Answer:
it must be less than 90 degrees
What is the Pythagorean triplet of 16?
The Pythagorean triplet of 16 is (8, 15, 17).
This can be calculated using the Pythagorean theorem, which states that in any right triangle, the sum of the squares of the two legs is equal to the square of the hypotenuse. Therefore, given a number, we can find a Pythagorean triplet by calculating the squares of the two legs and then finding the hypotenuse.
Formula:
a² + b² = c²
Find the square of the number.
16² = 256
Subtract the square from the number to get one leg of the triangle.
16 - 256 = -240
Take the square root of the result.
√(-240) = 8
Add the square to the number to get the other leg of the triangle.
256 + 16 = 272
Take the square root of the result.
√(272) = 15
Add the two legs together to get the hypotenuse.
8 + 15 = 23
Take the square of the result.
23² = 529
Subtract the sum of the two legs from the hypotenuse.
529 - 23 = 506
Take the square root of the result.
√(506) = 17
Therefore, the Pythagorean triplet of 16 is (8, 15, 17).
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Radicals
How Do I Simplify
(3√5+√3)(√5+ √3)
Answer:
18 + 4√15
Step-by-step explanation:
(3√5+√3)(√5+ √3)
= 3√5 (√5+ √3) + √3 (√5+ √3)
= 3√5 √5 + 3√5 √3 + √3 (√5+ √3)
= 3√5 √5 + 3√5 √3 + √3 √5 + √3 √3
= 18 + 4√15
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Please help
Solve the rational equation: 1/x+1 - 1/x+2 = 1/5
A. There is no solution.
B. x = −0.64, x = 1.44
C. x = −3.79, x = 0.79
D. x = −1, x = −2
The solution for the rational equation (1/(x + 1)) - (1/(x + 2)) = 1/5 is specified by the option C.
C. x = -3.79, x = 0.79
What is a rational equation?A rational equation consists of a fraction that has a polynomial numerator denominator.
The specified equation can be expressed as follows;
[tex]\dfrac{1}{x + 1} - \dfrac{1}{x+2} = \dfrac{1}{5}[/tex]
Finding the common denominator for the right hand side expression, we get;
[tex]\dfrac{ (x + 2) - (x + 1)}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]
[tex]\dfrac{1}{(x + 1) \times (x + 2)} = \dfrac{1}{5}[/tex]
[tex]\dfrac{1}{x^2+ 3\cdot x+ 2} = \dfrac{1}{5}[/tex]
Inverting both sides of the above equation, we get the following quadratic equation;
x² + 3·x + 2 = 5
x² + 3·x + 2 - 5 = 0
x² + 3·x - 3 = 0
The quadratic formula indicates that we get;
x = (-3 ± √(3² - 4×1×(-3))) ÷ (2 × 1)
x = (-3 + √(21)) ÷ 2 and x = (-3 - √(21)) ÷ 2
x ≈ 0.79 and x ≈ -3.79
The correct option is option C
C. x = -3.79, x = 0.79
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10 Two cyclists are traveling along a track in the same direction. Their motions are described
by the linear equations d = 10t and d-8t= 2, where t hours is the time and d miles is the
distance from a point on the track.
b When will the cyclists meet?
Answer:
They will meet in 1 hour
Step-by-step explanation:
(1) d = 10t
(2) d - 8t = 2 rearrange this equation to: d = 8t + 2
Set equation (1) equal to equation (2):
10t = 8t + 2
Solve for t:
10t - 8t = 2
2t = 2
t = 2/2 = 1 hr
Item 48 A couple has 5 children, all sons. If the woman gives birth to a sixth child, what is the probability that the sixth child will be a son
The probability that the sixth child will be a son is 50%. Each child, regardless of gender, has an equal chance of being born.
What is the probability that the sixth child will be a son?The probability of having a son as the sixth child can be calculated using the binomial formula. The binomial formula is used to calculate the probability of an event occurring after a certain number of trials, given the probability of success in each trial.In this case, the probability of having a son is the same for each trial (or birth), which is 0.5 (since the odds of having a boy or a girl are equal).Therefore, the probability of having a son as the sixth child can be calculated as follows:P(son) = (5 choose 6) x (0.5^6) = 0.015625
The binomial formula is used to calculate the probability of an event occurring after a certain number of trials, given the probability of success in each trial. In this case, the probability of having a son is the same for each trial (or birth), which is 0.5 (since the odds of having a boy or a girl are equal).Therefore, the probability of having a son as the sixth child can be calculated using the binomial formula as follows: P(son) = (5 choose 6) x (0.5^6) = 0.015625.
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Find the measurement indicated in each parallelogram.
Therefore , the solution of the given problem of parallelogram comes out to be option D 80 degrees.
Define parallelogram.A parallelogram is the name given to a quadrilateral in geometry. In a parallelogram, the opposing sides are parallel and of equal length. The rhombus, rectangle, and square are just a few shapes that are parallelograms.
Here,
Given : The parallelogram has M angle =100 degree
And to Find :L angle
In a parallelogram sum of the adjacent angle is 180°, So
So ,
Using this parallelogram property ,
we find :
=>100 + L =180
=> L = 80
Thus,
We get the L value using parallelogram properties.
Therefore , the solution of the given problem of parallelogram comes out to be option D 80 degrees.
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13yd 2ft 6in x 15 =
i need to know the answer to this problem
Using the unit conversion and converting all the distance units to inches, The final answer is 7575 inches.
What do you mean by unit conversion?Divide the smaller unit's value by the quantity of smaller units required to create the larger unit. Multiply to change from a larger to a smaller unit. Divide to change from a smaller unit to a larger one. We need to convert between units in order to ensure accuracy and prevent measurement misinterpretation. For example, we do not measure a pencil's length in kilometers. In this situation, one must convert from kilometers (km) to centimeters (cm).
What do you mean by equations?An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A collection of one or more linear equations containing the same variables is known as a system of linear equations in mathematics.
13 yard = 468inches
2ft = 24 inches
total 268+24+13 = 505inches
505*15 = 7575 inches
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need help with these 4
Thus, It is possible to visually assess whether a limit exists as x approaches a by looking at the function f (x) and g (x) graphs, which are 1 and 5 when x is very close to x=a.
How would you define limit?In mathematics, a limit is the value that a function, a sequence, or an index approaches as an input or an index gets closer to a particular value. Limits are essential to the study of calculus and mathematical analysis since they are used to define continuity, derivatives, and integrals.
Here,
From the function f (x) and g graphs shown here ( x)
1) lim f (x) plus lim g ( x )
= -1 + 2 = 1
2) f (-1) + lim g ( x)
= 3 + 2
= 5
Therefore , the solution of the given problem of limit comes out be 5.
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solve please im gonna fail
Answer:
The two little blue boxes are going
Step-by-step explanation:
Lets start with the 0s.
Two zeros is 0. so its
_ _ _ _ 0.
Now we add 2 and 0 which is 2.
_ _ _ 2 0
now we add 6 and 4, which is 10. We have to put the 1 above the 7 and 5 and we are going to put 0 down below
_ _ 0 2 0
now we are going to add 7 +5, but dont forget the 1! Its going to be 13. Put the 3 down below and put the 1 above the 2!
_ 3 0 2 0
Now its 2 + 1 which is 3
your answer is
33020
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.
What is an equivalent expression?The equivalent is the expression that is in different forms but is equal to the same value.
Simplify all the equations, then we have
A. 2 + x = 5, to simplify the equation, then we have
2 + x = 5
x = 3
B. x + 1 = 4, to simplify the equation, then we have
x + 1 = 4
x = 3
C. 9 + x = 6, to simplify the equation, then we have
9 + x = 6
x = - 3
D. x + (- 4) = 7, to simplify the equation, then we have
x - 4 = 7
x = 11
E. - 5 + x = - 2, to simplify the equation, then we have
- 5 + x = - 2
x = 3
The equations that are equivalent to each other will be 2 + x = 5, x + 1 = 4, and - 5 + x = - 2. Then the correct options are A, B, and E.
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n 2010, the population of a small town in Alabama was 8,250 people. By 2015, the population had decreased by 10%. From 2015, to 2020, the population then increased by 15%. What was the population of the town in 2020
The population of a city is increasing at a rate of 4% each year. In 2020, there were. 236,000 people in the city.
What is population?A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population.A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.Given, In 2015, the population of the town decreased by 10%, so [tex]8250 x 10/100 = 825[/tex] people left the town, bringing the population down to [tex]8250 - 825 = 7425.[/tex]
From 2015 to 2020, the population increased by 15% so [tex]7425 x 15/100 = 1113.75[/tex] people came back to the town, bringing the population to [tex]7425+1113.75 = 8538.75[/tex]
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8^x/2 divided by 4^x/3 equals 2^-5/2
The solution to the exponential equation 8^(x/2)/4^(x/3) = 2^(-5/2) is given as follows:
x = -6/5.
How to solve the exponential equation?The exponential equation for this problem is defined as follows:
[tex]\frac{8^{\frac{x}{2}}}{4^{\frac{x}{3}}} = 2^{-\frac{5}{2}}[/tex]
Both 8 and 4 are powers of 2, as follows:
8 = 2³.4 = 2².Applying the power of power rule (multiplying the exponents), the expression on the left side can be rewritten as follows:
[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{-\frac{5}{2}}[/tex]
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents, hence:
[tex]\frac{2^{\frac{3x}{2}}}{2^{\frac{2x}{3}}} = 2^{\frac{3x}{2} - \frac{2x}{3}}[/tex]
The subtraction is obtained as follows:
3x/2 - 2x/3 = 9x/6 - 4x/6 = 5x/6.
(as the least common factor of 2 and 3 is of 6).
Then the simplified expression is of:
[tex]2^{\frac{5x}{6}} = 2^{-\frac{5}{2}}[/tex]
As the exponential function y = 2^x is injective, the solution is obtained as follows:
5x/6 = -5/2.
10x = -12
x = -6/5.
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Adam is trying to spot a meteor. The probability he will see one in the next 10 minutes is 0.56.
What are the odds in favor of Adam seeing a meteor in the next 10 minutes?
Answer: The odds in favor of an event happening are the ratio of the probability of the event happening to the probability of the event not happening. To find the odds in favor of an event, you can use the formula:
Odds in favor = probability of event occurring / (1 - probability of event occurring)
In this case, the event is that Adam will see a meteor in the next 10 minutes. The probability that this event will occur is 0.56. Therefore, the odds in favor of this event occurring are:
Odds in favor = 0.56 / (1 - 0.56)
= 0.56 / 0.44
= 1.27
So, the odds in favor of Adam seeing a meteor in the next 10 minutes are 1.27 to 1.
It means that Adam is 1.27 times more likely to see a meteor in the next 10 minutes than not seeing one.
Step-by-step explanation:
The odds in favor of Adam seeing a meteor in the next 10 minutes are 14 : 11
For the 1996 General Social Survey, conducted by the National Opinion Research Center NORC, 842 replied "yes" and 982 replied "no. " Let π denote the population proportion who would reply "yes. " Find the P-value for testing H0 : π = 0. 5 using the score test, and construct a 95% confidence interval for π. Interpret the results
At a significance level of 0.05, the sample data is not consistent with the null hypothesis that the proportion of population who would respond "yes" is 0.5. The P-value of 0.0005 is less than 0.05, and also the sample proportion 0.4616 is not in the interval (0.477, 0.523) which we found as 95% Confidence interval.
Therefore, we reject the null hypothesis and conclude that the population proportion of "yes" responses is different from 0.5.
The P-value for a score test for H0: π = 0.5 can be found using the z-score and a standard normal table. The z-score is calculated as
[tex]z = \frac{x-0.5}{0.5\sqrt{\frac{x-0.5}{n} } }[/tex], that is
z = (x - 0.5) / (√(0.5(1 - 0.5) / n)
where x is the sample proportion of "yes" responses (842 / (842 + 982) = 0.4616), π is the population proportion of "yes" responses, and n is the sample size (842 + 982 = 1824).
[tex]z = \frac{0.4616-0.5}{0.5\sqrt{\frac{0.4616-0.5}{1824} } }[/tex]
= (0.4616 - 0.5)/ (√(0.5(1 - 0.5) / 1824)
This gives a z-score of -3.28.
To find the P-value, we can use the standard normal table to find the probability of observing a z-score less than -3.28. This P-value is approximately 0.0005, which is less than the commonly used significance level of 0.05. Therefore, we would reject the null hypothesis that π = 0.5.
To construct a 95% confidence interval for π, we can use the formula for a normal approximation interval:
π ± z×(√(π(1-π) / n)) that is
[tex]\pi \frac{+}{} z\frac{\pi (1 -\pi )}{n}[/tex]
Where π = 0.5, z = 1.96 (for a 95% confidence level), and n = 1824.
This gives a 95% confidence interval of (0.477, 0.523)
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The function f is defined by f(x) = mx + b, where m and b are constants. If f(0) = 18 and f(1) = 20, what is the
value of m?
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol.
What are 3 examples of a constant?A few more constant examples are :
The number of days in a week represents a constant.
In the expression 5x + 10, the constant term is 10.In 2a, 2 is a constant.In -7mn, -7 is a constant.In 3x, 3 is constant.A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.There are four major constants that appear within mathematical calculations. These math constants are used in a whole variety of equations and formulae and are repeatedly seen in a variety of areas.The easiest way we can find a constant term in math is to look first for stand-alone numbers, and then for coefficients and variables that can be solved for. A variable cannot be solved for and return only one value if it has an exponent, such as x^2.A function is called no constant if it takes more than one value (if there is more than one element in its range).Substitute:
m*o+b=18
m+b=20
Apply Zero Property of Multiplication:
b=18
m+b=20
Substitute into one of the equations:m+18=20
Rearrange unknown terms to the left side of the equation:m=20-18
Calculate the sum or difference:m=2
The solution of the system is:
b=18
m=2
The answer is b=18 m=2
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Sienna goes to the mall with $56. She spends $13 on food and $24 on a book. How much money does Sienna have left?
Answer: 19
Step-by-step explanation:
56-13=43
43-24=19
Answer: 19
Step-by-step explanation: 13 + 24 = 37
so (56 - 37 = 19)
HELP LIMITED TIME PLEASE HELP ASAP!!! THE PROBLEM I PUT IN PICTURES!
How do you solve complex fraction equations?
To solve complex fractions there are two methods -
1 - Divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator and then simplify further if necessary.
2 - Multiply the numerator and denominator of the overall complex fractions and then simplify further if necessary.
What is a complex fraction?
A rational expression with a fraction in the numerator, denominator, or both is referred to as a complex fraction.
There are two ways to solve a complex fraction -
Method 1 : Take an example - (1/3-1/4)/(1/8+1/2)
Step 1 - If necessary, combine the denominator and numerator into a single fraction.
Add the numerator -
=1/3-1/4
=(4-3)/12
=1/12
Add the denominator -
=1/8+1/2
=(1+4)/8
=5/8
Combine back to form a complex fraction -
=(1/12)/(5/8)
Step 2: Multiply the numerator by the denominator's reciprocal, then divide the result by the denominator.
Step 3: Simplify the rational expression if necessary.
=(1/12)×(8/5)
=8/60
=2/15
Method 2: Take an example - [(2x+1)/(x^2-25)]/[(4x^2-1)/(x-5)]
Step 1 - Divide the LCD of the smaller fractions by the numerator and denominator of the total complex fractions.
(x^2-25)=(x+5)(x-5)
The denominator of the denominator’s fraction has the following factor -
(x-5)
Using the highest exponent and combining all the other factors, we arrive at the LCD shown below for all the little fractions -
(x+5)(x-5)
By multiplying the LCD by the numerator and denominator -
=[{(2x+1)/(x+5)(x-5)}×(x+5)(x-5)]/[{(2x+1)(2x-1)/(x-5)}×(x+5)(x-5)]
=(2x+1)/(2x+1)(2x-1)(x+5)
Step 2 - Simplify the rational expression if necessary.
=(2x+1)/(2x+1)(2x-1)(x+5)
=1/(2x-1)(x+5)
Therefore, there are two methods to solve complex fractions.
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The sample points of a sample space are a equally likely events. b equally unlikely events. c simple events. d complex events.
The correct option is option A , the sample points of a sample space are equally likely events.
In probability when two the occurrence of two events are having a 50 - 50 possibility then those two events are said to be equally likely events. Example , on tossing a coin the probability of getting a H or a tail is 1/2 . Therefore, these events are said to be equally likely events.
Probability is a field of mathematics which tells us about the possibility of occurrence of an event. P = number of favorable outcomes / total number of outcomes , is the formula to calculate probability.
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A sample of 12th grade students who took the National Assessment of Education Progress year 2000 mathematics test had a mean score of 250. What is the population
On solving the provided question, we can say that by mean score the population will be 20192
What is mean?A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). Often referred to as the "mean," this is the most often used measure of central tendency. Simply dividing the dataset's total number of values by the sum of all of those values yields this result. Both raw data and data that have been combined into frequency tables can be used for calculations. Average refers to a number's average. It is straightforward to calculate:Divide by how many digits there are after adding up all the digits. the total divided by the count.
A sample of 12th grade students who took the National Assessment of Education Progress year 2000 mathematics test had a mean score of 250
200/4
= 50
50*e^{-2}
the population will be 20192
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tell which number is greater 56%, 5.6.
Answer:
5.6
Step-by-step explanation:
56% = 0.56
5.6 > 56%
Find the volume of the following figure.
(I need a answer to this very soon so if anybody can answer id really appreciate it :))
The volume of the prism is 103.32 cubic inches (optionD)
What is the volume of a prism?Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.
The formula for the volume of a prism is V=Bh , where B is the base area and h is the height.
The base area of the prism = 4.1×7.2 = 29.52 inches squared.
The height of the prism is 3.5 inches
Therefore volume = base area × height
volume = 29.52× 3.5 = 103.32 cubic inches.
Therefore the volume of the shape is 103.32 cubic inches.
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Trey and three of his friends are ordering a pizza. They plan to split the cost, and the want to spend at most $3.50 per person. Write and solve an inequality to find the cost of the pizza they should order.
The inequality to find the cost of the pizza they should order is c ≤ 14. The cost is at most $14.
How to express the inequality?Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.
Since Trey and three of his friends are ordering a pizza and they want to spend at most $3.50 per person. An inequality to find the cost of the pizza they can order is:
c ≤ (3.50 × 4)
c ≤ 14
The cost will be at most $14.
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Rewrite 21/3 as a whole number
Answer:
7
Step-by-step explanation:
As we want to find the whole number, and to do so we divide the numerator by the denominator. Since we are only interested in whole numbers, we ignore any numbers to the right of the decimal point.
21/3 = 7
What is the range of the function y = startroot x 5 endroot? y greater-than-or-equal-to negative 5 y greater-than-or-equal-to 0 y greater-than-or-equal-to startroot 5 endroot
The range of the function y = √(x +5) is y ≥ 0
What is the range of the function?The domain of a function is the set of all possible values of x
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
we have
y = √(x +5)
Remember that the radicand of the function must be greater than or equal to zero
so (x +5) ≥ 0
solve for x
x ≥ -5
The domain is the interval ----> [-5,∞)
For x= -5
y = √(-5 +5) = 0
so
The range is the interval ----> [0,∞)
y ≥ 0
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Write four different expressions for the perimeter of a square whose sides are all s 2 2 units long.
Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both.
What are expressions in maths?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression's structure is as follows: Expression: (Math Operator, Number/Variable, Math Operator)An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) You may think of expressions as being comparable to phrases. A phrase in language may contain an action on its own, but it does not constitute a whole sentence.For a square whose side are 2 units long is :
= 2 + 2 x 2 + 2
= ( 2 + 2 ) x 2
= 2 x 4
= 2 x 3 + 2 = 8
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Theater tickets sold for $7.50 on
the main floor and $, in the
balcony. The total revenue was
$3250, and there were 100 more
main-floor tickets sold than
balcony tickets. Find the number
of each type of ticket sold.
(in Substitution method)
Cant figure the work out :/
A school administrator wants to know what proportion of teachers in their state have a Master's degree. The administrator takes an SRS of 100100100 teachers from a statewide database containing every teacher, and they find 555555 teachers in the sample have a Master's degree. The administrator wants to use this data to construct a one-sample zzz interval for a proportion.Which conditions for constructing this confidence interval did their sample meet
When we construct the confidence interval their sample must have some conditions which are as follows,
The data should be a random sample from the population of interest.np^ ≥ 10 n(1 - p^) ≥ 10Individual observations can be taken as independent.Therefore , these are the conditions which the administrator should use to construct a one-sample z interval for a proportion.
When two ratios are equivalent to each other , they are said to be in a state called proportion. The proportion formula is used to see whether the given ratios or fractions are equal or not . The proportion formula can be given as, The product of means is equal to the the product of extremes. This can be written as ad = bc.
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I need help on these questions please help . ignore the writing
You will always get one triangle. This is because of the Triangle Angle Sum Theorem, which states that the sum of the measures of the angles of a triangle is always 180°.
What is triangle?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon.
The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.
The inner angles of every triangle sum up to 180°, 180°, 180°, 180°. Angles in a triangle are the total (sum) of the angles at each of its three vertices.
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[tex]h + 54 = 4 {}^{2} - 16 \div 4[/tex]
Value of h = ???
Answer:
[tex]h = -42[/tex]
Step-by-step explanation:
First, subtract 54 from both sides.
[tex]h = 4^2 - 16 \div 4 - 54[/tex]
Then, evaluate the right-hand expression using the order of operations:
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
We'll first evaluate the exponent in 4²:
[tex]4^2 = 4 \times 4 = 16[/tex]
[tex]h = 16 - 16 \div 4 - 54[/tex]
Next, we can evaluate the division:
[tex]16 \div 4 = 4[/tex]
[tex]h = 16 - 4 - 54[/tex]
Finally, perform the subtraction.
[tex]16 - 4 - 54 = -42[/tex]
[tex]h = -42[/tex]
Answer:
[tex] \sf \: h = - 42[/tex]
Step-by-step explanation:
Given equation,
→ h + 54 = 4² - 16 ÷ 4
Now the value of h will be,
→ h + 54 = 4² - 16 ÷ 4
→ h + 54 = 16 - 4
→ h + 54 = 12
→ h = 12 - 54
→ [ h = -42 ]
Hence, value of h is -42.