Please answer this questions step by step
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
A system of equations is: x = 10 and 3x + 5y = 20. In the system of equations, what is the value of y?
Answer:
2-
Step-by-step explanation:
[tex]x = 10 \\ 3(10) + 5y = 20 \\ 30 + 5y = 20 \\ 5y = - 10 \\ y = - 2[/tex]
Help!!! What is the difference ? (x - 8)/(3x) - (3x)/(x ^ 2)
Answer:
Given that you're providing only a single term, asking for a difference doesn't make a lot of sense. I assume you're asking to have the expression simplified?
If so, then it can be reduced to (x - 17) / 3x
Step-by-step explanation:
You can simplify by multiplying both terms each by a different ratio that equals one, but also gives the terms common denominator. Multiplying the first one by x²/x² and the second by 3x/3x will do that for you.
After that you can group the terms into one fraction and simplify:
[tex]\frac{x - 8}{3x} - \frac{3x}{x^2} \\\\= \frac{x - 8}{3x}\times\frac{x^2}{x^2} - \frac{3x}{x^2} \times\frac{3x}{3x} \\\\= \frac{x^3 - 8x^2}{3x^3} - \frac{9x^2}{3x^3} \\\\= \frac{x^3 - 8x^2 - 9x^2}{3x^3} \\\\= \frac{x - 8 - 9}{3x}\\\\= \frac{x - 17}{3x}\\[/tex]
Answer:
The difference of [tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex] is [tex]\mathbf{\frac{x-17}{3x}}[/tex]
Step-by-step explanation:
We need to find the difference: [tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex]
Simplifying to find the difference:
[tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex]
x is common in both 3x and x^2 so, we can cancel it out and we get:
[tex]=\frac{x-8}{3x}-\frac{3x}{x(x)}\\=\frac{x-8}{3x}-\frac{3}{x}[/tex]
Now, taking LCM of 3x and x we get 3x, We will multiply 3x with both terms and then solve we get:
[tex]=\frac{x-8-3(3)}{3x}\\=\frac{x-8-9}{3x}\\=\frac{x-17}{3x}[/tex]
It cannot be further simplified, so we get [tex]\frac{x-17}{3x}[/tex] as answer.
So, The difference of [tex]\frac{x-8}{3x}-\frac{3x}{x^2}[/tex] is [tex]\mathbf{\frac{x-17}{3x}}[/tex]
Bethany walks at a rate of 3 step every 2 seconds at this rate how many seconds will it take Bethany to walk 60 steps
Answer:
30seconds
Step-by-step explanation:
if it takes 2 seconds to walk 3steps then in 30 seconds she should have walked 60 steps.
Tori bought 24 candy bars for 69 cents each. She used partial products to find the total cost in cents. Which are NOT possible partial products for 24 × 69?
Answer:
Options A, B, C and D
Step-by-step explanation:
This question is not complete; here is the complete question.
Tori bought 24 candy bars for 69 cents each. She used partial products to find the total cost in cents. Which are NOT possible partial products for 24 × 69?
A. 24
B. 36
C. 180
D. 240
E. 1656
Cost of one candy = 69 cents
Since, cost of 24 candies = Cost of one candy × Number of candies
= 69 × 24
For partial product,
69 × 24 = (60 + 9)(20 + 4)
= 60(20 + 4) + 9(20 + 4)
= 60×20 + 60×4 + 9×20 + 9×4
= 1200 + 240 + 180 + 36
= 1656
Therefore, Options A, B, C and D are not possible partial products.
Conjecture: Any 2 circles in the plane are congruent. Do you agree or disagree
with the conjecture? If you agree, explain how you know. If you disagree, edit the
conjecture so it will always be true.
Answer:
Any 2 circles in the plane are similar.
Step-by-step explanation:
No, I disagree.
Any 2 circles in the plane are congruent only when their diameters have equal length.
Any 2 circles in the plane are similar.
Manuel incorrectly claimed that the surface area of the cylinder shown is about 190.0 in.2. Use a formula to find the surface area of the cylinder. Use 3.14 for π. What was his likely error?
The likely error in Manuel's claim is 552.61 in².
We have,
Height = 16 in
Diameter = 11 in
radius = 5.5 in
The surface area of a cylinder.
= 2πrh + 2πr²
= 2 x 3.14 x 5.5 x 16 + 2 x 3.14 x 5.5²
= 552.64 + 189.97
= 742.61 in²
Now,
Manuel incorrectly claimed that the surface area of the cylinder is
190.0 in²
Error = Correct surface area - Claimed surface area
Error = 742.61 in² - 190.0 in²
Error ≈ 552.61 in²
Thus,
The likely error in Manuel's claim is 552.61 in².
Learn more about cylinder here:
https://brainly.com/question/15891031
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Find the length of the segment with the end points (4,-3) and (7, 1) distance bridge math
Plz help due tomorrow
Answer:
15/16
Step-by-step explanation:
5×3=15
4×4=16
if they're two - you count them +
(my English is not very good :( )
1) Castel and Rob are selling cheesecakes for a school fundraiser. Customers can buy New York style
cheesecakes and apple cheesecakes. Castel sold 5 New York style cheesecakes and 6 apple cheesecakes
for a total of $85. Rob sold 6 New York style cheesecakes and 6 apple cheesecakes for a total of $90.
What is the cost each of one New York style cheesecake and one apple cheesecake?
Answer:
new York cheese cake $5
Apple cheese cake $10
pls help i will give brainliest
Answer:
the thrid one
Step-by-step explanation:
Which expression is equivalent to the given expression? 10q + 5
Answer: i think the answer is b
Step-by-step explanation:
think u
PLEASE HELP!!
what is true about the graph of the line y= -3x + 4?
a) the line has a slope of 4
b) the line has a slope of -4
c) the line crosses the y-axis below the origin
d) the line crosses the y-axis above the origin
Answer:
d) the line crosses the y-axis above the origin
Step-by-step explanation:
your welcome
Solve for X:
5x+3x=2(4x-5)-2
Answer: I got -1, I honest don’t know if i was doing it right so here is my explanation
Step-by-step explanation:
I distributed 2(4x-5)
5x+3x=20x-10-2
Sub 3x for 20x
5x=17x-10-2
Sub -10-2
5x=17x-12
Sub 5x-17x
12x=-12
Divide
Equals -1
Sry it took me a bite
Please answer this question
Jenny wants to save $900 to go to Puerto Rico. She saves $45 each week. Her brother gives her $180. Write an equation to find how many weeks she must save. (I need the equation)
Answer:
45x + 180 = 900
x being number of weeks
Step-by-step explanation:
The equation that can be used to find the number of weeks is 180+45x = 900 and the number of weeks she must save the money is 16 weeks.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
We have:
The amount of money Jenny saved each week = $45
The amount her brother gives = $180
Total amount Jenny wants to save = $900
Let's suppose the number of weeks is x
180+45x = 900 (as she has already $180 and each week she saves is
$45)
So from the above equation, we can find the number of weeks.
After solving the equation:
45x = 900 - 180
x = 16 weeks
Thus, the equation that can be used to find the number of weeks is 180+45x = 900 and the number of weeks she must save the money is 16 weeks.
Learn more about the linear equation here:
brainly.com/question/11897796
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What is the measure of ∠J?
Answer:
6 cm
Step-by-step explanation:
A fish tank has 150 gallons of water and is being drained at a rate of 1/2 gallon each second. A fish tank has 120 gallons of water and is being filled at a rate of 1/4 gallon each second. After how many seconds will the ywo fish tanks have the same amount of water?
Answer:
40! Seconds
Step-by-step explanation:
Calculation for After how many seconds will the two fish tanks have the same amount of water
First step
Based on the information given let the equation be :
150-1/2x=120+1/4x
Second step
Now let solve for x which means that x will be the number of second by multiplying both side by 4
4(150-1/2x)=4(120+1/4x)
=600-2x=480+x
Third step
Let Add 2x on both side
600=480+3x
Third step
Let Subtract 480 on both side
600-480=480-480+3x
120=3x
Last step is to divide both side by 3
120/3=3x/3
40=x
Hence:
x=40 seconds
Therefore After 40 seconds the two fish tanks will have the same amount of water.
ughhhhhhh help again please!!!
Answer:
90 degrees
Step-by-step explanation:
Assuming that this polygon is a square, x would be 90 degrees. In a square, all angles are right angles.
f(x) = -3x^2
Find f(-2)
9514 1404 393
Answer:
f(-2) = -12
Step-by-step explanation:
Put -2 where x is and do the arithmetic.
[tex]f(x)=-3x^2\\\\f(-2)=-3(-2)^2=-3\cdot4=\boxed{-12}[/tex]
WILL MARK BRAINLIST PLSSSSSSSSS
Answer:
Answer
Step-by-step explanation:
I believe it is the first or second choice. I believe it is the first choice, but it could be the second one.
Sorry hope it helps.
Giving brainliest
Math!!
Answer:
B
Step-by-step explanation:
Which is the best estimate of the mass of a skateboard.
a 3 liters
b 3 kilograms
c 30 grams
d 3 grams
Answer:
3 kilograms
Step-by-step explanation:
one is for liquids and the others are too small i think
The sum of two numbers is 51 and the greater number is twice the smaller number. Find the numbers.
a) set up the variables
Let _______ represent the first number Then _______ will represent the second number.
b) What is the equation that represents the above situation? c) Solve the equation.
Answer:
34 and 17
Step-by-step explanation:
x+y=51
2y=x
2y+y=51
3y=51
y=17
2(17)=x
x=34
6. Simplify the expression 2x + 8. when x=4
Answer:
16
if you are happy with my answer, please give brainliest :)
Step-by-step explanation:
Plug in:
8+8
Answer:
16
Step-by-step explanation:
2 × 4 = 8
8+8= 16
your answer is 16 when x equals 4
I
Write an equation of the line passing through the point (2, 3) and
PERPENDICULAR to the line y = -2x + 2.
Answer:
y= 1/2 x +7
the slope is 1/2 since hwne it's perpendicular, it's reciprocal and the sign also changes
Step-by-step explanation:
3= -4 +b
b= 7
Write 19/4 as a decimal
Rita collected and stored beads in 4 different bags.the table below shows the number and color of beeds in each bag.
Answer:
Add the table and i might answer correctly
Step-by-step explanation:
this is math pls help 3x + 2(5x − 7)
Answer: 13x - 14
Step-by-step explanation:
3x + 10x - 14
13x -14
Answer:
13x-14
Step-by-step explanation:
The solution to a system of linear equations is (0, 4).
One of the linear equations in the system is
y = 8x +4.
Which equation could be the other linear equation in the system?
• y=8
• y= 4.0
• y = 80
• y=4