Sheldon is 16 4/7 years old, while Leonard is 21 1/7.
We are given the correlations between two numbers in this sort of query, specifically the data when their ages are contrasted now and in the future.
Let x represent Leonard's age.
We can infer Sheldon's age from the question as being 4x - 68.
The following equation results from the question:
x + 12 = 2((4x - 68) + 12) - 24
Fix x,
=> x + 12 = 2(4x - 68 + 12) - 24
x + 12 = 2(4x - 56) - 24
x + 12 = 8x - 112 - 24
x - 8x = -136 - 12
-7x = - 148
x = 148 / 7 or 21 1/7
Now, simply multiply 4x by 68 to get Sheldon's age.
=> 4x - 68
=> 4 * 148/7 - 68
=> 592/7 - 68
=> 116/7 or 16 4/7
Leonard is therefore 21 1/7 years old, while Sheldon is 16 4/7.
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If 2x+y=4 and 2x-y=8, then what does 3x-y equal?
THE TRICK IS TO FIND THE VALUE OF X AND Y FIRST.
I WILL USE SUBSTITUTION TO SOLVE THIS SYSTEM OF EQUATIONS.
[tex]y = 4 - 2x......(3)equation[/tex]
[tex]2x - (4 - 2x) = 8 \\ 2x - 4 + 2x = 8 \\ 2x + 2x = 8 + 4 \\ 4x = 12 \\ \frac{4x}{4} = \frac{12}{4} \\ x = 3[/tex]
[tex]y = 4 - 2(3) \\ y = 4 - 6 \\ y = - 2[/tex]
THEN FOR 3X-Y PLUG IN THE VALUES YOU FOUND FOR X AND Y
[tex] = 3(3) - ( - 2) \\ = 9 + 2 \\ = 11 \\ 3x - y = 11[/tex]
ATTACHED IS THE SOLUTION
The weight M of an object on the moon varies directly as its weight E on earth. A person who weighs 162.71lb on earth weighs 27.66lb on the moon. How much would a 220lb person weigh on the moon?
A 220lb person on earth would weigh 23.81lb on moon
Given
Weight of an object on moon varies same as that on the planet earth
This means the weights are directly proportional
Weight of person on earth = 162.7lb
Weight of person on moon = 27.66lb
Also,
Weight of person on earth = 220lb
We need to find weight of this person on moon.
Let weight of person on moon be x
According to the data equation can be formed as
27.66 x 220 = 162.71x
3885.2 = 162.71x
x= 23.81
Hence the weight of the person on moon is 23.lb
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Which is true about investments and risk?
Answer:
Every investment carries some degree of risk, All investments carry some degree of risk. Stocks, bonds, mutual funds, and exchange-traded funds can lose value, even all their value, if market conditions sour. Even conservative, insured investments, such as certificates of deposit (CDs) issued by a bank or credit union, come with inflation risk. They may not earn enough over time to keep pace with the increasing cost of living.
Step-by-step explanation:
Sarah got a $60 gift card to Walmart. She uses the gift card to buy orange juice for $4.50. She also wants to use the gift card to buy shirts. Each shirt costs $2.29. Write an inequality to describe this situation, where n is the number of shirts Sarah wants to buy?Please answer quick, will give 18 points
ANSWER
[tex]4.50+2.29n\le60[/tex]EXPLANATION
We have that Sarah got a $60 gift card to use in Walmart.
This means that everything she can buy cannot be worth more than $60 (i.e. less than or equal to $60).
She buys orange juice for $4.50 and she wants to buy shirts (which cost $2.29 each)
Let n be the number of shirts Sarah wants to buy.
This means that the cost of n shirts is $2.29n.
Recall that she can only spend less than or equal to $60. This means that the sum of the cost of the orange juice and n shirts is less than or equal to $60.
That is:
[tex]4.50+2.29n\le60[/tex]That is the inequality that represents the situation.
Which inequality represents the compound inequality x > 3 and x < 5
Given:
x > 3 and x < 5
The inequality compound is:
[tex]3Answer: 3 < x < 5white ratio as a rate with a denominator of 1 2,400 copies in 3 minutes
Answer
Rate = 800 copies per minute
Explanation
Work = rate x time
Work = 2400 copies
Time = 3 minutes
Rate = work / time
Rate = 2400 / 3
Rate = 800 copies per minute
Therefore, rate is 800 copies per minute
Determine algebraically ifthe function is even, odd, or neither.f(x)=3x-2
A function is even if
[tex]f(-x)=f(x)[/tex]A function is odd if
[tex]f(x)=-f(x)[/tex]For the given question, we will test for both even and odd conditions
Step 1: Test for an even condition
[tex]\begin{gathered} f(-x)=3(-x)-2 \\ f(-x)=-3x-2 \\ \sin ce \\ f(-x)\ne f(x) \\ it\text{ is not an even function} \end{gathered}[/tex]Step 2: Test for an odd function
[tex]undefined[/tex]Write your answer as a fraction or as a whole or mixed number 3 7/10 * 4 5/6
Answer:
17 53/60
Step-by-step explanation:
Quadrilateral ABCD has coordinated a(-4,3) b(-3,6) c(0,8) d(-2,5). Prove that quadrilateral ABCD is a parallelogram and explain whether quadrilateral ABCD is a rectangle or not.
Quadrilateral ABCD has coordinate
A(-4, 3) , B(-3, 6) C(0,8) & D(-2,5)
so we will find the length of the sides
[tex]AB=\sqrt[]{(6-3)^2+(-3-(-4))}^2=\sqrt[]{9+1}=\sqrt[]{10}[/tex]for CD
[tex]CD=\sqrt[]{(5-8)^2+(-2-0)^2}=\sqrt[]{9+4}=\sqrt[]{13}[/tex]as we can see AB and CD is not equal to Quadrilateral is not equal.
now we compute the midpoint of the diagonals
midpoint of
[tex](x,y)=(\frac{-4-3}{2},\frac{3+6}{2})=(-\frac{7}{2},\frac{9}{2})[/tex]Suppose that the functions p and q are defined as follows.
p(x)=x² +6
q(x)=√x+1
Find the following.
(q. p) (3)=
(p.q) (3)=
The most appropriate choice for function can be given by
q[tex]o[/tex]p(3) = [tex]\sqrt{15}+1[/tex]
p[tex]o[/tex]q(3) = [tex]2\sqrt{3} + 10[/tex]
What is function?
A function from A to B is a rule that maps to each element of A a unique element of B.
A is called the domain of the function and B is called the co domain of the function.
We can do addition, subtraction, multiplication, division and composition on functions.
Let f and g be two functions
f[tex]o[/tex]g(x) = f(g(x)) and g[tex]o[/tex]f(x) = g(f(x))
This is known as composition of function.
Here,
[tex]p(x) = x^2 + 6\\q(x) = \sqrt{x} +1[/tex]
q[tex]o[/tex]p(x) = q(p(x))
=[tex]q(x^2+6)[/tex]
= [tex]\sqrt{x^2+6}+1[/tex]
q[tex]o[/tex]p(3) = [tex]\sqrt{3^2+6}+1[/tex]
= [tex]\sqrt{15}+1[/tex]
p[tex]o[/tex]q(x) = p(q(x))
= p([tex]\sqrt{x}+1[/tex])
= [tex](\sqrt{x}+1)^2+6[/tex]
= [tex]x + 1 + 2\sqrt{x} + 6[/tex]
= [tex]x + 2\sqrt{x} +7[/tex]
p[tex]o[/tex]q(3) = [tex]3 + 2\sqrt{3} +7[/tex]
[tex]2\sqrt{3} + 10[/tex]
[tex]2\sqrt{3} + 10[/tex]
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A toy store would like to open a new store in the city of Thousand Oaks, and they would like to know what proportion of households have kids. Out of 100 households sampled, 28 had kids. Based on this, to construct a 90% confidence interval for the true population proportion of Thousand Oaks households with kids, you need to use which one of the following calculators?
Answer: 55
Step-by-step explanation: It makes sense
The measure of the angle 6 = _____
Factor this polynomial. The image is attached here. Need help!
Answer:
[tex]4x^2+11xy-3y^2=(x+3y)(4x-y)[/tex]Step-by-step explanation:
To factor the following polynomial, break the expression into groups:
The grouping method can be used to factor polynomials whenever a common factor exists between the groupings. Just find families easier-to-factor groups that we can better approach the problem.
[tex]\begin{gathered} 4x^2+11xy-3y^2 \\ (4x^2-xy)+(12xy-3y^2) \end{gathered}[/tex]Then, factor it using factor by grouping:
[tex]\begin{gathered} x(4x-y)+3y(4x-y) \\ \text{ Since the two terms have (4x-y) as a common factor:} \\ (x+3y)(4x-y) \end{gathered}[/tex]The table below shows the number of house calls three different plumbers made on three different days.
Number of House Calls
Plumber A
Plumber B
Plumber C
Monday
2
8
8
Tuesday
4
7
10
Wednesday
3
9
9
The total amount of money earned by all three plumbers on Monday was $1,400. On Tuesday they earned a total of $1,660, and on Wednesday, they earned a total of $1,650. On Thursday, Plumber A made four house calls, Plumber B made six house calls, and Plumber C made three house calls. How much total money is earned on Thursday?
$250
$1,060
$1,090
$1,130
The total money that is earned on Thursday is $1090
How to determine the total money that is earned on Thursday?From the question, we have the following table of values
Monday Tuesday Wednesday
Plumber A 2 8 8
Plumber B 4 7 10
Plumber C 3 9 9
Using the given parameters in the question, we have the following system of equations
2a + 8b + 8c = 1400 --- (1)
4a + 7b + 10c = 1660--- (2)
3a + 9b + 9c = 1650 --- (3)
Subtract equation (2) from twice equation (1)
So, we have
(4a + 16b + 16c = 2,800) - (4a + 7b + 10c = 1,660)
This gives
9b + 6c = 1140 --- (4)
Subtract four times equation (3) from three times equation (2)
So, we have
12a+ 21b +30c = 4,980 -(12a + 36B + 36c = 6,600)
This gives
-15b - 6c = -1,620 --- (5)
Add equations (4) and (5)
(9b + 6c = 1140) + (-15b - 6c = -1620)
So, we have
-6B = -480
Divide by -6
b = 80
Substitute b = 80 in -15b - 6c = -1,620
-15 x 80 - 6c = -1,620
Evaluate
-1200 - 6c = -1,620
So, we have
-6c = -420
Divide
c = 70
In (2), we have
4a + 7b + 10c = 1660
This gives
4a + 7 * 80 + 10 * 70 = 1660
Evaluate
4a = 400
Divide
a = 100
On Thursday, we have
a = 4, b = 6 and c = 3
So, we have
Total = 4 * 100 + 6*80 + 3*70
Evaluate
Total = 1090
Hence, the total earnings is 1090
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Question 2 (4 points)y = x|d: {-8, -3, 4,7} {Blank 1:Blank 2:Blank 3:Blank 4
r: {8, 3, 4, 7}
Explanation:
y = |x|
domain = -8, -3, 4, 7
domain are the x values or input
r = range
Range are the y values or output
when x = -8
y = |-8| = 8
when x = -3
y = |-3| = 3
when x = 4
y = |4| = 4
when x = 7
y = |7| = 7
r: {8, 3, 4, 7}
blank 1 = 8
blank 2 = 3
blank 3 = 4
blank 4 = 7
Evaluate without a calculator.[tex] log_{4}(16) + log_{3}(27) [/tex]please show your work..!
Answer:
The value of the given expression is;
[tex]5[/tex]Explanation:
Given the logarithmic expression;
[tex]\log _416+\log _327[/tex]To solve, Recall the rules of logarithm;
[tex]\begin{gathered} \log _ax^y=y\times\log _ax\text{ ------1} \\ \log _aa=1\text{ -------2} \end{gathered}[/tex]Apply the above rules;
[tex]\begin{gathered} \log _416+\log _327 \\ \log _44^2+\log _33^3 \\ \text{Applying rule 1;} \\ 2\log _44+3\log _33 \end{gathered}[/tex]Aplplying rule 2;
[tex]\begin{gathered} 2\log _44+3\log _33 \\ =2(1)+3(1) \\ =2+3 \\ =5 \\ \log _416+\log _327=5 \end{gathered}[/tex][tex]\begin{gathered} \text{Note that from the rule 2;} \\ \log _aa=1 \\ so\text{ when a logarithm has the same number as the base it will equal to 1;} \\ \text{for example;} \\ \log _44=1 \\ \log _33=1 \\ \log _55=1 \end{gathered}[/tex]Therefore, the value of the given expression is;
[tex]5[/tex]Vă rog,Am nevoie urgent
Mulțumesc
Step-by-step explanation:
The Answer
I hope you are doing well and I don't want to be a part of this the only reason why you would want this
Which of the following statements is false?A. In the ordered pair (3, 7), 3 is the x-coordinateB. The point (0,5) is on the y-axis.OC The horizontal distance between the point located at (3,7) and the point located at (6, 7) is 3unitsOD. In the ordered pair (9.7), 7 is the x-coordinate,
Answer:
D. In the ordered pair (9,7), 7 is the x-coordinate
Explanation:
The ordered pairs have the form (x, y) where the first number is the x-coordinate and the second number is the y-coordinate. So, in the ordered pair (9, 7), 7 is the y-coordinate. This makes the last statement false and the answer is
D. In the ordered pair (9,7), 7 is the x-coordinate.
HELP ASAP I NEED ANSWER NOWW IT'S MISSING PLEASE HELP 50 POINTS
Answer:
Let [tex]g[/tex] equal the number of games.
Let [tex]r[/tex] equal the number of rides
System of Equations
[tex]2.50g+4r=52.50[/tex]
[tex]r=2g[/tex]
Step-by-step explanation:
One game costs $2.50, so [tex]g[/tex] games cost [tex]2.50g[/tex]. One ride costs $4.00, so [tex]r[/tex] rides cost [tex]4r[/tex]. The total [tex]2.50g+4r[/tex] equals $52.50: [tex]2.50g+4r=52.50[/tex]
Since Stella's number of rides she went on is twice the number of games she played, there are two times the number of games for her number of rides. [tex]r=2g[/tex]
What do we call the total area of all exposed surfaces of a geometric solid?
The total area of all exposed surfaces of a geometric solid is called surface area .
What does it mean by surface area of geometric solid ?The area is the entire amount of space filled by flat or two-dimensional objects. In other words, the number of square units that cover the surface of a closed figure is used to represent its area.
It is quantified in square inches, or square units. The area only has length and width since 2-dimensional shapes can be measured using them.
The area is a two-dimensional measurement of the size of a flat surface, whereas surface area is a measurement of a solid shape's exposed surface (three-dimensional).
The main distinction between area and surface area is this. However, both amounts are expressed in square units, which is the same for both. Learn the distinction between area and volume as well.
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Graph the line with the given slope that passes through the given point.
(a) slope:
3
4
,
point:
(1, 5)
The linear equation can be written as:
y = (3/4)*x + 17/4
And the graph can be seen at the end.
How to graph the linear equation?
A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Here we have the slope m = 3/4, so we get:
y = (3/4)*x + b
And the line passes through (1, 5), replacing these values in the equation we get:
5 = (3/4)*1 + b
5 - 3/4 = b
20/4 - 3/4 = b
17/4 = b
So the linear equation is:
y = (3/4)*x + 17/4
To graph the line we need other point, if we use x = 0 we get:
y = (3/4)*0 + 17/4 = 17/4
Then we have the points (1, 5) and (0, 17/4).
To graph the line, we just need to find these two points and connect them with a line, the graph can be seen below.
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I need help with please!!!
will give brainlist
Which graph represents the solution to one half m is greater than or equal to negative seven elevenths?
number line with closed circle on point negative 14 over 11 and arrow shaded to the right
number line with closed circle on point negative 7 over 22 and arrow shaded to the right
number line with closed circle on point negative 14 over 11 and arrow shaded to the left
number line with closed circle on point negative 7 over 22 and arrow shaded to the left
The solution to the inequality is m ≤ -14/11 which is the correct answer would be option (C).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
If it is "> or," the shaded arrow is drawn to the right of the inequality graph; if it is "or," it is drawn to the left.
Given the inequality, -1/2m ≥ 7/11,
Which represents the solution to one-half m is greater than or equal to negative seven elevenths
Solve for m:
⇒ -1/2m(-2) ≥ 7/11(-2)
m ≤ -14/11 [Because we are multiplying both sides by a negative value, the sign shifts]
The solution to the inequality is m ≤ -14/11 which the graph is attached below for m ≤ -14/11.
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Question 94 ptsONLY write your answer as a number. You do not needto write the unit measurement.Round you answer to the nearest tenth.15. A fireman leaned a 42-foot ladder against a building. If he placed the ladder 8.5 feetfrom the base of the building, what angle is formed between the ladder and the ground
The length of ladder is L = 42 foot.
The distance between base of building and ladder is b = 8.5.
Determine the measure of angle by using the trigonometry.
[tex]\begin{gathered} \cos \theta=\frac{8.5}{42} \\ \theta=\cos ^{-1}(0.20238) \\ =78.323 \\ \approx78.3 \end{gathered}[/tex]So measure of angle is 78.3 degree.
What is the actual distance between these two cities in kilometers?
1) Whenever we have problems that deal with the real distance and distance on the map, we can write out the following formula:
[tex]\begin{gathered} Scale=\frac{distance\: on\: the \: map}{real\: distance} \\ S=\frac{3.5}{R} \end{gathered}[/tex]So, let's call the Real distance "R". Note that in this question, 1 centimeter represents 20 kilometers
2) So, in order to plug that as the scale we need to convert kilometers to centimeters:
[tex]\begin{gathered} 1km--100000cm \\ 20km---x \\ x=2000000cm \end{gathered}[/tex]3) Finally, we can plug that into the formula and cross multiply the ratios this way:
[tex]\begin{gathered} \frac{3.5}{r}=\frac{1}{2000000} \\ r=2000000\times3.5 \\ r=7000000cm \end{gathered}[/tex]Converting it back to kilometers we can write:
[tex]\frac{7000000}{100000}=70km[/tex]How to solve it and how to calculate the gst and pst
Given:-
Given amount is $50.
Price of article is $24.
GST is 7%.
PST is 7%.
To find:-
The remaining amount.
The GST amount is,
[tex]\begin{gathered} 24\times\frac{7}{100}=0.24\times7 \\ \text{ =1.68} \end{gathered}[/tex]The PST amount is,
[tex]\begin{gathered} 24\times\frac{7}{100}=0.24\times7 \\ \text{ =1.68} \end{gathered}[/tex]So the total tax amount is,
[tex]1.68+1.68=3.36[/tex]Now the total amount of the article is,
[tex]24+3.36=27.36[/tex]So the remaining amount is,
[tex]50-27.36=22.64[/tex]So the remaining amount is $22.64
what is 1,235,721 + 9,576,345,123
The sum of the two numbers 1,235,721 and 9,576,345,123 is 9,577,580,844 after applying the arithmetic operation.
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that is +, -, ×, and ÷.
It is given that:
= 1,235,721 + 9,576,345,123
The above number expression is representing the sum of two big numbers.
After applying the arithmetic operation on the number expression:
1,235,721 + 9,576,345,123 = 9,577,580,844
Thus, the sum of the two numbers 1,235,721 and 9,576,345,123 is 9,577,580,844 after applying the arithmetic operation.
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Question A maritime flag is shown. What is the area of the shaded part of the flag
Answer:
There is no picture.
Step-by-step explanation:
If you ask a question, be mindful that people cannot read each other minds.
Find the area of the figure.
Based on the given figure, the area of the figure can be found to be 126.50 cm²
How to find the area?The figure given is a mix of a triangle and a rectangle. The area of the figure can then be found by finding the area of the triangle and the rectangle individually, and then summing them up.
The area of a rectangle is:
= Length x Width
= 8 x 11
= 88 cm²
The area of the triangle is:
= 1/2 x base x height
= 1/2 x 11 x 7
= 38.5 cm²
The area of the figure is:
= 88 + 38.5
= 126.50 cm²
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or each ordered pair, determine whety=5x-315x-3y=9(2,7)(-1,– 8)(3,4)(0,-9)