The scatter plot that supports this statement has to be a linear function (direct proportional relationship), with a positive slope.
Solve the following system of linear equations by graphing:- 4x + y = 12- 8x + 2y = 24
Given the following system of linear equations
[tex]\begin{gathered} -4x+y=12\ldots\ldots\text{.}.1 \\ -8x+2y=24\ldots\ldots.2 \end{gathered}[/tex]Let us now make 'y' the subject of the formula in the equations above (writing in slope-intercept form)
From equation 1
[tex]\begin{gathered} -4x+y=12 \\ y=4x+12 \\ \therefore y=4x+12 \end{gathered}[/tex]From equation 2
[tex]\begin{gathered} -8x+2y=24 \\ 2y=8x+24 \\ \text{Divide both sides by 2} \\ \frac{2y}{2}=\frac{8x}{2}+\frac{24}{2} \\ y=4x+12 \\ \therefore y=4x+12 \end{gathered}[/tex]Let us now plot the graph of the equations above
From the above equations written in slope-intercept form, it was observed that the two equations are the same. This means there will be only one graph representing them.
Lastly, since both solutions are the same so therefore the equations have an infinite number of solutions.
The correct answer is Option 3.
you invest $200 in an account that earns 3% annual interest. Written a function that represents the balance after t years
the fuction will be
[tex]y(t)=200(1.03)^t[/tex]A spinner with 10 equally sized slices that are all red. The dialIs spun and stops on a slide at random. What is the probability that the dial stops on a red slice?Write your answer as a fraction or a whole number.
We have to find the probability that the dial is spun and stops on a red slice.
As the 10 slices are red, the probability is success outcomes / possible outcomes = 10/10 = 1.
This means that there is 100% chance of getting a red slice.
Answer: the probability is 1.
Spiral Back : Proportions Set up the proportion The ratio of girls to boys at Rayburn Middle school is 5 to 8. If there are 64 boys, how many total students are Number of girls click to add text Total number of students Click to add text
40 girls
104 students
1) Given the ratio of girls to boys is 5:8 and there are a total of 64 boys we can write, and then cross multiply it (for this is a proportion):
[tex]\begin{gathered} \frac{5}{8}=\frac{x}{64} \\ 8x=320 \\ x=40 \end{gathered}[/tex]So there are 40 girls.
2) Hence, the number of students altogether is found by adding them up: 40+64 = 104
Answer the following question using arrangements with repetition, permutations, or combinations. Be sure to explain why the particular counting technique applies to the problem. A dog shelter is giving away 15 different dogs, but you have room for only 5 of them. How many different dog families could you have
In a dog shelter there are 15 different dogs and there is space for only 5 of them.
ExplanationTo determine the number of different dogs you could have.
Combinations should be used because no item may be selected more than once and the order does not matter.
[tex]\begin{gathered} 15_{C_5}=\frac{15!}{5!10!} \\ \frac{15!}{5!10!}=\frac{15\times14\times13\times12\times11\times10!}{5\times4\times3\times2\times1\times10!} \end{gathered}[/tex][tex]\begin{gathered} \frac{15\times14\times13\times12\times11}{5\times4\times3\times2\times1}=7\times13\times3\times11 \\ 3003. \end{gathered}[/tex]AnswerHence the number of different dogs you could have is 3003.
What does the constant 0.2 reveal about the rate of change of the quantity?
In this problem, we have an exponential decay function
so
the function is of the form
[tex]y=a(1-r)^x[/tex]In this problem we have
[tex]f(t)=310(0.2)^{24t}=310(1-0.8)^{24t}[/tex]therefore
The answer is
The function is decaying exponentially at a rate of 80% every 24 daysQuestion 5 of 5Which two ratios represent quantities that are proportional?A. and 1.1B. 2 and 1eC.andola36and48
From the quantities given in the option , check the ratios that are proportional.
[tex]\frac{21}{28}=\frac{12}{16}[/tex]Simplify the proportional ,
[tex]\frac{3}{4}=\frac{3}{4}[/tex]As you can see the ratio are proportional .
Hence the correct option is B.
Which of the following best describes control, a principal of experimental design?
Ok, to calculate this we need to divide the succesful outcomes by the size of the sample:
[tex]\text{Proportion}=\frac{26}{50}=0.52[/tex]The sample proportion is 0.52, option D.
Consider right triangle ADEF below.EFDWhich expressions are equivalent to cos(ZE)?
The cosine ratio is given in the form:
[tex]\cos\theta=\frac{adj}{hyp}[/tex]From the triangle in the question, the different sides are labeled with respect to angle E as follows:
[tex]\begin{gathered} hyp=EF \\ opp=DF \\ adj=DE \end{gathered}[/tex]Therefore, the cosine ratio for ∠E will be:
[tex]\cos(\angle E)=\frac{DE}{EF}[/tex]ANSWER
[tex]\begin{equation*} \cos(\angle E)=\frac{DE}{EF} \end{equation*}[/tex]Determine the y intercept of the graph of this equation: y=3x-15
EXPLANATION
Since we have the equation y= 3x - 15, the y-intercept is the point -15, or representing as an ordinated pair (0,-15)
Which system of equation is graphed? Mark only one oval Y-1/3x=0;x-y=-2X-y=2;y-3x=0Y-3x0;x-y=-2Y-1/3x=0;x-y=2
The formula to calculate the equation of a line between two points is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Let us pick any two points for both the two lines and find the equation of the lines.
Line 1
[tex]\begin{gathered} (x_1,y_1)=(-2,0) \\ (x_2,y_2)=(1,3) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{y-0}{x--2}=\frac{3-0}{1--2} \\ \frac{y}{x+2}=\frac{3}{1+2} \\ \frac{y}{x+2}=\frac{3}{3} \\ \frac{y}{x+2}=1 \\ y=1(x+2) \\ y=x+2 \\ x-y=-2...........1 \end{gathered}[/tex]Hence, the equation of the line is
[tex]x-y=-2..........1[/tex]Line 2
[tex]\begin{gathered} (x_1,y_1)=(0,0) \\ (x_2,y_2)=(1,3) \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \frac{y-0}{x-0}=\frac{3-0}{1-0} \\ \frac{y}{x}=\frac{3}{1} \\ \frac{y}{x}=3 \\ y=3x \\ y-3x=0.............2 \end{gathered}[/tex]Hence, the equation of the line is,
[tex]y-3x=0...............2[/tex]Therefore, the system of equations are
[tex]y-3x=0;x-y=-2\text{ \lparen Option 3\rparen}[/tex]Graph a triangle (LMN) and rotate it 180° around the origin to create triangle L′M′N′. (10 points)
Describe the transformation using words. Make sure you refer to the characteristics and the coordinates.
Draw a line through points L and L′ and through M and M′. What do you notice about the lines you drew? Do you think you would notice the same characteristics if you drew another line through points N and N′? How do you know?
Considering the rotation of 180º degrees around the origin of triangle LMN, it is found that the lines connecting the vertices at the original triangle and at the reflected triangle intersect at the origin.
180º rotation about the originThe rule for the vertices of the triangle when it is rotated 180º degrees about the origin is given as follows:
(x,y) -> (-x,-y).
Hence the signal of the x and the y-coordinates is exchanged.
We draw a triangle LMN with vertices given as follows:
L(1,2), M(7,2), N(1,10).
Hence, applying the rotation, the vertices of triangle L'M'N' are given as follows:
L'(-1,-2), M'(-7,-2), N(-1,-10).
Given two points, there is a single line connecting these two points. These lines can be found using a calculator, and are given as follows for each vertex:
L and L': y = 2x.M and M': y = 2/7x.N and N': y = 10x.These three lines have in common an intercept of 0, meaning that they are proportional relationships, that is, they intersect at the origin, as shown by the image shown at the end of the answer.
Learn more about rotations at brainly.com/question/26249005
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You want to buy a used truck and are interested in the fuel consumption rate for each of the three trucks you are considering. Using the information given, decide which of the used trucks gets the best gas mileage.:2007 Ford F-150: 250 miles on 15.6 gallons2008 Chevy Silverado: 500 miles on 29.4 gallons2006 Toyota Tundra: 428 miles on 26.4 gallons
Chevy Silverado
1) In this question, we are going to find the unit rate so that we can get the best relation: mileage/gas
2) Let's start with the 2007 Ford F-150:
[tex]\begin{gathered} m------------g \\ 250----------150 \\ x------------1 \\ 150x=250 \\ x=\frac{250}{150} \\ x=\frac{1.6m}{g} \end{gathered}[/tex]So that Ford F-150 makes 1.6 miles per gallon
b) Chevy Silverado:
[tex]\begin{gathered} m-----g \\ 500----29.4 \\ y------1 \\ 29.4y=500 \\ y=\frac{500}{29.4} \\ y=\frac{17.00m}{\text{gallons}} \end{gathered}[/tex]Thus, the Chevy Silverado makes 17 miles per gallon.
c) Toyota Tundra:
[tex]\begin{gathered} m-----g \\ 428----26.4 \\ z-----1 \\ 26.4z=428 \\ z=\frac{428}{29.4}=\frac{14.55m}{g} \\ z= \end{gathered}[/tex]3) Thus the best gas mileage is: Chevy Silverado
POSSIBLE POINTS: 16. What can be defined as the system of marks at fixed intervals, which define the relation between the units being used and their representatior on the graph?
A system of marks is used to represent convenient units in a particular context. The adavantage of using marks is that it helps you to graph adequately relation between different units. The important thing here is that each unit of the particular quantity (distance, time, weight, years, height, etc) is represented by one mark. Thus, one unit is one mark, two units are two marks, etc.
Furthermore, it is also possible to one mark represent 2 units, 3 units, or in general whichever amount of units. In this case, each mark is an interval between two fixed numbers. For example, if you have that one mark represents 5 units (it is made because there are a lot of situations in which the information requires bigger numbers), then, two marks will represent 10 units, three marks will represent 15 units, etc.
I just need r and s . I just need a brief explanation with the answer
In order to find r and s we need to solve the following system of equations:
[tex]\begin{gathered} r=30x+40 \\ s=130x-160 \\ r=s \end{gathered}[/tex][tex]\begin{bmatrix}r=30x+40 \\ r=130x-160\end{bmatrix}[/tex][tex]130x-160=30x+40[/tex][tex]\begin{gathered} 130x-30x=40+160 \\ 100x=200 \\ x=\frac{200}{100} \\ x=2 \end{gathered}[/tex]replace x = 2 in the initial equations
[tex]\begin{gathered} r=30\cdot\: 2+40 \\ r=60+40 \\ r=100 \end{gathered}[/tex][tex]\begin{gathered} s=130\cdot\: 2-160 \\ s=260-160 \\ s=100 \end{gathered}[/tex]take into account r and s are corresponding angles, that's why they are equal.
Easton is trying to pick out an outfit for the first day of school. He can choose from 2 pairs of pants, 6 t-shirts, and 2 pairs of shoes. How many different outfits does Easton have to choose from?
He needs to choose three things, and he have to wear at least one of them. We know that he has
2 pairs of pants
6 t-shirts
2 pairs of shoes,
so in total, he have
[tex]2\times6\times2=24[/tex]24 diferent outfits to choose from.
Li’s family has a coupon for $49 off a stay at any hotel. They do not want to spend more than $150 in all. An inequality representing this situation is x - 49 Less-than-or-equal-to 150. Explain how you would graph this inequality. What will be included in the solution set in the context of the problem?
the inequality is
[tex]x-49\le150[/tex]we have in the right side and horizontal line at y =150 in the left side we have a line y=x-49
If we graph the two lines we will obtain
where the shadded area is the area
[tex]undefined[/tex]Answer:
Step-by-step explanation:
ample Response/Explanation:The solution set includes all numbers less than or equal to 199. I would draw a closed circle at 199 and draw an arrow pointing to the left. In the context of the problem, only money values greater than or equal to 0 make sense.
when a constant force acts upon an object, the acceleration of the object varies inversely with its mass. when a certain constant force acts upon an object with mass 2kg the acceleration of the object is 38 m/s^2 . if the same force acts upon another object whose mass is 19 kg what is this object acceleration
When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. when a certain constant force acts upon an object with mass 2kg the acceleration of the object is 38 m/s^2 . if the same force acts upon another object whose mass is 19 kg what is this object acceleration.
Solution.
[tex]\begin{gathered} a\text{ }\propto\text{ }\frac{\text{ 1}}{m} \\ a\text{ = }\frac{k}{m}\text{ , where k is a constant} \\ \text{when a = 28, m =2} \\ 28\text{ = k/2} \\ k\text{ = 28 x 2 = 56} \\ a\text{ =}\frac{56}{m}\text{ ( relationship between a and m)} \\ \\ \text{when m= 19} \\ \text{ a= }\frac{56}{19} \\ \text{ a = 2.95 ms-}^2 \end{gathered}[/tex]At a local gym you can either pay $80 for a monthly pass and then pay $5 for each visit or you can pay $15 for each visit with no monthly pass what is the cost when at the point when either option cost the same
We have here two equations that we need to determine in order to solve the question.
First, we have:
1. If you pay $80 for a monthly pass and then you pay $5 for each visit.
2. You can pay $15 for each visit with no monthly pass.
In the first case, the expression that translates that in an equation is:
[tex]y=80+5x[/tex]In the second case, the expression is:
[tex]y=15x[/tex]Since y is the total cost to go to the gym, and we need to know what the cost is when either option cost the same, we can equate both equations as follows:
[tex]y=80+5x,y=15x\Rightarrow80+5x=15x[/tex]Then, we need to solve the last equation subtracting 5x to both side of it:
[tex]80+5x-5x=15x-5x\Rightarrow80=10x\Rightarrow\frac{80}{10}=\frac{10}{10}x\Rightarrow x=8[/tex]Thus, the value for x is 8. To find the value of the cost, we can substitute this value in either equation. The cost will be the same:
[tex]y=80+5\cdot(8)\Rightarrow y=80_{}+40\Rightarrow y=120[/tex]Or
[tex]undefined[/tex]Please help I will give brainliest
Answer:
y = -3x + 4
Step-by-step explanation:
Desmos works great for graphing equations like this! Here's how you can do it...
1) Enter the equation for the given line, followed by the point at which your other line must pass.
2) Then you can more easily and accurately see where to make your new line
Here is the demos graph for this equation...
Answer: y=-3x+4
Step-by-step explanation:
3x+y=3
-3x+3x+y=-3x+3
y=-3x+3 ==> slope is -3
y=-3x+b ==> x=1 and y=-7
-7=-3(1)+b
-7=-3+b
-7+3=-3+3+b
b=-4
y=-3x+4
A lender requires a minimum down payment of 16% of the value of the home. You have $30,000 cash available to use as a down payment toward a home. Determine the maximum home value that you can finance. You can afford to finance a home worth at most $.________Round your answer to the nearest dollar.
Let
x ----> the value of the home
Remember that
16%=16/100=0.16
so
the inequality that represents this situation is equal to
[tex]0.16x\leq30,000[/tex]Solve for x
[tex]\begin{gathered} x\leq\frac{30,000}{0.16} \\ x\leq\$187,500 \end{gathered}[/tex]The answer is $187,500What is the midpoint of the segment shown below? (3,5) (2, 2) - 10 10 O A. (5,7) O B. (2) O C. (5,3) OD. (5,7)
If we have a segment, we can find the coordinates of the midpoint by averaging the coordinates of the endpoints.
If the endpoints of the segment are (3,5) and (2,2), the coordinates of the midpoint will be:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2}=\frac{3+2}{2}=\frac{5}{2} \\ y_m=\frac{y_1+y_2}{2}=\frac{5+2}{2}=\frac{7}{2} \end{gathered}[/tex]Then, the midpoint has coordinates (5/2, 7/2).
Answer: (5/2, 7/2) [Option B]
5x + 9y + 10y = -86x + y + z = 06x - y - z = 0x = ?y = ? z = ?
We are asked to solve a system of three linear equation in three unknowns (x, y, and z)
Eq 1) 5 x + 9 y + 10 z = -8
Eq 2) 6 x + y + z = 0
Eq 3) 6 x - y - z = 0
So we start by combining Eq 2 and 3 as they are. Adding term by term each side of the equal sign:
6 x + y + z + 6 x - y - z = 0+ 0
12 x + 0 + 0 = 0
12 x = 0
then x = 0/12 = 0
So x is zero
and then we can find y in terms of z using either Eq 2 or Eq 3:
6 (0) + y + z = 0
then
y = -z
Now we use the values : x = 0 and y = - z in Eq 1):
5 (0) + 9 (-z) + 10 z = -8
0 - 9 z + 10 z = -8
z = -8
So we found the three values:
x = 0, y = - z = -(-8) = 8, and z = -8
x = 0, y = 8 , and z = -8
There were 80golfers in the first round of a tournament. Of the 80, 62.5% qualified for the next round. How many did not qualify?
Number of golfers that didn't qualify = 30
Explanation:Total number of golfers = 80
The percentage that qualified for the next round = 62.5% = 0.625
Number that qualified = 80 * 62.5%
= 80 * 0.625
Number of golfers that qualified = 50
Number of golfers that didn't qualify = Total number of golfers - Number of golfers that qualified
= 80 - 50
Number of golfers that didn't qualify = 30
How much will Barry pay Kim at the end of 4 years?
From the question
Kim loaned Barry $15,860 at an interest rate of 16% for 4 years
This implies
Principal (P) = $15,860
Interest Rate (R) = 16%
Time (T) = 4years
We are to find the amount Barry will pay Kim at the end of 4years
First, we need to find the interest I, using
[tex]I=\frac{\text{PRT}}{100}[/tex]By substituting values we get
[tex]I=\frac{\text{ \$15860}\times16\times4}{100}[/tex]Simplifying the expression we have
[tex]\begin{gathered} I=\frac{\text{ \$1,015,040}}{100} \\ I=\text{ \$10150.40} \end{gathered}[/tex]Hence, the interest to be paid is $10,150.40
Next, we will find the Amount Barry will pay Kim at the end of 4years
Amount (A) is given as
[tex]A=P+I[/tex]Substituting values
[tex]\begin{gathered} A=\text{ \$15,860}+\text{ \$10,150.40} \\ A=\text{ \$}26,010.40 \end{gathered}[/tex]Therefore the Amount to be paid back is $26,010.40
34% of 5.7 is what number?
Let's use a rule of three to solve this:
This way,
[tex]x=\frac{5.7\cdot34}{100}\Rightarrow x=1.938[/tex]Therefore, 34% of 5.7 is 1.938
a barrel shaped like cylinder is laid on its side and rolled up a ramp that is 196 m long. the barrel has a circular base that turns 49 times in being rolled up the ramp. what us the diameter of the circular base?use the value 3.14 for pie. round your answer to the nearest tenth.
We know that
• The ramp is 196 meters long.
,• The barrel has a circular base, it turns 49 times over the ramp.
Observe the ramp longitude is 49 times greater than the lateral surface of the barrel. Let's divide.
[tex]\frac{196}{49}=4[/tex]This means the circumference of the base of the barrel is 4 meters long.
The circumference length formula is
[tex]C=\pi d[/tex]Where d is the diameter. Let's replace the circumference and solve for d.
[tex]\begin{gathered} 4=3.14\cdot d \\ d=\frac{4}{3.14}\approx1.27 \end{gathered}[/tex]Therefore, the diameter is 1.27 meters long, approximately.For each expression, rewrite the expression to illustrate addition only. Evaluate eachexpression, if possible.A.-6 + 15 - 18 - 2B.2m – 8m - 9 - 1/2p
SOLUTION
A.
[tex]\begin{gathered} -6+15-18-2 \\ to\text{ illustrate addition only, the expression will be written as } \\ (-6)+15+(-18)+(-2) \\ \end{gathered}[/tex]To evaluate the expression further, we will have:
[tex]\begin{gathered} (-6)+15+(-18)+(-2) \\ -6+15-18-2 \\ =-11 \end{gathered}[/tex]B.
[tex]\begin{gathered} 2m-8m-9-\frac{1}{2}p \\ to\text{ illustrate addition only, the expression will be written as } \\ (2m)+(-8m)+(-9)+(-\frac{1}{9}p) \end{gathered}[/tex]To evaluate the expression further, we will have
[tex]\begin{gathered} (2m)+(-8m)+(-9)+(-\frac{1}{9}p) \\ 2m-8m-9-\frac{1}{2}p \\ -6m-9-\frac{1}{2}p \end{gathered}[/tex]The question is in the photo. I need the rest of this question answered, thanks.
Quadrilateral A:
If we reflect Quadrilateral A over the x-axis, the y-coordinates will have a reverse sign. So, the coordinates of Quadrilateral-2 B will be: (-2, 1), (-6, 1), (-3, 5), and (-6, 3).
If we slide Quadrilateral B 8 units to the right and 5 units down, we will be adding 8 on the x-coordinate and subtracting 5 on the y-coordinates of Quadriteral B.
Hence, the graph of Quadrilateral C is found here:
If we rotate Quadrilateral B by 90 degrees clockwise about point (-2, 1), the coordinates will become: (-2, 1), (-2, 5), (2, 2), and (0, 5). Here is the graph:
What we are doing on the Quadrilaterals above are reflection, translation, and rotation in that order. This transformations are called rigid transformation. When performing rigid transformation, the shape will stay in the same size. (7)
On the other hand, another form of transformation is dilation. Dilation is non-rigid transformation. Hence, when we dilate a figure, the size of the shape changes.
If we dilate a figure by a scale factor greater than one, the shape will get bigger. (5)
If we dilate a figure by a scale factor smaller than one, the shape will get smaller. (6)
If 96 of the 136 participants in the club activities are nonresidents, what is the ratio of residents to nonresidents who participate in club activities? write the ratio in lowest terms as a fraction or with a colon