Answer:
Step-by-step explanation:
We first need to find h. Since h is the x coordinate of Q, and Q is on the line 3x + 4y = 6, we will plug in the x value of h and the y value of 3 and solve for h:
3h + 4(3) = 6 and
3h + 12 = 6 and
3h = -6 so
h = -2
The coordinates for Q are (-2, 3). Now we can use that to find the slope of the line QR:
[tex]m=\frac{8-3}{3-(-2)}=\frac{5}{5}=1[/tex]
So the slope of QR is 1. Now we will choose one of the coordinates on line QR as our x and y coordinates to write the equation for the line in point slope form then in standard form:
y - 8 = 1(x - 3) and
y - 8 = x - 3 and
y - x = 5 or
-x + y = 5. If your teacher does not want you to lead with a negative:
x - y = -5 would be your equation in standard form.
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
You pull one card at random from a standard deck and you shuffle the remaining cards. Then you pull another card. Is the event independent or dependent?
Answer:
If an event is affected by previous events then it is a dependent event, while if an event is not affected by the previous event then it is an independent event.
Since we have replaced the card that we first drew from the deck, it wont affect the event of pulling a card second time.
So, we can say that it is an example of independent event.
please can someone help me solve this.. please help!!
Step-by-step explanation:
Hello,
Firstly just look to triangle BDE,
Here, you will find that,
140° = y+80° {the exterior and opposite interior angle of a triangle is equal}.
or, y= 140°-80° {shifting 80° to another side and subtracting it.}
Therefore, the value of y is 60°.
now, let's simply work with line EB or EG. we get;
angle GEF + y=180° { being a linear pair}.
or, angle GEF + 60°= 180°
or, angle GEF = 180°-60°
Therefore, the value of angle GEF = 120°.
now, looking in triangle EFG, we get;
angle GEF + 35°+x= 180° { the sum of interior angle of a triangle is 180°}.
or, 120°+35°+ x= 180°
or, x= 180°- 155°
Therefore, the value of x is 25°.
now, lastly finding the value of "z"
We find that x= z {being vertical opposite angle}
or, z =25°
Therefore, the value of z is 25°.
So, the values are,
x=25°
y=60°
and z= 25°
Hope it helps...
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)
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
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
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]
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
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
Please help
Maths....
6 cm from what im seeing
Answer: 7 cm
Step-by-step explanation:
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
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
I need domain and range
Answer:
-3 and infinity
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.
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
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].
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!
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:
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:)
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
*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.
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)
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.
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.
a blue die and a green die are rolled. find the probability that the blue and green are both less than 6
Answer
5/6 maybe
Step-by-step explanation:
determine the image of the point p[-3,10) under the translation [5,-7]
[tex](-3+5,10-7)=(2,3)[/tex]
Find the approximate volume of this prism (Image down below)
Answer:
about 62m^3
Step-by-step explanation:
Rory records the percentage of battery life remaining on his phone throughout a day. The battery life decreases as Rory uses the phone, but will increase or stay at 100% while charging. The graph represents the percentage of battery life remaining after a certain number of hours.
A graph titled Phone Battery Life. The horizontal axis shows Elapsed Time (hours) numbered 2 to 20, and the horizontal axis shows Battery Life (%) numbered 10 to 120. A line begins at 100% in 0 hours, to 20% in 8 hours, to 100% from 10 to 12 hours, to 60% in 16 hours, to 100% from 17 to 20 hours.
At which times could Rory's phone have been plugged into the charger? Select three options.
Answer:
9 hours
11 hours
19 hours
Step-by-step explanation:
The graph represents the percentage of battery life remaining after a certain number of hours is attached below.
At which times could Rory's phone have been plugged into the charger? Select three options.
6 hours
9 hours
11 hours
14 hours
19 hours
Answer: From the graph, the line segment with negative slope (that is decreasing value) shows that the phone is not plugged but being used while the line segment with positive slope (increasing value) or stays at 100% shows that the phone is plugged to the charger.
As shown, from 0 to 8 hours their is a decreasing value, the phone is not plugged. From 8 to 10 hours their is an increasing value therefore the phone is plugged also from 10 to 12 hours the phone is plugged since it is constant. From 12 to 16 hours it is not plugged. From 16 to 18 hours it is plugged and from 18 to 20 hours it is plugged.
From the options it is plugged at 9 hours, 11 hours and 19 hours
Answer:
B - 9 HOURS
C - 11 HOURS
E - 19 BHOURS
Step-by-step explanation:
i took the test
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:
solve this equation -2x+9=-5x-15
Answer:
x = -8
I hope this helps!