Answer:
x = 1, -5.56
Step-by-step explanation:
x^2 = -7x - 8
shift -7x and -8 to the other side . Remember when u shift minus changes into plus.
x^2 + 7x + 8 = 0
using quadratic equation formula
in quadratic equation one value comes positive and other comes in negative
a = 1 , b = 7 and c = 8
taking positive sign
x = (-b + [tex]\sqrt{b^2 - 4*a*c}[/tex]) /2*a
x = (-7 + [tex]\sqrt{7^2 - 4*1*8}[/tex] ) /2*1
x = (-7 + [tex]\sqrt{49 + 32}[/tex] ) /2
x = (-7 + [tex]\sqrt{81}[/tex] )/ 2
x = -7 + 9 / 2
x = 2/2
x = 1
taking negative sign
(-b - [tex]\sqrt{b^2 - 4*a*c}[/tex] ) /2*a
x = (-7 - [tex]\sqrt{7^2 - 4*1*8}[/tex] ) /2*1
x = (-7 - [tex]\sqrt{49 - 32}[/tex] ) /2
x = -7 - [tex]\sqrt{17}[/tex] / 2
x = -7 - 4.12 / 2
x = -11.12/2
x = -5.56
therefore x = 1 , - 5.56
Answer:
[tex]x = \frac{- 7 + \sqrt{17}}{2} \ , \ x = \frac{-7 - \sqrt{17}}{2}[/tex]
Step-by-step explanation:
[tex]x^2 = - 7x - 8\\\\x^2 + 7x + 8 = 0 \\\\[/tex]
[tex]x = \frac{- b \pm \sqrt{b^2 - 4ac}}{2a}\\\\[/tex] [tex][ \ a = 1 , \ b = 7 , \ c = 8 \ ][/tex]
[tex]x = \frac{-7 \pm \sqrt{49 - (4\times 8)}}{2} \\\\x = \frac{-7 \pm \sqrt{17}}{2} \\\\x = \frac{-7 + \sqrt{17}}{2} , \ , \frac{-7 - \sqrt{17}}{2}[/tex]
Which is a correct first step in solving 5 – 2x < 8x – 3?
5 < 6x – 3
3x < 8x – 3
5 < 10x – 3
2 – 2x < 8
Answer:
5 < 10x - 3
Step-by-step explanation:
5 - 2x < 8x - 3
Add '2x' to both the sides
5 - 2x + 2x < 8x + 2x - 3
5 < 10x - 3
Please help me solve my problem!!!
Evaluate the function
Answer:
224
Step-by-step explanation:
f(-7) = 4(-7)^2 - 4(-7)
=196 + 28
=224
The class aquarium holds 2 gallons of water. How many cups is this? How many fluid ounces is this?
Step-by-step explanation:
2 gallons = 2× 16 = 32 cups
2 gallons = 2 × 128 = 256 fluid ounces
In 32 cups the class aquarium holds 2 gallons of water.
In 256 ounces the class aquarium holds 2 gallons of water.
What is proportion?Proportion is an equation that defines that the two given ratios are equivalent to each other.
In other words, the proportion states the equality of the two fractions or the ratios.
The class aquarium holds 2 gallons of water.
1 gallon = 16 Cups
The class aquarium holds 2 gallons of water in the number of cups is;
2 gallons = 2× 16 = 32 cups
In 32 cups the class aquarium holds 2 gallons of water.
The class aquarium holds 2 gallons of water in the fluid ounces is;
1 gallons = 128 ounces
2 gallons = 2 × 128 = 256 fluid ounces
In 256 ounces the class aquarium holds 2 gallons of water.
Learn more about proportion here;
https://brainly.com/question/21636882
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The table represents the function f(x).
What is f(3)?
Answer:
f(3) = 9
Step-by-step explanation:
In the given figure,
when x=3,
f(x)=9
substituting x=3 in f(x),
=> f(3)=9
If you shift the quadratic function f(x) = x^2, right 12 units, what is the equation of the new function
Answer:
Step-by-step explanation:
Right is into positive territory.
y = x^2
Going right into positive territory means that the function becomes
y = (x - 12)^2
You need the value that will make x - 12 = 0. That number is 12.
6. A regular pyramid has a square base. The perimeter of the base is 64 inches and the height of the pyramid is 12 inches. What is the volume of the pyramid in cubic inches?
The volume is 1024. the base lengths are all 16 inches
Extend the sequence and then complete the
statements.
А
A (blank) is an ordered list of numbers that can
form a pattern.
А (blank)
is an element in a sequence.
You can (blank)
a sequence by finding and writing
more terms.
The next term in the sequence is A = (blank)
Answer:
l
Step-by-step explanation:
A sequence is an ordered list of numbers.....
A term is an element in a sequence.
You can expand a sequence by finding and writing....
The next term in the sequence is A = (general term)
(will give brainliest!)
Given the triangle below, which of the following is a correct statement?
a. sec∠B=3/7
b. cot∠B=3/2
c. sec∠B=7/3
d. cot∠C=1/2
Answer:
D) cot(C) = 1/2.
Step-by-step explanation:
We can go through each choice and examine is validity.
Choice A)
We have:
[tex]\displaystyle \sec B=\frac{3}{7}[/tex]
Recall that secant is the ratio of the hypotenuse to the adjacent.
With respect to B, the adjacent is 6 and the hypotenuse is 7.
Therefore, sec(B) should be 7/6 instead.
A is incorrect.
Choice B)
We have:
[tex]\displaystyle \cot B=\frac{3}{2}[/tex]
Cotangent is the ratio of the adjacent side to the opposite.
With respect to B, the adjacent side is 6 and the opposite side is 3.
Therefore, cot(B) = 6/3 = 2.
B is incorrect.
Choice C)
C is incorrect for the reasons listed in A.
Choice D)
We have:
[tex]\displaystyle \cot C=\frac{1}{2}[/tex]
Again, cotangent is the ratio of the adjacent side to the opposite.
With respect to C, the adjacent side is 3 and the opposite side is 6.
So, cot(C) = 3/6 = 1/2.
Therefore, D is the correct choice!
Need help on this!!! 10 points!!!
factorise x squared + x - 12
Answer:
(x+4)(x-3)
Step-by-step explanation:
Answer:
(x + 4)(x - 3)
Step-by-step explanation:
Given
x² + x - 12
Consider the factors of the constant term (- 12) which sum to give the coefficient of the x- term (+ 1)
The factors are + 4 and - 3 , since
4 × - 3 = - 12 and 4 - 3 = + 1 , then
x² + x - 12 = (x + 4)(x - 3) ← in factored form
a man spends ⅕ of his salary on shoes and ⅔ on school fees. what is the fraction of his salary left. pls help asap
Answer:
2/15
Step-by-step explanation:
1/5 + 2/3
= 3/15 + 10/15
= 13/15
15/15 - 13/15
= 2/15
I need help with math
I hope you understand....
Mark me as brainliest....
Thanks...
how many centimeters are in 5 inches? 1in. = 2.54 cm
5 in. = ?
Last year, samantha spent $2,478 for natural gas. This year, she decided to use balance billing. What will her monthly payment be this year?
Answer:
She will need to pay $206.50 per month.
Step-by-step explanation:
Divide the total cost ($2,478) by the number of months (12 mos) to obtain Sam's monthly payment:
$2,478
---------------- = $206.50/month
12 months
She will need to pay $206.50 per month.
4(5 square root x^2y) + 3(5 square root x^2y
Answer:
7(5sqrt ^2y)
Step-by-step explanation:
Answer: 7(5square root x^2y)
Step-by-step explanation:
By Factorisation
4(5[tex]\sqrt{ x^2y[/tex] )+ 3(5[tex]\sqrt{ x^2y[/tex] )= 4+3(5[tex]\sqrt{ x^2y[/tex] ) = 7(5[tex]\sqrt{ x^2y[/tex] )
In order to answer this question, remember that gasoline costs $2.56/gallon and the tank takes 15 gallons.
You have another person who wants to carpool with you and your friend. The tank will be split evenly. How much do you and your friend each save by having a third person sharing the tank of gas?
The tour operators thought it would be a good idea to get a souvenir T-shirt for each customer who went on the Ocean Bike Tour. They found a company who would sell them shirts with their logo for $6.25 per t-shirt. In your answer box, create a table like the one below and fill in the missing costs for 1 t-shirt up to 8 t-shirts.
Mia takes a job with a starting salary of $40,000 for the first year. She earns a 3% increase each year. Write an equation for the partial sum of the geometric sequence used to model the situation and explain what an, n, Sn, and r represent (use a_n to represent an).
Answer:
The partial sum that models the situation
is Sn=a1(1 - rn)/(1 - r).
n = number of years Mia works this job
an = Mia's salary during her nth year
Sn = total amount Mia earns after n years
r = percent increase, represented as a decimal, plus 1, because the total salary is needed and not just the amount of each increase
Answer:
The partial sum that models the situation
is Sn=a1(1 - rn)/(1 - r).
n = number of years Mia works this job
an = Mia's salary during her nth year
Sn = total amount Mia earns after n years
r = percent increase, represented as a decimal, plus 1, because the total salary is needed and not just the amount of each increase
Step-by-step explanation:
Which quadratic is written in graphing formRequired to answer. Single choice.
(10 Points)
f(x ) = 2x+4x^2+10
f(x ) = (x+2)^2+4
f(x) = (x+5)(x+4)
f(x) = 3x +7
Answer:
option B
Step-by-step explanation:
Option B is in vertex (or graphing ) form.
recall the equation for graphing form of a quadratic is
[tex]y = (x - h)^{2} + k[/tex]
what function is shown in the table
set up an equation and solve for x! 25 points!
Answer:
7
Step-by-step explanation:
70+16x-2
68+16x=180
16x=180-112
x=112/16
x=7
Answer:
x = 7
Step-by-step explanation:
70 + 16x - 2 = 180 degree (being co interior angle)
68 + 16x = 180
16x = 180 - 68
16x = 112
x = 112/16
x = 7
Picture is attached, please explain answer
Answer:
20 Yellow Counters
Step-by-step explanation:
You can see the clues with how the ratio changes.
To change from (1:4) => (5:1) is not because any were taken away from the value that is the Yellow counters, it is purely because the amount added to the blue counters was so large that they simply simplified the ratio.
The real value of the ratio if reverted back to it's original state would be:
=> (20:4)
95 blue counters is equivalent to 19 in the ratio. We know this because it increased from 1 to 20.
95/19 => 5
Each Ratio in the original one presented is equal to 5.
5 * 4 = 20 Yellow Counters
Answer:
sorry I don't Know ·ω·
Step-by-step explanation:
A circle passes through the point (2,2) and has its center at (1,-3). The radius of the circle is _ units.
Answer:
radius = [tex]\sqrt{26}[/tex] units
Step-by-step explanation:
The radius r is the distance from the centre to a point on the circle.
Using the distance formula to calculate r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (2, 2) and (x₂, y₂ ) = (1, - 3)
r = [tex]\sqrt{(1-2)^2+(-3-2)^2}[/tex]
= [tex]\sqrt{(-1)^2+(-5)^2}[/tex]
= [tex]\sqrt{1+25}[/tex]
= [tex]\sqrt{26}[/tex]
solve px-18=4 for x
Answer:
x=22/p
Step-by-step explanation:
1. Add 18 to 4
2. px=22
3. Divide by p to isolate x
4. 22/p=x
Answer:
x = 22 ÷ p
Step-by-step explanation:
px - 18 = 4
px - 18 + 18 = 4 + 18
px = 22
p · x = 22
x · p = 22
x · p ÷ p = 22 ÷ p
x = 22 ÷ p
The volume of a cylinder, V, in terms of radius, r,
and height, h, is given by V = πr 2
h. If a cylinder has
a height of 6 meters, express the radius as a function
of V and find the radius of a cylinder with volume of
300 cubic meters.
Answer:
See explanation
Step-by-step explanation:
Volume of a cylinder = πr²h
Solve for r
V = π * r² * h
r² = V/πh
Find the square root of both sides
r = √V/πh
If height = 6 meters and volume = 300 cubic meters. Find r
r = √V/πh
= √(300/3.14*6)
= √(300/18.84)
= √15.923566878980
r = 3.9904344223381
Approximately,
r = 4 meters
b = 9, c = 16
a =
help please ;(
Answer:
right triangle ?
a = 13.288 ?
Step-by-step explanation:
[tex]c^{2}[/tex] - [tex]b^{2}[/tex] = [tex]a^{2}[/tex]
256 - 81 = 175
[tex]\sqrt{175}[/tex] = 13.288
Which equation represents a quadratic function with a leading coefficient of 2 and a constant term of –3?
Answer:
[tex]2x^{2} +bx-3=0[/tex]
Step-by-step explanation:
General form. A quadratic function [tex]f(x)[/tex] is of the form [tex](ax^2+bx+c)[/tex] where [tex]a,b,c[/tex] ∈ R or C and [tex]a[/tex] ≠ [tex]0[/tex].
We obtain an equation when [tex]f(x)=0[/tex]
⇒ [tex]ax^{2} +bx+c=0[/tex] is an quadratic equation.
Solution.
Given, [tex]a=2,c=-3[/tex], but b is not given
Thus the quadratic function with leading coefficient [tex]a=2[/tex] and constant term [tex]c=-3[/tex] is given by
[tex]f(x)=2x^{2} +bx-3[/tex]
∴ the required quadratic equation is
[tex]2x^{2} +bx-3=0[/tex]
Y is inversely proportional to d^2 When d=10 y=4 D is directly proportional to x^2 When x=2, d=24 Find a formula for y in terms of x?
Answer:
y = 1.44x⁴
Step-by-step explanation:
From the question,
Y∝d²
To remove the proportionality sign we introduce a constant.
Y = kd²............... Equation 1
make k the subject of the equation
k = Y/d²............. Equation 2
Given: Y = 4, d = 10
Substitute these values into equation 2
k = 4/10²
k = 4/100
k = 0.04
Substitute these value of k in equation 1
Y = 0.04d²................ Equation 3
Similarly,
d∝x²,
d = Cx²
make C the subject of the equation
C = d/x²................... Equation 4
Given: d = 24, x = 2
Substitute into equation 4
C = 24/2²
C = 24/4
C = 6
Hence,
d = 6x²................... Equation 5
Substitute the value of d in equation 5 into equation 3
y = 0.04(6x²)²
y = 0.04(36x⁴)
y = 1.44x⁴
Hence the formula for y in terms of x is y = 1.44x⁴
Put these numbers in order from least to greatest.
1/8,0.13,1/2, and 7/8
Answer:
1/8, 0.13,1/2, 7/8 it already is in order
Step-by-step explanation:
Answer:
Step-by-step explanation: 1/8, 0.13,1/2, 7/8 it already is in order