Answer:
[tex]The[/tex] [tex]length[/tex] [tex]of[/tex] [tex]BC[/tex] [tex]is[/tex] [tex]\sqrt{55}[/tex] [tex](units)[/tex].
Step-by-step explanation:
Given ABC is a right triangle.
AC is the hypotenuse and BD is the altitude.
AB and BC are legs of the triangle ABC.
AC = 11 and DC = 5
Leg rule of geometric mean theorem:
[tex]\frac{hypotenuse}{leg}=\frac{leg}{part}[/tex]
[tex]\frac{AC}{BC}=\frac{BC}{DC}[/tex]
[tex]\frac{11}{x}=\frac{x}{5}[/tex]
Do cross multiplication.
[tex]11 * 5= x*x[/tex]
[tex]55=x^{2}[/tex]
Taking square root on both sides.
[tex]\sqrt{55} =\sqrt{x^{2} }[/tex]
[tex]\sqrt{55}=x[/tex], [tex]since[/tex] [tex]\sqrt{55}[/tex] [tex]cannot[/tex] [tex]be[/tex] [tex]reduced.[/tex]
The length of BC is [tex]\sqrt{55}[/tex].
Can anyone solve these equations?
The equation can be factorized as (x + 4/3) (x + 3/2).
The expression 2x² + bx - 9 will be prime for the the values of b = 18, 12, and -1.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
18. The zeroes of the expression ax² + b x + c can be found by,
x = [-b ± √(b² - 4ac)] / 2a
The given expression is 6x² + 17x + 12.
We have to factorize the expression.
x = [-17 ± √(17² - 4×6×12)] / [2 × 6]
= [-17 ± √(289 - 288)] / 12
= (-17 ± 1) / 12
x = -16/12 = -4/3 and x = -18/12 = -3/2
The expression can be factorized as (x + 4/3) (x + 3/2).
19. The expression is non factorable if the value of the discriminant is neither zero nor a positive perfect square.
For ax² + b x + c, Discriminant = b² - 4ac
The expression given is 2x² + bx - 9.
Discriminant = b² - (4 × 2 × -9) = b² + 72
When b = 18, b² + 72 = 396, not a perfect square root
When b = 3, b² + 72 = 81, a perfect square root
When b = 12, b² + 72 = 216, not a perfect square root
When b = -3, b² + 72 = 81, a perfect square root
When b = -7, b² + 72 = 121, a perfect square root
When b = -1, b² + 72 = 73, not a perfect square root
When b = 17, b² + 72 = 361, a perfect square root
So when b = 3, -3, -7 and 17, the expression is factorable.
When b = 18, 12, and -1, the expression is prime.
Hence the expression 2x² + bx - 9 is prime when the values of b are 18, 12, and -1.
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what does the entry of 1.00 indicate on the diagonal of the matrix?
Entry of 1.00 in the diagonal of the matrix indicate that it is a correlation matrix .
In the correlation matrix entries in the diagonal is equal to 1.00.In the table each random variable [tex]A_{i}[/tex] is correlated to the random variable [tex]A_{j}[/tex].They are related in the manner of value of A₁ : A₂ is same as the A₂ : A₁.For example :
A₁ A₂ A₃ A₄ A₅
A₁ 1
A₂ 2 1
A₃ 3 4 1
A₄ 5 6 7 1
A₅ 8 9 10 11 1
Diagonal values is always equal to 1 as the relation between A₁ to A₁ is always equal to one.
Therefore, the entry of one on the diagonal of the given matrix represents it is a correlation matrix.
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Please help me on this question.
For what value of x is line m parallel to line n?
Answer:
x=42
Step-by-step explanation:
Step 1) 105=3x-21
Step 2) 126= 3x
Step 3) 42=x
Which of the following can you use to justify the statement VWX~AZYX?
1. AA
2.SAS
3.SSS
4. Not similar
ΔVWX ≅ ΔZYX, to justify the statement SAS property is used.
Correct option is: 3
What is the SAS property in triangle?Congruent triangles exist if its two sides and also included angles are identical to that of other triangle's two sides and also included angle.
The triangles are considered to be congruent when all three pairs of matching sides are. Side-side-side is the name of this congruence shortcut (SSS). Side-angle-side (SAS) is an alternative simplification if two sets of side as well as the angles between them is known to just be congruent.
When determining if a collection of triangles is congruent, the Side-Angle-Side rule is utilized. According to the SAS rule, two sides and the included angle of one triangle must equal two sides and the included angle of another triangle in order for the two triangles to be considered congruent. An angle produced by two specified sides is called an included angle.
Correct option: 3
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The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $9. There was a total of $543 in revenue from the sale of 67 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
The system of equations that can find the number of student tickets sold is:
7x + 9y = 543
x + y = 67
Defining the variables that helped write the system are:
Let x be the number of student tickets sold
Let y be the number of adult tickets sold.
How to come up with the system of equations ?First, define the variables. In this case, we can say that x will be the number of student tickets while also making y the number of adult tickets.
The first equation would be:
Revenue of student tickets sold + Revenue of adult tickets = Total revenue
7x + 9 y = 543
The second equation is:
Number of student tickets + Number of adult tickets = Number of total tickets
x + y = 67
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Answer: The answer is 7x + 9y = 543x + y = 67.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
5. Number of cars of a particular model produced by a factory between 2006 and 2010 2006 35,000 2007 40,000 2008 45,000 2009 30,000 2010 35,000 2012
Answer:
The number of cars of a particular model produced by the factory between 2006 and 2010 are:
2006: 35,000
2007: 40,000
2008: 45,000
2009: 30,000
2010: 35,000
No data is available for 2012.
79% of 8400 + 66.66% of 4800 = 120% of 7200+ x% of 4784. what is the value of x?
(a) 33.33 (b) 25 (c) 11.11 (d) 20.13
The value of x = 25 % (option b) in 79% of 8400 + 66.66% of 4800 = 120% of 7200+ x% of 4784. by converting the percentages.
79% of 8400 = ( 79/100) x 8400
= 6636
66.66% of 4800 = (66.66/100)x4800
= 3199.68
120% of 7200 = (120/100)x7200
= 8640
x% of 4784 = (x/100) x 4784
we are given that, 79% of 8400 + 66.66% of 4800 = 120% of 7200+ x% of 4784. what is the value of x :
therefore, 6636 + 3199.68 = 8646 + (x/100) x 4784
(x/100) x 4784 = 6636 + 3199.68 - 8646
= 1189.68
(x/100) = 1189.68/4784
= 0.248
x = 0.248 x 100
therefore , the value of x is equals to 24.8 % or 0.248 which is approximated to 25 % that is option (b)
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if the variable num contains a positive integer, what are the only two possible results of the expression num % 2? 0 and 2 0 and 1 -1 and 1 1 and 2
The only two possible results of the expression num % 2 if the variable num contains a positive integer is 0 and 1.
Variables include effects like height, age, income, fiefdom of birth, academy grades, and kind of dwelling. There are two introductory types of variables order and numeric. also, each order is divided into two subcategories separate or nonstop for numeric variables, and nominal or ordinal for categorical variables. In this section, these orders are compactly described.
A quantifiable property with numerical values is known as a numeric variable( also known as a quantitative variable)( except figures which are canons standing up for orders). Both nonstop and separate numerical variables are possible.
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Leander, his brother, and a friend are sharing 36
dollars equally. How much money will each one get? What fractional part of the
$36 did each person get? * Write an equivalent fraction that represent the amount
each person received.
The amount of money each person gets is $12.
For a total amount of $36, each person gets a fraction of 1/3 of the whole amount.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
The number of people are = 3
The amount of money to be shred equally is = $36
Let the amount of money each person gets be = x
Then for 3 people the amount will be = 3x.
The formula to find the value of x is -
3x = 36
x = 36/3
x = 12
Therefore, each person get $12.
The fraction that represents the amount will be -
share of each person / total amount
Substitute the value into the expression -
12/36 = 1/3
Therefore, each person shares 1/3 of the money.
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Simplify the following using trigonometric identities:
( - tan² (x) + sec² (x) ) - sin² (x)
Answer:
cos^2 (x)
Step-by-step explanation:
Use two of the Pythagorean Identities. See image.
You can rearrange the Pyth Identities. Like subtract the same thing from both sides.
Your question simplifies in just two steps. See image.
Mr. Anderson and Mrs. Brown both recorded the number of push-ups done by students in their class. They made line plots to display the data.
Select whether the value of each statistics is greater for Mr. Anderson's class, equal in both, or greater in Mrs. Brown's class based on the line plots.
1. Number of students who did push-ups :
2. Maximum number of push-ups :
3. Mean number of push-ups :
There were 37 pupils that completed push-ups. The maximum number of push-ups allowed is 32.
What is line plot?A line chart, also known as a curve chart, is a type of chart that presents information as a succession of data points called "markers" that are connected by straight line segments. It is a simple form of chart that is used in many disciplines. A line plot is a linear graph that displays data frequency distributions along a number line. It is useful for analyzing data with a single specified value. Line plots are sometimes known as dot plots. A line plot depicting the distance traveled by 17 turtles in one hour is shown below (we know it is 17 turtles because there are 17 dots on the line plot).
Here,
Mr. Anderson's class=20
Mrs. Brown's class=17
Number of students who did push-ups is 37. Maximum number of push-ups is 32.
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write a function if the input value is 5 then the output should be 5,7,9,11,13
f(x)= x+2 a function if the input value is 5 then the output should be 5,7,9,11,13
g is a transformation f the function f.
We have to figure out the transformation and write the equation of g with respect to f.
g is (with respect to the function f):
• reflected upside down [reflected about x-axis]
• translated 3 units left
Reflection with respect to x-axis makes the function negative, so:
f(x) would be -f(x)
Then,
Translation "a" units to the left, makes a function f(x) into f(x+a), thus:
f(x) would be -f(x+3)
hence f(x)= x+2 a function if the input value is 5 then the output should be 5,7,9,11,13
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how many times greater is 6 x 10^6 than 4 x 10^4?
Answer:
Step-by-step explanation:
We have two values i.e., 6*10^6 and 4*10^4
we divide both of them
i.e., =6*10^6/4*10^4
we shift the 10^4 to the numerator which becomes 10^-4.
=6*10^6*10^-4/4
=6*10^2/4
=600/4
=150
so, 6*10^6 is 150 times greater than 4*10^4
however sums between 10 and 19 inclusive are forbidden
The result is true, the number is forbidden.
This rule can be expressed mathematically as:
10 ≤ x < 19
This statement is saying that any number x must be greater than or equal to 10, but less than 19. So if x is set to any number between 10 and 19, the statement will be false. For example, if x is set to 15, the statement becomes:
10 ≤ 15 < 19
Which is false. So any number between 10 and 19 is forbidden.
This can be calculated by first subtracting 10 from the number. For example, if the number is 17, we would subtract 10 to get 7. Since 7 is less than 19, the number is forbidden. We can also use this equation to check any given number:
x − 10 < 19
If the result is true, then the number is forbidden. For example, if x is set to 17, the equation becomes:
17 - 10 < 19
Which is true, so 17 is forbidden.
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Complete question:
What is the sum of any two numbers between 10 and 19?
Select the correct answer from each drop-down menu.
A company manufactures CD drives that theoretically experience disc-read errors 1.2% of the time.
If a CD drive is tested for 250 read operations and fails 4 times, the empirical probability that a CD drive will fail is 0.016%
If the theoretical model is valid, the company would expect the empirical probability to decrease as the number of read operations
decreases
increases
Reset
Next
Does it increase or decrease
When the empirical probability that a CD drive would fail is 0.016%, there are four possible failures.
what is probability ?The probability that a happening will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a value between 0 and 1 and 1, where about 0 represents how likely something event is always to occur and 1 represents certainty. A probabilities is a numerical illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100percentage or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a whole set of fairly probable options that lead to a specific occurrence.
given
Let n = number of operations and P = error.
P = .016
n = 250
Increase P and n.
.016 (250) = 4
When the empirical probability that a CD drive would fail is 0.016%, there are four possible failures.
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Ainsley works for the owners of a bookstore. Her starting salary is $24,500, and she gets a 3% raise each year.
a. Write an equation in function notation to represent Ainsley's salary as a function of the number of years she has been working at the bookstore.
b. What will Ainsley's salary be when she begins her fourth year working at the bookstore? Show your work.
The equation in function notation to represent Ainsley's salary is y = $24,500 * (1 + 0.03x) and Ainsley's salary will be $26,940 when she begins her fourth year working at the bookstore.
What is an equation in function notation?
An equation involving x and y, which is also a function, can be written in the form y = “some expression involving x”; that is, y = f ( x). This last expression is read as “ y equals f of x” and means that y is a function of x.
a. Let y be Ainsley's salary after x years of working at the bookstore.
The equation representing Ainsley's salary as a function of the number of years she has been working at the bookstore is y = $24,500 * (1 + 0.03x).
b. To find Ainsley's salary when she begins her fourth year working at the bookstore, we need to plug in x = 3 into the equation:
y = $24,500 * (1 + 0.03x)
y = $24,500 * (1 + 0.03 * 3)
y = $24,500 * 1.09
y = $26,940.
Hence, The equation in function notation to represent Ainsley's salary is y = $24,500 * (1 + 0.03x) and Ainsley's salary will be $26,940 when she begins her fourth year working at the bookstore.
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a ball is dropped from a height of 16 feet. each time it drops feet, it rebounds feet. (a) find the total vertical distance traveled by the ball
The total distance travelled by the ball after dropping from a height of 16 feet and rebounds 0.81 feet is equal to 168.4 feet.
Balls from a height = 16 feet
Rebounds = 0.81feet
It form a geometric progression pattern :
16 + 16(0.81) + 16(0.81)² + 16(0.81)³ + ......+ ∞
Using sum of geometric progression :
S = a / 1 - r
here a = 16
r = 0.81
S represents the sum .
The total distance travelled by the ball is double of the sum .
S = 16 / ( 1 - 0.81 )
= 16 / ( 0.19)
= 84.2 feet
Total distance travelled by the ball = 2 × 84.2 feet
= 168.4 feet
Therefore, the total distance travelled by the ball as per given situation is equal to 168.4 feet.
The above question is incomplete, the complete question is:
A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance traveled by the ball .
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evaluate the integral. 1 (x2 4)e−x dx 0
After evaluating the integral of equation is ( x ^2+4)×e−x dx
=ex ^2+4e−dx
There are occasions when it is possible to perform an apparently difficult piece of integration
by first making a substitution. This has the effect of changing the variable and the integrand.
When dealing with definite integrals, the limits of integration can also change. In this unit we
will meet several examples of integrals where it is appropriate to make a substitution.
(x^2 + 4)e−x dx = 0
(x ^2+4)×e−x dx
Multiply the terms
e(x ^2+4)−x dx
Multiply the terms
Evaluate
x dx
Multiply the terms x^ 1+1 d
Add the terms
x ^2d
Multiply the terms dx ^2
e(x ^2+4)−dx ^2
Simplify
e(x ^2 +4)
Apply the distributive property
ex ^2+e×4
Multiply the terms
ex^ 2+4e
ex ^2+4e−dx ^2
After evaluating the integral of equation is(x ^2+4)×e−x dx =ex ^2+4e−dx ^2
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Maggie reads 1/3 of a book every 3/4 of a Week. How manny books does Maggie read?
Answer:
4/9
Step-by-step explanation:
If Maggie reads 1/3 of a book in 3/4 weeks, you want to know how many books per week Maggie reads.
Books per weekTo find Maggie's reading rate in books per week, divide books by weeks:
(1/3 book)/(3/4 week) = (1/3)/(3/4) book/week
= (1/3) · (4/3) book/week = 4/9 book per week
Maggie reads 4/9 books per week.
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find n for which (5/6)^n is less than 0.00001
The n will be 12.175074 for which (5/6)^n is less than 0.00001.
We start by converting the target number to scientific notation: 0.00001 = 1 x 10^-5
Next, we take the logarithm base (5/6) of both sides:
n = log base (5/6) of (1 x 10^-5)
Using logarithm rules, we can simplify this to:
n = log base (5/6) of 1 - log base (5/6) of 10^-5
Using logarithm tables or a calculator, we find that:
log base (5/6) of 1 = 0
log base (5/6) of 10^-5 = -12.175074
So,
n = 0 - (-12.175074) = 12.175074
Therefore, n = 12.175074.
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Y= 2x + 1
y =x - 2
identify the point of intersection of a pair functions
Answer:
(-3,-5)
Step-by-step explanation:
2x+1=x-2
subtract 3 from both sides
x=(-3)
sub the value of x back into one of the equations
y=2(-3) + 1=-5
Express tan
I as a fraction in simplest terms.
The tangent of the corners of this right-angle triangle is 4/3.
What is the Pythagorean Theorem?The Pythagorean theorem states, "In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides." The sides of this triangle were called the perpendicular, the base, and the hypotenuse.
The tangent of a right triangle angle is equal to the ratio of the opposite side to the adjacent side. So if we call the other side "x", we can set the following formula:
tan(θ) = 8/x
where θ is the angle from height 8. We can find the value of x using the Pythagorean theorem.
[tex]x^2 + 8^2 = 10^2\\x^2 = 100 - 64\\x^2 = 36\\x = 6[/tex]
So the tangent values are:
tan(θ) = 8/6 = 4/3
Therefore, the tangent of the corners of this right triangle is 4/3.
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Based on the figure, select all true equations.
Answer:
B, C, E, F
Step-by-step explanation:
Solve for the missing angle first (which is 42°)
Listing all of the basic trig ratios (sohcahtoa):
sin x = opp/hyp
cos x = adj/hyp
tan = opp/adj
sin 48° = a/c
cos 48° = b/c
tan 48 = a/b
sin 42° = b/c
cos 42° = a/c
tan 42° = b/a
What proportion could you use to find the value of x?
A. 3/11=x/11
B. 3/x=x/11
C. 3+11/x=3/x
D. 11/x=x/11-3
The correct option: B. 3/x=x/11. is the proportion used to determine the the value of x.
Define the term proportion?Relationships among two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, each variable is consistently equal to the other's constant value. This "constant of proportionality" is the name of this constant.For the stated question:
The pair of sides x and 11 : as well as 3 and x are used to find the proportion.
Thus,
3/x = x/11
It is the correct relation to find the value of x.
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how many grams of carbs in an ounce
One ounce of food contains average about 28 grams of carbs.
One of the three macronutrients that the body needs for energy, carbohydrates can be found in a wide variety of foods. Sugar, starch, and fiber are the three elements that make up carbohydrates. Weight is measured in ounces, which weigh 28.35 grams. As a result, one ounce of food contains about 28 grams of carbs. Carbohydrates are crucial for supplying the body with the 4 calories per gram of energy it needs to function, fuel physical activity, and help with digestion. Foods like fruits, vegetables, grains, nuts, and dairy products all naturally include ounces of carbs. It is crucial to remember that there are several kinds of carbs, some of which are healthier than others.
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The complete question is
How many grams of carbs in an ounce of food ?
List the members of the set {2< x < 5}
Answer:
3 and 4 or {3,4}
Step-by-step explanation:
3 and 4 are the only numbers greater than 2, but less than 5.
assuming we know σ=5.5, construct a 85.0 percent confidence interval for the true population mean, μ, given that a random sample of 94 values was noted to have x¯=85.0.
The confidence interval is (84.41, 85.59), meaning that we are 85.0% confident that the true population mean, μ, lies between 84.41 and 85.59
How to construct the confidence intervalA 85.0% confidence interval for the true population mean, μ, can be constructed using the following formula:
x¯ ± (Zα/2 * σ/√n)
where
x¯ is the sample mean (85.0), Zα/2 is the critical value for a given confidence level σ is the population standard deviation (5.5)n is the sample size (94).Using the Z-score table for a confidence level of 0.85, we have
Zα/2 = 1.040.
Substitute the known values in the above equation, so, we have the following representation
CI = 85.0 ± (1.040 * 5.5/√94)
Evaluate
CI = 85.0 ± 0.59
This gives
CI = 84.41 to 85.59
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Solve 7(x + 3) = 2x + 1.
A. x = 3
B. x = 2
C. x = -4
D. x = -6
Answer:
C
Step-by-step explanation:
7(x + 3) = 2x + 1 ← distribute parenthesis on left side by 7
7x + 21 = 2x + 1 ( subtract 2x from both sides )
5x + 21 = 1 ( subtract 21 from both sides )
5x = - 20 ( divide both sides by 5 )
x = - 4
Answer:
x=-4
Step-by-step explanation:
7(x+3)=2x+1
distribute 7
7x+21=2x+1
subtract 1 from both sides
7x+20=2x
subtract 7x from both sides
20=-5x
divide both sides by -5
x=-4
Sue runs the 100-yd dash in 11.9 s, or
8.4 yd/s. If she could lower her time by
0.5 s, would she be better than average
for her age, which is 8.5 yd/s?
She needs to lower her head by 190 seconds by 0.5 seconds in order to go more quickly than the age-appropriate speed of 8.5 yards per second.
what is distance ?Distance is the broad, directionless movement of a moving object. Distance can be characterized as the amount of territory an object has covered, regardless of something like the originating or ending location. Distance is defined as the extent or size of the difference between two places. The space between two positions and the distance traveled between them are not the same thing, it should be emphasized. The distance traveled is the entire length of a path that connects two places. Distance is the actual travel distance of a body. It is also known as path length. For instance, OP = 360 m would be the length of the path for an object traveling from point O to point P.
given
V = D/t = 100/9.8 = 10.20 yd/sec is the speed with D = 100 yds, t = 9.8 s.
Convert the distance in yards for d = 100 meters, 1 yd/0.9144 m = 109.36 yds (1 yd = 0.9144 m d = 100 meters)
t=d/V=109.36 yards/10.20 yards per second = 10.72
The sprinter will finish the 100.0 meters in 10.72 seconds.
The sprinter's velocity is given by V = (10.20 yards per second)(0.9144 meters per yard) = 9.3 m/s.
Running 1.80 km in T = (1.80km * 1000m/1km)/9.33m/s will take 190 seconds.
She needs to lower her head by 190 seconds by 0.5 seconds in order to go more quickly than the age-appropriate speed of 8.5 yards per second.
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a study of 1000 randomly selected flights of a major airline showed that 769 of the flights arrived on time. what is the probability of a flight will not arrive on time?
The probability of a flight will not arrive on time is 231/1000
What is probability?Probability is the function that measures the chances that an outcome of a random event will be as expected. In this way you can measure how likely it is that an event will happen.
Probability requested is equivalent to:
Flights arrive on time= 769
Total flights = 1000
P(arrive on time) = Flights arrive on time / Total flights
P(arrive on time) = 769/1000
P (not arrive on time) = 1 - 769/1000
P (not arrive on time) = (1000 - 769)/1000
P (not arrive on time) = 231/1000
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