OA= (1,3,-1) and OD=(-1,0,n) find the value of n for which the length of AD is 7 units
Answer:
n = 5
Step-by-step explanation:
0A = (1,3,-1) and OD=(-1,0,n)
AD = √ (-1-1)^2 + (0-3)^2 + (n-(-1))^2
7 = √ (-2)^2 + (-3)^2 + (n+1)^2
7 = √4 + 9 + (n+1)^2
Now squaring both sides we have :
7^2 = (√4 + 9 + (n+1)^2)^2
49 = 4 +9 + (n+1)^2
49 = 13 + (n+1)^2
49 -13 = (n+1)^2
36 = (n+1)^2
Taking the square root of both sides we have :
√36 = √(n+1)^2
6 = (n+1)
6 = n + 1
6 - 1 = n
5 = n
Therefore n = 5
HELP ME!!! Find the y intercept of the line y=2x-11
Answer:
It would intercept the y-axis at y = -11
Step-by-step explanation:
Here is the work
Answer:
Step-by-step explanation:
the y interception is -11
Y=mx+b formula the b is for the y intercept and the m is the slope.
Given the regular octagon, what is the length of any side?
Answer:110
Step-by-step explanation:x^2+17x=15x+35
x^2+17x-15x-35=0
x^2+2x-35=0
delta=2^2-4*1*(-35)=4+140=144
x1=(-2+V144)/2=(-2+12)/2=10/2
x=5
so 15*5+35=75+35=110
Answer:
110Step-by-step explanation:
In a regular polygon, each side has the same length.
Therefore we have the equation:
[tex]x^2+17x=15x+35[/tex]
We must specify the domain:
[tex]x^2+17x>0\ \wedge\ 15x+35>0\\\\x(x+17)>0\ \wedge\ 15x>-35\\\\(x<-17\ \vee\ x>0)\ \wedge\ x>-\dfrac{7}{3}\Rightarrow x>0[/tex]
[tex]x^2+17x=15x+35\qquad\text{subtract}\ 15x\ \text{from both sides}\\\\x^2+17x-15x=15x-15x+35\\\\x^2+2x=35\qquad\text{add 1 to both sides}\\\\x^2+2x+1=35+1\\\\x^2+2(x)(1)+1^2=36\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=36\to x+1=\pm\sqrt{36}\\\\x+1=\pm6\qquad\text{subtract 1 from both sides}\\\\x+1-1=\pm6-1\\\\x=-7\ \vee\ x=5[/tex]
[tex]x<-7\notin\text{domain};\ x=5\in\text{domain}[/tex]
The length of a side:
[tex]x^2+17x=5^2+17(5)=25+85=110\\\\15x+35=15(5)+35=75+35=110[/tex]
Please help! Correct answers only!
There is a raffle with 200 tickets. One ticket will win a $550 prize, one ticket will win a $510 prize, one ticket will win a $280 prize, and the rest will win nothing. If you have a ticket, what is the expected payoff?
Answer:
" Expected Payoff " = $ 6.70
Step-by-step explanation:
Consider the steps below;
[tex]Probability of Winning the 550 Dollar Prize - 1 / 200,\\Probability * Money Won = " Expected Payoff " For The 550 Dollar Prize,\\\\1 / 200 * 550,\\" Expected Payoff " - 2.75 Dollars,\\\\Probability of Winning the 510 Dollar Prize - 1 / 200,\\\\1 / 200 * 510,\\" Expected Payoff " - 2.55 Dollars,\\\\Probability of Winning the 280 Dollar Prize - 1 / 200,\\\\1 / 200 * 280,\\" Expected Payoff " - 1.4 Dollars,\\\\[/tex]
[tex]Conclusion ; Expected Payoff = 6.70 Dollars[/tex]
a 150 adults complete a survey 80 of them a woman what the ratio
Answer:
The number of men to number of women be 7 : 8 .
Step-by-step explanation:
Answer:
7:8
Step-by-step explanation:
If < D is a right angle and < E is a right angle, and you said that < D is congruent to < E, the reason would be ____. Select one: a. Supplementary Angles are congruent b. All right angles are congruent c. Complementary Angles are congruent
Answer:
(B)All right angles are congruent
Step-by-step explanation:
Given that:
[tex]\angle D$ is a right angle, and\\\angle E$ is a right angle\\\\\angle D=90^\circ\\\angle E=90^\circ\\$Therefore: \angle D \cong \angle E[/tex]
The reason for this congruency is that both are right angles and in fact, all right angles are congruent.
Mrs. Meyer's soap is $3.99 for 12 ounces. What is the cost per ounce?
Answer:
It's about 33 cents per ounce. The exact answer would be 0.3325
Step-by-step explanation:
Answer:
0.33
Step-by-step explanation: i did it on a piece of paper
The table shows the scores of a biology test in Mrs. Smiths class . Find the mean of the data without Kim’s score.
A- 80
B- 87.2
C- 90
D- 84.5
Answer:
87.2
Step-by-step explanation:
90+93+87+83+86+90+82=611
611/7=87.29
answer is b
y=-3x + 6
y = 9
What is the solution to the systems of equations
Answer:
-1,9
Step-by-step explanation:
You use the equal values method to combine the two equations
-3x+6=9
then subtract 6 on both sides of the equal sign
nine minus six is 3
-3x=3
divide negative three on both sides to isolate the x value
to get....
x=-1
then plug the x value back in to find the y value
(you can plug in to one of them but I would plug into both of them just for double checking) ALWAYS CHECK YOUR WORK
3+6 is 9
9=9 check!
Answer:C -(-1,9)
Step-by-step explanation:
THIS QUESTION GOT ME STRESSIN HELPPP A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation. x + y = 24 3x + 5y = 100 What does the solution of this system indicate about the questions on the test? The test contains 4 three-point questions and 20 five-point questions. The test contains 10 three-point questions and 14 five-point questions. The test contains 14 three-point questions and 10 five-point questions. The test contains 20 three-point questions and 8 five-point questions.
Answer:
14 and 10
Step-by-step explanation:
14x5=70
10x3=30
100=70+30
Profit is the difference between revenue and cost. The revenue, in dollars, of a company that makes skateboards can be modeled by the polynomial 2x3 + 30x – 130. The cost, in dollars, of producing the skateboards can be modeled by 2x3 – 3x – 520. The variable x represents the number of skateboards sold. What expression represents the profit?
A. 27x – 650
B. 27x + 390
C. 33x – 650
D. 33x + 390
Answer:
We need to subtract both equations. 2x3+30x-130-2x3+3x+520
that gives
30x-130+3x + 520
33x+390
D is answer
Answer:
D. 33x + 390
Step-by-step explanation:
Profit is the difference between revenue and cost so subtract the given polynomials:
2x³ + 30x – 130 - (2x³ – 3x – 520) = 2x³ + 30x – 130 -2x³+3x+520
combine like terms: 33x +390
3х + y = 8
x - Зу = 11
Answer:
y = 8-3x and y = -11/3 + x/3
For the first equation you have to subtract 3x from both sides of the equation. for the second equation you have to move all terms that doesn't contain y to the right side and solve
Which of the following is an equivalent equation to find w
[tex]answer \\ w = \frac{ {8x}^{2} - 2y }{y} \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]
a food scientist wants to know if increasing the amount of lemon juice in a hummus recipe by 10% will increase the shelf life of the product, so he prepares 100 Badges of the recipe - 50 following the old recipe and 50 with extra lemon juice –and?checks each batch once per day to see how long it stays fresh. What type of data source is this?
Answer:
b. Experiment
Step-by-step explanation:
Setting up conditions so that you can examine the outcome is called an "experiment."
Answer:
[tex]\fbox{\begin{minipage}{10em}Option B-Experiment\end{minipage}}[/tex]
Step-by-step explanation:
As described, the food scientist performs the research based on the actual data, without using a computer or any simulation devices.
=> The data source is not generated from a computer simulation.
=> Option A-Simulation is incorrect.
The food scientist intentionally prepares the research by conducting an experiment, in which 100 badges are used, 50 badges following the old recipe and 50 badges with extra lemon juice.
=> This is not a subjective process, but a purposely attempting to observe the amount of lemon juice in a specific manner.
=> This is not a survey.
=> Option C-Survey is incorrect.
=> Option B-Experiment is correct.
Hope this helps!
:)
Which graph represents y<-3x?
Step-by-step explanation:
Desmos Graphing Calculator
Find the volume of prism
Pls!! Show how you got the volume pls
Find the missing exponet
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!
The graph of an absolute value function y=a|x| includes the points (1,6) and (-1,6)
Answer: y=6|x|
Step-by-step explanation:
I attached the graph too!
Order the simplification steps of the expression below using the properties of rational exponents. [tex]\sqrt[3]{7}=7^{\frac{1}{3}}[/tex]
A.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7^{\frac{1}{3}}\cdot ^{\frac{1}{3}}\cdot ^{\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7\\[/tex]
B.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}\cdot 7^{\frac{1}{3}}=7\cdot 7^{\frac{1}{3}}=3\cdot \frac{1}{3}\cdot 7=1\cdot 7=7[/tex]
C.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}}+\:^{\frac{1}{3}}+\:^{\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7[/tex]
D.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7\cdot \left(\frac{1}{3}+\frac{1}{3}+\frac{1}{3}\right)=7\cdot \frac{3}{3}=7\cdot 1=7[/tex]
The answer is C.) [tex]\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7[/tex]
what you plug in for calculator
\left(7^{\frac{1}{3}}\right)^3=7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}\cdot \:7^{\frac{1}{3}}=7^{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}=7^{\frac{3}{3}}=7^1=7
What is the range of the function?
A. (3)
B. {3, 9, 12)
C. (-2, 2, 3, 4, 9, 12)
O D. {-2, 2, 3, 4
The range is all the possible y values, so the set with all the arrows.
Answer: B. {3,9,12}
Answer:
B
Step-by-step explanation:
The range means the y coordinates or output
In this the output are the numbers on the right.
We can also find the answer by eliminating.
Option A could not be the answer because it is only one of the numbers from the range.
Option B is the answer because it includes all the numbers from the range.
Option C and Option D could not be the answer because they include other numbers from the domain (which we are not trying to find).
This is an example here below
Hope this helped!!
what number times there self eqaul to 64
Answer:
8
Step-by-step explanation:
8 times 8 = 64
Please help me with my question!!
Answer:
Step-by-step explanation:
y = 10x + 50
x ---> no of weeks
y - intercept = 50
y varies directly as x and inversely as z. If y = 5 when x = 3 and z = 4, find y when x = 6 and z = 8.
Answer:
y= 201/40
Step-by-step explanation:
y=k (x÷z)
5 = (3÷4)k
cross multiply
20=3k
k= 6.7 or 67÷10
y = 6.7 (x÷z) the law
y = (6÷8) × 6.7
y = 0.75 ×6.7
y= 5.025 or 201÷40
Which is a correct first step in solving 5 - 2x < 8x - 3?
5 < 6x-3
3x < 8x-3
5 < 10x - 3
2 - 2x < 8x
Answer:
5 < 10x-3
Step-by-step explanation:
5 - 2x < 8x - 3
Add 2x to each side
5 - 2x+2x < 8x - 3+2x
5 < 10x-3
Answer:
The answer is C.
Step-by-step explanation:
Trust me, I got you.
A multi level parking lot has 6 levels and there are total of 1,327 parking spots. There are 162 parking spots on the first level. The rest of the parking spots are distributed equally on the other 5 levels. How many parking spots are there on the top level? *
Answer:
233 parking spots
Step-by-step explanation:
1327 - 162 = 1165
1165 ÷ 5 = 233
Given: 3x < -6. Choose the solution set.
A. {x | x < -2}
B. {x | x > -2}
C. {x | x < 2}
D. {x | x > 2}
Answer:
When we divide the inequality by 3 we get x < -2 so the answer is A.
Mr Hassan gave his year 7 class a test on Friday. the highest possible mark for the test was 10.
Answer:
To solve this question, we just need to observe the given graph.
(A) How many pupils scored more than 8 in the test?
Each little square is equivalent to 0.5 units, so there are 5 students who fot more than 8. Specifically, 1 got 8 points and 4 students got 10.
(B) How many pupils are there in Mr. Hassan's Year 7 class?There are 33 pupils in total, remember that each little square is equivalent to 0.5 units.
(C) What assumption have you made in answering part b)?The assumption was that the majority of pupils scored less than 8.
Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function be written using
function notation?
f(y) = -1/3y+4/3
f(x) = -3x+4
f(x) = -1/3x + 4/3
f(y) = -3y+4
My question is 3x + (2− 4x)
Answer:
3x+(2-4x)
= 2 (3x+4x)
=2 (7x)
=2/7x
=7x/2
=3.5
Step-by-step explanation:=3.5
