The value of x for the triangle is equal to 17.32.
What is the Pythagorean theorem?Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Calculate the perpendicular side for both triangles by using the Pythagorean theorem.
H² = P² + B²
Here, H is the hypotenuse, P is perpendicular and B is the base.
For the first triangle, the perpendicular is calculated as,
P² = x² - 10²......................................................1
For the second triangle, the perpendicular will be,
P² = ( 30² - x² ) - 20² .......................................2
Equate the equation 1 and 2 and solve,
x² - 10² = ( 30² - x² ) - 20²
x² - 100 = 900 - x² - 400
2x² = 900 - 400 + 100
2x² = 600
x√ = 300
x =√300
x = 17.32
To know more about the Pythagorean theorem follow
https://brainly.com/question/343682
#SPJ1
10. The set of prime numbers greater than 11 with the cardinality of 5.
The set of prime numbers greater than 11 with the cardinality of 5 is {13, 17, 19, 23, 29}
How to determine the setFrom the question, we have the following parametes that can be used in our computation:
Set = prime numbers
Cardinality = 5
The cardinality implies that the number of elements in the set is 5
5 prime numbers greater than 11 are 13, 17, 19, 23, 29
Hence, the set is {13, 17, 19, 23, 29}
Read more about set at
https://brainly.com/question/24713052
#SPJ1
You’re help Is greatly appreciated!! I will mark BRAINLIEST as well
Answer:
1. -4/7
2. 4/3
3. x^2 + 16x + 63
4. x^2 + 19x + 90
Step-by-step explanation:
1. (1, 8) and (8, 4)
slope = m = (8 - 4)/(1 - 8) = -4/7
2. (2, 4) and (5, 8)
slope = m = (8 - 4)/(5 - 2) = 4/3
3. (x + 9)(x + 7) =
= x^2 + 7x + 9x + 63
= x^2 + 16x + 63
4. (x + 10)(x + 9) =
= x^2 + 9x + 10x + 90
= x^2 + 19x + 90
What is the opposite rational number of -3/2
The opposite rational number of -3/2 is -2/3.
Define rational number.p/q where q is not equal to 0 is the form of a rational number, which is a sort of real number in mathematics. A rational number is any fraction with a non-zero denominator. 1/2, 1/5, 3/4, and other like numbers are a few examples of rational numbers. A rational number is one that can be stated mathematically as the quotient or fraction pq of two numbers, p and q, with p being the numerator and q being the denominator. Every integer, such as 5 = 51, is a rational number, as is the number 37.
Given,
Rational number:
-3/2
Reciprocating,
-2/3
The opposite rational number of -3/2 is -2/3.
To learn more about rational number, visit:
https://brainly.com/question/24398433
#SPJ1
Given 3 + 7 + 11 + 15 + … find S20
Answer:
Hi
Please mark brainliest ❣️
Factor completely.
x^8 - 1/81
Please show a step-by-step/explanation on how you got your answer.
Answer: x(8) - /81
Step-by-step explanation:
Answer:
Step-by-step explanation:
As before any expression of the form (a^2-b^2) will always factor to (a-b)(a+b) in this case
x^8-1/81 = (x^4-1/9)(x^4+1/9) = (x^2-1/3)(x^2+1/3)(x^4+1/9) and if we completely factor it including square roots.\((x-\sqrt{1/3})(x+\sqrt{1/3})(x^2+1/3)(x^4+1/9)\)
Express 0.6(27..).)))) as a fraction
I assume you mean the number x = 0.6272727….
You have
10x = 6.272727…
1000x = 627.272727…
==> 1000x - 10x = 990x = 621
==> x = 621/990 = 69/110
Pleasere answerrrrrrr
Answer: the 2nd one
Step-by-step explanation: because i said so ur the dum one
The measures of the angles of a triangle are shown in the figure below. Solve for x.
34°
46°
x°
The measures of the angle x in the triangle is 100 degrees
How to determine the measures of the angle?From the question, we have the following parameters that can be used in our computation:
Angles = 34, 46 and x
The sum of angles in a triangle add up to 180 degrees
This is represented as
Sum of angles = 180
Substitute the known values in the above equation
So, we have
34 + 46 + x = 180
Evaluate the like terms in the above equation
So, we have
80 + x = 180
Evaluate the like terms in the above equation
So, we have
x = 100
Hence, the value of x is 100
Read more about triangles at
https://brainly.com/question/14285697
#SPJ1
How to do a arithmetic sequence
Answer:
See below.
Step-by-step explanation:
"...start with a number a, and add to it a fixed constant d, over and over again. This type of sequence is called an arithmetic sequence. Definition: An arithmetic sequence is a sequence of the form a, a + d, a + 2d, a + 3d, a + 4d, etc."
-hope it helps
Find the x-intercepts of the function: \(f(x)= cos(x) + sin(x) for 0\leq x \ \textless \ 2\pi\)
if a polygon is a triangle, then it has exactly three sides. is the converse of the conditional true?
Answer:
If a polygon is a triangle then it has exactly three sides
A polygon has 3 sides if and only if it is a triangle. Put it all together: Conditional: If a polygon is a triangle, then it has three sides. Converse: If a polygon has three sides, then it is a triangle.
Answer:
yes
Step-by-step explanation:
because the polygon it has tree sides it's called triangle hope it's helpThe temperature in march was less than 60 degrees everyday.
Which inequality shows the temperature in march?
Answer:
x-60
Step-by-step explanation:
because x is the degree it started with, and it was less 60 degrees everyday
Question content area top
Part 1
A new bank customer with $ wants to open a money market account. The bank is offering a simple interest rate of %.
a. How much interest will the customer earn in years?
Simplify each term. please help!! 30 points + brainliest :)
1. -(-3y)³
2. (2c)⁵
3. (-2m)⁴
4. (4g)³
5. (7j)²
6. (-5z)⁵
Answer:
1. 27y^3
2. 32c^5
3. 16m^4
4. 64g^3
5. 49j^2
6. -3125z^5
Step-by-step explanation:
Can you help answer my question too, please?
Help I'll give brainliest again to the first answer
Answer:
A ) 400 + 15c
Step-by-step explanation:
She earns 400 per week and 15 per customer so we have to add 15 to the 400, so we can remove option b and d
we can also remove option c because she isn't making 400 per new customer
4% is equivalent to what fraction
the value of 4% as a fraction is 1/25
4/100 is the fraction, but when 4 is divided into 100, it gives you 1/25 in simplest form.
kerry is going to use these instructions to make a fizzy drink
mix 7 parts apple juice with 3 parts lemonade
kerry thinks that she has 280ml of applejuice and 180 ml lemonade.
if kerry is correct what is the greatest amount of fizzy drink she can make?
second part:
kerry has 280 ml of applejuice but only has 160 ml of lemonade.
Does this affect the greatest amount of fizzy drink she can make?
Give a reason for your answer.
a) She can make 400 milliliters of the fizzy drink.
b) The change does not affect the greatest amount of drink.
If kerry is correct what is the greatest amount of fizzy drink she can make?We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.
If we divide the total amount of apple juice in 7 parts, then each part has:
280ml/7 = 40ml
Then we need 3 parts of 40ml of the lemonade, this is:
3*40ml = 120ml
Then the total amounf of drink fizz that she can make is:
280ml + 120ml = 400ml.
b) Now she has 160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.
Learn more about quotients:
https://brainly.com/question/629998
#SPJ1
On a number line , between which two consecutive whole number would 78 be located
Maria buys lunch every work day. She always eats at the same restaurant and spends no more than $5.25 for lunch. She has created a budget in which she has allowed herself $1700 for the year to buy lunches during her five-day work week. Assume Maria spends the maximum she allows for each lunch. Write an equation to determine how much of her budget, in dollars, remains unspent at the end of a particular week of the year? Include definitions of the variables you used. B = 26.25n- 1700, where B is her budget balance and n is the number of complete weeks of work O B= 1700 - 26,25n, where B is her budget balance and n is the number of complete weeks of work O B = 1700 - 5.25n, where B is her budget balance and n is the number of complete weeks of work O B = 5.25n - 1700, where B is her budget balance and n is the number of complete weeks of work
Let's begin by listing out the information given to us:
Maria spends $5.25 for every lunch;
Maria has 5 lunches every week (five-day work week) = 5 * ($5.25) = $26.25
Maria's budget = $1700
n = the number of complete weeks of work
Budget balance = Maria's Budget - (26.25 * the number of weeks)
B = 1700 - 26.25n
The events are not mutually exclusive, find the missing probability.
P(A) = 6
P (B) = 20
P(A/B) = ??
P(AVB) = 40
The missing probability is given as follows:
P(A and B) = 0.6375.
How to calculate a probability?The parameters that are needed to calculate a probability are given as follows:
Number of desired outcomes in the context of a problem/experiment.Number of total outcomes in the context of a problem/experiment.The probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.
The and probability is calculated as follows:
P(A and B) = P(A) + P(B) - P(A or B).
The parameters are given as follows:
P(A) = 5/16 = 0.3125.P(B) = 8/20 = 0.4.P(A or B) = 3/40 = 0.075.Hence:
P(A and B) = 0.3125 + 0.4 - 0.075
P(A and B) = 0.6375.
Learn more about the concept of probability at https://brainly.com/question/24756209
#SPJ1
How many solutions does the equation have? 2(x+3)=2x+6
Answer:
Infinitely Many Solutions
Step-by-step explanation:
Subtract 6 from both sides of the equation
2
the bakers want to sell their house for 145,500.After 2 months,the bakers decided to mark down the price of their house 8% to sell more quickly. How much are the bakers selling their house for now?
Answer:
133,860
Step-by-step explanation:
The baker was going to sell his house for 145,500 but he found that no one came to buy, so he decreased the amount by "8%".
* No we have our key elements:
- Starting amount = 145,500
- Rate of change = 8%
* We will get the "8%" of the number 145,500
- Firstly, "8%" means 8/100
- So, 0.08 will be our new rate of change.
* 145,500 will be multiplied by 0.08 to find the final answer because when we talk about the percentage of a number, we are going to talk about a part of it.
- 145,500 × 0.08 = 133,860 ; the same as
145,500 × 8/100 = 133,860
What fraction with a numerator of 2 is equivalent to 48?
Answer:
\(\frac{2}{\frac{1}{24} }\)
Step-by-step explanation:
2/x = 48
48x = 2
x = (2)/ (1/24)
\(\frac{2}{\frac{1}{24} }\) = 48
In a School sports day, the number of points the 8th grade team scores is given by 3x + 2y + z,
is the red team; y is yellow team, and z is the blue team. What is the total number of points scored by 10* graders when red scores 3 three points, yellow 5 points, and blue 2 points?
The total number of points scored is given by the equation A = 23 points
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the total points scored be represented as A
Now , the equation will be
Substituting the values in the equation , we get
A = 3x + 2y + z be equation (1)
where x = red team = 3 points
y = yellow team = 5 points
z = blue team = 2 points
So , A = 3 ( 3 ) + 2 ( 5 ) + 2
A = 9 + 10 + 2
A = 21 points
Hence , the equation is A = 21 points
To learn more about equations click :
https://brainly.com/question/19297665
#SPJ1
What is the sum of the first and second cube number
Answer:
9Step-by-step explanation:
What is the sum of the first and second cube number?
1³ + 2³ =
1 + 8 =
9
erify that the following function is a probability mass function, and determine the requested probabilities. [give exact answers in form of fraction.]
The probability of x = 1 is 0.2,x = 2 is 0.3, x = 3 is 0.5
Let X be a random variable with the following probability mass function:
f(x) =
x = 1: 0.2
x = 2: 0.3
x = 3: 0.5
This is indeed a probability mass function because the values of f(x) are all greater than or equal to 0, and the sum of the values of f(x) is equal to
To calculate the probability of x = 1, we can use the formula for probability mass functions: P(X = x) = f(x).
Therefore, the probability of x = 1 is 0.2.
To calculate the probability of x = 2, we can use the same formula: P(X = x) = f(x).
Therefore, the probability of x = 2 is 0.3.
To calculate the probability of x = 3, we can use the same formula: P(X = x) = f(x).
Therefore, the probability of x = 3 is 0.5.
Learn more about probability here:
https://brainly.com/question/11234923
#SPJ4
complete question
What is the probability of x = 1, x = 2, and x = 3?
Find the measure of the arc or angle indicated
The unknown angle in the cyclic quadrilateral is as follows:
∠R = 86 degrees
How to find arc angle?The diagram above is cyclic quadrilateral. A cyclic quadrilateral is a four sided shape that can be inscribed into a circle.
The sum of angles in a cyclic quadrilateral is 360 degrees. The opposite angles in a cyclic quadrilateral is supplementary.
Hence, let's find the unknown angle.
∠R = 1 / 2 (92 + 80)
∠R = 1 / 2 (172)
∠R = 86 degrees
Therefore, the unknown angle is 86 degrees.
learn more on arc angle here: https://brainly.com/question/9806509
#SPJ1
Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed.
The 99% confidence interval for the population proportion p is (0.776, 0.824).
To find the 99% confidence interval for a proportion, we can use the formula:
CI = p^ ± z*(SE)
where p^ is the sample proportion, SE is the standard error, and z is the critical value from the standard normal distribution corresponding to the level of confidence.
For a 99% confidence interval, the critical value z is 2.576.
Substituting the given values into the formula, we have:
CI = 0.80 ± 2.576*(0.03/√200)
Simplifying this expression, we have:
CI = 0.80 ± 0.024
This means that we are 99% confident that the true population proportion falls between 0.776 and 0.824. We can interpret this interval as a range of plausible values for the population proportion, based on the sample data.
To learn more about confidence interval here:
https://brainly.com/question/24131141
#SPJ1
Suppose an investigator takes a random sample of n = 50 birth weights from several teaching hospitals located in an inner-city neighborhood. In her random sample, the sample mean is y¯ = 3.15 kg and the standard deviation is 250 grams. (a) Calculate a 95% confidence interval for the population mean birth weight in these hospitals. (b) The typical weight of a baby at birth for the US population is 3.25 kg. The investigator suspects that the birth weights of babies in these teaching hospitals is different than 3.25 grams, but she is not sure if it is smaller (from malnutrition) or larger (because of obesity prevalence in mothers giving birth at these hospitals). Carry out the hypothesis test that she would conduct.
a)95% confidence interval for the population mean birth weight in these hospitals is (3078.9358,3221.0642).
(b)The P-value is 0.0068.
What is hypothesis testing?To test the null hypothesis and the alternative hypothesis, all analysts employ a random population sample. The null hypothesis typically states that two population parameters are identical; for instance, it can claim that the population mean return is equal to zero.
Why is hypothesis testing used?A strategy for determining how reliably one may extrapolate observed results in a study sample to the larger population from is provided by hypothesis testing, a procedure used to assess the strength of the evidence from the sample and give a framework for doing so.
C.I=x-t(alpha/2)xs/sqrt{n}
=3150+_2.01*250/sqrt{50}
=(3078.9358,3221.0642)
b) P value =P(t<-2.83)+P(t>2.83)
use calculator
=0.0034+0.0034
=0.0068
To learn more about hypothesis test visit link:
https://brainly.com/question/29519577
#SPJ4
Are these fractions equivalent or nonequivalent?
1 3
24 8
Click on the correct answer.
nonequivalent
equivalent
Answer: Easy, hope this helps!
Nonequivalent
Step-by-step explanation:
1/24 = 1/24
3/8 = 9/24
1/24 and 9/24 is nonequivalent