Answer:
x = -2
Step-by-step explanation:
Given equation:
8^x= 1/64
Ensure both sides of the equation are in power format by changing 1/64
1/64 = 64^-1
8^x = 64^-1
2^3(x) = 2^6(-1)
The bases will cancel out each other
3(x) = 6(-1)
3x = -6
x = -6/3
x = -2
Check
8^x = 1/64
x = -2
8^-2
= 1/8²
= 1/8*8
= 1/64
Find two consecutive positive intergers such that the square of the smaller interger is nineteen more than five times the larger interger.
Answer:
8 and 9
Step-by-step explanation:
Let the two consecutive integers be x - 1 and x
Smaller = x-1
Largere = x
If the square of the smaller integer is nineteen more than five times the larger integer, then;
(x-1)² = 19 + 5x
Expand
x²-2x+1= 19+5x
x²-2x-5x+1-19 -0
x²-7x-18 =0
Factorize
x²-9x+2x-18 =0
x(x-9)+2(x-9) = 0
(x+2) = 0 and x - 9 = 0
x = -2 and 9
SInce x cannot be negative;
x = 9
Smaller number = 9-1
Smaller number = 8
Hence the two consecutive integers are 8 and 9
A piece of ribbon is cut into two pieces in the ratio 3:7. The length of the shorter piece is 45cm. Calculate the length in cm of the longer piece of ribbon.
Answer:
105 cm
Step-by-step explanation:
3/7 = 45/x
cross-multiply:
3x = 315
x = 105
Someone please help me with this :/
5.Express the number 0.307 x 10-Bin
scientific notation,
A
3.07 x 10-9
B
3.07 x 10-6
3.07 x 10-1
3.07 x 10-8
Answer:
A
Step-by-step explanation:
Write the nunber in scientific notation which we need to add -1 to 10 power to made it 3.07.
What is the value of the rational expression
2x+1
when x = 5?
Step-by-step explanation:
2x+1
x = 5
2(5)+1
=10+1=11
Answer:
2(5)+1
10+1
11
Hope This Helps!!!
If there are twice as many bicycles as scooters and there are 945 vehicles in total. How many bicycles and scooters are there in Greenville?
Answer:
Bicycles = 315
Scooters = 630, basic mathematics. The most effective method for these questions is substitution. But I might have intermingled them so double check
A box is to be made out of a 12 by 20 piece of cardboard. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. Find the length L , width W , and height H of the resulting box that maximizes the volume.
Answer:
Box Dimensions:
L = 15.15 ul
W = 7.15 ul
h = x = 2.43 ul
V(max) = 263.22 cu
Step-by-step explanation:
We call x the length of the square to be cut in the corners then:
Are of the base of the box is:
(20 - 2*x) is the future length of the box and
(12 - 2*x) will be the width
The heigh is x then the volume of the box is:
V = ( 20 - 2*x )* ( 12 - 2*x ) * h
And the volume as a function of x is:
V(x) = ( 20 - 2*x) * ( 12 - 2*x ) * x or V(x) = (240 -40*x -24*x + 4*x²) * x
V(x) = 240*x - 64*x² + 4*x³
Taking derivatives on both sides of the equation we get:
V´(x) = 240 - 128*x + 12*x²
V´(x) = 0 240 - 128*x + 12*x² = 0 or 60 - 32*x + 3*x²
3*x² - 32*x + 60 = 0
Solving:
x₁,₂ = 32 ± √ (32)² - 4*3*60 ]/ 2*3
x₁,₂ = 32 ± √ 1024 - 720 )/6
x₁,₂ = ( 32 ± √ 304 )/6
x₁,₂ = ( 32 ± 17.44 )/6
x₁ = 8.23 ( we dismiss this solution because is not feasible 2*x > 12
x₂ = 2.43 u.l ( units of length)
Then
L = 20 - 2*x L = 20 - 4.85 L = 15.15 ul
W = 12 - 2*x W = 12 - 4.85 W = 7.15 ul
h = 2.43 ul
V = 2.43*7.15*15.15 cubic units
V = 263.22 cu
To see if when x = 2.43 function V has a maximum we go to the second derivative
V´´(x) = - 128 + (24)*2.43
V´´(x) = - 69.68 as V´´(x) < 0 then we have a maximum for V(x) in the point x = 2.43
Identify the range of the function shown in the graph.
Answer: Choice D) [tex]0 \le y \le 5[/tex]
This is because the smallest y can get is y = 0, while the largest it can get is y = 5. It can be anything in between these y values as well.
Visually, we look for the lowest and highest points. The range is the set of all possible y outputs. In contrast, the domain is the set of all allowed x inputs.
Answer:
in my opinion it's A.. hope it will help you.
two circles intersect each other in A and C. O the centre of the smaller circle, lies on circumference of the bigger circle D is a point on smaller circle and DC produce intersects the bigger circle in B. BO produce intersects AD inM. AO, OC andAB are drawn 1 IF IT IS FURTHER GIVEN THAT ACO.=D, PROVE THAT AD IS A TANGENT TO CIRCLE ABO
Answer:
ss
Step-by-step explanation:
s
Daine simplified the expression below.
8(1 + 2i) – (7 – 3i) = 1 + 5i
What mistake did Daine make?
Answer:
Step-by-step explanation:
8(1 + 2i) - (7 - 3i) = 8*1 + 8*2i + 7*(-1) - 3i*(-1)
= 8 + 16i -7 + 3i
= 8 - 7 + 16i + 3i
= 1 + 19i
Daniel forgot to multiply 2i by 8
Answer:
A , He did not apply the distributive property correctly for 8(1 + 2i).
on edge
Step-by-step explanation:
Select the correct measurement of the angle shown on the protractor. a protractor showing an angle with one side lined up with the base line and the other side going through the fifth tick mark after fifty five degrees 110° 120° 50° 60°
Answer:
110°
Step-by-step explanation:
Each tick line in a protractor shows 10°. So the next is 110° inclined.
Answer:
110 degrees hope this helps
Step-by-step explanation:
if r=1 and 0=5pi/6 what is the approximate arc length?
Answer:
B. 2.618 units
Step-by-step explanation:
the arc length = (5π/6) / 2π × 2×3.14×1
= 5/12 × 6.28
= 31.4/ 12
= 2.618 units
The arc length is = 2.618 units
what is arc length of a circle?Arc measure is a degree measurement, equal to the central angle that forms the intercepted arc. Arc length is a fraction of the circumference of the circle.
Given : r=1, [tex]\theta[/tex]= 5π/6
Now, arc length
= [tex]\theta[/tex]/ 2π * 2πr
= (5π/6) / 2π × 2×3.14×1
= 5/12 × 6.28
= 31.4/ 12
= 2.618 units
Learn more about arc length here:
https://brainly.com/question/1577784
#SPJ2
Write the equation of the line that contains the points (-2,5) and (6,9).
Answer: y=2/4x+6
I think it´s right sorry if it is´nt
Hihi , please help if able.
Step-by-step explanation:
the lines on the graph of inequality second option
This question is very important I will give Brainliest for the correct answer!! It's just perimeter but I'm a little confused.
If I eat 20 cupcakes and A=chicken nuggies what color is the imposter? True or false. extra points if you explain your answer.
Answer:
true
Step-by-step explanation:
because your susy
Which of the following is the best estimate of 7/8? ( Answer ASAP )
Answer:
C
Step-by-step explanation:
just round up to nearest number and 7/8 is 0.87 so it coloser to 1 than half and the others are way to big.
20 marbles in a bag. 4 are red, 5 are blue, 5 are black, 4 are white and 2 are yellow. What is the probability that he pulls out a red marble?
Answer:
1/5
Step-by-step explanation:
Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.
For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.
probability that he pulls out a red marble = number of red marbles / total number of marbles
= 4/20 = 1/5
Lift tickets at the resort cost $28 per day for adults and $19
per day for children under 12. The Scotts skied for 5 days.
A How much did the Scotts pay for lift tickets each day?
B. How much did the Scotts pay for lift tickets altogether?
Answer:
No solution is possible
Step-by-step explanation:
You didn't indicate the number of adults and children.
Find all values of x that satisfy the equation below. (x + 1)² - 25/9
= 0
Answer:
x = 8/3, 2/3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Multiple RootsStep-by-step explanation:
Step 1: Define
Identify
(x + 1)² - 25/9 = 0
Step 2: Solve for x
[Addition Property of Equality] Add 25/9 on both sides: (x + 1)² = 25/9[Equality Property] Square root both sides: x + 1 = ±5/3[Subtraction Property] Subtract 1 on both sides: x = ±5/3 - 1Evaluate Addition/Subtraction: x = 8/3, 2/3Step-by-step explanation:
Hey there!
Given equation is:
(x+1)² - 25/9 = 0
Then;
(x+1)² - (5/3)² = 0 ( since 5² = 25 and 3² = 9)
or, {(x+1)+5/3} { (x+1)-5/3} = 0. { use a² - b² = (a+b)(a-b) formula}
[tex]( \frac{3x + 3 + 5}{3} )( \frac{3x + 3 - 5}{3} ) = 0[/tex]
[tex]( \frac{3x + 8}{3} )( \frac{3x - 2}{3}) = 0[/tex]
Now;
Either;
( \frac{3x + 8}{3}= 0
or, X = 8/3
Or,
( \frac{3x -2}{3} = 0
x = 2/3
Therefore, X = 8/3 or 2/3.
Hope it helps!
Find the missing side!!
Answer:
the answer to the question is 12cm
Which best describes the relationship between the line that passes through the points (-6, -1) and (-11, 1) and the line
that passes through the points (-3, -8) and (-5, -13)?
A. perpendicular
B. parallel
C. neither perpendicular nor parallel
D. same line
Answer: A. perpendicular
Step-by-step explanation: First, you have to determine the slope of both lines and you can do so using the slope formula: (y2 - y1)/(x2 - x1). You should get the slope -2/5 for the first line and 5/2 for the second. Because one line has a slope that is the negative reciprocal of the other, these lines are perpendicular.
hey !! solve it
[tex] \sqrt{44 \times 11} [/tex]
Step-by-step explanation:
✓44×11
=✓2²×11²
=22
!!!!????!!!!!!
Answer:
22
Step-by-step explanation:
First, multiply 11 and 44
11 × 44 = 484
[tex]\sqrt{484}[/tex] = 22
---------------------------------------------------------------------------------------------------------------
Have a great summer :)
[tex]128^3+272^3 /128^2-128*272+272^2[/tex]
wait do you want it step by step or just the answer?
the answer is 400
through: (-2, -1), slope = -1
y= -1x -3
that's equation of the line
a fruit seller had thought to sell 120kg of fruit at 150 dollars / kg but sold it 5% less. find out how much dollars the seller lost
please answer this 2 question
Answer:
Step-by-step explanation:
AP 1 : 12, 15 , 18 , 21, 24, 27, 30 , 33 , 36, 39,.....
AP 2 : 17 , 21 , 25 , 29, 33, 37 , 41, 45,.....
AP formed with the common terms: 21, 33, 45 , ......
a = 21 , d = 33-21 = 12 ; n = 100
Sum = [tex]\frac{n}{2}(2a +(n-1)d)[/tex]
[tex]=\frac{100}{2}[2*21+99*12]\\\\=50 * [42+1188]\\\\=50*1230\\\\= 61500[/tex]
А
3
-2
-1
0
2
3
B.
-1
The distance AB rounded to the
nearest tenth = [?]
Hint: d= (x2 - 1)+ (y2 - yı)2
What should be filled in the blank spot you’ll be marked as brainliest if you are correct
Answer:
-4 square inches
Step-by-step explanation:
its because the 5 pictures together make 21
Which relationship has a zero slope? A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 2, 2, 2, 2. A two column table with five rows. The first column, x, has the entries, negative 3, negative 1, 1, 3. The second column, y, has the entries, 3, 1, negative 1, negative 3. A coordinate plane with a straight line starting at (negative 5, negative 5) and passing through the origin, and ending at (5, 5) A coordinate plane with a straight line starting iat (negative 2, 5) and passing the x-axis at (negative 2, 0), and ending at (negative 2, 5).
Answer:
y=3 x=1
Step-by-step explanation:
Answer:
above one is correct. I think so
In a regular polygon each interior angle is 120 greater than each exterior angle. Calculate the number of sides of the polygon.
Answer:
12 sides.
Step-by-step explanation:
the sum of every pair of interior and exterior angle is always 180 degrees.
x = exterior angle.
the interior angle is then x+120.
so then exterior and interior angle together must be 180.
x + x + 120 = 180
2x + 120 = 180
2x = 60
x = 30 degrees
how many sides ?
the sum of all exterior angles must be 360 degrees.
all exterior angles are the same (because all the interior angles must be the same due to "regular polygon").
so, how many times does 30 fit into 360 ?
360/30 = 36/3 = 12
it has 12 corners and also sides.