Rewriting the left-hand side as follows,
[tex](2\cos\theta-6\sin \theta)^2 +(6\cos \theta+2\sin \theta)^2\\\\=4\cos^2 \theta-24\cos \theta \sin \theta+36 \sin^2 \theta+36 \cos^2 \theta+24 \cos \theta \sin \theta+4 \sin^2 \theta\\\\=40\cos^2 \theta+40 \sin^2 \theta\\\\=40(\cos^2 \theta+\sin^2 \theta)\\\\=40[/tex]
answer this please tysm
Answer:
scalene
Step-by-step explanation:
hidhihihihihihi
Find the area of rhombus JKLM given the coordinates of the vertices. Round to the nearest tenth if necessary.
J(-2, -4), K(2, 2), L(6, -4), M(2, -10)
Answer:
The area of rhombus JKLM is 48 units²=====================================
Given Rhombus JKLM,Vertices at J(-2, -4), K(2, 2), L(6, -4), M(2, -10).To find The area of rhombus JKLMSolutionWe know that diagonals of rhombus are perpendicular to each other.
Hence its area is half the product of diagonals.
The diagonals are JL and KM and one of them is vertical and the other one horizontal since x- or y-coordinates are equal in pairs.
Let's find the length of diagonals, using the difference of coordinates:
JL = 6 - (-2) = 8 units,KM = 2 - (-10) = 12 units.Now find the area:
A = JL*KM /2 = 8*12 / 2 = 48 units²Rock Solid Bank and Trust (RSB&T) offers only checking accounts. Customers can write checks and use a network of automated teller machines. RSB&T earns revenue by investing the money deposited; currently, it averages 7.00 percent annually on its investments of those deposits. To compete with larger banks, RSB&T pays depositors 0.50 percent on all deposits. A recent study classified the bank’s annual operating costs into four activities.
Activity Cost Driver Cost Driver Volume
Using ATM Number of uses $ 4,200,000 5,600,000 uses
Visiting branch Number of visits 2,520,000 420,000 visits
Processing transaction Number of transactions 18,480,000 224,000,000 transactions
Managing functions Total deposits 16,800,000 $ 1,050,000,000 in deposits
Total overhead $ 42,000,000
Data on two representative customers follow.
Customer A Customer B
ATM uses 100 200
Branch visits 5 20
Number of transactions 40 1,500
Average deposit $ 6,000 $ 6,000
Required:
a. Compute RSB&T's operating profits.
b. Compute the profit from Customer A and Customer B, assuming that customer costs are based only on deposits. Interest costs = 0.50 percent of deposits; operating costs are 4 percent (= $42,000,000/$1,050,000,000) of deposits.
c. Compute the profit from Customer A and Customer B, assuming that customer costs are computed using the information in the activity-based costing analysis.
A) RSB&T's operating profits are 2,625,000.
B) The profit from Customer A = 42 and Customer B=42.
C) The profit from Customer A=77.7 and Customer B=-207.75(loss)
What does mean by profit?Profit is the term used to describe the financial gain experienced when the revenue from a commercial activity outweighs the costs, costs, and taxes incurred to maintain the activity in question.A business's financial gain when revenue exceeds costs and expenses is frequently referred to as profit. One cup of lemonade, for instance, costs a child at a lemonade stand one quarter. She then charges $2 for the beverage. She made $1.75 in profit on the cup of lemonade.All costs are first deducted from sales, and the result is then divided by sales. This creates the profit formula, which is expressed as a percentage. (Sales - Expenses) Sales = Profit is the formula.Data on two representative customers follow.
[A] Compute RSB&T's operating profits.
Computation of Operating Profits:-
Revenue 19,500,000
Interest to Depositors (1,875,000)
Overheads (15,000,000)
Total operating Profit 2,625,000
[B] Costs are based only on Deposits
Particulars A B
Revenue 312 312
Interest Cost -30 -30
Operating Cost -240 -240
Profits 42 42
[C] As per Activity based costing
Particulars A B
Revenue 312 312
Interest Cost -30 -30
ATM Uses -75 -150
Branch Visit -30 -120
Processing Transaction -3.3 -123.75
Managing Function -96 -96
Profits/Loss 77.7 -207.75
Therefore,
A) RSB&T's operating profits are 2,625,000.
B) The profit from Customer A = 42 and Customer B=42.
C) The profit from Customer A=77.7 and Customer B=-207.75(loss)
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FIND THE INDICATED PROBABILITY FOR THE FOLLOWING:
IF P(A OR B) = 0.9, P(A) = 0.5, AND P(B) = 0.6, FIND P(A AND B)
The value of the probability P(A and B) is 0.20
How to determine the probability?The given parameters about the probability are
P(A or B) = 0.9
P(A) = 0.5
P(B) = 0.6
To calculate the probability P(A and B), we use the following formula
P(A and B) = P(A) + P(B) - P(A or B)
Substitute the known values in the above equation
P(A and B) = 0.5 + 0.6 - 0.9
Evaluate the expression
P(A and B) = 0.2
Hence, the value of the probability P(A and B) is 0.20
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A store is having a sale on trail mix and jelly beans. For 3 pounds of trail mix and 8 pounds of jelly beans, the total cost is $29. For 5 pounds of trail mix and 2 pounds of jelly beans, the total cost is $20. Find the cost for each pound of trail mix and each pound of jelly beans.
Answer:
the price of one pound of trail mix is $3
the price of one pound of jelly beans is $2.5
Step-by-step explanation :
let t be the price of one pound of trail mix.
and b be the price of one pound of jelly beans.
This statement:
“For 3 pounds of trail mix and 8 pounds of jelly beans,
the total cost is $29”
Can be translated mathematically like this :
3t + 8b = 29
This statement:
“For 5 pounds of trail mix and 2 pounds of jelly beans,
the total cost is $20”
Can be translated mathematically like this :
5t + 2b = 20
We obtain a system of two equations :
3t + 8b = 29
5t + 2b = 20
Solving the system:
3t + 8b = 29 (equation 1)
5t + 2b = 20. (equation 2)
3t + 8b = 29
20t + 8b = 80 [4×(equation 2)]
3t + 8b = 29
17t = 51 [4×(equation 2) - equation 1]
3t + 8b = 29
t = 51/17 = 3
9 + 8b = 29
t = 3
8b = 20
t = 3
b = 20/8 = 5/2
t = 3
b = 5/2
t = 3
Therefore ,the solution to our system is (3 , 2.5)
Evaluate the expression. P(9, 2) · P(6, 5)
Answer:
51,840
Step-by-step explanation:
The format of P(n, r) is used for permutations,
where [tex]P(n, r) = \frac{n!}{(n - r)!}[/tex]
To evaluate this expression, P(9,2), we use the formula of permutation,
We have the value of n = 9 and r = 2, thus,
[tex]P(n, r) = P(9, 2) = \frac{9!}{(9 - 2)!} =\frac{9!}{7!} =\frac{9*8*7!}{7!} = 9 *8 =72\\[/tex]
To evaluate this expression, P(6, 5), we use the formula of permutation,
We have the value of n = 6 and r = 5, thus,
[tex]P(n, r) = P(6, 5) = \frac{6!}{(6 - 5)!} =\frac{6!}{1!} =\frac{6*5*4*3*2*1!}{1!} = 6*5*4*3*2 = 720[/tex]
Therefore the product of P(9, 2) · P(6, 5) is
72 · 720 = 51,840
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Complete the square -3x^2+12x-7
Answer:
[tex]-3(x-2)^2+5[/tex]
Step-by-step explanation:
First we can factor a -3 from the [tex]x^2[/tex] term and the [tex]x[/tex] term to get [tex]-3(x^2-4x)-7[/tex].
Then we want the stuff in the parentheses to have the form of [tex](x+b)^2[/tex], or equivalently, [tex](x^2+2b+b^2)[/tex] . So we can let [tex]2b = -4[/tex]. By solving it, we get [tex]b = -4/2 = -2[/tex]. Then our [tex]b^2[/tex] term should be [tex]b^2 = (-2)^2 = 4[/tex].
In order to make our [tex]b^2[/tex] term appear in the parentheses, we need to add and subtract our [tex]b^2[/tex] term, so we get [tex]-3(x^2 - 4x + 4 - 4) -7[/tex].
What we to keep inside our parentheses is [tex](x^2 - 4x + 4)[/tex] , so we can factor the [tex]-4[/tex] out of parentheses to get [tex]-3(x^2-4x+4-4)-7 = -3(x^2-4x+4)+(-3)(-4) - 7 = -3(x^2 - 4x + 4) + 12 - 7 = -3(x^2 - 4x + 4) + 5[/tex]
Finally, plugging [tex]b = -2[/tex] that we computed earlier into the equation [tex](x^2+2b+b^2) = (x+b)^2[/tex], we get [tex](x^2 - 4x + 4) = (x-2)^2[/tex].
So we have [tex]-3(x^2-4x+4)+5 = -3(x-2)^2+5[/tex].
In summary, the procedure is
[tex]-3x^2+12x-7 \\= &-3(x^2-4x) -7 \\= &-3(x^2-4x+4-4)-7 \\= -3(x^2-4x+4) + (-3)(-4)-7\\=-3(x^2-4x+4)+12-7\\= -3(x^2-4x+4)+5 \\= -3(x-2)^2+5[/tex]
Identify the slope and y-intercept of the line y = ×/2 -7
Answer:
Slope: [tex]-\frac{1}{5}[/tex] Y-intercept: (0,0)
Step-by-step explanation:
By putting this into a graph you can see that the y-intercept is (0,0). Also, by looking at the chart and using the walk, rise rule you can see that the slope is [tex]-\frac{1}{5}[/tex].
There are values of t so that the equation cos t = 5/3.
A. True
B. False
the statement is false, as there no exist a value of t such that cos(t) > 1.
Is the statement true or false?
Here we have the statement:
"There are values of t so that the equation cos(t) = 5/3"
Now, remember that the range of the sine and cosine equations is given by:
R: -1 ≤ y ≤ 1
And 5/3, the value in the statement, is larger than 1, which is the maximum in the range.
Then the statement is false, as there no exist a value of t such that cos(t) > 1.
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Please look at the attachment and help me with my question! (╥︣﹏᷅╥)
Peter:
£2.30 ÷ 6 = £0.38 each sausage
Paul:
£3.50 ÷ 10 = £0.35 each sausage
As you can tell, it is cheaper to buy from Paul because each sausage is £0.35 which is 3 pence less than buying from Peter.
In other words, the best value for money would go to the 10 pack sausage, saving £0.03 per unit of sausage.
However, that doesn't answer the question. You need to find how many packages you can get with your available £10.
£10 ÷ £2.30 = 4.34...
So, you can buy 4 packs of sausage from Peter - meaning you will get 24 sausages in total. This is because each pack contains 6 sausages, and you have 4 of this. (6x4=24)
£10 ÷ £3.50 = 2.85...
So, you can buy 2 packs of sausages from Paul & meaning you will get 20 sausages in toal because each package contains 10 sausages. (2x10 = 20)
Thus, you should buy from Peter because you get 24 sausages, instead of 20 sausages from Paul, in accordance to the £10 you can spend in both shops.
Hope this helps!
we conclude that the store where you can get more sausages is in Peter the Butcher.
Which shop is the best option?
You have £10.
Peter the Butcher sells 6 sausages for £2.30
The number of packages that you can buy is:
£10/£2.30 = 4.3
Rounding down to the next whole number, we conclude that here you can buy 4 packages, then:
4*6 = 24 sausages
4*£2.30 = £9.20
So here you can buy 24 sausages for £9.20
In Paul the butcher, you can buy 10 sausages for £3.50
Notice that here you can only buy 2 packages (because the cost of 3 packs would be £10.50, which is more than the amount you can spend).
Then here you only can get 20 sausages.
Then, we conclude that the store where you can get more sausages is in Peter the Butcher.
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x+2y=5 and 4x-12y=-20 substitution and elimination method
By solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.
Given two equations x+2y=5 and 4x-12y=-20.
We are required to solve the equations through elimination and substitution method.
Firstly we will solve the equations through elimination method.
x+2y=5-------------1
4x-12y=-20--------2
Multiply the equation 1 by 4 and then subtract the equation 2 from equation 1.
4x+8y-4x+12y=20+20
20y=40
y=2
Use the value of y in 1
x=5-2*2
x=5-4
x=1
From substitution method.
First find the value of x from first equation in terms of y.
x=5-2y-----4
Now put this value in second equation to get the value of y.
4(5-2y)-12y=-20
20-8y-12y=-20
20-20y=-20
-20y=-40
y=2
Put the value of y in equation 4.
x=5-2y
x=5-2*2
x=5-4
x=1
Hence by solving the equations x+2y=5, 4x-12y=-20 through elimination or substitution method we will get the value of x=1 and y=2.
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points a,b, and c make the triangle ABC and are at the coordinates A(-2,9), B(-33,13) and c(-21,25) point D is the midpoint of BC and AD is a median of ABC, the equation of the median can be given by ax+by=c where A B and C
what is most simple way to answer this
Answer:
[tex]2x+5y=41[/tex]
Step-by-step explanation:
Median of a triangle: A line segment that connects a vertex of a triangle to the midpoint of the opposite side.
Vertex: The point where any two sides of a triangle meet.
Given vertices of a triangle:
A = (-2, 9)B = (-33, 13)C = (-21, 25)Step 1Find the midpoint of BC (Point D) by using the Midpoint formula.
Midpoint between two points
[tex]\textsf{Midpoint}=\left(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\right)\quad \textsf{where}\:(x_1,y_1)\:\textsf{and}\:(x_2,y_2)\:\textsf{are the endpoints}}\right)[/tex]
Define the endpoints:
[tex]\text{Let }(x_1,y_1)=\sf B=(-33,13)[/tex][tex]\text{Let }(x_2,y_2)=\sf C=(-21,25)[/tex]Substitute the defined endpoints into the formula:
[tex]\textsf{Midpoint of BC}=\left(\dfrac{-21-33}{2},\dfrac{25+13}{2}\right)=(-27,19)[/tex]
Therefore, D = (-27, 19).
Step 2Find the slope of the median (line AD) using the Slope formula.
Define the points:
[tex]\textsf{let}\:(x_1,y_1)=\sf A=(-2,9)[/tex][tex]\textsf{let}\:(x_2,y_2)=\sf D=(-27,19)[/tex]Substitute the defined points into the Slope formula:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{19-9}{-27-(-2)}=-\dfrac{2}{5}[/tex]
Therefore, the slope of the median is -²/₅.
Step 3Substitute the found slope and one of the points into the Point-slope formula to create an equation for the median.
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-9=-\dfrac{2}{5}(x-(-2))[/tex]
Simplify and rearrange the equation so it is in standard form Ax+By=C:
[tex]\implies 5(y-9)=-2(x+2)[/tex]
[tex]\implies 5y-45=-2x-4[/tex]
[tex]\implies 2x+5y-45=-4[/tex]
[tex]\implies 2x+5y=41[/tex]
ConclusionTherefore, the equation of the median is:
2x + 5y = 41
X=y
Y=x
Is this is inverse equation
The inverse equation of x = y is y = x
What are inverse equations?Inverse equations are the opposite of an original equation
How to determine the inverse equation?The equation is given as
x = y
Swap the positions of x and y in the above equation
y = x
This means that the inverse equation of x = y is y = x
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(02.03)
Figure ABCD is transformed to A′B′C′D′, as shown:
A coordinate plane is shown. Figure ABCD has vertices A at 3 comma 1, B at 3 comma 4, C at 5 comma 5 and D at 5 comma 3. Figure A prime B prime C prime D prime has vertices A prime at negative 5 comma 1, B prime at negative 5 comma 4, C prime at negative 7 comma 5 and D prime at negative 7 comma 3.
Which of the following sequences of transformations is used to obtain figure A′B′C′D′ from ABCD? (4 points)
Group of answer choices
Reflection about the x-axis followed by a translation right by 2 units
Reflection about the y-axis followed by a translation left by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation right by 2 units
Counterclockwise rotation by 90 degrees about the origin followed by a translation left by 2 units
The sequence of transformation carried out on ABCD is; B: Reflection about the y-axis followed by a translation left by 2 units
What is the type of Transformation used?
As in rotation, reflection and translation the transformed image is congruent to the original figure (i.e all the points undergo same change). Thus, analyzing any one point will give the series of transformation undertaken.
Taking point A(3, 1) into consideration; Reflecting a point (x, y) over y axis, it becomes (-x, y).
Thus, reflecting A(3, 1) over y - axis gives the the new coordinates as (-3, 1)
Now, translating a point (x, y) k units left, gives a new coordinate (x - k, y).
Thus, translating point (-3, 1) 2 units left, gives the new coordinates as A'(-5, 1).
This is the coordinates for A'.
Thus, we can conclude by saying that the sequence of transformation carried out on ABCD is reflected about the y-axis followed by a translation left by 2 units.
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Please help, due in an hour. Two sides of a triangle are 12cm and 8cm. Complete the inequality to show the possible lengths for the third side. If the third side of the triangle is x then, _
Answer:
[tex]4 < x < 20[/tex]
Step-by-step explanation:
By the triangle inequality theorem, the sum of the length of the two smaller sides must be greater than the length of the largest side. If 12 cm was the length of the largest side, notice that [tex]8+x > 12 \Rightarrow x > 4[/tex]. Similarly, if x was the length of the largest side, we'd get the inequality [tex]12+8 > x \Rightarrow 20 > x[/tex]. Combining these inequalities, we get [tex]\boxed{4 < x < 20}[/tex].
mary is making a batch of chocolate chip cookies the recipe calls for 9 cups of flour and 2 4/7 cups of sugar she isshort on flour cuts the recipe down to 7 cups if flour how much sugar should she add
Answer:
2
Step-by-step explanation:
tammy smith deposits $5,000 in First Internet Bank's 5-year CD, which pays 5.22% compounded monthly.How much will she have in the account at the end of 5 Years? How much interest did she earn?
Answer: a) $ 6,487.47
b) $ 1,487.47
Step-by-step explanation:
irections: Simplify each expressio
25-(√16-1)-(3-9)²
Answer:
-14
Step-by-step explanation:
[tex]\sqrt{16} = 4\\\\(\sqrt{16} - 1) = (4 -1) =3\\\\(3-9) = (-6)\\\\(3-9) ^2 = (-6)^2 = 36\\\\25 - 3 - 36 = 25 - 39 = -14\\[/tex]
– 30% OF THE CELL PHONE USERS TODAY USE A MOTOROLA
PHONE. DETERMINE THE PROBABILITY THAT IF SIX CELL PHONE USERS
ARE SELECTED AT RANDOM, EXACTLY FOUR OF THEM USE A MOTOROLA CELL
PHONE.
Using the binomial distribution, there is a 0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.For this problem, the values of the parameters are given by:
p = 0.3, n = 6.
The probability that exactly four of them use a Motorola cell phone is given by P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
P(X = 4) = C(6,4) x (0.3)^4 x (0.7)² = 0.0595
0.0595 = 5.95% probability that exactly four of them use a Motorola cell phone.
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Find the slope of the line. On a coordinate plane, a line goes through (0, negative 6) and (2, 0). a. Negative one-third c. 3 b. One-third d. Negative 3 Please select the best answer from the choices provided A B C D
The slope of the line that passes through between (0, -6) and (2, 0) is: C. 3.
What is the Slope of a Line?The slope of a line can be defined as the measure of the ratio of the vertical distance to the horizontal distance that exists between two points on a coordinate plane.
How to Find the Slope of a Line?If we are given two points on a line, (x1, y1) and (x2, y2), the slope (m) is the rise/run = change in y / change in x = (y2 - y1)/(x2 - x1).
Given the following coordinates of two points as follows, (0, -6) and (2, 0), let:
(0, -6) = (x1, y1)
(2, 0) = (x2, y2)
Plug in the values into the slope formula to find the slope:
Slope (m) = (0 - (-6)) / (2 - 0)
Slope (m) = (0 + 6) / (2 - 0) [minus multiplied by minus is plus]
Slope (m) = (6) / (2)
Slope (m) = 3
Thus, the slope of the line that passes through between (0, negative 6) and (2, 0) is calculated as: C. 3.
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Which expressions are equivalent to 2(4f + 2g)?
Answer:
For example, 8f + 4g is one of the most used expression
Another example is 4 (2f + g), is correct too
HELP ASAP WILL GIVE BRAINLIEDT IF CORRECT!!!!!!!
Find the equation to the line below
Answer:
y = 3/2x + 2
Step-by-step explanation:
y = mx + c
y = gradient(x intercept) + y intercept
y = 3/2x + 2
Answer:
[tex]\sf y =\dfrac{3}{2}x+2[/tex]
Step-by-step explanation:
Equation of line:Pick any two points on the line.
(0,2) and (2 , 5)
(0,2) ⇒ x₁ = 0 & y₁ = 2
(2,5) ; x₂ = 5 & y₂ = 5
[tex]\sf \boxed{\bf Slope =\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\sf =\dfrac{5-2}{2-0}\\\\=\dfrac{3}{2}[/tex]
Equation of line in point slope form:
[tex]\sf y - y_1 =m(x -x_1)[/tex]
Point(0 ,2) and m = 3/2
[tex]\sf y - 2 = \dfrac{3}{2}(x -0)\\\\ y - 2 = \dfrac{3}{2}x\\\\[/tex]
Equation of line in slope y-intercept form:
[tex]\sf y =\dfrac{3}{2}x+2[/tex]
the number has 3 digits the number is less than 140 the number has 7 as a factor the number is even the sum of the digits is less than 9
Answer:
It could be 105, 112 or 133.
Step-by-step explanation:
Having 7 as a factor means it is a multiple of 7.
The first 3 digit multiple of 7: 100 ÷ 7 = 14 2/7 → first 3 digit multiple of 7 is 15 × 7 = 105
Last 3 digit multiple of 7 less than 140: 140 ÷ 7 = 20 → last 3 digit multiple of 7 less than 140 is 19 × 7 = 133
→ The possible multiples of 7 to consider are [15..19] × 7 which gives 105, 112, 119, 126 and 133.
The sum of the digits of these number is:
105 → 1 + 0 + 5 = 6
112 → 1 + 1 + 2 = 4
119 → 1 + 1 + 9 = 11
126 → 1 + 2 + 6 = 9
133 → 1 + 3 + 3 = 7
Of these sums only 6, 4 and 7 are less than 9, thus the possible numbers are 105, 112 or 113.
Match the matrix operations with the resulting matrices. Image Attached.
Answer:
1. 2A + 3A
2. 2A - B
3. 2A
4. 2(A-B)
Step-by-step explanation:
When multiplying matrix by a number you just multiply each number in the matrix by whatever you are multiplying. When adding 2 matrices you just add the corresponding number in each matrix. Ex: You add the top left number to the top left number. The same goes with subtraction.
Answer:
Behold!
Step-by-step explanation:
PLATO Type the correct answer in each box. Use numerals instead of words. In the figure, lines BD and QS are parallel. Two parallel lines B D, and Q S are intersected by a line A T at C, and R respectively such that the angle D C R is 77 degrees. Complete the given statement. The measure of ∠CRQ is °, and the measure of ∠CRS is °.
Answer:
c
Step-by-step explanation:
The measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.
In the figure, lines BD and QS are parallel. Two parallel lines B D, and Q S are intersected by a line AT at C, and R respectively such that the angle ∠DCR is 77 degrees.
We know that the angle ∠DCR & ∠SRT and ∠DCR & ∠SRT are corresponding angles. Then they are equal to each other.
∠DCR = ∠SRT = 77°
∠CRQ = ∠CRS
We know that the angle ∠CRQ and ∠CRS are supplementary angles. Then we have
∠CRQ + ∠SRT = 180°
∠CRQ + 77° = 180°
∠CRQ = 103°
Then the measure of the angle ∠CRQ is 103° and the measure of the angle ∠CRS will be 103°.
The diagram is given below.
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Instructions: Find the missing side of the triangle.
X= Answer
Answer: 15
Step-by-step explanation: Using the pythagorean theorem A^2 + B^2 = C^2 where C is the hypotenuse of the triangle and any A and B are any sides of the triangle that are not the hypotenuse; we can rewrite this as A^2 = C^2 - B^2 to find out the missing side. I picked A to be the unknown side but you could also choose B. We know the hypotenuse is 39, and side B is 36. 39^2 - 36^2, or 1521 - 1296, is 225.
Now we have A^2 = 225. To get rid of the square, we have to take the square root of both sides. The A^2 cancels to be A, and sqrt(225) is 15. Thus, side A, or the missing side is 15.
Hope this helped!
Lamar, an artist, plans to paint and sell some miniature paintings. He just bought some brushes for $10, and paint and canvas for each painting costs $45; he will sell each painting for $50. Once Lamar sells a certain number of his paintings, he will be breaking even. How many paintings will that be?
Answer:
2
Step-by-step explanation:
If he sells and makes x paintings, his expenses will he 10+45x and his revenue will be 50x.
50x = 45x + 105x = 10x = 2The break-even point is the point at which total cost and total income are equal. For breakeven, Lamar needs to sell 2 paintings.
What is breakeven?In economics, business, and especially cost accounting, the break-even point is the point at which total cost and total income are equal, i.e. "even."
Let the number of paintings that Lamar makes and sells at the break-even point be represented by x.
Given that Lamar bought some brushes for $10, and paint and canvas for each painting cost $45. Therefore, the total cost of making x number of paintings is,
Total cost of x painting = $10 + $45(x)
Also, the selling price of each painting is $50. Therefore, the revenue generated from x paintings is,
Revenue generated = $50(x)
Further, at the breakeven point, the total cost of production of any product is equal to the revenue generated by the product. Therefore, we can write,
Total cost of x painting = Revenue generated
$10 + $45(x) = $50(x)
10 + 45x = 50x
10 = 50x - 45x
10 = 5x
x = 10/5
x = 2
Hence, For breakeven Lamar needs to sell 2 paintings.
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The width of a rectangle measures
(7h+3) centimeters, and its length measures
(8h−4) centimeters. Which expression represents the perimeter, in centimeters, of the rectangle?
The expression that represents the perimeter of the rectangle is 30h - 2
How to determine the perimeter expression?The dimensions of the rectangle are given as:
Length = 7h + 3
Width = 8h - 4
The perimeter of the rectangle is given as:
P = 2 * (Length + Width)
Substitute the known values in the above equation
P =2 * (7h + 3 + 8h - 4)
Evaluate the like terms
P = 2 * (15h - 1)
Evaluate the product
P = 30h - 2
Hence, the expression that represents the perimeter of the rectangle is 30h - 2
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Sampson has been given the following budget guidelines. If his department’s budget is $50,000, how much can he spend in each budget category? Be sure to list dollars and cents (round to the nearest hundredth).
The amount he can spend on marketing is $8,333.33.
The amount he can spend on supplies is $16,666.67
The amount he can spend on trainings is $12,500
The amount he can spend on travel is $2,500
The amount he can spend on equipment is $10,000
How much can he spend on each category?The amount he can spend on each category can be determined by multiplying the fraction of that category by the total department's budget.
The amount he can spend on marketing : 1/6 x $50,000 = $8,333.33.
The amount he can spend on supplies: 1/3 x $50,000 = $16,666.67
The amount he can spend on trainings: 1/4 x 50,000 = $12,500
The amount he can spend on travel $2: 1/20 x 50,000 = 2,500
The amount he can spend on equipment $: 1/5 x 50,000 = 10,000
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Do companies that provide mobile wifi hotspots see your history?
Yes, companies that provide mobile wifi hotspots can see your history.
What is a Wi-Fi hotspots?A Wi-Fi hotspots can be defined as the hotspots that makes it possible for other mobile user connected to a wifi hotspots to browse or to connect to the internet.
For a mobile user to connect to the internet through the mobile wifi hotspot, the mobile hotspot wifi owner must have giving access to mobile user to browse .
Hence, companies that provide mobile wifi hotspots can see your history of the site you visit.
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