[tex] \huge \boxed{\mathfrak{Question} \downarrow}[/tex]
For what values of x is the equation x² − x = 20 true?
[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]
[tex] \sf \: x ^ { 2 } - x = 20[/tex]
Subtract 20 from both sides.
[tex] \sf \: x^{2}-x-20=0 [/tex]
To solve the equation, factor [tex]\sf\: x^{2}-x-20[/tex] using formula [tex]\sf\:x^{2}+\left(a+b\right)x+ab=\left(x+a\right)\left(x+b\right)[/tex]. To find a and b, set up a system to be solved.
[tex] \sf \: a+b=-1 \\ \sf \: ab=-20 [/tex]
As ab is negative, a and b have the opposite signs. As a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -20.
[tex] \sf1,-20 \\ \sf 2,-10 \\ \sf4,-5 [/tex]
Calculate the sum for each pair.
[tex] \sf1-20=-19 \\ \sf2-10=-8 \\ \sf 4-5=-1 [/tex]
The solution is the pair that gives sum -1.
[tex] \sf \: a=-5 \\ \sf \: b=4 [/tex]
Rewrite factored expression [tex]\sf \left(x+a\right)\left(x+b\right) [/tex] using the obtained values.
[tex] \sf\left(x-5\right)\left(x+4\right) [/tex]
To find equation's solutions, solve x-5=0 and x+4=0.
[tex] \bf \: x=5 \\ \bf x=-4[/tex]
⇨ The values of x are 5 & - 4.
If tom had 557 oranges and Billy had 676 more oranges than tom. How many oranges does Billy have.
Answer:
billy has 1233 oranges
Step-by-step explanation:
557+676=1233
you add 557 and 676 to figure out how much billy has
you can check your answer by subtracting 1233-557=676
Answer:
Billy has 1233 oranges.
Step-by-step explanation:
This is a simple, they have this many more than this person has, so an example is the B has 1 book, but Alex has a book collection of 10 books. They both have more than one book, but Alex has 10 books in total, with 9 more than B does.
So, for this question, Tom has 557, and Bill had 676 more than him, so that would mean you need to add 676 and 557 together to get 1233 oranges for just Billy. So that would be our answer.
4+2[10(2×7-11)-10]
Please help
Answer:
im pretty sure it equals 44. if you want to solve math problems in the future just use photòmath its a app
Segment addition postulate please help me
Answer:
which class
Step-by-step explanation:
.,........
Find the median of the data. 7, 5, 12, 8, 2, 9, 4
The median of the data is: 7
Sylvie is mixing concrete for her patio. For every 26.7 pounds of concrete mix, she needs to add 1 quart of water. Sylvie buys 80 kilograms of
concrete mix
1 kilogram 2.2 pounds
How many quarts of water, rounded to the nearest tenth, does Sylvie need to add to 80 kilograms of concrete mix?
Step-by-step explanation:
that back and forth between the different scales is the only task challenge. you need to focus to not mix things up.
so if I understand correctly, we should use the conversion rate of 1 kg = 2.2 pounds.
she should add 1 quart of water to every 26.7 pounds of concrete mix.
80 kg = 80×2.2 pounds = 176 pounds.
we need as many quarts of water as there are units of 26.7 pounds in 176 pounds.
176/26.7 = 6.5917603... quarts of water needed.
that would be rounded 6.6 quarts of water.
Amaya wants to jog 8 miles this week.She jogged 2 1/2 miles on Monday and 3 2/5 miles on wednesday. How many miles does Amaya still need to jog?
Answer:
2 1/10 miles.
Step-by-step explanation:
8 - (2 1/2 + 3 2/5)
= 8 - (5/2 + 17/5)
= 8 - (25/10 + 34/10)
= 8 - 59/10
= 80/10 - 59/10
= 21/10
= 2 1/10 miles.
Teacher: Who can tell me how to simplify 3 + 5 x 2 – 4?
Student -girl: I think you should do 3 + 5 first and the answer is 12.
Student -boy: I think you do 5 x 2 first and the answer is 9
Teacher: Why did the boy and girl get different answers?
Answer:
3+5×2-4
3+10-4
13-4
9
Step-by-step explanation:
But I solve like this and the answer is 9 I am student girl.
Answer:
The girl didn't follow PEMDAS
Step-by-step explanation:
PEMDAS is the order in which you solve mathematical equations.
Parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
If you add before multiplying you'll get a completely different answer.
The boy followed PEMDAS, while the girl didn't.
7. Find the representation of 4.18 as
an improper fraction and a mixed
number.
Step-by-step explanation:
Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are
2
numbers to the right of the decimal point, place the decimal number over
10
2
(
100
)
. Next, add the whole number to the left of the decimal.
4
18
100
Reduce the fractional part of the mixed number.
4
9
50
Convert
4
9
50
to an improper fraction.
Tap for more steps...
209
50
If the digits A, B and C are added, the sum is the two-digit number AB as shown. What is the value of C?
A
B
+ C
______
AB
Answer:
C=9
Step-by-step explanation:
If A, B, and C are all single digits the mimimum sum for AB would be 10 as it is a two-digit number (or 11 if you do not consider 0 a digit)
AB-(A+B)=C
10-(1+0)=9 or 11-(1+1)=9
therefore C=9
Solve [y] = -18.
Help pls
Answer:
[y]=-18 so y belongs to (-18,-17)
Step-by-step explanation:
Answer: hm shouldn’t that just be -18?
Step-by-step explanation:
What is 6a +9 ≤ -15?
Answer:
a = -5
Step-by-step explanation:
IF A = -5
6 ( - 5 ) + 9
- 30 + 9
-21
-21 is less than -15 so it works
length and width of a field are in the ratio 5.3 If the wilth of 아 the field is 42m, then its length is
Answer:
The length of the feild is:
(42 / 3) x 5 = 70m
So the length of the feild is 70m
Hope it helps, Brainliest please <3
f(x) = x-4.
find f(b)
Answer:
x0.4
Step-by-step explanation:
50 POINTSSSSSS
If C(n) = 20 - [tex]\frac{5}{8}[/tex] m, find C(0) and C(16). What is the zero of C?
PLS HELP ME SLOPE INTERCEPT FORMMM
through: (1, -1), parallel to y=5/3x
Step-by-step explanation:
the slope = 5/3
through (1, -1)
the equation :
y -(-1) = 5/3 (x -1)
y+1 = 5/3 x -5/3
y = 5/3 x -5/3 -1
y = 5/3 x - 8/3 or y = 5/3 x - 2⅔
(2sinx+3cosx)²+(3sinx-2cosx)²=13 prove plz
Answer:
LHS:-(4sin²x +9cos²x + 12sinxcosx) +(9sin²x+ 4 cos²x -12sinxcosx)
13 (sin²x + cos²x)
13*1 =
13RHSHP
Answer:
see explanation
Step-by-step explanation:
Using the identity
sin²x + cos²x = 1
Consider left side
(2sinx + 3cosx)² + (3sinx - 2cosx)² ← expand parenthesis using FOIL
= 4sin²x + 12sinxcosx + 9cos²x + 9sin²x - 12sinxcosx + 4cos²x
Collect like terms
= 13sin²x + 13cos²x ← factor out 13 from each term
= 13(sin²x + cos²x)
= 13 × 1
= 13
= right side , thus proven
Write the following numbers in words.
11)
644.112
12)
11.560
13)
200,006 4
14)
1.067
Answer:
Step-by-step explanation:
11)six hundred forty four and one hundred and twelve thousandths
you have piano lessons every 7 day and tuba lessons every 3 days today you have both lessons.
A. In how many days wil you have both lesson on the same day agian?
B. Not counting today or the day when you have the same lesson again, How many piano lesson will you have in between? Have many tuba lesson will you have in between?
Answer:
A.21 days
B.2, 6
Step-by-step explanation:
(a) In 21 days we will have both lessons on the same day again.
(b) Between each occurrence of having both lessons on the same day again, you will have 2 piano lessons and 6 tuba lessons.
a.
To find out when we will have both lessons on the same day again, we need to find the least common multiple (LCM) of 7 and 3.
The LCM of 7 and 3 is 21. This means that every 21 days, our piano and tuba lessons will align again.
b. Between each occurrence of having both lessons on the same day, you have 21 days. During these 21 days, you will have:
21 / 7 - 1 = 2 piano lessons.
21 / 3 - 1 = 6 tuba lessons.
So, between each occurrence of having both lessons on the same day again, we will have 2 piano lessons and 6 tuba lessons.
Learn more about the least common multiple here:
https://brainly.com/question/1494485
#SPJ3
Monique has 12$ in her account
Find the radius of the two other circles
Answer:
We draw the circles on a coordinate system. We know that a circle is has points that are equidistant from its centerpoint. So the point where these circles are tangent is the midpoint between the centerpoints.
We can use the midpoint formula.
M = ((x1 + x2) / 2 , (y1 + y2) / 2)
M = ((-2 + 6) / 2 , (3 + 9) / 2)
M = (2, 6)
These circles will have the same radii.
If we take the distance between the midpoint and (-2,3), we will have the radius of the circle with this centerpoint.
If we take the distance between the midpoint and (6,9), we will have the radius of the circle with this centerpoint.
Step-by-step explanation:
Sarah has saved $150. She wants to double the amount she saves each month. As an incentive, Sarah’s grandma says if she saves that amount, she will give her an additional $50 each month. What are the recursive formula and first term for Sarah’s saving’s?
Answer:
A₁ = $150.
Step-by-step explanation:
We know that:
Sarah has saved $150 at the moment.
She wants to double the amount that she saves each month, so the next month she needs to save 2*$150 = $300
And if she saves the $300, then her grandma will give her another $50.
Then, if the previous month Sarah saved A, then the next month she will get the double of A plus $50, which is:
2*A + $50
Then the recursive relation is just:
Where Aₙ is the amount that she saves in the n-th month, and the first term of the sequence is the initial amount that she saved, so we have:
A₁ = $150.
YALL I NEED HELP PLZ
Answer: 6.9
Step-by-step explanation: search sqrt 48
i need help pleaseee!!
Answer:
[tex]320 \sqrt{2} [/tex]
Una cisterna con forma de prisma rectangular mide 1.5 m de ancho, 2 m de largo y 1 m de alto. Si está vacía y se vierten en su interior 150 L de agua por minuto, ¿cuánto tiempo tardará en llenarse?
Step-by-step explanation:
V = 1.5 × 2 × 1 = 3 m³ = 3000 L
tiempo = 3000 ÷ 150 = 20 minutos
Evaluate each expression for t = 0, x = 1.5, y = 6, and z = 23
1. y + 5 = ??
2. z - 2x = ??
3. 2z - 2y = ??
4. 2.6y - 2x =??
5. 4(y - x) = ??
6. 4(2 + z) + 5 = ??
Answer:
1. 11
2. 20
3. 34
4. 12.6
5. 18
6. 105
Step-by-step explanation:
We are told that ---> t = 0, x = 1.5, y = 6, and z = 23
1. y + 5
= 6 + 5
= 11
2. z - 2x
= 23 - 2(1.5)
= 23 - 3
= 20
3. 2z - 2y
= 2(23) - 2(6)
= 46 - 12
= 34
4. 2.6y - 2x
= 2.6(6) - 2(1.5)
= 15.6 - 3
= 12.6
5. 4(y - x)
= 4(6 - 1.5)
= 24 - 6
= 18
6. 4(2 + z) + 5
= 4(2 + 23) + 5
= 8 + 92 + 5
= 105
2y+-1y+-1y+3=-13 solve for y
Answer:
There are no values of y
that make the equation true.
No solution
Help! I don’t get this ine
[tex]3|2x+4|-1=11 \ \ /+1\\\\3|2x+4|=12 \ \ /:3\\\\|2x+4|=4\\\\2x+4=4 \ \ \text{or} \ \ 2x+4=-4\\\\2x=0 \ \ \text{or} \ \ 2x=-8\\\\\boxed{x=0} \ \ \text{or} \ \ \boxed{x=-4}[/tex]
Which of the following transforms the graph of
y = x2 to the graph of y=x2-77
a translation 7 units to the right
a translation 7 units to the left
translation 7 units down
a translation 7 units up
Answer:
a translation 7 units down
Step-by-step explanation:
the value of -7 will be added to the value of y in the original one ( y = x2) and it will decrease it by 7 units
Answer:
c
Step-by-step explanation:
assignment said so
please help, this is geometry
Answer:
Step-by-step explanation:
The formula is the same almost as the previous question you posted.
You want to find the major arc. That's almost the whole circle. If it was the whole circle, the formula would be 2 * pi * r
But we only want a part of it. Just how big is the angle we use in the formula?
A circle has 360 degrees to go around it. We've cut out a slice of it that is 30 degrees.
The remaining part is 360 - 30 = 330
Arc length = angle / 360 * 2 * pi * r
r = 3 m
Arc length = 330 / 360 * 2 * pi * 3
Arc length = 0.9167 * 6 * 3.14
Arc length = 17.27
please help due today
Answer:
aabavcaca
Step-by-step explanation:
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