Answer:
[tex]\tt{} x_{1} = 4 \\ \tt{} x_{2} = 5 \\ [/tex]
Step-by-step explanation:
[tex]\tt{} \sqrt{ {x}^{2} - 16 } - 3 \sqrt{x - 4} = 0[/tex]
[tex]\tt{} \sqrt{ {x}^{2} - 16 } = 3 \sqrt{x - 4} [/tex]
[tex]\tt{}{x}^{2} - 16 = 9(x - 4)[/tex]
[tex]\tt{}(x - 4).(x + 4) = 9(x - 4)[/tex]
[tex]\tt{}(x - 4) \times (x + 4 - 9) = 0[/tex]
[tex]\tt{}( x - 4) \times (x - 5) = 0[/tex]
[tex]\tt{}x - 4 = 0 \\ \tt{}x - 5 = 0[/tex]
[tex]\tt{}x = 4 \\ \tt{}x = 5 \\ \\ [/tex]
[tex]\tt{} x_{1} = 4 \\ \tt{} x_{2} = 5 [/tex]
Answer:
x = 4, 5.
Step-by-step explanation:
√(x^2 - 16) - 3√(x - 4) = 0
√(x^2 - 16) = 3√(x - 4)
Square both sides of the equation:
x^2 - 16 = 9(x - 4)
x^2 - 9x - 16 + 36 = 0
x^2 - 9x + 20 = 0
(x - 4)(x - 5) = 0
x = 4, 5.
As the original equation contained square roots:
We test for extraneous solutions:
x = 4:
√(4^2 - 16) - 3√(4 - 4) = 0 - 3*0 = 0 so x = 4 is OK.
x = 5:
√(5^2 - 16) - 3√(5 - 4) = √9 - 3√1 = 0 so x = 5 is also OK.
A car is traveling at a rate of 72 miles per hour. What is the car's rate in feet per second? How many feet will the car travel in 2 seconds? In your computations,
use the fact that I mile is equal to 5280 feet. Do not round your answers,
Answer:
The rate of travel is 105.6 feet per second, so 211.2 feet could be travelled in 2 seconds.
Step-by-step explanation:
If you take 5280 times 72 it equals 380160 which is the total amount of feet travelled in an hour so you divide it by 60 giving you 6336 which is the total feet travelled in 1 minute and you divide it 1 more time to get 105.6 which is the total feet travelled in 1 second. Hope this helps!
Can someone help me with this please?
Answer: OO! i remember this but i forgot
Step-by-step explanation: ඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞ.
amogusඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞ.ඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞ.ඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞඞ.
What does m represent in the equation y = mx + b?
A. the y-intercept of the
graph of y = mx + b
B. the slope of the graph of
y = mx + b
C. the run in the ratio rise
/ run
D. None of these
Answer:
B. the slope of the graph of y = mx + b
Step-by-step explanation:
m is the slope.
y is the y value
x is the x value
b is the y intercept
the answer is
d. none of these
Sachin used synthetic division to divide a polynomial, p(x), by x + 5 and found that there was no remainder. What does this tell Sachin about how p(x) and x + 5 are related?
A. x + 5 is a factor of p(x)
B. p(x) divided by x + 5 is 0
C. x + 5 is not a factor of p(x)
D. x + 5 cannot be divided evenly into p(x)
Answer:
A
Step-by-step explanation:
The x + 5 is a factor of p(x) this represents that p(x) and x + 5 are related.
Given that,
Let us assume polynomial be p(x), and it is divided by x + 5.There is no remainder.Based on the above information, we can say that
x + 5 represent the factor of p(x).
Therefore we can conclude that the first option is correct.
Learn more: brainly.com/question/24169758
GIVING BRAINLIEST THOSE WHO PROVIDE PICTURES
graph the solution to this system of inequalities in the coordinate plane.
3y>2x+12
2x+y<-5
William says that 15 years from now, his age will be 3 times his age 5 years ago. if x represents William's present age, what equation represents his claim? What is Willaim's current age?
Answer:
x + 15 = 3 (x - 5)
William’s current age: 15. Years old
Step-by-step explanation:
x + 15 = 3(x-5)
x + 15 = 3x - 15
15 + 15 = 3x - x
30 = 2x
x = 15
The sum of two numbers is 179.
Their difference is 133. Find both numbers.
Answer:
156,23
Step-by-step explanation:
let the numbers be x and y and x>y
x+y=179
x-y=133
add
2x=312
x=156
156+y=179
y=179-156=23
Answer:
156 and 23
Step-by-step explanation:
We can use system of equations to solve this problem.Step 1: Set up the system of equations.
[tex]\left \{ {{x+y=179} \atop {x-y=133}} \right.[/tex]Step 2: Solve x + y = 179 for x.
[tex]x + y = 179[/tex] [tex]x + y - y = 179 - y[/tex] (Subtract y from both sides)[tex]x = -y + 179[/tex]Step 3: Substitute -y + 179 for x in x - y = 133.
[tex]x-y=133[/tex] [tex]-y+179-y=133[/tex] [tex](-y-y)+(179)=133[/tex] (Combine like terms)[tex]-2y + 179 = 133[/tex] [tex]-2y + 179 - 179 = 133 - 179[/tex] (Subtract 179 from both sides)[tex]-2y = -46[/tex] [tex]\frac{-2y}{-2} = \frac{-46}{-2}[/tex] (Divide both sides by -2)[tex]y = 23[/tex]Step 4: Substitute 23 for y in x = -y + 179
[tex]x = -23 + 179[/tex] [tex]x = 156[/tex]Therefore, the numbers are 156 and 23.
chu vi của một hình chữ nhật là 240 cm. Tính diện tích hình chữ nhật đó, biết tỉ số độ dài hai cạnh là 5 và 7
[3 - | -5/6 - 2(-3)|) ÷ (-17) What is the value of the expression? Enter your answer as a simplified fraction in the box.
HELP ME PLEASE!!
Answer:
-1/6
Step-by-step explanation:
i took the quiz
Help me show my work on 13.
Answer:
Just show basic multiplication skills that we learned in 3th grade i suppose since your teacher dosen't have a brain to figure this out
Find the slope of the line that passes through each pair of points A. (-3,4) and (2,-3)
Answer:
slope = (4-(-3))/(-3-2)=7/-5=-[tex]\frac{7}{5}[/tex]
Step-by-step explanation:
Answer: m=-7/5
Step-by-step explanation:
[tex](-3,4) (2-^-3) \\\\\frac{-3-4}{2-^-3} \\m=-\frac{7}{5}[/tex]
Please solve the math problem... I will mark you brainliest
-54/87 simplified to a fraction
Answer:
-18/29
Step-by-step explanation:
54 ÷ 3 = 18 - numerator
84 ÷ 3 = 29 - denominator
-54/84 = -18/29
Compare the graph of a linear inequality in two variables with the graph of a linear equation in two variables
Answer:
k but where is the graph
Step-by-step explanation:
a girl that is 5ft tall casts a shadow 4ft long. at the same time, a tree casts a shadow 24 ft long. how long is the tree?
Answer:
25 Feet
Step-by-step explanation:
Im sorry if i am wrong, but it is 25 because the girl is 5 feet, and one feet less of a shadow. So it is obvious to me that the tree is 1 foot larger.
Find the interval(s) on which the function is negative.
y = x^2 - 6x - 16
I. (-∞, -2)
II. (-∞, 3)
III. (-2, 8)
IV. (8,∞)
A. III only
B. I only
C. II only
D. I,II
Answer:
I am going to say that it is option A.
Step-by-step explanation:
I hope this helped out a lot!
please help on number 8!! it would be much appreciated
Answer:
a.) 135 degrees
b.) 45 degrees
c.) 45 degrees
Step-by-step explanation:
Use this link to see a visual representation on how to solve for these types of angles, it lets you click on any type of angle and see how it corresponds to other angles within the parallel line and traversal, give it a try!
https://www.mathsisfun.com/geometry/alternate-exterior-angles.html
Solve the equation. Prove that it makes the equation true.
3b-8=d-6
Answer:
um just one question are you sure it's supposed to be d-6 instead of b-6
Step-by-step explanation:
if it's b-6 instead of d then the answer is 1
A box of cereal states that there are 87 calories in a 3/4 cup serving. What is the unit rate for calories per cup? How many calories are in 2 cups of cereal?
Answer: for 2 cups, There are 232 Calories.
Step-by-step explanation:
Step 1
Let the calories in one cup be represented as C
Therefore
3/4 x C = 87 calories
C = 87 X 4 / 3 = 116
unit rate is 116 calories per cup.
Step 2- Solving the number of calories in 2 cups
1 cup serving = 116 calories
2 cups servings = 116 x 2= 232 calories
HEY I RLLLLLLY NEED HELP! 50 POINTS AND BRAINLIEST IS YOU'RE RIGHT!!!!
If
f(x) = 2x + 1
and
g(x) = x - 3
g(f(x)) = 2x + ????
I will report if you answer just for points. I'd love help please :P
Answer:
g(f(x)) = 2x - 2Step-by-step explanation:
Given:
f(x) = 2x + 1and
g(x) = x - 3Find g(f(x)), substitute the value of f(x) into equation:
g(f(x)) = g(2x + 1) = (2x + 1) - 3 = 2x - 2From the story the Black cat why did the man take out the cats eye
Answer:
Removing the cat's eye is the beginning of the end, so to speak, for the narrator. Until that moment, the cat had thus far escaped his drunken cruelty, so this act signifies that the narrator had reached a certain mental point: there were no longer any limits to his violent behavior.
Step-by-step explanation:
What is the factored form of this expression?
4t2 − 27t + 18
A.
(4t − 18)(t − 1)
B.
(4t − 3)(t − 6)
C.
(2t − 9)(2t − 2)
D.
(2t − 6)(2t − 3)
Answer:
B
Step-by-step explanation:
Answer:
Have a great rest of your day :)
Step-by-step explanation:
If (1 + 2x)^5+ (1 - 2x)^5 = a + bx + cx?
find the values of the constants a, b and c.
Answer:
steps below
Step-by-step explanation:
5th level of Pascal triangle: 1,5,10,10,5,1
(1+2x)⁵ = 1*1⁵*(2x)⁰+5*1⁴*2x+10*1³*(2x)²+10*1²*(2x)³+5*1¹(2x)⁴+1*1⁰*(2x)⁵
= 1 + 10x + 40x² + 80x³ + 80x⁴ + 32x⁵ .. (1)
(1-2x)⁵ = 1 - 10x + 40x² - 80x³ + 80x⁴ - 32x⁵ .. (2)
(1)+(2): (1+2x)⁵ + (1-2x)⁵ = 160x⁴ + 80x² +2
a + bx + cx ?? suppose it's ax⁴ + bx² + cx, if you have other set up.. adjust by yourself
a = 160, b = 80, c = 2
8 to the second power.(2+6) divided by 4=
The value of given numerical expression is 128.
The given numerical expression is [8²×(2+6)]/4.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
Now, the given expression can be solved as follows:
[8²×(2+6)]/4
= (64×8)/4
= 64×2
= 128
Therefore, the value of given numerical expression is 128.
To learn more about the exponents visit:
https://brainly.com/question/15993626.
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The 4th term in an arithmetic sequence is 18 and 9th term is 43. Find the first 5 terms of the sequence
Answer:
3, 8, 13, 18, 23
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₄ = 18 and a₉ = 43 , then
a₁ + 3d = 18 → (1)
a₁ + 8d = 43 → (2)
Subtract (1) from (2) term by term, eliminating a₁
5d = 25 ( divide both sides by 5 )
d = 5
Substitute d = 5 into (1) for value of a₁
a₁ + 3(5) = 18
a₁ + 15 = 18 ( subtract 15 from both sides )
a₁ = 3 , then
a₂ = a₁ + 5 = 3 + 5 = 8
a₃ = a₂ + 5 = 8 + 5 = 13
a₄ = a₃ + 5 = 13 + 5 = 18
a₅ = a₄ + 5 = 18 + 5 = 23
The first 5 terms are 3, 8, 13, 18, 23
Bridgette measured an Italian restaurant and made a scale drawing. The scale of the drawing was 8 millimeters: 5 meters. The restaurant's kitchen is 30 meters long in real life. How long is the kitchen in the drawing?
Answer:
The kitchen drawing is 48 millimeters long.
True or False?
VERY STUCK!!! PLEASE HELP!!!!
Answer:
I'm pretty sure it's True
Step-by-step explanation:
Congruent triangles are triangles that are the same shape and size. Each triangle has the numbers 71, 47, 62 so I'm assuming the answer is True
Hope that helped! Can I also get brainliest? I need a few more to advance, if not thank you anyways and have a nice day!!!
PLEASE HELP WILL MARK BRAINLIEST
What is -100 represented in exponents
Step-by-step explanation:
[tex] { - 100}^{1} [/tex]
a) 7x^2-7=0
b)x^2-x=0
c)5x-15=0
d)x^2-4x+4=9.(x-2)
e)3(x+3)-x^2-3x=0
Answer:
[tex]a)x = 1 \\ x = - 1 \\ b)x = 1 \\ x = 0 \\ c)x = 3 \\ d)x = 11 \\ x = 2 \\ e)x = 3 \\ x = - 3[/tex]
determine if the graph represents a function
Answer:
the asnwer is YES
Step-by-step explanation:
Answer:
Step-by-step explanation:
i think it 3256