Answer:
[tex]a = - \frac{3}{4}[/tex]
Step-by-step explanation:
The correct solution of the given equation is as follows :
We have,
[tex]\frac{1}{64} = 16^{2a}[/tex]
⇒ [tex]4^{- 3} = (2^{4} )^{2a}[/tex]
⇒ [tex]2^{(2 \times (-3))} = 2^{8a}[/tex]
⇒ [tex]2^{- 6} = 2^{8a}[/tex]
Comparing the power of equal base, we get
- 6 = 8a
⇒ [tex]a = - \frac{6}{8}[/tex]
⇒ [tex]a = - \frac{3}{4}[/tex]
Therefore, before equating the powers of two terms the base of the terms should be equal and here this is the error. (Answer)
Answer:
The bases were not the same when the exponents were set equal to each other.
16 should have been written as 4 squared.
The exponent on the right should be 4a instead of 8a.
The correct solution is a = -3/4
Step-by-step explanation:
correct on edge
Which expression is equivalent to 6^3?
6x3
6x6x6
6x6х6х6
3х3х3х3х3х3
Answer:
6x6x6
Step-by-step explanation:
The definition of an exponent is how many times a number is multiplied. For example, 7^5 is 7 multiplied by itself 5 times. (7x7x7x7x7)
Answer:
6x6x6!
Step-by-step explanation:
Have a nice day!
A Galapagos cactus finch population increases by half every decade. The number of finches is
modeled by the expression 45 • 1.54, where d is the number of decades after the population
was measured. Evaluate the expression to find the number of finches for d=-2.
Answer:
The number of fringes at [tex]d=-2[/tex] is given as 20.
Step-by-step explanation:
Question
A Galapagos cactus finch population increases by half every decade. The number of finches is modeled by the expression
,
where d is the number of decades after the population was measured. Evaluate the expression for d = −2
Given :
The number of finches is modeled by the expression :
⇒ [tex]45\cdot1.5^d[/tex]
where [tex]d[/tex] is the number of decades after the population was measured.
To evaluate the expression for d=-2
Solution:
In order to evaluate the given expression to find the number of finches at [tex]d=-2[/tex], we will plugin [tex]-2[/tex] for [tex]d[/tex] in the expression and simplify it.
Plugging in [tex]d=-2[/tex] in the expression:
⇒ [tex]45\cdot 1.5^{-2}[/tex]
Using negative exponent property. [[tex]a^{-x}=\frac{1}{a^x}[/tex]
⇒ [tex]45\cdot \frac{1}{1.5^2}[/tex]
⇒ [tex]45\cdot \frac{1}{2.25}[/tex]
⇒ [tex]20[/tex] (Answer)
Thus, the number of fringes at [tex]d=-2[/tex] is given as 20.
This means the number of fringes two decades ago was 20.
24 is 120% of what?, i need help so please tell ne the steps!?
Answer: it’s 20
We have, 120% × x = 24
or,
120/100 × x = 24
Multiplying both sides by 100 and dividing both sides by 120,
we have x = 24 × 100/120
x = 20
If you are using a calculator, simply enter 24×100÷120, which will give you the answer.
What is sinB? Who knows this one I’ll give you best brainliest
Answer:
sinB = Opposite/Hypotenuse
Step-by-step explanation:
no need for explanation
-3 - 6 ( 4x + 6 ) > -111
Answer:
-3 -24x - 36 > -111
-24x - 39 > -111
-24x > -72
x < 3
The probability that an event will happen is 5/8 . What is the probability that the event will not happen?
Answer:(please note im not sure)
3/8 (i think).
Step-by-step explanation:
The probability of this not happening in an event is 3/8.
Probability is a measure of the likelihood or chance that a particular event or outcome will occur. It quantifies the uncertainty associated with different possible outcomes in a given situation. In other words, probability helps us understand the likelihood of an event happening.
The probability of not happening of an event is calculated by subtracting the probability of happening of an event.
The probability of not happening of an event is,
P(not) = 1 - P
P(not) = 1 - 5/8
P(not) = 3 /8
Therefore, the probability that the event will not happen is 3/8.
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What number is 20% of 55
Answer:
11
Step-by-step explanation:
20·55/100=11
Answer: 11
Step-by-step explanation: First write 20% as a decimal by moving the decimal point 2 places to the left to get .20.
Next, the word "of" means multiply, so we have (.20)(55) which is 11.
So 11 is 20% of 55.
What number is 62% of 250? Round your answer to the nearest hundredth, if necessary.
Answer: 155
Step-by-step explanation: Well percent means over 100 so we can set up an equation for this problem by reading it from left to right.
What number means x, is means equals,
62% is 62/100, of means times 250.
So we have the equation x = 62/100 · 250.
Simplifying on the right side side of the equation, notice that 62/100 reduces to 31/50 so we have x = 31/50 · 250.
Think of the 250 as 250/1.
So we can cross cancel the 250 and 50 to 50 and 1.
So we 31 times 5 over 1 or 155.
So 155 is 62% of 250.
Round 23,865 to the nearest 1,000
Answer:
24,000
Step-by-step explanation:
What is 19 3/5 -18 4/5=
Answer:
1 -1/5 is the answer #markasbrainliest
11. Which equation would help you find the
1 missing side length in the right triangle shown
A - 122-102=c2
B- 122+ b2= 102
c. 12(2)+ 10(2) = c(2)
D. 122+ 102 = c3
Answer: A-122-102=c2
Step-by-step explanation: This is the answer to the missing side length in the right triangle shown.
Option B: 122 + b^2 = 102^2 is the correct equation to find the missing side length in the right triangle.
The equation that would help you find the missing side length in the right triangle is option B: 122 + b2 = 1022.
In a right triangle, the Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, 122 is the length of one side and 102 is the length of the other side. By rearranging the equation, you can solve for the missing side length, b.
Let's rewrite the equation using the proper square notation:
122 + b2 = 1022
122 + b2 = 10404
b2 = 10404 - 122
b2 = 10282
b = √10282
b ≈ 101.4
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I need this answered today
Answer:
The solution of the system is x=-2, y=-1
see the explanation
Step-by-step explanation:
we know that
When a system of linear equations is solved using a graph, the solution of the system of equations is the point of intersection of the two lines
In this problem
The intersection point both lines is (-2,-1)
therefore
The solution of the system is x=-2, y=-1
A right prism has a base that is an equilateral triangle. The height of the prism is equal to the height of the base. If the volume of the prism is 81, what are the lengths of the sides of the base?
Length of side of base is 5.45
Step-by-step explanation:
Step 1: Volume of a right prism = Area of the base × Height = 1/2 × base × height of base × height of prismHere, since the base is an equilateral triangle and it is given that height of the prism is equal to that of the base, measures of base and height are equal.
⇒ Volume = 1/2 × b × h × h (b and h are equal)
⇒ 81 = 1/2 × b³
⇒ b³ = 162
⇒ b = ∛162 = 5.45
Which expressions are equivalent to 5 (one-third x + 7) minus 3 (one-half x minus 4)? Select three options. 5 and one-third x minus 3 and one-half x + 35 minus 12 One-sixth x + 47 1 and two-thirds x + 35 minus 1 and one-half x + 12 5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4) 1 and one-third x + 35 minus 1 and one-half x minus 12
The equivalent options are:
"One-sixth x + 47" ⇒ 2nd
"1 and two-thirds x + 35 minus 1 and one-half x + 12" ⇒ 3rd
"5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)" ⇒ 4th
Step-by-step explanation:
The expression is: 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) to find the equivalent to it:
Open the bracketsAdd the like termsMultiply the bracket ( [tex]\frac{1}{3}[/tex] x + 7) by 5
∵ 5( [tex]\frac{1}{3}[/tex] x + 7) = 5(
Multiply the bracket ( [tex]\frac{1}{2}[/tex] x - 4) by - 3
∵ -3( [tex]\frac{1}{2}[/tex] x - 4) = -3(
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12
Add the like terms
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = ( [tex]\frac{5}{3}[/tex] x - [tex]\frac{3}{2}[/tex] x) + (35 + 12)
To add fraction with different denominators find the LCM of the two denominators and change them by it, then divide the LCM by each denominator and multiply the quotient by the corresponding numerator
∵ LCM of 3 and 2 is 6
∵ 6 ÷ 3 = 2, then multiply 5 by 2
∴ [tex]\frac{5}{3}[/tex] = [tex]\frac{10}{6}[/tex]
∵ 6 ÷ 2 = 3, then multiply 3 by 3
∴ [tex]\frac{3}{2}[/tex] = [tex]\frac{9}{6}[/tex]
∴ ( [tex]\frac{5}{3}[/tex] x - [tex]\frac{3}{2}[/tex] x) = [tex]\frac{10}{6}[/tex] x - [tex]\frac{9}{6}[/tex] x = [tex]\frac{1}{6}[/tex] x
∵ 35 + 12 = 47
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = [tex]\frac{1}{6}[/tex] x + 47
The 1st option is "One-sixth x + 47"
In the step 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12
∵ [tex]\frac{5}{3}[/tex] = [tex]1\frac{2}{3}[/tex] and [tex]\frac{3}{2}[/tex] = [tex]1\frac{1}{2}[/tex]
∴ [tex]\frac{5}{3}[/tex] x + 35 - [tex]\frac{3}{2}[/tex] x + 12 = [tex]1\frac{2}{3}[/tex] x + 35 - [tex]1\frac{1}{2}[/tex] x + 12
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = [tex]1\frac{2}{3}[/tex] x + 35 - [tex]1\frac{1}{2}[/tex] x + 12
The 2nd option is "1 and two-thirds x + 35 minus 1 and one-half x + 12"
∵ 5( [tex]\frac{1}{3}[/tex] x + 7) = 5(
∵ -3( [tex]\frac{1}{2}[/tex] x - 4) = -3(
∴ 5( [tex]\frac{1}{3}[/tex] x + 7) - 3( [tex]\frac{1}{2}[/tex] x - 4) = 5(
The 3rd option is "5 (one-third x) + (5) (7) minus (3) (one-half x) + (3) (4)"
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Answer:
[tex]5(\frac{1}{3}x)+5(7)-3 (\frac{1}{2}x)+(3)(4)[/tex]
[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+ 12[/tex]
[tex]\frac{1}{6}x+47[/tex]
Step-by-step explanation:
The given expression is [tex]5(\frac{1}{3}x+7)-3 (\frac{1}{2}x- 4)[/tex]
We expand to get:
[tex]5(\frac{1}{3}x)+5(7)-3 (\frac{1}{2}x)+(3)(4)[/tex]
[tex]\frac{5}{3}x+35-\frac{3}{2}x+ 12[/tex]
As mixed number coefficients:
[tex]1\frac{2}{3}x+35-1\frac{1}{2}x+ 12[/tex]
This simplifies to:
[tex]\frac{1}{6}x+47[/tex]
What is the true solution to 2 In 4x = 2 In 8?
O x=-4
X=-2
x=2
X=4
Answer:
The third answer choice (x = 2) is the correct one.
Step-by-step explanation:
2 ln 4x = 2 ln 8 simplifies to ln 4x = ln 8.
Next, ln 4x = ln 8 simplifies to 4x = 8, and, finally,
we get
x = 8/4 = 2.
The third answer choice (x = 2) is the correct one.
Answer:
the answer is C
Step-by-step explanation:
i took the test
2m^3-30m^2+108m please answer
Answer:
Step-by-step explanation:
2m^3 - 30m^2 + 108...factor out 2m
2m(m^2 - 15m + 54)
2m(m-9)(m-6) <====
Look at pic and answer pls
(a) [tex]x^{-5}[/tex]
(b) [tex]3x^{-7}[/tex]
(c) [tex]$\frac{4}{3}x^4[/tex]
Solution:
To write each of the given expression in the form [tex]ax^n[/tex]:
(a) [tex]\frac{x^3}{x^8}[/tex]
Using exponential rule: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]$\frac{x^3}{x^8}=x^{3-8}[/tex]
[tex]$\frac{x^3}{x^8}=x^{-5}[/tex]
(b) [tex]\frac{6x}{2x^8}[/tex]
Divide numerator and denominator by the common factor 2, we get
[tex]$\frac{6x}{2x^8}=\frac{3x}{x^8}[/tex]
Using exponential rule: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]$=3x^{1-8}[/tex]
[tex]$\frac{6x}{2x^8} =3x^{-7}[/tex]
(c) [tex]\frac{28x^6}{21x^2}[/tex]
Divide numerator and denominator by the common factor 7, we get
[tex]$\frac{28x^6}{21x^2}=\frac{4x^6}{3x^2}[/tex]
Using exponential rule: [tex]\frac{a^x}{a^y}=a^{x-y}[/tex]
[tex]$=\frac{4}{3}x^{6-2}[/tex]
[tex]$\frac{28x^6}{21x^2}=\frac{4}{3}x^4[/tex]
Find the length of the midsegment to the nearest tenth
31.0
70.0
35.0
16.7
Answer:
35.0 units
Step-by-step explanation:
we know that
A mid-segment of a triangle is a segment connecting the midpoints of two sides of a triangle. This segment is always parallel to the third side, and the length of the mid-segment is half the length of the third side
so
[tex]6x+5=\frac{1}{2}(3x+55)[/tex]
solve for x
[tex]12x+10=3x+55\\12x-3x=55-10\\9x=45\\x=5[/tex]
Find the length of the mid-segment
substitute the value of x
[tex]6(5)+5=35.0\ units[/tex]
Panchito Pantera has 100 coins(Quarters and dime). He has a totalof $22.How many quarters does he have?? dimes??
There are 20 dimes and 80 quarters
Solution:
Let "d" be the number of dimes
Let "q" be the number of quarters
1 dime = $ 0.10
1 quarter = $ 0.25
Panchito Pantera has 100 coins
Therefore,
number of dimes + number of quarters = 100
d + q = 100 ----------- eqn 1
He has a total of $22. Thus we frame a equation as:
number of dimes x 0.10 + number of quarters x 0.25 = 22
[tex]d \times 0.10 + q \times 0.25 = 22[/tex]
0.1d + 0.25q = 22 --------- eqn 2
Let us solve eqn 1 and eqn 2
From eqn 1,
d = 100 - q ------- eqn 3
Substitute eqn 3 in eqn 2
0.1(100 - q) + 0.25q = 22
10 - 0.1q + 0.25q = 22
0.15q = 22 - 10
0.15q = 12
Divide both sides by 0.15
q = 80
Substitute q = 80 in eqn 3
d = 100 - 80
d = 20
Thus there are 20 dimes and 80 quarters
4) Explain the difference between symmetry and congruency.
Answer:
Two figures are congruent if they can be superimposed so that they fit exactly. It can be shown that two plane polygons are congruent if and only if a one-to-one correspondence can be established between them such that corresponding sides have the same length and corresponding angles have the same measure.
Thus, figures that are the same size and shape are congruent. Corresponding parts of congruent figures are congruent. Congruent figures, such as those below, may be in different positions.
Congruent shapes
A figure has line symmetry if it can be folded in half and the two halves are congruent. The line made by the fold is the line of symmetry. Line symmetry is also called bilateral symmetry. Figures can have no lines of symmetry or an unlimited number of lines of symmetry.
Step-by-step explanation:
Final answer:
Symmetry refers to a balanced and proportional similarity an object exhibits across a dividing line, while congruency means two objects are identical in shape and size but may differ in position. Human bodies show bilateral symmetry, and symmetry is important for biological functionality and aesthetics. Congruency, meanwhile, is about identical geometry, regardless of orientation or position.
Explanation:
The difference between symmetry and congruency is foundational in understanding geometric principles. Symmetry refers to the balanced and proportional similarity that an object has with respect to a dividing line, plane, or center.
When an object exhibits symmetry, it means that if you were to fold it along its line of symmetry, the two halves would match up perfectly, reflecting one another. For instance, human body plans illustrate bilateral symmetry, where the body can be split into left and right halves that are mirror images of each other.
On the other hand, congruency is a concept that denotes when two shapes are identical in form and size, although they may be flipped, rotated, or moved. In geometry, when two figures are congruent, they have exactly the same dimensions and shape, but their positions may vary. A real-world example of congruence can be seen in the uniformity of manufactured products like tiles or bricks.
To observe how symmetry extends to our senses, consider that our eyes and ears are positioned symmetrically on either side of our head, providing balanced input to our brain which helps us navigate our environment effectively. This speaks to the importance of symmetry not just in aesthetics but also in biological functionality.
Henry had $24.12. His friend Greg had one-
half as much as Henry. Another friend Kasey
had one-fourth of what Henry has. How much
money do the three friends have altogether?
Henry:
Greg:
Kasey
Total:
Answer: $42.21
Step-by-step explanation:
Henry; $24.12
Gregg; $24.12 / 2= $12.06
Kasey; $ 24.12 / 4= $6.03
$24.12 + $12.06 + $6.03
Find the area of polygon
Answer:
of wut
Step-by-step explanation:
A daycare charges a base fee of 3 dollars plus 0.50 dollars per minute for late (after closing time) pick-ups. Albin
had to pay 10.50 dollars for a late pick-up.
Albin uses the equation, 10.50 = 0.50a + 3 to represent the situation.
What does the variable a represent in the equation?
Choose 1 answer:
Number of minutes of Albin's late pick-up
The part of the cost that depends on the number of minutes late
The number of dollars per minute late
The variable 'a' in Albin's equation represents the number of minutes Albin was late for picking up from the daycare, with 3 dollars as the base fee and 0.50 dollars charged for each minute late.
Explanation:The variable a in Albin's equation, 10.50 = 0.50a + 3, represents the number of minutes of Albin's late pick-up from the daycare. The base fee of the daycare is 3 dollars, which is a fixed amount, while 0.50 dollars is the rate charged per minute for being late. The equation is a way to calculate the total fee based on the minutes Albin is late.
For comparison, if we look at Aaron's Word Processing Service, the total cost of services would be represented by y = 31.50 + 32x, where 31.50 is a fixed cost and the cost for word processing is 32 dollars per hour (x). Similarly, for Svetlana's tutoring sessions, the total income she earns is given by y = 25 + 15x, where 25 is a one-time fee and 15 dollars per hour is her rate of earning.
If
A)8/17
B)8/15
C)15/17
D)15/8
Answer:
d) 15/8
Step-by-step explanation:
tgB = AC/AB = 15/8
The tangent of an angle is the length of the opposite side (AC) divided by the length of the adjacent side (AB).
What is the mixed number fraction of
6 2/5 - 2 9/10
Answer: srry ion k
Step-by-step explanation:
Next Tuesday, Cordelia is catering a proposal dinner for her brother. If she wants to serve her macaroni and cheese at this dinner for 2, she will use _____ cup(s) of Parmesan cheese. The recipe includes that 1/2 Cups of Parmesan cheese serves 4 people.
Answer: [tex]\frac{1}{4}\ cups[/tex]
Step-by-step explanation:
For this exercise it is important to analize the information given in the exercise.
According to the data provided in the exercise, the recipe says that [tex]\frac{1}{2}\ cups[/tex] of Parmesan serves four people.
The, let be "x" the amount of cups of Parmesan cheese that Cordelia will use for her brother's proposal dinner.
In this case, since the proposal dinner is for two people, you can set up the following proportion:
[tex]\frac{4}{\frac{1}{2}}=\frac{2}{x}[/tex]
Finally, you must solve for "x" in order to find its value, as you can observe below:
[tex]8=\frac{2}{x}\\\\8x=2\\\\x=\frac{2}{8}\\\\x=\frac{1}{4}[/tex]
Therefore, knowing the value of "x", you can determine that Cordelia will use [tex]\frac{1}{4}\ cups[/tex] of Parmesan cheese for the proposal dinner.
could you guys pleasenname the place value to which each number was rounded. 0.982 to 0.98
Answer: THOUSANDTHS
Step-by-step explanation:
Is 3/10 greater than 3/5
Answer:
No. 3/10 is NOT greater that 3/5.
Step-by-step explanation:
Take two pizzas for example. Cut one into 10 slices and the other into 5. Take three out of both and see which one has more of the pie gone.
Answer:No, You can set it up as a proportion to compare.
Step-by-step explanation:
You can check by changing 3/5 into 6/10(10 is a common denominator, what u do to the bottom, you must do at the top)and as you can see, 6/10 is more than 3/10.
2)x-5)+2-3(5-2x)=16
Answer:
Step-by-step explanation:
hello :
2(x-5)+2-3(5-2x)=16
2x-10+2-15+6x =16
8x-23 =16
8x =39
x = 39/8
just realized this is science not math O_o Determine if each description is mass or weight. Drag each description into the correct category.
This remains the same on the moon as on Earth.
This results from the pull of gravity.
This relates to the amount of matter in an object.
This will change in space.
mass(this is a category) weight (this is a category)
sorry i just realized its not mathematics O_o
This remains the same on the moon as on Earth. --> MASS
This results from the pull of gravity. --> WEIGHT
This relates to the amount of matter in an object. --> MASS
This will change in space. --> WEIGHT
mass is a SCALAR, weight is a VECTOR
Step-by-step explanation:
In physics:
- The mass of an object is a scalar quantity that gives a measure of the "amount of matter" in an object. It is an intrinsec property of the object, therefore its value does not depend on the location of the object.
- The weight of an object is the force of gravitational attraction exerted on the object. Being a force, it has a magnitude and a direction. Its magnitude is given by
[tex]F=mg[/tex]
where m is the mass of the object and g is the acceleration due to gravity at the location of the object. Therefore, its value depends on the location.
Now we can identify correctly each statement given:
This remains the same on the moon as on Earth. --> MASS
This results from the pull of gravity. --> WEIGHT
This relates to the amount of matter in an object. --> MASS
This will change in space. --> WEIGHT
mass is a SCALAR, weight is a VECTOR
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