Answer:
X is less than and equal to 4
What is the distance from (-5,2) and (0,4)?
Answer:
d = [tex]\sqrt{29}[/tex]
Step-by-step explanation:
The distance between two points is given by
d = [tex]\sqrt{ ( x2 - x1) ^2 - ( y2-y1)^2}[/tex] where ( x1,y1) and ( x2,y2) are the two points
d = [tex]\sqrt{( 0 - -5) ^2 + (4 - 2) ^2}[/tex]
d = [tex]\sqrt{5^2 + 2^2}[/tex]
d = [tex]\sqrt{25 +4}[/tex]
d = [tex]\sqrt{29}[/tex]
Answer: [tex]\Large\boxed{Distance=\sqrt{29} }[/tex]
Step-by-step explanation:
Given information
[tex](x_1,~y_1)=(-5,~2)[/tex]
[tex](x_2,~y_2)=(0,~4)[/tex]
Given the distance formula
[tex]Distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute values into the formula
[tex]Distance =\sqrt{((0)-(-5))^2+((4)-(2))^2}[/tex]
Simplify values in the parenthesis
[tex]Distance =\sqrt{(0+5)^2+(4-2)^2}[/tex]
[tex]Distance =\sqrt{(5)^2+(2)^2}[/tex]
Simplify the exponents
[tex]Distance =\sqrt{25+4}[/tex]
Simplify values in the radical sign
[tex]\Large\boxed{Distance =\sqrt{29}\approx5.4}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
The sum of a number and seven is six less than four times the number. Write an algebraic equation and solve to find the number.
Answer:
13/3 or 4.333
Step-by-step explanation:
Let the number be x
the sum of x and 7 is 6 less than 4x, giving the equation: x+7+6 = 4x
Solve:
x+7+6 = 4x
x+13 = 4x
13 = 3x
x = 13/3
The price of a product is reduced by 30%. By what percentage should be increased to make it 100%?
it should be 70 percent
Step-by-step explanation:
100 subtract by 30 is 70 percent
Pls answer before 8:00 pm
Answer:225 jeans.
Step-by-step explanation: What we need to do here is convert the number of jeans to a percentage. There were 25 jeans when 50 customers were surveyed and 25 is half of 50 or 50%. This means that if 450 pairs of pants are ordered half of them should be jeans. 450/2 = 225.
What is 57, 020, 000 expressed in scientific notation
Answer:
we write in form of (a x 10^n)
5.702 x 10⁷
Answer:
5.702 x 10^7
Step-by-step explanation:
In scientific notation, a number in the ones place is raised to a power of 10: the power will be positive if the original number is huge, and negative if the original number is small.
The number 57,020,000 is a huge number. We simply move the decimal 7 places to the left to get 5.072, and since we moved the decimal 7 places, 10 is raised to the power of 7.
Brainliest, please :) Hope this helps!
i need help w this pls
Answer: C
Step-by-step explanation: The y-intercept is 1/5 since the point on the y-axis is (0, 1/5). The slope is 2/3 because the other coordinate is up 2 and right 3 from (0, 1/5) *remember rise over run*. The shading means that the answer (y) must be less than or equal to 2/3x + 1/5, hence it being underneath the line.
. x is directly proportional to y. When x = 5, y = 3. Work out the value
of y when x =9
Answer: y = 5.4
Step-by-step explanation: This is a proportional statement. So we can set up a system of proportions.
So we know when x is 5, y is 3. Thus, we can set up a proportion [tex]\frac{x}{y}[/tex] such that substituting will give [tex]\frac{5}{3}[/tex].
Now, we know when x is 9, y is some unknown number. So we can set up the second proportion as [tex]\frac{9}{y}[/tex].
Since 5/3 and 9/y are directly proportional, these 2 expressions are therefore equal. So we have [tex]\frac{5}3}[/tex] [tex]= \frac{9}{y}[/tex].
Cross multiplying, we get [tex]5y = 27[/tex].
Dividing by 5, we get [tex]y = 5.4[/tex]
Hope this helped!
find the square roots by division method of
210,681
Answer: square of 459 is 210681
What is the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 2:3?
A.–6
B.–5
C.5
D.7
The y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C
How to determine the coordinatesLet's the point that divides the line segment as point S.
We have that,
Point S divides the line segment into ratio 2:3
The ratio 2:3 means that we are to divide the line segment into;
= 2+3
= 5 equal parts.
We then have that the horizontal distance between the two coordinates is 5
The vertical distance between the two coordinates is 10
Now, let's divide both vertical and horizontal distance into five equal parts,
Horizontal distance = 5/5 = 1
Vertical distance = 10/ 5 = 2
The horizontal distance is 1
The vertical distance is 2
For every one unit move to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.
The coordinate of point S that divides the line segment into 2 parts and 3 parts is (-5,5)
Thus, the y- coordinate that divides the directed line segment from J to K into a ratio of 2:3 is 5. Option C
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s−3(s+6)= ASAP I NEED ANSWER PLEASE
Answer: −2(
Answer:
Simplified: −2s − 18
Step-by-step explanation:
Simplify the expression.
PQR has the vertical P(0,4), Q(4,5), and R(4,1). Determine if PQR is the right triangle.
Answer:
no
Step-by-step explanation:
no it is not a right triangle
two angles share the same x but no angles share the same y
you can see this clearly when graphed
the answer is no
I
. If the results of a probability experiment can be any integer from 16 to 18 and the
probability that the integer is less than 20 is 0.88, what is the probability that the
integer be 20 or more?
Using the probability concept, considering complementary probabilities, there is a 0.12 = 12% probability that the integer is of 20 or more.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
If two events are complementary, the sum of their probabilities is of 1. In this problem, we have that an integer being less than 20 is complementary to an integer being 20 or more.
We have that:
There is a 0.88 probability that the number is less than 20.There is a x probability that the number is 20 or more.These events are complementary, hence:
0.88 + x = 1
x = 1 - 0.88
x = 0.12
There is a 0.12 = 12% probability that the integer is of 20 or more.
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Cody earned 600 from delivering groceries last year. He deposited this money in an account that pays an interest rate of 2% compounded annually. What will be his balance after 20 years. pls answer asap
The balance that Cody earned after 20 years is 891.57. Using the compound interest formula, the required value is calculated.
How to calculate the compound interest?The compound interest is calculated by
[tex]A = P(1 + \frac{r}{n} )^n^t[/tex]
Where,
A - Total amount (Future value)
P - Principal amount (Initial value)
r - The rate of interest
n - Number of times compounded per 't'
t - Total number of years the money is invested
Calculation:It is given that,
P = 600
r = 2% = 0.02
t = 20 years
n = 1 (since the amount is compounded annually)
Then,
[tex]A=600(1+\frac{0.02}{1})^1^*^2^0[/tex]
= 600 (1 + 0.02)²⁰
= 600 (1.02)²⁰
= 891.57
Therefore, the balance after 20 years is 891.57.
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The average telephone bill in a locality is $70, with a standard deviation of $40. In a sample of 50 randomly selected phone connections, what is the probability that the sample average will exceed $75?
Using the normal distribution, there is a 0.1894 = 18.94% probability that the sample average will exceed $75.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 70, \sigma = 40, n = 50, s = \frac{40}{\sqrt{50}} = 5.66[/tex]
The probability that the sample average will exceed $75 is one subtracted by the p-value of Z when X = 75, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (75 - 70)/5.66
Z = 0.88
Z = 0.88 has a p-value of 0.8106.
1 - 0.8106 = 0.1894.
0.1894 = 18.94% probability that the sample average will exceed $75.
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At Indianapolis Motor Speedway, one lap is 2.5 miles in length. The average speed of an Indy racing car is 190 miles per hour.
15. Find the length of one lap in yards.
16. How many seconds would it take to complete one lap?
Answer:
15. 4400 yards
16. 47.4 seconds
Step-by-step explanation:
15. 1 mile = 1760 yards
2.5 miles:
2.5(1760) = 4400 yards
16. t = 2.5/190 = 0.013150 h
1 hour = (60)(60) = 3600 seconds
Then 1 lap take
=(0.013150)(3600) = 47.4 seconds
Hope this helps
Find the rational roots f(x) =3x3+ 2x2 + 3x + 6
The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)
How to determine the rational root of the function f(x)?The function is given as:
f(x) = 3x^3 + 2x^2 + 3x + 6
For a function P(x) such that
P(x) = ax^n +...... + b
The rational roots of the function p(x) are
Rational roots = ± Possible factors of b/Possible factors of a
In the function f(x), we have:
a = 3
b = 6
The factors of 3 and 6 are
a = 1 and 3
b = 1, 2, 3 and 6
So, we have:
Rational roots = ±(1, 2, 3, 6)/(1, 3)
Split the expression
Rational roots = ±(1, 2, 3, 6)/1 and ±(1, 2, 3, 6)/3
Evaluate the quotient
Rational roots = ±(1, 2, 3, 6, 1/3, 2/3, 1, 2)
Remove the repetition
Rational roots = ±(1, 2, 3, 6, 1/3, 2/3)
Hence, the rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)
The complete parameters are:
The function is given as:
f(x) = 3x^3 + 2x^2 + 3x + 6
The rational roots of f(x) = 3x^3 + 2x^2 + 3x + 6 are ±(1, 2, 3, 6, 1/3, 2/3)
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Dividends Per Share Seventy-Two Inc., a developer of radiology equipment, has stock outstanding as follows: 60,000 shares of cumulative preferred 3% stock, $20 par and 400,000 shares of $25 par common. During its first four years of operations, the following amounts were distributed as dividends: first year, $32,000; second year, $72,000; third year, $80,000; fourth year, $100,000. Determine the dividends per share on each class of stock for each of the four years. Round all answers to two decimal places. If no dividends are paid in a given year, enter "0.00".
The dividends per share on each class of stock for each of the four years for Seventy-Two Inc. are as follows:
Cumulative Preferred Stock:Year 1 Year 2 Year 3 Year 4
Distributed Dividends $32,000 $40,000 $36,000 $36,000
Outstanding shares 60,000 60,000 60,000 60,000
Dividend per share $0.53 $0.67 $0.60 $0.60
Common Stock:Year 1 Year 2 Year 3 Year 4
Distributed Dividends $0 $32,000 $44,000 $64,000
Outstanding shares 400,000 400,000 400,000 400,000
Dividend per share $0 $0.08 $0.11 $0.16
Data and Calculations:3% Cumulative Preferred Common Stock
Outstanding shares 60,000 400,000
Par Value $20 $25
Total value $1,200,000 $10,000,000
Annual dividend $36,000 ($1,200,000 x 3%)
Year 1 Year 2 Year 3 Year 4
Distributed Dividends $32,000 $72,000 $80,000 $100,000
Cumulative Preferred $32,000 $40,000 $36,000 $36,000
Common Stock $0 $32,000 $44,000 $64,000
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PLEASE HELP ASAP!!! ALSO PLEASE ADD A DESEND EXPLANATION!! Find the original price if the price was: $8a after 60% increase.
Answer: $3.2a
Step-by-step explanation: We need to decrease $8a by 60 percent because $8a is the price after a 60% increase. 8 x 6/10 is 48/10 which as a mixed number is 4 8/10 or 4.8. Now, we subtract 4.8 from 8 which yields our answer of 3.2.
Perform the following mathematical operation, and report the answer tot he correct number of significant figures 0.396/0.5
Answer:
answer 0.8
Step-by-step explanation:
Solution
0.396 has 3 significant digits
0.5 has 1 significant digit.
Therefore the answer should be 1 significant digit.
0.396 / 0.5 = 0.792
Rounded to 1 sig dig, the answer = 0.8
Attached as photo. Please help
By Euler's method the numerical approximate solution of the definite integral is 4.189 648.
How to estimate a definite integral by numerical methodsIn this problem we must make use of Euler's method to estimate the upper bound of a definite integral. Euler's method is a multi-step method, related to Runge-Kutta methods, used to estimate integral values numerically. By integral theorems of calculus we know that definite integrals are defined as follows:
∫ f(x) dx = F(b) - F(a) (1)
The steps of Euler's method are summarized below:
Define the function seen in the statement by the label f(x₀, y₀).Determine the different variables by the following formulas:The table for x, f(xₙ, yₙ) and y is shown in the image attached below. By direct subtraction we find that the numerical approximation of the definite integral is:
y(4) ≈ 4.189 648 - 0
y(4) ≈ 4.189 648
By Euler's method the numerical approximate solution of the definite integral is 4.189 648.
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the mth term of a sequence 3,6,12,24,48,....... is 1536 . find value of m .
please help need ans asap !
best answer with formula will be marked brainliest
Answer:
Step-by-step explanation:
look at the screenshot and explain your answer pls
Answer:
f(x) = g(x) + 9 because it is shifted 9 to the right
A tap discharges 30 litres of water in 2 minutes. How many minutes will it take for a container with a capacity of 80 litres to be completely filled?
this is a rate question. please dont use algebra! thanks
Answer:
5.3333333 or 5 [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
30 divided by 2 equals 15.
80 divided by 15 equals 5.3333333 or 5 [tex]\frac{1}{3}[/tex].
Cos3A ×cos2A =cos A ×cos 2A -sin4A×sin A=prove it
Answer:
Step-by-step explanation:
cosA×cos 2A-sin4A×sinA
=cosAcos2A-2sin2Acos2A sin A
=cos 2A(cosA-2sin2AsinA)
=cos 2A(cosA-2×2sinAcosAsin A)
=cos2A×cosA(1-4sin²A)
=cos 2AcosA(1-4(1-cos²A))
=cos2A×cosA(1-4+4cos²A)
=cos 2A(-3cosA+4cos³A)
=cos 2A(4cos³A-3cosA)
=cos 2A×cos3A
pls help
heather had some candy to give to her five children. she first took eight pieces for herself and then evenly divided the rest amount her children. each child received four pieces. with how many pieces did she start?
Answer: She started with 28 pieces of candy.
Step-by-step explanation: In the beginning of the question it says that heather took 8 pieces. Then she divided the rest evenly amongst her 5 kids. Each received 4, so that make the equation 8+(5x4) which gives us 8+(20). Or 8+20 which is 28.
Answer:
She started with 28 candies.
Explanation:
Let the total amount of candies be c
Build equation:
heather took out 8 candies for herself→ remaining: c - 8
then divided the remaining candies to her five children→ each gets: (c - 8)/5
Here given each gets 4 candies
So,
(c - 8)/5 = 4
c - 8 = 5(4)
c - 8 = 20
c = 20 + 8
c = 28
How many grams of the isotope remains after 90 days?
Answer:
84,08964 [gr.].
Step-by-step explanation:
for more details see in the attachment.
sinx + siny=a
cosx + cosy=b
Find cos(x+y/2)
Using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].
What are the formulas for (sin x + sin y) and (cos x + cos y)?The formula for the addition of two Sine functions ([tex]\sin x+\sin y[/tex]) is [tex]\sin x + \sin y = 2\sin\frac{x+y}{2}\cos\frac{x-y}{2}[/tex].The formula for the addition of two Cosine functions ([tex]\cos x+\cos y[/tex]) is [tex]\cos x + \cos y = 2\cos\frac{x+y}{2}\cos\frac{x-y}{2}[/tex].Given that
[tex]\sin x + \sin y = a\\\cos x + \cos y = b[/tex]
Then using the above formulas, we get:
[tex]2\sin\frac{x+y}{2}\cos\frac{x-y}{2}=a[/tex] (1)
[tex]2\cos\frac{x+y}{2}\cos\frac{x-y}{2}=b[/tex] (2)
Dividing the equation (1) by (2), we get:
[tex]\dfrac{\sin\dfrac{x+y}{2}}{\cos\frac{x-y}{2}}=\dfrac{a}{b}\\\Longrightarrow \tan\dfrac{x+y}{2}=\dfrac{a}{b}[/tex] (3)
Now, we know that [tex]\cos\theta=\dfrac{1}{\sqrt{1+\tan^2\theta}}[/tex].
Thus, using the above formula, we get from (3):
[tex]\cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\tan^2\dfrac{x+y}{2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{1}{\sqrt{1+\dfrac{a^2}{b^2}}}\\\Longrightarrow \cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex]
Therefore, using the addition rule of the Sine function and the Cosine function, we obtain [tex]\cos\dfrac{x+y}{2}=\dfrac{b}{\sqrt{a^2+b^2}}[/tex].
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7. Find (f•g)(x) for the pair of functions.
f(x)=x+1
g(x) = 4x - 11
(f•g)(x) =
Answer:
(f•g)(x) = 4x² -7x -11
Step-by-step explanation:
The product of the two functions is the product of their respective definitions.
(f•g)(x)(f•g)(x) = f(x)•g(x) = (x+1)•(4x -11)
= x(4x -11) +1(4x -11) . . . . . use the distributive property
= 4x² -11x +4x -11 . . . . . . . and again
(f•g)(x) = 4x² -7x -11 . . . . . collect terms
just need these 3 please and thanks in advance
The conclusion that can be made based on the hypothesis is:
1. It's a valid conclusion.
2. It is a valid conclusion.
3. It is a valid conclusion.
How to illustrate the information?According to the law of detachment, when the conditional and the hypothesis are true, the conclusion will be true.
Therefore, if 6x < 42, the value of x will also be less than 6. This is valid.
When an angle is more than 90°, it's an obtuse angle and since A is 103°, it's valid.
Also, the statement about the violin being a string instrument is logically valid.
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The set of all triples of real numbers with the standard vector
addition but with scalar multiplication defined by
k(x, y, z) = (k2
x,k2
y,k2
z)
The given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").
What is a vector space?A vector space can be defined as a space (set) which comprises vectors, whose elements can be added under the associative and commutative operation, and can be multiplied by scalars under the associative and distributive operation.
This ultimately implies that, a vector space must be comprised of at least one element, which is generally regarded as its zero vector and the smallest possible vector space.
For every element {u, v and w} in vector (V), and element {a and b} in vector (F), this 8th axiom must be satisfied in order to have a vector space:
(k + m)u = ku + mu
Note: The above axiom (k + m)u = ku + mu is generally referred to as the "distributivity of scalar multiplication with respect to field addition."
Given the following vector:
k(x, y, z) = {k²x, k²y, k²z}
If x₁ · x₂ ≥ 0, then, (kx₁) · (kx₁) = k²x₁y₁ ≥ 0 [Closed in scalar multiplication].
If x₁ · x₂ ≥ 0, x₂ · y₂ ≥ 0, then (x₁ + x₂) · (y₁ + y₂):
x₁y₁ + x₂y₂ + x₁y₂ + x₂y₁ < 0
x₁y₁ + x₂y₂ < -(x₁y₂ + x₂y₁) [Not closed in vector addition].
In conclusion, we can infer and logically deduce that the given operation is not a vector space because it fails axiom 8 ("distributivity of scalar multiplication with respect to field addition").
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Complete Question:
Determine whether each set equipped with the given operations is a vector space. For those that are not vector spaces identify the vector space axioms that fail.
The set of all triples of real numbers with the standard vector addition but with scalar multiplication defined by k(x, y, z) = {k²x, k²y, k²z}.
