Answer:
find the value of:Cos = 0.54
3x + ky = 8
X – 2ky = 5
are simultaneous equations where k is a constant.
b) Given that y = 1/2 determine the value of k.
Answer:
(a): x is 3 and ky is -1
(b): k is -2
Step-by-step explanation:
Let: 3x + ky = 8 be equation (a)
x - 2 ky = 5 be equation (b)
Then multiply equation (a) by 2:
→ 6x + 2ky = 16, let it be equation (c)
Then equation (c) + equation (b):
[tex] { \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}[/tex]
Then ky :
[tex]{ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}[/tex]
[tex]{ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}[/tex]
Simultaneous equations are used to represent a system of related equations.
The value of k when [tex]y = \frac 12[/tex] is -2
Given that:
[tex]3x + ky = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]y = \frac 12[/tex]
Substitute [tex]y = \frac 12[/tex] in both equations
[tex]3x + ky = 8[/tex]
[tex]3x + k \times \frac 12 = 8[/tex]
[tex]3x + \frac k2 = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]x - 2k \times \frac 12 = 5[/tex]
[tex]x - k = 5[/tex]
Make x the subject in [tex]x - k = 5[/tex]
[tex]x = 5 + k[/tex]
Substitute [tex]x = 5 + k[/tex] in [tex]3x + \frac k2 = 8[/tex]
[tex]3(5 + k) + \frac k2 = 8[/tex]
Open bracket
[tex]15 + 3k + \frac k2 = 8[/tex]
Multiply through by 2
[tex]30 + 6k + k = 16[/tex]
[tex]30 + 7k = 16[/tex]
Collect like terms
[tex]7k = 16 - 30[/tex]
[tex]7k = - 14[/tex]
Divide both sides by 7
[tex]k = -2[/tex]
Hence, the value of constant k is -2.
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find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf sin\Theta=\dfrac{P}{H}}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{16}{26}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{8}{13}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=0.5[/tex]
Convert to p/q form[tex]\\ \sf\longmapsto sin\Theta=\dfrac{5}{10}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=\dfrac{1}{2}[/tex]
[tex]\\ \sf\longmapsto sin\Theta=sin30[/tex]
[tex]\\ \sf\longmapsto \Theta\approx30°[/tex]
Need help on #7 , #8 Asap
Simplify
1)a³b⁴/ ab³
2)2 (x³ )²
3)3x*2x³ y²
Answer:
1) a³b⁴/ ab³ = a²b
2)2 (x³ )² = 2x^6
3)3x*2x³ y² = 6x⁴y²
Write the ratio of detective headphones to total headphones in the sample. Then write the ratio as a decimal and as a percent
The question given is incomplete as the information about the headphones isn't given.
However, we can solve the problem by using hypothetical values.
Answer:
Kindly check explanation
Step-by-step explanation:
Given
Write the ratio of detective headphones to total headphones in the sample. Then write the ratio as a decimal and as a percent.
Let :
The number of defective headphones = 10
The total number of headphones on the sample = 50
To express as a ratio :
Defective headphones : total headphones
10 : 50 = 1 : 5
To express as a percentage ;
1 / 5 * 100% = 20%
A storeowner orders 25 calculators that cost $38 each. The storeowner can sell each calculator for $42. The storeowner sold 22 calculators to customers. He had to return 3 calculators that were never sold and pay a $2 charge for each returned calculator (although the initial cost is refunded). What is the storeowner's profit?
Answer:
Step-by-step explanation:
25*-30= -$750
Second: He sells 22 of those calculators for $35 each, so he is making money.
22*35= $770
Third: With the remaining three calculators, he must pay $2 each for returned calculators, so he is losing money again.
3*-2= -6
Add all the costs and sales together, and you get 770-750-6= $14 profit
However, the problem does not say if he gets his money back for the 3 returned calculators. In that case if he did, you would add the cost of each of those calculators to his profit. 30*3= 90
$90+$14= $104 profit
here u go
After getting RM24 from his mother, Samuel had 3 times as much as he had previously. How much did he have previously?
Answer:
Samuel had RM8 previously
Step-by-step explanation:
24÷3=8
Please hurry I will mark you brainliest
What is the slope of the line with an x-intercept of 4 and a y-intercept of -3?
the answer to this question is the slope is 43
Answer:
Therefore, the slope is 3/4
Step-by-step explanation:
An x -intercept is the value of x when y=0 , so an x-intercept of 4 can be written as a coordinate on the graph as (4,0)
Likewise, an
y -intercept is the value of y when x=0 , so an y -intercept of −3can be written as a coordinate on the graph as (0,-3)
Now we have two points(4,0) (0,-3)
To find the slope given two points, we use the formula
rise÷run , or y2−y1÷x2−x1 .
Plug in the given points into the formula
-3-0/0-4
-3/-4
3/4
Therefore, the slope is 3/4
Hope this helps!
Warren is on vacation and needs to arrange transportation. A rental car costs 40 dollars per day plus a one-time cost of 14 dollars for insurance. Construct a function C(x) that gives the total cost of renting a car for x days. C(x)=________.
If Warren has budgeted 254 dollars for the rental, how many days can he afford?
Answer:
C(x)=40x+14, 6 days
Step-by-step explanation:
C(x)= payment per day*x + initial payment. the payment per day is $40 while the initial payment is $14. so C(x)=40x+14.
C(x)=254=40x+14, 40x=240, x=6
Simplify 2m^2 – 2m + 3m^2
Answer:
5m^2-2m
Step-by-step explanation:
2m^2-2m + 3m^2
5m^2-2m
Answer:
5m² - 2m
Step-by-step explanation:
Given
2m² - 2m + 3m² ← collect like terms
= (2m² + 3m²) - 2m
= 5m² - 2m
Simplify: 5^(x+2)-4×5^x÷21×5^x
Answer:
(1/21)(21×5^(x+2)-4×5^2x)
Step-by-step explanation:
5^(x+2)-4×5^x÷21×5^x
= 5^(x+2)-4×5^2x/21
= 1/21(21×5^(x+2)-4×5^2x)
of (3, -2) reflected across the line x = 1 is?
Answer: (-1, -2)
===========================================================
Explanation:
Plot (3,-2) on the xy grid. Then draw a vertical line through 1 on the x axis.
Note that the horizontal distance from the point to the line is exactly 2 units. We move 2 units to the left to go from (3,-2) to (1,-2). Then we move another 2 units to the left to arrive at the final destination of (-1, -2)
In short, (3,-2) reflects over the vertical line x = 1 to get to (-1, -2)
See the diagram below.
find the surface area of the cylinder and round to the nearest tenth
Answer: A = 833.66 in^2
Step-by-step explanation:
Area of the base = (7^2)(pi) = 49 pi = 153.9 in^2
Height of the cylinder = 12 in
Circumference of the base = (2)(pi)(r) = 44in
Surface area = (2)(pi)(7)(12) + (2)(pi)(7) = 833.66 in^2
I need help please slope
Answer:
Step-by-step explanation:
The formula for slope is y2-y1/x2-x1 where y2 and x2 are the x and y coordinates from a coordinate pair and y1 and x1 are the coordinates from another coordinate pair. In this case, 2 coordinate pairs are given: (30,75) and (10, 35) 75-35/30-10 would be your slope, or, 40/20, or simplified, 2.
Your slope is 2
Na
C
9
Which rule describes the transformation?
Parallelogram ABCD is rotated to create image
A'B'C'D'.
SEE
0 (x, y) - (y, -x)
O (x, y) + (-y, x)
O (x, y) + (-X, -y)
(x, y) - (x,-y)
5
VX
4
R
D
2
1
C
-5.-5.4.-3.-2.-
23
4
SIB
Х
2
D
A
C
B
no
Answer:
(x, y) → (y, -x)
Step-by-step explanation:
The coordinates of the vertices of parallelogram ABCD are; A(2, 5), B(5, 4), C(5, 2), and D(2, 3)
The coordinates of the vertices of parallelogram A'B'C'D' are; A'(5, -2), B'(4, -5), C'(2, -5), and D'(3, -2)
The rule that escribes the transformation of the rotation of parallelogram ABCD to create the image A'B'C'D' is presented, by observation, is therefore;
(x, y) → (y, -x)
The resulting transformation used will be (x, y) -> (y, -x)
Transformation of coordinatesTransformation are rules applied to an object to change its orientation
For the given parallelogram, in order to know the rule used, we need the coordinate of the image and preimage
The coordinate of A is (2, 5) while that of A' is (5, -2).
From both coordinates, you can see that the coordinate was switched and the resulting y coordinate negated.
Hence the resulting transformation used will be (x, y) -> (y, -x)
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A recipe for eight flapjacks needs 2oz of butter, 3oz of sugar, and 4 oz of rolled oats. How many flapjacks can I make if I have 14 oz of butter, 15 oz of sugar, and 16 oz of rolled oats?
Answer:
Step-by-step explanation:
Eight flapjacks
2oz of butter
3oz of sugar
4 oz of rolled oats.
Each flapjack
Butter = 2/8 = 1/4 oz
Sugar = 3/8 oz
Rolled oats = 4/8 = 1/2 oz
How many flapjacks can I make if I have
14 oz of butter,
15 oz of sugar, and
16 oz of rolled oats?
Butter
= 14 oz ÷ 1/8 oz
= 14 × 8/1
= 112 flapjack
Sugar
= 15 oz ÷ 3/8 oz
= 15 × 8/3
= 120/3
= 40 flapjacks
Rolled oats
16 oz ÷ 1/2 oz
= 16 × 2/1
= 32 flapjack
Therefore,
Considering the quantity of rolled oats available, the number of flapjacks that could be made is 32
upon receiving your first salary, you deposited 3000 taka monthly in a fund for your future for 18 years. the fund earns 6% interest rate compounded monthly. after 18 years, you want it to make payments at the end of every quarter for five year 4.5% compounded quarterly, what is the amount of each annuity payment to you?
The Annuity payment will be "65,209.35 Taka". A further solution is provided below.
Given:
Monthly payment,
= 3000 Taka
Interest rate,
= 6% (compounded monthly)
Time,
= 18 years
The Future value will be:
→ [tex]FV = PMT\times \frac{((1+r)^{nt}-1)}{r}[/tex]
By putting the values, we get
[tex]=3000\times \frac{((1+\frac{6}{12\times 100} )^{12\times 18}-1)}{\frac{6}{12\times 100} }[/tex]
[tex]=3000\times \frac{((1+\frac{6}{1200} )^{216}-1)}{\frac{6}{1200} }[/tex]
[tex]=1,162,059.58 \ Taka[/tex]
hence,
The Annuity payment will be:
→ [tex]P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-4\times 5}}[/tex]
[tex]=P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-20}}[/tex]
By substituting all the values, we get
[tex]=65,209.35 \ Taka[/tex]
Thus the correct answer is "65,209.35 Taka".
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Find the area of the regular polygon. Round your answer to the nearest hundredth.
Answer:
Step-by-step explanation:
The central angle of a hexagon is 60 degrees. Drop a line from the center to the middle of the side marked 7.
Use the tan of the angle so formed (which is 30 degrees)
Tan(30)= opposite / height (which is the line you just drew).
Tan(30) = 3.5 / h
Tan(30) = 0.5774
Tan(30) = 3.5 / h multiply both sides by h
h*Tan(30) = 3.5 Divide by tan30
h = 3.5 / Tan(30)
h = 3.5 / 0.5774
h = 6.062
Now from both ends of the given side, draw 2 lines to the center. Find the area of that triangle.
Area of 1 triangle = 1/2 * b * h
area of 1 triangle = 1/2 * 7 * 6.062
Area of 1 triangle = 21.2176
There are 6 such triangles so multiply that number by 6
Answer: 6 * 21.2176
Answer: 127.31
Pls help I tried basic answers like 50+50+80 =180 but it’s wrong so pls help
Answer:
x = 65 degrees
Step-by-step explanation:
x° + x° + 50° = 180°
2x + 50° = 180°
2x = 180° - 50°
2x = 130°
x = 130°/2
x = 65°
Does this set of ordered Paris represent a function? Why or why not
Answer:
Me = no it doesn't....
you = why tho
me = becoz function not given .....
so lame joke ik...
The sum of two numbers is 83 if one of the number is 7 more than the other find the two numbers?
Answer:
48.5 and 34.5
Step-by-step explanation:
83 divided by 2 and then subtract 7
Answer:
45 and 38 equal 83 and 45 is 7 more than 38
I don't understand this one
Answer:
9/8 = n
Step-by-step explanation:
9 = 8n
Divide each side by 8
9/8 = 8n/8
9/8 = n
The lengths of the diameters of two concentric circles are 6 and 8. What is the distance between the circles?
Answer: 1 unit
Explanation:
The diameters are 6 and 8, which cut in half to 3 and 4 respectively.
The difference in these radii values is 4-3 = 1.
This is the distance from one circle's edge to the other circle's edge, such that we're on the same line that goes through the center of the circles. This is the gap width or ring width so to speak.
The points A,B,C and D divide the line segment AD in the ratio 4:3:1 , respectively , and AD = 72cm . What is the length of BD?
Segment addition postulate states that given points X, and Z, on a line, a point Y, can be located between X, and Z, ony if we have;
XZ = XY + YZ
The length of the segment BD is 36 cm
The reason the above value is correct is as follows:
Known:
The ratio in which the points A, B, C, and D divide the line segment = 4:3:1
The length of segment AD = 72 cm
Required:
The length of BD
Method:
Calculate the length of BC and CD and add their values to get BD
Solution:
Let the ratios be given unit proportions of the segment AD such that we have;
AB = 4 units
BC = 3 units
CD = 1 unit
By segment addition postulate, we have;
AD = AB + BC + CD
∴ AD = 4 units + 3 units + 1 unit = 8 units = 72 cm
∴ 1 unit = 72 cm/8 = 9 cm
1 unit = 9 cm
BD = BC + CD by segment addition postulate
BC = 3 units = 3 × 1 unit
∴ BC = 3 × 9 cm = 27 cm
BC = 27 cm
CD = 1 unit
∴ CD = 9 cm
∴ BD = 27 cm + 9 cm = 36 cm
The length of segment BD = 36 cm
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hi, please solve these three questions for me, i have to shoe solving steps.
question 3
Step-by-step explanation:
i only able to show you the step of question 3..so sorry
Joylin is writing an equation to model the proportional relationship between y, the total cost in dollars of downloading videos from a website, and x, the number of videos downloaded. She knows that the total cost to download 3 videos was $12. Her work to find the equation is shown below.
Joylin’s Work
Step 1
k = StartFraction 3 over 12 EndFraction = 0.25
Step 2
y = 0.25 x
Where did Joylin make her first error?
Answer:
Step-by-step explanation:
Jocelyn was attempting to find out how much she will be charged per download. She has the fraction upside down. To find the amount of money per download, the fraction should be $12/3downloads to get $4/1download. That is the slope of the equation, the rate of change or, for us, the fact that your cost will go up $4 for every single video you download. The equation would then be
y = 4x
The way she has it, we are paying only a quarter for a download. If that be the case, for 3 downloads we would only be paying .75, but it says we pay $12, so we know something is wrong right there.
Answer:
The answer is A
Step-by-step explanation:
The Vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).Find the length of each diagonal.Show me with the steps Please!
Answer:
13 and 17 units
Step-by-step explanation:
explaination is in pic.
The length of the diagonals of the quadrilateral AC and BD are 13 units and 17 units respectively, as per length between two points.
What is the length between two points in a plane?The length between two given points (x₁, y₁) and (x₂, y₂) will be:
√[(x₂ - x₁)² + (y₂ - y₁)²] units
Given, the vertices of a quadrilateral are A(4,-3),B(7,10),C(-8,2)and D(-1,-5).
Therefore, the diagonals of the quadrilateral will be AC and BD.
The coordinates of the diagonal AC are (4, - 3) and (- 8, 2).
Now, the length of the diagonal AC will be:
= √[(-8 - 4)² + (2 - (- 3))²] units
= √[(- 12)² + (5)²] units
= √[144 + 25] units
= √(169) units
= 13 units (length can't be negative)
Similarly, the coordinates of the diagonal BD are (7, 10) and (- 1, - 5).
Now, the length of the diagonal BD will be:
= √[(-1 - 7)² + (- 5 - 10)²] units
= √[(- 8)² + (- 15)²] units
= √[64 + 225] units
= √(289) units
= 17 units (length can't be negative)
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#SPJ2
Mahmoud earns $450 per week plus a 20% commission as a car salesman. He wants his
hourly salary to be at least $35.
The inequality that relates the number of hours to the weekly sales is:
[tex]450 + 0.20x \ge 35y[/tex]
The complete question implies that we define an inequality that represents the relationship between the number of hours worked in a week and the weekly sales
We make use of the following representation:
[tex]x \to[/tex] weekly sales from cars.
[tex]y \to[/tex] hours worked in a week
His weekly salary is then calculated as:
Salary (S) = Earnings per week + Commission * Sales from car
So, we have:
[tex]S = 450 + 20\% * x[/tex]
Express percentage as decimal
[tex]S = 450 + 0.20* x[/tex]
[tex]S = 450 + 0.20x[/tex]
Assume he works for y hours in a week.
His hourly rate is:
[tex]Hourly = \frac{S}{y}[/tex] --- i.e. weekly salary divided by number of hours
[tex]Hourly = \frac{450 + 0.20x}{y}[/tex]
For this rate to be at least [tex]\$35[/tex], the following condition must be true
[tex]Hourly \ge 35[/tex] --- i.e. is hourly rate must be greater than or equal 35
So, we have:
[tex]\frac{450 + 0.20x}{y} \ge 35[/tex]
Multiply both sides by y
[tex]450 + 0.20x \ge 35y[/tex]
Learn more about inequality:
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please answer this!!
Answer:
16
Step-by-step explanation:
if angle c is 45 then angle A is 45 also
Hence AB is equal to BC
Ivana wants to give books from her store to the local library. She needs to place 8 books in each box. If she has 1,125 books to give away, how many boxes will she need
Answer:
140.625
Step-by-step explanation:
1125 books, placed into 8 per boxes, 1125/8=140.625
