The following data table for two distinct linear functions utilizing identical x values for both functions is displayed:
[tex]\begin{tabular}{|c|c|c|}$\mathrm{x}$ & $\mathrm{y}=2 \mathrm{x}+7$ & $\mathrm{y}=-\mathrm{x}+4$ \\$-3$ & $2(-3)+7=-6+7=1$ & $-(-3)+4=3+4=7$ \\$-2$ & $2(-2)+7=-4+7=3$ & $-(-2)+4=2+4=6$ \\$-1$ & $2(-1)+7=-2+7=5$ & $-(-1)+4=1+4=5$ \\0 & $2(0)+7=0+7=7$ & $-(0)+4=0+4=4$ \\1 & $2(1)+7=2+7=9$ & $-(1)+4=-1+4=3$ \\2 & $2(2)+7=4+7=11$ & $-(2)+4=-2+4=2$ \\3 & $2(3)+7=6+7=13$ & $-(3)+4=-3+4=1$\end{tabular}[/tex]
The table demonstrates that the function y = 2x + 7 and the function y = -x + 4 both have values of 5 for x = -1.
As a result, the two functions' graphs will intersect at (1, 5)
First of all, we create 2 LINEAR function, i created the function f(x)=2x+5 and the function h(x)=3x+2, both are linear(without a quadratic term). Then
Choose a group of x values before creating the table. Add each x value from the left side column to the equation. To find the y value, evaluate the equation (middle column). Since the table of values really only contains x and y pairs, you can choose to omit the middle column from your table as an optional step.
you replace the x for a number:
Table 1 (F(X)=2X+5) Table 2 (H(X)=3X+2)
X=1----->Y=2+5=7 X=1------>Y=3·1+2=5
X=2---->Y=2·2+5=9 X=2----->Y=3·2+2=8
X=3---->Y=3·3+5=11 X=3----->Y=3·3+2=11
With both tables of data we can see that in the X=3/Y=11 point this two linear functions will intersect so the answer is that the two functions will intersect at (3,11)----->(X,Y)
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I need help look at the image attached
Answer:
[tex]\dfrac{(x-2)^2}{9}-\dfrac{y^2}{4}=1[/tex]
Step-by-step explanation:
Given points:
(2±3√2, ±2)(5, 0)(-1, 0)Standard equation of a horizontal hyperbola (opening left and right):
[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]
where:
center = (h, k)vertices = (h±a, k)Points (5, 0) and (-1, 0) are the vertices of the hyperbola.
The center (h, k) is midway between the vertices. Therefore:
[tex]\implies h=\dfrac{5-1}{2}=2[/tex]
[tex]\implies k=0[/tex]
Substitute the found values of h and k into the formula:
[tex]\dfrac{(x-2)^2}{a^2}-\dfrac{y^2}{b^2}=1[/tex]
Substitute point (5, 0) and solve for a²:
[tex]\implies \dfrac{(5-2)^2}{a^2}-\dfrac{0^2}{b^2}=1[/tex]
[tex]\implies \dfrac{3^2}{a^2}=1[/tex]
[tex]\implies \dfrac{9}{a^2}=1[/tex]
[tex]\implies 9=a^2[/tex]
Substitute one of the (2±3√2, ±2) points and the found value of a² and solve for b²:
[tex]\implies \dfrac{(2+3\sqrt{2}-2)^2}{9}-\dfrac{2^2}{b^2}=1[/tex]
[tex]\implies \dfrac{(3\sqrt{2})^2}{9}-\dfrac{4}{b^2}=1[/tex]
[tex]\implies \dfrac{18}{9}-\dfrac{4}{b^2}=1[/tex]
[tex]\implies 2-\dfrac{4}{b^2}=1[/tex]
[tex]\implies \dfrac{4}{b^2}=1[/tex]
[tex]\implies 4=b^2[/tex]
Substitute the found values of a² and b², together with the values of h and k, into the formula to create the equation of the hyperbola:
[tex]\dfrac{(x-2)^2}{9}-\dfrac{y^2}{4}=1[/tex]
identify if the following statement is a proper interpretation of a 95% confidence interval 95% of the population values will fall within this variable
option a , c and d are the correct statement or is a proper interpretation of a 95% confidence interval 95% of the population values will fall within this variable
What is the 95% confidence interval for a population mean?
It means that for any given number of samples, 95% of them will fall within 2 standard errors of the true mean of the population the sample is derived from.
a. In 95% of all samples, the sample mean will fall within 2 standard errors of the true population mean.
c. In 95% of all samples, the true population mean will be within 2 standard errors of the sample mean.
d. 95% of the population values will lie within 2 standard errors of the sample mean.
therefore option a , c and d are correct
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solve for x x/10 = 4
Equivalent expressions 4x+1/2+2x-3
The Equivalent expressions of 4x+1/2+2x-3 is 6x × 1/2 - 3 .
What are equivalent expressions?Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value(s) for the variable are entered, two algebraic expressions that are equivalent will have the same value (s). An expression that is equivalent to another expression but does not share its visual characteristics has the same value or worth. According to algebra, the equivalent formulae 2(2x - 3y + 6) and 4x -6y + 12 are the same. When two expressions can be written similarly or when they can be combined into a single, simpler expression, they are said to be equivalent. Furthermore, if values are replaced for the variable in two expressions and they both yield the same result, you can tell if the expressions are similar.
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The circumference of a circle changes from 20 to 4 after a dilation. What was the scale factor of the dilation?
O
25
O 5
O25
Answer:
1/5
Step-by-step explanation:
we know that
To find the scale factor divide the circumference of the dilated circle by the circumference of the original circle
so
Scale factor= 4/20=1/5
i rllly need this one pls help
The slope of the line is 2.
We are given a graph with coordinate axes, namely, the x-axis and the y-axis.The intersection of the coordinate axes is called the origin with coordinates (0, 0).The line is drawn in blue.The line passes through two dots, whose coordinates can be found using the graph.The coordinates of the points are (1, 1) and (-1, -3).The slope "m" of a line passing through points (x1, y1) and (x2, y2) is calculated as :m = (y2-y1)/(x2-x1)The slope of the line shown in the graph is :m = (-3-1)/(-1-1)m = -4/-2m = 2Thus, the slope of the line is 2.To learn more about slope, visit :
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Which is larger, 3.2 x 104 or 3.2 x 105?
Answer:
3.2 x 105
Step-by-step explanation:
its simple
Question 1
Solve the inequality.
5a<−35 or a−14>1
Answer:
The answer is
[tex]a < - 7 \: or \: a > 15[/tex]
Ava is older than Olivia. Their ages are consecutive even integers. Find Ava's age if the sum of Ava's age and 2 times Olivia's age is 74
Ava's age is 26 years when Ava and Olivia's ages are consecutive even integers and the sum of Ava's age and 2 times Olivia's age is 74.
According to the question,
Ava and Olivia's ages are consecutive even integers.
Now, let's take Olivia's age to be x years.
So, Ava's age would be (x+2) years because their ages are consecutive even integers. (Even numbers are the number which are divisible by 2.)
We have the sum of Ava's age and 2 times Olivia's age is 74.
So, we have the following expression:
(x+2+2x) = 74
3x+2 = 74
3x = 74-2
3x = 72
x = 72/3 (3 was in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 24 years
So, Olivia's age is 24 years.
Now, we have:
Ava's age = (x+2) years
Ava's age = (24+2) years
Ava's age = 26 years
Hence, Ava's age is 26 years.
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Mark raised $405 for his softball team's fundraiser. he wants to raise at least $825. write and solve an inequality to determine how much more money mark must raise to reach his goal. let d represent the amount of money in dollars mark must raise to reach his goal.
Answer: d ≥ 825-405
You're Welcome
Which are true about Figure 1 and Figure 2? Select all that apply. A. The figures have the same shape.B. The figures have the same size.C. Corresponding angles have the same measure.D. Corresponding sides have the same length.E. Corresponding side lengths have the same ratio.F. The figures are similar.
As we can see
A. The figures have the same shape. TRUE
B. The figures have the same size. FALSE
figure 1 is smaller than figure 2
C. Corresponding angles have the same measure. TRUE
as we can see in the image they have the same measure
D. Corresponding sides have the same length. FALSE
figure 1 is smaller than figure 2
E. Corresponding side lengths have the same ratio. TRUE
two figures are similar, the ratios of the lengths of their corresponding sides are equal.
F. The figures are similar. TRUE
because they have the same shape but the size is different
determine the test average for your math class after completing test
Considering the numeric value of the function f(x), the test average for your math class after completing test 2 was of 80.8.
How to find the numeric value of a function or of an expression?To find the numeric value of a function, we replace each instance of the variable in the function by the desired value.
For this problem, the function is given by:
f(x) = 79 + 0.9x.
The average after test 2 is represented by the numeric value when x = 2, hence we replace the lone instance of x on the function to find the average as follows:
f(2) = 79 + 0.9(2) = 80.8.
What is the missing information?
The problem asks for the test average for your math class after completing test 2.
The function that gives the average after test x is:
f(x) = 79 + 0.9x.
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A certain plant grows 1 1/6 inches each werk how long will it rake the plant to grow 6 1/6 inches?
A certain plant grows 1 1/6 inches each week. it will rake the plant to grow 6 1/6 inches is 5 weeks 2 days.
What is the definition of time?Time is ongoing progression of existence and things that happen in what seems to be an irrevocable order from the past, present, and forward into the future. It is a quantity that is part of several measurements that are used to compare the length of events or the gaps between them, to compare how long they last, to order events, and to measure how quickly the things change in the real world or in our conscious experience. Along with the three spatial dimensions, time is frequently referred to as a fourth dimension.
Time has long been an important subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without the circularity has consistently eluded scholars. Nevertheless, diverse fields such as the business, industry, sports, sciences, and the performing arts all incorporate some notion of time into their respective measuring systems.
A certain plant grows every week = [tex]1\frac{1}{6}[/tex] = [tex]\frac{7}{6}[/tex] inches
1 week = 7 days
Therefore in 1 day plant grows = [tex]\frac{\frac{7}{6} }{7}[/tex]
= [tex]\frac{1}{6}[/tex] inch
Now we have to calculate the number of days in which the plant grows [tex]6\frac{1}{6}[/tex] inches ≈ [tex]\frac{37}{6}[/tex] inch
Number of days = [tex]\frac{Total growth}{growth in one day}[/tex]
= [tex]\frac{37}{6}[/tex] ÷ [tex]\frac{1}{6}[/tex]
= [tex]\frac{37}{6}[/tex] × 6
= 37 days ≈ 5 weeks and 2 days
It will take plant 5 weeks 2 days to grow [tex]6\frac{1}{6}[/tex] inches.
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I am having a difficult time solving this. Please HELP!
The solution of the algebraic expression for the variable M is given as follows:
M = (4π²a³)/(T²G)
How to solve an algebraic expression for a variable?To solve an algebraic expression for a variable, we have to isolate this variable, as a function of the other variables in the expression.
In the context of this problem, the expression which we want to solve for M is given as follows:
T² = 4π²a³/GM
Applying cross multiplication to remove the fraction, we have that:
T²GM = 4π²a³
To isolate M, we apply the division, which is the opposite operation of the multiplication, as T²G are multiplying M, hence the simplified expression for M is given as follows:
M = (4π²a³)/(T²G)
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Help!A 2-column table with 5 rows. Column 1 is labeled Type of flower with entries lilies, daisies, carnations, asters, daffodils. Column 2 is labeled Amount with entries 60, 36, 72, 42, 24.
The florist makes the greatest number of identical arrangements with the lilies and the daisies. Which combination describes the arrangements?
A.6 arrangements with 10 lilies and 6 daisies
B.6 arrangements with 6 lilies and 10 daisies
C.12 arrangements with 10 lilies and 6 daisies
D.12 arrangements with 5 lilies and 3 daisies
The greatest number of identical arrangements the florist can make is .12 arrangements with 5 lilies and 3 daisies.
What is the greatest number of identical arrangements?The greatest number of identical arrangements with the lilies and the daisies the florist can make would be equivalent to the highest common factor of the number of lilies and daisies.
The highest common factor of two or more numbers is the highest number that can divide the numbers evenly without leaving any remainder. For example, the highest common factor of 4 and 8 is 4.
Factors of 60= 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, and 36.
Common factors = 1, 2, 3, 4, 6, 12
Highest common factor = 12
Number of daisies = 36 /12 = 3
Number of lilies = 60 / 12 = 5
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Translate this sentence into an equation. 67 is the difference of Gail's age and 15. Use the variable g to represent Gail's age.
The algebraic equation that represents the given sentence is:
g - 15 = 67.
Which algebraic equation represents the given sentence?We have to look at the description of the sentence, and then formulate expressions that represent this sentence.
The difference between two numbers x and y is represented by the following expression.
x - y.
Gail's age is represented by the following variable:
g.
Hence the difference of Gail's age and 15 is represented by:
g - 15.
The numeric value of this expression is of 67, hence the equation is:
g - 15 = 67.
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2ax-b=cx+b solve for x
The solution for x in the equation is x = 2b/(2a - c)
How to solve for x in the equation?The equation is given as
2ax - b = cx + b
Collect the like terms in the above equation
So, we have the following equation
2ax - cx = b + b
Evaluate the like terms in the above equation
So, we have the following equation
2ax - cx = 2b
Factor out x from the equation
x(2a - c) = 2b
Divide both sides by 2a - c
x = 2b/(2a - c)
Hence, the solution for x is x = 2b/(2a - c)
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Can someone like explain to me how to get this.
The probability of rolling an even number or a multiple of 3 is 3/4.
What is the probability?Probability determines the odds that a random event would happen. The probability the event takes place is 1 and the probability that the event does not happen is 0.
An even number is a number that is perfectly divisible by 2.
Probability of rolling an even number = number of sides that are even / total number of sides
Sides that are even = 2, 4, 6
Probability of rolling an even number = 3/6 = 1 / 2
Probability of rolling a multiple of 3 = number of sides that are multiples of 3 / total number of sides
Sides that are multiples of 3 = 3, 6
Probability of rolling a multiple of 3 = 2/6 = 1/2
The probability of event B or C = 1/4 + 1/2 = 3/4
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I REALLY NEED HELP WITH THIS!!
Determine the angles of a rotation
A) 90º clockwise
B) 90º counterclockwise
C) 180º
D) 270º clockwise
E) 270º counterclockwise
is 2 correct answers 
270 counter clockwise
Step-by-step explanation:
look at the rotation
I need help! This is due Friday and I don't know how to do all three questions.
Answer: Patrisha robbed 20+ banks
Bob has farted 30 times
Mary and John have 55 combined
Step-by-step explanation:
First one: She robbed 20 banks and then robbed more, giving 20+
Second one: 6 times a day for 5 days - 6x5=30
Third one: 25+30=55
Which of the following is both a perfect square and a perfect cube?
O64
O 1,000
16
081
Answer:
64
hope it helps
(6 ten thousands 3 hundreds) x 10
It should be noted that (6 ten thousands 3 hundreds) x 10 will give a value of 603000
How to calculate the value?Based on the information given, it should be noted that we want to calculate (6 ten thousands 3 hundreds) x 10
It should be noted that 6 ten thousands is 60000.
It should be noted that 3 hundreds will be 300.
Therefore, 6 ten thousands 3 hundreds x 10 will be:
= (60000 + 300) × 10
= 60300 × 10
= 603000
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A woman wants to measure the height of a nearby tower. The total length of the towers shawdow is 185 ft, and the poles casts a shawdow that is 6.5 ft long. How tall is the tower? Round your answer to the nearest foot.
yes you want to know about math then you will tell answer d
A baseball team has $1,400 to buy baseball uniforms. Each uniform costs $124. Does the team have enough money to buy 11 baseball uniforms? Use the drop-down menus to explain.
The total cost for 11 uniforms is
Choose...
.
Since
Choose...
is
Choose...
$1,400, the team
Choose...
enough money to buy 11 uniforms.
The team has enough money that will be used to buy 11 baseball uniforms.
How to illustrate the information?The information illustrated that the baseball team has $1,400 to buy baseball uniforms and each uniform costs $124.
It was also stated that the team needs to buy 11 uniforms. In this case, the cost of 11 uniforms will be the multiplication of the coat of each pair of uniform by the number of uniforms that will be bought.
This will be illustrated as:
= Amount of each uniform × Number of uniform
= $124 × 11
= $1364
Therefore, the total amount is $1364. Therefore, since the baseball team has $1400, the amount is enough.
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The table represents a continuous exponential function f(x).
x 2 3 4 5
f(x) 12 24 48 96
Graph f(x) and identify the y-intercept.
0
3
6
12
The graph of the continuous exponential function f(x) has been plotted and there is no y intercept in the graph
The domain is the set of all possible inputs of the given function.
The range is the set of all possible outputs of the given function
Here values of the x is the set of all possible inputs of the function and the values of (x) is the set of all possible outputs of the function.
Draw the graph using the given domain and range
From the given graph
We can see that there is no y intercept and x intercept
Hence, the graph of the continuous exponential function f(x) has been plotted and there is no y intercept in the graph
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The polynomial P(x) = x⁴ + 3x³ + cx² - 7x + 6 is divisible by x+3.
Determine the value of c and factor the polynomial fully.
The value of c is -3.
The factorization of the polynomial is [tex](x+3)(x^3-3x+2)[/tex].
Given that:-
Polynomial P(x) = x⁴ + 3x³ + cx² - 7x + 6 is divisible by (x + 3).
We have to determine the value of c and factorize the polynomial.
Using remainder theorem, putting x = -3 in the given polynomial, we get
[tex]P(-3)= (-3)^4+3(-3)^3+c(-3)^2-7(-3)+6=0[/tex]
P(-3) = 81 -81 +9c +21 +6 = 0
9c + 27 = 0
9c = -27
c = -27/9 = -3
Dividing the given polynomial x⁴ + 3x³ -3x² - 7x + 6 by (x + 3), we get,
[tex]x^3-3x+2[/tex]
Hence, the factorization of the polynomial is given by:-
[tex](x+3)(x^3-3x+2)[/tex]
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You buy a car that costs $24,211. The dealership is having a sale for 8% off and you have to pay 8.0% sales tax. How much will you pay?
He will pay $24.055 after discount and sales tax.
Define sales tax.A sales tax is a fee that is paid to the government when specified goods and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are typically used to describe taxes on goods and services that consumers pay directly to a governing authority.
Given Data
Car cost = $24.211
Discount = 8%
Car cost after discount:
= 24.211 - 8%
= 22.274
Car cost after sales tax:
= 22.274(8%)
= 22.274 (0.08)
= 1.781
Cost of car = 22.274 + 1.781
Cost of car = 24.055
He will pay $24.055 after discount and sales tax.
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Demuestra los valores de las funciones trigonométricas del ángulo de 0°
The values of the trigonometric functions of the 0° angle are, cos 0° = 1, sin 0° = 0 ,tan 0° = 0, cot 0° = ∞, sec 0° = 1 , cosec 0° = ∞.
What is trigonometric functions?The simplest definition of a trigonometric function is the function of an angle in a triangle, also known as a circular function. It implies that these trigonometric functions can be used to determine the relationship between a triangle's angles and sides. The fundamental trigonometric operations include sine, cosine, tangent, cotangent, secant, and cosecant.
Now given degree is 0 ,
So, we know that sin 0° = 0,
And cos 0° = 1,
⇒tanθ=sinθ/cosθ,
Here θ = 0°
⇒tan 0° = 0/1,
⇒tan 0° = 0,
Now as cot θ is the inverse of tan θ, we get,
⇒cot θ = 1/tan θ,
⇒cot 0°= 1/0,
⇒cot 0° = ∞,
Now we know that cosec θ is the inverse of sin θ, we get,
⇒cosec θ = 1/sin θ,
⇒cosec 0° = 1/0,
⇒cosec 0° = ∞
And we know that sec θ is the inverse of cos θ we get,
⇒sec θ = 1/cos θ,
⇒sec 0° = 1/1,
⇒sec 0° = 1.
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Write the equation for this graph using this format y= a |x-h| +k
The equation of the graph using the format y= a*|x-h|+k is y=|x+4|-5 .
In the question ,
From the graph we can see that the vertex of the graph is (-4,-5) ,
The absolute value equation of the graph is denoted by y=a*|x-h|+k ,
where (h,k) are the vertex of the graph .
Since (-4,-5) is the vertex , So h= -4 and k= -5 ,
Substituting the values of h and in the absolute value equation , we get
y=a*|x-(-4)|+(-5)
y=a*|x+4|-5
Take any point that lies on the graph ,
Selecting the point (1,0) which lie on the graph ,
Substituting the value as x=1 and y=0 , we get
0=a*|1+4|-5
5=a*|1+4|
5=5a
a=1 ,
Substituting the values of a=1 , h= -4 and k=-5 in the absolute value equation , we get y=|x+4|-5
Therefore , the equation of the graph using the format y= a*|x-h|+k is y=|x+4|-5 .
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A triangle has base 8 cm and perpendicular height 5.2 cm
Diagram not drawn accurately
8 cm
Work out the area of the triangle.
Optional working
5.2 cm
Answer:
cm²
Answer:
20.8 cm^2.
Step-by-step explanation:
Area = 1/2 * base * height
= 1/2 * 8 * 5.2
Answer:
A = 20.8 cm²
Step-by-step explanation:
We have just to use the following expression:
A = (Base x height) / 2
So:
A = (8 x 5.2) / 2
A = 4 x 5,2
A = 20.8 cm²