Answer:
A∩B = { 3 }
Step-by-step explanation:
A∩B means "the intersection of A and B" as in "all elements that appear in BOTH sets".
Only 3 appears in both sets.
) If 4x - 3y = 12 and y = -4, then x =
Answer:
x=0
Step-by-step explanation:
4x -3y =12
4x - 3(-4)=12
4x+12=12
4x=0
x=0
A rule for creating a pattern is given below. The rule begins with a number called the input and creates a number called the output. Rule: Multiply the input by 6 to get the output. Which input and output table works for the rule? Choose 1 answer:
2 is the input value, while 6 is the result.
We know the rule is Multiply the input by 6 to get the output.
= (2*5)-4
=10-4
=6.
A function rule is the equation-based relationship between dependent and independent variables. How to calculate the value of the dependent variable, say y, in terms of the independent variable, say x, is explained by the function rule of a particular function. A function table includes a function rule as well as input and output values. If we plug in various values for the input, we obtain corresponding values of output according to the function rule. The relationship between the input values x and the output values y always follows a pattern that is specified by the function rule.
Hence, the input and output value of a table is 2 and 6.
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you are working on an air conditioning system. A roll of cylindrical copper tubing has an outside diameter of 7/8 inch and an inside diameter of 3/4 inch. How much refrierant can 12 feet of the tubing hold?
The amount of refrierant the tubing can hold is 0.037 cubic feet..
How much refrierant can the tubing hold?A cylinder is a three-dimensional object that is made up of a prism with a circular base. In order to determine how much refrigerant that cylindrical coil can hold, the volume of the cylinder has to be determined.
First, the dimension of the inside diameter has to be changed to feet
1 inch = 1/12 feet
3/4 x 1/12 = 1/16 feet
Volume of a cylinder = πr²h
Where:
π = pi = 22/ 7r = radius = diameter / 2 = 1 /16 ÷ 2 = 1 /16 x 1/2 = 1/32h = heightVolume = 22/7 x (1/32)² x 12 = 0.037 cubic feet.
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Translate the following into a math expression:
twenty less than the product of five and a number
A: (x+5) - 20
B: 20-5x
C: 5x-20
D: 5/x - 20
Answer:
[tex]5x - 20[/tex]
Step-by-step explanation:
Product means the result of the multiplication of two numbers. A part of our expression will include the product of five and a number. We don't know what number it is, therefore, we'll call it [tex]x[/tex]. The product of those two numbers can be algebraically expressed as [tex]5x[/tex] (we usually eliminate the multiplication sign between numbers and variables).
We are then asked to express the number that is 20 less than the product we found earlier. To find this expression, we should subtract 20 from the product, giving us [tex]5x - 20[/tex].
Tyler has a shoe box in the shape of a right rectangular prism. He is filling the box with cubes that are each 1 cubic inch in order to find the volume of the box. He finds that 48 cubes completely fill the bottom of the box and that he can put 2 more layers of cubes in the box. What is the volume of the box in cubic inches?
The volume of Tyler's shoe box is 144 cubic inch
From the question, we are to calculate the volume of the shoe box.
From the given information, we have that
Tyler is filling the shoe box with cubes that are each 1 cubic inch.
and
He found out that 48 of the 1 cubic inch cube completely fills the bottom of the box
Also,
He observed that he can put 2 more layers of cubes in the box.
Thus,
The number of 1 cubic inch cube that would completely fill the box is
48 + (2×48)
= 48 + 96
= 144 cubes
Since the cubes are 1 cubic inch each,
Then,
The volume of the shoe box = 144 × 1 cubic inch
Volume of the shoe box = 144 cubic inch
Hence, the volume of Tyler's shoe box is 144 cubic inch
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You find that the number of messages you receive on your message board varies directly as the numbers of messages you post. When you post 5 messages, you receive 12 messages in return. Which variation equation can be used to predict how many messages you will post in order to receive 96 messages? A y = 12/5x - 96 B y = 5/12x + 96 C y = 12/5x
Answer: C) y=12/5x
Step-by-step explanation:
Divide 12 messages by 5 posts to find out how many messages you would receive for just posting 1 message (2.4)
Then determine how many times it goes into 96 (2.4 x 40 = 96)
What is (−116)(51)(−2)?
1,392
−1,392
11,832
−11,832
Answer:
11832 ............
Step-by-step explanation:
Y = (-116)(51)(-2)
Y = (-116) × (51) × (-2)
Let's multiply the +- symbols first ...... So ,. (-) × (+) × (-) = (+)NOTE :- (+) × (+) = (+) (+) × (-) = (-) (-) × (+) = (-) (-) × (-) = (+) After we multiply the numbers ...... (116) × (51) × (2) = 11832so combined the number and symbol ...... That's the Answer ... Answer : + 11832 = 11832Which explanation could be used to verify whether the functions are inverses?
Neither of the lines is parallel to the line y = x; therefore, the functions are inverses of each other.
Neither of the lines is parallel to the line y = x; therefore, the functions are not inverses of each other.
The point of intersection of the two functions is not on the line y = x; therefore, the functions are inverses of each other.
The point of intersection of the two functions is not on the line y = x; therefore, the functions are not inverses of each other.
The explanation that could be used to verify whether the functions are inverses is; The point of intersection of the two functions is not on the line y = x; therefore, the functions are not inverses of each other.
How to Interpret Function Inverses?
If we assume that (a, b) is a point that lies on both the graph y = f(x) and the graph y = f⁻¹(x), then from the second condition, it follows that the point (b, a) lies on the graph of f.
So, we’re looking for a function whose graph includes two points (a, b) and (b, a) and we want a ≠ b. An example is;
f(x) = -1/x³
So that the inverse function is f⁻¹(x) = 1/x^(1/3)
Thus, applying that concept to this question and we can conclude that the point of intersection of the two functions is not on the line y = x; therefore, the functions are not inverses of each other.
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ZRQT is a straight angle. What are mZRQS and
mZTQS?
mZRQS =
m/TQS=
RQS(9x+1)°
TQS(7x+3)°
The measure of the angle RQS is 100 degrees, and the measure of the angle TQS is 80 degrees.
What is an angle?When two lines or rays converge at the same point, the measurement between them is called a "Angle."
It is given that:
ZRQT is a straight angle
The sum of the angle RQS and angle TSQ will be 180 degrees
9x + 1 + 7x + 3 = 180
16x + 4 = 180
16x = 176
x = 176/16
x = 11
RQS(9x+1)° = 9x11 + 1 = 100
TQS(7x+3)° = 7x11 + 3 = 80
Thus, the measure of the angle RQS is 100 degrees, and the measure of the angle TQS is 80 degrees.
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Austin and Cody went to a carnival. They got to the carnival at nine minutes to nine in the morning and didn't leave until half past four in the afternoon. How long did Austin and Cody stay at the carnival?
Recipe ingredients remain in a constant ratio no matter how many servings are prepared. Which table shows a possible ratio table for ingredients X and Y for the given number of servings?
A 3-column table with 3 rows. Column 1 is labeled Servings 1, 2, 3. Column 2 is labeled x with entries 1, 2, 3. Column 3 is labeled Y with entries 2, 3, 4.
A 3-column table with 3 rows. Column 1 is labeled Servings 1, 2, 3. Column 2 is labeled x with entries 1, 2, 3. Column 3 is labeled Y with entries 2, 4, 8.
A 3-column table with 3 rows. Column 1 is labeled Servings 1, 2, 3. Column 2 is labeled x with entries 1, 2, 3. Column 3 is labeled Y with entries 2, 3, 5.
A 3-column table with 3 rows. Column 1 is labeled Servings 1, 2, 3. Column 2 is labeled x with entries 1, 2, 3. Column 3 is labeled Y with entries 2, 4, 6.
A table which shows a possible ratio table for ingredients X and Y for the given number of servings is table 4.
What is a proportion?A proportion can be defined as an equation which is typically used to represent (indicate) the equality of two (2) ratios. This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities.
Mathematically, a direct proportion can be represented the following equation:
y = kx
Where:
y and x are the variables.k represents the constant of proportionality.Since the recipe ingredients remain in a constant ratio, we have:
k = y/x
For table 1, we have:
k = 2/1 = 2.
k = 3/2 = 1.5.
k = 4/3.
For table 2, we have:
k = 2/1 = 2.
k = 4/2 = 2.
k = 8/3.
For table 3, we have:
k = 2/1 = 2.
k = 3/2 = 1.5.
k = 5/3.
For table 4, we have:
k = 2/1 = 2.
k = 4/2 = 2.
k = 6/3 = 2.
In conclusion, a table which shows a possible ratio table for ingredients X and Y for the given number of servings is table 4 as shown in the image attached below.
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Tracey paid $135 for an item that was originally priced at $260. What percent of the original price did Tracey pay?
Round your percentage answer to two decimal places.
Do NOT include a
%
symbol with your answer
Answer:
51.92
Step-by-step explanation:
135/260 = .51923076923 x 100 to get the percentage
51.923076923 and round
Amanda wants to project a movie from her phone to a screen on the wall. The side length of the screen on the wall is 56 in. The scale from the screen on the wall to the phone is 7 in. to 1 in. What is the side length of Amanda's phone?
The side length of Amanda's phone is 8 inches.
What is the side length?A scale drawing is either an enlarged or reduced image of another image or object. A scale drawing is enlarged or reduced using a scale. A scale is a used to determine the ratio between the scale drawing and the original diagram.
The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. The scale in this diagram is 7inches to 1 inches. This means that the screen on the wall is 7 times larger than her phone's screen.
In order to determine the side length of Amanda's phone, divide the scale of the screen by the side length of the screen on the wall.
Side length of Amanda's phone = 56 inches / 7 inches
= 8 inches
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write an absolute value equation that has the given solutions x=--10 and x=4
The suggested answers to the absolute value problem l x - 13 l = 7.
Except for 0, the absolute value is represented by a positive integer. In a variety of mathematical and physical situations, the notions of magnitude, distance, and norm are intimately related to the concept of absolute value.
In order to do this on a budget, find a number N that:
N-10=-(N + 4)
When we isolate N, we obtain:
2N= 10-4= 6
N= 6/2= 3
Following that, N-10= 3-10=-13, and N + 4= 3 + 4= 7.
as well as the fact that I-13I= I7I.
We can now express our equation as follows:
l x-13 l =7
As a result, where the roots (or solutions) of x = -10 and x = 4 are.
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Please can anyone help me
Answer:
x = 121°
Step-by-step explanation:
180° - 155° = 65°
360° - 304° = 56°
x = 65° + 56° = 121°
A 6.5 foot tall man casts a shadow that is 4.7 feet long. If the shadow of a flag pole is 8 feet long, how tall
is the flag pole?
The flag pole is
feet tall.
Enter an integer or decimal number [more..]
Round to the nearest tenth of a foot if needed.
Answer:
11.1
Step-by-step explanation:
This is a question involving ratios and proportions
The ratio of man's height to his shadow length = 6.5/4.7
The ratio of flagpole height to its shadow must be in the same ratio
If h is the height of the flagpole then h/8 is the ration of height to shadow length
Therefore,
[tex]\dfrac{6.5}{4.7} = \dfrac{h}{8}\\\\\mathrm{Multiplying \;both\;sides\;by\;8\;}\\\\\dfrac{6.5 \times 8 }{4.7} = h \\\\Or,\\h = \dfrac{6.5 \times 8 }{4.7} \\\\Which\;simplifies\;to:\\\\h = 11.0638\\\\h = 11.1 \;rounded\;to\;the\;nearest\;tenth\;of\;a\;foot[/tex]
Twice the difference of a number and three is four. Find the number.
Answer: 5
Step-by-step explanation:
2(x-3)=4
2x-6=4
Add 6to each side
2x=10
Divide each side by 2
X=5
Does this help?
Answers these please
Answer:
2. 4f+s, 3. 3c+10, 4. b-3, 5. f < 2t, 6. 3p + b, 7. 5w + 2, 8. c + 2w + f < 100
Question Find the equation of a line that contains the points (-7, 6) and (3, 8). Write the equation in slope-intercept form.
The equation of a line that contains the points (-7, 6) and (3, 8) is [tex]y=\frac{1}{5} x+\frac{37}{5}$$[/tex]
Find the line [tex]$y=m x+b$[/tex]passing through [tex]$(-7,6),(3,8)$[/tex]
Compute the slope [tex]$(-7,6),(3,8): \quad m=\frac{1}{5}$[/tex]
Compute the [tex]$y$[/tex] intercept: [tex]$\quad b=\frac{37}{5}$[/tex]
Construct the line equation [tex]$\mathrm{y}=\mathrm{mx}+\mathrm{b}$[/tex]where [tex]\mathrm{m}=\frac{1}{5}$ and $\mathrm{b}=\frac{37}{5}$[/tex]
[tex]y=\frac{1}{5} x+\frac{37}{5}$$[/tex]
The Slope intercept form is a system for determining a straight line's equation. The equation of a straight line is the relationship that
The slope- intercept form of a straight line is used to find a line's equation. The pitch of the line and the intercept cut by the line with the y- axis are needed for the pitch- intercept formula. Consider a straight line with pitch' m' and y- intercept For a straight line with a pitch, 'm,' and' b' as the y- intercept, the pitch intercept form equation is y = mx b. Then are some cases of pitch intercept forms.
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Which deciamal shows 0.06 as an equivalent number of thousands?
The decimal that shows 0.06 as an equivalent number of thousands is 0.060
How to determine the decimal that shows 0.06 as an equivalent number of thousands?The number is given as
0.06
To determine the equivalent number of the decimal in thousands, we simply add more zeros after the last significant digits
So, we have
Number = 0.0600000
Reduce the zeros till the thousandth place value
So, we have
Number = 0.060
Hence, the decimal that shows 0.06 as an equivalent number of thousands is 0.060
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What is the equation of the line that passes through (1, 3) and (-2, -3)?
Answer:
y = 2x + 1
Step-by-step explanation:
The slope is
[tex]\frac{-3-3}{-2-1}=2[/tex]
Substituting into point-slope form, the equation is
[tex]y-3=2(x-1)[/tex]
which rearranges into slope-intercept form as:
[tex]y-3=2x-2 \\ \\ y=2x+1[/tex]
I need help with this
Answer:
d is the answer to your question
Find the quotient and the remainder when x- + 5x + 2 is divided by x + 1
Answer: The quotient is when x+ 5x + 2 = 6
The reminder is when x+ 5x + 2 = -4
Step-by-step explanation:
Given data,
The quotient and the remainder when x + 5x + 2 is divided by x + 1
Let, f(x) = x + 5x + 2
g(x) = x+1
we can write,
g(x) = x+1 = 0
g(x) = x = -1
so, f(x) = x + 5x + 2
we can substitute x = -1 value
f(x) = x + 5x + 2
f(-1) = (-1) + 5(-1) + 2
f(-1) = (-1) - 5 + 2
f(-1) = (-1) - 3
f(-1) = -4
Therefore,
The quotient is when x+ 5x + 2 = 6
The reminder is when x+ 5x + 2 = -4
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Given a rectangle that is 46 cm longer than it is wide. Express the perimeter (in cm) of a rectangle in terms of its width w.
Answer:
2(46+w) + 2(w)
Step-by-step explanation:
Write an expression in factored form for the polynomial of the least possible degree graphed below.
The expression in factored form for the polynomial of the least possible degree is f(x) = (3 / 16) · (x + 2) · (x + 1) · (x - 2) · (x - 4).
How to write a polynomial in factored form
A polynomial can be written as a product of a constant named lead coefficient and binomials of the form x - r, where r is the root of the polynomial. A root is a value of x such that the polynomial is equal to zero and the lead coefficient can be determined by using the y-intercept of the graph, then:
f(x) = a · (x + 2) · (x + 1) · (x - 2) · (x - 4)
Where a is the lead coefficient.
If we know that f(0) = 3, then the value of the lead coefficient is:
3 = a · (0 + 2) · (0 + 1) · (0 - 2) · (0 - 4)
3 = 16 · a
a = 3 / 16
The expression in factored form for the polynomial of the least possible degree is f(x) = (3 / 16) · (x + 2) · (x + 1) · (x - 2) · (x - 4).
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Mia Wong is receiving the total accounts receivable of Wong's department store. Credit customers paid $90,000 this month. This represents 60% of all receivables due. What is Mia's total accounts receiving?
Mia's total accounts receiving is $1,50,000.
What is the total accounts receiving?Accounts receivable refers to the sum of money due to a company for goods or services delivered or utilized but not yet paid for by customers (AR). The balance sheet classifies accounts receivable as a current assets. Any money that clients owe for purchases they purchased using credit is referred to as "AR" (account receivable).Given :
receivables dues paid by customers = $90,000
Let Mia's total accounts receiving be $ x.
According to the question,
⇒ 60% of x = 90,000
⇒ [tex]\frac{60}{100} x[/tex] = 90,000
⇒ x = (90,000×100) /60
= 1,50,000
Therefore, Mia's total accounts receiving is $1,50,000.
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The hypotenuse of a right triangle is 13 cm long. The longer leg is 7cm longer than the shorter leg. Find the side lengths of the triangle.
Length of the shorter leg:
Length of the longer leg:
Length of the hypotenuse:
The information about the triangle will be:
Length of the shorter leg: = 5cm
Length of the longer leg: = 12cm
Length of the hypotenuse: = 13cm
How to illustrate the information?It should be noted that the formula for illustrating the information is:
c² = a² + b²
where c = hypothenuse
The shorter leg = x
Longer leg = x + 7
Hypothenuse = 13
Therefore, c² = a² + b²
13² = x² + (x + 7)²
169 = x² + x² + 14x + 49
169 = 2x² + 14x + 49
169 - 2x² - 14x - 49 = 0
-2x² - 14x + 120 = 0
Multiply through by minus
2x² + 14x - 120 = 0
Divide through by 2
x² - 7x - 60
x² - 12x + 5x - 60
x(x - 12) + 5(x - 12)
Therefore, the smaller length is 5cm and the bigger Length is 12cm
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Line h passes through point (3,0) and is perpendicular to the graph of y=1/5x-19. Line g is parallel to line h and passes through point (-1.15). What is the equation in slope intercept form of line g?
Answer:
y = -5x + 10
Step-by-step explanation:
Answer:
-5x + 10
Step-by-step explanation:
If a line 2 is perpendicular to line 1 and line 1 has slope m, then line 2 must have slope = [tex]\sf -\dfrac{1}{m}[/tex] which is the negative of the reciprocal of m
Essentially the product of the two slopes = -1
The line
[tex]y = \dfrac{1}{5}x - 19[/tex]
has slope of [tex]\dfrac{1}{5}[/tex] so the slope of line h which is perpendicular to this line must have slope = negative of reciprocal of [tex]\dfrac{1}{5}[/tex]
Reciprocal of [tex]\dfrac{1}{5}[/tex] is 5
Negative of reciprocal is thus -5
Equation of h is of the form
y = -5x + b where b is the y intercept, the value of y at x = 0
Since line h passes through (3, 0) we plug in these values for x and y and solve for b
0 = -5(3) + b
0 = -15 + b
15 = b (Adding 15 on both sides)
b = 15
Equation of line h is y = -5x + 15
Line g is parallel to line h. Parallel lines have the same slope so the equation for line g is
y = -5x + b (since slope of g = slope of h = -5)
Since this line passes through x = -1, y = 15 we can solve for b as before by plugging these values into the equation
15 = -5(-1) + b
15 = 5 + b
10 = b (Subtracting 5 on both sides)
b = 10
So equation of line g = -5x + 10
If b2 is changed from 7 to 9 what value will appear in c3 if c3 contains the formula =b2*2
The value of C3, when B2 is changed from 7 to 9 is 18.
Given that, B2 is changed from 7 to 9.
What is the formula?The formula is a fact or a rule written with mathematical symbols. It usually connects two or more quantities with an equal sign. When you know the value of one quantity, you can find the value of the other using the formula.
The given formula = B2 × 2
When B2 is 7, the value of C3 is 14
When B2 is changed from 7 to 9, the value of C3 is B2 × 2 = 9 × 2
=18
Therefore, the value of C3, when B2 is changed from 7 to 9 is 18.
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What are the solutions to the following inequality?
2x+6<4
We get that, the solution for the inequality 2 x + 6 < 4 will be x ∈ ( - ∞ , - 1 ).
We are given an inequality:
2 x + 6 < 4
We need to find the solution for the inequality.
2 x + 6 < 4
Subtract 6 from both the sides, we get that:
2 x + 6 - 6 < 4 - 6
2 x < - 2
Divide both the sides by 2, we get that:
2 x / 2 < - 2 / 2
x < - 1
x ∈ ( - ∞ , - 1 )
Therefore, we get that, the solution for the inequality 2 x + 6 < 4 will be x ∈ ( - ∞ , - 1 ).
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