6 7) through: (4, 5), parallel to y=-x
Answer:
Step-by-step explanation:
thank you for the points
a student is trying to solve the system of two equations given below:equation P: y + z = 6equation Q: 5y + 9z = 1Which of the following is a possible step used in eliminating the y-term?A: (y + z = 6) × 9B: (y + z = 6) × -5C: (5y + 9z = 1) × 9D: (5y + 9z = 1) × 5
we have the system
y + z = 6 ------> equation P
5y + 9z = 1 -----> equation Q
i will solve by elimination
step 1
Multiply the equation P by -5
so
(y + z = 6) *-5
-5y-5z=-30
adds equation Q
-5y-5z=-30
5y + 9z = 1
------------------
5z+9z=-30+1
therefore
the answer is the option Bplease help me......
write in y=mx+b form
Answer:
What?
Step-by-step explanation:
D.
[tex]g(x) = \frac{3}{x - 4} [/tex]find the domain, range and zeros/intercepts.The domain would be all real numbers not equal to 4. Right?How do I find the range and intercepts?
You are right about the domain
it is all real values of x except 4
So about the range we must make x subject of the formular so we know the values of y in which g(x) is defined
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Nov 03, 2:56:13 PM
Find the Area of the figure below, composed of a rectangle with two semicircles
removed. Round to the nearest tenths place.
Answer:
10
D(
PLEASE HELP 30 POINTS !!!!!!!!!!!!
Answer:
31.7 units²
Step-by-step explanation:
Since the two semicircles have the same radius, they have the same combined area as a full circle.
Rectangle: length 10; width 6
Circle: diameter 6; radius 3
area = area of rectangle - area of circle
area = LW - πr²
area = 10 × 6 - 3.14159 × 3²
area = 60 - 28.27431
area = 31.72569
Answer: 31.7 units²
12. Refer to a bag containing 13 red balls numbered 1-13 and 5 green balls numbered 14-18. Youchoose a ball at random.aa. What is the probability that you choose a red or even numbered ball? (3 points)b. What is the probability you choose a green ball or a ball numbered less than 5?(3 points)
Given
A bag contains 13 red balls numbered 1-13 and 5 green balls numbered 14-18.
And a ball is chosen at random.
To find:
a) The probability that you choose a ren or even numbered ball.
b) The the probability you choose a green ball or a ball numbered less than 5.
Explanation:
It is given that,
The total number of balls is (13+5)=18.
The number of red balls is 13 numbered from 1-13.
The number of green balls is 5 numbered from 14-18.
i) Then, the probability of getting a a red or even numbered ball is,
[tex]\begin{gathered} P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right) \\ =\frac{n\left(A\right)}{n\left(S\right)}+\frac{n\left(B\right)}{n\left(S\right)}-\frac{n\left(A\cap B\right)}{n\left(S\right)} \end{gathered}[/tex]Here,
[tex]\begin{gathered} n\left(A\right)=n\left(red\text{ balls}\right) \\ =13 \\ n\left(B\right)=n\left(even\text{ numbered balls}\right) \\ =9 \\ n\left(A\cap B\right)=n\left(red\text{ balls and even numbered balls}\right) \\ =6 \\ n\left(S\right)=n\left(Total\text{ number of balls}\right) \\ =18 \end{gathered}[/tex]That implies,
[tex]\begin{gathered} P\left(A\cup B\right)=\frac{13}{18}+\frac{9}{18}-\frac{6}{18} \\ =\frac{16}{18} \\ =\frac{8}{9} \\ =0.89 \end{gathered}[/tex]Hence, the probability of getting a red or even numbered ball is 0.89.
ii) Also,
The probability of getting a green ball or a ball numbered less than 5 is,
[tex]\begin{gathered} P\left(C\cup D\right?=P\left(C\right)+P\left(D\right)-P\left(C\cap D\right) \\ =\frac{n\left(C\right)}{n\left(S\right)}+\frac{n\left(D\right)}{n\left(S\right)}-\frac{n\left(C\cap D\right)}{n\left(S\right)} \end{gathered}[/tex]Here,
[tex]\begin{gathered} n\left(C\right)=n\left(green\text{ balls}\right) \\ =5 \\ n\left(D\right)=n\left(balls\text{ numbered less than 5}\right) \\ =4 \\ n\left(C\cap D\right)=n\left(a\text{ }green\text{ }ball\text{ }or\text{ }a\text{ }ball\text{ }numbered\text{ }less\text{ }than\text{ }5\right) \\ =0 \end{gathered}[/tex]Then,
[tex]\begin{gathered} P\left(C\cup D\right)=\frac{5}{18}+\frac{4}{18}-0 \\ =\frac{9}{18} \\ =\frac{1}{9} \\ =0.11 \end{gathered}[/tex]Hence, the probabilty of getting a green ball or a ball numbered less than 5 is 0.11.
What is the total surface area of the rectangular prism in square feet?39.25 ft?© 45 ft?B 78.5 ft?DNot here
We have that the total surface area of the rectangular prism is:
[tex]\begin{gathered} A_T=\text{ 2(4.5ft }\cdot\text{ 4ft) + 2(4.5 ft }\cdot\text{ 2ft)} \\ =2(18ft^2)+2(9ft^2) \\ =36ft^2+18ft^2 \\ =54ft^2 \end{gathered}[/tex]So the answer is 54 ft^2.
football field is 300 ft long and 160 ft wide , to nearest hundredth, how many acres in football field
What are the answers for these, please add workings so I can understand.
AA M2/L15 zearn.org Juanita swam Zearn Convert to Solve actice for a competition, Juanita swam 0.73 kilometer in the pool each day for 2 weeks How many meters did Juanita swim in those 2 weeks? 1 km = 1,000 m
10220 meters Juanita swim in those 2 weeks.
Given that,
Juanita practiced her swimming for a competition by swimming 0.73 kilometers in the pool every day for two weeks.
We have to find Juanita swam how many meters in those two weeks? 1 km = 1,000 m
First, we multiply the number of days swam by the amount of kilometers swan each day.
0.73×2 week
0.73×14days
10.22
The kilometers are then multiplied by the conversion rate to convert them to meters.
10.22 kilometers multiplied by a 1000 m to m conversion factor results in 10220 m.
Therefore, 10220 meters Juanita swim in those 2 weeks.
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f(x) = 2 + x^2, evaluate f(7)
ok
[tex]\begin{gathered} f(x)=2+x^2 \\ f(7)=2+(7)^2 \\ f(7)\text{ = 2 + 49} \\ f(7)\text{ = 51} \end{gathered}[/tex]Result
f(7) = 51
For the spring picnic, Mr. Jones served 85 hot dogs to 50 people. Mr. Jones expects 68 people at the fall picnic. Which proportion could be used to find how many hot dogs Mr. Jones needs for the fall picnic?
If Mr. Jones served 85 hot dogs to 50 people the proportion of hot dogs is:
[tex]\frac{85}{50}\text{ hot dogs/person}[/tex]If he expects 68 people at the fall picnic, the amount of hot dogs he will need is the number of people multiplied by this proportion:
[tex]\text{hot dogs = 68p }\cdot\frac{85}{50}\text{ hot dogs/p}[/tex]Answer
The proportion that could be used to find how many hot dogs Mr. Jones will need for the fall picnic is 85/50
He will need 115.6 hot dogs (since the number of hot dogs is a whole number, He will have to buy 116 hot dogs)
what is the slope of this line? y= -2x +6
Answer:
-2
Step-by-step explanation:
Slope is y = mx + b
Your equation is y = -2x + 6, simply pull the 'm' from the equation, that being -2.
Hope that helps.
Transform y = f(x) by reflecting it across the x-axis. Label the newfunction h(x). Compare the coordinates of the corresponding pointsthat make up the two functions. Which coordinate changes, x ory?
y = f(x)
Reflection, change the sign of the function
y = - f(x)
f(x) -f(x)
1 -1
2 -2
3 -3
8 -8
20 -20
The x coordinate will change.
How much you learned about the inverse, converse, and contrapositive of a conditional (if-then) statement, and how this can be applied in real life
A conditional statement can be written as:
[tex]p\rightarrow q[/tex]An example of this in real life is:
[tex]\text{If it rains then the floor gets wet.}[/tex]In this case:
p = it rains
q = the floor gets wet
The converse of that conditional is:
[tex]\begin{gathered} q\rightarrow p \\ \text{If the floor gets wet then it rains.} \end{gathered}[/tex]Notice that the conditional being true doesn't mean necessarily that its converse is true. For example, every time it rains the floor gets wet can be true, but the floor could get wet for other reasons, so the converse would not be true.
Also, the inverse of that conditional is:
[tex]\begin{gathered} \neg p\rightarrow\neg q \\ \text{If it does not rain then the floor does not get wet.} \end{gathered}[/tex]As we see, the inverse of a true conditional statement is not necessarily true.
And the contrapositive of that conditional statement is:
[tex]\begin{gathered} \neg q\rightarrow\neg p \\ \text{If the floor does not get wet then it does not rain.} \end{gathered}[/tex]Now, the contrapositive of a true conditional statement is always true. Notice that if every time it rains the floor gets wet, the only explanation for the floor not getting wet is that it does not rain.
Number 9, Im not quite sure on how to do these
Solution:
Given:
[tex]f(x)=2(x-3)^2+1[/tex]The equation of a parabola in vertex form is given by:
[tex]y=a(x-h)^2+k[/tex]The coordinates of the vertex is given by (h,k).
Hence, comparing both equations,
[tex]\begin{gathered} f(x)=2(x-3)^2+1 \\ y=a(x-h)^2+k \\ a=2 \\ h=3 \\ k=1 \end{gathered}[/tex]Therefore, the coordinates of the vertex is;
[tex](h,k)=(3,1)[/tex]Match the cards that have equivalent expressions. WILL GIVE BRAINLIEST!!!
Answer:
• 5x + 20 = 5(x + 4)
• 5(2x + 8) = 10x + 40
,• 5(x + 8) = 5x + 5.8
According to Hooke's Law, the force needed to stretch a spring is proportional to the distance the spring is stretched. If a force of 180 newtons stretches a spring 6 cm, what is the direct variation equation for this spring? If a force of 420 newtons was applied, what is the distance the spring will be stretched? Select all answers that apply.
[mark all correct answers]
a) f=6x
b) f=30x
c) f=70x
d)x=14
e) x=31.5
f) x=2.6
The direct variation equation is: b) f = 30x.
The distance 420 newtons will stretch is: d) x = 14.
How to Write a Direct Variation Equation?The direct variation equation can be defined as y = kx, where k is the constant of proportionality, which is k = y/x, while x and y are the variables.
Let y represent the distance the spring is stretched, while x represents the force that is applied to the spring.
If a force (f) of 180 newtons is applied to stretch a distance of the spring (x) to 6 cm, therefore:
Constant of proportionality, k = 180/6
Constant of proportionality, k = 30
To write the direct variation equation, substitute k = 30 into f = kx:
f = 30x.
To find the distance (x) the spring will be stretched when 420 newtons was applied, substitute f = 420 into y = 30x:
420 = 30x
420/30 = 30x/30
14 = x
x = 14
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Graph the line.2) Through (2, -6) and (-1,9)
Attached above is the graph of the line passing through the points (2, -6) and (-1,9).
How to plot the graph:
Firstly, we need to locate the first point (2,-6)
That means a point 2 on the x axis and -6 on the y-axis.
Then, next locate the second point (-1,9)
That means a point -1 on the x axis and 9 on the y-axis.
Then lastly, join the two points.
Write an equation for the line parallel to the given line that
contains C.
C(4,6); y= -4x+1
The equation of the parallel line is
The equation of the line parallel to the given line is y + 4x = 22
The given line is y= -4x+1
Slope of the line = -4
Slope of the parallel line= -4
Equation of the line parallel to the given line which passes through C(6,4)
y - 6 = - 4 ( x - 4 )
y - 6 = -4x + 16
y + 4x = 22
Hence the equation of the parallel line is y + 4x = 22
One that stretches on all sides and has no width is referred to in geometry as a line. A straight line is, to put it simply, a line without bends. An non-curved line that extends to infinity on both sides is said to be straight.
The general equation for a straight line is y = mx + c, where m stands for the line's slope and c for its y-intercept. The most frequently used straight line equation is one that has to do with geometry.
The equation of a straight line can be written in a number of different ways, such as point-slope form, slope-intercept form, general form, standard form, etc.
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what is the value of y in the triangle at the right? (sorry the picture is a little blurry)
Answer:
To find the length y from the given right anled triangle.
Since the given triangle is right anled triangle,
we have the following,
[tex]\sin \theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]Let,
hypotenuse =14
opposite side=y
Substitute the values we get,
[tex]\sin 30\degree=\frac{y}{14}[/tex]we know that, sin 30=1/2
Using this we get,
[tex]\frac{1}{2}=\frac{y}{14}[/tex][tex]y=\frac{14}{2}[/tex][tex]y=7[/tex]Answer is: option D: 7
25% of the students in a school are in sixth grade.A. How many sixth graders are there if the school has160 students?B. How many sixth graders are there if the school has28 students?C. If the school has x students, write an expression for the number of sixth graders in terms of x. D. How many students are in the school is 42 of them are sixth graders.
A.
Multiply the number of students (160) by the percentage that are in sixth grade (25%)
Express the percentage in decimal form = 25/100 = 0.25
160 x 0.25 = 40 students
B. Same process
28 x 0.25 = 7 students
C.
Multiply 0.25 by x
0.25x
D.
0.25x = 42
Solve for x
x =42/0.25
x= 168
Identify the local maximum and local minimum of the function shown in the graph below. You can assume that the maximum and minimum values lie on whole numbers
Given:
The graph of the function is given.
To find:
The local maximum and a local minimum of the function.
Explanation:
We know that,
The local minimum is a point within an interval at which the function has a minimum value.
So, the local minimum point is,
[tex](0,1)[/tex]The local maximum is a point within an interval at which the function has a maximum value.
So, the local maximum point is,
[tex](-3,4)[/tex]Final answer:
The local minimum point is,
[tex](0,1)[/tex]The local maximum point is,
[tex](-3,4)[/tex]I neeeeeeeeeeeeeeeeeedddddd helpppp!
Question: A shipment of 288 reams of paper was delivered. Each of the 30 classrooms received an equal share of the paper. Any extra reams of paper were stored After the paper was distributed to the classrooms, how many reams of paper were stored?
Answer:
18
Step-by-step explanation:
288/30=9 288-270= 18 9×30=270
Benjamin believes that [tex] \frac{1}{2} [/tex]% is equivalent to 50%. is he correct? why or why not?
First, we convert 1/2% to a decimal.
[tex]\frac{1}{2}\%=\frac{0.5}{100}=0.005[/tex]Similarly:
[tex]undefined[/tex]1. Tanisha drove 120 miles on 5 gallons of gas. How many miles can she drive t she has 12 gallons of gas?
The wavelength of a wave of frequency 100 Hz is 3.3m. Find it's speed
Answer:
330
Step-by-step explanation:
100*3.3=330
Step-by-step explanation:
Given:
Wavelength of wave : 3.3m
Frequency of wave : 100Hz.
speed/velocity : ?
As we know
velocity = wavelength × Frequency
= 3.3 × 100
=330ms−1
So the speed of the wave is 330 ms·¹
I need help with my math
The equation of a line is the form of
[tex]\begin{gathered} y\text{ = mx +c} \\ \text{where} \\ m\text{ = slope} \\ \text{and} \\ c\text{ = y-intercept} \end{gathered}[/tex]The equation of the line was, however, given as
[tex]5x-3y\text{ = (-9)}[/tex]To rewrite this equation in slope-intercept form, we must first find the slope and y-intercept from the equation by rearranging it
[tex]\begin{gathered} 5x+9=3y \\ 3y\text{ = 5x+9} \\ \frac{3y}{3\text{ }}=\frac{5x}{3}+\frac{9}{3} \\ y\text{ = }\frac{5}{3}x+3 \\ \text{From here the slope, m =}\frac{5}{3} \\ \text{and } \\ \text{the y-intercept, c = 3} \end{gathered}[/tex]Hence the required equation is y =(5/3)x +3. The answer is the third option
Please help,quick! *I need an equation!*
Any 1 solved is appreciated please:)
2.If a number decreased by 20, the result is 13. What is the number?
3. This week, a construction company had expenses of $900, which was $50 more than the expenses from last week. What were last week's expenses?
4.Sara's mom split her gift card among her 4 children. If each child received $15, how much was on the gift card originally?
I'd appreciate it if you just solved 1, or all of them. Either way, thank you.
Answer: for 2 its 33, for 3 its 850, for number 4 its 60
Step-by-step explanation:
1: 20+13=33, so 33-20=13
2: 900-50=850
4: 15x4=60
Find the range and standard deviation of the set of data.4, 7, 4, 7, 7, 9, 11The range is(Simplify your answer.)
SOLUTI0N
Step 1 :
In this question, we are meant to find the range and standard deviation of the set of the data:
4, 7, 4, 7, 7, 9, 11
For the Range, we have that:
[tex]\begin{gathered} \text{Range = Highest number - Smallest number } \\ =\text{ 11 - 4} \\ =7 \end{gathered}[/tex]Step 2 :
For the Standard Deviation,
We have that :
[tex]\text{Standard Deviation =}\frac{\sqrt[]{\sum ^{\infty}_{n\mathop=0}(X_{i\text{ }}-X)^2}}{n}[/tex]So, we need to evaluate using the following process,
[tex]\begin{gathered} \text{Mean, X = }\frac{4\text{ + 7 + 4 + 7 +7 + 9 + 11}}{7} \\ =\frac{49}{7} \\ =\text{ 7} \end{gathered}[/tex]Next, we evaluate the following :
Variance =
[tex]\frac{(4-7)^2+(7-4)^2+(4-7)^2+(7-7)^2+(7-7)^2+(9-7)^2+(11-7)^2}{7}[/tex]=
[tex]\begin{gathered} \frac{9\text{ + 9 + 9 + 0 + 0 + 4 + 4}}{7} \\ =\text{ }\frac{35}{7} \\ =\text{ 5} \end{gathered}[/tex]Next, we have that :
Standard Deviation =
[tex]\sqrt[\square]{Variance}[/tex]=
[tex]\begin{gathered} \sqrt[\square]{5} \\ =\text{ 2. 236} \\ =\text{ 2. 2}4\text{ ( nearest hundredth )} \end{gathered}[/tex]CONCLUSION:
The Range = 7 and the Standard Deviation = 2. 24