The present age of Lia is 35 and the present age of Myra is 5.
The sum of Lia's age and Myra's age is 40.
Let the present age of Myra is x and the present age of Lia is y.
So the equation should be
x + y = 40..................(1)
After 10 year the age of Myra is x + 10 and age of Lia is y + 10.
In 10 year Lia will be three time a older than Myra.
y + 10 = 3(x + 10)
Simplify
y + 10 = 3x + 30
Subtract 10 on both side, we get
y = 3x + 20
Now putting the value of y in the equation 1.
x + 3x + 20 = 40
4x + 20 = 40
Subtract 20 on both side, we get
4x = 20
Divide by 4 on both side, we get
x = 5
The present age of Myra is 5.
Now putting the value of x in equation 1
x + y = 40
5 + y = 40
Subtract 5 on both side, we get
y = 35
The present age of Lia is 35.
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The complete question is:
The sum of Lia's age and Myra's age is 40. In 10 year Lia will be three time a older than Myra. How old is each person?
find the derivatives of the following functions (2x³-5x²+6x-3)/x² y=sin^-1(x)+cos^-1(x)-Inx y=5^x-6cosec1/2(x)+3/7(cos5x)-2
Answer:
Below
Step-by-step explanation:
1) The derivative of (2x³-5x²+6x-3)/x² is (6x²-10x+6-3x)/x³
2) The derivative of sin^-1(x)+cos^-1(x)-Inx is (1/(√(1-x²))*dx + (-1/(√(1-x²))*dx )- (1/x)*dx
3) The derivative of 5^x - 6cosec1/2(x) + 3/7(cos5x) - 2 is (ln(5) * 5^x) - (6*(-csc(x)cot(x))dx) + (3/7(-5sin(5x))*dx)
Two families visited an amusement park. the first family bought 2 hot dogs and 3 bottles of waters, which totaled $18. the second family bought 4 hot dogs and 2 bottles of waters, which totaled $28. how much did one hot dog cost? a. $2 b. $4c. $5 d. $6
Answer:
d. $6
Step-by-step explanation:
The diameter of a hat is 6.8 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
2.17 inches
10.68 inches
21.35 inches
36.29 inches
Answer:
Step-by-step explanation:
c is the correct answer
Answer: c
Step-by-step explanation:
At a pizza shop, 6 slices of pizza and 2 drinks cost the same as 5 slices of pizza and 5 drinks. Each slice of pizza costs $4.50. Find the cost in dollars of each drink.
Answer:
Each drink costs $1.50
Step-by-step explanation:
Let d = the cost of a drink
6(4.50) + 2d = 5(4.5) + 5d Distribute the 6 and 5
27 + 2d = 22.50 + 5d Subtract 2d from both sides
27 + 2d - 2d = 22.50 + 5d - 2d
27 = 22.50 + 3d Subtract 22.50 from both sides
4.5 = 3d Divide both sides by 3
1.50 = d
Solve -2(8n - 3) = 43(n + 7). write the solution as an integer or decimal. Show your work (simply).
n = __
Answer:
n = - 5
Step-by-step explanation:
- 2(8n - 3) = 43(n + 7) ← distribute parenthesis on both sides
- 16n + 6 = 43n + 301 ( subtract 43n from both sides )
- 59n + 6 = 301 ( subtract 6 from both sides )
- 59n = 295 ( divide both sides by - 59 )
n = - 5
Answer:
n=7.14
Step-by-step explanation:
-2(8n-3)=43(n+7)
distribute
-16n+6=43n+301
add 16n on both sides
6=43n-301
add 301 on both sides
307=43n
divide both sides by 43
n=7.1395
suppose that shoe sizes of american women have a bell-shaped distribution with a mean of 8.04 and a standard deviation of 1.53 . using the empirical rule, what percentage of american women have shoe sizes that are less than 11.1 ?
The percentage of American women that have shoe sizes that are at least 11.1 is; 0.0015
Empirical Rule
We are given;
Mean; x' = 8.04
Standard deviation; σ = 1.53
Using the empirical rule, we can have the data either 1, 2, or 3 standard deviations from the mean.
Thus;
At 1 standard deviation from the mean, we have;
8.04 ± 1(1.53)
⇒ (6.52, 8.56)
At 2 standard deviations from the mean, we have;
8.04 ± 2(1.53)
⇒ (5, 11.08)
At 3 standard deviations from the mean, we have;
8.04 ± 3(1.52)
⇒ (3.48, 12.6)
We can see that the one with at least 12,6 is 3 standard deviations from the mean which from the empirical rule is 99.7%
Thus;
percentage of American women have shoe sizes that are at least 12.6 = 100% - 99.7% - 0.15%
P(x ≥ 12.6) = 0.15% = 0.0015
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HELP MEEEE!!!
i really need helppp
The value of a and b are 1 and 6 respectively.
The equation of the line is y = 1 / 3 x + 1.
How to find the equation of a line?The equation of a line can be represented in slope intercept form as follows:
y = mx + b
where
m = slope of the lineb = y-interceptTherefore, let's find the value of a and b using the line.
Hence, using (3, 2) and (12, 5)
slope = 5 - 2 / 12 - 3
slope = 3 / 9
slope = 1 /3
Therefore, let's find the y-intercept using (3, 2)
y = 1 / 3 x + b
2 = 1 /3 (3) + b
2 - 1 = b
b = 1
Therefore, the equation is y = 1 / 3 x + 1.
Let's find a and b
a is the y-intercept. Therefore, a = 1
using (b, 3)
y = 1 / 3 x + 1
3 = 1 / 3 (b) + 1
3 - 1 = b / 3
b = 2 × 3
b = 6
Therefore,
a = 1 and b = 6
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can you describe the set {x ∈ z : −1 ≤ x < 43} in interval notation? why/why not?
The interval notation for the set {x ∈ Z : −1 ≤ x < 43} is [-1, 43).
An "interval" in mathematics refers to a set of numbers between two given endpoints, where the endpoints can be included or excluded from the set, depending on the specific interval notation being used.
In the case of the set {x ∈ Z : −1 ≤ x < 43}, we are looking at all integers (x ∈ Z) that satisfy the inequality −1 ≤ x < 43.
This means that we are looking at all integers greater than or equal to −1 and less than 43.
Here we need to express this set in interval notation, we have to decide whether or not to include the endpoints −1 and 43.
Since the inequality symbol used is "<" for 43, we will exclude 43 from the set and use a parenthesis around 43 in the interval notation to indicate that it is not included in the set.
Therefore it can be written as, [-1, 43).
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-cos(x y)sin(y) sin(x y)cos(y)
On the left side of the expression, the first term is cos(x y)sin(y) and the second term is sin(x y)cos( y ).cos(x y)sin(y) sin(x y)cos(y) = cos(x y)sin(y) − sin(x y)cos(y)
We can use the trigonometric identity sin(A)cos(B) - cos(A)sin(B) to simplify the expression.
On the left side of the expression, the first term is cos(x y)sin(y) and the second term is sin(x y)cos( y ).
We can rearrange the terms and apply the identity, which gives us:
On the left side of the expression, the first term is cos(x y)sin(y) and the second term is sin(x y)cos( y ).
cos(x y)sin(y) − sin(x y)cos(y)
the complete question is :
What is the result of cos(x y)sin(y) - sin(x y)cosy?
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sam is going to assemble a computer by himself. he has choice of chips from two bands, a hard dive from four, memory from three and an accessory bundle from five local stores. how many different ways can sam order the parts?
The total number of different combinations Sam can make is 120.
Computer Assembly Options CalculationThe number of different ways that Sam can order the parts is given by the product of the number of choices he has for each part:
Chips: 2 options
Hard Drive: 4 options
Memory: 3 options
Accessory Bundle: 5 options
Therefore, the total number of different combinations Sam can make is 2 x 4 x 3 x 5 = 120.
This is about a person named Sam who is assembling a computer and has a choice of parts from different brands and stores. The problem is to calculate the number of different combinations of parts he can choose from. The solution involves finding the number of options he has for each part (chips, hard drive, memory, and accessory bundle) and then multiplying these numbers to get the total number of combinations.
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Find the length of BC
Our legs range in length from 15 to 36. (A & B). A hypotenuse is 39.
What is Pythagorean Theorem?Any right triangle has a square whose side is the hypotenuse, which is the side across from the right angle, and whose area is equal to the sum of the squares' areas whose sides are the two legs (the two sides that meet at a right angle). The square on the hypotenuse is equal to the sum of the squares on the other two sides for all right-angled triangles, according to Pythagoras' theorem. The longest side is called the hypotenuse, and it is always perpendicular to the right angle. A right angle is formed in this triangle using the formula a 2 = b 2 + c 2.We must apply Pythagorean Theorem in order to solve for this.
In order to find the hypotenuse (C), or the side that is opposite the 90-degree angle, we add the squares of the legs (A & B). This is known as the Pythagorean Theorem.
A² + B² = C² is the Pythagorean Theorem's formula.
We have two different leg lengths: 15 and 36. (A & B).
Square 15 and 36.
15² = 225
36² = 1,296
Let's add the side lengths now that we have them.
225 + 1,296 = 1,521.
We now need to square root our sum in order to find C.
39 is the square root of 1,521.
39 is your hypotenuse.
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there are 10 members on a board of directors. if they must elect a chairperson, a secretary, and a treasurer, how many different slates of candidates are possible?
There are 720 different slates of candidates possible.
Permutation:
The permutation is a statistical method that determines the number of possible arrangements. In permutation, the order of selection is important and replacements are not allowed.
Permutation can be divided into three different types:
Permutation of n different objects.Repetition, where repetition is allowed.A permutation is when the objects are not distinctThe general formula of Permutations:
[tex]^nP_r=\frac{n!}{(n-r)!}[/tex]
n= total number of members.
r=number of members selected.
Here n=10 and r= 3
Now substitute the values in the above formula:
[tex]^nP_r=\frac{10!}{(10-3)!} \\\\^nP_r=\frac{10!}{7!}\\\\^nP_r= \frac{10*9*8*7!}{7!} \\\\^nP_r=10*9*8\\\\^nP_r=720[/tex]
Therefore, there are 720 different slates of candidates possible.
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If triangle ABC is rotated 90 degrees clockwise about the origin followed by dilation by a factor of 2 about the origin, what will be the resulting coordinates of the vertices of the transformed triangle A' B'C'?
For a ΔABC when rotated 90° clockwise and dilated with a factor of 2 the new vertices becomes option C: A'(0,4), B'(6,-4) and C'(-2,-2).
What is dilation?
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.
The vertices of triangle ABC are - A(-2,0), B(2,3) and C(1,-1).
When an object is rotated at an angle of 90° clockwise the formula for the vertices becomes (x,y) → (y,-x)
So, the new vertices are -
A(-2,0) → [(0),-(-2)] → a(0,2)
B(2,3) → [(3),-(2)] → b(3,-2)
C(1,-1) → [(-1),-(1)] → c(-1,-1)
When an object is dilated by a factor of 2 the formula for the vertices becomes (x,y) → (2x,2y)
So, the new vertices are -
a(0,2) → [2(0),2(2)] → A'(0,4)
b(3,-2) → [2(3),2(-2)] → B'(6,-4)
c(-1,-1) → [2(-1),2(-1)] → C'(-2,-2)
Therefore, the new vertices are A'(0,4), B'(6,-4) and C'(-2,-2).
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Hong ordered some books online for $8 each. He paid a total of $5 for shipping. The total cost of the purchase was 133 how many books did he buy?
Write an equation that could be used to answer the question above. First chose the appropriate form. Then, fill in the blanks with the numbers 8, 5, and 133. Let B represent the number of books.
A. _b + _ = _
B. _b - _ = _
Answer: He bought 16 books
Step-by-step explanation: $133-$5=$128 (taking away shipping)
$128/8=16 (separating non-shipping price into groups of $8 to compensate for the cost of books)
A: 8b+5=133
B: 8b-133=5
b=16
The population of a city increases by a rate of 3% a year. In 2000 the population was at 250,000.
A. Write an equation to model the scenario.
B. What was the population in 2010?
Answer: 325000
Step-by-step explanation:
In 2000 the population was 250,000 and it would grow 3 percent a year which is 7500 so that means we add 75000 since 7500 X 10 = 75000 so we add it which gives us 325000 in 2010.
the sum of lisa's age and myra's age is 40. in to years, lisa will be 3 times as old as myra. how old is each person now?
The age of Lisa and Myra now is 35 years old and 5 years old, respectively.
To determine how old each person now, use algebraic expression and equation.
Let x = current age of Lisa
y = current age of Myra
If the sum of Lisa's age and Myra's age is 40, then we can express it as:
x + y = 40
x = 40 - y
If in 10 years, Lisa will be 3 times as old as Myra, then we can express it as:
x + 10 = 3(y + 10)
x + 10 = 3y + 30
x - 3y = 20
Substitute the equation for x into the 2nd equation and solve for y.
x - 3y = 20
(40 - y) - 3y = 20
40 - 4y = 20
4y = 20
y = 5
Substitute the value of y into the equation for x and solve.
x = 40 - y
x = 40 - 5
x = 35
Therefore, Lisa is 35 years old while Myra is 5 years old.
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The two polygons are similar. Find the values of x and y.
Answer:
x = 7.5
y = 166º
Step-by-step explanation:
4 ------ 6
5 ------ x
4x = 30
x = 7.5
116 + 61 + 90 + (y - 73) = 360
y - 73 = 360 - 267
y = 93 + 73
y = 166
Answer:
The other answer shows how to get it but for points just showing his answers are right.
Step-by-step explanation:
Vereenvoudig die volgende verhoudings: 4:6
Answer:
Die verhouding 4:6 kan vereenvoudig word tot 2:3 door beide syfers de deel deur 2 te deel.
condense the equation
2log9= log3 - logx
Answer:
[tex]x=\frac{1}{27}[/tex]
Step-by-step explanation:
Solve for x.
We need to use the quotient property of logarithms.
Quotient Property of Logarithms: [tex]\log _{b} (x)-\log _{b} (y)=\log _{b} (\frac{x}{y} )[/tex]
Apply the property to our equation.
[tex]\log(\frac{3}{x})=2\log(9)[/tex]
Simplify the right side by moving the 2 inside the logarithm.
[tex]\log(\frac{3}{x})=\log(9^2)[/tex]
For the equation to be equal, the argument of the logarithms on both sides of the equation must be equal.
[tex]\frac{3}{x}=9^2[/tex]
Evaluate [tex]9^2[/tex].
[tex]\frac{3}{x}=81[/tex]
Multiply both sides of the equation by x.
[tex]\frac{3}{x}x=81x[/tex]
Cancel the common factor of x on the left side.
[tex]3=81x[/tex]
Divide both sides by 81.
[tex]\frac{3}{81} =\frac{81x}{81}[/tex]
[tex]\frac{3}{81} =x[/tex]
Simplify the fraction.
[tex]x=\frac{1}{27}[/tex]
question 6: orthogonal matrices let r be an n×northogonal matrix. 1. what values can the determinant of r take? 2. what values can the real eigenvalues take?
An orthogonal matrix has determinant and real eigenvalues of either 1 or -1, depending on the orientation and reflection properties of the matrix.
An orthogonal matrix is a special type of square matrix where the transpose of the matrix is equal to its inverse.
The determinant of an orthogonal matrix is either 1 or -1. This is because the determinant of a matrix represents the scaling factor of the matrix and an orthogonal matrix can only scale the space by a factor of 1 or -1.
The determinant of 1 indicates that the matrix preserves orientation, while a determinant of -1 indicates that the matrix reflects the space.
The real eigenvalues of an orthogonal matrix are either 1 or -1. This is because an orthogonal matrix preserves the magnitude of vectors, and therefore, the eigenvalues must be either 1 or -1.
The number of eigenvalues equal to 1 is equal to the number of dimensions preserved by the matrix, and the number of eigenvalues equal to -1 is equal to the number of dimensions reflected by the matrix.
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Solve for x help pleaseee
The value of x in the triangle is 14.4 units.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the length of x in the right triangle as follows;
Using similar triangle ratios,
x / 18 = 24 / 30
cross multiply
30x = 24 × 18
30x = 432
divide both sides of the equation by 30
x = 432 / 30
x = 14.4
Hence,
x = 14.4 units
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Need help asappppp thank youuuuu
30 * x⁵y⁸ will be the volume of the given rectangular prism.
What is volume?Volume, which is measured in cubic units, is the 3-dimensional space occupied by matter or encircled by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume. Volume is another word for capacity.
Given a rectangular prism whose sides are mentioned in the problem.
From the general formula of the Volume of Cuboid:
Volume of cuboid = length *width*height
In our case,
Length = 3x²y²
Width = 5x²y⁴
Height = 2xy²
Thus,
volume of rectangular prism = 3x²y²* 5x²y⁴ * 2xy²
volume of rectangular prism = 30 * x⁵y⁸
therefore, the volume of the given rectangular prism will be 30 * x⁵y⁸.
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Deepak used 32% of his salary to pay the house rent which amounted to 16,000. What is his total salary?
Answer:
50,000
Step-by-step explanation:
just need this is it thanks very much
The maximum profit that the florist will earn from selling celebration bouquets is $675.
The maximum is given by the vertex of the graph.The florist will break even after 20 one-dollar increases.
Break-even is when profit is zero.The interval of the number of one-dollar increases for which the florist makes a profit from celebration bouquets is [tex](0,20)[/tex].
To make a profit, [tex]P(x)>0[/tex].Which two angles are adjacent?
Answer:
Any angles that share a common vertex and side are adjacent angles.
Solve 8x−14≤10. Make sure to write your inequality so that x comes first. (1 point)
(If anyone knows the answer to Lesson 11 inequalities unit test on connections PLS PLS help me!!!)
The solution to the inequality equation given above would be = X ≥ 3
What is inequality equation?An Inequality equation is defined as the type of equation that is used to show the relationship between two variables that are not equal using the following symbols such as < or >.
The equation given are as follows:
= 8x−14≤10
Bring the like terms together;
= 8x ≤ 10+14
= 8x ≤ 24
= X ≥ 24/8
= X ≥ 3
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The solution to the inequality equation is expressed as; x ≤ 3
What is inequality equation?Equations and inequalities are considered to be both mathematical sentences that are formed by relating two expressions to each other. In an equation, the two expressions are considered as equal which is shown by the symbol =. Meanwhile in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
The equation we are to solve is; 8x − 14 ≤ 10
Add 14 to both sides to get;
8x ≤ 24
Divide both sides by 8 to get;
x ≤ 3
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PLS DO NUMBER NUMBER 6 WILL GIVE 75 pts
Answer:
Step-by-step explanation:
THE CONSTANT RATE WILL BE 2.5 so that would =75%
Solve for x. Write the equation and show ALL STEPS to solve.
The value of x is 16 and the values of given angles are 45,45.
What are parallel lines ?
Parallel lines can be defined as the lines which are equi distant to each other and they never intersect each other.
Given Two angles,
3x - 3 and 2x+13
Here two angles are vertically opposite angles
so we know that vertically opposite angles are always equal.
3x - 3 = 2x + 13
3x - 2x = 13 + 3
x = 16
SO, the value of x = 16
and 3x - 3 = 3*16 - 3 = 48 - 3 = 45
2x + 13 = 2*16 + 13 = 45
Therefore, The value of x is 16 and the values of given angles are 45,45.
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8) which inequality represents the solution to the given inequality? State the letter of the correct answer.
7< z/28
A) z<196
B) z>196
C) z>4
D) z<4
Answer:
B
Step-by-step explanation:
7 ≤ [tex]\frac{z}{28}[/tex] ( multiply both sides by 28 to clear the fraction )
196 ≤ z , then
z ≥ 196
Simplify 2^5x2^2 / 2^7x2^3 leaving your answer in index form
The simplified form of the expression is [tex]2^{-3}[/tex].
What is expression?
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. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression is,
=> [tex]\frac{2^5\times 2^2}{2^7 \times 2^3}[/tex]
We know that [tex]a^x\times a^y = a^{x+y}[/tex] then
=> [tex]\frac{2^{5+2}}{2^{7+3}}[/tex]
=> [tex]\frac{2^7}{2^{10}}[/tex]
Now [tex]\frac{a^x}{a^y}=a^{x-y}[/tex] then
=> [tex]2^{7-10}[/tex]
=> [tex]2^{-3}[/tex]
Hence the simplified form of the expression is [tex]2^{-3}[/tex].
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