Answer:
First, a rational number is defined as the quotient between two integer numbers, such that:
N = a/b
where a and b are integers.
Now, the axiom that we need to use is:
"The integers are closed under the multiplication".
this says that if we have two integers, x and y, their product is also an integer:
if x, y ∈ Z ⇒ x*y ∈ Z
So, if now we have two rational numbers:
a/b and c/d
where a, b, c, and d ∈ Z
then the product of those two can be written as:
(a/b)*(c/d) = (a*c)/(b*d)
And by the previous axiom, we know that a*c is an integer and b*d is also an integer, then:
(a*c)/(b*d)
is the quotient between two integers, then this is a rational number.
Find x. Assume that segments that appear tangent are tangent.
Answer:
27
Step-by-step explanation:
FE is tangent to the circle with center D at point E and DE is radius.
[tex] \therefore FE \perp DE \implies m\angle FED = 90\degree [/tex]
DE = x
DF = x + 18
FE = 36
By Pythagoras theorem:
[tex] DF^2 = DE^2 + FE^2 [/tex]
[tex] (x+18)^2 = x^2 + 36^2 [/tex]
[tex] x^2 + 36x + 324= x^2 + 1296[/tex]
[tex] 36x + 324= 1296[/tex]
[tex] 36x = 1296-324[/tex]
[tex] 36x = 972[/tex]
[tex] x = \frac{972}{36}[/tex]
[tex] x =27[/tex]
The value of x from the given figure, which is radius of a circle is 27 units.
From the given figure, FE=36 units, DE=x units and FD=x+18 units.
What is the angle formed with tangent and radius?Tangent and radius of a circle meet at 90°. If we draw a radius that meets the circumference at the same point, the angle between the radius and the tangent will always be exactly 90°.
Using Pythagoras theorem, we have
FD²=FE²+DE²
⇒ (x+18)²=36²+x²
⇒ x²+36x+324=1296+x²
⇒ 36x=1296-324
⇒ 36x=972
⇒ x=972/36
⇒ x=27 units
Hence, the value of x from the given figure, which is radius of a circle is 27 units.
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Evaluate the expression shown below and write your answer as a fraction in simplest form. 3 (-20 8 Answer: Submit Answer attempt 1 out of 2 O
Answer:
[tex] -\frac{1}{40} [/tex]
Step-by-step explanation:
To evaluate [tex] -\frac{3}{8} - (-\frac{7}{20}) [/tex], start by opening the bracket.
When opening the bracket, we would be multiplying negative sign by negative sign, which equal positive sign.
Thus,
[tex] -\frac{3}{8} + \frac{7}{20} [/tex]
Solve further by performing addition operation to make both fractions one
The common denominator of 8 and 20 is 40,
[tex] \frac{5(-3) +2(7)}{40} [/tex]
[tex] \frac{-15 + 14}{40} [/tex]
[tex] \frac{-1}{40} = -\frac{1}{40} [/tex]
The answer of given expression in simplest form is: [tex]\dfrac{-1}{40}\\[/tex]
The given expression is:
[tex]-\dfrac{3}{8} - (-\dfrac{7}{20})[/tex]
Multiplying negative sign with negative sign will result in positive sign of the latter term.
The simplification will be done as follows:
[tex]\\-\dfrac{3}{8} - (-\dfrac{7}{20})\\\\= -\dfrac{3}{8} + \dfrac{7}{20}\\\\=\dfrac{-3 \times 5 + 7 \times 2}{40}\\\\= -\dfrac{1}{40}\\[/tex]
In the above process, we the lcm of 8 and 20 was taken which is equal to 40.
Thus, the simplest form of the given expression is [tex]\dfrac{-1}{40}\\[/tex].
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If tan Θ=3/4, then evaluate 3sin Θ +2cos Θ
Answer:
[tex]3\sin\theta+2\cos\theta=\dfrac{17}{5}[/tex]
Step-by-step explanation:
Given that,
The value of [tex]\tan\theta=\dfrac{3}{4}[/tex]
We know that, [tex]\tan\theta=\dfrac{\text{perpendicular}}{\text{base}}[/tex]
[tex]H^2=B^2+P^2[/tex]
H is hypotenuse
[tex]H^2=3^2+4^2\\\\H=5[/tex]
[tex]\sin\theta=\dfrac{P}{H}\\\\=\dfrac{3}{5}[/tex]
And, [tex]\cos\theta=\dfrac{B}{H}=\dfrac{4}{5}[/tex]
So,
[tex]3\sin\theta+2\cos\theta=3\times \dfrac{3}{5}+2\times \dfrac{4}{5}\\\\=\dfrac{9}{5}+\dfrac{8}{5}\\\\=\dfrac{17}{5}[/tex]
So, the value is 17/5.
Sixty percent of the cost of the dining set is the same as one half the cost of the dining set decreased by $180. What is the cost of the dining set?
Answer:
The cost of the dining set = $200
Step-by-step explanation:
Let
Cost of the dining set=x
Sixty percent of the cost of the dining set
= 60% of x
=60/100 * x
= 0.6x
One half the cost of the dining set decreased by $180.
=1 1/2 of x - 180
= 1.5 * x - 180
= 1.5x - 180
Sixty percent of the cost of the dining set is the same as one half the cost of the dining set decreased by $180
0.6x = 1.5x - 180
Collect like terms
0.6x - 1.5x = -180
-0.9x = -180
Divide both sides by -0.9
x= -180 / -0.9
=200
x= $200
Check:
0.6x
= 0.6(200)
=120
1.5x - 180
=1.5(200) - 180
= 300 - 180
=120
Different amounts of force are applied to the same boat over several trials, and the acceleration is measured. In a graph of acceleration versus net force, what does the slope of the graph represent?
the speed of the boat <-- MY ANSWER
the inverse of the mass of the boat
the mass of the boat
the inverse of the speed of the boat
Thank you :)
Answer: The inverse mass of the boat (B)
Step-by-step explanation:
The relationship between force, mass and acceleration is: [tex]F = ma[/tex]. So, the slope of the graph represents the inverse of the mass of the boat.
From the question, we understand that the graph is acceleration vs net force.
This means that, the points on the graph will be:
[tex](F_1,a_1)[/tex] and [tex](F_2,a_2)[/tex]
The slope (m) of a linear graph is:
[tex]m =\frac{y_2 - y_1}{x_2 - x_1}[/tex]
In this case, it will be:
[tex]m =\frac{a_2 - a_1}{F_2 - F_1}[/tex] ---- slope
Recall that:
[tex]F = ma[/tex]
Make mass (m) the subject
[tex]m = \frac Fa[/tex]
See attachment for further explanation
Hence, the slope of the graph represents (b) the inverse of the mass of the boat
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zalman started solving 53 times 26 by breaking the problem into parts. Here is what he has done so far 50 times 20=1000 50 times 6=300 3 times 20= 60 what does he still need to multiply
Answer:
3 * 6 = 18
Step-by-step explanation:
53 * 26 =
= (50 + 3) * (20 + 6)
= 50 * 20 + 50 * 6 + 3 * 20 + 3 * 6
= 1000 + 300 + 60 + 18
Answer: 3 * 6 = 18
Call: Im(formula = Repair.Costs ~ Miles.Driven, data = Dataset) Residuals: Min 1Q Median 3Q Max -247.81 -144.68 29.07 64.89 343.86 Coefficients: Estimate (Intercept) 72.807562 Miles.Driven 0.009792 Std. Error 89.456108 0.001601 t value 0.814 6.117 Pr>It) 0.432 5.2e-05 *** Signif. codes: 0) ****' 0.001 '**'0.01 '*' 0.05'.'0.1''1 Residual standard error: 180.3 on 12 degrees of freedom Multiple R-squared: 0.7572, Adjusted R-squared: 0.7369 F-statistic: 37.42 on 1 and 12 DF, p-value: 5.2e-05
Using these regression results, what is the estimated repair cost on a car that has 74,000 miles on it?
Answer:
797.42
Step-by-step explanation:
Given the Output of a linear regression data using R;
From the result table;
Intercept = 72.807562
Gradient or slope = 0.009792
General form of a linear equation:
y = mx + c
Where y = response variable ; x = explanatory variable ; c = intercept and m = gradient / slope
Hence, the regression equation becomes :
y = 0.009792x + 72.807562
Using these regression results, what is the estimated repair cost on a car that has 74,000 miles on it?
x = 74,000
y = 0.009792(74000) + 72.807562
y = 724.608 + 72.807562
y = 797.42
Answer:
The estimated repair cost on a car that has 74,000 miles on it is $797.42.
Step-by-step explanation:
The statement: Im(formula = Repair.Costs ~ Miles.Driven, data = Dataset) implies that the variable "Repair.Costs" is the dependent variable and the variable "Miles.Driven" is the independent variable.
From the provided data the regression equation formed is:
[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]
Compute the estimated repair cost on a car that has 74,000 miles on it as follows:
[tex]\text{Repair.Costs}=72.807562+0.009792\cdot \text{Miles.Driven}[/tex]
[tex]=72.807562+0.009792\cdot 74000\\\\=72.807562+724.608\\\\=797.415562\\\\\approx 797.42[/tex]
Thus, the estimated repair cost on a car that has 74,000 miles on it is $797.42.
Simplify (5ab4c)(-abc2)
Answer: -5a²b⁵c³
Step-by-step explanation: 5ab⁴c can be thought of as 5a¹b⁴c¹ and in the second part of the problem, since there is no coefficient on -a¹b¹c², we can give it a coefficient of 1.
Now simply multiply the coefficients
and add the exponents to get -5a²b⁵c³.
is 7.401 larger or smaller then 7.04
Answer:
Larger
Step-by-step explanation:
Since, 7.401 > 7.04
Therefore, 7.401 is larger than 7.04.
Answer:
Larger.
7.401 = 7.40 (rounding)
7.40 > 7.04
Bye!
make h the subject A=1/2(a+c)h
Answer:
h = [tex]\frac{2A}{a+c}[/tex]
Step-by-step explanation:
Given
A = [tex]\frac{1}{2}[/tex](a + c)h
Multiply both sides by 2 to clear the fraction
2A = (a + c)h ( divide both sides by (a + c) )
[tex]\frac{2A}{a+c}[/tex] = h
Answer:
[see below]
Step-by-step explanation:
[tex]a = 1/2(a+c)h\\\\1/2(a+c)h = a\\\\2 * 1/2(a+c)h = a * 2\\\\h(a+c)=2a\\\\\frac{h(a+c)}{a+c}=\frac{2a}{a+c}; a \neq -c\\\\\boxed{h=\frac{2a}{a+c}; a \neq -c}[/tex]
Hope this helps.
y=3/2x+5 in standard form
Answer:
3x -2y = -5
Step-by-step explanation:
Standard form is ...
ax +by = c
where the leading coefficient (a, or b if a=0) is positive and a, b, c are mutually prime.
Multiplying the equation by 2 gives ...
2y = 3x +5
We can subtract 2y+5 to get standard form:
3x -2y = -5
An account earned interest of 5% per year. The beginning balance was $250. The equation t=log1.05E250 represents the situation, where t is the time in years and E is the ending balance.
Answer:
t=3 years
Step-by-step explanation:
t=log1.05E250
t= time in years
E= ending balance.
Interest=5% per year
Ending balance=$289.41
Note: write Log 1.05 as written in the question
t= log1.05 E/250
=log1.05 (289.41 / 250)
=Log 1.05 (1.15764)
=Log (1.15764) / log (1.05)
= 0.0636 / 0.0212
=3
Therefore,
t=3 years
Which are vertical angles?
O AFE and BFD
O BFC and DFE
O AFE and CFD
O BFC and EFA
Answer:
✔️AFE AND BFD
Step-by-step explanation:
vertical angles are angles are formed from a pair of intersecting lines. The vertical angles are angle AFE and BFD
What are vertical angles?These angles are formed from a pair of intersecting lines, The meet at a point X in a figure.
from the given figure, we need to find which of the angles are vertical angles. Since vertical angles are equal, hence the measure of this angles must be equal.
From the diagram, the vertical angles are angle AFE and BFD
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Graph the image of the given segment under a di6with scale factor -1/3 and center of dilatation (0,0). Line on graph is A (-6,9) B (-3,3) please explain to me how I solve this.
Answer:
A ' = (2, -3)
B ' = (1, -1)
See attached image below for the diagram
========================================================
Explanation:
Point A is originally at (-6, 9). It moves to A ' (2,-3) after applying the scale factor. This is because we basically multiply the scale factor (-1/3) by each coordinate of point A
-6 * (-1/3) = 2
9 * (-1/3) = -3
The negative scale factor is like a mirror in a way. Points in negative regions move to positive regions, and vice versa. Since |-1/3| = 1/3 is less than 1, this means the new point (2,-3) is closer to (0,0) compared to its original counterpart.
Point B follows the same idea
B(-3,3) moves to B ' (1, -1) after multiplying each coordinate by -1/3
-------------
Side note: The segment A'B' is 1/3 as long compared to segment AB.
g 3.23 Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it. (a) What is the probability that the first marble you draw is blue
Answer:
[tex]P(Blue) = 0.3[/tex]
Step-by-step explanation:
Given
Red = 5
Blue = 3
Orange = 2
Required
Probability that the first marble is Blue
First, the total number of marble has to be calculated;
[tex]Total = Red\ Marble + Blue\ Marble + Orange\ Marble[/tex]
[tex]Total = 5 + 3 + 2[/tex]
[tex]Total = 10[/tex]
The probability of Blue being the first is calculated as thus;
[tex]P(Blue) = \frac{n(Blue)}{Total}[/tex]
[tex]P(Blue) = \frac{3}{10}[/tex]
[tex]P(Blue) = 0.3[/tex]
Hence, the required probability is 0.3
I have a rectangular garden. I usually grow
carrots in 2/5 of my garden but I want to
take 1/4 of the carrots section to grow
strawberries. After I make this change, how
much of my whole garden will be
strawberries?
Answer:
[tex]\frac{1}{10}[/tex]
Step-by-step explanation:
If you originally have [tex]\frac{2}{5}[/tex] of your garden reserved for carrots, are taking [tex]\frac{1}{4}[/tex] of the carrot space ( [tex]\frac{2}{5}[/tex] ) for strawberries, then the total amount of your garden left for strawberries will be [tex]\frac{2}{5}\cdot\frac{1}{4}[/tex]
[tex]\frac{2}{5}\cdot\frac{1}{4} = \frac{2}{20}[/tex]
[tex]\frac{2}{20}[/tex] simplifies down to [tex]\frac{1}{10}[/tex].
Hope this helped!
For parts a through f., A denotes an mxn matrix. Determine whether each statement is true or false. Justify each answer. a. A null space is a vector space. Is this statement true or false?
A. True because the null space of an mx n matrix A is a subspace of Rm
B. False, a column space is a vector space, but a null space is not a vector space
C. False, a vector space is a null space, but a null space is not necessarily a vector space
D. True because the null space of an mxn matrix A is a subspace of Rn
Answer:
D. True because the null space of an m x n matrix A is a subspace of [tex]$R^n$[/tex]
Step-by-step explanation:
A null space is also the vector space.
We know that a null set satisfies the following properties of a vector space.
Now let [tex]$x,y \in Null (A), \alpha \in IR$[/tex] , then
[tex]A[\alpha x+y] = \alpha A(x)+ A(y) = \alpha . 0 + 0 = 0$[/tex]
Thus, [tex]$ \alpha x+y \in Null (A)$[/tex]
Hence, option (d) is true.
. Which category(s) does 75% belong? I. Real II. Whole III.Rational IV. Integer V. Irrational VI. Natural *
A. III and IV only
B. I and III only
C. I, II, IV, V, and VI only
D. I, II, III, IV, and VI only
E. I, II, and III
Answer: B.) 1 and 111 only
Real, rational
Step-by-step explanation: Real is an encompassing terms when defining numbers as it includes all integers, whole, rational and irrational numbers. Therefore 75% belondmgs to a category of real numbers.
75% which is equivalent to 75/100 is a rational number as it can be written in the form p/q . where both p and q are integers and q is not 0. This also means 75% is not an irrational number.
75% = 0.75 is neither a whole number nor an integer as it contains decimal.
75% is not a natural number as natural numbers are counting numbers starting from 1.
Order these from least to greatest. -13/8, -2.1, -26/13, -9/4 I know how to do this I'm just to lazy too and I want to chat.
Answer:
-9/4, 2.1, -26/13, -13/8
Step-by-step explanation:
10y-3(y+5) what’s the answer
Answer:
7y-15
Step-by-step explanation:
10y-3(y+5)
=10y-3y-15
=7y-15
Hope it helped :)
Which of the following is required by k-means clustering ? a. defined distance metric b. number of clusters c. initial guess of centroids d. all of the above
Answer:
d. all of the above
Step-by-step explanation:
K-means clustering is a term used to describe a technique of vector quantization, that attempts to partition "n" observations into "k" clusters whereby each observation refers to the cluster with the closest mean which represents a model of the cluster.
This implies that the K-means algorithm recognizes the "k" number of centroids, and then assigns every data point to the closest cluster while the centroids remain as small as possible.
Hence, the following is required of K-means clustering:
1. defined distance metric
2. number of clusters
3. initial guess of centroids
Therefore, in this case, the correct answer is option D: All of the above.
Write the rule that transforms p(x) into q(x), where q(x)=2p(x+3)−6
Answer: - A horizontal shift of 3 units to the left.
- A vertical dilation of factor 2.
- A vertical shift of 6 units down.
Step-by-step explanation:
Here we have 3 transformations:
I will start giving general cases for each transformation:
Horizontal shift.
When we have a function f(x), an horizontal shift to the right of N units (N positive) is written as:
g(x) = f(x - N)
So in our case, we have a shift to the LEFT of 3 units.
Vertical dilation/contraction.
A vertical dilation/contraction of factor A, is written as:
g(x) = A*f(x)
if A > 1, this is a dilation, if A < 1, this is a contraction.
In the case of our problem, we have A = 2.
Vertical shift:
A vertical shift is written as:
g(x) = f(x) + N.
If N is positive, we have a shift of N units up, if N is negative, we have a shift of N units down.
in this case, N = -6.
Then the transformations are:
q(x) = 2*p(x -(-3)) - 6
- A horizontal shift of 3 units to the left.
- A vertical dilation of factor 2.
- A vertical shift of 6 units down.
The length of the longer leg of a right triangle is 19 cm more than five times the length of the shorter leg. The length of the hypotenuse is 20 cm more than five times the length of the shorter leg. Find the side lengths of the triangle
Answer:
13 cm, 84 cm, 85 cm
Step-by-step explanation:
Let the sides of triangle are be a, b, c
a = x, b = 5x + 19, c = 5x + 20As per Pythagorean theorem:
c² = a² + b²(5x+20)² = (5x +19)² + x²25x² + 200x + 400 = 25x² + 190x + 361 + x²x² - 10x - 39 = 0Solving the quadratic equation we get:
x= 13Then:
a= 13 cmb = 5*13 +19 = 84 cmc= 5*13 + 20 = 85 cm24a + 72b - 40c what’s the answer can somebody help me I’m confused
Answer:
8⋅(3a+9b−5c)
Step-by-step explanation:
The equation in a simple form by using the greatest common factor is
8 ( 3a + 9b -5c ).
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.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The greatest common factor is the largest positive number which can be divided into given numbers evenly.
The expression will be simplified as below:-
E = 24a + 72b - 40c
Take the number 8 common from the expression.
E = 8 ( 3a + 9b -5c ).
Therefore, the equation in a simple form by using the greatest common factor is 8 ( 3a + 9b -5c ).
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X+y+z=1
X-2y+3z=2
X+z-5=0
x+y+z=1
x=1/(y+z)
1/(y+z)-2y+3z=2
1-2y²-2yz+3yz+3z²=2(y+z)
(1-2y²+yz+3z²)/2=y+z
z=(1-2y²+yz+3z²)/2 -y/1
z=(1-2y²+yz+3z²-2y)/2
Bank A charges $30 monthly fee for a check account bank B charges $15 a month How much would Keiko pay at each bank each month
Answer:
Keiko would pay $30 a month at bank A.
Keiko would pay $15 a month at bank B.
Both bank A and bank B combined would be $45 a month.
Step-by-step explanation:
Write an expression to match this situation and combine like terms: Ling has 4m pounds of flour. She buys another 2 packages of flour, each weighing m pounds. How much flour does ling have in terms of m?
Answer:
4m + 2m = 6m
Step-by-step explanation:
For a 7 1/2 hour day, Ed makes $90. How much does he make in 1 hour?
Answer:
he makes $12 an hour
Step-by-step explanation:
Ed makes $6 in one hour.
To find out how much Ed makes in one hour, we can divide the total amount he makes in a 7 1/2 hour day by the number of hours in a day.
First, let's convert 7 1/2 hours to a mixed fraction.
7 1/2 hours = 7 + 1/2 = 14/2 + 1/2 = 15/2 hours.
Now, we can calculate how much Ed makes per hour by dividing the total amount he makes ($90) by the number of hours (15/2):
Amount per hour = $90 ÷ (15/2) = $90 × (2/15) = $6.
Therefore, Ed makes $6 in one hour.
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the supplement of a 45 degree angle is
Answer:
135°
Step-by-step explanation:
The supplement of an angle is the measure in which, when combined with the previous angle, will total up to 180°. Since we already know the measure of 1, we can easily find the supplement, assuming [tex]x[/tex] is the supplement of 45.
[tex]45 + x = 180\\\\x = 180-45\\\\x=135[/tex]
Hope this helped!
can someone help me with this
if xy=4 then what is d²y/dx² × d²x/dy²
please read carefully there not the same so they don't equal one
Answer:
Actually, this is equal to 1.
Step-by-step explanation:
Hello, please consider the following.
First of all, we assume x and y different from 0.
[tex]xy=4\\\\y=\dfrac{4}{x}\\\\x=\dfrac{4}{x}\\\\\text{So}\\\\y'(x)=\dfrac{-4}{x^2}\\\\y''(x)=\dfrac{-4*(-2)}{x^3}=\dfrac{8}{x^3}\\\\x''(y)=\dfrac{8}{y^2}\\\\\text{So, we can conclude}[/tex]
[tex]\dfrac{d^2y}{dx^2}\cdot \dfrac{d^2x}{dy^2}=\dfrac{8}{x^3}\cdot\dfrac{8}{y^3}\\\\=\dfrac{64}{(xy)^3}\\\\\text{We replace xy by 4}\\\\=\dfrac{64}{4^3}\\\\=\dfrac{64}{64}\\\\=\large \boxed{\sf \bf \ 1 \ }[/tex]
Thank you