Answer:
[tex]x=\frac{5+\sqrt{15}}{2},\:x=\frac{5-\sqrt{15}}{2}[/tex]
Step-by-step explanation:
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=2,\:b=-10,\:c=5[/tex]
[tex]x_{1,\:2}=\frac{-\left(-10\right)\pm \sqrt{\left(-10\right)^2-4\cdot \:2\cdot \:5}}{2\cdot \:2}[/tex]
[tex]\sqrt{\left(-10\right)^2-4\cdot \:2\cdot \:5}[/tex]
Apply exponent rule: (-a)^n=a^n, if n is even
[tex]\left(-10\right)^2=10^2[/tex]
[tex]=\sqrt{10^2-4\cdot \:2\cdot \:5}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:4\cdot \:2\cdot \:5=40[/tex]
[tex]=\sqrt{10^2-40}[/tex]
[tex]10^2=100[/tex]
[tex]=\sqrt{100-40}[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:100-40=60[/tex]
[tex]=\sqrt{60}[/tex]
[tex]60\:\mathrm{divides\:by}\:2\quad \:60=30\cdot \:2[/tex]
[tex]=2\cdot \:30[/tex]
[tex]30\:\mathrm{divides\:by}\:2\quad \:30=15\cdot \:2[/tex]
[tex]=2\cdot \:2\cdot \:15[/tex]
[tex]15\:\mathrm{divides\:by}\:3\quad \:15=5\cdot \:3[/tex]
[tex]=2\cdot \:2\cdot \:3\cdot \:5[/tex]
[tex]2,\:3,\:5\mathrm{\:are\:all\:prime\:numbers,\:therefore\:no\:further\:factorization\:is\:possible}[/tex]
[tex]=2\cdot \:2\cdot \:3\cdot \:5[/tex]
[tex]=2^2\cdot \:3\cdot \:5[/tex]
[tex]=\sqrt{2^2\cdot \:3\cdot \:5}[/tex]
Apply Radical Rule:
[tex]=\sqrt{2^2}\sqrt{3\cdot \:5}[/tex]
Apply Radical Rule:
[tex]\sqrt{2^2}=2[/tex]
[tex]=2\sqrt{3\cdot \:5}[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]=2\sqrt{15}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-10\right)\pm \:2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]\mathrm{Separate\:the\:solutions}[/tex]
[tex]x_1=\frac{-\left(-10\right)+2\sqrt{15}}{2\cdot \:2},\:x_2=\frac{-\left(-10\right)-2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]\frac{-\left(-10\right)+2\sqrt{15}}{2\cdot \:2}[/tex]
Apply Rule -(-a)=a
[tex]=\frac{10+2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4[/tex]
[tex]=\frac{10+2\sqrt{15}}{4}[/tex]
[tex]=\frac{2\left(5+\sqrt{15}\right)}{4}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:2[/tex]
[tex]=\frac{5+\sqrt{15}}{2}[/tex]
[tex]\frac{-\left(-10\right)-2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]=\frac{10-2\sqrt{15}}{2\cdot \:2}[/tex]
[tex]\mathrm{Multiply\:the\:numbers:}\:2\cdot \:2=4[/tex]
[tex]=\frac{10-2\sqrt{15}}{4}[/tex]
[tex]=\frac{2\left(5-\sqrt{15}\right)}{4}[/tex]
[tex]\mathrm{Cancel\:the\:common\:factor:}\:2[/tex]
[tex]=\frac{5-\sqrt{15}}{2}[/tex]
[tex]\mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:}[/tex]
[tex]x=\frac{5+\sqrt{15}}{2},\:x=\frac{5-\sqrt{15}}{2}[/tex]
[tex]Evaluating Combination Notation & Problem Solving[/tex]
Evaluate the following combinations. Write also your solutions.
Answer:
Step-by-step explanation:
1. ⁷C₅ = ⁷C₂ = 7 x 6 / 2 = 21
2. ⁹C₈ = ⁹C₁ = 9
3. ¹²C₅ = 12 x 11 x 10 x 9 x 8 / 2 x 3 x 4 x 5
= 11 x 9 x 8 = 11 x 72 = 792
4. ²⁰C₁₇ = ²⁰C₃ = 20 x 19 x 18 / 2 x 3
= 19 x 3 = 57
5. ¹⁶C₁₃ = ¹⁶C₃ = 16 x 15 x 14 / 2 x 3
= 8 x 5 x 14 = 40 x 14 = 560
6. ⁷C₄ + ¹¹C₉ = ⁷C₃ + ¹¹C₂ = (7 x 6 x 5 / 2 x 3) + (11 x 10 / 2)
= 35 + 55 = 90
7. ⁷C₃ + ⁷C₄ + ⁷C₅ = 2(⁷C₃) + ⁷C₂ = (2 x 7 x 6 x 5 / 2 x 3) + (7 x 6 / 2)
= 70 + 21 = 91
Legit only this much I can do now.
Hope it is enough.
If the graph of f " (x) is continuous and has a relative maximum at x = c, which of the following must be true?
The graph of f has an x-intercept at x = c.
The graph of f has an inflection point at x = c.
The graph of f has a relative minimum at x = c
None of the above is necessarily true.
Answer:
None of the above is necessarily true.
Step-by-step explanation:
I've attached an example of such a function to show this.
Write the following number in standard form. One hundred four billion, twenty- seven thousand, five hundred seventy-one
Answer:
104,000,027,571
Step-by-step explanation:
billions, millions, thousands, hundreds
If y varies directly as x, and x =9 when y =15, Find y when x =21
y = x
15 = 9
y = 21
9y = 315
y = 315/9
y = 35
Answer:
35
Step-by-step explanation:
y is propotional to x, means, if x changes, y changes.
Considering, y depends on x only. Introduce a constant.
y = kx
When x = 9, y = 15,
=> 15 = k(9) => 5/3 = k
When x = 21, note that k is constant.
=> y = kx = (5/3)*21
= 35
c. Describe how you could compare the corresponding sides and angles of
figure WXUY and its image, figure STUV.
Step-by-step explanation:
please provide the figure. without the figure cannot find the answer
Work out value x, give answer to 1 decimal place
Answer:
x ≈ 44.6°
Step-by-step explanation:
perimeter of a perfect circle: 2πr = 2π(9) = 18π
perimeter of the circle arc : 25 - 2(9) = 7
The central angle in a full circle is 360 degrees. In the segment of the circle is x degrees. The value of x is obtained using proportionality.
[tex] \frac{360}{x} = \frac{18\pi}{7} \\ \\ x = \frac{7 \times 360}{18\pi} = 44.56[/tex]
can anybody explain how to subtract mixed fractions?
Answer:
convert the mixed fractions to improper fractions (where the numerator is greater than or equal to the denominator): multiply the whole number part by the fraction's denominator, add that to the numerator, write the result on top of the denominator.if the denominators are not the same, work out the common denominator and rewrite the fractions with the same denominatorssubtract by subtracting the numerators and writing the result over the denominatorconvert back to mixed fractions by dividing the numerator by the denominator, write down the whole number answer, write down the remainder above the denominator.
Example
[tex]3\frac23-1\frac45[/tex]
convert to improper fractions:
[tex]\dfrac{3 \times 3+2}{3}-\dfrac{1 \times 5+4}{5}=\dfrac{11}{3}-\dfrac{9}{5}[/tex]
common denominator = 3 × 5 = 15, so:
[tex]\dfrac{11}{3}-\dfrac{9}{5}=\dfrac{11\times 5}{3\times 5}-\dfrac{9\times 3}{5\times 3}=\dfrac{55}{15}-\dfrac{27}{15}[/tex]
subtract:
[tex]\dfrac{55}{15}-\dfrac{27}{15}=\dfrac{55-27}{15}=\dfrac{28}{15}[/tex]
convert back to mixed fractions:
[tex]28 \div 15=1 \textsf{ remainder }13=1 \frac{13}{15}[/tex]
To subtract mixed fractions, we must follow the steps:
Convert the mixed fraction to improper fraction.2. Multiply the denominator and the numerator by the LCM of the denominators to make the denominators same. P.S: (If the denominators are the same, you can skip this step).
3. Simplify the fractions. (The denominators do not change).
4. (Optional) Convert the fractions to mixed fraction.
Solving an example:Let's take an example.
⇒ [tex]4 \frac{2}{5} - 3 \frac{3}{8}[/tex]Step-1: Convert the fractions to improper fraction:
⇒ [tex]4 \frac{2}{5} - 3 \frac{3}{8}[/tex]⇒ [tex]\frac{(4)(5) + 2}{5} - \frac{(3)(8) + 3}{8}[/tex]⇒ [tex]\frac{20 + 2}{5} - \frac{24+ 3}{8}[/tex]⇒ [tex]\frac{22}{5} - \frac{27}{8}[/tex]Step-2: Make the denominators same:
⇒ [tex]\frac{22}{5} - \frac{27}{8}[/tex]⇒ [tex]\frac{(22)(8)}{(5)(8)} - \frac{(27)(5)}{(8)(5)}[/tex]⇒ [tex]\frac{176}{40} - \frac{135}{40}[/tex]Step-3: Subtract:
⇒ [tex]\frac{176}{40} - \frac{135}{40}[/tex]⇒ [tex]\frac{41}{40}[/tex]Step-4: Convert the fraction to mixed fraction:
⇒ [tex]\frac{41}{40}[/tex]⇒ [tex]\frac{40}{40} + \frac{1}{40}[/tex]⇒ [tex]1 + \frac{1}{40}[/tex]⇒ [tex]1\frac{1}{40}[/tex]Solve : 21 divided by -3 =
Answer:
-7
Step-by-step explanation:
21 divided by -3 = -7
-7 times -3 =21
New shoes are on SALE. You find a pair you like for $85 dollars. But you only have $45 with you. So, you pay $40 and
charge the balance. At 8% interest, what will the balance owed be in six months? (Assume no payments made and simple interest.)
0 0 0 0
a) $24.25
b) $35.50
c) $46.80
d) $50.00
Answer:
C) $46.80
Explanation:
The price of new shoes = $85
The amount paid for the shoes = $ 40
The balance amount for the shoes = $85 - $40 = $ 45
The rate of interest = 8%
The time period = 6 months = 0.5 years
Simple interest:
Simple interest = = $1.8
So, Amount = Principal + Interest
or, Amount = $45 + $1.8 = $ 46.8
The balance amount owned in six months is $46.8
Answer:
$46.8
Step-by-step explanation:
i took the test
2 5/8 -1 1/4 fraction
Answer:
11/8 or 1 3/8
Step-by-step explanation:
hope this helps
20. Which student's score was closest to
average?
pls answer ASAP I will make you brainist however you spell it
Answer:
CStep-by-step explanation:
Comparing the difference with the average in absolute value
3, 4, 2, 5, 7The smallest number is 2 indicating the closest to average score
Matching student is C
If f(x)=8x^3-6x^2+x-3 and g(x)=0, find (f o g)(x) and (g o f)(x)
Answer:
(f o g)(x) = -3
(g o f)(x) = 0
Step-by-step explanation:
See attached image
2 mangoes cost $3.00 at the store. What is the cost per mango?
Answer:
1 mango = $1.50
Step-by-step explanation:
2 mangoes - $3
1 mango - $?
3 / 2 = 1.5
So:
1 mango = $1.50
Hope this helped!
(Let me know if I got something wrong!)
Answer: $1.50
Step-by-step explanation:
The total cost of mangoes cost $3.00, and the person bought two.
To find the cost per mango, you can divide 3 by 2.
3/2 is 1.5, so each mango costs $1.50
hope this helped :)
The policy of the Broadway Pawnshop is to lend up to 35% of the value of a borrower’s collateral. John wants to use a $3,000 ring and a $1,200 necklace as collateral for a loan. What is the maximum amount that he could borrow from Broadway?
Answer:1
3,000 + 1,200 = 4,200
add value of items
2
35 / 100 = .35
divide percentage by 100 to get decimal
3
4,200 * .35 = $1,470
multiply value of items by decimal to find collateral
RESULT
$1,470
Step-by-step explanation:
The maximum amount that he could borrow from Broadway is $1,470.
Calculation of the maximum amount:Since The policy of the Broadway Pawnshop is to lend up to 35% of the value of a borrower’s collateral. John wants to use a $3,000 ring and a $1,200 necklace as collateral for a loan.
Here the total amount should be
= $3,000 + $1,200
= $4,200
And, there is 35%
So, the maximum amount should be
= 35% of $4,200
= $1,470
Hence, The maximum amount that he could borrow from Broadway is $1,470.
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Students at a local school can join one club. The chart below shows how many students are in each club. What percentage of the total number of students are in the outdoor club? (3 points - 2 pts for each correct answer, 1 pts total for showing work) Number of Students Percent of Students Club Photography Coding 32 16% 64 32% Outdoor 40 Gaming 64 Show your work below: =
Answer:
20%
Step-by-step explanation:
If you already know that 64 students equals 32% you can fill the gaming club in for 32%. Since 100% is the goal you can add 32+32+16 to get 80 and subtract that from 100 to get the remaining percent.
solve this -5x=3x-24
Answer:
x=19/3 x=6 1/3 x=6.333333333
Step-by-step explanation:
Tanya is given the graphs of the following functions. The functions Latex: f(x) f ( x ) and Latex: g(x) g ( x ) are linear, and the function Latex: s(x) s ( x ) is quadratic. f ( x ) = 3 x − 8 g ( x ) = − 2 x + 5 s ( x ) = 4 x 2 − 9 x + 2 Tanya is then asked to find the graph of Latex: (f\cdot g)(x) ( f ⋅ g ) ( x ) and the graph of Latex: (g\cdot s)(x)\textsf{.} For each combined function, she is given four options to choose from. What clues will help Tanya identify the correct graph of Latex: (f\cdot g)(x)\textsf{?} What clues will help Tanya identify the correct graph of Latex: (g\cdot s)(x)\textsf{?}
The functions (f.g)(x) and (g.s)(x) are illustrations of composite function
The values of the composite functions are:
(fg)(x) = -6x^2 + 31x - 40 and (gs)(x) = -8x^3 + 38x^2 -49x+ 10
How to determine the equation of the composite functionThe equation of the functions are given as:
f(x) = 3x - 8
g(x) = -2x + 5
s(x) = 4x^2 - 9x + 2
.
The composite functions are calculated using:
(fg)(x) = f(x) * g(x)
So, we have:
(f g)(x) = (3x - 8) * (-2x + 5)
Evaluate the product
(fg)(x) = -6x^2 + 15x + 16x - 40
Evaluate the like terms
(fg)(x) = -6x^2 + 31x - 40
Also, we have:
(gs)(x) = g(x) * s(x)
So, we have:
(gs)(x) = (-2x + 5) * (4x^2 - 9x + 2)
Expand
(gs)(x) = -8x^3 + 18x^2 -4x + 20x^2 - 45x + 10
Collect like terms
(gs)(x) = -8x^3 + 18x^2 + 20x^2-4x - 45x + 10
Evaluate the like terms
(gs)(x) = -8x^3 + 38x^2 -49x+ 10
Hence, the values of the composite functions are:
(fg)(x) = -6x^2 + 31x - 40 and (gs)(x) = -8x^3 + 38x^2 -49x+ 10
Read more about composite functions at:
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Choose the equation below that represents the line that passes through the point (-2, -1) and has a slope of 5. (5 points)
O. y- 1 = 5(x - 2)
O. y + 1 = 5(x + 2)
O. y + 2 = 5(x + 1)
O. y-2-5(x - 1)
Step-by-step explanation:
That's the solution;
Final answer; y + 1 = 5 ( x + 2 )
4+ x/7 =2
A.-14
B.10
C.12
D.42
Answer:
The answer is A
Step-by-step explanation:
Answer:
its 14
Step-by-step explanation:
1.Subtract 4 from both sides of the equation
2.Simplify
3.Multiply all terms by the same value to eliminate fraction denominators
Simplify
4.Solution
A survey of athletes at a high school is conducted, and the following facts are discovered: 21% of the athletes are football players, 27% are basketball players, and 4% of the athletes play both football and basketball. An athlete is chosen at random from the high school: what is the probability that the athlete is either a football player or a basketball player? Probability =
Answer:
40% (probability that an athlete is a football player OR a basketball player, but not both) I think this is what its asking, but the wording isn't super clear.
44% (probability an athlete is a football player, basketball player, or both)
Step-by-step explanation:
probability of only football player (21%-4%) plus probability of only basketball player (27-4%)
=17%+23%
=40%
Find the measure of the angle. (final)
Answer:
39˚
Step-by-step explanation:
The whole thing is a right angle, and we know that because of the square thing at the top.
These two angles are complementary, so we can subtract 51 from 90.
90-51=39˚
If one angle of an equilateral triangle was 60 degrees, then what is the angle of the other two?
2|x+7|-10>14
Inequality
Answer: x>5 or x<−19
I need to buy enough white boards for 172 students and there are 25 in a pack when the pack arrives 12 whiteboards are damaged. How many whiteboards are undamaged?
Answer:
There are 163 whiteboards undamaged.
Step-by-step explanation:
So first we know that 12 are damaged and there are 172 students. So first we need to find out how many whiteboards did you buy without knowing there will be 12 damaged. The answer is 7 because there are 25 per pack. And 7 * 25 = 175. You can't buy less because you rather buy extra rather then not enough. Now knowing that, what is 175 - 12 because 12 was damaged.
175 - 12 = 163.
There are 163 whiteboards undamaged.
163 white boards are undamaged
Step-by-step explanation:
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
Given;
172 Students
25 in a pack
12 whiteboards are damaged
To Find;
How many whiteboards are undamaged?
Solution;
we need 172 whiteboard but one pack consist of 25 whiteboards
⇒ 172/25 = 6.88
≈ 7 pack
Total whiteboard we buy
⇒ 7 × 25 = 175
Out of which 12 whiteboard are damaged
↓ Undamaged whiteboard ↓
→ 175 - 12 = 163 ←
thus, 163 whiteboards are undamaged
⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻⁻
~[RevyBreeze]~
Equivalent Expression for 8b +8 - 4b
Answer:
4b +8
Step-by-step explanation:
8b +8 - 4b
Combine like terms
8b -4b +8
4b +8
Larry opened a bank account that earns simple interest with an initial deposit of $2,200. He made no other transactions throughout the year. At the end of the year, Larry had $2260.50 in his account. What was the simple interest rate
Answer:
r=(1/t) (A/P-1) = 2.75%
The simple interest rate is 2.75%
Which one of these are the right answers. Help ASAP.
Which of the following is a true statement?
3/4>9/12
3/5<4/7
6/7<5/8
5/12>3/8
Can any show me another one simple way to do this.
Answer:
The answer is the last one 5/12 > 3/8
Step-by-step explanation:
Convert the fractions to regular numbers so 5/12 just do 5 ÷ 12 and 3/8 do 3 ÷ 8 whatever side has the arrow opened to means that's should be the bigger number for example 2 > 1 is true because 2 is greater than 1 but 2 < 1 is false
Answer:
5/12>3/8
Step-by-step explanation:
you need a common denominator
you multiply 5/12 by 2 the top and the bottom to get 10/24
then you multiply 3/8 by 3 the top and the bottom to get 9/24
10/24>9/24
i-Ready
Write and Evaluate Algebraic Expressions -- Instruction – Level
1) The school is planning a field trip to the science center. Tickets are originally $28, but school
groups receive an $8 discount on each ticket that is purchased. The expression t(28 – 8)
represents the total cost for t tickets.
2) What does the quantity 28 - 8 represent?
Order of Operations
) the discounted price of each ticket
Evaluate inside parentheses.
Multiply or divide.
2
• Mrs. Price purchases 24 tickets for the students
in her class. Evaluate the expression for t = 24.
Add or subtract.
3
t(28 - 8) = 24(28 – 8)
= 24 (13
7
8
9
X
4
5
6
The cost of 24 tickets for the students is $480.
The given expression is t(28-8) represents the total cost for t tickets.
Mrs. Price purchases 24 tickets for the students in her class. Evaluate the expression for t=24.
Substitute t=24 in the given expression t(28-8), we get
24(28-8)
= 24×20
= $480
Therefore, the cost of 24 tickets for the students is $480.
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One number is 2 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 416, find the numbers