To find the missing side length of the acute angled triangle apply the cosine law as follow:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
As given in the question,
Given triangle is acute angled triangle.
Let us consider the measure of two sides and its included angle of the acute angled triangle is given.
Let the triangle be ABC,
Side opposite to ∠A, ∠B , and ∠C are a , b, and c respectively.
Apply cosine law to find the measure of the missing side in the acute angled triangle:
a² = b² + c² - 2bccosA
b² = a² + c² - 2accosB
c² = b² + a² - 2abcosC
Therefore, to get the measure of the missing side length in the acute angled triangle apply cosine law.
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Radicals
How do I Simplify
(4√5-3)(√5-2)
Answer:
26 - 11√5
Step-by-step explanation:
(4√5-3)(√5-2)
= 4√5 (√5-2) -3 (√5-2)
= 4√5 √5 + 4√5 ⋅ -2 -3 (√5-2)
= 4√5 √5 + 4√5 ⋅ -2 -3√5 -3 ⋅ -2
= 26 - 11√5
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As an estimation we are told 5 miles is 8 km.
Convert 52 km to miles.
Answer:
32.5 miles
Step-by-step explanation:
We can convert 52 km to miles using the given estimation.
To convert 52 km to miles, create a proportion where x is how many miles are in 52 km:
[tex]\frac{5}{8}[/tex] = [tex]\frac{x}{52}[/tex]
Cross multiply and solve for x
8x = 260
x = 32.5
So, in 52 km, there are approximately 32.5 miles
52 km is approximately equal to 32.5 miles.
What is the proportion?A mathematical assessment of two numbers is called a proportion. If two sets of provided numbers rise or fall in the same relation, then the ratios are said to be directly proportional to each other.
If we are given the estimation that 5 miles is approximately 8 km, we can use this ratio to convert 52 km to miles.
Let's set up a proportion:
5 miles / 8 km = x miles / 52 km
Cross-multiplying, we get:
5 miles × 52 km = 8 km × x miles
260 miles = 8x
To solve for x, divide both sides of the equation by 8:
260 miles / 8 = x
x ≈ 32.5 miles
Therefore, 52 km is approximately equal to 32.5 miles.
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Grandma Meyer uses the recipe to make a soup.
Part A: How much vegetable stock and cream are needed?
Answer:
um u gotta give numbers how r we gonna answer?
Step-by-step explanation:
Which number is less than -1.5?
1. -1
2.-1.5
3.-1 1/3
4.-1 2/3
Answer:
4.) -1 2/3
Step-by-step explanation:
it means -1.66666666
Help on this which one is the answer???:((:))
Answer:
A
Step-by-step explanation:
Find all the missing elements:
B
40°
a
120°
A
8
С
C = [?]° a = [ ] C = [ ]
Enter
Answer:
a=10.8; c=4.3
Step-by-step explanation:
The sum of all the angles in a triangle is 180 degrees.
Two of the angles are given as 40 deg and 120 deg.
Subtract the measures of both from the sum to get the last angle:
180-40-120=20; ∠C=20°
Using Law of Sines: [tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]
[tex]\frac{a}{sin120}=\frac{8}{sin40}; a=\frac{8*sin120}{sin40}; a=10.77837084[/tex]
[tex]\frac{c}{sin20}=\frac{8}{sin40}; a=\frac{8*sin20}{sin40}; c=4.25671109[/tex]
Answer:
c=20 a=10.8 c=4.3
Step-by-step explanation:
Identify similarities and differences in finding the volume of cylinders, cones, and spheres.
The volume of the cone is one third the volume of the cylinder.
The volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter
How to illustrate the information?Similar to a prism, a cylinder has two bases, but they are circles rather than polygons. A cylinder's sides are also curved rather than flat. A cone has a vertex that is not on the base and a single circular base. The sphere is a figure in space with equal distances between each of its points and the center.
The cone's volume is one-third that of the cylinder. A sphere's volume is 2/3 that of a cylinder with the same radius, and its height is equal to its diameter.
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Mario's pizzeria puts olive pieces along the outer edge (periphery) of the crust of its 18-inch (diameter) pizza. Assuming that the pizza is cut into eight slices and that there is at least one olive piece per inch of crust, find how many olive pieces you will get in one slice of pizza.
Answer:
Radius= 9 in.
Circumference= 2π*9=56 (rounded)
So you'd get at least 56 pieces in the crust of the pizza.
Divide the answer by 8 to get the average number of piece per slice.
56/8
= 7 pieces approximately.
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How many pieces of 2/3 yard can I cut if I have 6 1/3 yards of material
Answer:
9
Step-by-step explanation:
6 1/3 yards of material is 19/3 yards total. 6 yards broken into thirds is 18/3. 18 divided by 2 is 9. There are 9 total pieces to cut, and an extra 1/3 left over
Pls help me with this no links please and Thank you
Answer:
im sorry you need to take a better pic i can see the graphs
What is the area of a square that has a side length of (4x+5)?
Is the equation a linear equation? xy+2y=8
Answer:
NO it is not linear
Step-by-step explanation:
hey please, i wanna help you and everybody viewing this go to m a t h w a y put your answer in and when it asks to "how should i answer" look up determine if linear.
Need this question quick 20 points
On solving the provided question we can say that the rectangular form of the equation is y = -1
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
Ф = [tex]\pi[/tex]/2
y = - 1
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How do you compare two slopes on a graph?
Two slopes can be compared on a graph by analyzing the steepness of the lines and their direction (positive or negative).
The steepness of a line on a graph is determined by its slope, which is the ratio of the change in y to the change in x (rise over run). A steep line has a large slope, meaning that for a small change in x, there is a large change in y. A shallow line has a small slope, meaning that for a small change in x, there is a small change in y. To compare two slopes, one can compare the steepness of the lines by comparing the absolute value of the slopes.
If one line has a larger absolute value than the other, it is steeper. Additionally, one can also compare the direction of the slope, which is determined by the sign of the slope. A positive slope indicates that the line is increasing and a negative slope indicates that the line is decreasing. By comparing the steepness and direction of the slopes, one can determine whether the two lines are parallel or not, and whether they are going in the same direction or not.
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A type of medicine is given in a 100-milligram dosage. The medicine comes in 14-gram bottles. How many 100-milligram dosages are in a bottle?
Answer:
140 doses
Step-by-step explanation:
1 gram = 1000 milligrams
1 gram = 10 doses
10*14 = 140
Does 3 4 5 make a right triangle?
Answer:
Yes
Step-by-step explanation:
The side lengths are a Pythagorean triple.
It takes 52 yards of fabric to make 8 costumes for the dance recital. How many yards are needed to make one costume?
Make a Ratio Table
(MUST INCLUDE THE TABLE!!)
Total 6.5 yards , fabaric are needed to make one costume for the dance recital.
We have , Total lengths of fabaric present for making costumes = 52 yards
Total number of costumes for the dance recital made from 52 yards = 8
we have to calculate the length of fabaric in yards are used for make one constume .
Let the " x yards " be the fabric length used to make one constume.
Now, total fabric length used to make 8 conatumes = 8x yards
but it will be equals to 52 yards . So, we get a simple linear equation with one variable, i.e
=> 8x = 52
=> x = 52/8
=> x = 6.5
So, the required fabric length is 6.5 yards .
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A website lists homes for sale in a suburban town. The site provides information including neighborhood, selling price, number of bedrooms, and whether the home has a garage. What are the individuals in this setting?
homes
neighborhoods
selling prices
bedrooms
answer is homes
Based on the description above, the individuals in this setting is option A: homes.
Whys the setting home?The website lists homes for sale in a suburban town and provides information such as neighborhood, selling price, number of bedrooms, and whether the home has a garage.
In this case each house is an instance or a data point of a "home" object, these objects have different attributes or features like neighborhood, selling price, number of bedrooms and garage, these attributes are used to describe the characteristics of the home, they are also called features.
Therefore, each home is an individual unit being sold on the market. Neighborhoods, selling prices, and bedrooms are attributes or characteristics of the homes, and they help provide more information about each individual home being listed.
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Assume that lines which appear tangent are tangent
Answer:
B
Step-by-step explanation:
Remark
This is a monster when you first come across it, but later on you will not be fooled.
Construction
Draw a line from E to the center of the circle. Label the center of the circle OOE and OF are both radii. They form the central angle of the ArcEFSolution
Find the value of Arc EF
The value of Arc EF = 360 - 244 = 116
The value of <FOE also = 116. (The arc and the central angle are equal.)
ΔFOE = 116 degrees See above statement
ΔFOE is isosceles Two of it's sides are radii.
The two base angles can be solved. Call each one x
2x + 116 = 180 All triangles have 180 degrees
-116 -116 Subtract 116 from both sides
2x = 64 Divide by 2
x = 32 <EFO = 32
<EFO = 90 Where the tangent meets the radius forms a 90o angle.
<EFO + GFE = 90
32 + GFE =90
GFE = 90 - 32
GFE = 58
Answer: B
Answer:
b
Step-by-step explanation:
360-244/2= 116/2=58 or b
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What is the percent that the temperature of a ufo that hits in the middle of the Arctic and is eaten by a giraffe is 72 degrees?
Answer:
67°
Step-by-step explanation:
TYAJSJSHSSNDNDBSBSBSBBSD
Simplify 16x+34(12x−4)
Answer:
424x - 136
Step-by-step explanation:
16x + 34 ( 12x - 4 )
= 16x + 408x - 136
= 424x - 136
Carla Arslanian is 55 years old. She wants to purchase a $100,000, 10 year term life insurance policy. The premium per $1000 is $8.95. What is her annual premium?
Answer:
$863
Step-by-step explanation:
Given: Carla Arslanian is 55 years old. She wants to purchase a $100,000, 10-year term life insurance policy.
To find: What is her annual premium?
Solution: Insurance companies use mathematical calculation and statistics to calculate the number of insurance premiums they charge their clients.
Annual premium = face value x rate $100
Annual premium (for building) = $100,000 ÷ $1000 x 10 = $1000.
The sum of the annual premium is $863.
What is the smallest multiple of 6 greater than 115?
Answer:
120
Step-by-step explanation:
First, divide 115 by 6:
115/6 =
(114 + 1)/6 = ==> 114 is a multiple of 6
114/6 + 1/6 = ==> distribution property
19 + 1/6 = ==> simplify
19 1/6 ==> the smallest integer greater than 19 1/6 is 20
Hence, multiply 20 by 6 to get 120.
(x - 13)
155 solve for x
It equals 180 but I don’t know how to solve it
The solution of x in the given linear equation (x - 13 + 155 = 180) is equal to 38.
To solve the equation (x - 13 + 155 = 180), we need to pursue the following steps.
Step 1. Move all terms to the left:
⇒(x - 13 + 155 - (180)) = 0
Step 2. Add all the numbers jointly, and all the variables
⇒(x - 38) = 0
Step 3. Get rid of parentheses
⇒x - 38 = 0
Step 4. Transfer all terms including x to the left, and all other terms to the right
⇒x = 38
Hence, the required solution of x in the given linear equation (x - 13 + 155 = 180) is 38.
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You have $1000 to invest in two different accounts. In order to save the money you need for college, you need to average 6.6 percent interest. If the two accounts pay 5 percent and 7 percent interest, how much should you invest in each account?
A) $800 in 5%, $200 in 7%
b) $400 in 5%, $600 in 7%
C) $200 in 5%, $800 in 7%
D) $500 in 5%, $500 in 7%
Answer:
B) $400 in 5%, $600 in 7%
Step-by-step explanation:
First, convert R as a percent to r as a decimal
r = R/100
r = 6.6/100
r = 0.066 rate per year,
Then solve the equation for A
A = P(1 + r/n)nt
A = 10,000.00(1 + 0.066/12)(12)(7.5)
A = 10,000.00(1 + 0.0055)(90)
A = $16,382.75
Therefore, you will need to invest $400 in 5%, $600 in 7% acoounts
Answer:
Step-by-step explanation:
C) $200 in 5%, $800 in 7%
You need to split it in half then multply then add
Answer:
378 because 6×7 is 42 and 16×21 is 336 and them and get. 378
what can 16 and 4 both be divided by
Answer:
4
Step-by-step explanation:
they can both be divided by 4
Find the Surface area and volume of the larger figure:
scale factor = 1:3
SA = 81 cm^2
V = 135 cm^3
Plz help
A cylindrical aluminum soda can is to hold 12 ounces of tasty beverage. What are the dimensions of the can that will minimize the amount of aluminum used
A cylindrical can with volume 355 ml will use the least aluminum if its radius is about 3.84 cm and its height is about 7.67 cm.
What is a reasonable approximation for the volume of a soda can?The soda cans are advertised as having a volume of 12 ounces, or 355 milliliters. The remaining head space is just under 25 ml. The can weighs about 13 g by itself. 39 g, or about 11%, of sugar, make up 355 ml of Coke.
How much pressure does a 12 oz. soda can typically hold?When canned at 4 °C and stored at 20 °C, 12 oz. soda cans typically have pressures of about 120 kPa and 250 kPa, respectively. A 7UP® can that has been refrigerated contains 210 kPa of pressure. Pepsi-Cola®, on the other hand, has 276 kPa at about 16 °C.
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maggie has a rectangular box with a length of 6 1/2 of 9 inches and hieght of 3 1/2 inches
what is the volume of the box
V = & x w x h
V = 6 1/2 x 9 x 3 1/2
V = 204 3/4
So answer is 204 3
4