Answers
Answer:
x = 5
Step-by-step explanation:
Step-by-step explanation:
Given,
[tex] \sqrt{x + 11} - x = - 1[/tex]
To Find:
Value of xSolution:
Square both sides, then solve.
[tex] \rm \implies \: \: \sqrt{(x + 11} ) {}^{2} = ( - 1 + x) {}^{2} [/tex]
[tex] \implies \rm \: x + 11 = - (1 + x) {}^{2} [/tex]
[tex] \rm \implies \: \: x + 11 = 1 - 2x + x {}^{2} [/tex]
[tex] \rm \implies \: 1−2x+x {}^{2}=x+11[/tex]
[tex] \rm \implies1+x {}^{2} −3x=11[/tex]
[tex] \rm \implies1+x {}^{2} −3x−11=0[/tex]
[tex] \rm \implies {x}^{2} - 3x - 10 = 0[/tex]
Factor the LHS
[tex] \implies \rm \: (x - 5)(x + 2) = 0[/tex]
Bring terms equal to 0, that is
[tex] \implies \rm(x - 5) = 0[/tex]
Solve for x[tex] \implies \rm \: x = 5+ 0 = \boxed 5[/tex]
AND set x+2 equal to 0,
[tex] \rm\implies \: x + 2 = 0[/tex]
Solve for x[tex] \rm \implies \: x = - 2[/tex]
So the possible two values are 5 & -2.
But, after plugging the values for verifying each,the most accurate is 5.
So, the value of x is 5.
Related Questions
Which statement is true about points located in quadrant Ill in the coordinate
plane?
O A. The x-coordinate is negative, and the y-coordinate is positive.
B. The x-coordinate is positive, and the y-coordinate is negative.
C. The x-coordinate is negative, and the y-coordinate is negative,
D. The x-coordinate is positive, and the y-coordinate is positive.
Please answer TODAY DEC 15
I WILL GIVE 100 POINTS TO THE FIRST PERSON THAT ANSWERS
Answers
Answer: C
Step-by-step explanation
I Think Its C
More than half of the students were excited about the project. In fact, were excited. If 10 students were not
excited about the project. how many students were excited?
Answers
Answer:1/2 divided by 10
Step-by-step explanation:
"select all the numbers that are solutions to the equation x^3=27"
Answers
3^3 = 27
the cubed root of 27 is 3
The x = ∛27 and x = 3 are solution to the equation x³=27 option (B) and option (C) are correct.
What is a cube root?It is defined as the sum of two or more numbers. The original number is obtained by multiplying the cube root of a number three times; for example, the cube root of x is z.
We have equation:
x³ = 27
Taking cube root both side
∛x³ = ∛27
x = ∛27
x = 3
Thus, the x = ∛27 and x = 3 are solution to the equation x³=27 option (B) and option (C) are correct.
Learn more about the cube root here:
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What is the vertex of the following: y=1/4x^2+2x+6
Answers
Answer:
Yea i definitly just lost brain cells
Step-by-step explanation:
A cylindrical soup can has a radius of 8.4 cm and a height of 13.2 cm. What is the volume of the soup can to the nearest tenth of a cubic centimeter?
A= 110.9 cm3
B= 348.3 cm3
C= 673.8 cm3
D= 2926.1 cm3
Answers
Answer:
D. 2926.1 cm3
Step-by-step explanation:
To calculate volume of a cylinder, you need to use the equation V = pi r² h, where r is radius and h is height.
you have the right numbers to plug in, so pi times 8.4² times 13.2, which gives you 2926.05 which you round up to 2926.1 cm³
Camilla has already baked five pies and she can make one pie with additional cup of sugar she buys how many additional cups of sugar does Camila need in order to bake a total of 49 pies
Answers
I used to know a Camilla, she cheated on me for my brother...pain
Rain minus the \
How many 1/3 yard lengths are in 1 yard
Answers
Answer:
3
Step-by-step explanation:
1/3 yard lengths times 3 equals 3 (or 1 yard).
There are 3 numbers of 1/3 yard lengths are in 1 yard.
What is the arithmetic operator?A summation, which is the result of adding two or more numbers or quantities, is also known as a sum.
A mathematical operation known as subtraction involves two values that will be subtracted to produce a new value.
Multiplication is the general procedure in mathematics in which we multiply two or more numbers to each other to find a new multiplied number.
Division is divide of any two numbers so it will give a new divided value for example 4/2 will gives us 2.
1 yard = 1/3 yard + 1/3 yard + 1/3 yard
The lowest common multiple of the right hand will be 3
So,
1 yard = (1 + 1 + 1)/3 yard
1 yard = 3/3 yards
1 yard = 1 yard
Hence in 1 yard, there is a total of 3 numbers of 1/3 yards.
To learn more about the arithmetic operator
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The right hexagonal pyramid has a hexagon base with equal-length sides. The lateral faces of the pyramid are all triangles (that are exact copies of one another) with heights of 18 ft. Find the surface area of the pyramid.
Answers
Answer:
208
Step-by-step explanation:
The answer is 208 first I multiplied 18x8=144 than 8ft*5=40
40+8=48 than I did 40 +24=64 after that I added 144+64=208 so surface area of the pyramid will be 208ft2
Answer:
352
Step-by-step explanation:
The baker pays $0.60 per pound for sugar and $1.35 per pound for butter. Which expression shows how much the baker will spend
if he buys 4 pounds of butter and 10 pounds of sugar?
Answers
Explanation: You need to multiply the amount it costs by the amount needed and you get the answers.
$0.60 x 10 = $6.00
$1.35 x 4 = $5.40
The graph shows the number of centimeters a particular plant grows over time. Given the points (0,0) and (5,8), how many centimeters does the plant grow per week?
can someone help me with this problem please?
Answers
Answer:
8 cm
m = -------------- This is the desired rate of change, the amount the plant
5 wk grows per 1 week.
Step-by-step explanation:
Moving from point (0, 0) to point (5, 8), we see that the x-coordinate (the 'run') increases by 5 wk and the y-coordinate (the 'rise') increases by 8 cm. Thus we have the rate of change
8 cm
m = -------------- This is the desired rate of change, the amount the plant
5 wk grows per 1 week.
Find the area of the shaded regions below. Give your answer as a completely simplified exact value in terms of pi (no approximations).
Answers
Answer:
area = 4π-8 cm²
Solve the inequality.
p + 14 ≥ 2
Answers
Answer:
p [tex]\geq[/tex] -12
Step-by-step explanation:
Subtract 14
p [tex]\geq[/tex] -12
The solution to the inequality from the information given is p ≥ -12
What is inequality?Inequality shows the relationship between two expressions and this relationship is identified by using the inequality signs (<, >, ≤, ≥).
The solution to the inequality p + 14 ≥ 2 can be determined by having the variables on one side and the numbers on the other side. To do that:
Let us subtract 14 from both sides of the equation we have:
p + 14 - 14 ≥ 2 - 14
p ≥ -12
Learn more about inequality here:
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A worker at a snack stand opened a new box of cups. On the first day, the worker used 30 cups from the box. On the second day, the worker used 15% of the remaining cups in the box. A total of 90 cups were used on the second day. What was the original number of cups in the box before any cups were used?
Answers
Answer:
630 cups
Step-by-step explanation:
Percentages
This problem is most easily solved backward, i.e., from the final data up to the beginning.
There was a new box of cups and the worker at a snack stand opened it. He first used 30 cups from the box and the second day he uses 15% of the remaining cups in the box, and we are told that represents 90 cups.
If 15% (0.15) equals 90 cups, then the number of cups before the second day was 90/0.15 = 600 cups.
On the first day, we used 30 cups, thus the original number of cups in the box was 600+30=630 cups
Can somebody help me ??
Answers
Answer:
y = 98
z = 21
Step-by-step explanation:
in the picture, y and 82 are supplementary angles because the are same side interior angles. This means that we can create this equation:
y = 180 - 82
we get y = 98
<Y and <4z + 14 are vertical angles, so we can also say that they are equal to each other. So we can create this equation:
4z + 14 = 98
subtract 14 from both sides:
4z = 84
divide both side by 4 to find z:
z = 21
Answer:
y = 82
z = 21
Step-by-step explanation:
You can get y almost immediately.
82 and y are supplementary. Interior angles on the same side of the transversal = 180
82 + y = 180 Subtract 82 from both sides
y = 180 - 82
y = 98
y and 4z + 14 are equal.
y = 4z + 14 Substitute for y
98 = 4z + 14 Subtract 14 from both sides.
98-14 = 4z
84 = 4z Divide by 4
84/4 = 4z/4
21 = z
HELP WHATS THE ANSWER
Answers
Answer:
The answer is 0, hope this helps
Round 4,368 to the nearest ten
Answers
Answer:
4,370
Step-by-step explanation:
If you are looking for the nearest ten in 4,368, you round up the number 8. Eight is greater than five and not less than four, therefore, the answer is 4,370. Good Luck on whatever assignment you're doing!
4370
Explanation:
5 or more you round to the next number. In this case 8 is above 5 so you round to the next number of 68 which is 70
Please help with math
Answers
Answer:
B) 10^0
Step-by-step explanation:
Well when dividing an exponent, you subtract the exponents but keep the base, this is the rule of exponents.
So in this case you got 10^-3/10^-3
SO you subtract the wo exponents and don’t forget to keep the sign
-3-(-3)
or -3+3
so 0
so final answer is 10^0
Answer:
The correct answer is B. 10(0).
Step-by-step explanation:
10^3 =
10 x 10 x 10 =
1,000
-------------------------
1,000 ÷ 1,000 = 1
10(0) = 1
Therefore, the correct answer is B. 10(0).
Hope this helps! :D
simplify x^2 + ax - 2a^2÷
3a^2 - 2ax - x^2?
Answers
Answer:
[tex] - \frac{x + 2a}{3a + x} [/tex]
Step-by-step explanation:
[tex] \frac{ {x + ax - 2 {a}}^{2} }{3a {}^{2} - 2ax - {x}^{2} } [/tex]
i) write ax as a difference
[tex] \frac{ {x}^{2} + 2ax - ax - 2 {a}^{2} }{3 {a}^{2} - 2ax - x {}^{2} } [/tex]
ii) write -2ax as a difference
[tex] \frac{ {x}^{2} + 2ax - ax - 2a {}^{2} }{3a {}^{2} + ax - 3ax - x {}^{2} } [/tex]
iii) factor out x from the expression
[tex] \frac{x(x + 2a) - ax - 2 {a}^{2} }{3 {a}^{2} + ax - 3ax - {x}^{2} } [/tex]
iv) factor out -a from the expression
[tex] \frac{x(x + 2a) - a(x + 2a)}{3 {a}^{2} + ax - 3ax - {x}^{2} } [/tex]
v) factor out a from the expression
[tex] \frac{x(x + 2a) - a(x + 2a)}{a(3a + x) - 3ax - {x}^{2} } [/tex]
vi) factor out -x from the expression
[tex] \frac{x(x + 2a) - a(x + 2a)}{a(3a + x) - x(3a + x)} [/tex]
vii) factor out x+2a from the expression
[tex] \frac{(x + 2a)(x - a)}{a(3a + x) - x(3a + x)} [/tex]
viii) factor out 3a+x from the expression
[tex] \frac{(x + 2a)(x - a)}{(3a + x)(a - x)} [/tex]
ix) factor out the negative sign from the expression and rearrange the term
[tex] \frac{(x + 2a)( - ( - a - x))}{(3a + x)(a - x)} [/tex]
x) reduce the fraction a-x
[tex] \frac{(x + 2a)( - 1)}{(3a + x)} [/tex]
[tex] - \frac{x + 2a}{3a + x} [/tex]
Find 56(−4⋅27). Write your answer in simplest form.
Answers
Answer:
[tex]-6048[/tex]
Step-by-step explanation:
[tex]---------------------------------[/tex]
[tex]56\left(-4\cdot27\right)[/tex] = [tex]-6048[/tex] [tex]because[/tex]
[tex]---------------------------------[/tex]
[tex]56\left(-4\cdot27\right)[/tex] = [tex]?[/tex]
[tex]\left(-4\cdot27\right)[/tex] = [tex]-108[/tex]
[tex]56\left(-108\right)[/tex] = [tex]?[/tex]
[tex]56\left(-108\right)[/tex] = [tex]-6048[/tex]
[tex]---------------------------------[/tex]
Hope this helps! <3
[tex]---------------------------------[/tex]
Please can someone help me please
It is attached
Answers
(y+1)^3
Using , (a+b)^3=a^3a^2b+3ab^2+b^3expand the expression
y^3+3y^2+3y+1=
Answer
What does x, and y equal
Answers
Answer:
x = 1.25
y = 1.75
Step-by-step explanation:
Since, the line that is 8 units long is parallel to the line that is ten units long.
Therefore, both the triangles are similar by AA postulate.
Corresponding sides of of the similar triangles are in proportion.
Therefore,
[tex] \frac{5}{x + 5} = \frac{7}{y + 7} = \frac{8}{10} \\ \\ \implies \frac{5}{x + 5} = \frac{8}{10} \\ \\ 5 \times 10 = 8(x + 5) \\ \\ 50 = 8x + 40 \\ \\ 50 - 40 = 8x \\ \\ 10 = 8x \\ \\ \frac{10}{8} = x \\ \\ x = 1.25 \\ \\ \\ \frac{7}{y + 7} = \frac{8}{10} \\ \\ 7 \times 10 = 8(y + 7) \\ \\ 70 = 8y + 56 \\ \\ 70 - 56 = 8y \\ \\ 14 = 8y \\ \\ \frac{14}{8} = y \\ \\ y = 1.75[/tex]
Aaliyah is working two summer jobs, making $7 per hour walking dogs and making $10 per hour tutoring. In a given week, she can work no more than 17 total hours and must earn no less than $140. Also, she must work at least 2 hours walking dogs and at most 13 hours tutoring. If xx represents the number of hours walking dogs and yy represents the number of hours tutoring, write and solve a system of inequalities graphically and determine one possible solution.
Answers
Answer:
140 >/ 7x + 10y (read as 140 is greater than or equal to 7x plus 10y)
x + y /< 17 - to represent the number of hours she can work
she will work at least 10 hours walking dogs and at least 7 tutoring
Step-by-step explanation:
Q.23 Prove that: (sin4A - cos4A + 1) = 2sin2A
Answers
Answer:
Step-by-step explanation:
I think you have the question incomplete, and that this is the complete question
sin^4a + cos^4a = 1 - 2sin^2a.cos^2a
To do this, we can start my mirroring the equation.
x² + y² = (x + y)² - 2xy,
This helps us break down the power from 4 to 2, so that we have
(sin²a)² + (cos²a)² = (sin²a + cos²a) ² - 2(sin²a) (cos²a)
Recall from identity that
Sin²Φ + cos²Φ = 1, so therefore
(sin²a)² + (cos²a)² = 1² - 2(sin²a) (cos²a)
On expanding the power and the brackets, we find that we have the equation proved.
sin^4a + cos^4a = 1 - 2sin^2a.cos^2a
Write the following series in sigma notation. 4 +13 +22 + 31 +40 +49 +58
Answers
Answer:
Step-by-step explanation:
what is 457 times 3792 divided by 382 + 39281.028
Answers
Answer: 43817.5306178
Step-by-step explanation:
What is long division answer to 6 divided by 92
Answers
A surveyor is trying to find the length of a lake. He finds a baseline distance AB of 125 m. Angle A is measured to be 41.6° and angle B is measured at 124.3°. Find the length of the lake d. Please and Thank you.
Answers
Answer:
[tex]d = 340.7m[/tex]
Step-by-step explanation:
See attachment for question illustration
From the attachment, we have:
[tex]AB = 125m[/tex]
[tex]<A = 41.6[/tex]
[tex]<B = 124.3[/tex]
Required
Solve d
First, we need to calculate <C
[tex]<A + <B + <C = 180[/tex] --- angles in a triangle
[tex]41.6+ 124.3 + <C = 180[/tex]
[tex]165.9+ <C = 180[/tex]
Make <C the subject
[tex]<C = 180 - 165.9[/tex]
[tex]<C = 14.1[/tex]
Next, we apply Sine's law to solve for d
[tex]\frac{A}{Sin\ A} = \frac{B}{Sin\ B} =\frac{C}{Sin\ C}[/tex]
In this case:
[tex]\frac{d}{Sin\ 41.6} = \frac{125}{Sin\ 14.1}[/tex]
Make d the subject
[tex]d = \frac{125 * sin\ 41.6}{sin 14.1}[/tex]
[tex]d = \frac{125 * 0.66392621265}{0.24361501178}[/tex]
[tex]d = \frac{82.9907765812}{0.24361501178}[/tex]
[tex]d = 340.663639629[/tex]
[tex]d = 340.7m[/tex]
Hence, the base of the lake is approximately 340.7m
can u pls help me with this question
Answers
helpp hurrryyyyyyyyyy
Answers
Answer:
N=10
Step-by-step explanation:
Find the value of n.
2.8 ÷ n = 0.028
Answers
Answer:
100
Step-by-step explanation:
2.8/n = 0.028
2.8/0.028 = n
100 = n