15b^2 + 4b - 4 =0 factorize
A Quadratic equation can have the form:
\(ax^2+bx+c=0\)Where "a" is the Leading coefficient.
In this case, you have the following Quadratic equation:
\(15b^2+4b-4=0\)You can rewrite it as following:
\(15x^2+4x-4=0\)The steps to factorize it are shown below:
1. Use the Quadratic formula:
\(x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}\)2. You can see that:
\(\begin{gathered} a=15 \\ b=4 \\ c=-4 \end{gathered}\)3. Substitute values into the Quadratic formula and evaluate:
\(\begin{gathered} x=\frac{-4\pm\sqrt[]{4^2-4(15)(-4)}}{2(15)} \\ \\ x_1=\frac{2}{5} \\ \\ x_2=-\frac{2}{3} \end{gathered}\)4. Substituting the variable "x" by the variable "b", you can write it in the following factor form:
\(15(b-\frac{2}{5})(b+\frac{2}{3})=0\)The answer is:
\(15(b-\frac{2}{5})(b+\frac{2}{3})=0\)the graph of f(x) = x is shifted up 9 units, what would be the equation of the new graph?
If the graph of f(x) = x is shifted up 9 units, the equation of the new graph would be g(x) = x + 9.
What is a translation?In Mathematics, the translation of a geometric figure to the left simply means subtracting a digit from the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is shifted up simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image or parent function.
Translating the graph of the parent function f(x) = x by shifting it nine (9) units up, we have the following equation:
f(x) = x → g(x) = f(x) + 9
g(x) = x + 9
In this context, we can logically deduce that the parent function f(x) was shifted by nine (9) units up to create function g(x) as shown in the graph attached below.
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What is the cost of a pair of shoes if they retail for $18.50, have a tax of 6%, and you have a coupon for 20% off after taxes
Answer:
$15.69
Step-by-step explanation:
multiply the retail price by 1.06 to get the price after taxes.
find the discounted price by multiplying the price after taxes(19.61) by 0.8 since it is 20% off to get the answer
Explain your answer !!
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f(n)=3+4)2 find the 4 terms of the sequence
Answer:25 + 24 + 49 :)
Step-by-step explanation:
Hope this helped :)
How do i write the prime factorization of 360 using division by primes?
What is the constant of proportionality in the equation y=5/4x
The constant of proportionality in the equation is 5/4
What is constant of proportionality?The constant connecting two given numbers in what is known in a proportional relationship is the constant of proportionality.
The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.
In the problem, y = 5/4x
The constant term 5/4 as used in the equation is used t multiply the input x values to get the out put y values
The term helps in relating x to y
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The sixth number 20210A is prime for only one digit A. What is A?
9514 1404 393
Answer:
A = 9
Step-by-step explanation:
Beyond the first few primes, all prime numbers end in one of the odd digits, 1, 3, 7, or 9. We can reduce this list by using a couple of simple divisibility rules.
The sum of the digits is 2+0+2+1+0+A = A+5. The number will be divisible by 3 if A+5 is divisible by 3. That will be the case for A=1 and A=7.
The sum of odd digits is A+1+0 = A+1. The sum of even digits is 0+2+2 = 4. When these sums are equal, the number is divisible by 11. That will be the case for A=3.
So, we have ruled out all digits except 9. If the number is prime it must be ...
202109
A = 9
_____
Additional comment
To make sure the number is prime, we would need to check divisibility by all primes less than √202109 ≈ 449.
Answer: 9
the answer is 9 because if i root 202109 i get about 446 and if its decimal it prime
A 12 oz box of sugar costs $3.10 and a 36 oz box of sugar costs $7.90. Which box of sugar is the better buy?
Answer: 36 oz box
Step-by-step explanation:
3.1/12=0.258333
7.9/360.291444
Thus, the 36 oz box is the better buy
does anyone know what 4/9 - 3/9 - 5/9 + 5 - 8 is simplified? if u do it would help me greatly. thank you.
Answer:
-31/9 which is also equal to -3 4/9
Step-by-step explanation:
Four different exponential functions are represented below.
Drag the representation of each function into order from greatest y-intercept to least y-
intercept.
The graph of the function y = 2x⁴ - 5x³ + x² - 2x + 4 is plotted and attached.
How to solve
We have the 4 functions as shown in the image attached.
The y - intercept is the point where the graph intercepts the y - axis.
Function [1] -
y = 4 + 2x
y - intercept is 4
Function [2] -
y = 5ˣ + 1
y - intercept is 2.
Function [3] -
the y-intercept is 1.
Function [4] -
the y - intercept is at -1.
Therefore, the greatest y-intercept is of function -
f(x) = 2x + 4
and the least y-intercept is of the function shown in graph [4] or function [4].
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Answer:
Carlos puts $3 into his bank account and it grows by 50% each year
f(x)=4^x+1
(The Table)
(The Graph)
6 * 10x^{-3}/8*10x^{-6}
The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4 × 10³
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
6 × 10⁻³ / 8 × 10⁻⁶
Simplifying the expression
6 × 10⁻³ / 8 × 10⁻⁶
This can be written as
6/8 × 10⁻³/10⁻⁶
Reduce the fraction
3/4 × 10⁻³/10⁻⁶
Apply the division law of indices
3/4 × 10⁻³ ⁻ ⁽⁻⁶⁾
3/4 × 10⁻³ ⁺ ⁶
3/4 × 10³
Hence, the value is 3/4 × 10³
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whats is the spread of 4, 6, 7, 9, 9
So, the spread of the numbers 4, 6, 7, 9, 9 is 5.
What is spread?Spread can refer to different things depending on the context. Here are a few examples:
In finance, spread refers to the difference between the bid price and the ask price of a security or asset. The bid price is the highest price a buyer is willing to pay for a security, while the ask price is the lowest price a seller is willing to accept. The spread represents the cost of trading that security or asset and is typically measured in basis points (hundredths of a percentage point).
In sports betting, spread refers to the point spread or handicap that is assigned to a team in order to make the betting odds more even. For example, if a football team is favored to win by 7 points, they may be assigned a -7-point spread, meaning they would have to win by more than 7 points for a bet on them to be successful.
In epidemiology, spread refers to the transmission of a disease from one person to another. The spread of a disease can be influenced by a variety of factors, including the infectiousness of the disease, the proximity and frequency of contact between people, and the effectiveness of measures to prevent transmission (such as vaccines or masks).
In cooking, spread can refer to a variety of ingredients that are used to spread on bread or crackers, such as butter, jam, or peanut butter.
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There are 6 acts in a talent show.
An acrobat, a dancer, a guitarist, a singer, a violinist, and a whistler.
A talent show host randomly schedules the 6 acts.
Compute the probability of each of the following events.
Event A: The acrobat is first, the singer is second, the violinist is third, and the whistler is fourth.
Event B: The first four acts are the whistler, the acrobat, the guitarist, and the dancer, In any order.
Write your answers as fractions in simplest form.
P(A) =
P (B) =
The probability of Event A is 1/360 and the probability of Event B is 1/15.
For Event A, we can calculate the probability by considering the order in which the acts are scheduled.
There are 6 acts, so there are 6 possible choices for the first act. After the first act is scheduled, there are 5 remaining acts, so there are 5 possible choices for the second act.
Similarly, there are 4 possible choices for the third act, and 3 possible choices for the fourth act.
Finally, there are 2 possible choices for the fifth act, and only 1 choice remains for the last act.
Therefore, the total number of possible ways to schedule all 6 acts is:
6 x 5 x 4 x 3 x 2 x 1 = 720
Since we are only interested in one specific order of the first four acts, we need to count the number of ways to schedule the remaining two acts after the first four have been scheduled in the desired order.
There are 2 remaining acts, so there are 2 possible choices for the fifth act.
Only one act remains for the last slot.
Therefore, the total number of ways to schedule all 6 acts such that the acrobat is first, the singer is second, the violinist is third, and the whistler is fourth is:
1 x 1 x 1 x 1 x 2 x 1 = 2
Thus, the probability of Event A is:
P(A) = 2/720 = 1/360
For Event B, we want to count the number of ways to schedule the first four acts as the whistler, the acrobat, the guitarist, and the dancer, in any order.
There are 4 acts, so there are 4 possible choices for the first act. After the first act is scheduled, there are 3 remaining acts, so there are 3 possible choices for the second act.
Similarly, there are 2 possible choices for the third act, and only one choice remains for the fourth act.
Therefore, the total number of possible ways to schedule the first four acts is:
4 x 3 x 2 x 1 = 24
Since we do not care about the order in which the last two acts are scheduled, we can simply choose any two acts from the remaining 2. There are 2 ways to do this.
Therefore, the total number of ways to schedule all 6 acts such that the first four acts are the whistler, the acrobat, the guitarist, and the dancer, in any order is:
24 x 2 = 48
Thus, the probability of Event B is:
P(B) = 48/720 = 1/15
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C is the point on line y= 2x+1 where x= 2. Find coordinates of midpoint of BC
Answer:
Step-by-step explanation:
Not going to happen without knowing where B exists.
C has coordinates found by y = 2(2) + 1 = 5
(2, 5)
IF B is at (Bx, By)
the midpoint of the segment BC is
(½(Bx + 2), ½(By + 5))
Help please f/18 = -6
Answer:
f=-108
Step-by-step explanation:
f/18=-6
f= -6 x 18
f= -108
Answer:
f=-108
Step-by-step explanation:
Since F divided by 18 is -6, just multiply -6 and 18 to get the answer
Tom is 8 years older than Jerry. The sum of their age is 80. What is Tom's age?
Answer: Tom is 46 years old and Jerry is 34 years old.
if the number is divisible both 3 and 4, find the greatest common fact
Evaluate A^2-B^2 for A = 3 and B = -4
A.) -7
B.) -2
C.) 25
Answer:
A.) -7
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightStep-by-step explanation:
Step 1: Define
A² - B²
A = 3
B = -4
Step 2: Evaluate
Substitute: 3² - (-4)²Exponents: 9 - 16Subtract: -7what is the value of x in the eqation 3 [2x+5]=3x+4x
Answer:
x = 15
Step-by-step explanation:
3 ( 2x + 5 ) = 3x + 4x
Distribute;
3 ( 2x + 5 ) = 3x + 4x
6x + 15 = 3x + 4 x
Combine like terms;
6x + 15 = 3x + 4x
6x + 15 = 7x
Inverse operations;
6x + 15 = 7x
-6x -6x
15 = x
Find the surface area and volume of a sphere.
A = 4 r²
V = 4/3r³
A sphere has a radius of 4 inches.
Area (to the nearest tenth) =
Volume (to the nearest tenth) =
sq. in.
cu. in.
\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary. B = 103°, a = 12 cm, c = 22 cm (5 points) a 128.62 cm2 b 132 cm2 c 29.69 cm2 d 257.23 cm2
The area of the triangle, Rounded to the nearest hundredth, is approximately 132.02 cm².
The area of a triangle with the given measurements, we can use the formula for the area of a triangle using side lengths and an included angle. The formula is:
Area = (1/2) * a * c * sin(B)
where a and c are the side lengths, B is the included angle between those sides, and sin(B) represents the sine of angle B.
Let's calculate the area using the given measurements:
B = 103° (included angle)
a = 12 cm
c = 22 cm
First, we need to convert the angle from degrees to radians, as the sine function operates on radians. We can use the conversion: radians = degrees * (π/180).
B in radians = 103° * (π/180) ≈ 1.8 radians
Next, we can substitute the values into the formula:
Area = (1/2) * a * c * sin(B)
= (1/2) * 12 cm * 22 cm * sin(1.8 radians)
Using a calculator, we can evaluate sin(1.8 radians) ≈ 0.9833.
Area ≈ (1/2) * 12 cm * 22 cm * 0.9833
≈ 132.02 cm² (rounded to the nearest hundredth)
Therefore, the area of the triangle, rounded to the nearest hundredth, is approximately 132.02 cm².
Among the given options, the closest match is:
b) 132 cm² (rounded to the nearest whole number)
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thx guysssssssssssssssssssssssssssssssssssssssss
(30 points easy) write the equation of side B seat inside AC to determine if the three points could form a right triangle
write the equation of the line for side B C, and side AC, If the points were connected, could this be a right triangle explain why
(use the graph in the photo)
Answer:
Side BC: y = -2x + 10
Side AC: y = 2x + 4
Yes, these three points could form a right triangle. This is because the slopes of the two lines, Side BC and Side AC, are opposite reciprocals of each other. This means that when the two lines intersect, they will form a right angle.
Carlos read 150 words in one minute. He
read 5 times as many words as his younger
brother. How many words did his younger brother
read in one minute?
Answer:
30
Step-by-step explanation:
150/5 = 30
Answer: 30
Step-by-step explanation:
Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.
Is the product positive or negative? Why?
The multiplication expression with eight rational factors are ''positive''.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Jared writes a multiplication expression with eight rational factors. Half of the factors are positive and half are negative.
Since, Multiplication of four positive numbers are always gives a positive number and multiplication of four negative numbers are always gives a positive number.
Hence, The multiplication expression with eight rational factors are positive.
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Please help I need due ....
Answer:
The answer is 22 2/5
Step-by-step explanation:
So the correct is B
#11-14 Answers are on the side
GEOMETRY 100 POINTS
Find the length of BC
Answer:
x = 16
Step-by-step explanation:
Opposite sides are equal in a parallelogram
AD = BC
5x - 12 = 3x + 20
5x - 3x = 20 + 12
2x = 32
x = 32/2
x = 16
The area of a rectangle is 3x2 - 12x square yards. If the width is 3x yards, what is the length of the rectangle?
Answer:
x - 4 yards.
Step-by-step explanation:
Given:
Area of rectangle = 3x^2 - 12x square yards
Width = 3x yards
To find:
Length of rectangle
Solution:
The area of a rectangle is equal to the product of its length and width.
Area of rectangle = Length * Width
Substituting the given values, we get:
3x^2 - 12x = Length * 3x
Length =( 3x^2 - 12x )3x
Length = x-4
Therefore, the length of the rectangle is x - 4 yards.
Answer: The length of the rectangle is x - 4 yards.
Step-by-step explanation:
We can create an equation to solve this word problem, where the variable L = length.
3x × L = \(3x^2 - 12x\)
We need to solve for the variable L, to find the length of the rectangle.
First lets factor the right side of the equation to make it easier to divide with.
3x × L = \(3x^2 - 12x\)
We can factor out 3x from the right side of the equation.
3x × L = 3x(x - 4)
Now we need to get the variable L by itself (isolating the variable). In order to do that, we can divide both sides by 3x.
3x × L = 3x(x - 4)
/3x /3x
L = x - 4
The length of the rectangle is x - 4 yards.