First, we need to find the equation for the two equations.
The equation graphed has a y-intercept of 3 and a slope of
[tex]m=\frac{-6}{3}=-3[/tex]therefore, the equation of the line is
[tex]\boxed{y=-\frac{1}{2}x+3.}[/tex]For the second equation, we know what it has a slope of 3; therefore it can be written as
[tex]y=3x+b[/tex]Now, we also know that this equation passes through the point y = -5, x = 2; therefore,
[tex]-5=3(2)+b[/tex]which gives
[tex]-5=6+b[/tex][tex]b=-11[/tex]Hence, the equation of the line is
[tex]\boxed{y=3x-11}[/tex]Now we have the equations
[tex]\begin{gathered} y=-\frac{1}{2}x+3 \\ y=3x-11 \end{gathered}[/tex]equating them gives
[tex]-\frac{1}{2}x+3=3x-11[/tex]adding 11 to both sides gives
[tex]-\frac{1}{2}x+14=3x[/tex]adding 1/2 x to both sides gives
[tex]14=\frac{7}{2}x[/tex]Finally, dividing both sides by 7/2 gives
[tex]\boxed{x=4\text{.}}[/tex]The corresponding value of y is found by substituting the above value into one of the equations
[tex]y=-\frac{1}{2}(4)+3[/tex][tex]y=1[/tex]Hence, the solution to the system is
[tex](4,1)_{}[/tex]-Determine whether each relation is a function. Explain your answerA. {(7,4),(6,3),(5,2)}B. {(15,0),(15,-2)}C. {(0,1),(2,1),(0,3)}
A. it is a fuction because for every number in the first position of the pairs it is one and only one second position number.
B. it's not a function because the number 15 has two different pairs
C. it's not a function because zero has two different pairs, 1 and 3.
In the accompanying diagram of parallelogramABCD, m_A = (2x + 10) and mZB = 3x. Find thenumber of degrees in m_B.D3x(2x + - 10)ABBYour answer
Answer
Angle B = 102°
Angle A = 78°
Explanation
The first thing to note in answering this is that for parallelograms,
- Opposite angles are equal to each other.
- Adjacent angles (angles close to each other) sum up to give 180°.
So, in the given parallelogram, we can see that the two angles given are adjacent angles. Hence,
2x + 10° + 3x = 180°
5x + 10° = 180°
5x = 180° - 10°
5x = 170°
Divide both sides by 5
(5x/5) = (170°/5)
x = 34°
So, we can solve for Angle B now
Angle B = 3x = 3 (34°) = 102°
Angle A = 2x + 10° = 2(34°) + 10° = 68° + 10° = 78°
Hope this Helps!!!
16. The graph shows the relationship between the total cost and the amount of rice purchased 32 20 Total price ($) Amount of rice (lb) Part A: What does the ordered pair (6, 30) represent? Part B: Which point on the graph represents the unit price? Part C: How many pounds would you have to buy for the total cost to be $20? Explain how to find the answer
For the information given in the statement you have:
Part A: According to the graph, the point (6,30) means that the total cost of 6 pounds of rice is $30.
Part B: The unit price per pound of rice can be seen in the graph at point (1,4), that is, the price of 1 pound of rice is $ 4.
Part C: To find out how many pounds you would have to buy for the total cost to be $ 20 you have to find the point whose second coordinate is 20, that is, point (4,20), then you would have to buy 4 pounds of rice for the total cost to be $20.
Oliver Queen is able to hit the bull's-eye (center of the target) 87% of the time. If he shoots 29 arrows, what is the probability that he hits the bull
eye exactly 13 times?
The probability that he hits the bull's-eye in one shot is given by p = 0.87
Then, the probability that the hits the bull's-eye m times in n shots is given by:
[tex]P(m|n)=\frac{n!}{m!(n-m)!}p^m(1-p)^{n-m}[/tex]For n = 29 and m = 13 we have:
[tex]\begin{gathered} P(13|29)=\frac{29!}{13!16!}0.87^{13}\cdot0,13^{16} \\ P(13|29)=4.0\cdot10^{-8} \end{gathered}[/tex]in the graph of y= 8x + 5, 8 is theof the line
the function is:
[tex]y=8x+5[/tex]where 8 is the slope of the function
The average daily high temperatura for the month of may in Ocala, Florida is approximated by the fuction f(n)= 0.2n + 80, where n is the day of the month. May has 31 days. The maximum daily high temperature ocurred on May 31 st. What was the msximum temperature?
n = day of the month
Therefore,
The maximum temperature for may 31st will be
[tex]\begin{gathered} f(n)=0.2n+80 \\ f(31)=0.2(31)+80 \\ f(31)=6.2+80=86.2\text{ } \end{gathered}[/tex]A fireworks rocket is launched from a hill above a lake. The rocket will fall into the lake after exploding in the air. The rocket’s height above the surface of the lake is given by the function g(x)= -16x2 + 64x + 80 where x is the number of seconds after the rocket is launched. The function can also be written in factored form as g(x) = -16 (x + 1)(x - 5).When does the rocket hit the ground?
We are giving the function as;
[tex]g(x)=-16x^2+64x+80[/tex]If we factorize g(x) we have that
[tex]g(x)=-16(x+1)(x-5)[/tex]T0 find if the object has be launched and find the x value of the object
Therefore,
[tex]\begin{gathered} -16(x+1)(x_{}-5)=0 \\ \Leftrightarrow(x+1)(x_{}-5)=0 \\ \leftrightarrow x=-1\text{ or x=5} \end{gathered}[/tex]it will take the rocket 5 seconds to reach the ground.
Choose the linear equation that best fits the data on the graph
We have several points in a graph and want to know what of the options is the best fit.
Due the options has very diferent slopes for the line we can solve the problem by inspection, so:
• The slope of the line must be negative, because the points data show a negative slope. ,So, the options A and B are discarded.
,• The points show a big slope. For Option C, when x = 4, y = -7 that is near from data, for Option D, when x =4, y = -1 which is very far from data.
So the correct answer is the option C.
A tire company wants to determine if tires made with a new type of tread will last longer than the tires made with the original type of tread. The company has access to 24 different vehicles. The vehicles will be driven for one year and the depth of the remaining tread will be measured. The average depth for the new type of tread will be compared to the average depth of the original type of tread.Which of the following describes a matched pairs design for this experiment?A. Each of the 24 vehicles is numbered 1–24. These numbers are put into a random number generator. The first 12 unique numbers generated will represent the vehicles that will receive the tires with the new tread. The remaining 12 vehicles will receive the tires with the original tread.B. There are six vehicles of each vehicle type: sedan, SUV, minivan, and truck. For each type, the vehicles will be numbered 1–6, and a random number generator will be used to pick three unique numbers. These three vehicles will receive tires with the new tread and the other three vehicles in the group will receive tires with the original tread.c. There are six vehicles of each vehicle type: sedan, SUV, minivan, and truck. Each vehicle type is numbered 1–4, and these numbers are entered into a random number generator. The first two unique numbers selected will represent the group of vehicles that will receive tires with the new type of tread. The remaining two groups will receive tires with the original type of tread.D. The vehicles will be put into groups of two based on the size of the vehicle, with the largest two put together, the next largest two, etc. For each of the 12 groups of two, one of the vehicles is selected and a coin will be flipped. If it is heads, this car will receive tires with the new tread and the other vehicle will receive tires with the original tread. If it is tails, then the opposite will be done.
A matched pairs design is a special case of a randomized block design. It can be used when the experiment has only two treatment conditions; and subjects can be grouped into pairs, based on some blocking variable. Then, within each pair, subjects are randomly assigned to different treatments.
Based in the definition above, the correct answer is D.
Sarah wanted to catch Jim. However , although they started at the same time, Jim traveled at 80 km/h and Sarah traveled at 120 km/h . How much of a head start did Jim have if it took three hours for Sarah to catch him ?
Jim traveled at 80 km/h and Sarah traveled at 120 km/h
It took 3 hours for Sarah to catch Jim.
Let's find out how much distance both covered.
[tex]Jim\colon\; d=r\cdot t=80\cdot3=240\: km[/tex]So, Jim traveled 240 km
[tex]Sarah\colon\; d=r\cdot t=120\cdot3=360\: km[/tex]So, Sarah traveled 360 km
This means that Jim must have started 360 - 240 = 120 km ahead.
Therefore, Jim had a head start of 120 km
Solve each quadratic equation.f(x) = (x + 7)2 – 2
Let's find the solutions:
[tex]\begin{gathered} f(x)=0 \\ \mleft(x+7\mright)^2-2=0 \end{gathered}[/tex]Solve for x:
Add 2 to both sides:
[tex]\begin{gathered} (x+7)^2-2+2=0+2 \\ (x+7)^2=2 \end{gathered}[/tex]Take the square root of both sides:
[tex]\begin{gathered} \sqrt[]{(x+7)^2}=\pm\sqrt[]{2} \\ x+7=\pm\sqrt[]{2} \end{gathered}[/tex]Subtract 7 from both sides:
[tex]\begin{gathered} x+7-7=\pm\sqrt[]{2}-7 \\ x=\pm\sqrt[]{2}-7 \\ so\colon \\ x=\sqrt[]{2}-7\approx5.586 \\ x=-\sqrt[]{2}-7\approx-8.414 \end{gathered}[/tex]You can verify the results using the graph:
Identify the statement that best describes the output for the following R command. filter (Fingers, SSLast != “NA”)a) A list of the values in SSLast that are “NA”.b) A list of the values in SSLast excluding the “NA” values.c) A list of all the values in SSLast, but not in Fingers.d) A list of all values in Fingers excluding the “NA” values.
solution
filter(Fingers, SSLast != "NA") includes only cases for which the variable SSLast is not equal to NA. Therefore
answer:
b) A list of the values in SSLast excluding the “NA” values.
Can you help me on either of these questions it doesn't matter you can pick
12)
The midpoint of NH can be calculated using the formula:
[tex]M_{NH}=\frac{N+H}{2}...(1)[/tex]From the graph, we identify:
[tex]\begin{gathered} N=0 \\ \\ H=-6 \end{gathered}[/tex]Now, using equation (1):
[tex]\begin{gathered} M_{NH}=\frac{0-6}{2}=\frac{-6}{2} \\ \\ \Rightarrow M_{NH}=-3 \end{gathered}[/tex]According to the graph, this is the point K
y = -x - 2 y + 2 = -x Graph each system. Tell whether the system hasA.no solutionB.one solutionC. infinitely many solutionsD. Cannot determine
To graph each equation in the system, you can give it x-values, plug into the equations, and get values for Y.
Since a single line passes through two points, just take two values of x for each equation. So, for the first you have for example
*If x = 3
[tex]\begin{gathered} y=-x-2 \\ y=-3-2 \\ y=-5 \\ \text{ So} \\ (3,-5) \end{gathered}[/tex]*If x = -4
[tex]\begin{gathered} y=-x-2 \\ y=-(-4)-2 \\ y=4-2 \\ y=2 \\ \text{ So,} \\ (-4,2) \end{gathered}[/tex]For the second equation you have for example
*If x = 1
[tex]\begin{gathered} y+2=-x \\ y+2=-1 \\ y+2-2=-1-2 \\ y=-3 \\ \text{ So,} \\ (1,-3) \end{gathered}[/tex]*if x = -1
[tex]\begin{gathered} y+2=-(-1) \\ y+2=1 \\ y+2-2=1-2 \\ y=-1 \\ \text{ So,} \\ (-1,-1) \end{gathered}[/tex]Now, graphing the equations you have
As you can see, the lines associated with this system of equations overlap, that is, they share infinite solution points.
Therfore, the correct answer is C. infinitely many solutions.
given the polygon below, if
The value of ∠Q = 130
A polygon is a flat or plane two-dimensional closed shape with straight sides. It doesn't have any curved edges. A polygon's sides are also known as its edges.
Given that in the polygon ∠T = ∠S and ∠S = 115
We have to find q
The formula to calculate the sum of the inner angles of an n sides polygon is
(n-2) x 180
= (5-2) x 180
= 3 x 180
= 540
Sum of inner angles of polygon = 540
Since T = S
In the polygon P = R = 90
Q = 540 – 2 x 115 – 2 x 90
Q = 540 – 230 – 180
Q = 540 – 410
Q = 130
Therefore the value of ∠Q = 130
To learn more about polygons visit
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Hello, I'm finding this a tad bit difficult.A little help please. Question 1a. Calculate the total are including the frame.Question 1b: Calculate the external perimeter of this picture frame.
Part a.
In the first part of the problem we need to calculate the total area including the frame, for this, we use the formula for the area of a parallelogram:
In this case, the values of a, b and c are:
[tex]\begin{gathered} a=42\operatorname{cm} \\ b=65\operatorname{cm} \\ c=0.39m=39\operatorname{cm} \end{gathered}[/tex]Thus, the area is:
[tex]\begin{gathered} A=65\operatorname{cm}\times39\operatorname{cm} \\ A=2,535\operatorname{cm}^2 \end{gathered}[/tex]2,535 centimeters squared.
Part b.
In this part, we are asked to find the external perimeter of the picture frame.
For this, we use the formula to find the perimeter of a parallelogram:
Substituting the values of a and b from part a into the perimeter formula:
[tex]\begin{gathered} P=2(a+b) \\ P=2(42\operatorname{cm}+65\operatorname{cm}) \\ P=2(107\operatorname{cm}) \\ P=214\operatorname{cm} \end{gathered}[/tex]The perimeter of the frame is 214 centimeters.
Answer:
A. Area
[tex]2,535\operatorname{cm}^2[/tex]B. Perimeter
[tex]214\operatorname{cm}[/tex]Four different stores have the same digital camera on sale. The original price and discounts offered by each store are listed below. Rank the stores from the cheapest to most expensive sale price of the camera.
Store A: price $99.99 and discount of 15%
Store B: price $95.99 and discount of 12%
Store C: price $90.99 and discount of 10%
Store D: price $89.99 and successive discounts of 5% and 5%
Answer:
Step-by-step explanation:
store A $99.99 x 0.15= 14.9985
99.99-14.9985 = 84.99
store B $95.99 X 0.12= 11.5188
95.99 - 11.5188= 84.47
store C $90.99 x 0.10= 9.099
90.99-9.099= 81.891
store D = $89.99 x 0.05=4.4995
89.99- 4.4995= 85.4905 x 0.05= 4.27
85.4905- 4.27= 81.22
STORE D
STORE C
STORE B
STORE A
write the number in standard notation:3.92x10^7
We will write it as follows:
[tex]3.92\cdot10^7=39200000[/tex]I don't understand how to do a certain equation i have no clue what its called
Answer:
y =24 -x
Explanation:
Mr Ledger has 24 donuts and if he uses x donuts then the amount he will have left will be
[tex]24-x[/tex]and since we are calling this amount left y, we can say
[tex]y=24-x[/tex]which is our answer!
When Mr Ledger uses 18 donuts, the number left will be
[tex]\begin{gathered} y=24-18, \\ y=6. \end{gathered}[/tex]And when Mr Ledger uses 22 donuts, we will have left
[tex]\begin{gathered} y=24-22, \\ y=2. \end{gathered}[/tex]donuts.
The graph of the two points is given below.
What is the area of trapezoid KLMO?A) 224cm^2B) 112 cm^2C) 128 cm^2D) 96 cm^2
Given:
The length of the bases of the trapezoid
[tex]\begin{gathered} KL=a=12cm \\ \\ OM=b=16cm \end{gathered}[/tex]Height of the trapezoid:
[tex]LN=h=8cm[/tex]Required:
The area of trapezoid KLMO
Explanation:
The formula for area of trapezoid is given by
[tex]A(trapezoid)=\frac{a+b}{2}\times h[/tex]Substituting the given values in the above equation we get
[tex]\begin{gathered} A(trapezoid\text{ }KLMO)=\frac{a+b}{2}\times h \\ \\ A(trapezoid\text{ }KLMO)=\frac{12+16}{2}\times8=\frac{28}{2}\times8=14\times8=112cm^2 \end{gathered}[/tex]Final answer:
The area of trapezoid KLMO is 112 sq.cm
Given a student has a dog, what is the probability that a student also has a cat?62.9%57.1%41.8%36.3%
The given problem is a conditional probability problem.
Probability that a student has a cat given that he/she has a dog is represented as:
[tex]Pr(C|D)=\frac{Pr(CnD)}{Pr(D)}[/tex][tex]\begin{gathered} \text{CnD}=16 \\ \text{Sample space=28+16+24}=68 \end{gathered}[/tex]Thus,
[tex]Pr(\text{CnD)}=\frac{16}{68}=0.2353[/tex][tex]\begin{gathered} Number\text{ of dogs only=28} \\ Pr(D)=\frac{28}{68}=0.4117 \end{gathered}[/tex]Therefore,
[tex]undefined[/tex]I need help with the Try it! section. i will flow a walk through if you can give one
Solution
For this case we need to remember that the general equation for a line is given by:
y= mx+ b
Where m represent the slope and b the intercept
And we can find the slope with this formuala:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]And we can use (50, 725) and (100,1325) and we have:
[tex]m=\frac{1325-725}{100-50}=12[/tex]And the intercept would be:
725 = 50*12 +b
b= 725 - 600
b= 125
and the equation would be given by:
y= 12 x + 125
And the y intercept represent the starting value of 125$ no matter the number of guests
Find the volume of the solid. Use 22/7 for II
We have a rectangular solid prism. The formula to find the volume of this prism is as follows:
[tex]V=\text{lwh}[/tex]Where:
• l = length,. In this case, we have that ,l = 6cm,.
,• w = width,. In this case, we have that ,w = 5cm,.
,• h = height,. In this case, ,h = 1cm,.
Then, we have:
[tex]V=6\operatorname{cm}\cdot5\operatorname{cm}\cdot1\operatorname{cm}=30\text{cubic cm.}[/tex]Therefore, the value for the volume of the rectangular prism is equal to 30 cubic centimeters (30cm³) (30 cubic cm) (last option).
I need help with this question(Please no long explanation just the answer)
To find the answer to this question, we only have to add $12.80 once more time to the Simple Interest Earned.
[tex]12.80+38.40=51.2[/tex]At the fourth year, the Simple Interest Earned is $51.2 and the new account balance is $451.2.
Find the value of X in the length of MO
We are given that:
N is between M & O
[tex]\begin{gathered} MN=2x+4 \\ MO=6x \\ NO=28 \\ \\ \text{If N is the midpoint of M \& O, we have:} \\ MN=NO \\ 2x+4=28 \\ \text{Subtract ''4'' from both sides, we have:} \\ 2x=28-4 \\ 2x=24 \\ \text{Divivde both sides by ''2'', we have:} \\ x=\frac{24}{2}=12 \\ x=12 \\ \\ \therefore x=12 \end{gathered}[/tex]We will obtain the value of MO by substituting the value of ''x'' into MO. We have:
[tex]\begin{gathered} MO=6x \\ x=12 \\ MO=6(12)=72 \\ MO=72 \\ \\ \therefore MO=72 \end{gathered}[/tex]Which of the geometric objects are scaled versions ofeach other?For the objects that are scaled versions of each otherfill out the table withFigure Type- Figure Labels (smallest to largest)-Figure Ratio (might be extended ratio)Ive filled out the circles for you as an example and because the ratio involves radials. Figure labels| figure ratioCircle- J,L,G | √2: √ 5 :3
I will do the squares for you
All squares are similar
E K and C are squares so they are scaled versions of each other
The length of the top side of E 2 is units
The length of the top side of K is 3 units
The length of the top side of C is 5 units
From smallest to largest is E, K, C
Figure ratio is 2,3,5
The rectangles are done in the same manner
D is a 2 by 4
F is a 2 by 6
I is a 3 by 6
D and I are similar
D,I the ratio is 2:3
Triangles work like rectangles
B is a 2 by 3
H is a 3 by 5
A is a 4 by 6
B and A are similar
B,A the ratio is 2:4
The doctor orders 3000 mL D5RL to run at 300 ml/hr. How long will this IV infusion run
we know that
the infusion run at 300 ml/hr
so
Applying proportion
Find out how long for 3,000 ml
Which inequality is true when the value of u is 1? O-- 10 > -1.5 u – 10 > 1.5 O –u – 10 – 1.5 O – 10 >1.5
First, let's solve each one of the inequalities for u
1) -u-10>-1.5
u<-10+1.5
u<-8.5 then this statement is not true for u=1
2) u-10>1.5
u>1.5+10
u>11.5 then this statement is not true for u=1
3) -u-10<1.5
u>-10-1.5
u>-11.5 which is true for u=1
4)-u-10>1.5
u<-11.5 which is not true for u=1
then the correct option will be -u-10<1.5Solve each equation for the variable. -10 = Зm +5
-10 = Зm +5
Subtract 5 from both sides of the equation:
-10-5 = 3m+5-5
-15 = 3m
Divide both sides by 3
-15/3 = 3m/3
-5= m
m= -5
A line passes through the point (4,7) and has slope of 5/4. Write an equation in slope intercept form for this line.
Given the point (4,7) and the slope 5/4, we can use the line equation in the form slope-point to get the following:
[tex]\begin{gathered} (x_0,y_0)=(4,7) \\ m=\frac{5}{4} \\ y-y_0=m(x-x_0) \\ \Rightarrow y-7=\frac{5}{4}(x-4)=\frac{5}{4}x-\frac{5\cdot4}{4}=\frac{5}{4}x-5 \\ \Rightarrow y=\frac{5}{4}x-5+7=\frac{5}{4}x+2 \\ y=\frac{5}{4}x+2 \end{gathered}[/tex]therefore, the equation in slope intercept form is y = 5/4x + 2