Answer:
[tex](-3,-12)[/tex]
[tex]x=-3, y=-12[/tex]
Step-by-step explanation:
So we have the system:
[tex]3x+y=-21\\y=4x[/tex]
To solve this, we can do some substitution. Substitute the y in the first equation for the 4x in the second:
[tex]3x+y=-21\\3x+(4x)=-21[/tex]
Combine like terms:
[tex]7x=-21[/tex]
Divide both sides by 7. The left side cancels:
[tex](7x)/7=(-21)/7\\x=-3[/tex]
So we determined that x is -3. Now, plug this number back into the second equation:
[tex]y=4x\\y=4(-3)=-12[/tex]
So the solution is:
[tex](-3,-12)[/tex]
Answer:
[tex]\Large \boxed{x=-3 \ } \\ \\ \Large \boxed{y=-12}[/tex]
Step-by-step explanation:
3x + y = -21
y = 4x
Substitue y = 4x in the first equation.
3x + 4x = -21
Combine like terms.
7x = -21
Divide both sides by 7.
x = -3
Let x = -3 for the second equation.
y = 4(-3)
Multiply.
y = -12
The solution for the system of equations is x = -3 and y = -12.
To estimate your average monthly salary, divide your yearly salary by the number of months in a year. Write and solve an equation to determine your yearly salary when your average monthly salary is $4,559.
Answer:
yearly salary = $54,708
Step-by-step explanation:
Let monthly salary be x
Let yearly salary be y
Let number of months be n
To estimate your average monthly salary, divide your yearly salary by the number of months in a year. This can be written as
x = y divided by n
[tex]x = \frac{y}{n}[/tex]
Therefore, writing an equation to determine yearly salary is the same as making the yearly salary 'y' the subject of the formula above:
[tex]x = \frac{y}{n}\\cross-multiplying\\n\ \times\ x= y\\y\ =\ nx[/tex]
where y = ???
x = $4,559
n = 12 months
[tex]y = 4,559\ \times\ 12 \\= \$\ 54,708[/tex]
Therefore yearly salary = $54,708
The population of a certain country is expected to double every 32 years. The population of this country was 4.2 million people in the year 2000. To the nearest tenth of a present, by which percentage rate is the population expected to increase each year
Answer:
2.2%
Step-by-step explanation:
Given the following :
Population in year 2000 (A) = 4.2 million
Expected population every 32 years = 2 *A
The growth rate per year =?
The population figure after 32 years = (2 * 4.2 million) = 8.4 million
Using the exponential growth formula :
P(t) = A × (1 + r)^t
(1 + r) = g = Total growth percent
A = Initial population
t = time
P(t) = 8.4 million
8,400,000 = 4,200,000 × g^32
g^32 = (8400000/4200000)
g^32 = 2
Taking the root of 32 on both sides
g = 1.02189714865
g = (1 + r)
1.02189714865 = 1 + r
r = 1.02189714865 - 1
r = 0.02189714865
.rate = 0.02189714865 * 100
= 2.18971486541%
= 2.2% ( nearest tenth)
Gerardo compró un servicio de limpieza para su negocio que le cobra $300 por cada uno de los dos primeros servicios y $150 por servicio adicional. Esta vez Gerardo ha requerido 5 servicios en total, por lo que se ha hecho acreedor a una promoción de $100 de descuento, ¿cuánto pagará Gerardo en total por sus servicios?
Answer:
CT= $950
Step-by-step explanation:
Dado la siguiente información:
Servicio= $300 primeros dos
Servicio adicional= $150
Descuento= $100
Para calculate el costo total, tenemos que usar la siguiente formula:
CT= 300x + 150y - 100
x= costo normal
y= costo promocional
CT= 300*2 + 150*3 - 100
CT= $950
PLEASE HELP!!! offering 25 points brainiest and 5 stars with thanks
Answer:
.3
Step-by-step explanation:
P( defective) = number defective/ total
= 3/10
.3
Answer:
[tex]\huge\boxed{0.3}[/tex]
Step-by-step explanation:
Total CDs = 10
Defective CDs = 3
P(Defective) = 3/10
P(Defective) = 0.3
5(5x+3) -4(2x-9)=0
pls help
Answer:
x = -3
Step-by-step explanation:
See steps of solution:
5(5x+3) -4(2x-9)=0 ⇒ parenthesis25x + 15 - 8x + 36 = 0(25x -8x) + (15 + 36) = 0 ⇒ grouping like terms17x +51 = 017x = -51 ⇒ subtract 51 from both sidesx = -51/17 ⇒ divide both sides by 17x = -3 ⇒ answerAnswer is -3
Answer:
x = -3
Step-by-step explanation:
5(5x+3) - 4(2x-9) = 0 Multiply out.
5*5x + 5*3 - 4*2x + 36 = 0
25x + 15 - 8x + 36 = 0 Combine like terms.
25x - 8x + 15 + 36 = 0
17x + 51 = 0 Subtract 51 from both sides.
17x = - 51 Divide each side by 17.
17x/17 = -51/17
x = - 3
is 32k+24=8(4k+3) true? a.True b.False
Answer:
a. True.
Step-by-step explanation:
32k + 24 = 8(4k + 3)
32k + 24 = 32k + 24
32k - 32k = 24 - 24
0 = 0
Since 0 does equal 0, the statement is a. True.
Hope this helps!
Answer:
[tex]\Large \boxed{\mathrm{a. \ True}}[/tex]
Step-by-step explanation:
[tex]32k+24[/tex]
[tex]\sf Factor \ out \ 8 \ from \ the \ expression.[/tex]
[tex]8(4k)+8(3)[/tex]
[tex]8(4k+3)[/tex]
[tex]32k+24=8(4k+3)[/tex]
[tex]\sf The \ equation \ is \ true.[/tex]
Find the the domain codomain and range of the graph
Answer:
Domain: All Real numbers
CoDomain : All Real numbers
Range: [tex]\left\{y|y\geq 0 \right\}[/tex]; that is: Real numbers larger than or equal to zero
Step-by-step explanation:
Notice that the graphed function can use any Real number x (from - infinity to + infinity) and produce an output. Therefore, the Domain of the function plotted in graph 3 is : All Real numbers.
The set of possible outputs (CoDomain) is also the set of all Real numbers (notice that the y-axis extends form - infinity to + infinity
But the Range (the actual set of the collection of outputs of the function) is just a subset of the CoDomain consisting of the Real numbers larger than or equal to zero (notice that the drawing of the function touches the x axis and lies completely on the upper half of the plane.
Cos 3 A + COS5A + COS7A+ Cos 15 A = 4 COS 4A COS5A COS6A
Your question has been heard loud and clear.
Lhs = 2cos[5A+3A/2]cos[5A-3A/2]+2cos[15A+7A/2]cos[15A-7A/2]
=2cos4AcosA+2cos11Acos4A
=2cos4A[cosA+cos11A]
=2cos4A[2cos[11A+A/2]Cos[11A-A/2]
=2cos4A2cos5Acos6A
=4cos4Acos5Acos6A=Rhs
Thank you
Which of the following are irrational numbers?
86
-29
88.80
[tex] \sqrt{46} [/tex]
Answer:
sqrt 46
Step-by-step explanation:
irrational numbers are numbers cannot be define in a fraction. sqrt of 46 will give you infinite decimal which could not be express in a fraction form.
Does anyone know this
(20 POINTS!) If the point (x, y) is on the y-axis, which of the following must be true? x = 0 or y = 0
Answer:
x = 0
Step-by-step explanation:
because the x coords are still 0 and y is changing.
How might constructions prove to be useful in your life?
Step-by-step explanation:
Constructions are useful in life. From learning it, you are able to use the required tools, and get familiarized with different shapes and angles. This would help you prepare for the task of proving theorems that involved those shapes and angles. It is not the end, ultimately, it prepares you for real life. Constructions are applied in building houses, estates, etc, and constructions of roads, bridges, etc.
i need help (3/4)x+2=(3/8)x-4
Answer:
x = -16
Step-by-step explantion:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Hope this helps!
(・∀・(・∀・(・∀・*)
I have a shuffled deck of 52 playing cards. A deck of cards has four different suits, with an even number of cards in each. I pick a card at random. What is the probability of me picking any card which is in the spades suit, as a decimal?
Answer:
The probability is 0.25
Step-by-step explanation:
Here is a probability question.
We want to know the probability of picking a card which is in the spades suit.
Now, what we know is that there are a total of 52 cards and we have 4 suites.
Each suite have equal number of cards. So definitely the number of cards in the spades suit will be 52/4 = 13 cards
Thus, the probability of picking any card in the spades suit = number of cards in the spades suit/ Total number of cards in the deck
Mathematically that would be 13/52 = 1/4 = 0.25
An underwater canyon begins at 40 feet below sea level and is 105 feet deep. what is the elevation of the bottom of the canyon
Answer:
145 feet
Step-by-step explanation:
The computation of the elevation of the bottom of the canyon is shown below;
Given that
A = sea level
B = The point at which the canyon starts
C = Canyon bottom
AB = 40 feet
BC = 105 feet
Based on the above information
The AC or elevation of the canyon bottom is
AC = AB + BC
= 40 feet + 105 feet
= 145 feet
10+(-3)
What is the answer and how u get the answer?
Answer:
7
Step-by-step explanation:
This is so because (+) × (-) is (-).
Just like (+) × (+) is (+) and (-) × (-) is (-).
So 10 + (-3) = 10 - 3 = 7.
Answer:
[tex]7[/tex]
Step-by-step explanation:
[tex]10 + ( - 3) \\ \\ (+) \: \times \: (- )= (- ) \\ so \: 10 - 3 \\ = 7[/tex]
Simplify the expression where possible. (r^3)^ -2
Answer:
Step-by-step explanation:
We apply the properties of the power.
[tex]\left(r^3 \right)^{-2}=r^{3*(-2)}=r^{-6}=\dfrac{1}{r^6}[/tex]
Answer:
r^-6 OR 1 / (r^6)
Step-by-step explanation:
For this expression, we can use exponential power rules to simplify.
Power to a power, you multiply the exponents.
So, (r^3)^-2 == r^-6
We can use the fact that negative exponents will be the base to the power in the denominator.
r^-6 == 1/(r^6)
Cheers.
the cost of renting a car for one day and driving m miles if the rate is $49 per day plus 5 cents per mile
Answer:
[tex]Total\ Rent = 49 + 5m[/tex]
Step-by-step explanation:
Given
Rent per day = $49
Addition = 5 cents per mile
Required
Determine the rent for a day and m miles
First, we need to generate a formula from the given parameters;
Let d represent number of days and m represent additional miles;
[tex]Total\ Rent = 49 * d + 5 * m[/tex]
[tex]Total\ Rent = 49 d + 5 m[/tex]
Solving for the rent for a day and m miles
We have that: d = 1 and m = m
Substitute these in the formula above
[tex]Total\ Rent = 49 * 1 + 5 * m[/tex]
[tex]Total\ Rent = 49 + 5m[/tex]
Hence, the total rent is
[tex]Total\ Rent = 49 + 5m[/tex]
can someone please help me
Answer:
m = 20a = 48These are the answers.Step-by-step explanation:
1. m/-8 = -2.5
*-8 = *-8
m = -2.5*-8
m = 2.5*8
m = 20
2. 7/8a = 42
*8 *8
7a = 336
/7 /7
a = 336/7
a = 48
Hope this helped,
Kavitha
WILL GIVE BRAINLIEST
In the following graph, ∆ABC is congruent to ∆A’B’C’. A teacher asks Janine to state the translation rule for this transformation. She focuses on point C’ and states that “the translation rule is
(x,y)→(x-2, y-6).
In other words, to shift from the blue to the red triangle, you must shift each point two units to the left and six units down. Janine made an error.
Explain how to correct her rule by either using transformation notation showing each step or explain using 2-3 sentences.
Answer:
Given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down, which is also T₍₋₃, ₋₅₎, by transformation notation
Step-by-step explanation:
The coordinates of the point C is (1, -1)
The coordinates of the point C' is (-2, -6)
Therefore, the translation required to shift the point C from to point C' is found as follows;
The difference between the x, and y-coordinates of the points C and C' are given as follows;
Δx, C to C' = (-2 - 1) = -3
Δy, C to C' = (-6 - (-1)) = (-6 + 1) = -5
Therefore, the the transformation from C to C' it T₍₋₃, ₋₅₎
Which can be presented as, given that the triangle with point C is the blue triangle and the triangle with the point C' is the red triangle, then to shift from the blue triangle to the red triangle, you must shift each point two units to the left and five units down.
Simplify 8x - 3 (x + 1) - 4.
Answer:
5x-1
Step-by-step explanation:
8x-3(x+1)-4
{open the brackets}3x-3
8x-3x-3-4
5x+(-7), which is 5x-7
If a translation of (x, y) + (x +6, y-10) is applied to
figure ABCD, what are the coordinates of D'?
B
O (-5,-2)
O (1, -12)
(4, -15)
O (-9, 6)
6
5
-32
2
3
х
D
с
The coordinates of the point D of the rectangle after the translation is given by D' ( 1 , -12 )
What is Translation?A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.
A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.
Given data ,
Let the coordinates of the rectangle be ABCD
Now , the coordinate of the point D be D ( -5 , -2 )
And , the translation rule is ( x , y ) → ( x + 6 , y - 10 )
So , the point after translation be D'
where D' = D ( -5 + 6 , -2 - 10 )
The coordinates of D' = D' ( 1 , -12 )
Hence , the coordinates after translation is D' ( 1 , -12 )
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Divide each polynomial by a monomial. (4x^4+2x^3+2x^2)÷10x
Answer:
2/5x³ + 1/5x² + 1/5x
Step-by-step explanation:
You have to divide each term in the polynomial by the monomial.
(4x⁴ + 2x³ + 2x²)/10x
2/5x³ + 1/5x² + 1/5x
The solution is, 2/5x³ + 1/5x² + 1/5x is the answer of the division.
What is division?Division is the process of splitting a number or an amount into equal parts. Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
here, we have,
given that,
(4x^4+2x^3+2x^2)÷10x
now,
we have to divide each term in the polynomial by the monomial.
so, we get,
(4x⁴ + 2x³ + 2x²)/10x
=(4x⁴/ 10x + 2x³/ 10x + 2x²/ 10x )
=2/5x³ + 1/5x² + 1/5x
Hence, The solution is, 2/5x³ + 1/5x² + 1/5x is the answer of the division.
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weight to the nearest pound of 17 cats:10, 15, 9, 8, 11, 10, 9, 8, 13, 9, 12, 10, 13, 11, 9, 12, 10
Answer:
Step-by-step explanation:
+ si
Express the interval shown on the number line in inequality notation.
==============================================
Explanation:
The left endpoint is -2. The right endpoint is 10. Both endpoints are open holes, meaning we do not include them as part of the green shaded solution region. If x is a solution, then the solution can be described as [tex]-2 < x < 10[/tex] which converts to the interval notation [tex](-2, 10)[/tex]. The curved parenthesis says "do not include the endpoint".
Note: this is not ordered pair notation (x,y). Unfortunately math tends to reuse symbols so it might be a bit confusing at first.
Find m<LMN if m<LMT=23° and m<TMN=144°
Answer:
167°
Step-by-step explanation:
<LMN = <LMT + <TMN
23° + 144° = 167°
<LMN = 167°
(2x2 + 2x + 3) - (x2 + 2x + 1) =
O A. x2 + 4
O B. x2 + 4x + 2
O C. x2 + 4x + 4
O D. x2 + 2
Answer:
[tex] \boxed{\sf D. \ x^2 + 2} [/tex]
Step-by-step explanation:
[tex] \sf Simplify \ the \ following: [/tex]
[tex] \sf \implies (2 {x}^{2} + 2x + 3) - ( {x}^{2} + 2x + 1)[/tex]
[tex] \sf - ( {x}^{2} + 2x + 1) = - {x}^{2} - 2x - 1 : [/tex]
[tex] \sf \implies (2 {x}^{2} + 2x + 3) - {x}^{2} - 2x - 1[/tex]
[tex] \sf Grouping \ like \ terms: [/tex]
[tex] \sf \implies (2 {x}^{2} - {x}^{2}) + (2x - 2x)+ (3 - 1)[/tex]
[tex] \sf 2 {x}^{2} - {x}^{2} = {x}^{2} : [/tex]
[tex] \sf \implies {x}^{2} + (2x - 2x)+ (3 - 1)[/tex]
[tex] \sf 2x - 2x = 0 : [/tex]
[tex] \sf \implies {x}^{2} + 0+ (3 - 1)[/tex]
[tex] \sf 3 - 1 = 2 : [/tex]
[tex] \sf \implies {x}^{2} +2[/tex]
Mr Hassan gave his year 7 class a test on Friday. The highest possible mark for the test was 10.
Answer/Step-by-step explanation:
a. From the bar graph, 1 student scored 9, 4 students scored 10.
Therefore, the no. of students who scored above 8 is: [tex] 1 + 4 = 5 [/tex]
b. From the graph, we have the following:
3 students scored 1
5 students scored 2
2 students score 4
6 students scored 5
12 students scored 8
1 student scored 9
4 students scored 10
Total no. of pupils in year 7 class = 3 + 5 + 2 + 6 + 12 + 1 + 4 = 33 students
c. It is assumed that all the students in Mr Hassan's year 7 class took the test.
What is the slope of the line represented by the equation y = 4/5x- 3?
-3
-4/5
4/5
3
Answer:
m= 4/5
Step-by-step explanation:
The equation of the line is in slope-intercept form.
y=mx+b
where m is the slope and b is the y-intercept.
Basically, the number that is being multiplied by x is the slope, and the number added or subtracted from that is the y-intercept.
We are given the equation:
y= 4/5x -3
4/5 is the coefficient of x. 3 is being subtracted from 4/5x.
Therefore, the slope of the line is 4/5 and the y-intercept is -3.
The question asks us to find the slope of the line, so the answer is 4/5.
The slope of the line represented by the equation y = 4x/5 - 3 is 4/5.
Given that an equation y = 4x/5 - 3 we need to find the slope of the equation.
In the slope-intercept form of a linear equation (y = mx + b), "m" represents the slope of the line.
The slope determines how steep or shallow the line is. It also tells us the rate at which the line is rising or falling as we move along the x-axis.
In the given equation, the coefficient of "x" is 4/5. This is the slope of the line.
To understand this better, compare the equation with the slope-intercept form: y = mx + b.
In the given equation, m (the slope) is 4/5. It means that for every 1 unit increase in the x-coordinate, the y-coordinate increases by 4/5 (or decreases by 4/5 if the slope were negative).
So, the line rises (or falls) at a rate of 4/5 for every unit increase along the x-axis.
In this case, since the slope is positive, the line will rise as we move from left to right on the coordinate plane.
Graphically, the line with a slope of 4/5 would look like a rising line, making an angle with the positive x-axis, and moving upwards from left to right.
So, the slope of the line represented by the equation y = (4/5)x - 3 is 4/5.
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A survey of 2690 musicians showed that 368 of them are left-handed. Find a point estimate for p, the population proportion of musicians that are left-handed.
Answer: 0.137.
Step-by-step explanation:
Let p be the population proportion of musicians that are left-handed.
Given: Sample size : n= 2690 [subset of population]
Number of musicians that are left-handed: x= 368
Then the sample proportion: [tex]\hat{p}=\dfrac{368}{2690}\approx0.137[/tex]
Since sample proportion is the best point estimate of the population proportion.
Hence, a point estimate for p, the population proportion of musicians that are left-handed is 0.137.