Answer:
x + y = 29 equation 1
Five more than means add 5+5 three times the smaller number:
3x equals the larger number: = y 3x + 5 = y equation 2
From equation 1x + y = 29subtract x from both sidesy = 29 - x
We now have two things that are both equal tothe larger number y.
They must be equal to each other.
3x + 5 = 29 - x
Add x to both sides 3x + x + 5 = 29 - x + x4x + 5 = 29
subtract 5 from both sides 4x + 5 - 5 = 29 - 54x = 24
divide both sides by 44x/4 = 24/4x = 6
We now know x = 6
We also know y=29-x y = 29 - 6y = 23
Your numbers are 6 and 23
Step-by-step explanation:
Salena is buying school supplies. Pencils are sold in packages of 12, while erasers are sold in packs of 10.She wants to buy the smallest number of both pencils and erasers so that she has an eraser for every pencil. How many packages of pencils and erasers should Salena buy?
12 x 5 = 60
10x 6= 60
so 5 packs of pencils and 6 packs of erasers.
estimate the sum
1. 359=
814=
+ 207=
2. 6428=
7154=
+ 9345=
According to the solving the estimated sum of the numbers:
2,0401,38022,93014,42022,610What is the total and difference of the estimates?To estimate implies to come up with a solution that is close but not accurate. It's a reasonable solution to a problem. A sum is the solution to an addition issue. A difference is a solution to a subtraction issue.
How do you write a rough estimate?To get the total, we round each number to the closest tenth and then add the rounded figures. Let us calculate 38 + 23. 38 is more like 40 than 30. As a result, 38 is rounded up to 40.
According to the given data:1 435 + 678 + 925 = 2,038
on round of = 2040
2.359 + 814 + 207 = 1,380
on round of = 1380
3. 6428 + 7154 + 9345 = 22,927
on round of = 22930
4. 2987 + 6873 + 4555 = 14,415
on round of = 14420
5. 6759 + 8210 + 7642 = 22,611
on round of = 22610
2,040
1,380
22,930
14,420
22,610
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I understand that the question you are looking for is:
Estimate the sum:
1 435 + 678 + 925 =
2.359 + 814 + 207 =
3. 6428 + 7154 + 9345 =
4. 2987 + 6873 + 4555 =
5. 6759 + 8210 + 7642 =
The length of a rectangle is 3 meters less than 2 times the width. the perimeter is 24 meters. find the width.
The width of the rectangle is: 3 meters.
What is the Perimeter of a Rectangle?Perimeter of a rectangle is determined using the formula:
Perimeter = 2(length + width)
Given the parameters below:
Width of the rectangle = w meters
Length of the rectangle = 2w - 3 meters
Perimeter of the rectangle = 24 meters
Therefore:
2((2w - 3) + w) = 24
Solve for w (width of the rectangle)
2((2w - 3 + w) = 24
2(3w - 3) = 24
6w - 6 = 24
6w = 24 - 6
6w = 18
6w/6 = 18/6
w = 3
Therefore, the width of the rectangle is: 3 meters.
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Let f(x)=x-2 and g(x)=x²-3 x+2 . Perform each function operation and then find the domain. g(x) / f(x)
The division of f (x) and g (x) is x - 1 and the domain is [ 1 , ∞ ].
Given,
f (x) = x - 2
g (x) = x ² - 3 x + 2
The question states to find the division of the function f, that is, f (x) = x - 2, and function g, that is, g (x) = x ² - 3 x + 2
Performing the division operation on these functions is just like simple division.
This implies, dividing the two functions f (x) and g (x), we get
g (x) / f (x) = x² - 3x + 2 / x - 2
x - 1
___________
x - 2 | x² - 3x + 2
x² - 2x
____________
-x + 2
-x + 2
____________
0
=> g (x) / f (x) = x - 1
This implies that the division of the two functions f (x) and g (x) gives x - 1
To find the domain :
y = x - 1
=> x ≥ 1
=> Domain = [ 1 , ∞ ]
Therefore, we get the division of f (x) and g (x) as x - 1 and the domain as [ 1 , ∞ ].
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Which equation is a linear function?
A) y=-3x2 - 5x+3
B) y=5.2x-3
C) -5y+ 3x = 7
D) y = -5√x + 11
Answer:
A.
Step-by-step explanation:
D: there is no square root
for both C and B there is no decimal.
A should end up being y=-8x+5 which is in y=mx+b form
Evaluate -3|15-8|.
-7
-21
18
Answer:
18=49
Step-by-step explanation:
Jabria added water to a tank by opening a value to produce a constant stream of water after 7 minutes the tank contained 3,482 gallons of water she waited 12 more minutes and observed that the tanks contained 7,298 gallons of water how much water was in the tank when Jabria began adding water?
Using a linear function, it is found that 1466 gallons of water were in the tank when jabria began adding water.
What is Mathematical function ?
Function is defined as the expression or relation between any given two variables such as x and y and there must be an independent variable and dependent variable.
A linear function is modeled by: y = mx + b
where,
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, we have given that in 12 minutes, the amount of water increased by 3456 gallons, hence the slope is given by :
m = 3456/12 = 288.
In 7 minutes, the tank contained 3,482 gallons of water, hence the initial amount was given by :
3482 - 7 x 288 = 1466
1466 gallons of water were in the tank when jabria began adding water.
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Last year, a popular brand of running
shoes cost $75.99 per pair. The new
model of the same shoe costs $95.99 per
pair. What is the percent of increase in
price for the pair of running shoes?
Round to the nearest tenth if necessary.
Answer:
answers is 26.3%.
Step-by-step explanation:
you will say ( NEW price-OLD price)
95.99-75.99=20
20/75.99*100%
=26.3%
Which statement describes the end behavior of this function?
9(x) = }|x
3| - 7
• A.
As x approaches negative infinity, g(x) is no longer continuous.
• B.
As x approaches positive infinity, g(x) approaches positive infinity.
• C.
As x approaches positive infinity, g(x) approaches negative infinity.
• D.
As x approaches negative infinity, g(x) approaches negative infinity.
The correct option for the end behaviour of function is option C. As x approaches positive infinity, g(x) approaches positive infinity.
What is defined as the end behaviour of function?End behavior of such a function f refers to the behavior of the function's graph at the "ends" of a x-axis. In other sayings, the end behavior of a function defines the graph's trend when we look to the right end of x-axis (as x approaches +) and the left end of the x-axis (since x approaches ).We have been assigned the following function:
g(x) = 1/2|x - 3| - 7
Behavior at the end: As x approaches negative and positive infinity, the limit of g(x) is reached.
Infinity minus one:
lim g(x) = lim 1/2|x - 3| - 7
x → -∞ x → -∞
lim g(x) = 1/2|-∞ - 3| - 7 = | -∞ | = ∞
x → -∞
Thus, the negative end behaviour is ∞ .
Infinity plus one:
lim g(x) = lim 1/2|x - 3| - 7
x → ∞ x → ∞
lim g(x) = 1/2|∞ - 3| - 7 = | ∞ | = ∞
Thus, positive end behaviour is also ∞ .
As a result, it approaches positive infinity in both cases, and the correct option is C.
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The correct question is-
Which statement describes the end behavior of this function?
g(x) = 1/2|x - 3| - 7
A. As x approaches positive infinity, g(x) approaches negative infinity.
B. As x approaches negative infinity, g(x) approaches negative infinity.
C. As x approaches positive infinity, g(x) approaches positive infinity.
D. As x approaches negative infinity, g(x) is no longer continuous.
Give possible values for the measures of angles A and C if ABC is an obtuse triangle.
( In triangle ABC, the measure of angle B is 50 degrees)
The possible values of angles A and C are;
60° and 70° or 55° and 75°
How to find the angles in a triangle?
An acute triangle is a triangle that has all the measures of its angles to be less than 90°. This means that none of the angles is greater than 90°
Since sum of the angles in a triangle is equal to 180°, then it means that;
∠A + ∠B + ∠C = 180°
We are given that;
∠B = 50°
Thus;
50° + ∠A + ∠C = 180°
∠A + ∠C = 180° - 50°
∠A + ∠C = 130°
It should be noted that all the angles of the acute triangle are also different.
Thus, the possible values of A and C are 60° and 70° or 55° and 75° because their sum must be equal to 130°
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3 4/15 divided by (8 times 6 3/10)
let's first of all, convert all the mixed fractions to improper fractions and then proceed.
[tex]\stackrel{mixed}{3\frac{4}{15}}\implies \cfrac{3\cdot 15+4}{15}\implies \stackrel{improper}{\cfrac{49}{15}} ~\hfill \stackrel{mixed}{6\frac{3}{10}}\implies \cfrac{6\cdot 10+3}{10}\implies \stackrel{improper}{\cfrac{63}{10}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\cfrac{3\frac{4}{15}}{ ~~ 8\cdot 6\frac{3}{10} ~~ }\implies \cfrac{\frac{49}{15}}{ ~~ 8\cdot \frac{63}{10} ~~ }\implies \cfrac{\frac{49}{15}}{ ~~ \frac{252}{5} ~~ }\implies \cfrac{49}{15}\cdot \cfrac{5}{252}\implies \cfrac{49}{252}\cdot \cfrac{5}{15} \\\\\\ \cfrac{7}{36}\cdot \cfrac{1}{3}\implies \cfrac{7}{108}[/tex]
For every three girls taking classes at a
martial arts school, there are 4 boys
who are
taking classes. If there are 236 boys
taking
classes, predict the
number of girls taking
classes at the school.
Answer:
We would predict 177 girls
Step-by-step explanation:
We can set up a proportion
[tex]\frac{Girls}{Boys}[/tex] = [tex]\frac{Girls}{Boys}[/tex] Put in the number that I know and solve for the number that I do not know.
[tex]\frac{3}{4}[/tex] = [tex]\frac{g}{236}[/tex] I can cross multiply to solve for x
4g = 3(236)
4g = 708 Divide both sides by 4
g = 177
What is the equation for the graph shown?
The equation of the line shown in the reference graph, attached hereby, that passes through the points (-6, 0) and (0, 4) is [3y = (2x + 12)].
As per the question statement, we are provided with a straight line, drawn on the cartesian quadrants that pass through two points, (-6, 0) and (0, 4).
We are required to determine the equation of the line.
To solve this question, we need to know the formula to determine the linear equation of a line passing through two points, (x₁, y₁) and (x₂, y₂), which goes as [tex][(y-y_{1})=(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}) (x-x_{1})][/tex].
Here, let us consider, (-6, 0) to be (x₁, y₁), and (0, 4) to be (x₂, y₂). Therefore, using these values in the above mentioned equation, we get
[tex](y-0)=[\frac{4-0}{0-(-6)}][x-(-6)]\\ or, y=(\frac{4}{6})(x+6)\\ or, y=(\frac{2}{3})(x+6)\\or, 3y=2x+12[/tex]
Equation: An equation is a mathematical statement having two separate expressions, connected by an equal signLine: A line is an one-dimensional figure, having infinite length but no width.To learn more about Equations of Lines, click on the link below.
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help me this is transformations review
The triangle UVW have vertices at U(-3, -4), V(-3, -3) and W(-2, -4). UVW is reflected across x = -2 to get U'(-1, -4), V'(-1, -3) and W'(-2, -4)
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformations are rotation, translation, reflection and dilation.
Translation is the movement of a point either up, down, left or right in the coordinate plane.
The triangle UVW have vertices at U(-3, -4), V(-3, -3) and W(-2, -4). UVW is reflected across x = -2 to get U'(-1, -4), V'(-1, -3) and W'(-2, -4)
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Marisa said that multiplying 8.0 by 106 would increase the value of the 8 because there would be 6 more zeros to the right of the decimal point. Explain what is wrong with Marisa's statement.
May you help me?
Answer:
The value behind a decimal point isn't increased by zeros, zeros are actually just placeholders
Step-by-step explanation:
Please help!! Thanks!
What is the range of the function y = |x+2 | −2 if the domain is a x € R?
The range of the function f(x) = | x + 2| - 2 for all x belongs to real is [-2,∞].
What are closed and open interval ?Closed interval includes the points and we denote it by third brackets and open interval do not include the points and denoted by first brackets.
According to the given question we have to determine the range of the function y = |x + 2| - 2 where domain of x ∈ R.
We know, |x + 2| ≥ = 0.
∴ | x + 2 | - 2 ≥ -2 and f(x) = | x + 2 | - 2 so, f (x) ≥ - 2, ∀ x ∈ R.
There fore the range of the function f(x) is [ -2, ∞ ].
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solve for the indicated variable a/b = c for b
Answer:
b = [tex]\frac{a}{c}[/tex]
Step-by-step explanation:
[tex]\frac{a}{b}[/tex] = c ( multiply both sides by b )
a = bc ( isolate b by dividing both sides by c )
[tex]\frac{a}{c}[/tex] = b
The question is listed below:
Answer:
[tex]3\sqrt{5}[/tex]
Step-by-step explanation:
Factor out a [tex]\sqrt{5}[/tex] from the [tex]\sqrt{80}[/tex], and you will get [tex]\sqrt{5} * \sqrt{16}[/tex]
Then you get: [tex]4\sqrt{5}[/tex], since the square root of 16 is just 4. Then we have this expression:
[tex]4\sqrt{5} -\sqrt{5}[/tex], which gives us [tex]3\sqrt{5}[/tex].
Hope this helps
3) Tim has 5/10 of a book left to read for school. Tim read 1/8 of a book on Monday. Tim reads 10/13 times faster on weekends. How many more books does Tim need to read?
The fraction that's left to read in the book is 3/8.
How to calculate the fraction?From the information given, it should be noted that Tim has 5/10 of a book left to read for school. Tim read 1/8 of a book on Monday.
Therefore, the fraction that will be left to read will be:
= 5/10 - (1/8)
= 20/40 - 5/40
= 15/40
= 3/8.
The fraction that is left will be 3/8.
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Let f(x)=3 x²-11 x-4 and g(x)=3 x+1 . What are f . g and f/g and their domains?
If the two functions be f(x) = 3x² - 11x - 4 and g(x) = 3x + 1 then
(fg)(x) = f(x)g(x) = [tex]$$9x^3[/tex] - 30x² - 23x - 4
(f/g)(x) = f(x)/g(x) = x - 4
What is meant by function operation?
Function operations are the rules we use to solve functions. There is a specific way to deal with function addition, multiplication, and division.
Function composition is a mathematical operation that takes two functions f and g and produces a function h = g f such that h(x) = g(f(x)). The function g is applied to the result of applying the function f to x in this operation.
Let the two functions be f(x) = 3x² - 11x - 4 and g(x) = 3x + 1.
(fg)(x) = f(x)g(x)
= (3x² - 11x - 4) (3x + 1)
simplifying the above equation, we get
= 3x² [tex]*[/tex] 3x + 3x² [tex]*[/tex] 1 - 11x [tex]*[/tex] 3x - 11x [tex]*[/tex] 1 - 4 [tex]*[/tex] 3x - 4 [tex]*[/tex] 1
= [tex]$$9x^3[/tex] - 30x² - 23x - 4
Therefore, (fg)(x) = f(x)g(x) = [tex]$$9x^3[/tex] - 30x² - 23x - 4
(f/g)(x) = f(x)/g(x)
Where, f(x) = 3x² - 11x - 4 and g(x) = 3x + 1.
f(x)/g(x) = (3x² - 11x - 4)/(3x + 1)
= [(3x + 1)(x - 4)]/(3x + 1)
canceling the common factors we get
= x - 4
Therefore, f(x)/g(x) = x - 4
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PLS HELP MEEE what is equation y??
what are the rules for dividing integers
Answer: Positive ÷ positive = positive.
Negative ÷ negative = positive.
Negative ÷ positive = negative.
Step-by-step explanation: The division of two positive integers results positive integer.
Positive (+) ÷ Positive (+) = Positive (+)
The division of two negative integers results positive integer.
Negative (+) ÷ Negative (+) = Positive (+)
The division of two different sign integers results negative integer.
What is the expression ∛(a)⁷ written as a variable raised to a single rational exponent?
The expression ∛(a)⁷ raised to a single rational exponent is [tex]a^{\frac{7}{3} }[/tex] .
A rational number is one that can be defined as the ratio or fraction a/b of two numbers, where a and b are the numerator and denominator, respectively. Here the integer numbers a and b are co prime numbers.
For example 8/7 is a rational number and all integers are rational numbers.
Any combination of terms that have undergone operations like multiplication,addition, subtraction, division is known as an algebraic expression.
it is given that the expression is of the form ∛(a)⁷ .
We know that the n-th root of a variable x ([tex]\sqrt[n]{x}[/tex]) can also be written as
[tex]x^{\frac{1}{n} }[/tex].
Therefore ∛(a) can be written as [tex]a^{\frac{1}{3} }[/tex] . Now the complete expression is ∛(a)⁷.
So [tex](a^{\frac{1}{3} })^7=a^{\frac{7}{3} }[/tex] and we know that 7/3 is a rational number.
Therefore the expression can be written as [tex]a^{\frac{7}{3} }[/tex] using rational exponents.
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Select the step that is not part of the process for copying ∠CAB.
A - Draw a line and mark A' on it.
B - Set the compass to length AB.
C - Place the compass point at A' and mark an arc crossing the new line.
D - Label the intersection of the arc and the new line C'.
The only one that is not part of the process for copying ∠CAB is; Option D: Label the intersection of the arc and the new line C'.
What are the steps in copying an angle?The steps for constructing a copy of an angle using only a compass and a straightedge are as follows;
Step 1: Mark the point that will be the vertex of the new angle, and label it P.
Step 2: Draw a ray from P in any direction, with any length. This ray will be one of the sides of the new angle.
Step 3: Place the compass point on the vertex of the original angle, and adjust the compass width to a convenient size.
Step 4: Use the compass to draw an arc intersecting both rays of the original angle at two points, J and K.
Step 5: Move the compass (without changing the width) to point P, and make an arc intersecting the existing ray of the angle. Mark the intersection point, and label it M.
Step 6: Set the compass point on the original angle at point J, and set its width to the length of line segment JK.
Step 7: Move the compass point to M on the new angle, and draw an arc cutting the previous arc. Mark the intersection point and label it L.
Step 8: Draw a ray from point P through point L. The new angle is a copy of the original angle.
Looking at the given options, the only one that is not part of the process for copying ∠CAB is; Option D: Label the intersection of the arc and the new line C'.
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Answer:
d
Step-by-step explanation:
Discuss the advantages and disadvantages of histograms versus stem-and-leaf plots.
Data of different sizes can be easily arranged with histograms, but not with stem-and-leaf diagrams. This is a drawback.
What are Stem-and-leaf charts?Stem-and-leaf charts often include the original data values while histograms do not. This is a crucial advantage the former has over the latter.
The primary benefit of stem-and-leaf charts over histograms is that they display the original data values.
In contrast to stem-and-leaf charts, which lack this capability, histograms make it straightforward to organize data of various sizes. This is a serious disadvantage.
In conclusion, a stem-and-leaf display, sometimes referred to as a stem-and-leaf plot, is a tool that shows quantitative data graphically to assist visualize the form of a distribution.
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pls do the table in the picture
Step-by-step explanation:
(a-b)+ccase 1 a=0.5 , b=2 , c=-1
(0.5-2)-1 = -1.5 - 1
= -2
case 2 a=3 , b=-4 , c=-2
(3+4) -2 = 7 - 2
= 5
case 3 a=-8 , b=5 , c=3
(-8+5)+3 = -3+3
= 0
-(a-b)-ccase 1 a=0.5 , b=2 , c=-1
-(0.5-2)+1 = -(-1.5)+1
= +1.5 + 1
= 2.5
case 2 a=3 , b=-4 ,c=-2-(3+4)+2 = -(7) +2
= -5
case 3 a=-8 , b=5 , c=3
-(-8-5) -3 = -(-13) -3
= +13 -3
= 10
A group of friends decides to attend a concert. The group pays $125 per ticket and each person chips in $6 for parking. A total of $85 is spent on concessions. If the group spent $740, how many friends are in the group?
ASAPPP!!
PLS SOMEONE HELP ME WITH THIS
Answer:
Remove 1 stripyRemove 3 stripyAdd 2 plainsAdd 5 plainsHope this helps!
Let g(x)=3 x+2 and f(x)=x-2 / 3 . Find each value.
(f⁰g)(-2)
Value for (f⁰g)(-2) = -6/3
What is the domain of the function (f⁰g)(-2)?Given :
g(x) = 3x + 2
f(x) = (x-2)/3
Now,
(f⁰g)(x) = f(g(x))
(f⁰g)(-2) = f(g(-2))
substitute x = -2
g(-2) = 3(-2) + 2 = -4
f(g(-2)) = f(-4)
(f⁰g)(-2) = f(-4) = -6/3
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