add 4 to both sides:
−4x − 4 + 4= −4 + 4
−4x = 0
Divide both sides by -4:
-4x/-4 = 0/-4
x = 0
Answer: 0
Step-by-step explanation:
The Changs received a delivery of fuel oil totaling 35.00 gallons. The oil cost $3.05 per gallon. What did the Changs pay for the delivery
Answers
Answer:
$106.75
Step-by-step explanation:
Since the cost of a gallon of oil cost $3.05, we are going to have the equation y = 3.05x, where x represents the number of gallons of oil.
Since the Changs have 35 gallons of oil, the equation would be;
3.05(35) = 106.75
The Changs paid $106.75 for the delivery.
3.
The table shows the estimated number of deer living in a forest over a five-year period. Are the data best represented by a linear, exponential, or quadratic model? Write an equation to model the data.
A. quadratic; y = 91x2 + 0.77
B. exponential; y = 91 • 0.77x
C. linear; y = 0.77x + 91
D. quadratic; y = 0.77x2 + 91
Answers
Answer:
B. exponential; y = 91 • 0.77x
Step-by-step explanation:
I just substituted the x on all of them and only one got the correct y which is B.
...............................................................................................................................................
The Answer is B.
y=91*0.77^x
...............................................................................................................................................
Answer:
B. exponential; y = 91 • 0.77x
Step-by-step explanation:
Just is
How do radical expressions relate to everyday life , give atleast 3 examples !!!!!
Answers
1) Architecture
2) Carpentry
3) Masonry
it is used to calculate formulas such as home inflation
At 11:00 a.m., John started driving along a highway at constant speed of 50 miles per hour. A quarter of an hour later, Jimmy started driving along the same highway in the same direction as John at the constant speed of 65 miles per hour. At what time will Jimmy catch up with John?
Answers
Answer:
12:05 pm
Step-by-step explanation:
Let z be the number of hours, from 11:00 am, when Jimmy would catch up with John. The time that Jimmy will have to drive to catch up with John is z - 1/4 as he started a quarter of an hour late. When Jimmy would catch up with John, they would have traveled the same distance. Hence
50 z = 65 (z - 1/4)
Solve for t
50z = 65z - 65/4
z = 65/60 = 1.083 hours = 1 hour and 5 minutes
Jim will catch up with John at
11:00 am + 1 hour 5 minutes = 12:05 pm
Answer From Gauth Math
Sequence Problem Below
Answers
Answer:
[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\dddddd \displaystyle \Large \boldsymbol{} t_1=\boxed{5} \\\\d=\boxed{-4} \\\\t_n=\boxed{9-4n}[/tex]
Step-by-step explanation:
[tex]\displaystyle\large \boldsymbol{Rule: t_n=S_{n}-S_{n-1}} \\\\\\S_n=7n-2n^2 \ \ \ \ then \\\\\Longrightarrow S_{n-1}=7(n-1)-2(n-1)^2 =7n-7-2n^2+4n-2 \\\\then \\\\\\S_{n}-S_{n-1}=7n\!\!\!\!\!\!\diagup-2n^2\!\!\!\!\!\!\diagup-7n\!\!\!\!\!\!\diagup+7+2n^2\!\!\!\!\!\!\diagup-4n+2=9-4n \\\\t_n=9-4n => t_1=5\\\\d=t_2-t_{1}=1-5=-4[/tex]
what is the value of x
Answers
Answer: 24(option A) is the answer
exterior angle = 360/n
so, n = 15
then, 360/15 = 24
The rate of change is constant in each table. Find the rate of change. Explain what the rate of change means for the situation. (Help ASAP)
Is it a, b, c or d?
Answers
Answer:
C.
Step-by-step explanation:
212/4 = 53, so 53/1, or 53 miles are driven every hour.
On Monday a post office employee processed a batch of letters, on Tuesday she processed three times as many, and on Wednesday she processed 5,000 cards. In the 3 days she processed 15,000 letters. How many did she process on Tuesday
Answers
Let the number of letters processed on Monday = x
She processed 3 times letters on Tuesday.
Therefore, number of letters processed on Tuesday = 3x
Number of letters processed on Wednesday = 5000
Total number of cards processed in 3 days = 15000
Therefore, equation for the situation will be,
x + 3x + 5000 = 15000
4x = 15000 - 5000
4x = 10000
x = 2500
Since, number of letters processed on Tuesday = 3x
Therefore, number of letters processed on Tuesday = 3(2500)
= 7500
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find the surface area
Answers
Answer:
160π in²
Step-by-step explanation:
The formula for the surface area of a cylinder is: A = 2πrh + 2πr²
From here we can plug in what we know (r = 4, h = 16):
A = 2π(4)(16) + 2π(4²)
A = 128π + 32π
A = 160π in²
The surface area of a cylinder is 160π in².
What is the surface area of a cylinder?The surface area of a cylinder is also called the total surface area of the cylinder.
Suppose that:
Radius of the considered cylinder = 'r' units
Height of the considered cylinder = 'h' units
The formula for the surface area of a cylinder is:
A = 2πrh + 2πr²
From here we can plug in what we know that,
(r = 4, h = 16):
A = 2π(4)(16) + 2π(4²)
A = 128π + 32π
A = 160π in²
Hence, the surface area of a cylinder is 160π in².
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200 students in a class took an examination in French and English. 180 of them passed in English and 80 passed in both French and English. 40 students did not pass in any of the subjects Illustrate the information on a Venn diagram How many passed in French? What is the probability of meeting a student who passed in one subject only?
Answers
Answer:
500
Step-by-step explanation:
What is the reciprocal of 7/9 it’s a fraction by the way
Answers
Answer:
9/7
Step-by-step explanation:
Reciprocal means 1 over the number
1 / (7/9)
1 * 9/7
9/7
Answer:
[tex] = \frac{9}{7} [/tex]
Step-by-step explanation:
Reciprocal means inverse:
[tex] {( \frac{7}{9} })^{ - 1} = (\frac{9}{7} ) {}^{1} \\ \\ = \frac{9}{7} [/tex]
Evaluate the expression when b= -6.
b^2-6b+4
Answers
-6(-6) = 36
Answer:
76
Step-by-step explanation:
when b = -6
b^2 - 6b + 4
(-6)^2 - 6(-6) + 4
36 + 36 + 4 = 76
(remember, a negative times a negative always equals a positive)
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