Answer
y = ½x + 5
If y is the total amount Juanita makes for x inches of finished lanyard,
Base fee = y-intercept = 5
Cost per inch = Slope = 0.5 = ½
Explanation
To write the expression for this, we need to write the equation for the line representing the whole function
The slope and y-intercept form of the equation of a straight line is given as
y = mx + b
where
y = y-coordinate of a point on the line.
m = slope of the line.
x = x-coordinate of the point on the line whose y-coordinate is y.
b = y-intercept of the line.
From the gaph, we can easily see that
b = y-intercept = point where the line crosses the y-axis = 5
For the slope, for a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as
[tex]Slope=m=\frac{Change\text{ in y}}{Change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1}[/tex]For this question,
(x₁, y₁) and (x₂, y₂) are (2, 6) and (6, 8)
[tex]\text{Slope = }\frac{8-6}{6-2}=\frac{2}{4}=\frac{1}{2}=0.5[/tex]Recall,
y = mx + b
m = slope = 0.5 = ½
b = y-intercept = 5
y = ½x + 5
If y is the total amount Juanita makes for x inches of finished lanyard,
Base fee = y-intercept = 5
Cost per inch = Slope = 0.5 = ½
Hope this Helps!!!
how many bites have their second, third and fourth digit equal to 0
How many bytes have their second, third, and fourth digit equal to 0.
If we refer to 8-bits, we would have a value from 00000000 to 11111111, there would be a total of 256 values.
[tex]2^8=256[/tex]Considering that we only need it to have its second, third and fourth digit equal to 0, we can add the values from 2^0 up until 2^4
[tex]2^0+2^1+2^2+2^3+2^4=1+2+4+8+16=31[/tex]That would be equal to 31 bytes.
Can please help mii here
Answer:
the function Is y= -x+5 .........
I need help with this practice problem *you can pick more than one answer
Solution:
Consider the following trigonometric equation:
[tex]3\cot (\theta)=-\sqrt[]{3}[/tex]This is equivalent to:
[tex]\cot (\theta)=-\frac{\sqrt[]{3}}{3}[/tex]now, consider the following trigonometric circle and the above equation:
According to this trigonometric circle and the definition of the cotangent function, we can conclude that the general solution would be:
[tex]\theta=\frac{2\pi}{3}+\pi n[/tex]PLEASE 95 POINTS TO WHOEVER ANSWER'S THIS QUESTION
The coordinate plane below shows the map of a school and some of the locations:
What is the distance between Math and English, rounded to the nearest tenth of a unit?
The distance between points Math(-3, -5), and English(2, 2) is 8.60 units after using the distance formula.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
Math(-3, -5)
English(2, 2)
Using distance formula:
D = √[(x₂ - x₁)² + (y₂ - y₁)²]
D = √[(2 - (-3))² + (2 - (-5)₁)²]
D = √74
D = 8.60 units
Thus, the distance between points Math(-3, -5), and English(2, 2) is 8.60 units after using the distance formula.
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Write the coordinates of the vertices after a rotation 90° counterclockwise around the origin.
Q=
R=
S=
T=
Check the picture below.
what multiplication expression can you use to find 3/8 divided by 3/4
The multiplication expression will be (3/8 × 4/3) and the resultant answer of this expression will be 1/2.
What do we mean by expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, the expression to solve the given fractions will be:
3/8 ÷ 3/4 that is (3/8 × 4/3)Now, also solve as follows:
3/8 × 4/312/241/2Therefore, the multiplication expression will be (3/8 × 4/3) and the resultant answer of this expression will be 1/2.
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Answer:
3/8 x 4/3
(That equals 1/2)
hope this helps. Currently doing this i-Ready lesson right now.
Two machines worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charge a total of $2250. What was the rate charged per hour by each mechanic if the sum of the two rates was $125 per hour?
Solution:
Let's make,
mechanic #1's rate = x
mechanic #2's rate = y
Note that their rate is dollars per hour.
Now, mechanic #1 worked for 20 hours. Then, we get the following equation:
20x = money earned by mechanic #1
On the other hand, mechanic #2 worked for 15 hours. Then, we get the following equation:
15y = money earned by mechanic #2
together they charged a total of $2250. So the amount of money earned by both mechanics is:
20x + 15y = 2250 EQUATION 1
On the other hand, the sum of the two rates was:
x + y = 125 EQUATION 2
From the equation, if we solve for x, we get:
x = 125-y EQUATION 3
plug (125-y) in for "x" in equation 1 to get everything in terms of one variable:
20(125-y)+15y = 2250
this is equivalent to
2500-20y +15y = 2250
this is equivalent to
2500 -5y = 2250
this is equivalent to
-5y = 2250 -2500
this is equivalent to:
-5y = -250
or
5y = 250
solving for y, we get:
[tex]y\text{ =}\frac{250}{5}=50[/tex]now, replacing this into equation 3, we get:
x = 125-y = 125 - (50) = 75
so that, we can conclude that the correct answer is:
mechanic #1 charged 75 $/hr
mechanic #2 charged 50 $/hr
Problem 2: Solve the matrix equation for "x" and "y" 8 -X 2 13 4 1- [ 3 -9 10 -4y 5 6 [ 0 16
Solve the operation of the matrix
[tex]\begin{gathered} 2\begin{bmatrix}{8} & {-x} & {} \\ {5} & {6} & {} \\ & {} & {}\end{bmatrix}{}-\begin{bmatrix}{3} & {-9} & {} \\ {10} & {-4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{16} & {-2x} & {} \\ {10} & {12} & {} \\ {} & & {}\end{bmatrix}-\begin{bmatrix}{3} & {-9} & {} \\ {10} & {-4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \\ \begin{bmatrix}{13} & {-2x+9} & {} \\ {0} & {12+4y} & {} \\ {} & {} & {}\end{bmatrix}=\begin{bmatrix}{13} & {4} & {} \\ {0} & {16} & {} \\ {} & {} & {}\end{bmatrix} \end{gathered}[/tex]From this result we know that
[tex]\begin{gathered} -2x+9=4 \\ 12+4y=16 \end{gathered}[/tex]Now clear x and y from the equations
[tex]\begin{gathered} -2x+9=4 \\ -2x=-5 \\ x=-\frac{5}{-2} \\ x=\frac{5}{2} \end{gathered}[/tex][tex]\begin{gathered} 12+4y=16 \\ 4y=4 \\ y=\frac{4}{4} \\ y=1 \end{gathered}[/tex]x is 5/2 and y is 1
(3x-3) = 48 Find the value of X
Answer:
17
Step-by-step explanation:
3x-3=48
3x = 48+3
3x= 51
x= 51/3 = 17
Apr 20, 11:27:10 AMA series of coins are stacked to represent a right circular cylinder (on the left). Thecoins are then "slid" to represent a distorted cylinder (on the right). The samenumber of congruent coins was used in each stack. Which of the following statementswill be TRUE regarding these stacks of coins?
The picture provides to stacks of coins and the number of coins used in both stacks are the same. One stack is straight while the other has been slightly distorted. Nonetheless, since the stacks of coins are congruent, the volume would be the same.
Mrs.smith deposits $980 in a saving account that pays 3.1% interest compounded daily
The amount at the end of 30 days, when interest compounded daily is found as $982.53.
What is referred as the compound interest?Compound interest is investment determined on the preliminary principal plus all previous periods' accumulated interest. The power of compound interest is the ability to generate "interest on interest." Interest could be compounded at any time, from continuously to everyday to annually.The formula for calculating the compound interest is;
A = P(1 + r/100n)∧nt
Where,
CI = compound interestP = principal amount = $980r = rate of interest = 3.1%n = number of time interest compounded = 30 dayst = time in years = 1 months; 1/12 year.A = amount after given time.Now put the values in the formula.
A = 980(1 + 3.1/3000)∧30(1/12)
A = 980(1.0025)
A= 982.53
Thus, the amount at the end of 30 days, when interest compounded daily is found as $982.53.
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The complete question is-
Mrs.smith deposits $980 in a saving account that pays 3.1% interest compounded daily. Calculate the total amount for 30 days.
helpppppppppppppppppppppppp
Answer:
Many solutions
If the second term of an arithmetic sequence is 7 and the fourth term is 1, what is the 15th term? (non complicated answer would be extremely appreciated <3)
⇒[tex]T_{n} =a+(n-1)d[/tex] is the formula to find the general term of the arithmetic sequence.
⇒Note to find the second term we will plug in 2 in the place of n in the formular and simplify.
⇒[tex]T_{2} =a+(2-1)d\\T_{2} =a+(1)d\\T_{2} =a+d[/tex]
⇒It is given that the second term is 7 meaning in the place of [tex]T_{2}[/tex] in the equation above since we do not know the value of a and d we will plug in 7 and have the equation [tex]7=a+d[/tex] as our first equation.
⇒ For the fourth term [tex]T_{4}[/tex] we follow the same step of using the general formula to find the nth term by plugging in 4 in the place of n and and simplify
[tex]T_{4} =a+(4-1)d\\T_{4}=a+(3)d\\T_{4}=a+3d[/tex]
In the place of [tex]T_{4}[/tex] plug in 1 for the fourth term is equal to 1 to have the second equation
[tex]1=a+3d[/tex]
Note we can now use the two equations we have now to find the value of a which is the first term and d which is the difference.
7=a+d......1st equation
1=a+3d...2nd equation
∴from the first equation by making a the subject of the equation we get
a=7-d
from the second equation making a the subject of the equation we get a=1-3d
Now let us equate first equation and the second equation since they are both equal to a and solve for d.
[tex]7-d=1-3d\\-d+3d=1-7\\2d=-6\\\frac{2d}{2} =\frac{-6}{2} \\d=-3[/tex]
⇒Now you can see that we have the difference of the arithmetic sequence equal to -3
⇒To find the value of a you can use any of the equations from the ones we created . I will use the equation a=7-d
[tex]d=-3\\a=7-d\\a=7-(-3)\\a=7+3\\a=10[/tex]
⇒ to get the 15th term we will go back to the general formula of finding the nth term in the place if n we will plug in 15 and simplify the formula
[tex]T_{15} =a+(15-1)d\\T_{15}=a+(14)d\\T_{15}=a+14d\\[/tex]
⇒Now we find that the 15th term is equal to a plus 14(d)
⇒Note we already have the value of a and we can just plug them in to find the value of the 15th term and simplify.
[tex]a=10,d=-3\\T_{15}=a+14d\\\\T_{15}=10+14(-3)\\T_{15}=10-42\\T_{15}=-32[/tex]
⇒The 15th term is -32
HELP HELP HELP MEEEEEEEEE PLEASEEEEEEEEE
Answer:
see explanation
Step-by-step explanation:
the domain is the x- coordinates (input) of the ordered pairs, note repeated values are only listed once , then
domain { - 3, 0, 1, 2 }
the range is the y- coordinates (output) of the ordered pairs , note repeated values are only listed once, then
range { 1, 2, 4, 5 }
For the relation to be a function then each value of x must map to one unique value of y.
here - 3 → 1 and 2 → 1
Thus the relation is not a function
which of the following is the measure of the supplement of angle CAB
EXPLANATION
The measure of the
By applying this theorem we can get the value of the angle CAB as shown as follows:
180 - 90 - 42 = 48 degrees
Then, by the supplementary angles theorem, we can assevere that the sum of supplementary angles is equal to 180 degrees.
180 - 48 = 132 degrees
Hence, the value of the supplementary angle is 132 degrees.
what would (9, 10) be after a rotation 270 degrees counterclockwise around the origin?
The new coordinates of the point (9, 10) after a rotation of 270 degrees counter-clockwise around the origin are (10, -9).
The coordinates of the point are (9, 10). We perform a transformation on the point. The type of transformation performed is rotation. The rotation is done at an angle of 270 degrees in a counter-clockwise direction around the origin. First of all, we need to convert the angle of rotation from degrees to radians. The angle θ is 270*(π/180) = 3π/2. Let the original coordinates be denoted by (a, b) and the coordinates after rotation be (x, y). We can write the following equations using the theory of rotation.
x = a×cos(θ) - b×sin(θ) = 9×cos(3π/2) - 10×sin(3π/2) = 0 - 10(-1) = 10
y = b×cos(θ) + a×sin(θ) = 10×cos(3π/2) + 9×sin(3π/2) = 0 + 9(-1) = -9
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Explain negative exponents. Why do you find the reciprocal of the base and then, make the exponent positive?
Answer:
Step-by-step explanation: A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.
HELP!!!!
the quantity negative 7 minus one fifth times p end quantity plus the quantity nine tenths times p minus 2 end quantity
negative 8 over 15 times p plus negative 5
7 over 10 times p minus 9
7 over 20 times p minus 5
8 over 10 times p plus negative 9
The expression "negative 7 minus one fifth times p end quantity plus the quantity nine tenths times p minus 2 end quantity" is given as "7 over 10 times p minus 9".
The correct answer is option B
How to evaluate fractions?negative 7 minus one fifth times p end quantity plus the quantity nine tenths times p minus 2 end quantity
= (-7 - 1/5 × p) + (9/10 × p - 2)
open parenthesis
= (-7 - 1/5p) + (9/10p - 2)
= -7 - 1/5p + 9/10p - 2
= -1/5p + 9/10p - 2 - 7
= (-2p + 9p) / 10 - 9
= 7p/10 - 9
= 7/10p - 9
Therefore, the solution to the fractional expression (-7 - 1/5 × p) + (9/10 × p - 2) is 7/10p - 9
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Is it a
linear function?
Answer:
No
Step-by-step explanation:
Well, by looking at the x factors, none of them repeat so it is a function. To determine if it's linear, you can look to see if the change is consistent. From 0 to 2 is +2, and from 10 to 6 is -4. From 2 to 4 is +2, but from 6 to 4 is -2. Since it doesn't go down the table at a set rate, it isn't linear. So, it is a function, but not a linear function
this is a 4 question part which price has the lowest unit per ounce choice a 6 ounces of chocolate chips for $ 2.49 choice b 8 ounces of chocolate chips for $ 3.32 I will ask the other 3 questions soon
For choice (a);
[tex]\begin{gathered} 6\text{ ounces of chocolate for 2.49} \\ \text{Per ounce=}\frac{2.49}{6} \\ \text{Per ounce=\$0.415} \end{gathered}[/tex]For choice (b);
[tex]\begin{gathered} 8\text{ ounces of chocolate for 3.32} \\ \text{Per ounce=}\frac{3.32}{8} \\ \text{Per ounce=\$0.415} \end{gathered}[/tex]Both options (a) and (b) have the same price per ounce which is $0.415.
Therefore, none of them is a cheaper option.
x = y + 3
(2y + x = 12
Answer:
X is 6, Y is 3
Step-by-step explanation:
The first equation states that x=y+3, so we can substitute x for y+3 in the second equation. We get 2y+y+3=12.
Combine like terms: 3y+3=12
Subtract 3: 3y=9
Divide by 3: y=3
Substitute y=3 into the first equation: x=3+3
Simplify: x=6
Answer:
first one is
x= 6
second one is
y = 3
Step-by-step explanation:
just use the solving eqautions method- I will give you a chart on how
two angles are supplementary. One angle measures 12 degrees less than 3 times the other. find the measure of each angle
Angle 1 = A
Angle 2 = B
They are supplementary, that means that they add 180 degrees, then: A + B = 180
One angle measures 12 degrees less than 3 times the other, tahn means: A - 12 = 3B
Equation 1: A + B = 180
Equation 2: A - 12 = 3B
Solving for A in equation 1:
A + B = 180
A = 180 - B
Using this value into equation 2, and solving for B:
A - 12 = 3B
(180 - B) - 12 = 3B
180 - B - 12 = 3B
168 = 3B + B = 4B
4B = 168
B = 168/4 = 42
B = 42
Using the expression we found for A:
A = 180 - B = 180 - 42 = 138
A = 138
Answer
42 degrees and 138 degrees
Use your answers from #1 and #2 to find the length of each arc between gondola cars. Use 3.14 for pi and round to the nearest hundredth. You must write out all the numbers you are multiplying together, meaning, show your work for full credit.
We have a SkyWheel.
We know that the angle between the gondolas is 360/41 = 8.78°.
The radius of the wheel is 181/2 = 90.5.
We know have to calculate the length of the arc between gondolas.
The length of the arc L can be calculated using proportions: the length of the arc is to the angle between gondolas as the total circumference of the wheel is to 2*pi (or 360°).
We can express this as:
[tex]\frac{L}{\theta}=\frac{C}{2\pi}[/tex]If we rearrange, we can solve for L:
[tex]\begin{gathered} \frac{L}{\theta}=\frac{C}{2\pi} \\ \frac{L}{\theta}=\frac{2\pi r}{2\pi} \\ \frac{L}{\theta}=r \\ L=\theta\cdot r=(\frac{2\pi}{41})\cdot90.5=(\frac{2\cdot3.14}{41})\cdot90.5=13.86ft \end{gathered}[/tex]NOTE: we have to express the angle theta (that is the angle between the gondolas) in radians when we want to calculate a length. That is why this angle is expressed as the total angle of the circle (2*pi) divided the 41 gondolas.
If we use 8.78°, we should express it as:
[tex]L=\theta\cdot r=8.78\degree\cdot(\frac{2\pi}{360\degree})\cdot90.5ft=13.86ft[/tex]With the factor 2pi/360 we are converting the angle in degrees into radians in order to calculate the length.
Answer: the length of the arc between gondolas is 13.86 ft.
Assume that a sample is used to estimate a population mean . Find the margin of error M.E. that corresponds to a sample of size 5 with a mean of 75.2 and a standard deviation of 21.2 at a confidence level of 98% Report ME accurate to one decimal place because the sample statistics are presented with this accuracy M.E. Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.
We have the following:
[tex]\begin{gathered} df=n-1 \\ =5-1 \\ df=4 \end{gathered}[/tex]therefore:
[tex]\begin{gathered} ME=t_{critical}\cdot\frac{s}{\sqrt{n}} \\ ME=3\text{.}747\cdot\frac{21.2}{\sqrt{5}} \\ ME=35.52 \end{gathered}[/tex]The margin the error that corresponds to a sample of size of 5 with mean 75.2 and a standard deviation of 21.2 at a confidence level of 98% is 35.52
If Ashley had 4 yards of yarn and Ramon had 11 feet of yarn, who had more yarn?
Answer:
Step-by-step explanation:
Ashley had more yarn, 1 yard = 3 ft 3 times 4 = 12 so 3 yards is 12 feet.
Answer:
Ashley has more yarn than Ramon.
Step-by-step explanation:
1 yard is 3 feet, so thats 4 (yards) time 3 (feet per yard) is 12. Ashley has 12 feet of yarn. Ramon has 11. 12 is greater than 11, so Ashley has more yarn.
Two consecutive terms in an ARITHMETIC sequence are given. Find the recursive function.
An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.
The recursive formula have the following format:
[tex]a_{n+1}=a_n+d[/tex]Where 'd' is the common difference between each term.
From the text, we know that
[tex]\begin{gathered} a_3=5 \\ a_4=8 \end{gathered}[/tex]Plugging those values in our formula, we find that the common difference between our terms is 3.
This gives us the following recursive function:
[tex]f(n+1)=f(n)+3[/tex]Evaluating the function at '5' and '6', we get the following:
[tex]\begin{gathered} f(5)=f(4)+3=8+3=11 \\ f(6)=f(5)+3=11+3=14 \end{gathered}[/tex]b. Lynn is traveling in Mexico. She exchanges $200 for pesos. If the exchange rate is 19.29 pesos per US dollar, how many pesos should she expect to receive from the exchange pesos
The expected pesos after exchange are 3858 , we can find out by using the concept of exchange rate.
How to calculate currency after exchange rate?
Multiplying the money you have budgeted by the exchange rate .
for example,
If "a" is the money in one currency , you have
"b " is the exchange rate
"c" is the expected money in another currency after exchange.
So, a * b = c
Here, a= $200
b=19.29
now, c = 200 * 19.29
= 3858.
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how do I translate six more than four times a number z into a variable expression
For the relationship, two variables are needed.
One of the variable is given as 'z'. Let the other one be 'x'.
Then you need to translate that 'x' is six more than four times a number 'z'.
This can be expressed as,
[tex]x=6+4z[/tex]Thus, the right side of the expression represents the relationship "six more than four times a number z".
which is the best estimate for the average rate of change for the quadratic function graph on the interval [tex]0 \leqslant x \leqslant 4[/tex]
The average rate of change of the given quadratic function on the interval
[tex]0\le x\le4[/tex]is the slope of the secant line connecting the points
[tex](0,f(0))\text{ and (4,f(4)}[/tex]In other words, the average rate of change is
[tex]m=\frac{f(4)-f(0)}{4-0}[/tex]From the graph, we can see that f(0)=0 and f(4)=-4. By substituying these values into the last equation, we obtain
[tex]\begin{gathered} m=\frac{-4-0}{4-0} \\ m=-\frac{4}{4} \\ m=-1 \end{gathered}[/tex]Hence the average rate of change for the given quadratic function whose graph is shown on 0≤x≤4 is -1
Determine the present value P that must be invested to have the future A at simple interest rate r after time t A= $3000.00 r=15,0% t= 9 months Round up to nearest cent as needed
Answer:
$2696.63
Explanation:
The future value A and the present value P are related by the following equation
A = P(1 + rt)
Where r is the interest rate and t is the time.
Now, we need to convert 9 months to years as follows
9 months x 1 year / 12 months = 0.75 years
Then, replacing A = 3000, r = 15% = 0.15 and t = 0.75, we get:
3000 = P(1 + 0.15(0.75))
3000 = P(1 + 0.1125)
3000 = P(1.1125)
Now, we can solve for P
P = 3000/1.1125
P = 2696.63
Therefore, the present value is $2696.63