Find the solutions to the equation below.
Check all the apply.
16x^2 - 64 = 0
A. x = 4
B. x = 2
C. x = -64
D. x = -2
E. x = -4
F. x = -8
Answers
Answer:
x = 2
x = - 2
Step-by-step explanation:
⇒ 1: Common Factor
16x² - 64 = 016(x² - 4) = 0⇒ 2: Use the sum-product pattern
16 (x² - 4) = 016 (x² + 2x - 2x - 4) = 0⇒ 3: Common factor from the two pairs
16((x² + 2x) + (-2x - 4) = 016(x(x+2)-2(x+2))=0I dont feel like adding more details.
- rewrite in factored form
16(x(x+2)-2(x+2))=0
16(x-2)(x+2)=0
- create seperate equations
16(x-2)(x+2)=0
x-2=0
x+2=0
- solve
*rearrange and isolate the variable to find each solution
x = -2
x = 2
Answer:
B.x=2
Step-by-step explanation:
[tex]16x ^{2} - 64 = 0[/tex]
[tex]16x ^{2} = 64[/tex]
[tex]4 ^{2} {x}^{2} = {4}^{3} [/tex]
[tex] {x}^{2} = \frac{4 ^{3} }{4 ^{2} } [/tex]
[tex]x^{2} = 4[/tex]
[tex] \sqrt{x ^{2} } = \sqrt{4} [/tex]
[tex]x = 2[/tex]
Related Questions
Brenda walked a distance represented by the expression 5(2y + 4). It is 5 times the
distance John walked. Interpret the expression 2y + 4 and identify the correct choice.
Answers
Answer:
Option DStep-by-step explanation:
Let the distance Brenda walked is B and distance John walked is J.
We have
B = 5Jand
B = 5(2y + 4)Comparing the two equations we see
J = 2y + 4It means 2y + 4 is the distance walked by John
Correct answer choice is D
The measures of two angles of a triangle are 29° and 61°. Is the triangle acute, right, or obtuse? Use geometric terms in your explanation.
Answers
x + 29 + 61 = 180
x + 90 = 180
x = 180 - 90
Other angle = 90
As one of the angle is 90, the triangle is right angles triangle
Which of these figures has a line of symmetry drawn correctly?
Shape A and Shape B
Shape B and Shape D
Shape A
Shape C
Answers
Use 2-3 sentences to explain, in your own words, why the two acute angles in a right
triangle are complementary using the following vocabulary words: right triangle, acute
angles, angle sum theorem, and degrees.
Answers
Answer:
In a right triangle, we know that there is one 90 degree angle and two acute angles. The angle sum theorem states that the sum of all angles in a triangle equal 180 degrees. For this reason, we know that these two acute angles must equal 90 degrees or be complementary angles to add up with the 90 degree right angle and equal 180.
I hope this helps!
Answer:
In a right triangle, the angle opposite the hypotenuse is always 90 degrees. The angle sum theorem states that the sum of the interior angles of a triangle is 180 degrees. Therefore, the other two angles sum to 90 degrees, which means they are complementary. They are also acute angles, since they are each less than 90 degrees.
The rectangle on the right is a scaled copy of the rectangle on the left. Identify the scale factor. Express your answer as a whole number or fraction in simplest form.
Answers
Answer:
scale factor is 3/2
Step-by-step explanation:
to find scale factor, new image divided by original image.
Make sure you rotate the image on the right so it matches the image on the left. 3 corresponds to 9/2 and 5 corresponds to 15/2.
[tex]\frac{9}{2}[/tex] ÷ [tex]\frac{3}{1} \\[/tex]
[tex]\frac{9}{2}[/tex] × [tex]\frac{1}{3}[/tex]
[tex]\frac{9}{6}[/tex]
reduce
[tex]\frac{3}{2}[/tex]
What is the domain of the function y=\sqrt{x}
What is the domain of the function y = StartRoot x EndRoot?
Answers
Answer: C (third choice)
Step-by-step explanation:
Square roots cannot hold negative x values as it will create an imaginary number.
Therefore the starting value of x must be starting at 0 and then moving to infinity
Answer:
c
Step-by-step explanation:
im stuck, i dont know where i went wrong. Will brain list, pls help. Evaluate x³-2x²+3x-7/x-1
Answers
Answer: hii
hopefully this helps you!
Step-by-step explanation:
Simplify the expression.
- Matthew <3
Please help me with this
Answers
Answer:
8. 133°
9. 124°
Step-by-step explanation:
Because all triangles add up to 180°, the sum of all interior angle will add up to 180°.
8) 94 + 39 = 133
180 - 133 = 47
47° is the measure of the unknown interior angle, but we need the exterior and all straight lines are 180° angles, so we need to subtract.
180 - 47 = 133°
9)
81 + 43 = 124
180 - 124 = 56 (interior angle)
180 - 56 = 124° (exterior angle)
What is the slope of a line perpendicular to the line whose equation is
5x – 2y = -10. Fully simplify your answer.
Answers
use the slope intercept y=mx+b
The figure above includes one cylinder and two identical rectangular prisms. The volume of one rectangular prism is 800 m3. The volume of the entire figure is?
Answers
Answer:
1,720m
Step-by-step explanation:
I took the test
PLEASE RESPOND FAST FOR BRAINLIEST.
Data Set 1 has a mean of 173.5 and a MAD of 3.9.
Data Set 2 has a mean of 161.2 and a MAD of 4.1.
What can be concluded about the two distributions?
Select each correct answer.
The means-to-MAD ratio is 3.
The distributions are different.
The means-to-MAD ratio is 4.
The distributions are somewhat similar.
Answers
Answer:
Option D, The distributions are somewhat similar
Step-by-step explanation:
Step 1: Determine the means-to-MAD ratio
Data Set 1 → Mean = 173.5, MAD = 3.9
Data Set 2 → Mean = 161.2, MAD = 4.1
[tex]Ratio = \frac{Mean\ of\ 2 - Mean\ of\ 1}{MAD\ of\ 2 - MAD\ of\ 1}[/tex]
[tex]Ratio = \frac{161.2 - 173.5}{4.1 - 3.9}[/tex]
[tex]Ratio = \frac{-12.3|}{0.2}[/tex]
[tex]Ratio = -61.5[/tex]
Step 2: Determine if the distributions are similar or not
Since the MAD of set 2 is somewhat similar to MAD of set 1, the distributions are somewhat similar.
Answer: Option D, The distributions are somewhat similar
CAN SOMEONE PLS ANSWER THIS QUESTION FAST
I WILL MARK BRAINLIEST
Answers
Answer:
B 5
Step-by-step explanation:
it is the same ratio as the red
Please help fast!!!!
How many solutions does the equation y + 12 = y + 10 + 2 have?
O Zero
One
O Two
O Infinitely many
Answers
Answer:
Infinitely many
Step-by-step explanation:
Given:
[tex]y + 12 = y + 10 + 2[/tex]
Solve:
Subtract y from both sides
[tex]y+12-y=y+10+2-y[/tex]
Simplify
[tex]12=10+2[/tex]
Now add : 10 + 2
[tex]12=12[/tex]
Both side are equal
Since both sides are equal then answer = Infinitely many
[RevyBreeze]
Video One, a Blu-ray disc player manufacture, produces two model of Blu-ray players. The mini-blue,
which can only play a Blu-ray disc and the media-blue that plays Blu-ray disc and contains a
personal DVR. The players are assembled on two different assembly lines. Line 1 can assemble 2
units of the mini-blue model and 12 units of the media-blue model per hours, and Line 2 can
assemble 5 units of the mini-blue model and 5 units of the media-blue model per hours. The
company needs to produce at least 20 units of the mini-blue model and 70 units of the media-blue
model to fill an order.
Let x = the number of hours for Line 1
Let y = the number of hours for Line 2.
Write the system of inequalities that represents the minimum number of Blu-ray disc player that
need to be produced to fill the order.
Answers
Answer:
This question is very big, you should shorten your question a bit so that I can answer it quickly, the rest is just that I did not understand the question a bit
Debbie receives 25% commission on all sales. Her sales totalled $400. How much commission does she earn?
Answers
Answer:
$100
Step-by-step explanation:
Debbie's earnings are found by multiplying her commission rate by her sales:
0.25 × $400 = $100
Debbie earns $100 commission on her sales.
Decide if each set might produce one or more gaps when represented by a histogram. 1.The ages of students in a sixth-grade class. 2. The ages of people in a elementary school. 3. The ages of people eating in a family restaurant.
4. the ages of people who watch football. 5. The ages of runners in a marathon.
Answers
The set of data that might produce one of more gaps on thr histogram are:
the ages of people who watch football; andthe ages of people eating in a family restaurant.What is a Histogram?A histogram is a graphical representation of data such that the data is organized by data points into user-specified ranges.
The categories of people highlighted above will cause gaps because there is an increased likelihood that their ages will vary greatly or be distanced from the mean.
Learn more about Histograms at:
https://brainly.com/question/2962546
x= 1+ root 2. find (x-1/x)³
I m in grade 9
Answers
Answer:
2√2 / (5√2 + 7)
Step-by-step explanation:
Given :
x = 1 + √2Expanding
(x - 1 / x)³(1 + √2 - 1)³ / (1 + √2)³(√2)³ / (1 + √2)³2√2 / 1 + 2√2 + 3(1)(√2)(1 + √2)2√2 / 1 + 2√2 + 3√2 + 62√2 / (5√2 + 7)Answer:
[tex]-14\sqrt{2}+20[/tex]
Step-by-step explanation:
[tex]\textsf{Substituting}\quad x=1+\sqrt2\quad\textsf{into}\quad\left(\dfrac{x-1}{x}\right)^3[/tex]
[tex]\implies \left(\dfrac{(1+\sqrt2)-1}{(1+\sqrt2)}\right)^3[/tex]
[tex]\implies \left(\dfrac{\sqrt2}{1+\sqrt2}\right)^3[/tex]
[tex]\textsf{Apply exponent rule}:\left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}[/tex]
[tex]\implies \dfrac{(\sqrt2)^3}{(1+\sqrt2)^3}[/tex]
Expand numerator:
[tex](\sqrt{2} )^3=\sqrt{2}\sqrt{2}\sqrt{2}=2\sqrt{2}[/tex]
Expand denominator:
[tex]\begin{aligned}(1+\sqrt2)^3 & = (1+\sqrt2)(1+\sqrt2)(1+\sqrt2)\\ & =(1+\sqrt2)(1+2\sqrt{2}+2)\\ & =1+2\sqrt{2}+2+\sqrt{2}+2\sqrt{2}\sqrt{2}+2\sqrt{2}\\ & = 7+5\sqrt{2}\end{aligned}[/tex]
[tex]\implies \dfrac{(\sqrt2)^3}{7+5\sqrt2}[/tex]
Substituting expanded numerator and denominator:
[tex]\implies \dfrac{2\sqrt{2}}{7+5\sqrt2}[/tex]
[tex]\textsf{Mulitply by conjugate :}\quad\dfrac{7-5\sqrt2}{7-5\sqrt2}[/tex]
[tex]\implies \dfrac{2\sqrt{2}(7-5\sqrt2)}{(7+5\sqrt2)(7-5\sqrt2)}[/tex]
[tex]\implies \dfrac{14\sqrt{2}-20}{49-50}[/tex]
[tex]\implies \dfrac{14\sqrt{2}-20}{-1}[/tex]
[tex]\implies -14\sqrt{2}+20[/tex]
The function f is defined by the following rule.
f(x) = 4x+5
=
Complete the function table.
Answers
the answers are as follows:
• -15
• -7
• 5
• 13
• 21
Drag each equation to the correct location on the table.
Match the inequalities with the value of a for which they hold true.
2a + 3 < 9 − 3a
5a − 4a + 6 < 8
2a + 3 > 10 − 3a
4 + 3a + 8 < 16
3a − 2a + 1 > 2
14 + 5a < 12a + 1
Answers
a=1
-2a + 3 < 9 − 3a
5a − 4a + 6 < 8
2a + 3 > 10 − 3a
a=2
-4 + 3a + 8 < 16
14 + 5a < 12a + 1
3a − 2a + 1 > 2
An arithmetic series contains 14 numbers. The first number is 12. The last number is 38. What is the sum of the series?
312
350
494
700
Answers
Answer: The answer is B:350
Step-by-step explanation:
edge
Answer:
B
Step-by-step explanation:
Got it right
Here help my sis needs help
Answers
Let's complete
(2,8)(3,12)(4,16)Rule following=4n
(5,20)(6,24)#2
The rule is 4n
#3
Let's see
4n=48n=12ydComplete part (a) and part (b) given the following system of equations x-y=0 2x + 3y = -5 Solve this system graphically.
Answers
Answer:
(-1, -1)
Step-by-step explanation:
x - y = 0 ------> x = y
2x + 3y = -5
2(y) + 3y = -5
5y = -5
y = -1
x - (-1) = 0
x = -1
The solution to this system is (-1, -1). To solve graphically, plot both functions and you will see that they intersect at (-1, -1).
I hope this helps!
6. Kayla is planning to buy a new phone. Rongers charges $0 for down payment plus $127 monthly fee. Fidoll charges $363 for down payment plus $94 monthly fee.
a) When will the two plans charge the same amount (the same number of months for both plans)?
b) If both plans are contracted for 2 years (24 months), which plan would you recommend to Kayla? Explain.
Answers
Answer:
See below ↓↓
Step-by-step explanation:
Plan 1
0 + 127xPlan 2
363 + 94xPart A
Equating them
⇒ 127x = 363 + 94x
⇒ 33x = 363
⇒ x = 11 months [They will be same at this point]
Part B
⇒ Plan 1 : 127(24) = $3048
⇒ Plan 2 : 363 + 94(24) = 2256 + 363 = $2619
⇒ I would recommend Plan 2 as it costs less for the time period of 2 years
How many feet are represented by a 4 inch line if it is drawn to a scale of 1/2 inch equals 1 foot
Answers
Answer:
8 feet are represented by a 4-inch line.
Step-by-step explanation:
Scale:
1/2 (0.5) in. = 1ft
1/2x = 1
x = 2
4x in. = ? ft
4(2) in = ? ft
4 x 2 = 8
8 feet are represented by a 4-inch line.
hope this helps!! p.s. i really need brainliest :)
CAN SOMEBODY HELP ME PLEASE
Answers
Answer:
g-intercept: (0, 48)n-intercepts: (6, 0), (-4, 0), (2, 0)Step-by-step explanation:
The g-intercept is the point where the function graph crosses the vertical axis. The value there is g(0). It is found by evaluating the function when n=0.
g(0) = (0 -6)(0 +4)(0 -2) = (-6)(4)(-2) = 48
The g-intercept is (0, 48).
__
The n-intercepts are the points where the function graph crosses the horizontal axis. These are the values of n that make g(n) = 0. For each of the binomial factors, that value of n will be the value that makes the factor 0:
n -6 = 0 ⇒ n = 6
n +4 = 0 ⇒ n = -4
n -2 = 0 ⇒ n = 2
The n-intercepts are (6, 0), (-4, 0), and (2, 0).
Answer:
g intercepts: 48
n intercepts: 6, -4, 2
Step-by-step explanation:
Part 1:
To find the g intercepts, set n to 0 everywhere.
You then get:
g(0) = (-6)*(4)*(-2)
g(0) = 48
Part 2:
To find the n intercepts, set g to 0.
You then get:
(n-6) * (n+4) * (n-2) = 0
Solve for n in each part seperately to find all intercepts:
n-6 = 0 -> n = 6
n+4 = 0 -> n = -4
n-2 = 0 -> n = 2
the diagonal of a rectangular garden measures 111/4m while it's width measures 63/4m . Calculate the perimeter of the garden
Answers
Answer:
Step-by-step explanation:
The diagonal of a rectangular garden forms a hypotenuse with the width and length sides. We can use the Pythogorean Theorem to calculate the remaining side.
Let W, L, and H stand for the Width, Length, and Hypotenuse, all in meters.
W^2 + L^2 = H^2
Enter the data:
(63/4)^2 + L^2 = (111/4)^2
248.06 + L^2 = 770.06
L^2 = 522
L = 22.847 meters
Perimeter is 2W + 2L
Perimeter = 2(63/4) + 2(22.847)
Perimeter = 77.19 meters
A company’s stock increases from $18.30 to $54.90 over a 3-year period. What is the percent increase?
Answers
(200% increase)
Answer:
the answer is 66.67%
Step-by-step explanation:
54.90-18.30=36.60
36.60÷54.90×100=66.666666666... or 66.67%
You spin the spinner once.
6
3
5
What is P(6)?
Write your answer as a decimal.
4
Answers
Answer:
0.25
Step-by-step explanation:
Every number has equal probability here
The perimeter of a rectangle is 120 meters and the length is 20 meters longer than the width. Find the dimensions of the rectangle. Let x = the length and y = the
2+2y = 12)
width. The corresponding modeling system is 2x + 2y =120 x-y = 20
Solve the system graphically
Answers
The dimension of the rectangle is 40meters by 20meters
What is the perimeter of a figure?The perimeter of a figure is the sum of all the external sides of the figure
The formula for calculating the perimeter of rectangle = 2(l+w)
If the length is 20 meters longer than the width, then;
l = 20 + w
Substitute
120 = 2(20+2w)
60 = 20 + 2w
30 = 10 + w
w = 20 meters
Since l = 20 + w
l = 20 + 20
l = 40 meters
Hence the dimension of the rectangle is 40meters by 20meters
Learn more on perimeter of figure here: https://brainly.com/question/22447290
Please help in stuck on this one
Answers
Answer:
Step-by-step explanation:
a.
[tex]2^3*2^{-3}=2^0\\b.\\\frac{2^3}{2^5} =2^{-2}\\c.\\2^{-3}*5^{-3}=10^{-3}[/tex]
