Using Simplification , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 , the correct option is (a) and (d) .
In the question ,
it is given that
the equation is (6x+2)/3 = 2 - (3x+14)
solving the brackets on the right side of the equation ,
(6x+2)/3 = 2 - 3x - 14
(6x+2)/3 = -3x - 12 ....option(a)
On Cross Multiplying , we get
6x + 2 = 3(-3x - 12)
6x + 2 = -9x - 36 ....option(d)
Therefore , all the equations that are equivalent to (6x+2)/3 = 2 - (3x+14) are (6x+2)/3 = -3x - 12 and 6x + 2 = -9x - 36 .
The given question is incomplete , the complete question is
Using Simplification , Select all equations that are equivalent to
(6x+2)/3 = 2 - (3x+14)
(a) (6x+2)/3 = -3x-12
(b) (6x+2) = 2 - (3x+14)
(c) 2x + 2/3 = 2 - (3x+14)
(d) 6x+2 = -9x-36
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Please help me with this (ASAP) 15 POINTS
Circle 10cm find the diameter of the circle
Answer:
Diameter = 3.1831 cm (aprox)
Step-by-step explanation:
Diameter = circle / π
π ≈ 3.1414
Then:
Diameter = 10 / 3.1418
Diameter = 3.1831 cm
Simplify the radical expression (3+√6)(3-√6)
Applying the distributive property, the given radical expression can be represented by 15.
Properties of Multiplication
The properties of multiplication are:
Distributive: a(b±c)= ab±ac Commutative: a . b = b. a Associative: a(b+c)= c(a+b) Identity: b.1=bThe question gives [tex](3+\sqrt{6} )(3-\sqrt {6} )[/tex]. Therefore, you should analyze the properties presented previously, and after that, you should identify which was used.
Here, it is possible to see that you can apply the distributive property. See below.
[tex](3+\sqrt{6} )(3-\sqrt {6} )\\ 9-3\sqrt {6} +3\sqrt {6}+6[/tex]
9+0+6=15
Then, the radical expression (3+√6)(3-√6)=15
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What are the domain and range of f(x) = logx-5?
John read 7 and 1/2 pages in 2/5 of an hour at what rate in pages per hour did he read?
When John read 7 and 1/2 pages in 2/5 of an hour, the rate in pages per hour that he read is 18.75 per pages.
What is rate?It should be noted that rate is used to show the comparison between two things.
In this case, John read 7 and 1/2 pages in 2/5 of an hour.
The number of pages read per hour will be the division of the values given. This will be:
= 7 1/2 ÷ 2/5
= 7.5 / 0.4
= 18.75 pages
The pages is 18.75 pages.
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Translate the following equation into a verbal sentence x/4 - y = -2(x/y)
The given equation x/4 - y = -2(x/y) can be expressed in a verbal sentence as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.
How to express the mathematical equation in the form of a verbal sentence?
To express the mathematical equation in the form of a verbal sentence, we have to express the operations by using sentences.
Let's take an example,
x + y = 4.
Then the verbal form will be the sum of two numbers is 4.
Hence, the given expression can be expressed as the difference between the fourth fraction of x and y is equal to minus of twice the fraction of x and y.
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I need help please because I am failing in math
Answer:
what do you need help with?
Answer:
Step-by-step explanation:
You need a picture of the item.
Given that £1 = $1.62
how much is $405 in £
Answer:
£250
Step-by-step explanation:
Divide $405 by $1.62 which is 250.
Multiply that by £1 which is £250.
engineers must consider the diameters of heads when designing helmets. the company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6.4-in and a standard deviation of 0.9-in. due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 1.4% or largest 1.4%. what is the minimum head diameter that will fit the clientele? min
The largest head diameter that can accommodate the clientele is 8.5743
Mean, u = 6.4
Standard deviation = 0.9
We must utilize the inverse of the common normal table to obtain our values.
the smallest head width possible.
P(Z < z) = 1.4%
P(Z < z) = 0.014
P(Z < -2.0749) = 0.014
z = -2.0749
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
We already have:
z = -2.0749
u = 6.5
s.d = 1
Replacing numbers,
x = (-2.0749 × 1) + 6.5
x = 4.4251
The clientele requires a minimum head breadth of 4.4251.
The largest head width that can be accommodated.
P(Z > z) = 1.4%
1 - P(Z < z) = 0.014
P(Z < z) = 1 - 0.014 = 0.981
P(Z < 2.0749) = 0.981
Using the z-score calculation,
(x - μ) ÷ σ = [tex]Z_{0.019}[/tex]
Let x be the heads' breath.
Making x the focus of the equation,
x = z × σ + μ
z = 2.0749
u = 6.5
s.d = 1
Substituting figures,
x = (2.0749 × 1) + 6.5
x = 4.4251
x = 8.5743
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At the bakery, they have 4 and a 1/8 pies for sale. They sell 1⁄4 of a pie for$5. How many pieces do they have to sell, and how much money will they make?
The number of pieces the bakery will sell is 16 and a half. The total amount of money they will make is $82.5.
What is the number of pieces of pies to be sold?To get the number of pieces of pies that they have to sell, we need to first determine how many 1/4 pies are in 4 and 8 pieces of bread. Going by that, we can see that:
1/4x of 4 = 16.
Also, 1/4x of 1/8 = 1/2.
So, the total number of pies that they have to sell is 16 and a half.
Now if 1/4 of a pie costs $5, then 4 1/8 will be equal to 33/8 × 5 ÷ 1/4.
This is equal to 165/8 × 4 = $82.5
So, the total amount of money that the bakery will make will be $82.5.
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2. Identify the proportional relationship.
7x-2=y y + 1 = 3x y = 5x y=2x +4
Find all the zeros of the equation.
[tex]2x^4+70x^2-72=0[/tex]
Answer:
x = 1, -1
x = 6i, -6i
Answer:
1, -1, 6i, -6i
Step-by-step explanation:
What are the roots of the equation x 2 + 16 x + 80 = 0 x 2 +16x+80=0 in simplest a + b i a+bi form?
The quadratic equation x² + 16 · x + 80 has two roots: x₁ = - 1 / 10 + i (4 / 5), x₂ = - 1 / 10 - i (4 / 5).
How to determine the roots of a quadratic equation
In this question we find a quadratic equation of the form a · x² + b · x + c = 0, whose roots can be found by using the quadratic formula:
x = - b / (2 · a) ± [1 / (2 · a)] · √(b² - 4 · a · c)
Where b² - 4 · a · c is the discriminant of the quadratic formula, which offers three cases of solutions:
b² - 4 · a · c > 0: Two different real roots. b² - 4 · a · c = 0: Two equal real roots. b² - 4 · a · c < 0: Two conjugate complex roots.If we know that a = 1, b = 16 and c = 80, then the roots of the quadratic equation are, respectively:
x = - 16 / 160 ± (1 / 160) · √(16² - 4 · 1 · 80)
x = - 1 / 10 ± (1 / 10) · √(- 64)
x = - 1 / 10 ± i (4 / 5)
The roots are - 1 / 10 + i (4 / 5) and - 1 / 10 - i (4 / 5).
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I need help like asap !!!
only numbers and decimal points
Answer:
use pythagoras theorm you will get 20.35 ft
Step-by-step explanation:
Answer:
20.3490
Step-by-step explanation:
a^2+b^2=c^2
15.5^2+13.2^2=c^2
240.25+174.24=c^2
414.49=c^2
c=20.3590
A palindrome is a word or number that is the same when read forwards or backwards. For example, DAD is a palindrome, and so is
RACECAR. 484 is a palindrome number, and so is 9229.
What is the sum of a three digit palindrome number that ends in 71 and a four digit palindrome number that ends in 83?
Answer:
4054
Explanation:
171 is the three-digit palindrome that ends with 71
3883 is the four-digit palindrome that ends with 83
171 + 3883 = 4054
Isabel and Khalil buy peaches and apricots. At the fruit stand, peaches cost $0.85 each, and apricots cost $0.55 each. Tax is included in the cost of each fruit. The friends have $5 to spend. Which is a possible combination of the number of peaches and apricots they can get for $5? Responses 1 peach, 8 apricots 1 peach, 8 apricots 2 peaches, 5 apricots 2 peaches, 5 apricots 3 peaches, 7 apricots 3 peaches, 7 apricots 4 peaches, 3 apricots 4 peaches, 3 apricots
The possible combination of the number of peaches and apricots they can get for $5 is 2 peaches and 5 apricots.
What is the possible combination?The equation that represents the total cost of peaches and apricots is:
Total cost = (number of peaches x cost of one peach) + (number of apricots x number of apricots)
$5 = ($0.85 x p) + ($0.55 x a)
Total cost of buying 1 peach and 8 apricots:
($0.85 x 1) + ($0.55 x 8) = $5.25
Total cost of buying 2 peaches and 5 apricots:
($0.85 x 2) + ($0.55 x 5) = $4.45
Total cost of buying 3 peaches and 7 apricots:
($0.85 x 3) + ($0.55 x 7) = $6.40
Total cost of buying 4 peaches and 3 apricots:
($0.85 x 4) + ($0.55 x 3) = $5.05
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If the weight of 7 sheets of paper is 28 g, find how many papers will weigh 1 .5 kg?
Answer:
Step-by-step explanation:
weight of 1 sheet= (28/7)g
=4g
1.5kg=1.5 X 1000g
=1500g
no. of papers that will weigh 1.5 kg= 1500/4
=375
Answer: 375 sheets of paper
Step-by-step explanation: First, to find the weight of one sheet of paper, we can do 28 divided by 7 to get 4 grams. Then, since 1.5 kg is 1500 grams, we can do 1500 divided by 4, which equals 375. So, 375 sheets of paper will weigh 1.5 kg.
hope this helps!
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amy gets 7 our of 8 math problems correct, mark gets 7 out of 11 problems correct ,and carol gets 7 out of 9 math problems corect. order these fractions from least to Greatest
Answer:
[tex]\frac{7}{11}[/tex], [tex]\frac{7}{9}[/tex], [tex]\frac{7}{8}[/tex]
Hope this helps!
Step-by-step explanation:
One way to find this out is by just plain dividing the numbers, 7 ÷ 11 is 0.636363..., 7 ÷ 9 is 0.7777777..., and 7 ÷ 8 is 0.875. 7/11 is the smallest of all of them, then 7/9, and then 7/8.
4. Which theorem would explain why TU > SV?
Answer:
B. Hınge theoremStep-by-step explanation:
We can observe:
ST = UV, marked as equal;VT = TV, common side;m∠TVU = 45° > m∠STV = 44°, as marked.According to Hınge theorem if two sides of different triangles are equal and the angles between the two sides are different, then the larger angles has greater side opposite to it.
As TU is opposite to the larger angle, and SV is opposite to smaller angle, then TU > SV.
Correct angle choice is B.
(b) Expand and simplify.
(2x - 5) (x - 3)
help me pls
[tex] = 2x(x - 3) - 5(x - 3) \\ = 2 {x}^{2} - 6x - 5x + 15 \\ = 2 {x}^{2} - 11x + 15 [/tex]
ATTACHED IS THE SOLUTION
Daniela needs to rent a car while on vacation. The rental company charges $19.95, plus 18 cents for each mile driven. If Daniela only has $50 to spend on the car rental, what is the maximum number of miles she can drive?
Daniela can drive a maximum of
going over $50. Round your answer to the nearest mile.
miles without the cost of the rental
Answer:
167 miles without the cost of the rental
Step-by-step explanation:
Daniela needs to rent a car while on vacation. The rental company charges $19.95, plus 18 cents for each mile driven. If Daniela only has $50 to spend on the car rental, what is the maximum number of miles she can drive? Round your answer to the nearest mile.
equation: where m = miles driven
50 = 0.18m + 19.95
subtract 19.95 from both sides:
50 - 19.95= 0.18m + 19.95 - 19.95
30.05 = 0.18m
divide both sides by 0.18:
30.05/0.18 = 0.18m/0.18
m = 166.9444
rounded: 167 miles without the cost of the rental
Answer:
167 :)
Step-by-step explanation:
it's math :)
A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the
function S=18.95 +0.50M, where M is the number of miles driven.
The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I=4.80 +0.15M.
Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.
An equation relating C to M is (C) = 23.75 + 0.65M.
Given,
In the question:
The standard charge S (in dollars) is given by the
function S=18.95 +0.50M, where M is the number of miles driven.
The insurance charge I (in dollars) is given by the function I=4.80 +0.15M.
and, Let C be the total charge (in dollars) for a rental that includes insurance.
To find the An equation relating C to M.
Now, According to the question:
By the topic:
The total Charge (C) = The standard Charge (S) + The insurance charge (I)
Thus,
The total Charge (C) = 18.95 +0.50M + 4.80 +0.15M.
Combine like terms:
The total Charge (C) = 18.95 + 4.80 + 0.50M + 0.15M
The total Charge (C) = 23.75 + 0.65M
Hence, An equation relating C to M is (C) = 23.75 + 0.65M.
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[tex]\frac{2}{5} a^{\frac{2}{2} } + C[/tex]
By simplifying 2/5 + [tex]a^{2/2}[/tex] C we get the solution as (2a + 5C) / 5.
What is simplification?To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.Start by resolving all of the terms enclosed in parenthesis to simplify mathematical equations using the order of operations. The exponents should then be solved, followed by any necessary multiplication. Division problems are next, followed by adding and subtracting to wrap things out.Given equation ,
2/5 + [tex]a^{2/2}[/tex] C
We know that , [tex]a^{2/2}[/tex] = a
So the equation becomes ,
2/5 a + C
By simplifying,
2a / 5 + C
= 2a / 5 + 5C / 5
By combining fractions ,
(2a + 5C) / 5
Thus solution is (2a + 5C) / 5 .
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Use either long division or synthetic division to solve:
(2i^4 +-6i³+-25i² +31i+-30)/(i +-5)
Answer:
[tex]\textsf{Quotient}: \quad 2i^3+4i^2-5i+6[/tex]
[tex]\textsf{Simplified Quotient}: \quad 2-7i[/tex]
Step-by-step explanation:
Long division method
Divide the first term of the dividend by the first term of the divisor, and put that in the answer.Multiply the divisor by that answer, put that below the dividend.Subtract to create a new dividend.Repeat.Given rational expression:
[tex]\dfrac{2i^4-6i^3-25i^2 +31i-30}{i -5}[/tex]
Solve using long division:
[tex]\large \begin{array}{r}2i^3+4i^2-5i+6\phantom{)}\\i-5{\overline{\smash{\big)}\,2i^4-6i^3-25i^2 +31i-30\phantom{)}}}\\{-~\phantom{(}\underline{(2i^4-10i^3)\phantom{-b00000000000.)}}\\4i^3-25i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(4i^3-20i^2)\phantom{))))))))))))}}\\-5i^2+31i-30\phantom{)}\\-~\phantom{()}\underline{(-5i^2+25i)\phantom{........}}\\6i-30\phantom{)}\\-~\phantom{()}\underline{(6i-30)\phantom{}}\\0\phantom{)}\end{array}[/tex]
Therefore, the quotient is:
[tex]2i^3+4i^2-5i+6[/tex]
Imaginary number rule
[tex]i^2=-1[/tex]
Simplify the quotient:
[tex]\implies 2i^3+4i^2-5i+6[/tex]
[tex]\implies 2i^3+4(-1)-5i+6[/tex]
[tex]\implies 2i^3-4-5i+6[/tex]
[tex]\implies 2i^3-5i-4+6[/tex]
[tex]\implies i(2i^2-5)+2[/tex]
[tex]\implies i(2(-1)-5)+2[/tex]
[tex]\implies-7i+2[/tex]
[tex]\implies 2-7i[/tex]
Container A has 600 mL of water and is being filled at a rate of 12 mL per minute. Container B has 1500 mL of water and is being drained at 12 mL per minute. How many minutes, m, will it take for the two containers to have the same amount of water?
Answer:
It will take 37.5 minutes for both containers to reach the same amount of water which is 1050 mL
Step-by-step explanation:
1500 - (12 × 37.5) = 1050
600 + (12 × 37.5) = 1050
What is 3/4-3/10for IXL “L.12
The difference of the given fractions is 9/20.
The given fractions are 3/4 and 3/10.
What is subtraction of fractions?Subtracting fractions include the subtraction of two or more fractions with the same or different denominators. Like fractions can be subtracted directly but for unlike fractions we need to make the denominators same first and then subtract them.
The difference of the given fractions is
3/4 - 3/10
= 15/20 - 6/20
= 9/20
Therefore, the difference of the given fractions is 9/20.
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you are 5 feet tall. if the angle of elevation of a tower is 23 degree and you are standing 10 feet away from the base of the tower, how tall is the tower?
The height of the tower is 9.24 feet. That is, the tower is 9.24 feet tall
Calculating the height of a towerFrom the question, we are to determine how tall the tower is
From the given information,
From a distance of 10 feet, the angle of elevation of the tower at a height 5 feet from the ground is 23 degrees.
Let x represent the length of the tower from a point 5 feet from the ground.
Thus,
The height of the tower will 5 + x feet
Now, we will determine x
Using SOH CAH TOA
tan 23° = x / 10
x = 10 × tan 23°
x = 4.24 feet
Height of the tower is 5 + x feet
Therefore,
Height of the tower = 5 + 4.24 feet
= 9.24 feet
Hence,
The height is 9.24 feet
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A dolphin was swimming at 20 feet below sea level. Then it dove to 45 feet below its original position. Write an expression that represents the change in depth of the dolphin's dive.
The expression that represents the change in depth is |-45 + 20|
How to determine the change in depth expression?From the question, the endpoints are given as
Initial point = 20 feet below the sea level
Final point = 45 feet below the sea level
Rewrite the endpoints properly
This is done as follows
Initial point = -20
Final point = -45
The distance expression between the endpoints is then calculated as
Distance = |Final point - Initial point|
Substitute the known values in the above equation
So, we have the following equation
Distance = |-45 + 20|
Hence, the distance expression is |-45 + 20|
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Use mental math to subtract 3,273-1,256=
Answer:
Ima say 2017
Step-by-step explanation:
PLEASE HELP ASAP express
Answer: 5+3*3(3)-2= 30
Step-by-step explanation: Replacing x with 2 and using PEMDAS
