Given:
A line passes through the points (-1, -1) and (5,8).
To find:
Which points lie on the same line?
Solution:
If a line passes through two points, then the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
A line passes through the points (-1, -1) and (5,8). So, the equation of the line is:
[tex]y-(-1)=\dfrac{8-(-1)}{5-(-1)}(x-(-1))[/tex]
[tex]y+1=\dfrac{8+1}{5+1}(x+1)[/tex]
[tex]y+1=\dfrac{9}{6}(x+1)[/tex]
[tex]y+1=\dfrac{3}{2}(x+1)[/tex]
Multiply both sides by 2.
[tex]2(y+1)=3(x+1)[/tex]
[tex]2y+2=3x+3[/tex]
[tex]2y=3x+3-2[/tex]
[tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex]
So, the equation of the line is [tex]y=\dfrac{3}{2}x+\dfrac{1}{2}[/tex].
Now, check each point for this equation.
Putting [tex]x=-3[/tex], we get
[tex]y=\dfrac{3}{2}(-3)+\dfrac{1}{2}[/tex]
[tex]y=\dfrac{-9+1}{2}[/tex]
[tex]y=\dfrac{-8}{2}[/tex]
[tex]y=-4[/tex]
Similarly,
For [tex]x=9,y=15[/tex].
For [tex]x=1,y=2[/tex].
For [tex]x=4,y=6.5[/tex].
For [tex]x=3,y=5[/tex].
For [tex]x=-2,y=-2.5[/tex].
Therefore, the points (-3,-4), (9,14), (1,2) and (3,5) lie on the same line but the points (4,7) and (-2,-2) are not on that line.
PLEASE HELP! PLEASE SHOW WORK
Use the following expression to answer this three part question:
f(x) = 2x2 + 4x − 6
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
Answer:
Step-by-step explanation:
The graph of a quadratic function is a U-shaped curve called a parabola. One important feature of the graph is that it has an extreme point, called the vertex. If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function.
Can you help me with this question? It’s in the photo
Answer:
Option (d), (e) and (f) are correct.
Step-by-step explanation:
In triangle MNP, angle P = 90 degree
Cos M = 7 / 12
Now according to the right angle triangle
[tex]NP^2 = NM^2 - PM^2\\\\NP^2 = 12^2 - 7^2\\\\NP = \sqrt95[/tex]
Now
[tex]Sin M = \frac{sqrt95}{12}\\\\Cos N = \frac{95}{12}[/tex]
the quantity of the square of the sum of 4 times
x and 3, divided by the difference of x and 10
Answer:
Step-by-step explanation:
(4x+3)²÷(x-10)
=(16x²+24x+9)÷(x-10)
x-10) 16x²+24x+9 (16x+184
16x²-160x
- +
------------------
184x+9
184x-1840
- +
----------------
1849
----------------
Please help with (ii). thank you!!!
Answer:
Exact surface area = 500+20pi square cm
=============================================================
Explanation:
A = area of the bottom face = 10*12 = 120B = area of the left face = 7*12 = 84C = area of the right face = 7*12 = 84D = area of the front face = 7*10-0.5*pi*2^2 = 70 - 2piE = area of the back face = 7*10-0.5*pi*2^2 = 70 - 2piF = area of the top face = 2*3*12+0.5*2*pi*2*12 = 72+24piAll areas mentioned are in square cm, which can be abbreviated to cm^2.
Faces A,B,C are straight forward as they are simply rectangles. The remaining 3 other faces are a bit tricky.
Faces D and E involve subtracting off the area of a semicircle of radius 2 from a 7 by 10 rectangle area. The formula pi*r^2 is the area of a full circle, while 0.5*pi*r^2 is the area of a semicircle. From there, I then plugged in r = 2.
The top face is really a combination of 3 different pieces (two flat, one curved in the middle). Each flat part is of area 3*12 = 36, so that doubles to 2*3*12 when accounting for both flat parts. The curved portion will involve the lateral surface area of a cylinder formula which is
LSA = 2*pi*r*h
but since we're only dealing with half the lateral area, we multiply that by 0.5 to get 0.5*2*pi*r*h. From there, I plugged in r = 2 and h = 12.
-----------------------
In summary we have these six areas for the faces
bottom = 120left = 84right = 84front = 70 - 2piback = 70 - 2pitop = 72 + 24piAdd up those sub areas to get the full surface area of this particular 3D solid.
120+84+84+(70-2pi)+(70-2pi)+(72+24pi)
(120+84+84+70+70+72)+(-2pi-2pi+24pi)
500+20pi
This is the exact surface area in terms of pi. If you want the approximate version of this, then you could replace pi with 3.14 and compute to get 562.8 cm^2
Use more decimal digits in pi to get a more accurate value. If you use your calculators version of pi, then you should get somewhere around 562.831853 cm^2
In this case, I think it's better to stick with the exact surface area (unless your teacher instructs otherwise).
What is the recursive formula for this geometric sequence?
-3, -21, -147, -1029, ..
Answer:
b . is the answer
Step-by-step explanation:
ha ahhgahga
instructions: state what additional information is required in order to know that the triangle in the image below are congruent for the reason given.
Given: AAS
Answer:
QP ≈ HG
Common side between those angles are QP and HG
so, they should be congruent to prove AAS
Answered by GAUTHMATH
Help me with this problem
Answer:
x = 30
Step-by-step explanation:
If A parallel to B , then
2x and 4x are same- side interior angles and sum to 180° , that is
2x + 4x = 180
6x = 180 ( divide both sides by 6 )
x = 30
simplify 2a+5b/4+3a+2b/8
Answer:
Step-by-step explanation:
Combine like terms
[tex]2a + \frac{5b}{4}+3a + \frac{2b}{8}=2a + 3a +\frac{5b}{4}+\frac{2b}{8}\\\\ = 2a + 3a + \frac{5b}{4}+\frac{b}{4}\\\\= 5a + \frac{5b+b}{4}\\\\= 5a +\frac{6b}{4}\\\\= 5a + \frac{3b}{2}[/tex]
Answer:
[tex]2a+5\frac{b}{4}+3a+2\frac{b}{8}[/tex]
First multiply by 8
[tex]2\cdot8a+5\cdot8\cdot\frac{b}{4}+3\cdot8\cdot a+2\frac{b}{8}\cdot8[/tex]
We multiple and divide where we can
[tex]16a+10b+24a+2b[/tex]
And now it's simple
30a+12b
Which property of math is the young student learning with the following equation? 3 x (4 + 7) = (3 x 4) + (3 x 7)
The property of math they are learning is the distributive property
Solve the equation to find a positive value of c: 3^2 + 4^2 = c^2
Answer:
The answer is c=5,-5
On a standard baseball field, consecutive bases are 90 feet apart. How far does the catcher have to throw the ball to get from home plate to 2nd base
Carlos and Maria drove a total of 197 miles In 3.8 hours. Carlos drove the first part of the trip and averaged 55 miles per hour. Maria drove the
remainder of the trip and averaged 47 miles per hour. For approximately how many hours did Maria drive? Round your answer to the nearest tenth if
necessary.
Answer:
1.5 hours
Step-by-step explanation:
Carlos = x
Maria = y
55x + 47y = 197
x + y = 3.8
x = 3.8 - y
55(3.8 - y) + 47y = 197
209 - 55y + 47y = 197
-8y = -12
y = 3/2 = 1.5
On a coordinate plane, a line goes through (negative 3, negative 4) and (3, 0).
What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept?
The slope is Negative three-halves and contains the point (0, 2).
The slope is Negative two-thirds and contains the point (0, −2).
The slope is Three-halves and contains the point (0, 2).
The slope is Negative three-halves and contains the point (0, −2
Answer:
The slope is Negative three-halves and contains the point (0, 2).
Step-by-step explanation:
(-3,-4)(3,0)
M= -4/-6 = 2/3
⊥M = -3/2
0 = 2/3(3) + B
B=2
1
What is the value of x in the equation x - y = 30, when y = 152
200
[tex]\displaystyle\bf 1) \ if\ y=152 \Longrightarrow x=30+152=182 \\\\2) \ if \ y =200 \Longrightarrow x=200+30=230\\\\3) \ if \ y=80 \Longrightarrow x=30+80=110\\\\4) \ if \ y=4 \Longrightarrow x=4+30=34 \\\\5)\ if \ y=8 \Longrightarrow x=30+8=38[/tex]
17.27. How many Social Security numbers (see Exercise 8.12) have their nine digits in strictly increasing order
Answer:
"10 possibilities" is the appropriate response.
Step-by-step explanation:
The numbers will be:
⇒ [tex]123 \ 456 \ 789[/tex]
Now anyway we commence with right and afterwards remove nine from eight and seeing as maintain the sequence growing.
then,
[tex]012345678[/tex][tex]012345679[/tex][tex]012345689[/tex][tex]012345789[/tex][tex]012346789[/tex][tex]012356789[/tex][tex]012456789[/tex][tex]013456789[/tex][tex]023456789[/tex]Thus, the above is the correct answer.
Find a number such that if 16 is added to it, the ratio of the result to the original number is 4:3
Answer:
48
Step-by-step explanation:
let the number be x and x + 16 the result of adding 16 to it, then
the ratio of the result to the original is
[tex]\frac{x+16}{x}[/tex] = [tex]\frac{4}{3}[/tex] ( cross- multiply )
4x = 3(x + 16) = 3x + 48 ( subtract 3x from both sides )
x = 48
a. 65
b. 67
c. 43
d. 23
y = RootIndex 3 StartRoot x EndRoot. y = negative (0.4) RootIndex 3 StartRoot x minus 2 EndRoot
Which of the following describes the graph of the transformed function compared with the parent function? Select all that apply.
Answer:
- Reflected over the x-axis
- Compressed by a factor of 0.4.
- Translated 2 units left
Step-by-step explanation:
Given
[tex]y = \sqrt[3]{x}[/tex]
[tex]y' = -(0.4)\sqrt[3]{x-2}[/tex]
Required
The transformation from y to y'
First, y is reflected over the x-axis.
The transformation rule is:
[tex](x,y) \to (x,-y)[/tex]
So, we have:
[tex]y = \sqrt[3]{x}[/tex] becomes
[tex]y' = -\sqrt[3]{x}[/tex]
Next, it was compressed by a scale factor of 0.4
The rule is:
[tex]y' = k * y[/tex]
Where k is the scale factor (i.e. k = 0.4)
So, we have:
[tex]y' = 0.4 * -\sqrt[3]{x}[/tex]
[tex]y' = -(0.4)\sqrt[3]{x}[/tex]
Lastly, the function is translated 2 units left;
The rule is:
[tex](x,y) \to (x-2,y)[/tex]
So, we have:
[tex]y' = -(0.4)\sqrt[3]{x - 2}[/tex]
Answers:
-reflected over the x-axis
-translated 2 units right
-compressed by a factor of 0.4
Which statement about these two restaurant meals is correct? A. Neither meal contains any nutrients. B. Meal A is the more healthful choice. C. Meal B is the more healthful choice. D. Both meals are healthful choices.
Answer:
D. Both meals are healthful choices
50 pts pls help
What is the range of the function shown on the graph above?
Answer:
[0, 7]Step-by-step explanation:
The range is the set of y-values.
The graphed function has its range between 0 and 7, both inclusive.
So the range is:
y ∈ [0, 7]what is the binary 11110-10101
Será - 12 esta noche. El meteorólogo predice que mañana al mediodía hará 25 ° más de temperatura. ¿Cuál será la temperatura mañana al mediodía?
Respuesta:
13 °
Explicación paso a paso:
La temperatura de esta noche = - 12
La temperatura prevista para mañana = 25 ° más cálida que la temperatura de esta noche
La temperatura prevista para mañana será;
La temperatura de esta noche + 25 °
Temperatura prevista para mañana = (-12 ° + 25 °)
Temperatura prevista para mañana = 13 °
Write down five numbers so that:the mean is 6,the median is 5 and the mode is 4
Answer:
4 , 4 , 5 , 6 , 11
Step-by-step explanation:
Mode = 4
So at least two times 4 should be there in the data.
And median is 5. So the middle term ( 3rd term} should 5.
Let x and y be the 4th term and 5th term
Data set:
4 , 4 , 5 , x , y
Mean =6
[tex]\frac{4+4+5+x+y}{5}=6\\[/tex]
4+4+5 +x + y = 6*5
13 + x + y = 30
x + y = 30 - 13
x + y = 17
x ,y can be any numbers that sum up to 17.
x , y can be 10 , 7 or 6, 11
Data set: 4 , 4 , 5 , 6, 11
please help!!
The length of side AC is | 3,4,5,6 | units.
The area of triangle ABC is | 5,10,15,20 | square units.
Look at ∠A, the angle which resides on (1, 3). If we count 5 units down, you find the other endpoint on side AC. Hence, the length of side AC is 5 units. This figure is equal to the height of the graphed triangle.
If we mirror this process with the figure representing the triangle's length, side BC, we get 4 units.
The formula for calculating a triangle's area is [tex]\frac{1}{2}bh[/tex]. In this context, the base of the triangle is the same as the length. Now, let's plug in the base and the height.
[tex]\frac{1}{2}(4)[/tex] × [tex](5) = 10[/tex]
The area of triangle ABC is 10 squared units.
Answer:
first box: 5 second box: 10
Step-by-step explanation:
A line has slope 3 and y–intercept 4.
Which answer is the equation of the line?
Answer:
y= 3x+4
Step-by-step explanation:
Slope-intercept form of an equation is
y=mx+b
m=slope
b=y-intercept
Just plug the values in and you get y=3x+4
Calculate the sum of the integers from 52 to 108
Answer:
4560
Step-by-step explanation:
Find an ordered pair to represent t in the equation t = u + v if u = (-1, 4) and v = (3, -2)
Given:
[tex]u=(-1,4)[/tex]
[tex]v=(3,-2)[/tex]
The equation is:
[tex]t=u+v[/tex]
To find:
The ordered pair to represent t in the given equation.
Solution:
We have,
[tex]t=u+v[/tex]
Substituting the given values, we get
[tex]t=(-1,4)+(3,-2)[/tex]
[tex]t=((-1)+3,4+(-2))[/tex]
[tex]t=(-1+3,4-2)[/tex]
[tex]t=(2,2)[/tex]
Therefore, the ordered pair to represent t in the given equation is (2,2).
Choose the smallest number. 3/18 10/3
Answer:
3/18
Step-by-step explanation:
3/18= 0.16
10/3= 3.33
Answer:
3/18
Step-by-step explanation:
3/18 , 10/3
Simplify it to the smallest size
3/18 , 10/3
1/6 , 10/3
1/6 = 3/18
____ more than 3455 is two hundred seventy -eight thousand five hundred eighty three
Answer:
275 128
Step-by-step explanation:
You have to subtract 3455 from two hundred seventy eight thousand five hundred eighty three(278 583) so you will get the answer 275 128.
278 583-3455=275 128
I'm sure with this answer
to make sure you can add 3455 to 275 128 and you will get the answer as 278 583
Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit but the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.
Answer:
there are 2 apples in the basket
there are 10 banana in the basket
Step-by-step explanation:
According to the Question,
We have, Battle is making fruit baskets, which include apples and bananas to send to some of her real estate clients. She wants each basket to have at least 12 pieces of fruit.let x for apple And y for banana So, x+y=12---Equation 1
And, the fruit should weigh no more than 80 ounces total. On average each apple weighs 5 ounces and each banana weighs 7 ounces.Thus, 5x+7y=80 ----Equation 2
Now, (Equation 1) × 5 Subtract with (Equation 2) We get,
2y = 20 ⇒ y=10 (there are 10 banana in basket)
Put value of y=10 in Equation 2 we get5x+70=80 ⇔ x=2(there are 2 apples in basket)
