Answers
Missing side length of the given measures of the triangle is equal to x = 1/2 units (approximately).
As given,
Given measures of the triangle ABC are
Angle A=(18 +18)°
=36°
Consider side opposite to ∠A=a ,∠B=b ,∠C=c
Given side length
AC=b
=20
AB=c
=12
BC=c
=x+12
Using cosine law
cos A= (b²+c²-a²)/2bc
⇒cos36°= [20²+12²-(x+12)²]/2(20)(12)
⇒(1+√5)/4=(544-x²-24x-144)/480
⇒x²+24x-280+120√5=0
⇒x²+24x-11.7=0
Now, x = [-24±√24²-4(1)(-11.7)]/2(1)
= (-24±24.955)/2
≈ (-24 ±25)/2
Hence, x = (-24+25) /2
= 1/2
or x = -24.5 side length cannot be negative.
Therefore, Missing side length of the given measures of the triangle is equal to x = 1/2 units (approximately).
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Related Questions
1. Maria's new car costs $280 per month for
car payments and insurance. She estimates
that gas and maintenance cost 15 cents per
mile.
a) Express her total monthly cost as a
function of the miles driven during the
month.
b) What is the slope of the graph of the cost
function?
Answers
From the situation described, it is found that:
a) The linear function that expresses her monthly cost is:
C(m) = 280 + 0.15m.
b) The slope of the graph of the cost function is of 0.15.
What is a linear function?A linear function, in slope-intercept format, is modeled according to the following rule:
y = mx + b
In which the coefficients are described as follows:
The coefficient m is the slope of the function, which is the rate of change of the function, that is, the change in y divided by the change in x.The coefficient b is the y-intercept of the function, which is the the value of y when the function crosses the y-axis(x = 0).In the context of the cost function in this problem:
The intercept is the fixed cost per month, for cay payments and insurance, of $280.The slope is the variable cost, which is the cost per mile of 15 cents = $0.15.Hence the parameters of the function are given as follows:
m = 0.15, b = 280.
The cost function for a mileage of m miles is, considering the above coefficients, is given by:
C(m) = 0.15m + 280.
With the slope of 0.15 already explained.
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Kiley and her parents traveled to visit her grandmother. They drove 24.3 miles from their house to the airport in 12 hour. At the airport, they exited the car and walked for 34 hour to the waiting area by the gate to board their plane. Their walk covered 1.2 miles. From the waiting area, they walked another 0.1 mile to board the plane. The plane left the gate 45 minutes after they arrived at the waiting area. The plane flew 346 miles in 214 hours. After the plane landed, Kiley and her parents walked for 30 minutes, covering 1.1 miles, before they found a cab. It was a 15-minute cab ride to get to Kiley’s grandmother’s house, which was 12.3 miles away.Answer the following questions about Kiley’s trip. All questions are written in terms of an average rate. Assume that an average rate includes the time that Kiley is at rest (that is, not moving).In this task, you will write the ratio of miles to hours for each leg of Kiley’s trip. You will then, express the ratio as a decimal number. Next, you will find the unit rate in miles per hour (mph) for each leg of the trip. If your unit rate includes a repeating decimal number, you must indicate which digits repeat (for example, write 0.3¯when the 3 repeats.) A description of each leg is listed below in parts A through F.
Answers
Given:
The car ride from Kiley's house to the airport.
Distance =24.3 miles.
Time =1/2 hour.
We know that
[tex]\text{Average rate =}\frac{\text{Distance}}{\text{time}}[/tex]Substitute Distance =24.3 miles and time =1/2 hour to compute the average rate of the car ride from Kiley's house to the airport.
[tex]=\frac{24.3\text{ miles}}{\frac{1}{2}\text{hours}}[/tex][tex]\text{ Use }\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a}{b}\times\frac{d}{c}\text{.}[/tex][tex]=24.3\times\frac{2}{1}\text{ miles per hour}[/tex][tex]=24.3\times2\text{ miles per hour}[/tex][tex]=48.6\text{ miles per hour}[/tex]Hence the average rate of the car ride from Kiley's house to the airport is 48.6 miles per hour.
2)
Given that they walked 3/4 hours to the waiting area and covered the distance of 1.2 miles.
Distance =1.2 miles.
Time =3/4 hours.
we know that
[tex]\text{Average rate =}\frac{\text{Distance}}{\text{time}}[/tex]Substitute distance =1.2 miles and time =3/4 hours to compute the average rate of the walk from the car to the waiting area by the gate, at the airport.
[tex]=\frac{1.2\text{ miles}}{\frac{3}{4}\text{ hours}}[/tex][tex]=1.2\times\frac{4}{3}\text{ miles per hour.}[/tex][tex]=\frac{1.2\times4}{3}\text{ miles per hour.}[/tex]Multiplying 1.2 and 4, we get 4.8
[tex]=\frac{4.8}{3}\text{ miles per hour.}[/tex]Dividing 4.8 by 3, we get 1.6
[tex]=1.6\text{ miles per hour.}[/tex]Hence at the airport, the average rate of the walk from the car to the waiting area by the gate is 1.6 miles per hour.
Use the Distance Formula to write an equation of the parabola with vertex (0,0) and directrix y = -6
An equation of the parabola is y=
Answers
Answer:
x^2 + y^ = 36
Step-by-step explanation:
See attached worksheet.
a large national study finds that 10% of pregnant women deliver prematurely. a local obstetrician is seeing 20 pregnant women in the next week at their clinic. (round answers to 3 decimal places)
Answers
The probability that fewer than 3 women will deliver prematurely is 1/20.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. The total number of positive outcomes as well as the probability of any given event depend on each other. The probability is typically defined as the proportion of favorable outcomes to all outcomes in the sample space. Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).So, 10% of 20:
20/100 × 10 = 2 (Which is less than 3)Then, Premature delivery (Of fewer than 3 women) = 1Total events = 20P(E) = favourable/total events1/20Therefore, the probability that fewer than 3 women will deliver prematurely is 1/20.
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The correct question is given below:
A large national study finds that 10% of pregnant women deliver prematurely. a local obstetrician is seeing 20 pregnant women in the next week at their clinic. what is the probability that fewer than 3 of them will deliver prematurely?
Write a simplified equation in point-slope form.
Line 2: contains (1,2) and (4, -7)
Answers
Answer:
y = -3x + 5
Step-by-step explanation:
(1, 2) and (4, -7)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -7 - 2 -9
m = ------------- = ------------- = -------- = -3
x₂ - x₁ 4 - 1 3
y - y₁ = m(x - x₁)
y - 2 = -3(x - 1)
y - 2 = -3x + 3
+2 +2
----------------------
y = -3x + 5
I hope this helps!
-2,-14) and (h,28) slope is 6
Answers
[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-14})\qquad (\stackrel{x_2}{h}~,~\stackrel{y_2}{28}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{28}-\stackrel{y1}{(-14)}}}{\underset{run} {\underset{x_2}{h}-\underset{x_1}{(-2)}}} \implies \cfrac{28 +14}{h +2}~~ = ~~\text{\LARGE 6}\implies \cfrac{42}{h+2}=6 \\\\\\ 42=6h+12\implies 30=6h\implies \cfrac{30}{6}=h\implies \boxed{5=h}[/tex]
Milly measured a cereal box It is two inches wide six inches long and twelve inches tall what is the volume of the cereal box
Answers
The volume of the cereal box is 144 square inches its width is two inches, its length is six inches and its height is 12 inches.
What is the volume of a rectangular prism?The top, bottom, and lateral faces of a rectangular prism are all rectangles, and all the pairs of opposing faces are congruent. A rectangular prism is a three-dimensional structure with six faces.
The rectangular prism's base area is equal to lw (using the area of a rectangle formula)
The height of the rectangle prism is equal to h.
Thus, V = lw ×h = lwh is the formula for the rectangular prism's volume.
Given,
width = 2 inches
length = 6 inches
height = 12 inches
The volume of a rectangular prism is simply length× width× height.
Volume = 6× 2× 12
= 144 square inches.
Therefore, the volume of the cereal box is 144 square inches.
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Solve the equation below for x. 100 = 25e3 In4 O A. 4 B. 3 e O C. X=In4 - 3 c In100 3. In25 O D.
Answers
Dividing the given equation by 25 we get:
[tex]\begin{gathered} \frac{100}{25}=\frac{25e^{3x}}{25}, \\ 4=e^{3x}\text{.} \end{gathered}[/tex]Applying the natural logarithm to the above equation we get:
[tex]\ln (4)=\ln (e^{3x})=3x\ln (e)=3x\text{.}[/tex]Finally, solving for x we get:
[tex]x=\frac{\ln (4)}{3}\text{.}[/tex]Answer: Option A.
what is the standard deviation of 0,0,1,1,1,2,2,3,5
Answers
Based on the numbers given in the distribution, the standard deviation can be found to be 1.49
How to find the standard deviation?To find the standard deviation, you first have to find the mean of the distribution:
= (0 + 0 + 1 + 1 + 1 + 2 + 2 + 3 + 5 ) / 9
= 15 / 9
= 1.67
You can then find the variance using financial calculators to be:
= 2.2222222
The standard deviation is:
= √variance
= √2.2222222
= 1.49
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You bike 11 1/4 miles from your house to a. State park. You travel 1/6 of that distance in the woods. You bike along the bank of a stream for the last 2/5 of the woods. On how many miles of your trip do you bike along the bank of the stream?
Answers
Answer:
9/10 mile
Step-by-step explanation:
Distance from house to state park = 11 1/4 miles = 45/4 miles
Distance through woods
[tex]\dfrac{1}{6}\cdot \dfrac{45}{4}\\\\=\dfrac{9}{4} \text { miles}\\[/tex]
Since the distance along the stream is 2/5 of the distance in the woods,
the distance biked along the stream
= 9/4 x 2/5 = 18/20 = 9/10 mile
1. By what factor does organism A's population grow in the first five days? Express your answer as an exponential expression. (2 points)
2. The expression showing organism A's decrease in population over the next 3 days is
(
1
2
)
3
(
2
1
)
3
. This can be written as (2–1)3.
Write (2–1)3 with the same base but one exponent. (2 points)
3. By combining the increase and decrease, find an exponential expression for the total change in organism A's population after 8 days. Show your work. (2 points)
Answers
Using an exponential function, it is found that:
a) During the first five days, the population of organism A grew by a factor of 2^5.
b) During the next three days, the population of organism B decayed by a factor 2^(-3).
c) The expression for the total change is of 2².
What is an exponential function?An exponential function is modeled according to the following rule:
[tex]y = ab^x[/tex]
In which:
a is the initial value of the exponential function.b is the rate of change of the exponential function.For the first five days, the population doubles each day, hence the rate of change is of:
b = 2.
The growth factor will be of:
y = 2^5 = 32
During the next three days, the population cuts in half each day, hence the rate of change is of:
b = 0.5.
Then the decay factor is of:
y = (0.5)³ = (1/2)³ = 2^(-3).
Applying properties of exponents, over the entire period, the change in the population will be of:
2^5 x 2^(-3) = 2^(5 - 3) = 2².
As when we multiply two terms with the same base and different exponents, we keep the bases and add the exponents.
What is the missing information?The problem is given by the image at the end of the answer.
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y = x + 3
y = x^2 + 5x - 2
solve simultaneous equation
Answers
By solving the simultaneous equation value of x = -5, -2 and y = 1, 4.
How to solve simultaneous equation?
1. Use the elimination method to get rid of one of the variables.
2. Find the value of one variable.
3. Find the value of the remaining variables using substitution.
Given that,
y = [tex]x[/tex]+3
y = [tex]x^{2} +5x-2[/tex]
First both equation are equal
[tex]x+3 = x^{2} +5x-2\\x^{2} +4x-5 =0\\x^{2} +5x-x-5=0\\x(x+5)-1(x+5)=0\\x=1, -5[/tex]
Then, substitute the value of x in y =x+3
y = x+3
at x= -5
y= -2
at x= 1
y = 1+3
y = 4
Hence, By solving the simultaneous equation value of x = -5, -2 and y = 1, 4.
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The hypotenuse of a right triangle measures 20 cm and one of its legs measures 7 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answers
Answer:
19
Step-by-step explanation:
The square value of the measure of hypotenuse is equal to the square measure of sum of two legs.
Let x represent the missing leg:
[tex] {20}^{2} = {7}^{2} + {x}^{2} [/tex]
400 = 49 + x^2 subtract 49 from both sides
351 = x^2 find the root for both sides
The root of 351 is between 18 and 19 but it is closer to 19 since 19×19 = 361 and since we are asked to round to the nearest tenth the answer is 19.
carson flips over the cards of a standard 52-card deck one at a time. what is the probability that he flips over the ace of spades before any face card (jack, queen or king)?
Answers
The probability that the ace of spades will be revealed before any face card (the jack, queen, or king) is 0.0769.
What in mathematics is probability?Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.
The likelihood is based on the range of potential outcomes. the total number of possible outcomes. As an illustration, since there is only one way to get a head and a total of two possible results, the likelihood of flipping a coin and getting heads is one in two. a tail or a head.
According to given data;
Let's look at the first few probabilities; we're going to do this in reverse order, in order to find a pattern:
P(O,O,O,AS)=39/52)*(38/51)*(37/50)*(1/49)
=(39*38*37/3!)/(52*51*50/3!)*1/49
P(O,O,AS)=(39/3)(52/3)×1/49
but we know that;
(n/2)=n(n-1)/2!
P,(O,O,AS) =(39/2)/(52/2) *1/50
P(AS)=(39/0)/(52/0) *(1/52)
We now have
P(AS)+P(O,AS)+P(O,O,AS)+P(O,O,O,AS)
FROM THIS CALCULATE ;
P=0.0769
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2 odd numbers that are a factor of 30 and multiples of 5
Answers
Answer:
Step-by-step explanation:
The required two odd numbers are 3 and 5.
We have to determine, It is a factor of 30 and a multiple of 3 what are 2 numbers.
To obtain the factor of 30 and 2 numbers is calculated in the following steps.
The Factors of 30 are,
30 = 2 , 3 , 5 ,
And multiply the terms by 2,
After multiply by 2 all the term become even.
Then,
The 2 odd numbers are: 3, 5
Hence, The required two odd numbers are 3 and 5.
what is the equivalent fraction?
Answers
The equivalent fraction of 1 2/3 + 1 1/2 is 1 4/6 + 1 3/6
What are expressions?Expressions are mathematical statements that are represented by variables, coefficients and operators.
How to evaluate the fraction expression?The fraction expression is given as
1 2/3 + 1 1/2
Express the mixed numbers as improper fractions
So, we have
1 2/3 + 1 1/2 = 5/3 + 3/2
Rewrite as equivalent fractions
1 2/3 + 1 1/2 = 10/6 + 9/6
Express the improper fractions as mixed numbers
So, we have
1 2/3 + 1 1/2 = 1 4/6 + 1 3/6
Hence, the value of the expression is 1 4/6 + 1 3/6
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Domain and Range, please help!!
Answers
Answer:
Step-by-step explanation:
Increasing
Domain: (-∞,∞)
Domain: -∞<x<∞
Range: (-∞,∞)
Range: -∞<y<∞
Write an equation of the line in point-slope form that passes through the given points.
(4,-5) and (-4,-8)
Answers
Answer: y+5=3/8*(x-4)
Step-by-step explanation: Find the slope using m = y2-y1/x2-x2 which is the change of y over change of x, so the slope is m=3/8. Use the slope 3/8, and a given point (4, -5) to substitute for x1 and y1 in point slope form y -y1 = m(x-x1). So y-(-5)=3/8*(x-(4)). Now we simplify the equation so it's y+5=3/8*(x-4).
HELP IM CONFUSED. NEED HELP ASAP
Answers
Answer:
Yeah good job! u got it right :)
Step-by-step explanation:
How to find perimeter?
Frist you will add up all the sides
then thats your answer :)
In this case the same logic applies
Hope this helps :3
X
3
2
1
0
-1
-2
-2
Y
12
10
8
6
4
2
0
Find the domain and range
Answers
Answer:
domain: all x-values
Step-by-step explanation:
4 2/5 divide 1 1/5 need answer
Answers
Answer:
5 3/5
Step-by-step explanation:
assuming you are dividing fractions, here are your steps
Whoever can answer this gets branliest!!
A baseball player batted 544 times in a season, with a batting average of 0.294. Using the formula below, find the number of hits he made.
The batting average formula is a = h/n where a is the batting average ,h is the number of hits and n is the number of times at bat
A. 148 hits
B. 160 hits
C. 159 hits
D. 165 hits
Answers
Answer:
B. 160 hits
Step-by-step explanation:
544 × .294 = 159.936, which rounds to 160.
if y = 10x^2, find the value of y when x = 3
evaluate the given expression for the given value of y
x-2
when x=4 =
when x=-7 =
Answers
Where x = 3, and the value of y = 90;
For the expression y = x -2, when x = 4, y = 2, when x = -2, y = -9
What is the computation for the above?Given:
y = 10x²................................1
Where x = 3, We make the required substitution
y = 10 x (3)²
y = 10 x 9
Hence,
y = 90
For the given expression:
Y = x -2.....................................2
Where x = 4, We make the required substitution
= 4 -2
hence,
y = 2
Where x = -7, We make the required substitution
y = 7
y = -7-2
Hence
y = -9
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What are the domain and range of this relation? pt2
Answers
Answer:
Domain: { -5, -1, 1, 3, 4}
Range: { -2, 1, 5}
Step-by-step explanation:
Domain = X-Values
Range = Y-Values
Every possible X-Value is the domain, and likewise with the Range.
Meaning if it was a line that went on forever through Y-1 the the Domain would be X = {-[infinity], +[infinity]} and the range would be Y = {1}
Hope this helps.
Consider a goodness-of-fit test with a computed value of chi-square27. 385 and a critical value13. 388, the appropriate decision would be to __________.
Answers
Since the chi-square 27.385 is greater than 13.388 at the provided critical value level value, the null hypothesis is accepted.
What is conclusion of hypothesis testing?The hypothesis test makes an announcement the outcome of an assumption in five to six fundamental phases. The technique to be used is based on the idea of correlating the standardized sample equivalent of a parameter to the critical boundary that allows the null hypothesis to be accepted.For the given question;
27. 385 is the chi-square value.13.388 is the critical value.The hypotheses for the goodness of fit test are as follows:
Null: a expected value does not differ significantly from the observed values.Alternative: the expected value differs significantly from the observed values.The chi-square test has one tail.
The criterion is as follows:
The null hypothesis is dismissed if the test statistic exceeds the critical value.If the test statistic is less than the critical value, this same null hypothesis is rejected.Thus, the null hypothesis is accepted at the provided level of critical value because the chi-square 27.385 is more than 13.388.
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9. Solve
x(c- b) = g solve for x
Answers
For the given equation, on rearranging, the value of x becomes = x = g / (c-b)
What does the math term "rearranging" mean?
Rearranging parts is the act of rearranging counters, numbers, etc. to alter the way a number is shown visually; for instance, the number "4" could be shown in either of the two ways shown below.
A formula's components must be rearranged so that a different variable is the subject in order to change the formula's subject. Understanding inverse operations and how to solve equations is really helpful.
Given,
x(c- b) = g
On rearranging the equation,
x = g / (c-b)
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A number x divided by 36
Answers
Answer:
x/36 is what you're looking for my guy
A scale drawing of an elephant is shown. The actual
elephant that the model is based on is 216 inches long.
What is the scale factor for the model?
A. 1:30
B. 30:1
C. 208.8
D. 1555.2
Answers
The scale factor for the model of the elephant is 1 : 30 (option A).
What is the scale factor?A scale drawing is either a smaller or a larger version of an original image. For example, a map is a smaller version of a city, country or area.
A scale factor provides information on the relationship that exists between the scale drawing and the actual image. The scale factor shows the rate of reduction or enlargement of the original image.
Scale factor = actual length of the elephant / length of the elephant in the model
216 / 7.2 = 30
The scale factor is 1 : 30
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What is 20% of a 400 liter tank?
Answers
20% of a 400 liter tank is 80 liters.
I WILL GIVE 20 POINTS IF THE ANSWER IS CORRECT AND A GOOD EXPLANATION
Answers
The surface area of a cylinder is equal to 208π square units.How to calculate the surface area of right cylinder?The surface area is the sum of the areas of all faces of the solid. In the case of a right cylinder, the surface area is the sum of the two areas of the circular base and the lateral area (A), in square units, whose formula is described below:A = 2π · r² + 2π · r · h (1)Where:r - Base radiush - HeightIf we know that r = 8 and h = 5, then the surface area of the right cylinder is:A = 2π · 8² + 2π · 8 · 5A = 208πThe surface area of a cylinder is equal to 208π square units.