==================================
Explanation:
Consecutive integers are integers like 1,2,3,... or 6,7,8... so they are integers that follow one after another.
Consecutive odd integers are sequences like 3,5,7,... or 21,23,35... meaning they are odd integers following one after another as close as possible.
If x is some integer, then 2x is always even and 2x+1 is always odd
let 2x+1 be that first odd integer
adding on 2 leads to the next odd integer: (2x+1)+2 = 2x+3
adding on another 2 leads to the next one: (2x+3)+2 = 2x+5
The three expressions
2x+1
2x+3
2x+5
represents three consecutive odd integers. They must add to 105
(2x+1)+(2x+3)+(2x+5) = 105
(2x+2x+2x)+(1+3+5) = 105
6x+9 = 105
6x = 105-9
6x = 96
x = 96/6
x = 16
Meaning that
2x+1 = 2(16)+1 = 33 = first odd integer
2x+3 = 2(16)+3 = 35 = second odd integer
2x+5 = 2(16)+5 = 37 = third odd integer
As a check
33+35+37 = 105
which confirms the answer
Rhoda is asked to graph this system of equations: 5x - 6y = 4 3y + 2x = 7 How many times will the lines intersect? O A. The lines will intersect infinitely many times, because they are identical. O B. The lines will not intersect, because this system has no solutions. O C. The lines will intersect once, because this system has one solution. D. There is no way to tell without graphing the lines first.
Answer:
C. The lines will intersect once, because this system has one solutionStep-by-step explanation:
System of equations:
5x - 6y = 4 3y + 2x = 7The system of linear equations has one solution if the lines intersect, no solution if the lines are parallel, infinitely many solutions if lines are same
Let's put the lines into slope-intercept form to compare
Line1
5x - 6y = 46y = 5x - 4y = 5/6x - 4/6Line 2
3y + 2x = 73y = -2x + 7y = -2/3x + 7/3As we see lines have different slopes so they are different and they intersect once
This system has one solution
Answer:
C. The lines will intersect once, because this system has one solution
Step-by-step explanation:
On Friday, the tent will be on sale for $15 off the price of $219.00
What will Amber's total savings be if she buys the tent on
Friday? Include $0.06 in sales tax on every $1 when
calculating the cost. Show how you found your answer.
Answer:
Step-by-step explanation:
219*0.06=13.14
219+13.14=232.14 regular price after tax
really, she is paying 232.14 regularly, not 219
15*0.06=0.90
15-0.90=14.10
232.14-14.10=218.04 discounted price after tax
this means that she save $14.10 off of the regular price if she buys the tent on friday
can i get brainliest please?
In order to convert this equation to Slope-Intercept Form, you must first isolate y.
What is the first step in isolating y?
3x+2y=4
Use Division Property of Equality to divide the equation by 3.
Use Addition Property of Equality to add 2y to both sides of the equation.
Use the Subtraction Property of Equality to subtract 3x from both sides of the equation.
Use Subtraction Property of Equality to subtract 4 from both sides of the equation.
Answer:
use the subtraction property of equality to subtract 3x from both sides of the equation
Step-by-step explanation:
y is on the left so move everything else to the right side
According to the Subtraction Property, both sides of an equation remain equal following a subtracting of the same amount from both sides of the equation
The first step in isolating y in the equation 3·x + 2·y = 4 is the option;
Use the Subtraction Property of Equality to Subtract 3·x from both sides of the equationReason:
The slope and intercept form of the straight line equation is the the equation in the form y = m·x + c
Where;
m = The slope of the equation
c = The y-intercept
The given equation is 3·x + 2·y = 4
To isolate y, the terms containing y, are placed on one side of the equation, while the other terms are placed on the other side as follows;
First step; 3·x + 2·y - 3·x = 4 - 3·x (Subtraction property of equality)
Second step; 2·y = 4 - 3·x
Third step; [tex]\dfrac{2 \cdot y}{2} = \dfrac{4 - 3 \cdot x}{2}[/tex] → y = 2 - 1.5·x (Division property of equality)
y = 2 - 1.5·x = -1.5·x - 2
y = -1.5·x - 2 Equation in slope and intercept form
Therefore, the first step is use the Subtraction Property of Equality to Subtract 3·x from both sides of the equation
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Miss Kent reminds her students that every two inches on the model represents 25 feet on the actual statue. Based on Martina's measurements what is the area in square feet of the tablet on the actual Statue of Liberty show your work
Answer:
78.125 ft²
Step-by-step explanation:
The dimension of the tablet is given as:
Length = 1 in
Width = ½ in
First,we need to determine the measurements in feet.
Using the scale measurement:
Scale: 2 in =25 ft
Divide both sides by 2
2 in/2 = 25 ft/2
1 in = 12.5 ft
So, Length = 12.5 ft
Divide the scale measurement by 4
2 in/4 = 25 ft/4
½ in = 6.25 ft
So,
Width = 6.25 ft
Area is calculated as:
Area = Length * Width
Area = 12.5 ft * 6.25 ft
Area = 75.125 ft²
y + 1 = - 2x
Rewrite the equation in y=Mx+b form
Answer:
the correct answer is Y=-2x-1
Please help! Chapter test review tomorrow!!!!!
Answer:0D is the answer
Step-by-step explanation:
The switchboard in a Denver law office gets an average of 8.2 incoming phonecalls during the noon hour on Thursdays. Find the probability that more than 4 calls will be received during the noon hour, on some particular Thursday. Assume calls are independent of each other.
Answer:
The probability that more than 4 calls will be received during the noon hour, on some particular Thursday is 0.9113.
Step-by-step explanation:
The random variable X can be defined as the number of incoming phone calls during the noon hour on Thursdays.
The random variable X describes a finite number of occurrences of an event in a fixed time interval.
The random variable X follows a Poisson distribution with parameter λ = 8.2.
The probability mass function of X is:
[tex]P(X=x)=\frac{e^{-8.2}(8.2)^{x}}{x!};x=0,1,2,3...[/tex]
Compute the probability of more than 4 calls as follows:
[tex]P(X>4)=1-P(X\leq 4)[/tex]
[tex]=1-\sum\limits^{4}_{x=0}{\frac{e^{-8.2}(8.2)^{x}}{x!}}\\\\=1-[0.00027+0.00225+0.00923+0.02524+0.05174]\\\\=1-0.08873\\\\=0.91127\\\\\approx 0.9113[/tex]
Thus, the probability that more than 4 calls will be received during the noon hour, on some particular Thursday is 0.9113.
Sales Tax. The sales tax on a purchase of L dollars is 6%. Write an algebraic expression that represents the total amount of sales tax.
Answer:
The value is [tex]T = 0.06L [/tex]
Step-by-step explanation:
From the question we are told that
The sales tax is [tex]k = 6\%[/tex]
Generally the total amount of sales tax is mathematically represented as
[tex]T = 6\% \ of \ L[/tex]
=> [tex]T = \frac{6}{100} * L[/tex]
=> [tex]T = 0.06L [/tex]
Please help with this!
9514 1404 393
Answer:
-11
Step-by-step explanation:
DeYanna's cards are ...
black: 2, 4, for a total value of 2+4 = 6
red: 7, 10, for a total value of -(7+10) = -17
Then the total value of DeYanna's cards is ...
6-17 = -11
X cannot equal 3 on a number line
Answer:
Yes it can
Step-by-step explanation:
math
Answer:
So whats the question
Step-by-step explanation:
Write the equation of a line with slope 3 and y-intercept −3.
PLS I NEED ASAP
HELP ME ANSWER THIS MGA LODI NG BAYAN HAHAHA SERIOUS NA
Answer:
[tex]( {x}^{} + 2) {}^{2} = {x}^{2} + 4x + 4[/tex]
[tex](2x - 3) {}^{2} = {4x}^{2} - 12x + 9[/tex]
[tex] {(3x + 4)}^{2} = {9x}^{2} + 24x + 16[/tex]
[tex] {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} [/tex]
[tex] {(2x + 3y)}^{2} = 4x {}^{2} + 12xy + 9y {}^{2} [/tex]
A "roll" of nickels contains 40 nickels. How much money is a "roll" worth? A 5¢ B. 20¢ c. $1.00 D. $2.00 E. $4.00
Answer:
D
Step-by-step explanation:
a nickel = 5 and 5 x 40 = 200 so it would be 2.00
find the surface area and volume of a rectangular solid with length 10, width 7, height 12
surface area______square inches
volume_____cubic inches
Answer:
Surface area is =548
Volume = 840 in³
Step-by-step explanation:
l × w, l × w, w × h, w × h, l × h, l × h
70 + 70 + 84 + 84 + 120 + 120 = 548
l × w × h = 840
Faheem wants to write equations in the form y = mx + b for the lines passing through point P that are parallel and perpendicular to line t. First he finds the slopes of these 2 lines. What could he do next to find the y-intercepts?
Answer:
Substitute the slope and the coordinates of point P in y = mx + b and then solve for b for each equation.
Step-by-step explanation:
WILL GIVE BRAINLIEST make sure to show all of your work
Let the graph of g be a translation 3 units up, followed by a vertical stretch by a factor of 2 and a reflection in the x-
Axis of the graph of
f(x) =3x^2-3x write a rule for g
G(x) =
15 points!!!!
Answer:
The answer is [tex]g(x)= -6x(x-1)+3[/tex]
Step-by-step explanation:
we know that f(x) is written as [tex]3x^{2}-3x[/tex]
to show that the graph is being translated up, vertically stretching, and reflecting across the x axis, we need to factor the function.
[tex]f(x)= 3x^{2}-3x \\ 3x(x-1)\\[/tex]
now we can incorporate the changes to this graph.
multiply 3x by 2 and -1. (2 for a stretch and -1 for a reflection).
[tex]-6x(x-1)[/tex]
tack on the +3 to show a translation of 3 units up.
[tex]-6x(x-1)+3[/tex]
therefore, [tex]g(x)= -6x(x-1)+3[/tex]
hope this helps!
The rule for the graph of g after all transformations of the function f(x) = 3x² -3x is;
g(x) = 6x² + 3x + 6
The graph of f(x) is given as;
f(x) =3x^2-3x
According to the parameters given;
First, the graph of g is a translation 3 units up, therefore, we have;
g(x) = f(x) + 3g(x) = 3x² - 3x + 3Secondly, followed by a vertical stretch by a factor of 2 and a reflection in the x axis.
This means that the graph must be multiplied by 2 and x values containing x be now regarded as -x
g(x) = 6x² - 3x + 6And a reflection in the x-axis yields;
g(x) = 6(-x)² -3(-x) + 6g(x) = 6x² + 3x + 6Ultimately, the rule for the graph of g is;
g(x) = 6x² + 3x + 6.
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You have been waiting for months. The latest version of your favorite video game comes out today. You have mowed lawns, done extra chores, and saved up gift money. The new game costs $49.99. You have exactly $50.00 saved. So you are good to go, right?
In 3 to 5 sentences explain if you have enough money to buy that game in Pennsylvania where sales tax is 6%. If you have enough money, will you have change? If you do not have enough money, how much more do you need?
if I had enough money, of course I will have change.
Find the percent for the fraction 2/3. Round your answer to the nearest tenth?
Answer: 33.33%
Step-by-step explanation:
Please help!!
Rewrite the expression with rational exponents.
\root(6)(x^(7))
Answer:
[tex]x^{\frac{7}{6} }[/tex]
Step-by-step explanation:
Rob makes $15.20 an hour mowing lawns. How much does Rob make if he mowed lawns for 2 hours on Monday and 3 hours on Tuesday?
Answer:
if rob makes $15.20 an hour and on Monday decides to mow two lawns for 2 hours an easy way to do it is by multiplying 15×2=30 then add 0.20+0.20 you get 30.4 that the amont he makes on monday for tuesday just 15.2+30.4 and get $45.60
can someone help me with a b and c please
Answer:
c.in this 2014,396.12million pets were owned
What’s 96 dived by 7
Answer:
Exact Form:
96 /7
Decimal Form:
13.71428571 …
Mixed Number Form:
13 5 /7
Step-by-step explanation:
Reduce the expression, if possible, by cancelling the common factors.
More than 3, 000, 000, 000 pencils are manufactured in country A annually. Write this number in scientific notation
Answer:
3.0 times 10 with 8 as the exponent
Step-by-step explanation:
Count the amount of times you move the decimal point.
That number is the exponent number.
If you are counting left it is positive, if you are counting right it is negative.
Answer:
Step-by-step explanation:
Count the number of zeros.
There are 9 of them.
So the answer is 3 * 10^9
Write the equation of a line perpendicular to 6y-2x=-8 and passes through the point(-2,1) in slope-
intercept form
Answer:
y = -3x + 17/10
Step-by-step explanation:
First you want to move the 2x to the other side of the equal sign for the proper way of slope-intercept form. Which makes it 6y=2x-8.
You still want to make sure that y is by itself so you divide the whole equation by 6 which makes it y=1/3x-8/6.
We have to find the slope of the a perpendicular line now and to do so, you must take the slope of the given line and make it into the opposite reciprocal.
To do that you take 1/3 and reciprocate it, which makes it 3.
Then flip the sign to make it opposite. Like making a positive into a negative and a negative into a positive. Therefore the slope of the perpendicular line is -3.
Now we must make it past through point (-2,1). To do that you have to adjust the y-intercept. Because of that, the y-intercept is 1.7 or 17/10.
The equation of the slope is y=-3x+17/10
What is 0.934 (34 repeating) as a fraction?
Answer:
185 ove r198
Step-by-step explanation:
A contractor has submitted bids on three state jobs: an office building, a theater, and a parking garage. State rules do not allow a contractor to be offered more than one of these jobs. If this contractor is awarded any of these jobs, the profits earned from these contracts are $10 million from the office building, $5 million from the theater, and $2 million from the parking garage. His profit is zero if he gets no contract. The contractor estimates that the probabilities of getting the office building contract, the theater contract, the parking garage contract, or nothing are .15, .30, .45, and .10, respectively.
1. Write the probability distribution of x .
2. Find the mean and standard deviation of x .
Answer:
The probability distribution of x is
Profits in millions (x) Probability of getting contract (P(x))
$10 0.15
$ 5 0.30
$ 2 0.45
$ 0 0.10
The mean is [tex]E(X) = 3.9 millions [/tex]
The standard deviation is [tex]s = 3.01 \ millons [/tex]
Step-by-step explanation:
Generally the probability distribution of x is
Profits in millions (x) Probability of getting contract (P(x))
$10 0.15
$ 5 0.30
$ 2 0.45
$ 0 0.10
Generally the mean is mathematically represented as
[tex]E(X) = x * p(x)[/tex]
=> [tex]E(X) = [10 * 0.15 ] + [5 *0.30 ] + [2 * 0.45 ] + [0 * 0.10] [/tex]
=> [tex]E(X) = 3.9 millions [/tex]
Now
[tex] E(X^2) = x^2 * p(x)[/tex]
=> [tex] E(X^2) = (10 ^2 * 0.15) + (5 ^2 * 0.30) +(2 ^2 * 0.45) + (0 * 0.10)[/tex]
=> [tex] E(X^2) = 24.3 [/tex]
Gnerally the variance is mathematically represented as
[tex]V(X) = E(X^2) - [E(X)]^2[/tex]
=> [tex]V(X) = 24.3 - 3.9^2[/tex]
=> [tex]V(X) = 9.09 [/tex]
Gnerally the standard deviation is mathematically represented as
[tex]s = \sqrt{V(X)}[/tex]
=> [tex]s = \sqrt{9.09[/tex]
=> [tex]s = 3.01 [/tex]
He started by making mini sandwiches. If he has 4 friends coming over and he made 3
sandwiches for each one of them, how many sandwiches did he make?
1 point
Your answer
Answer: 12
Step-by-step explanation:
if 1 friend = 3 sandwiches, and you have 4 friends, you multiply the 3 by 4 and get 12
Joe deposits $700 into an account that pays simple interest at a rate of 4% per year. How much will he be paid in the first 3 years?
Answer:
784
Step-by-step explanation:
Will award brainiest if you answer correctly
Answer:
7 units because (6x-22)=(2×+6)