Answer:
see explanation
Step-by-step explanation:
(a)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (P(16, 9) and (x₂, y₂ ) = Q(22, 24)
[tex]m_{PQ}[/tex] = [tex]\frac{24-9}{22-16}[/tex] = [tex]\frac{15}{6}[/tex] = [tex]\frac{5}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{2} }[/tex] = - [tex]\frac{2}{5}[/tex] , then
y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation
To find c substitute (5, 1) into the partial equation
1 = - 2 + c ⇒ c = 1 + 2 = 3
y = - [tex]\frac{2}{5}[/tex] x + 3 ← equation of perpendicular line
(b)
Given PN = 2NQ , then N sections PQ in the ratio 2 : 1
Using the Section formula to find coordinates of N
N = ( [tex]\frac{16(1)+22(2)}{1+2}[/tex] , [tex]\frac{9(1)+24(2)}{1+2}[/tex] )
= ( [tex]\frac{16+44}{3}[/tex], [tex]\frac{9+48}{3}[/tex] )
= ( [tex]\frac{60}{3}[/tex], [tex]\frac{57}{3}[/tex] )
= (20, 19 )
Find the missing height of the solid figure
9514 1404 393
Answer:
5 in
Step-by-step explanation:
The figure's angles are presumed to be right angles everywhere, so the left-side vertical dimension is equal to the right-side vertical dimension.
The right side is marked as 15 inches.
The left side has two vertical segments, one of which is 10 inches. Since the total left-side height must be the same as the right-side height, we have ...
10 in + ? = 15 in
? = 5 in . . . . . . subtract 10 in
The missing height is 5 inches.
Write the equation of the line, in slope-intercept form, with the
following information:
slope: -2
y-intercept: (0, -3)
Factor the following quadratic expression n^2+ 4n-12
Answer:
(n + 6)(n - 2)
Step-by-step explanation:
Given
n² + 4n - 12
Consider the factors of the constant term (- 12) which sum to give the coefficient of the n- term (+ 4)
The factors are + 6 and - 2 , since
6 × - 2 = - 12 and 6 - 2 = + 4
Then
n² + 4n - 12 = (n + 6)(n - 2) ← in factored form
What is the simplified value of the exponential expression 27 ^1/3
Answer:
27^1/3=3^3×1/3=3^1=3
therefore required answer is 3.
Answer:
3
Step-by-step explanation:
(27)^1/3
(3^3)^1/3
3
As 3*3*3 is 27 so we can write 3^3 ...both power got cancelled hence we got 3 as a answer
What is the dominan and range of the relation below? Answer using set notation.
Answer:
domain: -2 < x < 4
range: -3 < y < 1
HELPPPPPPPPPPPPPPPPppppppppppppppp
Answer:
i go for 3
Step-by-step explanation:
What is the value of x?
(9x - 3)
(6x)
48°
Enter your answer in the box.
X=
Answer: x = 9
Step-by-step explanation:
The sum of three interior angles of a triangle is 180°.
(9x - 3) + (6x) + 48° = 180°
9x - 3 + 6x + 48 = 180
15x + 45 = 180
15x = 135
x = 9
given the following sequences : -17 -25 -33 -41... write an explicit formula and find the 28th term in this sequence
Answer:
a(n) = -8n -9
a(28) = -233
Step-by-step explanation:
a(n) = a(1) + (n - 1)d
n is the nth term, a(1) is the first term, d is the common difference.
*d = -25 - (-17) = -8
a(n) = -17 + (n - 1)(-8)
= -17 + (-8n + 8)
= -17 - 8n + 8
= -8n - 9
For the 28th term
a(28) = -8(28) - 9
= -224 - 9
= -233
please how do you solve 60cos25
Answer:
60cos(25)=54.378467222199
Which inequality does the graph represent?
1. x>17
2.x<17
3.x<_17
4.x>_17
Answer:
1. x > 17
Step-by-step explanation:
When the point on the graph is an open circle you are going to be using < or > as an open circle means greater than or less than
Immediately we can eliminate number 3 and 4
When the line is going in the direction of the right than the inequality sign will face the variable (x)
the numbers are getting larger meaning that x is greater than the constant (17)
Hence, your answer is x > 17
Extra notes:
when the point on the graph is a closed circle ( filled in ) then you will use ≤ or ≥ as a closed circle means greater than or equal to or less than or equal to
Answer:
1. x > 17
Step-by-step explanation:
I l l l
17 18 19 20
-------------------------------->
Hope this helps
Plz help with this problem
A diver found a school of fish 85 feet below the surface of the ocean. He found coral 95 feet deeper than the fish. How many feet deep from the surface was the coral?
Answer:
180 feet
Step-by-step explanation:
85+95=180 because depth + depth.
The total deep 180 feet from the surface was the coral.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
Given that diver found the school of fish 85 feet below the surface of the ocean. Which he found coral 95 feet deeper than the fish.
The total deep from the surface was the coral.
Therefore, it could be;
depth + depth.
85 + 95 = 180
Hence, the total deep 180 feet from the surface was the coral.
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
A $100 tablet is marked up by 10% and then the new price is marked down by 10%. What is the final price?
Answer:
$99
Step-by-step explanation:
So the initial price of the tablet was $100. It was marked up by 10% and then marked down by 10%. We are asked to find the final price.
To find the final price, lets first find the price after the tablet price was marked up by 10%. This means that the tablet price increased by 10%. To find the price, we can add 10% of the new original price (or 10% times $100) original price ($100):
$100 + ($100 × 0.1) = $100 + $10 = $110
We could have also multiplied $100 by 1.1 (or 1 + 10%) to find the new price.
So now we know that the new price after the tablet is marked up by 10% is $110. Now, to find the final price, we have to find the price after the new price is marked down by 10%. We can do this by taking the new price ($110) and subtracting 10% of the new price (or 10% times $110):
$110 - ($110 × 0.1) = $110 - $11 = $99
So the final price of the tablet would be $99.
I hope you find my answer to be helpful. Happy studying.
What could this answer be??
The number in the parentheses is the rate of change. Because this number is less than 1 it is a decrease, so it is a decay.
The percent decrease is 1 - 0.63 = 0.37 = 37% decrease
When the function ƒ(x) = 4x−2 is evaluated for x = 3, the output is:
-4
-6
-16
-none
Answer:
None
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
f(x) = 4x - 2
x = 3
Step 2: Evaluate
Substitute in x [Function]: f(3) = 4(3) - 2Multiply: f(3) = 12 - 2Subtract: f(3) = 10A model rocket is launched vertically from a platform 64 feet above the ground. The height of the rocket reaches during the flight is modeled by the equation h(t) = -16t² + 128x, where h is the height of the rocket and t is the time in seconds since the launch. Determine algebraically the time when the ball hits the ground.
Answer:
do not know why asking questions
What is the value of x?
Find all of the missing angles, #1-22. pleasssseeee helpppppp
pls help me multiple choice!
Answer:
100. degrees was right for me so it could be for you
Solve the following system of equations using Substitution, showing all work.
2x+y=9
3x−2y=17
Answer:
(x,y)=(5,-1)
Step-by-step explanation:
1. 2x+y=9 ---> y=9-2x
2. Substitute y=9-2x into 3x-2y=17 ---> 3x-2(9-2x)=17 ---> 3x-18+4x=17 --> 7x=35 ---> x=5.
3. Substitute x=5 into 2x+y=9 ---> 2*5+y=9 ---> y=9-10 ---> y= -1
Nine scores have an average of 8. Scores x and x+1 are added, and these increase the average to 9. Find x
Answer:
x must be 13
Step-by-step explanation:
Represent the nine scores by a, b, c, d, e, f, g, h, i.
Write the following equation to indicate that the average of these nine scores is 8:
a+b+c+d+e+f+g+h+i
----------------------------- = 8, or a+b+c+d+e+f+g+h+i = 72 if we multiply both
9 sides of this equation by 9.
Next, we add scores x and x+ 1 to
a+b+c+d+e+f+g+h+i + x + x + 1
and divide the result by 11, as there are now 11 scores instead of just 9:
a+b+c+d+e+f+g+h+i + x + x + 1
----------------------------------------------
11
Earlier, we saw that a+b+c+d+e+f+g+h+i = 72. We can now replace
a+b+c+d+e+f+g+h+i in the above fraction by 72:
72 + 2x + 1
------------------- = 9 (as the new average is 9)
11
Multiplying both sides of this equation by 11 results in:
73 + 2x = 99, or 2x = 26.
Then x must be 13, and x + 1 must be 14.
one package of strawberries costs $4.50 how many will 3 packages cost?
if you can please show your work:)
I think you have to multiply them to get the answer $13.5
A watering can contained 5 ½ quarts water. After all the plants were watered, only 4 cups remained.
How many cups of water were used to water the plants?
7 cups
18 cups
40 cups
84 cups
Answer: 18 cups
Step-by-step explanation:
Answer:
the answer is 18 cups :))
what is the inequality for more than 100,000
Answer:
>100,000
Step-by-step explanation:
If a fair die is rolled twice and two numbers X1=result of the first roll and X2=result of the second roll are obtained. Given that X1+X2=7, what is the probability that X1 =4 or X2 =4
Answer:
P = 2/3 = 0.67
Step-by-step explanation:
Assuming that X1 + X2 = 7
The total number of outcomes such that X1 + X2 = 7 are:
X1 = 3, X2 = 4
X1 = 4, X2 = 3
X1 = 1, X2 = 6
X1 = 6, X2 = 1
X1 = 2, X2 = 5
X1 = 5, X2 = 2
So there are 6 total outcomes such that X1 + X2 = 7
Now, the probability that X1 = 4 is equal to the quotient between the number of outcomes where X1 = 4 (only one outcome) and the total number of outcomes (6)
Then:
p = 1/6
And the probability that X2 = 4 is calculated in the same way, then the probability is:
q = 1/6
Now, the probability that X1 = 4 or X2 = 4 is the sum of both probabilities we've found above, then:
P = p + q = 1/6 + 1/6 = 2/6 = 2/3 = 0.67
Solve the equation and check.
37x + 16 = 6(6x + 6)
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution is
(Simplify your answer.)
B. The solution is all real numbers.
OC. There is no solution.
Answer:
x = 20.
Step-by-step explanation:
37x + 16 = 6(6x + 6)
Distribute.
37x + 16 = 36x + 36
Subtract 36x from both sides.
x + 16 = 36
Subtract 16 from both sides.
x = 20.
The solution is 20.
Proof
37x + 16 = 6(6x + 6)
37(20) + 16 = 6(6(20) + 6)
740 + 16 = 6(120 + 6)
756 = 6(126)
756 = 756.
%
Jaden goes to her dance class every
10 days and Scarlett goes to the same dance
class every 5 days. If they are together at the
class on Saturday, what is the next day they
will be together at the dance class?
Answer:
tuesday is answere .........
The sum of two numbers is 54 and the difference is 8. What are the numbers?
Answer:
23 and 31 are the numbers you are searching for.
Step-by-step explanation:
23 + 31 = 54
31 - 23 = 8
Have a nice day!
plz help I am being timed
Answer:
24
Step-by-step explanation:
What is 0.00047 in standard form.
Step-by-step explanation:
0.00047. = 47÷10 000
=4.7×10/10^-5
= 4.7×10^-4