Answer:
(x + [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] )(x + [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] )
Step-by-step explanation:
solve the polynomial for x then express in product of factor form
Solve
x² + x - 10 = 0 ( add 10 to both sides )
x² + x = 10
Using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2([tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] = 10 + [tex]\frac{1}{4}[/tex]
(x + [tex]\frac{1}{2}[/tex] )² = [tex]\frac{41}{4}[/tex] ( take the square root of both sides )
x + [tex]\frac{1}{2}[/tex] = ± [tex]\sqrt{\frac{41}{4} }[/tex] = ± [tex]\frac{\sqrt{41} }{2}[/tex] ( subtract [tex]\frac{1}{2}[/tex] from both sides )
x = - [tex]\frac{1}{2}[/tex] ± [tex]\frac{\sqrt{41} }{2}[/tex]
Thus corresponding factors are
(x - (- [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] ) ) and (x - (- [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] ), that is
(x + [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] ) and ( x + [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] )
Thus
x² + x - 10 = ( x + [tex]\frac{1}{2}[/tex] + [tex]\frac{\sqrt{41} }{2}[/tex] )(x + [tex]\frac{1}{2}[/tex] - [tex]\frac{\sqrt{41} }{2}[/tex] ) ← in factored form
Solve for x:
9x - 3 - 8x = 7 - x
x= -7
B. x=-2
c. x = 4
D. x = 5
Answer:
x = 5
Step-by-step explanation:
[tex]9x - 3 - 8x = 7 - x\\x - 3 = 7 - x\\[/tex]
Move x's to one side, and numbers to the other.
Make it the opposite sign when you move it over. Since I'm subtracting 3, I'm going to add it to the other side, and add x. And then divide by 2 to solve for x
[tex]x + x = 7 + 3\\\\\frac{2x}{2} = \frac{10}{2}\\\\x = 5\\\[/tex]
Sherry brings two containers of cookies to a party. Each container contains 6 cookies. Sally shows up with a dozen cookies. Sandy arrives with 2 cookies and 10 donuts. How many cookies will Harry need to bring if the total cookie count is 4 dozen
Answer:
22 cookies
Step-by-step explanation:
A dozen items means 12 number of items.
Number of cookies brought by Sherry = No. of containers multiplied by number of cookies in one container
= 2 [tex]\times[/tex] 6 = 12
Number of cookies brought by Sally = A dozen cookies = 12
Number of cookies brought by Sandy = 2
Number of cookies brought by Sherry, Sally and Sandy together = 12 + 12+2 = 26
Total number of cookies to be brought = 4 dozen = 48 cookies
Number of cookies to be brought by Harry = Total number of cookies to be brought - Number of cookies brought by Sherry, Sally and Sandy together
48 - 26 = 22 cookies
Estimate the product of 41.03 x 0.513.
Answer
Roughly, it would be 20.5
The exact answer is 21.05
Step-by-step explanation:
To roughly get the estimate you round it to the nearest 1st decimal place in this case. So it'd be 41.0 x 0.5
Elias completely covered a square canvas using 77.8 in.² of fabric without any overlap. Which measurement is closest to the side length of this canvas in inches? A. 8 in. B.9 in. C. 19 in. D. 39 in.
Answer:
B. 9 in
Step-by-step explanation:
The area covered by the fabric ([tex]A[/tex]) is represented by the following formula:
[tex]A = l^{2}[/tex]
Where [tex]l[/tex] is the side length of the canvas, measured in inches, and which is now cleared:
[tex]l = \sqrt{A}[/tex]
If [tex]A = 77.8\,in^{2}[/tex], then:
[tex]l = \sqrt{77.8\,in^{2}}[/tex]
[tex]l \approx 8.82\,in[/tex]
Which corresponds to option B.
How many solutions exist for the given equation?
12x + 1 = 3(4x + 1) - 2
zero
one
two
infinitely many
Answer:
infinitely many
Step-by-step explanation:
12x + 1 = 3(4x + 1) - 2
Distribute
12x + 1 = 12x + 3 - 2
Combine like terms
12x+1 = 12x +1
Subtract 12x from each side
1 =1
Since this is always true, we have infinite solutions
Answer:
[tex]\Huge \boxed{\mathrm{infinite \ solutions}}[/tex]
Step-by-step explanation:
[tex]\sf 12x + 1 = 3(4x + 1) - 2[/tex]
Using distributive property.
[tex]\sf 12x + 1 = 12x+3 - 2[/tex]
[tex]\sf 12x + 1 = 12x+1[/tex]
Subtracting 1 from both sides.
[tex]\sf 12x=12x[/tex]
Dividing both sides by 12.
[tex]\sf x=x[/tex]
All real numbers are solutions.
There are infinite solutions.
A certain shade of lavender is created by adding 5 cups of purple paint to 8 cups of white paint. a. How many cups of purple paint should be added to 1 cup of white paint? Cups of white paint Cups of purple paint 1 8 b. What is the constant of proportionality?
Answer:
a. [tex]\frac{5}8[/tex] cups of purple paints required.
b. [tex]\frac{5}8[/tex]
Step-by-step explanation:
Given that
Number of purple paints required with 8 cups of white paint = 5
To find:
a. Number of cups of purple paint needed to be added to 1 cup of white paint ?
b. Constant of proportionality.
Solution:
Answer a. We can use unitary method here to find the number of cups of purple paint that are to be added to 1 cup of white paint.
Let us use the given statement:
8 cups of white paint require = 5 cups of purple paint
Let us divide both sides by 8:
1 cup of white paint require = [tex]\frac{5}8[/tex] cups of purple paint
Answer b.
Constant of proportionality is nothing but the ratio of two numbers which are present in a proportion.
Here, the ratio between number of cups of purple paint and number of cups of white paint is:
5:8 or [tex]\frac{5}8[/tex].
so, the answer is: [tex]\frac{5}8[/tex]
Can any kind soul draw answer this question
PLISSSSS!
Draw a Venn Diagram
Answer:
Please see attached picture for full solution.
HELP PLZ ITS FOR SCHOOL
Answer:
a)5:2
b)14
c)17
Step-by-step explanation:
The ratio for babies to nursery workers is 5:2
To find the answer to b, we find how much you have to multiply 2 by to get 35, which is 7 and multiply that by the number of workers, 2, so you need 14 workers
To find the answer to c multiply 2 bye 3.5 to get 7 and multiply 5 by 3.5 to get 17.5 now rounf down so the answer to c is 17
Answer:
a)5:2 b)14 c)17
Step-by-step explanation:
If n-8=-3, what is 3n?
Greetings from Brasil...
Let's isolate N. For that we will pass the - 8 to the second member:
n - 8 = - 3
n = - 3 + 8
n = 5
3n = 15Victoria and her friends are going on a road trip that is 632.64 miles long. If they have 32.3 miles until their destination, how far have they already traveled? Answer in decimal form.
The Venn diagram represents different categories of real numbers. Which category on the Venn diagram is represented by 4π? A) Irrational Numbers B) Integers C) Natural Numbers D) Rational Numbers
Answer:
Irrational Number
Step-by-step explanation:
The Venn diagram is not attached; However, the question can still be answered
Given
[tex]Number = 4\pi[/tex]
Required
What category of number is the given number
[tex]Number = 4\pi[/tex]
Substitute [tex]\frac{22}{7}[/tex] for [tex]\pi[/tex]
[tex]Number = 4 * \frac{22}{7}[/tex]
[tex]Number = \frac{4 *22}{7}[/tex]
[tex]Number = \frac{88}{7}[/tex]
[tex]Number = 12.5714285714......[/tex]
Notice that there's .... at the end of the number;
This implies that, the decimal number still extends
Numbers like 12.5714285714...... are categorized as irrational numbers because it can't be changed back to a fraction
Answer:
A. irrational number
Step-by-step explanation:
I took the test
If a and b are the zeroes of the polynomial x2 + 5x + 8, then the value of a2 + b2
is..............(Pls help)
Answer:
9
Step-by-step explanation:
If α and β are the zeros of ax² + bx + c = 0 , then
α + β = [tex]\frac{-b}{a}[/tex] ( sum of zeros ) and
αβ = [tex]\frac{c}{a}[/tex] ( product of zeros )
Given
x² + 5x + 8 = 0
with a = 1, b = 5, c = 8 , with zeros a and b, then
a + b = [tex]\frac{-5}{1}[/tex] = - 5
ab = [tex]\frac{8}{1}[/tex] = 8
Thus
(a + b)² = a² + 2ab + b² , that is
(- 5)² = a² + 2(8) + b²
25 = a² + 16 + b² ( subtract 16 from both sides )
9 = a² + b²
The area of a rectangular football field is 7200m² while its perimeter is 360m. Calculate the;
dimension of the field
(60 m ; 120 m)
Step-by-step explanation:A = l×w = 7200m²
P = 2w + 2l = 360m
lw = 7200 => l = 7200/w
2(w + l) = 360 => w + l = 180
w + 7200/w = 180
w² + 7200 - 180w = 0
w² - 60w - 120w + 7200 = 0
w(w - 60) - 120(w - 60) = 0
(w - 60)(w - 120) = 0
w₁ = 60m => l₁ = 7200/60 = 120 m
w₂ = 120m => l₂= 60 m
Solve for y.
6 = -2/9v
Answer:
: 1: Exact form : v = - 1/27
: 2 : Decimal form : v = -0.037037037037037037037037...
Step-by-step explanation: Multiply the equation to remove your variable (v) from the denominator.
I hope this helps you out.
Kojo wants to be an author. To improve his writing skills, every day after school he writes 3 pages of a story he is working on. Kojo has been writing his story for ddd days. He has a total of 81 pages completed.
Answer:
81= 3 times x
its right on khan.
Step-by-step explanation:
Round 24.772 to each value listed below
Nearest tens:
Nearest tenths:
Nearest whole:
Nearest hundredths
Answer:
Nearest tens: 20
Nearest tenths: 24.8
Nearest whole: 25
Nearest hundredths: 24.77
Answer:
Nearest tens: 20 ⇔ the ones digit is 4, no rounding up
Nearest tenths: 24.8 ⇔ the hundredths is 7, need to round up
Nearest whole: 25 ⇔ the tenths digits is 7, need to round up
Nearest hundredths: 24.77 ⇔ the thousandths digit is 2, no rounding up
Hope this helps!! :)
Please let me know if you have any question
(-14+3/2b)-(1+8/2b)
Answer:
[tex]\Large \boxed{\frac{-5}{2}b -15}[/tex]
Step-by-step explanation:
[tex]\displaystyle (-14+\frac{3}{2}b )-(1+\frac{8}{2} b)[/tex]
Distributing the negative sign to the terms in the bracket.
[tex]\displaystyle -14+\frac{3}{2}b -1-\frac{8}{2} b[/tex]
Grouping the like terms in the expression.
[tex]\displaystyle (-\frac{8}{2} b +\frac{3}{2}b) +(-1-14)[/tex]
Combining the like terms in the expression.
[tex]\displaystyle (\frac{-8+3}{2}b) +(-15)[/tex]
[tex]\displaystyle (\frac{-5}{2}b) +(-15)[/tex]
I need help with this is my last one
Answer:
1. Quadrant 2
2. Quadrant 1
3. Quadrant 2
4. Quadrant 4
5. Quadrant 4
6. Quadrant 2
7. Quadrant 2
8. Quadrant 3
Step-by-step explanation:
For this problem, we just need to follow the pattern of positive and negatives associated with each quadrant.
The first quadrant (+, +)
The second quadrant (-, +)
The third quadrant (-, -)
The fourth quadrant (+, -)
Using these patterns we can state what order pair correlates to which quadrant.
(-2.5, 2.1) --> Q2
(1/2, 3/4) --> Q1
(-10, 13) --> Q2
(2.5, -5.5) --> Q4
(9, -10) --> Q4
(-12, 3.4) --> Q2
(-5/8, 5) --> Q2
(-6.4, -6.3) --> Q3
Cheers.
Find the product of 10n5 and 6n2
[tex]10 \times 10 \times 10 \times 10 \times 10 = 2000[/tex]
[tex]6 \times 6 = 36[/tex]
= 2036n
K - 8 = -7 What is K?
Answer:
1
Step-by-step explanation:
To find the answer of a negative and a positive, you subtract and then keep the symbol of the bigger number. So in the equation 1-8 you subtract 1 from 8, then keep the symbol of the 8 (which is a negative) since it is the bigger number. 1 minus 8 is 7, and the symbol is negative, so the answer is -7. This makes K=1.
if bob simsim went to the cinema and brought 200g of popcorn and he ate 100g of popcorn how many grams of popcorn does he have left?
Answer:
He has 100 g left.
Step-by-step explanation:
We start with 200 g, then bob eats 100 g, 200-100=100 grams!
What is -5 5/8+ 3 1/2
f(x) = 5x + 12. Find f−1(x)
Answer:
(x-12)/5
Step-by-step explanation:
v=pi r^2 h solve for pi
please help asap
will mark brainliest
Answer:
[tex]\pi=\frac{v}{hr^2}[/tex]
Step-by-step explanation:
So we have:
[tex]v=\pi r^2h[/tex]
And we want to solve for π.
First, divide both sides by h:
[tex]\frac{v}{h}=\pi r^2[/tex]
Now, divide both sides again by r²:
[tex]\pi=\frac{v}{hr^2}[/tex]
And this is our answer :)
Answer:
[tex]\frac{v}{r^{2} h} = \pi[/tex]
Step-by-step explanation:
Simply divide both sides by [tex]r^{2}h[/tex] to get pi by itself.
[tex]6\sqrt{7-11}\sqrt{7+2}\sqrt{7}[/tex]
Answer:
[tex]=36\sqrt{7}i[/tex]
Step-by-step explanation:
sqrt of 7-11=2i
simplify to [tex]6\cdot \:2\sqrt{9}\sqrt{7}i[/tex]
then sqrt of 9=3
then we simplify again to [tex]=36\sqrt{7}i[/tex]
hope this helps and if you don't mind please consider giving me brainliest
1. 4x– 15 = 17 - 4x+10x
Help?
Answer:
x=-16
Step-by-step explanation:
4x– 15 = 17 - 4x+10x
4x+4x-10x = 17+15
-2x=32
-x=16
x=-16
d = b^2 -4ac solve for a 2/3 (x-18y) = 6y solve for x
Answer:
a = [tex]\frac{b^2-d}{4c}[/tex]
x = 27y
Step-by-step explanation:
Order of Operations: BPEMDAS
Question 1
Step 1: Write out discriminant
d = b² - 4ac
Step 2: Subtract b² on both sides
d - b² = -4ac
Step 3: Divide both sides by -1
b² - d = 4ac
Step 4: Divide both sides by 4c
a = [tex]\frac{b^2-d}{4c}[/tex]
Question 2
Step 1: Write out equation
2/3(x - 18y) = 6y
Step 2: Distribute parenthesis
2/3x - 12y = 6y
Step 3: Isolate x by adding 12y on both sides
2/3x = 18y
Step 4: Divide both sides by 2/3
x = 27y
how to do this question plz answer me step by step plzz
Answer:
Adult's ticket is 7, child's ticket is 2
Step-by-step explanation:
Let adult's ticket be "x" and child's ticket be "y"
So, for family 1, the equation would be: 2x+3y=20
And, for family 2, the equation would be: 1x+4y=15
Use the substitution method in the second equation to know what x in terms of y is:
x + 4y = 15 (substact 4y from both sides)
x= 15 - 4y
Plugin y into the first equation:
2(15-4y)+3y=20 (distribute)
30-8y+3y=20 (simplify)
30-5y = 20 (get y by itself)
-5y = -10 (divide by -5)
y = 2
Now that you know the value of y (child's ticket), figure out x by plugging in 2 into any of the equations (I chose the second):
1x+4(2) = 15 (simplify)
x + 8 = 15 (subtract 8)
x = 7
Answer:
price of adult ticket=7 £
price of childrens' ticket =2 £
Step-by-step explanation:
let x be price for adult and y price for for children
family 1 : 2x+3y=20
family 2: x+4y=15
solve by eliminating : multiply equation 2 by (2) to eliminate x
2x+3y=20
2x+8y=30
subtract the two equations:
2x+3y-2x-8y=20-30
-5y=-10
y=-10/-5
y=2( the price for children)
x+4y=15
x+4(2)=15
x=15-8
x=7 ( the price for adults)
check : 2x+3y=20
2(7)+3(2)=14+6=20
what value of x makes this inequality true?
x+9 < 4x
Answer:
X>3
Step-by-step explanation:
X+9<4X
x-x+9<4x-x
9<3x
3<x
5+2x=2x+6 please answer
If we firstly consider only the terms in x.
subtract 2x from both sides of the equation
⇒5+2x
−2x=2x−2x
+6
Observe that the x terms are eliminated and we are left with
5+0=0+6 that is 5=6 which is invalid
There is no solution to this equation.
Answer:
no solution
Step-by-step explanation:
Given
5 + 2x = 2x + 6 ( subtract 5 from both sides )
2x = 2x + 1 ( subtract 2x from both sides )
0 = 1 ← not possible
Thus indicates the equation has no solution