The measure of the diagonal KI is approximately 6.465 centimeters.
The diagonals of the quadrilateral RISK are represented by line segments RS and KI, both measured in centimeters. There are two triangles forming the quadrilateral: [tex]\triangle RIS[/tex], [tex]\triangle RKS[/tex]
By Law of Sine and Law of Cosine we determine the measures of all internal angles:
Triangle RIS
[tex]RS^{2} = RI^{2}+IS^{2}-2\cdot RI\cdot IS \cdot \cos I[/tex] (1)
[tex]\frac{RS}{\sin I} = \frac{RI}{\sin S'} = \frac{IS}{\sin R'}[/tex] (2)
Triangle RKS
[tex]RS^{2} = RK^{2} + KS^{2}-2\cdot RK\cdot KS\cdot \cos K[/tex] (3)
[tex]\frac{RS}{\sin K} = \frac{RK}{\sin S''} = \frac{KS}{\sin R''}[/tex] (4)
[tex]S = S' + S''[/tex] (5)
[tex]R = R' + R''[/tex] (6)
By (1) and (3) we find the values of angles I and K:
[tex]I = \cos^{-1}\left(\frac{RI^{2}+IS^{2}-RS^{2}}{2\cdot RI\cdot IS} \right)[/tex]
[tex]I \approx 90.261^{\circ}[/tex]
[tex]K = \cos^{-1}\left(\frac{RK^{2}+KS^{2}-RS^{2}}{2\cdot RK\cdot KS} \right)[/tex]
[tex]K\approx 94.903^{\circ}[/tex]
By (2) and (4) we find the remaining angles for each triangle:
[tex]S' = \sin^{-1}\left[\left(\frac{RI}{RS} \right)\cdot \sin I\right][/tex]
[tex]S' \approx 38.682^{\circ}[/tex]
[tex]R' = \sin^{-1}\left[\left(\frac{IS}{RS} \right)\cdot \sin I\right][/tex]
[tex]R' \approx 51.057^{\circ}[/tex]
[tex]S'' = \sin^{-1}\left[\left(\frac{RK}{RS} \right)\cdot \sin K\right][/tex]
[tex]S'' \approx 28.969^{\circ}[/tex]
[tex]R'' = \sin^{-1}\left[\left(\frac{KS}{RS} \right)\cdot \sin K\right][/tex]
[tex]R'' \approx 56.128^{\circ}[/tex]
Then, we have the values of angles R and S by (5) and (6):
[tex]S \approx 67.651^{\circ}[/tex], [tex]R \approx 107.185^{\circ}[/tex]
The measure of the diagonal KI is found by the Law of Cosine:
[tex]KI = \sqrt{IS^{2}+SK^{2}-2\cdot IS\cdot SK\cdot \cos S}[/tex]
[tex]KI \approx 6.465\,cm[/tex]
The measure of the diagonal KI is approximately 6.465 centimeters.
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f(x) = -x - 14
Find x if f(x) = -2
Answer:
x = -12
Step-by-step explanation:
First, you want to plug in f(x)'s value into the equation.
-2 = -x-14
Then solve for x:
x=-14+2
x=-12
What is 2a・420 divided by 3z when z=34 and a=56
461.176470588
Explanation:
2×56=112
112×420=47040
---------------------------------
3×34=102
---------------------------------
47040÷102=461.176470588
these are so confusing, can someone explain how to do this
Answer:
4
Step-by-step explanation:
x/2 +6 = 8
subtract 6 from both sides
x/2 = 2
multiply by the reciprocal of 1/2 which is 2. That cancels out the 2 on the x side and x is equal to 4
Hope that helps
Answer:
x = 4
Step-by-step explanation:
The left side of the equation has a variable term (x/2) and a constant term (6).
The right side of the equation has a constant term (8).
This is the form you expect to see for a "two-step" linear equation. It is solved in 2 steps.
Step 1:
Subtract the left-side constant from both sides.
x/2 +6 -6 = 8 -6
x/2 = 2 . . . . . simplify
Step 2:
Multiply both sides of the equation by the reciprocal of the coefficient of x. The coefficient of x is 1/2. Its reciprocal is 2/1 = 2. When you multiply both sides by 2, you get ...
2(x/2) = 2(2)
x = 4 . . . . . . simplify
_____
Additional comment
The idea of a multiplicative inverse (reciprocal) is that a number multiplied by its reciprocal is 1.
[tex]\dfrac{2}{1}\times\dfrac{1}{2}=\dfrac{2}{2}=1[/tex]
1 is the "identity element" for multiplication. That means whatever you multiply by 1 retains its original identity. Multiplying x by 1 gives x.
When we solve an equation of this sort, we use these properties of multiplication (inverse, identity element) to "get rid of" the coefficient of x.
As always, the rules of equality say that whatever you do to one side of the equation must also be done to the other side. So, when we multiply x/2 by 2, we must also multiply the other side of the equation by 2.
__
Don't let the presentation of the x-term throw you. It can be written several ways that all mean the same thing.
(1/2)x . . . . with or without the parentheses
0.5x
x/2
4 more to go-2 + (-2) × -2 + (-2) ÷ -2
Let's se
-2+(-2)(-2)+(-2)/(-2)-2+(-2)^2+1-1+21Done!
The area of a rectangle is 52 in^2. If the length is 9 inches more than the width, find the
dimensions of the rectangle.
Answer:
width=4in.
length=13in
Step-by-step explanation:
let the width of the rectangle be x
then the length will be x+9
Area= length×width
52= (x+9)x
52= x²+9x
x²+9x-52=0
x²+13x-4x-52=0
x(x+13) - 4(x+13)= 0
(x-4)(x+13)=0
x=4 or -13
dimension cannot be negative
hence x=4in
the width is 4in. and the length is 4+9=13in.
The solution is, width=4in.
length=13in
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
The area of a rectangle is 52 in^2.
If the length is 9 inches more than the width.
let the width of the rectangle be x
then the length will be x+9
Area= length×width
so, we have,
52= (x+9)x
52= x²+9x
x²+9x-52=0
x²+13x-4x-52=0
x(x+13) - 4(x+13)= 0
(x-4)(x+13)=0
x=4 or -13
dimension cannot be negative
hence x=4in
so, we get,
the width is 4in. and the length is 4+9=13in.
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Can someone please help me with 54? It’s the last one and it’s due in 1 hour Tysm if you do!!
Answer:
4
Step-by-step explanation:
Well 3 x 4 equals 12, 12 x 4 equals 48, and so on.
hope this helps!
Find the distance between the origin and (-12,-9)
Answer:
Distance (d) = 15
Step-by-step explanation:
The given requires the distance between the point of origin, (0, 0), and (-12, 9). We can use the following distance formula for this problem:
[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{(x_2-x_1)^2\:+\:(y_2-y_1)^2}}[/tex]
Let (x₁, y₁) = (0, 0)
(x₂, y₂) = (-12, 9)
Substitute these values into the distance formula.
[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{(x_2-x_1)^2\:+\:(y_2-y_1)^2}}[/tex]
[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{(-12\:-\:0)^2\:+\:(9-0)^2}}[/tex]
Perform the required subtraction within each parenthesis:
[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{(-12)^2\:+\:(9)^2}}[/tex]
Next, take the squared values of -12 and 9 under the radical:
[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{144\:+\:81}}[/tex]
Add 144 and 81:
[tex]\displaystyle\mathsf{Distance(d)=\:\sqrt{225}}[/tex]
Distance (d) = 15
Answer:Therefore, the distance between the point of origin and (-12, 9) is 15.
Ricky spends $103. 19 in additional interest and charges on monthly payments as the result of a prior bankruptcy. If Ricky had been able to save this money for one year and then put it into a savings account earning 3. 1% simple interest, how much money could he have in savings after two more years? a. $1,238. 28 b. $1,276. 67 c. $1,315. 06 d. $2,476. 56.
The amount of money he could have in savings after two more years is:c. $1,315. 06.
First step is to calculate the 12 month saving
Saving= 12 month × $103.19
Saving = $1238.28
Second step is to calculate the interest earned
Interest = Prt
Interest= $1238.28×·0.031×1
Interest= $38.39
Third step is to calculate the balance after 2 years
Saving= $1238.28 +(2 years × $38.39)
Saving= $1238.28 +$76.78
Saving= $1315.06
Inconclusion the amount of money he could have in savings after two more years is:c. $1,315. 06.
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Sophia drew a scale drawing of the elementary school. The scale of the drawing was 1 centimeter : 4 meters. The schoolyard is 52 meters wide in real life. How wide is the schoolyard in the drawing
Answer:
13 cm
Step-by-step explanation:
The scale of the drawing was 1 centimeter : 4 meters.
x cm : 52 m Divide by 4
13 cm : 52 m
what is the answer in the remainder
Answer:
12 with a remainder of 5
Step-by-step explanation:
have a good day! :)
please help me write an expression for area and perimeter for this rectangle
[tex]\text{Given that ,}\\\\\text{Length,}~ l = (2y+5)~\text{units.}\\\\\text{Width, } w= 3~\text{units.}\\\\\\\text{Area} = lw = (2y+5)(3) = (6y+15) ~~ \text{units}^2.\\\\\\\text{Perimeter} =2(l+w) = 2(2y+5 +3) = 2(2y+8) = (4y+16)~~ \text{units}.[/tex]
Please help answer this question also with explanation
If a bank represents deposits with positive numbers and withdrawals as negative numbers, what could 10 + (-60) represent?
Answer:
A $10 deposit followed by a $60 withdrawal
Step-by-step explanation:
The 10 is positive, so it would represent a deposit, and the 60 is negative, so it would represent a withdrawal.
Johnny kicks a ball into the air. Assume the path of the ball can be modeled with a quadratic function. The ball reaches a height of 10 feet and lands on the ground 3 seconds later. Draw and label a graph that models the path of the ball. Write an equation that models the path of Johnny’s ball.
An equation that models the path of Johnny’s ball is [tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]
The maximum height is given as:
[tex]h_{max}= 10ft[/tex]
And the time spent is:
[tex]t = 3s[/tex]
So, the vertex of the ball would be:
[tex]Vertex = (t/2,h_{max})[/tex]
This gives
[tex]Vertex = (3/2,10)[/tex]
[tex]Vertex = (1.5,10)[/tex]
Rewrite properly as:
[tex](h,k) = (1.5,10)[/tex]
The ball is on the floor after 3 seconds.
So, another point on the graph is:
[tex](x,y) = (3,0)[/tex]
A quadratic equation is represented as:
[tex]y=a(x - h)^2 + k[/tex]
Substitute [tex](x,y) = (3,0)[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]
[tex]0=a(3 - 1.5)^2 + 10[/tex]
[tex]0=a(1.5)^2 + 10[/tex]
Evaluate the exponent
[tex]0=2.25a + 10[/tex]
Subtract 10 from both sides
[tex]2.25a =- 10[/tex]
Divide both sides by 2.25
[tex]a = -\frac{10}{2.25}[/tex]
Multiply by 4/4
[tex]a = -\frac{40}{9}[/tex]
Substitute [tex]a = -\frac{40}{9}[/tex] and [tex](h,k) = (1.5,10)[/tex] in [tex]y=a(x - h)^2 + k[/tex]
[tex]y = -\frac{40}9(x - 1.5)^2 + 10[/tex]
See attachment for the graph that models the path
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What is the equation of the line that passes through the points (-4, 2) and (-2, 10)?
Answer:
y=4x+18
Step-by-step explanation:
HOPE THIS HELPS :)
For f(x) = 4 - x and g(x) = 3x² + x + 5, find the following functions.
a.
(fog)(x); b. (gof)(x); c. (fog)(3); d. (gof)(3)
Arrange in descending order: 101.121, 111.101, 101.112, 110.111
Answer:
111.101, 110.111, 101.121, 101.112
Step-by-step explanation:
Descending order means values starting with big ones and ending with the small ones.
So, in this case,
111.101, 110.111, 101.121, 101.112Hope it helps :)
if x is reduced by 25%. the result will be
[tex]\huge\color{skyblue}\boxed{\colorbox{black}{Answer♡}}[/tex]
[tex]a \: number \: x \: is \: reduced \: by \: 25\%[/tex]
[tex]25\% \: of \: x \: means \: ( \frac{25}{100} )(x) = 0.25x \\ \\=> x - 0.25x \\ = > 0.75x[/tex]
hope helpful~
The reduced quantity if x is reduced by 25% is 0.75x.
What is percentage?A percentage, often known as percent, is a division by 100. Percentage, which means "per 100," designates a portion of a total sum. 45 out of 100 is represented by 45%, for instance. Finding the percentage of a whole in terms of 100 is what percentage calculation is. Both manual calculation and the use of internet calculators are options.
Given:
x is reduced by 25%,
Calculate the 25% of x as shown below,
25 / 100 × x
0.25x
Calculate the reduced quantity,
Reduced quantity = x - 0.25x
Reduced quantity = x(1 - 0.25)
Reduced quantity = 0.75x
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frEE po ints
Lets say you own a ferret store and you have 20,female ferrets worth $400 and 2, male ferrets worth 350 dollar ferrets. you sell 1male ferret and 8 female ferrets how much money do you get from the sellings?
pt.b
your store gets robbed and you loose 800 dollars worth of female ferrets and 350bucks worth of male ferrets how many ferrets do you have in still have in toatal?
Answer:
Part A, 3550$
Part B, Ten female ferrets left
Step-by-step explanation:
help me with this pls
Answer:
-49
Step-by-step explanation:
Make sure you understand the difference between
-3² and (-3)²
-3² means square 3, then take its opposite. -3² is the same as -(3²) = -9
(-3)² means square the number -3, which means that (-3)² = (-3) × (-3) = 9
Ok, now we can start. Use the correct order of operations.
-3² + (2 - 6)(10) =
= -9 + (-4)(10)
= -9 + (-40)
= -9 - 40
= -49
X
-9
-5
-1
3
Y
- 2
0
2
4
What is the slope of the line?
ok done. Thank to me :>
4.5 times 9 times 6.5 please make it a fraction or whole number also no links bots or anything like that please
Answer:
263.25
Step-by-step explanation:
Your welcpme and stay safe
Answer:
fraction; 263.25/100
whole number; 263
Step-by-step explanation:
4.5 × 9 × 6.5;
4.5 × 6.5 = 29.25
29.25 × 9 = 263.25
Explain why the square root of a number is defined to be equal to that number to the 1/2 power
Answer:
Because square root is essentially the same thing as the power to a half
sqrt(x) is the same as (x)^1/2
Just checking, am I correct?
Answer: yes!
Step-by-step explanation:
Answer: As to what I am seeing i think you are doing fine
Step-by-step explanation:
Great Job
. . . .. . . .. . . .. so easy
Answer:
i aint smart but im a the last one 4/8
Answer:
The answer is 4/8.
Step-by-step explanation:
Because 4 is half of 8 while the others are either 1 more or 1 less then half or just don't make half at all. So the only answer here that makes sense is 4/8
(pls do tell me if I'm wrong)
(Look at the picture ) Consider the graph of the function f below.
N0.6
(4.6
6
(3.4)
21 8(2.2)
-6
-8
-4
-2
0
2
4
6
8
What is the value of f (4)?
1
A
B
3
С
6
D
14
Answer:
yes u picked C thats the correct answer
Step-by-step explanation:
A small jar of mustard holds 75% as much as a large jar of mustard. If the large jar holds 36 ounces, how much does the small jar hold?
Answer:
27 ounces
Step-by-step explanation:
36 / 4 = 9 x 3 = 27
2+5+8+….+3n-1=n(3n+1)/2
Answer:
all you do is() first divide then go from left to right answers 4
M(ax+by+c)=0 make y subject
[tex]M(ax+by +c)=0\\\\\implies ax+by +c =0\\\\\implies by = -ax-c\\\\\implies y = \dfrac{-ax -c}{b}\\\\\implies y = - \left(\dfrac{ax+c}b \right)[/tex]
What is the equation of the line in standard form?
(2,2)
Step-by-step explanation:
You have to add them together and minus the negatives