We are given the following equation
\(-3\mleft(x-14\mright)+9x=6x+42\)Let us solve the equation for x.
Step 1:
Multiply the term -3 with the terms in the parenthesis.
\(\begin{gathered} -3(x-14)+9x=6x+42 \\ -3x+42+9x=6x+42 \end{gathered}\)Step 2:
Simplify the terms on the left-hand side of the equation
\(\begin{gathered} -3x+42+9x=6x+42 \\ 42+6x=6x+42 \end{gathered}\)Step 3:
Combine the like terms together.
\(\begin{gathered} 42+6x=6x+42 \\ 42-42=6x-6x \\ 0=0 \end{gathered}\)This means that this equation has an infinite number of possible solutions.
If you notice the left and right side of the equation are exactly the same.
\(42+6x=6x+42\)This means that whatever value of x you put into this equation, the equation will always be satisfied.
Try substituting some values for x.
\(\begin{gathered} 42+6(1)=6(1)+42 \\ 42+6=6+42 \\ 48=48 \end{gathered}\)\(\begin{gathered} 42+6(-2)=6(-2)+42 \\ 42-12=-12+42 \\ 30=30 \end{gathered}\)Hence, the given equation has an infinite number of possible solutions.
Find the volume of the triangular prism?
Answer:
i not understand this question plase ask full question
3 1/2 - 9 3/4 please solve
Answer:
-6 1/4
Step-by-step explanation:
3 1/2 - 9 3/4
Get a common denominator
3 1/2 * 2/2 - 9 3/4
3 2/4 - 9 3/4
Subtract the smaller number from the larger number and take the sign of the larger
9 3/4 - 3 2/4
6 1/4
The sign is negative for 9 3/4 so
- 6 1/4
A probability experiment consists of rolling a 6-sided die. Find the probability of the event bel
rolling a number less than 5
The probability is
(Type an integer or decimal rounded to three decimal places as needed.)
The probability of rolling a number less than 5 is 0.667.
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event asked. The value is expressed from zero to one. An outcome is a value we can obtain.
As we are given a 6-sided dice therefore,
Total possible outcomes = 6
Favorable outcomes (that is less than 5) = 4 [that are; 1, 2, 3, 4]
probability = number of favorable outcomes/number of possible outcomes
probability = 4/6
4/6 = 2/3
= 0.6666666666666
To round the value to three decimal places, we need to see if the fourth value after decimal is more than 5 or not. If it is more than 5, preceding digit is increased by 1. therefore, by applying the rule to the value we get
= 0.667 [rounded to three decimal places as needed]
therefore, the probability of the event given, that is rolling a number less than 5 is 0.667.
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Which expression is equivalent to 6√8 √√2?
A. 48√/2
B. 24
C. 24√2
D. 48
Answer:
\(6 \sqrt{8} \sqrt{2} = 6 \sqrt{16} = 6(4) = 24\)
B is the correct answer.
For the question of total area of the cuboid is 200cm^.
I understand where we divide 150 by 4.
But why do I need to multiply by 5, when there are 6 faces.
You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.
When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.
A cuboid has six faces, but each face has a pair that is identical in size and shape.
Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.
To find the surface area of a cuboid, you can add up the areas of all its faces.
However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:
(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.
By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.
Essentially, you are considering one face from each pair and then summing their areas.
Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.
When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.
Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.
Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.
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Find the area of the polygon.
16 ft
14 ft
2 ft
2 ft
Answer:
448ft
Step-by-step explanation:
16 x 14 x 2 x 2
\ / \ /
224 x 4
\ /
448
The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is three times the measure of the first angle. The third angle is 29 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.
====================================================
Explanation:
The three angles add to 180, so x+y+z = 180
The second and third angles add to 3 times the measure of the first, so y+z = 3x
The third angle is 29 more than the second, so z = y+29
----------------------------
The system of equations is
\(\begin{cases}x+y+z = 180\\\\y+z = 3x\\\\z = y+29\end{cases}\)
For now, let's focus on the second and third equations only.
Start with y+z = 3x. Replace z with y+29 which is valid because of the third equation.
So we'll have
y+z = 3x
y+y+29 = 3x
2y+29 = 3x
Let's isolate y
2y+29 = 3x
2y = 3x-29
y = (3x-29)/2
y = 3x/2 - 29/2
y = 1.5x - 14.5
We'll use this later.
--------------------------
Go back first equation of the system. Plug in z = y+29
x+y+z = 180
x+y+y+29 = 180
x+2y+29 = 180
Then plug in y = 1.5x - 14.5 we found earlier
x+2y+29 = 180
x+2(1.5x-14.5)+29 = 180
x+3x-29+29 = 180
4x = 180
x = 180/4
x = 45
---------------------------
We can use this x value to find y
y = 1.5x - 14.5
y = 1.5*45 - 14.5
y = 53
and use this to find z
z = y+29
z = 53+29
z = 82
As a check, x+y+z = 45+53+82 = 180 to help confirm the answer. I'll let you check the other equations.
g The equation for the change of position of a train starting at x = 0 m is given by The dimensions of b are Select one: a. L-1T-1 b. LT-1 c. T-3 d. LT-2 e. LT-3
Answer:
B. LT⁻¹Step-by-step explanation:
The question is incomplete. Here is the complete question,
The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__
from the equation of motion given, the constant b is the velocity of the body. For us to get the dimension of b, we have to find the dimension of the velocity .
Since velocity is the rate of change of displacement of a body, then;
VELOCITY = DISPLACEMENT/TIME
displacement is measured in metres while time in seconds.
expressing the formula in terms of its fundamental unit,
v = metre/secs
Since the fundamental quantity of the metre is length (L) and that of seconds is the time (T); the dimensions is expressed as;
V = L/T
V = L * 1/T
V = L * T⁻¹
V = LT⁻¹
Hence the dimension of b is LT⁻¹.
Note that the dimension of a body is written in terms of its fundamental quantities.
The dimensions of b from the given equation are; B: LT⁻¹
Dimensional Analysis
The complete question is;
The equation for the change of position of a train starting at x = 0 m is given by x =(1/2)at² + bt³. The dimensions of b are__
Now, in that equation above, b represents the velocity of the motion. Now, the formula for velocity is;
Velocity = Distance/Time
Now, distance is also called Length and represented by L in basic parameters units while Time is represented by T.
Thus, the dimensions of b are; L/T or expressed as LT⁻¹
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Serenity is making beaded jewelry with no more than 920 beads she currently has in stock. Bracelets use 15 beads
and necklaces use 70 beads.
x= the number of bracelets
y = the number of necklaces
The inequality is written as 15x + 70y ≤ 920. Then the region below the line is the solution to inequality.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
Serenity is assembling beaded jewelry with no more than 920 beads she presently has in inventory. Bracelets use 15 beads and necklaces use 70 beads.
Let 'x' be the number of bracelets and 'y' be the number of necklaces. Then the inequality is given as,
15x + 70y ≤ 920
The region below the line is the solution to inequality.
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What is the slope of a line that is perpendicular to the line 2y – 3x = 8?
Answer:
\( = \frac{3}{2} \)
Step-by-step explanation:
\(y = mx + c\)
Here,
m => slopec => interceptIn this equation ,
\(2y - 3x = 8\)
to find the value of m or the value of slope we have to solve for y
Let's solve,
\(2y - 3x = 8 \\ 2y = 8 + 3x \\ \frac{2y}{2} = \frac{8 + 3x}{2} \\ y = 4 + \frac{3x}{2} \\ y = \frac{3x}{2} + 4\)
So, the slope is,
\( = \frac{3}{2}\)
Which of the following input/output pairs is valid for the graph below?
Identify the correct output for each given input to spot the right answer.
According to the graph, the outputs for the inputs 2, 3, -3 and 4 are:
\(\begin{gathered} 2\rightarrow1 \\ 3\rightarrow3 \\ -3\rightarrow-9 \\ 4\rightarrow5 \end{gathered}\)From the given options, the only one that is correct is: input 4, output 5.
Therefore, the correct choice is the last option:
\(\text{Input: 4, Output: 5}\)NO LINKS!! URGENT HELP PLEASE!!!
Please help me with Growth rate and Initial Value only
Answer:
growth rate: 4
y-value: 19
equation: y=4x+19
Step-by-step explanation:
Growth Rate:
The growth rate of a linear function is constant. This means that the function will increase or decrease by the same amount for every unit increase in x.
This can be found by dividing the change in y-values by the change in x-values.
For the question:
The change in y-values is 11-7=4,
and the change in x-values is +1.
Therefore, the growth rate is 4.
\(\hrulefill\)
Initial Value: The initial value of a linear function is the value of the function when x is 0.
In this case, the initial value is 19.
This can be found by looking at the y-value of the point where x is 0.
In this case, the y-value is 19.
\(\hrulefill\)Equation: The equation of a linear function is y = mx + b, where m is the slope and b is the y-intercept.
Using the table you provided, we can find the slope by using two points on the line.
Let’s use (-3, 7) and (1, 23).
The slope is (y2-y1)/(x2-x1)=(23-7)(1-(-3)=16/4=4
Now,
Taking 1 point (-3,7) and slope 4.
we can find the equation by using formula:
y-y1=m(x-x1)
y-7=4(x+3)
y=4x+12+7
y=4x+19
Therefore, the equation of the given table is y=4x+19\(\hrulefill\)
Answer:
Growth rate: 4
Initial value: 19
Equation: y = 4x + 19
Step-by-step explanation:
The slope of a linear function represents its growth rate.
Therefore, the growth rate of a linear function can be found using the slope formula.
Substitute two (x, y) points from the table into the slope formula, and solve for m. Substituting points (0, 19) and (1, 23):
\(\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{23-19}{1-0}=\dfrac{4}{1}=4\)
Therefore, the growth rate of the linear function is 4.
The initial value of a linear function refers to the y-intercept, which is the value of the y when x = 0.
From inspection of the given table, y = 19 when x = 0.
Therefore, the initial value of the linear function is 19.
To write a linear equation given the growth rate (slope) and initial value (y-intercept), we can use the slope-intercept formula, which is y = mx + b. The slope is represented by the variable m, and the y-intercept is represented by the variable b.
As the growth rate of the given linear function is 4, and the initial value is 19, substitute m = 4 and b = 19 into the slope-intercept formula to create the equation of the linear function represented by the given table:
\(\boxed{y=4x+19}\)
who contributed proof of complex functions to geometry
We can see here the proof of complex functions to geometry was contributed by the Norwegian mathematician Caspar Wessel.
What is complex function?A complex function is one that accepts a complex number as input and outputs another complex number. It is a function that, in other words, has the complex numbers as a codomain and a subset of the complex numbers as its domain.
Wessel demonstrated in his article that complex functions and complex numbers may both be used to represent curves and points in the plane. This research was a significant advancement in the field of complex analysis and opened the path for its growth into a potent instrument for addressing geometric problems.
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Please help! The question is in the image.
Answer:
Step-by-step explanation:
Drag each number to a box to complete the table. Each number may be used once or not at all
Each number should be dragged to a box to complete the table as follows;
Kilometers Meters
1 1,000
2 2,000
3 3,000
5 5,000
8 8,000
What is a conversion factor?In Science and Mathematics, a conversion factor can be defined as a number that is used to convert a number in one set of units to another, either by dividing or multiplying.
Generally speaking, there are one (1) kilometer in one thousand (1,000) meters. This ultimately implies that, a proportion or ratio for the conversion of kilometer to meters would be written as follows;
Conversion:
1 kilometer = 1,000 meters
2 kilometer = 2,000 meters
3 kilometer = 3,000 meters
4 kilometer = 4,000 meters
5 kilometer = 5,000 meters
6 kilometer = 6,000 meters
7 kilometer = 7,000 meters
8 kilometer = 8,000 meters
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
In the figure below, =m∠1 = 32°. Find m∠2.
The required measure of supplymentary angle m∠2 is 58°.
Here, two supplymentary angles are given ∠1 and ∠2 where m∠1 = 32°, m∠2 is to be determined.
The angle can be defined as the one line inclined over another line. Unit of the measure of angle are degree and radians.
Here,
For supplymentary angles, the sum of the angle is equal to 90°. So,
m∠1 + m∠2 = 90
From the given,
32 + m∠2 = 90
m∠2 = 90 - 32
m∠2 = 58°
Thus, the required measure of supplymentary angle m∠2 is 58°.
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Gentoo penguin can swim at a rate of 17 miles per hour. How many miles can a penguin swim in 4 hours? Use the expression rt, where r represents rate and t represents time.
Answer:
68
Step-by-step explanation:
R=17 t=4
S=68
Select ALL of the solutions of the following system of linear inequalities below.
The solutions of the system of inequalities are:
(0, 3)
(6, 2)
How to find the solutions of the system?Here we have the graph of a system of inequalities, the solutions are all the points on the area where the two shaded regions intercept (it would be on the purple area).
And we can see that one line is solid, the points on that line are solutions, the other line is dashed, the points on that line are not solutions.
Then the points that are solutions are:
(0, 3)
(6, 2)
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Jug A contains 6/7 as much water as Jug B.Jug C contains 3/5 as much water as Jug A.Find the ratio of the volume of water in Jug B to the volume of water as Jug C.
The ratio of the volume of water in Jug B to the volume of water in Jug C is 35:18.
Let's assume the volume of water in Jug B is x.
According to the given information, Jug A contains 6/7 as much water as Jug B. Therefore, the volume of water in Jug A can be calculated as (6/7) * x.
Similarly, Jug C contains 3/5 as much water as Jug A. Hence, the volume of water in Jug C can be expressed as (3/5) * [(6/7) * x].
To find the ratio of the volume of water in Jug B to the volume of water in Jug C, we divide the volume of water in Jug B by the volume of water in Jug C:
(x) / [(3/5) * (6/7) * x]
Simplifying the expression, we get:
x / (18/35 * x)
The x values cancel out, leaving us with:
1 / (18/35)
To simplify further, we multiply the numerator and denominator by the reciprocal of the denominator:
1 * (35/18)
The final ratio is:
35/18
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4. It takes 2 minutes to boil a single
egg. How many minutes will it take
to boil 5 eggs?
a. 10
b. 4
c. 2
d. 5
\(\huge\text{Hey there!}\)
\(\large\text{\#4). It takes 2 MINUTES to boil a SINGLE egg. How MANY minutes}\\\large\text{ to boil 5 eggs?}\)
\(\large\text{\bf{Keyterm(s)}}\downarrow\\\large\text{\bf{2 minutes to boil ONE egg}}\\\large\text{\bf{Number of minutes it will take to boil FIVE eggs}}\)
\(\textsf{Well, if one egg takes approximately two minutes, then we have we have to}\\\textsf{MULTIPLY 2 from 5, to find out your answer!}\)
\(\large\text{\bf{2(5)}}\\\large\text{\bf{2 minutes * 5 eggs = 10 minutes to boil FIVE eggs}}\\\boxed{\boxed{\large\text{\bf{Answer: A. 10}}}}\huge\checkmark\)
\(\text{Good luck on your assignment and enjoy your day!}\)
~\(\frak{Amphitrite1040:)}\)
How would I do this?
Answer:
A general rule when dealing when exponents:
An exponent of 0 is will always result in 1
An exponent of 1 results in the base number itself. The answer would be B, 1
Mark as brainliest if possible :)
Answer: B. 1
Step-by-step explanation: 4.51 to the power of 0 is 1.
Everything to the power of 0 will always equal 1.
I need some help!! I wil try to give brainliest!!!
How many degrees is 5pi/4 radians?
Answer: 225
Step-by-step explanation:
Create a ratio part/whole for radians = part/whole for degrees
\(\frac{\frac{5\pi }{4} }{2\pi } = \frac{x}{360}\) Keep change flip because you are dividing fractions for left side
\(\frac{5\pi }{4} (\frac{1}{2\pi }\)) = \(\frac{x}{360}\)
\(\frac{5}{8} (\frac{360}{1} ) =x\)
x = 225
HELP I JUST WANT TO FINISH GET MY CREDIT AND GRADUATE 70 POINTS HELP ASAP What are the values of x and y in the matrix subtraction below? [[- 20, 16], [4, 0], [9, - 6]] - [[- 5, 1], [- 6, 7], [0, 11]] = [[x, y], [10, - 7], [9, - 17]]
SOLUTION
We want to solve the question below
We can see that a matrix was subtracted from another. In Addition or subtraction of matrix, we just add or subtract the element. So
We have in the first row
\(\begin{gathered} -20-(-5)=x \\ -20+5=x_ \\ x=-15 \end{gathered}\)And
\(\begin{gathered} 16-1=y \\ 15=y \\ y=15 \end{gathered}\)Hence x = -15 and y = 15, the first option is correct
16 families went on a trip which cost them Rs 2,16,352. How much did each
family pay?
Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522
Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.
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Answer:
Step-by-step explanation
1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.
Now let's check if this result is correct:
1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.
So we have shown that each family paid **Rs 13,522** for the trip
Help pls 20 POINTS math
j/−2+7=−12
Answer:
Step-by-step explanation:
j/-2 =-12-7
j=(-19)*(-2)
j=38
Calculate the volume of the triangular prism shown below. Give your answer in cm³. 5 cm 9 cm 11 cm 6 cm
The volume of the triangular prism is 135 cm³.
To calculate the volume of a triangular prism, we multiply the area of the triangular base by the height of the prism.
Given the dimensions provided:
Base: Length = 5 cm, Width = 9 cm
Height: 6 cm
To find the area of the triangular base, we use the formula for the area of a triangle:
Area = (1/2) * base * height
Substituting the values:
Area = (1/2) * 5 cm * 9 cm
Area = 22.5 cm²
Now, to calculate the volume of the prism, we multiply the area of the base by the height:
Volume = Area * Height
Volume = 22.5 cm² * 6 cm
Volume = 135 cm³
Consequently, the triangular prism has a 135 cm3 volume.
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The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answer:
Step-by-step explanation:
3.6*
It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2
For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.
We get
36 = s^2
Now, we need to get the square root of both sides, which gives us
s = √36 s = 6 cm
Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.
Therefore, the perimeter of the square is 24 cm.
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T/F. victor found 5 cars online that he will go to see. the prices of the cars are: $5,000; $4,500; $5,500; $3,999; and $4,999. the median car price is $4,799.60.
False
The median car price is the one right in the middle of the price list. To find the median, we first need to rank the prices from lowest to highest.
The ordered price list looks like this:
$3,999; $4,500; $4,999; $5,000; The median price is $4,999, which is the median price. The average price is not $4,799.60.
Median is a measure of the central tendency of a dataset. The value that separates the top and bottom halves of the record. To find the median, we need to enter the values in the dataset in order from lowest to highest. If the dataset has an odd number of values, the median is the mean.
For example, given the following five values: For 3, 5, 7, 9, 11, the median is the median, so the median is 7. If the dataset has an even number of values, the median is the average of the two middle values. For example, given the following 6 values:
For 3, 5, 7, 9, 11, 13, the median is (7 + 9)/2 = 8. In this case, there are 5 values, which are odd, so the median is the median. , which is $4,999.
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Does a linear relation exist between age and HDL cholesterol? A. There appears to be a positive linear association because r is positive and greater than the critical value. B. There is little or no evidence of a linear association because r is positive and greater than the critical value. C. There appears to be a negative linear association because r is negative and less than the negative critical value. D. There is little or no evidence of a linear association because the absolute value of r is less than the critical value. More
Answer:
The correct answer is - option D. There is little or no evidence of a linear association because the absolute value of r is less than the critical value.
Step-by-step explanation:
Given:
Age Cholesterol
49 55
27 45
52 40
38 57
44 28
The linear correlation coefficient between age and HDL cholesterol can be computed by the=
r = Cov (X, Y)/ δx.δy
=v∑XY /√∑X2. ∑Y2
rv= negative 0.192
The absolute value of r is less than the critical value so there is no or very little evidence of linear association.