Answer:
Step-by-step explanation:
Part A:
y=1.5x+4.25
Part B:
16.25=1.5x+4.25
Minus 4.25 from both sides
12=1.5x
Divide both sides by 1.5 and you will get x=8
Cliek an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan click the trashcan to clear all your answers
Factor completely, then place the answer in the proper location on the grid
2107.57a+ 30
123456789
===============================================================
Explanation:
I'll use the variable x in place of 'a'
The expression we need to factor is [tex]21x^2-57x+30[/tex] which is in the form [tex]ax^2+bx+c[/tex]
So,
a = 21b = -57c = 30We'll plug those three values into the quadratic formula
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-57)\pm\sqrt{(-57)^2-4(21)(30)}}{2(21)}\\\\x = \frac{57\pm\sqrt{729}}{42}\\\\x = \frac{57\pm27}{42}\\\\x = \frac{57+27}{42} \ \text{ or } \ x = \frac{57-27}{42}\\\\x = \frac{84}{42} \ \text{ or } \ x = \frac{30}{42}\\\\x = 2 \ \text{ or } \ x = \frac{5}{7}\\\\[/tex]
The two roots of [tex]21x^2-57x+30 =0[/tex] are [tex]x = 2 \text{ and } x = \frac{5}{7}[/tex]
The root x = 2 leads to the factor (x-2) after subtracting 2 from both sides.
The root [tex]x = \frac{5}{7}[/tex] leads to the factor (7x-5) after first multiplying both sides by 7, and then subtract 5 from both sides.
So we have this set of steps:
[tex]x = \frac{5}{7}\\\\7x = 5\\\\7x-5=0\\\\[/tex]
The two factors are (x-2) and (7x-5).
This leads to (x-2)(7x-5)
The last step is to replace x with 'a' so that the variables match up.
We arrive at (a-2)(7a-5)
However, as the next section shows, we have a bit of a problem. Don't worry, it can be easily fixed.
---------------------
Let's expand out that factored expression we found earlier.
[tex](a-2)(7a-5)\\\\b(7a-5)\ \text{ ..... let b = a-2}\\\\7ab - 5b\\\\7a(b) - 5(b)\\\\7a(a-2) - 5(a-2)\ \text{ ..... plug in b = a-2}\\\\7a^2-14a - 5a+10\\\\7a^2-19a+10\\\\[/tex]
That's not good. We should have arrived at the original expression [tex]21a^2-57a+30[/tex]. To fix this discrepancy, we can stick a 3 out front and then notice that:
[tex]3(a-2)(7a-5) = 3(7a^2-19a+10) = 21a^2-57a+30[/tex]
The error has been fixed.
We have the full factorization of 3(a-2)(7a-5)
The order of the factors doesn't matter, so we could have written the answer as 3(7a-5)(a-2). Usually the factor without any variables will be listed first.
Based on the screenshot you posted, if that '7' is locked in place, then the only possible answer is 3(7a-5)(a-2) since you'll have 3 in the first slot, then a ( in the next slot. The other slots are filled out in a similar manner. There are no spaces between any symbol or letter.
*FIRST PERSON TO GET IT RIGHT AND ANSWER FIRST GETS BRAINLIEST*
In an aquarium, there are starfish and octopi in a tank. The total number of animals in the tank is 30. The total number of legs in the tank is 171. Assuming that all animals have all their legs, find the number of each type of animal in the tank. (Starfish have 5 legs and Octopus have 8 legs)
(solve this using Elimination Method, MUST SHOW WORK)
Answer:
23 starfish, 7 octopi
Step-by-step explanation:
x=starfish
y=octopi
x+y=30
5x+8y=171
-5(x+y=30)
5x+8y=171
-5x-5y=-150
5x+8y=171
3y= 21
y=7
x+7=30
x=23
23 starfish, 7 octopi
The area of a rectangle is 65 square inches.
The length is x + 5, and the width is x – 3.
Find the value of x, and the dimensions of the rectangle.
A = lw
x=
length =
width=
Answer:
x=-10,8
length=13
width=5
Step-by-step explanation:
(x+5)(x-3)=65
x^2+2x-15-65=0
x^2+2x-80=0
(x+10)(x-8)=0
x=-10,8
x+5
(-10)+5=-5, negative length does not make sense
x+5
8+5=13
x-3
(-10)-3=-13, negative width does not make sense
x-3
(8)-3=5
Answer:
x=8
length= 13inches
width=5inches
Step by step explanation:
A=lw
65= (x+5)(x-3)
65= x²-3x+5x-15
x²+2x-80=0
x²+ 10x - 8x - 80 = 0
x(x+10) -8(x+10) = 0
(x-8)(x+10)=0
x= 8 or -10
x cannot be negative
hence x= 8
length= x+5
=8+5
=13inches
width= x-3
=8-3
=5inches
The table shows the linear relationship between the number of pages left to read in an
the number of hours a student has already spent reading the novel. Mark each stateme
or false. If false, rewrite the statement correctly.
HOURS
READ
RE
9. The student reads at a rate of 48 pages per hour.
1
4
10. The number of pages in the novel is 644.
8
12
11. The situation can be represented by the
equation y = -48x + 692.
14
The table is an illustration of a linear function
9. The student's rate
Take any two points from the table
[tex](x,y) =\{(1,644)\ (4,500)\}[/tex]
The rate is then calculated using:
[tex]Rate = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
This gives
[tex]Rate = \frac{644 -500}{1-4}[/tex]
[tex]Rate = \frac{144}{-3}[/tex]
[tex]Rate = -48[/tex]
The statement that the student reads at a rate of 48 pages per hour is true
10. The pages in the novel
From the table, there are 644 pages left, after the student read for 1 hour.
This means that there are more than 644 pages in the novel.
The statement that the number of pages in the novel is 644 is false
11. The linear equation
This is calculated as:
[tex]y = Rate(x -x_1) + y_1[/tex]
So, we have:
[tex]y = -48(x -1) + 644[/tex]
[tex]y = -48x +48 + 644[/tex]
[tex]y = -48x +692[/tex]
The statement that the situation can be represented by the equation y = -48x + 692 is true
Read more about linear equations at:
https://brainly.com/question/15602982
Answer:
Step-by-step explanation:
HELP HELP HELP HELP HELP What is the range of the data shown in this stem-and-leaf plot?
Stem Leaf
1 3 7 7
2 2 4 4 4 5
3 1 5 8 9
4 0 6 7
Key: 2|1=21
======================================================
Explanation:
The smallest data value is 13. This is due to the stem 1 and leaf 3.
The largest is 47. This is from the stem 4 and leaf 7.
The span between these items is 47-13 = 34
anybody help please hehehe
Answer:
It is the second one 20^247
Step-by-step explanation:
PLS HELP ASAP ILL GIVE BRAINLKEST THANKS
Answer:
C
Step-by-step explanation:
y = 10
x = 8
The y intercept is 0 and the line runs through (0,0)
m = y / x This formula can only be used when the y incept is 0.
m = 10/8
m = 5/4
Equation
y = 5/4 x
3
which equation is equivalent to -2 (x+3) - 4x = 10?
Answer:
-6x -6= 10
Step-by-step explanation:
-2(x +3) -4x= 10
Expand:
-2(x) -2(3) -4x= 10
-2x -6 -4x= 10
Simplify:
-6x -6= 10
Thus, the second option is correct.
Write the equation of the line that passes through (-4,1) and is perpendicular to the line y=2x+3
Answer: y = -(1/2)x - 1
Step-by-step explanation:
y=2x+3
This is written in the format of y = mx + b, where m is the slope and b the y-intercept. The slope of this reference line is 2. Perpendicular lines will have a slope that is the negative inverse of the slope of the reference line. That means out new line will have a slope of -(1/2):
y = -(1/2)x + b
We can find b by entering the x and y for the given point (-4,1) and solve for b:
y = -(1/2)x + b
1 = -(1/2)(-4) + b
1 = 2 + b
b = -1
y = -(1/2)x - 1
This equation is perpendicular to y=2x+3 and goes through point (-4,1). See attachment.
Luis tiene la mitad de la edad de Juan menos un año, Pedro tiene un tercio menos edad que Luis
Answer:
dude I would love to help but I don't speak taco bell I'm sorry :/
Order these numbers from least to greatest
Answer:
5.125 < 5.14 < 5.15 < 5 2/9
Step-by-step explanation:
i changed 103/20 to a decimal to make it easier and just left 5 2/9 the same, hope this helps <3
A total of 11 trucks was used to carry 126 tonnes of iron. Some of the trucks carry
16 tonnes each, and the rest carry 6 tonnes each. Form an equation and solve it to
find the number of 16 tonne trucks.
Step-by-step explanation:
x = number of trucks with 16 tonnes capacity
y = number of trucks with 6 tonnes capacity
x + y = 11
16x + 6y = 126
the first equation gives us
x = -y + 11
and we use that in equation 2 :
16(-y + 11) + 6y = 126
-16y + 176 + 6y = 126
-10y = -50
10y = 50
y = 5
x = -y + 11 = -5 + 11 = 6
the number of 16 tonne trucks was 6.
Find the zeros of ƒ(x) = x3 + 6x2 + 8x.
A) x = 0, –2, –4
B) x = 0, 2, 4
C) x = 2, 4
D) x = –2, –4
Answer:
Option A: [tex]x=0[/tex], [tex]x=-2[/tex], and [tex]x=-4[/tex]
Step-by-step explanation:
[tex]f(x)=x^3+6x^2+8x[/tex]
[tex]0=x^3+6x^2+8x[/tex]
[tex]0=x(x^2+6x+8)[/tex]
[tex]0=x(x+2)(x+4)[/tex]
[tex]x=0[/tex], [tex]x=-2[/tex], and [tex]x=-4[/tex]
[tex]x^3+6x^2+8x = 0\\\\\implies x^3+2x^2 +4x^2+8x =0\\\\\implies x^2(x+2) +4x (x+2) =0\\\\\implies (x+2)(x^2 +4x) = 0\\\\\implies x (x+2) (x+4)=0\\\\\text{Hence,} \\\\x = 0 ,-2,-4[/tex]
4
en 2 = 21,426
6%-
*8 = 21 - 22 - 24
8
-8=24
16
44-8-8=24 -
2x
47.
4y
Answer:
Step-by-step explanation:
BOX #1 -- 2x
BOX #2 -- 4x
BOX #3 -- 8
BOX #4 -- 16
BOX #5 -- 4
HELP SOLVE THIS QUICK
y = 6x + 20
y = -4x + 150
Answer:
13
Step-by-step explanation:
set equations equal to each other and solve for x
6x + 20 = -4x + 150
10x = 130
X = 13
The year the Greek city of Helike disappeared is -1/5 times the year the US Civil War ended. Let w represent the year the Civil War ended. Write an expression in terms of w to represent the year of Helike’s disappearance.
Variables:
w= The\ year\ Civil\ War\ ended
The year the Greek city of Helike disappeared is -1/5(w)
sry if im wrong i hope this helps tho :)
Answer:
Hope this helps
Step-by-step explanation:
-1/5x=w
w=1865
so -1/5x=1865
x=-9325
A company rents out 11 food booths and 20 game booths at the county fair. The fee for a food booth is $100 plus $9 per day. The fee for a game booth is $95 plus $6 per day. The fair lasts for d days, and all the booths are rented for the entire time. Enter a simplified expression for the amount in dollars, that the company is paid. The expression is?
Answer:
3000 +219d
Step-by-step explanation:
The food booth rental revenue is ...
11(100 +9d) = 1100 +99d
The game booth rental revenue is ...
20(95 +6d) = 1900 +120d
Then the total revenue is ...
(1100 +99d) +(1900 +120d) = 3000 +219d
How to derive Universal Law of Gravitation ?
Answer:
These are the answers
Step-by-step explanation:
The orbit of a planet is an ellipse, with the Sun at one of the two foci.
A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
Hope it helped !
Answer:
The universal law of gravitation states that every particle attracts every other particle in the universe with a force that is directly proportional to the ...
Bernoulli formula: define focal length
Si unit of thrust: newton's third law of motion examples
The swimming team has competed in 45 races this season. They have won 30 races so far. How many races will the team need to win today for the team to have a 75% success rate? 8 10 12 15.
The number of races the team need to win today for the team to have a 75% success rate is 15
Number of attempt = 45
Number of winnings = 30
Percentage won so far = 30/45 × 100
= 66.67%
let
x = Number of races that tfe team needs to win to have 75% success rate
(30 + x) / (45 + x) = 0.75
Cross product
30 + x = 0.75(45 + x)
30 + x = 33.75 + 0.75x
x - 0.75x = 33.75 - 30
0.25x = 3.75
x = 3.75 / 0.25
x = 15
Therefore, the number of races the team need to win today for the team to have a 75% success rate is 15
Learn more about percentage:
https://brainly.com/question/7225231
IS IT VALID OR NOT (explaining would be helpful) you want to determine how many students consider math to be their favorite school subject. you randomly survey 75 students. thirty-three students consider math to be their favorite subject while forty-two does not. so, you conclude that 40% of students at your school consider math to be their favorite subject.
Answer:
I would say not valid
Step-by-step explanation:
well, it would actually be 44% since 33/75= 0.44 to represent the number of ppl hat consider math their favorite subject
Use substitution to solve each system of equations
2x -y = 6
-3y = -6x + 18
I need help with this question
Answer:
Option D
Step-by-step explanation:
a^2 + b^2 = c^2
5^2+b^2=9^2
25+b^2=81
b^2=56
b=2√14
Please help I’ll give brainliest ASAP
Answer:
1 I don't know if those are questions but try if they are try the first one a
×-2+2×+4+2×-2=180 what does x equal in this equation.
Answer:
x = 36
Here's how I got that:
- Group like terms -
x - 2 + 2x + 4 + 2x - 2 = 180
↓
5x - 2 + 4 - 2 = 180
↓
5x = 180
- Divide both sides by 5 -
5x/5 = 180/5
↓
x = 36
~ That's all folks ~
-Siascon
Given that f(x) = 10 - 3x and g(x) = x-3/2 find the value of fg(4)
Answer:
-1
Step-by-step explanation:
(fg)(x) is the product of f(x) and g(x).
We can find (fg)(4) by first finding f(4) and g(4) and then multiplying the results together:
f(x) = 10 - 3x, so f(4) = 10 - 3(4) = -2, and
g(x) = x - 3/2, so g(4) = 4 - 3/2 = 1/2
Then (fg)(4) = (-2)(1/2) = -1
Please quickly answer number 6 will give brainliest
.guys can you solve anything please
Answer:
3.a)2[tex]\sqrt[3]{2}[/tex]
5.a) x=2
Step-by-step explanation:
Answer:
1. If 3^x = 1 then x =0
Step-by-step explanation:
3^0 = 1
3. 2, 9 3, 7, 5, the median is 5
4.3,5,3,4,3 the mode is 3
5. A cube whose volume is 8^3 =(512cm^3)
3. B
A coin weighs 8/15 ounces. A different coin weighs 4/15 ounces.
How much do the two coins weigh together?
12/15 ounces
this is because 8/15 + 4/15 = 12/15
hope this is helpful!
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
x + 2y = -16
Answer:
y = -1/2x - 8
Step-by-step explanation:
You are looking for the equation in the form of y=mx + b, so you need y on the left hand side without x. Subtract x from both sides.
2y = -x - 16
Now you want 1y instead of 2y. So divide everything by 2.
y = -1/2x - 8
During a cold winter day, the temperature change was - 2.3 f per hour for a period of 6.5 hours. What was the change in temperature during that time?
Answer:
-14.95 FStep-by-step explanation:
Given:
Temperature change rate is - 2.3 F per hourTime is 6.5 hoursThe change in temperature is:
temperature change rate * time -2.3 * 6.5 = -14.95 F