Step-by-step explanation:
Algebra is a topic that covers linear equations, system of equations, sequences, exponential functions, polynomials, quadratic, exponents, radicals, functions, and more. I'm going to give use algebraic formulas and not all the topics.
Like Terms Rule: If two terms that share the same variable are separated by a binary operation, we can combine them.
For example, look at
[tex]6 + 7x + 9x[/tex]
We can combine 7x and 9x.
[tex]7x + ( + 9x) = 16x[/tex]
Add the coeffceint and keep the variable.
16x+6
Solving Algebraic Equations:
Alot questions in Algebra asks you to isolate a variable. For example,
[tex] \frac{x}{2} + 6 = 9[/tex]
First step, is to get the x variable by itself. To do this subtract 6 by both sides. Why? Because Subtraction is a inverse operation off addition. Remeber the Golden Rule of Algebra,
WHAT WE DO TO ONE SIDE. WE DO TO THE OTHER.
[tex] \frac{x}{2 } = 3[/tex]
Now, we multiply both sides by 2 because multiplying is the inverse operation of division and vice versa.
[tex]x = 6[/tex]
If we plug this in, it is indeed true.
[tex] \frac{6}{2} + 6 =[/tex]
[tex]3 + 6 = 9[/tex]
Some other rules are
If we multiply a term by a one term, we only affect the term that is being multiplied, for example
[tex]2x \times 3[/tex]
2 and 3 are both real numbers so we just multiply 2 and 3. and put x behind the answer.
[tex]2 \times 3 = 6(x)[/tex]
[tex]2x \times 3 = 6x[/tex]
When we multiply 2 variables, we put the variable near each other. For example,
[tex]x \times y = xy[/tex]
When we add term, we add the coeffcient parts
[tex]y + y = 1y + 1y = 2y[/tex]
Know that
[tex]y = 1y[/tex]
When we multiply same term variables, we get
[tex]x \times x = {x}^{2} [/tex]
There is more formulas for Algebra. But these are the basicis.
An airplane landed at a point 100 km east and 420 km south from where it took off. If the airplane flew in a straight line from where it took off to where it lands, how many kilometers did it fly? Enter only the number rounded to the nearest kilometer.
Answer:
[tex]\sqrt{100^2 + 420^2}[/tex]
[tex]\sqrt{100^2+420^2}=20\sqrt{466}\quad \left(\mathrm{Decimal:\quad }\:431.74066\dots \right)[/tex]
Step-by-step explanation:
Pls help ASAP will give brainliest
Answer:
hope it help you.........
Answer:
[tex]\boxed {\boxed {\sf y= -1.2 }}[/tex]
Step-by-step explanation:
We are asked to solve the following equation for y.
[tex]-2y-4.2= 1.8 + 3y[/tex]
To solve for y, we have to isolate the variable by performing the inverse operations. First, move all the terms without a variable or the constants to one side, and the terms with a variable to the other side.
4.2 is being subtracted and the inverse operation of subtraction is addition. Add 4.2 to both sides.
[tex]-2y-4.2 +4.2= 1.8 + 3y+ 4.2[/tex]
[tex]-2y=1.8 + 4.2 + 3y[/tex]
[tex]-2y= 6 + 3y[/tex]
3y is being added and the inverse operation of addition is subtraction. Subtract 3y from both sides.
[tex]-2y-3y= 6+ 3y -3y[/tex]
[tex]-2y-3y= 6[/tex]
[tex]-5y=6[/tex]
y is being multiplied by -5. The inverse operation of multiplication is division. Divide both sides by -5.
[tex]\frac {-5y}{-5}= \frac{6}{-5}[/tex]
[tex]y=- 1.2[/tex]
Check the answer by substituting -1.2 back into the original equation.
[tex]-2 (-1.2)-4.2 = 1.8 + 3(-1.2)[/tex]
[tex]2.4-4.2=1.8 + - 3.6[/tex]
[tex]-1.8 = -1.8[/tex]
This checks out, so we know our answer is correct.
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!! Determine the Value of K in the diagram ( secant lines to circles).
Answer:
6
Step-by-step explanation:
5
Answer:
k = 10
Step-by-step explanation:
Given 2 secants from an external point to the circle, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
2x(2x + kx) = 3x(3x + 5x)
4x² + 2kx² = 3x × 8x = 24x² ( subtract 4x² from both sides )
2kx² = 20x² ( divide both sides by 2x² )
k = 10
I need help !!!PLEASE
Answer:
answer
volume= 252 yd^3 .
find the following ratios right triangle. PLS HURRY and disregard my answers.
Answer:
sinA= 5/13; cosB= 5/13
Step-by-step explanation:
sine is opposite over hypotenuse so 5/13. cosine is adjacent over hypotenuse so 5/13
Which of the following equations is the translation 2 units down of the graph of y = Ixl?
y= - 21
y = 1x + 21
y = Ixl - 2
y = x + 2
Answer:
Answer:
The answer is: y = |x| - 2
.......plz answer it plz
Answer:
a: x=90 b: x=45 y=45 c: y=68 x=68
Use the discriminant to determine the number of real solutions to the equation,
10n^2 = 10 - 8n
Answer:
2 real solutions
Step-by-step explanation:
Get all the terms to one side
10n^2 = 10 - 8n
10n^2 +8n -10 =0
ax^2 +bx+c =0
The discriminant is
b^2 -4ac
8^2 - 4(10)(-10)
64 +400
464
If the discriminant is greater than 0 we have 2 real solutions
Please help please with geometry
Answer:
33
Step-by-step explanation:
HJ = HI + IJ
HJ = 3x - 9, HI = x and IJ = x + 5
So 3x - 9 = x + x + 5
Solve for x
Combine like terms
3x - 9 = 2x + 5
Add 9 to both sides
3x = 2x + 14
Subtract 2x from both sides
x = 14
Find HJ
HJ = 3x - 9
We have found that x = 14
HJ = 3(14) - 9
Multiply 3 and 14
HJ = 42 - 9
Subtract
HJ = 33
2. What is the sum of iº + kº?
Find the perimeter of the figure.
31 cm
18 cm
25 cm
Drawing not to scale
C.
b. 80 cm
68 cm
d.
87 cm
a.
74 cm
I need help!
Its a triangle
[tex]\\ \sf\longmapsto Perimeter=31+18+25[/tex]
[tex]\\ \sf\longmapsto Perimeter=48+25[/tex]
[tex]\\ \sf\longmapsto Perimeter=73cm[/tex]
42:-Its rectangle
[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(15+10)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(25)[/tex]
[tex]\\ \sf\longmapsto Perimeter=50ft[/tex]
Answer:
a and c
Step-by-step explanation:
The perimeter is the sum of the 3 sides, that is
perimeter = 25 + 18 + 31 = 74 cm → a
-------------------------------------------------------------------
The opposite sides of a rectangle are equal, so
perimeter = (2 × 10) + (2× 15) = 20 + 30 = 50 ft → c
Help ASAP I’ll mark you as brainlister
Answer: Try 2. This is my best guess
Sz – [32 – (10z + 2)]
A rectangle field is 10m longer than its width. If the perimeter is 300cm, find;
i) Its width
ii) the area if the rectangular field
Answer:
w = 70 cm
A = 5600cm^2
Step-by-step explanation:
P = 2(l+w) where l is the length and w is the width
300 = 2(l+w)
We know the length is 10 longer than the width
l = w+10
300 = 2(w+10+w)
Divide each side by 2
300/2 = (w+10+w)
150 = (2w+10)
Subtract 10 from each side
150-10 = 2w
140 = 2w
Divide by 2
140/2 = w
70 = w
Now find the area
A = l*w
A = (w+10) * w
= (70+10) *70
= 80*70
5600
Warren is on vacation and needs to arrange transportation. A rental car costs 40 dollars per day plus a one-time cost of 14 dollars for insurance. Construct a function C(x) that gives the total cost of renting a car for x days. C(x)=________.
If Warren has budgeted 254 dollars for the rental, how many days can he afford?
Answer:
C(x)=40x+14, 6 days
Step-by-step explanation:
C(x)= payment per day*x + initial payment. the payment per day is $40 while the initial payment is $14. so C(x)=40x+14.
C(x)=254=40x+14, 40x=240, x=6
Please help me to solve this question
Answer:
x = 64°, y = 32°
Step-by-step explanation:
The sum of the angles on a straight line = 180° , then angles on PS are
2x + y + 20 = 180 ( subtract 20 from both sides )
2x + y = 160 → (1)
Angles on QT are
x + 3y + 20 = 180 ( subtract 20 from both sides )
x + 3y = 160 → (2)
Solve (1) and (2) simultaneously
Rearrange (1) expressing y in terms of x by subtracting 2x from both sides
y = 160 - 2x → (3)
Substitute y = 160 - 2x into (2)
x + 3(160 - 2x) = 160 ← distribute and simplify left side
x + 480 - 6x = 160
- 5x + 480 = 160 ( subtract 480 from both sides )
- 5x = - 320 ( divide both sides by - 5 )
x = 64
Substitute x = 64 into (3)
y = 160 - 2(64) = 160 - 128 = 32
Then
x = 64°, y = 32°
Jim is swimming part of a lap around his 100-foot diameter pool. If he swims around the outside edge, how far does he swim if he travels a 60° arc, rounded to the nearest foot? Use 3.14 for pi.
answer:
have any notes for reference?
Step-by-step explanation:
Can some one help me on this math question its confusing ill give brainly when right!!!
Answer:
s - t = 10 - -7 = 17
Step-by-step explanation:
I only see
s - t
nothing else is there to evaluate (or calculate).
s - t = 10 - -7 = 17 (as a double "-" always turns into a "+").
you really needed help with that ?
Answer:
= s-t
= 10 - (-7)
= 10 + 7
= 17
✌✌✌✌
find the sum or difference of 24-16
Answer:
24+16= 40
24-16=8 if it's wrong, try and make ur question more specific, thanks
Answer:
8 or 40
Step-by-step explanation:
24-16=8
24+16=40
Simplify each numerical expression.
1) 6 + 2 x 8 - 12 + 9 - 3
Answer:
16
Step-by-step explanation:
using BODMAS rule
6 + 16 - 12 + 9 - 3............step 1
22 - 3 - 3....…...................step 2
16
what is the graph of the following function??
PLEASE HELP!!
Answer:
umm it's a piecewise function and I think the graph is correct I don't really understand what you mean by what is the "graph" of the following function since the graph is already there...
Step-by-step explanation:
Find the coordinates of U' after a reflection across parallel lines; first across the line x=-2 and then across the line x=-1 write your answer in form (a,b)
Answer:
U in the line x=-2: (-4,0)
U in the line x=-1: (-2-0)
Step-by-step explanation:
...............
HElp Please its Pre-Calculus Matrix
The determinant is C. -541.
Using a cofactor expansion along the first row:
[tex]\begin{vmatrix}-8&-4&-1\\1&7&-3\\8&9&9\end{vmatrix} = -8\begin{vmatrix}7&-3\\9&9\end{vmatrix} + 4\begin{vmatrix}1&-3\\8&9\end{vmatrix} - \begin{vmatrix}1&7\\8&9\end{vmatrix} \\\\= -8(7\times9-(-3)\times9) + 4(1\times9-(-3)\times8) - (1\times9-7\times8) \\\\ = -8(63+27) + 4(9+24) - (9-56)\\\\= \boxed{-541}[/tex]
find x giving your answer to 1 decimal place
Step-by-step explanation:
[tex] \frac{ \sin(81) }{x} = \frac{ \sin(40) }{7} \\ x \times \sin(40) = 7 \times \sin(81) \\ x = \frac{7 \times \sin(81) }{ \sin(40) } = 10.75 = 10.8 \: cm[/tex]
Answer:
x is 10.8 cm
Step-by-step explanation:
from Lami's theorem:
[tex] \frac{7}{ \sin(40 \degree) } = \frac{x}{ \sin(81 \degree) } \\ \\ x = \frac{7 \sin(81 \degree) }{ \sin(40 \degree) } \\ \\ x = 10.8 \: cm[/tex]
Find the common ratio for the geometric sequence
Answer:
1/4
Step-by-step explanation:
Once upon a time there was a farmer whose family raised pigs and chickens. If you counted 24 heads and 80 feet, how many chickens were there? How many pigs were there?
Answer:
Number of chickens = 8
Number of pigs = 16
Step-by-step explanation:
Let the pigs = p
Let the number of chickens = c
Number of heads = 24
p + c = 24 ----------------(I)
p= 24 - c
Number of feet = 80
Chicken has 2 legs and pig has 4 legs
4p + 2c = 80 --------------(II)
Substitute p = 24 - c in equation (II)
4*(24 - c) + 2c = 80
4*24 - 4*c + 2c = 80
96 - 4c + 2c = 80 {Combine like terms}
96 - 2c = 80 {subtract 96 from both sides}
-2c = 80 - 96
-2c = -16 {Divide both sides by (-2)}
c = -16/-2
c = 8
Plugin c = 8 in equation (I)
p + 8 = 24
p = 24 - 8
p = 16
What is the quotient of 8.8 x 107 and 8.0 x
102 expressed in scientific notation?
Answer:
88,000,000 and 800
Step-by-step explanation:
Answer:1.1×105
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
At the Scott wedding, 12 guests sat on the groom's side and 10 guests sat on the bride's side. At the Smith wedding, 13 guests sat on the bride's side and 18 guests sat on the groom's side. Which wedding had a lower ratio of guests of the groom to guests of the bride?
A. not enough information
B. the Smith wedding
C. neither, the ratios are equivalent
D. the Scott wedding
Answer:
D. The Scott Wedding
Step-by-step explanation:
Scott: 12 guests on the groom's side and 10 guests on the bride's side
Smith: 18 guests on the the groom's side and 13 guests on the bride's side
6. Alex and Brian park their bikes side-by-side. Alex leaves to visit friends, and Brian leaves 30 minutes later,
headed for the same destination. Alex pedals 5 miles per hour slower than Brian. After 1 hour, Brian passes Alex. At
what speed are they each pedaling?
Answer:
See below.
Step-by-step explanation:
When Brian passes Alex they both have travelled the same distance.
Call this distance d.
Let the speed that Brian passes = x miles/hour.
Distance = speed * time so:
For Alex:
d = (x - 5) * 1.5 ( Alex cycles for 1 + 30 minutes = 1.5 hours)
For Brian:
d = x * 1
So substituting d = x in Alex's equation:
x = 1.5(x - 5)
x = 1.5x - 7.5
7.5 = 0.5x
7/5 / 0.5 = x
15 = x.
ANSWER:
Brian's speed is 15 miles/hour.
Alex's speed is 15 - 5 = 10 miles/hour.
What is the sale price of this bed after the discount has been taken off the standard price?
Answer:
585 is the answer of your question.
Step-by-step explanation:
because formula is
Mp _ d% of mp
