The two binomial factors of the expression x² - 100 are ( x + 10 ) and ( x - 10 ).
What are the binomial factors of the expression?Given the expression in the question:
x² - 100
To factor the expression x² - 100 as the product of two binomials, simply apply the difference of squares formula.
The difference of squares formula states that:
a² - b² can be factored as (a + b)(a - b).
x² - 100
Replace 100 with 10²:
x² - 10²
Now, apply the difference of squares:
a² - b² = (a + b)(a - b)
x² - 10²
a = x and b = 10
x² - 10² = ( x + 10 )( x - 10 )
Therefore, the binomial factors are ( x + 10 ) and ( x - 10 ).
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The expression x^2-100 is a difference of squares and can be factored into the product of two binomials as (x + 10)(x - 10).
To factor the expression x^2-100 as the product of two binomials, we can recognize that it is a difference of squares. A difference of squares can be factored into the form (a + b)(a - b), where a and b are the square roots of the terms in the expression. In this case, the square root of x^2 is x, and the square root of 100 is 10. Therefore, the factored form of x^2-100 using two binomials is (x + 10)(x - 10).
What is the equation of the line that contains point ( -2,1) and has a slope of 4
Final answer:
The equation of the line that contains the point (-2,1) and has a slope of 4 is y = 4x + 9.
Explanation:
To find the equation of a line that contains a given point and has a given slope, you can use the point-slope form of a linear equation, which is y - y1 = m(x - x1). In this case, the given point is (-2,1) and the given slope is 4. Plugging these values into the point-slope form, we get y - 1 = 4(x - (-2)).
Simplifying the equation, we have y - 1 = 4(x + 2). To get the equation in slope-intercept form, solve for y by distributing 4 to both terms inside the parentheses: y - 1 = 4x + 8. Finally, move the constant term (-1) to the other side of the equation: y = 4x + 8 + 1. The equation of the line is y = 4x + 9.
Which expression is equivalent
to the one shown above?...
Answer:
A. [tex]7-3.25+4[/tex]
Step-by-step explanation:
Because [tex]5^2=5\times5=25[/tex], the expression [tex]7-3\times5^2+4[/tex] can be rewritten as [tex]7-3\times25+4[/tex].
PLEASE HELP
Which x value would make the following expression undefined? *
(81x^2 – 25) * 6/18x + 10
Answer
Given expression,
[tex](81x^2-25)\times \dfrac{6}{18x+10}[/tex]
We have to find the value of x for which the expression is undefined.
Simplifying the given expression
[tex]((9x)^2-5^2)\times \dfrac{3}{9x+5}[/tex]
[tex](9x-5)(9x+5)\times \dfrac{3}{9x+5}[/tex]
[tex]3(9x-5)[/tex]
On solving we can see that the expression is defined for all value of x.
Simplify the following equation. (6x+4)+(5-2x)
Answer:
the correct answer is...
Step-by-step explanation:
4x+9
1. Find the Median Average of these distances run by 8 marathon runners:
10 km, 15 km, 12 km, 14 km, 8km, 16 km, 11 km, 15 km
Answer:
13
Step-by-step explanation:
Organizing the numbers
8 10 11 12 14 15 15 16
The median are both 12 and 14 but to get one median you add the two numbers 12 + 14 which equals 26. 26 divided by 2 numbers equals 13
Determine the number of x-intercepts that appear on a graph of each function.f (x) = (x + 5)3(x - 9)(x + 1)
Answer:
there are three x-intercepts
Step-by-step explanation:
-5, -1, 9 are all the x-intercepts that appear on the graph.
Answer: 3
Step-by-step explanation:
egde
The model below shows the number 7.77. ONES TENTHS HUNDREDTHS 7 . 7 7 Using the model of 7.77, how does the 7 in the tenths place compare to the 7 in the place to its right?
The 7 in the tenth place is equal to 7 times the value on the right
Crude oil is leaking from a tank at the rate of 10% of the tank volume every 3 hrs. If the tanker originally contained 500,000 gallons of oil, how many gallons of oil remain in the tank after 4 hrs? Round to the nearest gallon.
Answer:
434,470 gallons
Step-by-step explanation:
The exponential equation for the volume v remaining after t hours can be written as ...
v(t) = (initial amount)×(decay factor)^(t/(decay time))
v(t) = 500,000×(1 -10%)^(t/3)
Then after 4 hours, the remaining volume is ...
v(4) = 500,000×(0.90^(4/3)) ≈ 434,470 . . . . gallons
_____
Comment on the form of the equation
The decay factor is related to the decay rate by ...
decay factor = 1 - (decay rate)
and the decay time is the time applicable to that decay rate. Here, the rate is 10% every 3 hours, so the decay time is 3 hours for a decay rate of 10%.
Each student receives one of 4 calculator models and one of 3 types of ruler. How many possible outcomes are there if a student gets one ruler and one calculator?
Answer:
24 possible outcomes
Step-by-step explanation:
Combination has to do with selection. For example, if r object is selected from a pool of n objects, the number if possible ways can be expressed according to the combination formula:
nCr = n!/(n-r)!r!
Applying this in question, if each student receives one of 4 calculator models and one of 3 types of ruler, the number of ways this can be done is:
4C1 × 3C1
4C1 = 4!/(4-1)!1! {If a student gets one calculator)
4C1 = 4×3×2/3×2
4C1 = 4ways
3C1 = 3!/(3-2)!1! {If a student gets a ruler}
3C1 = 3×2/1
3C1 = 6ways
Total number of possible outcomes if a student gets one ruler and one calculator will be 4×6 = 24ways
What’s the answer to this
Step-by-step explanation:
undefined
Answer:
C) Undefined
Step-by-step explanation:
When the slope on a graph is straight there is no slope so therefore it is undefined.
Solve the equation 2x2 + 15x – 9 = -26 to the nearest tenth.
The reciprocal parent function is translated 5 units right and 3 units up. Write an equation to represent the new function.
Transformations:
y=ax-h+k
Answer:
The new function is [tex]y=\frac{1}{x-5}+3[/tex] , where x ≠ 5
Step-by-step explanation:
The reciprocal parent function is [tex]f(x)=\frac{1}{x}[/tex] , where x ≠ 0
The translation of f(x) to the right h units is f(x - h)
The translation of f(x) up k units is f(x) + k
The translation of f(x) to the right h units and up k units is f(x - h) + k
∵ The equation of the reciprocal parent function is [tex]y=\frac{1}{x}[/tex]
∵ The function is translated 5 units right
∴ h = 5
- That means 5 is subtracted from x ⇒ (x - 5)
∵ The function is translated 3 units up
∴ k = 3
- That means y added by 3
∴ [tex]y=\frac{1}{x-5}+3[/tex]
The new function is [tex]y=\frac{1}{x-5}+3[/tex] , where x ≠ 5
PLEASE HELP!!!! The edges of the diameter of a circle are at (-3,-8) and (5,7).
Write the equation of the circle in general form.
Please show your work.
Answer:
x^2 + y^2 -2x +y -71 = 0
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so is ...
((-3, -8) +(5, 7))/2 = (-3+5, -8+7)/2 = (1, -1/2)
The square of the radius of the circle can be found from the Pythagorean theorem. The x- and y- differences between an end point and the center are the legs of a right triangle with r as the hypotenuse.
r^2 = (5 -1)^2 +(7 -(-1/2))^2 = 4^2 +7.5^2 = 16 +56.25
r^2 = 72.25
__
The standard form equation of the circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
(x -1)^2 +(y -(-1/2))^2 = 72.25
Eliminating parentheses, we have ...
x^2 -2x +1 +y^2 +y +0.25 = 72.25
Subtracting the right-side constant and rearranging to descending powers, we find the general form of the equation to be ...
x^2 + y^2 -2x +y -71 = 0
_____
Comment on the work
Of course, you know that ...
(a -b)^2 = a^2 -2ab +b^2
This helps you simplify the squares of binomials.
Does anyone know what 8x1/6 is?
Answer: 1.33333333333
Step-by-step explanation: 8x1=8
8/6=1.33333333333
Which statements describe negative integers? Check all that apply A ship sank to 25 meters below sea level. Josué climbed up 32 stairs. A rollercoaster went 50 feet up a hill. Jack lost $20.
Answer:
A and D
Step-by-step explanation:
Answer:
The answer is A and D
X
- 78.3
= -66.5
-66.5 -
=
Answer:x= -54.7
Step-by-step explanation:
-66.5-66.5= -133+ 78.3= -54.7
You have learned some new ways in this module to prove that triangles are similar Please describe some of these new postulates and include a diagram on the whiteboard to help explain how they are applied.
Answer:
TA = 6 units
GT = 10 units
Step-by-step explanation:
Angle G is common to both triangles, so that's a congruent angle.
Since RT is parallel to EA,
Angle R = Angle E
And
Angle T = Angle A
When two triangles have the same distribution of angles, they are similar (by AAA).
Therefore GRT and GEA are similar
GE/GR = GA/GT
8/5 = 16/(16-x)
16-x = 16 × 5/8
16 - x = 10
x = 16 - 10
x = 6
GT = 16 - x = 16 - 6 = 10
Which statement is true about the similarity of two squares of different sizes ABCD and WXYZ?
A) ABCD can be carried onto WXYZ using only dilation.
B) ABCD can be carried onto WXYZ using only rotation.
C) ABCD can be carried onto WXYZ using only reflection.
D) ABCD can be carried onto WXYZ using only translation.
Answer:
the correct A
Step-by-step explanation:
Answer: A) ABCD can be carried onto WXYZ using only dilation.
Step-by-step explanation:
Kailey wrote 8,912,000 in scientific notation as 89.12 times 10 Superscript 5. Which statement best describes Kailey's work? Kailey is correct: 89.12 times 10 Superscript 5 equals 8,912,000. Kailey is not correct: the exponent of ten should be negative. Kailey is correct: it is written as a decimal number multiplied by a power of ten. Kailey is not correct: 89.12 times 10 Superscript 5 is not written in scientific notation.
Answer:
D. Kailey is not correct: [tex]89.12 \times 10^5[/tex] is not written in scientific notation.
Step-by-step explanation:
We have been given that Kailey wrote 8,912,000 in scientific notation as [tex]89.12 \times 10^5[/tex]. We are asked to choose the statement that best describes Kailey's work.
We know that to convert a number into scientific notation, we write the given number as product of two numbers. One factor is a number between 1 and 10, while the 2nd factor is power of 10.
Upon looking at [tex]89.12 \times 10^5[/tex] , we can see that 1st factor is 89.10, which is greater than 10. This means that Kailey did not write 8,912,000 in scientific notation.
Therefore, option D is correct choice.
Answer:
d
Step-by-step explanation:
what is the area of the polygon
Answer:
Step-by-step explanation:
to find the area of a regular polygon, all you have to do is follow this simple formula: area = 1/2 x perimeter x apothem. Here is what it means: Perimeter = the sum of the lengths of all the sides. Apothem = a segment that joins the polygon's center to the midpoint of any side that is perpendicular to that side.
At the electronics store, Martin earns a 4.5% commission on his monthly sales.If his sales for January were $1,350, how much of a commission did he earn?
Answer:
60.75
Step-by-step explanation:
Since he earns a 4.5% commission
you need to find 4.5% of $1,350
1350 x 0.045 = 60.75
A company advertises two car tire models. The number of thousands of miles that the standard model tires last has a mean \mu_S = 60μ S =60 and standard deviation \sigma_S = 5σ S =5. The number of miles that the extended life tires last has a mean \mu_E = 70μ E =70 and standard deviation \sigma_E = 7σ E =7. If mileages for both tires follow a normal distribution, what is the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire?
Answer:
0.123
Step-by-step explanation:
Use the random variable E - S, which will follow a normal distribution with a mean of 70 - 60 = 10 and SD = \sqrt{5^2+7^}
P(E - S < 0) = 0.123
The probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.
What is the normally distributed data?Normally distributed data is the distribution of probability which is symmetric about the mean.
The mean of the data is the average value of the given data. The standard deviation of the data is the half of the difference of the highest value and mean of the data set.
A company advertises two car tire models. The number of thousands of miles that the standard model tires last has a mean and standard deviation,
[tex]\mu_S= 60[/tex]
[tex]\sigma_S = 5[/tex]
The number of miles that the extended life tires last has a mean and standard deviation,
[tex]\mu_E = 70[/tex]
[tex]\sigma_E = 7[/tex]
Use the E-S random variable rule,
[tex]E=\mu_E-\mu_s\\E=70-60\\E=10[/tex]
Similarly, the value of S,
[tex]E=\sqrt{\sigma^2_E+\sigma^2_s}\\S=\sqrt{7^2+5^2}\\S=\sqrt{49+25}\\S=\sqrt{74}\\S=8.60[/tex]
For this E-S value, the value of probability from the table of normal distribution, we get as 0.123.
[tex]P(E - S < 0)=0.123[/tex]
Thus, the probability that a randomly selected standard model tire will get more mileage than a randomly selected extended life tire is 0.123.
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Please help Asap will mark (Brainliest)
Kyleigh put a large rectangular sticker on her notebook. The height of the sticker measures 16 centimeters. The base is half as long as the height.The area of the notebook that the sticker covers is ____________ square centimeters.
Answer: The area of the notebook that the sticker covers is 128 cm^2
Step-by-step explanation:
The equation for the area of a rectangle should be:
[tex]A=bh[/tex]
-The height of the stickers measures 16 cm:
[tex]height = 16cm[/tex]
-So, if the base is half as long as the height, you divide it by 2:
[tex]base=\frac{16}{2}=8cm[/tex]
-Then, you substitute it:
[tex]A=16[/tex] · [tex]8[/tex]
-Result:
[tex]128cm^2[/tex]
A one-night stay at the Great Wolf Lodge is
$249. If you have a coupon for 10% off the
room rate and sales tax is 12.75%, find the
total cost for one night.
After applying a 10% coupon and 12.75% sales tax, the total cost for one night at the Great Wolf Lodge is approximately $252.67.
Explanation:To find the total cost for one night at the Great Wolf Lodge including a 10% discount and 12.75% sales tax, we first need to calculate the amount of the discount. Since the discount is 10% off, you would multiply the original cost of $249 by 0.10 to get $24.9. Then subtract this from the original cost to find the discounted cost: $249 - $24.9 = $224.1. Next, apply the 12.75% sales tax to the discounted cost. Multiply $224.1 by 0.1275 to get $28.5725. Add this to the discounted cost: $224.1 + $28.5725 = $252.6725. So, including the discount and sales tax, the total cost for one night would be approximately $252.67.
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To find the total cost for one night, calculate the discount, subtract it from the original price, calculate the sales tax, and add it to the discounted price.
Explanation:To find the total cost for one night at the Great Wolf Lodge, you need to calculate the discount from the coupon and add the sales tax to the discounted room rate.
The total cost for one night at the Great Wolf Lodge, after applying the 10% discount and including the 12.75% sales tax, is $252.68.
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Bradley spins the spinner below 30 times. A success occurs when the spinner lands on a number that is greater than 6.
Answer:A. 1/4 - 3/4
Step-by-step explanation:For future students
I need help ASAP. Thank you
3x^2 + 23x - 36
^
3x to the power of 2 btw for the first part.
Answer:
.
Step-by-step explanation:
(3x-4)(x+9)
you can continue doing it :)
1. Find the circumference of a circle with a radius of 5 meters.
A regular heptagon has a side length of 13.9 and an apothem of 14.4. Find the area of the regular heptagon.
Answer: 700.56
Step-by-step explanation:
A heptagon has 7 sides, therfore a regular heptagon will have 7 equal sides
n = 7 (number of sides)
s = 13.9 (length of each sides of the heptagon)
r = 14.4 (The apothem)
The area of the regular heptagon can be calculated by:
Area = ½ n × s × r
Area = ½ × 7 × 13.9 × 14.4
Area = 700.56 square units
A bag contains 52 balls lettered from a to z and A to Z (i.e. uppercase or lowercase letters). One ball is withdrawn. What is the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D)?
the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D) is 0.557
Step-by-step explanation:
Here we have ,A bag contains 52 balls lettered from a to z and A to Z (i.e. uppercase or lowercase letters). One ball is withdrawn. We need to find What is the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D)? Let's find out:
There are 26 lowercase letters and 26 uppercase letters ! According to question we need to choose a ball which is either a lowercase ( i.e. from 26 letters ) or earlier in the alphabet than d ( or D ) which is A or B or , C .
Probability = (Favorable outcome)/(Total outcome)
Favorable outcome = 26+3=29
Total Outcome = 52
So ,
⇒ [tex]Probability = \frac{29}{52}[/tex]
⇒ [tex]Probability = 0.557[/tex]
Therefore , the probability that the ball will have a letter that is lower case or earlier in the alphabet than d (or D) is 0.557
Final answer:
To calculate the probability of drawing a ball that is lower case or earlier in the alphabet than 'd', we count the number of qualifying balls (29) and divide by the total number (52), resulting in a probability of 29/52.
Explanation:
The student's question is about calculating the probability of drawing a ball from a bag that either contains a lower case letter or a letter that comes earlier in the alphabet than the letter 'd'. Given that the bag contains 52 balls, with each letter of the alphabet represented in both upper and lower case, we can calculate the probability by counting the number of balls that satisfy the condition and dividing by the total number of balls.
There are 3 letters in the alphabet before 'd' (‘a’, ‘b’, and ‘c’) and each comes in two forms (upper and lower case), so there are 3 * 2 = 6 balls that meet the 'earlier in the alphabet than d' criterion. Since there are 26 letters in the alphabet and each has a lower case form, there are 26 balls that are lower case.
To avoid double-counting the lower case balls ‘a’, ‘b’, and ‘c’, we subtract those 3 balls from the 26 lower case balls, resulting in 23. Adding these 23 to the 6 balls already counted, we have a total of 29 balls that satisfy either condition. The probability is therefore 29/52.
What is the only unknown (variable) needed to find the volume of a sphere?
Sphere
The radius of the sphere is the only unknown variable need to find the volume of a sphere.
Step-by-step explanation:
Sphere is a geometrical three dimensional round figure with every point on its surface equidistant from its center. It is a three dimensional representation of a circle. A line which connects from the center to the surface is called radius of the sphere.The diameter of the sphere is the longest straight line which passes through the center of the sphere.
The volume of sphere is given by:
Volume of sphere(V) = [tex]\frac{4}{3}\pi r^{3} \\[/tex]
where V is the volume of the sphere
r is the radius of the sphere
[tex]\pi = \frac{22}{7}[/tex] = 3.14
Hence the only unknown variable to find the volume of a sphere is the radius.