Answer:
[tex]slope = \frac{y_2 - y_1}{x_2-x_1}\\\\4 = \frac{p-2}{1-4} \\\\4 \times -3 = p -2\\\\-12 + 2 = p \\\\p = -10 \\\\Equation \ of \ line : \\\\(y -y_1) = m(x - x_1)\\\\y - 2= 4(x-4)\\\\y - 2 = 4x -16\\\\y = 4x -14[/tex]
Hi there! The slope formula is:
[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
We know that the slope is 4 but we are missing the value of p. (Define m = slope)
What we have now are:
two ordered pairs (4,2) and (1,p)value of slope = 4We are going to substitute these values and solve the equation for p-term.
[tex] \large{4 = \frac{2 - p}{4 - 1} } \\ \large{4 = \frac{2 - p}{3} } \\ \large{4(3) = \frac{2 - p}{3} (3)} \\ \large{12 = 2 - p} \\ \large{p = 2 - 12 \longrightarrow \boxed{p = - 10}}[/tex]
Hence, the value of p is -10.
Next, we have to write the equation of a line in point-slope form. The point-slope form is:
[tex] \large \boxed{y - y_1 = m(x - x_1)}[/tex]
Define that (x1, y1) = ordered pairs
Since we have two given points, we can either use the first point or second point. Both work.
First Point
For our first ordered pairs (4,2), substitute x1 = 4 and y1 = 2 in the equation.
[tex] \large{y - 2 = 4(x - 4)}[/tex]
Hence, the equation of a line in point-slope form as in (4,2) is y-2=4(x-4)
Second Point
For our second ordered pairs (1,p), we know that p = -10 from the equation that we solved. Therefore (1,p) = (1,-10). Substitute x1 = 1 and y1 = -10 in the equation.
[tex] \large{y - ( - 10) = 4(x - 1)} \\ \large{y + 10 = 4(x - 1)}[/tex]
Hence, the equation of a line in point-slope form as in (1,-10) is y+10 = 4(x-1)
Answer
The value of p is -10 (p = -10)y - 2 = 4(x-4) —> use (4,2) to form an equation. y + 10 = 4(x-1) —> use (1,-10) to form an an equation.Both equations work for point-slope form.
Questions can be asked through comment.
Hope this helps, and Happy Learning! :)
pls help me i really need it
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of slides ridden and y represent the total cost. Hence:
1) For option 1, the table is shown. It passes through (2,10) and (6, 20). The equation is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-10=\frac{20-10}{6-2} (x-2)\\\\y=2.5x+5[/tex]
2) For option 2, the equation is given by y = 5x + 7.5
3) For option 3, the graph passes through (30, 100) and (10, 40). Hence the equation is:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-40=\frac{100-40}{30-10} (x-10)\\\\y=3x+10[/tex]
Option 2 has the highest rate
There are 54 benches and 6 picnic tables in a park. What is the ratio
of the number of picnic tables to the number of benches in its
simplest form??????????????????????????????/
Answer:
1 picnic table : 9 benches
Step-by-step explanation:
You just simplify the equation down to its simplest form, so since they both have the gcf of 6, you divided both sides by 6, which results in the answer above.
Given sin theta=1/3 and 0 < theta< π/2; find tan 2 theta.
Answer:
tan2θ = 4√2/7
Step-by-step explanation:
Given sin theta=1/3 and 0 < theta< π/+
Required
tan 2 theta
tan2 theta = 2tanθ/1-tan²θ
Get tan θ
sinθ = opp/hyp
adj = √3²-1²²
adj = √9-1
adj = √8
tanθ = opp/adj = 1/2√2
tan2 theta = 2(1/2√2/1-(1/2√2)²
tan2θ = 1/√2/1-1/8
tan2θ = 1/√2/7/8
tan2θ = 8/7√2
Rationalize
tan2θ = 8√2/14
tan2θ = 4√2/7
Jenna is opening a clothing store. She plans to start by selling T-shirts. If it
costs her $7 for each shirt, $2 for ink per shirt, and $0.10 a bag, what is her
unit cost per shirt?
O A. $9.10
O B. $2.10
O c. $4.55
O D. $7.00
Her unit cost per shirt is,
= $9.10
What is Addition?The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.
Given that;
Jenna's unit cost per shirt is, $9.10
Here, We have;
Cost for each shirt = $7
Cost for ink per shirt = $2
Cost of a bag = $0.10
Hence, Cost of T-shirt is,
= Cost for each shirt + Cost for ink per shirt + Cost for bag
= $7 + $2 + $0.10
= $9.10
Thus, Her unit cost per shirt is,
= $9.10
Learn more about the addition visit:
https://brainly.com/question/25421984
#SPJ5
Which of these is the cross section if the slice is made perpendicular to the base?
A. square
B. triangle
C. rectangle
D. rhombus
***(NO LINKS AND ANSWER SERIOUSLY)***
Hi there!
[tex]\large\boxed{\text{ C. Rectangle}}[/tex]
If cross sections were made perpendicular to the base, they would assume the shape of the lateral sides.
Thus, the cross sections would be rectangles. The correction answer is C.
Simon is playing a game with letter tiles.
Answer:
so what should I do
Step-by-step explanation:
hope it helps
what is the answer to this problem?
Ellie is running down the street at 10 m/s. She sees a double-tall latte on the road ahead of her and starts sprinting. After 5 seconds have passed, Ellie is running 15 m/s. Assuming she does not change directions, what was Ellie’s acceleration?
Answer:
2m/s²
Step-by-step explanation:
acceleration = change in velocity/time taken
a = v-u/t
Given
v = 15m/s
u = 5m/s
time t = 5secs
Substitute
a = 15 - 5/5
a = 10/5
a = 2m/s²
Hence Ellie’s acceleration is 2m/s²
I need helppp pls I’m confused
Answer:
30 ft²
Step-by-step explanation:
Area of a paralleogram formula:
A = bh
A = (6)(2)
A = 12
Area of a rectangle:
A = bh
A = 6(3)
A = 18
Combined:
12 + 18
30
A car wash detailed 288 cars in 8 hours. At what rate did the car wash detail cars in cars per hour?
A.
34 cars per hour
B.
37 cars per hour
C.
36 cars per hour
D.
35 cars per hour
Answer:
a
Step-by-step explanation:
I need help pls! Giving brainliest and extra points!
Answer:
y = 8x+6
Step-by-step explanation:
First find the slope since it is a linear function
m = (y2-y1)/(x2-x1)
= (18-2)/(1 1/2 - -1/2)
=16 / (1 1/2 +1/2)
= 16/2
= 8
The linear function is in the form
y = mx+b where m is the slope
y = 8x+b
Substitute the other point into the equation to determine b
10 = 8(1/2) +b
10 = 4+b
10-4 = b
6 = b
y = 8x+6
formula of slope , if angle is give
Answer:
formula of slope if angle is given:
Tan (angle given)
Step-by-step explanation:
4•(-6) • (-2) =
plz help
Answer:
should be 48
Step-by-step explanation:
Answer:
48
Step-by-step explanation:
Apply rule- a * (-b) = -a * b
4 * (-6)
= -24(-2)
= 48
Hope this helps:)
can someone please help me figure this out? this is a summative and I'm failing for the year. it's algebra 1.
Part (a)
x = number of bass caughty = number of trout caughtx and y are nonnegative whole numbers.
3x represents the total weight of all the bass, since one bass weighs 3 pounds. Similarly, 2y is the total weight of the trout with each one being 2 pounds. Adding up all the weight of all the fish, we get 3x+2y. This is set equal to 34 pounds which is the total stated weight caught.
In short, we end up with the equation 3x+2y = 34
Now onto the second equation. The expression 5x represents how many points Pat gets from catching x bass, because he gets 5 points per bass. Then we subtract off 2y to represent Pat losing 2 points per trout he catches. Overall, his point total is 5x-2y. This is set equal to his point total of 14.
The second equation is 5x-2y = 14
------------
Answer:
3x+2y = 34
5x-2y = 14
Both equations are needed to form this particular system.
===================================================
Part (b)
We could use a number of methods to solve for (x,y). Possibly the most efficient is elimination. Why? Because note how we have 2y up top and -2y down below. They add to 0y which is just 0. The y terms go away, and are eliminated. Afterward, all we're left with is x in which we can solve for just like any other single variable equation. More info is in part (c).
===================================================
Part (c)
Refer to the answer in part (a). We'll add straight down. So that means we have these three sets of addition operations.
3x+5x becomes 8x2y + (-2y), aka 2y-2y, becomes 0y and the y terms go away34+14 simplifies to 48After those three sets of addition operations, we're left with the much simpler equation 8x = 48. To solve this, we divide both sides by 8 and we get x = 6. This says Pat caught 6 bass.
Use this value of x to find y. So we'll plug x = 6 into either equation involving x,y and solve for y
3x+2y = 34
3(6)+2y = 34
18+2y = 34
2y = 34-18
2y = 16
y = 16/2
y = 8
So we can see that Pat caught 8 trout as well.
The check portion is shown in the attached image below. Effectively, all we're doing is replacing x and y with 6 and 8 respectively. Then we're simplifying both sides. Getting the same number on both sides results in a true equation, and therefore verifies we have the correct (x,y) solution.
Solution: (x,y) = (6,8)
Interpretation: Pat caught 6 bass and 8 trout
SOLVE 23 ASAP PLEASE!!
A = ( - 3 , 2 ) ..**&**.. B = ( 4 , 5 )
_________________________________
Slope = [ y(B) - y(A) ] ÷ [ x(B) - x(A) ]
Slope = [ 5 - 2 ] ÷ [ 4 - ( - 3 ) ]
Slope = [ 3 ] ÷ [ 4 + 3 ]
Slope = 3 ÷ 7
Slope = 3/7
_________________________________
y - y(A) = Slope × ( x - x(A) )
y - 2 = 3/7 × ( x - ( - 3 ) )
y - 2 = 3/7 ( x + 3 )
y - 2 = 3/7 x + 9/7
y = 3/7 x + 9/7 + 2
y = 3/7 x + 9/7 + 14/7
y = 3/7 x + 23/7
please help. The graph of y = f(x) is shown below. What are all of the real solutions of f(x) = 0?
Answer:
(-4,0) (-5,0) and (1,0)
Step-by-step explanation:
Write the rule for the nth term of geometric sequence a1=6 and r=3
Step-by-step explanation:
Hey there!
Given;
a1 = 6
and r = 3
Then;
Let's see, we have a1 "first term" and r "common ratio". So, firstly use the formula.
[tex]nth \: term \: of \: geometric \: sries = {a}^{} . {r}^{n - 1} [/tex]
Now, keep all values.
[tex]nth = 6 \times {3}^{n - 1} [/tex]
So, it becomes like this.
Therefore, the rule is nth= 6*3^n-1.
Hope it helps!
60% of the students on the field trip love the museum. If 24 students love the museum, how many students went on the field trip?
Answer:
40
60% of 40 is 24
so the answer would be 40
what is the value of x?
Answer:
12
Step-by-step explanation:
The graph compares the weights in pounds of 100 dogs and cats that are brought in to a veterinarian's office.
Two box and whisker plots showing weights of cats and dogs on a number line from 0 to 100. The upper plot represents the dog weights. For this upper plot, the minimum number is 10, the maximum number is 95, the right side of the box is 70, the left side of the box is 35, and the bar in the box is at 50. The lower plot represents cat weights. For this lower plot, the minimum number is 1, the maximum number is 18, the right side of the box is 13, the left side of the box is 6, and the bar in the box is at 10.
How many more dogs than cats were over 10 pounds?
10
30
50
100
Answer:
100
Step-by-step explanation:
Calculate the volume of a cube with side length of 7mm.
Answer:
[tex] {7}^{3} = 7 \times 7 \times 7 = 147 {m}^{3} \\ to \: calculate \: the \: volume \: of \: a \: cube \: we \: need \: to \: use \: this \: formula \\ {x}^{3} \\ x = side \: length[/tex]
hiii please help!! i'll give brainiest if you get it correct - find the volume.
Answer:
Step-by-step explanation:
volume=area of side triangle×distsnce between triangles
=1/2×20×8×5
=400 in³
Answer:
the answer would be 400
Step-by-step explanation:
20×8×5×.5
Devon writes a number pattern. He starts with 3 and follows the rule “multiply by
2." Which numbers could be in Devon's pattern
Answer:
3,6,12,24.48,96,192
Step-by-step explanation:
solve the inequality 14≥3x+2
Answer:
4 ≥ x
Step-by-step explanation:
14 ≥ 3x + 2
14 - 2 ≥ 3x
12 ≥ 3x
4 ≥ x
Solving the inequality 14 ≥ 3x+2 we get x ≥ 4.
What is inequality?In mathematics, an assertion of an order connection greater than, greater than, or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
Given:
14 ≥ 3x+2
Switch sides
3x+2 ≥ 14
Subtract 2 from both sides of the equation, we get
3x + 2 - 2 ≥ 14 - 2
Simplifying the above equation
3x ≥ 12
Divide both sides by 3, we get
3x/3 ≥ 12/3
x ≥ 4
Therefore, the value of x ≥ 4.
To learn more about inequality
https://brainly.com/question/25275758
#SPJ2
how to represent -23/6 on number line
Multiply. Express your answer in simplest form. 3 1/2 x 1 2/5. Show work.
Answer:
4 9/10
Step-by-step explanation:
Give the trigonometric ratio as a fraction:
Tan Z
X
24
26
Y
10
z
Answer:
your answer is B
Step-by-step explanation:
Answer:
24/ 10
Step-by-step explanation:
We know,
tan θ = opposite/adjacent
∴ tan Z = 24/ 10
Find m
p (8x+2)
q (10x-19)
r (16x-7)
Answer:
you have to add all the angles of a triangle so the value of m is 6
Help pls 40 points
Maths genius awakee!
Two experiments were carried out to find the relationship between the variables x and y. Both
experiments showed that the relationship between x and y is in accordance to 3(9^x) = 27^y and log2 y = 2 + log2 (x - 2). Find the value of x and y that satisfy both experiments.
Answer:
X=5/2 , y=2
Step-by-step explanation:
Sorry if I'm not correct
F4 ke?
How is 80.106 written in expanded form?
Pls answer !!
Answer:
B
Step-by-step explanation:
This is pretty self explanatory and easy..