Step-by-step explanation:
the equation is
2x² + 3x - 8 = 0
the generic solution to such a quadratic equation is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 2
b = 3
c = -8
x = (-3 ± sqrt(9 - 4×2×-8))/(2×2) =
= (-3 ± sqrt(9 + 64))/4 = (-3 ± sqrt(73))/4
x1 = (-3 + sqrt(73))/4 = (-3 + 8.544003745)/4 =
= 1.386000936... ≈ 1.39
x2 = (-3 - sqrt(73))/4
but that would negative, and therefore not a wanted solution.
x ≈ 1.39
is the targeted solution.
Comparing Domain and Range
Which sets of values belong to the domain and range of a relation?
Domain
Quick
Chock
output values
values for the independent variable
input values
values for the dependent variable
Range
Try It #4
For the function f (x) = | 2x − 1 | − 3, find the values of x such that f(x) = 0.
Answer:
x=2 or x= -1
Step-by-step explanation:
when f(x) = 0
⇒| 2x-1 | =3
case(i) (x>1/2)
2x-1=3
x=2
case(ii) (x<1/2)
-(2x-1)=3
2x-1=-3
x=-1
case(iii) (x=1/2)
[tex]0=3[/tex] absurd.
Can someone solve this?
Answer:
[tex]\frac{5}{6}[/tex], [tex]\frac{5}{6}[/tex], and "Yes"
Step-by-step explanation:
We will do as the instructions say.
-> See attached.
Simplify the expression completely.
The solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
The given expression will be solved as follows:-
E = [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]
E = [tex]\sqrt{7\times 7\times 3\times xy^7\times x^5y^5[/tex]
E=[tex]\sqrt{7\times 7\times 3\times x^6y^{12}[/tex]
E = 7x³y⁶√3.
Therefore the solution of the given expression [tex]\sqrt{7xy^7}\sqrt{21x^5y^5}[/tex]will be 7x³y⁶√3.
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How much simple interest is earned on an investment of 1,250 if the money is invested for 5 years at an annual interest rate of 4.5%
Work Shown:
i = P*r*t
i = 1250*0.045*5
i = 281.25
In the following exercises, multiply the binomials. Use any method.
256. (r + s)(3r + 2s)
Answer:
Hence the expression [tex]$$(4z-y)(z-6)=4z^2-yz-24z+6y$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (4z-y)(z-6).We have to multiply the given expression.Multiply the (4 z-y) by -6, multiply the (4 z-y) by z then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 4z & - & y \\ \times & {} & {} & {} & z & - & 6 \\ \end{matrix}$$[/tex]
________________
[tex]$$\begin{matrix}{} & {} & {} & - & 24z & + & 6y \\ 4{{z}^2} & - & yz & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
______________________
[tex]$$\begin{matrix}4{{z}^2} & - & yz & - & 24z & + & 6y \\ \end{matrix}$$[/tex]
с
Instructions: Find the value of the trigonometric ratio. Make sure to simplify the fraction
if needed.
Tan A
Check
50
30
A
40
B
Using relations in a right triangle, it is found that:
tan(A) = 3/4 = 0.75.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this triangle:
The adjacent side to A has length 40.The opposite side to A has length 30.Hence the tangent of A is:
tan(A) = 30/40 = 3/4 = 0.75.
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A scientist has 50 grams of a radioactive element. The amount of radioactive element remaining after t days can be
determined using the equation f()-50
50 (1) ³ . After two days the scientist receives a second shipment of 50 grams of the
same element. The equation used to represent the amount of shipment 2 remaining after t days is f(t)-50
(1)- 50 (2)
of the following is an equivalent form of the expression for the amount remaining in shipment 2?
•(9²
5
50.
19
t
50-(³
The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
What is the radioactive element about?Note that:
f(t)= 50 (1/2)^ [tex]\frac{t-2}{5}[/tex]
f(t)= 50 (1/2)^ [tex]\frac{\frac{t}{5} } - {\frac{2}{5} }[/tex]
Note also that in indices, [tex]x^{-y}[/tex] = 1/ [tex]x^{y}[/tex]
Then: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
([tex]50 \frac {1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
= 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
Therefore, The option that is the equivalent form of the expression for the amount remaining in shipment 2 is the second option: 50 ([tex]\frac{1}{2} ^ \frac{t}{5} / \frac{1}{2} ^ \frac{2}{5}[/tex])
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Evaluate the expression for x = 6.
12 + 2x -
5
O A. 19
O B. 79
O C. 14
O D. 54
A=[37], B =[²7], C = [= ² =8].
Which matrix represents (A - B) - C?
2. If (300) (30,000) = 9 x 10m, then m =
How to find the answer to0.291×0.34
Answer:
0.291×0.34=0.09894
Answer: 0.09894
We are going to use long division:
write the equation for a polynomial of least degree with integer coefficients given the following zeros: -2, -6, -10i. leave your answer in factored form, but make sure there are no irrational or imaginary numbers
The equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0
What is a polynomial?A polynomial is an algebraic equation with at least the power of its variable 3.
Analysis:
if -2, -6, -10i are the zeroes of the polynomial, it means x = -2, x = -6, x = -10i
if x = -2, (x+2) is a factor, (x+6) is a factor.
convert x = -10i to a real number,
i = [tex]\sqrt{-1}[/tex]
-10[tex]\sqrt{-1}[/tex] = 10[tex]\sqrt{- -1}[/tex] = 10[tex]\sqrt{1}[/tex] = 10
x = 10, so (x-10) is a factor.
Therefore equation of the polynomial in factored form is (x+2)(x+6)(x-10) = 0
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Hurrry help number is chosen at random form 1 to 50 find the probiotic of selecting prime numbers
Answer: [tex]\frac{3}{10}[/tex] or 30%
Step-by-step explanation:
We will divide the wanted outcomes by the possible outcomes.
[tex]\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{number of prime number}}{\text{number of numbers 1 through 50}} =\frac{15}{50}=\frac{3}{10}\;\; \text{or 30\%}[/tex]
The prime numbers from one through fifty are; 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47.
-> This is 15 numbers
increase the number 1.25 by 8/25 of it
Answer: 1.65
Step-by-step explanation:
First, we must find 8/25 of 1.25. This is using multiplication.
1.25 * 8/25 = 0.4
Now, we can increase 1.25 by 8/25 of it. This is using addition.
1.25 + 0.4 = 1.65
What is the slope of line a? 48 POINTS
Answer:
-3
Step-by-step explanation:
[tex]Slope = \frac{Change in Y}{Change in X}[/tex]
Take two points
(1, -5) and (-1, 1)
Plug in their y and x coordinates
[tex]\frac{-5 - 1}{1-(-1)} =\frac{-6}{2} = -3[/tex]
Answer:
1st answer is correct.
Step-by-step explanation:
First, let us take two coordinates of the line.
( 0 , -2 ) ⇒ ( x₁ , y₁ )
( -1 , 1 ) ⇒ ( x₂ , y₂ )
We have to use the below formula to find the slope of the line.
Slope = m
[tex]m = \frac{y_1-y_2}{x_1-x_2}[/tex]
Let us find it now.
[tex]m = \frac{-2-1}{0-(-1)}\\m = \frac{-3}{1}\\m=-3[/tex]
The school tuck-shop has milk in 700mL and 1L cartons. If there are 60 cartons and 48L of milk in total, how many 700 mL cartons are there?
60 × 48 = 2880 L
2880 ÷ 700 = 4
Answer:
20 1 Liter Cartons
40 700 ml Cartons
Step-by-step explanation:
Let A be the number of 700ml cartons.
Let B be the number of 1 L cartons
We are told that A + B = 60 cartons total
Rearrange to isolate A: A = 60 - B
700ml is 0.700L
Total volume of milk is 48L
Total volume (in liters) of the 700 ml cartons is from (0.70 L)A
Total volume from the 1L cartons is (1 L)B
Total = (0.70)A + 1B = 48 L
Now use the rearranged equation for A in the above espression:
(0.70)A + 1B = 48 L
(0.70)(60-B) + 1B = 48 L
42 - 0.70B + B = 48
0.30B = 6
B = 20
A is 60 - B or 40
=============
CHECK:
B: 20*(1 L) = 20 L
A: 40*(0.70 L) = 28 L
Total = 48 L YES
The height of a cone is twice the radius of its base.
2x
X
What expression represents the volume of the cone, in
cubic units?
O 2x³
O 47x³
Answer: O253
Step-by-step explanation:
The correct expression which represents the volume of the cone is,
V = 2x³π/3
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.
Given that;
The height of a cone is twice the radius of its base.
Let radius of cone = x
Then, The height of cone = 2x
Hence, The volume of cone is,
V = 1/3πr²h
V = 1/3 × π × x² × 2x
V = 2x³π/3
Thus, The correct expression which represents the volume of the cone is,
V = 2x³π/3
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In a class of 40 students, 20% are females. How many males are in the class?
Answer:
In a class of 40 students, 20% are females. How many males are in the class?
ANSWER
= 32
if in a class of 40 students 20% are females that means 80% of the class are males...
Please answer with everything needed i appreciate everyones help:)0)
Answer:
1/3
Step-by-step explanation:
please mark brainliest if correct
PLEASE HELP THIS IS MY LAST TEST QUESTION!!!14x^5y^4+21x^3y^2/7x^3y
Answer: =2x²y³+3y.
Step-by-step explanation:
[tex]\frac{14x^5y^4+21x^3y^2}{7x^3y} =\frac{7x^3y*(2x^2y^3+3y)}{7x^3y}= 2x^2y^3+3y.[/tex]
In the formula d = startroot (x 2 minus x 1) squared (y 2 minus y 1) squared endroot, how does each subtraction expression relate to the pythagorean theorem?
Each subtraction expression, in relation with the Pythagoras Theorem, represents the length of one side of a right-angled triangle with a hypotenuse of length d.
What is Pythagoras Theorem?
The Pythagoras Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the remaining two sides in a right-angled triangle.
The formula for Pythagoras Theorem is given by,
[tex]h^{2}=a^{2} +b^{2}[/tex]
Here, h is the hypotenuse, a and b are the two legs of the right-angled triangle.
Each Subtraction in view of Pythagoras Theorem
It is is given that,
[tex]d =\sqrt{(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2} }[/tex]
or [tex]d^{2} =(x_{2} - x_{1} )^{2}+(y_{2} -y_{1} )^{2}[/tex]
Therefore, d is the hypotenuse and each subtraction term represents one leg of the right-angled triangle in accordance with the Pythagoras Theorem.
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The FBI wants to determine the effectiveness of their 10 Most Wanted list. To do so, they need to find out the fraction of people who appear on the list that are actually caught. In an earlier study, the population proportion was estimated to be 0.26. How large a sample would be required in order to estimate the fraction of people who are captured after appearing on the 10 Most Wanted list at the 98% confidence level with an error of at most 0.04?
The sample size required to estimate the fraction of people who are captured after appearing on the 10 most wanted list is 228.
Given standard deviation of 0.26 ,margin of error of 0.04, and confidence interval of 98%.
We have to determine the sample size required to estimate the fraction of people who are captured after appearing on the 10 ost wanted list.
We can find the sample size with the help of margin of error.
Margin of error is the difference between the calculated values and real values.
Margin of error=z*σ/[tex]\sqrt{n}[/tex]
where σ is standard deviation,
n is sample size and z is critial z value.
We have to find the z value for 98% confidence level from z table.
z value=2.326.
Put the values in the formula of margin of error.
0.04=2.326*0.26/[tex]\sqrt{n}[/tex]
[tex]\sqrt{n}[/tex]=2.326*0.26/0.04
[tex]\sqrt{n}[/tex]=15.119
squaring both sides we get
n=228.58
By rounding we get
n=228.
Hence the sample size needed is 228.
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Suppose a large shipment of televisions contained 19% defectives. If a sample of size 479 is selected, what is the probability that the sample proportion will be greater than 17%
The value is P(p'-p > 0.17) = 0.09
From the question we are told that
The population proportion is p=0.19
The sample size is n = 479
Generally given that the sample size is large enough , i.e n > 30 then the mean of this sampling distribution is mathematically represent
[tex]u_{x} =p=0.19[/tex]
Generally the standard deviation is mathematically represented as
σ[tex]=\sqrt{ \frac{p(1-p)}{n}[/tex]
σ= [tex]\sqrt{ \frac{0.19(1-0.19)}{479}[/tex]
σ=0.017
Generally the the probability that the sample proportion will differ from the population proportion by greater than 17% is mathematically represented as
[tex]P(p'-p > 0.17) =P (z > \frac{0.17}{0.017} )[/tex]
[tex]P(p'-p > 0.17) =P (z > 10 )[/tex]
[tex]P(p'-p > 0.17) =P (z > 10 ) - P (z > -10 )[/tex]
From the z table the area under the normal curve to the left corresponding to 10 and - 10 is
[tex]P(p'-p > 0.17) = 0.97042 - 0.87450\\P(p'-p > 0.17) = 0.09[/tex]
So, the value of probability is greater than 17% is P(p'-p > 0.17) = 0.09
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The probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.
The true proportion of the sample or the mean of the sample = 19%, that is, μ = 19% or 0.19.
The sample size (n) = 479.
The sample proportion is to be calculated at the point 17% or 0.17.
The standard error (s) = √{μ(1 - μ)/n} = √{0.19(1 - 0.19)/479} = 0.0179.
We are asked to calculate the probability that the sample proportion is greater that 17% or 0.17.
This is written as P(X > 0.17) = P(Z > {(0.17-0.19)/0.0179}) = P(Z > -1.1173) = 1 - P(Z ≤ -1.1173) = 1 - 0.1304 = 0.8696 or 86.96%.
To calculate this using the calculator, we use the calculator function:
Normalcdf(0.17,10000000,0.19,0.0179) = 0.8677 or 86.77%.
Thus, the probability that the sample proportion will be greater than 17% is 0.8677 or 86.77%.
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Use a graphing calculator to find the value of the correlation coefficient r to determine if there is a strong correlation among the data.
(1, 7), (2, 5), (3, -1), (4, 3), (5, -5)
The value for r = - 0.8535 , there is strong correlation between the variables.
What is a correlation coefficient ?Correlation coefficient describes the relationship between the two variables in the data .
The data given is
(1, 7), (2, 5), (3, -1), (4, 3), (5, -5)
Assuming Linear Regression ,
The data is plotted on the graphing calculator
The value for r = - 0.8535
as the value is in the range of - .85 to -1 , therefore there is strong correlation between the variables.
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A study conducted at a certain college shows that 51% of the school's graduates find a job in their chosen field within a year after graduation. Find the probability that 5 randomly selected graduates all find jobs in their chosen field within a year of graduating. Round to the nearest thousandth if necessary.
Answer:
0.035
Step-by-step explanation:
Since all of them find a job, the probability is
[tex]51\%\times51\%\times51\%\times51\%\times51\%\\\\=(51\%)^5\\\\=0.035[/tex]
(rounded to the nearest thousandth)
Simplify.
6a2−4b2+4abc−9b2−4a2+8abc
Answer:
[tex]\huge\boxed{\sf 2a^2-13b^2+12abc}[/tex]
Step-by-step explanation:
Given expression:[tex]=6a^2-4b^2+4abc-9b^2-4a^2+8abc\\\\Combine \ like \ terms\\\\=6a^2-4a^2-4b^2-9b^2+8abc+4abc\\\\=2a^2-13b^2+12abc\\\\\rule[225]{225}{2}[/tex]
Answer:
Hello! The answer is: [tex]2a^2 - 13b^2 + 12abc[/tex]
Step-by-step explanation:
[tex]6a^2 - 4b^2 + 4abc - 9b^2 - 4a^2 + 8abc[/tex]
Rearrange to combine like terms:
[tex]6a^2 - 4a^2 - 4b^2 - 9b^2 + 4abc + 8abc[/tex]
Combine like terms:
[tex]2a^2 - 13b^2 + 12abc[/tex]
math. is 1.096 x 10 ^4 the right answer?
Work Shown:
[tex]1.04 \cdot 10^4 + 5.6 \cdot 10^2\\\\10,400 + 560\\\\10,960\\\\1.096 \cdot 10^4\\\\[/tex]
Note: Something like [tex]5.6 \cdot 10^2[/tex] means we move the decimal point two spots to the right to get to 560. If the exponent was negative, then we move that many spaces to the left.
Over which interval are the exponential and linear function approximately the same?
hard to tell but from 0.75 to 1
Simplify
(13x² +10) - 9x²