Answer: [tex]\sqrt{(-16)^{2} } =16[/tex]
Step-by-step explanation:
I looked it up on my calculator. I hope this helps!! :)
meijun had some money. she used 1/3 of it on a watch and 1/9 of it on a gift. the watch and the gift cost $144 altogether. how much money did she have at first?
Answer:
$324
Step-by-step explanation:
let x be the amount of money she had at first , then
[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{9}[/tex] x = 144 ( multiply through by 9 to clear the fractions )
3x + x = 1296
4x = 1296 ( divide both sides by 4 )
x = 324
she had $324 at first
If a and b are two distinct primes, the ab2 has ___ positive divisors.
The number ab², where a and b are prime numbers, has 6 divisors.
How many divisors are for the given expression?Remember that any number can be written as a product of primes, for example, 15 can be written as:
15 = 3*5
Where 3 and 5 are primes.
Such that the divisors of 15 are the factors made with the primes on the right side.
So for the number:
N = a*b^2 = a*b*b
The divisors are:
a, b, a*b, b*b
And trivially, itself and 1, so there are a total of 6 divisors.
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I also dont get this :(
An equation is formed of two equal expressions. If x is increased by 5 then the value of y is increased by 10.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
Given that y=2x+1, now if the value of x increased by 5. then the value of y will be,
[tex]y_1=2(x+5)+1\\y_1 = 2x + 11[/tex]
Now if we compare y and y₁, then it can be said that if x is increased by 5 then the value of y is increased by 10.
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find the distance between the pair of points (7,6) and (4,10)
Answer:
5 units
Step-by-step explanation:
to find out the answer for this you must first find the distance between 7 and 4 and then 6 and 10
then you would square them and then add them
lastly you would take the square root of that and youd have your answer
so
7 - 4 = 3
6 - 10 = -4 (just use 4)
3^2 + 4^2 = 9 + 16 = 25
then you take the square root of this
sqrt(25) = 5
that is your answer
To solve this problem, you will use the Distance Formula to find the distance between two coordinate points.
Set Up the Distance FormulaThe Distance Formula is defined as follows:
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
We must title our points by the standard coordinate naming system:
[tex](x_1, y_1) \ \text{and} \ (x_2, y_2)[/tex]
Therefore, our points can be labeled:
[tex]x_1 = 7[/tex][tex]y_1 = 6[/tex][tex]x_2 = 4[/tex][tex]y_2 = 10[/tex]Substitute Known Values for VariablesNow, substitute the known values as the variables in the Distance Formula:
[tex]d=\sqrt{(4 - 7)^2 + (10 - 6)^2}[/tex]
You must know the BPEMDAS acronym, which stands for:
Brackets
Parentheses
Exponents
Multiplication
Division
Addition
Subtraction
Simplify the expression using BPEMDAS:
[tex]d=\sqrt{(-3)^2 + (4)^2}[/tex]
Remember that when a number is raised to the 2nd power, it is the same thing as multiplying the number by itself:
[tex]-3\times-3 = 9[/tex]
[tex]4\times4=16[/tex]
Simplify further by removing the parentheses:
[tex]d=\sqrt{9+16}[/tex]
Compute the additive operation:
[tex]d=\sqrt{25}[/tex]
Simplify the RadicandThe number that is placed inside of a square root symbol (or a radical symbol) is referred to as the radicand.
In this situation, the radicand is 25.
To simplify the radicand, you may either use a calculator to compute the result, or you can determine which number raised to the 2nd power will result in a final answer of 25.
In this case, we can determine that 5² will result in a final answer of 25.
[tex]5^{2} = 25[/tex]
The final answer is 5 units.
A student wanted to find the sum of all the even numbers from 1 to 100. He said: The sum of all the even numbers from 1 to 100 is twice the sum of all the odd numbers from 1 to 100. The sum of all the odd numbers from 1 to 100 is 1002. Explain why each of these statements is incorrect. HELP ME ASAP
Statement 1
Twice the sum of the odd numbers would be:
[tex]2(1+3+5+\cdots+99)=2+6+10+\cdots+198[/tex], which is not equal to the sum of all the even numbers from 1 to 100.
Statement 2
The sum of all the odd numbers from 1 to 100 can be thought of as an arithmetic sequence containing 50 terms, with first term 1 and common difference 2. This means the sum of the series would be:
[tex]\frac{50}{2}[2(1)+(50-1)(2)]=2500[/tex]
which is not equal to 1002.
The statement 1 and the statement 2 are incorrect.
The sum of the arithmetic series of first term a₁ and common difference d will be s= n/2{2a₁+(n-1)d
Statement 1:
Given in statement 1, Twice the sum of the odd numbers would be:
2(1+3+5+7.......+99)=2+6+10+14+.....198
which is not equal to the sum of all the even numbers from 1 to 100.
Statement 2:
The sum of all the odd numbers from 1 to 100 can be calculated as follows where this is an arithmetic sequence of 50 terms, where the first term is 1 and the common difference is 2. This means the sum of the arithmetic series would be:
s= n/2{2a₁+(n-1)d}
putting the above formula
a₁=1
n=50
d=2
s= 50/2{2(1)+(50-1)2} = 25{2+98} =2500 ≠1002
which is not equal to 1002.
Therefore statement 1 and 2 are incorrect.
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If the hypotenuse of a 30-60-90 degree triangle is 14, what is the short leg?
Answer:
7 units
Step-by-step explanation:
The short leg is opposite the 30 degree angle
sin 30 = opposite side/ hypotenuse
Hypotenuse * sin 30 = opposite side = 14 * 1/2 = 7 units
Find two positive numbers such that their sum is 60 and their product is a maximum. Select one: O a. 30 and 30 O b. 25 and 35 O c. 1 and 59 O d. 20 and 40
Answer:
B: 25 and 35
Step-by-step explanation:
25 product 35 875
Account earns 8.5% interest. If you invest $6,609 now how much interest will you earn in 5years
Answer:
simple interest is $281(nearest whole number)
Step-by-step explanation:
S. I=PXTXR
100
P=$6609
T=5
R=8.5 or 85/10
S. I=6609X5X85
100X10
=280.8825
=281
A farmer has decided to divide his land area in half in order to plant soy and corn. Calculate the area of the entire area so he knows how much soil is needed.
A parallelogram with a height of 6 yards and side length 9 yards. The height forms a triangle with the slanted side of the rhombus with a base of 2.5 yards. Rhombus is split into a soy half and a corn half.
Each bag of soil covers 20 square yards. How many bags should the farmer purchase?
The farmer should purchase 2 bags of soil for his farm.
What is Area of rectangle?Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.
The shape of the farm, according to the picture is a parallelogram. the total area can be calculated as follows:
Area = b X h
where
b = base
h = height
base = 6.5 + 2.5 = 9.0 yards
height = 6 yards
Area = 6 × 9 = 54 square yards.
40 square yards requires 1 bag of soil .
54 square yards will require ?
cross multiply
Bags required = 54 / 40 = 1.35 bag
Thus, the farmer will require 2 bags of soil for his farm.
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Students returning to a secondary school have to pass through a check point at the rate of 50 per though. The average time for checking is 35 seconds. The arrival rate and service rate follow a Poisson distribution. There is a delay and the principal is willing to include another check point to reduce the average time of checking to 28 seconds if the idle time is less than 10% and the average queue length is more than 10 students, check whether the introduction of an extra check point is justifiable.
The average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
How to explain the information?Since the arrival rate and service rate follow a Poisson distribution, we can use the Poisson arrival rate formula to calculate the average queue length.
Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)
For the given problem, the average queue length is:
Average queue length = (50 * 35) / (1 - 50 * 35)
= 175
Since the average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.
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The power 3 Superscript negative 3 equals StartFraction 1 Over 27 EndFraction . Which expression is equivalent to 3 Superscript negative 3?
Applying the negative exponent, it is found that the equivalent expression to [tex]3^{-3}[/tex] is [tex]\frac{1}{27}[/tex].
How to deal with a negative exponent?When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator, as follows:
[tex]a^{-b} = \frac{1}{a^b}[/tex]
Hence, in this problem, the equivalent expression is:
[tex]3^{-3} = \frac{1}{3^3} = \frac{1}{27}[/tex]
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You have loaned a friend $100 and will charge him 5% annua simple interest when he pays it back.
The annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount of borrowed amount.
We have:
You have loaned a friend $100 and will charge him 5% annually.
As we know:
A = P(1 + rt)
P = $100
r = 5% = 0.05
t = 1 years
A = 100(1 + 0.05×1)
A = $105
I = A - P = 105 - 100 = $5
Thus, the annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.
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Celia needs 75% of the marks in an exam to pass. She gets 4/5 of the marks. Does she pass the course? Show your working to justify your answer
Answer:
Yes, she passes with 80%
Step-by-step explanation:
4 divided by 5 = 0.8
0.8 multiplied by 100 = 80%
80% is greater than the required 75% needed to pass
Answer:
Yes
Step-by-step explanation:
First lets establish the key points
We know she needs 75% to pass and she gets 4/5 of the marks
Lets make 4/5 a decimal 4/5 X 2/2 is 8/10 better know as .8
.75 = 75%
.8 = 80%
80% > 75%
Meaning She PASSED!!!
If angle 1= 105°, angle 12= (3x + 15)°, and angle 7 = (8y-5)°, determine the values
of x and y?
The value of the variable x is 30° and the value of the variable y is 10°.
The missing diagram is attached below.
What is an angle?The angle is the distance between the intersecting lines or surfaces.
Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.
Vertically opposite angle – When two lines intersect, then their opposite angles are equal.
Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.
If angle ∠1 = 105°, angle ∠12 = (3x + 15)°, and angle ∠7 = (8y-5)°.
∠1 = ∠5 = ∠9 = 105° (corresponding angles)
∠1 = ∠4 = 105° (Vertical opposite angles)
∠1 + ∠2 = 180° (linear angle)
∠2 = 75°
∠2 = ∠3 = 75° (Vertical opposite angles)
∠3 = ∠8 = ∠12 = 75° (corresponding angles)
Then the value of x and y will be
∠9 = ∠12
∠1 = ∠12
105° = (3x + 15)°
3x = 90°
x = 30°
∠6 = ∠7
75° = (8y – 5)°
8y = 80°
y = 10°
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Determine whether each ordered pair is a solution to the inequality x+5y<2.
Select all that apply:
(−8,−1)
(−1,0)
(4,2)
(9,6)
(0,10)
Two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.
What is inequality?The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.
Given inequality is:-
x + 5y < 2.We will check all the points for the inequality:-
(−8,−1) → x + 5y < 2. → -8 +(5 x -1) < 2 → -13 < 2 It is inequality
(−1,0) → x + 5y < 2 → -1 < 2 It is inequality
(4,2) → x + 5y < 2 → 14 < 2 wrong
(9,6) → x + 5y < 2 → 39 < 2 wrong
(0,10) → x + 5y < 2 → 50 < 2 wrong
Therefore the two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.
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If f(n)= n²-n, then f(-4) is
O-20
12
-12
20
Answer:
20
Step-by-step explanation:
Plug in -4 for n:
(-4)^2 - (-4) = 16 + 4 = 20
3 more than half a number
Answer:
3 + a/2
Step-by-step explanation:
3 + a/2
What is 4 third written in expanded form
Frankie’s weekly budget includes a long-term goal of purchasing a car. He is saving $15 a week toward that goal. He is considering saving up his money to purchase his grandmother’s older car. Frankie knows his grandmother has maintained the car and it is in good condition. She is also giving him a greatly discounted price of $800. What should Frankie consider before buying the car? Check all that apply. what he will be giving up if he spends $800 on the car the cost to maintain (oil, tires, gas, brakes) and insure the car how many of his friends have cars his short- and long-term financial goals if an alternate mode of transportation, such as a bicycle or the bus, is sufficient for his needs
The decision of purchasing a car must be taken by Frankie after considering the following points:
1. what he will be giving up if he spends $800 on the car
2. The cost to maintain and ensure the car
3. his short- and long-term financial goals
4. if an alternate mode of transportation, such as a bicycle or the bus, is sufficient for his needs.
What is the point he must know about purchasing a car?Frankie is an individual person when he wants to purchase a car that is his long-term goal.
he must consider various things before making such a big expenditure.
The points to be noted before purchasing a car are:
what is the cost for Frankie for spending $800?
What will be the maintenance and insurance cost?
He must check his other short and long-term goals before purchasing a car.
Is the expense of the car a necessity for Frankie or he can use public transport.
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Answer:
Step-by-step explanation: thank me later
A,B,E
4x+7-(x+6)=68
Solve.
[tex]4x + 7 - (x + 6) = 68 \\ \\ 4x + 7 - x - 6 = 68 \\ \\ 3x + 1 = 68 \\ \\ 3x = 68 - 1 \\ \\ 3x = 67 \\ \\ x = \frac{67}{3} \\ \\ x = 22.3[/tex]
The value of x is 67/3 or 22.3 .
Hi!
__________________________________________________________
[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]
x=
[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]
First let's distribute the minus sign.
[tex]\twoheadrightarrow\sf 4x+7-x-6=68[/tex]
[tex]\bullet[/tex] Add 6 to both sides
[tex]\twoheadrightarrow\sf 4x+7-x=74[/tex]
[tex]\bullet[/tex] Subtract the x's
[tex]\twoheadrightarrow\sf 3x+7=74[/tex]
[tex]\bullet[/tex] Subtract 7 from both sides
[tex]\twoheadrightarrow\sf3x=67[/tex]
[tex]\bullet[/tex] Divide both sides by 3
[tex]\twoheadrightarrow\sf x=\cfrac{67}{3}[/tex]
[tex]\bullet[/tex] Great job! We solved for the variable
--
Hope that this helped! Best wishes.
[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]
--
Solve the following subtraction problem. Remember to borrow as necessary.
9cu yd113cu in
− 4cu ft129cu in
−−−−−−−−−−−−−−−−−−−−−−
The subtraction of the expression will be 238 cubic feet, 551 cubic inches.
What is subtraction?It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.
The expressions are given below.
9 cubic yd 113 cubic in and 4 cubic ft 129 cubic in
1 cubic yard = 27 cubic feet
1 cubic feet = 1728 cubic inches
Then the subtraction will be
242 cu ft 1841 cu in
− 4 cu ft 1290 cu in
238 cu ft 551 cu in
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Determine algebraically whether the function is even, odd, or neither: f(x)=3x ³ +5
What is the rule for the reflection?
rx-axis (x, y) - (-x, y)
ry-axis (x, y) (-x, y)
rx-axis (x, y) - (x, y)
ry-axis (x, y) (x, −y)
When reflected over ry-axis (x, y) (-x, y) , rx-axis (x, y) (x,-y) , Option A and D is the correct answer.
What is rule for the reflection ?The rule for reflection is when an object or a coordinate point is reflected over x axis then the coordinate of the x axis remains the same while the y coordinate changes to be additive inverse.
Vice Versa happens when reflected over y axis.
So,
rx-axis (x, y) - (-x, y) --> (x,-y)
ry-axis (x, y) (-x, y)
Therefore Option A and D is the correct answer.
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Answer: its A not A & D
Step-by-step explanation:
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 80% salt. She wants to obtain 120 ounces of a mixture that is 70% salt. How many ounces of each solution should she use?
Giving the brainliest to those who answer!
Solve for x:
5(1 – x) = 20
x = __
[tex]5(1-x)=20\\5-5x=20\\5x=-15\\x=-3[/tex]
Hii!
__________________________________________________________
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex]
The value of x is -3! ^^
[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]
[tex]\bullet[/tex] First multiply 5 times 1 and -x
[tex]\twoheadrightarrow\sf 5(1-x)=20[/tex]
[tex]\twoheadrightarrow\sf 5-5x=20[/tex]
[tex]\bullet[/tex] Now subtract 5 from both sides
[tex]\twoheadrightarrow\sf -5x=15[/tex]
[tex]\bullet[/tex] Now divide both sides by -5
[tex]\twoheadrightarrow\sf x=-3[/tex]
--
Hope that this helped! Best wishes.
--
Determine whether each ordered pair is a solution to the inequality −7x−y>2.
Answer:
[tex]x < - \frac{2 + y}{7} [/tex]
Step-by-step explanation:
[tex] - 7x > 2 + y \\ x < - \frac{2 + y}{7} [/tex]
3.
2. The diagram below is divided into equal parts. Which fraction of the parts is
white?
Mark only one oval.
Option 1
Option 3
37
314
I
Option 2
47
Option 4
4/3
Step-by-step explanation:
simply count them.
there are 7 little rectangles building the whole.
from these 7, 4 are gray and 3 are white.
so, 3 of 7 are white.
that means,
3/7 of all the parts are white.
7. Sapna travelled 48 km to meet her parents. She travelled the first 18 km by car and the remaining distance by train. Find the fraction of the journey sapna travelled by car and train
The fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
We know that fraction is an expression in mathematics used to denote the division of two whole numbers.
Given that the total distance = 48 km.
The distance Sapna traveled by car = 18 km.
So, the fraction is = distance traveled by car/total distance = 18/48 = 3/8
The distance Sapna traveled by train = 48 - 18 km = 30 km.
So, the fraction is = distance traveled by train/total distance = 30/48 = 5/8
Therefore the fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.
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...............
................
Let the numbers be x and x/7
Now
sum=824x+x/7=8248x/7=8248x=824(7)8x=5768x=721The numbers are
721 and 721/7=103Answer:
7x+X=824
8X/8=834/8
x=108
Step-by-step explanation:
hope I helped