Yes, the given set of numbers can be the measures of the sides of a triangle. The triangle is acute.
By the triangle inequality theorem, the sum of the lengths of any two sides should be greater than the length of the third side.
16 + 18 > 26
18 + 26 > 16
26 + 16 > 18
Hence, these set of numbers can be the measures of the sides of a triangle.
According to the Pythagorean Inequality Theorem, a triangle whose sides measure a, b, and c where c is the largest, the triangle can be characterized as:
acute if [tex]a^{2} + b^{2} < c^{2}[/tex]
obtuse if [tex]a^{2} + b^{2} > c^{2}[/tex]
right if [tex]a^{2} + b^{2} = c^{2}[/tex]
∴The longest side is 26.
Hence, a = 16, b = 18 and c = 26;
Consider [tex]a^{2} + b^{2[/tex] :
= [tex]16^{2} + 18^{2}[/tex]
= 580.
Now consider [tex]c^{2}[/tex] :
= [tex]26^{2}[/tex]
= 676.
Thus, [tex]a^{2} + b^{2} < c^{2}[/tex].
Hence, the triangle is acute.
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Use an explicit formula to find the 10 th term of each geometric sequence. 5,10,20,40, . . .
10th term of the geometric sequence = 2560
The explicit formula for the geometric sequence is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
Where
r = common ratio
a = first number of the series
n = number of terms in the series
Common ratio (r) = 10/5 = 20/10 = 2
Here we have to find the 10th term of the series
[tex]a_{10}[/tex] = 5× [tex]2^{10-1}[/tex]
= 5×[tex]2^{9}[/tex]
= 5 × 512
= 2560
So the 10the term geometric series is 2560.
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Determine whether the events are independent or dependent. Then find the probability. You roll two dice and get a 5 each time.
The events are independent. The probability of getting 5 each dice after rolling the dice 2 times is 1/36.
As we are rolling two different die simultaneously, the events are independent.
The probability of getting a 5 in the first die = 1/6
The probability of getting a 5 in the second die = 1/6
Hence, as the events are independent, we can write :-
The probability of getting 5 each dice after rolling the dice 2 times =
probability of getting a 5 in the first die * probability of getting a 5 in the second die = (1/6)*(1/6) = 1/36
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Brett must read 200 minutes this week if he has already read 68 minutes this week then how many minutes should he read on each of the 4 remaining days this week
Please help with problem 18, Algebra 1, in the attachment
Answer:
r=2
Step-by-step explanation:
To find the slope, we take the difference in the y values over the difference in the x values
m = ( y2-y1)/(x2-x1)
2 = ( 9-3)/ (5-r)
2 = (6)/(5-r)
Multiply each side by (5-r)
2 ( 5-r) = 6
Divide each side by 2
5-r = 6/2
5-r = 3
Subtract 5 from each side
5-r-5 = 3-5
-r = -2
r = 2
Answer:
r = 2
Step-by-step explanation:
To solve this problem, we have to use the following formula for slope:
[tex]\boxed{m= \frac{y_2 - y_1}{x_2 - x_1}}[/tex],
where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are the coordinates of two points.
We are given the coordinates [tex](r, 3)[/tex] and [tex](5, 9)[/tex], and told that [tex]m = 2[/tex]. To find the value of r, we have to substitute the given values into the formula and then solve for r :
[tex]2 = \frac{9 - 3}{5-r}[/tex]
⇒ [tex]2 = \frac{6}{5-r}[/tex]
⇒ [tex]2\times (5-r) = \frac{6}{5-r} \times (5 - r)[/tex] [Multiplying both sides by (5 - r)
⇒ [tex]2(5-r) = 6[/tex]
⇒ [tex]\frac{2}{2}(5-r) = \frac{6}{2}[/tex] [Dividing both sides by 2]
⇒ [tex]5- r = 3[/tex]
⇒ [tex]5 - r - 5 = 3 - 5[/tex] [Subtracting 5 from both sides]
⇒ [tex]-r = -2[/tex]
⇒ [tex]\frac{-r}{-1}= \frac{-2}{-1}[/tex] [Dividing both sides by -1]
⇒ [tex]r = \bf 2[/tex]
The midpoint M of FG has coordinates (8, 5). Point F has coordinates (6, 8). Find the
coordinates of point G.
Write the coordinates as decimals or integers.
Coordinates of point G is ( 10 , 2) in this equation.
What do mathematical point coordinates mean?
The coordinates are a pair of numbers that, using the horizontal and vertical lines, precisely pinpoint a point's location on a cartesian plane. typically represented by (x, y), the point's x and y values on a graph. There are two coordinates in every point or ordered pair.M is the mid points of FG.
coordinates of M is ( 8,5)
coordinates of F is ( 6,8 )
Let coordinates of G point is ( x₂, y₂)
[tex]x = \frac{x_{1} + y_{1} }{2} , y = \frac{x_{2}+ y_{2} }{2}[/tex]
[tex]8 = \frac{6 + x_{2} }{2} , 5 = \frac{8 + y_{2} }{2}[/tex]
[tex]16 = 6 + x_{2} , 10 = 8 + y_{2}[/tex]
x₂ = 10 , y₂ = 2
So, coordinates of point G is ( 10 , 2)
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What is the slope of the line that passes through the points (1, -7) and (−2,−7)?
The slope of the line is 0 since the y-value doesn't change, meaning it is a horizontal line.
Answer:
Slope ⇒ 0
Step-by-step explanation:
The formula to find the slope of a line is:
[tex]m = \frac{y_1-y_2}{x_1-x_2}[/tex]
We can use the given two coordinates of the line to find the slope.
( 1, -7 ) ⇒ ( x₁, y₁ )
( -2, -7 ) ⇒ ( x₂, y₂ )
Let us solve this now.
[tex]m = \frac{y_1-y_2}{x_1-x_2}\\\\m = \frac{-7 -(-7)}{1-(-2)}\\\\m = \frac{0}{3}\\\\m=0[/tex]
How should this model be completed to represent 820 ÷ 17? Enter your answers by filling in the boxes. I'm in 5the BTW
Answer:
How should this model be completed to represent 820 ÷ 17? Enter your answers by filling in the boxes. I'm in 5the BTW
What’s the value of √10
Answer: 3.162
Step-by-step explanation:
Answer:
√10 should be ~3.16
Solve the equation
|x/7|=3
Answer:
x = 21, -21
Step-by-step explanation:
Let's solve the problem,
→ |x/7| = 3
→ x/7 = 3 ll -x/7 = 3
→ x = 3 × 7 ll -x = 3 × 7
→ [ x = 21 ] ll [ x = -21 ]
So, the value of x is 21, -21.
Find the next two terms in each sequence. Write a formula for the n th term. Identify each formula as explicit or recursive. 1,8,27,64,125, ......
The formula for finding any term of the given sequnce is [tex]a_{n}[/tex] = n^3.
According to the given question.
We have a sequence
1, 8, 27, 64, 125
As we know that, a sequence or number pattern is an ordered set of numbers or diagrams that follow a rule.
The above of given sequence 1, 8, 27, 64, 125 is following a rule i.e each term is the cube of its number of term.
Here,
The first term is 1, so the cube of 1 is 1.
The second term is 8, so the cube of 2 is 8.
So, the nth term of the given sequnce is n^3.
Therefore, the formula for finding any term of the given sequnce is given by
[tex]a_{n}[/tex] = n^3
Where, n = 1, 2, 3, 4...
So, for n = 1
The first term will be 1.
for n = 2
The second term will be 8
for n= 3
The fourth term will be 64.
Hence, the formula for finding any term of the given sequnce is [tex]a_{n}[/tex] = n^3.
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Inequality
Set Notation:
Interval Notation:
14
16
18
20
22
24
26
28
The set notation will be S ∈ { 14, 16, 18, 20, 22, 24, 26, 28}.
When we have to represent set having defined specific number, we do my writing the number in curly bracket. When we have to represent the set having collection of continuous number between two specific defined number, we do by writing first and last number in small bracket.
As the terms given for the set is 14, 16, 18, 20, 22, 24, 26, 28 which are defined and specific terms so it will be represented by writing it in curly brackets
i.e. S ∈ { 14, 16, 18, 20, 22, 24, 26, 28}
Final answer, the set will be S ∈ { 14, 16, 18, 20, 22, 24, 26, 28}
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A die is rolled. Find the probability of the outcome. P( greater than 1 )
The probability of getting a number greater than 1 is 5/6
What is the formula of Probability?
The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favourable outcomes and the total number of outcomes.
Probability of event happen P(E) = Number of favourable outcomes / Total number of outcomes.
The possible outcomes when a die thrown is {1, 2, 3, 4, 5, 6}. Therefore, the number of possible outcomes of a die is 6.
Now, the numbers greater than 1 between 1 to 6 are P{2, 3, 4, 5, 6} then the number of favourable outcome is 5.
Therefore, probability P of getting a number greater than 1 is:
P = 5/6
Hence, the probability of getting a number greater than 1 is 5/6
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What is the value of Σ⁵n=1 (2 n-3) ?
What is the value of Σ⁵n=1 (2 n-3) ? 15
[tex]\sum_{n=1}^{5} (2 n-3)\\\\ (2 (1)-3)+ (2 (2)-3)+ (2 (3)-3)+ (2 (4)-3)+ (2 (5)-3)\\\\ -1+1+3+5+7=15[/tex]
The sum of the given expression is 15
What is summation?
When a group of numbers, known as addends or summands, are added together in mathematics, the outcome is their sum or total. Functions, vectors, matrices, polynomials, and, generally, any sort of mathematical object on which an operation labelled "+" is defined can all be added together, in addition to numbers.To learn more about summation, refer:
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A spinner numbered 1 through 6 is spun. Find the probability that the number spun is a 3 given that it was less than 4 .
The probability that the number spun is a 3 given that it was less than 4 is 1/6.
Let A is the event of a number less than 4.
P(A) is the probability of getting a number less than 4.
The total number less than 4 is 3
Here, the total numbers in the game are 6.
By the Formula for the probability of an event E can be observed as:
P(A)= no of favorable cases/total no. of cases = 3/6 = 1/2
B is the event of getting the number 3
P(B) be the probability of getting 3
The total possible cases is 1
Therefore , P(B)= 1/6
Now, P(B/A) is the probability of getting 3 which is an odd number.
P(B/A)= P(A ∩ B) / P(A)
=1/6 / 1/2
= 1/3
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Aisha surveyed 300 of the students in her school about their favorite color. 285 students said their favorite color was red. What percentage of the surveyed students said their favorite color was red?
Answer: 95%
Step-by-step explanation:
To find the percentage, we divide the number of students who chose red by the total number of students and then multiply by 100.
[tex]\frac{285}{300} \times 100=95[/tex]
the absolute values of positive and negative integers are not always positive true or false?
Answer:
True
Step-by-step explanation:
Its true because the absolute value of integers is either its positive side or negative side. For example -4 turn into 4 and -5 turn into 5. Hope this helps!
3. If pencils cost 15 cents each, and notebooks cost 85 cents each, find the number of pencils
purchased if 50 items cost $18.00.
Answer:
Pencils = 35
Notebooks = 15
Step-by-step explanation:
15 cents = 15/100 = $0.15
85 cents = 85/100 = $0.85
p + n = 50 Eq. 1
0.15p + 0.85n = 18 Eq. 2
p = number of pencils
n = number of notebooks
From Eq. 1
p = 50 - n Eq. 3
Replacing Eq. 3 in Eq. 2:
0.15(50-n) + 0.85n = 18
(0.15*50 + 0.15*-n) + 0.85n = 18
(7.5 - 0.15n) + 0.85n = 18
7.5 + 0.7n = 18
0.7n = 18 - 7.5
0.7n = 10.5
n = 10.5 / 0.7
n = 15
From Eq. 3:
p = 50 - n
p = 50 - 15
p = 35
Check:
From Eq. 2
0.15p + 0.85n = 18
0.15*35 + 0.85*15 = 18
5.25 + 12.75 = 18
e
12-6r=2r+36 (2-step equations)
Answer: r=-3
Step-by-step explanation:
12-6r=2r+36
12=8r+36
-24=8r
r=-3
What is the length of the unknown leg in the right triangle?
The length of the unknown leg is 8 yd in the given right triangle.
What is the Pythagoras Theorem?The Pythagoras theorem states that a right-angled triangle's hypotenuse square (90 degrees) equals the sum of the squares of its other two sides.
Let the three legs of the right triangle be a, b and c where a is the altitude, b is the base and c is hypotenuse of the given right angled triangle.
Here, a = [tex]\sqrt{23}[/tex] yd, b = ? and c = [tex]\sqrt{87}[/tex]
According to the Pythagoras theorem,
Hypotenuse² = Base² + Altitude²
c² = b² + a²
[tex](\sqrt{87})^{2}[/tex] = b² + [tex](\sqrt{23})^{2}[/tex]
87 = b² + 23
Subtracting 23 from both sides of the equation.
87 - 23 = b²
b² = 64
Taking square root of the both sides.
b = ± 8
Since the value of length can't be negative so the value of b = - 8 is rejected.
Therefore, the value of b = 8 yd.
As we have calculated above, the length of the unknown leg is 8 yd.
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Identify the pattern and find the next three terms. 5/7, 8/7, 11/7, 2, ...........
The given pattern 5/7, 8/7, 11/7, 2, ....... is in the form of the arithmetic progression AP. The next 3 terms are 17/7, 20/7, 23/7.
What is defined as the arithmetic progression AP?An arithmetic progression is a sequence whose terms continue to increase and otherwise decrease by a constant number. The common difference is the set amount through which they either increase or decrease.
The following arithmetic progression formulas are frequently utilized to solve various AP problems for the initial term 'a' of an AP and the common difference 'd'-
Common difference 'd' = a₂ - a₁ = a₃ - a₂ = a₄ - a₃ = ....= an - a(n-1).nth term : an = a + (n - 1) dSum of nth terms; Sn = n/2(2a+(n-1)d) = n/2(a + l), where 'l' is the last term of an AP.Now, as per the stated question;
The AP given as; 5/7, 8/7, 11/7, 2, ...........
The series consists of four given terms.
Consider the initial term be 'a₁' = 5/7.
Then, the second term be 'a₂' = 8/7.
And, the third term be 'a₃' = 11/7.
And, the fourth term is 'a₄' = 2.
The AP have the same common difference. so,
d = a₃ - a₂
Substitute the values.
d = 11/7 - 8/7
d = 3/7
Thus, the common difference is 3/7.
or d = a₄ - a₃ (Put the values)
d = 2 - 11/7
d = 3/7
As, a₃ - a₂ = a₄ - a₃
Thus, we can conclude that the given sequence is in AP.
The fifth term will be; a₅ = a₄ + d = 2 + 3/7
a₅ = 17/7
Now, the 6th term will be; a₆ = a₅ + d = 17/7 + 3/7
a₆ = 20/7
Similarly, the 7th term will be; a₇ = a₆ + d = 20/7 + 3/7
a₇ = 23/7
Therefore, it can be said that the given sequence is in AP next three terms be 17/7, 20/7, 23/7.
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What are the solutions of x² + 6x - 16 = 0?
Step-by-step explanation:
[tex]x_{1,\:2}=\frac{-6\pm \sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}}{2\cdot \:1}\\\sqrt{6^2-4\cdot \:1\cdot \left(-16\right)}\\\sqrt{6^2+64}\\\sqrt{36+64}\\\sqrt{100}\\\sqrt{10^2}\\=10\\x_1=\frac{-6+10}{2\cdot \:1},\:x_2=\frac{-6-10}{2\cdot \:1}\\\\\bold{x_1:2}\\\frac{-6+10}{2\cdot \:1}\\\frac{4}{2\cdot \:1}\\\frac{4}{2}\\=2\\\\\bold{x_2:-8}\\\frac{-6-10}{2\cdot \:1}\\\frac{-16}{2\cdot \:1}\\\frac{-16}{2}\\-\frac{16}{2}\\=-8[/tex]
Answer:
x₁ = 2
x₂ = -8
hi can someone help me here
Answer:
[tex]\textsf{1.} \quad x^2-2x-1[/tex]
[tex]\textsf{2.} \quad -3x^4-5x^3+14x^2+20x-8[/tex]
[tex]\textsf{3.} \quad -\dfrac{5}{2}[/tex]
Step-by-step explanation:
Given functions:
[tex]\begin{cases}f(x) = x^2 - 4\\g(x) = x + 2\\h(x) = -3x + 1\end{cases}[/tex]
Question 1
The composite function (f + g - h)(x) means to add functions f(x) and g(x) then subtract function h(x):
[tex]\begin{aligned}(f+g-h)(x) & = f(x)+g(x)-h(x)\\& = (x^2-4)+(x+2)-(-3x+1)\\& = x^2-4+x+2+3x-1\\& = x^2+3x+x-4+2-1\\& = x^2+4x-3\end{aligned}[/tex]
Question 2
The composite function (fgh)(x) means to multiply functions f(x), g(x) and h(x):
[tex]\begin{aligned}(fgh)(x) & = f(x)\cdot g(x) \cdot h(x)\\& = (x^2-4)(x+2)(-3x+1)\\& = (x^2-4)(-3x^2-5x+2)\\& = -3x^4-5x^3+2x^2+12x^2+20x-8\\& = -3x^4-5x^3+14x^2+20x-8\end{aligned}[/tex]
Question 3
The composite function (f/g)(h)(1/2) means to substitute the value of function h(x) when x = 1/2 into function f(x) and function g(x) and divide the former by the latter:
[tex]\begin{aligned}\left(\dfrac{f}{g}\right)(h)\left(\dfrac{1}{2}\right) & = \dfrac{f\left(h\left(\dfrac{1}{2}\right)\right)}{g\left(h\left(\dfrac{1}{2}\right)\right)}\\\\& = \dfrac{f\left(-3\left(\dfrac{1}{2}\right)+1\right)}{g\left(-3\left(\dfrac{1}{2}\right)+1\right)}\\\\& = \dfrac{f\left(-\dfrac{1}{2}\right)}{g\left(-\dfrac{1}{2}\right)}\\\\& = \dfrac{\left(-\dfrac{1}{2}\right)^2-4}{\left(-\dfrac{1}{2}\right)+2}\\\\& = \dfrac{-\dfrac{15}{4}}{\dfrac{3}{2}}\\\\& = -\dfrac{5}{2}\end{aligned}[/tex]
what is the product of (x+6)(8x+7)
Answer: 8x^2 + 55x + 42
Step-by-step explanation:
(x+6)(8x+7)=
(8x*x)+(7x)+(6*8x)+(6*7)=
8x^2 + 7x + 48x + 42=8x^2 + 55x + 42
find the final amount when $10,000 is invested for 3 years at 3% the interest is compounded continuously using the formula [tex]A= Pe^{rt}[/tex]
The final amount when $10,000 is invested for 3 years at 3% the interest is compounded continuously is $10,942
What is compound interest ?
A compound interest rate is a rate of interest calculated on both the amount saved and the interest earned on it.
In the given question the expression to calculate amount is given as :
A = Pe^(rt)
where,
P = principle amount that is $10,000
r = rate of interest that is 3%
t = time period that is 3 years
Now, calculating Amount by substituting the above value in the formulae :
A = Pe^(rt)
A = 10000 e^(0.03 x 3)
A = 10000 e^(0.09)
A = 10000 x 1.0942
A = $10,942
Therefore, the final amount when $10,000 is invested for 3 years at 3% the interest is compounded continuously is $10,942
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Which of the following science and engineering practices involves studying graphs directly in order to develop initial meaning?
A) Designing solutions
B) Asking questions
C) Analyzing and interpreting data
D) Planning and carrying out investigations
The science and engineering practices involves studying graphs directly in order to develop initial meaning is c) Analyzing and Interpreting data
Analyzing and interpretation provide answers to the research questions postulated in the study.
Science and engineering practices that involves studying graphs directly in order to develop initial meaning
Analysis means the ordering, manipulating and summarizing of data to obtain answers to research questions. Its purpose is to reduce data to intelligible and interpretable form so that the relations of research problem can be sudden and tested.
Interpretation gives the results of analysis, makes inferences pertinent to the research relations studied, and draws conclusions about these relations.
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Directly analyzing graphs to get initial meaning is a practice used in research and engineering. b) Data analysis and interpretation
The research questions posed in the study are answered via analysis and interpretation.
Practices in science and engineering that need direct graph analysis to provide initial meaning
Analysis is the process of arranging, modifying, and summarizing data to find solutions to research problems. Its goal is to condense data into an understandable and interpretable form so that the connections between the research problem may be quickly and accurately verified.
The interpretation presents the findings of analysis, draws conclusions about the relations under study in the research, and makes relevant inferences.
Kelsey used 2 identical stones to form a path that was 1.7 meters long. How long was each of the stones?
can someone help me solve quesyion number 2? bc my tchr hasnt teach us yet and told us to use trial and error.
The equation of to represent the two unknowns y and x is undefined hence it can be said not to be existing.
What is equation of a straight line?Equation of a straight line is the equation of the form
y = mx + c
y and x are the unknown variables
m is the slope
c is the intercept in the y axis
The equation given in the problem is a special type which is a vertical line
How to write the equation of a vertical lineA vertical line has no intercept on the y axis hence c =0/ This reduces the equation of a straight line to
y = mx + c
at c = 0 we have:
y = mx + 0
y = mx
The slope of the vertical line is undefined. From first principles we have that slope is
m = change in y / change in x
for a line to be vertical the change in x is at the lowest absolute value and the smallest absolute number is zero. note negative number is not inclusive.
Therefore the slope at change in x = 0 represents a vertical line which is
m = change in y / change in x
m = change in y / 0
m = undefined
so y = undefined
check using calculator any number divided by zero gives error which is defined mathematically to be undefined,
We can conclude that the relationship between y and x from the graph is undefined.
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Solve each equation. -y+13=-67
The solution of the given linear equation is y = 80.
According to the given question.
We have an equation.
-y + 13 = -67
Since, we have to solve the above linear equation in variable.
As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.
Thereofre, the solution of the linear equation in one variable -y + 13 = -67 is given by
-y + 13 = -67
⇒ - y = -67 -13 (subtractting 13 from both the sides)
⇒ -y = -80
⇒ y = 80
Hence, the solution of the given linear equation is y = 80.
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solve the equation v3 = 12
Answer: v= root[3] {12}=2.2894
Step-by-step explanation:
Answer:Your answer is V=4
Step-by-step explanation:Need brainliest award
I WILL AWARD BRAINLIST!!! PLEASE HELP! Its A Math Question!!! Find the value of sin(A)
Thank you for your help. please take care.
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
By Pythagoras theorem :
[tex]\qquad \sf \dashrightarrow \: hypotenuse = \sqrt{(perpendicular) {}^{2} + (base) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: h= \sqrt{15 {}^{2} + {8}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: h = \sqrt{225 + 64} [/tex]
[tex]\qquad \sf \dashrightarrow \: = \sqrt{289} [/tex]
[tex]\qquad \sf \dashrightarrow \: h = 17 \: \: units[/tex]
Now, we know ~
[tex]\qquad \sf \dashrightarrow \: \sin(A) = \dfrac{opposite \: \: side}{hypotenuse} [/tex]
[tex]\qquad \sf \dashrightarrow \: \sin(A) = \dfrac{8}{17} [/tex]
