A linear equation in the slope-intercep form is y = mx + b.
To find the equation, follow the steps below.
Step 01: Substitute the point (0, 10) in the equation.
[tex]\begin{gathered} y=mx+b \\ 10=m\cdot0+b \\ 10=b \end{gathered}[/tex]Then,
[tex]y=mx+10[/tex]Step 02: Substitute the point (-5, 0).
[tex]0=-5m+10[/tex]Subtract 10 from both sides:
[tex]\begin{gathered} 0-10=-5m+10-10 \\ -10=-5m \end{gathered}[/tex]And divide both sides by -5:
[tex]\begin{gathered} \frac{-10}{-5}=\frac{-5}{-5}m \\ 2=m \end{gathered}[/tex]Step 03: Write the linear equation.
[tex]y=2x+10[/tex]Answer:
[tex]y=2x+10[/tex]Which phrase represents the algebraic expression for n-4.A) The quotient of a number and 4. B) 4 less than a number. C) 4 minus a number. D) 4 more than a number.
B) 4 less than a number.
. Identify the difference. -2-(-6)
In this case,
This difference is made this way:
-2 - (-6) =
-2 +6 = 4
So there we have this identity. The minus before the parentheses turns the minus into plus sign.
A pool is filled to 3/4 of its capacity 1/9 of water in the pool, evaporates. If the pool can hold 24,000 gallons when it is full, how many gallons of water will have to be added in order to fill the pool?A. 6,000B. 8,000C.12,000D.16,000
First, the pool was filled to 3/4 of its capacity, which is equal to:
[tex]24000\cdot\frac{3}{4}gal=18000gal.[/tex]Then, 1/9 of the water evaporated remaining 8/9 of the 18000 gal:
[tex]18000\text{gal}\frac{8}{9}=16000gal.[/tex]Therefore, to fill the pool we need to add:
[tex]24000-16000[/tex]gallons of water.
Answer: B. 8000.
List the angle measures of △VWX in order from smallest to largest. Assume that t is a positive number.
Explanation
To begin with, we will first have to obtain the length of side VX
[tex]VX^2=WX^2+VW^2-2\times WX\times VWcosw[/tex]In our case
[tex]\begin{gathered} WX=28t \\ VW=95t \\ w=94^0 \end{gathered}[/tex]Thus
[tex]\begin{gathered} VX^2=(28t)^2+(95t)^2-2\times(28t\times95t)cos94 \\ \\ VX^2=784+9025+371.104 \\ VX^2=100180.10 \\ \\ VX=100.90t \end{gathered}[/tex]Next, we will determine the angles at V and X
using sine rule
[tex]\begin{gathered} \frac{sin94}{100.9t}=\frac{sinV}{28t} \\ \\ sinV=\frac{28t\times sin94}{100.9t} \\ \\ sinV=0.27683 \\ \\ V=16.07^0 \\ \end{gathered}[/tex]Then, we will get the measure at X
[tex]180^0-16.07^0-94=69.93^0[/tex]Therefore, the order from smallest to largest angles will be
m
OR
m
Ashley‘s Internet service is terribly unreliable in fact on any given day there’s a 60% chance that her Internet‘s connection will be lost at some point that day what is the probability that her Internet service is not broken for seven days in a row inner a fraction or round your answer to four decimal places if necessary.
Let the event that her internet will be broken be A
The event that her internet will not be broken be B
Therefore:
[tex]\begin{gathered} P(A)=60\%=0.60 \\ P(B)=1-0.60=0.4 \end{gathered}[/tex]Thus, the probability that her internet is not broken for 7 days in a row:
[tex]P(B\text{ for 7 days\rparen=P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}\times\text{P\lparen B\rparen}[/tex]Substitute the value:
[tex]P(B\text{ for 7 days\rparen=0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4}\times\text{0.4=0.001634}[/tex]Round to four decimal places is 0.0016
Answer: 0.0016
Find the tangent of the angle whose measure is pi/2....pi divided by 2.
We have the following:
[tex]\begin{gathered} \tan \theta=x \\ \tan \frac{\pi}{2}=x \end{gathered}[/tex]the value of pi / 2 is not defined
Solve the following logarithmic equation. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.(Simplify your answer. Type an exact answer. Use a comma to separate answers as needed.)
Hello
We are given a log funtion to solve and see if it have a solution.
[tex]\log _2(x+2)=\log _2(15)[/tex]Step 1
we apply log rules
[tex]\begin{gathered} \log _2(x+2)=\log _215 \\ x+2=15 \end{gathered}[/tex]Step 2
Solve for x
[tex]\begin{gathered} x+2=15 \\ x=15-2 \\ x=13 \end{gathered}[/tex]From the calculation above, the solution of the set is 13; i.e x = 13
Evaluate.C15 3 It says I need to evaluate 15^C 3
Explanation
We are required to determine the value of the following:
[tex]_{15}C_3[/tex]This is achieved thus:
We know that the combination formula is given as:
Therefore, we have:
[tex]\begin{gathered} _{15}C_3=\frac{15!}{3!(15-3)!} \\ _{15}C_3=\frac{15!}{3!12!} \\ _{15}C_3=\frac{15\cdot14\cdot13\cdot12!}{3!12!} \\ _{15}C_3=\frac{15\cdot14\cdot13}{3!}=\frac{15\cdot14\cdot13}{3\cdot2\cdot1} \\ _{15}C_3=5\cdot7\cdot13 \\ _{15}C_3=455 \end{gathered}[/tex]Hence, the answer is:
[tex]455[/tex]The probability that a tourist- will spot a Cheetah in Kruger National park is 0.4, the probability that he will spot a Tiger, is 0.7, and the probability that he will spot a Cheetah, or a Tiger or both is 0.5. What is the probability that the tourist will spot: (a) both animals? (b) neither of the animals? (c) Determine with appropriate reason whether the event of spotting a Cheetah and a Tiger are independent or not?
Since the probability of Cheetah is 0.4
Since the probability of Tiger is 0.7
Since the probability of Cheetah or Tiger or both is 0.5
Let us draw a figure to show this information
Then we need to find both animals (x)
Since
[tex]0.5+x=0.7+0.4-x[/tex]Add x to both sides and subtract 0.5 from both sides
[tex]\begin{gathered} 0.5+x+x=0.7+0.4-x+x \\ 0.5+2x=1.1 \\ 0.5-0.5+2x=1.1-0.5 \\ 2x=0.6 \end{gathered}[/tex]Divide both sides by 2 to find x
[tex]\begin{gathered} \frac{2x}{2}=\frac{0.6}{2} \\ x=0.3 \end{gathered}[/tex]a) The probability of both animals is 0.3
Since the total of probability is 1, then to find the neither subtract (0.4 + 0.7 - 0.3) from 1
[tex]\begin{gathered} N=1-(0.4+0.7-0.3) \\ N=1-0.8 \\ N=0.2 \end{gathered}[/tex]b) the probability of neither is 0.2
Events A and B are independent if the equation P(A∩B) = P(A) · P(B)
Since
[tex]P(Ch\cap T)=0.3[/tex]Since P(Ch) . P(T) = 0.4 x 0.7 = 0.28
Then
[tex]P(Ch\cap T)\ne P(Ch).P(T)[/tex]c) The events are not independent
You invent a game that is played on a perfect 12 foot by 12 foot square. What is the longest distance between any two points on the square? A. 12 feetB. 15 feetC. 17 feetD. None of the aboveI will really appreciate the help on this problem.
The given figure is a square that measures 12 foot by 12 foot. please see illustration below;
The square in the sketch above shows the longest distance between two opposite diagonals, and that is the hypotenuse, labelled as a.
In the triangle ADC, using Pythagoras' theorem;
[tex]\begin{gathered} AD^2+DC^2=AC^2 \\ 12^2+12^2=a^2 \\ 144+144=a^2 \\ 288=a^2 \\ \sqrt[]{288}=a \\ a=16.97 \end{gathered}[/tex]The longest distance which is a (that is AC) is approximately 17 ft as shown above (16.97 ft).
use the generic rectangle 3x-8)² and -7x⁴(3x-2) what's the product and sum?
In this case the answer is very simple .
Step 01:
Data:
eq1. (3x - 8)²
eq2. -7x⁴(3x-2)
Step 02:
Sum.
eq.1 + eq.2
(3x - 8)² + (-7x⁴(3x-2))
(9x² - 2*3x*8 - 64) + (-21x⁴ - 14x⁴)
9x² -
Glven: 3x - 2 = 2(x + 1)Prove: x=4REASONSTATEMENT1. 3x - 2 = 2(x + 1)30.2. 3x - 2 = 2x + 231.3. X-2= 232.4. x= 433.Word Bank:A. Distributive PropE. Transitive PropC. Substituion PropD. Subtraction PropB. GivenF. Addition Prop
you have the following equation:
3x - 2 = 2(x+1)
You have to specify the property used in each step to get the solution of the previous equation. You obtain the following:
1. 3x - 2 = 2(x + 1) given
2. 3x - 2 = 2x + 2 distribution prop
3. 3x - 2x - 2 = 2x - 2x + 2 subtraction 2x both sides - subtraction prop
x - 2 = 2
4. x - 2 + 2 = 2 + 2 summation 2 both sides - addition prop
x = 4
Alec wants to purchase a new phone that costs $219.00. His current average net pay is $212.34 each week. What percent of his weekdy net pay does Alec need to save each week, for the next seven weeks, to reach
his goal? Round to the nearest hundredth (1 point)
9.69%
14.73%
O 21.76%
31.28%
Answer:
14.73%
Step-by-step explanation:
firstly let's divide the phone price into 7 equal parts. by this equation 219.00/7=31.28
So Alec needs to save $31.28 but we want the percentage.
by equation x%*212.34=31.28
x=(31.28*100)/212.34=3128/212.34=14.73
so Alec needs to save 14.73% of 212.34 each week.
A rectangular room is 1.8 times as long as it is wide, and its perimeter is 29 meters. Find the dimension of the room. The length is : meters and the width is meters.
Let's say x is going to be the number meters of the width of the room:
x: width
Since its lenght is 1.8 as it is width, then it will be 1.8 · x long:
1.8x: lenght
Step 2: relating the expressions for each side to its perimeterWe know that the perimeter of a rectangle is given by
Perimeter = 2· (width + lenght)
We know that the perimeter is 29 meters, then
Perimeter = 29
↓
29 = 2· (width + lenght)
We do know an expression for its width and lenght, we replace them:
29 = 2· (width + lenght)
↓
29 = 2· (x + 1.8x)
Step 3: finding xSince x + 1.8x = 2.8x:
29 = 2· (x + 1.8x)
↓
29 = 2· (2.8x)
↓ 2· 2.8 = 5.6
29 = 5.6x
↓ dividing both sides by 5.6
29/5.6 = 5.6x/5.6
5.2 = x
Final step: finding its dimensionsSince
x: width
then
Width = 5.2 meters
Since
1.8x: lenght
then
Lenght = 1.8 · 5.2 meters = 9.36 meters
Answer: the dimensions of the room are Width = 5.2 meters and Lenght = 9.36 meters
What is 13.496 rounded to the nearest tenth?A.13B.13.4C.13.5D.14
1) When we need to round up or down to the nearest tenth, it's necessary to consider the hundredth's place.
2) Note this number:
We can see that 13.496 is greater than 13.45 so it is closer to 14 than 13, then we can round it off to the nearest greater number than 4.
3) Thus, we can round it off to:
[tex]13.5[/tex]hello I just need help with these no need to explain just the answers please
The two pairs of angles are supplementary
Here, we want to complete the given sentence
We want to find the relationship between two parallel lines which are cut by a transversal
A figure showing the described relationship is given below;
Now, we want to find the relationship between the two marked angles
From what we have, the two marked angles are supplementary
What this mean is that both angles add up to 180 degrees
Suppose that the velocity v (t) (in meters per second) of a sky diver falling near the Earth’s surface is given by the following exponential function, where time t is the time after diving measured in seconds.
The equation of the velocity is given by the exponential:
[tex]v(t)=53-53e^{-0.24t}[/tex]Let us say that the sky driver's velocity will be 47 m/s at t₁. Then, using the expression above:
[tex]\begin{gathered} v(t_1)=47 \\ 53-53e^{-0.24t_1}=47 \end{gathered}[/tex]Solving for t₁:
[tex]\begin{gathered} \frac{53-47}{53}=e^{-0.24t_1} \\ \ln (\frac{6}{53})=-0.24t_1 \\ t_1=9.1s \end{gathered}[/tex]In which of the following triangles does m
Okay let's analyze each triangle
In triangles A, B, and D the angle
Kuta Sotware - Infinite Algebra 2 Solving Inequalities Solve each inequality and graphite 10 > Kuin Software - Infinite Algebra 2 Graphing Linear Inequalities Sketch the graph of each linear inequality. Name Samante 1) yz-2x-2 Y-2-2 2). ys - !
Could you please send a picture of the inequality you are asked to solve?
I'll be closing the session now if you cannot do it. Please ask your question again, and send the image in the question itself to avoid this problem of your uploaded images and messages not getting to me.
Thank you, and please re-submit your question request.
Solve by using a proportion. Round answers to the nearest hundredth if necessary. 1. You jog 3.6 miles in 30 minutes. At that rate, how long will it take you to jog 4.8 miles? 2. You earn $33 in 8 hours. At that rate, how much would you earn in 5 hours?
EXPLANATION
Let's see the facts:
rate ---> 3.6 miles / 30 minutes
The unit rate is:
Unit rate = 0.12 miles/minute
Now, dividing the needed 4.8 miles by the unit rate will give us our desired number:
Time= 4.8 miles/ 0.12miles/minute = 40 minutes
The answer is 40 minutes.
Part 1: Factorial! 3. What are the pros and cons to using the factorial function on your calculator in terms of understanding and/or thecalculation itself?
Explanation
We are required to determine the pros and cons of using the factorial function on the calculator.
Hence, the answers are:
- Pros
• It makes calculation easier.
,• It makes calculations to be done in an efficient manner.
,• It helps students to solve complicated questions seamlessly.
- Cons
• It cannot help with large numbers as the calculator has limited space for answer preview.
,• It does not help to understand better how the calculation is done.
hector recorded the amount of rainfall in the desert each month over a period of two years. the list shows the number of inches fell for each month for year 1 and year 2 year 1: 2,2,0,0,0,1,2,2,3,2,2,2year 2:1,1,0,0,0,0,2,2,2,1,2,1 whats the difference in rain fall between the mean of the rain fall in two years hurry its a test
ANSWER
The difference is 0.5
EXPLANATION
We have to find the mean of the rain fall for each year. To do this we have to add all the data and then divide by the total number of data.
Year 1: number of data = 12:
[tex]\bar{x_1}=\frac{2+2+0+0+0+1+2+2+3+2+2+2}{12}=\frac{18}{12}=\frac{3}{2}=1.5[/tex]Year 2: number of data = 12:
[tex]\bar{x_2}=\frac{1+1+0+0+0+0+2+2+2+1+2+1}{12}=\frac{12}{12}=1[/tex]The difference is:
[tex]\bar{x}_1-\bar{x}_2=1.5-1=0.5[/tex]students at a local school were asked about how many hours do you spend on homework each week? the table shows the results of the survey classify the statement below as a true or false more students study for 3 to 4 hours than for 5 to 6 hours the statement is (true or false) because.... students study for 3 to 4 hours and..... students study for 5 to 6 hours.
The total of students that study for 3 to 4 h is 147
The total of students that study for 5 to 6 h is 107
Then, the statement: "more students study for 3 to 4 hours than for 5 to 6 hours" is true because 147 students study for 3 to 4 hours and 107 students study for 5 to 6 hours.
Two cars are driving on the same road, in the same
direction. They start driving from the same place and are
traveling at a constant speed. The second car started
driving 1.5 hours after the first car started driving. If the
second car drives 60 miles per hour and the first drives 40
miles per hour, how many miles will each car have
traveled when the second car catches up to the first?
Answer:
180 miles
Step-by-step explanation:
distance = rate x time
t = time
1st car:
distance = 40t
2nd car:
distance = 60(t - 1,5)
When the car catch up to each other the distances will be the same, so set the equation equal to each other. Calculate the time and then put the time back into either equation and solve for the distance.
40t = 60(t-1.5) Distribute the 60
40t = 60t -(60)1.5
40t = 60t - 90 Subtract 60t from both sides of the equation
-20t = -90 Divide both sides by -20
t = 4.5
Now that we know the time, substitue that back into either equaiton and solve for the time
distance = 40 (4.5)
180 miles
Match each step with the correct expression to factor s2 + 78 + 6 by using the decomposition method.
We have the following:
[tex]s^2+7s+6[/tex]solving:
[tex]\begin{gathered} \text{step 1} \\ s^2+s+6s+6 \\ \text{step 2} \\ s\mleft(s+1\mright)+6\mleft(s+1\mright) \\ \text{step 3} \\ (s+1)(s+6) \end{gathered}[/tex]Area of a sector A sector with a radius of \maroonD{8\,\text{cm}}8cmstart color #ca337c, 8, start text, c, m, end text, end color #ca337c has an area of \goldE{56\pi\,\text{cm}^2}56πcm
To find the angle of the sector, follow the steps below.
Step 01: Find the total area of the circle.
The area (A) of a circle with radius r is:
[tex]A=\pi r^2[/tex]Knowing that r = 8 cm, then the area is:
[tex]\begin{gathered} A=8^2\pi \\ A=64\pi\text{ cm}^2 \end{gathered}[/tex]Step 02: Find the central angle.
To find the angle, use proportions.
Knowing that:
When angle = 2π, A = 64π,
Then when angle is x, A = 56π
[tex]\begin{gathered} \frac{x}{2\pi}=\frac{56\pi}{64\pi} \\ \\ \text{ Multiplying both sides by 2}\pi: \\ \frac{x}{2\pi}*2\pi=\frac{56\pi}{64\pi}*2\pi \\ x=\frac{56*2}{64}\pi \\ x=\frac{112}{64}\pi \\ \\ \text{ Dividing both the numerator and the denominator by 16:} \\ x=\frac{\frac{112}{16}}{\frac{64}{16}}\pi \\ x=\frac{7\pi}{4} \end{gathered}[/tex]Answer: The central angle measure is:
[tex]\frac{7\pi}{4}[/tex]Compute the area of each triangle. Round to the nearest tenth.
The triangle ΔDEF has the following coordinates
[tex]\lbrace D(-1,6),E(-4,-6),F(3,-5)\rbrace[/tex]To find the area of a triangle in coordinate geometry, we have a formula. Given 3 vertices A(x1, y1), B(x2,y2) and C(x3,y3), the area of this triangle is given by
[tex]Area(\Delta ABC)=\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]Using this formula for our problem, we have
[tex]Area_{\Delta DEF}=\frac{1}{2}|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))|[/tex]Solving this equation, we have
[tex]\begin{gathered} Area_{\Delta DEF}=\frac{1}{2}|(-1)((-6)-(-5))+(-4)((-5)-6)+3(6_{}-(-6))| \\ =\frac{1}{2}|(-1)((-6+5)+(-4)(-5-6)+3(6_{}+6)| \\ =\frac{1}{2}|(-1)(-1)+(-4)(-11)+3(12)| \\ =\frac{1}{2}|1+44+36| \\ =\frac{1}{2}|81| \\ =\frac{81}{2} \\ =40.5 \end{gathered}[/tex]And this is our answer Area(ΔDEF) = 40.5
Use the graph of 'f' in the figure below to answer the following questions. 1. State the domain and range of 'f'.2. Find the average rate of change of 'f' over the interval [0,6].
The domain of the given function corresponds to:
[tex]\lbrack-4,-2)\cup(-2,6)[/tex]And the range of the function is:
[tex](-2,6)[/tex]The average rate of change of f over the interval [0,6] is:
[tex]\frac{5.5-(-2)}{0-6}=\frac{7.5}{-6}=-\frac{5}{4}=-1.25[/tex]Help me pls on math homework!!!!!
He sold 28 watermelons on Friday.
How to find the number of watermelons sold on Friday?The number of watermelons sold during the entire week is of 60, hence we find the daily amounts and add them, and this has to reach 60. The daily amounts are given as follows:
Monday: x.Tuesday: 2x. (twice as many as Monday).Wednesday: 0.5x. (half as many as Monday).Thursday: 18.Friday: 6x + 4. (four more than twice the amount sold on Monday).Hence the following equation is built, and we can solve for the unknown variable x as follows:
x + 2x + 0.5x + 18 + 6x + 4 = 60.
9.5x = 38
x = 38/9.5
x = 4
Then the amount sold on Friday is calculated as follows:
Friday = 6x + 4 = 6(4) + 4 = 24 + 4 = 28 watermelons.
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He sold 28 watermelons on Friday
What is the number of watermelons he sold on Friday?The total number of watermelons sold for the whole summer week is 60
He sold x watermelons on Monday
On Tuesday, he sold twice the numbers sold on Monday: 2x
On Wednesday, he sold half the numbers sold on Monday: x/2
On Thursday, he sold 18
On Friday, he sold:
= 2(x+2x) + 4 = 2(3x) + 4 = 6x + 4
And we know that the total number of watermelons is 60. Therefore:
x + 2x + x/2 + 18 + 6x+4 = 60
9.5x + 22 = 60
9.5x = 60 - 22
9.5x = 38
x = 4
since the amount sold on Friday is 6x+4:
= 6 x 4 + 4
= 24 + 4 = 28
Therefore, he sold 28 watermelons on Friday
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Find an equation for the line that passes through the points (-2,-6) and (6,-4).
Answer:
[tex](y+6)=\frac{2}{8} (x+2)[/tex]
Step-by-step explanation:
First, find the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
-4+6=2
6+2=8
m=2/8
With the slop, you have everything you need to stick one of your points in point-slope form. I chose (-2,-6)
[tex](y-y1)=m(x-x1)\\(y+6)=\frac{2}{8} (x+2)[/tex]
Really, that's all you need as it is not an equation of a line. Not the most useful form, but works as an answer.