Law of cosine helps us to know the third side of a triangle. The length of the third side of the ΔHIJ, h is 6.698 inches.
What is the Law of Cosine?The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,
[tex]c =\sqrt{a^2 + b^2 -2ab\cdot Cos\theta}[/tex]
where
c is the third side of the triangle
a and b are the other two sides of the triangle,
and θ is the angle opposite to the third side, therefore, opposite to side c.
As it is given that the length of the first two sides of the triangle is i=6.6inches and j=6.4 inches, while the measure of the ∠H=62°. Therefore,
the length of the third side with the help of cosine rule can be written as,
[tex]h =\sqrt{i^2 + j^2 -2ij\cdot Cos(\angle H)}\\\\h =\sqrt{(6.6)^2 + (6.4)^2 -(2 \times 6.6 \times 6.4)\cdot Cos(62^o)}\\\\h = 6.6976 \approx 6.698[/tex]
Hence, the length of the third side of the ΔHIJ, h is 6.698 inches.
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Please answer!!
6.7.32
For what value of x is the given parallelogram a
rhombus?
(6x +13)
(9x-5)
The given parallelogram is a rhombus when x=
Answer:
x = 6
Step-by-step explanation:
(9x - 5)° = (6x +13)°
9x - 5 = 6x + 13
9x - 6x = 13 + 5
3x = 18
x = 18/3
x = 6
The given parallelogram is a rhombus when x = 6
The value of 'x' for which the parallelogram will be a rhombus is x = 3.
What is a rhombus?A quadrilateral with all equal sides is a rhombus.
Rhombuses are a particular kind of parallelogram in which all of the sides are equal since the opposite sides of a parallelogram are equal.
A rhombus has 360° of interior angles total.
A rhombus's adjacent angles add up to 180°.
A rhombus's diagonals are perpendicular to one another and cut each other in half.
One more property of rhombus is that the diagonals bisect the originating angles.
Therefore, The values of 'x' for which this parallelogram will be a rhombus is, 6x + 13 = 9x - 5.
6x - 9x = - 5 - 13.
- 3x = - 18.
3x = 18.
x = 6.
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Please do number 13 for me
Y = A system of equations. Y equals StartFraction 2 over 3 EndFraction x plus 3. X equals negative 2.X + 3 x = –2
Answer: The solution is the pair (-2, 5/3)
Step-by-step explanation:
The system of equations is:
y = (2/3)*x + 3
x = -2
When we have a system of equations, we usually start by isolating one of the variables in one of the equations and then replacing it in the other ones (in that way, we can "remove" variables, until we have only one and we can solve the problem)
In this case, we have already isolated the variable x in the second equation, then we can just replace it in the first one, to get:
y = (2/3)*(-2) + 3
y = -4/3 + 3 = -4/3 + 9/3 = (-4 + 9)/3 = 5/3
y = 5/3
Then the solution of this system is
x = -2
y = 5/3
Which also can be represented with the ordered pair (-2, 5/3)
Simplify:
4y - 1/2 (-3/4+2/3y)
Answer:
11/3y-3/8
Step-by-step explanation:
Distribute -1/2 through the parentheses
4y-3/8-1/3
calculate the difference
Answer- 11/3y-3/8
Given the following equations, at which point will the graphs intersect?
f(x) = 5x + 1
g(x) = -2x + 15
(0,0) (1,15) (-2,-9) (2,11)
Answer:
(2,11)
Step-by-step explanation:
f(x) = 5*2 + 1 = 11
g(x) = -2 *2 + 15 = 11
what is the actual length?
Answer:
Step-by-step explanation:
2ft
A water tank in the shape of a pyramid has a rectangular base with dimensions of 10 feet by 15 feet. The height of the rectangular pyramid is 12 feet. Water fills half the volume of the water tank. How many more cubic feet of water is needed to finish filling the water tank?
(Explanations are appreciated along with your answer.)
600ft³ will be the required volume
Volume of pyramidThe formula for calculating the volume of the rectangular prism is expressed as:
V = 1/3lwhGiven the following information
l = 10 feet
w = 15feet
h = 12 feet
Get the volume
V = 1/3(10 * 15 *12)
V = 1/3(1800ft³)
V = 600ft³
Hence 600ft³ will be the required volume
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Solve using the substitution method. 3x +2y= 19 xy= 15
Answer:
when x = 3 1/3, y = 4.5
or
when x =3 , y = 5
Step-by-step explanation:
Here, we want to solve using substitution
xy = 15
let x = 15/y
Put this into the first equation;
3(15/y) + 2y = 19
45/y + 2y = 19
Multiply through by y
45 + 2y^2 = 19y
2y^2 -19y + 45 = 0
2y^2 - 10y - 9y + 45 = 0
2y(y-5) -9(y-5) = 0
(2y-9)(y-5) = 0
2y-9 = 0
or y-5 = 0
2y = 9 or y = 5
y = 9/2 or y = 5
y = 4.5 or y = 5
Recall;
x = 15/y
x = 15/4.5 or x = 15/5
x = 3 1/3 or x = 3
On the first day of ticket sales the school sold 8 senior citizen tickets and 1 child ticket for a total of $97. The school took in $102 on the second day by selling 6 senior citizen tickets and 4 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.
Answer:
A senior citizen ticket costs $11, and a child ticket costs $9.
Step-by-step explanation:
Let s = price of 1 senior citizen ticket, and let c = price of 1 child ticket.
First day:
8s + c = 97
Second day:
6s + 4c = 102
We have a system of 2 equations in 2 unknowns.
8s + c = 97
6s + 4c = 102
We will use the addition method to solve the system.
Multiply both sides of the first equation by -4. Write the second equation below it and add the equations.
-32s - 4c = -388
(+) 6s + 4c = 102
----------------------------
-26s = -286
Divide both sides by -26.
s = 11
Now substitute s with 11 in the first original equation and solve for c.
8s + c = 97
8(11) + c = 97
88 + c = 97
Subtract 88 from both sides.
c = 9
Answer: A senior citizen ticket costs $11, and a child ticket costs $9.
Emerson struck out 122 times in 350 at bats. What is his percentage of strike outs?
Answer:
Around 35%
Step-by-step explanation:
122/350 = 0.35
Answer:
32%
Step-by-step explanation:
We are told out of 350 times, he stuck out 122 times. As a fraction, we can say he struck out 122/350 times.
As a fraction, we can easily convert this to a decimal by dividing the numerator (top number) by the denominator (bottom number).
So, 122/350 = 0.32.
Now, we can easily convert this to a percentage by multiplying by 100.
0.32 x 100 = 32%
Which statement best describes the area of Triangle ABC shown below?
А
с
00
(5 points)
O It is twice the area of a square of side length 4 units.
O It is one-half the area of a square of side length 4 units.
It is twice the area of a rectangle with sides 4 units x 3 units.
It is one-half the area of a rectangle with sides 4 units x 3 units.
Answer:
Would be the 3rd one I believe
Step-by-step explanation:
The statement that is true is:
It is one-half the area of a rectangle with sides of 4 units x 3 units is true.
What is a triangle?A triangle is a 2-D figure with three sides and three angles.
The sum of the angles is 180 degrees.
We can have an obtuse triangle, an acute triangle, or a right triangle.
We have,
The area of the triangle.
= 1/2 x base x height
Now,
Base = 4 units
Heights = 3 units
So,
Area = 1/2 x 4 x 3 = 6 units²
Now,
It is twice the area of a square of the side length of 4 units.
6 units² < 16 units²
This is not true.
It is one-half the area of a square of side length 4 units.
1/2 x 16 units² = 6 units²
8 units² = 6 units²
This is not true.
It is twice the area of a rectangle with sides 4 units x 3 units.
2 x 12 units² = 6 units²
24 units² = 6 units²
This is not true.
It is one-half the area of a rectangle with sides 4 units x 3 units.
1/2 x (4 x 3) units² = 6 units²
6 units² = 6 units²
This is true.
Thus,
It is one-half the area of a rectangle with sides of 4 units x 3 units is true.
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GUYSS PLEASEEEE NO ONE IS HELPING MEEE I NEED THSISSSSSSS 30PTSS
Step-by-step explanation:
how do you write over the thing so I can give you the answer or can I just tell you the answer in text messages
Answer:
uh what
Step-by-step explanation:
mickel and 4 friend bought a total of 95 raffle tickets if the ticket were dived equaly among themselves how many tickets did each person get?
Answer:
19
Step-by-step explanation:
5 people in total, divide equally from 95
Answer:
Step-by-step explanation:
95/4=23.75
Round 23.75 --> 24.00 raffle tickets each.
What is the range of the data set below?
25, 24, 24, 24, 33
Answer:
9
Step-by-step explanation:
the range is the difference between the greatest value and the smallest one. The greatest value in the data set is 33, and the smallest is 24.
So u just subtract 24 from 33:
33 – 24 = 9
and that's your range! hope this helps!
PLEASE HELP ASAP!!
Please could I have the answers or step by step I don’t mind just PLEASEE help asap!!
I need an answer for this it’s due today plss
Answer:
128
Step-by-step explanation:
2^4/2^-3
= 2^7
=128
PLEASE HELP (don't put fake answers !!)
Answer:
=33.55 m^2
Step-by-step explanation:
The area of the trapezoid is
A = 1/2 a(b+c) where a is the height and b and c are the bases
A = (1/2 *5.5)(5+7.2)
= 2.75(12.2)
=33.55 m^2
Answer:
i resubmitted my Persuasive Argument: Letter to Gov. Abbott Choice
Step-by-step explanation:
Which situation would not be represented by the integer -9?
a hole 9 feet deep
9 dollars withdrawn from the bank
a football pass of 9 yards
a temperature of 9° below zero
If you deposit $6000 into an account paying 8% annual interest compounded monthly, how much money will be in the account after 7 years?
Answer:
$10278
Step-by-step explanation:
Given data
P= $6000
R= 8%
T= 7 years
The compound interest formula is
A=P(1+r)^t
substitute
A=6000(1+0.08)^7
A=6000(1.08)^7
A=6000*1.713
A=$10278
Please answer the correctly in the picture below 8TH GRADE MATHENMATICS?!
Answer:
B 3.5
Step-by-step explanation:
Hope it Helps!
One hundred grams of radium are stored in a container. The amount RR (in grams) of radium present after tt years can be modeled by R=100e−0.00043tR=100e−0.00043t. After how many years will only 5 grams of radium be present? Round your answer to the nearest whole year.
Answer:
6967 years
Step-by-step explanation:
Given the exponential function :
R=100e−0.00043t
Time = t in years
R = final amount
Number of years in which only 5 grams of radium will be present :
R = 5
Plugging into our formula :
5 = 100 * e^−0.00043t
5 / 100 = e^−0.00043t
0.05 = e^−0.00043t
Take the In of both sides
−2.995732 = - 0.00043t
t = −2.995732 / - 0.00043t
t = 6966.819
t = 6966.819 years
t = about 6967 years
Which number below is a perfect square? 100 90 50 75
Can someone help me I'm confused
Answer:
I think its 5 t shirts for 11 dollars?
Step-by-step explanation:
Answer:
When she buys 0 t-shirts, the price is $0.
Step-by-step explanation:
Answer fast!!!!!!!!!
Answer:
$0.52 = 0.52
Step-by-step explanation:
I think so.....
The volleyball team needs new uniforms. The students plan to sell plush toy eagles (the school mascot) for $5 each. The students find three companies on-line that sell stuffed mascots. Company A sells 12 eagles for $34.56. Company B sells 15 eagles for $42.90. Company C charges $51.30 for 18 eagles. Which company has the best buy?
Answer:
Step-by-step explanation:
A=34.56/12=$2.88 each
B=42.90/15=$2.86 each
C=51.30/18=$2.85 each
So C is the cheapest.
Dane needs to cut 4 strips of border for his rectangular project board. The project board has a length of 12 1/2 inches and a width of 6 1/4 inches. How much border will Dane have left if the border comes in a 60-inch roll?
HELP I NEED HELP ASAP
Answer:
I think it's A
Step-by-step explanation:
the line is going up and the more it goes up it looks like it will be 2.5
What equation models the data in the table if d = number of days and c = cost?
Help this is due today and I don’t know how to do it you please show me the steps:)
Answer:
628 inches²
Step-by-step explanation:
the equation for surface area is SA=2(lw+lh+hw) so..
1. 2×(16×14 + 16×3 + 3×14)
2. 2×(224+48+42)
3. 2×314
4. 628
Hope this helps! :)
the numerical coefficient in the expression -3×y² is
The numerical coefficient for the expression how much of the variables, in this case xy^2 there are in number form. There is only one number in this question so it makes it fairly straight forward. The answer is -3.