To find the slope of the line we have to use this equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Now we have to replace two coordiantes in the line, so I was able to see the coordinates: (0,40) and (20,50), sothe equation become:
[tex]m=\frac{50-40}{20-0}[/tex]and we simplify so:
[tex]m=\frac{10}{20}=\frac{1}{2}[/tex]So the slope is 1/2
Compare f(0) and g(0)f(0) is <, =, or > to g(0)
From the graph of f(x), it can be obseved that function f(x) value at x = 0 is -3, which means that f(0) = -3.
From the graph of g(x), it can be observed that g(0) = 0.
As value 0 is greater than -3. So f(0) is lesser than g(0).
Answer: f(0) < g(0)
What is the slope of the line that passes through the points (2,8) and (12,20)?
The slope of the line with that passes through the coordinates (2,8) and (12,20) is 6/5.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 2,8 )
x₁ = 2y₁ = 8Point 2( 12,20 )
x₂ = 12y₂ = 20Slope m = ?
To find the slope m, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 20 - 8 )/( 12 - 2 )
Slope m = ( 12 )/( 10 )
Slope m = 12/10
Slope m = 6/5
Therefore, the slope of the line is 6/5.
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Jake and Joshua have new jobs selling gift cards at a local convenience store at the cash register, but their pay is different. Jake earns a foundational wage of $6 per hour, as well as $8 for each gift card sold. Joshua gets $4 for each gift card sold and earns a foundational wage of $6 per hour. If they each sell a certain number of gift cards in one hour, they will end up earning the same amount of pay. How many gift cards would that make up to?Write a system of equations, graph them, and type the solution.
Let x be the number of cards Jake and Joshua sell within one hour. Therefore, their earnings are given by the following expressions,
[tex]\begin{gathered} Ja=6+8x \\ Jo=6+4x \end{gathered}[/tex]Then, set Ja=Jo (both earn the same amount),
[tex]\begin{gathered} Ja=Jo \\ \Rightarrow6+8x=6+4x \end{gathered}[/tex]Solving for x,
[tex]\begin{gathered} \Rightarrow8x=4x \\ \Rightarrow4x=0 \\ \Rightarrow x=0 \end{gathered}[/tex]Then, they will earn the same within one hour only if both sell zero cards within the hour.
Graphing the system of equations,
As one can see, the intersection point is (0,6), which stands for 0 cards and $6
If f(x) = 8x2 - 18x + 5, find when f(x) = -4
Setting the given equation equals -4 we get:
[tex]\begin{gathered} 8x^2-18x+5=-4 \\ 8x^2-18x+5+4=0 \\ 8x^2-18x+9=0 \end{gathered}[/tex]Notice that:
[tex]8x^2-18x+9=8(x^2-\frac{9}{4}x+\frac{9}{8})=8(x-\frac{3}{2})(x-\frac{3}{4})[/tex]Therefore, f(x)=-4 when x=3/2 or x=3/4.
What fraction of $36,000 is $27,000?
We need to keep in mind that
36000 is 1
In order to know the fraction we need to divide 27000 between 36000, and then simplify the fraction
[tex]\frac{27000}{36000}=\frac{27}{36}=\frac{3}{4}[/tex]the fraction of 36000 that is 27000 is 3/4
Calculate the answers. 13. An orbiting satellite is positioned 3,105 mi above the earth (rearth = 3,959 mi) and orbits the earth once every 201.3 min. Assuming its orbit is a circle, find the distance traveled in 50.0 min.
first you will calculate the speed of the orbiting satelite
[tex]\text{speed = }\frac{dis\tan ce}{time}[/tex]distance = circumference of the of the orbit
[tex]\begin{gathered} \text{circumference = 2}\times\pi\times\text{ r} \\ r\text{ = radius of the earth + the height of the satelite above the earth} \\ r\text{ = 3105+3959 =7064mi} \end{gathered}[/tex][tex]\text{circ of the orbit = }2\text{ }\times3.142\times7064=\text{ 44390.176}[/tex][tex]\text{speed = }\frac{44390.176}{201.3}\text{ = 220.52mi/min}[/tex]distance covered in 50.0 min
distance = speed X time
[tex]\text{distance = 220.52}\times50=11026mi[/tex]the distance traveled is 11026 mi
In AOPQ, 0 = 500 cm, p = 600 cm and q=380 cm. Find the measure of P to thenearest 10th of a degree.
Answer: Triangle has three sides, which are:
[tex]\begin{gathered} O=500\operatorname{cm} \\ P=600\operatorname{cm} \\ Q=380\operatorname{cm} \\ \end{gathered}[/tex]We need to find the angle p, that is right across the side P:
[tex]\angle A=\arccos (\frac{b^2+c^2+a^2}{2bc})=0.97895\text{rad}=56.09\text{degres}[/tex]This is the value of angle A
At 3:00 PM a man 138 cm tall casts a shadow 145 cm long. At the same time, a tall building nearby casts a shadow 188 m long. How tall is the building? Give your answer in meters. (You may need the fact that 100 cm = 1 m.)
A tall man(138cm) casts a shadow of 145cm
A building nearby casts a shadow of 188m
Using the information you have to determine the height of the building.
First step is to convert the units of the height of the man and the length of his shadow from cm to meters:
100cm=1m
So 145cm=1.45m
And 138co=1.38m
Now that the measurements are expressed in the same units you can determine the height shadow ratio of the man and use it to calculate the height of the bulding.
[tex]\frac{\text{height}}{\text{shadow}}=\frac{1.38}{1.45}[/tex]Compare this ratio with the ratio between the heigth/shadow ratio of the building to determine the heigth of the building.
Said height will be symbolized as "x"
[tex]\begin{gathered} \frac{1.38}{1.45}=\frac{x}{188} \\ x=(\frac{1.38}{1.45})188 \\ x=178.92m \end{gathered}[/tex]The building is 178.92m
linear equation in deletion method2x + y − 3z = 13x − y − 4z = 75x + 2y − 6z = 5
The given system is:
[tex]\begin{gathered} 2x+y-3z=1\ldots(i) \\ 3x-y-4z=7\ldots(ii) \\ 5x+2y-6z=5\ldots(iii) \end{gathered}[/tex]Add (i) and (ii) to get:
[tex]\begin{gathered} 2x+y-3z=1 \\ + \\ 3x-y-4z=7 \\ 5x-7z=8\ldots(iv) \end{gathered}[/tex]Multiply (ii) by 2 to get:
[tex]6x-2y-8z=14\ldots(v)[/tex]Add (iii) and (v) to get:
[tex]\begin{gathered} 6x-2y-8z=14 \\ + \\ 5x+2y-6z=5 \\ 11x-14z=19\ldots(vi) \end{gathered}[/tex]Multiply (iv) by 2 to get:
[tex]10x-14z=16\ldots(vii)[/tex]Subtract (vii) from (vi) to get:
[tex]\begin{gathered} 11x-14z=19 \\ - \\ 10x-14z=16 \\ x=3 \end{gathered}[/tex]Put x=3 in (iv) to get:
[tex]\begin{gathered} 5\times3-7z=8 \\ -7z=8-15 \\ -7z=-7 \\ z=1 \end{gathered}[/tex]Put x=3 and z=1 in (i) to get:
[tex]\begin{gathered} 2(3)+y-3(1)=1 \\ 6+y-3=1 \\ y+3=1 \\ y=-2 \end{gathered}[/tex]So the values are x=3,y=-2 and z=1.
You have 1/4 of a quiche left over from lunch. If you sent 4/6 of the leftover quiche home with your brother, how much of the quiche do you have left in the dish?
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
If the brother took home 4/6, that means that you still have 2/6.
[tex]\frac{1}{4}[/tex] x [tex]\frac{2}{6}[/tex] = [tex]\frac{2}{24}[/tex] which is the same as 1/12
Please help thank you sm it would be very helpful and very much appreciated ♥️‼️
2. Write the formula for the circumference of a circle.
a. Calculate the circumference of circle B if the diameter is 8 inches.
b. Calculate the radius of circle B if the circumference is 94.2 square centimeters.
Step-by-step explanation:
2. C = [tex] 2 \pi r [/tex]
a. to find radius from diameter in order to calculate the value of the circumference we have to divide the diameter by 2
d/2 = 8/2 = 4
Next, Find the circumference
C = [tex] 2 \pi r [/tex]
C = [tex] 2 \cdot 3.142 \cdot 4 [/tex]
C = 25.13
b. Rearrange formula for circumference to find the value of the radius
Where, C = [tex] 2 \pi r [/tex]
Make r the subject of formula
C/[tex] 2 \pi [/tex] = [tex] 2 \pi r [/tex] /[tex] 2 \pi [/tex]
94.2/2 × 3.142 = r
94.2/6.3 = r
r = 14.95 ≈ 15
2.circumference= pi×diameter
a)25.136 inches
b)14.99 cm
Step-by-step explanation:
a) pi × 8
3.142× 8= 25.136
b) diameter = radius × 2
circumference = pi × diameter OR pi × radius×2
because we are trying to find the radius we will use the pi × 2 radius.
94.2= 3.142 × 2 radius
94.2 ÷ 3.142= 2 radius
29.981 = 2 radius
29.981 ÷ 2 = radius
14.99 = radius
If f(x) = ln [ sin2(2x)(e-2x+1) ] , then f’(x) is
I want to solve ?
Here we will write our function in regular form using an identity.
[tex]log(ab)=loga+logb[/tex][tex]log(a/b)=loga-logb[/tex]Therefore, the rule of our function [tex]f(x)[/tex] will be as follows.
[tex]f(x)=ln(sin^2(2x))+ln(e^{-2x}+1)[/tex]The derivative of the natural logarithm [tex]ln(x)[/tex] function is of the following form.
[tex](ln(x))'=\frac{x'}{x}[/tex]It is found by dividing the derivative of the function in [tex]lnx[/tex] by the function in [tex]lnx[/tex].
For example:
[tex](ln(5x))'=\frac{(5x)'}{5x} =\frac{5}{5x} =\frac{1}{x}[/tex]According to this information, let's take the derivative of our function.
[tex]f'(x)=\frac{2sin(4x)}{sin^2(2x)} +\frac{-\frac{2}{e^{2x}} }{e^{-2x}+1}[/tex][tex]f'(x)=4cot(2x)-\frac{2}{1+e^{2x}}[/tex]Rules:[tex]((sin2x)²)'=2.2sin(2x)cos(2x)=2sin(4x)[/tex][tex](e^x)'=x'.e^x[/tex]As an incoming college freshman, Tina received a 10-year $15,100 Federal Direct
Unsubsidized Loan with an interest rate of 4.29%. She knows that she can begin making
loan payments 6 months after graduation but interest will accrue from the moment the
funds are credited to his account. How much interest will accrue while she is still in
school and over the 6-month grace period for this freshman year loan?
O $2,813.28
O $2,915.06
O $3,001.32
O $3,102.38
The interest that will accrue while the college freshman is still in school and over the 6-month grace period for this freshman year loan is, approximately, B. $2,915.06.
How is the interest determined?The interest for federal college loans is based on the simple interest formula instead of compounding.
By compounding, we mean that interest is computed on the principal and accumulated interest.
Federal Direct Unsubsidized Loan = $15,100
Number of years for college = 4 years
The number of years before repayment = 4.5 years (4 years + 6 months)
Simple interest for 4.5 years = $2,915.06 ($15,100 x 4.29% x 4.5 years)
On the other hand, one can compute the compounded interest using an online finance calculator.
Compounded Interest:N (# of periods) = 4.5 years
I/Y (Interest per year) = 4.29%
PV (Present Value) = $15,100
PMT (periodic payment) during the 4.5 years = $0
Results:
FV = $18,241.85
Total Interest = $3,141.85
Thus, the interest is Option B.
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Enter the missing values in the area model to find 10(8y + 5)+510BoyAccording to the model above, 10(8y + 5) =Submit Answeatte
Note you have to use the value outside the bracket to multiply the inner value.
I think I’m off to a good start but I’m still confused
The radius is given 3.5 ft and height is given 14 ft.
ExplanationTo find the surface area of cylinder,
Use the formula.
[tex]S=2\pi rh+2\pi r^2[/tex]Substitute the values.
[tex]\begin{gathered} S=2\pi r(h+r) \\ S=2\times3.14\times3.5(14+3.5) \\ S=384.65ft^2 \end{gathered}[/tex]The volume of cylinder is determined as
[tex]V=\pi r^2h[/tex]Substitute the values
[tex]\begin{gathered} V=3.14\times3.5^2\times14 \\ V=538.51ft^3 \end{gathered}[/tex]AnswerThe surface area of cylinder is 384.65 sq.ft.
The volume of cylinder is 538.51 cubic feet.
The area of a rectangle is 28m^2, and the length of the rectangle is 5 meters less than three times the width. Find the dimensions of the rectangle. L:W:
The area of a rectangle is given by the formula
[tex]A=L*W[/tex]where
A=28 m2
L=3W-5
substitute given values in the formula
[tex]\begin{gathered} 28=(3w-5)W \\ 28=3w^2-5w \\ 3w^2-5w-28=0 \end{gathered}[/tex]Solve the quadratic equation
Using the formula
we have
a=3
b=-5
c=-28
substitute
[tex]w=\frac{-(-5)\pm\sqrt{-5^2-4(3)(-28)}}{2(3)}[/tex][tex]w=\frac{5\pm19}{6}[/tex]The solutions for w are
w=4 and w=-2.33 ( is not a solution because is a negative number)
so
The width w=4 m
Find out the value of L
L=3w-5=3(4)-5=7 m
therefore
L=7 mW=4 m4. Driving on the highway, you can safely drive 65 miles per hour. How far can you drive in ‘h’ hours? What is the domain of the function which defines this situation?A) 65B) the number of hours you driveC) the distance you driveD)the amount of gas you use
Answer:
[tex]\text{ The number of hours you drive.}[/tex]Step-by-step explanation:
For distance, we can apply the following equation:
[tex]\begin{gathered} d=s*h \\ where, \\ s=\text{ speed} \\ h=\text{ hours} \end{gathered}[/tex]Since we know that we can safely drive 65 miles per hour, the domain will be defined by the number of hours you drive:
[tex]d=65h[/tex]What’s the total of all the present values of the payments? $320,640 $787,116 $878,611 $987,116
The total of all the present values of the payments is $2,973,483.
What is the present value?The present value is the future cash flows discounted to the present day's values.
The present value can be determined using an online finance calculator that inputs the future cash flows, the interest rate, and the period.
How is the total present value determined?The total present value is a function of the summation of the four present values.
Since the present values are given, computing the total involves the mathematical operation of addition.
Present Values:1st payment $320,640
2nd payment $787,116
3rd payment $878,611
4th payment $987,116
Total PV $2,973,483
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Answer:
The correct answer is $878,611 for plato users
Step-by-step explanation:
The function table below is intended to represent the relationship y=-5x+1. However, one of the entries for y does not correctly fit the relationship with x.
Answer:
Step-by-step explanation:
none of the answers are correct
how would I solve and what would the answer be?
Given that:
f(x) = |x| and g(x) = x + 6
[tex](f\circ g)(x)=|x+6|[/tex]and
[tex](g\circ f)(x)=|x|+6[/tex]24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas Choose the correct letter
Since 24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas
These are 2 equal ratios, then
They will be 2 equal fractions
[tex]\frac{24\text{ miles}}{1\text{ gallon}}=\frac{60\text{ miles}}{2.5\text{ gallons}}[/tex]The correct answer is D
prism x imprison wire similar. the volume of prison why is 92 cm3 find the volume of prism x.
If they are similar, then their side measures are proportional
Prism X, volume = 92 cm^3
The expression (222)(x?) is equivalent to z What is the value of p?
SOLUTION;
Step 1:
[tex]undefined[/tex]At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 breadsticks, and 2 juice drinks costs $12. A second order of 5 slices of pizza, 2 breadsticks, and 3 juice drinks costs $15. If four breadsticks and a juice drink cost $.30 more than a slice of pizza, write a system that represents these statements. p: slices of pizza b: bread sticks d: juice drinks Choose the correct verbal expressions for problems into a system of equations or inequalities.
p = slices of pizza
b = bread sticks
d = juice drinks
Equation 1
3p + 4b + 2d = 12
Equation 2
5p + 2b + 3d = 15
Equation 3
4b + 1d = 1p + 0.3
That's all
what is 0.09 as a percentage?
Sheldon is painting a wall in his house and is using a paint roller.The paint roller had a radius of 1 inch and a height of 8 inches.How many square inches of space Sheldon paint with one revolution of paint roller?Round to nearest tenths
The information we have about the paint roller:
Radius: r=1in
Height: h=8in
To find the answer to how many square inches of space he can paint with one revolution, it is useful to visualize the surface area of a cylinder:
The circles are the top and bottom of the cylinder, and the rectangle is the body of the cylinder (the paint roller). The area of this rectangle is the area that the paint roller will paint with one revolution.
Calculate the area of the rectangle:
To find the area, first, we need to find the length "L":
This length L is equal to the circumference of the circle defined as follows:
[tex]L=2\pi r[/tex]So to find L we substitute r=1in and pi=3.1416:
[tex]\begin{gathered} L=2(3.14216)(1\text{ in)} \\ L=6.2832in \end{gathered}[/tex]And finally, to find the area of the rectangle and thus, the area that the paint roller covers with one revolution, we multiply the length by the height:
[tex]A=h\times L[/tex]Where "A" is area.
Substituting h and L:
[tex]\begin{gathered} A=8in\times6.2832in \\ A=50.2656in^2 \end{gathered}[/tex]Rounding our answer to the nearest tenths:
[tex]50.2656\approx50.3[/tex]Answer: 50.3 square inches
All of the following ratios are equivalent except 8 to 12 15/102/36:9
False
1) Let's examine those ratios, and simplify them whenever possible:
[tex]\begin{gathered} \frac{15}{10}=\frac{3}{2} \\ \frac{2}{3} \\ \frac{6}{9}=\frac{2}{3} \\ \frac{8}{12}=\frac{2}{3} \end{gathered}[/tex]2) Simplifying those ratios, all the following but 15/10 are equivalent to 8/12
3) So this is a false statement to say that all of those are equivalent except 8 to 12.
The formula to calculate the gravitational force between two objects is F_g=\frac{GM_1M_2}{r^2},F
g
=
r
2
GM
1
M
2
, where M_1M
1
and M_2M
2
are the masses of the objects, GG is the gravitational constant and rr is the distance between the objects. Solve for M_2M
2
in terms of F_g,F
g
, G,G, M_1M
1
and r.r.
The expression for M in terms of other variables is M = Fr^2/Gm
Subject of formulaThe variable being calculated is the formula's subject. On one side of the equals sign, it is identifiable as the letter on its own.
In order to make one of the the variables the subject of the formula, we place rewrite the expression in a different form.
Given the formula to calculate the gravitational force between two objects as;
Fg = GMm/r^2
We are to make M the subject of the formula in terms of other variables.
F = GMm/r^2
Cross multiply
Fr^2 = GMm
Divide both sides by Gm
Fr^2/Gm = GMm/Gm
Fr^2/Gm = M
Swap
M = Fr^2/Gm
This gives the expression for the variable M.
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In a cricket match, you have a squad of 15 players and you need to select 11 for a game. The two opening batsmans are fixed and the rest of the players are flexible. How many batting orders are possible for the game?
The number of batting orders that are possible for the game is 1365 orders.
What are combination?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!
n = the number of items.
r = how many items are taken at a time.
This will be:
15! / 11! (15 - 11)!
= 15! / 11! 4!
= 15 × 14 × 13 × 12 / 4 × 3 × 2
= 1365 orders
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There is a 50% chance of rain here and a 10% chance of rain on Mars. Therefore, there is a 45% chance that it will rain in neither place.
The statement that " There is a 45% chance that it will rain in neither place" is true.
In the question ;
it is given that
Probability of raining here = 50% = 0.5
Probability of raining on mars = 10% = 0.1
So, the probability of not raining here = 1-0.5 = 0.5
and probability of not raining on mars = 1-0.1 = 0.9
Hence the probability of rain in neither place = (probability of not raining here)×(probability of not raining on mars) .
Substituting the values , we get
probability of rain in neither place = 0.5×0.9
= 0.45
= 45%
Therefore , the statement " There is 45% chance that it will rain in neither place" is true.
The given question is incomplete , the complete question is
There is a 50% chance of rain here and a 10% chance of rain on Mars. Therefore, there is a 45% chance that it will rain in neither place.
Is the statement True or False ?
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