[tex]\mathsf{\heartsuit\;\; (\sqrt{8})^2 = \sqrt{64}}\\\\\mathsf{\heartsuit\;\; [(8)^\frac{1}{2}]^2 = \sqrt{(8)^2}}\\\\\mathsf{\heartsuit\;\; (8)^\frac{2}{2} = [(8)^2]^\frac{1}{2}}\\\\\mathsf{\heartsuit\;\; 8 = [8]^\frac{2}{2}}\\\\\mathsf{\heartsuit\;\; 8 = 8}\\\\\mathsf{\heartsuit\;\; Option\;(A)\;is\;the\;Answer}[/tex]
The number which will make the equation true, when placed in the box is: A. √8.
How to solve for the unknown number?In order to determine the unknown number, we would assign a variable (x) to the unknown number and then evaluate the resulting algebraic equation as follows:
x² = √64
x² = 8
Taking the square root of both sides, we have:
x = √8.
Read more on algebraic equation here: brainly.com/question/13170908
#SPJ2
15 Points!
I have tried multiple times on this question and I don't understand it. Matikas is writing a coordinate proof to show that the midpoints of a quadrilateral are the vertices of a parallelogram. He starts by assigning coordinates to the vertices of quadrilateral RSTV and labeling the midpoints of the sides of the quadrilateral as A, B, C, and D.
Enter the answers, in simplified form, in the boxes to complete the proof.
Answer:
coordinate of point A is (a,b)
coordinate of point C is (2c,d)
slope of AD and BC =[tex]\frac{b}{a-c}[/tex]
Step-by-step explanation:
According to midpoint formula
If we have points P [tex](x_{1} ,y_{1} )[/tex] and Q [tex](x_{2} ,y_{2} )[/tex]
then the coordinate (x,y) of mid point of line PQ is given by
[tex]x=\frac{x_{1} +x_{2} }{2}[/tex] and [tex]y=\frac{y_{1} +y_{2} }{2}[/tex]
now from the given diagram A is the mid point of line joining R(0,0) and S(2a,2b)
Using midpoint formula, coordinates of point A is given by
[tex]x=\frac{0+2a}{2}= a[/tex] and [tex]y=\frac{0+2b}{2} =b[/tex]
so we have
coordinate of point A is (a,b)
Also C is the midpoint of line joining T (2c,2d) and V(2c,0)
coordinate of point C is given by
[tex]x= \frac{2c+2c}{2} =2c[/tex] and [tex]y=\frac{2d+0}{2} =d[/tex]
so we have
coordinate of point C is (2c,d)
it is given that coordinate of point B is (a+c, b+d) and coordinate of D is (c,0)
If we have points P [tex](x_{1} ,y_{1} )[/tex] and Q [tex](x_{2} ,y_{2} )[/tex]
then the slope of PQ =[tex]\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]
hence slope of AD= [tex]\frac{0-b }{c-a} [/tex]
=[tex]\frac{-b}{c-a}[/tex]
=[tex]\frac{-b}{-(a-c)}[/tex]
=[tex]\frac{b}{a-c}[/tex]
and slope of BC =[tex]\frac{d-(b+d)}{2c-(a+c)}[/tex]
=[tex]\frac{d-b-d}{2c-a-c}[/tex]
=[tex]\frac{-b}{c-a}[/tex]
=[tex]\frac{b}{a-c}[/tex]
so we have
slope of AD and BC =[tex]\frac{b}{a-c}[/tex]
Answer:
Co-ordinates of A are ( a, b )
Co-ordinates of C are ( 2c, d )
Slope of line segments AD and BC is [tex]\frac{-b}{c-a}[/tex]
Step-by-step explanation:
We know that, the co-ordinates of the mid-point of a line segment having end points (x,y) and [tex](x_{1} , y_{1} )[/tex] is [tex](\frac{x+x_{1} }{2} , \frac{y+y_{1} }{2} )[/tex]
Now as 'A' is the mid-point of the line segment RS having end points (0,0) and (2a,2b).
The co-ordinates of A will be ( [tex]\frac{0+2a}{2}[/tex], [tex]\frac{0+2a}{2}[/tex] ) i.e [tex]( a, b )[/tex]
Now as 'C' is the mid-point of the line segment TV having end points (2c,2d) and (2c,0).
The co-ordinates of C will be ( [tex]\frac{2c+2c}{2}[/tex], [tex]\frac{2d+0}{2}[/tex] ) i.e. [tex]( \frac{4c}{2} , \frac{2d}{2})[/tex] i.e. [tex]( 2c, d )[/tex].
Further, we need to find the slope of line segments AD and BC.
AD has end points [tex]( a, b )[/tex] and [tex]( c, 0 )[/tex]. Then the slope of AD will be [tex]\frac{0-b}{c-a}[/tex] i.e [tex]\frac{-b}{c-a}[/tex]
Similarly, BC has end points [tex]( a+c, b+d )[/tex] and [tex]( 2c, d )[/tex]. Then the slope of BC will be [tex]\frac{d-b-d}{2c-a-c}[/tex] i.e [tex]\frac{-b}{c-a}[/tex]
Hence, the slope of AD and BC is [tex]\frac{-b}{c-a}[/tex].
Does cell division always mean an organism is growing?
Your car averages 34 miles per gallon on the highway. If gas costs $2.10 per gallon, how much does it cost in dollars per mile, to drive your car on the highway?
(A) $.06/mi (B) 16 mi/dollar (C) $16/mi (D) 0.06 mi/dollar
Answer:
Your answer is (A) $.06/mi
Step-by-step explanation:
Martha states that -6 is a rational number.Wich is a correct explanation for this statement?
A)The number -6 is the opposite of 6
B) The number -6 is a negative integer
C) The number -6 can be written as -6/1
D)The number -6 is less than 0
Answer:
It would be C
Step-by-step explanation:
The number is between integers, so it can't be an integer or a whole number. It's written as a ratio of two integers, so it's a rational number and not irrational.
Answer:
C.
Step-by-step explanation:
because if -6 is a rotational number it should also be able to be translated into a fraction form
Tony went to the candy store and saw that his favorite candy was on sale. The original price is $1.49 per candy bar. Today, the store is selling it for $1.25 per candy bar. How much greater (in dollars) is the original price than the sale price?
Answer:
$0.24
Step-by-step explanation:
1.49 - 1.25 = 0.24
Answer:
$0.24
Step-by-step explanation:
alma is finding the measures of the angles in a triangle that have the ratio 1:3:5. circle her mistake and correct it
x + 3x +5x = 180
8x = 180
x = 22.5
Answer:
error in summing terms in x
Step-by-step explanation:
x + 3x + 5x = 180 ( collect like terms on left )
9x = 180 ← ( 9x not 8x )
divide both sides by 9
x = 20
Alma made a calculation error in solving for the angles with a ratio of 1:3:5. The correct values for x, which is the smallest angle, should be 20 degrees with the middle and largest angles being 60 degrees and 100 degrees respectively.
Alma is attempting to solve for the measures of angles in a triangle with a ratio of 1:3:5. However, there seems to be a mistake in her calculation. To correct it, we start with her equation x + 3x + 5x = 180, which represents the fact that the sum of the angles in a triangle is always 180 degrees (Theorem 20).
Combining like terms we do have 9x = 180. Solving for x gives us x = 20.
Therefore, the measure of the smallest angle is 20 degrees, the middle angle is 60 degrees, and the largest angle is 100 degrees.
1) 3 - 7 x 5 + 2 x 4=
2) 7 - 2 x 5 + 9 x 3=
3) 2 - 8x + 3x When x = 5
4) 4 - 2x + 5x when x= 4
5) z divided 2 - 4z + 3(z-3) when z =8
GEMDAS!
1:
3 - 7 x 5 + 2 x 4
3 - 35 + 2 x 4
3 - 35 + 8
3 - 27
-24
2:
7 - 2 x 5 + 9 x 3
7 - 10 + 9 x 3
7 - 10 + 27
7 + 17
24
3:
2 - 8x + 3x When x = 5
2 - 8(5) + 3(5)
2 - 40 + 15
2 - 25
-23
4:
4 - 2x + 5x when x= 4
4 - 2(4) + 5(4)
4 - 8 + 20
4 + 12
16
5:
z ÷ 2 - 4z + 3(z - 3) when z = 8
8 ÷ 2 - 4(8) + 3(8 - 3)
8 ÷ 2 - 32 + 24 - 9
4 - 32 + 24 - 9
4 - 8 - 9
-13
I might've did #5 incorrect.... Really really sorry...
Miguel has two same size rectangles divivded into the same number of equal parts. One rectangle has 3/4 of the parts shaded, and the other has 5/8 of the parts shaded. Into how many parts could each rectangle be divided?
Final answer:
Each rectangle can be divided into 8 equal parts, allowing [tex]\frac{3}{4}[/tex] and [tex]\frac{5}{8}[/tex] to be expressed with the same denominator for comparison.
Explanation:
To determine how many parts each rectangle can be divided, we need to find a common denominator that allows us to express [tex]\frac{3}{4}[/tex] and [tex]\frac{5}{8}[/tex] using the same size parts. The smallest number that both denominators 4 and 8 can divide into without a remainder is 8. Therefore, the first rectangle can be divided into 8 equal parts, with 6 of those parts being shaded (since [tex]\frac{3}{4}[/tex] is equivalent to [tex]\frac{6}{8}[/tex]). The second rectangle is already divided into 8 equal parts with 5 of those parts being shaded.
HELP ASAP! WILL MARK AS BRAINLIEST (if you get answers correct)
1. (-6,-1), (-2,-3)
a. (-4,-2)
b. (2,-5)
c. (-2,1)
d. (-3.5,-2.5)
2. (-4,-5), (2,3)
a. (-4.5, 2.5)
b. (-3,-4)
c. (8,11)
d. (-1,-1)
3. (-3,-1), (3,5)
a. (-2,4)
b. (0,2)
c. (-3,-3)
d. (9,11)
4. What is the midpoint between (-3,-2) and (4,7)?
a. (2.5, 0.5)
b. (3.5, 4.5)
c. (-7, -9)
d. (0.5, 2.5)
Answer:
Step-by-step explanation:
If you want the mid point for these questions then for the 1st
1. add -6 and -2 which is -8 then divide by 2 which is -4, then add -1 and -3 which is -4 and then divide by 2 which is -2. so the mid point is (-4,-2)
2. its the same as above first add -4 and 2 which is -2 then divide by 2 which is -1, then add -5 and 3 which is -2 and divide by 2 which is -1. the point is (-1,-1)
3. -3+3=0 dived by 2 which is 0, -1+5=4 divide by 2 which is 2
point is (0,2)
4. -3+4=1 divide by 2 which is 1/2 =0.5, -2+7=5 then divide by 2 which is 5/2=2.5. point is (0.5,2.5)
HELP !!! Use the elimination method to solve the system of equations.
4x + 3y = 11
x - y = 8
Answer:
C. (5, -3)
Step-by-step explanation:
4x + 3y = 11
x - y = 8 (multiply by 3) --> 3x - 3y = 24
4x + 3y = 11
3x - 3y = 24
---------------------add
7x = 35
x = 5
5 - y = 8
y = 5 - 8
y = -3
(5, -3)
Answer:
C. (5, -3)
Step-by-step explanation:
Rewrite the first equation.
Multiply the second equation by 3 and write it under the first equation.
4x + 3y = 11
3x - 3y = 24
Now add the equations.
7x = 35
Divide both sides by 7.
x = 5
Substitute 5 for x in the original first equation:
4(5) + 3y = 11
20 + 3y = 11
3y = -9
y = -3
Solution: (5, -3)
plz help Pru, Piper, and Phoebe share spices in the ratio 5:3:4. If Pru has 24 more spices than Piper, how many spices does Phoebe have?
Answer:
Step-by-step explanation:
Pru, Piper, Phoebe ratio 5:3:4vadded = 12
What this means is Pru has 5/12 of the total amount, Piper has 3/12 of the total amount, and Phoebe has 4/12 of the total amount of spices.
pru = piper + 24
5/12x = 3/12x + 24
5/12x - 3/12x = 24
2/12x = 24
x = 24 / (1/6)
x = 24 * 6
x = 144 spices in total
Pru has : 5/12(144) = 720/12 = 60 spices
Piper has : 3/12(144) = 432/12 = 36 spices
Phoebe has : 4/12(144) = 576/12 = 48 spices
I hope this can help.
Answer:
48
Step-by-step explanation:
Pru, Piper, and Phoebe share spices in the ratio 5:3:4
5+3+4=12
So Pru has 5/12 share of spices, Piper has 3/12 share of spices, and Phoebe has 4/12 share of spices.
If Pru has 24 more spices than Piper, (5/12 - 3/12)=2/12 share of spices =24
Total spices = 24x12/2 = 144
Phoebe has 4/12x144 = 48 spices
Which property is demonstrated?
Answer:
associative property of multiplication
Step-by-step explanation:
edge 2021
Find (f • g) when f(x) = x^2 + 5x + 6 and g(x) = 1/x+3
Answer:
option D
Step-by-step explanation:
[tex]f(x) = x^2 + 5x + 6[/tex]
[tex]g(x)= \frac{1}{x+3}[/tex]
(fog)(x) = f(g(x))
Plug in g(x) in f(x)
We plug in 1/x+3 in the place of x in f(x)
[tex]f(g(x))= f(\frac{1}{x+3})= (\frac{1}{x+3})^2 + 5(\frac{1}{x+3}) + 6[/tex]
To simplify it we take LCD
LCD is (x+3)(x+3)
[tex]\frac{1}{(x+3)(x+3)}+5\frac{1*(x+3)}{(x+3)(x+3)}+\frac{6(x+3)(x+3)}{(x+3)(x+3)}[/tex]
[tex]\frac{1}{x^2+6x+9}+\frac{(5x+15)}{x^2+6x+9}+\frac{6x^2+36x+54}{x^2+6x+9}[/tex]
All the denominators are same so we combine the numerators
[tex]\frac{1+5x+15+6x^2+36x+54}{x^2+6x+9}[/tex]
[tex]\frac{6x^2+41x+70}{x^2+6x+9}[/tex]
Option D is correct
Answer:
The correct option choice is D. 6x^2 + 41x + 70 / x^2 +6x + 9
In an ordinary annuity, when does the interest on a yearly investment start building interest?
Answer:
The interest on a yearly investment start building interest - at the end of the first period.
Step-by-step explanation:
In an ordinary annuity, the interest on a yearly investment start building interest - at the end of the first period.
An ordinary annuity is a series of payments, where all the payments are of the same amount and are paid at the same intervals of time. The interest is calculated at the end of first period.
Can someone show me an example of long division?
Answer:
When you have large numbers to divide,
draw a tableau for long division on the side.
Write the steps that will be your guide,
D, M, S, B and R – Abide by to long divide!
Step-by-step explanation:
Answer:
Step-by-step explanation:
find the prime factorization of 3,240
Answer:
Answer: 3240 = 2^3×3^4×5
Factor the following integer:
3240
The last digit of 3240 is 0, which means it is even. Therefore 3240 is divisible by 2:
3240 = 2 1620:
3240 = 2×1620
The last digit of 1620 is 0, which means it is even. Therefore 1620 is divisible by 2:
1620 = 2 810:
3240 = 2×2×810
The last digit of 810 is 0, which means it is even. Therefore 810 is divisible by 2:
810 = 2 405:
3240 = 2×2×2×405
405 is not divisible by 2 since 405 is odd and 2 is even:
3240 = 2×2×2×405 (405 is not divisible by 2)
The sum of the digits of 405 is 4 + 0 + 5 = 9, which is divisible by 3. This means 405 is divisible by 3:
405 = 3 135:
3240 = 2×2×2×3×135 (135 is not divisible by 2 since 405 is not)
The sum of the digits of 135 is 1 + 3 + 5 = 9, which is divisible by 3. This means 135 is divisible by 3:
135 = 3 45:
3240 = 2×2×2×3×3×45 (45 is not divisible by 2 since 135 is not)
The sum of the digits of 45 is 4 + 5 = 9, which is divisible by 3. This means 45 is divisible by 3:
45 = 3 15:
3240 = 2×2×2×3×3×3×15 (15 is not divisible by 2 since 45 is not)
The sum of the digits of 15 is 1 + 5 = 6, which is divisible by 3. This means 15 is divisible by 3:
15 = 3 5:
3240 = 2×2×2×3×3×3×3×5 (5 is not divisible by 2 since 15 is not)
Divide 3 into 5:
| 1 | (quotient)
3 | 5 |
- | 3 |
| 2 | (remainder)
5 is not divisible by 3:
3240 = 2×2×2×3×3×3×3×5 (5 is not divisible by 2 or 3)
No primes less than 5 divide into it. Therefore 5 is prime:
3240 = 2×2×2×3×3×3×3×5
There are 3 copies of 2, 4 copies of 3 and 1 copy of 5 in the product:
Answer: 3240 = 2^3×3^4×5
3,240 =
= 324 × 10 =
= 4 × 81 × 10 =
= 2^2 × 3^4 × 2 × 5 =
= 2^3 × 3^4 × 5As a salesperson at trading cards unlimited Justin receives a monthly base pay Plus commission on all of that he sells. If he sells for $100 worth of merchandise in one month he is paid $500 if he sells $700 of merchandise in one month he is paid $575 find Justin’s salary when he sells $2500 worth of merchandise
Answer:
If he sells $2500 worth of merchandise, his salary is $800.
Step-by-step explanation:
You can find a function that gives you his salary as a function of the sales.
You have two points: (100, 500) and (700, 575).
y = mx + b
m = (575 - 500)/(700 - 100) = 75/600 = 0.125
Now use point (100, 500) to find b.
y = mx + b
500 = 0.125(100) + b
500 = 12.5 + b
b = 487.5
y = 0.125x + 487.5
If he sells $2500, then x = 2500.
y = 0.125x + 487.5
y = 0.125(2500) + 487.5
y = 800
If he sells $2500 worth of merchandise, his salary is $800.
In May, 2018 a store had a furniture with a listed price of $550, having a sales tax of 3% on the listed price. Next month the price increased by 33 1/3 %. What sales tax should be paid in dollars on the new price?
The sales tax that should be paid in dollars on the new price is $22
Further explanationOrder of Operations in Mathematics follow this following rule :
ParenthesesExponentsMultiplication and DivisionAddition and SubtractionThis rule is known as the PEMDAS method.
In working on a mathematical problem, we first calculate operation that is in parentheses, follow by exponentiation, then multiplication or division, and finally addition or subtraction.
Let us tackle the problem !
Given:
Initial Price = $550
Sales Tax = 3%
Percentage of Price Increase = 33¹/₃ %
Unknown:
Final Sales Tax = ?
Solution:
[tex]\texttt{Final Price} = \texttt{Initial Price} \times (100\% + \texttt{Percentage of Price Increase} )[/tex]
[tex]\texttt{Final Price} = \$550 \times (100\% + 33\frac{1}{3}\% )[/tex]
[tex]\texttt{Final Price} = \$550 \times (100\% + \frac{100}{3}\% )[/tex]
[tex]\texttt{Final Price} = \$550 \times (\frac{300}{3}\% + \frac{100}{3}\% )[/tex]
[tex]\texttt{Final Price} = \$550 \times (\frac{400}{3}\%)[/tex]
[tex]\texttt{Final Price} = \$550 \times (\frac{4}{3})[/tex]
[tex]\texttt{ }[/tex]
[tex]\texttt{Final Sales Tax} = 3\% \times \texttt{Final Price}[/tex]
[tex]\texttt{Final Sales Tax} = 3\% \times \$550 \times (\frac{4}{3})[/tex]
[tex]\texttt{Final Sales Tax} = \frac{3}{100} \times (\frac{4}{3}) \times \$550[/tex]
[tex]\texttt{Final Sales Tax} = \frac{4}{100} \times \$550[/tex]
[tex]\texttt{Final Sales Tax} = 4 \times \$5.5[/tex]
[tex]\texttt{Final Sales Tax} = \$22[/tex]
[tex]\texttt{ }[/tex]
Learn moreInfinite Number of Solutions : https://brainly.com/question/5450548System of Equations : https://brainly.com/question/1995493System of Linear equations : https://brainly.com/question/3291576Student's Shirt : https://brainly.com/question/909783Answer detailsGrade: Middle School
Subject: Mathematics
Chapter: Percentage
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point , Multiplication , Division , Exponent , PEMDAS , percentange , percent , cookies , chocolate , chip , paper , fourth , pieces
The sales tax should be paid in dollars on the new price is [tex]\boxed{\$ 22}.[/tex]
Further Explanation:
Given:
The listed price of furniture is [tex]\$550.[/tex]
The sales tax is of [tex]3\%[/tex] on the listed price.
The price is increased by [tex]33\dfrac{1}{3}\%.[/tex]
Calculation:
The increased price of the furniture can be obtained as follows,
[tex]\begin{aligned}{\text{Increased price}} &= 550 + \left( {33\frac{1}{3}\% \times 550} \right)\\&= 550 + \left( {\frac{{33.34}}{{100}} \times 550} \right)\\&= 550 + 0.3333 \times 550\\&= 550 + 183.32\\&= 733.32\\\end{aligned}[/tex]
The new price of the furniture is [tex]\$ 733.32.[/tex]
The sales tax is of [tex]3\%[/tex] on the listed price.
The sales tax can be obtained as follows,
[tex]\begin{aligned}{\text{Sales tax}} &= 3\% {\text{ of new price}}\\&= \frac{3}{{100}} \times 733.32\\&= \$ 22\\\end{aligned}[/tex]
The sales tax should be paid in dollars on the new price is [tex]\boxed{\$ 22}.[/tex]
Learn more:
Learn more about inverse of the function https://brainly.com/question/1632445 Learn more about range and domain of the function https://brainly.com/question/3412497 Learn more about profit and loss https://brainly.com/question/2479097
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Investment and return
Keywords: May, 2018, store, furniture, listed, price, listed price, $550, sales, sales tax, 3%, tax on listed price, next month, price increased, increased price, month[tex], 33 1/3%[/tex], paid, dollars, new price.
Which statement about the graph y= 4x - 10 is NOT true?
A. The slope of the line can be written as 4/1
B. The graph crosses the y-axis 10 units below the origin
C. The line has a constant rate of change
D. The graph contains the point (4, -10)
Answer:
D. The graph contains the point (4, -10)
Step-by-step explanation:
We have been given an equation of a function: [tex]y=4x-10[/tex]. We are asked to find which of the given statements are not true about our given function.
A. The slope of the line can be written as 4/1.
We can see from our given equation that slope is 4 we can write 4 as 4/1 as it will not change value of 4, therefore, option A is true.
B. The graph crosses the y-axis 10 units below the origin.
Since we know that b represents y-intercept, where line crosses y-axis. y-intercept for our given equation is -10, which means that our given line crosses y-axis at -10 (10 units below the origin), therefore, option B is true.
C. The line has a constant rate of change.
We can see that slope of line is 4 which means with each increase in x, y will increase by 4 units, which remains constant, therefore, option C is true indeed.
D. The graph contains the point (4, -10)
Since we know that y-intercept is -10, which occurs at x equals 0, therefore, the graph does not contain the point (4,-10) and option D is not true.
Phillip bought 12 used cds and dvds. CDs cost 2 each and dvds cost 3 each. He spent 32 not including tax. How many dvds did Phillip buy?
Answer:
Eight
Step-by-step explanation:
We have two conditions:
(1) C + D = 12
(2) 2C + 3D = 32 Subtract D from each side of Equation (1)
C = 12 - D Multiply both sides by 5
2(12 – D) + 3D = 32 Remove parentheses
24 – 2D + 3D = 32 Combine like terms
24 + D = 32 Subtract D from each side
D = 8
Philip bought eight DVDs.
I need help with a and b
You travel 12 miles north and then 5 miles west from your home. How far are you from home?
Answer:
13 Miles
Step-by-step explanation:
This problem could be solved using the Pythagorean theorem.
a² + b² = c²
a = 12 b = 5
12² + 5² = 169
√169 = 13
Therefore, you are 13 miles away from your house!
the quotient of 32 times a number and 4 is 16
Answer:
x=2
Step-by-step explanation:
32x ÷ 4 = 16
32x = 64
x = 2
Answer:
x = - 3.5
Step-by-step explanation:
32 * ( x + 4 ) = 16
x + 4 = 16 / 32
x + 4 = 0.5
x = 0.5 - 4
x = - 3.5
What are the factors of x2 – 100?
(x – 50)(x + 50)
(x – 10)(x + 10)
(x – 25)(x + 4)
(x – 5)(x + 20)
Answer:
(x-10)(x+10)
Step-by-step explanation:
Here, the given expression,
[tex]x^2-100[/tex]
[tex]=(x)^2-(10)^2[/tex]
By using the identity [tex]a^2-b^2=(a+b)(a-b)[/tex]
[tex]=(x+10)(x-10)[/tex]
[tex]=(x-10)(x+10)[/tex] ( By the commutative property )
Since, further factorization is not possible,
Hence, the factors of [tex]x^2-100[/tex] are,
[tex](x-10)(x+10)[/tex]
Second option is correct.
If the speed limit of the highway is 60 mph which car exceed the speed limit assume other cars were traveling at a constant speed a car traveled at 183 miles in three hours a car that travel 236 miles in four hours a car that traveled 290 miles in five hours or a car that traveled 342 miles in six hours
Answer:
The first car
Step-by-step explanation:
183/3 = 61mph
Answer:
183/3 or Option A
Step-by-step explanation:
Edge 2021
thats where i got the correct answer plus i took the test
What is the solution set of x2 – 10 = 30x?
So for this, I will be completing the square to solve for x. Firstly, add 10 and subtract 30x on both sides of the equation:
[tex]x^2-30x=10[/tex]
Next, we want to make the left side of the equation a perfect square. To find the constant of this soon-to-be perfect square, divide the x coefficient by 2 and square the quotient. Once you get that result, add it to both sides of the equation:
[tex]30\div 2 = 15\\15^2=225\\\\x^2-30x+225=235[/tex]
Now, factor the left side:
[tex](x-15)^2=235[/tex]
Next, square root both sides:
[tex]x-15=\pm\ \sqrt{235}[/tex]
Now, add 15 to both sides of the equation:
[tex]x=15\pm \sqrt{235}[/tex]
This is the exact solution. To find the approximate solution, solve the left side twice -- once with the plus sign, once with the minus sign:
[tex]x=30.33,-0.33[/tex]
Answer:In short:
Exact Solution: [tex]x=15\pm\sqrt{235}[/tex]Approximate Solution (Rounded to the hundredths): [tex]x=30.33,-0.33[/tex][tex]x^2-10=30x\qquad\text{subtract 30x from both sides}\\\\x^2-30x-10=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a},\ x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\text{We have}\ a=1,\ b=-30,\ c=-10\\\\\text{Substitute.}\\\\b^2-4ac\to(-30)^2-4(1)(-10)=900+40=940\\\\\sqrt{b^2-4ac}=\sqrt{940}=\sqrt{4\cdot235}=\sqrt4\cdot\sqrt{235}=2\sqrt{235}\\\\x_1=\dfrac{-(-30)-2\sqrt{235}}{2(1)}=\dfrac{30-2\sqrt{235}}{2}=15-\sqrt{235}\\\\x_2=\dfrac{-(-30)+2\sqrt{235}}{2(1)}=\dfrac{30+2\sqrt{235}}{2}=15+\sqrt{235}[/tex]
[tex]Answer:\ \boxed{x=15-\sqrt{235}\ and\ x=15+\sqrt{235}}[/tex]
a file is 284 megabytes is being downloaded. If the download is 15.3% complete how many megabytes have been downloaded
Answer:
43.452
Step-by-step explanation:
284 times .153 = 43.452
I WILL AWARD BRAINLIEST!
The Patronete Winery's tastiest wine must have a 12% alcohol content. How many gallons of wine with a 9% alcohol content must be mixed with 3,000 gallons of wine with a 15% alcohol content in order to achieve the desired 12% alcohol content?
Answer:
3000 gallons of 12 percent is required
Step-by-step explanation:
We can use the formula
percentage * amount + percentage * amount = percentage*total amount
We have 9 percent and 15 percent wine that we are mixing to get 12 percent wine.
We are adding g gallons and 3000 gallons to get a total of (g+3000) gallons
Substituting this information in
.09 *g + .15 * 3000 = .12 (g+3000)
Distribute
.09g +450 = .12g+360
Subtract .9g from each side
.09g-.09g +450 = .12g-0.09g+360
450 = .03g + 360
Subtract 360 from each side
450-360 = .03g
90 =.03g
Divide each side by .03
90/.03 = .03g/03
3000 = g
if i clock out at 1:46 and i have 30 Minutes what time do i go in?
I will get in 2:16.
Now it is given that I clock out or I got out when the time was 1 hour 46 minutes.
And I have 30 minutes to go in.
So after 30 minutes, the time will be :
1 hour + 46 minutes
+ 30 minutes
1 hour + 76 minutes
Now we know that 60 minutes = 1 hour
So the time will be 2 hours and 16 minutes.
Therefore, the time at which I will get in after 30 minutes is 2:16
Learn more :
https://brainly.com/question/11780640
PLEASE HELP!! what is the units digit of 23^23
HURRY! PLEASE answer in 1 MINUTE!
Thanks!
The units digit of 23^23 is 7. This is found using the power cycle of 3 (the units digit of the base number), which is 3, 9, 7, 1 and the remainder when the exponent 23 is divided by the length of this power cycle (4).
Explanation:To find the units digit of 2323, one needs to understand a pattern in power cycles. For any number, the units digit will repeat in a certain cycle when the number is raised to higher powers. For number 3, every fourth power goes back to the value 1. Thus, the cycle for the number 3 is 3, 9, 7, 1.
Here’s how the calculation works:
For finding the pattern cycle we ignore any digits other than the units digit. This means we only need to look at the pattern in powers of 3 (not 23). Determine which number of the cycle to use. The exponent 23 divided by the length of the cycle (4) leaves a remainder of 3 (because 23/4= 5 remainder 3). So we use the third number in the cycle, which is 7. Hence, the units digit of 2323 is 7.Learn more about Units Digit here:https://brainly.com/question/17038912
#SPJ2