Answer:
y=8X
Explanation:
The ratio 13 to X = 13:X
The ratio 104 to y = 104:y
If they are equivalent, we have that:
[tex]13\colon X=104\colon y[/tex]We write the ratios in fraction form.
[tex]\frac{13}{X}=\frac{104}{y}[/tex]We then make y the subject of the equation.
[tex]\begin{gathered} 13y=104X \\ y=\frac{104X}{13} \end{gathered}[/tex]We can simplify further to get:
[tex]\begin{gathered} y=\frac{13\times8X}{13} \\ y=8X \end{gathered}[/tex]This is the equation that represents y in terms of X.
The solution set of which of the following equations is the set of real numbers that are 3 units from -2?
A |x+2|=3
B|x-2|=3
C |x+3|=-2
D |x-3|=2
E |x+3|=2
The solution set of real numbers that are 3 units from -2 is :
|x +2| = 3
What is a solution set?Any value of a variable that makes the specified equation true is referred to as a solution. A solution set is the collection of all variables that satisfy the equation. To find the solution set of an equation with a given domain, first plug each domain value into the equation to obtain the respective range values. Make ordered pairs out of these values and write them down as a set. That set is our solution.Here
Function : |x +2| = 3
since ,
|x +2| = 3 => x + 2 = 3 ∨ x + 2 = -3
x = 3 - 2 ∨ x = -3 - 2
x = 1 ∨ x = -5
| - 2 - 1 | = | -3| = 3
| -2 -(-5) | = | -2 + 5 | = 3.
To learn more about solution set refer to :
https://brainly.com/question/10588366
#SPJ13
ABCD is a quadrilateral
Work out the length of BC
Give your answer correct to 1 decimal place.
Using the law of cosines, the length of BC in the given quadrilateral is: 8.1 cm.
What is the Law of Cosines?The law of cosines that can be used to find the length of a side of a triangle with a known included angle and two sides is:
c² = a² + b² - 2 × a × b × Cos C.
Considering right triangle ABD,
BD = a
DC = b
BC = c
Use the Pythagorean theorem to find the length of BD in the quadrilateral as shown in the diagram:
BD = √(7.5² + 5²)
BD = √(7.5² + 5²)
BD = 9.0 cm
Use the law of cosines to find the length of BC:
BC² = BD² + DC² - 2 × BD × DC × Cos <BDC.
Substitute
BC² = 9.0² + 13² - 2 × 9.0 × 13 × Cos 38
BC² = 250 - 184.4
BC² = 65.6
BC = √65.6
BC = 8.1 cm
Learn more about the law of cosines on:
https://brainly.com/question/4372174
#SPJ1
what’s is the expression that is equivalent (x^2-3x)(4x^2+2x-9)?
4x^4-10x^3-15x^2+27x
(use foiling)
Por C?AnswerExample0 How many ways can 4 candy bars be chosenfrom a store that sells 30 candy bars?С27,4052 How many ways can 13 students line up for lunch?113 How many ways can you make a 3-letterarrangements out of the letters in the wordTRAPEZOID.4 How many ways can you choose 2 books from ashelf of 40 books-5 How many ways can 12 swimmers finish in first,second, and third place?.L11---How many ways can Mrs. Sullivan choose twostudents from 27 to help put away calculators atthe end of class?----1-111
1) How many ways can 4 candy bars be chosen from a store that sells 30 candy bars?
In this case we can combine 30 types of candy bars in a set of 4 bars.
This can be calculated as a combination of 30 in 4 with no repetition:
[tex]\begin{gathered} C(n,r)=\frac{n!}{(n-r)!r!} \\ C(30,4)=\frac{30!}{(30-4)!4!}=\frac{30!}{26!4!}=\frac{30\cdot29\cdot28\cdot27}{4\cdot3\cdot2\cdot1}=\frac{657720}{24}=27405 \end{gathered}[/tex]Answer: 27,405 possible combinations (C).
2) How many ways can 13 students line up for lunch?
In this case we have a permutation of 13 in 13 with no repetition.
We can calculate this as:
[tex]\begin{gathered} P(n,r)=\frac{n!}{(n-r)!} \\ P(13,13)=\frac{13!}{(13-13)!}=\frac{13!}{1}=6227020800 \end{gathered}[/tex]Answer: 6,227,020,85)00 possible permutations (P).
3) How many ways can you make a 3-letter arrangements out of the letters in the word TRAPEZOID.
In the word we have 9 letters with no repetition, so we have to calculate a permutation (as order matters) of 9 letters in 3 places.
We can calculate this as:
[tex]P(9,3)=\frac{9!}{(9-3)!}=\frac{9!}{6!}=9\cdot8\cdot7=504[/tex]Answer: 504 possible permutations (P).
4) How many ways can you choose 2 books from a shelf of 40 books.
In this case, the order does not matter, so it is a combination of 40 in 2.
This can be calculated as:
[tex]C(40,2)=\frac{40!}{(40-2)!2!}=\frac{40!}{38!2!}=\frac{40\cdot39}{2\cdot1}=\frac{1560}{2}=780[/tex]Answer: 780 possible combinations (C)
5) How many ways can 12 swimmers finish in first, second, and third place?
In this case, the order does matter, so we have a permutation of 12 in 3:
[tex]P(12,3)=\frac{12!}{(12-3)!}=\frac{12!}{9!}=12\cdot11\cdot10=1320[/tex]Answer: 1320 permutations (P)
6) How many ways can Mrs. Sullivan choose two students from 27 to help put away calculators at the end of class?
The order does not matter between the two students, so it is a combination of 27 in 2:
[tex]C(40,2)=\frac{27!}{25!2!}=\frac{27\cdot26}{2\cdot1}=351[/tex]Answer: 351 combinations (C)
PLEASE SHOW YOUR WORK THIS IS DO IN AN HOUR AND I HAVE TO SUMBIT A PHOTO OF THE WORK AND THE WORK PAGE PLEASE IN NEED OF HELP
Answer:
[tex]\frac{21}{2} * \frac{2}{21} = 1[/tex]10 1/2 as an improper fraction is [tex]\frac{21}{2}[/tex]
the reciprocal of 10 1/2 is [tex]\frac{2}{21}[/tex]
so [tex]\frac{21}{2} * \frac{2}{21} = 1[/tex]
below is an image of the rest of the answers
P.L.Z HELP. 50pts
Sal's Sandwich Shop sells wraps and sandwiches as part of its lunch specials. The profit on every sandwich is $2, and the profit on every wrap is $3. Sal made a profit of $1,470 from lunch specials last month. The equation 2x + 3y = 1,470 represents Sal's profits last month, where x is the number of sandwich lunch specials sold and y is the number of wrap lunch specials sold.
Change the equation to slope-intercept form. Identify the slope and y-intercept of the equation. Be sure to show all your work.
Slope-intercept form: y=-2/3=x+490 The slop is -2/3 and the y-intercept is unknown.
Describe how you would graph this line using the slope-intercept method. Be sure to write using complete sentences.
Write the equation in function notation. Explain what the graph of the function represents. Be sure to use complete sentences.
Graph the function. On the graph, make sure to label the intercepts. You may graph your equation by hand on a piece of paper and scan your work or you may use graphing technology.
Suppose Sal's total profit on lunch specials for the next month is $1,593. The profit amounts are the same: $2 for each sandwich and $3 for each wrap. In a paragraph of at least three complete sentences, explain how the graphs of the functions for the two months are similar and how they are different.
Answer:
[tex]y=-\dfrac{2}{3}x+490[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Given equation:
[tex]2x + 3y = 1470[/tex]
To change the equation to slope-intercept form, isolate y:
[tex]\implies 2x + 3y -2x=1470 -2x[/tex]
[tex]\implies 3y=-2x+1470[/tex]
[tex]\implies \dfrac{3y}{3}=\dfrac{-2x+1470}{3}[/tex]
[tex]\implies y=-\dfrac{2}{3}x+\dfrac{1470}{3}[/tex]
[tex]\implies y=-\dfrac{2}{3}x+490[/tex]
Therefore:
[tex]\textsf{Slope} =-\dfrac{2}{3}[/tex][tex]\textsf{$y$-intercept}=490[/tex]To graph this line with the slope-intercept method:
Plot the y-intercept at (0, 490).The slope gives us the change in y-values over the change in x-values (rise over run). Therefore, use the slope to plot the next few points by mapping 3 units to the right and 2 units down each time:To write the equation in function notation, replace the y-variable for f(x).
[tex]\implies f(x)=-\dfrac{2}{3}x+490[/tex]
The graph of the function represents:
The number of wrap lunch specials sold given the number of sandwich lunch specials sold.The y-intercept of the graph is (0, 490).
To find the x-intercept, set the function to zero and solve for x:
[tex]\implies -\dfrac{2}{3}x+490=0[/tex]
[tex]\implies -\dfrac{2}{3}x=-490[/tex]
[tex]\implies -2x=-1470[/tex]
[tex]\implies x=735[/tex]
Therefore, the x-intercept is (735, 0).
The graph of the function is attached.
If Sal's total profit on lunch specials for the next month is $1,593 (where the profit amounts are the same) the equation would be 2x + 3y = 1593 and the function would be:
[tex]g(x)= -\dfrac{2}{3}x+531[/tex]
As the coefficient of the x-variable has not changed, the slopes of the two functions are the same.
As the total profit has changed, the intercepts are different.
The y-intercept of the first function is (0, 490) and its x-intercept is (735, 0). Whereas the y-intercept of the second function is (0, 531) and its x-intercept is (796.5, 0).
HELP ME FIND X AND Y
<EOG =90° AS INDICATED IN THE DIAGRAM
<EOF+<FOG=<EOG(THEY MAKE THE ANGLE)
[tex]27 + 3y = 90 \\ 3y = 90 - 27 \\ 3y = 63 \\ \frac{3y}{3} = \frac{63}{3} \\ y= 21[/tex]
<AOB =180°( STRAIGHT LINE )
<AOE+EOF+<FOG+<GOB=<AOB(THWY MAKE THE ANGLE)
[tex]x + 27 + 3(21) + 8x + 18 = 180[/tex]
[tex]x + 27 + 63 + 8x + 18 = 180 \\ x + 8x + 27 + 63 + 18 = 180 \\ 9x - + 108 = 180 \\ 9x = 180 - 108 \\ 9x =72 \\ \frac{9x}{9} = \frac{72}{8} \\ x = 9[/tex]
ATTACHED IS THE SOLUTION
How much must be deposited today into the following account in order to have a $125,000 college fund in 16 years? Assume no additional deposits are made. An account with monthly compounding and an APR of 7.3%
The amount that must be deposited to get a final amount of
$ 125,000 is $ 26.34 .
What is compound interest and how is it calculated?
The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest.
Mathematically, A = P (1 + (R/n))^t
Given, the amount that will be developed after interest is laid
= A = $125,00
Also, number of years for which amount is loaned = n = 16 years
Annual Percentage Rate of the loan availed = R = 7.3
Frequency with which interest is paid out per year = 1
Following the formula established in the literature, we have:
125000 = P(1 + 7.3)⁴ ⇒ P = 125000/(1 + 7.3)⁴ ⇒ P = 125000/8.3⁴ = 26.34
Therefore, the amount that must be deposited to get a final amount of
$ 125,000 is $ 26.34 .
To learn more about this, tap on the link below:
https://brainly.com/question/24924853
#SPJ13
Write a number that satisfies the given condition. An integer between - 0.6 and 0.4. The integer between -0.6 and 0.4 is
Answer:
I think the answer is 0.
Step-by-step explanation:
-0.6,-0.5,-0.4,-0.3,-0.2,-0.1,0,0.1,0.2,0.3,0.4
Pls help will mark brainliest!!
Answer:
59 degrees(triangle on the right)
Step-by-step explanation:
The total degrees of a triangle is 180 so add 76+45=121.
180-121=59
Given m ||n, find the value of x and y.
Answer: The correct answer is x=18 and y=59
Step-by-step explanation:
Opposite angles are congruent:
(6x+13) = (7x-5)
Solve for x:
6x+13−7x=7x−5−7x
−x+13−13=−5−13
−x=−18
x=18
Plug x value in for y:
Y=180-(7x-5)
Y=180-(126-5)
Y=180-121
Y=59
In one of its Spring catalogs , Bean advertised footwear on 29 of its 192 catalog pages. Suppose we randomly survey 20 pages. We are interested in the number of pages that advertise footwear. Each page may be picked at most once.
A. In words, define the random variable X.
B. List the values that X may take on.
C. How many pages do you expect to advertise footwear on them ?
D. Calculate the standard deviation .
A) The random variable X is The number of pages that advertise footwear
B) X = 1, 2, 3.....20
C) On average 3.02 pages expect to advertise footwear on them
Bean advertised footwear on 29 of its 192 catalog pages.
we randomly survey 20 pages
the random variable X is
X = The number of pages that advertise footwear
It is given that 20 pages have been surveyed
so, X = 1, 2, 3.....20
The average value for binomial distribution can be calculated as follows
μ = np
= 20 (29/192)
= 580/192
=3.02
On average 3.02 pages expect to advertise footwear on them
Therefore, A) The random variable X is The number of pages that advertise footwear
B) X = 1, 2, 3.....20
C) On average 3.02 pages expect to advertise footwear on them
To learn more about probability refer here
https://brainly.com/question/251701
#SPJ1
quick Sarah is walking diagonally across a park as modeled by the equation y = x − 1. Suppose Marcus starts walking at the point (0, 9) so his path is perpendicular to Sarah's. At what point will Sarah's path and Marcus's path intersect?
The Sarah's path and Marcus path will intersect at the point (5,4) .
In the question ,
it is given that
the park is modeled by the equation y = x − 1 .
On comparing with the slope intercept form ,
we get
the slope as 1 .
Since both the paths are perpendicular ,
the slope for Marcus path is -1 .
hence the equation of line with slope -1 and passing through the point (0,9) is y = (-1)x + c
9 = (-1)0 + c
9 = c
so equation is y = (-1)x + 9
So to find the point of intersection , we solve both the equations .
Substituting y = x − 1 in y = (-1)x + 9 ,
we get
x − 1 = (-1)x + 9
x - 1 = -x + 9
x + x = 9 + 1
2x = 10
x = 5
So, y = 5 - 1 = 4
the point of intersection is (5,4) .
Therefore , The Sarah's path and Marcus path will intersect at the point (5,4) .
Learn more about Equations here
https://brainly.com/question/19700463
#SPJ1
In the diagram below line FG is // to line HI, and line segments BC and AD intersect at E.
The measure of angle GBE = 3x+20, and the measure angle ECD = x.
The values of the angle x in the line segments is 40 degrees.
How to find the measure of angle?When parallel lines are are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, linear angles, vertically opposite angles etc.
Therefore, the line FG is parallel to line HI. The line segment BC and AD are the transversal lines that cut across the parallel lines FG and HI.
Therefore,
3x + 20 + x = 180 (Same interior angles)
Same interior angles are supplementary. That is the angles sum up to 180 degrees.
Therefore,
3x + 20 + x = 180
4x + 20 = 180
4x = 160
divide both sides by 4
x = 160 / 4
x = 40 degrees
learn more on angles here: https://brainly.com/question/13873168
#SPJ1
Pls pls help due tomorrow!
If the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6
The equation is
y = -x
The slope intercept form
y = mx+b
Where m is the slope of the line
Comparing the slope intercept form and the given equation
Slope of the line m = -1
The line is passing through the points (-8,2)
The point slope form of the line
[tex](y-y_1)=m(x-x_1)[/tex]
Substitute the values in the equation
y-2 = -1(x-(-8))
y-2 = -1(x+8)
y-2 = -x-8
y = -x-8+2
y = -x-6
Hence, if the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6
Learn more about slope intercept form here
brainly.com/question/9682526
#SPJ1
Does this graph represent a function? Why or why not
x-3 divided by x^2 + 5x + 2
Answer:
[tex]6x - \frac{3}{X^2} + 2[/tex]
Step-by-step explanation:
Hope this is correct and helps you! :))
this exercise refers to choosing two cards from a thoroughly shuffled deck. assume that the deck is shuffled after a card is returned to the deck. if you do not put the first card back in the deck before you draw the next, what is the probability that the first card is a 10 and the second card is a jack?
Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.
Solve the problem?
Given that a card is selected from a 52-card deck that has been thoroughly shuffled without being replaced, the following card is drawn.
A: The top card is a 4, and B: The next card is an ace.
Probability =A∩B
After this first card is pulled, if 10is drawn, we have 51 cards left with 4 aces in them. This is the probability we need to discover for
P(A). = 10/52
P(B) = number of aces in 51 cards divided by 51, thus = 4/51
Hence A∩B =10/52×10/51
= 100/2652
(From this, we can see that, after changing the card count, A and B are independent.
Additionally, we multiply the probability for both.)
To learn more about probability refer
https://brainly.com/question/13406107
#SPJ4
Use the figure to find measures of the numbered angles.
The measure of the numbered angles formed by the common transversal to the two parallel lines are;
[tex] \angle 1 = 113^{ \circ} [/tex]
[tex] \angle 2 = 67^{ \circ} [/tex]
[tex] \angle 3 = 67^{ \circ}[/tex]
[tex]\angle 4 = 113^{ \circ} [/tex]
What are the relationships between the angles formed by the common transversal to two parallel lines?The relationships between the angles are;
Corresponding angles are congruentVertical angles are congruentSame side exterior angles are supplementarySame side interior angles are supplementaryAlternate interior angles are congruentAlternate exterior angles are congruentThe given angle is 113°
According to corresponding angles theorem, we have;
[tex] \angle 1 = 113^{ \circ} [/tex]
[tex]\angle 1 \: and \: \angle 4 [/tex] are vertical angles
According to vertical angles theorem, we have;
[tex]\angle 1 = \angle 4 = 113^{ \circ} [/tex]
[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are same side exterior angles.
According to same side exterior angles theorem, we have;
[tex] \angle 3 \: and \: 113^{ \circ} [/tex] are supplementary angles. Which gives;
[tex] \angle 3 + 113^{ \circ} = 180^{ \circ} [/tex]
[tex] \angle 3 = 180^{ \circ} - 113^{ \circ} = 67^{ \circ}[/tex]
[tex] \angle 2 \: and \: \angle 3 [/tex] are vertical angles, which gives;
[tex] \angle 2 = \angle 3 [/tex] = 67°
Learn more about the angles formed by two parallel lines that have a common transversal here:
https://brainly.com/question/1751268
#SPJ1
4x - 7<-27 or 29 4x - 7
Answer:x= 1/4=0.250
Step-by-step explanation:
The volume of this cube is 27 cubic centimeters. What is the value of p?P=___centimeters
a student reflects four point across the y ax is and recorded his work
Reflection across the y axis the y coordinate values remains the same but the x coordinates value changes sign. For example
[tex](x,y)\rightarrow(-x,y)[/tex]Therefore,
[tex]\begin{gathered} (6,8)\rightarrow(-6,8) \\ (1,1)\rightarrow(-1,1) \\ (0,3)\rightarrow(0,3) \\ (3,2)\rightarrow(-3,2) \end{gathered}[/tex]Set D has an error.
- What is the perimeter of a right triangle witha hypotenuse that measures 6 square root 5 cm and onealeg that measures 4 square root 5 cm
Which integer is the farthest from the origin on a number line? A. -11 O B.-1 Oc. O D. 10
In order to determine the farthest integer related to the origin ona a number line, apply the absolute value of the given numbers, this gives you the distance of the specific number to the origin.
The absolute value of a number, negative or positive, is always equal to the same positive number.
Then,for the given asnwer choices you have:
|-11| = 11 where the bars |-11| expresses absolute
PLEASE HELP ME ASAP :,)
Answer:
154 feet squared
Step-by-step explanation:
1. Divide 14 by 2
2. Use the equation pie times radius squared
3. Answer is 153 foot squared
A $350,000 house is assessed at % of its value. If the yearly tax rate is $3.25 per hundred of assessed value, what is the yearly tax on this property?
F. $2,275
G. $1,600
H. $5,687
J. $6,405
K. $8,000
Given the circle below, find the value of x.251L (9x+26)*
Given the following:
Then:
[tex]a=\frac{b-c}{2}[/tex]In this case, we are given:
a = (9x + 26)
b = 251
To find c, we rest a whole circle (360) and rest angle b:
[tex]c=360-251=109[/tex]And now, we use the formula from above:
[tex]9x+26=\frac{251-109}{2}[/tex]And solve for x:
[tex]\begin{gathered} 9x+26=\frac{142}{2} \\ . \\ 9x=71-26 \\ . \\ x=\frac{45}{9} \\ . \\ x=5 \end{gathered}[/tex]The answer is the last option, x = 5
determine the equation of the line from the graph
Answer:
y = -x + 1
Step-by-step explanation:
y =mx + b
It is crossing the y axis at 1 that is the b
The slope (m) is -1. From one point on the line to another you go down 1 and left 1. That represents a negative slope of 1
Please help me on this question need it by today
The measures of the interior angles of four regular polygons are shown below. Which expression best represents the measure in degrees of the interior angle of a regular polygon having n sides?
ANSWER
[tex]\frac{180(n-2)}{n}[/tex]EXPLANATION
We want to find the expression that best represents the measure of the interior angle of a regular polygon with n sides.
The general formula for finding the total angle in a regular n sided polygon is given as:
[tex]180(n-2)[/tex]Therefore, to find the measure of each interior angle of the polygon, we have to divide the total angle by the number of sides.
That is:
[tex]\frac{180(n-2)}{n}[/tex]Hence, that is the expression that best represents the measure in degrees of the interior angle of a regular polygon having n sides.
