For triangle ABC, tell what information is given (i.e. SAS, SSS, ASA, etc.) in Column A. Solve for the indicated angle or side in Column B. If there are two solutions, give both. Express answers to the nearest tenth.
1. A=52°, b=120, c = 160, find a
2. a=13.7, A=2543°, B=78°, find b
3. A=38°, B=63°, c=15, find b
4. a=1.5, b=2.3, c=1.9, find B
5. b=795.1, c=775.6, B=51.85°, find C
6. b=40, c=45, A=51°, find a
7. b=50, a=33, A=132°, find B
8. a=20, b=12, c=28, find C
9. a=125, A=25°, b=150, find B
10. b=15.2, A=12.5°, C=57.5°, find c
Answers
Using the laws of sines and cosines, answers to the questions are as follows,
1. A=52°, b=120, c = 160,
SAS property, a=128
2. a=13.7, A=25.43°, B=78°,
AAS property, b=31.21
3. A=38°, B=63°, c=15,
ASA property, b=14
4. a=1.5, b=2.3, c=1.9,
SSS property, B=84
5. b=795.1, c=775.6, B=51.85°,
SAS property, C=50
6. b=40, c=45, A=51°,
SAS property, a=37
8. a=20, b=12, c=28
SAS property, C=120
9. a=125, A=25°, b=150
SAS property, 2 solutions are there, B1=149, B2=30.4
10. b=15.2, A=12.5°, C=57.5°
SAS property, c=14
What are the laws of sine and cosine?
We can determine a triangle's one side's length or one of its angles' measurements using the laws of sine and cosine.
In most cases, the unknown sides or angles of an oblique triangle are calculated using the law of sines formula.
The equation that connects the lengths of the triangle's sides and the cosines of its angles is known as the law of cosine or cosine rule.
1. Given A=52°, b=120, c = 160.
If we construct the triangle, we see that it is satisfying the SAS property
By using the law of cosine we get,
[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{120^{2}+160^{2}-2.120.160.\cos 52}\\a=127.9[/tex]
2. Given, a=13.7, A=25.43°, B=78°
From angle A, angle B, and side a, we calculate side b, by using the Law of Sines,
[tex]\frac{b}{a}=\frac{\sin B}{\sin A}\\b=a.\frac{\sin B}{\sin A}\\b=13.7. \frac{\sin 78}{\sin 25.43}\\b=31.21[/tex]
3. A=38°, B=63°, c=15
From angle A and angle B, we calculate angle C,
[tex]A+B+C=180\\C=180-A-B\\C=180-38-63\\C=79[/tex]
Next, From angle A, angle C, and side c, we calculate side a, by using the Law of Sines
[tex]\frac{a}{c}=\frac{\sin A}{\sin C}\\a=c.\frac{\sin A}{\sin C}\\a=15. \frac{\sin 38}{\sin 79}\\a=9.41[/tex]
Calculation of the third side b of the triangle using a Law of Cosines,
[tex]b^{2}=a^{2} +c^{2}-2.a.c.\cos B\\b=\sqrt{a^{2}+c^{2}-2.a.c.\cos B}\\b=\sqrt{9.1^{2}+15^{2}-2.9.41.15.\cos 63}\\b=13.68[/tex]
4. a=1.5, b=2.3, c=1.9
Calculation of the inner angles of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{1.5^{2}+1.9^{2}-2.3^{2} }{2 . 1.5.1.9}\\B=84.15[/tex]
5. b=795.1, c=775.6, B=51.85°
From angle B, side c, and side b, we calculate side a. by using the Law of Cosines and quadratic equation:
[tex]b^2 = c^2 + a^2 - 2.c. a. {\cos B} \\ 795.1^2 = 775.6^2+a^2-2. 775.6. a . \cos 51\ \\ a > 0 \\ a = 989.175[/tex]
Calculation of angle C of the triangle using a Law of Cosines
[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{989.175^{2}+795.1^{2}-775.6^{2} }{2 . 989.795}\\C=50.5[/tex]
6. b=40, c=45, A=51°
Calculation of the third side a of the triangle using a Law of Cosines
[tex]a^{2}=b^{2} +c^{2}-2.b.c.\cos A\\a=\sqrt{b^{2}+c^{2}-2.b.c.\cos A}\\a=\sqrt{40^{2}+45^{2}-2.0.45.\cos 51}\\a=36.87[/tex]
8. a=20, b=12, c=28
Calculation of angle C of the triangle using a Law of Cosines
[tex]c^{2}=a^{2}+b^{2}-2.a.b.{\cos C}\\C=arc {\cos} \frac{a^{2}+b^{2}-c^{2} }{2.a.b} \\ C=arc {\cos} \frac{20^{2}+12^{2}-28^{2} }{2 . 20.12}\\C=120[/tex]
9. a=125, A=25°, b=150
2 solutions are possible for this,
solution for B1:
From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:
[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 28.21[/tex]
Calculation of angle B of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+28.21^{2}-150^{2} }{2 . 125.28}\\B=149[/tex]
solution for B2:
From the angle A, side b, and side a, we calculate side c. by using the Law of Cosines and quadratic equation:
[tex]a^2 = b^2 + c^2 - 2b c \cos A \ \\ 125^2 = 150^2 + c^2 - 2 \cdot \ 150 \cdot \ c \cdot \ \cos 25\degree \ \ \\ c > 0 \ \\ c = 243.679[/tex]
Calculation of angle B of the triangle using a Law of Cosines
[tex]b^{2}=a^{2}+c^{2}-2.a.c.{\cos B}\\B=arc {\cos} \frac{a^{2}+c^{2}-b^{2} }{2.a.c} \\ B=arc {\cos} \frac{125^{2}+243^{2}-150^{2} }{2 . 125.243}\\B=30.28[/tex]
10. b=15.2, A=12.5°, C=57.5°
From angle A and angle C, we calculate angle B:
[tex]A+B+C=180\\B=180-A-C\\B=180-12.5-57.5\\B=110[/tex]
From the angle A, angle B, and side b, we calculate side a, by using the Law of Sines.
[tex]\ \\ \dfrac{ a }{ b } = \dfrac{ \sin A }{ \sin B } \\ a = b \cdot \ \dfrac{ \sin A }{ \sin B } \\ a = 15.2 \cdot \ \dfrac{ \sin 12.30 }{ \sin 110\degree } = 3.5[/tex]
Calculation of the third side c of the triangle using a Law of Cosines
[tex]c^{2}=a^{2} +b^{2}-2.a.b.\cos C\\c=\sqrt{a^{2}+b^{2}-2.a.b.\cos C}\\c=\sqrt{15.2^{2}+3.5^{2}-2.15.4.\cos 57.30}\\c=13.64[/tex]
Therefore, we have found the solutions of all of the above bits using the law of sine and cosine.
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Related Questions
Solve the system of equations by graphing.
1. y = x - 1
y = 2x - 2
2. y = 4x
y = x + 3
3. y - x = 1
y = x - 2 + 3
Answers
Answer:
Step-by-step explanation:
1) x - 1 = 2x - 2
-x = -1
x = 1
2) 4x = x + 3
3x = 3
x = 1
3) x + 1 = x + 1
infinite solutions (parallel lines)
For graphing, just look at the y-intercept, in the equation y = mx + b.
b is the y-intercept, so, for you plot the y-intercpet on the y-axis. You look at m, which is the slope. For positive, you go up how many ever it says in the numerator and then to the right how many ever it says in the denominator. For a negative you do the same thing except you go down and then to the right, or up and to the left. For positive there is only up and then to the right. I hope this answers your question.
a hemispherical tank is filled with water and has a diameter of 10 feet. if the water weighs 62.4 pounds per cubic foot. what is the total weight of the water in a filled tank
Answers
The total weight of the water in a filled tank will be equal to 16,336 Pounds.
What is Volume?
Every three-dimensional item takes up space in some way. The volume of this area is what is used to describe it. The area covered within an entity's three-dimensional bounds is referred to as its volume. The object's size is another name for it.
As per the given data in the question,
Radius, r = 10/2 = 5 ft.
Use the equation of the volume of a sphere,
V = 4/3πr³
We only require half of it then,
V = 2/3πr³
V = 261.8 ft³
So, the total weight will be,
W = 261.8 × 62.4
W = 16,336 Pounds.
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(a) The diameter of Mars at its equator is approximately 6.79*10^3 kilometers. Write this number in standard notation.
Answers
Answer:
6790 km
Step-by-step explanation:
move the decimal 3 places to the right.
The average height of children who are 2 years old is 34 inches. A random sample of 35 children who are 2 years old in a large daycare franchise is collected, and they are found to average 29.50 inches with a standard deviation of 1.70 inches. The researchers are suspicious that the children at the daycare are not growing as quickly as they should be.
a. Write the hypotheses.
b. Calculate the test statistic.
c. Calculate the P-value
d. What is the conclusion for the hypothesis test?
Answers
There is sufficient evidence to support the claim.
What is sufficient evidence ?
Sufficient evidence is admitted evidence that has enough overall weight, in terms of relevance and credibility, to legally justify a particular conclusion.
This is left tailed test .
The null and alternative hypothesis is ,
H0 : mu= 34
Ha :mu < 34
Test statistic(t) = (x)
n= root (29.5 - 34) / 1.70
root 35
Test statistic = -15.66
P-value = 0
Alpha = 0.05
P-value <Alpha
Reject the null hypothesis .
There is sufficient evidence to support the claim.
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find the coordinaates of the turning point on the curve with equation y=9+18x-3x>2
Answers
The coordinates of the turning point on the curve with the quadratic equation y = 9 + 18x - 3x² is (3,36).
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
It is given that:
The quadratic equation is:
y = 9 + 18x - 3x²
To find the turning point:
Graph the above quadratic equation;
From the graph:
The maximum point from where the graph starts to decrease is (3,36)
Thus, the coordinates of the turning point on the curve with the Quadratic equation y = 9 + 18x - 3x² is (3,36).
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What is the area of the triangle?
7 cm
10 cm
Area = [?] cm²
Enter
Answers
Answer:
35cm^2
Step-by-step explanation:
Things To Keep In Mind:
Height: 7 cm
Length: 10 cm
(L*H)/2=area of triangle
7*10=70
70/2=35
If there are any problems with this answer please feel free to tell me, thanks :)
M < a = ?
M < d = ?
please help!!
Answers
Answer:
m∠A = 60
m∠D = 60
Step-by-step explanation:
∆ABC and ∆DEF are congruent triangles
So,
m∠A = m∠D
x + 30 = 2x
2x - x = 30
x = 30
So,
m∠A = x + 30 = 30 + 30 = 60
m∠D = 2x = 2(30) = 60
Thus, m∠A and m∠D are 60°
someone please help i’ve been struggling for 20 minutes
Answers
The number of leaves on a tree which is 2 yards tall and receives 9 hours of sunlight is 324 leaves.
How many leaves are on the tree?The number of leaves on a tree = zHeight of the tree in yards = yHours of direct sunlight the tree receives = xz = k × y × x
Where,
k = constant of proportionalityIf y = 10 yards, x = 3 hours, z = 540 leaves
z = k × y × x
540 = k × 10 × 3
540 = 30k
k = 540/30
k = 18
Then, find z when y = 2 yards and x = 9 hours
z = k × y × x
= 18 × 2 × 9
z = 324 leaves.
In conclusion, given the constant of proportionality, the number of leaves on the tree is 324 leaves.
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Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent
Answers
Rate percent is 10%
What is rate percent ?A coefficient that is a quotient of two values, where the denominator is written in percentage points and has the same units as the numerator when it is multiplied by a unit of time.
According to the given information
Sum of money ( principal ) P = 5000 rupees
Interest obtained in money = 1500 rupees
Time duration T = 3 years
According to the given information
I = P × T × [tex]\frac{R}{100}[/tex]
1500 = 500 × 3 × R/100
Rate percent is 10%
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Margo borrows $1000, agreeing to pay it back with 7% annual interest after 9 months. How much interest will she pay?
Answers
The interest over 18 months will be $105.00 if Margo borrows $1000, agreeing to pay it back with 7% annual interest.
What is simple interest?It is defined as the interest on the based on the principal amount, it does not include the compounded amount. The interest calculate on the initial amount or borrowed amount.
It is given that:
Margo borrows $1000, agreeing to pay it back with 7% annual interest after 9 months
I = Prt
= 1.5 x 7%
= 1.5 x .07
= 0.105
= $1000 x .105
= $105.00
Thus, the interest over 18 months will be $105.00 if Margo borrows $1000, agreeing to pay it back with 7% annual interest.
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A house was valued at $95,000 in the year 1991. The value appreciated to $165,000 by the year
2008.
Use the compound interest formula S = P(1 + r) to answer the following questions.
A) What was the annual growth rate between 1991 and 2008?
T =
Round the growth rate to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
T =
%.
C) Assume that the house value continues to grow by the same percentage. What will the value
equal in the year 2011?
value = $
Round to the nearest thousand dollars.
Answers
Hello,
I hope you and your family are doing well!
A) To find the annual growth rate between 1991 and 2008, we can use the compound interest formula:
S = P(1 + r)
Where S is the final value of the house, P is the initial value of the house, and r is the annual growth rate.
Plugging in the values from the problem, we get:
165,000 = 95,000(1 + r)
Dividing both sides of the equation by 95,000 gives:
1.737 = 1 + r
Subtracting 1 from both sides of the equation gives:
0.737 = r
The annual growth rate between 1991 and 2008 is 0.737.
B) To express the growth rate in percentage form, we can multiply it by 100%:
0.737 * 100% = 73.7%
So the annual growth rate between 1991 and 2008 was 73.7%.
C) To find the value of the house in the year 2011, we can use the compound interest formula again, with the initial value of the house set to the final value in 2008:
S = P(1 + r)
Plugging in the values from the problem, we get:
S = 165,000(1 + 0.737)
Solving for S gives:
S = 165,000 * 1.737 = 285,195
So the value of the house in the year 2011 will be approximately $285,195. Rounded to the nearest thousand dollars, this is $285,000
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Happy Holidays!
The formula A=23.1 е⁰⁰¹⁵²⁺ models the pollution of US state, a, in millions ,t years after 2000.
A. What was the population of the state in 2000 ?
b. When will the population of the state reach 28.3 million?
a. In 2000 , the population of the state was million.
Answers
The population of the state in 2000 was 23.1 million and the population will be 28.3 million after 13.4 years.
What is an exponential function?The definition of an exponential function is given by the equation
y = aeᵇˣ, where bx is an exponent.
The given equation is [tex]A = 23.1e^{0.0152t}[/tex].
To find the population of the state in 2000, substitute t = 0 in the given equation:
[tex]A =23.1e^{0.0152(0)}\\\\A = 23.1[/tex]
Now, Substitute A = 28.3 into the given equation and solve for t:
[tex]28.3=23.1e^{0.0152t}\\\\e^{0.0152t}=1.2251\\\\0.0152t=\ln(1.2251)\\\\0.0152t=0.2030\\\\t=13.4[/tex]
Hence, the population of the state in 2000 was 23.1 million and the population will be 28.3 million after 13.4 years.
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The owner of a factory wants to determine a confidence interval for the average wages at his factory. The population average wages is unknown. However, the owner was able to take a random sample of 64 workers. He found that the average salary for this sample of workers is $50,000. The population standard deviation is $3000. He calculated a 99% confidence interval for the population average wages at the factory. Which of the following choices is correct? Assume the distribution of wages is normally distributed.
Answers
4,034.06 ,5,965.94 are confidence interval for the population average wages at the factory.
What is confidence interval estimation?
Your estimate's mean plus and minus the range of that estimate's fluctuation is called a confidence interval.
If you repeat your test, you can expect your estimate to fall between these numbers with a reasonable degree of certainty. Another term for probability in statistics is confidence.
The formula for confidence interval estimation is:
μ = M ± Z(sM)
where:
M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = √(s2/n)
M = 50000
Z = 2.58
sM = √(30002/64) = 375
μ = M ± Z(sM)
μ = 50000 ± 2.58*375
μ = 50000 ± 965.94
μ = 4,034.06 ,5,965.94
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WIL GIVE BRAINLIEST!!!!
What is the value of x in simplest radical form?
Look at the provided picture!!!
Answers
Answer: b
Step-by-step explanation:
3^2 + x^2 = 9^2
9 + x^2 = 81
x^2 = 72
x = sqrt(72)
If the ratio of hotels to office buildings with 4 to 9 find the ratio of office buildings to hotels
Answers
The ratio shows how many times one value is contained in another value.
The ratio of office buildings to hotels will be 9 : 4.
What is a ratio?The ratio shows how many times one value is contained in another value.
Example:
There are 3 apples and 2 oranges in a basket.
The ratio of apples to oranges is 3:2 or 3/2.
We have,
The ratio of hotels to office buildings = 4 : 9
Now,
The ratio of office buildings to hotels will be 9 : 4.
Thus,
The ratio of office buildings to hotels will be 9 : 4.
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Which expression is equivalent to 5–√3⋅4–√5
5
3
⋅
4
5
?
Answers
The expression that is equivalent to ∛ 5 * [tex]\sqrt[5]{4}[/tex] is [tex]5^{1/3}*4^{2/5}[/tex]
What are radicals in math?A radical in mathematics is the opposite of an exponent, which is symbolized by the sign "n√" also known as root.
The number before the symbol or radical is regarded as an index number or degree, and it can either be a square root or a cube root and so on.
How to find the equivalent expressionThis equation represents exponents in fraction form and the basics for the calculation is from
x^(b/n)
[tex]\sqrt[n]{x}^{b}[/tex]
Rewriting the expression is done as below
∛ 5
= [tex]5^{1/3}[/tex]
and
[tex]\sqrt[5]{4}[/tex]
[tex]= 4^{2/5}[/tex]
combining both gives
∛ 5 * [tex]\sqrt[5]{4}[/tex]
[tex]5^{1/3}*4^{2/5}[/tex]
[tex]5^{1/3}*4^{2/5}[/tex] is the equivalent expression
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h
41. What is the solution of the system? (1 point)
y=9x-2
y=7x+3
5 41
2 29
5'5
1 13
22
29 need help quickly question is in unit eight lesson two semester final exam on Pecos
Answers
The solutions of the given system of Equations are (5/2, 41/2).
What are the Solutions of Equations:The set of values for each variable in a system of linear equations is referred to as the solution set.
The intersection or meeting points of the lines or planes used to illustrate the linear equations are also known as the solutions.
The elimination method is one way of resolving a system of linear equations. To obtain the equation in one variable using this technique, simply add or subtract the equations.
Here we have
y = 9x-2 --- (1)
y = 7x+3 --- (2)
From (1) and (2)
=> 9x - 2 = 7x + 3
=> 9x - 7x = 3 + 2
=> 2x = 5
=> x = 5/2
Substitute x = 5/2 in (1)
=> y = 9(5/2) - 2
=> y = (45/2) - 2
=> y = (45 - 4)/2
=> y = 41/2
Therefore,
The solutions of given system of Equations are (5/2, 41/2).
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can someone help me with this circle question asap
Answers
The point which satisfies equation is (-2,4)
What is circle?
A circle could be a form consisting of all purposes during a plane that are at a given distance from a given point, the centre.
Main body:
The center of circle formula is also known as the general equation of a circle. In a circle, if the coordinates of the center are (h,k), r is the radius, and (x,y) is any point on the circle, then the center of circle formula is given below:
Formula of circle =
(x - h)² + (y - k)² = r²
According to question:
center of circle = (2,1)
diameter of circle = 10 units
radius = 5 units
equation of circle ⇒
(x - 2)² + (y - 1)² = 25
for a point to lie on circle , it need to satisfy the equation of circle:
A) (1,-3)
⇒(1 - 2)² + (3 - 1)²
⇒(-1)² +2²
⇒5
so it does not lie on circle.
B) (-2,4)
⇒(-2 - 2)² + (4 - 1)²
⇒-4²+3²
⇒ 25
so, it satisfies the equation.
hence, the point which satisfies equation is (-2,4)
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given the graph of f(x)on the right,determine the type of the function help for number 2
Answers
The type of the function for the given graph f(x) on the right is odd function.
What is meant by a function?An exact one of each element of Y is assigned to each element of X via a mathematical function from a set X to a set Y. The sets X and Y are denoted by the terms "domain" and "codomain," respectively.
The link between varying amounts and other variables was the foundational idea behind functions. The effect of time on a planet's position serves as an example of this. The infinitesimal calculus was used to develop the concept in the past, beginning at the end of the 17th century and continuing through the 19th century.
An odd function's graph possesses rotational symmetry with respect to the origin, which means that it doesn't change after being rotated by 180 degrees around the origin.
Therefore, The type of the function for the given graph f(x) on the right is odd function.
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which equation in point-slope from is equivalent to y=-3/4x + 9?
A. y-9=-3/4(x-0)
B. y-1=-3/4(x-9)
C. y-3/4=9(x-0)
D. y-1=9(x+3/4)
Answers
Answer:
Step-by-step explanation:
I know that in point-slope form, the equation is y - y1 = m(x - x1)
Fill in y1 and x1 with the points given in the multiple choices.
If you look at Letter A, it shows the point (0,9). If you fill that in the formula. You solve the equation:
y - 9 = -3/4(x - 0)
y - 9 = -3/4x
+9. =. +9
y = -3/4x + 9
Therefore your answer is letter A.
In a video game, Clare scored 50% more points than Tyler. If c is the number of points that Clare scored and t is the number of points Tyler scored, which equations, are correct?
Answers
Answer:
c= 1.5t, c=t+0.5t and c=(1+0.5)t
Step-by-step explanation:
Given that, Clare scored 50% more points than Tyler, c is the number of points that Clare scored and t is the number of points that Tyler scored,According to question,c = 150% of tc = 1.5tHence, the correct options are c = 1.5t, c = t+0.5t and c = (1+0.5)t
Find m in equation, W=1/2*m*v squared?
Answers
Answer: To find the value of m in the equation W = 1/2 * m * v^2, you need to know the values of W and v. The variable m represents the mass of the object, and W represents the kinetic energy of the object. The equation states that the kinetic energy of an object is equal to 1/2 of its mass multiplied by its velocity squared.
If you are given the values of W and v, you can solve for m by rearranging the equation as follows:
m = 2 * W / v^2
Plugging in the values of W and v will give you the value of m.
For example, if W = 100 joules and v = 10 meters per second, the equation would be:
m = 2 * 100 joules / 10 m/s^2 = 20 kilograms
This is the mass of the object.
[tex]m=\frac{2W}{v^{2} }[/tex].
Step-by-step explanation:1. Write the expression.[tex]W=\frac{1}{2} mv^{2}[/tex]
2. Divide both sides of the equation by [tex]\frac{1}{2}[/tex] and [tex]v^{2}[/tex].[tex]\frac{W}{\frac{1}{2} v^{2} }=m\\ \\[/tex]
3. Rewrite and simplify.[tex]m=\frac{W}{\frac{1}{2} v^{2} }\\ \\m=\frac{2W}{v^{2} }[/tex].
The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle. Use words, numbers, or models to justify your answer.
Answers
The vertices of a rectangle are W(1, 2) X(4, 2) Y(4, 23) and Z(1, 23) Find the perimeter of the rectangle is 16.
Step-by-step explanation:We could use the distance formula to find the distance between the points in this problem, but when we look we see that the sides of the rectangle are parallel to the x and y-axis for each pair of sides. The first two points have a distance of 3 because 4-1=3. Since it is a rectangle, the opposite side will have the same length. For the sides perpendicular, we look at the points with the same x coordinate. Using (4,2) and (4,-3), we can calculate the length of the side by finding the distance by adding the absolute values of the y coordinate. 2+3=5. This means that the triangle has two sides with a length of 5 and two sides with a length of 3. Adding these together, 5+5+3+3 = 16.
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A rectangle is 5 inches long and 2x inches wide. The value of the perimeter in inches) is equal to the value of the area (in square inches). Find x.
Answers
Answer:
the width of the rectangle is -5/3 inches.
Step-by-step explanation:
To find the perimeter of the rectangle, we add together the lengths of all four sides. Since the rectangle is 5 inches long and 2x inches wide, the perimeter is given by:
Perimeter = 5 + 2x + 5 + 2x = 10 + 4x
To find the area of the rectangle, we multiply the length by the width. The area is given by:
Area = 5 * 2x = 10x
Setting the perimeter equal to the area, we have:
10 + 4x = 10x
Subtracting 10 from both sides, we have:
4x = 10x - 10
Combining like terms, we have:
-6x = -10
Dividing both sides by -6, we have:
x = 10 / -6
Simplifying, we have:
x = -5/3
Please help me on math very easy graphing! thank you!! due soon
Answers
Answer:
4x=4 or 4tims x =y
Step-by-step explanation:
1x4=4
3x4-=12
Mickey Here Hi justice as more point because you deserve it
Answers
Answer:
second
Step-by-step explanation:
2x+5>7
2x>2
x>1
therefore, second
In a certain rental shop, they have 63 vehicles. They allow you to rent bicycles and tricycles free for the first hour.If they had 149 tires in all, how many bicycles and tricycles do they have?
Answers
Answer:
There Are 40 Bicycles And 23 Tricycles
Step-by-step explanation:
Let, x be bicycles and y be tricycles
Condition 1;
: x + y= 63
: x =63-y
Condition 2;
Number Of Tires=149
:2x + 3y =149 [2x=Two Tires Of Bicycle And
3y=Three Tires Of Tricycle]
:x = 149-3y/2
Combination 1 & 2;
63-y = 149-3y/2
126-2y = 149-3y
y=23
x = 63-23
=40
What is the remainder that the number 10^2023 leaves after division by 13?
Answers
Applying the property of exponents, the remainder that the number 10^2023 leaves after division by 13 is 9.
What is remainder?The remainder is the amount left over after a division operation.
What is exponent?An exponent is a number that indicates how many times a base number is used as a factor in a multiplication expression.
From the property of exponent:
We can rewrite 10^2023 as (10^13)^155 * 10^8:
10^2023 = (10^13)^155 * 10^8
We can then use the property of exponents to simplify:
10^2023 = (10^(13*155)) * 10^8
Since 10^13 is congruent to 1 mod 13, 10^(13*155) is congruent to 1 mod 13 as well. Therefore, 10^2023 is congruent to 10^8 mod 13.
We can find the remainder by calculating 10^8 mod 13:
10^8 = 100000000
After dividing 100000000 by 13, we get a remainder of 9.
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A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:
Machining,
hours
Polishing, hours Assembling,
hours
Product I 3 1 2
Product II 2 1 1
Product III 2 2 2
Product IV 4 3 1
The firm has available to it on weekly basis, 480 hours of machining time, 400 hours
of polishing time and 400 hours of assembling time. The unit profits on the productare Birr 360, Birr 240, Birr 360 and Birr 480, respectively. The firm has a contract
with a distributor to provide 50 units of product I, and 100 units of any combination
of products II and III each week. Through other customers the firm can sell each
week as many units of products I, II and III as it can produce, but only a maximum
of 25 units of product IV. How many units of each product should the firm
manufacture each week to meet all contractual obligations and maximize its total
profit? Make a mathematical model for the given problem. Assume that any
unfinished pieces can be finished the following week.
Answers
Profit is the money you have left after paying for business expenses.
What is profit?Profit is the term used to describe the monetary gain experienced when the revenue from a business activity outpaces the costs, costs, and taxes incurred to maintain the activity in question.Any earnings go back to the company's owners, who can choose to keep the money for themselves, give it to shareholders as dividends, or put it to use again in the company.A business's profit is the money left over after all costs have been deducted. Any business, whether it be a lemonade stand or a publicly traded multinational corporation, has as its main objective making money. As a result, a business's success is measured by its profitability in all of its forms.Depending on the analyst, profitability before taxes and other expenses may be more important to them than top-line profitability. Others are only interested in profitability after expenses have been covered.
The production of the products are given below with the profit as well:
a. Production of Product 1 = 50 units per week
b. Production of Product 2 = 0 units per week
c. Production of Product 3 = 145 units per week
d. Production of Product 4 = 10 units per week
e. Total Profit = $1250 per week
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Answer:
Step-by-step explanation:
A local manufacturing firm produces four different metal products, each of
which must be machined, polished and assembled. The specific time
requirements (in hours) for each product are as follows:
Machining,
hours
Polishing, hours Assembling,
hours
Product I 3 1 2
Product II 2 1 1
Product III 2 2 2
Product IV 4 3 1
the manager of a theater wants to know whether the majority of its patrons are adults or children. One day, 5100 tickets were sold and the receipts totaled $29,484. The adult admission is $7.50, and the children's admission is $4.50. How many adult patrons were there
Answers
We can estimate the number of adult partons at 2187 by solving equations.
What do we mean by equations?The equals sign is a symbol used in mathematical formulas to denote the equality of two expressions.
A function is an equation that has only one answer for y for every possible value of x.
When utilizing a function, each input of a specific type receives exactly one output.
A function is commonly referred to as f(x) or g instead of y. (x).
Because f(2) instructs us to do so, we should figure out the value of our function when x is equal to 2.
So, the total number of adults present was thus:
Let a be an adult, and b and c be kids.
Ticket totals:
a + c = 5200
c = (5200-a)
Total amount:
7.50a + 4.50c = 29961
In the first equation, swap out c with (5200-a).
7.5a + 4.5(5200-a) = 29961
7.5a + 23400 - 4.5a = 29961
7.5a - 4.5a = 29961 - 23400
3a = 6561
a = 6561/3
a = 2187
Therefore, we can estimate the number of adult partons at 2187 by solving equations.
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