Equation of the line
The equation of a line can be expressed in slope-intercept form as follows:
y = mx + b
Where m is the slope of the line and b is the y-intercept.
We are given the equation of a line:
y = -5x + 3
This line as a slope of m=-5 and the intercept with the y-axis is y=3
We are required to find the equation of another line that is parallel to the given line. Parallel lines have the same slope. Thus the slope of our new line is also m=-5.
We are also given the y-intercept of the new line (0,4). This means the value of b is 4.
Knowing the values of m and b, we can write the equation of the required line as:
y = -5x + 4
I’m doing order of operation (14+16)/2-10
To solve this question, follow the steps below.
Step 01: Solve the operation inside the parentheses.
[tex]\begin{gathered} \frac{\mleft(14+16\mright)}{2}-10 \\ \frac{30}{2}-10 \end{gathered}[/tex]Step 02: Solve the division.
[tex]15-10[/tex]Step 03: Solve the subtraction.
[tex]5[/tex]Answer: 5.
To adopt a dog from an animal shelter, you must pay $90 for vaccinations, $75 to spay or neuter the dog, and $40 for a wellness exam by a veterinarian. a. Write an expression in simplest form that represents the amount (in dollars) it costs to adopt x dogsb. What does the coefficient of the expression in part (a) represent?
1) Gathering the data
pay $90 for vaccinations,
$75 to spay or neuter the dog,
and $40 for a wellness exam
Let x be the price of the dog.
2) Since all of these expenses represent money out, or less money in your wallet. And all of these prices refer to the adoption of one dog then We can state
C=(90+75+40)x
C= 205x
Given: _A and B form a linear pair,_B and C are complementary, and m_A = 103°Prove: m C = 13°Statement:Reason:1. _A and B form a linear pair 1. Given2. m A+ m B = 180°2. Postulate3. mA = 103°3. Given4. 103° + m B = 180°4. Substitution5. m2B = 77°5.[?]6. B and C are complementary 6. Given7. m B + m C = 90°7. Definition8. 77° + m2 = 90°8. Substitution9. m C = 13°9.Select the reason that bestsupports Statement 5 in thegiven proof.A. Multiplication Property of EqualityB. Subtraction Property of EqualityC. Division Property of EqualityD. Addition Property of Equality
SOLUTION
Statement 4, states that
[tex]103^o+mWhat is the product of 8V 5 and 5/10 in simplest radical form?
Given the numbers:
[tex]8\sqrt[]{5},5\sqrt[]{10}[/tex]The product of the numbers will be:
[tex]\begin{gathered} 8\sqrt[]{5}\times5\sqrt[]{10}=8\times5\sqrt[]{5\times10}=40\sqrt[]{50} \\ \\ 50=25\times2=5^2\times2 \\ \\ 40\sqrt[]{50}=40\sqrt[]{5^2\times2}=40\times5\sqrt[]{2}=200\sqrt[]{2} \end{gathered}[/tex]So, the answer will be:
[tex]200\sqrt[]{2}[/tex]A circular pool with a radius of 3 m sits in a rectangular yard that is 14 m by 8 m. What area of the yard is NOT covered by the pool?
SOLUTION:
Step 1:
In this question, we are given the following:
A circular pool with a radius of 3 m sits in a rectangular yard that is 14 m by 8 m. What area of the yard is NOT covered by the pool?
Step 2:
The area of the yard that is NOT covered by the pool is given as :
[tex]\text{Area of the Rectangular yard - Area of the circular pool}[/tex][tex]\text{( Length }X\text{ Breadth ) - ( }\pi r^2\text{ )}[/tex][tex]\begin{gathered} (\text{ 14 X 8 ) - (}\frac{22}{7}X\text{ 3 X 3 )} \\ =\text{ 112 - (}\frac{198}{7}) \\ =\text{ 112 - 28.28571429} \\ =\text{ 83.71428571} \\ \approx83.71m^2\text{ ( 2 decimal places)} \end{gathered}[/tex]CONCLUSION:
The area of the yard NOT covered by the pool is:
[tex]83.71m^2\text{ ( 2 decimaal places)}[/tex]Suppose that an item regularly costs $100.00 and is discounted 24%. If it is then marked up 24%, is the resulting price $100.00? If not, what is it?
Given the cost of item =$ 100
If it is discounted 24%
So, the discount will be = 24% of 100 = 0.24 x 100 = $24
The cost after discount = 100 - 24 = $76
If it is marked up 24%
so, the rise will be = 24% of 76 = 0.24 x 76 = $18.24
The cost after marked up = 76 + 18.24 = $94.24
So, the answer is : No, and the cost will be = $94.24
(-4, 6); slope = - 3/4write the linear equation in slope intercept form given
We know the slope = -3/4 and a point = (-4, 6) of a line, and we wnat to find the equation in the slope-intercept form, so:
[tex]\begin{gathered} \text{The general slope-intercept form of a line is:} \\ y=mx+b \\ \text{Where m is the slope and b is the value of y-intercept} \end{gathered}[/tex]In this case, m=-3/4 and evaluating the point (-4, 6) we can find the value of b:
[tex]\begin{gathered} \text{With m=-3/4 and the point (x, y) = (-4, 6):} \\ 6=-\frac{3}{4}(-4)+b \\ 6=3+b \\ b=6-3 \\ b=3 \end{gathered}[/tex]We found that b = 3, so the equation of the line is:
[tex]y=-\frac{3}{4}x+3[/tex]What expression shows 50 + 30 written as a product of 2 factors?
(A)5(10+ 7)
(B)5(10+ 3)
(C)10(5+ 2
(D)10(5+ 3)
need answers fast pleazz
Answer:
D
Step-by-step explanation:
distribute the 10 to (5+3) and you get 50+30
A gets you 50+35
B gets you 50+15
C gets you 50+20
D gets you 50+30
I worked on this and I can't seem to find the answer
1 liter = 1000 milliliters.
thus, 75791 liters =
[tex]75791\times1000=75791000[/tex]thus, 75791000 milliters.
Multiply 3x11/12 and reduce to lowest terms Convert into a mix number
Multiply 3x11/12 and reduce to lowest terms Convert into a mix number
we have
3*(11/12)=11/4
convert to mixed number
11/4=8/4+3/4=2+3/4=2 3/4
answer is 2 3/4Given the parallelogram TVWY shown above, determine how triangles TUZ and WXV can be shown to be similar. A. Since ZTU VWX and VX = XW, the triangles are similar by angle-side. B. Since TUZ WXV and TU = UZ, the triangles are similar by angle-side. C. Since TUZ VWX and ZTU WXV, the triangles are similar by angle-angle. D. Since TUZ WXV and ZTU VWX, the triangles are similar by angle-angle.
Notice that triangles TUZ and WXV have an angle with the same measure; therefore, we need two additional corresponding similar angles, or two corresponding similar sides, or one side and an angle to prove similarity.
Options A is not possible since it would imply that triangle TUZ has two 90°-inner angles.
Option B states a relation between two sides of triangle TUZ, not between two sides (one of each triangle). Option B cannot be the answer.
According to the figure, angles TUZ and WXV have to be congruent; therefore, option C cannot be the answer.
The only valid alternative is option D, option D is the answer.
If 8% of the sheet aluminum is lost to scrap when forming a fuel tank, what is the weight of the tank if the raw sheets of aluminum weigh 200 pounds?
Solution:
Step 1: Calculate 8% of the raw sheets of aluminum :
[tex]200\text{ x 0.08 = 16}[/tex]This is the weight that is lost in the production of the fuel tank.
Step 2: Calculate the weight of the tank :
200 pounds - 16 pounds = 184 pounds.
So that, we can conclude that the correct answer is:
184 pounds.
John was asked to place the numbers shown below in order from greatest to least. 0.2 , -0.3, 1.6, 120%, -2%, 3.8, --33, 3.14 After ordering the numbers from greatest to least, what number would John have in the 3rd position?
Let's begin by listing out the information given to us:
0.2, -0.3, 1.6%, 120%, -2%, 3.8, -33, 3.14
In sorting the numbers from the greatest to the least, we must bear the following in mind:
I. Any number having a negative parenthesis is lower than zero
II. % means 100; any number having % means the real value of the number is multiplied by 100
0.2 = 0.2
-0.3 = -0.3
1.6% = 1.6 * 100 = 160
120% = 120 * 100 = 12000
-2% = -2 * 100 = -200
3.8 = 3.8
-33 = -33
3.14 = 3.14
Rearranging from the greatest to the least, we have it thus:
120%, 1.6%, 3.8, 3.14, 0.2, -0.3, -33, -200
The number in the third position is 3.8
input is complete.A parallelogram has a base of 9 units and an area of 12 square units. What is the corresponding height for that base? Remember: Area parallelogram = b × h
As written in the Question Tab, the area of the parallelogram can be solved by multiplying the base and the height. Since we already have the base = 9 units and its area which is 12 square units, the first and last thing to do is divide the area by the base to solve the height of the parallelogram. See computation below:
[tex]\begin{gathered} \text{area = base}\times\text{height} \\ 12=9\times h \\ Divide\text{ both sides by 9.} \\ \frac{12}{9}=\frac{9h}{9} \\ \frac{4}{3}or\text{ 1.33 = h} \end{gathered}[/tex]Therefore, the height of the parallelogram is 4/3 or 1.33 units.
Solve the equation for y in terms of x. In other words, algebraically rearrange the equation so that the y variable is by itself one side of the equation. Type your answer in the form y=mx+b. If you have a value that is not an integer then type it rounded to the nearest hundredth. Do not put spaces between your characters.5x+2y=0y=Answer
we have the equation
5x+2y=0
solve for y
step 1
subtract 5x on both sides
5x+2y-5x=0-5x
simplify
2y=-5x
step 2
Divide by 2 on both sides
2y/2=-5x/2
y=-(5/2)x
y=-2.50xQuestion 7 of 10Use the properties of logarithms to expand the following expression.(√log(x+4)5x³Your answer should not have radicals or exponents.You may assume that all variables are positive.
We have:
[tex]\begin{gathered} log(\sqrt{\frac{(x+4)^5}{x^3}}) \\ =log(\frac{(x+4)^2\sqrt{x+4}}{x\sqrt{x}} \end{gathered}[/tex]Applying properties of logarithms:
[tex]\begin{gathered} =log((x+4)^2\sqrt{x+4})-log(x\sqrt{x}) \\ =2log(x+4)+log(\sqrt{x+4})-logx-log\sqrt{x} \end{gathered}[/tex]Solve this system of equations by graphing. First graph the equations, and then type the solution.x+3y=6y=1/2x+7
Given the system of equations;
[tex]\begin{gathered} x+3y=6---(1) \\ y=\frac{1}{2}x+7---(2) \end{gathered}[/tex]We shall first of all re-arrange the equations in the slope-intercept form;
[tex]y=mx+b[/tex]Note that the second one has already been expressed in the slope-intercept form. For the first one we would now have;
[tex]\begin{gathered} x+3y=6 \\ 3y=-x+6 \\ \text{Divide both sides by 3;} \\ \frac{3y}{3}=-\frac{x}{3}+\frac{6}{3} \\ y=-\frac{1}{3}x+2 \end{gathered}[/tex]To plot this equations on a graph we take two extreme points. We can do this by finding the value of y when x = 0, and y when x = 0.
For the first equation, we would have;
[tex]\begin{gathered} y=-\frac{1}{3}x+2 \\ \text{When x}=0 \\ y=-\frac{1}{3}(0)+2 \\ y=0+2 \\ y=2 \\ \text{That means we have the point }(0,2) \\ \text{Also, when y}=0 \\ 0=-\frac{1}{3}x+2 \\ \frac{1}{3}x=2 \\ \text{Cross multiply this and you'll have;} \\ x=2\times3 \\ x=6 \\ We\text{ now have our second point, }(6,0) \end{gathered}[/tex]Hence, for the first equation we have the two points;
[tex]\begin{gathered} A(0,2) \\ B(6,0) \end{gathered}[/tex]For the second equation;
[tex]\begin{gathered} y=\frac{1}{2}x+7 \\ \text{When x}=0 \\ y=\frac{1}{2}(0)+7 \\ y=0+7 \\ y=7 \\ \text{This means we have the point }(0,7) \\ \text{Also, when y}=0 \\ 0=\frac{1}{2}x+7 \\ -\frac{1}{2}x=7 \\ \text{Cross multiply and you'll have;} \\ x=7\times(-2) \\ x=-14 \\ \text{That means we now have the second point which is }(-14,0) \end{gathered}[/tex]For the second equation we now have the points;
[tex]\begin{gathered} A(0,7) \\ B(-14,0) \end{gathered}[/tex]We can now input both sets of coordinates and our graph would come out as shown below.
The point of intersection as we can see is at where x = -6 and y = 4. Therefore;
ANSWER:
The solution to the system of equations as shown on the graph is;
[tex](-6,4)[/tex]the cost of 3D movie tickets is $12 for 1 ticket, $24 for 2 tickets, and $36 for 3 tickets. determine whether the cost is proportional to the number of tickets by graphing on the coordinate plane. explain your reasoning
Explanation
1 ticket =$12
2 ticket =$24
3 ticket =$36
Which of the following is the graph of the quadratic function y = x2 - 6x -
Therefore,
From the graph above,
The correct answer is OPTION C
What happens to the graph when you change the value of a?
we have that
the value of a represent a vertical dilation
so
We stretch the graph in the vertical direction by a scale factor of
If the value of a> 1
then
we have stretching of the graph
If the value of 0 < a < 1
then
we have a compress of the graph
3. The angle of depression of an aeroplane measured from a control tower, PQ, of height 88.9 m is 48°. When the plane moves along the runway from point Ato point Band stops, the angle of depression becomes 25.2°. The distance from point P to point Ais given as 119.6 m. Complete the diagram below to represent this informatior Р brid (ii) Leaving your answers correct to ONE decimal place calculate (a) Durmine the distance from the control tower to point A. (2) (b) Calculate the distance moved by the plane from its initial position.
The Solution:
Part (a)
Representing the problem fully in a diagram, we have:
Part (b)
We are required to find the length of QA= x.
We shall use Trigonometrical Ratio as below:
[tex]\begin{gathered} tan48^o=\frac{opposite}{adjacent}=\frac{88.9}{x} \\ \\ tan48=\frac{88.9}{x} \end{gathered}[/tex]Making x the subject of the formula, we get
[tex]x=\frac{88.9}{tan48}=80.0459\approx80.0m[/tex]Thus, the distance from the control tower to point A is 80.0 meters.
Part (c)
We are required to find the length of AB= y.
Considering triangle PQB, we have:
[tex]\begin{gathered} tan25.2=\frac{88.9}{x+y}=\frac{88.9}{80+y} \\ \\ 0.47056=\frac{88.9}{80+y} \end{gathered}[/tex]Solving for y, we get
[tex]\begin{gathered} 80+y=\frac{88.9}{0.47056} \\ \\ y=188.922-80 \\ y=108.922\approx108.9m \end{gathered}[/tex]Thus, the distance moved by the plane from its initial position is 108.9 meters.
Find the length of AB.6 in A30°BAB = [ ?Round your answer to the nearest hundredth.
Prepare an amortization schedule for the first three months on a loan of $87000 at 6% for 20 years
First, we need to calculate the value of the monthly payments. We can use the general ordinary anuity formula:
[tex]PV=\text{PMT}\cdot\lbrack\frac{1-(1+i)^{-n}}{i}\rbrack[/tex]Where PV=$87000
n=20
i=0.06
Replace the given values and solve for PMT:
[tex]\begin{gathered} 87000=\text{PMT}\cdot\lbrack\frac{1-(1+0.06)^{-20}}{0.06}\rbrack \\ 87000=\text{PMT}\cdot\lbrack\frac{1-0.3118}{0.06}\rbrack \\ 87000=\text{PMT}\cdot\lbrack\frac{0.6882}{0.06}\rbrack \\ 87000=\text{PMT}\cdot11.4699 \\ \text{PMT}=\frac{87000}{11.4699} \\ \text{PMT}=7585.06 \end{gathered}[/tex]Now that you have the payment, you can construct the table of the amortization schedule with the know information:
To calculate the missing information, start by calculating the interest component of the payment (interest paid) by multiplying the periodic interest by the remaining principal.
The monthly interest is the yearly interest divided by 12, then:
[tex]MI=\frac{0.06}{12}=0.005[/tex]And the interest paid is then:
[tex]\begin{gathered} IP=MI\cdot\text{ Remaining principal} \\ IP=0.005\cdot87000\text{ (for the first payment)} \\ IP=435 \end{gathered}[/tex]Now, calculate the principal paid by subtracting the interest paid from the payment amount:
[tex]\text{ Principal paid=7585.06-435}=7150.06\text{ (first payment)}[/tex]Then, by putting the values on the amortization schedule:
The remaining principal is 87000-7150.06 (principal paid).
Now for the second payment, calculate the interest paid with the new remaining principal:
[tex]\begin{gathered} IP=0.005\cdot79849,94\text{ (for the second payment)} \\ IP=399,25 \end{gathered}[/tex]And the principal paid is:
[tex]\text{ Principal paid=7585.06-399.25}=7185.81\text{ (second payment)}[/tex]The remaining principal is:
[tex]RP=79849.94-7185.81=72664.13[/tex]Thus:
And for the third month, you apply the same calculations and the amortization schedule is:
QuestionA cylinder has height 6 meters and radius 5 meters. Find the a. volume and b. surface area. Use 3.14 for. Do not round.
Problem: A cylinder has a height 6 meters and a radius 5 meters. Find the a. volume and b. surface area. Use 3.14 for. Do not round.
Solution:
Remember that the volution of cylinder is given by the following equation:
[tex]V\text{ =}\pi\text{r}^2h[/tex]where r is the radius of the cylinder and h is the height of the cylinder. In this case, we have that:
[tex]V\text{ =}\pi\text{r}^2h=\pi5^2\text{ x 6 = 150}\pi\text{ = 471.23}[/tex]So we can conclude that the volume of the cylinder is 471.23
Now, for surface area, remember that the surface area for the cylinder is given by the following equation:
[tex]V=2\pi r^2+\text{ }2\pi rh[/tex]where r is the radius of the cylinder and h is the height of the cylinder. In this case, we have that:
[tex]V=2\pi r^2+\text{ }2\pi rh\text{ = 2}\pi(5)^2\text{ + 2}\pi(5)(6)\text{ = 110}\pi\text{ = 345.57}[/tex]So we can conclude that the surface area for the cylinder is 345.57
can someone help me with this one ? list the first 15 perfect cubes:
We have the following exercise
What is a cube of a number x?
The answer is to multiply this number or quantity 3 times. For example:
1^3 = 1 x 1 x 1 = 1,
2^3 = 2x 2 x 2 = 8
4^3 = 4x4x4 = 64
and so on.
Equivalently, let represent with a stick a unity 1: so for example
So if we want 2^3, is the same to say:
that is 2^3 = 8
When given two points and asked to find the equation of the line in slope-intercept form, what are the correct steps? Place a number next to the step to put them in order.
Given
given two points and asked to find the equation of the line in slope-intercept form
Find
what are the correct steps? Place a number next to the step to put them in order.
Explanation
to find the equation of the line in slope intercept form form given two points.
step 1 :
find the slope.
step 2
write equation in point slope form
step 3.
pick a point form the given points , substitue it into the point slope form
step 4.
write the equation in slope intercept form by simplifying
Final Answer
Hence , the correct order is 2 , 1 , 4 , 3
Solve the equation for the variable. 5.3 = 2 - 2.7 I
We are asked to solve for the variable in the equation:
5.3 = z - 2.7
SO we need to isolate the variable "z" on one side of the equal sign. for that we add 2.7 to both sides:
5.3 + 2.7 = z - 2.7 + 2.7
combining like terms we get:
8 = z + 0
8 = z
Therefore z is 8.
graph the line that passes through the given point and has the given slope m(1,7); m=-5/2
Given that the line passes through the points;
[tex](1,7)[/tex]And slope;
[tex]m=-\frac{5}{2}[/tex]Michael and Larry scored 18 points in a basketball game. Michael scored twice as many points as Larry. How many points did Larry score?6 8 10 12
Let Larry score x, Michael scored 2x
x + 2x = 18
3x = 18
x = 18/3 = 6 points.
Therefore, Larry scored 6 points. Option A
It used to cost $33.00 to buy a case of 23 bottles of Sriracha. Because of the shortage, each case is now $50.00. How MUCH MORE is each bottle of Sriracha?
The amount of money that each bottle of sriracha would cost more would be = $0.82
What is product shortage?Product shortage is definitely as the decrease in the availability of a product in the market or decrease in its production.
The cost of a case of sriracha = $33.00
The amount of a case after the shortage = $50.00
The amount of bottles that is found in case = 23
The amount of each bottle before shortage = 23/33 = $0.70
The amount of each bottle after shortage = 50/33 =
$1.52
The amount of money that each bottle of sriracha would cost more = 1.52 - 0.70 = $0.82
Learn more about cost price here:
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