Answer:
[tex]\boxed {\boxed { \sf 12 \ inches}}[/tex]
Step-by-step explanation:
The area of a triangle can be calculated using the following formula.
[tex]a=\frac{1}{2} bh[/tex]
The area of the triangle is 24 square inches and the base is 4 inches long.
a= 24 in² b= 4 inSubstitute the values into the formula.
[tex]24 \ in^2 = \frac {1}{2} * 4 \ in * h[/tex]
Multiply on the right side of the equation.
[tex]24 \ in ^2 = ( \frac{1}{2} * 4 \ in ) * h[/tex]
[tex]24 \ in ^2 =2 \ in *h[/tex]
We are solving for the height of the triangle, so we must isolate the variable h. It is being multiplied by 2 inches. The inverse of multiplication is division, so we divide both sides by 2 inches.
[tex]\frac { 24 \ in ^2 }{2 \ in }= \frac{ 2 \ in *h}{ 2 \ in}[/tex]
[tex]\frac { 24 \ in ^2 }{2 \ in }= h[/tex]
[tex]12 \ in = h[/tex]
The height of the triangle is 12 inches.
What is the slope of the line shown below?
A. -13/6
B. 6/13
C. 13/6
D. -6/13
-
Answer:
13/6
Step-by-step explanation:
We can use the slope formula
m = ( y2-y1)/(x2-x1)
= (6 - -7)/(1 - -5)
= ( 6+7)/ (1+ 5)
= 13/6
what is the least number to be added to 1500 to make it a perfect square?
Answer:
21
Step-by-step explanation:
√1500 = 38.7
Round to nearest whole number
≈39
39²-1500
= 1521 - 1500
= 21
(5, 4)
11-5-2)
16.nat's the slope-intercept form of the equation of the line graphed in this figure?
O A. y = 5/3x + 1
O B.y=-3x + 1
O C. y = 3x + 1
O D.y = -5/3X - 1
Answer:
The answer is B. y=3/5x+1A box contains 40 identical discs which are either red or white if probably picking a red disc is 1/4. Calculate the number of;
1. White disc.
2. red disc that should be added such that the probability of picking a red disc will be 1/4
How do i do this equation
-3(-2y-4)-5y-2=
Answer:
Step-by-step explanation: distribute -3 to the parenthesis (-2y-4) to eliminate the parenthesis. you’ll be left with 6y +12 -5y-2. From there you combine like terms. do 6y-5y= 1y or just y and 12-2 = 10. your answer would be 10
Partition the circle into 4 equal sections. What unit fraction of the circle’s area does each section represent?
Answer:
1/4
Step-by-step explanation:
If the 4 sections have equal areas, then each section has 1/4 of the original circle's area.
If Q(x) = x2 – 2 – 2, find Q(-3).
Answer: A (10)
Step-by-step explanation:
Plug in Q(-3) into formula x^2-x-2
(-3)^2-(-3)-2= 9+3-2
=10
The rationalisation factor of 2 + √3 is
step by step for BRAINLIST
Answer:
rationalising factor wud be
2 - root3
as on multiying both and applying identity we end up
2^2 - (root3)^2
4 - 3 = 1
we got a rational number so rationalisng factor is
2 - root3
woman has 7 coworkers' man. How many different possible groups of four people could do the project, if one out of three is women? g
Answer: 24ways
Step-by-step explanation:
Given data:
No of men in the workplace = 7
No of women in the workplace = 1
How many ways can a group of 4 people carry out a project if on out of the 3 must be a woman.
Solution.
A group of 4 can carry out the project with one be a woman
This means there must be 3 males and 1 female in the group
= 4p3
= 24ways
The project can be carried out by 4 groups in 24 ways
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = - 8p^2 + 24,000p. What unit
price should be established for the dryer to maximize revenue? What is the maximum revenue?
The unit price that should be established to maximize revenue is $|
(Simplify your answer.)
Here we have a problem of maximization and quadratic equations.
The unit prize that maximizes the revenue is $1,500, and the maximum revenue is $18,000.
We know that the revenue equation is:
R(P) = - 8p^2 + 24,000p
Where the variable p is the price.
Now we want to find the value of p that maximizes the revenue.
To do it, we can see that the revenue equation is a quadratic equation with a negative leading coefficient.
This means that the arms of the graph will go downwards, then the maximum point of the graph will be at the vertex.
Remember that for an equation like:
y = a*x^2 + b*x+ c
The x-value of the vertex is at:
x = -b/(2*a)
Then for the equation:
R(P) = - 8p^2 + 24,000p
The vertex is at:
p = -(24,000)/(2*-8) = 1,500
The value of p that maximizes the revenue is p = $1,500
To get the maximum revenue, we need to evaluate the revenue equation in that p value.
R(1,500) = - 8*(1,500)^2 + 24,000*1,500 = 18,000
And the revenue equation is in dollars, then the maximum revenue is 18,000 dollars.
If you want to learn more, you can read:
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p = 1500 $ the unit price
R(p) = 18000000 $ maximum revenue
We will use two different procedures to calculate the maximum revenue.
That is equivalent to solve the problem and after that to test the solution
The first one is:
R(p) = - 8*p² + 24000*p
we realize that R(p) is a quadratic function ( a parabola) of the form:
y = a*x² + b*x + c ( c = 0 in this case)
We also know that as the coefficient of p² is negative the parabola opens downwards then the vertex is a maximum value for R(p), and the x coordinate of p is:
x = p = - b/2*a then by substitution
p = - ( 24000)/ 2 ( - 8)
p = 1500 $ and for that value of p
R(p) = - 8 ( 1500)² + 24000* (1500) = - 18000000 + 36000000
R(p) = 18000000 $
The second procedure is solving with the help of derivatives.
R(p) = - 8*p² + 24000*p
Tacking derivatives on both sides of the equation we get:
R´(p) = -16p + 24000
If R´(p) = 0 then -16p + 24000 = 0
p = 24000/ 16 p = 1500
if we check for the second derivative
R´´(p) = -16 -16 < 0 therefore there is a maximum value for R(p) when p = 1500, and that value is:
By substitution in R(p)
R(p) = -8 *(1500)² + 24000* 1500
R(p) = - 18000000 + 36000000
R(p) = 18000000 $
13 is subtracted from the product of 4 and a certain number. The result is equal to the sum of 5 and the original number. Find the number.
Answer:
Step-by-step explanation:
4x - 13 = x + 5 Add 13 to both sides
4x = x + 18 Subtract x
3x = 18 Divide by 3
x = 6
Need Help
*Please Show Work*
Hi there! :)
Answer:
y = -2x + 3
Step-by-step explanation:
We can write an equation in slope-intercept form. Use the slope formula to find the rate of change in the table:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in values from the table:
[tex]m = \frac{5 - 7}{-1 - (-2)}[/tex]
Simplify:
m = -2 (rate of change)
Use a point from the table (-2, 7) and the slope to solve for the equation for the linear function:
7 = -2(-2) + b
7 = 4 + b
7 -4 = b
b = 3
Rewrite:
y = -2x + 3 is the equation for the linear function.
200,000=2x10 to the power of 6
False.
2x10^6 you move the decimal point 6 places to the right. ( add 6 zeros after the 2)
2x 10^6 = 2,000,000
HELPPPPP ASP PLZZZZZ
Answer:
[tex](f-g)(x)[/tex]
[tex]f(x)-g(x)[/tex]
[tex]x^{2} -6x-27-x+9[/tex]
[tex]x^{2} -7x-18[/tex]
----------------------
[tex](f*g)(x)[/tex]
[tex]=f(x)g(x)[/tex]
[tex](x^{2} -6x-27)(x-9)[/tex]
[tex]=x^{3} -15x^{2}+27x+243[/tex]
----------------------
[tex]\frac{f}{g} (x)[/tex]
[tex]\frac{x^{2} -6x-27}{x-9}[/tex]
[tex]\frac{(x-9)(x+3)}{x-9}[/tex]
[tex]x+3[/tex]
-----------------------
[tex](f+g)(x)[/tex]
[tex]f(x)+g(x)[/tex]
[tex]=x^{2} -6x-27+x-9[/tex]
[tex]=x^{2} -5x-36[/tex]
------------------------
OAmalOHopeO
------------------------
Which statement about this function is true?
O A.
The value of a is positive, so the vertex is a minimum.
OB.
The value of a is negative, so the vertex is a minimum.
OC.
The value of a is negative, so the vertex is a maximum.
OD
The value of a is positive, so the vertex is a maximum.
Answer:
b
Step-by-step explanation:
The value of a is negative, so the vertex is a minimum.
Intro to Translations
Acellus
Find the image of the given point
under the given translation.
P(-1,2)
T(x, y) = (x + 2, y - 4)
P' = ([?], [])
Enter the number that belongs
in the green box.
Answer:
(1,-2)
Step-by-step explanation:
P(-1,2) and (x, y) -> (x + 2, y - 4). Plugging in x and y in the transformation, the transformed points are (-1+2, 2-4) = (1,-2)
solve for x. Solve for x solve for x solve for x
Answer:
x=29
Does the answer help you?
Answer:
x=29
Step-by-step explanation:
Calculate how much 10% acid solution and how much pure acid must be mixed to end up with exactly 12 liters of 30% acid solution. Rounding to the nearest hundredth of a liter, you'll need ___ liters of the pure acid.
Answer:
2.67 liters
Step-by-step explanation:
Let "a" represent the number of liters of pure acid needed to make the desired solution. Then the amount of acid in the mix is ...
(100%)x +(10%)(12 -x) = (30%)(12)
(90%)x = 12(20%) . . . . . subtract (10%)(12)
x = 12(2/9) . . . . . divide by 90%
x = 2 2/3 . . . liters
You'll need 2.67 liters of the pure acid.
1 What is the product of 2r^2- 5 and 3r
Answer:
Step-by-step explanation:
3r(2r^2 - 5)
6r^(2 + 1) - 5*3r
6r^3 - 15r
Consider the line =−−7x4y−6.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
4/7
Step-by-step explanation:
Original equation, in general form: -7x - 4y - 6
Rearrange to get: 4y = -7x - 6
Divide both sides by 4 to get: y = -7/4(x) - 1.5
To find the slope of a line perpendicular to another line, take the original gradient, and find the negative inverse
So for here,
Original gradient: -7/4
Negative: 7/4
Negative Inverse: 4/7 (which is our gradient)
Done!
PLEASE HELP !! (2/5) -50 POINTS-
Answer:
[tex]X=\begin{bmatrix}5\\ 14\\ -10\end{bmatrix}[/tex]
Step-by-step explanation:
Our approach here is to isolate X, and simplify this solution. We want to begin by subtracting matrix 2, as shown below, from either side - the first step in isolating X. Afterwards we can multiply either side by the inverse of matrix 1, the co - efficient of X, such that X is now isolated. We can then simplify this value.
Given,
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ \:\:\:3&-2&-1\end{bmatrix}[/tex] : Matrix 1
[tex]\begin{bmatrix}3\\ -1\\ 8\end{bmatrix}[/tex] : Matrix 2
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}X+\begin{bmatrix}3\\ -1\\ 8\end{bmatrix}=\begin{bmatrix}6\\ 4\\ 5\end{bmatrix}[/tex] ( Subtract Matrix 2 from either side )
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}X=\begin{bmatrix}6\\ 4\\ 5\end{bmatrix}-\begin{bmatrix}3\\ -1\\ 8\end{bmatrix}[/tex] ( Simplify )
[tex]\begin{bmatrix}6\\ 4\\ 5\end{bmatrix}-\begin{bmatrix}3\\ -1\\ 8\end{bmatrix} = \begin{bmatrix}6-3\\ 4-\left(-1\right)\\ 5-8\end{bmatrix}=\begin{bmatrix}3\\ 5\\ -3\end{bmatrix}[/tex] ( Substitute )
[tex]\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}X=\begin{bmatrix}3\\ 5\\ -3\end{bmatrix}[/tex] ( Multiply either side by inverse of Matrix 1 )
[tex]X=\begin{bmatrix}1&2&3\\ -3&5&5\\ 3&-2&-1\end{bmatrix}^{-1}\begin{bmatrix}3\\ 5\\ -3\end{bmatrix}=\begin{bmatrix}5\\ 14\\ -10\end{bmatrix}[/tex] - let's say that this is Matrix 3. Our solution would hence be Matrix 3.
A team wishes to purchase 10 shirts of the same color. A store sells shirts in 3 different colors. What must the inventory of the store be in order to conclude that there are at least 10 shirts in one of the three colors?
Answer:
30
Step-by-step explanation:
prove that is here
[tex]1 - cos {2}a \div 1 - sin a{2} = tan {2} a[/tex]
[tex]\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}[/tex]
LHS[tex]\boxed{\sf \dfrac{cosA}{sinA}=cotA}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}[/tex]
[tex]\\ \sf\longmapsto 1-cot2A[/tex]
[tex]\\ \sf\longmapsto 1-\dfrac{1}{tan2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{tan2A-1}{tan2A}[/tex]
[tex]\\ \sf\longmapsto tan2A[/tex]
Convert degrees to radians
Answer:
it's answer is
[tex] \frac{25}{18} [/tex]
evaluate the expression 4x^2-6x+7 if x = 5
Answer:
77
Step-by-step explanation:
4x^2-6x+7
Let x = 5
4* 5^2-6*5+7
4 * 25 -30 +7
100-30+7
7-+7
77
Please help with questions 1-4.
Observe the quantities, ie. see what happens if you increase one or decrease the other.
To simplify imagination, expose one quantity. I will expose y.
1.
[tex]-\frac{y}{4}=2x\implies y=-8x[/tex]
So what is their variation or proportion? If I increase x then y is getting more and more negative. So is this direct or inverse or nothing? It is direct.
2.
[tex]14x=\frac{14}{y}\implies y=x, y\neq0[/tex] again if I increase x then y will match, will also increase. This is again direct.
3.
[tex]y=\frac{13}{x}, x\neq0[/tex] this time if I increase x, y will get smaller. When x is exactly 13, y will be 1 and when x is 10000, y will be 0.0013. This is inverse. One quantity gets really small when other quantity gets really big.
4.
[tex]y=x-2[/tex] if I increase x then y will also increase even though by slightly less (-2) it will still increase. However since there is no multiplication this is not a direct variation nor is it inverse. It is nothing/no-variation.
Hope this helps :)
Find the value of the logarithm. log 122
Answer:
2.086
Step-by-step explanation:
Log 122 is equal to 2.086
What is the difference between a line graph and a scatter plot?
Step-by-step explanation:
scatter plot s are similar to line graphs in that they start with mapping quantitive data points. The difference is that with a scatter plot, the decision is made the the individual points should not be connected directly together with a line but, instead express a trend
If (x - 2) and (x + 1) are factors of
x + px? + qx + 1, what is the sum of p and q?
Answer:
p + q = -3
Step-by-step explanation:
First we need to take the original equation, and factor it to a form that's easier to get two binomial factors from (i.e., let's get a quadratic):
x^3 + px^2 + qx + 1
= x (x^2 + px + q) + 1
Now that we have factored out the x, we have a quadratic trinomial which we know can be broken down into two linear binomials. The problem gives us two linear binomials, so let's take a look.
(x - 2) (x + 1) = (x^2 + px + q)
x^2 - 2x + x -2 = x^2 + px + q
Now let's solve.
x^2 - x - 2 = x^2 + px + q
-x - 2 = px + q
From here, we can easily see that p = -1 (the coefficient of x) and q = -2.
Hence, p + q = -1 + -2 = -3.
Cheers.
Luke owns a trucking company. For every truck that goes out, Luke must pay the driver $17 per hour of driving and also has an expense of $1.75 per mile driven for gas and maintenance. On one particular day, the driver drove an average of 40 miles per hour and Luke's total expenses for the driver, gas and truck maintenance were $522. Write a system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove. Define the variables that you use to write the system.
Answer:
17h+1.75m=522 m=40h
Step-by-step explanation:
Let h= {the number of hours the driver drove}
Let m= the number of miles driven
The driver makes $17 for each hour working, so if the driver worked for hh hours, Luke would have to pay him 17h17h dollars. The cost of gas and maintenance is $1.75 per mile, so for mm miles Luke's costs would be 1.75m1.75m dollars. The total cost of the route 17h+1.75m17h+1.75m equals \$522:$522:
17h+1.75m=522
17h+1.75m=522
Since the driver drove an avearge of 40 miles per hour, if the driver drove hour, he would have driven 40 miles, and if the driver drove hh hours, he would have driven 40h40h miles, therefore mm equals 40h:40h:
m=40h
m=40h
Write System of Equations:
17h+1.75m= 522
m=40h
The truck is going for a run for 6 hours and the system of the equation to solve a further problem related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
The following are the different costs of the truck that Luke must be pay while running a truck:
Luke must pay the driver $17 per hour of driving.A truck has an expense of $1.75 per mile driven for gas and maintenance.Let ' x ' be the total time of driving a truck in hours.
and ' y ' be the total mile distance that is covered by the truck.
Therefore, the system of the equation for the overall running cost for a truck is given below.
[tex]\rm{Cost}=17x+1.75y[/tex]
Now, On one particular day, the driver drove an average of 40 miles per hour, and Luke's total expenses for the driver, gas and truck maintenance were $522.
Thus,
The total distance traveled by truck is 40x.
That is,
[tex]y=40x[/tex]
Substitute the values and solve them further.
[tex]522=17x+1.75y\\522=17x+1.75 \times 40x\\522=17x+70x\\522=87x\\x=6[/tex]
Thus, the truck is going for a run for 6 hours and the system of the equation to solve the further problems related to this is [tex]\rm{Cost}=17x+1.75y[/tex]
To know more about variables, please refer to the link:
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