Answer:
y-3= 2(x-1)
Step-by-step explanation:
1. The equation of a line in point slope form is y-y1= m(x-x1)
2. m=slope and (x1,y1) is the point the line passes through
3. The point the line passes through is (1,3)
4, The slope is 2
5. Therefore the answer is y-3=2(x-1)
Answer:
y-3=2(x-1)
Step-by-step explanation:
Point slope form is y-y1=m(x-x1)
Now we just need to plug in what you have into this equation.
y-3=2(x-1) and this is the point slope form for this line.
PLZ HELP ME 100 POINT AND BRAINEST Solve the Quadratic Equation X^2 = -8x -7
A. 7, -1
B. -1, -7
C. 8, 1
D. 7,1
E. -8, -1
Answer:
B
Introduction:Given equation: [tex]x^2 = -8x -7[/tex]
To solve the quadratic equation, we will need to set one side of the equation equal to 0. This can be done by subtracting x² on both sides.
[tex]\implies x^2 - x^2= -8x -7 - x^2[/tex]
[tex]\implies 0= -8x -7 - x^2[/tex]
To further simplify, we can factor -1 from the expression on the R.H.S. Then, we can cancel the -1 since there is a 0 on the other side.
[tex]\implies 0= -1(8x + 7 + x^2)[/tex]
[tex]\implies 0= 8x + 7 + x^2 = x^2 + 8x + 7[/tex]
Finally, factor the expression on the right hand side.
Factoring a quadratic equation can be done in 2 ways.
1) Splitting methodIn this method, we split the middle term into two suitable terms. The suitable terms must follow two conditions.
The product of the suitable terms must be equal to the product of the first and last terms of the expression. The sum of the suitable terms must be equal the middle term.Then, we factor the first two terms of the expression and the last two terms of the expression. Eventually, we will get a common expression. So, we can further factorize to get a product of two expressions.
However, this method follows a condition. If the middle term cannot be split into two suitable terms, then the second method should be followed to determine a solution. 2) The Quadratic FormulaIn this method, we will compare our equation with the standard form equation to determine the a, b, and c variables. Then, we plug the variables into the formula and simplify to get the roots (solutions).
[tex]\text{Quadratic Formula:} \ \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]
We can use any method to solve for the roots. First, let us check whether the middle term could be split into two suitable terms such that those terms could meet the criteria stated above.
-----------------------------------------------------------------------------------------------------
Solving for x using the splitting methodWe can see that 8x is the middle term and it can be split into the sum of 7x and x. The product of the (middle term) coefficients is 7. The product of the coefficients (first and last terms) is also 7. Since both products match, we can use the splitting method to factorize the expression.
[tex]\implies 0= x^2 + 8x+ 7[/tex]
[tex]\implies 0= x^2 + x + 7x+ 7[/tex]
Now, factor the first two terms and the last two terms separately.
[tex]\implies 0= x^2 + x + 7x+ 7[/tex]
[tex]\implies 0= x(x + 1) + 7(x+ 1)[/tex]
We can see a common expression. Finally, let us factor the common expression to get a product of two expressions.
[tex]\implies 0= (x + 7)(x + 1)[/tex]
Since the factorized expression equals to 0, we can set each expression (inside the parentheses) equal to 0.
[tex]\implies x + 7 = 0; x + 1 = 0[/tex]
[tex]\implies x = -7; x = -1[/tex]
Solving for x using the Quadratic formulaNow, let us try to solve using the Quadratic formula.
[tex]0= x^2 + 8x+ 7[/tex]
Tip: Standard form: 0 = ax² + bx + c
Comparing both equations will allow us to determine the a, b, c variables.
⇒ a = 1; b = 8; c = 7
Now, let us plug these values into the quadratic formula and simplify.
[tex]\implies \dfrac{-b\ \± \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]\implies \dfrac{-8\ \± \sqrt{8^{2} - 4(1)(7)} }{2(1)}[/tex]
[tex]\implies \dfrac{-8\ \± \sqrt{64 - 28} }{2}[/tex]
[tex]\implies \dfrac{-8\ \± \sqrt{36}}{2} = \dfrac{-8\± 6}{2} = \dfrac{-8 + 6}{2},\ \dfrac{-8 - 6}{2} = \dfrac{-2}{2} ,\ \dfrac{-14}{2} = -1 , -7 \ \text{(B)}[/tex]
Therefore, in both methods, the answer is -1, -7 (B).
Learn more about quadratic formula: brainly.com/question/22364785
Learn more about splitting method: brainly.com/question/13874704
The area of a compact disc is 78.53 square centimeters. What is the radius of the disc? Use pi = 3.14
Answer:
r = 5 cm
Step-by-step explanation:
A = πr²
78.53 = (3.14)r²
divide by 3.14
25 = r²
r = ±5
r = 5
solve the equation -3+(1) −3+(1)
Answer:
-4
Step-by-step explanation:
you can just plug this into a calculator.
OR you could take -3+1 and get -2 and then subtract that from 2 (-3+1=2) and then you get -4
Answer:
-4
Step-by-step explanation:
-3 + (+1)= -2
2(-3 + (+1)) = -4
Figure A is a scale image of Figure B.
27
Figure A
Figure B
45
35
What is the value of x?
Greetings from Brasil...
According to the statement, one figure is scaled in relation to another, so we can apply similarity to polygons.....
So
BIG/small = BIG/small
or
small/BIG = small/BIG
27/X = 45/35
OR
35/45 = X/27
27/X = 45/35
45X = 27·35
45X = 945
X = 945/45
X = 218. Laurenpacksanorderofblocksin 2 crates and 7 stacks. How many blocks does Lauren pack?
Answer:
14
Step-by-step explanation:
(multiply 2by7)
2×7
=14
Find the measure of angle A. This is for my math class, and I’ve been stuck on this for a while. Please help!
Answer:
x = 7.6°, so A = 18.8°
Step-by-step explanation:
What we need to know in order to utilize algebra is the total sum of all triangle's angle. It's 180°. So, we can write
25 + 17x - 1 + 3x - 4 = 180
20x + 28 = 180
20x = 152
x = 7.6°
Now what you need to do is substitute 7.6° into each expression 17x - 1 and 3x - 4.
In each expression below identify the coefficient constant and variable
Answer:
The expression is missing in the question.
The expression is 4x +450
The variable is x and the coefficient is 4
Step-by-step explanation:
In an expression, a variable is a quantity which is not fixed value and can be of any arbitrary value. A variable is the unknown in the expression. In any expression, the variable are represented by alphabets such as a, b, c, x, y or z etc.
The numeric quantity which lies in the front of a variable is known as a coefficient. It can be any numeric values. For example, 9x --- here 9 is the coefficient of variable x, 4x -- here 4 is the coefficient.
Evaluate the expression when x = 5 and z= 7.
5z +x
Simplify your answer as much as possible.
Answer:
12
Step-by-step explanation:
We are given the expression:
[tex]\frac{5z+x^2}{x}[/tex]
and asked to evaluate when x= 5 and z=7. Therefore, we must substitute 5 for x and z for 7.
[tex]\frac{(5(7)+(5)^2)}{5}[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
First, evaluate the exponent.
(5)²= 5*5= 25
[tex]\frac{(5(7)+25)}{5}[/tex]
Next, multiply 5 and 7.
5*7=35
[tex]\frac{(35+25)}{5}[/tex]
Next, add 35 and 25.
25+25=60
[tex]\frac{60}{5}[/tex]
Finally, divide 60 by 5.
[tex]12[/tex]
The expression (5z+x²)/x when x=5 and z=7 is 12.
If the first differences of a sequence are a constant -7 and the third term is 22, find the first 5 terms of the sequence.
Answer:
36, 29, 22, 15, 8
Step-by-step explanation:
Step 1: State known information
First difference is -7
Third term of the sequence is 22
Step 2: Find first 5 terms
You just need to add and subtract 7 to 22 and the answer 5 times
1. 36 +7
2. 29 +7
3. 22 <- We know 22 is the 3rd term
4. 15 -7
5. 8 -7
Therefore the first 5 terms of the sequence is 36, 29, 22, 15, 8
Solve each equation using the Zero Product Property and the Distributive Property (as necessary)
11. f(x)=3x(2x-6)
12. f(x)=3x(x+7)-2(x+7)
Answer:
11) x=1 or x=3.
12) x=2/3 or x=-7.
Step-by-step explanation:
So we have two equations:
[tex]f(x)=3x(2x-6)\\f(x)=3x(x+7)-2(x+7)[/tex]
And we want to solve them. To do so, make each of them equal 0 and then solve for x:
11)
[tex]f(x)=3x(2x-6)\\0=3x(2x-6)[/tex]
Using the Zero Product Property, either one or both of the factor must be zero for this to be true. Therefore, make each factor equal to zero and solve:
[tex]3x=0 \text{ or } 2x-6=0[/tex]
Divide the left by 3. On the right, add 6 and then divide by 2:
[tex]x=0\text{ or } 2x=6\\x=0 \text{ or } x=3[/tex]
Therefore, the solutions to the first equation is:
x=1 or x=3.
12)
[tex]f(x)=3x(x+7)-2(x+7)[/tex]
First, use the distributive property to group the terms together. The equation is equivalent to:
[tex]f(x)=(3x-2)(x+7)[/tex]
Now, set the function to zero and solve:
[tex]0=(3x-2)(x+7)[/tex]
[tex](3x-2)=0 \text{ or } x+7=0\\3x=2 \text{ or } x=-7\\x=2/3 \text{ or } x=-7.[/tex]
Therefore, the answer is:
x=2/3 or x=-7.
Answer:
[tex]\large \boxed{{\bold{11.} \ x=0, \ x=3}} \\ \\ \large \boxed{{\bold{12.} \ x=-7, \ x=2/3}}[/tex]
Step-by-step explanation:
We will set the outputs of the functions to 0 and solve for x.
0 = 3x(2x - 6)
Set factors equal to 0.
First possibility:
3x = 0
x = 0
Second possibility:
2x - 6 = 0
2x = 6
x = 3
0=3x(x+7)-2(x+7)
Take (x+7) as a common factor.
0 = (3x-2)(x+7)
Set factors equal to 0.
First possibility:
x + 7 = 0
x = -7
Second possibility:
3x - 2 = 0
3x = 2
x = 2/3
X + + x plus StartFraction x Over 7 EndFraction plus StartFraction 1 Over 11 EndFraction left-parenthesis x plus StartFraction x Over 7 EndFraction right-parenthesis equals 60.(x + ) = 60
Answer:
[tex]x = \frac{770}{16}[/tex]
Step-by-step explanation:
Given
[tex]x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60[/tex]
Required
Solve for x
[tex]x + \frac{x}{7} + \frac{1}{11} (x + \frac{x}{7}) = 60[/tex]
Start by solving the bracket [Take LCM]
[tex]x + \frac{x}{7} + \frac{1}{11} (\frac{7x + x}{7}) = 60[/tex]
[tex]x + \frac{x}{7} + \frac{1}{11} (\frac{8x}{7}) = 60[/tex]
Open the bracket
[tex]x + \frac{x}{7} + \frac{8x}{77} = 60[/tex]
Take LCM
[tex]\frac{77x + 11x + 8x}{77} = 60[/tex]
[tex]\frac{77x + 11x + 8x}{77} = 60[/tex]
[tex]\frac{96x}{77} = 60[/tex]
Multiply both sides by 77
[tex]77 * \frac{96x}{77} = 60 * 77[/tex]
[tex]96x = 60 * 77[/tex]
Divide both sides by 96
[tex]\frac{96x}{96} = \frac{60 * 77}{96}[/tex]
[tex]x = \frac{60 * 77}{96}[/tex]
Divide the numerator and denominator by 6
[tex]x = \frac{10 * 77}{16}[/tex]
[tex]x = \frac{770}{16}[/tex]
Answer:
48.125
Step-by-step explanation:
What equation represents a population of 300 animals at the crease and an annual rate of 23%
Answer:
300 + 69xStep-by-step explanation:
Given initial population of animals = 300 animals
If the population increases by 23% annualy, yearly increment will be expressed as:
Yearly increment = 23% of 300
Yearly increment = 0.23*300
Yearly increment for = 69
Let the total number of years of be x
Increment after x years = 69x
Increase in population of animals after x years with an annual rate of 23% = Initial population + Increment after x years
= 300 + 69x
Hence, the equation represents a population of 300 animals at the increase and an annual rate of 23% is expressed as 300 + 69x
HELP ASAP I HAVE 48 MINUTES LEFT
The graph of y = |xl is transformed as shown in the graph below. Which equation represents the transformed
function?
y=|1/4x|
y=|2x|
y=|4x|
y=|1/2x|
Answer:
y = |1/4x|
Step-by-step explanation:
The slope is 1/4
The Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 90% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 110 pints of a mixture that is pure fruit juice
Answer:
The pints of each of the two existing types of drinks are 22 and 88 respectively.
Step-by-step explanation:
We are given that the Royal Fruit Company produces two types of fruit drinks. The first type is 70% pure fruit juice, and the second type is 95% pure fruit juice. The company is attempting to produce a fruit drink that contains 90% pure fruit juice.
Let the first type of fruit drink pints in the mixture be 'x' and the second type of fruit drink pints in the mixture be 'y'.
So, according to the question;
The first condition states that we have to make 110 pints of a mixture of two types that is pure fruit juice, that means;x + y = 110
x = 110 - y ---------------- [equation 1]
The second condition states that the first type is 70% pure fruit juice, and the second type is 95% pure fruit juice, that means;[tex]0.70x+0.95y=0.90\times 110[/tex]
[tex]70x+95y=9900[/tex]
[tex]70(110-y)+95y=9900[/tex]
[tex]7700-70y+95y=9900[/tex]
[tex]25y=9900-7700[/tex]
[tex]y=\frac{2200}{25}[/tex]
y = 88
Now, putting the value of y in equation 1 we get;
x = 110 - y
x = 110 - 88 = 22
Hence, the pints of each of the two existing types of drinks are 22 and 88 respectively.
5h-2(11-h)=h-4
what’s the value of h
Answer:
The correct answer is h = 3.
Step-by-step explanation:
To solve this problem, we should first use the distributive property on the left side of the equation. This means that we can multiply each of the terms inside the parentheses by -2 (be careful that you distribute the negative as well). This is modeled below:
5h - 2(11 - h) = h - 4
5h - 22 + 2h = h - 4
Next, we can combine like terms on the left side of the equation.
7h - 22 = h - 4
Now, we can subtract h from both sides of the equation to move all of the variable terms to the left side of the equation.
6h - 22 = - 4
Next, we can add 22 to both sides of the equation to isolate the variable term on the left side of the equation.
6h = 18
Finally, we can divide both sides by 6 in order to get the variable completely isolated.
h = 3
Therefore, the correct answer is h = 3.
Hope this helps!
A comfy jacket is normally $200. It is on sale for 40% off. What is the sale price?
Answer:
120
Step-by-step explanation:
First find the discount
200 * 40%
200 * .40
80
Subtract the discount from the original price
200-80
120
The sale price is 120
Answer:
[tex]\huge \boxed{\mathrm{\$ \ 120}}[/tex]
Step-by-step explanation:
Calculating the discount on the jacket.
[tex]200 \cdot 40\% \\ \\ 200 \cdot 0.4 \\ \\ 80[/tex]
The discount on the jacket is $80.
Let’s find the sale price of the jacket.
[tex]\sf sale \ price = original \ price - discount.[/tex]
[tex]200-80 \\ \\ 120[/tex]
The sale price of the jacket is $120.
A dealer sold a painting for $800. She made a profit of 25% on the price she paid for it. Calculate the price she paid for the painting.
She paid $640 for the painting
Step-by-step explanation:
her selling price SP = 800
CP+25%of CP = 800
1.25CP=800
CP=640
Answer:
$640
Step-by-step explanation:
paint sold for $800
profit 25%
the price she paid for the painting = $800 / 1.25 = $640
which expression is equivalent to 4n+ 28
A 28n + 4
B 4(n+28)
C 4( +7)
D 32
Answer:
It would be B
Step-by-step explanation:
Which equation is equivalent to 7w – 1 = –15?
A: 1 - 7w = -15
B: 7w = -15 + 1
C: 7w = –15 – 1
D: 7w = 15 - 1
Answer:
i believe the answer is A
Step-by-step explanation:
midpoint of the segment with endpoints A(-5, -2) and B(-7, 6).
(-6,2)
Inbox me on fb for more help with math same name as my brainly
Answer:
(-6,2)
Step-by-step explanation:
I need help on this problem. (-5)^5/(-5)^-6
Answer: (-5)¹¹ of (-5)^11
Step-by-step explanation:
Since the base of the two exponents are teh same at -5, we can subtract the exponents.
5-(-6)=11
Now, we know that the new exponent will be 11, with the base staying the same.
Read the table. 1/2 = 2 gallons 1 = 4 gallons 1 1/2 = 6 gallons. If this goes on. how much gallons is 6 1/2?
Answer:
24 1/2
Step-by-step explanation:
Every 1/2 is 2 gallons.
1/2 x 2 gallons = 4 gallons.
The whole number in 6 1/2 is 6.
1 x 6 = 6.
Now, we multiply 6 by 4 because each 1 = 4 gallons.
6 x 4 = 24.
There is still an 1/2 left in 6 1/2.
You add that.
Your answer is 24 1/2.
Hope this helps you!
Find m∠PQR. A. 81 B. 90 C. 77 D. 72
Work Shown:
Angle PQR = (far arc - near arc)/2
Angle PQR = ( (major arc PR) - (minor arc PR) )/2
Angle PQR = ( (2x+252) - (2x+108) )/2
Angle PQR = 144/2
Angle PQR = 72
Notice how we didn't need to find the value of x at all.
What is the value of
3 - x if x = 6?
Answer:
-3
Step-by-step explanation:
3-x if x=6
3-6
-3
Hope this helps ;) ❤❤❤
Answer: -3
Step-by-step explanation: In this case, we are given that x = 6.
So we have 3 - 6 which is -3.
Pls help with questions
1. What is the volume of a cylinder that has a radius of 5 inches and height of 9 inches?
2. Mrs.vega brought a new aquarium for her turtles. How much space will the turtles have in the aquarium if the length is 5.2 ft, the width is 1.8 ft and the height is 2 ft?
Step-by-step explanation:
1. volume = πr²h
= π×(5²)×9
= π×225
= 225π
= 707.1 cubic inches
2. volume = lwh
= 5.2 × 1.8 × 2
= 18.72 square feets
Question 4 (1 point)
(01.02)
Evaluate the following expression using the given values: (1 point)
Find x - 3y if x = 3 and y=-2.
A -9
B -3
C 3
D 9
Answer: 9
Step-by-step explanation:
plug in numbers to get 3+6
add them
boom
Answer:
D. 9
Step-by-step explanation:
Plug in 3 as x and -2 as y in the expression:
x - 3y
3 - 3(-2)
3 + 6
= 9
The record high temperature in Alabama is 112f and the record low temperature is -27f. What is the difference between the highest and lowest temperature? A. 139 degrees B. 27 degrees C. 85 degrees D. 112 degrees
Answer:
(A) 139°
Step-by-step explanation:
What we are trying to find here is the distance between -27 and 112.
To do this, we have to think of it as a number line.
The distance from -27 to 0 is 27 units, and the distance from 0 to 112 is 112 units.
So the total distance is [tex]112+27=139[/tex]
Hope this helped!
please help me on this
Answer:
Step-by-step explanation:
coordinate of O(2,1),Y(3,-2),T(-3,-3)
let the reflected points are O',Y',T'
distance of O from y=2 is 1 unit.
∴ ordinate of O' =1+2(1)=3
or O' is (2,3)
distance of Y from y=2 is2+2=4
ordinate of Y'=-2+2(4)=6
so coordinate of Y' is (3,6)
distance of T from y=2 is (2+3)=5
so ordinate of T' =-3+2(5)=7
coordinate of T' is(-3,7)
(6x3 + 3x² + 3) + (2x - 5x + 1)
the sum is?
Step-by-step explanation:
(6x^3 + 3x² + 3) + (2x^3 - 5x + 1)
6x^3 + 2x^3 = 8x^3
3x^2 + 0 = 3x^2
-5x + 0 = -5x
3 + 1 = 4
8x^3 + 3x^2 - 5x + 4 is the answer because you have to put all the terms that were solved together. This will lead to 8x^3 + 3x^2 - 5x + 4. And, standard form is ax^2 + bx + c. So, 8x^3 + 3x^2 - 5x + 4 is the answer.
8x^3 + 3x^2 - 5x + 4
Hope this helped,
Kavitha
Answer:
= 8x³ + 3x² - 5x + 4
Step-by-step explanation:
(6x³ + 3x² + 3) + (2x³ - 5x + 1)
= 6x³ + 3x² + 3 + 2x³ - 5x + 1 remove parentheses
= 6x³ + 2x³ + 3x² - 5x + 1 group like terms
= 8x³ + 3x² - 5x + 3 + 1 add similar elements
= 8x³ + 3x² - 5x + 4
How can you invest your money as a student or a teenager???
Answer:
Buy stuff and sell them at a higher price
Step-by-step explanation:
Answer:
get a job
Step-by-step explanation: