The standard form of the linear equation 15( y - 1/3 ) = x is 3x - 45y = -15.
What is the given equation in standard form?The standard form of a linear equation is expressed as;
Ax + By = C
Where A and B are the coefficient of x and y respectively, C is the constant term.
Given the equation in the question;
15( y - 1/3 ) = x
Multiply both sides by 3
3(15( y - 1/3 )) = 3x
First, apply distributive property to remove the parenthesis.
15( 3y - 1 ) = 3x
45y - 15 = 3x
3x = 45y - 15
Now, move all terms containing variables to the left and side of the equation and reorder the equation in form of Ax + By = C
3x - 45y = -15
Therefore, the standard form of the equation is 3x - 45y = -15.
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Find the exact value of sin 120° in simplest form with a rationaldenominator.
Perform the indicated operation.Subtract (4x^2-5) from the sum of (x^2 - 5x + 1) and (3x^2 – 3x+4)The answer is
We have the sum of
[tex]\mleft(x^2-5x+1\mright)+(3x^2-3x+4)[/tex]we sum similar terms
[tex]4x^2-8x+5[/tex]then we subtract (4x^2-5) from the result of the sum above
[tex](4x^2-8x+5)-\mleft(4x^2-5\mright)=4x^2-8x+5-4x^2+10[/tex]then we sum similar terms, and we find the answer
[tex]-8x+10[/tex]This hutch is made up of two rectangular prisms. 1 7 ft 2 ft 2 127 ft 22 ft 4 ft What is the total volume of this hutch, in cubic feet?
Answer
40 cubic feet
Step-by-step explanation
The volume of a rectangular prism is calculated as follows:
[tex]V=whl[/tex]where w is the width, h is the height and l is the length of the prism.
The hutch is made up of two rectangular prisms, one with a width of 1 1/3 ft, a height of 2 1/2 ft, and a length of 4 ft. The other one has a width of 2 2/3 ft, a height of 2 1/2 ft, and a length of 4 ft.
To calculate the volume of the hutch, first, we need to calculate the volume of each prism, and then add them.
The volume of the smaller prism is:
[tex]\begin{gathered} V_1=1\frac{1}{3}\cdot2\frac{1}{2}\cdot4 \\ V_1=13\frac{1}{3}\text{ cubic feet} \end{gathered}[/tex]The volume of the bigger prism is:
[tex]\begin{gathered} V_2=2\frac{2}{3}\cdot2\frac{1}{2}\cdot4 \\ V_2=26\frac{2}{3}\text{ cubic feet} \end{gathered}[/tex]Finally, the volume of the hutch is:
[tex]V_1+V_2=13\frac{1}{3}+26\frac{2}{3}=40\text{ cubic feet}[/tex]Four friends are playing a game. 36 cards are dealt out between the friends. Which equation can be used to find how many cards each person receives
Given
Four friends are playing a game.
36 cards are dealt out between the friends.
To find: Which equation can be used to find how many cards each person receives.
Explanation:
It is given that,
Four friends are playing a game.
36 cards are dealt out between the friends.
Let x be the number of cards received by each person.
Then,
[tex]\begin{gathered} 4x=36 \\ x=\frac{36}{4} \\ x=9 \end{gathered}[/tex]Hence, each person receives 9 cards.
Thus,
[tex]undefined[/tex]An industrial machine made 1,629 cans of diet sodas and 6 times as many
regular sodas over the course of 46 minutes. The regular sodas were then
placed into 3 shipping boxes with each shipping box containing the same
number of sodas. How many regular sodas were in each shipping box.
Each of the shipping boxes contains 2172 cans of regular soda.
Ratios and fractions are the main bases on which proportion is explained. Two ratios are equal when they are expressed as a fraction in the form of a/b, ratio a:b, and then a proportion.
The industrial machine made a total of 1629 cans of diet soda which is 6 times as much regular soda in 46 minutes.
Then, the total number of regular sodas made will be:
R = 4 × Total number of diet soda
R = 4 × 1629 cans
R = 6516 cans
The regular sodas were packed in 3 shipping boxes with each having the same number of soda cans.
Therefore, the number of cans of regular sodas in each box will be:
N = 6516/3
N = 2172 cans
There are 2172 cans of regular sodas in each shipping box.
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Instructions: State the domain and range of the given function.
In this problem, we are going to state the domain (x-values)of the given scatter plot.
Notice that we are given individual points. That means the domain will also have individual values, or the x-vaues of the points.
In your graph, we are given th following points:
(2,2)
(2,10)
(3,7)
(5,5)
(8,5)
So, the domain for the graph will have the values 2, 3, 5, 8, or the first option on your dropdown menu.
Which of the following systems of equations has the solution (1, 4)? y = –3x – 1y = –x + 5 y = 3x + 1y = x – 5y = –x – 5
Step 1
To find the systems of equations that has the solution (1,4). The value of x, 1 input into the equations must give 4 as the value of y. We will now test the options.
1) y=-3x-1
[tex]\begin{gathered} y=-3(1)-1 \\ y=-4 \\ False \end{gathered}[/tex]2) y=-x+5
[tex]\begin{gathered} y=-(1)+5=4 \\ True \end{gathered}[/tex]3) y=3x+1
[tex]\begin{gathered} y=3(1)+1=4 \\ True \end{gathered}[/tex]4) y=x-5
[tex]\begin{gathered} y=1-5=-4 \\ false \end{gathered}[/tex]5) y=-x-5
[tex]\begin{gathered} y=-(1)-5=-6 \\ False \end{gathered}[/tex]Answer;
[tex]\begin{gathered} y=-x+5 \\ y=3x+1 \\ \end{gathered}[/tex]The sum of nine and a number is forty less than fifteen
Answer:
x = -34
Step-by-step explanation:
Lets use "x" as the missing number
9 + x = 15 - 40
9 + x = -25
x = -25 - 9
x = -34
B.__ angles form a straight line.
Complete the sentences
A. All right angles are 90 degrees (by definition)
B. supplemenatry angles form straight line (by definition)
C. If two angles form a linear pair, then the are supplementary (by definition)
D. When two lines intersect, the inverse angles are congruent.
In the given image of two intersecting lines, you have m∠1 = 67°
E. angle 2 and angle 1 are supplementary, then;
m∠2 + m∠1 = 180°
m∠2 = 180° - m∠1
m∠2 = 180° - 67°
m∠2 = 113°
F. angle 3 and angle 1 are congruent, then:
m∠3 = m∠1 = 67°
Due to the given image, you have the following expressions:
2x + x + 60° = 180° supplementary angles
3x + 60° = 180° subtract 60 both sides
3x = 180° - 60°
3x = 120° divide both sides by 3
x = 120/3
x = 40°
Furthermore, for y, you have:
x + y + y + 20° = 180° supplementary angles
x + 2y + 20° = 180° replace x = 40
40 + 2y + 20° = 180°
2y + 60° = 180° subtract 60 both sides
2y = 180° - 60°
2y = 120°
y = 120/2 divide by 2 both sides
y = 60°
Answer: 180 degree's make up a straight line.
Step-by-step explanation:
Solve
-21 < 3x - 12 < 6
Answer:
-3 < x < 6
Step-by-step explanation:
-21 < 3x - 12 < 6
first lets add 12 to everything
-9 < 3x < 18
now lets divide everything by 3
-3 < x < 6
3.168×10 9 and 4.8 \times 10^24.8×10 2 expressed in scientific notation?
The value of 3.168 × 10^9 × 4.8 × 10^2 in scientific notation is 15.2064 × 10^11.
What is scientific notation?It should be noted that scientific notation is used to express the numbers that are either too large or too small.
The expression is illustrated as:
= 3.168 × 10^9 × 4.8 × 10^2
= 15.2064 × 10^11
It should be noted that the exponent is that we add the powers.
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what is the area of a parallelogram with a side of 11 8 and 10
The area of the parallelogram with dimensions 11.8 units and 10 units is 118 square units
How to find the area of a parallelogramParallelogram is a general term that refers to quadrilaterals with the opposite sides parallel to each order
Area refers to the space covered by an object or extent covered
Hence to find the pace covered by the parallelogram which is the area of the parallelogram we multiply the both sides as follows
let the length, L = 11.8 units and width, w = 10 units
Area of parallelogram = L * w
= 11.8 * 10
= 118 square units
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An inverse variation includes the points (-4, 3) and (-1, n). Find n.
In a inverse variation you have two variables, in this case (x,y) x and y, and a constant value k in the form:
[tex]y=\frac{k}{x}[/tex]When x increase y decreases and when x decreases y increases (inverse variation)
As you have two (x,y) data;
(-4, 3 ) and (-1 , n)
And both have the same constant k.
[tex]\begin{gathered} 3=\frac{k}{-4} \\ \\ n=\frac{k}{-1} \end{gathered}[/tex]Solve in the first equation the k:
[tex]\begin{gathered} k=-4\cdot3 \\ k=-12 \end{gathered}[/tex]Use the value of k= -12 to find n in the second equation:
[tex]n=\frac{-12}{-1}=12[/tex]Then , the value of n is 12Mavis says that -7/9 * 6 is less than 7/9 * (-6) explain whether or not maybe this is correct
EXPLANATION
-7/9*6 is the same number that 7/9*(-6) because by the property of the products ---> the order of symbols doesn't change the solution : -a*b= a*-b
indicate the equation of the given line in standard form show all your work for full creditthe line containing the diagonal ,BD,of a square whose vertices areA(-3,3) B(3,3) C (3,-3) and D (-3,-3)find two equations one for each diagonal
ANSWER:
x + y = 0
x - y = 0
EXPLANATION:
Given the coordinates:
A(-3,3)
B(3,3)
C(3,-3) and
D (-3,-3)
One diagonal is line AC.
Find the slope of AC:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\text{ }\frac{-3-3}{3-(-3)}=\frac{-6}{6}=\text{ -1}[/tex]Solpe of AC = -1
Using the slope intercept form, y = mx+b, we have:
y = -1x + b
y = -x + b
The equation for AC:
y = -x
The other diagonal is BD.
find the slope of BD:
[tex]m\text{ = }\frac{y2-y1}{x2-x1}=\text{ }\frac{-3-3}{-3-3}=\frac{-6}{-6}=\text{ 1}[/tex]Slope of BD = 1
The equation of BD:
y = 1x
y = x
Therefore the equation of both lines in standard form will be:
AC ==> x + y = 0
BD ==> x - y = 0
On a recent test, Mark got 6 questions out of 40 wrong. Which answer best describes the percent of questions he got correct?
answer 85%
Step-by-step explanation:
6-40=34
100 divide by 40
2.5 times 34
Solve for x
23x-5
21x+5
Plot the given parabola on the axes. Plot the roots, the vertex and two other points.
Solution
Step 1:
The first two points are the roots of the parabola.
To get the roots of the parabola, equate y = 0
[tex]\begin{gathered} \text{y = x}^2\text{ + 2x - 35} \\ x^2\text{ + 2x - 35 = 0} \\ x^2\text{ + 7x - 5x - 35 = 0} \\ x(x\text{ + 7)-5(x + 7) = 0} \\ (x\text{ + 7)(x - 5) = 0} \\ x\text{ = -7 , x = 5} \\ \text{The parabola intercept x-axis at (-7, 0) and (5 , 0)} \end{gathered}[/tex]Step 2:
Find the y-intercept.
To find the y-intercept, plug x = 0
[tex]\begin{gathered} \text{y = x}^2\text{ + 2x - 35} \\ y=0^2\text{ + 2}\times0\text{ - 35} \\ y\text{ = -35} \\ y-\text{intercept is (0 , -35)} \end{gathered}[/tex]Step 3:
Find the vertex
[tex]\begin{gathered} \text{The vertex is (}\frac{-b}{2a}\text{ , y)} \\ b\text{ = 2, a = 1} \\ x\text{ = }\frac{-b}{2a} \\ x\text{ = }\frac{-2}{2\times1} \\ x\text{ = }\frac{-2}{2} \\ x\text{ = -1} \\ y=(-1)^2\text{ + 2(-1) - 35} \\ y\text{ = 1 - 2 - 35} \\ y\text{ = -36} \\ \text{Vertex = (-1, -36)} \end{gathered}[/tex]Final answer
All the five points are:
Roots (x-intercept) = (-7, 0) , (5 , 0)
y-intercept = (0, -35)
vertex = (-1, -36)
Other point = (-5, -20)
Use this description to write the quadratic function in vertex form:The parent function f(x)=x^2 is vertically stretched by a factor of 2 and translated 14 units right and 6 units up.
The vertex form is given by:
[tex]y=a(x-h)^2+k[/tex]The parent function is:
[tex]f(x)=x^2[/tex]The function is vertically stretched by a factor of 2 :
[tex]2f(x)=2x^2[/tex]and translated 14 units right:
[tex]2f(x-14)=2(x-14)^2[/tex]and 6 units up:
[tex]2f(x-14)+6=2(x-14)^2+6[/tex]Answer:
[tex]g(x)=2(x-14)^2+6[/tex]Dakota fills a measuring cup 5/8 cup of sugar 2 times to make a cake. Which multiplication equation shows the total amount of sugar Dakota uses?
We have that Dakota fills a measuring cup 5/8 cup of sugar two times. The multiplication equation that shows the total amount of sugar is:
[tex]2\cdot\frac{5}{8}=\frac{10}{8}=\frac{8}{8}+\frac{2}{8}=1+\frac{2}{8}=1\frac{2}{8}[/tex]We needed to multiply the fraction 5/8 by 2, and then solve for the given operations.
Therefore, the answer is the last option:
2 x 5/8 = 10/8 = 1 2/8 cups of sugar
According to the propertyWhich choice is equivalent to the quotient below!
Answer:
A
Step-by-step explanation:
Because square root of 30 is 5.4 rounded, and square root of 6 is 2.4 rounded, so 5.4 divided 2.4 is 2.25, and square root of 5 (Answer choice A) is 2.25 rounded as well. They are more accurate when not rounded btw u can check yourself:) HAVE A GREAT DAY/NIGHTT!
Choose the answer that represents the product below as an exponentialexpression(8.2). (8.2). (8.2)A. 3.8.2B. 8.2^4C. 3^8.2D. 8.2^3
We have
[tex]\mleft(8.2)\cdot(\mright?8.2)\cdot(8.2)[/tex]the base is 8.2 and the exponent is the number of times the number repeated in this case it is 3 therefore the answer is
[tex]8.2^3[/tex]ANSWER
D. 8.2^3
I am stuck on trying to solve these two problems can someone please help me with themWrite an equivalent fraction for each problem below. 24/42 and 16/20
ANSWER :
The equivalent fractions are :
24/42 = 4/7
16/20 = 4/5
EXPLANATION :
From the problem, we have the fractions 24/42 and 16/20
For 24/42
We need to think of a number that the numerator and the denominator will be divisible of.
24 and 42 are both divisible by 6.
That will be :
[tex]\frac{24}{42}\rightarrow\frac{24\div6}{42\div6}=\frac{4}{7}[/tex]Therefore, the equivalent fraction for 24/42 is 4/7
For 16/20
We will do the same procedure, 16 and 20 are divisible by 4.
That will be :
[tex]\frac{16}{20}\rightarrow\frac{16\div4}{20\div4}=\frac{4}{5}[/tex]The equivalent fraction for 16/20 is 4/5
factor this polynomial completely[tex] {x}^{2} - 8x + 16[/tex]
Solution.
[tex]\begin{gathered} Given \\ x^2-8x+16 \\ =x^2-4x-4x+16 \\ =x(x-4)-4(x-4) \\ =(x-4)(x-4) \end{gathered}[/tex]The answer is (x-4)(x-4)
this one is way to hard
f(5) = -4(5 - 1)
f(5) = -4(4)
f(5) = - 16
what is the range of the relation[(-5,0),(-4,-3),(-3,4),(-1,0),(-4,-1)]
The range is the set of values that the relation takes for the domain for which it is defined.
Is the set of values of the dependent variable.
In this case, we have the relation [(-5,0),(-4,-3),(-3,4),(-1,0),(-4,-1)].
The dependant variable takes the values: 0, -3, 4, 0 and -1. Some values are repeated.
We put the repeated values only once and sort to write the range.
Then, the range is R = {-3, -1, 0, 4}.
Answer: Range = {-3, -1, 0, 4}
help me please
thank you
In interval notation, the inequality is [tex](-\infty, -4][/tex].
use a calculator.15. Select all the numbers that are solutions to the equation x2 = 15. (2 pt)A. 225B. 225C. 7.5D. 715E. -V15
√15, and -√15
1) Considering the equation below, let's solve it:
[tex]\begin{gathered} x^2=15 \\ \sqrt[]{x^2}=\sqrt[]{15} \\ x=\sqrt[]{15},\text{ -}\sqrt[]{15} \end{gathered}[/tex]2) So the answer is √15, and -√15
Since (√15)² = 15 and (-√15)²=15
Write the equation below in standard form. Show work. 8/3y = 5/6x - 2
To write the equation in standard form:
Step 1. Multiply the expression by 6
[tex]\begin{gathered} (\frac{8}{3}y=\frac{5}{6}x-2)\cdot6 \\ 16y=5x-12 \end{gathered}[/tex]Step 2. Clear the independent term
[tex]\begin{gathered} 16y=5x-12 \\ 16y-5x=-12 \end{gathered}[/tex]The equation in standard form is 16y-5x=-12
A={1,2,3,4,5} and B={6,7,8,9}. Find A∪B
Answer:
{1, 2, 3, 4, 5, 6, 7, 8, 9}
Step-by-step explanation:
[tex]A \cup B[/tex] represents the set of all elements in [tex]A[/tex] or [tex]B[/tex].
