Answer:
[tex]101 * 102 = 10302[/tex]
Step-by-step explanation:
Given
[tex](x + a)(x + b) = x^2 + (a + b)x + ab[/tex]
Required
Find 101 * 102
[tex]101 * 102 =[/tex]
Express as a sum of 100
[tex](100 + 1) * (100 + 2)[/tex]
Compare this to [tex](x + a)(x + b)[/tex]
We have that:
[tex]x = 100[/tex]
[tex]a = 1[/tex]
[tex]b = 2[/tex]
Recall that:
[tex](x + a)(x + b) = x^2 + (a + b)x + ab[/tex]
Substitute 100 for x, 1 for a and 2 for b
[tex](100 + 1) * (100 + 2) = 100^2 + (1 + 2) * 100 + 1 * 2[/tex]
[tex](100 + 1) * (100 + 2) = 100^2 + 3 * 100 + 2[/tex]
[tex](100 + 1) * (100 + 2) = 10000 + 300 + 2[/tex]
[tex](100 + 1) * (100 + 2) = 10302[/tex]
Hence:
[tex]101 * 102 = 10302[/tex]
Write an equation for the line in slope- intercept form. 2. Х -4 -2 o 2 4. -2 4
Answer:
y= -2x-3
Step-by-step explanation:
this is because the y intercept is at negative 3 and the rise over run is down 1 over 2
what is the slope of the line that passes through the points (7, -5) and (10, -7.5)?
A:
[tex] \frac{5}{6} [/tex]
B:
[tex] \frac{6}{5} [/tex]
C:
[tex] - \frac{5}{6} [/tex]
D:
[tex] - \frac{6}{5} [/tex]
Answer:
C. [tex]-\frac{5}{6}[/tex]
Step-by-step explanation:
just use the equation [tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex] So our first point (7,-5) will be [tex]x_1=7,y_1=-5[/tex]and our second point (10, -7.5) will be [tex]x_2=10,y_2=-7.5[/tex] Then substitute[tex]slope=\frac{(-7.5)-(-5)}{(10)-(7)}=\frac{-2.5}{3}=-\frac{5}{6}[/tex]110 meters of fencing are used to fence a rectangular pasture of 750 square meters of farmland. If the length of the pasture is longer than the width, what is the width of the pasture in meters?
Answer:
25mStep-by-step explanation:
Perimeter of the rectangular pasture P = 2(L+W)
Area A = LW
L is the length
W is the width
Given
Perimeter = 110m
Area = 750m
If the length of the pasture is 40m longer than the width, then L = W+40
110 = 2L+2w
55 = L+W .....1
750 = LW.....2
Solving simultaneously
from 1; L = 55-W
substitute into 2;
750 = (55-W)W
750 = 55W-W²
-W²+55W -750 = 0
W²-55W+750 = 0
(W²-25W)-(30W+750) = 0
W(W-25)-30(W-25) = 0
(W-25)(W-30) = 0
W-25 = 0 and W-30 = 0
w = 25m and 30m
Since L = 55-W
L = 55-25 = 30m and;
L = 55-30 = 25m
Since we are told that length id longer than the width then, the width we are going to use is 25m
Leon drove from his house in Cincinnati to his sister’s house in Cleveland, a distance of 252 miles. It took him 4.5 hours. For the first half-hour, he had heavy traffic, and the rest of the time his speed was five miles per hour less than twice his speed in heavy traffic. What was his speed in heavy traffic?
Answer:
Speed in heavy traffic is 32 miles per hour
Step-by-step explanation:
Total distance = 252miles
Total time = 4.5hours = 4 hours + 30minutes
Let the speed in heavy traffic = x
distance = time * speed
First half hour
D1 = 0.5*x
The speed after the traffic = 2x - 5
D2= 4* (2x - 5)
Total distance = D1 + D2
[tex]\frac{x}{2}[/tex] + 8x - 20 = 252
[tex]\frac{17x}{2}[/tex] = 272
x = [tex]\frac{272}{17}*2[/tex]
x = 32 miles per hour
what is this !?help please!
Please help me my homework is due tomorrow use the screen shot
Answer:
1/5
Step-by-step explanation:
(5^7*5^5)/5^13 (when multiplying numbers with the same base, add the exponents)
= (5^12)/5^13 (when dividing exponents with the same base, subtract the exponents)
= 1/5^1 (anything to the first power is itself)
= 1/5
the ratio of 70 to 210
If you're looking for the lowest ratio for 70 to 210, it should be
1:3
70min=70×60=4200sec
ratio=4200/210
=210×20/210
=20/1
=20:1
I am less than 10 l am not a multiple of 2 l am a composite number.
Answer:
9 is the answer
Step-by-step explanation:
if it was less then ten and not a multiple of 2 then i will ether be 1 3 5 7 9 but the composite numbers are 4 6 8 9 so since it is not a factor of 2 it has to be 9. so 9 is the answer
The number which is less than 10, not a multiple of 2, and is a composite number, is 9.
What is multiplication?One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical sizes.
Given:
I am less than 10 l am not a multiple of 2 l am a composite number,
The numbers which are less than ten are,
9, 8, 7, 6, 5, 4, 3, 2, 1, 0
The numbers which are not the multiple of 2 are shown below,
9, 7, 5, 3, 1, 0
The numbers which are composite are shown below,
9 = 3 × 3
Thus, The number is 9.
To know more about multiplication:
https://brainly.com/question/1135170
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524800 in scientific notation?
Answer:
5.248 x 10^5
Step-by-step explanation:
there should be one digit and then however many decimals after. the exponent is positive because the original number is larger than one's digit.
Write a equation in slope-intercept form of the line that passes though (-5,19) and (5,13)
Answer:
y= -3/5x + 16
Step-by-step explanation:
slope intercept form: y=mx+b
1. Find the slope: rise over run so 13-19/ 5-(-5) = -3/5
M=-3.5
2. Find the y - intercept by using the point slope form: b= 16
So, y= -3/5x + 16
Hope this helps :)
Name the zero(s) of f (x).
Answer:
(a, 0) and (b, 0)
General Formulas and Concepts:
Alg I
Zeros of a Quadratic FunctionReading a Cartesian GraphStep-by-step explanation:
We are looking for the zeros of f(x). The blue quadratic is the graph of f(x). Zeros mean the coordinates when the graph crosses the x-axis. Therefore, our correct answer is the last choice.
All of the points in the picture are on the same line.
YA
(6, 10)
(a, 8)
(4,5)
(2, 2)
1. Find the slope of the line. Explain or show your reasoning,
2. Write an equation for the line.
3. Find the values for a and b. Explain or show your reasoning
4. What is the y-coordinate when x = 0? Explain or show your reasoning.
Answer:
Did you ever get the answers??
The equation of the line is y = 2x - 2.
What is the point-slope form of a line?If m is the slope of the line that passes through the point (x₁, y₁), then the equation of the line is y - y₁ = m (x - x₁).
The graph of the line is given.
(1)
The line passes through points (2,2) and (6,10).
The slope of the line is:
m = (10 - 2)/(6 - 2)
m = 8/4
m = 2
(2)
The equation of the line with a slope of m =2 and passes through (2,2) is:
y - 2 = 2(x - 2)
y = 2x - 4 + 2
y = 2x - 2 (1)
(3)
The line passes through points (4,b) and (a,8), therefore, from equation (1):
b = 2(4) - 2
b = 6, and
8 = 2a - 2
2a = 10
a = 5
(4)
Substitute x = 0 into equation (1):
y = 2(0) - 2
y = -2
Hence, the equation of the line is y = 2x - 2.
Learn more about the point-slope form of a line:
https://brainly.com/question/29503162
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Lawrence bought 2/3 pound of roast beef. He used 3/4 of it to make a sandwich. How much beef did he use for his sandwich A 5/12 pound B 1/2 pound C 5/7 pound D 6/7 pound
Answer:
B) 1/2 pound
Step-by-step explanation:
Lawrence bought 2/3 pound of roast beef.
He used 3/4 of it to make a sandwich.
The amount of beef that he used for his sandwich is calculated as:
3/4 of 2/3 pounds of roast beef
3/4 × 2/3
= 6/12 pound
= 1/2 pound
Option B is the correct Option.
***Answer when you can!***
Evaluate functions from their graph
g(-4)=??
Answer:
1
Step-by-step explanation:
That is the y coordinate when x is -4Leila was asked to solve the equation 2 over 3 left parenthesis x plus 5 right parenthesis equals 29. The first step she did to solve the equation was 2 over 3 left parenthesis x right parenthesis plus 2 over 3 left parenthesis 5 right parenthesis equals 29. What property did she use in this step?
A.associative
B.commutative
C.distributive
D.reflexive
Which answer is right !
20 points
Need help ASAP!!!!!!!
Answer:
I can't see the assignment question. It says there is nothing attached...
Step-by-step explanation:
I will give brainliest
A. 2x-1+3x=0
B. 5x-1=0
1) How can we get Equation B from Equation A?
Choose 1 answer:
(Choice A) Add/subtract the same quantity to/from both sides
(Choice B) Add/subtract a quantity to/from only one side
(Choice C) Rewrite one side (or both) by combining like terms
(Choice D) Rewrite one side (or both) using the distributive property
BRAINLIEST ON THE LINE INFO IN PHOTO BELOW
Answer:
32 days is my final answer
Step-by-step explanation:
The triangles in the picture are congruent by which method
surface area of a net
Answer:
Step-by-step explanation:
This is really a sloppy diagram. You have to know if the base of the triangle is 5 or 10.
It is 5. So the area of 1 of the triangles is 1/2 * b * h
b = 5
h = 8.7
Area = 1/2 * 8.7 * 5 = 21.75
There are 4 such triangles. The total area = 4 * 21.75 = 87 sqr in
Which of Earth’s spheres encompasses all of
Earth’s water?
a. the hydrosphere
b. the atmosphere
c. the asthenosphere
d. the geosphere
Answer:
The answer is A.
Step-by-step explanation:
All of earths bodies of water including groundwater. the hydrosphere also includes the cryosphere, which is made up of the worlds ice sheets and sea ice.
Answer:
a. the hydrosphere
Step-by-step explanation:
hydro means water
CAN SOMEONE HELP ME WITH PATTERN 1
Hey I need some help!! Does anyone mind giving me the answers and explain how? I really don’t understand. PS the question is in the pic, I will mark u brainlist if you help!! Have a wonderful day everyone!!!!! Technically I’m supposed to match them btw!
Answer:
2x2x2x5
Step-by-step explanation:
2x2x2x5 equals 40
The monthly payment for a car lease is $530 for 18 months. The down payment is $2,000. The residual value is $7,000. What is the total cost of the lease? A. $18,540 B. $20,540 C. $25,540
Answer:
18540
Step-by-step explanation:
18 times 530 = 9540
9540 + 2,000 + 7,000= 18540
I did 18 times 530 because it said 530 for 18 months
The First-person to get correct will get BRAINLESIT
I think of a number, multiply it by four, and subtract three. I get eleven. a) Using the statement above, form an equation. Use the letter 'x' for the unknown number.
b) Solve the equation
caculate the diffrence of 13.9-1.149
Answer:
12.751
Step-by-step explanation:
13.9 - 1.149
--Subtract--
Answer:
12.751
Step-by-step explanation:
Just do subtraction.
Which of these is a factor of 10?
A. 20
B. 2
C. 4
Answer:
B. 2
Hope this helps!
Step-by-step explanation:
The factors of 10 are 1, 2, 5, and 10. You can also look at this the other way around: if you can multiply two whole numbers to create a third number, those two numbers are factors of the third. 2 x 5 = 10, so 2 and 5 are factors of 10. 1 x 10 = 10, so 1 and 10 are also factors of 10.
Use this new algebraic method to find equations for the line with the following properties:
A slope of −3, passing through the point (15,−50).
Show your work in the sketch box on the left.
Step 1: Substitute values for m, x, and y.
Step 2: Solve equation for b.
Step 3: Rewrite your equation with only m and b.
What is the equation of this line?
Answer:
Y = -3x + 90
Step-by-step explanation:
Y= Mx + b
M - (-3)
X - 15
Y - (-50)
Y = Mx + b
50 = (-3)(15) + b
50 = -45 + b
95 = b
Y = -3x + 90
Hope this helps
Which of the following equations have no solutions?
Choose all answers that apply:
A
5x +5 = -4x - 5
B
- 4x + 5 = -4x - 4
C
-4x +5 = -4x - 5
D
4x + 5 = -4x + 5
I need help plsssssss
Answer:
C. y= 7x
Step-by-step explanation: