===================================================
Explanation:
Rearrange 0 = x + 2 + x^2 into x^2 + x + 2 = 0
Note that we have something in the form ax^2 + bx + c = 0
where a = 1, b = 1, c = 2
Plug these three values into the discriminant formula
d = b^2 - 4ac
d = 1^2 - 4*1*2
d = 1 - 8
d = -7
The discriminant for the quadratic equation 0 = x squared + x + 2, using the formula b squared - 4ac, and substituting the values a = 1, b = 1 and c = 2, is -7.
Explanation:The question is asking for the value of the discriminant for the quadratic equation 0 = x2 + x + 2. The discriminant is part of the quadratic formula and its value can be computed using the formula b2 - 4ac. In this equation, a = 1, b = 1, and c = 2. By substituting these values into the formula, we get: (1)2 - 4 * 1 * 2 = 1 - 8 = -7. Therefore, the value of the discriminant for the given equation is -7.
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Solve the quadratic equation by factoring. 9x^2+24x+20=4
A. x=4/3
B. x=-3/4
C. x=4
D. x=-4/3
D. -4/3
Let's solve your equation step-by-step.
9x2+24x+20=4
Step 1: Subtract 4 from both sides.
9x2+24x+20−4=4−4
9x2+24x+16=0
Step 2: Factor left side of equation.
(3x+4)(3x+4)=0
Step 3: Set factors equal to 0.
3x+4=0 or 3x+4=0
x= −4 /3
Hope This helps
Answer:
D. x = [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
Step 1: Subtract 4 from both sides.
9x^2 + 24x + 20 − 4 = 4 − 4
9x^2 + 24x + 16 = 0
Step 2: Factor left side of equation.
(3x+4)(3x+4) = 0
Step 3: Set factors equal to 0.
3x+4=0 or 3x+4=0
x = [tex]-\frac{4}{3}[/tex]
I hope this helps your assignment! Anyways, have a fantastic day! :D
a toy company's total payment salaries for the first two months of 2005 is $21, 894. write and solve an equation to find the salaries for the second month if the first month's salaries are $10,205.
Solution: Second month = m
The equation is
m + 10205 = 21894
m = 11689
So the second month will be $11,894. :)
To solve for the second month's salaries, subtract the first month salary from the total for two months. The solution to the equation $21,894 - $10,205 gives this salary: $11,689.
Explanation:The subject of this problem is a toy company's salary expenses over a course of two months. Let's denote the salary expenses for the second month as X. We know from the problem that the total salary expenses for the first two months (January and February) are $21,894. Furthermore, we know that the salary expenses for January are $10,205.
We can write an equation to express these facts as follows: X (which is the salary expenses for February) is equal to the total salary for the two months minus the salary for January, or in mathematical notation, X = $21,894 - $10,205.
We solve this math equation by subtracting $10,205 from $21,894, giving us X = $11,689. Therefore, the second month's salaries total $11,689.
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shelby's monthly periodic rate is 1.95%. what is the APR?
Monthly periodic rate = 1.95%
The APR is the annual periodic rate
The annual periodic rate is the monthly rate multiplied by 12, because there are 12 months in a year
APR = monthly periodic rate X number of months in a year
= 1.95% X 12
= 23.4%
By using the concept of Annual Periodic rate and Monthly periodic rate,
Annual periodic rate of Shelby = 23.4%
What is Annual Periodic Rate and Monthly periodic rate?
At first it is important to know about Periodic rate.
Periodic rate is the rate that can be charged on loans for a certain period.
If the periodic rate is calculated over a month then it is called monthly periodic rate.
If the periodic rate is calculated over a year then it is called Annual periodic rate.
Here,
Monthly periodic rate of Shelby = 1.95%
Annual periodic rate of Shelby = [tex]1.95 \times 12[/tex]
= 23.4%
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Hi I would really iike if someone helped me with this homework that I have I don't understand. an aquarium in the shape of a parallelepiped ABCDEFGH length AB = 80cm, width AD = 40cm, height DH = 50cm. a) we put HM = x cm give a frame for x b) give, according to x, the volume of water contained in the aquarium. This volume will be expressed in cm ^ 3 then in liters.
170^3 this is the answer just make sure you do you're work.
Evaluate the surface integral. s y ds, s is the helicoid with vector equation r(u, v) = u cos(v), u sin(v), v , 0 ≤ u ≤ 6, 0 ≤ v ≤ π.
Compute the surface element:
[tex]\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv[/tex]
[tex]\vec r(u,v)=(u\cos v,u\sin v,v)\implies\begin{cases}\vec r_u=(\cos v,\sin v,0)\\\vec r_v=(-u\sin v,u\cos v,1)\end{cases}[/tex]
[tex]\|\vec r_u\times\vec r_v\|=\sqrt{\sin^2v+(-\cos v)^2+u^2}=\sqrt{1+u^2}[/tex]
So the integral is
[tex]\displaystyle\iint_Sy\,\mathrm dS=\int_0^\pi\int_0^6u\sin v\sqrt{1+u^2}\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\left(\int_0^\pi\sin v\,\mathrm dv\right)\left(\int_0^6u\sqrt{1+u^2}\,\mathrm du\right)[/tex]
[tex]=\dfrac23(37^{3/2}-1)[/tex]
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
An organization of berry farmers releases a study reporting that people who eat blueberries every day have a lower cholesterol level.
Which statement describes the best conclusion to draw from the study?
Answer:
C
Step-by-step explanation:
I would say that the study reveals that there may be a correlation between eating blueberries and a lower cholesterol level.
The best conclusion from the study is that the consumption of blueberries might be associated with lower cholesterol levels. However, it's important to note that correlation does not mean causation and other factors could be at play.
Explanation:The statement that comes closest to an appropriate conclusion from the study is that the possible consumption of blueberries might be associated with lower cholesterol levels. However, it is important to remember that correlation does not necessarily imply causation. While the organization of farmers showed a connection between eating blueberries and lower cholesterol, this does not necessarily mean eating blueberries directly causes lower cholesterol. Other factors could be involved. For instance, those who eat blueberries daily might generally lead healthier lifestyles, contributing to lower cholesterol levels.
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Lines a and b are parallel and lines e and f are parallel.
What is the value of x?
Answer:
the answer is 82
Step-by-step explanation:
The answer would be 82
Hannah is saving money for a car. She earns $160 each week working part time after school and on the weekends at Papa's Pizza. Hannah currently has $1,280 in savings. Her parents put $50 in her savings account each week and she saves one-half of her paycheck each week. Which expression represents the situation? (n represents the number of weeks) A) 1,280 + 130n B) 1,280 + 160n + 50n C) 1,280 + 160n 2 D) 1,280 + 160n + 50n 2
Answer:
it is A
Step-by-step explanation:
Anna's scores for a video game are 670, 575, 400, 575, 1250, 720, and 885. Which statement about the data is correct?
Answer:
Step-by-step explanation:
what are the statements about the data?
Answer
C) The mean is greater than the median.
Step-by-step explanation:
To find the median, order the scores from LEAST to GREATEST.
400, 575, 575, 670, 720, 885, 1250.
The mean is the middle number, which is 670.
To find the mean, average the scores:
400 + 575 + 575 + 670 + 720 + 885 + 1250
7
= 725
725 > 670; therefore, the mean is greater than the median.
If B=26° and b=18 then find c (picture provided)
Answer:
c. 41.1
Step-by-step explanation:
To find a, we'll use the Law of Sines that says:
[tex]\frac{b}{sin(B)} = \frac{c}{sin(C)}[/tex]
And we'll isolate c to get:
[tex]c = \frac{sin(C) * b}{sin(B)}[/tex]
Then we will plug-in the information we already have :
[tex]c = \frac{sin(90) * 18}{sin(26)} = 41.06[/tex]
So, let's round it to 41.1 to match the answer number C.
Answer:
The correct answer is option C. 41.1
Step-by-step explanation:
Points to remember:-
Trigonometric ratio
Sin θ = opposite side/Hypotenuse
From the figure we can see a right triangle triangle FGH.
To find the value of c
It is given that, B=26° and b=18
Sin26 = opposite side/Hypotenuse = b/c
c = 18/Sin26 = 41.1
Therefore the correct answer is option c. 41.1
Find the area of the shaded sector (It is 45 degrees with a radius of 7) Help!!!
Answer:
Step-by-step explanation:
The formula for the area of a sector is
[tex]A_{s} =\frac{\theta }{360}*\pi r^2[/tex]
where theta is the angle given as 45 and r is the radius (7). Plugging in we get
[tex]A_{s}=\frac{45}{360}*\pi (7)^2[/tex]
Simplify a bit to get
[tex]A_{s}=\frac{1}{8}*49\pi[/tex]
which gives you, in terms of pi:
[tex]A_{s}=\frac{49\pi }{8}[/tex]
or if you need to use the decimal form, rounded to the hundredths position:
A = 19.24
If a certain negative number is multiplied by six, the result is the same as 20 less than the original number. What is the value of the original number?
The original negative number in the problem is found by setting up the equation 6x = x - 20 and solving for x, which results in the original number being -4.
Explanation:If a certain negative number is multiplied by six, the result is the same as 20 less than the original number. To solve for the original number, we can set up an equation based on the given condition. Let's assume the original number is x.
According to the problem, 6 times x equals x subtracted by 20:
6x = x - 20
To solve for x, we'll first move all terms involving x to one side of the equation by subtracting x from both sides:
6x - x = -20
This simplifies to:
5x = -20
Now, divide both sides by 5 to isolate x:
x = -20/5
x = -4
Therefore, the value of the original number is -4.
Let f(x)= cos(2x) +e^(-x). for what value of x on the interval (0,3) will f have the same instantaneous rate of change as the average rate of change of f over the interval?
[tex]f(x)[/tex] is continuous on [0, 3] and differentiable on (0, 3), so the mean value theorem applies here. It says that there is some [tex]c[/tex] in the open interval (0, 3) such that
[tex]f'(c)=\dfrac{f(3)-f(0)}{3-0}[/tex]
We have
[tex]f'(x)=-2\sin2x-e^{-x}[/tex]
so
[tex]-2\sin2c-e^{-c}=\dfrac{\cos6+e^{-3}-2}3\implies c\approx1.5418[/tex]
Please help!!!!!!!!!!
Answer:
Step-by-step explanation:
65 - Acute
72 - Acute
96 - Obtuse
Answer:
(a)
Step-by-step explanation:
Given 3 sides of a triangle a, b and c where c is the longest side, then
• If a² + b² = c² ⇒ triangle is right
• If a² + b² > c² ⇒ triangle is acute
• If a² + b² < c² ⇒ triangle is obtuse
Here a = 65, b = 72 and c = 96
65² + 72² ? 96²
4225 + 5184 ? 9216
9409 > 9216 ⇒ triangle is acute
Given the similarity statement ΔDEF ∼ ΔXYZ, which angle corresponds with ∠Z?
A. ∠F
B. ∠Y
C. ∠E
D. ∠D
Answer:
F
Step-by-step explanation:
In congruent triangles, or similar triangles, the letters in the same place will also be congruent
Answer:
the answer is A
Step-by-step explanation:
40 points PLEASE HURRY!!!
Noya needs to determine the number of books that will fit into a box. If the box has a length of 18 inches and each book is 2/9 of an inch thick, which expression can be used to determine the number of books that will fit into the box?
A. 18 divided by 2/9
B. 18 x 2/9
C.2/9 divided by 18
D.9/2 divided by 18
Answer:
A. 18 divided by 2/9
Step-by-step explanation:
To determine the number of boos that will fit into a box that is 18 inches long, we divide the length of the box by the length of the books
18 inches divided by 2/9 inches per book
This tells us how many books
copy dot flip
18 * 9/2
81 books
Determine the critical? value(s) for a? left-tailed test of a population mean at the alphaequals0.01 level of significance based on a sample size of nequals15.
Answer: 2
Step-by-step explanation:
The model represents an equation. What value of x makes the equation true?
A)
3
4
B)
9
2
C) −
3
4
D) −
9
2
Answer:
B) 9/2
Step-by-step explanation:
Subtracting 5x+7 from both sides leaves 2x = 9.
Dividing the 9 into two parts, we find ...
x = 9/2
Answer: 9/2 your welcome i got a 100% on the test by the way
Step-by-step explanation:
Please help me out with this
Answer:
81.75 ft²
Step-by-step explanation:
The area (A) of a trapezoid is calculated using the formula
A = [tex]\frac{1}{2}[/tex] h (a + b)
where a, b are the parallel bases and h is the perpendicular height
Calculate h using the right triangle and the sine ratio
sin30° = [tex]\frac{opposite }{hypotenuse}[/tex] = [tex]\frac{h}{10}[/tex]
Multiply both sides by 10
10 × sin30° = h, thus
h = 5
a = 12 and b = 8.7 + 12 = 20.7, hence
A = [tex]\frac{1}{2}[/tex] × 5 × (12 + 20.7)
= 0.5 × 5 ×32.7
= 81.75 ft²
What is an equivalent form of the function f(x) = x^2 +8x+15 that reveals the zeros of the function? A. y= (x-3)^2-5 B. f(x) = (x-3)^2-5 C. f(x) = (x+3)(x+5)
ANSWER
C. f(x) = (x+3)(x+5)
EXPLANATION
The given function is
[tex]f(x) = x^2 +8x+15[/tex]
The factored form of the function reveals the zeros of the function.
From the factored form, we apply the zero product principle to get the zeros.
From the given options, the factored form of the polynomial is
[tex]f(x) = (x+3)(x+5)[/tex]
What is the degree of x 6 + 4x – 3?
Answer:
The degree of a polynomial is the highest degree of its monomials with non-zero coefficients
Step-by-step explanation:
not sure
The maximum power of the polynomial x⁶ + 4x - 3 that is degree will be 6.
What is a polynomial?A polynomial expression is an algebraic expression with variables and coefficients. Unknown variables are what they're termed. We can use addition, subtraction, and other mathematical operations. However, a variable is not divisible.
A polynomial's degree is the greatest exponent of its variable term. The variable in this example is x, and the maximum exponent of x is 6, which is the degree of the polynomial. As a result, the polynomial x⁶ + 4x - 3 has a degree of 6.
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Help Plz ASAP!!!!!
Arianna's register shows a deposit on 9/5 in the amount of $310.25 an ATM withdrawal on 9/8 in the amount of $60.00 and check #149 on 9/14 in the amount of $240.67. No other Transactions were made
What should the balance be in Arianna register? Use this bank statement
A.-$32.63
B.$448.72
C.$587.88
D.877.82
Answer:
Step-by-step explanation:
Observe in the attached image that the final balance in your account on 9/1 is $578.30.
Then:
*On 9/6 he makes a payment of $140.30
*On 9/8, he makes a withdrawal from an ATM of $120
This means that:
$140.30 + $120 = $260.30
Then:
*On 9/18 you receive a deposit of $356.22
This means that:
$356.22
So, we have:
Beginning Balance: $578.30.
Total Withdrawals: $260.30
Total Deposits: $356.22
Final Balance = Beginning balance + Total Deposits - Total Withdrawals
Final Balance= $578.30 + $356.22 - $260.30
Final balance= $674.22
Then:
Date Description Debits(-) Credits(+) Balance
9/6 Auto Pay 140.30 438.00
9/8 ATM 120.0 318.00
9/18 Deposit 356.22 674.22
The balance in Arianna's register after the transactions will be $587.88. Then the correct option is C.
What is a bank transaction?
A monetary transfer is a record of money entering and exiting your account and is known as a bank transaction.
Arianna's register shows a deposit on 9/5 in the amount of $310.25 an ATM withdrawal on 9/8 in the amount of $60.00 and checks #149 on 9/14 in the amount of $240.67.
No other Transactions were made.
Then the balance be in Arianna's register will be
→ $ 578.37 + $ 310.25 - $ 60 - $ 240.67
→ $ 587.88
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Can someone please help me on this question.
Answer:
Step-by-step explanation:
[tex]3x^{2} + 5x-12=0[/tex]
[tex]-12=-5x-3x^{2}[/tex]
[tex](-12=-5x-3x^{2} ) * -1[/tex]
[tex]\sqrt{12=5x+3x^{2}[/tex]
in the triangle below what ratio is sec H
For this case we have that by definition:
[tex]Secant (A) = \frac {1} {Cosine (A)}[/tex]
Then, we find the cosine of the angle H, this will be given by the leg adjacent to H on the hypotenuse of the triangle.
[tex]Cos (H) = \frac {g} {f}[/tex]
So, the secant of H is given by:[tex]Sec {H} = \frac {1} {\frac {g} {f}}\\Sec {H} = \frac {f} {g}[/tex]
Answer:
Option C
(05.06)
Which of the following points lie in the solution set to the following system of inequalities?
y ≤ x − 5
y ≥ −x − 4
A) (−5, 2)
B) (5, −2)
C) (−5, −2)
D) (5, 2)
the answer for this question is (B) 5,-2
Find the number of ways to listen to 4 different CDs from a selection of 15 cds?
A. 1355
B. 2730
C. 360,360
D. 32,760
Answer: letter a should be the correct answer
Step-by-step explanation:
D is the answer for this question
A rectangular prism has a volume of 2320.5 in.? a width of 12.75 inches and a height of 14 inches what is the length?
Answer:
13
Step-by-step explanation:
Volume = length x width x height
2320.5 = l x 12.75 x 14
2320.5 = l x 178.5
2320.5/178.5 = l
l = 13
Please please help please
Answer:
130.5 in²
Step-by-step explanation:
The area (A) of a regular pentagon is
A = [tex]\frac{1}{2}[/tex] × perimeter × apothem
perimeter = 8.7 × 5 ← pentagon has 5 sides
= 43.5 in
A= 0.5 × 43.5 × 6 = 130.5 in²
A fish tank is a cube. Its side length is 4 1/2 feet. The volume of water needed to completely fill the fish tank is ___ cubic feet.
The equation for the volume of a cube is V=s^3, where V is volume and s is side length. Plug in and solve:
V=4.5^3
V=4.5*4.5*4.5
V=91.125ft^3
Hope this helps!!
Find the period of the function. y=3 sin x/8
Answer:
The period of given function is [tex]Period = 16\pi [/tex]
So, Option B is correct.
Step-by-step explanation:
In this question we need to find the period of the function y= 3 sin x/8
The formula used to find period of function is: [tex]\frac{2\pi }{b}[/tex]
We need to know the value of b.
To find the value of b we compare the standard equation with the equation of function given.
Standard Equation: y = a sin(bx - c) +d
Given Equation: y= 3 sin(x/8)
Comparing we get:
a= 3
b= 1/8
c= 0
d=0
So, we get the value of b i.e 1/8. Putting it in the formula to find period of given function.
[tex]Period = \frac{2\pi }{b}[/tex]
[tex]Period = \frac{2\pi }{\frac{1}{8}}[/tex]
Solving,
[tex]Period = 2\pi *8[/tex]
[tex]Period = 16\pi [/tex]
So, the period of given function is [tex]Period = 16\pi [/tex]