Answer:
y- intercept = - 39
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 12x + 2 ← is in slope- intercept form
with slope m = 12
Parallel lines have equal slopes, thus
y = mx + c ← is the partial equation
To find c substitute (4, 9) into the partial equation
9 = 48 + c ⇒ c = 9 - 48 = - 39 ← y- intercept
Answer:
y-intercept = -39
Step-by-step explanation:
if two lines are parallel it means they have the same gradient so we compare the equation given to the default equation of a line
y=mx+c
y=12x+2
comparing we have the gradient m=12 now finding the equation of the line parallel to the given line we use
y-y1=m(x-x1)
y1=9 and x1=4
y-9=12(x-4)
y-9=12x-48
y=2x-48+9
y=2x-39
comparing to the default equation of a line y=mx+c where c is the y-intercept
therefore the y-intercept is -39
Solve 2(x - 5) = 48 - 4(x + 1)
Answer:
x = 9
Step-by-step explanation:
first remove the brackets
2x - 5 = 48 - 4x + 1
then take numbers to the opposite sides
2x + 4x = 48 + 5 + 1
I have used addition because since your taking-5 to the other side it becomes+5 and -4 becomes +4
now solve
2x + 4x= 6x
48+5+1= 54
6x = 54
now solve for x
divide both sides by 6x
x = 9
How can you change a rational number to a decimal? Can you give an exsample?
Answer:
1/2=0.5
Step-by-step explanation:
¼=0.25
¾=0.75
need help will give 5 stars.
Answer:
t=0.64
Step-by-step explanation:
h = -16t^2 +4t +4
We want h =0 since it is hitting the ground
0 = -16t^2 +4t +4
Using the quadratic formula
a = -16 b = 4 c=4
-b ± sqrt( b^2 -4ac)
----------------------------
2a
-4 ± sqrt( 4^2 -4(-16)4)
----------------------------
2(-16)
-4 ± sqrt( 16+ 256)
----------------------------
-32
-4 ± sqrt( 272)
----------------------------
-32
-4 ± sqrt( 16*17)
----------------------------
-32
-4 ± sqrt( 16) sqrt(17)
----------------------------
-32
-4 ± 4 sqrt(17)
----------------------------
-32
Divide by -4
1 ± sqrt(17)
----------------------------
8
To the nearest hundredth
t=-0.39
t=0.64
Since time cannot be negative
t=0.64
Answer:
0.64
Step-by-step explanation:
0 = -16t^2 + 4t + 4
-4(4t^2 - t -1) = 0
t = [-(-1) +/- sqrt (1 - 4*4*-1)] / 8)
t = 0.64, -0.39
answer is 0.64
If 4SINB=3SIN(2A+B) :
Prove that:7COT(A+B)=COTA
Answer:
Step-by-step explanation:
Given the expression 4sinB = 3sin(2A+B), we are to show that the expression 7cot(A+B) = cotA
Starting with the expression
4sinB= 3sin(2A+B)
Let us re write angle B = (A + B) - A
and 2A + B = (A + B) + A
Substituting the derived expression back into the original expression ww will have;
4Sin{(A + B) - A } = 3Sin{(A + B)+ A}
From trigonometry identity;
Sin(D+E) = SinDcosE + CosDSinE
Sin(D-E) = SinDcosE - CosDSinE
Applying this in the expression above;
4{Sin(A+B)CosA - Cos(A+B)SinA} = 3{Sin(A+B)CosA + Cos(A+B)sinA}
Open the bracket
4Sin(A+B)CosA - 4Cos(A+B)SinA = 3Sin(A+B)CosA + 3Cos(A+B)sinA
Collecting like terms
4Sin(A+B)CosA - 3Sin(A+B)cosA = 3Cos(A+B)sinA + 4Cos(A+B)sinA
Sin(A+B)CosA = 7Cos(A+B)sinA
Divide both sides by sinA
Sin(A+B)CosA/sinA= 7Cos(A+B)sinA/sinA
Since cosA/sinA = cotA, the expression becomes;
Sin(A+B)cotA = 7Cos(A+B)
Finally, divide both sides of the resulting equation by sin(A+B)
Sin(A+B)cotA/sin(A+B) = 7Cos(A+B)/sin(A+B)
CotA = 7cot(A+B) Proved!
what is nine and forty-two hundredths
Answer:
9.42
Step-by-step explanation:
Breaking the phrase down:
'Nine' would be the number 9 in the ones place.
'And' represents the decimal in a number. ('.')
'Forty-Two Hundredths" is 0.42.
So, "nine and forty-two hundredths" would be 9.42.
Hope this helps.
Solve. 4x−y−2z=−8 −2x+4z=−4 x+2y=6 Enter your answer, in the form (x,y,z), in the boxes in simplest terms. x= y= z=
Answer:
(-2, 4, 2)
Where x = -2, y = 4, and z = 2.
Step-by-step explanation:
We are given the system of three equations:
[tex]\displaystyle \left\{ \begin{array}{l} 4x -y -2z = -8 \\ -2x + 4z = -4 \\ x + 2y = 6 \end{array}[/tex]
And we want to find the value of each variable.
Note that both the second and third equations have an x.
Therefore, we can isolate the variables for the second and third equation and then substitute them into the first equation to make the first equation all one variable.
Solve the second equation for z:
[tex]\displaystyle \begin{aligned} -2x+4z&=-4 \\ x - 2 &= 2z \\ z&= \frac{x-2}{2}\end{aligned}[/tex]
Likewise, solve the third equation for y:
[tex]\displaystyle \begin{aligned} x+2y &= 6\\ 2y &= 6-x \\ y &= \frac{6-x}{2} \end{aligned}[/tex]
Substitute the above equations into the first:
[tex]\displaystyle 4x - \left(\frac{6-x}{2}\right) - 2\left(\frac{x-2}{2}\right)=-8[/tex]
And solve for x:
[tex]\displaystyle \begin{aligned} 4x+\left(\frac{x-6}{2}\right)+(2-x) &= -8 \\ \\ 8x +(x-6) +(4-2x) &= -16 \\ \\ 7x-2 &= -16 \\ \\ 7x &= -14 \\ \\ x &= -2\end{aligned}[/tex]
Hence, x = -2.
Find z and y using their respective equations:
Second equation:
[tex]\displaystyle \begin{aligned} z&=\frac{x-2}{2} \\ &= \frac{(-2)-2}{2} \\ &= \frac{-4}{2} \\ &= -2\end{aligned}[/tex]
Third equation:
[tex]\displaystyle \begin{aligned} y &= \frac{6-x}{2}\\ &= \frac{6-(-2)}{2}\\ &= \frac{8}{2}\\ &=4\end{aligned}[/tex]
In conclusion, the solution is (-2, 4, -2)
Answer:
x = -2
y =4
z=-2
Step-by-step explanation:
4x−y−2z=−8
−2x+4z=−4
x+2y=6
Solve the second equation for x
x = 6 -2y
Substitute into the first two equations
4x−y−2z=−8
4(6-2y) -y -2 = 8
24 -8y-y -2z = 8
-9y -2z = -32
−2(6-2y)+4z=−4
-12 +4y +4z = -4
4y+4z = 8
Divide by 4
y+z = 2
z =2-y
Substitute this into -9y -2z = -32
-9y -2(2-y) = -32
-9y -4 +2y = -32
-7y -4 = -32
-7y =-28
y =4
Now find z
z = 2-y
z = 2-4
z = -2
Now find x
x = 6 -2y
x = 6 -2(4)
x =6-8
x = -2
If sin Θ = 5 over 6, what are the values of cos Θ and tan Θ?
Answer:
Check explanation
Step-by-step explanation:
Sin∅=5/6
Opp=5. Hyp=6
Adj= (√6²+5²)
= √11
Cos∅=(√11)/6
Tan∅=5/(√11)
simpily 2^3×3^2=6^5
Answer:
2^3×3^2=6^5 equation is wrong because
2×2×2×3×3=72
6^5=6×6×6×6×6=36×36×6=7776
the two numbers are not equal
Mate, I think your question is wrong ! ;(
[tex]Corrected \\ Question...\\[/tex] (2^3)^2*(3^2)^3=6^5
what is the answer to 1/8=s-3/4
Answer:
7/8 =s
Step-by-step explanation:
1/8=s-3/4
Add 3/4
1/8 + 3/4 = s -3/4 +3/4
1/8 + 3/4 = s
Get a common denominator
1/8 + 3/4 *2/2 = s
1/8 + 6/8 =s
7/8 =s
1/8 = s - 3/4
1/8 = s -6/8 ( * 2/2)
7/8 = s
s = 7/8
During a catered lunch =, an average of 4 cups of tea are poured per minute. The lunch will last 2 hours. How many gallons of tea should the caterer bring if there are 16 cups in one gallon?
Answer:
30 gallons of tea
Step-by-step explanation:
We are looking at the average of cups of tea per minute but we are given the time frame of lunch in hours, so first, we have to convert the hours to minutes:
There are 60 minutes in 1 hour and lunch is 2 hours long. So, multiply 60 by 2 to get 120 minutes total.
Next, we have to find out the number of cups of tea poured during the lunch. We have been told already that an average of 4 cups of tea are poured a minute.
Therefore, multiply 4 by the total number of minutes for lunch. You will multiply 4 by 20 to get 480 cups of tea poured in total during the catered lunch.
Finally, we have to see how many gallons of tea the caterer should bring. We should know that there are 16 cups in one gallon.
That means we have to divide the total number of cups poured by 16. Divide 480 by 16 to get 30 gallons of tea that the caterer should bring.
PLZ HELP I WILL MARK YOU AS BRAINLIEST
The ages of two groups of karate students are shown in the following dot plots: The mean absolute deviation (MAD) for group A is 2.07 and the MAD for group B is 5.51. Which of the following observations can be made using these data? Group A has greater variability in the data. Group A has less variability in the data. Group B has a lower range. Group B has a lower mean.
Answer:
Group A has less variability in the data.
Step-by-step explanation:
Examining the data for both groups virtually as represented on the dot plot, we can easily tell that the data in group A are less spread compared to group B data.
Group A has a range value of 10 (14 - 4), while group B has a range value of 19 (26 - 7).
Therefore, "Group A has less variability in the data."
how many are 6 raised to 4 ???
Answer:
[tex]\large \boxed{1296}[/tex]
Step-by-step explanation:
6 raised to 4 indicates that the base 6 has an exponent or power of 4.
[tex]6^4[/tex]
6 is multiplied by itself 4 times.
[tex]6 \times 6 \times 6 \times 6[/tex]
[tex]=1296[/tex]
A white-tailed deer can sprint at speeds up to 30 miles per hour. American bison can run at speeds up to 3,520 feet per minute. Which animal is faster and by how many miles per hour? There are 5,280 feet in one mile. A deer is 10 miles per hour faster than a bison.
3520/5280 = 2/3 of a mile per minute.
2/3 x 60 minutes per hour = 40 miles per hour.
40-30 = 10
Bison runs 40 miles per hour
The bison runs 10 miles an hour faster than the deer
Answer:
American bison is faster than the white-tailed deer by 10 more miles per hour.
Step-by-step explanation:
In 1 hour there are 60 minutes.
=> 3520 feet = 1 minute
=> 60 minutes = 3520 x 60
=> 211200 feet = 60 minutes
So, 211200 feet can be converted in miles.
=> 1 mile = 5280 feet
=> 211200 feet = x miles
=> x = 211200 / 5280
=> x = 40 miles per hour.
So, a white-tailed deer can run up to 30 miles per hour.
an American bison can run up to 40 miles per hour.
American bison runs 10 more miles per hour than a white-tailed deer.
solve for x 3(x+2) + 4(x-5)=10
Answer:
x= 3.43
Step-by-step explanation:
First, use the distributive property and multiply 3 by x and 3 by 2:
3x + 6
next use the distributive property again and multiply 4 by x and -5:
4x - 20
Combine Like terms: 3x + 6 + 4x - 20
3x + 4x = 7x
6 - 20 = -14
Now Add 14 to both sides: 7x - 14 = 10
10 + 14 = 24
Now divide 7 by both sides: 7x = 24
24 / 7 = 3.428571429 = 3.43
Answer:
x=24/7 or 3 3/7
Step-by-step explanation:
3(x+2) + 4(x-5)=10 parenthesis first
3x+6+4x-20=10
7x-14=10 addition on both sides
7x-14+14=10+14
7x=24
x=24/7
check the answer:
3(x+2) + 4(x-5)=10
3(24/7+2)+4(24/7-5)=10
72/7+6+96/7-20=10
168/7-14=10
24-14=10
10=10 correct
*PLEASE ANSWER TY* What is the volume of a hemisphere-shaped coffee if the width of the coffee cup is about 16.51 centimeters? (Use 3.14)
Answer:
Option (1)
Step-by-step explanation:
By the property of the liquids,
"Liquids have a fixed volume but don't have the fixed shape. If we put a liquid in a bottle or a cup it will acquire the shape of a bottle or cup."
In our question, coffee when kept in a cup will take the shape of the cup which is a hemisphere.
Volume of a hemisphere = [tex]\frac{2}{3}\pi r^{3}[/tex]
Where 'r' = radius of the hemisphere
Radius of the cup = [tex]\frac{16.51}{2}[/tex] cm
Volume of the hemisphere = [tex]\frac{2}{3}\pi (\frac{16.51}{2} )^{3}[/tex]
= [tex]\frac{2}{3}\pi (8.255)^3[/tex]
= 1177.5778
≈ 1177.58 cm³
Therefore, Option (1) will be the answer.
Maggie drew lines of best fit for two scatter plots, as shown. Which statement best describes the placement of the lines Maggie drew?
Answer:
B. Only line B is a well-placed line of best fit.
Step-by-step explanation:
A good line of best fit is a line drawn to represent, as much as possible, all data points. As long as the data points are clustered along the line, and are not farther from each other, the line is a best fit for such data points.
Therefore, from the two lines drawn by Maggie, Line B seems to be the only well-placed line of best fit, as virtually all the data points are clustered along the line, compared to Line A. Line A only runs across 2 data points. The rest data points are scattered far apart from the line.
Therefore, the statement that best describes the placement of the line of best fit drawn by Maggie is: "B. Only line B is a well-placed line of best fit."
Answer:
Only line B
Step-by-step explanation:
Line A is too low on the graph to be best fit for the plot
A son is 8 years old. His father is 5 times as old. How old was the father when his son was born?
Answer:
he was 32
Step-by-step explanation:
8x5 is 40 because he was born 8 years ago you subtract 8 from 40 to get 32
Emma changed £500 into rand before going on holiday to South Africa.
The rate of exchange at the time was £1 = 10.4 rand.
Emma spent 4000 rand on holiday. When she got home, she changed her leftover rand into pounds.
The exchange rate was now £1 = 9.8 rand. How much money did she get back in pounds?
Answer:
I'm sorry but I can give exact numbers but I would like to help work it out so...
Step-by-step explanation:
So overall she had £500 to start with
And £1 is equal to 10.4 rand
So you would divide 100 by 10.4 and get the potential difference between the average of money which she has then because she spent 400 rand in holiday you would divide 400 by the amount of the potential difference which was given then change that back to pounds
Hope this helps
If this seems incorrect please comment and I will change my answer thanks:)
Hi how do I solve this simultaneous equation
Answer:
M (-3, -5/2)
N (3, -1)
Step-by-step explanation:
Solve the first equation for x.
4y = x − 7
x = 4y + 7
Substitute into the second equation.
x² + xy = 4 + 2y²
(4y + 7)² + (4y + 7)y = 4 + 2y²
Simplify.
16y² + 56y + 49 + 4y² + 7y = 4 + 2y²
18y² + 63y + 45 = 0
2y² + 7y + 5 = 0
Factor.
(y + 1) (2y + 5) = 0
y = -1 or -5/2
Plug back into the first equation to find x.
x = 4(-1) + 7 = 3
x = 4(-5/2) + 7 = -3
M (-3, -5/2)
N (3, -1)
Can you help Jorge organize the results into a two-way frequency table? Please answer this ASAP
Answer:
The table is attached!
Step-by-step explanation:
6 students play both musical instrument and a sport3 students play neither a musical instrument nor a sport14 students in total play a sportGiven: There are 24 students in the class
The number of students that does not play a sport is 24 - 14 = 10
The number of students that does not play a musical instrument but play a sport = 14 - 6 = 8
The frequency table thus is attached below:
Joey intends to roll a six-sided number cube 100 times. What probability model can he use to predict whether or not each roll will give a result that is divisible by 3?
Options :
A. Each roll has a 0.117 probability of being divisible by 3.
B. Each roll has a 0.333 probability of being divisible by 3.
C. Each roll has a 0.5 probability of being divisible by 3. D. Each roll has a 0.667 probability of being divisible by 3.
Answer: B. Each roll has a 0.333 probability of being divisible by 3.
Step-by-step explanation:
Sample space for a six-sided number cube :
1, 2, 3, 4, 5, 6
Number of outcomes divisible by 3:
(3, 6) = 2
Probability of an event = Number of required outcomes / total number of possible items
Probability (getting a number divisible by 3):
(Number of outcomes divisible by 3 / total outcomes in sample space)
Probability (getting a number divisible by 3):
2 / 6 = 1/3
= 0.333
30 times the square of a nonzero number is equal to eight times the number what is the number
Answer: 4/15
Step-by-step explanation:
Answer:
[tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Number sentence: [tex]30x^{2}[/tex] = [tex]8x[/tex]
You can start by applying algebra to the left side of the equation by dividing each side by x. This should be how it looks now: 30x = 8
Now divide each side by 30 to keep reducing it: [tex]x = \frac{8}{30}[/tex]
Now that we have [tex]\frac{8}{30}[/tex], we can reduce that by dividing the top and bottom by 2:
[tex]\frac{8}{30} = \frac{4}{15}[/tex].
Therefore, the number is [tex]\frac{4}{15}[/tex].
Need help with mark brainlist.
Nam worked on a job for 10 days. On each of the last 2 days, he worked 2 hours more than the mean number of hours he worked per day during the first 8 days. If he worked 69 hours in all, how many hours did he work during the last 2 days together?
Answer: 17 hours
Step-by-step explanation:
Given that On each of the last 2 days, he worked 2 hours more than the mean number of hours he worked per day during the first 8 days. That is he worked additional 4 hours for the two days.
Let the total hours for the 8 days = E
The mean = E/8 = 0.125E
For the two last days, he worked
( 0.125E + 2 ) × 2 = 0.25E + 4
If he worked 69 hours in all, then
E + 0.25E + 4 = 69
Collect the like terms
1.25E = 69 - 4
1.25E = 65
E = 65/1.25
E = 52.
Now find the mean of the first 8 days
Mean = 52 / 8 = 6.5 hours
Nam works during the last 2 days together for:
(6.5 + 2)×2
8.5 × 2 = 17 hours
the perimeter of square is 76 cm find are of square
Answer:
Given the information above, the area of the square is 361 cm²
Step-by-step explanation:
A square is a shape with four equal sides. So, in order to find the area of the square, we must find the length of each individual side. We can do this by dividing the perimeter by 4 because a square has 4 equal sides meaning they have the same lengths.
The perimeter of the square is 76. So, let's divide 76 by 4.
76 ÷ 4 = 19
So, the lengths of each sides in the square is 19cm.
In order to find the area, we must multiply the length and the width together. Since a square has equal sides, then we will multiply 19 by 19 to get the area.
19 × 19 = 361
So, the area of the square is 361 cm²
Answer:
361 cm^2
Step-by-step explanation:
The area of a square can be found by squaring the side length.
[tex]A=s^2[/tex]
A square has four equal sides. The perimeter is the sum of all four sides added together. Therefore, we can find one side length by dividing the perimeter by 4.
[tex]s=\frac{p}{4}[/tex]
The perimeter is 76 centimeters.
[tex]s=\frac{76 cm}{4}[/tex]
Divide 76 by 4.
[tex]s=19 cm[/tex]
The side length is 19 centimeters.
Now we know the side length and can plug it into the area formula.
[tex]A=s^2\\s=19cm[/tex]
[tex]A= (19 cm)^2[/tex]
Evaluate the exponent.
(19cm)^2= 19 cm* 19cm=361 cm^2
[tex]A= 361 cm^2[/tex]
The area of the square is 361 square centimeters.
determine the image of the point p[-3,10) under the translation [5,-7]
[tex](-3+5,10-7)=(2,3)[/tex]
I need domain and range
Answer:
-3 and infinity
Step-by-step explanation:
which transformations can be used to map a triangle with vertices A(2, 2), B(4,1), C(4, 5) to A'(-2,-2), B'(-1.-4). C'(-5, -4)?
Answer:
C!
Step-by-step explanation:
Please help
Maths....
6 cm from what im seeing
Answer: 7 cm
Step-by-step explanation:
A combination lock uses three numbers between 1 and 46 with repetition, and they must be selected in the correct sequence. Is the name of "combination lock" appropriate? Why or why not? Choose the correct answer below. A. No, because the multiplication counting rule would be used to determine the total number of combinations. B. Yes, because the combinations rule would be used to determine the total number of combinations. C. No, because factorials would be used to determine the total number of combinations. D. No, because the permutations rule would be used to determine the total number of combinations.
The correct answer is D. No because the permutations rule would be used to determine the total number of combinations.
Explanation:
The difference between a combination and a permutation is that in permutations the order is considered. This applies to the numbers in a lock because these need to be in order. Therefore, to analyze the permutations in a lock, the rule for permutations should be used. This includes the general formula P (n,r) =[tex]\frac{n!}{(n-r) !}[/tex]; in this, n is the number of objects and r refers to the objects used in a permutation. Thus, the term "combination" is inappropriate because this is a permutation, and the permutation rule should be used.
solve this equation -2x+9=-5x-15
Answer:
x = -8
I hope this helps!
