1) Slope is the ----- of a line. It is also known as the ------ rate of change.
Slope means steepness and it is a constant rate of change meaning that it does not change.
2) If a line is slanting upwards we say it has a ------ slope.
Slanting upward means a positive slope, for example when you are moving uphill.
If a line is slanting downwards we say it has a ------ slope
Slanting downward means a negative slope, for example when you are moving downhill.
3) A slope of zero means the line is -----
a Slope of 0 means that the line is horizontal. for example when you are moving on a straight road.
4) An undefined slope means the line is -----
An undefined slope means that the line is vertical. for example when you are climbing a vertical wall.
5) All straight line graphs are known as ------ relationships.
They are known as linear relationships.
6) To find the slope of a line we use the formula ----- over ------
We use the slope formula that is rise over run.
Chauncey is studying a 250-mg sample of a radioasubstance has a half-life of 5 days. Write an equatsubstance, s, is left after n days?aS =b= 250 (3)s = 250 (3)s = 250 (0.5)s = 250 (0.5)$5nd
Answer:
[tex]s=250(0.5)^{\frac{n}{5}}[/tex]Step by step explanation:
Exponential functions are represented by the following expression:
[tex]\begin{gathered} f(x)=ab^x \\ \text{where,} \\ a=\text{initial amount} \\ b=\text{decay factor} \\ x=\text{time(days)} \end{gathered}[/tex]Then, for this situation, we have an initial amount of 250, a decay factor of (0.5) in 5 days:
[tex]s=250(0.5)^{\frac{n}{5}}[/tex]what is the area of a semicircle with a diameter of 2 ?
we have that
the area of semicircle is equal to
[tex]A=\frac{1}{2}\cdot\pi\cdot r^2[/tex]we have
r=2/2=1
substitute
[tex]\begin{gathered} A=\frac{1}{2}\cdot\pi\cdot1^2 \\ A=\frac{\pi}{2} \end{gathered}[/tex]area is equal to pi/2 square unitsA computer system was purchased by a small business for $12,000 and, for tax purposes, is assumed to have a salvage value of $2,000 after 8 years. If its value is depreciated linearly from $12,000 to $2,000, find the linear equation that relates the value V in dollars to the time t in years. A video production company is planning to produce instructional videotape. The producer estimates that it will cost $84,000 to shoot the video and $15 per unit to copy and distribute the tape. The wholesale price of the tape is $50 per unit. How many units must be manufactured and sold each month for the company to break even?
Second question
In order to break even,
total revenue must be equal to total cost. In this case, there is no profit
Let x represent the number of units of tape that would be manufactured to break even.
From the information given,
cost of shooting the video = 84000
If the cost of producing a unit is $15, it means that the cost of x units would be 15x
The total cost of producing x units is
15x + 84000
The wholesale price of the tape is $50 per unit. It means that the revenue from selling x units would be 50x
To break even, it means that
15x + 84000 = 50x
50x - 15x = 84000
35x - 84000
x = 84000/35
x = 2400
2400 units must be manufactured and sold each month for the company to break even
Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 10 people took the trip. She was able to purchase coach tickets for $200 and first-class seats for $940 Sheyee her total budget for airfare for the trip, which was $4220. How many first-class tickets did she buy? How many coach tickets did she buy? number of first-class tickets bought = number of coach tickets bought =
Answer:
• The number of first-class tickets bought = 3
,• The number of coach tickets bought =7
Explanation:
Let the number of first-class tickets bought = x
Let the number of coach tickets bought = y
A total of 10 people took the trip:
[tex]\implies x+y=10[/tex]Her total budget for the trip's airfare = $4220.
[tex]\implies200y+940x=4220[/tex]Next, solve the two equations simultaneously:
[tex]\begin{gathered} x+y=10\implies x=10-y \\ 940x+200y=4220 \end{gathered}[/tex]Substitute x into the second equation:
[tex]\begin{gathered} 940(10-y)+200y=4220 \\ 9400-940y+200y=4220 \\ 9400-740y=4220 \\ 9400-4220=740y \\ 5180=740y \\ \frac{5180}{740}=y \\ y=7 \end{gathered}[/tex]Recall: x=10-y
[tex]\begin{gathered} x=10-7 \\ x=3 \end{gathered}[/tex]Thus:
• The number of first-class tickets bought, x = 3
,• The number of coach tickets bought, y =7
what is the ratio 250 pieces of red construction paper and 114 blue construction paper
Answer
Check Explanation
Explanation
We need to find the ratio of red construction paper to blue construction paper.
250 : 114
Divide both sides by 2
125 : 57
That's how far we can go, since there is no number that can divide these two numbers.
Hope this Helps!!!
Pamela's mother purchased five boxes of candy bars. If each box contains 20 bars, how many candy bars does Pamela's mother have? Explain your answer.
If each box contains 20 bars and Pamela's mother purchased 5 boxes
To get the number of candy bars Pamela's mother have, we will simply multiply the number of box by the number oc candy in each box
That is; 5 x 20bars = 100 candy bars
Hence Pamela's mother have 100 candy bars
What is the measurement of the exterior angle in the diagram below?A. 100B. 30C. 70D. 88
i need help with -1=-4/7t
The equation is:
[tex]-1\text{ = -}\frac{4}{7}\text{ t}[/tex]To find t you need to isolate t.
First, pass the 7 multiplying and the 4 dividing:
[tex]-1\cdot\frac{7}{4}=-t[/tex]Finally, pass the minus sign:
[tex]-t\text{ = (-1)}\cdot t=-1.\frac{7}{4}\Rightarrow\text{ t = (-1)}\cdot\frac{7}{4}\frac{1}{(-1)}=\frac{7}{4}[/tex]Seth charges $42 for 2 hours of baseball lessons. Bennie charges $65 for 3 hours of baseball lessons. Who offers the better deal? Why?
Answer:
Seth offers the better deal, because his charge per hour is lower.
Explanation:
Given that;
Seth charges $42 for 2 hours of baseball lessons.
Seth's Charge rate per hour would be;
[tex]\begin{gathered} r_s=\frac{\text{ \$42}}{2\text{ hours}} \\ r_s=\text{ \$21 per hour} \end{gathered}[/tex]Also, Bennie charges $65 for 3 hours of baseball lessons.
[tex]\begin{gathered} r_b=\frac{\text{ \$65}}{3\text{ hours}} \\ r_b=\text{ \$21.67 per hour} \end{gathered}[/tex]From the given deals, the deal with the lower Charge rate per hour offers the better deal.
So, Seth offers the better deal, because his charge per hour is lower.
A glass jar contains 3 red, 13 green, 4 blue, and 8 yellow marbles. If a single marble is chosen at random from the jar, what is the probability of choosing a(a) red marble? (b) green marble? (c) blue marble?
Solution
(a) red marble?
[tex]p=\frac{\text{red}}{\text{total}}=\frac{3}{3+13+4+8}=\frac{3}{28}[/tex](b) green marble?
[tex]p=\frac{\text{gren}}{\text{total}}=\frac{13}{3+13+4+8}=\frac{13}{28}[/tex](c) blue marble?
[tex]p=\frac{\text{blue}}{\text{total}}=\frac{4}{3+13+4+8}=\frac{4}{28}[/tex]Five CDs cost $80 . If each CD costs the same, how much does one cost
solution:
5 CDs ----> $80
1 CDs ----> x
then
[tex]x=\frac{80}{5}=16[/tex]answer: one CD cost $16
Use a properly of equality to solve this equation: 4.5x = 18
To solve the equation you can use the property of the multiplicative inverse, like this
[tex]\begin{gathered} 4.5x=18 \\ \frac{1}{4.5}\cdot4.5x=18\cdot\frac{1}{4.5} \end{gathered}[/tex]Dividing by 4.5 into both sides of the equation is the same as multiplying by the multiplicative inverse of 4.5 on both sides of the equation
[tex]x=\frac{18}{4.5}[/tex]Therefore,
[tex]x=4[/tex]A sailmaster decides to stitch a strip of binding right round the edge of a sail which is the shape of a right- angled triangle. The vertical and horizontal edges of the sail are 6.5m and 2.6m respectively. What length of binding is needed for the job?
First, we will use the Pythagorean theorem to compute the hypotenuse:
[tex]\begin{gathered} h^2=(6.5m)^2+(2.6m)^2 \\ =42.25m^2+6.76m^2 \\ =49.01m^2. \end{gathered}[/tex]Then:
[tex]h\approx7.0m.[/tex]Therefore, the sail master will need:
[tex]6.5m+2.6m+7m=16.1m[/tex]of blinding.
Answer: 16.1m
Janelle invests in a piece of art that cost 600 British Pounds. A study found that art appreciates in value at a rate of 3.97% per year. Assuming this pattern continues, how much, in British Pounds, will Janelle's piece of art be valued at after 10 years? Round your answer to the hundredths place.
Step-by-step explanation:
The art piece originally costs £600.
And it appreciates at a rate of 3.97% each year.
And we want to find the value of the art after 10 years.
We can write an exponential function to model the situation. The standard exponential function is given by:
[tex]f(t)=a(r)^t[/tex]Where t is the time in years.
Since it appreciates at a rate of 3.97% each year, the value after each year will be (100% + 3.97%) or 103.97%.
103.97% = 1.0397. So, r = 1.0397:
[tex]f(t)=a(1.0397)^t[/tex]Our a is the initial value. Therefore:
[tex]f(t)=600(1.0397)^t[/tex]Then the value of the piece of art after 10 years is:
[tex]f(10)=600(1.0397)^{10}=885.58793\approx885.59[/tex]Hence, It will be worth about £885.59 after 10 years.
Math help question one and two
We can determine that the option D is better fit of equation model which calculated as follows :
First, insert the value x to the formula (y)
y = 0.07(100) + 0,94
y = 7 + 0,94
y = 7,94
Given the bone chips (x) is 100, then the bone tools (y) is 8.
The value of bone tools (y) which is 8 is the result of rounded of value (y) 7,94.
2. The answer for question no. 2 is B
The equation models the line of best fit for data is y = -0,35x + 31,6
We can prove it as follows :
First step is value of race (x) of the first column which given by 1 to the formula .
y = -0,35(1) + 31,6
y = -0,35 + 31,6
y = 31,25
Next, we check that given the value of the Time (y) of Race (x) value of 1 is 31,1.
Hence, it shows that the equation models the line of best fit for data is y = -0,35x + 31,6
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A complex number zı has a magnitude z1] = 2 and an angle 6, = 49°.=Express zy in rectangular form, as 21 == a +bi.Round a and b to the nearest thousandth.21 =+iShow Calculator
Complex numbers can be written in two forms:
[tex]\begin{gathered} z=a+b\cdot i \\ z=r\cdot e^{i\theta} \end{gathered}[/tex]Where a and b are known as the real and the imaginary part and r and theta are the magnitude and the angle of the number. In this case we are given these last two quantities and we have to find a and b. One way to do this is recalling an important property of the exponential expression above:
[tex]e^{i\theta}=\cos \theta+i\sin \theta[/tex]Then the exponential form of a number is equal to:
[tex]z=r\cdot e^{i\theta}=r\cdot(\cos \theta+i\sin \theta)=r\cos \theta+i\cdot r\sin \theta[/tex]And since we are talking about the same number then this expression must be equal to that given by a and b:
[tex]a+i\cdot b=r\cos \theta+i\cdot r\sin \theta[/tex]Equalizing terms without i and those with i we have two equations:
[tex]\begin{gathered} a=r\cos \theta \\ b=r\sin \theta \end{gathered}[/tex]Now let's use the data from the exercise:
[tex]\begin{gathered} r=\lvert z_1\rvert=2 \\ \theta=\theta_1=49^{\circ} \end{gathered}[/tex]Then we have:
[tex]\begin{gathered} a=2\cdot\cos 49^{\circ} \\ b=2\cdot\sin 49^{\circ} \end{gathered}[/tex]Using a calculator we can find a and b:
[tex]\begin{gathered} a=1.312 \\ b=1.509 \end{gathered}[/tex]Then the answers for the two boxes are 1.312 and 1.509
Solve the system of linear equations by eliminations-- 3x + 4y = 186x+2y = -6does thia system have a solution?
10Ana wants to multiply out the brackets in the expression 2(3a-1).She writes 2(3a-1)=6a - 1.Ana is wrong. Explain why.1Show Your WorkYou have responded to 9 of 10 questions
Answer:
[tex]2(3a-1)=6a-2[/tex]Step by step explanation:
To multiply the expression 2(3a-1), we need to use the distributive property of multiplication which states that:
[tex]a(b+c)=a\cdot b+a\cdot c[/tex]Then, for the expression 2(3a-1), the correct answer would be:
[tex]\begin{gathered} 2(3a-1)=2\cdot3a-2\cdot1 \\ 2(3a-1)=6a-2 \end{gathered}[/tex]Supposed to 25% of the time Danny eat out twice a month 30% of the time he eats out once a month and 45% of the time he doesn’t eat out at all in a given month what is the expected value for the number of times daily eats out during a month
Answer
Expected value = 0.8 times per month
Explanation
The mean of the probability distribution is called expected value and it is given as
E(X) = Σxᵢpᵢ
where
xᵢ = each variable = Number of times Danny eats out
pᵢ = probability of each variable
n = number of variables
p = probability of one variable
We need to set up the probability distribution first
xᵢ | pᵢ
2 | 0.25
1 | 0.30
0 | 0.45
E(X)
= (2 × 0.25) + (1 × 0.30) + (0 × 0.45)
= 0.5 + 0.3 + 0
= 0.8
Hope this Helps!!!
To start a new business Beth deposits $1500 at the end of each six-month period in an account that pays 8%, compounded semiannually. How much will she have at the end of 9 years?
The amount Beth deposit every six-month is A = $1500.
The rate percent is 8% or 0.08.
The time after which futre value determined is t = 9 years.
Determine the rate percent for semi-annually.
[tex]\begin{gathered} i=\frac{0.08}{2} \\ =0.04 \end{gathered}[/tex]Determine the value of time (t) for semi-annualy.
[tex]\begin{gathered} n=2\cdot9 \\ =18 \end{gathered}[/tex]The formula for the future value is,
[tex]FV=\frac{A}{i}\lbrack(1+i)^n-1\rbrack[/tex]Substitute the values in the formula to determine the future value.
[tex]\begin{gathered} FV=\frac{1500}{0.04}\lbrack(1+0.04)^{18}-1\rbrack \\ =37500\lbrack(1.04)^{18}-1\rbrack \\ =38468.11933 \\ =38468.12 \end{gathered}[/tex]So answer is 38468.12
Rangers wanted to estimate the total number of elk in region of Montana. they tagged 12 elk and sent them back to the area. two months later the Rangers observed 4 of the tagged elk out of 25 total Elk observed. estimate the size of the elk population in that region of Montana
Total number of elks tagged = 12
Number of a sample of the tagged elks from 25 total Elk observed = 4
Total number of 25 Elk observed = 12/4 = 3
Size of the elk population in the region of Montana = 3 x 25
= 75
Sketch a graph of g (x) = V (x-3) + 2 Label at least 4 points including X-and y-intercepts, explain
The equation is given as
[tex]g(x)=\sqrt[]{x-3}+2[/tex]To find the coordinates of the equation,
Hence the graph of the equation is
Nick used a rope to make a rectangle and a circle below. If 10 cm rope was left, what was the original length of the rope? cm 10 cm 7 cm
To find the original length of the rope, we must find the length of rope used in the rectangle and in the circle, and add it to the length of rope that was leftover.
The length of rope used in the rectangle would be the perimeter of the rectangle, the perimeter of the rectangle is the sum of all his sides.
Perimeter of a rectangle = side + side + side + side
[tex]\text{Perimeter rectangle= 10+7+10+7=34 cm}[/tex]The question gives us the perimeter of the circle, 20 cm this measure was the length of rope used in the circle.
[tex]\text{Perimeter circle= 20 cm}[/tex]Now the total length of the rope was: The sum of the perimeters of both rectangle and circle and the length of rope that was left.
Total length rope = 34 + 20 + 10 = 64 cm
which word phrase represents the following expression n-3A) the quotient of n and 3B) 3 less than nC) n less than 3
Answer:
B) 3 less than n
Explanation:
Given the expression:
[tex]n-3[/tex]This means that the value of n is being reduced by 3.
Thus, the appropriate word phrase is: 3 less than n.
The correct choice is B.
Susan is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be 4 inches. The area of the pennant must be at least 12 square inches. (The pennant has to be seen in the photo.) Write an Inequality that describes the possible heights (in inches) of the triangle. Use h for the height of the triangular pennant.
Susan is making a pennant in the shape of a triangle for her senior class photo. She wants the base length of this triangle to be 4 inches. The area of the pennant must be at least 12 square inches. (The pennant has to be seen in the photo.) Write an Inequality that describes the possible heights (in inches) of the triangle. Use h for the height of the triangular pennant.
Remember that
the area of the triangle is
[tex]A=\frac{1}{2}b\cdot h[/tex]we have
b=4 in
at least -----> is greater than or equal to
so
[tex]A\ge12\text{ in2}[/tex]therefore
[tex]\begin{gathered} \frac{1}{2}\cdot(4)\cdot h\ge12 \\ \text{solve for h} \\ 2h\ge12 \\ h\ge6\text{ in} \end{gathered}[/tex]the height of triangle must be greater than or equal to 6 inches
For her cell phone plan heather pays 30 dollars per month plus 0.05 per text. She wants to keep her cell phone bill under 60 dollars per month. Which inequality represents the number of texts t heather can send each month while staying within her budget?
The inequality represents the number of texts t heather can send each month while staying within her budget is t<600.
Given, heather pays 30 dollars per month plus 0.05 per text.
She wants to keep her cell phone bill under 60 dollars per month.
hence texts she can send = 0.5 × 600
= $30
hence for $30 heather can text upto 600 texts.
so, cell phone plans + text
= $30 + $ 30
= $60
so, the inequality represents the number of texts t heather can send each month while staying within her budget is t<600
Hence the inequality is t<600
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Brady creates the graph below to keep track of the approximate height of the grass on hislawn over timeWhat is the dependent variable in the situation?Brady's Lawnthe number of days it takes for the grass togrow an inchthe height of the grass, in inchesthe number of inches the grass grows eachdayHeight of Grass (inches)the amount of time that has passed. In days2468 10 12 14 16 18 20Time (days)
Answer:
The height of the grass, in inches
Explanation:
The dependent variable is the variable whose value changes whenever the other variable (independent) changes.
From the graph, the height of the grass (in inches) depends on the time in days.
Therefore, the dependent variable in this situation is the height of the grass, in inches
The coach of a soccer team keeps many stats on her teams performance. For example, she records if the team was ahead, behind, or tired with the opponent at the end of each half.pic is the summary of the data she got after 60 games. Supposed the coach continue recording the end-of-half results for 80 more games. In how many of these 80 games will the team be tied at the end of neither half. Use the data to make a prediction
Given:
The stat of the team is given in the table.
Required:
We have to find in how many of 80 games will the team be tied at the end of neither half.
Explanation:
The total number of games given in the table is
[tex]4+8+12+3+6+9+5+4+9=60[/tex]The number of games in which the team has tied at the end of neither half is
[tex]4+8+3+6=21[/tex]Then the percentage of the team has tied at the end of neither half is
[tex]\frac{21}{60}\times100=0.35\times100=35\text{ \%}[/tex]Hence the number of games in which the team be tied at the end of neither half in those 80 games is
[tex]35\text{\% of }80=\frac{35}{100}\times80=0.35\times80=28[/tex]Final answer:
Hence the final answer is
[tex]28[/tex]For each of the following, find the Lateral Area, Surface Area, and Volume. Leave answers in terms ofFt, and if applicable, round to the nearest tenth.1. TA =V=A sphere with radius of 21 cm.
Given a sphere with radius R, the volume and the surface area formulas are expressed as:
[tex]\begin{gathered} V=\frac{4}{3}\pi R³ \\ \\ A=4\pi R² \end{gathered}[/tex]Now, if we have a sphere of radius R = 21 cm = 0.688976 ft. Then, using the formulas:
For the volume
[tex]\begin{gathered} V=\frac{4}{3}\pi(0.688976)³ \\ \\ \therefore V=1.37\text{ ft^^b3} \end{gathered}[/tex]For the surface area
[tex]\begin{gathered} A=4\pi(0.688976)² \\ \\ \therefore A=5.97\text{ ft^^b2} \end{gathered}[/tex]Use the correct trigonometric function to solve for both x and y .
As per given by the question.
There are given that a triangle.
Now,
Suppose given triangle is ABC.
Then, redraw the given triangle.
Now,
For finding the value of x, and y;
First find the value of x with the help of sine trigonometric function.
So,
[tex]\sin 35^{\circ}=\frac{AB}{AC}[/tex]Then,
Substitute the value x for AB and 22 for AC.
SO,
[tex]\begin{gathered} \sin 35^{\circ}=\frac{AB}{AC} \\ \sin 35^{\circ}=\frac{x}{22} \\ 0.57=\frac{x}{22} \\ x=0.57\times22 \\ x=12.54 \end{gathered}[/tex]Now,
For finding the value of y,
Here, use pythagoras theorem in triangle ABC.
So, from the pythagoras theorem;
[tex]AB^2+BC^2=AC^2[/tex]Then,
Substitute the value in above formula;
So,
[tex]\begin{gathered} AB^2+BC^2=AC^2 \\ x^2+y^2=(22)^2 \end{gathered}[/tex]Now, put the value 12.54 for x,
So,
[tex]\begin{gathered} x^2+y^2=(22)^2 \\ (12.54)^2+y^2=(22)^2 \\ 157.25+y^2=484 \\ y^2=484-157.25 \\ y^2=326.75 \end{gathered}[/tex]Then,
[tex]\begin{gathered} y^2=326.75 \\ y=\sqrt[]{326.75} \\ y=18.076 \end{gathered}[/tex]Hence, the value of x is 12.54 and the value of y is 18.076.