Answer:
x=-3
Step-by-step explanation:
The values of y with respect to the points created is constant, hence the two points will have the same y values but difference their respective x values
m=[tex] \frac{y2 - y1}{x2 - x1} [/tex]hence, [tex] \frac{x +3}{ - 5 - x } = 0[/tex]x+3=0x=-3What is x−16=−88? I don't know what it is
Answer:
x = -72
Step-by-step explanation:
So first you need to get x on its own, so you you need to get rid of -16 by adding +16 which you get 0.
so now x=-88
whatever you do on one side you do on the other, so add 16 to the other side (-88) so you get -72.
x = -72
so the answer is -72
Thank you <3
WORD PROBLEMS INVOLVING SIMULTANEOUS EQUATIONS:
The cost of a bottle of water is Rsx.
The cost of a bottle ofjuice is Rsy.
The total cost of 9 bottles of water and 3 bottles of juice is Rs 153.
The total cost of 6 bottles of water and 5 bottles of juice is Rs 147.
Find the cost of a bottle of water and the cost of a bottle of juice.
Step-by-step explanation:
9x + 3y = 153
6x + 5y = 147
the first equation can be divided by 3 and then multiplied by 2. and from that we can subtract equation 2 :
9x + 3y = 153 | /3
3x + y = 51 | ×2
6x + 2y = 102
- 6x + 5y = 147
-----------------------
0 -3y = -45
3y = 45
y = 15
3x + y = 51
3x + 15 = 51
3x = 36
x = 12
1 bottle of water costs Rs 12.
1 bottle of juice costs Rs 15.
Given the equation 6x + 18 = 72:
Part A: Write a short word problem about a purchase made to illustrate the equation. (6 points)
Part B: Solve the equation showing all work. (4 points)
Part C: Explain what the value of the variable represents. (2 points)
The short word problem that illustrates the given equation is seen below. The value of the variable is 9.
Expression of the algebraic equation into word problems:Linear algebra equations are equations that can be expressed in word problems and these equations can be used to solve real-life scenarios. These algebraic equations are designed by the application of the desired set of variables with its arithmetic operations.
A.
In a food factory, Eighteen fried chickens are added to the six times the number of food plates is seventy-two. How much-fried chicken goes into each food plate?
B.
6x + 18 = 72
Subtract 18 from both sides;
6x + 18 - 18 = 72 - 18
6x = 54
Divide both sides by 6.
6x/6 = 54/6
x = 9
C.
The value of the variable is 9, and according to the example we used, it represents the number of chickens that goes into each plate of food.
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13. What is the length of the missing side, x?
40 in.
51°
35 in.
49 in.
74°
55°
X
For the given triangles the length of the missing side x is 56in.
As given in the question,
Two triangles are given ,
Let the triangle with measurement 40in. and 35in. be A and another is B.
In triangle A,
Let missing angle be α
Sum of all the angles in the interior of a triangle is equal to 180°
51°+ 74° + α = 180°
⇒α = 55°
In triangle B.
Let missing angle be β,
74° + 55° + β = 180°
⇒β= 51°
By AAA both the triangles are similar.
Length of corresponding sides are in proportion.
40: x = 35 : 49
⇒x = ( 40×49)/35
⇒x= 56in.
Therefore, for the given triangles the length of the missing side x=56in.
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What is the m
9.4
m
15.1
K
Step-by-step explanation:
imagine a circle with J being the center, and JK being the radius.
then
sin(J) = 15.1/JK
cos(J) = 9.4/JK
we have one trigonometric function, where we don't need to calculate JK first : tangent.
tan(J) = sin(J)/cos(J) = 15.1/JK / 9.4/JK = 15.1/9.4 =
= 1.606382978...
J = 58.09705252...° ≈ 58.1°
When f(x) equals X -7/2, what is the value of (F•F^-1) (3)
The value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.
The given function is f(x)=x-7/2.
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The inverse of the given function is
y=x-7/2
Replace y with x and x with y, we get
x=y-7/2
y=x+7/2
[tex]f^{-1}(x)[/tex]=x+7/2
When x=3
[tex]f^{-1}(3)=3+7/2[/tex]
=6.5
f(6.5)=6.5-7/2
=6.5-3.5
=3
Therefore, the value of [tex]f.f^{-1}(x)[/tex] is 3 from the given function.
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how many ways are there to put $4$ balls into $3$ boxes, given that the balls are not distinguished and neither are the boxes?
Answer:
Step-by-step explanation:
think that there are 15 ways ... call the boxes A, B, and C.
You could put all four b***s into either box A, or box B, or box C ---> 3 ways.
You could put three ball into one box and the other ball into another box:
-- 3 into A, 1 into B, 0 into C; or 3 into A, 0 into B, 1 into C; or 1 into A, 3 into B, 0 into C; or 1 into A, 0 into B, 3 into C; or 0 into A, 3 into B, 1 into C; or 0 into A, 1 into B, 3 into C ---> 6 ways
You could put two balls into one box and the other two balls into another box:
-- 2 into A, 2 into B, 0 into C; or 2 into A, 0 into B, 2 into C; or 0 into A, 2 into B, 2 into C ---> 3 ways.
You could put two b***s into one box and one ball into each of the other two boxes:
-- There are three boxes that could get the two b***s ---> 3 ways
Total: 3 + 6 + 3 + 3 = 15 ways.
which expression is equivalent to 2 over 5 x 2 over 28
answer:
look
step-by-step explanation:
over? you would have 2 ÷ (5 x 2) ÷ 28. in fraction form.
What amount of pure acid must be added to 400 mL of a 40% acid solution to produce a 60% acid solution?
Answer:
600ml
Step-by-step explanation:
Write a system of equations to describe the situation below, solve using any method, and fill
in the blanks.
Sidney wants to take group fitness classes at a nearby gym, but needs to start by selecting a
membership plan. With the first membership plan, Sidney can pay $36 per month, plus $2 for
each group class she attends. Alternately, she can get the second membership plan and pay
$35 per month plus $3 per class. If Sidney attends a certain number of classes in a month,
the two membership plans end up costing the same total amount. How many classes per
month is that? What is that total amount?
If Sidney attends
Submit
classes per month, each membership plan costs $
The system of equation to describe the situation below is x= 1.
What is equation?
an equation is a formula that is to expresses the equality of two expressions, by the connecting them with in the equals sign.
The process of equting one thing with another is called the equation of science with objective.
Sol- Based on the given condition-
The formulate is- 36+2x=35+3x
Rearrange variables to the left side of the equation
2x-3x=35-36
Combine like terms
-x= 35-36
Calculate the sum or difference
-x=-1
Devide both side of the equation by the coefficient of variable we get
X=1
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A line is subdivided according to the golden ratio, with a smaller piece having a length of 5 meters. What is the length of the entire line?
The length of the entire line which is subdivided according to golden ratio is 13.09 meters.
What is Golden Ratio?
The golden ratio is a special number approximately equal to 1.618
We find the golden ratio when we divide a line into two parts so that, the whole length divided by the long part is also equal to the long part divided by the short part
Let smaller part of a line be b and long part be a
Golden ratio = a + b/a = a/b = 1.618
According to the given question:
Length of smaller part of line = 5 meters
Let the longer length of the line be x
∴ Total length of line = 5 + x
Using Golden ratio to find the entire length of line
x/5 = 1.618
x = 8.09
Calculating length of entire line = 5 + x = 5 + 8.09 = 13.09
∴ Length of entire line is 13.09 meters
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The difference between five-halves of a number
and 17 is 48.
The required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
What are algebraic expressions ?An algebraic expression (or) a variable expression is a aggregate of phrases through the operations together with addition, subtraction, multiplication, division, etc. For instance, allow us to have a study the expression 5x + 7. Thus, we will say that 5x + 7 is an instance of an algebraic expression.
CalculationWords can be expressed algebraically.
The algebraic expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
Let the number be x.
Five-halves of x is: 5/2x
So the difference between and 17 is:
5/2x - 17 = 48 or 17 - 5/2x = 48
Combine both expressions
[tex]| 17 - \frac{5}{2}x|[/tex] = 48
Hence, the required expression is: [tex]| 17 - \frac{5}{2}x|[/tex] = 48
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if a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 17 feet, what angle does the ramp make with the ground? round to 2 decimal places.
The angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.
What is trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry". Therefore, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians.
Given, the length of the ramp = h = 17 feet
Height at which ramp is placed on truck = p = 4 feet
Let the angle that the ramp makes with the ground = ∅
Taking the length and height of ramp as basis, on assuming a right triangle with the length as hypotenuse and the height as perpendicular, we have:
sin ∅ = Perpendicular/Hypotenuse = h / p = 17/4 = 4.25
⇒ ∅ = sin⁻¹ (4.25) ⇒ ∅ = 10.48°
Thus, the angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.
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\frac{2x^3t^3}{xt^2}\:\cdot \frac{\left(3xt\right)^3}{9x^2t}
Answer:
[tex]6x^{3}t^{3}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{\left(3xt\right)^3}{9x^2t}[/tex]
[tex]\textsf{Apply exponent rule} \quad (ab)^c=a^c \cdot b^c:[/tex]
[tex]\implies \dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{3^3x^3t^3}{9x^2t}[/tex]
[tex]\implies \dfrac{2x^3t^3}{xt^2}\:\cdot \dfrac{27x^3t^3}{9x^2t}[/tex]
[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{b} \cdot \dfrac{c}{d}=\dfrac{ac}{bd}:[/tex]
[tex]\implies \dfrac{2x^3t^327x^3t^3}{xt^29x^2t}[/tex]
Collect like terms:
[tex]\implies \dfrac{2 \cdot 27x^3x^3t^3t^3}{9x^2xt^2t}[/tex]
Multiply the numbers 2 and 27:
[tex]\implies \dfrac{54x^3x^3t^3t^3}{9x^2xt^2t}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \dfrac{54x^{3+3}t^{3+3}}{9x^{2+1}t^{2+1}}[/tex]
[tex]\implies \dfrac{54x^6t^6}{9x^3t^3}[/tex]
Separate like terms:
[tex]\implies \dfrac{54}{9} \cdot \dfrac{x^6}{x^3}\cdot \dfrac{t^6}{t^3}[/tex]
Divide the numbers 54 and 9:
[tex]\implies 6 \cdot \dfrac{x^6}{x^3}\cdot \dfrac{t^6}{t^3}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies 6 \cdot x^{6-3}\cdot t^{6-3}[/tex]
[tex]\implies 6 \cdot x^{3}\cdot t^{3}[/tex]
[tex]\implies 6x^{3}t^{3}[/tex]
Mason is a songwriter who collects royalties on his songs whenever they are played in a commercial or a movie. Mason will earn $30 every time one of his songs is played in a commercial and he will earn $80 every time one of his songs is played in a movie. Mason earned a total of $470 in royalties on 9 commercials and movies. Write a system of equations that could be used to determine the number of commercials and the number of movies on which Mason's songs were played. Define the variables that you use to write the system.
Answer:
Get the roundend answer to 10
Step-by-step explanation:
Expand & simplify: (7-3x)(2x-4)(x+1)
will mark brainliest
Find the x-intercept and the y-intercept of the graph of the equation.
4x + 5y = 20
The x-intercept is
The y-intercept is
(Type an integer.)
(Type an integer.)
The x-intercept and y-intercept of the graph is (5,0) and (0,4)
How to find the intercept ?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilized (0, b). The y value of the y intercept point is represented by b in the equation.
1. To find the x-intercept we put y=0
The equation becomes
4x + 5(0) = 20
4x = 20
x = [tex]\frac{20}{4}[/tex]
x = 5
∴ The x-intercept is (5,0)
2. To find the y-intercept we put x=0
The equation becomes
4(0) + 5y = 20
5y = 20
y = [tex]\frac{20}{5}[/tex]
y = 4
∴ The y-intercept is (0,4)
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Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $60 for every hour they work. If the plumber charges Jerald a total of $305, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.
35x + 60 = 305; x = 7 hours
35x − 60 = 305; x = 10.4 hours
60x + 35 = 305; x = 4.5 hours
60x − 35 = 305; x = 5.7 hours
Answer:
60x + 35; x = 4.5 hours
(x is not actually equal to 4.5, it is equal to 4.67)
Step-by-step explanation:
The description says that the plumber charges a one time fee of 35 dollars to come to someones house, and then 60 dollars an hour. The total pay is 305 dollars. x will be the number of hours that the plumber works.
60x + 35 = 305
Subtract 35 from both sides: 60x = 280
Divide by 60: x = 280/60
Simplify: x=14/3
Fraction to decimal: x=4.67
Answer: C (60x + 35 = 305; x = 4.5 hours)
It's right trust me! Wish you luck!
Brainliest?
Evaluate 3 (2x - 1).
Answer:
6x - 3
Step-by-step explanation:
3 ( 2x - 1 )
= 3 ( 2x ) - 3 ( 1 )
= 6x - 3
Answer:
x=1/2 or 0.5 or just 6x-3
Step-by-step explanation:
3(2x-1)
distribute.
6x-3
get 6x alone
6x=3
divide
x=3/6
x=1/2 or 0.5
What are the terms of this algebraic equations 3+6ab+c? 3,6ab 6ab,c 3,6ab, and c
The terms of the algebraic equation 3+6ab+c are (d) 3, 6ab and c
How to determine the terms of the equation?The algebraic equation is given as
3 + 6ab + c
Consider an equation represented as
x + y
The terms of the equation are x and y
Also, for an equation represented as
x + y + z;
The terms are x, y and z
Using the above as a guide, the terms of 3 + 6ab + c are 3, 6ab and c
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Compare the slope-intercept and point-slope forms of a linear equation.
It is possible to determine a line's direction and steepness by looking at its slope.
What is slope?Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
A line's basic formula in gradient intercept form is y=mx + b. It is rewritable in point-slope form.
When y-b is equal to m(x-0), the location is the y-intercept (0,b).
The basic equation for a line with m=slope and (k,h) a position on the line is y-h=m(x-k).
By determining y and adding constant variables, the equation can be recast in slope-intercept form.
Y = mx-mk + h, where h-mk = b is the y-intercept in this form.
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Find the equation of the vertical line that passes through point M(−2, 6)
The equation for the vertical line that goes through point M(−2, 6) is x = -2.
Answer:
The equation of a straight line is:
y = mx + b;
y, x are variables, m is the slope of the line and b is the y intercept.
The slope of a vertical is undefined. Since the line passes through the point M(−2, 6), hence the equation of the vertical line is:
x = -2
There are 14 students in a homeroom. How many different ways can they be chosen
to be elected President, Vice President, Treasurer, and Secretary?
There are 24,024 different ways to choose a President, Vice President, Treasurer, and Secretary from a group of 14 students.
Permutation is the arrangement of objects in a specific order. It is the number of different ways in which a set of objects can be arranged in a specific order. The formula to calculate permutation is:
[tex]P(n, r) = n! / (n - r)![/tex]
Permutations are commonly used in mathematics, science, and engineering, and are useful for solving problems that involve counting the number of possible arrangements of objects or events.
We can use the formula for permutations to find the number of ways to choose the four officers from a group of 14 students.
The number of permutations of n objects taken r at a time is given by:
[tex]^nP_r = n! / (n - r)![/tex]
where n! denotes n factorial, which is the product of all positive integers up to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
In this case, we want to choose 4 students from a group of 14, and the order in which they are chosen matters (since we are electing them to specific positions). So we have:
n = 14
r = 4
The number of ways to choose the four officers is therefore:
[tex]^1^4P_4 = 14! / (14 - 4)! = 14 \times 13 \times 12 \times 11 = 24,024[/tex]
Therefore, there are 24,024 different ways to choose a President, Vice President, Treasurer, and Secretary from a group of 14 students.
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the price of a car was increased by 4% to £22 what was the price before
13.80
Step-by-step explanation:
22 - 4% is your answer
Which equation show the relationship between the number of
hours, x, and the number of dogs groomed, y?
y = 15x
y = 5x
y = 30x
y=3x
The relation that can be formed by obersving the Cartesian Plane is y = 5x
What is Co-ordinate Geometry?
The study of geometry using coordinate points is known as coordinate geometry (or analytic geometry). It is possible to estimate the distance between two points, divide lines in a m:n ratio, identify the midpoint of a line, calculate the area of a triangle in the Cartesian plane, and so on using coordinate geometry.
Solution:
By analysing the given Cartesian Plane
it can be observed that the rate of change of y with respect to x
is 5 times
Therefore, the relation that can be formed by obersving the Cartesian Plane is y = 5x
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Matteo buys a basil plant that is 22 cm tall and grows 1/2 a centimeter every day.
A. Write an equation that can be used to solve for the number of days until the plant has a height of 30 cm. Use d to represent the number of days. Label each part of your equation with what it represents.
B. How much does the plant still have to grow?
C. Solve for the value of d. What does this value represen in this problem?
PLEASE SOLVE ALL
A) The equation is 22 + (d * 1/2) = 30
B) The plant that still have to grow 8 cm more
C) d = 16 days, d represents the number of days
Step-by-step explanation:
Given:
Initial height (basil plant at buying) = 22cm
Plant grows on everyday = 1/2cm
A) Given:
Total height (to be grown) = 30 cm.
The equation is,
Initial height+ ( number of days * plant grows on everyday) = Total height
22 + (d * 1/2) = 30 → equation 1
B) The plant that still have to grow = Total height - Initial height
= 30 - 22
= 8 cm
C) Solving the value d using equation 1:
22 = 30 - (d * 1/2)
44 = 60 - d
d = 16 days
Hence, A) The equation is 22 + (d * 1/2) = 30.
B) The plant that still have to grow 8 cm more.
C) d = 16 days, d represents the number of days.
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T
4) a) On the grid, draw
the line y = 3
b) On the grid, draw
the line x = -2
6
5
4
-3-
2
1-
-3 -2 -1 0
-1-
-2
1
2
3
4
5
Fe
Be
1.
2.
3
4
Answer:
Step-by-step explanation:
Please help with the unfilled spots! :)
The value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex],according to the question.
What do you mean by XY coordinates?
The x and y coordinates are a component of the x-axis and y-axis in a 2D space in the Cartesian coordinate system. The x and y coordinates for a point in space are expressed as an ordered pair (x, y). The position of the point on the x-axis is shown by the first number, while its location on the y-axis is indicated by the second number.
According to the data in the given question,
We have:
The coordinates of points A are (-9,-6).
The coordinates of points W are (-1,-12).
In this question,
[tex](x_{1},y_{1})= (-9,-6)[/tex]
[tex](x_{2},y_{2})= (-1,-12)[/tex]
Therefore, the value of [tex](x_{1},y_{1})= (-9,-6)[/tex] and the value of [tex](x_{2},y_{2})= (-1,-12)[/tex].
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a yield sign measures 24 inches on each of its three sides. what is the area of the sign? (round your answer to one decimal place.)
A yield sign measures 24 inches on each of its three sides ( equilateral )then the area of the sign is 249.4
Given,
24 inches on each of its three side. (See in attached picture)
Consider ADB,
As it is an equilateral triangle, BD = BC/2 = 12 inches
By Pythagoras theorem,
AB^2 = BD^2 + AD^2
24^2 = 12^2 + AD^2
24^2 – 12^2 = AD^2
576-144 = AD^2
432= AD^2
20.78= AD
Area = ½ (base * height)
= ½ (24*20.78)
= 249.4
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Expand and Simplify (x+5)(x-2)
Answer:
[tex]x^2+3x-10[/tex]
Step-by-step explanation:
To expand you must do this:
[tex]x*x+(-2x)+(5x)-10\\x^2-2x+5x-10\\x^2+3x-10[/tex]