By using a² + b² = c² this formula we can find the missing length of a triangle.
A triangle is right-angled if one of the three angles is 90°, i.e., any two sides are perpendicular.
If we know two other sides of the right triangle, all you need to do is apply the Pythagorean theorem:
a² + b² = c²
If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root:a = √(c² - b²)
If leg b is unknown, then:b = √(c² - a²)
For hypotenuse c missing, the formula is:c = √(a² + b²)
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What are the multiples of 42?
The first 10 multiples of 42 are as follows:
42, 84, 126, 168, 210, 252, 294, 336, 378, 420.
What are multiples?In mathematics, multiplying any number by integer results in a multiple.
In other terms, it can be argued that b is a multiple of the supplied two numbers, a, and b if b = na for some integer n, known as the multiplier.
This is comparable to saying that if an is not zero, then b/a is an integer.
When a and b are both integers and b is a multiple of a, then an is said to be a divisor of b.
So, the multiples of 42 are:
42, 84, 126, 168, 210, 252, 294, 336, 378, 420
Therefore, the first 10 multiples of 42 are as follows:
42, 84, 126, 168, 210, 252, 294, 336, 378, 420.
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Correct question:
What are the first 10 multiples of 42?
For the polynomial function f(x) = -2x4 + 8x2 - 8, find all local and global extrema.
A.) No global extrema exist.
B.) The only extrema point is (0, -8).
C.)The local and global extrema are: (-√2.0), (0.-8) and (√2.0).
D.)No local extrema exist.
The derivative for [tex]y=eu(x)[/tex]; [tex]u(x)[/tex] is a function in terms of [tex]x[/tex] is [tex]\frac{dy}{dx}[/tex]=[tex]eu'(x)[/tex]+ [tex]u(x)e[/tex].
Definition of derivative-A derivative is the rate of change of a function with respect to a certain variable . Derivatives are fundamental to the solution of problems in calculus and differential equations.
There are certain rules of differentiation which help us to evaluate the derivatives of some particular functions. :
Power Rule.
Sum and Difference Rule.
Product Rule.
Quotient Rule.
Chain Rule.
Given: [tex]y=eu(x)[/tex]
Explanation:-This equation can be solved using the product rule of derivatives .
According to the product rule derivative of uv will be taken as -
u(v)' + v(u)'
where (') represents derivative of the variable.
Therefore accordingly, [tex]y=eu(x)[/tex]
Differentiating with respect to [tex]x[/tex],
[tex]\frac{dy}{dx} =e(u(x))'+u(x)(e')[/tex]
[tex]\frac{dy}{dx} =eu'(x)+u(x)e[/tex]
So, finally the derivative of the function in terms of x is [tex]\frac{dy}{dx}[/tex] = [tex]eu'(x)+[/tex][tex]u(x)e[/tex]
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which two figures of the following labels correctly refer to the angels shown in the figure?
A.
B.
C.COD
D.
Which tool is used to make chart 1 look like chart 2 in Excel?
The answer is data labels tool.Data Labels tool is used make chart 1 look like chart 2.When you select the chart and right click and select the option to add data labels.So the required labels will be displayed.
what is excel chart?A chart is a visual display of data in which the data is displayed by symbols such as bars in a bar chart or lines in a chart.It can help people to understand information easily.
How many types of charts?There are following types of charts.
column charts
line charts
bar charts
area charts
pie charts
Now for opening chart tools in excel.you can
click the insert tab and then click the arrow next to chart.click chart type and then double click the chart you want to add.So you can insert chart into excel sheet.
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NEED HELP!!!
The graph shows a linear relationship between y, the number of bicycles, and x, the number of tires.
Which statement is true?
Select TWO correct answers.
A. Range: {0, 1, 2, 3, 4, 5}
B. Domain: {0, 1, 2, 3, 4, 5}
C.Range: {0, 2, 4, 6, 8, 10}
D. Domain: 0 ≤ x ≤ 5
E. Domain: {0, 2, 4, 6, 8, 10}
F. Range: 0 ≤ y ≤ 10
The Range={0, 1, 2, 3, 4, 5}
Domain={0, 2, 4, 6, 8, 10}
So, options A and E are correct.
What is meant by range and domain?Its arguments are a group of values that can be plugged into a function's domain. This set includes the x values for a function like f(x). Its range refers to the set of digits that the function considers. The function prints these values in the order they are entered after the insertion of an x value.
Another approach to defining the scope and range of functions is through the use of graphs. Since "domain" refers to the set of possible input values, the full set of input values shown on the x-axis is the domain of a graph. On the y-axis, the range's varied output values are visible.
From the graph the points are (0, 0), (1, 2), (2,4), (3,6), (4,8), (5,10)
So, Range={0, 1, 2, 3, 4, 5}
Domain={0, 2, 4, 6, 8, 10}
Therefore, options A and E are correct.
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Is algebra 8th or 9th grade?
Algebra is advised for ninth grade, and pre-Algebra is taught in eighth grade, according to the Common Core standards that California enacted two years ago and is just now starting to apply.
what is algebra ?In algebra, definite or fixed numbers with values like 2, 9, 0.068, etc. are used. Introduction to algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are only a few of the many sub-disciplines of algebra.
here ,
The option to take it in the eighth grade may be given to students who demonstrated extraordinary potential in the subject.
Algebra is often taught in the eighth grade in many schools today, while certain students who meet a certain threshold can finish the subject in the lower grades.
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suppose i work at a call center and i have to track the urgency of the incoming calls. in one day, i had 20 calls. 5 were classified as urgent and 15 were classified as no rush. what is the mode of this data?
The mode of the data at the call center will be 15 which are the non urgent s that was received.
What is the mode of a data set?The mode of a data set is defined as the value of the set of data that appeared or occurred the most. When two values have the same number of occurrences or frequency, it is said that the data set is bimodal or has two modes.
From the scenario given,
The number of calls received in a day = 20 calls.
The number of calls that are urgent = 5
The number of calls that are not urgent = 15
Therefore, the mode of this data set would be the number of non urgent calls which is 15.
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How do you solve a 2x2 matrix 2x2?
To solve a 2x2 matrix equation of the form Ax = b, where A is a 2x2 matrix, x is the variable (a column vector), and b is a known column vector.
You can use the following steps:
Find the inverse of the matrix A. This will allow you to multiply both sides of the equation by A^(-1), which will isolate the variable x on the left side of the equation.To find the inverse of a 2x2 matrix A, use the following formula:A^(-1) = (1/det(A)) * adj(A)
where det(A) is the determinant of matrix A and adj(A) is the adjugate of matrix A. The transposition of a matrix's cofactor matrix is adjugate. The cofactor matrix is a matrix of the determinants of the minors of the original matrix, each of which is multiplied by a cofactor (-1)^(i+j). The minors of a matrix are the determinants of the square submatrices formed by deleting one row and one column from the matrix. The determinant of a matrix is a scalar value that can be computed from its elements.
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what is the 95% confidence interval for the difference in the two means (construction site minus undisturbed location)?
The 95% confidence interval for the difference in the two means = (-2.56 , 0.16)
What is Confidence Interval?
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Given,
Sample statistics size(n) mean(x) s.d(s)
Construction site 16 x₁ = 5.584 1.812
Undistributed Location 16 x₂ = 6.789 1.945
Standard error = 0.665
Degree of freedom = 30
Critical T-value for 95% confidence interval is 2.0423
The 95% confidence interval for the difference in the two means
(construction site - undistributed location)
= x₁ -x₂ ± (t-value) (standard error)
= 5.584 - 6.786 ± (2.0423) (0.665)
= -1.2020 ± 1.358130
= (-1.2020 - 1.358130 , -1.2020 + 1.358130)
= (-2.56 , 0.156)
= (-2.56 , 0.16)
for complete question see the attachment
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Given,
Sample statistics size(n) mean(x) s.d(s)
Construction site 16 x₁ = 5.584 1.812
Undistributed Location 16 x₂ = 6.789 1.945
Standard error = 0.665
Degree of freedom = 30
Critical T-value for 95% confidence interval is 2.0423
The 95% confidence interval for the difference in the two means
(construction site - undistributed location)
= x₁ -x₂ ± (t-value) (standard error)
= 5.584 - 6.786 ± (2.0423) (0.665)
= -1.2020 ± 1.358130
= (-1.2020 - 1.358130 , -1.2020 + 1.358130)
= (-2.56 , 0.156)
= (-2.56 , 0.16)
How many solutions will the linear equation 2x 5y 7 has?
The linear equation 2x + 5y = 7 has infinitely many solutions.
In this question we need to determine the number of solutions of the linear equation 2x + 5y = 7.
We know that an equation of the form ax + by + c = 0, where a, b and c are real numbers such that a ≠ 0 and b ≠ 0, is called as a linear equation in two variables.
Also as we know a linear equation in two variables has infinitely many solutions. The graph of linear equation in two variables is a straight line. Every point on the straight line represents a solution of the linear equation.
Here we have a linear equation in two variables 2x + 5y = 7.
By rearranging given linear equation we get,
5y = 2x - 7
y = (2x - 7)/5
Here we will get different values of y for different values of x
Therefore, the linear equation has infinitely many solutions.
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find the indicated critical value z0.11(round to two decimal places as needed.
The indicated critical value of z₀.₁₁ is 0.54.
What does it mean round to two decimal places?
The second place to the right of the decimal point, or the hundredths place, is used to round a decimal value to two decimal places. For instance, you can round 2.83620364 to two decimal places as 2.84 and 0.7035 to two decimal places as 0.70.
A crucial value is the test statistic's value that establishes a confidence interval's upper and lower boundaries or the level of statistical significance for a given test.
The critical value of z₀.₁₁ is z₀.₁ ₊ ₀.₀₁ = 0.5438
The round to two decimal places of 0.5438 is 0.54.
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The total of the age of Ann, Bob and Chri i 31 year. What will the total of their age be in three year’ time?
The total of their age be in three years time is 40 years.
As per the given data:
The total of the age of Ann, Bob and Chri is 31 years.
Let the present age of Ann is 'x' years.
Then the age of Ann after 3 years will be x+3
Let the present age of Bob is 'y' years.
Then the age of Bob after 3 years will be y+3
Let the present age of Chri is 'z' years.
Then the age of Chri after 3 years will be z+3.
The total of the age of Ann, Bob and Chri is 31 years.
x + y + z = 31.....(i)
The total of the age of Ann, Bob and Chri after 3 years is ( x + 3 + y + 3 + z + 3 ) years.
= ( x + 3 + y + 3 + z + 3 )
= ( x + y + z + 9 )
From equation (i)..... ( x + y + z = 31 )
= 31 + 9
= 40 years
Therefore the answer is 40 years.
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What is the nature of roots of 2x² 6x 3 0?
Answer:
The roots are imaginary.
Step-by-step explanation:
⭐ What is "the nature of the roots"
The nature of the roots are how the roots of a quadratic exist.⭐What are the different types of "the nature of the roots"?
The roots could be real numbers, distinct, and rational/irrationalThe roots could be real, equal, and rationalThe roots could be imaginary⭐How do we determine "the nature of the roots"?
Substitute the values of the coefficients (a,b, and c) of a quadratic equation into the quadratic formula( [tex]x =\frac{ -b+/-\sqrt{b^2-4ac} }{2a}[/tex])If the value of the discriminant in the quadratic formula ([tex]b2-4ac[/tex])>0: the roots are real numbers, distinct, and rational/irrationalIf the value of the discriminant in the quadratic formula ([tex]b2-4ac[/tex])=0: the roots are real, equal, and rationalIf the value of the discriminant in the quadratic formula ([tex]b2-4ac[/tex])<0: the roots are imaginaryTo solve this problem, substitute the values of the coefficients of the given quadratic equation into the quadratic formula:
[tex]x =\frac{ -6+/-\sqrt{6^2-4(2)(30)} }{2(2)}[/tex]
Now, compute only the discriminant ([tex]b^2-4ac[/tex]).
[tex]b^2-4ac = 36-4(60)[/tex]
[tex]b^2-4ac = 36-240[/tex]
[tex]b^2-4ac = -204[/tex]
[tex]b^2-4ac[/tex]< 0. Therefore, the roots are imaginary.
the probability that the same kayla will score above 80% on a mathematics test is 0.70. kayla will take four tests this semester. we want to find the probability she will score above 80% on exactly three out of the four tests. what is the probability of kayla scoring above 80% on exactly three out of the four tests?
The probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.
Probability
Given that the probability Kayla will score above 70% on a mathematics test is 0.60, and Kayla will take four tests this semester, and we want to find the probability she will score above 70% on exactly three out of the four tests, to determine what is the probability of Kayla scoring above 70% on exactly three out of the four tests, the following calculation must be performed:
0.6 x 0.6 x 0.6 x 0.4 = X
0.216 x 0.4 = X
0.0864 = X
0.0864 x 100 = 8.64
Therefore, the probability of Kayla scoring above 70% on exactly three out of the four tests is 8.64%.
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What are the 4 ways to write a solution to an inequality?
Compare kx <5 and kx =5 for any nonzero number k.
(Hint: Pick a value of k and discuss the graph of the inequality versus the graph of the equation.)
The graph of k x = 5 will be a line parallel to Y axis and the graph of k x < 5 will be the region where the value of x does not exceed 5/k.
What is Linear Inequality?Linear Inequalities are the expressions which have a left and a right hand side connected with inequality signs like >, <, ≥ and ≤.
Consider k x = 5
⇒ x = 5/k
This means that, for a nonzero constant k, the value of x will be the same throughout, which is 5/k.
If k = 1, then the value of x will be 5 throughout.
If k = 2, then the value of x will be 5/2 = 2.5 throughout.
and so on.
So the graph of k x = 5 will be a line parallel to the Y axis passing through the point x = 5/k for some constant k.
Now let us consider k x < 5.
⇒ x < 5/k
This means that for any nonzero constant k, the value of x will not be equal or never exceed 5/k.
If k = 1, then the value of x will be less than 5 throughout.
If k = 2, then the value of x will be less than 5/2 = 2.5 throughout.
and so on.
So the graph of k x < 5 includes the region where value of x does not exceed 5/k.
Hence the graph of k x = 5 and k x < 5 is a line parallel to Y axis and the region which does not exceed 5/k respectively.
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1.5(x-5)=1 solve for x
Answer: 5.66
Step-by-step explanation:
1.5(x-5)= 1
1.5x - 7.5 = 1
Add 7.5 on both sides
1.5x = 8.5
Divided 1.5 into both sides
x = 5.66
what does 12 times a number g mean?
Answer:
The Answer is 12 g because 12* g =12g
The ratio of soccer balls to basketballs at Andrew’s school is shown on the ratio table. What number completes the ratio table to make an equivalent ratio? [Type your answer as a number.]
soccer balls 30 ?
basket balls 25 5
Answer:
10
Step-by-step explanation:
30-25=5
10-5=5
30:10
25:5
Find the slope between each points.
(-8,18) and (-14,-3)
Answer:
the slope between the two points is 3.5.
Step-by-step explanation:
To find the slope between two points, you can use the formula: slope = (y2 - y1) / (x2 - x1). Plugging in the coordinates for the two points, we get: slope = (-3 - 18) / (-14 - (-8)). Simplifying the expression, we get: slope = -21 / -6Which simplifies to slope = 3.5, So slope between the two points is 3.5.
Answer:
Slope: 7/2
Step-by-step explanation:
Slope formula:
m=(y2-y1)/(x2-x1) ==> where m=slope, (x1, y1), (x2, y2)
(x1, y1), (x2, y2) ==> (x1=-8, y1=18), (x2=-14, y2=-3)
m=(-3-18)/(-14-(-8)) ==> plugin y2=-3, y1=18 and x2=-14, x1=-8
m=(-(3+18))/(-14+8)
m=(-21)/(-6) ==> simplify
m=21/6 ==> m=7/2
The difference between a number p and 6 is -14
Equation:
Solution:p=
The value of p in the equation p - 6 = -14 is -8.
What is the value of p in the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this situation, the difference between a number p and 6 is -14.
It should be noted that the equation van be illustrated as:
p - 6 = -14
Collect like terms
p = -14 + 6
p = -8
The value of p is -8.
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What is the range of f )= 4?
Answer: the range is 4
Step-by-step explanation:
Is 12345 divisible by 3?
Yes it is divisible by 3. A number is fully divisible by three if its digit sum is also divisible by three, according to the rule of divisibility for three.
what is divisibility test?The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.
here
add all the numbers,
1 + 2+ 3 + 4+ 5 = 15
and 15/3 = 5
so it is divisible by 3
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Carlos plays an arcade game. The scatter plot shows his score and the number of minutes
he plays. A good line of fit is drawn through the points (6, 50) and (12, 80).
What is the slope of the line of fit?
m =?
Answer:
The slope of this line (m) is 5
Step-by-step explanation:
Slope is the change in y over the change in x.
The y values are 80 and 50 (6,50) (12,80) You find the change by subtracting these values
80 -50 = 30
The x values are 12 and 6 (6,50) (12,80) You find he change by subtracting these values.
12 - 6 = 6
[tex]\frac{30}{6}[/tex] this reduces to 5
a pet shop pays $40 for a dog bed, and then sells it to a customer for $75. what is the percent markup
How many different possible outcomes are there when two six sided dice are rolled?
Answer:
36 different ones
Step-by-step explanation:
When two dice are rolled, there are now 36 different and unique ways the dice can come up. This figure is arrived at by multiplying the number of ways the first die can come up (six) by the number of ways the second die can come up (six)
What is the value of TT in math?
Answer:
22/7 or 3.14
the value of pie is 22/7 or if you write it in decimals it will be 3.14.
Is 5 A All real number?
Yes, 5 is a all real number.
What is real number?A real number is a number that can take on any value on the real number line, which is an infinite line that extends from negative infinity to positive infinity. Real numbers are used in mathematics to represent quantities such as distance, area, and time. They can also be used to represent irrational numbers, such as pi, and numbers with recurring decimals, such as 1/3.
A real number is any number that is either a rational number (fractions and whole numbers) or an irrational number (numbers that cannot be expressed as a fraction or a whole number). This includes all integers, fractions, and decimals. 5 is an integer, so it is included as a real number.
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In which number does the digit 6 have a value that is 10 times as great as the digit 6 in the number 62,045?
A. 640,488
B. 814,694
C. 28,367
D. 56,808
The number where the digit 6 have a value that is 10 times as great as the digit 6 in the number 62,045 is A. 640,488.
How to illustrate the place value?It should be noted that a place value is the value that is represented based on the position of a number.
In this case, the digit of 6 in 62,045 is 60000. From the options, the digit of 6 in 640488 is 600000. This is 10 times the value.
Therefore, the number where the digit 6 have a value that is 10 times as great as the digit 6 in the number 62,045 is 640,488. The correct option is A.
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What is y =- 3 on a graph?
Answer:
A line.
Step-by-step explanation:
Graphing y = -3 will give you a horizontal line 3 units below the x-axis.
To imagine this, we can create a bunch of points, each with a y coordinate of -3. For example: (-2, -3), (-1, -3), (3, -3), (6,-3). Graphing these will lead to a horizontal line!