Answer:
We typically construct graphs with the input values along the horizontal axis and the output values along the vertical axis. The most common graphs name the input value x and the output value y , and we say y is a function of x , or y=f(x) y = f ( x ) when the function is named f .
Step-by-step explanation:
1. In questions 18-1d, choose Yes or No
to tell if the number 1/2 will make each
equation true.
1a. 1/18 + 1/2 = 10/18 yes or no
1b. 1/3 + 1/2 =1/5 yes or no
1c. 5/8 - 1/2 = 1/8 yes or no. 1d. 3/4 - 1/2 = 1/4 yes or no
Answer:
Yes, No, Yes, Yes
Step-by-step explanation:
1a = Yes
1b= No
1c= Yes
1d =Yes
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simplify: (8^2/3)^4
Answer:
[tex](8^{\frac{2}{3} } )^{4} = 256[/tex]
Step-by-step explanation:
Given
[tex](8^{\frac{2}{3} } )^{4}[/tex]
Required
Simplify
To simplify this, we apply law of indices but first we start by solving the expression in bracket.
8 =2 * 2 * 2
8 = 2³
So, we substitute 2³ for 8
[tex](8^{\frac{2}{3} } )^{4}[/tex] becomes
[tex]((2^{3})^{\frac{2}{3} } )^{4}[/tex]
From law of indices
[tex]a^{n} = (a^{m})^{\frac{n}{m} }[/tex] ==> [tex](a^{m})^{\frac{n}{m} } = a^{n}[/tex]
So, [tex](2^{3})^{\frac{2}{3} } = 2^{2}[/tex]
At this point we have
[tex]((2^{3})^{\frac{2}{3} } )^{4}[/tex] = [tex](2^{2})^{4}[/tex]
Also, from law of indices
[tex](a^{m})^{n} = a^{m.n}[/tex]
So,
[tex]((2^{3})^{\frac{2}{3} } )^{4}[/tex] = [tex](2^{2})^{4}[/tex]
[tex](2^{2})^{4} = 2^{2*4}[/tex]
[tex](2^{2})^{4} = 2^{8}[/tex]
[tex](2^{2})^{4} = 256[/tex]
Hence,
[tex](8^{\frac{2}{3} } )^{4} = 256[/tex]
The length of a rectangle garden is represented by 3x - 4 and the width is represented by 2x - 5. Which of the following represents the total area of the garden?
Answer:
area of rectangle garden=6x^2-23x+20
Step-by-step explanation:
given lengtarden=l=3x-4
width of rectangle garden=b=2x-5
area of rectangle garden=a=lb
=(3x-4)(2x-5)
=6x^2-15x-8x+20
=6x^2-23x+20
area of rectangle garden=6x^2-23x+20 answer
A new pair if shoes will cost you $86 if you buy them on black friday. They will be dicounted 45%. How much will you save if you wait until black Friday
Answer:
saving amount=$38.7
Step-by-step explanation:
given cost price=$86
discount on black friday=45%
selling price=cost price(1-discount%)
selling price=86(1-[tex]\frac{45}{100}[/tex])
selling price=86([tex]\frac{55}{100}[/tex])
selling price=$47.3
saving amount=$86-$47.3=$38.7
saving amount=$38.7 answer
To find the savings on the shoes, multiply the original price by 45% to find the discount amount, then subtract it from the original price. The savings amount to $38.70.
You want to know how much you will save on a new pair of shoes that costs $86 if they are discounted by 45% on Black Friday. To calculate the savings, you need to calculate 45% of the original price and then subtract that amount from the original price.
Step-by-Step Calculation:
Calculate 45% of $86: (0.45 × $86 = $38.70).
Subtract the discount from the original price: ($86 - $38.70 = $47.30).
Therefore, if you wait until Black Friday, you will save $38.70 on the shoes.
15 people received an email and sent it to 3 different friends each, who in turn each sent it to 2 new people. What percent of the total number of people who received the e-mail are the original 15 people?
The original 15 people are 10% of the total number of people who received the mail.
Step-by-step explanation:
Given,
Number of people who received mail = 15
Mail further sent to 3 more friends;
Number of people who received mail from 15 people = 15*3 = 45 people
Number of people who received mail from 45 people = 45*2 = 90 people
Total number of people = 15+45+90 = 150 people
Now,
Percent of original people = [tex]\frac{Number\ of\ original\ people}{Total\ number\ of\ people}*100[/tex]
Percent of original people = [tex]\frac{15}{150}*100=10\%[/tex]
The original 15 people are 10% of the total number of people who received the mail.
Keywords: multiplication, percentage
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Marisa has 24 quarters to play games at a carnival. She only wants to play Ring Toss and Knock Down the Clown. If each game costs 3 quarters, and she plays Ring Toss at least three times, how many different ways can Marisa play the two games?
A. 12 ways
B. 8 ways
C. 6 ways
D. 4 ways
Answer:
D.
Step-by-step explanation:
24 divided by 3 is 8 divided by 2 because of the two games is 4
11. Higher Order Thinking Cora makes this
design with square and triangular tiles.
What is the area of the design? How did
you calculate your answer?
Step-by-step explanation:
With no photo of the design is imposible to calculate exactly the design area. However:
We know that the area of a square is:
[tex]A_{sq}=L^2[/tex] where L is the leght of the square's side
Also, the area a triangle is:
[tex]A_{tr}=\frac{h*b}{2}[/tex] where h is the height and b is the base (see the figure)
So, the total area, assuming that all square tiles are equal between them (the same for the triangular ones):
[tex]A_{total}=A_{sq}*n_{squaretiles}+A_{tr}*n_{triangtiles}[/tex]
Name two coordinates that are on the line: [tex]y = 12[/tex]
Name two coordinates that are on the line: [tex]x = -5[/tex]
Write the equation of the line that passes through the point (3, -5) and is perpendicular to the line x = 4.
60 Point offer.
(1, 12)
(420, 12)
Any coordinate with a y value of 12 lies on the line y = 12.
-----
(-5, 69)
(-5, 13)
Any coordinate with an x value of -5 lies on the line x = -5.
-----
Since the equation must be perpendicular to the line x = 4, which is a vertical line, it must also be written in the form x = a.
Since the x coordinate is 3, the equation of the line is simply x = 3.
Students were asked to write 6x^5 + 8x-3x^3+7x^7 in standard form
The standard form is [tex]7x^7 + 6x^5 -3x^3 + 8x[/tex]
Solution:
Given that we have to write the given equation in standard form,
[tex]6x^5 + 8x - 3x^3 + 7x^7[/tex]
In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to write
The terms are ordered from biggest exponent to lowest exponent
In the given equation,
[tex]6x^5 + 8x - 3x^3 + 7x^7[/tex]
7 is the highest exponent. So we write the standard form as,
[tex]7x^7 + 6x^5 -3x^3 + 8x[/tex]
Thus the terms are arranged from highest exponent to lowest exponent
The standard form of the polynomial in 6x^5 + 8x-3x^3+7x^7 is
7x^7 +6x^5+ 8x-3x^3 ].
What are polynomials in standard form?Polynomials can simply be explained as expressions of algebraic inclinations that bear variables and coefficients.
When polynomials are expressed in a way where the term with the highest degree is written first, the polynomial is said to be in its standard form.
Therefore, 7x^7 +6x^5+ 8x-3x^3 is the standard form
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Find the minimum or maximum value of f(x) = x2 + 6x +11 .
Answer:
Therefore the Minimum value of f(x) is 2.
Step-by-step explanation:
Given:
[tex]f(x)=x^{2} + 6x+11[/tex]
To Find:
minimum or maximum value of f(x)
Solution:
To find minimum or maximum value of f(x)
Step 1 . Find f'(x) and f"(x)
[tex]f(x)=x^{2} + 6x+11[/tex]
Applying Derivative on both the side we get
[tex]f'(x)=\dfrac{d(x^{2})}{dx}+\dfrac{d(6x)}{dx}+\dfrac{d(11)}{dx}[/tex]
[tex]f'(x)=2x+6+0[/tex]
Again Applying Derivative on both the side we get
[tex]f''(x)=\dfrac{d(2x)}{dx}+\dfrac{d(6)}{dx}[/tex]
[tex]f''(x)=2[/tex]
Step 2. For Maximum or Minimum f'(x) = 0 to find 'x'
[tex]2x+6=0\\\\2x=-6\\\\x=\dfrac{-6}{2}=-3[/tex]
Step 3. IF f"(x) > 0 then f(x) is f(x) is Minimum at x
IFf"(x) < 0 then f(x) is f(x) is Maximum at x
Step 4. We have
[tex]f''(x)=2[/tex]
Which is grater than zero
then f(x) is Minimum at x= -3
Therefore the Minimum value of f(x) is 2.
The minimum value is 2 when x = -3.
The minimum or maximum value of the function f(x) = x^2 + 6x +11, we need to complete the square or use the vertex formula for a quadratic function.
The function is a parabola that opens upwards (since the coefficient of the x2 term is positive). To complete the square, we group the x-terms and add and subtract the square of half the coefficient of x:
f(x) = (x^2 + 6x + 9) + 11 - 9
f(x) = (x + 3)^2 + 2
The minimum value of this parabola occurs at the vertex, which is (-3, 2).
What is the approximate area of the shaded sector in the circle shown below?
Answer:
I think it is B. 52.3
Answer:
13.1 in
Step-by-step explanation:
apex
If f(n) = (2n + 3)2 – 2n, which statement is true?
1. f(3) = 75
2. f(2)= 619
3. f(5) = 16
4. f(-4)= -3
Upon evaluating the function f(n) = (2n + 3)2 – 2n at the given values, the true statement is f(3) = 75.
Explanation:To determine which statement about the function f(n) = (2n + 3)2 – 2n is true, we must evaluate the function at the given values of n.
For f(3), we calculate (2·3 + 3)2 – 2·3 = (6 + 3)2 – 6 = 92 – 6 = 81 – 6 = 75.For f(2), we calculate (2·2 + 3)2 – 2·2 = (4 + 3)2 – 4 = 72 – 4 = 49 – 4 = 45, not 619.For f(5), we calculate (2·5 + 3)2 – 2·5 = (10 + 3)2 – 10 = 132 – 10 = 169 – 10 = 159, not 16.For f(-4), we calculate (2·(-4) + 3)2 – 2·(-4) = (-8 + 3)2 – (-8) = (-5)2 – (-8) = 25 + 8 = 33, not -3.Therefore, the statement that is true is f(3) = 75.
The following dot plot shows the pulse rates of runners after finishing a marathon
Which of the following data sets is represented in the dot plot?
A. {145, 165, 175, 1853}
B. {145, 150, 150, 152, 153, 160, 163, 165, 170, 170, 178, 179, 185}
C. {1, 5, 6, 1}
D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}
Answer: D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}
Step-by-step explanation:
In the given dot plot that is showing the pulse rates of runners after finishing a marathon, it can be seen that ,
There are 1 dot on 145, 5 dots on 165, 6 dots on 175 and 1 dot on 185.
So , the data sets is representing this would be {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185} , which has the same number of values as the dot plot.
Hence, the data set representing the dot plot would be :
D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}
The data set that represented by the dot plot given is:
D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}
In a dot plot, each data point in a data set is represented by a dot.
To find out the data set that is represented in the dot plot, list out the data points as plotted on the dot plot given.
Thus:
145 - 1 dot = 145165 - 5 dots = 165, 165, 165, 165, 165175 - 6 dots = 175, 175, 175, 175, 175, 175185 - 1 dot = 185Therefore, the data set that represented by the dot plot given is:
D. {145, 165, 165, 165, 165, 165, 175, 175, 175, 175, 175, 175, 185}
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What is its constant speed?
Answer:
So the Conclusion is that 4000 km/h is the constant speed.
Step-by-step explanation:
Given:
Time (hrs) | Distance (km)
0.5 | 2000
1 | 4000
1.5 | 6000
To Find:
Constant Speed:
Solution:
We know ,
[tex]Speed =\frac{Distance}{Time}[/tex]
For the first case we have
[tex]Speed=\frac{2000}{0.5} =4000\ km/h[/tex]
For the second case we have
[tex]Speed=\frac{4000}{1} =4000\ km/h[/tex]
For the third case we have
[tex]Speed=\frac{6000}{1.5} =4000\ km/h[/tex]
So the Conclusion is that 4000 km/h is the constant speed
Find the value of each of the following:
(i)
3.5 – 1.4 + 2.9
Answer:
[tex]3.5 - 1.4 + 2.9 \\ = 5[/tex]
hope this helps you
Answer:
3.5 - 1.4 + 2.9 = 5
Step-by-step explanation:
3. 5 - 1.4 + 2.9
At first, we will add 3.5 and 2.9 and then we will subtract 1.4 from the sum of 3.5 and 2.9.
So, 3.5 - 1.4 + 2.9
= (3.5 + 2.9) - 1.4
= 6.4 - 1.4
= 5
So, the value of 3.5 - 1.4 + 2.9 is 5.
Rewrite the expression with a rational exponent as a radical expression.
(4^2/5)^1/4
a.)^10sqrt4
b.)^4sqrt4
c.)^5sqrt4^2
d.)sqrt4^10
sqrt=square root
Answer:
First option is correct.
[tex]\sqrt[10]{4}[/tex]
Step-by-step explanation:
Given:
The given expression is [tex](4^{\frac{2}{5}})^{\frac{1}{4}}[/tex]
We write the given expression with a rational exponent as a radical expression such as.
[tex]=(4^{\frac{2}{5}})^{\frac{1}{4}}[/tex]
Simplify the above equation by multiplication of powers.
[tex]=(4^{\frac{2}{5}\times \frac{1}{4}})[/tex]
[tex]=(4^{\frac{1}{5}\times \frac{1}{2}})[/tex]
[tex]=(4^{\frac{1}{5\times 2}})[/tex]
[tex]=(4^{\frac{1}{10}})[/tex]
[tex]=\sqrt[10]{4}[/tex]
Therefore, The answer is [tex]=\sqrt[10]{4}[/tex].
Write an equation in point-slope form for the Line through the given point with the given slope.
(3,-8); m= -0.24
the equation is y-y1 =m (x,x1)
Solve 5n^2=5 with the quadratic formula
Answer:
n = 1
Step-by-step explanation:
First, rearrange the equation to standard form 0 = ax² + bx + c, when everything equals 0.
5n² = 5
5n² - 5 = 0
State the variables a, b and c.
a = 5; b = 0; c = -5
Substitute a, b, and c into the quadratic formula.
[tex]n = \frac{-b ±\sqrt{b^{2}-4ac} }{2a}[/tex]
[tex]n = \frac{-0 ±\sqrt{0^{2}-4(5)(-5)} }{2(5)}[/tex] Substitute
[tex]n = \frac{\sqrt{100} }{10}[/tex] Simplify inside the √ and bottom
[tex]n = \frac{10}{10}[/tex] Simplify the top
[tex]n = 1[/tex] Final answer
Therefore the solution is n = 1.
The quadratic formula usually is written with x, but it can be solved with any variable in standard form.
What does it mean to be a storehouse of value?
O
A. It serves as a valid currency.
O
B. The item is divisible and each unit is worth the same
O
C. Any item that can be traded for another item.
O
D. Any item that maintains its worth over time.
Final answer:
Being a storehouse of value means the item retains its worth over time, allowing it to be saved, stored, and reliably used later as a medium of exchange, like money or other assets with lasting value.
Explanation:
To be a storehouse of value means that the item, such as money, can retain its worth over some time. Unlike goods that may deteriorate, go out of style, or otherwise lose value, a storehouse of value allows individuals to save and store their wealth, retrieving it later with confidence that it will still be valuable.
Money is a common store of value since you do not need to spend it right away and can trust that even with the potential erosion of value due to inflation, it will remain a valid medium for future transactions.
Goods such as houses, artworks, or financial assets are also considered stores of value, but money is distinguished by its liquidity—being readily exchangeable for other goods or services. Although not perfect due to inflation, money's role as a medium of exchange in financial markets and aggregate expenditure makes it a convenient choice for storing value, especially when compared to the barter system.
In conclusion, option D - Any item that maintains its worth over time, accurately describes a storehouse of value.
True or false:
The solution, root, x-intercept, and zero of a problem are the same.
The terms 'solution,' 'root,' 'x-intercept,' and 'zero' are related in mathematics, but they are not always the same.
Explanation:The statement in the question is false. Though the terms 'solution,' 'root,' 'x-intercept,' and 'zero' are related in mathematics, they are not always the same.
In quadratic equations, for example, the 'solution' refers to the values of x that make the equation equal to zero, while 'root' refers to the values of x that satisfy the equation. 'X-intercept' refers to the points on the graph where the equation intersects the x-axis, while 'zero' refers to the x-values for which the equation equals zero.
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Ashely’s group was responsible for painting windows on the set of a school play. the group painted at this rate, how many windows would they paint for 3 hours?
Answer:
x:3
Step-by-step explanation:
Complete the statement to describe the expression abc + def.
The expression consists of
terms, and each term contains
factors.
Reng
Answer:
1) Two terms
2) Three factors
Step-by-step explanation:
We are given the following expression:
abc + def
We have to compete the given statement with the help of given expression.
The given expression consist of two terms, abc and def.Each term contain 3 factors:abc - 3 factors: a, b and c
def - 3 factors: d, e and f
The expression abc + def consists of two algebraic terms, each with three factors.
Explanation:The expression abc + def consists of two terms, and each term contains three factors. To elaborate, a term in algebra is a single part of an expression separated by plus or minus signs. The given expression has two distinct groupings separated by a plus sign: 'abc' and 'def'. Each of these groupings is considered a term. Moreover, within each term, there are three variables multiplied together, hence each term contains three factors. Understanding this fundamental concept of terms and factors is crucial for manipulating algebraic expressions, factoring, and solving equations more efficiently.
Add 20 7/12 + 4 2/10
Well ,I am not sure about the answer....
Triangle SQT is isosceles. The measure of angle STQ is 48°. Triangle S Q T is cut by perpendicular bisector T R. The lengths of line segments S R and R Q are congruent. Side lengths S T and T Q are congruent. Angles S T R and R T Q are congruent. What is the measure of Angle S T R? 24° 38° 48° 76°
Answer:
[tex]m\angle STR=24^o[/tex]
Step-by-step explanation:
we know that
[tex]m\angle STQ=m\angle STR+m\angle RTQ[/tex] ---> by addition angle postulate
we have
[tex]m\angle STQ=48^o[/tex] ----> given problem
[tex]m\angle STR=m\angle RTQ[/tex] ----> given problem
substitute in the expression above
[tex]48^o=2m\angle STR[/tex]
Divide by 2 both sides
[tex]m\angle STR=24^o[/tex]
Answer:
A.24
Step-by-step explanation:
Jillian ran for two weeks. During the first week, she ran 12 miles. During the next week, she ran 15 miles. What is the ratio of miles ran to total numbers of miles in both weeks?
What is 20 times 4 and add 5?
20 times 4 add 5 is
20*4+5
20*4=80
80+5=85
85 is your answer
Answer: 85.
Step-by-step explanation: 20 times 4 equals 80, add 5 to that makes 85.
And the equation in mathematical form: ( 20 X 4 ) = 80 + 5 = 85.
Hope this helps, if not, comment below please!!!!!
Dan and £9.10 per hour how much will he earn for five hours
Answer:
He will earn 45.50 in five hours.
Step-by-step explanation:
Answer:
45.5
Step-by-step explanation:
9.10*5
please help!!!
thank you will give brainlist!!!!
Answer:
The options 3, 4, and 5 are functions.
Step-by-step explanation:
If there is more than one value of y for a given single value of x then this is called a relation but not a function.
That geometrically means that if you can draw a vertical line that intersects the graph that is plotted from the given points that intersect the graph at more than one point then this graph is called a relation and not a function.
Here, in option one the points on the graph are given to be (6,-6), (-3,12), (6,-1) and (-8,13), which is not a function as there are two values of y for x = 6.
Now, in option two the points on the graph are given to be (0,0.5), (2,1), (1,2.5) and (0,2), which is also not a function as there are two values of y for x = 0.
Now, in option three the points on the graph are given to be (8,7), (7,8), (6,5) and (5,6). this can be a function.
Now, in option four the points on the graph are given to be (-2,7), (-3,9), (-5,9) and (-8,11). this can be a function.
Finally, in option five the points on the graph are given to be (-3,0), (-5,8), (-7,8) and (-9,0). this can be a function. (Answer)
fastas soon as possible............Find HCF
Answer:
[tex]y^4+1+\dfrac{1}{y^4}[/tex]
Step-by-step explanation:
Consider expression
[tex]y^7-\dfrac{1}{y^5}[/tex]
Rewrite it:
[tex]\dfrac{y^7\cdot y^5-1}{y^5}=\dfrac{y^{12}-1}{y^5}[/tex]
Consider the numerator:
[tex]y^{12}-1=(y^4)^3-1^3[/tex]
Use formula:
[tex]a^3-b^3=(a-b)(a^2+ab+b^2)[/tex]
So,
[tex](y^4)^3-1^3=(y^4-1)((y^4)^2+y^4\cdot 1+1^2)=(y^4-1)(y^8+y^4+1)[/tex]
Now,
[tex]\dfrac{y^7\cdot y^5-1}{y^5}=\dfrac{(y^4-1)(y^8+y^4+1)}{y^5}=\dfrac{y^4-1}{y}\cdot \left(y^4+1+\dfrac{1}{y^4}\right)[/tex]
Hence,
[tex]GCF(y^7-\frac{1}{y^5}, y^4+1+\frac{1}{y^4})=y^4+1+\dfrac{1}{y^4}[/tex]
Answer:
Step-by-step explanation:
Consider expression
Rewrite it:
Consider the numerator:
Use formula:
So,
Now,
Hence,
Answer:
Step-by-step explanation:
find the range of the function below if the domain is {-1,0,2}
f(x)=x^2 -2x +3
Answer:
{3, 6}
Step-by-step explanation:
f(x) is the same thing as y. f(x) or y are the values that are shown in the range.
The domain represents all possible values of x. Data must be in an (x, y) form, where any value of "y" would need a partner, "x".
Substitute all of the possible x-values into the formula to find all possible y-values (the range).
f(x) = x² - 2x + 3
f(-1) = (-1)² - 2(-1) + 3
f(-1) = 1 + 2 + 3
f(-1) = 6
f(x) = x² - 2x + 3
f(0) = (0)² - 2(0) + 3
f(0) = 0 - 0 + 3
f(0) = 3
f(x) = x² - 2x + 3
f(2) = (2)² - 2(2) + 3
f(2) = 4 - 4 + 3
f(2) = 3 Do not write repeated numbers
The possible y-values are 3 and 6.
Writ the range in set notation in the brackets {}. Order the numbers from least to greatest.
Range is {3, 6}.
The range of a function with a specified domain is equal to {3, 6}.
Range of the function:
The function is f(x) = x² - 2x + 3. Given the domain {-1, 0, 2}, we can find the corresponding range by evaluating the function at each point in the domain:
For x = -1: f(-1) = (-1)² - 2(-1) + 3 = 6.
For x = 0: f(0) = 0² - 2(0) + 3 = 3.
For x = 2: f(2) = 2² - 2(2) + 3 = 3.
The range of this function for the given domain is {3, 6}.