2. Graph the following inequality on the axes provided below: 6x + 2y = 8 -10 8 6 4 2 -101-8-6 1-4-2 -2 2 4_LG_L 8 10 -4 -6 -8 -10 True or False: (1,1) is a solution to the inequality. Explain using evidence from your graph.
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We are given the following inequality
[tex]6x+2y<8[/tex]Let us first convert the inequality into slope-intercept form
[tex]\begin{gathered} 6x+2y<8 \\ 2y<-6x+8 \\ y<-\frac{6x}{2}+\frac{8}{2} \\ y<-3x+4 \end{gathered}[/tex]Comparing this inequality with the standard slope-intercept form we see that
Slope = -3 and y-intercept = 4
So the graph of the inequality is
The area left to the red line represents the solution of the inequality.
Now we need to check if the point (1, 1) lies left to the red line.
We can clearly see that point (1, 1) is just left to the red line hence it is a solution.
Therefore, it is true.
Related Questions
ill take a pic of it
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The line passes through the points given.
Select any two points from the table, (-4,2) and (-3,5).
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Hence the slope is:
[tex]\begin{gathered} m=\frac{5-2}{-3-(-4)} \\ m=\frac{3}{1} \\ m=3 \end{gathered}[/tex]The slope is 3.
Which of the following correctly identifies the vertices that lie on the major axis of the conic section shown below? (x - 2) 3-2*) (y+5) = 1 4 9 O A. (2,-2) and (2,-8) O B. (-5,5) and (-5,-1) O C. (5,5) and (-1,-5) O D. (0,-5) and (4,-5)
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General equation of an ellipse:
[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]where (h,k) is the center, and a and b are some constants.
If b² is greater than a², then the y-axis is the major axis.
In this case, the ellipse is defined by the next equation:
[tex]\frac{(x-2)^2}{4}+\frac{(y+5)^2}{9}=1[/tex]This means that:
[tex]\begin{gathered} b^2=9 \\ b=\sqrt[]{9} \\ b=3 \end{gathered}[/tex]And, h = 2, k = -5
The vertices on the major axis are computed as follows:
(h, k+b) and (h, k-b)
Substituting with h = 2, k = -5, and b = 3, the vertices are:
(2, -5+3) and (2, -5-3)
(2, -2) and (2, -8)
what is 5/8 out of 100
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5/8 of 100 can be obtained by applying the rule of three:
[tex]\begin{gathered} 1\text{ ----- 100} \\ 5/8\text{ ----x} \end{gathered}[/tex]then, x is given by
[tex]\begin{gathered} x=\frac{\frac{5}{8}\cdot100}{1} \\ x=62.5 \end{gathered}[/tex]then, the answer is 62.5.
Sonia has $725,000 she wants to save. If the FDIC insurance limit per depositor, per bank, is $250,000, which of these ways of distributing her money between three banks will guarantee that all her money is insured?
$220,000 in Bank A, $230,000 in Bank B, $275,000 in Bank C
$220,000 in Bank A, $250,000 in Bank B, $255,000 in Bank C
$240,000 in Bank A, $230,000 in Bank B, $255,000 in Bank C
$240,000 in Bank A,, $245,000 in Bank B 245,000 in Bank c
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As per the dividing method, there are 3 ways of distributing her money between three banks.
Dividing method:
Division is the process of repeated subtraction.
This method, we start from the number called dividend in the number line and keep subtracting the number called divisor till we reach at 0 that is called remainder, and the number of steps we go on backward counting is the quotient or result of division.
Given,
Sonia has $725,000 she wants to save.
FDIC insurance limit per depositor, per bank, is $250,000
So, here we need to find the ways of distributing her money between three banks will guarantee that all her money is insured.
We know that, he limit is $250,000.
So, we have to divide the total amount within these limit across three bank.
Therefore, the possible ways of dividing the amount is given below:
Way 1:
if $250,000 deposited in bank A,
$250,000 deposited in bank B and
remaining money $175,000 will be deposited in bank C.
Way 2:
if $200,000 deposited in bank A,
$250,000 deposited in bank B,
$225,000 deposited in bank C.
Way 3:
If $225,000 deposited in bank A,
$225,000 deposited in bank B,
and $ 225,000 in bank C.
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A package of 5 pairs of insulated socks costs 27.95$. What is the unit price of the pairs of ?
Answers
Answer:
$5.59
Step-by-step explanation:
You want the unit price of a pair of socks, given that 5 pairs cost $27.95.
Unit priceThe unit price is found by dividing the price by the number of units.
$27.95/5 = $5.59
The unit price of a pair of socks is $5.59.
shows four types of polygons which type of polygon shown has no pairs of parallel sides
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Accoring to the given figures, the pentagon is the one without parallel sides.
Hence, the answer is Pentagon.Where may estimation of decimals be useful in every-day life? Give an example
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You can use decimal numbers (those numbers that have a comma after an interger part and before the decimal part)
You can use decimal numbers in real life in measures as:
Examples:
weight (you can weight 132,27 lb)
volumen of soda (you can drink a glass of soda of 8,45 oz = 0,25 L)
The temperature ( the temperature can be 89,9 F)
All the examples above have decimal number that can be useful in every-day life.
Samantha started with $25 in her account. she saves $7 per week. Australia has no money in his account, but adds $15 per week. for how many weeks will Australia have more money in his account than Samantha
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In this problem we can made a function to calculate the total amount for Samantha (S) and total amound of Australia (A) fon any time:
[tex]\begin{gathered} S=25+7t \\ A=0+15t \end{gathered}[/tex]when t is the number of weeks. if we made equal the ecuation we will have the time when they would have the same amound:
[tex]\begin{gathered} S=A \\ 25+7t=15t \end{gathered}[/tex]and we solve for t
[tex]\begin{gathered} 25=15t-7t \\ 25=8t \\ \frac{25}{8}=t \\ 3.125=t \end{gathered}[/tex]This means that in the next full number Australia will have more money than Samantha, so in 4 weeks this is going to happen.
You are redecorating your room and the only thing left to paint is your door. You're onlygoing to paint the side that faces the inside of your room. The door is 6 feet 10 inchestall and 30 inches wide. You need to know the surface area of the side of the door todetermine how much paint to buy. The hardware store sells paint by how much coversa square foot. What is the surface area of the garage door? Round your answer to thenearest square foot. (Hint: 1 square foot = 144 square inches) (gridded response)
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The roblem tells us that a door needs to be painted on only one side that measures 6 ft and 10 in height by 30 in wide.
We need to find the area to be painted in order to buy the appropriate quantity of paint. The answer has to be given in square feet at the end.
We start by recalling that the door is represented by a rectangle, and the area of such is given by the height times the wid
given that the measure of arc AD=(17×+2), measure of arc AC=(7×-10),and measure of angle ABC=(4×+15) find the measure of angle ABC
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In the given figure, angle ABC is formed by a tangent and a secant.
The angle formed by tangent and secant is given by
[tex]m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC})[/tex]Where mAD and mAC are the intercepted arcs.
For the given case,
[tex]\begin{gathered} m\angle ABC=(4x+15)\degree \\ m\bar{AD}=(17x+2)\degree \\ m\bar{AC}=(7x-10)\degree \end{gathered}[/tex]Let us substitute the given values into the above formula and solve for x
[tex]\begin{gathered} m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC}) \\ (4x+15)\degree=\frac{1}{2}\lbrack(17x+2)\degree-(7x-10)\degree\rbrack \\ 2\cdot(4x+15)\degree=(17x+2)\degree-(7x-10)\degree \\ 8x+30=17x+2-7x+10 \\ 8x-17x+7x=2+10-30 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}[/tex]The value of x is 9
So, the measure of angle ABC is
[tex]\begin{gathered} m\angle ABC=4x+15 \\ m\angle ABC=4(9)+15 \\ m\angle ABC=36+15 \\ m\angle ABC=51\degree \end{gathered}[/tex]Therefore, the measure of angle ABC is 51°
Express the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x).
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Answer:
y = 5u², u=x-6
Explanation:
Given the function:
[tex]y=5(x-6)^2[/tex]We want to express f(x) as a composition of two functions.
Let u = x-6
[tex]\implies y=5u^2[/tex]Therefore, the function y=5(x−6)² as a composition y=f(g(x)) of two simpler functions y=f(u) and u=g(x)
[tex]\begin{gathered} y=5u^2\text{ where:} \\ f(u)=5u^2 \\ u=g(x)=x-6 \end{gathered}[/tex]Use the distance formula to find the distance between the points given.(3,4), (4,5)
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Solution:
To find the distance between two points, the formula is
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Where
[tex]\begin{gathered} (x_1,y_1)=(3,4) \\ (x_2,y_2)=(4,5) \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]d=\sqrt{(4-3)^2+(5-4)^2}=\sqrt{1^2+1^2}=\sqrt{1+1}=\sqrt{2}\text{ units}[/tex]Hence, the answer is
[tex]\sqrt{2}\text{ units}[/tex]1. ¿Qué expresiones a continuación se pueden usar para encontrar el área del prisma rectangular de abajo? ¡ELIJA TODOS LOS QUE SE APLIQUEN! Nota: Puede probarlos todos para asegurarse de que sean iguales. * 15 (5x2x3) + (2x3x3) (5x2) + (5x2) + (5x2) + (5x2) 5x2x2 2 (5x2) + 2 (5x2) + 2 (2x2)
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We need to find the area of the prism given in the following image:
You need to add the surfaces of ALL rectangles in the image (recall that the area of a rectangle is : Base x Height)
So for this prism we have:
FOUR rectangles that measure 5 x 2
and also TWO small squares of area 2 x 2
So we need to select all the formulas they give you that read like the addition of the two above:
(5x2) + (5x2) + (5x2) + (5x2) + (2x2) + (2x2)
It can also be written as:
2 (5x2) + 2 (5x2) + 2 (2x2)
Classify each set of measures as AAS, ASA, SSA, SAS, or SSS. Then find the indicated length or angle measure (to the nearest tenth).
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Hello there. To solve this question, we'll have to remember some properties about triangles.
Given the triangle:
Notice in this case we have two consecutive angles and a side between them. This is a case of ASA (angle-side-angle).
With respect to the side with measure x, we have two consecutive angles then the side, hence AAS.
To find x, we'll have to apply the law of sines:
[tex]\dfrac{A}{\sin(\alpha)}=\dfrac{B}{\sin(\beta)}=\dfrac{C}{\sin(\gamma)}=2R[/tex]In this case, the angle opposite to x measures 73º and the angle opposite to 4 measures 85º, hence:
[tex]\dfrac{x}{\sin(73^{\circ})}=\dfrac{4}{\sin(85^{\circ})}[/tex]Multiply both sides by a factor of sin(73º)
[tex]x=\dfrac{4\sin(73^{\circ})}{\sin(85^{\circ})}[/tex]Using a calculator, we get the following approximation (rounding to the nearest tenth):
[tex]x\approx3.8[/tex]This is the measure of x we're looking for.
10 × 1/3
make sure the answer is a fraction and that u explain
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multiply the top and bottom ----> 10*1 and 1*3
10/3 would be your answer
laws of exponent : multiplication and power to a power5x3 • 2 x ²
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Multiplication of coefficients and variable
It's given the expression:
[tex]5x^3\cdot2x^2[/tex]Which is a perfect square?583644
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Solution:
A perfect square is a number that can be expressed as the product of an integer by itself or as the second exponent of an integer.
Hence,
[tex]36=6^2=6\times6[/tex]Therefore, the perfect square is 36.
A gamer spinner, circle O, is divided into 3 regions as shown. RP is a diameter. what is the area of the shaded sector ROS if RP=8 in a m
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we get that the radius is 4 and the angle is 135° which is radians 3/4 pi
so the area is
[tex]A=\frac{\pi}{2}\cdot4^2-\frac{\pi}{8}\cdot4^2=8\pi-2\pi=6\pi\approx18.85[/tex]If a rectangle has a perimeter of 70, a length of x and a width of x-9, find the value of the length of the rectangle040 3113O 22
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The formula for the perimeter of rectangle is,
[tex]P=2(l+w)[/tex]Substitute 70 for P, x for l and (x - 9) for w in the formula to determine the value of x.
[tex]\begin{gathered} 70=2(x+x-9) \\ 35=2x-9 \\ 2x=35+9 \\ x=\frac{44}{2} \\ =22 \end{gathered}[/tex]So value of x is 22.
Suppose you are completely locked out outside of your house. You remember that you left your bedroom window, which is 12 feet above the ground, unlocked from the inside (meaning you can climb up the window if you have a ladder, which you do!). You go to your garage, grab the 20 ft ladder and place it so that it reaches exactly to your bedroom window. What is the angle of elevation needed to reach your window? How far away will the bottom of the ladder be from your house?
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A diagram of the situation is shown below:
In order to determine the angle of elevation x, use the sine function, as follow:
sin x = opposite side/hypotenuse
the opposite side is the distance from the ground to the wi
12 is what percent of 18
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We have that
[tex]12\cdot\text{ }\frac{100}{18}=\text{ }\frac{1200}{18}\text{ = 66.6666}[/tex]So the answer is: 66.6666 .
A trapezoid has a height of 16 miles. The lengths of the bases are 20 miles and 35miles. What is the area, in square miles, of the trapezoid?
Answers
Given:
A trapezoid has a height of 16 miles.
The lengths of the bases are 20 miles and 35 miles.
To find:
The area of the trapezoid.
Explanation:
Using the area formula of the trapezoid,
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]On substitution we get,
[tex]\begin{gathered} A=\frac{1}{2}(20+35)\times16 \\ =\frac{1}{2}\times55\times16 \\ =440\text{ square miles} \end{gathered}[/tex]Therefore the area of the trapezoid is 440 square miles.
Final answer:
The area of the trapezoid is 440 square miles.
How many ways can Rudy choose 4 pizza toppings from a menu of 16 toppings if each can only be chosen once
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ANSWER:
1820 different ways
STEP-BY-STEP EXPLANATION:
We can use here combination rule for selection:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]In this case n is equal to 16 and r is equal to 4, therefore, replacing and calculating the number in different ways, there:
[tex]\begin{gathered} _{16}C_4=\frac{16!}{4!(16-4)!}=\frac{16!}{4!\cdot12!} \\ \\ _{16}C_4=1820 \end{gathered}[/tex]So in total there are 1820 different ways Rudy can choose 4 pizza toppings.
question 1 A new streaming company charges a rate of $5.99 per month. in order to generate some additional revenue upfront the company is offering a VIP rate of only $3.49 Per month to any subscriber who purchases a VIP pass for one time fee of $21 set up in solving any qualities to determine how many months it would take for subscriber to save money by purchasing the VIP pass
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21 + 3.49x < 5.99x
x > 8.4
Explanations:The normal monthly rate = $5.99
The VIP monthly rate = $3.49
The one time VIP fee = $21
Let the number of months be x
At normal rate, the total charge for x months = 5.99x
For the VIP:
The total charge for x months = 21 + 3.49x
For a subscriber to save money by purchasing the VIP pass, it means the total charge for the VIP must be less than the total charge for the normal subscribers5.99x
Therefore, the inequality to determine how many months it will take for a subscriber to save money by purchasing the VIP pass is:
21 + 3.49x < 5.99x
Solve the inequality above:
21 < 5.99x - 3.49x
21 < 2.5x
2.5x > 21
x > 21/2.5
x > 8.4
Therefore, for a subscriber to save money by purchasing the VIP pass, it would take more than 8.4 months
helpppppppppp!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:f(x) = 1/4x
Step-by-step explanation:
Assuming this is a linear equation, we simply use the two points given to find the slope (or gradient depending on where you’re from), to find the equation. So just do rise over run:
Edited: I divided backwards, apologies!
-3 - (-2)/-8 - (-12) = -5/-20 = 1/4x.
Will give brainliest thank you..!
Answers
Answer:
4
Step-by-step explanation:
4
4
4
4
Write an equation for the description.Two-thirds a number x plus 6 is 10.
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We have the next description:
- Two-thirds a number x plus 6 is 10.
To represent the description we can use the next equation:
[tex]\frac{2}{3}x+6=10[/tex]can anyone help me?
solve using system of linear equations using elimination
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Answers
The values of the variables are x = 2, y = -2 and z =0
How to solve the system of equations?From the question, the system of equations is given as
x – y - 3z = 4
2x + 3y – 3z = -2
x + 3y – 2z = -4
Subtract the second equation from the third
This action will eliminate (y)
So, we have
x + 3y – 2z = -4 - (2x + 3y – 3z = -2)
Evaluate
-x + z = -2
Make x the subject
x = z + 2
Substitute x = z + 2 in x – y - 3z = 4 and x + 3y – 2z = -4
z + 2 – y - 3z = 4
z + 2 + 3y – 2z = -4
Evaluate
-2z - y = 2
-z + 3y = -6
Double -z + 3y = -6
-2z + 6y = -12
Subtract -2z + 6y = -12 from -2z - y = 2 to eliminate z
7y = -14
Divide
y = -2
Substitute y = -2 in -z + 3y = -6
-z + 3(-2) = -6
Evaluate
-z - 6 = -6
Evaluate
z = 0
Recall that x – y - 3z = 4
So, we have
x + 2 - 3(0) = 4
Evaluate
x = 2
Hence, the solution is x = 2, y = -2 and z =0
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PLSSS HELPPPPPthe number of stores opened by a coffee company can be modeled by the exponential function graphed on the grid. Based on the graph, which statement does not appear to be true.
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Let's analyze the statements to see which one is not true.
Statement F. The coffee shop company had opened 400 stores by the end of 1992.
The horizontal axis on the graph (the x-axis) represents the number of years that have passed since 1992, thus the year 1992 is at x=0 on the graph.
The vertical axis (the y-axis) represents the number of stores.
As we can see in the following diagram, the red point represents the number of stores at x=0 (at the year 1992):
it is true that the coffee shop had 400 stores by the end of 1992.
Statement G. The coffee shop opened 100 stores in 1 year.
To see if this is true, we look at x=1, which represents 1 year, and check for the number of stores corresponding to 1 year:
This point is at (1,500) --> After 1 year there were 500 stores.
Since they started with 400 stores, this means that it is true that they opened 100 stores in 1 year.
Statement H. Every year the number of stores the coffee company opened increased by 25%.
We can find if this is true just by looking at the form of the graph. This graph has an exponential curve which means that the growth increases at every step. Thus there is an increase in the coffee shop that they open every year. This statement is true.
Statement J. Since 1992 the coffee shop company has opened 250 stores each year.
As we saw with the previous statement, the number of shops opened every year is not constant, it increases with time. Thus, since they do not open the same amount of shops every year, this option the one that is not true.
Answer: Statement J
simplify the rational expression. 18x3y5 45x5y9
Answers
8y+63x+9
