Answers
Answer:
3x + 5y = 15
Find gradient:
coordinates taken: (5, 0), (0, 3)
[tex]\rightarrow \sf \dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\rightarrow \sf \dfrac{3-0}{0-5}[/tex]
[tex]\rightarrow \sf -\dfrac{3}{5}[/tex]
Here the y-intercept: 3gradient: -3/5
equation:
[tex]\sf \bold{ y = m(x) + b}[/tex]
[tex]\rightarrow \sf y = -\dfrac{3}{5} x + 3[/tex]
[tex]\rightarrow \sf y = -\dfrac{3}{5} x + \dfrac{15}{5}[/tex]
[tex]\rightarrow \sf 5y =-3x+15[/tex]
[tex]\rightarrow \sf 3x+5y =15[/tex]
Take two points
(0,3)(5,0)x intercept=a=5y intercept=b=3So
equation of line in intercept form
[tex]\\ \rm\rightarrowtail \dfrac{x}{a}+\dfrac{y}{b}=1[/tex]
[tex]\\ \rm\rightarrowtail \dfrac{x}{5}+\dfrac{y}{3}=1[/tex]
Multiply each by 15[tex]\\ \rm\rightarrowtail 3x+5y=15[/tex]
Related Questions
-5x-21 find value of x
Answers
Answer:
The value of x = -21/5
Step-by-step explanation:
=> -5x-21 =0
=> -21 = 5x
=> -21/5 = x
Answer:
Step-by-step explanation:
you want to set the equation equal to 0
-5x - 21 = 0
add 21 to both sides to get the variable by itself
-5x = 21
divide both sides by -5
x = - 21/5
If x = 2and y = - 2 , find the value of 4x ^ 2 * y ^ - 2
Answers
=========================================================
Plug in the values of the variables & simplify:-
[tex]\longrightarrow\pmb{4x^2y^2}[/tex]
The values of the variables are:-
[tex]\bigstar{\boxed{x=2~and~y=-2}[/tex]
Simplify:-
[tex]\longrightarrow\pmb{4(2)^2(-2)^2}[/tex]
[tex]\longrightarrow\pmb{4*4-4}[/tex]
[tex]\longrightarrow\pmb{16-4}[/tex]
[tex]\longrightarrow\pmb{12}[/tex]
==========================================================
note:-Hope everything is clear; if you need any clarification/explanation, kindly let me know, and I'll comment and/or edit my answer :)
Answer:
the answer for this is 4.
X + 4y = 7 4x - 3y = 9 equivalent equation and solution
Answers
Answer:
x = 3, y = 1
Step-by-step explanation:
Given:
[tex]\begin{bmatrix}x+4y=7\\ 4x-3y=9\end{bmatrix}[/tex]
Solve:
[tex]\mathrm{Substitute\:}x=7-4y[/tex]
[tex]\begin{bmatrix}4\left(7-4y\right)-3y=9\end{bmatrix}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\begin{bmatrix}28-19y=9\end{bmatrix}[/tex]
[tex]\mathrm{For\:}x=7-4y[/tex]
[tex]\mathrm{Substitute\:}y=1[/tex]
[tex]x=7-4\cdot \:1[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x=3[/tex]
[tex]\mathrm{The\:Answer\:to\:the\:system\:of\:equations\:are:}[/tex]
[tex]x=3,y=1[/tex]
Check Answer:
3 + 4(1)
7 (1) = 7
True
4(3) - 3(1)
12 - 3 = 9
True
Hence, x = 3 , y =1
~lenvy~
∠C and ∠D are complementary.
Let m∠C=(8x)° and m∠D=(5x−1)°.
What is the value of x?
Enter your answer in the box.
x =
Answers
Answer:
x = 7Step-by-step explanation:
Complementary angles are angles that add up to 90°.
We have C and D as complementary.
Their sum is:
m∠C + m∠D = 90Substitute values and solve for x:
8x + 5x - 1 = 9013x = 90 + 113x = 91x = 91/13x = 7Answer:
x = 7
Step-by-step explanation:
Complementary angles are two angles that sum up to 90°. In this case, we are given that ∠C and ∠D are complementary. This means that the sum of ∠C and ∠D is equivalent to 90°.
⇒ ∠C + ∠D = 90°
⇒ 8x + 5x - 1 = 90° [∠C = 8x; ∠D = 5x - 1]
⇒ 13x - 1 = 90°
⇒ 13x = 90 + 1
⇒ 13x = 91
⇒ 13x/13 = 91/13
⇒ x = 91/13 = 7
A rental car company charges $36.39 per day to rent a car and $0.09 for every mile
driven. Miguel wants to rent a car, knowing that:
He plans to drive 225 miles.
• He has at most $480 to spend.
Which inequality can be used to determine x, the maximum number of days Miguel
can afford to rent for while staying within his budget?
Answers
Answer:
12 days
Explanation:
480 >/= 36.39x + 20.25
The inequality to determine x, the maximum number of days Miguel
can afford to rent while staying within his budget is
202.5 + 36.39x ≤ 480
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Charges per day = $36.39
Charges per mile = $0.90
Total miles = 225
Total charges for 225 miles.
= 225 x 0.90
= $202.5
The maximum amount to spend = $480
The inequality for the maximum number of x days.
202.5 + 36.39x ≤ 480
Thus,
The inequality to determine x, the maximum number of days is
202.5 + 36.39x ≤ 480
Learn more about inequalities here:
https://brainly.com/question/20383699
#SPJ2
Select the expression that represents the following problem: A glass hols 1/4 liter of liquid. How many glasses of liquid are in 5 liters
Answers
1 glass..........1/4 liter
n glass.......... 5 liters
n = 1 x 5 : 1/4
n = 5 x 4
so there are 20 glasses
Solve the system of equations by substitution. X + y = 32 y = 7x The solution of the system is (Simplify your answer. Type an ordered pair.)
if you can can you please write out the steps
Answers
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
Let's solve ~
The given equations are :
[tex]\qquad \sf \dashrightarrow \:x + y = 32[/tex]
and
[tex]\qquad \sf \dashrightarrow \:y = 7x[/tex]
Now, plug in the value of y from equation 2 into equation 1 to find out the value of x ~
[tex]\qquad \sf \dashrightarrow \:x + y = 32[/tex]
[tex]\qquad \sf \dashrightarrow \:x + 7x = 32[/tex]
[tex]\qquad \sf \dashrightarrow \:8x = 32[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 32 \div 8[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 4[/tex]
Now, plug the value of x in equation 2 to find y
[tex]\qquad \sf \dashrightarrow \:y = 7x[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 7 \times 4[/tex]
[tex]\qquad \sf \dashrightarrow \:y = 28[/tex]
➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖
Ken wants to build a table and put a border around it. The table and border must have an area of 3,276 square inches. The table is 36 inches wide and 72 inches long without the border. Which quadratic equation can be used to determine the thickness of the border, x? 4x2 216x 2,592 = 0 4x2 216x − 684 = 0 2x2 216x − 3,276 = 0 x2 108x 3,276 = 0.
Answers
The quadratic equation that can be used to represent the thickness of the border is 4x²+18x-3258=0.
What is a quadratic equation?A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.
It is written in the form of ax²+bx+c.
As it is given that the length and the width of the centre area are 72 inches and 36 inches, respectively. When the dimensions of the centre area are converted into the feets, it will be,
[tex]\rm Length = \dfrac{72\ inches}{12} = 6\ feet[/tex]
[tex]\rm Width= \dfrac{36\ inches}{12} = 3\ feet[/tex]
If we take the borders of the table into account, the length and the breadth of the table will become,
Length = (6+x+x) = (6+2x)
Width = (3+x+x) = (3+2x)
We know that the area of a rectangle is given as the product of the length and width, and also it is mentioned that the area of the entire table is 3,276 square feet. Therefore, the area of the table can be written as,
[tex]{\rm Area=Length \times Width}\\\\3276 = (6+2x)(3+2x)\\\\3276= 18+ 12x+ 6x + 4x^2\\\\4x^2+18x+18-3276=0\\\\4x^2+18x-3258=0\\[/tex]
Thus, the quadratic equation that can be used to represent the thickness of the border is 4x²+18x-3258=0.
Learn more about Quadratic Equation:
https://brainly.com/question/2263981
please help!! it is due today and i will give 50 points
Answers
Answer:
E) 36 ft²
Step-by-step explanation:
Formulae
Area of a triangle = 1/2 x base x heightArea of a rectangle = width x lengthThe shape is made up of 2 congruent triangles and 3 different rectangles.
Area of triangle = 1/2 x 3 x 4 = 6 ft²
Area of rectangle 1 = 2 x 4 = 8 ft²
Area of rectangle 2 = 2 x 3 = 6 ft²
To calculate the area of the 3rd triangle, we need to use Pythagoras' Theorem to determine the length of the hypotenuse of the right triangle.
a² + b² = c²
⇒ 3² + 4² = c²
⇒ 25 = c²
⇒ c = √(25)
⇒ c = 5 ft
Therefore, area of rectangle 3 = 2 x 5 = 10 ft²
Total Surface Area
Total SA = 2 triangles + rectangle 1 + rectangle 2 + rectangle 3
= (2 x 6) + 8 + 6 + 10
= 36 ft²
Which of the following linear equations represents the data chart?
Answers
Answer:
option C
Step-by-step explanation:
y = -x + 7
Hope this helps you
need some help with these questions in the image
Answers
a. answer:_77
2_ (7 * 9) _ 16
2_ (63) _16
_61_16
_77
1. What is the magnitude and direction of RS with tail and head points R(4, -6) and S(-2, 1)?
a.9.2 units, 49.4° south of east
b.10.4 units, 40.6 ° south of east
c.9.2 units, 49.4 ° north of west
d. 10.4 units, 40.6 ° north of west
Answers
The magnitude and the direction of the vector formed by (4, 6) and (-2, 1) are [tex]\sqrt{85}[/tex] (approx. 9.2 units) and 49.4° north of west. (Correct choice: C)
How to find the magnitude and the direction of a vectorFirst, we need to determine the expression of [tex]\overrightarrow {RS}[/tex] by vector sum:
[tex]\overrightarrow{RS} = S(x,y) - R(x,y)[/tex]
[tex]\overrightarrow{RS} = (-2, 1) - (4, -6)[/tex]
[tex]\overrightarrow {RS} = (-6, 7)[/tex]
The magnitude and the direction of the vector are determined by Pythagorean theorem and inverse trigonometric functions, respectively:
Magnitude[tex]\|\overrightarrow{RS}\| = \sqrt{(-6)^{2}+7^{2}}[/tex]
[tex]\|\overrightarrow{RS} \| = \sqrt{85}[/tex]
Directionθ = tan⁻¹ (7/-6)
θ ≈ 130.601°
The magnitude and the direction of the vector formed by (4, 6) and (-2, 1) are [tex]\sqrt{85}[/tex] (approx. 9.2 units) and 49.4° north of west. (Correct choice: C) [tex]\blacksquare[/tex]
To learn more on vectors, we kindly invite to check this verified question: https://brainly.com/question/13322477
(Little tricky; worth extra points )
Which series of transformations shows that pentagon A is congruent to Pentagon B?
A. Reflect pentagon A over the y-axis, rotate it 180 degrees clockwise about the origin, and translate it 3 units up
B. Rotate pentagon A 90 degrees clockwise about the point (1,1) reflect it over the x-axis, and translate it 3 units to the left.
C. Rotate pentagon A 90 degrees clockwise about the origin, reflect it over the x- axis, and translate it 6 units to the left.
D. Reflect pentagon A over the y-axis and translate it 2 units to the left and 8 units up.
Answers
Answer:
i am pretty sure it's A or B
Step-by-step explanation:
hope this helps
→(·°ω°·)←
sin^-1(√3-1/2√2)
please give me answer
Answers
use a calculator and the correct answer is 0.019134405
and then round off the that answer into 2 significant number
sin^-1(√3-1/2√2)
please give me answer
A number line going from negative 10 to positive 10. Use the number line to help you answer the question. Which statements are true? Check all that apply. –4 < –8 |–4| < |–8| |–5| > 1 –5 > |1| |–2| = |2|
Answers
Answer:
2. |-4| < |-8|
3. |-5| > 1
5. |-2| = |2|
Answer:
2,3,5 are correct
Step-by-step explanation:
i took the test
A shop increases all their prices by 9% A picture frame increases by £153 Find the new price of the picture frame.
Answers
The new price of the picture frame is £1853
Discounts and incrementsGiven the following parameters
Percentage increase = 9%
Increment = £153
Determine the original value if the frame
9% of x = £153
0.09x = £153
x = £153/0.09
x = £1700
New price = £1700 + £153
New price = £1853
Hence the new price of the picture frame is £1853
Learn more on discount here; https://brainly.com/question/1548141
Evaluate the quotient of 1.05 x 103and 1 x 103:
1.05 x 10 -6
1.05 x 10 9
1.05 x 10 6
1.05 x 10 0
Answers
Answer:
1.05 x 10^0.
Step-by-step explanation:
1.05 x 10^3 / 1 x 10^3
= 1.05/1 x 10^(3-3)
= 1.05 x 10^0
Will choose Brainliest.
Jessica and Martha each have a bag of cookies with unequal quantities. They have 30 cookies total between the two of them. Each of them ate 6 cookies from their bag. The product of the number of cookies left in each bag is not more than 80.
How many more cookies will Jessica have than Martha?
If x represents the number of cookies Jessica started with, complete the statements below.
The inequality that describes the relationship between the number of cookies each one of them has is x^2- _ x + 224 ≥ 0
Jessica has at least
_ cookies more than Martha.
Answers
That part is total cookies as per algebraic formula x^2-(a+b)x+ab=0
Hence
The inequality is
[tex]\\ \rm\rightarrowtail x^2-30x+224>=0[/tex]
[tex]\\ \rm\rightarrowtail (x-14)(x-16)>=0[/tex]
[tex]\\ \rm\rightarrowtail 14\leqslant x\leqslant 16[/tex]
Solution range
[14,16]Atleast means the range
16-142Atleast 2 more than Martha
Find the measure of
Answers
Explanation: the ) like marking in both symbolizes that both
convert 0.001 * km ^ 3 into m ^ 3
Answers
Answer:
[tex]1,000,000 \: {m}^{3} [/tex]
Step-by-step explanation:
[tex]0.001 \: {km}^{3} \\ \\ = 0.001 \times {(1000)}^{3} \\ \\ = 0.001 \times 1,000,000,000 \\ \\ = 1,000,000 \: {m}^{3} [/tex]
The coach of Darnel's baseball team recorded how many runs the team scored in each game last season. This box plot shows the results. please
Answers
The fraction of the game that Daniel's team scores 2 or more runs is 1/4 of the game.
What are box plots?A box plot is used to study the distribution and level of a set of scores. Scores are distributed into 4 groups. Each group has a value of 25%
The first quartile, is the first line on the box. The first quartile represents 1/4 of the score.
To learn more about box plots, please check: https://brainly.com/question/27215146
type of angle that has the sallest measure
Answers
Answer: acute angle
Step-by-step explanation: acute angle is the smallest starting from 0 to 90 DDegrees .
HELP ME PLS. brainy reward it is about hangers.
The Problem: 20/3x = 5(x+1/2) + 4/3
20/3 , 1/2 , 4/3 are fractions. Solve for x
Answers
Answer:
x=23/10
Step-by-step explanation:
the dash is a fraction
PLS HELP WILL MARK YOU BRAINLIEST! NO FAKE ANSWERS! A local grocery store released the following statistics on the average volume of products sold per month in its two branches over the past six months.
Answers
Answer:
a. House hold laundry
b. Beverages
c. Snacks
Step-by-step explanation:
Do mark brainliest.
#a
For branch A
Household laundryFor branch B
Snacks#b
For branch A
snacksFor branch B
Canned goods#c
Branch A
20+25+15+28+20108Branch B
20+18+30+23+20111Branch B performed better
Graph a rectangle with an area of 12 square units. State the lengths of each of the sides. Write your answer LxW (length of one side X length of the other side) please help
Answers
A rectangle with area of 12 square units would have sides of length 4 units and 3 units. Area would therefore be 4 x 5.
What are the side lengths of this rectangle?A rectangle must be such that one side is longer than the other side.
The area of a rectangle is found as:
= Length x Width
As the area is 12, the length and width have to be numbers that when multiplied, will give you 12.
The factors of 12 which allow this to happen are:
= 1, 2, 3, 4, 6, 12
From here you can use 3 and 4.
Find out more on the area of a rectangle at https://brainly.com/question/2607596.
Inscribed angle
Help please
Answers
Answer:
x = 3
Step-by-step explanation:
The measure of the inscribed angle is half of measure of the intercepted arc .
Find the half of 192.
192/2 = 96
The inscribed angle is 96°.
Create an equation and solve for x.
31x + 3 = 96
31x + 3 - 3 = 96 - 3
31X = 93
31x/31 = 93/31
x = 3
Please help me yall I am so done with hw
Answers
Cities are pretty far from each other so you would have to use miles
Answer: the answer is d which is Miles .
Step-by-step explanation: it is Miles because there is a far distance bbetween Cities .HOPE IT HELPS YOU .PLEASE GIVE BRAINLIEST . THANKS .
How you should answer:
1. Known:
2.Unknown:
3.Rationle:
4.Equation and Solution:
Steps on how to answer:
-State the known
-State the unknown and represent it with a variable
-Provide a rationale for your approach
-Include the equation, exact answer, and decimal approximation
Answers
Question 1
Focus on the triangle on the left.
sine is the ratio of opposite over hypotenuse
sin(angle) = opposite/hypotenuse
sin(44) = w/30
w = 30*sin(44)
w = 20.839751 approximately
Now move onto the triangle on the right. We'll use cosine this time.
cos(angle) = adjacent/hypotenuse
cos(x) = w/45
cos(x) = 20.839751/45
cos(x) = 0.463106
x = arccos(0.463106) ... arccosine is the same as [tex]\cos^{-1}[/tex]
x = 62.412286
Answers:w = 20.839751 approximatelyx = 62.412286 approximately==========================================================
Question 2
Focus on the triangle on the left.
sin(angle) = opposite/hypotenuse
sin(32) = w/5
w = 5*sin(32)
w = 2.649596
Now move to the triangle on the right.
sin(angle) = opposite/hypotenuse
sin(x) = w/5
sin(x) = 2.649596/5
sin(x) = 0.5299192
x = arcsin(0.5299192) .... arcsine is the same as [tex]\sin^{-1}[/tex]
x = 31.999996
Answers:w = 2.649596 approximatelyx = 31.999996 approximately==========================================================
Question 3
This time we use the tangent ratio.
Focus on the triangle that has legs of w and 16.
tan(angle) = opposite/adjacent
tan(70) = 16/w
w*tan(70) = 16
w = 16/tan(70)
w = 5.823524
Now let y = x+w and focus on the largest triangle this time.
tan(angle) = opposite/adjacent
tan(41) = 16/y
y = 16/tan(41)
y = 18.405895
This leads to:
y = x+w
x = y-w
x = 18.405895 - 5.823524
x = 12.582371
Answers:w = 5.823524 approximatelyx = 12.582371 approximatelyThe students in a class collected data on the number of minutes some of them spend
brushing their teeth every day. That data is shown in the dot plot below.
What was the median number of minutes students brushed
their teeth?
Answers
Answer:
2.5
Step-by-step explanation:
BASED ON GIVEN DATA:
⇒ 2 STUDENTS SPENT 2.5 (2 1/2) MINUTES
⇒ 1 STUDENT SPENT 3 MINUTES
⇒ 1 STUDENT SPENT 4.5 MINUTES
THE MOST COMMON AMOUNT OF TIME TAKEN IS 2.5 MINUTES BECAUSE OF THE 2 STUDENTS.
Answer: 0.5 minutes
Step-by-step explanation:
If there are 40% of girls and 250 are boys, find
(i) the total number of students
(ii) the number of girls.
Answers
Step-by-step answer:
If there are 40% students that are girls , and the rest are 250 boys. Then that must mean there are 60% boys. Because that is the compliment.
i)
Because we know that 60% of the people in the group are boys, and that the amount of boys amounts to 250, we can model an equation like this.
[tex]Total * 0.6 = 250[/tex].
[tex]Total = 250/0.6[/tex]
[tex]Total = 417[/tex]
There are 417 students
ii)
Because we know that the total amount is 417, we can find the amount of girls there are by multiplying the total by the percentage.
[tex]417 * 0.4 = 167[/tex]
There are 167 students that are girls.