SOLUTION
We want to identify the equation that represents the data in the table.
Let's put the first values for x and y from the table, that is x = -2 and y = 11 and see if it works for the first option
[tex]y=x+5[/tex]This becomes
[tex]\begin{gathered} y=x+5 \\ y=-2+5 \\ y=3 \end{gathered}[/tex]Since we didn't get y = 11, but we got y = 3, then the first option is wrong.
Let's try the next one
[tex]y=-3x+5[/tex]This becomes
[tex]\begin{gathered} y=-3x+5 \\ y=-3(-2)+5 \\ y=6+5 \\ y=11 \end{gathered}[/tex]So, we got y = 11, this option should be the correct answer, but let us confirm with the next values of x and y which are (0, 5).
So we will put x = 0, if we get y = 5, then the option is correct, so
[tex]\begin{gathered} y=-3x+5 \\ y=-3(0)+5 \\ y=0+5 \\ y=5 \end{gathered}[/tex]Since we got y = 5, this option is correct.
Hence, the answer is the 2nd option.
[tex]y=-3x+5[/tex]What is the standard form of the equation of a line passing through points (2,3) and (2,-5)?
Answer:
[tex]x\text{ = 2}[/tex]Explanation:
Here, we want to find the standard form of the equation
We have the standard form as:
[tex]Ax\text{ + By = C}[/tex]We can arrive at this using the two-points form:
This is:
[tex]\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{y-y_1}{x-x_1}[/tex](x1,y1) = (2,3)
(x2,y2) = (2,-5)
Now, as we can see, the line is a vertical line since the x-value is the same
Thus, we have it that:
[tex]x\text{ = c}[/tex]where c will represent the x-intercept
Thus, we have the equation of the line as:
[tex]x\text{ = 2}[/tex]Consider the expression 6+(x+3)^2. Tabulate at least SIX different values of the expression.
Considering the expression 6+(x+3)^2. the table of at least SIX different values of the expression is
x y
0 15
1 22
2 31
3 42
4 55
5 70
How to determine the he table of at least SIX different values of the expressionThe table is completed by substituting the values of x in the given expression as follows
6 + ( x + 3 )^2
for x = 0, y = 6 + ( 0 + 3) ^2 = 15
for x = 1, y = 6 + ( 1 + 3) ^2 = 22
for x = 2, y = 6 + ( 2 + 3) ^2 = 31
for x = 3, y = 6 + ( 3 + 3) ^2 = 42
for x = 4, y = 6 + ( 4 + 3) ^2 = 55
for x = 5, y = 6 + ( 5 + 3) ^2 = 70
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write each of the following numbers as a power of the number 2
Answer
The power on 2 is either -3.5 in decimal form or (-7/2) in fraction form.
Explanation
To do this, we have to first note that
[tex]\begin{gathered} \sqrt[]{2}=2^{\frac{1}{2}} \\ \text{And} \\ 16=2^4 \end{gathered}[/tex]So, we can then simplify the given expression
[tex]\begin{gathered} \frac{\sqrt[]{2}}{16}=\frac{2^{\frac{1}{2}}}{2^4}=2^{\frac{1}{2}-4} \\ =2^{0.5-4} \\ =2^{-3.5} \\ OR \\ =2^{\frac{-7}{2}} \end{gathered}[/tex]Hope this Helps!!!
Which statement best describes the area of the triangle shown below?
ANSWER
Option D - The area of this triangle is one-half of that of a square that has area of 12 square units
EXPLANATION
We want to the best description of the area of the triangle given.
To do this, we have to first find the area of the triangle.
The area of a triangle is given as:
[tex]A\text{ = }\frac{1}{2}(b\cdot\text{ h)}[/tex]Where b = base and h = height
From the diagram, we have that:
b = 4 units
h = 3 units.
Therefore, the area of this triangle is:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}(4\cdot\text{ 3)} \\ A\text{ = }\frac{1}{2}(12) \\ A\text{ = 6 square units} \end{gathered}[/tex]Checking through the options, we see that the only correct option is Option D.
This is because the area of this triangle (6 square units) is one-half of that of a square that has area of 12 square units
The ratio of students polled in 6th grade who prefer lemonade to iced tea is 8:4, or 2:1. If there were 39 students in 6th grade polled, explain how to find the number of students that prefer lemonade and the number of students that prefer iced tea. Be sure to tell how many students prefer each.
Since we know the ratio is 2:1, then to find the number of students who like iced tea we convert the ratio to a fraction:
[tex]\frac{1}{2}[/tex]this means that one of two students preferred iced tea.
To find the number of students who prefer iced tea we multiply the total number of students by the fraction, then:
[tex]39\cdot\frac{1}{2}=\frac{39}{2}=19.5[/tex]Since we can't have a fraction of a student, we conclude that 19 students prefer iced tea and 20 prefer lemonade.
I resolved this problem for a test already but it looks like the graph it’s not ok can you help me?
SOLUTION
The function given is
[tex]f(x)=2x+1[/tex]To obtain the slope, we compare the equation above with the standard form of a slope intercept form.
Hence,, slope intercept is given as
[tex]\begin{gathered} y=mx+c \\ \text{Where m=slope.c=intercept on y (0,c)} \end{gathered}[/tex]Comparing with the function given, we have
[tex]\begin{gathered} M=2,c=1 \\ \text{Hence } \\ \text{slope}=2,\text{ y-intercept=(0,1)} \end{gathered}[/tex]Therefore
The slope = 2 and the y-intercept= (0,1 )
The graph of the functionis given in the image below
GRAPH each triangle and CLASSIFY the triangle according to its sides and angles.
Answer:
[tex]\Delta CAT\text{ is an ISOSCELES triangle}[/tex]Explanation:
To properly classify the traingle, we need to get the length of the sides
To get the length of the sides, we need to get the distance between each two points using the distance between two points formula
Mathematically,we have the formula as:
[tex]D\text{ = }\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where (x1,y1) refers to the coordiantes of the first point while (x2,y2) refers to the coordinates of the second point
let us get the coordinates of the individual points as seen from the plot shown
C (1,8)
A (5,10)
T (7,6)
So, let us find the distance between each two points
For AC, we have:
[tex]D\text{ = }\sqrt[]{(5-1)^2+(10-8)^2}\text{ = }\sqrt[]{20}[/tex]For AT, we have:
[tex]D=\sqrt[]{(7-5)^2+(6-10)^2\text{ }}\text{ = }\sqrt[]{20}[/tex]Lastly, for CT, we have:
[tex]D\text{ = }\sqrt[]{(7-1)^2+(6-8)^2\text{ }}\text{ = }\sqrt[]{40}[/tex]From our calculations, we can see that AC = AT
If we have a triangle which has two of its sides equal in length (the angle facing these sides would be same too), we call this an isosceles triangle
So, the class of triangle CAT is isosceles triangle
Question 39.Find the inverse of the given function. Graph both functions on the some set of axes and show the line y=x as a dotted line in the graph.
First, to find the inverse of a function, call the original function "x" and call call "x" in the original function as the inverse function:
[tex]\begin{gathered} f(x)=5x+1 \\ x=5f^{-1}(x)+1 \end{gathered}[/tex]Now, we solve for the inverse function:
[tex]\begin{gathered} x=5f^{-1}(x)+1 \\ 5f^{-1}(x)+1=x \\ 5f^{-1}(x)=x-1 \\ f^{-1}(x)=\frac{x}{5}-\frac{1}{5} \end{gathered}[/tex]To graph lines, we can find two points in it and draw a line that passes through both.
Let's pick x = 0 and x = 1 for the first equation:
[tex]\begin{gathered} f(0)=5\cdot0+1=1 \\ f(1)=5\cdot1+1=6 \end{gathered}[/tex]So, we plot the points (0, 1) and (1, 6).
For the inverse, we can simply invet the coordinates, which is the same as picking x = 1 and x = 6:
[tex]\begin{gathered} f^{-1}(1)=\frac{1}{5}-\frac{1}{5}=0 \\ f^{-1}(6)=\frac{6}{5}-\frac{1}{5}=\frac{5}{5}=1 \end{gathered}[/tex]Thus, we have the points (1, 0) and (6, 1).
The line y = x is jus the diagonal that passes though point (0, 0) and (1, 1), for example.
Putting these points and drawing the lines, we get:
Write a multiplication expression to represent each situation. Then find each product and explain its meaning. Ethan burns 650 calories when he runs for 1 hour. Suppose he runs 5 hours in one week.
We know that
• Ethan burns 650 calories per hour.
If he runs 5 hours we just have to multiply this time with the given rate.
[tex]650\cdot5=3,250[/tex]Therefore, Ethan burns 3,250 calories in 5 hours.writing equations in slope-intercept form common core algebra 1question 1
The equation of the line in the slope-intercept form is y = mx + b, where "m" is the slope and "b" is the y-intercept.
"b" is the point (0, yi).
"m" can be found using 2 points P₁ (x₁, y₁) and P₂ (x₂, y₂), according to the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, to solve this question, follow the steps below.
(a) First graph
Step 01: Find the y-intercept and another point in the graph.
To find the points in the graph, choose a x-value and find its corresponding y-value.
Choosing x = 0, y = 2.
P₁ = (0, 2).
Choosing x = -3, y = -2.
P₂ = (-3, -2).
Step 02:
Describe it and decide if normal curve could be used as model
Answer:
The symmetric is symmetric
The distribution is unimodal
The mean, median, and mode are equal
A normal distribution is appropriate
Explanation:
The normal distribution is symmetric and unimodal, where the mode, the median, and the mean are equal. This distribution has the following shape
Therefore, the normal curve can be used as a model for the distribution.
So, the answers are:
The symmetric is symmetric
The distribution is unimodal
The mean, median, and mode are equal
A normal distribution is appropriate
factor the following by taking on the greatest common factor 14a^3 + 35a^2 +42a
Let's break apart each term into its factors:
[tex]\begin{gathered} 14a^3=2\cdot7\cdot a\cdot a\cdot a \\ 35a^2=5\cdot7\cdot a\cdot a \\ 42a=2\cdot3\cdot7\cdot a \end{gathered}[/tex]The common factors are
7 * a
That is,
[tex]7\cdot a=7a[/tex]Now, factorizing the expression, we have:
[tex]\begin{gathered} 14a^3+35a^2+42a \\ =7a(2a^2+5a+6) \end{gathered}[/tex]Answer[tex]7a(2a^2+5a+6)[/tex]Factor Problem Completely 16n^3 - 56n^2 + 8n - 28
Given
The equation is given as
[tex]16n^3-56n^2+8n-28[/tex]Explanation
Factorisation the equation,
[tex]4(4n^3-14n^2+2n-7)[/tex]Factorise the polynomial.
[tex]4(2n-7)(2n^2+1)[/tex]AnswerHence the answer is
[tex]4(2n-7)(2n^2+1)[/tex]Problem Solving
20. A city is building 3 parks in a new subdivision. Each park
will be 1.25 acres. How many total acres will the 3 parks
be?
According to the solving all three parks will cover surface of 37.5 acres in total.
How much area of land is in acres?The imperial and US customary systems both utilize the acre as a unit of land area. An acre is approximately equal to approximately 4,047 [tex]m^{2}[/tex].
How much area will 3 parks cover?Area covered by 3 parks can be calculated by multiplying the area of one park by three.
so, area covered by 3 parks=3×1.25
area covered by 3 parks=3.75
As you know multiplication is the repeated addition so we can obtain the same results by adding 1.25 three times to itself.
These three parks will cover total area of 3.75acres.
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Given that angle A lies in Quadrant III and sin(A)= −17/19, evaluate cos(A).
As we know;
[tex]sin^2(x)+cos^2(x)=1[/tex]We will use this equality. We take the square of the sine of the given angle and subtract it from [tex]1[/tex].
[tex]sin^2(A)=(-\frac{17}{19} )^2=\frac{289}{361}[/tex][tex]sin^2(A)+cos^2(A)=1[/tex][tex]sin^2(A)=1-cos^2(A)[/tex][tex]\frac{289}{361}=1-cos^2(A)[/tex][tex]cos^2(A)=1-\frac{289}{361} =\frac{72}{361}[/tex][tex]\sqrt{cos^2(A)} =cos(A)[/tex][tex]\sqrt{\frac{72}{361} }=\frac{6\sqrt{2} }{19}[/tex]In the third region the sign of cosines is negative. Therefore, our correct answer should be as follows;
[tex]cos(A)=-\frac{6\sqrt{2} }{19}[/tex]solve 6 + 5 on the sqr root of 249 - 2x = 7
ANSWER
x = 124
EXPLANATION
First we have to clear the term that contains x in the equation. In this case, this term is the second term. So we have tu subtract 6 from both sides of the equation:
[tex]\begin{gathered} 6-6+\sqrt[5]{249-2x}=7-6 \\ \sqrt[5]{249-2x}=1 \end{gathered}[/tex]Then, we have to eliminate the root. Note that in the expression inside the root there are two terms. To do this, we have to apply the "opposite" operation on both sides of the equation, which in this case is exponent 5:
[tex]\begin{gathered} (\sqrt[5]{249-2x})^5=1^5 \\ 249-2x=1 \end{gathered}[/tex]Now we do something similar to the first step. We want to leave on one side of the equation only the term that contains x and the rest on the other side. To do this we can either add 2x on both sides, or subtract 249 from both sides. We'll apply the first option because then we'll have a positive coefficient for x:
[tex]\begin{gathered} 249-2x+2x=1+2x \\ 249=1+2x \end{gathered}[/tex]However, we now have to subtract 1 from both sides of the equation:
[tex]\begin{gathered} 249-1=1-1+2x \\ 248=2x \end{gathered}[/tex]Finally, to find x, we have to divide both sides by 2:
[tex]\begin{gathered} \frac{248}{2}=\frac{2x}{2} \\ 124=x \end{gathered}[/tex]Hence, the solution to the equation is x = 124.
Can you please help me find the area of the shaded triangle? Thank you :)
Area of shaded triangle = Area of triangle - area of circle
Area of triangle = 1/2 x base x height
Base= 16 yds
Height= 19 yds
Area of triangle = 1/2 x 16 x 19 = 8 x 19 =152 square yard
[tex]\begin{gathered} \text{Area of circle = }\pi\times r^2 \\ \pi=3.14 \\ r=5\text{yds} \\ \text{Area of circle = 3.14 }\times5^2=78.5yard^2 \end{gathered}[/tex]Area of shaded triangle = 152 - 78.5 =73.5 square yard
Determine if the 2 lines are parallel, perpendicular, or neither based on their slope-intercept equations.
Equations of lines G & H;
Line G: y=-6x + 14
Line H: y=6x-14
O Perpendicular
O Not Enough Information
O Parallel
O Neither
POSS
10 11
12 13 14 15
Answer:
perpendicular because the slopes are opposite
Step-by-step explanation:
What is the y-intercept of the line x+2y=-14? (0,7) (-7,0) (0,-7) (2,14)
3. The data in the table gives the number of barbeque sauce bottles (y) that are sold with orders of chicken wings (x) for each hour on a given day at Vonn's Grill. Use technology to write an equation for the line of best fit from the data in the table below. Round all values to two decimal places.
1) Let's visualize the points
2) To find the equation for the line of best fit we'll need to follow some steps.
2.1 Let's find the mean of the x values and the mean of the Y values
2.2 Now It's time to find the slope, with the summation of the difference between each value and the mean of x times each value minus the mean over the square of the difference of the mean of x and x.
To make it simpler, let's use this table:
The slope then is the summation of the 5th column over the 6th column, we're using the least square method
[tex]m=\frac{939.625}{1270.875}=0.7393\cong0.74[/tex]The Linear coefficient
[tex]\begin{gathered} b=Y\text{ -m}X \\ b=14.625-0.73(19.875) \\ b=0.11625\cong0.12 \end{gathered}[/tex]3) Finally the equation of the line that best fit is
[tex]y=0.73x+0.12[/tex]Shanice has 4 times as much many pairs of shoes as does her brother Ron. If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does. How many pairs of shoes will Shanice have left after she gives Ron the shoes?
Let's define:
x: pairs of shoes of Shanice
y: pairs of shoes of Ron
Shanice has 4 times as much many pairs of shoes as does her brother Ron, means:
x = 4y (eq. 1)
If Shanice gives Ron 12 pairs of shoes, she will have twice as many pairs of shoes as Ron does, means:
x - 12 = 2y (eq. 2)
Replacing equation 1 into equation 2:
4y - 12 = 2y
4y - 2y = 12
2y = 12
y = 12/2
y = 6
and
x = 4*6 = 24
After she gives Ron the shoes, she will have left 24-12 = 12 pairs of shoes
want to graph xdont you need to find out what x is?-3x-6y=0
We have a equation of a line in the form:
[tex]-3x-6y=0[/tex]This goes through the point (0,0).
With another point, we can graph the line.
For example, for x=2, we have:
[tex]\begin{gathered} -3(2)-6y=0 \\ -6-6y=0 \\ -6y=6 \\ y=-1 \end{gathered}[/tex]So the point (2,-1) belongs to the line.
We can graph the line passing through those points:
i inserted a picture of the questioncan you state whether the answer is A, B, C OR D
Looking at the triangles, they are both right triangles. They have congruent legs = 12. They have congruent acute angles of 45 degerees. Thus, they are congruent triangles. The answer is True
The table shows a linear relationship between x and y. Drag and drop the options provided into the correct boxes to complete the equation. х 1 0 6 -4 41 у 9 -39 The equation that represents the relationship Is y = -8 -41 ON 9 4 O?
To calculate the equation first we need to choose two points of the table
P1 (1,1)=(x1,y1)
P2(0,9)=(x2,y2)
then we calculated the slope m
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]substituting the points we have
[tex]m=\frac{9-1}{0-1}=\frac{8}{-1}=-8[/tex]then we can calculate the equation
[tex](y-y1)=m(x-x1)[/tex][tex](y-1)=-8(x-1)[/tex][tex]y-1=-8x+8[/tex][tex]y=-8x+8+1[/tex]the equation is
[tex]y=-8x+9[/tex]The pentagonal prism below has a height of 13 units and a volume of 247 units ^3. Find the area of one of its bases.
• Volume of pentagonal prism = area of base x height
Volume = 247 unis^3
height = 13 units
Replacing:
V = A x h
A = V / h
A = 247/13 = 19 units^2
Please assist me. I have no idea how to start this equation
Part a
Remember that the linear equation in slope-intercept form is
y=mx+b
where
m is the slope or unit rate
b is the y-intercept or initial value
In this problem
the equation is of the form
C=m(n)+b
where
m=8.50
b=350
therefore
C=8.50n+350Part b
A reasonable domain for n (number of cups)
Remember that the number of cups cannot be a negative number
so
the domain is the interval [0, infinite)
but a reasonable domain could be [0, 500]
Find out the range
For n=0 -----> C=350
For n=500 ----> C=8.50(500)+350=2,100 ZAR
the range is the interval [350,2,100]
Part c
calculate the cost
For n=100 cups ----> C=8.50(100)+350=1,200 ZAR
For n=200 cups ----> C=8.50(200)+350=2,050 ZAR
For n=400 cups ---> C=8.50(400)+350=3,750 ZAR
Part d
Average cost
Divide the total cost by the number of cups
For 100 cups ------> 1,200/100=12 ZAR per cup
For 200 cups ----> 2,050/200=10.25 ZAR per cup
For 400 cups ----> 3,750/400=9.38 ZAR per cup
Part e
it is better to order more cups, to reduce the initial ZAR 350 cost.
Part f
In this problem we have the ordered pairs
(200, 2150) and (400, 3750)
Find out the slope m
m=(3750-2150)/(400-200)
m=8 ZAR per cup
Find out the linear equation
C=mn+b
we have
m=8
point (200,2150)
substitute and solve for b
2150=8(200)+b
b=2150-1600
b=550
therefore
The linear equation is
C=8n+550Part g
A reasonable domain could be [0, 600]
Find out the range
For n=0 ------> C=550
For n=600 ----> C=8(600)+550=5,350
The range is the interval [550,5350]
Part h
The gradient is the same as the slope
so
slope=8
that means ----> the cost of each cup is 8 ZAR
Part i
For n=600
C=8(600)+550=5,350 ZAR
Part j
we have the inequality
8n+550 < 8.50n+350
Solve for x
550-350 < 8.50n-8n
200 < 0.50n
400 < n
Rewrite
n > 400
For orders more than 400 cups is more effective to order from Cupomatic
Verify
For n=401
C=8n+550=8(401)+550=3,758 ZAR
C=8.50n+350=8.5(401)+350=3,758.5 ZAR
the cost is less in CUPOMATIC, is ok
the answer is
For orders more than 400 cups is more effective to order from CupomaticStatusRecovery8Help ResourcessAABC ~ AXYZFind the missing side length, s.B.3 65А&Х-ZCross multiplySE ][?] = [ ]153s
Since triangles ABC and XYZ are similar, the ratio between their corresponding sides is constant; thus,
[tex]\begin{gathered} \frac{AB}{XY}=\frac{BC}{YZ} \\ \Rightarrow\frac{3}{5}=\frac{6}{s} \end{gathered}[/tex]Solving for s,
[tex]\begin{gathered} \frac{3}{5}=\frac{6}{s} \\ \Rightarrow\frac{3}{5}\cdot s=\frac{6}{s}\cdot s \\ \Rightarrow\frac{3s}{5}=6 \\ \Rightarrow\frac{3s}{5}\cdot5=6\cdot5 \\ \Rightarrow3s=30 \\ \Rightarrow s=\frac{30}{3} \\ \Rightarrow s=10 \end{gathered}[/tex]Thus, the result of the cross multiplication is 3s=30 and the answer is s=10
3. Convert the angle 3π/4 to degrees.
Answer:
135°
Step-by-step explanation:
To convert an angle from radians to degrees, multiply by [tex]180/\pi[/tex].
[tex]\frac{3\pi}{4} \cdot \frac{180}{\pi}=135^{\circ}[/tex]
$1750 is invested in an account earning 3.5% interest compounded annualy. How long will it need to be in an account to double?
Given :
[tex]\begin{gathered} P\text{ = \$ 1750} \\ R\text{ = 3.5 \%} \\ A\text{ = 2P} \\ A\text{ = 2}\times\text{ 1750 = \$ 3500} \end{gathered}[/tex]Amount is given as,
[tex]\begin{gathered} A\text{ = P( 1 + }\frac{R}{100})^T \\ 3500\text{ = 1750( 1 + }\frac{3.5}{100})^T \\ \text{( 1 + }\frac{3.5}{100})^T\text{ = }\frac{3500}{1720} \end{gathered}[/tex]Further,
[tex]\begin{gathered} \text{( 1 + }\frac{3.5}{100})^T\text{ = 2} \\ (\frac{103.5}{100})^T\text{ = }2 \\ (1.035)^T\text{ = 2} \end{gathered}[/tex]Taking log on both the sides,
[tex]\begin{gathered} \log (1.035)^T\text{ = log 2} \\ T\log (1.035)\text{ = log 2} \\ T\text{ = }\frac{\log \text{ 2}}{\log \text{ 1.035}} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} T\text{ = }\frac{0.3010}{0.0149} \\ T\text{ = 20.20 years }\approx\text{ 20 years} \end{gathered}[/tex]Thus the required time is 20 years.
Is x5 + x2 + x a polynomial? Explain why or why not.
A polynomial is a mathematical expression formed by variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponentiation of variables.
The expression:
[tex]x^5+x^2+x[/tex]Is formed by the addition of three terms, each consisting of the variable x raised to a positive integer quantity. Therefore, the given expression is a polynomial.
