The leg length is 9/ root2
Here we are given a right angle triangle , and in a right triangle , sum of squares of sides is equal to the square of hypotenuse.
[tex]a^{2}+b^{2} =c^{2}[/tex]
This is right angle scalene triangle as the two angles other than right angle are 45° each.
Hence ,
In this case we have
[tex]a^{2}+a^{2} =c^{2}[/tex]
[tex]2a^{2}=c^{2}[/tex]
[tex]a^{2}=\frac{c^{2} }{2}[/tex]
Taking square roots on both sides
[tex]a=\frac{c}{\sqrt{2} }[/tex]
Here we have hypotenuse c given as 9
Hence, the leg length is [tex]a =\frac{9}{\sqrt{2} }[/tex]
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Find the first five terms of each sequence. a n =-2 n+3
The formula for estimating the nth term of an arithmetic sequence is:
a n = a₁ + (n-1)d
The first five terms of a n = -2n + 3 = 1, -1, -3, -5, -7
What is meant by arithmetic sequence?A succession of numbers merged together to make a sequence exists comprehended as an arithmetic sequence.
A series of numbers named an arithmetic progression or arithmetic sequence (AP) contains a constant difference between the terms.
The formula for estimating the nth term of an arithmetic sequence exists:
a n = a₁ + (n-1)d
The four quantities in the formula exist a n, a₁, n, d.
The first 5 terms are a n = -2n + 3
a₁ = -2 + 3 = 1
a2 = -4 + 3 = -1
a3 = -6 + 3 = -3
a4 = -8 + 3 = -5
a5 = -10+3 = -7
Therefore, the first 5 terms of the sequence be 1, -1, -3, -5, -7.
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Rob has $1.65 in nickels and dimes.He has 25 coins in all. How many of each kind of coin are there
rob has 8 dimes and 17 nickels in $1.65
WHAT ARE LINEAR EQUATION ?There is only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All the points fall on the same line when the values that together make a linear equation true are determined and plotted on a coordinate grid.
CALCULATIONLet n represent nickels & d dimes
given: n + d = 25 #1 (number of coins)
given: .05n + .10d = 1.65 #2 (amount in dollars)
n = 25 - d #3 (rewrite of #1)
.05(25 -d) + .10d = 1.65 (substitute #3 in #2)
1.25 - .05d + .10d = 1.65 (multiply out the left side)
.05d = .40 (collection of like terms)
d = 8 (divided both sides by.05)
n + 8 = 25 (substitute answer for d in #1)
n = 17 (subtract both sides by 8)
There are 8 dimes and 17 nickels.
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You buy a new car for $22,000. The value of the
car decreases by 12.5% each year.
Answer:
Thus the value of the car decreases by $2,750 every year.... Making it $19,250 in the first year and $16,500 in the second
Step-by-step explanation:
12.5/100×22,000
2750
What is y-8={3}(x+1)y−8=3(x+1)y, minus, 8, equals, 3, left parenthesis, x, plus, 1, right parenthesis written in standard form?
The equation written in standard form is expressed as 3x - y = -11
Linear equation in standard formThe standard form of a linear equation is expressed as Ax + By = C
Given the equation below;
y - 8 = 3(x+1)
Expand
y- 8 = 3x + 3
Collect the like terms
y-3x = 3 + 8
y - 3x = 11
-3x + y = 11
3x - y = -11
Hence the equation written in standard form is expressed as 3x - y = -11
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I'm more sophisticated than my little sister. I save my money in a bank account that pays me 3% interest on the money in the account at the end of each month. (If I take my money out before the end of the month, I don't earn any interest for the month.) I started the account with $50 that I got for my birthday. How much money will I have in the account at the end of 10 months? How many months will it take to have at least $100? Justify your answer with a mathematical model of the problem situation.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months}\dotfill &10 \end{cases} \\\\\\ A=50\left(1+\frac{0.03}{1}\right)^{1\cdot 10} \implies A=50(1.03)^{10}\implies A \approx \text{\LARGE 67.20}[/tex]
well, let's check how long till you'd have $100 first
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$100\\ P=\textit{original amount deposited}\dotfill &\$50\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ n= \begin{array}{llll} \textit{times it compounds per \underline{month}} \end{array}\dotfill &1\\ t=\underline{months} \end{cases}[/tex]
[tex]100=50\left(1+\frac{0.03}{1}\right)^{1\cdot t} \implies 100=50(1.03)^t\implies \cfrac{100}{50}=1.03^t \\\\\\ 2=1.03^t\implies \log(2)=\log(1.03^t)\implies \log(2)=t\log(1.03) \\\\\\ \stackrel{\textit{about 23 months and 13 days}}{\cfrac{\log(2)}{\log(1.03)}=t\implies \text{\LARGE 23.45}\approx t}[/tex]
Solve the equation. 125x³+216=0 .
1/3 divided by 7/9 solution
Answer:
3/7.
Step-by-step explanation:
1/3 / 7/9
Invert the 7/9 and multipliply:
= 1/3 * 9/7
= 9 / 21
= 3/7
An aeroplane flies 500km in one hour. How long does it take to f a distance of 10925km? for class 4
Answer:
It will take 22 hours
Step-by-step explanation:
10925 ÷ 500 = 21.9 = 22 hours
how to do:
5n - 7n = 14
Please show the step by step process! (:
Answer: n=-7
Step-by-step explanation:
5n - 7n = 14
(5-7)n=14
-2n=14
-2n/(-2)=14/(-2)
n=14/(-2)
n=-7
The equation is,
→ 5n - 7n = 14
Solving for the value of n,
→ 5n - 7n = 14
→ -2n = 14
→ n = -(14//2)
→ [ n = -7 ]
Thus, the value of n is -7.
help me number 2 please
The following volume quantities are listed below:
a) 2 pints, 1 qt
b) 12 pints, 6 qt
c) 5 pints, 2.5 c
d) 6.75 pints, 3.375 fl oz
How to convert an unit to another by using unit conversions
In this question we must transform a quantity in a unit to another quantity in a unit of the same kind. For instance, if we have a quantity in a mass unit, then we only can convert it into another mass unit.
Herein we have four unit conversion cases for volumes, both pints and quarts are volume units commonly used in the United States. There are the following equivalencies:
1 quart = 2 pints = 4 cups = 32 fluid ouncesNow we proceed to convert each quantity to pints and quarts by cross multiplication:
a) 32 fl oz × 2 pints / 32 fl oz = 2 pints, 32 fl oz × 1 qt / 32 fl oz = 1 qt
b) 24 c × 2 pints / 4 c = 12 pints, 24 c × 1 qt / 4 c = 6 qt
c) 10 c × 2 pints / 4 c = 5 pints, 10 c × 1 qt / 4 c = 2.5 c
d) 108 fl oz × 2 pints / 32 fl oz = 6.75 pints, 108 fl oz × 1 qt / 32 fl oz = 3.375 fl oz
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Six years ago, Lucia’s age was 1/3 the age she will be in 6 years. How old is Lucia now? Enter an integer.
Answer:
Lucia is 12 years old now
Over the last 3 evenings, Heather received 61 phone calls at the call center. She received 7 more calls on the second evening than on the first evening. On the third evening, she received 2 times as many calls as the second evening. How many phone calls did she receive each evening?
Answer:
for real even great Britain cant get this because ya
Step-by-step explanation:
Simplify.
8√2 / 6-3√8
The rationalized expression in general term is given by: (-8 -4√2) / 3
What is rationalization?Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.
As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.
(8√2 / 6-3√8 ) Multiply by ( 6+3√8)/( 6+3√8)
(8√2 / 6-3√8 )( 6+3√8)/( 6+3√8)
8√2(6+3√8) / (6-3√8)² Expand the denominator using the FOIL method.
8√2(6+3√8) / (36 - 18√8 + 18√8 - 72)
8√2(6+3√8) / -36
48√2 + 24√2√8 / -36 ::::. √8 = 2√2
48√2 + 96 / -36
-12(4√2 + 8) / 12x3
(-8 -4√2) / 3 is the result.
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Create Write a real-world situation to explain the
inequality-$15 < $7.
Answer: Maggie went to the store and bought 3 cartons of organic eggs for $23, and a bag of flour for $7. She had $15 dollars in her bank account. But the checkout total was $30. So the bank charged her credit card of her $15 dollars. Now she has a -$15 dollar fine that needs to be paid to her card.
Step-by-step explanation:
Maggie went to the store and bought 3 cartons of organic eggs for $23, and a bag of flour for $7. She had $15 dollars in her bank account. But the checkout total was $30. So the bank charged her credit card of her $15 dollars. Now she has a -$15 dollar fine that needs to be paid to her card.
Write the following
numbers in descending
order.
0.741, 0.7041, 0.7412,
0.70411, 0.744
Answer:
0.744-0.741-0.7412-0.7041-0.70411
Step-by-step explanation:
Answer:
0.7440.74120.7410.704110.7041Step-by-step explanation:
Decending order- From greatest to least
To order them start with the dight with the highest number in the place that isn't equal. In this case it the 4 in the hundredths place so are top 3 numbers are 0.741, 0.7412, and 0.744. As this point you continue to look at the greatest number when the dights aren't equal so the top three would be ordered 0.744,0.7412
0.744,0.7412, and 0.741. As for the bottom 2 numbers you do the same thing with the top three numbers so the rest of the list is 0.70411 and 0.7041
Write an equation of each line in standard form with integer coefficients.
2y = -4x-12
The equation of the line in standard form of 2y = -4x - 12 is 4x + 2y = -12.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.
Given the equation 2y = -4x - 12, to write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
2y = -4x - 12
4x + 2y = -12
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In this problem, you will investigate the relationships among three points of concurrency in a triangle.
d. Make a conjecture about the relationships among the circumcenter, centroid, and orthocenter.
The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. The circumcenter, centroid, and orthocenter are all collinear.
What is the relationship between the centroid circumcenter and orthocenter?The circumcenter, centroid, and orthocenter are all collinear.
The centroid separates the line connecting the circumcenter and orthocenter in the proportion of 2 :1
i.e, CSOC = 21.
Where, C-Coordinate of the centroid. O-Coordinate of the orthocenter.
The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. A centroid is the point at which the lines drawn from the midpoints of each side of a triangle intersect at the opposite vertex.
Any triangle's orthocenter, centroid, and circumcenter are collinear. The centroid divides the distance between the orthocenter and the circumcenter in a 2:1 ratio. The line connecting these three points is known as the triangle's Euler line. to represent the ABC triangle's circumcircle.
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The sun is at a focus of Earth's elliptical orbit.
a. Find the distance from the sun to the other focus.
The distance from the sun to the other focus is 5.01 × 10⁹ m.
What is the distance from the sun?
(a) The distance from the center of an ellipse to a focus is an where a is the semi major axis and e is the eccentricity. Thus, the separation of the foci ( in the case of Earth's orbit ) is;
2ae = 2(1.50 × 10¹¹)(0.0167) = 5.01 × 10⁹ m.
(b) To express this in terms of solar radii, we set up a ratio;
(5.01 × 10⁹)/(6.96 × 10⁸) = 7.2
Thus, we can conclude that the distance from the sun to the other focus is 5.01 × 10⁹ m.
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Complete question is;
The Sun's center is at one focus of Earth's orbit. How far from this focus is the other focus, (a) in meters and (b) in terms of the solar radius, 6.96 × 10⁸ m? The eccentricity is 0.0167, and the semimajor axis is 1.50 × 10¹¹ m.
Find the sum of each finite series. Σ⁸ n=1 (7-n)
The sum of the finite series [tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex] is 20
Given a finite series:
[tex]\sum\limits^{8}_{n=1} {(7-n)}[/tex]
Recall the properties of summation notation:
Σₙ b. f(n) = b Σₙ f(n) where b is a constant.
Σ (a + b) = Σ a + Σ b
[tex]\sum\limits^p_{n=1} {b} =b.p[/tex] where b is a constant
Using the above summation properties, we can write:
[tex]\sum\limits^{8}_{n=1} {(7-n)}=\sum\limits^{8}_{n=1} {7}-\sum\limits^{8}_{n=1} {n}[/tex]
=7 . 8 - (1+2+3+ ...+8)
= 56 - 8/2 (1+8)
= 56 - 4 . 9
= 56 - 36 = 20
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Figure ABCD is a rhombus. Find the
value of x.
B
5x-8
D
A
3x + 10
x = [?]°
A Figure ABCD is a rhombus. The angles of A and C are equal by alterenate interior angle. The value of x in the figure ABCD rhombus is 9 degree.
What is a rhombus?We know that rhombuses are a particular type of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal.
The Solution to an equation is finding values of the variable in the considered equation for which the equation considered evaluates to be true.
For a solution, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, thus solution to a system is the intersection of all its equation at single point
WE know that the diagonals of a rhombus bisect each other, we know that triangle DEC is a right triangle.
Since the side lengths of a rhombus are equal, so the angles of A and C are equal by alterenate interior angle.
Now, 5x-8 = 3x + 10
i.e. 5x - 3x = 10 + 8
i.e. 2x = 18
i.e. x = 9
Therefore the value of x in the figure ABCD is 9 degree.
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expand the expression as a product of factors.
(x+y)^5
Answer: 7+8y
Step-by-step explanation:
Solve the equation.
2|2x+3|=|x-3|
There should be two solutions.
Please show the steps and give an explanation on how to solve it and why.
Answer:
x= -3
Step-by-step explanation:
[tex]2(2x + 3) = x - 3 \\ 4x + 6 = x - 3 \\ 4x = x - 3 - 6 \\ 4x - x = - 3 - 6 \\ 3x = - 9 \\ x = \frac{ - 9}{3} \\ x = - 3[/tex]
Answer:
[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]
Step-by-step explanation:
Given absolute value equation:
[tex]2|2x+3|=|x-3|[/tex]
The absolute value of a number is its positive numerical value.
Therefore, the expressions inside the bars should be set to both positive and negative. Rewrite the absolute value equation as four equations without absolute value bars and simplify:
[tex]\textsf{Positive = Positive}: \quad 2(2x+3)=x-3[/tex]
[tex]\textsf{Positive = Negative}: \quad 2(2x+3)=-(x-3)[/tex]
[tex]\begin{aligned}\textsf{Negative = Positive}: \quad -2(2x+3) &=x-3\\ \implies 2(2x+3) &=-(x-3)\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Negative = Negative}: \quad -2(2x+3) &=-(x-3)\\ \implies 2(2x+3)&=x-3\end{aligned}[/tex]
From inspection of the equations:
Positive = Positive is equal to Negative = Negative, and Negative = Positive is equal to Positive = Negative,so there are only two unique equations to be solved.
Equation 1
[tex]\begin{aligned}2(2x+3) & =x-3\\4x+6 & = x-3\\4x+6-x&=x-3-x\\3x+6&=-3\\3x+6-6&=-3-6\\3x & =-9\\\dfrac{3x}{3} & = \dfrac{-9}{3}\\ x&=-3 \end{aligned}[/tex]
Equation 2
[tex]\begin{aligned}2(2x+3)&=-(x-3)\\4x+6&=-x+3\\4x+6+x&=-x+3+x\\5x+6&=3\\5x+6-6&=3-6\\5x &=-3\\ \dfrac{5x}{5}&=\dfrac{-3}{5}\\x &=-\dfrac{3}{5} \end{aligned}[/tex]
Therefore, the solutions are:
[tex]x=-3 \textsf{ \quad or \quad} x=-\dfrac{3}{5}[/tex]
Nicolas has 1400 pokemon cards. Of these cards, 40% are water pokemon and 15% are considered rare pokemon, the rest are rock pokemon. How many rock pokemon cards does Nicolas have? (I have completely forgotten this skill)
Answer:
630 rock cards
Step-by-step explanation:
aight so 40 % of 1400 is 560 , and 15% of 1400 is 210 . add those and you get 770 . so you got 770 water and rare . you subtract that by 1400 and you got 630 !!
Answer: 476 rock type pokemon cards
Step-by-step explanation: Let's do this! 40% of 1400 is 560, and 15% of 560 is 84. 560 - 84 = 476.
A pendulum moving in simple harmonic motion is modeled by the function , where s is measured in inches and is measured in seconds. determine the first time when the distance moved is 4 inches.
The maximum displacement, the frequency, and the time required for one cycle are 1/5 inch, 1/π Hz and π sec.
What is displacement?A displacement is a vector in geometry and mechanics that has a length equal to the shortest distance between a point P's initial and final positions. It calculates the length and angle of the net motion, or total motion, in a straight line from the starting point to the destination of the point trajectory. The translation that links the starting point and the ending point can be used to spot a displacement.
Therefore, the instantaneous speed is different from velocity, which is the rate at which the distance traveled along a particular path changes over time. The temporal rate of change of the position vector can also be used to describe velocity.
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Three classes have a total of 66 students. The students need to make teams of 7 for a Math competition. How many complete teams can they make?
10 teams
8 teams
3 teams
9 teams
(1+2)+6=1+(2+6) which property is this
Answer:
Associative.
Step-by-step explanation:
The associative property is the property that means an equation's result will be the same regardless of grouping the factors together or reversing the equation.
e.g
[tex](a - b) \times c = c \times (b-a)[/tex]
A box contains 7 blue marbles, 6 red marbles, 2 white marbles, and 3 black marbles. If one marble is chosen at random, what is the probability that it will be red?
A. 0.11
B. 0.17
C. 0.33
D. 0.39
E. 0.67
The probability that the chosen marble will be red is, 0.27.
Probability:
Probability is calculated by using the formula,
P(A) = n(A)/n(S)
Where,
P(A) is the probability of an event “A”
n(A) is the number of favorable outcomes.
n(S) is the total number of events in the sample space.
Given,
A box contains 7 blue marbles, 6 red marbles, 2 white marbles, and 3 black marbles.
Here we need to find If one marble is chosen at random, then what is the probability that it will be red.
According to the formula,
number of favorable outcomes = 6
total number of events in the sample space = 7 + 6 + 2 + 3 = 22.
Then the probability of getting red marbles is,
=> P(A) = 6/22.
It can be simplified as,
=> P(A) = 3/11
=> P(A) = 0.27
Therefore, the probability of getting red marble is 0.27.
Here in the options, the option 0.27 is not present.
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Which statement correctly describes the inverse of the following function?
12345
A. It is a horizontal shift.
B. It is not a function.
C. It is a function.
D. It is negative.
2
3
4
5
6
7
It is not a function. which is the correct answer would be option (B)
Given that,
A function is shown in the figure with its domain and range.
To determine the inverse function.
What is the function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
Since the two preimages of the value 5 are present in the domain
So that is why the inverse function of a given function is not possible.
Therefore, It is not a function.
Hence, the correct answer would be option (B)
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What is the arithmetic mean between 20 and 56?
Answer:
35, the population size is 2.
can someone please help me
for the first one x = 12
second one is 2
Answer:
x = 12
x = 2
Step-by-step explanation:
Basically the triangles are congruent. Therefore, the sides are equal to each other. Set both equations equal to each other and solve for x.
