Which line is the graph of the function y=x - 7?
Given the function :
[tex]y=x-7[/tex]To find which line represents the given function , find x- intercept and y - intercept
So, the y- intercept of the function is the value of y when x = 0
So, when x = 0
y = 0 - 7 = -7
The x - intercept is the value of x when y = 0
So, when y = 0
0 = x - 7
x = 7
So, the function passes through the points ( 0 , -7 ) and ( 7 , 0 )
Now, look to figure to find which line is the correct line
So, it will be the line D, because he is the only line is passing through one of the points.
The answer is : D
Let p be a figure is a triangle and let a be a figure is a polygon. Write the inverse
Given that
p is " a figure is triangle"
q is " a figure is polygon"
Then, the inverse of the logic statement will be
~p is " a figure is not a triangle"
~q is " a figure is not a polygon"
Now combining both of the statement together, it will be
If a figure is not a triangle, then it is not a polygon. Which is a false statement.
Therefore, the correct option is Option 4.
Find the area of the parallelogram below using the Formula: A = bh
Given:
The base 10 cm and height 3 cm.
Required:
Find the area of the parallelogram.
Explanation:
We know the formula for area of parallelogram
[tex]A=base\times height[/tex]We have base = 10 cm and height = 3 cm
[tex]\begin{gathered} A=3\times10 \\ A=30\text{ cm}^2 \end{gathered}[/tex]Answer:
The area is 30 cm square.
Find the shortest distance from A to B in the diagram below.A. 17 mB. 329−−√ mC. 505−−−√ mD. 10 m
Let us sketch out the part of the image needed,
To solve for the shortest distance from A to B, we will apply the Pythagoras theorem which states,
[tex]\text{Hypotenuse}^2=Opposite^2+Adjacent^2[/tex]Given data
[tex]\begin{gathered} \text{Hypotenuse}=a=\text{?} \\ \text{Opposite}=b=3=8m \\ \text{Adjacent}=c=6m \end{gathered}[/tex]Solving for a,
[tex]a^2=b^2+c^2[/tex]Substituting the values of b=8m and c=6m
[tex]\begin{gathered} a^2=(8m)^2+(6m)^2 \\ a^2=64m^2+36m^2 \\ a^2=100m^2 \\ \end{gathered}[/tex]Take the square root of both sides
[tex]\begin{gathered} \sqrt[]{a^2}=\sqrt[]{100m^2} \\ a=10m \end{gathered}[/tex]Hence, the shortest distance from A to B is 10m.
The correct option is D.
5. Assume that the sales of a certain automobile parts company are approximated by a linear function. Suppose that sales were $200,000 in 1981 and $1,000,000 in 1988. Let x = 0 represent 1981 and x = 7 represent 1988. (a) Find the equation giving the company's yearly sales. (b) Find the approximate sales in 1983. (c) Estimate sales in 1999.
a)
The equation of the line in the slope-intercept form has the next form
[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept
So first we need to calculate the slope, the slope is given by the next formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are points where the line passes through.
In our case
(0,200000)
(7,1000000)
We substitute the data
[tex]m=\frac{1,000,000-200,000}{7-0}=\frac{800000}{7}[/tex]Then we need to calculate the y-intercept that is b
x=0 and y=200000
[tex]200000=\frac{800000}{7}(0)+b[/tex]We isolate the b
[tex]b=200000[/tex]The linear equation is
[tex]y=\frac{800000}{7}x+200000[/tex]b)
If x=0 represents 1981, therefore x=2 represents 1983
We substitute in the equation above x=2
[tex]y=\frac{800000}{7}(2)+200000=\frac{3000000}{7}=428571.43[/tex]The approximate sales in 1983 are $428571.43
c)
if x=0 represents 1981, therefore x=18 represents 1999
[tex]y=\frac{800000}{7}(18)+200000=2257142.86[/tex]The estimated sales in 1999 are $2257142.86
If a student (represented by initials) was chosen at random, find P(HH|C).
The conditional probability formula is given as
[tex]P(HH|C)=\frac{P(HH\cap C)}{P(C)}[/tex]where
[tex]P(HH\cap C)[/tex]denotes the probability of the intersection zone.
From the given picture, we can note that the number of elements in each of the above zones are:
[tex]\begin{gathered} n(HH\cap C)=4 \\ \text{and} \\ n(C)=10 \end{gathered}[/tex]Then, we have
[tex]P(HH|C)=\frac{P(HH\cap C)}{P(C)}=\frac{4}{10}[/tex]by symplifing this result, we have
[tex]P(HH|C)=\frac{2}{5}[/tex]Cone A has a radius 18 inches and Cone B has a radius of 48inches. If the cones are similar and the volume of Cone A is 54 ft^3,find the volume of Cone B.
Answer:
1023.9 ft^3
Explanation:
The below formula can be used to find the volume of a cone;
[tex]V=\pi\times r^2\times\frac{h}{3}[/tex]where r = radius of the base
h = height of the cone
Given the radius of cone A as 18 inches(18/12 = 1.5 ft) and the volume of cone A as 54 ft^3, we can go ahead and solve for the height of cone A;
[tex]\begin{gathered} 54=3.14\times(1.5)^2\times\frac{h_A}{3} \\ h_A=\frac{162}{7.065} \\ h_A=22.93ft \end{gathered}[/tex]We're told that cone A and B are similar, therefore the ratios of the radii and heights must be the same;
[tex]\begin{gathered} \frac{h_B}{h_A}=\frac{48}{18} \\ h_B=\frac{22.93\times48}{18} \\ h_B=61.14ft \end{gathered}[/tex]Since we now know that the height of cone B to be 61.14ft and we're given the radius of cone B to 48 inches (48/12 = 4ft), we can go ahead and determine the volume of cone B as shown below;
[tex]\begin{gathered} V_B=3.14\times(4)^2\times\frac{61.14}{3} \\ V_B=1023.9ft^3 \end{gathered}[/tex]The number of guests , g, comeing for dinner is not 8 how do u write that as an inquality??
By definition, the following symbol meanas "not equal to":
[tex]\ne[/tex]An inequality relates two expressions. When you use the symbol shown above, you are indicating that the expressions are not equal.
In equations you use the "equal sign":
[tex]=[/tex]That indicates that the expresions related are equal; it indicates and equality.
In this case, the statement given in the exercise says that "g" (that represents the number of guests that coming for dinner) is not 8. So this indicates that "g" is not equal to 8.
Based on the above, you can write this situation as the following inequality:
[tex]g\ne8[/tex]The answer is:
[tex]g\ne8[/tex]Consider a linear function y = ax modeling a vehicle traveling at a constant speed. For this model, y is the distance ofthe vehicle from its starting point and x is the time the vehicle has been traveling. Which of the following is the best Interpretation of a vertical change of 10 units up?A)The transformed function models the same vehicle but measures distance from a location 10 miles from the starting point.B)The transformed function models the same vehicle but measures the time from 10 hours before the vehicle started moving.C)The transformed function models the same vehicle but the vehicle is traveling 10 mph faster.D)The transformed function models the vehicle 10 cars ahead of the original vehicle.
Given the function, y = ax
Given that y is the distance of the vehicle from its starting point, it means that the initial position of y is zero. A vertical change of 10 units up is a movement along the y axis. Therefore, the interpretation would be
A)The transformed function models the same vehicle but measures distance from a location 10 miles from the starting point.
Carlos knows that he had deposited $100 in a bank account that earns 25% interest compounded quarterly. How much money will he have in 4 years?
We have the following:
To calculate the total amount of money compounded monthly or quarterly we use the formula below n = number of times interest is compounded per year
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where P is $100, r is 25% or 0.25 and n is 4, replacing:
[tex]\begin{gathered} A=100(1+\frac{0.25}{4})^{4\cdot4} \\ A=100\cdot1.0625^{16} \\ A=100\cdot2.648 \\ A=264.8 \end{gathered}[/tex]Therefore, in 4 years have $264.8
if f(x)=5x, what is f^-1(x)
We want to find the inverse of the function f(x) = 5x. For this purpose, we use the following procedure:
Let´s the function:
[tex]f(x)\text{ = 5x}[/tex]this is equivalent to say
[tex]y\text{ = 5x}[/tex]Now, we resolve the above equation in terms of x. That is:
Topic 6: Rate of change Note: A rate of change is a rate that describes how one quantity changes in relation to another. A constant rate of change is the rate of change of a linear relationship. Ex 6: Find the rate of change below AND explain it in words.
Rate of Change
As stated in the question, the rate of change measures how one quantity changes with respect to another.
The question talks about two quantities: The number of hours passed and the number of candies sold. The corresponding data is shown in the table.
Let's call H to the number of hours passed and C to the number of candies sold. We are interested in calculating the changes of C divided by the changes of H as follows:
[tex]r=\frac{\text{change of C}}{change\text{ of H}}[/tex]Take the first two rows of the table. The change of C is 9 - 5 = 4. The change of H is 8 - 7 = 1, thus the rate of change is:
[tex]r=\frac{9-5}{8-7}=\frac{4}{1}=4[/tex]This means 4 candies are sold per hour.
Now take the second and the third rows.
[tex]r=\frac{13-9}{9-8}=\frac{4}{1}=4[/tex]Again, we get 4 candies per hour.
You can use any pair of rows (including non-continuous rows) and you will get the same result.
Based on those results, we can conclude the rate of change is constant and has a value of 4 candies per hour.
solve the following quadratic function by utilizing the square root method. simplify your answer y=49x^2-1
y=49x^2-1
y = 49x² - 1
49x² - 1 = 0
49x² = 1
x² = 1/49
sqrt(x²) = sqrt(1/49)
x = +1/7
x = -1/7
Answer:
x = 1/7
What is the measure of angle zxv 138° 68° 94° 112°
The sum of all angles at a point on a line is equal to 180°.
In the given figure, at line YXT, sum of all angles at X = 180
SOo, angle YXZ + angle ZXT = 180°
It is given that angle YXZ = 68°
SUbstitute the value and solve for ZXT
YXZ + ZXT = 180
68 + ZXT = 180
Angle ZXT = 180 - 68
Angle ZXT = 112°
Angle ZXV is the sum of angle ZXT and TXV
Angle ZXV = Angle ZXT + Angle TXV
Angle ZXV = 1
I need help with 3 topics with different things in the 6th grade
The given number is,1428
The digits in the one's place are 8
And the digits in the hundreds place is 4.
26 Anna is drawing a picture on a square piece of paper that has an area of 729 in.1 What is the minimum side length of a square clipboard that Anna could use that would support the whole sheet of paper? A. 9 in. B. 27 in. C. 182.25 in. D. 364.5 in. 27] A basketball has a diameter of 9.5 cm. Which of the expressions shows how to determine the volume of air the basketball can
Answer:
B. 27in
Monica went to purchase a new bike when she went to visither grandmother in California. The bicyde cost $89.00. Thesales tax in California is 7.5% How much will she pay in taxeswhen purchasing the bike in California? Monica lives in Ohio.The sales tax in Ohio is 7% She can purchase the same bikefor the same original cost in Ohio. If she waits until she getshome to purchase the bike, how much will she savepurchasing the bike in Ohio
Data:
Cost of the bike: $89.00
Salex tax California: 7.5%
Sales tax in Ohio: 7%
1. As the bike cost without tax $89.00 to find how much will she pay in taxes in California (C) you find the 7.5% of $89.00:
[tex]C=89.00\cdot\frac{7.5}{100}=6.675[/tex]In California she pays in tax $6.6752. As the bike has the same cost $89.00 to find how much she will save purchasing the bike in Ohio you:
- calculate the 7% of $89.00
[tex]89.00\cdot\frac{7}{100}=6.23[/tex]In Ohio she pays in tax $6.23- Find the difference between the tax she pays in California and the tx she pay in Ohio:
[tex]6.675-6.23=0.445[/tex]If she purchase the bike in Ohio she will save $0.445What amount must be deposited now in order to withdraw ₱5,000 at the beginning of each month for 4 years, if interest is 12% compounded monthly?
Given:
The final amount is given as A = ₱5,000.
The number of years is T = 4.
The number of times compounded is each month, n = 12 per year.
The rate of interest is r = 12% = 0.12.
The objective is to find the amount to be deposited.
Explanation:
The general formula to calculate the principal amount is,
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ P=\frac{A}{(1+\frac{r}{n})^{nt}}\text{ . . . . . . .(1)} \end{gathered}[/tex]On plugging the given values in equation (1),
[tex]\begin{gathered} P=\frac{5000}{(1+\frac{0.12}{12})^{12(4)}} \\ =\frac{5000}{(1+0.01)^{48}} \\ =3101.302025\ldots\text{..} \\ =3101.3 \end{gathered}[/tex]Hence, the amount to be deposited is ₱3101.3
2. What is the volume and surface area of the square pyramid? (Spts each) Volume = Surface Area = Identify the needed values. (1pt each) B = = 3n.. P= Sin. h = 8 in. (=
Volume of the square pyramid = 64 in³
Surface area of square pyramid = 144 in²
B = 64 in²
P = 32 in
h = 3 in
l = 5 in
Explanation:The base is a square.
Volume of a square pyramid = area of base × height/3
h = height = 3 in
Area of base = side length²
side length = 8 in
Area of base = 8² = 64
Volume of the square pyramid = 64 × 3/3 = 192/3
Volume of square pyramid = 64 in³
B = area of base
B = 64 in²
P = perimeter of base
perimeter of base = 4(length) = 4(8)
perimeter of base = 32 in
P = 32 in
Surface area of square pyramid = Area of base + 1/2 × perimter of base × slant height
l = slant height = 5 in
l = 5 in
Surface area of square pyramid = 64 + 1/2(32)(5)
Surface area of square pyramid = 64 + 80
Surface area of square pyramid = 144 in²
Use a calculator to evaluate the trigonometric function for the indicated value.Round your answer to four decimal places.
Given:
There are given the trigonometric funtion:
[tex]sec(20^{\circ}20^{\prime}18^{\prime}^{\prime})[/tex]Explanation:
According to the question:
First, we need to convert all minutes into degrees.
So,
To find the minute to a degree, we need to divide by 60 degrees.
Then,
[tex]\begin{gathered} 20^{\prime}=\frac{20}{60} \\ =0.33^{\circ} \end{gathered}[/tex]Then,
[tex]1^{\prime}^{\prime}=\frac{1}{60}^{\prime}[/tex]Then,
[tex]\begin{gathered} 18^{\prime}^{\prime}=\frac{18}{60}^{\prime} \\ =0.3^{\prime} \end{gathered}[/tex]Then,
[tex]\begin{gathered} 0.3^{\prime}=\frac{0.3}{60}^{\circ} \\ =0.005^{\circ} \end{gathered}[/tex]So,
The final trigonometric function will be:
[tex]sec(20^{\circ}+0.33^{\circ}+0.005^{\circ})=sec(20.335^{\circ})[/tex]Then,
The value of the given sec function is:
[tex]sec(20.335^{\circ})=\frac{1}{cos(20.335^{\circ)}}[/tex]Then,
[tex]\begin{gathered} sec(20.335^{\operatorname{\circ}})=\frac{1}{cos(20.335^{\operatorname{\circ}})} \\ =\frac{1}{0.9} \\ =1.11 \end{gathered}[/tex]Final answer:
Hence, the value of the given expression is 1.11
Solve the equationbelow:71<-Ea+3A qq=1-87B a=16
Solve the equation;
[tex]\begin{gathered} \frac{7}{8}=q+\frac{1}{2} \\ \\ \text{Subtract }\frac{1}{2}\text{ from both sides} \\ \frac{7}{8}-\frac{1}{2}=q+\frac{1}{2}-\frac{1}{2} \\ \text{Take the LCM of the fractions on the left side} \\ \frac{7-4}{8}=q \\ \frac{3}{8}=q \end{gathered}[/tex]The answer is
q = 3/8
Option C is the correct answer
tammy is going to rent a truck for one day. there are two companies she can choose from, and they have the following prices. company A charges $75 and allows unlimited millage company B has an initial fee of $55 and charges an additional $0.80 for every mile driven.for what mileage will company A charge less than company B?use m for the number of miles driven and solve your inequality for m.
Company A-> charges $75 and unlimited millage.
Company B-> initial fee $55 and charges +$0.8 for every mile driven.
The inequality that represents for what millage will company A charges less than company B is:
Let m be the number of miles
[tex]\begin{gathered} 75<55+0.8m \\ 75-55<0.8m \\ 20<0.8m \\ \frac{20}{0.8}For 25 miles company A will charge less than company B.In how many ways can the letters in the word ATONEMENT be arranged?
Given:
The word is ATONEMENT.
The number of letters in this word are 9 and unique letters are 6.
Arrangement of the letter is calculated as,
[tex]\begin{gathered} n\text{ letters are arranged in n! ways} \\ Arrangement=9!\text{ } \end{gathered}[/tex]But as the 3 letters are repeated 2 times.
So, the number of unique arrangements are,
[tex]\text{Arrangement}=\frac{9!}{2!2!2!}=\frac{362880}{8}=45360[/tex]Answer: Number of arrangements are 45360.
Hello, please help me with this geometry on circles and ratios.
To determine the tangent angle of a circle
[tex]\begin{gathered} arcBDC\colon arcBC=3\colon2of360^0\text{ } \\ arc\text{ BDC = }\frac{3}{5}X360^0=216^0 \\ arc\text{ BC = }\frac{2}{5}x360^0=144^0 \end{gathered}[/tex]Measure of angle A = 1/2 of arc BDC - arc BC
[tex]\begin{gathered} mHence the measure of angle 36°8. For numbers 8a-8c, tell whether each expression was rewritten using the Commutative Property or the Associative Property. Choose the correct property of addition. Associative Property 8a. + (2 + 4) = 5 + (4 + 2 Commutative Property Associative Property 8b. 1 히 6 Commutative Property Associative Property 8c. ( 13 + 35) + + (33 + 1 Commutative Property
(a)
[tex]\begin{gathered} \frac{5}{7}+(\frac{2}{9}+\frac{4}{7})=\frac{5}{7}+(\frac{4}{7}+\frac{2}{9}) \\ \text{This expression was re-written using the Commutative property} \end{gathered}[/tex](b)
[tex]\begin{gathered} (\frac{1}{8}+\frac{5}{6})+\frac{1}{6}=\frac{1}{8}+(\frac{5}{6}+\frac{1}{6}) \\ \text{This expression was re-written using the associative property} \end{gathered}[/tex](c)
[tex]\begin{gathered} (1\frac{2}{5}+3\frac{1}{3})+\frac{4}{5}=(3\frac{1}{3}+1\frac{2}{5})+\frac{4}{5} \\ \text{This expression was re-written using the Commutative property} \end{gathered}[/tex]The Commutative property of addition (and multiplication) states that the numbers we are dealing with in math can have their positions changed, without making any difference to the final answer.
In number 8(a), the fractions in parenthesis swapped places but this wouold not affect the answer.
The Associative property of addition (and multiplication) states that when two or more numbers are added (or multiplied) the results remain the same regardless of the change in grouping of the parenthesis.
In number 8(b), the first and second expression were grouped into parenthesis. But when the second and third expression were regrouped into the parenthesis, the answer would remain the same.
Find all the solutions to the following equation that are on the interval [0,2pie] by solving for theta
First, add 1 to both members of the equation:
[tex]\begin{gathered} 2\sec \theta\tan \theta+2\sec \theta+\tan \theta=-1 \\ \Rightarrow2\sec \theta\tan \theta+2\sec \theta+\tan \theta+1=0 \end{gathered}[/tex]Next, factor out 2secθ from the first two terms, and group the third and fourth therms:
[tex]\Rightarrow2\sec \theta(\tan \theta+1)+(\tan \theta+1)=0[/tex]Factor out (tanθ+1):
[tex]\Rightarrow(\tan \theta+1)(2\sec \theta+1)=0[/tex]Since the product of two factors is equal to 0, then, the equation is true whenever each of them is equal to 0 separately. This leads to two cases:
Case 1: tanθ+1=0
[tex]\begin{gathered} \tan \theta+1=0 \\ \Rightarrow\tan \theta=-1 \\ \Rightarrow\theta=\arctan (-1) \\ \Rightarrow\theta=\frac{3}{4}\pi+n\pi \end{gathered}[/tex]
For n=0 and n=1, we get solutions on the interval [0,2π)
[tex]\Rightarrow\theta_1=\frac{3\pi}{4};\theta_2=\frac{7\pi}{4}[/tex]Case 2: 2secθ+1=0
[tex]\begin{gathered} 2\sec \theta+1=0 \\ \Rightarrow2\sec \theta=-1 \\ \Rightarrow\sec \theta=-\frac{1}{2} \end{gathered}[/tex]
Since the absolute value of the secant function is always greater or equal to 1, there are no real solutions for this case.
Therefore, all the solutions to the equation in the interval [0,2π) are:
[tex]\begin{gathered} \theta_1=\frac{3\pi}{4} \\ \theta_2=\frac{7\pi}{4} \end{gathered}[/tex]
Simplify the expression below x^2-8x-9/ 5x^2-45r
We were given that:
[tex]x^2-8x-\frac{9}{5x^2}-45r[/tex]The vertices of a triangle are S(-2, -2), T10,-2) and R(4, 4). Prove algebraically that this is a right - angledtriangle. (7A)
Right Triangle
If one of the interior angles of a triangle measures 90°, then we call the triangle a right triangle.
We must prove one of the angles formed by two of the sides of the triangle measures 90°. Those sides must be perpendicular to each other.
If two lines with slopes m1 and m2 are perpendicular, then:
m1 * m2 = -1
We'll calculate the slopes of each line defined by their endpoints (x1, y1) and (x2, y2) with the formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Calculate the slope of the segment ST:
[tex]m_1_{}=\frac{-2+2}{10+2}=0[/tex]This represents a horizontal line.
Now for segment TR:
[tex]\begin{gathered} m_2=\frac{4+2}{4-10} \\ m_2=\frac{6}{-6}=-1 \end{gathered}[/tex]For segment SR:
[tex]m_3=\frac{4+2}{4+2}=1[/tex]Note the product of m2 and m3 is -1, thus the triangle is right-angled at vertex R.
Calculate the future value (in dollars) of $1,450 deposited into an account earring an annual simple interest rate of 5% compounded daily after 3 years. Round to the nearest cent
Principal (P)= $1,450
Simple Interest rate (R) = 5%
time (T) = 3 years
n = 365
Future value = Amount. + Principal
[tex]FV=P(1+\frac{r}{n})^{nt}-P+P=P(1+\frac{r}{n})^{nt}[/tex][tex]\Rightarrow FV=1450(1+\frac{0.05}{365})^{365\times3}=1684.54[/tex]Therefore, the Future value = $1684.54
at the end of the summer, Caitlin had saved $120 for her summer job
From the present question, we know that Caitlin saved $ 120 from the summer job, and is depositing weekly $5 in her account. It means that:
after 1 week, it will be $120 + $5 = $125
after 2 weeks, $125 + $5 = $130
after 3 weeks, $130 + $5 = $135
4 weeks, $135 + $5 = $140
We can use this data to complete the table as follows:
From this, we can conclude that her account balance is proportional to the number of weeks of deposit because this is increasing with time.