Answer:
2(x - 10)(x + 10)
Step-by-step explanation:
Given
2x² - 200 ← factor out 2 from each term
= 2(x² - 100) ← x² - 100 is a difference of squares and factors as
x² - 100 = x² - 10² = (x - 10)(x + 10), hence
2x² - 200 = 2(x - 10)(x + 10)
Answer:
Step-by-step explanation:
If your equation is [tex]2x^2-200[/tex] and you're to factor it, the first thing you do is set the expression equal to 0 so you can solve for x.
[tex]2x^2-200=0[/tex]
There's a couple of different ways in which to approach this. You can factor out a 2:
[tex]2(x^2-100)=0[/tex]
and solve it from there. The Zero Product Property says that if the equation is equal to 0, then either 2 has to equal 0 or [tex]x^2-100[/tex] has to equal 0. We know that 2 does not equal 0, so [tex]x^2-100=0[/tex]
Add 100 to both sides in the equation:
[tex]x^2=100[/tex]
and then take the square root of both sides. Because this is a second degree polynomial, we expect to have 2 solutions, and we do. Don't forget that when you take the square root of a number you have to alow for both the positive and the negative of the result. Our factored form of the given equation then is that x = 10 and x = -10.
what is a rational number whose square root is a whole number?
Answer:
4
Step-by-step explanation:
For example, 4.
4 is rational since it can be written as a fraction of integers. 4 = 4/1
The square root of 4 is 2, and 2 is a whole number.
What is the solution set of y=x? - 5x + 7 and y = 2x + 1?
Separate your x and y values with a comma.
) and (
Does anyone know this?
Answer:
The solutions are (6,13) and (1,3)
Step-by-step explanation:
We want to solve
[tex]y=x^2-5x+7[/tex]
and
[tex]y=2x+1[/tex]
We equate both equations to get:
[tex]x^2-5x+7=2x+1[/tex]
[tex]x^2-5x-2x+7-1=0[/tex]
[tex]x^2-7x+6=0[/tex]
We split the middle term to get:
[tex]x^2-6x-x+6=0[/tex]
[tex]x(x-6)-1(x-6)=0[/tex]
[tex](x-6)(x-1)=0[/tex]
[tex](x-6)=0,(x-1)=0[/tex]
[tex]x=6,x=1[/tex]
When x=6, y=2(6)+1=13
When x=1, y=2(1)+1=3
The solutions are (6,13) and (1,3)
What is the simplified expression for the expression below? 4(3x – 2) + 6x(2 – 1) 24x – 3 18x – 8 18x – 7 24x – 14
Answer:
18x-8
Step-by-step explanation:
Given expression:
=4(3x-2)+6x(2-1)
The expression has to be simplified using the basic rules of mathematics,
In order to simplify the given expression,
We can see that the expression written in second bracket (2-1) which can be solved so,
=4(3x-2)+6x(1)
Multiplying 4 inside the bracket (3x-2)
=12x-(4)(2)+6x
=12x-8+6x
=18x-8 ..
Answer:
The answer is 18x - 8
Step-by-step explanation:
What is an inequality to represent the perimeter of a triangle if two sides measure 3 meters and 8 meters
Answer:
16 m < P < 19 m
Step-by-step explanation:
we know that
The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
x----> the length of the third side
Applying the triangle inequality theorem
1) 3+8 > c
11 > c
c < 11 m
2) c+3 > 8
c> 5 m
so
the measure of the third side must be
5 m < c < 8 m
therefore
The perimeter of the triangle is equal to
P=3+8+c
P=11+c
The inequality is equal to
(11+5) m < P < (11+8) m
16 m < P < 19 m
1.3,5/4,1 8/25 in order from least to greatest
Answer:
5/4, 1.3, 1 8/25
Step-by-step explanation:
5/4=1.25
1 8/25=1.32
---------------
The numbers 1.3, 5/4, 1, and 8/25 can be rearranged from least to greatest as 0.32, 1, 1.25, 1.3 once they're all converted to decimals. Converting fractions and whole numbers to decimals is a crucial skill in Mathematics and can simplify problems like this.
Explanation:To answer your question, the numbers 1.3,5/4,1 and 8/25 can be put in order from least to greatest by first converting them all to decimals or fractions. Given in their current form 5/4 equals 1.25 as a decimal and 8/25 equals 0.32 as a decimal. Hence we can put them into increasing order as 0.32, 1, 1.25, 1.3.
Understanding how to convert between fractions, decimals, and whole numbers is an essential skill in mathematics, and it can make problems like this easier to understand and solve. For instance, understanding that the fraction 5/4 is equivalent to the decimal 1.25 makes it easier to compare with other numbers.
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Write and solve of the following linear equation. Show or explain your work.
Three consecutive integers have a sum of 246. What are the three integers
Answer:
The three integers are 81,82 and 83
Step-by-step explanation:
Let
x,x+1 and x+2 ----> the three consecutive integers
we know that
[tex]x+(x+1)+(x+2)=246[/tex]
Solve for x
[tex]3x+3=246[/tex]
[tex]3x=246-3[/tex]
[tex]x=243/3[/tex]
[tex]x=81[/tex]
therefore
[tex]x=81[/tex]
[tex]x+1=81+1=82[/tex]
[tex]x+2=81+2=83[/tex]
The table shows the functions representing the height and base of a triangle for different values of x
ANSWER
B. A(x)=0.5 (f .g)(x)
EXPLANATION
The area of a triangle is calculated using the formula:
Area=0.5 Base × Height
The base is given by
g(x)=2x
and the height of the function is
[tex]f(x)= {x}^{2} + 3[/tex]
This implies that:
A(x)=0.5f(x) × g(x)
A(x)=0.5 (f .g)(x)
the number of cells in a sample doubles every minute. A doctor with a sample of 25 cells and predicted that, after 5 minutes, he would have 32 cells. Is his prediction reasonable? Explained
Answer: No, his prediction is unreasonable. After 5 minutes, the number of cells would be 400, not 32. See the explanation below for details.
-------
Remember:
[tex]a_{n}[/tex] = [tex]n[/tex]th term[tex]n[/tex] = number of terms[tex]a_{1}[/tex] = first term[tex]r[/tex] = common ratio-------
Identify the given information.
[tex]a_{1}[/tex] = 25
[tex]r[/tex] = 2
Use the explicit formula for geometric sequences.
[tex]a_{n} = a_{1} r^{n - 1}[/tex]
Substitute the given values.
[tex]a_{n} = (25)(2)^{n - 1}[/tex]
Substitute in 5 for [tex]n[/tex] to find out how many cells there would be after 5 minutes.
[tex]a_{5} = (25)(2)^{5 - 1} \\\\a_{5} = (25)(2)^{4} \\\\a_{5} = (25)(16)\\\\a_{5} = 400[/tex]
Final answer:
The doctor's prediction of 32 cells after 5 minutes is not reasonable, because based on exponential growth of doubling every minute, 25 initial cells should grow to 800 cells in that time period.
Explanation:
The given question involves the calculation of cell numbers in a growing population, which relates to the field of exponential growth. Using the information provided that the number of cells doubles every minute, we can apply the formula for exponential growth, which is [tex]2^{n}[/tex], where 'n' is the number of generations or minutes in this case.
Starting with 25 cells, after 5 minutes, the expected number of cells would be calculated by multiplying 25 by 25 (since the cells double every minute). This calculation gives us 25 * 32, which equals to 800 cells after 5 minutes. Therefore, the doctor's prediction that there would only be 32 cells after 5 minutes is not reasonable, as the correct calculation suggests the number should be much higher.
Amplitude of y=-3sin5x
Answer:
Amplitude is 3
Step-by-step explanation:
in y=-3sin5x
the number in front of sign is always the amplitude. Its not negative 3 because the negative simply means it reflects across the x-axis
ANSWER
The amplitude is 3
EXPLANATION
The amplitude of a periodic function is the distance from the midline of its graph to the peak.
The given function is:
[tex]y = - 3 \sin(5x) [/tex]
This function is of the form:
[tex]y = a \: \sin(bx) [/tex]
The of this function is
[tex] |a| [/tex]
By comparing the two functions, we have a=-3.
Therefore the amplitude of the given function is
[tex] | - 3| = 3[/tex]
A county in Alabama has a population of 90,000 people. It has an area of 800 mi2. How many people are there per square mile?
Answer:
112.5 people per square mile
Step-by-step explanation:
Find the "unit rate:"
90,000 people
----------------------- = 112.5 people per square mile
800 miles²
If a minivan averages 25.8 miles per gallon, how many miles will it travel on 23 gallons of gas
Answer:
Step-by-step explanation:
25.8/1=593.4/23
593.4 is the answer
Final answer:
To find out how many miles a minivan will travel on 23 gallons of gas with an average of 25.8 miles per gallon, multiply the gallons by the mpg to get 593.4 miles.
Explanation:
To calculate the distance a minivan will travel on 23 gallons of gas when it averages 25.8 miles per gallon, we simply multiply the number of gallons by the miles per gallon (mpg).
The formula to use is:
Distance = Number of Gallons × Average Miles per Gallon
Using the given values:
Distance = 23 gallons × 25.8 mpg
We calculate:
Distance = 593.4 miles
Therefore, the minivan can travel 593.4 miles on 23 gallons of gas, assuming it maintains the average fuel economy of 25.8 miles per gallon.
Write an equation that gives the proportional relationship of the graph.
A) y = 1/5x
B) y = 5x
C) y = 6x
D) y = 30x
Answer:
B) y = 5x
Step-by-step explanation:
We need to find the slope
m = (y2-y1) /(x2-x1)
We have 2 points (0,0) and (6,30)
m = (30-0)/(6-0)
= 30/6
=5
The slope is5
y = mx+b
The y intercept is 0
y = 5x+0
y = 5x
Answer:
B:)
Step-by-step explanation:
Wanahton is cooking a breadstick on a rectangular baking sheet measuring 9\dfrac129
2
1
9, start fraction, 1, divided by, 2, end fraction inches (\text{in})(in)left parenthesis, i, n, right parenthesis by 13\,\text{in}13in13, space, i, n. Assuming the breadstick width is negligible, what is the longest breadstick Wanahton could bake by fitting it straight along the diagonal and within the baking sheet to the nearest inch?
Answer:
The longest bread stick is approximately 16 in
Explanation:
The diagram representing the tray is shown in the attached image
From the diagram, we can note that the diagonal of the tray represents the hypotenuse of a right-angled triangle having legs 9.5 in and 13 in
Therefore, to get the length of the hypotenuse, we can use the Pythagorean equation which is as follows:
c² = a² + b²
where c is the length of the hypotenuse and a and b are the length of the two legs
Substitute with the givens in the above equation to get the length of the hypotenuse as follows:
c² = (9.5)² + (13)² = 259.25
c = 16.1 in which is approximately 16 in
From the above, we can conclude that:
The longest bread stick that can be fit straight along the diagonal of the tray is approximately 16 in
Hope this helps :)
What is the y-intercept of the function f(x)=-2/9x+1/3?
To find the y intercept replace the x in the equation with zero and solve
-2/9(0) + 1/3
0 + 1/3
The y-intercept is:
(0, 1/3)
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
y intercept is 1/3
Step-by-step explanation:
[tex]f(x)=-\frac{2}{9} x+ \frac{1}{3}[/tex]
To find y intercept we plug in 0 for x
Y intercept point is a point where the graph f(x) crosses y axis.
At y intercept, the value of x is 0
to find y intercept we plug in 0 for x
[tex]f(0)=-\frac{2}{9} (0)+ \frac{1}{3}[/tex]
[tex]f(0)=\frac{1}{3}[/tex]
What experimental of rolling a 2 or 3
Answer:
Option 1: 0.32
Step-by-step explanation:
Let
P(A) be the experimental probability of getting two
And
P(B) be the experimental probability of getting three
The dice is rolled 360 times.
So the sample space is n(S) = 360
P(A) = n(A)/n(S)
= 54/360
= 0.15
And
P(B) = n(B)/n(S)
= 62/360
= 0.172
As both the events A and B are mutually exclusive,
P(A or B) = P(A) + P(B)
= 0.15 + 0.172
=0.322
Rounding of to one decimal gives us:
0.32
So the probability of rolling a two or three is 0.32 ..
Leticia invests $200 at 5% interest. If y represents the amount of money after x time periods, which describes the graph of the exponential function relating time and money?
Answer:
[tex]y=200(1.05)^{x}[/tex]
Step-by-step explanation:
This is a compound interest problem. The principal is given as 200 and the interest rate as 5%. We can use the compound interest formula to determine the relationship between time and money;
[tex]A=P(1+r)^{n}[/tex]
where;
A is the amount of money
P is the principal invested
r is the rate of interest
n is the time duration
Substituting the information given we have;
[tex]y=200(1+\frac{5}{100})^{x}\\\\y=200(1.05)^{x}[/tex]
which is an exponential function
Find the attached for the graph of this exponential function.
Question 3(Multiple Choice Worth 4 points) (08.05) Jemma wants to solve the following system using the elimination method: y = x − 6 y = 6x − 19 What number should the equation y = x − 6 be multiplied by to eliminate x?
1
2
4
-6
Answer:
-6.
Step-by-step explanation:
y = x - 6
y = 6x - 19
To eliminate x the first equation should be multiplied by -6 giving:
-6y = -6x + 36
Adding this to the second equation will eliminate x.
(3square root8x^5)-(4square root256y^3)
Write in exponential form
and simplify
Answer:
[tex]2x^\frac{5}{3} - 4y^\frac{3}{4}[/tex]
Step-by-step explanation:
Given equation:
[tex]\sqrt[3]{8x^5} - \sqrt[4]{256y^3}[/tex]
([tex](8x^5)^\frac{1}{3} - (256y^3)^\frac{1}{4} \\ (8^\frac{1}{3} . x^\frac{5}{3} ) - (256^\frac{1}{4}. y^\frac{3}{4})\\ 2x^\frac{5}{3} - 4y^\frac{3}{4}[/tex] !
The initial equations of (3√8x^5) and (4√256y^3) are first changed to exponential form and then simplified to final forms of 6x^2√x and 64y respectively. The final simplified form of the entire equation therefore becomes 6x^2√x - 64y.
Explanation:The given expression is (3√8x^5) - (4√256y^3). Lets breakdown and simplify each component firstly.
The first expression, 3√8x^5, can be written as 3*(8x^5)^(1/2). The number 8 can be expressed as 2^3 and x^5 as (x^2)^(5/2). So, 3√(8x^5) simplifies to 3*2x^2*√(x) = 6x^2√x.
For the second expression, 4√256y^3, can be written as 4*(256y^3)^(1/2). The number 256 can be expressed as 2^8 and y^3 as (y^2)^(3/2). So, 4√(256y^3) simplifies to 4*16y = 64y.
Now, putting these values back into the original equation, we get: 6x^2√x - 64y
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Ummmm ignore the writing by total are. I don’t understand this,so can you guys do one or both for me please.Im most grateful.
You just have to split the figures in different parts...
- First Picture:
- the total length is 130, so the upper and bottom rectangles have 50ft. as showed, and the middle one is 130-(50x2) = 30
- The second step is get the 2 holes área to subtract from the “total rectangle without holes area” (30x40=1200)x2 and then (20,150-1400=18,750) so, the total area from the rectangle with the holes is 18,750!
Find the slope of (0, 3), (4, 0). Reduce all fractional answers to lowest terms.
The formula to find slope is:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
[tex]y_{2} = 0\\y_{1} =3\\x_{2} = 4 \\x_{1} = 0[/tex]
so...
[tex]\frac{0-3}{4-0}[/tex]
[tex]\frac{-3}{4}[/tex] <<<the slope
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
-3/4
Step-by-step explanation:
The slope is given by
m = (y2-y1)/(x2-x1)
= (0-3)/(4-0)
= -3/4
PLEASE HELP RIGHT AWAY
Answer:
No teen sent texts fewer than 1630 or more than 1854 texts in a month
Step-by-step explanation:
margin of error gives the difference that may come in the sample results from the actual population results.
Given:
Average teen sends 1742±112 texts per month
here ±112 is margin of error, calculating maximum difference:
1742+112=1854
1743-112=1630
No teen sent texts fewer than 1630 or more than 1854 texts in a month !
PLEASE HELP
I WILL MARK BRAINIEST
Answer:
1: Rhombus
2: Square
3: Rectangle
4: Trapezoid (isosceles trapezoid to be exact)
Answer:
1. convex
2. square
3. rectangle
4. trapezoid
Step-by-step explanation:
solve for x. round to the nearest hundredth if necessary.
Answer:
[tex]x= 11.47[/tex]
Step-by-step explanation:
By definition the cosine of an angle is the quotient between the side adjacent to the angle and the hypotenuse.
In other words:
[tex]cos (\alpha) = \frac{adjacent}{hypotenuse}[/tex]
In this triangle the length of the side adjacent to the 55 degree angle is x, and the length of the hypotenuse is 20
So:
[tex]cos(55\°) = \frac{x}{20}[/tex]
Now we solve the equation to find the value of x
[tex]x = 20cos(55\°)[/tex]
Finally
[tex]x= 11.47[/tex]
Answer:
11.47
Step-by-step explanation:
Given
Two angles of 90 and 55 degrees
and a side of length 20
Finding third angle= 180-(90+55)
= 35
Finding x:
Using Law of Sines to find length of side x
x/sinX=y/SinY
x/sin35=20/sin90
x=20sin35
x=11.47 !
Paul has 183 stamps his friends gave 15 stamps for his birthday how many stamps does Paul have after he received stamps from his friend?
Answer:
198.
Step-by-step explanation:
183+15=198
Hello!
If Paul already has 183 stamps, just add 15 more because that is how much his friend gave him and you will get 198 stamps
Which logarithmic graph can be used to approximate the value of y in the equation 3^y = 4?
Answer:
c
Step-by-step explanation:
$3.36 for 1.4 pounds of grapes what is the unit rate per pound of grapes??????? I really need to know.... Yeet
Answer: 2.4 per pound you have to divide $3.36 and 1.4 pounds and you get your answer. Please mark me the brainliest answer? Hope this helped have a good day :)
OMG IS THAT A CURSED IMAGE?!?!?! :D
Based on the information given the unit rate per pound is 2.4.
Using this formula
Unit rate per pound=Costs/Pounds
Where:
Cost=$3.36
Pounds=1.4 pounds of grapes
Let plug in the formula
Unit rate per pound=$3.36/1.4
Unit rate per pound=2.4
Inconclusion the unit rate per pound is 2.4.
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John is 1/8 meter shorter than Paul, and Paul is 0.25 meter taller than Andrew. If John’s height is 1 3/4 meters, what is Andrew’s height?
Andrew is 1 5/8 meters tall.
Andrew's height is 5.75 meters
Calculating variable dependent parameter -A variable dependent parameter equation is an equation where we solve a given problem from the statements and the data mentioned in it.
How to find Andrew's height in the given problem ?Let the height of Andrew be x meters
Given Paul is 0.25 meters taller than Andrew .
∴ Paul's height = 0.25 + x meters
Also given that John is 1/8 meters shorter than Paul .
John's height = 1/8(0.25 + x) meter
Also given that John's height is 3/4 meters.
⇒ 3/4 = 1/8(0.25 + x)
⇒ 6 = (0.25 + x)
∴ x = 5.75
Therefore the height of Andrew is 5.75 meters.
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Evaluate the function!!! 10 points. Help needed!
ANSWER
[tex]f( - 3) = - \frac{9 }{7} [/tex]
EXPLANATION
The given function is
[tex]f(x) = \frac{2 {x}^{2} }{3x - 5} [/tex]
We want to find f(-3)
We substitute x=-3 into the function to get;
[tex]f( - 3) = \frac{2 {( - 3)}^{2} }{3( - 3) - 5} [/tex]
Simplify;
[tex]f( - 3) = \frac{2 \times 9 }{ - 9- 5} [/tex]
[tex]f( - 3) = - \frac{18 }{ 14} [/tex]
[tex]f( - 3) = - \frac{9 }{7} [/tex]
which is the slope of the line y= -3x+2?
Answer:
The slope is -3
Step-by-step explanation:
This is because the slope of a line in an equation is m. In the equation given m=-3, so that makes the slope -3.
Answer:
I'm pretty sure the slope is -3.
The area of the figure is blank
square units.
The area of the figure is 2×3+(2×2)/2=8 square units.