The question is worded a bit strangely (in my opinion anyway), but I think your teacher wants you to describe how exponents work.
Let's say we had the expression [tex]5^3[/tex]
The base is 5 as its the bottom most value (think of something like the base of a tree or building). The exponent is 3.
The exponent of 3 tells the reader to multiply the base 5 by itself 3 times like so
[tex]5^3 = 5*5*5 = 125[/tex]
With larger exponents, it becomes more tedious to write out all the repeated multiplications, which is why many calculators have an exponent button to save time.
An exponent signifies how many times a base is multiplied by itself. The expression "5 squared" (5²) means 5 x 5 = 25. Similarly, "5 cubed" (5³) means 5 x 5 x 5 = 125. This concept of exponentiation is essential in mathematics for representing repeated multiplication of a number.
An exponent indicates the number of times a base is multiplied by itself. For example, the exponent "2" in the expression "5²" means that the base "5" is multiplied by itself, resulting in 5 x 5 = 25. This is also known as squaring a number. Similarly, an exponent of "3" denotes cubing, which means the base is multiplied by itself three times. For instance, 5³ equals 5 x 5 x 5, which equals 125.
It's also important to understand that when we talk about exponents, we are often referring to powers. If the base is "b" and the exponent is "n", then the expression can be written as bn, indicating a chain of multiplications of "b", "n" times. For instance, witnessing an expression like (10²)³, we multiply the exponents to get a new exponent (2 x 3 = 6), resulting in 10⁶.
The concept of exponents is a foundational element in various mathematical operations and is crucial for understanding more complex mathematical concepts.
Tamara has a $50 gift card to the theater. Each movie costs $8. She can decide how many movies to see by solving the inequality 50 – 8m ≥ 0. Which is the correct solution?
Answer: Second option.
Step-by-step explanation:
Given the following Inequality provided in the exercise:
[tex]50 - 8m \geq 0[/tex]
You need to solve for "m".
Then, you can follow the steps below in order to find the solution of the inequality:
Step 1: You must apply the Subtractrion property of Inequality and subtract 50 from both sides:
[tex]50 - 8m-(50) \geq 0-(50)\\\\- 8m \geq -50[/tex]
Step 2: Now you need to apply the Division property of Inequality and divide both sides of this inequality by -8 (Since you are dividing both sides by a negative number the direction of the inequality changes). Then, you get:
[tex]\frac{- 8m}{-8} \geq \frac{-50}{-8}\\\\m\leq \frac{25}{4}\\\\m\leq6.25[/tex]
Notice that this solution matches with the second option.
draw 5 angles so that ∟2 and ∟3 are acute vertical angles,∟ 1 and ∟2 are supplementary , ∟2 and ∟5 are complementary and∟ 4 and ∟5 are adjacent.
Answer:
Figure is attached:
Acute angles are angles whose measures are less than 90°, so it needs to be less than a right angle.
Vertical angles are angles formed by two intersecting lines. When these lines intersect they form 4 angles in the middle. They are called vertical when they are opposite of each other like the figure attached.
Supplementary angles are two angles that sum up to 180° or they make up a straight line.
Complementary angles are two angles that sum up to 90°.
Adjacent angles are angles that are next to each other.
In the problem above. How much money will be saved per year
Answer: i would help but i'm confused....what problem? can yhu attach it so i could help??! - Lexi@helps
Step-by-step explanation:
Solve for t: 3x8= t+15
Hey there!
I'm going to set up the equation slightly different.
[tex](3)(8)=t+5\\24=t+5\\t+15=24\\t+15-15=24-15\\t = 9 \checkmark[/tex]
Answer:
t = 9
Step-by-step explanation:
3x8 = t + 15
24 = t + 15
t = 24 - 15
t = 9
Yvette earns a $45,000 salary plus a 12% commission on any sales over $10,000. Last year Yvette made $30,000 in sales. How much did Yvette
earn in salary plus commission?
O A. $46,000
OB. $46,200
OC. $46,500
OD. $47,400
O E.
$48,600
Option D
The total earnings of Yvette is $ 47, 400
Solution:
Given that, Yvette earns a $45,000 salary plus a 12% commission on any sales over $10,000
Last year Yvette made $30,000 in sales
Subtract 10,000 from her sales to get the amount she earns commission on:
30,000 - 10,000 = 20,000
Since Yvette gets 12% commission
So amount earned as commission would be 12% of $20,000
[tex]\text{Commission}=20000\times \frac{12}{100}\\\\\text{Commission}=20000\times 0.12\\\\\text{Commission}=2400\left\\\\[/tex]
Yvette also gets a salary of $45,000, so Yvette's total earnings would be $45,000 plus $2,400
[tex]Total\ Earnings = 45000 + 2400 = 47400[/tex]
Thus total earnings of Yvette is $ 47, 400
Answer:
D
Step-by-step explanation:
solve for x: 12x-20=6(x-20)-9x
Answer:
Step-by-step explanation:
12x-20=6(x-20)-9x
Opening bracket
12x - 20 = 6x - 120 - 9x
Collecting like terms
12x - 6x + 9x = -120 + 20
15x = -100
Dividing by 15
15x/15 = -100/15
x = -20/3
x = - 6 2/3
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
12x - 20 = 6( x - 20) - 9x
pay attention to the brackets as you simplify.
Let's work on it:
12x - 20 = 6x - 120 -9x
Collecting like terms to further simplify the equation.
12x - 6x + 9x = -120 + 20
15x = -100
Let's make x the subject formula by dividing through by 15
Therefore:
x = -100 / 15
Divide through by 5
x = -20 / 3
Since nothing can easily divide through, we turn it to a mixed fraction
x = - 6 2/3
( Minus six whole number, two divided by three)
Find the distance from the point A(-2,3) to the line y=1/2x+1. Round your answer to the nearest tenth.
To find the distance from a point to a line, we can use the distance formula. For this problem, the distance from point A(-2,3) to the line y=1/2x+1 is approximately 2.5 units.
Explanation:To find the distance from a point to a line, we can use the formula for the distance between a point and a line. The formula is:
d = |Ax + By + C| / √(A^2 + B^2)
In this case, the equation of the line is y = (1/2)x + 1, which can be rewritten as 2x - y + 2 = 0. Plugging in the coordinates of point A in the equation, we get:
d = |(2 * -2) + (-1 * 3) + 2| / √((2^2) + (-1^2)))
After completing the calculation, rounding the answer to the nearest tenth, the distance from point A(-2,3) to the line y = (1/2)x + 1 is approximately 2.5 units.
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Each person that works at a company is given a 5-digit code. These employees must enter their codes on a keypad to enter and exit the office building. The company has 80 employees.
a) How many codes are possible if there are no restrictions?
b) What is the probability of someone entering a 5-digit code at random and gaining entry?
Answer:
A) 100000
B) 80/100000
Step-by-step explanation:
A) it is a simple matter of multiplying the possibilities of the digit it could be to the second one then to the third and so on and so forth
B) if a person were to enter a 5 digit code at random say it be 00000 then that person would have 80 out of a 100000 chance of unlocking the door as there are only 80 access codes that are correct
There are 100,000 possible 5-digit codes. The probability of a random 5-digit code granting access is 0.0008 or 0.08%.
Explanation:This problem involves combinatorics and probability.
a) If each digit of the 5-digit code can be any number from 0-9, then for each digit, 10 possibilities exist. Hence the total number of possibilities for a 5-digit code would be 10*10*10*10*10, which is 100,000. So there are 100,000 possible 5-digit codes.
b) Probability is defined as the number of ways an event can occur over the total number of outcomes. If each 5-digit code is unique and assigned to only one employee, with 80 employees, there are 80 valid codes. Therefore, the probability of someone entering a 5-digit code at random and gaining entry would be 80 (the number of successful outcomes) divided by 100,000 (the total number of possible outcomes), which is 0.0008 or 0.08%.
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Look at the following sequence.
128, 320, 800, 2000, . . .
If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose “not geometric.
Answer:
geometric sequence
Step-by-step explanation:
If the sequence is geometric then there must be a common ratio r between consecutive terms, that is
320 ÷ 128 = 2.5
800 ÷ 320 = 2.5
2000 ÷ 800 = 2.5
Since there is a common ratio r = 2.5 between consecutive terms.
Then the sequence is geometric
Which describes a method for solving systems of equations in which you
plug in an expression for one variable written in the terms of the other?
Substitution method is used for solving systems of equations in which you plug in an expression for one variable written in the terms of the other
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The method described is called substitution method.
In the substitution method, we start by solving one equation for one of the variables in terms of the other variable.
Then, we substitute the expression we found for that variable into the other equation.
This allows us to solve for the other variable.
Finally, we substitute the value we found for that variable back into one of the original equations to solve for the first variable.
Hence, substitution method is used for solving systems of equations in which you plug in an expression for one variable written in the terms of the other
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If p = 19 then
what does the
following
expression:
(2p - 10) = 2
equals?
Answer:
14
Step-by-step explanation:
(2(19)-10)=2
(38-10)=2
(28)=2
÷2. ÷2
14
solve the equation
[tex] \frac{3}{8}x - 17 = 10[/tex]
Answer:
x = 72
Step-by-step explanation:
To solve for 'x', isolate it. This means to keep 'x' on one side of the equal sign, while moving the other numbers to the other side. The numbers on the other side will tell you what 'x' equals to.
When 'moving' a number to the other side, you cancel it out where it originally is by doing reverse operations. (Reverse operation pairs are addition/subtraction and division/multiplication). To keep an equation balanced, what you do to one side you have to do to the other.
[tex]\frac{3}{8}x-17=10[/tex] Keep 'x' on the left and move everything over.
[tex]\frac{3}{8}x-17+17=10+17[/tex] Add 17 to both sides. "-17" cancels out on the left.
[tex]\frac{3}{8}x=27[/tex] Simplified right side
[tex]\frac{3}{8}x/\frac{3}{8}=27/\frac{3}{8}[/tex] Because 3/8 originally multiplies with 'x', do the reverse: divide both sides by 3/8.
[tex]x=27/\frac{3}{8}[/tex] To divide a fraction, change to multiplication and flip the fraction's top and bottom numbers.
[tex]x=27*\frac{8}{3}[/tex] Combine the factors into one fraction.
[tex]x=\frac{27*8}{3}[/tex] Multiply 27 by 8 in the numerator.
[tex]x=\frac{216}{3}[/tex] Simplify the fraction by dividing top by bottom.
[tex]x=72[/tex] Final answer, solved for 'x'
a restaurant automatically add an 18% tip to the bill. if the tip was $9, what was the bill before the tip was added, in dollars ?
Answer:
$50
Step-by-step explanation:
If the tip was $9, you can find the total price by dividing 9 by .18. .18 is 18% but as a decimal (move to the left two decimal places). 9/.18 = 50.
You can also check the answer by finding the 18% tip of $50. 50*.18=9.
Which inference can be made about the cars?
Answer:
Bout which cars?
Step-by-step explanation:
Sorry, but I think you've missed out a part of the question
Choose the equation that represents this situation. Use n to represent the
number of lawns mowed and tto represent total earnings.
Carson earns $15 for each lawn he mows. What are his total earnings?
Answer:
Step-by-step explanation:
He earns $15n
answer asap i will make you brainliest!!!
ers as the elements in the rows near the bottom.
C.
have higher atomic numbers than the elements in the rows near the bottom.
D.
have lower atomic numbers than the elements in the rows near the bottom.
Answer:
Step-by-step explanation:
What is the following quotient 2/13+11
Answer:
[tex]\frac{145}{13}[/tex]
Step-by-step explanation:
2÷13+11
= (2÷13)+11
= (2÷13)+(11×13÷13)
=(2÷13)+(143÷13)
= 145÷13
.
Writing the Equation of
a
What is the equation of a line that is parallel to the line 2x + 5y = 10 and passes through the point (-5, 1)? Check all
that apply.
y=-2x-1
2x + 5y = -5
y=-2x-3
2x + 5y = -15
1= -2.(x + 5)
Answer: 2x + 5y = -5
Step-by-step explanation:
Two lines are said to be parallel if they have the same slope.
The equation of the line given :
2x + 5y = 10
To find the slope , we will write it in the form y = mx + c , where m is the slope and c is the y - intercept.
2x + 5y = 10
5y = -2x + 10
y = -2/5x + 10/5
y = -2/5x + 2
This means that the slope is -2/5 ,the line that is parallel to this line will also have a slope of -2/5.
using the formula:
[tex]y-y_{1}[/tex] = m ([tex]x-x_{1}[/tex] ) to find the equation of the line , we have
y - 1 = -2/5(x -{-5})
y - 1 = -2/5 ( x + 5 )
5y - 5 = -2 ( x + 5 )
5y - 5 = -2x - 10
5y + 2x = -10 + 5
therefore :
2x + 5y = -5 is the equation of the line that is parallel to 2x + 5y = 10
Answer: 2x + 5y = -5
Step-by-step explanation:please see attachment for explanation
1. Jason was asked to factor 25x2 - 1 on his algebra test. Which of the following
could best reflect Jason's answer?
The best reflection of Jason's answer among the given options is option : [tex]\((5x + 1)(5x - 1)\).[/tex]
The correct option is (H).
To factor [tex]\(25x^2 - 1\)[/tex], Jason likely used the difference of squares formula. This formula states that for any expressions [tex]\(a\) and \(b\), \(a^2 - b^2\)[/tex] can be factored as [tex]\((a + b)(a - b)\).[/tex]
In our case, [tex]\(a = 5x\) and \(b = 1\)[/tex]. So, we apply the difference of squares formula:
[tex]\[25x^2 - 1 = (5x)^2 - 1^2\][/tex]
[tex]\[= (5x + 1)(5x - 1)\][/tex]
This factorization is a result of recognizing that [tex]\(25x^2 - 1\)[/tex] can be written as [tex]\((5x)^2 - 1^2\),[/tex] fitting the difference of squares pattern.
Now, let's compare Jason's answer to the options given:
- Option F: [tex]\((5x-1)(5x-1)\)[/tex] is not correct. This represents the square of [tex]\(5x - 1\),[/tex] not a difference of squares.
- Option G: [tex]\((5x+1)(5x+1)\)[/tex]is not correct. This also represents the square of [tex]\(5x + 1\),[/tex] not a difference of squares.
- Option H:[tex]\((5x+1)(5x-1)\)[/tex] is correct. This represents the correct factorization using the difference of squares formula.
- Option J: Prime. This is incorrect because [tex]\(25x^2 - 1\)[/tex] can indeed be factored as [tex]\((5x + 1)(5x - 1)\).[/tex]
Therefore, the best reflection of Jason's answer among the given options is option H: [tex]\((5x + 1)(5x - 1)\).[/tex]
complete question given below:
Jason was asked to factor 25x^2-1 on his algebra test. Which of the following could best reflect Jason's answer?
F. (5x-1)(5x-1)
G. (5x+1)(5x+1)
H .(5x+1)(5x-1)
J .Prime
to prove that LMN~XYZ by the SSS similarly theorem using the information provided in the diagram, it would be enough additional information to know that.
a) LM is 3 units and XZ is 5 units
b) LM is 4 units and XZ is 6 units
c) LM is 5 units and XZ is 3 units
d) LM is 6 units and XZ is 4 units
I believe the answer would be B because it makes the most sense putting the figures scaled in my head with the already designated lengths
To prove that LMN~XYZ by the SSS similarly theorem , the measure of sides are LM is 4 units and XZ is 6 units
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be ΔLMN
Let the second triangle be ΔXYZ
Now , the corresponding sides are
LM / XY = LN / XZ
On simplifying , we get
The corresponding sides of similar triangles are in the same ratio
So , LM is 4 units and XZ is 6 units
Hence , the triangles are similar by SSS theorem
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N=2pt3q2
Make p the subject
Answer:P=N/(2t3q2)
Step-by-step explanation:
N=2pt3q2
Divide both sides by 2t3q2
N/(2t3q2)=(2pt3q2)/(2t3q3)
N/(2t3q2)=p
Model 55% during a 10-by-10 grid
The correct answer is that 55 squares on a 10-by-10 grid would be shaded to represent 55%.
To solve this problem, we need to calculate the total number of squares on a 10-by-10 grid and then determine what 55% of that total would be.
First, we calculate the total number of squares on the grid:
[tex]\[ \text{Total squares} = 10 \times 10 \\\[ \text{Total squares}= 100 \][/tex]
Next, we find 55% of the total number of squares:
[tex]\[ \text{Number of shaded squares} = \frac{55}{100} \times 100 \][/tex]
[tex]\[ \text{Number of shaded squares} = 55 \][/tex]
So, to represent 55% on a 10-by-10 grid, we would shade 55 out of the 100 squares.
Answer the image. Also, you don't need to explain your answer.
Answer:
5G/10
Step-by-step explanation:
What is the zero of the function below?
f(x) =
[tex] 3\sqrt{x + 3} - 6[/tex]
Answer:
Step-by-step explanation:
[tex]3\sqrt{x+3}-6=0\\\\3\sqrt{x+3}=6\\\\\sqrt{x+3}=\frac{6}{3}\\\\\sqrt{x+3}=2\\\\Takesquarebothsides,\\\\x+3=2^{2}\\\\x+3=4\\\\x=4-3\\\\x=1[/tex]
Practice
Simplify each expression by combining like terms.
1. 6x + 4x
2. – 5y + 2y
3. – 3m - 8(m + 1)
4. -81r - 2) + 6(r - 2) -
5. 9m - 7m + 13
b) Find the value of x. Show algebraic support.
hint: sum of the exterior angles is 360
Answer:
x = 16
Step-by-step explanation:
Given that the sum of the exterior angles is 360°
Sum the given exterior angles and equate to 360
47 + 93 + 46 + 3x + 62 + 4x = 360, that is
248 + 7x = 360 ( subtract 248 from both sides )
7x = 112 ( divide both sides by 7 )
x = 16
According to the histogram, how many people took the test?
Answer:
23
Step-by-step explanation:
you add all the numbers
The table shows values for functions f(x) and g(x) .
x f(x)=0.5x g(x)=−0.5x+1
−2 4 2
−1 2 32
0 1 1
1 12 12
2 14 0
What is the solution to f(x)=g(x) ?
Select each correct answer.
x=−2
x=−1
x = 0
x = 1
x = 2
Answer:x f(x)=0.5x g(x)=−0.5x+1
This implies that f(x)= 0.5 and
g(x)= -0.5x + 1
-0.5x + 1= 0.5
-0.5x= 0.5-1
-0.5x=-0.5
x= -0.5/-0.5
x=1
Step-by-step explanation:
Final answer:
To solve f(x) = g(x), set 0.5x equal to −0.5x + 1. Solve for x by combining like terms, which gives x = 1 as the solution.
Explanation:
To determine the solution to f(x) = g(x), we set the two functions equal to each other and solve for x.
The function f(x) is given by f(x) = 0.5x, and the function g(x) is given by g(x) = −0.5x + 1.
Setting f(x) equal to g(x), we have:
0.5x = −0.5x + 1
To solve for x, we'll combine like terms by adding 0.5x to both sides, which gives us:
0.5x + 0.5x = 11x = 1
When we divide both sides by 1, we get:
x = 1
So the solution to f(x) = g(x) is when x = 1.
Solve.
−35x+15>720
Drag and drop a number or symbol into each box to show the solution.
options:
< > -3/20, -1/4, 3/20, 1/4
Answer:
[tex]x<-\frac{1}{4}[/tex]
Step-by-step explanation:
The correct question is
Solve. −3/5x+1/5>7/20 Drag and drop a number or symbol into each box to show the solution
we have
[tex]-\frac{3}{5}x+\frac{1}{5} >\frac{7}{20}[/tex]
Solve for x
Multiply by 20 both sides
[tex]-12x+4 >7[/tex]
subtract 4 both sides
[tex]-12x >7-4[/tex]
[tex]-12x >3[/tex]
divide by -12 both sides
Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol
[tex]x<-\frac{3}{12}[/tex]
simplify
[tex]x<-\frac{1}{4}[/tex]
Answer:
x < 1/4
Step-by-step explanation:
you're supposed to add or subtract the constant, and then do the same to the other constant, them bring down the coefficient and you'll get your answer.
hope this helps
What is the vertex of the function f (x) = x2 - 10x?
(5,-25)
(5.-75)
(-5,75)
(-5,25)
Option A
The vertex is (h, k) = (5, -25)
Solution:
Given function is:
[tex]f(x) = x^2-10x[/tex]
The vertex form is given as:
[tex]y = a(x-h)^2+k[/tex]
where (h, k) is the vertexRewrite the equation in vertex form
[tex]f(x) = x^2-10x[/tex]
Complete the square for [tex]x^2-10x[/tex]
Use the form [tex]ax^2+bx+c[/tex] to find the values of a, b, c
a = 1 , b = -10, c = 0
Consider the vertex form of a parabola
[tex]a(x+d)^2+e[/tex]
Substitute the values of a and b into the following formula to find "d" :
[tex]d = \frac{b}{2a}\\\\d = \frac{-10}{2 \times 1}\\\\d = -5[/tex]
Find the value of "e" using the formula,
[tex]e = c - \frac{b^2}{4a}\\\\e = 0 - \frac{(-10)^2}{4 \times 1}\\\\e = -25[/tex]
Substitute the value of a, d, e into vertex form
[tex]a(x+d)^2+e\\\\1(x-5)^2-25\\\\(x-5)^2-25[/tex]
Set y equal to above equation
[tex]y = (x-5)^2-25[/tex]
Compare the above equation with vertex form
[tex]y = a(x-h)^2+k[/tex]
[tex]y = (x-5)^2-25[/tex]
We find, h = 5 and k = -25
Thus the vertex is (h, k) = (5, -25)