Answers
Answer:
(a) When a = 4 and b = -5, a² + b² - a·b = 61
(b) When a = 4 and b = -5, a³·b + a·b² = -220
(c) [tex]When \ a = 4 \ and \ b = -5, \ \dfrac{a - b}{a + b} + a -b = 0[/tex]
(d) When a = 4 and b = -5, (a + b)² - (a - b)² = 82
Step-by-step explanation:
The question relates to evaluation of expressions, given the values of the variables, "a" and "b"
Where;
a = 4 and b = -5
(a) For a² + b² - a·b, we have;
a² + b² - a·b = 4² + (-5)² - 4 × (-5) = 16 + 25 + 20 = 41 + 20 = 61
(b) For a³·b + a·b² we have;
a³·b + a·b² = 4³·(-5) + 4·(-5)² = 64 × (-5) + 4 × 25 = -320 + 100 = -220
(c) For [tex]\dfrac{a - b}{a + b} + a -b[/tex], we have;
[tex]\dfrac{a - b}{a + b} + a -b = \dfrac{4 - (-5)}{4 + (-5)} + 4 - (-5) = \dfrac{4 + 5}{4 -5} + 4 + 5= \dfrac{9}{-1} + 4 + 5 = -9 + 4 + 5 = 0[/tex]
[tex]\therefore when \ a = 4 \ and \ b = -5, \ \dfrac{a - b}{a + b} + a -b = 0[/tex]
(d) For (a + b)² - (a - b)² we have;
(a + b)² - (a - b)² = (4 + (-5))² - (4 - (-5))² = (4 - 5)² - (4 + 5)² = (-1)² - 9² = 1 + 81 = 82
When a = 4 and b = -5, (a + b)² - (a - b)² = 82
Related Questions
A water tank fills as shown in the graph below. What is the slope of the line?
Answers
Answer:
1/3
Step-by-step explanation:
I have a bag with yellow and blue marbles in it. At the moment, the ratio of blue marbles to yellow marbles is 4:3. If I add 5 blue marbles and remove 3 yellow marbles, the ratio will be 7:3. How many blue marbles were in the bag before I added more?
Answers
Answer:
4:7 7 being to total number of marbles (part to whole ratio)
There are 16 blue marbles were in the bag before I added more.
What is mean by Ratio?A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.
Given that;
The ratio of blue marbles to yellow marbles is 4 : 3.
And, If I add 5 blue marbles and remove 3 yellow marbles, the ratio will be 7:3.
Now,
Since, The ratio of blue marbles to yellow marbles is 4 : 3.
Hence, Number of blue marbles = 4x
Number of yellow marbles = 3x
And, If I add 5 blue marbles and remove 3 yellow marbles, the ratio will be 7:3.
Then, We can formulate;
⇒ 4x + 5 / 3x - 3 = 7x / 3x
⇒ (4x + 5) / (3x - 3) = 7 / 3
⇒ 3 (4x + 5) = 7 (3x - 3)
⇒ 12x + 15 = 21x - 21
⇒ 15 + 21 = 21x - 12x
⇒ 36 = 9x
⇒ x = 4
Thus, The number of blue marbles = 4x
= 4 × 4
= 16
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A 4-pound bag of carrots costs $2.48. What is the unit price? *
Answers
Answer:
0.62 cents per pound
Step-by-step explanation:
2.48/4
to find price per pound which is the unit price
2.48/4=0.62
brainliest appreciated
You drop a ping pong ball into a measuring cup. The water started at 200 mL but after you drop the ping pong ball the water rises to 400mL. What is the volume of the ping pong ball?
Answers
Answer:
200
Step-by-step explanation:
Someone help ASAP plssss
Answers
Answer:
49
Step-by-step explanation:
you are given the hypotenuse of 60 and a leg of 35
a^2 + b^2 = c^2
35^2 + b^2 = 60^2
1225 +b^2 = 3600
-1225 -1225
2375
B^2 = square root 2375
48.73 round up to 49
Okay I need 1 and 2 please help
Answers
Answer:
1. x=2 y=4
2. x=2 y=2
Step-by-step explanation:
I dont understand pls help me
Answers
Answer:
the answer is the option B 35
Step-by-step explanation:
first, add 4 and 3. you will get 7. Next, multiply 7 by 5 and you will get the answer :35
[tex]5(3 + 4) \\ 5(7) \\ 35[/tex]
which ends up to be 15+20=35
What effect does inflation have on the prices of goods and services?
A. Prices decrease
B. Prices double
C. Prices increase
D. Prices stay the same
Answers
Answer:
C, price increases
Step-by-step explanation:
this is correct I promise you.
Answer:
C
Step-by-step explanation:
Prices increase because there is a higher demand for the product, but it does not double because each individual seller can set their price.
Plz help I do t have much time!!!!!!!!! Which expression is represented by the model?
A.
B.
C.
D.
Answers
Answer:
4x-3 or A
Step-by-step explanation: because there are 4 x's and 3 "-" which makes it 4x-3
Answer:
Hi, this is a strange problem but I believe the answer is A) 4x-3.
Step-by-step explanation:
I think the X symbols represent "X"es and the dashes represent single negative digits. I may be wrong, but I think this is what your teacher is most likely looking for. Good luck! :)
Donna rides her bike at a rate of 19/2 mph how many miles can donna travel in 1/3 of an hour
Answers
Answer:
19/2 = 9.5. This is the speed she can ride in a single hour. At that speed, she would travel 9.5/3 miles in 1/3 of an hour. 9.5/3 = 3.1666666666666667
Step-by-step explanation:
Emily Elizabeth has $1.50 in dimes and nickels. She has 22 coins in all. How many nickels does she have?
Answers
Answer:
[tex]14[/tex]
Step-by-step explanation:
We can set up the following system of equations:
[tex]\begin{cases}10d+5n=150\\d+n=22\\\end{cases}[/tex], where [tex]d[/tex] is the number of dimes she has and [tex]n[/tex] is the number of nickels she has.
Multiplying the second equation by -5 and adding both equations lets us isolate and solve for [tex]d[/tex]:
[tex]10d+5n+(-5(d+n))=150+(-5(22)),\\5d=40,\\d=8[/tex]
Plugging [tex]d=8[/tex] into any of the two equations will let us solve for [tex]n[/tex]:
[tex]8+n=22,\\n=\fbox{$14$}[/tex].
Therefore, she has 14 nickels.
Evaluate the expression for the given value of the variable.
46 + 1/5r
r = -1/2
Answers
Answer:
[tex]45\frac{9}{10}[/tex] or [tex]45.9[/tex]
Step-by-step explanation:
All we have to do here is substitute the given value of [tex]r[/tex] into the given expression. Therefore, after substituting [tex]r=-\frac{1}{2}[/tex] into [tex]46+\frac{1}{5}r[/tex], we get:
[tex]46+\frac{1}{5}r[/tex]
[tex]= 46+\frac{1}{5}*(-\frac{1}{2} )[/tex] (Substitute [tex]r=-\frac{1}{2}[/tex] into [tex]46+\frac{1}{5}r[/tex])
[tex]=46-\frac{1}{10}[/tex] (Multiply)
[tex]=45\frac{9}{10}[/tex] or [tex]45.9[/tex] (Simplify)
Hope this helps!
Hey there!
The answer to your question is [tex]45\frac{9}{10}[/tex]
We can find this by simply plugging in the "r" value into the given equation.
46 + [tex]\frac{1}{5}[/tex] ([tex]\frac{-1}{2}[/tex])
Now we evaluate the equation:
46 + [tex]\frac{1}{5}[/tex] ([tex]\frac{-1}{2}[/tex])
46 + [tex]\frac{-1}{10}[/tex]
[tex]45\frac{9}{10}[/tex]
Hope this helps and have an amazing day!
3
The following scores of an AP Bio course are listed below. Mr. B wants to figure out the class median for the set of data.
99, 68, 79, 81, 99, 65, 73, 96, 87, 83, 73, 73, 86, 83, 72, 73
What is the median score of data?
79
B 80
73
D 96
81
Answers
Which inequality is NOT satisfied by this table of values?
Answers
Answer: y < -2x-4
Step-by-step explanation:
Answer:
I hope this helps
Answer: y < x-1
Step-by-step explanation:
Please help me! I will brainliest u
Answers
Answer:
<
Step-by-step explanation:
Answer:
m D = m C
Step-by-step explanation:
I'll explain later... I have exams hhh
need rn! worth 25 points (you MUST answer BOTH questions) 谢谢你！
Answers
Answer:
Number 1 - 3 terms (B)Number 2 - 2nd and 3rd optionsNumber 1 Explanation:
Terms are separated by addition or subtraction signs.There are three parts separated by two addition/subtraction signs.That means there are three terms.Number 2 Explanation:
Polynomials can't have negative exponents.Polynomials can't have fractional exponents on variables or roots of variables.For the first option, [tex]\frac{1}{x}[/tex] can also be written as [tex]x^{-1}[/tex], so it has a negative exponent and is not a polynomial.The second and third options follow polynomial rules.The fourth option has [tex]x^{\frac{1}{2} }[/tex], which is the same thing as [tex]\sqrt{x}[/tex]. Polynomials can't have roots of variables (or fractional exponents on variables), so this isn't a polynomial.7 1/2 ÷ 3 3/4 equals?
Answers
Answer:
2
Step-by-step explanation:
Gabriella earns a commission of 6% for every house she sells each month. This month she sold 3 houses totaling $895,000. How much did she earn commission this month?
Answers
Answer:
$53,700
Step-by-step explanation:
Commission earned = percentage commission x total number of houses sold
[tex]\frac{6}{100}[/tex] x $895,000 = $53,700
Solve the perimeter formula for an isosceles triangle, P = 2a + b for a.
a = P + 2b
a = P – 2b
Answers
Answer:
The solution for a is a = [tex]\frac{P-b}{2}[/tex]
Step-by-step explanation:
To solve an equation for one of its variables, do that
Separate the term of this variable on one side and the other terms on the other sidesMake the coefficient of the variable equals1 (if it is not 1)Let us solve the question
∵ The perimeter formula for an isosceles triangle is P = 2a + b
∵ We need to solve it for a
→ By using the first step above, subtract the two sides by b to move it
from the right side to the left side
∵ P - b = 2a + b - b
∴ P - b = 2a
→ By using the second step above, divide both sides by 2
∵ [tex]\frac{P-b}{2}[/tex] = [tex]\frac{2a}{2}[/tex]
∴ [tex]\frac{P-b}{2}[/tex] = a
→ Switch the two sides
∴ a = [tex]\frac{P-b}{2}[/tex]
∴ The solution for a is a = [tex]\frac{P-b}{2}[/tex]
Plssssss help asp it about math and other things pls
Answers
Answer:
1) Actual cost was $5,762.50
2) Joe's birthday is on January 1st.
Step-by-step explanation:
1) To find this, since we know they were wrong by an identical amount and one was over and the other was under, we can average the cost to find the difference between the amounts. Then we can add that difference to the lower (or subtract it from the higher) amount:
6950 - 4575 = 2375
2375 / 2 = 1187.50
4575 + 1187.50 = $5,762.50
2) Joe could turn 21 on January 1st, but was 20 on December 31st. Next year Joe would turn 22 on January 1st.
I hope this helps!
-TheBusinessMan
Zohad has $30 in a savings account that earns 15% interest per year. How much interest will he earn in 4 years?
Answers
Answer:
30/100 X 15 = 4.50
4.50 X 4 = 18
$18
At one location, the temperature increased from -7° F to 40 F between 5:00 a.m. and 9:00 a.m. By 11:00 a.m., the temperature was 3.5 times greater than the 9:00 a.m. temperature. What was the total increase in temperature between 5:00 a.m. and 11:00 a.m., in degrees Fahrenheit?
Answers
Answer:
the answer is 82 F add the temperature together
The total increase in temperature between 5:00 a.m. and 11:00 a.m., in degrees Fahrenheit, is 164.5°F.
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that at one location, the temperature increased from -7° F to 40 F between 5:00 a.m. and 9:00 a.m. By 11:00 a.m., the temperature was 3.5 times greater than the 9:00 a.m. temperature.
The temperature will be calculated as,
Temperature = ( 40 - (-7) x 3.5
Temperature = 47 x 3.5
Temperature = 164.5°F
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How do you solve this? 35=y-6
Answers
Answer:
Rewrite the equation as y−6=35 .
y−6=35
Move all terms not containing y to the right side of the equation.
y=41
Step-by-step explanation:
3 people can build a shed in 8 hours.
How long would it take 5 people?
Give your answer in minutes.
Answers
Answer:
The answer is 288 minutes
This one is hard but I hope someone can help me out
Answers
Step-by-step explanation:
please where is the question
Answer:
that one seems a little bit too hard....
A snowboarder is going down a mountain at a rate of 2000 feet per 20 minutes. At this rate how many feet will he have traveled after 4 hours?
Answers
Answer: 24,000 feet
Step-by-step explanation:
Well there is 60 minutes in an hour. So every 60 minutes you add by 6000
and 6000 x 4= 2400
:)
Item 10
Find the interquartile range of the data.
8, 2, 14, 12, 10, 4, 4, 6
Answers
Answer:
7
Step-by-step explanation:
What is the probability of the complement of spinning an even number by using the spinner below?
A spinner is split into 8 equal parts labeled 1, 2, 3, 4, 1, 2, 3, 5.
StartFraction 3 over 8 EndFraction
One-half
StartFraction 5 over 8 EndFraction
StartFraction 7 over 8 EndFraction
Answers
Answer:
C
Step-by-step explanation:
What is the equation, in slope-intercept form, of the line plotted on the graph below?
A. y= - 2/3 x - 1
B. y= 2/3 x -1
C. y= 3/2 x - 1
D. y= 3/2 x - 1
Answers
(It looks like you may have accidentally typed answers C and D as the same.)
Mika has a goal of folding at least 120 paper swans. He can fold 12 paper swans per hour. Which inequaility can Mika use to find h, the number of hours he should fold paper swans to meet or exceed his goal?
Answers
Answer: it would take him 10 hours to make 120 paper