To find the quadratic equation with roots 6 and -5 and a leading coefficient of 3, we use the format 3(x - 6)(x + 5) and expand it to get the equation 3x² - 3x - 90 = 0.
Explanation:The quadratic equation with roots 6 and -5 and a leading coefficient of 3 can be written in the standard form ax² + bx + c = 0, where a, b, and c are constants. Since the roots are 6 and -5, and the leading coefficient (a) is 3, we can use the fact that a quadratic equation with roots r and s can be written as a(x - r)(x - s). Thus, our equation becomes 3(x - 6)(x + 5).
Expanding this, we have:
3(x² + 5x - 6x - 30)3(x² - x - 30)3x² - 3x - 90The quadratic equation with the given roots and leading coefficient is 3x² - 3x - 90 = 0.
What is the exact value of arcsin(−2√2)
Answer:
π4;3π4
Step-by-step explanation: Trig table gives:
sinx=√22 --> arc x=π4
Unit circle gives another arc x that has the same sin value:
x=π−π4=3π4
The exact value of [tex]\(\arcsin(-2\sqrt{2})\)[/tex] is not defined within the real numbers because the sine function has a range of [tex]\([-1, 1]\)[/tex], and the argument [tex]\(-2\sqrt{2}\)[/tex] lies outside this interval. The arcsine function, [tex]\(\arcsin(x)\)[/tex], is only defined for [tex]\(x\)[/tex] in the interval [tex]\([-1, 1]\)[/tex] .
To illustrate, the sine function reaches its maximum value of [tex]\(1\)[/tex] at [tex]\(\frac{\pi}{2}\)[/tex] and its minimum value of [tex]\(-1\)[/tex] at [tex]\(-\frac{\pi}{2}\)[/tex]. Any value outside the interval [tex]\([-1, 1]\)[/tex] is not within the domain of the inverse sine function. Therefore,[tex]\(\arcsin(-2\sqrt{2})\) does not have a real value.[/tex]
However, if we were to consider complex numbers, we could use Euler's formula and the definition of the complex logarithm to find a complex value for [tex]\(\arcsin(-2\sqrt{2})\)[/tex]. The general formula for the arcsine of a complex number [tex]\(z\)[/tex] is given by:
[tex]\[ \arcsin(z) = -i \ln\left(iz + \sqrt{1 - z^2}\right) \][/tex]
For [tex]\(z = -2\sqrt{2}\)[/tex], we would have:
[tex]\[ \arcsin(-2\sqrt{2}) = -i \ln\left(-2i\sqrt{2} + \sqrt{1 - (-2\sqrt{2})^2}\right) \][/tex]
Simplifying the expression under the square root:
[tex]\[ \sqrt{1 - (-2\sqrt{2})^2} = \sqrt{1 - 8} = \sqrt{-7} \][/tex]
Since [tex]\(\sqrt{-7} = i\sqrt{7}\)[/tex], we can continue the calculation:
[tex]\[ \arcsin(-2\sqrt{2}) = -i \ln\left(-2i\sqrt{2} + i\sqrt{7}\right) \][/tex]
This expression involves the complex logarithm, which is multi-valued due to the periodicity of the complex exponential function. Therefore, the value of [tex]\(\arcsin(-2\sqrt{2})\)[/tex] in the complex plane is not unique and requires careful handling of the branch cuts of the logarithm function. However, as stated earlier, within the realm of real numbers, [tex]\(\arcsin(-2\sqrt{2})\)[/tex] is undefined.
Solve for x:
-15x – 3 > 42
Answer: X < -3
Step-by-step explanation:
-15x - 3 > 42
-15x - 3 + 3 > 42 + 3
-15x > 45
-15x/-15 > 45/-15
Since we are dividing by a negative, we flip the >
x < -3
So, let's check
-4 < -3
-15*-4 - 3 > 42
60 - 3 > 42
57 > 42
Now, let's see if -3 will work.
-15*-3 - 3 > 42
45 - 3 > 42
42 > 42 (False)
Okay, now let's try 4
-15*4 - 3 > 42
-60 - 3 > 42
-63 > 42
This is false, so it is x < -3
The correct answer is x < -3
Explanation:
To solve our equation we first need to set out our equation, -15x – 3 > 42. Next, we add 3 to both sides of our equation, -15x - 3 + 3 > 42 + 3 = -15x > 45. Then, we multiply both sides by -1(Or in other words, reverse the inequality), -15x * -1 > 45 * -1 = 15x < -45. And then, we divide both sides by 15, 15x/15 < -45/15 = x < -3. Finally, we have our answer of x < -3.
Hope This Helps!!!
-AnimeDabGirl
F(x)=5x-3 what does f(5)=
f(5) means that x=5
Now, we solve 5x-3 because we know what x is.
5(5)-3
25-3
22
F(5)=22
Answer:
F (5)= 22
Step-by-step explanation:
what is 6.5 as a fraction
Answer:
13/2 is 6.5 as a fraction
Find the constant of variation for the relationship described in the table.
x f(x)
–2 –60
1 30
4 120
5 150
90
30
f(x)
x
Answer:
i believe the answer is 30
Step-by-step explanation:
Divide. 413÷129 Enter your answer, as a mixed number in simplest form, in the box.
For this case we must divide the following expression:
[tex]\frac {413} {129}[/tex]
The expression can not be simplified. When dividing we have that its decimal form is given by:
3,201550
If we convert to a mixed number we have:
[tex]3 \frac {26} {129}[/tex]
Verifying:
[tex]3 \frac {26} {129} = \frac {129 * 3 + 26} {129} = \frac {413} {129}[/tex]
Answer:
[tex]3 \frac {26} {129}[/tex]
Nicole drove
355 miles using 17 gallons of gas. At this rate, how many gallons of gas would she need to drive 284 miles?
Answer:
13.6 i believe, but that could, should be right tho.
Step-by-step explanation:
355/17=20.88235294 then 284/20.88235294=13.6
For this case, you want to know how many gallons of gasoline Nicole needs to drive 284 miles, knowing that with 17 she drove 355 miles. For this, we make a rule of three:
[tex]355 \ miles -----------> 17 \ gallons\\284 \ miles -----------> x[/tex]
Where "x" represents the number of gallons consumed in 284 miles.
[tex]x = \frac {284 * 17} {355}\\x = 13.6 \ gallons[/tex]
So, Nicole will need 13.6 gallons of gas to drive 284 miles
Answer:
13.6 gallons
please help me Find the legth of x
Answer: 6
=====================================
Explanation:
The triangles are similar triangles (we can use the AA similarity theorem to prove this). So the vertical sides pair up, and the horizontal sides pair up, to form the proportion below
x/4.5 = 8/6
Note the order of the terms. I'm dividing the upper triangle's sides by the corresponding lower triangle's sides. Cross multiply and solve for x
x/4.5 = 8/6
6x = 4.5*8
6x = 36
x = 36/6
x = 6
I need help with 9 & 10 please!
How many 1/2’a are in 7
Answer:
There are 14 halves in seven.
Step-by-step explanation:
7(1/2)=14
7(2)=14
OR, you could just count by halves until you reach 7, but that takes a while. (;
Which logarithmic equation is equivalent to the exponential below? e^a= 35
Answer:
[tex]log_{e}[/tex] 35 = a
Step-by-step explanation:
using the law of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
[tex]e^{a}[/tex] = 35 ⇒ [tex]log_{e}[/tex] 35 = a
Marie plants flowers in a planter that is 1 1/2 feet long and 1 2/3 feet wide. She plans to cover the entire area with fertilizer. How much area will she need to spread with fertilizer
Answer:
2 3/6
Step-by-step explanation:
You must turn 1 2/3 and 1 1/2 into improper fractions. You then multiply them and get an answer of 15/6, but since 6 can go into 15 twice (6x2=12+3=15), you get a whole of 2 and 3/6.
Final answer:
Marie will need to cover an area of 2 1/2 square feet with fertilizer for her planter that is 1 1/2 feet long and 1 2/3 feet wide.
Explanation:
The question asks to calculate the area that needs to be covered with fertilizer for a planter with given dimensions.
Step-by-Step Solution:
Convert the dimensions of the planter into improper fractions for easier multiplication. The length is already given as an improper fraction (1 1/2 feet which is 3/2 feet). The width is 1 2/3 feet, which is 5/3 feet when converted.
Multiply the length by the width to find the area in square feet: (3/2) × (5/3) = 15/6 square feet.
Simplify the calculated area if necessary. The area 15/6 can be simplified to 2 1/2 square feet.
Therefore, Marie will need to spread fertilizer over an area of 2 1/2 square feet.
The length of a rectangle is three centimeters more than twice the width. The perimeter is 78 centimeters. Define a variable and write and solve an equation to find out how long and wide the rectangle is?
I need to find the length? how?
Help!
If I were to Buy a bright bomer from the item shop and buy the glider. The Bright bomer is Rare and so is the glider. How much?
Answer: 2000 v-bucks
Step-by-step explanation: The bright bomber costs 1,200 and the glider costs 800
Which expression is equivalent to -9( -2x - 3)
Answer:
-18x+ 27
Step-by-step explanation:
Michelle multiple 3.4×52. she incorrectly wrote 1,768 as her product.
Answer:
Wrong Answer 176.8
Step-by-step explanation:
Multiply 3.4 * 52 = 176.8
using the random digits table from the lesson, start with the number in the tenth column, eighth row. list that number and next 4 numbers in the column.
First number
54, 50, 98, 82, 71, 19, 99, 09, 10
second number
09, 54, 98, 10, 19, 99, 71, 50, 82
third number
54, 99, 19, 98, 71, 50, 09, 10, 82
fourth number
99, 10, 98, 19, 54, 50, 09, 71, 82
fifth number
10, 99, 82, 19, 50, 54, 71, 09, 98
Answer:
19, 82, 54, 09 and 99
Step-by-step explanation:
From the random table, row numbers are given on the left side of the table and the column numbers are given on the top of the table.
On seeing them, the number on the tenth column and eighth row is 19.
The next 4 numbers on the same column are the elements in the 9th, 10th, 11th and 12 rows and on the same tenth column.
They are:
82, 54, 09 and 99.
Answer:
19, 82, 54, 09 and 99
Step-by-step explanation:
From the random table, row numbers are given on the left side of the table and the column numbers are given on the top of the table.
On seeing them, the number on the tenth column and eighth row is 19.
The next 4 numbers on the same column are the elements in the 9th, 10th, 11th and 12 rows and on the same tenth column.
They are:
82, 54, 09 and 99.
Step-by-step explanation:
Two factory plants are making TV panels. Yesterday, Plant A produced 6000 panels. Seven percent of the panels from Plant A and 2 % of the panels from Plant B were defective. How many panels did Plant B produce, if the overall percentage of defective panels from the two plants was 4 % ?
Answer:
1% of 4000 + 4% of B = 2% of (4000 + B)
40 + 0.04*B = 0.02( 4000 + B)
40 + 0.04* B = 80 + 0.02*B
40 + 0.04*B - 80 - 0.02B = 0
0.02*B - 40 = 0
0.02*B = 40
2B = 4000
B = 2000
Step-by-step explanation:
Plant B produced 1000 panels.
The total number of defective panels from Plant A is 7% of 6000,
= (7/100) x 6000
= 420 panels.
and, total number of defective panels from Plant B is 2% of x,
= (2/100) x
= (1/50) x.
The overall number of defective panels from both plants is 4% of the total number of panels
= (4/100)(6000 + x)
= (1/25) (6000 + x).
Now, set up the equation:
420 + (1/50) x = (1/25) (6000 + x)
To solve for x, we can multiply both sides of the equation by 50 * 25 to eliminate the fractions:
50 . 25 . 420 + 50 x = 25 (6000 + x)
125000 + 50x = 150000 + 25x
50x - 25x = 150000 - 125000
25x = 25000
x = 25000 / 25
x = 1000
Therefore, Plant B produced 1000 panels.
Learn more about Equation here:
https://brainly.com/question/29657983
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HELP RIGHT AWAY PLEASE!!!!
The graph shows two lines, A and B:
A graph is shown with x and y axes labeled from 0 to 6 at increments of 1. A straight line labeled A joins the ordered pair 2, 0 and the ordered pair 0, 4. Another straight line labeled B joins the ordered pair 0, 1 and the ordered pair 5, 6.
Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?
(1, 2) is the solution to line A but not to line B.
(1, 2) is the solution to both lines A and B.
(0, 1) is the solution to both lines A and B.
(0, 1) is the solution to line A but not to line B.
Answer:
(1,2) is the solution to both lines a and b
Step-by-step explanation:
You find the slope using 2 point and do y2-y1/x2-x1 . To create the equations for the two lines you do y=mx+b where m=slope and b=y-intercept.
Express 1.05 as a percent
1. 05 × 100
105%
(You move the decimal over twice)
Answer: 105%
Step-by-step explanation:
What is the graph of the inequality?
x > -3
Help!
Profit P(x) can be calculated as revenue minus cost. R(x) = 55x - 2x2 C(x) = 21x + 97 P(x) = - 2x2 + 34x - 97 Calculate the x-value that maximizes profit.
8.5
Step-by-step explanation:The vertex of a quadratic ax²+bx+c is located at x = -b/(2a). When the x² coefficient is negative, the vertex represents a maximum.
For P(x), the x-value of the maximum profit is ...
... x = -34/(2(-2))
... x = 8.5
You can buy 5 pounds of grapes for $9.95 .what is a proportion that gives the cost c if you buy 4 pounds of grapes
9.95 / 5 = 1.99
4 x 1.99 = 7.96
$7.96
How many permutations are possible for 11 objects taken 7 at a time? 330 5,040 237,600 1,663,200
The number of permutations possible for 11 objects taken 7 at a time is 1663200
Using the permutation formula :
nPr = n!/(n - r)!Here ,
n = 11 ; r = 7Inputting our values:
11P7 = 11!/(11 - 7)!
Evaluate:
11P7 = 1663200
The graph shows calories compared to grams of protein.
What information can you draw from the point (3, 12) on the graph?
There are 3 calories in 1 gram of protein.
There are 3 calories in 12 grams of protein.
There are 12 calories in 3 grams of protein.
There is 1 calorie in 4 grams of protein.
Hello :3
Your answer would be C. (or "There are 12 calories in 3 grams of protein).
Hope This Helps (Hope i am not to late sorry if i am)
Cupkake~
evaluate the expression 2m +n for m=13 and n=3
Answer:
This is equal to 29
Step-by-step explanation:
2(13)+3=29
Which value is the same as 2 tenths?
Answer:
0.2
Step-by-step explanation:
2/10=0.2
I need to know where did kellys collection go the most?
Answer:
What options are there
Step-by-step explanation:
Answer:
Step-by-step explanation:
Between the third and fourth months, the size of K's collection grew by 3. This is the steepest slope / greatest rate of change.
use the law of sines to find the length of side c
Look at the picture.
The law os sine:
[tex]\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
We have
[tex]m\angle A=46.7^o\\\\m\angle C=48^o\\\\a=44\\\\c=?[/tex]
Substitute:
[tex]\dfrac{c}{\sin48^o}=\dfrac{44}{\sin46.7^o}\\\\\boxed{c=44.93}\to\boxed{A.}[/tex]
Answer:
A!
Step-by-step explanation:
Explain when you know you need to rename a mixed number to subtract
When subtracting mixed numbers, rename the mixed number if the subtrahend is larger than the minuend by converting them into improper fractions and then subtracting the numerator while keeping the denominator the same.
Explanation:When subtracting mixed numbers, you may need to rename the mixed number if the subtrahend is larger than the minuend.
This means that the whole number part of the subtrahend is greater than the whole number part of the minuend, or the fractions have different denominators.
To rename the mixed number, you convert it into an improper fraction.
Once both mixed numbers are in the same form, you can subtract them by subtracting the numerator and keeping the denominator the same. Finally, simplify the answer if needed.