The ordered pairs of the function, h(x) = 3x², are (1,3) and (-1,3).
According to the question,
We have the following information:
h(x) = 3x²
Now, we will look at the options to know the correct option of ordered pairs.
Now, in the options, there are only two values of x (1 and -1). So, we will solve the given function using these two values and we will find the value of h(x).
h(x) = 3x²
h(1) = 3*1*1
h(1) = 3
So, the first ordered pair is (1,3).
When x = -1:
h(x) = 3x²
h(-1) = 3*-1*-1
h(-1) = 3
Now, the second ordered pair of the function is (-1,3).
Hence, the correct options are A and C.
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Timothy plans to add a railing parallel to a flight of stairs that goes down to the basement in his house. Each step has the dimensions shown in the sketch.
What will be the length of the railing?
The length of the railing is 105.81 inches.
Given,
The stair has 7 steps
The rise of each step = 8.5 inches
The tread of each step = 12.5 inches
Slope of each step = x
We have to find the length of the railing.
Length of railing = 7x
Then,
Slope of step, x can be determined using Pythagorean theorem.
Let rise be the height of the right angled triangle and tread be the base of the triangle
Then,
Hypotenuse= Slope, x = [tex]\sqrt{Rise^{2} + Tread^{2} }[/tex]
x = [tex]\sqrt{8.5^{2}+ 12.5^{2} }[/tex]
x = [tex]\sqrt{72.25 + 156.25}[/tex]
x = √228.5
x = 15.12 inches
That is,
The slope, x of one step is 15.12 inches
Now,
Length of the railing = 7x = 7 × 15.12 = 105.81 inches
Therefore,
The length of the railing is 105.81 inches.
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41 is 10 1/4% of what number
By the concept of percentage, 41 is [tex]10\frac{1}{4}[/tex] % of the number 400.
What is meant by percentage?The percentage is a comparative figure denoting one-hundredth of any quantity. One percent (symbolized as 1%), being the hundredth component, is represented as 100 percent, while 200 percent signifies twice the amount specified. Percent is derived from the Latin word per centum, which means "by the hundred." In the 16th century, the Latin expression was adopted by English. Later, it was shortened to % with a period in the end. The present one-word form % was created after the period was eliminated and the two elements were combined. In essence, percentages are fractions with a denominator of 100. The percent symbol (%) is placed next to a number to indicate that it is a percentage.
Let the number be x.
Then, according to the question
[tex]10\frac{1}{4}[/tex] can be written as 41/4
So,
41/400 × x = 41
41 x = 41 ×100
x =400
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If the p-value is 0.023 from a hypothesis test is compared to a significance level of 0.05, what conclusion would we make?
Group of answer choices
A) Accept the null hypothesis.
B) Reject the alternative hypothesis.
C) Fail to reject the null hypothesis.
D) Reject the null hypothesis.
If the p-value is 0.023 from a hypothesis test is compared to a significance level of 0.05, the conclusion which we would make is: A) accept the null hypothesis.
What is a p-value?A p-value is also referred to as the probability value and it can be defined as a probability which arises when the null hypothesis (H₀) is true of obtaining a sample result that is at least as unlikely as what is originally observed.
In Mathematics, the following rules are applicable to both a p-value and a hypothesis test:
Accept the null hypothesis when the p-value is greater than the significance level (alpha).Reject the null hypothesis when the p-value is less than the significance level (alpha).In this context, we can logically deduce that the null hypothesis would be accepted because the p-value (0.023) is greater than a significance level of 0.05 and not statistically significant.
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The problem is sketch the graph of each line
The required sketch graph of given straight line is shown below in the image.
Explain the concept of equation of line.
The general equation of line is written as Y = mx + c where, m is the gradient of straight line, c is the point where the line cut y-axis.
According to the question:we have, line y = x - 1
So, slope of line is 1 and y-intercept is -1
Thus,required graph of straight line is
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Five students were looking at a large poster of the periodic table. They noticed the elements were arranged in rows and columns. They also noticed the elements were nged in order from 1-118. They had different ideas about the arrangement of the elements on the periodic table. This is what they said:
Damon: I think the elements are arranged by increasing mass.
Flo: I think the elements are arranged according to their properties.
Sienna: I think the elements are arranged by when they were discovered.
Kyle: I think the elements are arranged according to how common they are.
Glenda: I don't agree with any of you. I think there must be a different reason for the arrangement.
WHO DO YOU AGREE WITH?
The person that I agree with is Glenda I don't agree with any of you. I think there must be a different reason for the arrangement.
What is a periodic table?The periodic table, commonly known as the periodic table of (chemical) elements, is a table that displays the chemical elements in a tabular format.
The chemical elements are ordered from left to right and top to bottom by increasing atomic number, or the number of protons in an atom's nucleus, which generally corresponds to increasing atomic mass.
The elements in the periodic table are organized into rows, called periods, in ascending atomic number order. Vertical columns, referred to as groups, in which the elements have similar qualities.
I agree with Glenda because they're arranged in atomic number.
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développer l'expression suivante
3−3(−3x−5)(−3x+5)−4(3x−2)(2x+3)
3-3(9x²+15x-15x+25)-4(6x²+9x-4x+6)
3-27x²-75-24x²-20-24
3-51x²-119
-116-51x²
ASAPPPPP PLEASE HELPPP!!!!!!!!!!
Between 50 and 100 books are stored on a shelf. Exactly 20 percent of them are textbooks. Exactly one-seventh of them are novels. Can the exact number of books on the shelf now be determined? Why or why not?
Answer:
no
Step-by-step explanation:
the percentage has nothing to do with how many of them there are, forgive me if im wrong
The exact number of books on the shelf cannot be determined based on the information given.
What is an expression?An expression is a grouping of one or more mathematical or logical operators, operands (values, variables, or other expressions), and brackets in mathematics and computer programming that denote a computation that can be evaluated to generate a value.
We know that between 50 and 100 books are stored on a shelf, so let's assume the number of books is some integer value between 50 and 100, inclusive. Let's call this value "n".
Exactly 20% of the books are textbooks, which means there are 0.2n textbooks on the shelf.
Exactly one-seventh of the books are novels, which means there are (1/7)n novels on the shelf.
We know that n, 0.2n, and (1/7)n are all integers because they represent whole numbers of books. We can write this as:
n = a
0.2n = b
(1/7)n = c
where a, b, and c are integers.
From the second equation, we know that 0.2n is a multiple of 1/10. From the third equation, we know that n is a multiple of 7. Therefore, we can rewrite these equations as:
n = 10b
n = 7c
Since n is equal to both 10b and 7c, we know that n must be a multiple of the least common multiple of 10 and 7, which is 70.
So, n must be a multiple of 70, and therefore must be one of the integers 50, 70, or 90. However, we cannot determine which of these three values is the correct one based on the information given, because all three satisfy the conditions in the problem:
If n=50, then 20% of the books (i.e., 10 books) are textbooks, and 1/7 of the books (i.e., 7.14 books, which we round down to 7) are novels.
If n=70, then 20% of the books (i.e., 14 books) are textbooks, and 1/7 of the books (i.e., 10 books) are novels.
If n=90, then 20% of the books (i.e., 18 books) are textbooks, and 1/7 of the books (i.e., 12.86 books, which we round down to 12) are novels.
Therefore, the exact number of books on the shelf cannot be determined based on the information given.
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A footballb team lost the same number of yards on each of 3 consecutive plays.what is the total change in yards from where the team started? Someone pls help I dont understand.
The total change in yards where the team started is 3x
How to determine the total change in yards?The given parameters in the question are:
Yards per play = unknown
Number of plays = 3 consecutive plays
Represent the yards per play with x
So, we have
Yards per play = x
The total change in yards is the amount of yard per play multiplied by the number of plays
This is represented as
Total change = Yards per play * Number of plays
Substitute the known values in the above equation So, we have the following equation
Total change = x * 3
Evaluate
Total change = 3x
Hence, the total change is 36 yards
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i bet u cant solve it
For the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.
As given in the question,
Given :
Pair of parallel lines are AG and BH.
CF is the transversal.
Transversal CF intersect line AG at point D and
Transversal CF intersect line BH at point E
Four pair of corresponding angles
Two pair of alternate interior angles
Corresponding pair of angles in the pair of parallel lines are congruent.
∠ADE ≅ ∠BEF
∠ADE and ∠BEF are corresponding angles.
Therefore, for the given pair of parallel lines AG and BH , CF is the transversal then ∠ADE and ∠BEF are corresponding angles.
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What must be added to 3/8 to make a whole?
Answer:1/2
Step-by-step explanation:
in exercises 10-11, find the value of x so that the function has the given value.
10. m(x) = -3/5x - 4; m(x) = 2
11. w(x) = 5/6x - 3; w(x) = -18
The value of x so the the the function has the given value is as follows:
m(x) = 2; x = - 10w(x) = - 18; x = - 18How to find the value of the input of a function?A function relates an input to an output.
In other words, a function is a special relationship among the inputs and their outputs codomain) where each input has exactly one output value.
Therefore, let's find the value of x so that the function has the given values.
m(x) = -3/5x - 4; m(x) = 2
let's find the value of x when m(x) = 2
2 = - 3/5x - 4
2 + 4 = - 3/5x
6 = - 3/5 x
cross multiply
-3x = 30
x = 30 / - 3
Hence,
x = - 10
w(x) = 5/6x - 3; w(x) = -18
let's find the value of x when w(x) = -18
- 18 = 5/6x - 3
- 18 + 3 = 5 / 6 x
- 15 = 5 / 6 x
5x = - 90
x = -90 / 5
Hence,
x = - 18
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find the missing value ratio inches :2 and years: 3,1,8
Answer: The missing values in the ratio table will be 0.666 and 5.33 inches.
Step-by-step explanation:
As the ratio of the terms is equal. The value of x and y is ,
2/3 = x/1
x=2/3
x=0.66 inches
In order to obtain y,
2/3 = y/8
y=2×8/3
y=16/3
y=5.33 inches.
Write the expression as a power and evaluate it. 8•2^7 and 16•32
The expression as a power is ____
The expression as a power is 2^10 and 2^9
What is index form?Index form of a number can be defined as the number that is written in the form of an exponential expression.
It is also described as a single number that is raised to another variable or number.
It is important to note the following index forms with base of 2, we have;
2^1 = 22^2 = 42^3 = 82^4 = 162^5 = 322^6 = 64We have the expression as;
8•2^7
Substitute the values
2^3 . 2^7
Add the powers
2^3 + 7
2^10
16•32
Substitute the values
2^4 . 2^5
Add the powers
2^ 4 + 5
2^9
The expression is written as; 2^ 10 and 2^9
Hence, the values are 2^10 and 2^9
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Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24. Find the percent tip.
The percentage of the tip will be equal to 24.81%.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Mia was out at a restaurant for dinner when the bill came. Her dinner came to $28. After adding in a tip, before tax, she paid $37.24.
The percentage tip will be calculated as,
P = ( (37.24 - 28 ) / 37.24
P = 9.24 / 37.24
P = 0.2481 x 100
P = 24.81%
Therefore, the percentage of the tip will be equal to 24.81%.
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please help meee :((
The system of conics has two solutions.
(x−4)2+(y+1)2=9
(x−4)29+(y+1)281=1
What are the solutions to this system of conics?
Answer:
(1, -1) and (7, -1)===============
Given system(x − 4)² + (y + 1)² = 9(x − 4)² / 9 + (y + 1)² / 81 = 1Solve it by eliminationMultiply the second equation by 9 and subtract from the first one:
(y + 1)² - (y + 1)² / 9 = 0(y + 1)²/8 = 0(y + 1)² = 0y + 1 = 0y = - 1Substitute y and solve for x(x − 4)² + (-1 + 1)² = 9(x - 4)² = 9x -4 = ± 3x = 4 ± 3x = 1 and x = 7Answer:
[tex]\left(\; \boxed{1}\:,\boxed{-1}\;\right)\; \textsf{and}\;\left(\; \boxed{7}\:,\boxed{-1}\;\right)[/tex]
Step-by-step explanation:
Given system of conics:
[tex]\begin{cases}(x-4)^2+(y+1)^2=9\\\\\dfrac{(x-4)^2}{9}+\dfrac{(y+1)^2}{81}=1\end{aligned}[/tex]
Multiply the second equation by 81:
[tex]\implies \dfrac{81(x-4)^2}{9}+\dfrac{81(y+1)^2}{81}=81[/tex]
[tex]\implies 9(x-4)^2+(y+1)^2=81[/tex]
Rearrange to make (y + 1)² the subject:
[tex]\implies (y+1)^2=81-9(x-4)^2[/tex]
Substitute into the first equation and simplify:
[tex]\implies (x-4)^2+81-9(x-4)^2=9[/tex]
[tex]\implies -8(x-4)^2=-72[/tex]
[tex]\implies (x-4)^2=9[/tex]
Solve for x:
[tex]\implies \sqrt{ (x-4)^2}=\sqrt{9}[/tex]
[tex]\implies x-4=\pm3[/tex]
[tex]\implies x=4\pm3[/tex]
[tex]\implies x=1, 7[/tex]
Substitute the found values of x into the first equation and solve for y:
[tex]\begin{aligned}x=1 \implies (1-4)^2+(y+1)^2&=9\\(-3)^2+(y+1)^2&=9\\9+(y+1)^2&=9\\(y+1)^2&=0\\y+1&=0\\y&=-1\end{aligned}[/tex]
[tex]\begin{aligned}x=7 \implies (7-4)^2+(y+1)^2&=9\\(3)^2+(y+1)^2&=9\\9+(y+1)^2&=9\\(y+1)^2&=0\\y+1&=0\\y&=-1\end{aligned}[/tex]
Therefore, the solution to the given system of conics is:
(1, -1) and (7, -1)What is the reason for each step in the solution of the equation?
18−2x=4x
Drag and drop the reasons into the boxes to correctly complete the table.
Answer:
Given
Addition property of equality
Division property of equality
Step-by-step explanation:
The first line is given.
Next 2x was added to each side. The addition property of equality says that for an equation to stay in balance, it you add something to one side of the equation, you have to add that same thing to the other side of the equation.
The same is true for the division property.
Which relation is a function?
Answer:
The bottom right
Step-by-step explanation:
A relation is just a set of ordered pairs. A function is a special relation. In a function every input (x) has only one output (y).
You can use the vertical line test. If you took your pencil and vertical passed over the graph left to right. If there is any point that more than one point would be under the pencil, the relation is not a function.
Rewrite this number in appropriate scientific notation:
answer=
464, 400,000
You may use either X or to represent multiplication.
Kepteo can cultivate a piece of land in7hrs. While wanjiku can do the same work in 5 hrs . Find the time they will take to cultivate the piece of land when working together
The time is 2 our 55 minutes when they will take to cultivate the piece of land when working together.
What is mean by Fraction?
A fraction is a part of whole number, and a way to split up a number into equal parts.
Or, A number which is expressed as a quotient is called fraction.
It can be written as the form of p : q, which is equivalent to p / q.
Given that;
Kepteo can cultivate a piece of land in 7 hr.
Wanjiku can do the same work in 5 hr.
Now,
Since, Kepteo can cultivate a piece of land in 7 hr.
Hence, Kepteo make work in 7 h
So, In 1 hour kepteo work = 1/7
And, Since, Wanjiku can cultivate a piece of land in 5 hr.
Hence, Wanjiku make work in 5 h
So, In 1 hour Wanjiku work = 1/5
Thus, They make with together = 1/7 + 1/5
= 12/35
Hence, When they working, they make = 12/35 work per hour
So, They need number of hour to working together = 35/12 hour
= 2 hour 55 minutes.
Thus, The time is 2 our 55 minutes when they will take to cultivate the piece of land when working together.
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If a plant grows 15 cm in 3 hrs. Determine which expression correctly represents a unit rate for the situation.
The unit rate of the plant growth is 5cm per hour
How to calculate the unitThe unit rate refers to amount the plant will grow 1 hour
from the relationship
15 cm = 3 hours
? cm = 1 hour
cross multiplying
3 * ? = 15 * 1
? = 15 / 3
? = 5 cm
The plant's unit rate of growth is 5cm per hour
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Use the difference of two squares to find each product.
17•7
The product of 17×7 using the difference of two squares is 119.
= 17×7
=(12+5)(12-5)
=12(12-5)+5(12-5)
=12×12-12×5+5×12-5×5
=12²-5²
=144-25
=119
The difference between two squares is a theorem that tells us if a quadratic equation can be written as a product of two binomials, in which one shows the sum of the square roots and the other one is the difference of the square root.
I hope this answer helps.
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Express 6 + √ − 81 as a simplified complex number
The given algebraic expression can be simplified as 6+9i.
Complex NumberA complex number is represented by the following form: a+bi, where a and b are real numbers. The variables: a is the real part and bi imaginary part. See an example: 7 + 14i , then:
7 real part14i imaginary partRegarding operations math, the same properties used for real numbers can be applied to complex numbers. And for solving the operations math with these numbers, it is important to know that i²= -1. Thus, 2i² = 2*(-1)= -2.
When you subtract or sum complex numbers, you can only subtract or sum: the real part with the real part of each complex number and the imaginary part with the imaginary part of each complex number. Here, you can see examples:
(5 + 2i) + (5 + 2i) = 10+4i
(4 + 9i) - (1 + 5i) = 1+4i
Therefore, the result for the 6 + √− 81 will be:
6+ √81i²
6+9i
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how are the zeros of a polynomial function related to the equation and graph of a function
The way that zeros of a polynomial function is related to the equation and graph of a function because they act as solutions to the equation and also x-intercepts of a graph.
What graphing relationship does a zero have?When the quadratic equation's graph crosses the x-axis, those points are known as the zeros of the equation.
The graph's x-intercepts and a function's zeros are the same thing. If the zero of f has an odd multiplicity, the graph of f will cross the x-axis at that x value. The x-axis will be touched by the graph of f if it has an even multiplicity zero.
Hence, A polynomial's zeros are the answers to any equation such as p(x) = 0, where p(x) stands for the polynomial. Since the values of x where y = 0 if we graph this polynomial as y = p(x). In other words, these are the graph's x-intercepts.
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Find the distance between the two points rounding to the nearest tenth (if necessary).
(-3, 5) and (1,−1)
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~1 - (-3)~~)^2 + (~~-1 - 5~~)^2} \implies d=\sqrt{(1 +3)^2 + (-1 -5)^2} \\\\\\ d=\sqrt{( 4 )^2 + ( -6 )^2} \implies d=\sqrt{ 16 + 36 } \implies d=\sqrt{ 52 }\implies d\approx 7.2[/tex]
if Julie average arts test score at 85 and what would you predict her average math test score would be
1. Her Average would be 80
2. Yes, there are more dots around points 80.
State whether the simplification below is true or false 5^-2=1/25
Answer:
true
Step-by-step explanation:
5^ -2
(1/5)^2
1/25
Answer:
That's true :
5^-2= 1/5^2= 1/25
so yes : 5^-2=1/25
Step-by-step explanation:
You buy 3 gallons of milk at $2.48/gallon, 2 gallons of
ice cream at $1.49/gallon, and 4 lbs of strawberries at
$0.58/1b. What is your total cost?
(1 point)
O$9.51
O$12.74
0$4.55
O$10.67
The total cost is $12.74
In this question, we have been given the cost of 1 gallon of milk, 1 gallon of ice-cream and 1 1b of strawberry.
1 gallon of milk costs $2.48,
1 gallon of ice-cream costs $1.49
and 1b of strawberry costs $0.58
You buy 3 gallons of milk, 2 gallons of ice cream, and 4 lbs of strawberries.
So by unitary method total cost would be,
(3 * 2.48) + (2 * 1.49) + (4 * 0.58) = $12.74
Therefore, the total cost is $12.74
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A cell phone plan costs $100 to start. Then there is a $25 charge each month. What is the total cost (start-up fee and monthly charge) to use the cell phone plan for 1 month? 6 months? Be sure to show your work. What is the total cost for months? Enter your first and last name below and then click start. If this is your second attempt, be sure to put a "2" after your name so I know it is your second attempt. Graph the cost of the cell phone plan over a period of two years, using months as the units of time. Be sure to label your axes and scale them by labeling each gridline with a number.
The $100 start-up fee and $25 monthly rental gives;
The cost of using the phone for 1 month = $125
The cost of using the phone for 6 months = $250
The cons of using the phone for n months = $(100 + 25·n)
Please find attached the graph of the cellphone plan over a period of two years (24 months)
What is a graph of a function?A graph is a visual representation of the variation of one variable of a function with respect to other variables of the function.
The start-up fee of the cell phone plan = $100
The amount charged each month = $25
First part;
The total cost for the start-up fee and monthly rental for 1 month = $100 + $25
The total cost for 1 month = $125
The total cost for 6 months = $100 + 6 × $25 = $250
The total cost for n months = 100 + n × 25 = $(100 + 25·n)
Please find the graph of the total cost to the number of months created with MS Excel
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The cost of 5 kg of potatoes is £3.40
The cost of 2 kg of carrots is 32p
Work out the total cost of 11 kg of potatoes and 1½ kg of carrots.
Answer:
i know i know its is 8.78 pounds it is easy
Step-by-step explanation:
what you do is that i am smart
The required total cost of the 11 kg of potatoes and 1½ kg of carrots is $7.72.
Given that,
The cost of 5 kg of potatoes is £3.40 the cost of 2 kg of carrots is 32p working out the total cost of 11 kg of potatoes and 1½ kg of carrots.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Cost of potatoes per kg = 0.68
Cost of 11 kg of potatoes = 0.68×11 = $7.48
Cost of the carrots per kg = 0.16
Cost of 1.5 kg carrot = 0.24
Total cost of the 11 kg of potatoes and 1½ kg = 7.48 + 0.24= $7.72.
Thus, the required total cost of the 11 kg of potatoes and 1½ kg of carrots is $7.72.
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41% adults favor the use of unmanned drones by police agencies. Twelve U.S. adults are randomly selected. Find the probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is (a) exactly three, (b) at least four, (c) less than eight.
P(3)=
P(x >4)=
P(x<9)=
The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is;
(a) exactly three = 0.1314
(b) at least four = 0.7953
(c) less than eight = 0.93382
How to solve Binomial Probability Distribution Problems?The binomial probability distribution is the probability of exactly x successes on n repeated trials, with p probability. The formula is;
P(X = x) = ⁿCₓ * pˣ * (1 - p)^(n - x)
We are given;
p = 41% = 0.41
n = 12
Thus;
1) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is exactly three;
P(3) = ¹²C₃ * 0.41³ * (1 - 0.41)^(12 - 3)
P(3) = 0.1314
2) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is at least four;
P(x ≥ 4) = P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12)
P(x ≥ 4) = 0.7953
3) The probability that the number of U.S. adults who favor the use of unmanned drones by police agencies is less than eight using binomial probability calculator is;
P(X < 8) = 0.93382
Read more about Binomial Probability Distribution at; https://brainly.com/question/15278907
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