Answer:
Ted has 10 books and Omar has 15 books
Step-by-step explanation:
Hey there!
In order to find how many books each of the boys have, we can make a system of equations
First equation: O+T=25
Second equation: O=2T-5
After making the equations, you can use substitution by plugging in 2T-5 For O in the first equation:
2T-5+T=25
Simplify LHS
3T-5=25
Take 5 to the other side
3T=30
Divide by 3 on both sides to get T by itself
T=10
So this means that Ted has 10 books
Now we can plug this into the second equation
*note that you can plug 10 into the first equation too*
O=2(10)-5
Simplify RHS
O=20-5
Combine like terms
O=15
This means that Omar has 15 books
So, Ted has 10 books and Omar has 15 books
The 25th term of an arithmetic series is 44.5
The sum of the first 30 terms of this arithmetic series is 765
Find the 16th term of the arithmetic series.
Show your working clearly.
Answer:
[tex]a_{16}=26.5[/tex]
Step-by-step explanation:
Arithmetic series: [tex]a_n=a+(n-1)d[/tex]
Sum of arithmetic series: [tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
(where a is the first term and d is the common difference)
Given:
[tex]a_{25}=44.5[/tex][tex]S_{30}=765[/tex][tex]\implies a_{25}=44.5[/tex]
[tex]\implies a+(25-1)d=44.5[/tex]
[tex]\implies a+24d=44.5[/tex]
[tex]\implies S_{30}=765[/tex]
[tex]\implies \dfrac{30}{2}[2a+(30-1)d]=765[/tex]
[tex]\implies 30a+435d=765[/tex]
Rewrite [tex]a+24d=44.5[/tex] to make a the subject:
[tex]\implies a=44.5-24d[/tex]
Substitute found expression for a into [tex]30a+435d=765[/tex] and solve for d:
[tex]\implies 30(44.5-24d)+435d=765[/tex]
[tex]\implies 1335-285d=765[/tex]
[tex]\implies 285d=570[/tex]
[tex]\implies d=2[/tex]
Substitute found value of d into [tex]a=44.5-24d[/tex] and solve for a:
[tex]\implies a=44.5-24(2)=-3.5[/tex]
Therefore:
[tex]\implies a_{16}=-3.5+(16-1)2=26.5[/tex]
is it possible to mass the sum of $153 in $5 bills? explain your answer
Answer:
Step-by-step explanation:
Let me see if I understand what you mean. Do you mean can you have 153 dollars in your pocket when all you have is 5 dollar bills?
If that is what you mean, then no that isn't possible. You can get 150 dollars or you can get 155 dollars, but you can't get 153.
In order to do the problem, using only 5 dollar bills, the number you choose must end in 0 or 5. If it ends in anything else, the task is impossible.
PLEASE HELPPP!!!!
1. ) The points (-2, 6), (-1, 3), (0, 2), and (1, 3) are on the graph of my function. What is the equation?
2. ) My parabola intersects the x-axis at points (-2, 0) and (2, 0) and the y-axis at point (0, -4). What is the equation?
3.) The table of values below describe the relationship for my function.
x values: -2, -1, 0 , 1
y values: 4, 1, 0, 1
What is the equation?
4.) To find my equation, shift f(x) = x2 + 5 left 3.
What is the equation?
Answer:
1) [tex]y=x^2+2[/tex]
2) [tex]y=x^2-4[/tex]
3) [tex]y=x^2[/tex]
4) [tex]y=x^2+6x+14[/tex]
Step-by-step explanation:
Question 1
Given points: (-2, 6) (-1, 3) (0, 2) (1, 3)
This is likely to be a quadratic equation with a vertex of (0, 2) since the points (-1, 3) and (1, 3) are symmetrical about x = 0
Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex)
[tex]\implies y=a(x-0)^2+2[/tex]
[tex]\implies y=ax^2+2[/tex]
To find a, input one of the points into the equation:
[tex](1, 3)\implies a(1)^2+2=3\implies a=1[/tex]
Therefore, the equation of the graph is [tex]y=x^2+2[/tex]
Question 2
If the parabola intersects the x-axis at (-2, 0) and (2, 0) then
[tex]y=a(x+2)(x-2)[/tex]
We are told that the y-intercepts if (0, -4). Input this into the equation to find a:
[tex]\implies a(0+2)(0-2)=-4[/tex]
[tex]\implies -4a=-4[/tex]
[tex]\implies a=1[/tex]
Therefore,
[tex]\implies y=(x+2)(x-2)[/tex]
[tex]\implies y=x^2-4[/tex]
Question 3
Given points: (-2, 4) (-1, 1) (0, 0) (1, 1)
This is likely to be a quadratic equation with a vertex of (0, 0) since the points (-1, 1) and (1, 1) are symmetrical about x = 0
Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]
(where (h, k) is the vertex)
[tex]\implies y=a(x-0)^2+0[/tex]
[tex]\implies y=ax^2[/tex]
To find a, input one of the points into the equation:
[tex](-2,4)\implies a(-2)^2=4\implies a=1[/tex]
Therefore, the equation of the graph is [tex]y=x^2[/tex]
Question 4
[tex]f(x) = x^2 + 5[/tex]
If we wish to move the function to the left by 3 units, we substitute x for [tex]x+3[/tex]:
[tex]\begin{aligned}\implies f(x+3) & =(x+3)^2+5\\ & = x^2+6x+9+5\\ & = x^2+6x+14\end{aligned}[/tex]
[tex]\implies y=(x+3)^2+5[/tex]
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answer:
a) Team C - lowest average/mean
b) Team A - greatest variability/range
Step-by-step explanation:
Hope this helps!
PLEASE GUYS CAN SOMEONE HELP ME WITH THESE, POINTS TO THE KIND AND SMART PERSON TO ANSWER THESE SORT OF TEDIOUS QUESTIONS HELP ASAP
Step-by-step explanation:
1.
a. true
b. false (the arc angles are relative to the center of the circle)
c. true (as the central angle of a circle is twice any inscribed angle subtended by the same arc)
d. true (but note that the arc angle of YE is again measured via the center of the circle and twice as large as the angle S)
2.
EGS is an isoceles triangle (that means both legs are equally long).
remember the extended Pythagoras for general triangles :
c² = a² + b² - 2ab×cos(C)
c being the side opposite of the angle C.
let's say c is our long baseline, since we have is opposite angle 124°, and a = b = GE = GS, we have
3.8² = a² + a² - 2aa×cos(124) = 2a² - 2a²×cos(124) =
= 2a²(1 - cos(124))
2a² = 3.8²/(1 - cos(124))
a² = 3.8²/(2(1 - cos(124)))
a = GS = sqrt(3.8²/(2(1 - cos(124)))) =
= 2.151883096... ≈ 2.2 cm
3.
circumference
16pi = 2pi×r
r = 8
area = pi×r² = pi×8² = 64pi
yes, the statement is true.
4.
a half-circle has 180°.
the arc angel AD is a full half-circle (because AD is a diameter), so it is 180°.
the angle ACB is the arc angle AB = 40°. so, the arc angle BD must be the rest of the 180° = 180 - 40 = 140°.
5.
diameter = 50 ft.
so, the radius or distance from the center to the circle arc is 50/2 = 25 ft.
the length of a chord is
c = 2×sqrt(r² - d²)
with r being the radius, d being the distance of the chord from the center.
40 = 2×sqrt(25² - d²)
20 = sqrt(625 - d²)
400 = 625 - d²
-225 = -d²
225 = d²
d = 15 cm
so, the distance of the chord from the center is 15 cm.
6.
the arc angles RE and TS are equal. that means the arc lengths of RE and TS are equal.
and that means the arc lengths of RS and ET are equal. the chords between 2 points on a circle must have the same length, when the arc lengths between these 2 points are the same.
7.
they are equally long.
as we saw in 5., the length of a chord depends on the radius of the circle and the distance of the chord from the center.
since both chords are in the same circle (with the same radius), and they both have the same distance from the center, they can only be equally long, as there is no other element to name them different.
8.
the angle NPE is half of the angle NAE (= the arc angle NE).
the arc angle NE = 63×2 = 126°
the angle PET is half of the angle PAT (= the arc angle PT).
the arc angle PT = 19×2 = 38°
the arcs NP and ET cover the rest of the whole circle circumference (360°).
so, arc angle NP + arc angle ET = 360 - 38 - 126 = 196°
but arc angles NP and ET must be equal (as per the problem definition).
therefore, 2 equal arc angles = 196°
1 arc angle = NP = 196/2 = 98°
there are 90 girls in third year, 25 of whom Study biology what percentage of third year girls study biology
Answer:
27.7% of third year girls study biology
Which number is a rational number?
13
549
16
√34
Answer:
all numbers except √34
Step-by-step explanation:
the top three are whole numbers and therefore rational
1. Consider the pyramid.
(a) Draw and label a net for the pyramid.
(b) Determine the surface area of the pyramid. Show your work.
Answer: 224
Step-by-step explanation:
on the white boards
Answer:
i did it
Step-by-step explanation:
You and your friend are sharing three eighths of a bag of candy. How much of the bag will each of you get if you share it evenly?
Answer:
3/16
Step-by-step explanation:
3/8 / 2 = 3/16
Therefore you and your friend will each get 3/16.
How do I find the surface area of of rectangle
A small bus has seats for 16 passengers. Which equation can be used to find the number of passenger seats, n, in b small
buses?
A
n = 16-b
B
b = 16n
C
b = 16+n
D
n = 16b
Answer:
D, n=16b
Step-by-step explanation:
There are 16 busses, each of which can hold 16 seats. There are n of those busses.
Therefore, 16*n = the total number of seats on the busses altogether.
PLEASE HELP I AM CHOOSING BRAINLIEST
Answer:
0
Step-by-step explanation:
since (x + 7) is a factor (aka. a multiple of) (x + 7) that means there cannot be a remainder. h(x) = n(x+7) , n being any whole number
for example
2(x+7) would be a factor of (x+7) and 2(x+7)/(x+7) = 2 will not leave a remainder
Please help i need answers now!, I will give full points to whoever helps me and I’ll give Brainlyest too
Answer:
182
Step-by-step explanation:
We need to find 3/4 of 242. To do this, multiply 3/4 by 242:
[tex]\sf \implies \dfrac34 \times 242=\dfrac34 \times \dfrac{242}{1}=\dfrac{3 \times 242}{4 \times 1}=\dfrac{726}{4}=181.5[/tex]
181.5 rounded is 182.
Therefore, approximately 182 students went on the field trip.
What is the area of a square that had side length of x-6?
area square= side²
= (x-6)²
= x²-12x+36
Answer:
36
Formula:
Side² = Area
Step-by-Step Explanation
-6 x -6 = 36
what is pi and why do we need it
Answer:
Pi is the number you get from dividing the circumfrence by the diameter of a perfect circle. It is important because without this, we wouldnt have perfect circles and even wheels could be disformed and cause crashes.
Answer:
Pi is an infinite number. We need it to find the area and circumference of a circle.
Step-by-step explanation:
A lender estimates the closing costs on a home loan will be 3.75% of the loan amount of $120,000. the actual closing costs are listed below. closing cost charge loan origination $300 title insurance $600 attorney’s fees $1,250 appraisal $550 inspection $525 recording fees $125 escrow $2,000 evaluate the lender’s good faith estimate. a. the lender made an excellent estimate; it was equal to the actual closing costs. b. the lender made a very good estimate; it was within 0.25% of the actual closing costs. c. the lender made a fairly good estimate; it was between 0.25% and 0.5% of the actual closing costs. d. the lender made a poor estimate; it was off by more than 0.5% of the actual closing costs.
The lender’s good faith estimate is that he made a poor estimate; it was off by more than 0.5% of the actual closing costs.
What is closing cost?All the expenduture and charges charged by a lander and other parties is called the closing cost.
A lender estimates the closing costs on a home loan will be 3.75% of the loan amount of $120,000. Thus, the estimate closing cost is,
[tex]C_{ec}=\dfrac{3.75}{100}\times120000\\C_{ec}=4500[/tex]
The actual closing costs are listed below.
Loan origination $300Title insurance $600 Attorney’s fees $1,250 Appraisal $550 Inspection $525 Recording fees $125 Escrow $2,000.The total annual cost is,
[tex]C= $300 +$600 +$1,250 +$550 +$525 +$125 +$2,000\\C=4800[/tex]
Total annual cost is $300 more than the estimate closing cost. In the percentage form,
[tex]p=\dfrac{4800-4500}{4500}\times100\\p=6.66\%[/tex]
Thus, the lender’s good faith estimate is that he made a poor estimate; it was off by more than 0.5% of the actual closing costs.
Learn more about the closing cost here;
https://brainly.com/question/20108287
Answer:
Its D trust me
I got it right from the other person
A cylinder has a radius of 17 yards it’s volume is 15,426. 82 yd.³ what is the height of the cylinder
i don’t understand how to solve this, can you help me. I tried dividing by 3 but it’s not right.
Answer:
Hello Camila Sofia Pazos Motta, you have to divide by pi, not 3.
Step-by-step explanation:
Given: x1 = 6, x2 = 2.5, y1 = 2.4. Find y2 if the points are (a) directly proportional or
(b) inversely proportional
a) The value of y₂ is 1 for the direct proportionality case.
b) The value of y₂ is 5.76 for the inverse proportionality case.
How to predict a value by apply proportionality model
Proportionality represents a family of relationships between two variables, which can be linear and nonlinear. Direct proportionality represents a linear relationship, whereas inverse proportionality represents a kind of nonlinear relationship.
Here are two mathematical representations of the relationships described above:
Direct proportionality[tex]y \propto x[/tex]
[tex]\frac{y_{2}}{y_{1}} = \frac{x_{2}}{x_{1}}[/tex] (1)
Inverse proportionality[tex]y \propto \frac{1}{x}[/tex]
[tex]\frac{y_{2}}{y_{1}} = \frac{x_{1}}{x_{2}}[/tex] (2)
If we know that x₁ = 6, x₂ = 2.5, y₁ = 2.4, then the value of y₂ for each case are, respectively:
Direct proportionalityy₂ = 2.4 × (2.5/6)
y₂ = 1
Inverse proportionalityy₂ = 2.4 × (6/2.5)
y₂ = 5.76
To learn more on proportions, we kindly invite to check this verified question: https://brainly.com/question/2548537
the difference of 20 and x
Answer:
20-x
Step-by-step explanation:
you need the value of x to answer
A circle that has (-2,4) and (4,2) as endpoints of a diameter.
Use the given information to write the standard equation of the circle.
I WILL MARK BRAINLIEST IF YOU GIVE ME THE CORRECT ANSWER!
Answer:
[tex]\implies (x-1)^2+(y-3)^2=10[/tex]
Step-by-step explanation:
End points of the diameter of the circle are:
[tex](-2,\:4) \implies x_1= -2, \: y_1= 4[/tex]
[tex](4,\:2) \implies x_2= 4, \: y_2= 2[/tex]
Equation of circle in diameter form is given as:
[tex](x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0[/tex]
Plugging in the values of [tex]x_1, \: y_1,\:x_2, \: y_2[/tex] in the above equation, we find:
[tex][x-(-2)](x-4)+(y-4)(y-2)=0[/tex]
[tex]\implies (x+2)(x-4)+(y-4)(y-2)=0[/tex]
[tex]\implies x^2-2x-8+y^2-6y+8=0[/tex]
[tex]\implies x^2-2x+1-9+y^2-6y+9-1=0[/tex]
[tex]\implies (x^2-2x+1)-9+(y^2-6y+9)-1=0[/tex]
[tex]\implies (x-1)^2+(y-3)^2-10=0[/tex]
[tex]\implies (x-1)^2+(y-3)^2=10[/tex]
This is the required equation of circle in standard form.
The cost of shirts are 3 for $40.65 what is the unit cost per shirt?
Answer: $13.55 per shirt
Step-by-step explanation:
3 for $40.65
you must first divide 40.65 by 3 to find the cost of 1 shirt which the answer is $13.55. I hope this helps! Have a good day! :)
Since we are given the price of 3 shirts, we can work backwards to do $40.65 divided by 3 to get the unit cost per shirt, in which we get $13.55.
Glad to help!
I'd appreciate if you marked this as brainliest, if not I understand :)
choose the imensions that represen this rectlangl
answer
length:2/5
width: 3/6
length:2/4
width:3/4
length:2/3
width:3/5
length:2/3
width:3/4
Answer:B
Step-by-step explanation:I hope it help
d) The phys-ed. department bought a total
of 27 bats and balls for the baseball team.
Three times the number of bats minus
the number of balls is 21. Find the
number of bats and balls.
1. Jakob plays the violin. His bow is 8 decimeters long.
How many meters long is Jakob's bow?
Answer:
0.8 meters
Step-by-step explanation:
1 decimeter is 0.1 meters
so,
[tex]\frac{1}{0.1} = \frac{8}{x}\\x = 8*0.1\\x = 0.8[/tex]
who can help me with my math
Step-by-step explanation:
I am always available to help, post your worry
A square tile is decorated with dots and triangle patterns.
The tile is rotated into this new position.
Which tile sections should have a dot?
(sections have been numbered to help you identify them for your answer)
Answer
Who is your school?
Who is your class?
Who is the chapter
PLEASE HELP ME TO FIND THE VALUE OF X AND Y
Answer:
x=85/5
x= 17
y=95/5
y=19
Step-by-step explanation:
vertically opp angles are equal
Answer:
vertical angles here make an X
1. 5y and 95 are vertical
2. 5x and 85 are vertical
3. x = 17
4. y = 19
.
Step-by-step explanation:
angles MPL and NPO are equal
5x = 85
x = 17
angles MPN and LPO are equal
5y = 95
y = 19
Ada got a new puppy for Christmas. She went to the pet store to buy the
things she needed for her puppy. She bought a collar for $18.37, an
identification tag for $15.67, a chew toy for $8.23, puppy shampoo for
$19.26, and a food and water dish for $21.28. The pet store gave her an
$7.50 discount for spending more than $50.00. How much did Ada spend
altogether?
Answer:
Hope it helps you.
Amy fills an ice cream cone to the top edge. The diameter of the ice cream cone is 2 inches and its height is 6 inches. Don fills a bowl (V = 5 cubic inches) with ice cream. Amy has how much more ice cream than Don?
Answer:
1.28 in³
Step-by-step explanation:
Volume of Amy's cone
Cone = 1/3πr²hCone = 1/3 x 3.14 x 1² x 6Cone = 2 x 3.14 = 6.28 in³Volume of Don's bowl
It's given to be 5 in³Difference
Amy's cone - Don's bowl6.28 - 51.28 in³Answer:
So obviously in the context of this question you are meant to find the volume. Since Don's bowl already has a given value of 5 cubic inches we will use that same unit when calculating amy's ice cream cone volume.
Step-by-step explanation:
You are given that amy has a cone and need to find the volume. The formula for the volume of a cone is (V=πr^2*h/3).
π = pi or 3.14......
r = radius (in this case the opening/ diameter of the ice cream cone is given as 2 inches and the radius is half of diameter so d/2 = r (r=1)
h = height (in this case it is given that height is 6 inches)
Remember all variable units must be kept the same so in this case all units are inches.
Now Plug in and solve V = [tex]3.14*(1)^{2} *\frac{(6)}{3}[/tex]
Remember order of operations / PEMDAS (in this case, do exponent first then just multiply from left to right and at the end divide that number by 3.
V= 6.28 cubic inches (since all our units were inches and we are finding cubic volume of a cone)
Now Amy volume of cone - Don volume of bowl = your answer. 6.28-5 = 1.28 cubic inches
