a. 5²
b. 7⁴
c. 2³
d. 9⁵
Explanation:
An exponent is the number of times a number is multiplied by itself.
a. 5x5 = 5² ( five is multiplied two times)
b. 7 x 7 x 7 x 7 = 7⁴ ( seven is multiplied four times)
c. 2 x 2 x 2 = 2³ ( two is multiplied three times)
d. 9 x 9 x 9 x 9 x 9 = 9⁵ ( nine is multiplied five times)
Final answer:
Exponential abbreviations express repeated multiplication of the same number as a base raised to a power. For example, 5x5 becomes 5², and 7x7x7x7 becomes 7⁴. This notation simplifies multiplication into a more compact and manageable form.
Explanation:
Writing Multiplications as Exponential Abbreviations
To write the given multiplications as exponential abbreviations, we look for repeated factors and express them as a base number raised to the power of how many times it occurs. Here's how to do it:
a. 5x5 is 5 multiplied by itself 1 more time, so it is written as 5².b. 7 x 7 x 7 x 7 is 7 multiplied by itself 3 more times, so it is written as 7⁴ (7 to the fourth power).c. 2 x 2 x 2 is 2 multiplied by itself 2 more times, so it is written as 2³.d. 9 x 9 x 9 x 9 x 9 is 9 multiplied by itself 4 more times, so it is written as 9⁵ (9 to the fifth power).This process simplifies multiplication by using exponents to indicate the number of times a base is used as a factor.
If f(x) =4x^2 + 1 and g(x) =x2 -5, find (f+g)(x)
The value of [tex](f+g)(x)[/tex] is [tex]5 x^{2}-4[/tex]
Explanation:
Given that the functions [tex]f(x)=4 x^{2}+1[/tex] and [tex]g(x)=x^{2}-5[/tex]
We need to determine the value of [tex](f+g)(x)[/tex]
The value of [tex](f+g)(x)[/tex] can be determined by substituting the value of [tex]f(x)[/tex] and [tex]g(x)[/tex] and simplifying the terms.
Thus, let us assign [tex]f(x)=4 x^{2}+1[/tex] in the function [tex](f+g)(x)[/tex], we have,
[tex]4 x^{2}+1+g(x)[/tex]
Now, let us assign [tex]g(x)=x^{2}-5[/tex] in the function [tex](f+g)(x)[/tex], we get,
[tex]4 x^{2}+1+x^{2}-5[/tex]
Grouping the like terms, we have,
[tex]4 x^{2}+x^{2}+1-5[/tex]
Adding the like terms, we get,
[tex]5 x^{2}-4[/tex]
Hence, the value of [tex](f+g)(x)[/tex] is [tex]5 x^{2}-4[/tex]
F(x)=12x+1
Find f(4)
f(4) is 49
Explanation:
Given:
f(x) = 12x + 1
f(4) = ?
we have to substitute the value of x = 4 in the given equation.
f(4) = 12 X 4 + 1
f(4) = 49
Whenever there is such type of question then we have to just put the value of x in the equation. In case of f '(4) then we have to differentiate the given equation with respect to x first and then substitute the value of x in the differentiated equation.
Therefore, f(4) is 49
Is area a function of the radius ? Is radius a function of area?
Answer: The area (A) of a circle is a function of its radius (r) and is given by the function A = f(r) = πr2.
Step-by-step explanation: google help
The area is a function of the radius and the radius is a function of the area.
Is the area a function of the radius?
For a circle of radius R, we can write the area as:
A = pi*R^2
So we can write the area in terms of the radius, meaning that yes, the area is a function of the radius of a circle.
Is the radius a function of the area?If we take the above equation and we isolate R, we get:
R = √(A/pi)
So you can also write the radius in terms of the area, meaning that the radius is also a function of the area.
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Four more than five times a number is two less than the number
make it into an algebraic expression
Answer:
4+5x<x
Step-by-step explanation:
four more than is saying addition so youd add the 4 and the 5x together. the less than is referring to the less than sign. and the number is referring to x.(;
A Pentagon is transformed according to the rule R0, 180°. Which is another way to state the transformation?
(x,y)>(-x,-y)
(x,y)>(-y,-x)
(x,y)>(x,-y)
(x,y)>(-x,y)
The another way to state the transformation would be [tex](x,y)>(-x,-y)[/tex]
Solution:
Rotation about the origin at [tex]180^\circ[/tex]: [tex]R_{180^\circ}A \rightarrow O = R_{180^\circ} (x, y) \rightarrow (-x,-y)[/tex]
The term R0 means that the rotation is about the origin point. Therefore, (R0,180) means that we are rotating the figure to [tex]180^\circ[/tex] about the origin.
So, the transformation of the general point (x,y) would be (-x,-y) when it is rotated about the origin by an angle of [tex]180^\circ[/tex].
Hence according to the representation, the expression would be [tex](x, y) \rightarrow (-x, -y)[/tex].
The transformation R0, 180° is equivalent to reflecting each point (x, y) in a Pentagon across the origin, resulting in the new coordinates (-x, -y).
The transformation rule R0, 180° involves rotating a point (x, y) within a Pentagon by 180 degrees around the origin. In this transformation, each point is mirrored or reflected across the origin. To express this transformation differently, we can say that (x, y) is mapped to its mirror image in both the x-axis and y-axis. In other words, the x-coordinate is reversed (negated), and the y-coordinate is also reversed (negated).
So, the alternative way to state this transformation is: (x, y) > (-x, -y). This means that any point (x, y) in the original Pentagon will become (-x, -y) after the transformation.
For example, if we have a point (2, 3) within the Pentagon, applying the transformation yields (-2, -3). This means the point's x-coordinate is changed from 2 to -2, and the y-coordinate is changed from 3 to -3. This transformation is essentially a 180° rotation or a reflection through the origin.
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Which equation represents a function?
OA) x = -2y2
OB) x = y2 - 9
OC) x2 + y2 = 1
OD) y= 3x2 + 2
The correct equation which represents a function is,
⇒ y= 3x² + 2.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
To find the correct equation which represents a function.
Now, We know that;
The equation that represents a function is option D,
⇒ y= 3x² + 2.
This is because for every value of x, there is a unique value of y.
In other words, each x value has only one corresponding y value.
And, The other options either have multiple outputs for the same input or do not qualify as a function for other reasons.
Thus, The correct equation which represents a function is,
⇒ y= 3x² + 2.
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The storm dropped 1 3/12 feet of snow during the first hour and 9/12 foot more during the second hour. how much snow fell during those to hours?
i need help
Answer:
your answer would be 2
Step-by-step explanation:
Convert 1 3/12 into an improper fraction which is 5/4
Then add it with 9/12
5
/4 + 9
/12
(5 × 12) + (9 × 4)
---------------------------
4 × 12
= 96/48
= 96 ÷ 48
-------------------
48 ÷ 48
= 2
2 is your answer hope this helps :)
Answer:
2 feet
Step-by-step explanation:
To find the total amount of snow that fell, we add
1 3/12 + 9/12
add the fractions
3/12+9/12 = 12/12 =1
Add the whole numbers
1 plus the whole number from the fraction
1+1 =2
Which of the following best explains the value of sinä on the u
sual holnw?
carol invests 6250 at a rate of 2 per year compound interest calculate the total amount carol has after 3 years
Answer:
$6,632.55
Step-by-step explanation:
What a coincidence I was doing the same question. Ok so you should know about the Compound Interest formula which is A=P (1+r/100) n. (n) is btw in the exponent.
A= ?
P=6250
r=2
n=3
Anyways we will input everything we are given so it will be:
A=6250(1+2/100)3
Since A is final amount - it will be our answer which is $6,632.55
Final answer:
Carol invested $6,250 at a rate of 2% per year compound interest. After 3 years using the compound interest formula A = P(1 + r/n)^(nt), her investment will grow to $6,632.55.
Explanation:
Carol invested $6,250 at a rate of 2% per year compound interest. To calculate the total amount Carol has after 3 years, we can use the formula:
A = P(1 + r/n)^(nt)
Where:
A is the amount of money accumulated after n years, including interest. P is the principal amount (the initial amount of money). r is the annual interest rate (decimal). n is the number of times that interest is compounded per year. t is the time the money is invested for in years.
Since the interest is compounded yearly, n will be 1. Assuming the 2% interest rate is already in decimal form (0.02), and the time is 3 years, we substitute these values into the formula:
A = 6250(1 + 0.02/1)^(1*3)
A = 6250(1 + 0.02)^3
A = 6250(1.02)^3
A = 6250 * 1.061208
A = $6632.55
Therefore, after 3 years, Carol's investment will have grown to $6632.55.
make b the subject of the formula a = *square root* b+6
The required formula with b subject is [tex]b = a^{2} - 6[/tex].
Given that ,
a is the subject of the formula,
[tex]a = \sqrt{ b + 6}[/tex]
We have to make b is the subject for the formula,
[tex]a = \sqrt{ b + 6}[/tex]
Squaring both the sides,
[tex]a^{2} = b + 6[/tex]
[tex]b = a^{2} - 6[/tex]
Hence , The required formula with b subject is [tex]b = a^{2} - 6[/tex]
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To make b the subject of the formula a = √(b+6), you need to isolate b on one side of the equation. The solution is b = a² - 6.
Explanation:To make b the subject of the formula a = √(b+6), we need to isolate b on one side of the equation. Here are the steps:
Square both sides of the equation to remove the square root: a² = b + 6Subtract 6 from both sides: a² - 6 = bTherefore, b = a² - 6.
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Which is the largest: 27/30, 28/32, 38/40, 36/39, 75/85
I need help with this question please?
ANSWER ASAP!!!!!!!!!
The fish is 2.25 ft above the water surface.
Step-by-step explanation:
Step 1: Given expression for height of the fish above the water surface, y = -16x² + 12x where x is time in seconds. Find height after 0.375 seconds⇒ y = -16(0.375)² + 12 × 0.375
= -2.25 + 4.5
= 2.25 ft
The graph below shows a system of equations:
The x-coordinate of the solution to the system of equations is _____
Answer:
the x-coordinate is 1 in the graph
Marcus has 824 marbles and wants to put marbles into 5 bags to give as gifts. Marcus knows he cannot divide the marbles evenly, but he wants to use as many of the marbles as possible, while making sure there is the same amount in each bag. How many marbles will be in each bag Please Explain.
Answer:
there will be 164 marbles in each bag
Step-by-step explanation:
The question is simply asking you to divide the total number of marbles by five; for each bag. 824/5= 164.8 and 164.8 rounded down; (underline means important), is 164 marbles.
Answer:
164
Step-by-step explanation:
How many values are in the range 35 to 95?
62
61
60
59
Answer:
Option B, 61
Step-by-step explanation:
Step 1: Find the range
To find the range, subtract the lowest number from the highest number.
Example: 1, 50
What is the highest number: 50
What is the lowest number: 1
50 - 1 = 49
Problem: 96, 35
What is the highest number: 96
What is the lowest number: 35
96 - 35
61
Answer: Option B, 61
Answer:
Only one value is in the range,
61
Step-by-step explanation:
Calculate range by subtracting the smaller value from the larger value
96 - 35 = 61
Only one of the given options corresponds with the solution of the range, which is 61, or the second option.
Hope this helps :)
A flower garden is shaped like a circle. Its diameter is 36 yd. A ring-shaped path goes around the garden. The width of the path is 5 yd.
The gardener is going to cover the path with sand. If one bag of sand can cover 4 yd", how many bags of sand does the gardener need? Note that sand comes
only by the bag, so the number of bags must be a whole number. (Use the value 3.14 for n.)
Answer:
3
Step-by-step explanation:
subtract six hundred fifty three thousand from two million.
Answer:
2,000,000- 653,000= 1,347,000
Step-by-step explanation:
first write this in a equation with numbers
2,000,000- 653,000
million = 1,000,000
hundred thousand= 100,000
now solve the equation
2,000,000- 653,000= 1347000
DIUILUUUUUUUUULIC POLL
8
Stephanie is paid $1898 per fortnight and Tahlia $3821 per month. Calculate each person's
equivalent annual income. Who earns more per week and by how much?
1
.
1
L
ol
Final answer:
Stephanie's annual income is $49,348, while Tahlia's is $45,852, making Stephanie's weekly earnings $67.61 higher than Tahlia's. Stephanie earns $949.38 per week, and Tahlia earns $881.77 per week.
Explanation:
To calculate each person's equivalent annual income, we must standardize their earnings to a common time frame. We consider a year to have 26 fortnights and 12 months.
Stephanie's Annual Income
Stephanie is paid every fortnight, so we multiply her fortnightly income by the number of fortnights in a year:
$1898 per fortnight x 26 fortnights per year = $49,348 per year.
Tahlia's Annual Income
Tahlia is paid monthly, so we multiply her monthly income by the number of months in a year:
$3821 per month x 12 months per year = $45,852 per year.
To determine who earns more per week, we divide the annual income by the number of weeks in a year (52). Stephanie earns $949.38 per week ($49,348 / 52), while Tahlia earns $881.77 per week ($45,852 / 52). Stephanie earns more per week by:
$949.38 - $881.77 = $67.61.
Therefore, Stephanie earns $67.61 more than Tahlia per week.
HELP. Y=-3x + 6
Y=2x - 4
How many solutions can be found for the system of linear equations represented on the graph?
A) no solution
B) one solution
C) two solutions
D)infinitely many solutions
Answer:
one solutions
Step-by-step explanation:
graph both points on a graph if they cross you have one solution, if they never meet you have no solution and if it's one line you have infinite solutions
Final answer:
The two given linear equations y = -3x + 6 and y = 2x - 4 have different slopes, which means they will intersect at exactly one point, indicating that there is one solution to the system.
Explanation:
To find out how many solutions can be found for the system of linear equations represented on the graph, we can observe the slopes and y-intercepts of the given equations. The two equations are:
y = -3x + 6
y = 2x - 4
These are both linear equations in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The first equation has a slope of -3 and the second has a slope of 2. Because the slopes are not equal, these lines are not parallel and will, therefore, intersect at one point. When two lines intersect at exactly one point, the system of equations has one solution.
Moreover, since they intersect, they do not have the same line, so they do not have infinitely many solutions. Therefore, the correct answer is one solution (B).
PLEASE ANSWER ASAP!
Dylan solved an inequality to determine the amount of lemonade, in cups, that fit in a cooler already containing ice and lemon wedges. His solution is graphed on the number line below.
How should the graph be interpreted? Select two options.
1. at most 19 cups
2. 19 cups or less
3. more than 19 cups
4. a minimum of 19 cups
5. no fewer than 19 cups
Answer:
1 + 2
Step-by-step explanation:
When we look at the number line, we can see that the inequality is:
x ≤ 19
This means that all values of "x", must be equal to or less than 19.
To find the correct answer choices, we must keep that equation in mind.
1. at most 19 cups - this answer choice does work, because it shows that 19 is the limit (which is what our inequality represents)
2. 19 cups or less - this answer choice works as well because it shows that 19 is the maximum and all other values of "x" must be below that.
3. more than 19 cups - this goes against our inequality, since "x" can't exceed 19. This means that this answer choice must be incorrect.
4. a minimum of 19 cups - this answer choice also cannot be correct since it shows that "x" can go over 19 (which we know is false).
5. no fewer than 19 cups - this is also wrong because it wants "x" to go over the value of 19, which it can't do.
Answer:
Step-by-step explanation:
A and b
•
If AB = 4x + 9, BC = 5x + 2, and AC = 56, find the measure of AB and BC.
Answer:
Step-by-step explanation:
Given that
AB=4x+9
BC=5x+2
Then, AC=56
From vector
AC=AB+BC
Then,
56=4x+9+5x+2
56=9x+11
Subtract 11 from both sides
56-11=9x+11-11
45=9x
Divide both sides by 9
45/9=9x/9
5=x
Then, x=5
Now,
1. AB=4x+9, x=5
AB=4(5)+9
AB=20+9
AB=29
2. Also
BC=5x+2
BC=5(5)+2
BC=25+2
BC=27
What does the value of y have to be so that
(3, y) and (-5,6) have a slope of -1 between them?
Answer:
y= -2
Step-by-step explanation:
Please see attached picture for full solution.
(From the 4th to 5th line, I multiplied both sides by 8)
The sum of three consecutive odd numbers is 123 what is the smallest of the three numbers
Answer:
39
Step-by-step explanation:
Let the three consecutive odd numbers be:
x+2, x+4, x+6.
The sum of the consecutive numbers is 123 i.e
x+2 + (x+4) + (x+6) = 123
x + 2 + x + 4 + x + 6 = 123
3x + 12 = 123
Collect like terms
3x = 123 — 12
3x = 111
Divide both side by the coefficient of x i.e 3
x = 111/3
x = 37
Now let us find the value of the three odd numbers. This is illustrated:
1st : x + 2 = 37 + 2 = 39
2nd : x + 4 = 37 + 4 = 41
3rd : x + 6 = 37 + 6 = 43
The smallest of the three consecutive odd numbers is 39
Can you please show me what 56%/43% is?
Answer: 1.3
Step-by-step explanation:
Step 1: convert to decimal
56% = 56/100 = 0.56
43% = 43/100 = 0.43
Step 2; divide the values
0.56/0.43= 1.3
I hope this helps.
What are the x-intercepts of the graph of the function below?
y= x2 + 2x-15
O A. (5,0) and (3,0)
O B. (-5,0) and (-3,0)
O C. (-50) and (3,0)
OD. (5,0) and (-3,0)
Answer:
C. (-5,0) and (3,0)
Step-by-step explanation:
y= x² + 2x-15
y = 0
x² + 2x-15 = 0
(x - 3) (x + 5) = 0
x = 3 or x = -5
The x-intercepts of the graph of the function are (-5,0) and (3,0).
Option C is the correct answer.
What is a function?A function has an input and an output.
A function can be one-to-one or onto-one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To find the x-intercepts of the graph of the function,
We need to set y = 0 and solve for x.
So we have:
x² + 2x - 15 = 0
Factoring this quadratic equation.
(x + 5) (x - 3) = 0
Setting each factor equal to zero.
x + 5 = 0 or x - 3 = 0
Solving for x.
x = -5 or x = 3
Therefore,
The x-intercepts of the graph of the function are (-5,0) and (3,0).
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0.1 percent as fraction in simplest form ?
Answer:
1/10
Step-by-step explanation:
Answer:
1/10
Step-by-step explanation:
In its simplest form, expressing the decimal as a fraction to its simplest form will give one over ten.
Therefore if you divide 1/10, the answer will be 0.1. it is also called one-tenth.
Although there are other expressions or fractions that give 0.1, but 1/10 is the simplest of them all, and the question specified to use it in its simplest form.
Which property is illustrated in this equation?
32 • 15 = (3210) + (325)
A. Associative Property
B. Commutative Property
C. Distributive Property
D. Identity Property
Answer:
c)
Step-by-step explanation:
c). Distributive Property
32*15 = 32*(10+5) = 32*10 + 32*5
=320 + 160 = 480
The product of two consecutive odd integers is equal to 30 more than the first. Find the integers.
This is solving quadratic word problems.
Answer:
The integers are
5 and 7
Step-by-step explanation:
Let
x ---> the first consecutive odd integer
x+2 ---> the second consecutive odd integer
we know that
The algebraic expression that represent this situation is
[tex]x(x+2)=x+30[/tex]
solve for x
[tex]x^2+2x=x+30\\x^2+2x-x-30=0\\x^2+x-30=0[/tex]
Solve the quadratic equation
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} +x-30=0[/tex]
so
[tex]a=1\\b=1\\c=-30[/tex]
substitute in the formula
[tex]x=\frac{-1\pm\sqrt{1^{2}-4(1)(-30)}} {2(1)}[/tex]
[tex]x=\frac{-1\pm\sqrt{121}} {2}[/tex]
[tex]x=\frac{-1\pm11} {2}[/tex]
[tex]x=\frac{-1+11} {2}=5[/tex]
[tex]x=\frac{-1-11} {2}=-6[/tex] ---> is not a odd integer
For x=5
The numbers are
[tex]x=5\\x+2=7[/tex]
so
5 and 7
The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 A cube of gold weighs 652 grams. Calculate the length of the edge of the cube in centimeters. Answer with two decimal places.
The length of the edge of the cube is 3.23 cm .
Step-by-step explanation:
We have , The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 or [tex]y = 19.3x^3[/tex] . A cube of gold weighs 652 grams i.e. y = 652 . Let's calculate value of x from above data:
[tex]y = 19.3x^3[/tex]
⇒ [tex]y = 19.3x^3[/tex]
⇒ [tex]652= 19.3x^3[/tex]
⇒ [tex]19.3x^3=652[/tex]
⇒ [tex]\frac{19.3}{19.3}x^3=\frac{652}{19.3}[/tex]
⇒ [tex]x^3=\frac{652}{19.3}[/tex]
⇒ [tex]\sqrt[\frac{1}{3} ]{x^3} = \sqrt[\frac{1}{3} ]{\frac{652}{19.3}}[/tex]
⇒ [tex]({x^3})^\frac{1}{3} =({\frac{652}{19.3}})^\frac{1}{3}[/tex]
⇒ [tex]x =(33.78)^\frac{1}{3}[/tex]
⇒ [tex]x =3.23[/tex]
Therefore, the length of the edge of the cube is 3.23cm.
Which of the following expressions are equivalent to 4+(14-2)4+(14−2)4, plus, left parenthesis, 14, minus, 2, right parenthesis?
Choose 3 answers:
Choose 3 answers:
(Choice A)
A
4-(-14-2)4−(−14−2)4, minus, left parenthesis, minus, 14, minus, 2, right parenthesis
(Choice B)
B
(4-14)-2(4−14)−2left parenthesis, 4, minus, 14, right parenthesis, minus, 2
(Choice C)
C
4-(-14)-(2)4−(−14)−(2)4, minus, left parenthesis, minus, 14, right parenthesis, minus, left parenthesis, 2, right parenthesis
(Choice D)
D
4+14+(-2)4+14+(−2)4, plus, 14, plus, left parenthesis, minus, 2, right parenthesis
(Choice E)
E
-(-4-14)-2−(−4−14)−2
To simplify the expression 4 + (14 - 2), subtract 2 from 14, then add 4 to get the equivalent expression. The three equivalent expressions are: 20, -12, and 16.
To simplify the expression 4 + (14 - 2), we need to perform the operations inside the parentheses first. This means subtracting 2 from 14, which gives us 12. Then, we add 4 to 12, resulting in 16. Therefore, the expression 4 + (14 - 2) is equivalent to 16.
The three expressions that are equivalent to 4 + (14 - 2) are:
A. 4 - (-14 - 2) = 4 - (-16) = 4 + 16 = 20
B. (4 - 14) - 2 = -10 - 2 = -12
C. 4 - (-14) - (2) = 4 + 14 - 2 = 16