The Hike 4 Life company manufactures hiking boots. The production facility has foxed costs of $400 a day and the cost of making 1 pair of boots is $4.75. Which of the following equations
represents the daily production cost based on the number of pairs of boots manufactured each day?
Answers
The equation that represents the daily production cost based on the number of pairs of boots manufactured each day is C(x) = 4.75x + 400.
What are linear equations?
Linear equations are a subset of first order equations. Linear equations are defined for lines in the coordinate system. One homogeneous variable of degree one constitutes a linear equation in one variable (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.
Given, the daily production cost (in $) = C(x)
The number of pairs of boots manufactured = x
The cost of making a pair of boots = $ 4.75
The fixed cost of production each day = $ 400
Thus, net cost of making 'x' boots added to the daily fixed production cost will give the daily production cost.
Therefore, C(x) = 4.75x + 400, is the correct equation.
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Related Questions
How many units are (-2,-3) & (5,7) from each other on the coordinate plane
Answers
Let's begin by listing out the information given to us:
(x, y) = (-2, -3), (5, 7)
The distance between the two points is given by:
[tex]\begin{gathered} d=\sqrt[]{\mleft(\mleft(x_2-x_1\mright)^2+\mleft(y_2-y_1\mright)^2\mright)} \\ d=\sqrt[]{(5--2)^2+(7--3)^2} \\ d=\sqrt[]{7^2+10^2} \\ d=\sqrt[]{49+100} \\ d=12.207\approx12.21 \\ d=12.21 \end{gathered}[/tex]Based on this data what is the probability that the next car will not be white why
Answers
The probability of the next car not being a white car is 0.92
What is probability?The probability of an event is the chance or the likelihood that the event would occur.
Note that the chance or the likelihood is represented as a numerical value
How to determine the probability?The complete question is added as an attachment
From the attached question, we have the following parameters
P(White Vehicle) = 0.25
P(Car) = 0.36
P(White Car) = 0.08
Using the complement rule of probability, we have the following equation
P(White Car) + P(Not White Car) = 1
Substitute the known values in the above equation
So, we have the following equation
0.08 + P(Not White Car) = 1
Subtract 0.08 from both sides of the equation
So, we have
P(Not White Car) = 1 - 0.08
Evaluate the difference
P(Not White Car) = 0.92
Hence, the probability that the next car will not be a white car is 0.92
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When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones. Explain why you regroup before the next step
Answers
When using the standard algorithm to find the product 5,917x29, the first step is multiplying 9 ones by 7 ones, it's important to regroup in order to correctly multiply the values.
How to illustrate the information?Using partial products or multiplying in parts is how the conventional method does multiplication. A word that also signifies multiplication is "product," so keep that in mind. Any two numbers, regardless of how tiny or how large, can be multiplied using this standard technique.
The top number is multiplied by the bottom number, one digit at a time, working your way from right to left, using this procedure.
In this case, it should be noted that the value of 5,917 × 29 is 171593.
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The function f(x) = 2x − 1 is transformed to function g through a horizontal shift of 7 units left. What is the equation of function g?
Replace the values of h and k in the equation.
g(x) = 2x+h + k
Answers
When the function f is transformed to g, the equation is g(x) = 2x + 14 - 1
How to determine the equation of function g?The equation of function f is given as
f(x) = 2x - 1
The transformation is given as
Horizontal shift of 7 units left.
The above transformation rule can be represented as
Horizontal shift of 7 units left.: (x, y) = (x + 7, y)
When the above rule is applied, we have the following equation
g(x) = f(x + 7)
So, we have
g(x) = 2(x + 7) - 1
Open the brackets
g(x) = 2x + 14 - 1
Hence, the equation of function g is g(x) = 2x + 14 - 1
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The Life time in hours of a certain aircraft has the normal distribution with mean 80, Standard devation 16. What is the probability that the aircraft Will last 100 hours
Answers
1.25 is the probability that the aircraft Will last 100 hours.
What is probability?The area of mathematics described as probability concerns with numerical representations of the likelihood that an event will occur or that an assertion is correct. An event's probability is a number between 0 and 1, where, roughly speaking, 0 indicates the event's impossibility and 1 represents certainty.
Given Data
Mean = 80
Standard deviation = 16
P( x < 100)
P( x < 100) = P( Z< [tex]\frac{x- mean}{standard deviation}[/tex])
P(x<100 ) = P( Z < [tex]\frac{100-80}{16}[/tex])
P(x< 100) = P(Z< [tex]\frac{20}{16}[/tex])
P(x < 100) = 1.25
1.25 is the probability that the aircraft Will last 100 hours.
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1/16x+1/320y-29=0 rewrite the equation as a function of x
Answers
The equation as a function of x is y = 9280 -20x
What is equation ?Equations are logical assertions in mathematics that have two algebraic expressions on either side of an equals (=) sign. The expression on the left and the expression on the right are shown to be equal in reference to one another. LHS = RHS (left hand side = right hand side) appears in all mathematical equations. You can solve equations to determine an unknown variable's value, which corresponds to an unknown quantity. It is not an equation if there is no "equal to" sign in the statement. It shall be taken into account as an expression.
The equation is =[tex]\frac{1}{16}x + \frac{1}{320}y - 29= 0[/tex]
Now rearranging the function we write
[tex]\frac{y}{320}= 29 -\frac{x}{16}[/tex]
y = 9280 -20x
The equation as a function of x is y = 9280 -20x
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A company borrows $68,000 for 8 years at a simple interest rate of 15.5%. Find the interest paid on the loan and the total amount paid.
Answers
The interest paid on the loan and the total amount paid are $84,320 and $152,320 respectively.
It is given in the question that:-
Money borrowed by the company (Principal) = $68,000
Time period for which the money is borrowed = 8 years
Simple Interest rate = 15.5 %
We have to find the interest paid on the loan and the total amount paid.
We know that,
Simple interest = (Principal * Interest * Rate)/100
Hence, we can write,
Simple interest = (68000 * 15.5 * 8)/100 = $84,320
Also, we know that,
Amount = Principal + Interest
Hence, we can write
Amount = 68,000 + 84,320 = $152,320
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A high school band raises $6, 764 to buy instruments
and uniforms for its members. Half the money is spent
on new instruments. They buy 38 new uniforms with
the remaining money.
Answers
Answer:
$89 dollars per uniform
Step-by-step explanation:
Total amount of money raised= $6,764.
Money spent on new instruments= $6,764÷1/2 = $3382
The number of new uniforms bought with the remaining money= 38.
How much was spent on one= $3,382÷38 = $89
Two accounts each begin with a deposit of $9000. Both accounts have rates of 3.1%, but one account compounds interest once a year while
the other account compounds interest continuously. Make a table that shows the amount in each account and the interest earned after one
year, five years, ten years, and 20 years.
Answers
Given : Initial deposit or the principal amount = $ 9000
Rate of interest = 3.1 %
Compound interest annually
= principal (1 + r/ 100)^t
here put value principal rate and time period 1, 5 10 and 20 years
and we get the amount for each time period
than for interest = amount - principal we get interest
as that we calculate all value:
given in the attachment
When do we use compound interest ?When interest on a balance in a savings or investment account is reinvested, you receive compound interest, which results in higher interest payments. Money makes money, a wise man once said. And money makes money by making more money. Compound interest speeds up the long-term growth of your savings and investments.
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Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.a. What is her ending balance after the year, to the nearest cent?b. How much interest does she earn, to the nearest cent?c. What is her annual percentage yield to the nearest hundredth of a
Answers
Joanne deposits $4,300 into a l-year CD at a rate of 2.3%, compounded daily.
a. What is her ending balance after the year, to the nearest cent?
b. How much interest does she earn, to the nearest cent?
c. What is her annual percentage yield to the nearest hundredth
Remember that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$4,300
t=1 year
r=2.3%=2.3/100=0.023
n=365
Part a
Find out the value of A
substitute the given values in the formula
[tex]A=4,300(1+\frac{0.023}{365})^{365\cdot1}[/tex]A=$4,400.04
Part b
I=A-P
I=4,400.04-4,300
I=$100.04
Part c
we have
4,300 -----> represent 100%
so
Applying proportion
Find out how much percentage is 4,400.04
100/4,300=x/4,400.04
x=(100/4,300)*4,400.04
x=102.33%
therefore
102.33-100=2.33%
The vertices of triangle FGH are F(-5,1,) G(-2,4), and H(-1,2) the vertices of triangle F’G’H are F’(-5,-1) G(-2,-4) H (-1-2)Identify the transformation of triangle FGH to triangle F’G’H A. A translation across the x-axis B. A reflection across the x-axis C. A dilation D. A rotation
Answers
The transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.
What do we mean by reflection across the x-axis?The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).A graph will appear to be inverted or on the other side of an axis, such as the x-axis, when it is reflected along that axis.If you look closer, you'll notice that it's symmetrical, meaning that each point is equally spaced from the axis of reflection and the axis of its reflection.As a result, if you reflect a point (x, y) along the x-axis, its x abscissa will remain the same but its y ordinates will negate. So (x,y) becomes (x, -y)
So, the difference between the vertices of triangle FGH and F’G’H is the y-coordinates of the F’G’H triangle are inverse of the y-coordinates of the FGH triangle.
And as we know that in reflection across x-axis the x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse.Therefore, the transformation of △FGH to △F’G’H is (B) the reflection across the x-axis.
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3. a) Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. The actual
was 4.1 ft. What is John's percent decrease on his measurement?
measurement
Answers
Jack's percentage decrease on his measurement of painting by 18%.
What is meant by percentage change?
Measures of percent change include percent increase and percent decease, which indicate how much an element of a variable changes in terms of intensity, size, extent, or value.
Given that,
Jack's measurement for his room = 5 ft (taking this as old value)
Actual measurement for Jack's room = 4.1 ft (taking this as new value)
Using formula for Percent change = [tex]\frac{new - old}{old}[/tex] × 100% = [tex]\frac{4.1 - 5}{5}[/tex] × 100%
= [tex]\frac{-0.9}{5}[/tex] × 100% = -0.18 × 100%
= -18%
Here, minus sign represents the decrease in percentage.
Hence, Jack's percentage decrease on his measurement of painting by 18%.
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Correct question will be :
Jack needs to purchase a painting for his room. Jack measured the painting as 5 ft. But the actual measured painting is 4.1 ft. What is Jack's percent decrease on his measurement of the painting?
15 POINT AND BRANLIEST
A 15-gallon gas tank. If you can drive 330 miles on a full tank of gas, what is the unit rate of miles per gallon he gets?
Answers
The unit rate he can drive in mile per gallon is 22 miles per gallon.
How to find unit rate?Unit rate can be defined as the ratio between two measurements with the second term as 1.
In other words, a unit rate describes the ratio of two different units for the quantity of one.
Therefore, the unit rate in miles per gallon can be calculated as follows:
Hence,
unit rate = number of miles / number of gallons
number of miles = 330 miles
number of gallons = 15 gallons
unit rate = 330 / 15
Therefore,
unit rate = 22 miles per gallon
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Perform the indicated operation. Don't forget to simplify if possible.
Subtract 6x + 2 from 4x-6.
Answers
Answer: 2x + 8
Step-by-step explanation:
( 6x + 2 ) - ( 4x - 6 ) =
6x - 4x = 2x
2 - -6 = 8
Each of the four shapes represents a positive whole number. The sum of the shapes in
each row and column is displayed at the end of each row and column. Using this
information, determine the numerical value of each shape.
Answers
The numerical value of each of the four given shapes filled in the rows and columns are;
pentagon shape = 8star shapes = 6spiral shapes = 3rectangle shape = 5How to find numerical value of each shape.let
pentagon shape = AStar shape = BSpiral shape = Crectangle shape = DRow 1: There are 2 stars, one pentagon and one spiral shape.
A + 2B + C = 23 .....(equation 1)
Row 2: There are 2 spiral shapes and 2 rectangle shape.
2C + 2D = 16 ......( equation 2)
Row 3: There are 1 star, one pentagon and 2 rectangle shape.
A + B + 2D = 24 ....(equation 3)
Row 4: There are 3 spiral shapes and one star shape.
B + 3C = 15 ....(equation 4)
Column 1:
2C + A + D = 19 ....(equation 5)
Column 2:
2B + C + D = 20 .....(equation 6)
From equation 4;
B = 15 - 3C
From equation 2:
D = 8 - C
Substitute B = 15 - 3C into equation 1;A + 2B + C = 23
A + 2(15 - 3C) + C = 23
A + 30 - 6C + C = 23
A = 5C - 7
Substituting D = 8 - C and A = 5C - 7 into equation 5;2C + A + D = 19
2C + (5C - 7) + 8 - C = 19
6C + 1 = 19
6C = 18
C = 3
Substitute 3 for C inA = 5C - 7
A = 5(3) - 7
A = 8
Substitute 3 for C inB = 15 - 3C
B = 15 - 3(3)
B = 6
Substitute 3 for C inD = 8 - C
D = 8 - 3
D = 5
Therefore, there are 8 pentagon shape, 6 star shapes, 3 spiral shapes and 5 rectangle shape.
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solve for x if the equation is[tex]3 \sqrt{x + a - z = b} [/tex]
Answers
EXPLANATION
Given the expression:
[tex]b=\sqrt[3]{x+a-z}[/tex]Applying the cubic power to both sides:
[tex]b^3=(\sqrt[3]{x+a-z})^3[/tex]Simplifying the cubic root with the cubic power:
[tex]b^3=x+a-z[/tex]Subtracting -a to both sides:
[tex]b^3-a=x+a-a-z_{}[/tex]Adding z to both sides:
[tex]b^3-a\text{ +z = x + a - a -z + z}[/tex]Simplifying terms:
[tex]b^3-a+z=x[/tex]Switching sides:
[tex]x=b^3-a+z[/tex]Assume that when you take a bath, you fill a tub to the haltway point. The tub measures 5 feet by 2 feet by 2.7 feet. When you take a shower, you
use a shower head with
flow rate of 2.03 gallons per minute, and you typically spend 9 minutes in the shower. There are 7.5 gallons in one cubic
foot. Complete parts (a) through (c) below.
a. Do you use more water taking a shower or taking a bath? Select the correct choice below
and fill in the answer box to complete your choice.
(Round to one decimal place as needed.)
O A. Shower; you use
more cubic feet of water than taking a bath.
• B. Bath; you use
more cubic feet of water than you do taking a shower.
Answers
The person is therefore using more water for bathing than for showering, according to the conclusion.
Half of the tub's total water is consumed while taking a bath.
Water used divided by volume equals
[tex]\frac{volume}{2}[/tex]
= [tex]\frac{(5)(3)(2.8)}{2}[/tex]
=[tex]\frac{42}{2}[/tex]
=21 cubic feet.
The following will provide the total amount of water utilized while having a shower:
Total water Equals rate ×time
= 1.52 × 12
= 18.24 gallons.
So, if there are 7.5 gallons in a cubic foot, the amount of water in cubic feet will be amount
=[tex]\frac{18.24}{7.5}[/tex]
=2.432 cubic feet.
The person is therefore using more water for bathing than for showering, according to the conclusion.
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n
Find the value of x that makes m ||
(180 − x)°
m
An
to
W
Answers
Answer:
The value of x will be 90°
a₁ = 4; a = (a)²-3 (n ≥2) list the first five terms
Answers
The first five terms of the given sequence are 4, 1, 6, 13, 22
We can solve this problem by following a few steps.
The formula to find the next four terms is, a = (n)²- 3, (n ≥2) as per the question.
Where n is the sequence of the number ( n = 2, 3, 4, 5, 6, etc. )
So, for the 2nd term A₂ = 2² - 3 = 4 - 3 = 1 [As n = 2 for the second term ]
Similarly, for the 3rd term A₃ = 3² - 3 = 9 - 3 = 6 [ As n = 3 for the third term ] ,
for the 4th term A₄ = 4² - 3 = 16 - 3 = 13 [ As n = 4 for the second term ] ,
for the 5th term A₂ = 5² - 3 = 25 - 3 = 22 [As n = 5 for the second term ]
Now, we can conclude that the first five terms of the given sequence are 4, 1, 6, 13, 22
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The correct question is :
a₁ = 4; a = (n)²-3 (n ≥2) list the first five terms
Simplify
Y exponent -5/ y exponent -4
Answers
Answer:
"Simplify" is an instruction to rewrite the expression with as few symbols as possible. 5y-4 and 5/y4 have the same number of symbols.
A possible alternative direction might have been to rewrite without the negative exponent.
Answer:
[tex]\frac{1}{y}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
given
[tex]\frac{y^{-5} }{y^{-4} }[/tex]
= [tex]y^{(-5-(-4))}[/tex]
= [tex]y^{(-5+4)}[/tex]
= [tex]y^{-1}[/tex]
= [tex]\frac{1}{y}[/tex]
Determine the solution of the given system of equations.
-x+y=-5
-4x - 5y=7
Answers
Answer:
x =2 y = -3
Step-by-step explanation:
hope it helps!!!!!
Help.
A. RS
B. ST
C. Ut
Answers
Answer: THE ANSWER TO THAT IS B
Step-by-step explanation:
find the slope of the line that goes through the given points (-2,-4) (1/4,5)
Answers
Solution
find the slope of the line that goes through the given points (-2,-4) (1/4,5)
[tex]\begin{gathered} slope\text{ =m} \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} x_1=-2 \\ x_2=\frac{1}{4} \\ y_1=-4 \\ y_2=5 \end{gathered}[/tex][tex]m=\frac{5--4}{\frac{1}{4}--2}=\frac{9}{2.25}=4[/tex]Therefore the slope of the line = 4
Show how you can make a ten to find the sum of 6+5
Answers
By rewritting the 6 as 5 + 1 we will get:
1 + 5 + 5 = 1 + (5 + 5) = 11
How to make a ten to simplify the sum?
One trick we do a lot when we do additions os making tens (or hundreds, thousands, etc... depending on the case).
This means that we play with the numbers in such a way that we can make tens, in this case we have the sum:
6 + 5
We can rewrite this as:
6 + 5 = 1 + 5 + 5
Using the associative property we rewrite:
1 + 5 + 5 = 1 + (5 + 5)
1 + (5 + 5) = 1 + 10 = 11
The sum is equal to 11.
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The line y=kx+4 goes through the point (2,-2)
K=-3
Sketch the graph of the line (need ASAP!)
Answers
The graph of the linear equation:
y = -3x + 4
Can be seen in the image at the end.
How to sketch a graph of the line?
Here we know that the equation for the line is:
y = k*x + 4
We know that this line goes through the point (2, -2), then we can replace these values in the above line so we get the value of k.
-2 = k*2 + 4
With this, we can find the value of k.
-2 - 4 = k*2
-6 = k*2
-6/2 = k = -3
Then the line is:
y = -3*x + 4
If we evaluate in x = 0, we get:
y = -3*0 + 4 = 4
So, at this point we know that the line passes through points (0, 4) and (2, -2), so to graph the line, we just need to graph these two points and draw a line that connects them, like in the example below.
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The height of a wave in California varies directlywith the seconds that pass by. At 4 seconds,the wave is 6 feet high. Find the constant ofvariation.Weight varies directly with arit
Answers
The constant variation of hight(y) to seconds(x) is 3y/2x.
What is the constant variation?The quantity that connects two variables that are directly or inversely proportional to one another is known as the constant of variation. By dividing the y-coordinate by the x-coordinate, we can find k when given any point because it is constant (the same for every point). For instance, the constant of variation is k = = 3 if y varies directly as x and y = 6 when x = 2.So, let the second be 'x' and the height is 'y'.
At 4 seconds the wavelength is 6 ft high.
Constant variation:
y/x = 6/4 = 3/23y/2xSo,
x = 4, x = 8, x = 12y = 6, y = 12, x = 18Therefore, the constant variation of hight(y) to seconds(x) is 3y/2x.
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Given P(A) = 0.2, P(B) = 0.31 and P(AB) = 0.152, find the value of
P(AUB), rounding to the nearest thousandth, if necessary.
Answers
Probability - The value of P(AUB) = 0.557
What is Probability ?
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.
Given,
P(A) = 0.2,
P(B) = 0.31 and
P(A/B) = 0.152,
Since, we know that
P(A⋃B) = P(A)+P(B)-P(A⋂B)
So, we have to find P(A⋂B)
We know that,
P(A/B) = P(A⋂B)/P(B)
Putting the values we get,
0.152 = P(A⋂B) / 0.31
P(A⋂B) = 0.152 x 0.31
P(A⋂B) = 0.047
Now, lets find the value of P(A⋃B)
P(A⋃B) = P(A)+P(B)-P(A⋂B)
Putting the values we get,
P(A⋃B) = 0.2 + 0.31 + 0.047
P(A⋃B) = 0.557
Hence the value of P(A⋃B) = 0.557
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Use the number line to answer the question.
A number line is shown with end points 0 and 2. Hash marks are at every 0.2. Heavy marks are at 0, 1, and 2.
Zach bought 8 pieces of bubble gum that were $0.20 each. He used a number line to find the total cost. Choose the numbers to complete the sentences.
Zach started on the number line at 0.2 for the cost of one piece of gum. He moved
Choose...
hash marks. The total cost is
Choose...
.
Answers
Zach began at 0.2 for the price of one piece of gum on the number line. Has moved eight times. The whole price is $1.60.
Since each hash mark is worth.2, moving eight times will result in 1.6, or eight times $0.20.
This is further explained below.
What is a Number line?Generally, A number line is a depiction of a graded straight line that is used to represent real numbers visually.
It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
A horizontal line with evenly spaced numerical increments is referred to as a number line.
How the number on the line may be answered depends on the numbers present. How a number is utilized depends on the issue it is associated with, such as when graphing a point
In conclusion, On the number line, Zach started at 0.2, which was equal to the cost of one piece of gum. Has relocated a total of eight times. The whole cost is a dollar and sixty cents.
Moving eight times will result in 1.6, which is equal to eight times $0.20, given that each hash mark is worth.2.
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2) Jennifer makes a hexagon by arranging 6 equilateral triangles, each of which has a vertex at
the center of the hexagon. If the length of one side of a triangle is 4, what is the area in
square units of the hexagon? Leave in simplest radical form if necessary. Show work and
circle final answer
Answers
The area in square units of the hexagon will be 12√3.
What is Hexagon?
A polygon with six sides are called a hexagon.
Given that;
Jennifer makes a hexagon by arranging 6 equilateral triangles.
The length of one side of a triangle is 4.
Now, To find the area of hexagon, we find the height of the equilateral triangle and then multiply by the 6.
So, In ΔABC;
AB = BC = CA = 4
Then, Measure of DC = BD = 2
Now, using Pythagoras theorem to find height of triangle (AD) as;
AD² = AC² - DC²
AD² = 4² - 2²
AD² = 16 - 4
AD² = 12
Take square root both side;
AD = √12
AD = 2√3
So, The area of hexagon = 6 × Height of triangle
= 6 × 2√3
= 12√3
Thus, The area in square units of the hexagon will be 12√3.
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Solve the quadratic equation using the method indicated. See attached photo. Thanks in advance!
Answers
The quadratic formula is given by th following formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a, b and c are the coefficients of the quadratic equation. In this case, you have:
a = 6
b = 9
c = -22
replace the previous values into the quadratic formula and simplify:
[tex]\begin{gathered} x=\frac{-9\pm\sqrt[]{(9)^2-4(6)(-22)}}{2(6)} \\ x=\frac{-9\pm\sqrt[]{609}}{12} \\ x_1\approx1.31 \\ x_2\approx-2.81 \end{gathered}[/tex]Hence, the solutions for the given equation are 1.31 and -2.81