[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{0}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{4}}} \implies \cfrac{0 +3}{-2} \implies \cfrac{ 3 }{ -2 } \implies - \cfrac{3}{2}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{3}{2}}(x-\stackrel{x_1}{4}) \implies y +3 = - \cfrac{3}{2} ( x -4) \\\\\\ y+3=- \cfrac{3}{2}x+6\implies {\Large \begin{array}{llll} y=- \cfrac{3}{2}x+3 \end{array}}[/tex]
Answer:
y = -1.5x + 3
Step-by-step explanation:
gradient = (-3 - 0) / (4 - 2) = -3/2 = -1.5.
equation on line through two points is given by
y - y1 = m (x - x1)
where y1 and x1 are the coordinates of the point and m is the gradient.
we can choose either point to use in the equation.
y - 0 = -1.5 (x - 2) = -1.5x + 3
y = -1.5x + 3
La señora Luisa pide un presupuesto para reparar ocho joyas. El encargado de la joyería le dice que cobrará $6 por la primera joya, y por cada pieza sucesiva lo triple que la anterior. ¿Cuánto le cobrará el joyero a la señora Luisa?
The amount that the jeweler would charge Mrs. Luisa, given the prices of the successive jewelry would be $ 19, 680
How to find the total cost ?The charge for repairing the jewelry pieces is calculated in a geometric progression:
= 6, 63, 63 ², 63 ³, ..., 63 ⁷
The sum of the first n terms in such a progression is:
S = a x (r ⁿ - 1) / ( r - 1 )
Seeing as there are 8 pieces of jewelry, the total cost to Mrs. Luisa would be:
S = 6 x ( 3 ⁸ - 1) / ( 3 - 1 )
S = 6 x ( 6561 - 1 ) / 2
S = 6 x 6560 / 2
S = 3 x 6560
S = $ 19, 680
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Pls help asap RSM QUESTION!!!
what is greater 54300ml or 54L?
Answer:
54300 ml is greater than 54 L. This is because 54300 ml is equivalent to 54.3 L, which is larger than 54 L.
Given f of x is equal to the quantity x plus 3 end quantity over the quantity x squared plus 2 times x minus 3 end quantity and g(x) = x + 2, evaluate (g – f )(2).
The composite function (g - f)(2) when evaluated is 3
Evaluating the composite functionsFrom the question, we have the following parameters that can be used in our computation:
f(x) = (x + 3)/(x² + 2x - 3)
Also, we have
g(x) = x + 2
The composite function (g - f)(2) is calculated as
(g - f)(2) = g(2) - f(2)
Where, we have
g(2) = 2 + 2 = 4
Also, we have
f(2) = (2 + 3)/(2² + 2(2) - 3) = 1
So, we have
(g - f)(2) = 4 - 1
Evaluate
(g - f)(2) = 3
hence, the composite function (g - f)(2) when evaluated is 3
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4 2/3 divided by 7 write the quotient in simplified fraction
Answer: The correct answer is 42
Step-by-step explanation:
Answer:
8/21
Step-by-step explanation:
4 2/3=8/3, times 1/7 (or divide by 7) equals 8/21.
write equivalent fraction for 1 1/5 and 1 1/3
Answer:
1 1/5 = 6/5
1 1/3 = 4/3
Step-by-step explanation:
hope this helps, if you’re looking for 1 1/5 + 1 1/3 please tell me and I will solve that for you
On an overnight camping trip, the Adventure Scouts could choose to sleep in a cabin, in a tent, or outside under the stars. A total of 115 scouts went on the trip. Twice as many scouts slept in a cabin as slept in a tent. The same number of scouts slept outside as slept in a cabin.
How many Adventure Scouts slept outside?
There are 58 Adventure Scouts slept outside on the camping trip.
Let's denote the number of scouts who slept in a cabin, tent, and outside as c, t, and o, respectively. We know that the total number of scouts is 115, so:
c + t + o = 115
We also know that twice as many scouts slept in a cabin as slept in a tent, so:
c = 2t
And we know that the same number of scouts slept outside as slept in a cabin, so:
o = c
We can use these equations to solve for the number of scouts who slept outside:
c + t + o = 115
2t + t + t = 115 (substituting c = 2t and o = c)
4t = 115
t ≈ 28.75
Since we can't have a fractional number of scouts, we need to round this up or down. However, we also know that the number of scouts who slept outside is the same as the number who slept in a cabin, which means that either c or o must be even (since c is twice t). Therefore, we'll round t up to 29 and use that to solve for c and o:
c = 2t ≈ 58
o = c ≈ 58
So, we can conclude that 58 Adventure Scouts slept outside on the camping trip.
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Answer:
46
Step-by-step explanation:
You need to find how many Adventure Scouts slept outside. Start with the information in the problem.
A total of 115 scouts went camping.
Twice as many slept in a cabin as slept in a tent.
The same number slept outside as slept in a cabin.
You can use a diagram to model the problem. Fewer scouts slept in a tent than the other choices. So, start with the scouts who slept in a tent.
Twice as many scouts slept in a cabin as slept in a tent. So, draw 1 box to represent the number who slept in a tent and 2 boxes to represent the number who slept in a cabin.
tent
cabin
outside
The same number of scouts slept outside as slept in a cabin. There are 2 boxes for scouts who slept in a cabin. So, draw 2 boxes to represent the number who slept outside.
tent
cabin
outside
There are 5 boxes in the diagram in all. There were 115 scouts on the trip altogether. So, each box represents 115÷5 scouts. Divide.
2 3
5
1 1 5
– 1 0
1 5
– 1 5
0
Each box represents 23 scouts. There are 2 boxes for the scouts who slept outside. Multiply to find the number of scouts who slept outside.
2 3
× 2
4 6
46 Adventure Scouts slept outside.
QUESTION 1
Use the sine rule to find x. Rationalise and leave your answer in surd form; a+b√c
Use special angles where Sine 30 = and sine 45 = 2x-1 45 2x + 2 30
It can be seen that x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.
How to solveTo find x using the sine rule, we need to solve the equation:
sine(45) / x = sine(30) / (2x + 2√3)
Simplifying this equation, we have:
(2x - 1) / x = 1 / (2x + 2√3)
Cross-multiplying and simplifying further, we get:
(2x - 1)(2x + 2√3) = x
Expanding the brackets, we have:
[tex]4x^2 + 4\sqrt3x - 2x - 2\sqrt3 = x[/tex]
Rearranging the terms and simplifying, we get:
[tex]4x^2 - 3x - 2\sqrt3 = 0[/tex]
Using the quadratic formula, we can solve for x:
x = (-(-3) ± √((-3)^2 - 4(4)(-2√3))) / (2(4))
x = (3 ± √(9 + 32√3)) / 8
Therefore, x = (3 ± √(9 + 32√3)) / 8, which can be expressed in surd form as (3 + √(9 + 32√3)) / 8 or (3 - √(9 + 32√3)) / 8.
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Given △RST≅△LMN, m∠R=65°, and m∠M=70°, what is the measure of ∠T?
Enter your answer in the box.
m∠T=
Answer: ∠T=45°
Step-by-step explanation:
If triangle RST is congruent to triangle LMN, then the angles R=L, S=M, and T=N. Knowing that the sum of angles in a triangle= 180 degrees, then:
∠R+∠S+∠T=180°
∠R=65°
∠M=∠S=70°
180°-∠R-∠S=∠T
180°-65°-70°=
∠T=45°
Find the area of a rectangle with a base of 9 feet and a height of 7 feet
Answer:
63
Step-by-step explanation:
b x h = A
9 x 7 = 63
Stuck on question number 3
Answer:90
Step-by-step explanation:
Sarah spends 30 minutes reading,20 minutes writing,and 20 minutes doing her math. How many minutes does she spends on school work in all
Answer:
She spends 70 minutes in total or 1h 10min
PLEASE MARK IT THE BRAINLIEST!!!!!
If it rains tomorrow, the probability is 0.7 that John will practice his cello. If it does not rain tomorrow, there is only a 0.6 chance that John will practice.
Suppose the chance of rain tomorrow is 60%.
What is the probability that John will practice his cello?
P(John will practice) =
(Type an integer or a decimal.)
Answer:
0.66
Step-by-step explanation:
please read attachments
Help please I will give brainlist!!
The angles in the circle are as follows:
mBC = 107°m∠BAC = 53.5° mBC = 92°How to find arc angles?The central angle of an arc is the central angle subtended by the arc.
The measure of an arc is the measure of its central angle.Therefore,mBC = 107 degrees
The angle subtended by an arc at the center is twice the angle subtended at the circumference.
Therefore, m∠BAC = 107 / 2 = 53.5 degrees
The inscribed angle is half the intercepted arc angle.
Therefore, to find mBC, we solve:
46 = 1 / 2
Next, we cross multiply mBC = 46 × 2
Therefore, mBC = 92 degrees
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Help Quickly! The table shows bear population data gathered by researchers in the Wild Horse Forest. If the total bear population was 2,008 bears in May 2002, estimate the number of total bears counted in 2002 to complete the chart. (Click the picture to zoom in more)
A. 1,060 bears
B. 2,008 bears
C. 1,101 bears
D. 1,823 bears
The number of total bears counted in 2002 will be: A. 1060 bears.
How to determine the total bear estimateTo determine the total bear estimate, we will use the mark-recapture formula. In this formula, we equate the number of the population to MC/R where:
M = Number marked initially
C = Number captured in the second sample
R = The recaptured number
Also, R/C = M/N
For the given problem,
M = 2008
C = 38
R = 72
So, N = 2008 * 38/72
= 1059 approximately 1060 bears.
So, the bear population will amount to 1060.
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Which of the following is the result of expanding
8.5
15.5
32
60
Based on the information, the required result of the expansion for the expression is 8.
How to calculate the value of the expressionIn mathematics, an expression is a combination of numbers, variables, operators, and/or functions that can be evaluated to obtain a numerical or symbolic result. Expressions can take many forms, but typically involve some combination of mathematical symbols such as +, -, ×, ÷, =, and parentheses.
The given expression is 2x-3 .
when x =1, we will get 2(1)-3 = 2-3 =-1
When x=2, we will get, 2(2) -3 = 4-3 =1
When x=3, we will get 2(3)-3 = 6-3=3
When x=4, we will get 2(4)-3 = 8-3=5
The required result of the expansion is -1+1+3+5=8
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The parabola y = x, squared is shifted down by 3 units and to the left by 2 units.
It's important to note that shifting a function involves changing the corresponding variables (x or y) in the equation to achieve the desired translation.
The parabola y = x^2 represents a standard upward-opening parabola with its vertex at the origin (0, 0). To shift this parabola down by 3 units, we subtract 3 from the y-coordinate of each point on the original parabola. Thus, the equation of the shifted parabola becomes y = x^2 - 3.
Similarly, to shift the parabola to the left by 2 units, we subtract 2 from the x-coordinate of each point on the original parabola. The equation of the parabola shifted down by 3 units and to the left by 2 units is y = (x + 2)^2 - 3.
In the shifted parabola, the vertex will be at the point (-2, -3). The parabola retains its general shape, but its position in the coordinate plane has changed. It is now translated 2 units to the left and 3 units down compared to the original parabola y = x^2.
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Indicate which of the following variables are continuous.
1. Length of a frog's jump.
2. Monthly TV cable bills.
3. Lottery revenues of states.
4. Number of wheels of a car.
5. Monthly spendings of a family.
O 1, 2, 3 and 5
O 1, 4 and 5
O 1, 2, 3 and 4
O 1 and 2
The correct variables which are continuous are,
1. Length of a frog's jump.
2. Monthly TV cable bills.
3. Lottery revenues of states.
4. Number of wheels of a car.
We have to given that;
To find correct variables which are continuous.
Since, The number of wheels of a car is a discrete variable, because it can only take certain integer values (2, 3, 4, etc.), while the other variables can take any real value within a certain range.
Hence, The correct variables which are continuous are,
1. Length of a frog's jump.
2. Monthly TV cable bills.
3. Lottery revenues of states.
4. Number of wheels of a car.
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An amount of $21,000 is borrowed for 13 years at 8.75% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Answer: To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the final amount
P is the initial principal (the amount borrowed)
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time period in years
In this case, we have:
P = $21,000
r = 8.75% = 0.0875
n = 1 (interest is compounded annually)
t = 13 years
So, plugging these values into the formula, we get:
A = 21,000(1 + 0.0875/1)^(1*13)
A = 21,000(1.0875)^13
A = $58,150.51
Therefore, if the loan is paid in full at the end of the 13-year period, $58,150.51 must be paid back, which includes the original principal plus the interest accrued over the 13-year period.
Step-by-step explanation:
The table below shows the demand for a new bath soap in a shop for each of the last 7 months.
Month 1 2 3 4 5 6 7 8
Demand 23 29 33 40 41 43 49 52
Calculate a 3-month moving average for months two to nine.
Find the derivative of the function
thank you guys sm
The derivative of the function is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = log₂ ( 3x + 4 )³
On simplifying , we get
On taking the derivative of the function , we get
f' ( x ) = d/dx ( log₂ ( 3x + 4 )³ )
d/dx ( log₂ ( 3x + 4 )³ ) = 1/ ln ( 2 ) [ d/dx( 3x + 4 )³ ]
On applying chain rule , we get
f' ( x ) = 1/ ln ( 2 ) 1/( 3x + 4 )³ ( 9 ( 3x + 4 )² )
So , cancelling out the similar terms , we get
f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
Hence , the derivative is f' ( x ) = 9 / ( 4 + 3x ) ( ln 2 )
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Dos ángulos de un cuadrilátero miden 60° y 80°. Los otros dos ángulos están en una
proporción de 2:9. ¿Cuáles son las medidas de esos dos ángulos?
Answer:
La suma de los cuatro ángulos de un cuadrilátero es igual a 360 grados. Entonces, si dos ángulos miden 60° y 80°, la suma de esos ángulos es de 140 grados.
Los otros dos ángulos están en una proporción de 2:9, lo que significa que la suma de sus medidas es de 11 partes. Si representamos las medidas de estos ángulos como 2x y 9x, respectivamente, entonces podemos escribir la ecuación:
2x + 9x = 11 partes
11x = 11 partes
x = 1 parte
Por lo tanto, el ángulo más pequeño mide 2x = 2 partes o 2 × 1 = 2 grados, y el ángulo más grande mide 9x = 9 partes o 9 × 1 = 9 grados.
En resumen, los dos ángulos faltantes miden 2° y 9°.
Step-by-step explanation:
Help Screenshot need help
The probability that the student was female and got grade C is P ( A ) = 0.12833
Given data ,
Let the table represent the group of students with their gender and the grades in school
Now , the probability that the student was female = total number of females / total number of students
So , probability that the student was female = 22/60
Now , the probability that the student got grade C = 21/60
So , the compound probability P ( A ) = probability that the student was female and got grade C
On simplifying , we get
P ( A ) = ( 22/60 ) ( 21/60 )
P ( A ) = 462/3600
P ( A ) = 0.12833
Hence , the probability is P ( A ) = 0.12833
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Given f(x) = x2 – 7x + 10 and g(x) = x – 5, find (f + g)(x).
Answer:
b,x²-6x+5
Step-by-step explanation:
(f+g)(x)=f(x)+g(x)
=x²-7x+10+(x-5)
=x²-7x+10+x-5
=x²-7x+x+10-5
=x²-6x+5
Paige Inc. has a division that makes paint and another division that constructs houses. The paint division incurs the following costs for one litre of paint: Direct materials R1.10 Direct labour R1.45 Variable overhead R0.90 Fixed overhead R1.15 Total R4.60 The Paint Division can make 1 000 000 litres per year, and is operating at capacity. The Construction Division currently buys paint from an outside supplier for R5.20 per litre (the same price that the Paint Division receives). What is the minimum transfer price?
The solution is, $85,500 are the total cost savings for Leather Stuff.
Explanation:
In this case, we need to calculate the saving per zipper which is external price minus agreed transfer price.
Then, we will multiply the saving per zipper by the quantity of zipper required by Leather Stuff, which is 90,000 zippers.
Cost saving per zipper
= External price - Agreed transfer price
= $3.50 - $3.25
= $0.25
Total cost saving
= $0.95 x 90,000 zippers
= $85,500
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complete question:
Quinn Inc. has a number of divisions. One division, Style, makes zippers that are used in the manufacture of boots. Another division, LeatherStuff, makes boots that use the zippers and needs 90,000 zippers per year. Style incurs the following costs for one zipper: Direct materials $0.23 Direct labor 0.20 Variable overhead 0.95 Fixed overhead 1.32 Total $2.70 Quinn has capacity to make 950,000 zippers per year, but due to a soft market, only plans to produce and sell 620,000 zippers next year. LeatherStuff currently buys zippers from an outside supplier for $3.50 each (the same price that Style receives). Assume that Style and LeatherStuff have agreed on a transfer price of $3.25. What are the total cost savings for LeatherStuff?
Find the value of x. Round to the nearest tenth, if necessary. NEED ANSWERS FAST WILL MARK BRAINLIEST
Answer:
Step-by-step explanation:
[tex]28^{2} = 11^2 + x^2\\ 784 = 121 + x^2\\x^2 = 663\\x = 25.74\\x[/tex]≅ [tex]26[/tex]
plot -8/5 and 1.8 on number line
The points are shown on the number line as below.
The given numbers are,
-8/5 and 1.8
Now convert -8/5 into decimal form
therefore,
Divide 8 by 5 we get,
-8/5 = -1.6
Since we know that,
On a number line, arithmetic procedures can be better described. To begin, one needs understand how to locate numbers on a number line. A number line's midway point is zero.
Positive numbers occupy the right side of the zero on the number line, whereas negative numbers occupy the left side of the zero. The value of a number diminishes as we travel to the left side. 1 is greater than -2, for example.
Integers, fractions, and decimals may all be simply expressed on a number line.
The points are plotted on number line shown below.
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I ne table below represents the function r, and the tonowing grapn represents the function g.
0 1
-6 -5 -4 -3 -2 -1
-10 -8
-2
22
X
f(x) 8-2-8
Complete the following statements.
The functions / and g have
The y-intercept of fis
the y-intercept of g.
Over the interval [-6, -3), the average rate of change of fis
9
-4 -2
6
4
the average rate of change of g.
Since the average rates of change of f and g cannot be determined from the given information provided.
We can find the average rate of change of function f over the interval [-6, -3) as:
The average rate of change of f;
= (f (6) - f (3)) / (6 - 3)
= (71 - 59) / 2 = 6
We have the two given points to set up equations:
-53 = a(3)^b - 41
-53 = a(5)^b - 41
0 = a(3^b - 5^b)
Since 3^b ≠ 5^b, we must have a = 0, that means g is not a valid exponential function passing through the given points.
Therefore,
We can conclude, that the average rates of change of f and g cannot be determined.
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If f(x) = (3+x)/(x-3) , what is f(a+2)
Answer:
Step-by-step explanation:
f(x) = [tex]\frac{3+x}{x-3}[/tex]
f(a+2) = [tex]\frac{3+a+2}{a+2-3}[/tex]
f(a+2) = [tex]\frac{5+a}{a-1}[/tex]
Solve these using quadratic formula
Write out your work!
I need the vertex
Axis of symmetry
Intercepts -also include the function to find the intercepts-
The vertex is at (1, 4).
The vertex is at (-1, -4).
The axis of symmetry is x = 1.
The axis of symmetry is x = -1.
The x-intercepts are (3, 0) and (-1, 0).
The x-intercepts are approximately (-2.3, 0) and (0.3, 0).
The y-intercept is (0, 3).
The y-intercept is (0, -6).
We have,
To solve the equations using the quadratic formula, we need to rewrite them in the standard form ax² + bx + c = 0.
-x² + 2x + 3 = 0 can be rewritten as -1x² + 2x + 3 = 0
Here, a = -1, b = 2, and c = 3
Using the quadratic formula, we have:
x = (-b ± √(b² - 4ac)) / 2a
x = (-2 ± √(2² - 4(-1)(3))) / 2(-1)
x = (-2 ± √(16)) / -2
x = 1 ± 2
So, x = 3 or x = -1
2x² + 4x - 6 = 0 is already in the standard form with a = 2, b = 4, and c = -6
Using the quadratic formula, we have:
x = (-4 ± √(4² - 4(2)(-6))) / 2(2)
x = (-4 ± √(52)) / 4
x = (-2 ± √(13)) / 2
To find the vertex of each parabola, we can use the formula x = -b / 2a and then substitute the value of x into the equation to find y.
For -x² + 2x + 3 = 0
We have a = -1 and b = 2, so the vertex is at
x = -b / 2a = -2 / (2(-1)) = 1.
Substitute x = 1 into the equation to find y:
y = -1(1)² + 2(1) + 3 = 4.
So the vertex is at (1, 4).
For 2x² + 4x - 6 = 0,
We have a = 2 and b = 4, so the vertex is at x = -b / 2a = -4 / (2(2)) = -1. Substitute x = -1 into the equation to find y: y = 2(-1)² + 4(-1) - 6 = -4.
So the vertex is at (-1, -4).
The axis of symmetry is a vertical line that passes through the vertex.
For -x² + 2x + 3 = 0, the axis of symmetry is x = 1.
For 2x² + 4x - 6 = 0, the axis of symmetry is x = -1.
To find the x-intercepts, we can set y = 0 in each equation and solve for x using the quadratic formula.
For -x² + 2x + 3 = 0, we have:
x = (-2 ± √(2² - 4(-1)(3))) / 2(-1)
x = (-2 ± √(16)) / -2
x = 1 ± 2
So the x-intercepts are (3, 0) and (-1, 0).
For 2x² + 4x - 6 = 0, we have:
x = (-4 ± √(4² - 4(2)(-6))) / 2(2)
x = (-4 ± √(52)) / 4
x = (-2 ± √(13)) / 2
So the x-intercepts are approximately (-2.3, 0) and (0.3, 0).
To find the y-intercept, we need to set x = 0 and solve for y.
Setting x = 0 in -x² + 2x + 3 = 0.
-0 + 0 + 3 = 3
Therefore, the y-intercept is (0, 3).
Setting x=0 in 2x² + 4x - 6.
2(0)² + 4(0) - 6 = -6
Therefore, the y-intercept is (0, -6).
Thus,
The vertex is at (1, 4).
The vertex is at (-1, -4).
The axis of symmetry is x = 1.
The axis of symmetry is x = -1.
The x-intercepts are (3, 0) and (-1, 0).
The x-intercepts are approximately (-2.3, 0) and (0.3, 0).
The y-intercept is (0, 3).
The y-intercept is (0, -6).
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