Answer:
y = 4. So this is your width.
Step-by-step explanation:
Use the distributive property to do 2(2y-3) = 2*2y-2*3 = 4y-6. So we have
4y-6+2y = 18. Combine like terms 4y and 2y to get 6y.
6y-6 = 18. Add 6 to both sides to solve for 6y
6y = 24. Divide by 6 to solve for y
y = 4. So this is your width.
length = x
________________
| |
y | | width = y
| |
_________________
x
The width of the rectangle is determined to be 4 inches.
To find the width of the rectangle, we need to set up equations based on the information given. The length (L) is described as being 3 inches less than twice the width (W), so we can express that as L = 2W - 3. The perimeter (P) of a rectangle is calculated as P = 2L + 2W. We are told the perimeter is 18 inches, so we have 18 = 2(2W - 3) + 2W. Simplifying this equation, we get 18 = 4W - 6 + 2W, which combines to 18 = 6W - 6. Adding 6 to both sides gives us 24 = 6W, and dividing both sides by 6 yields W = 4 inches. Therefore, the width of the rectangle is 4 inches.
The process used here is similar to working through proportions and scale factors. For instance, if one is working with scale models, as in the miniature fish pond example, the scale factor is used to determine the dimensions in the model based on actual size dimensions. However, in this case, the given equations allowed us to find the width directly.
How do we express one-half of the difference of a number cubed and one?
Answer:
1/2(x^3 - 1) or we could write it as (x^3 - 1) / 2.
Step-by-step explanation:
A number cubed is x^3. Difference of this and 1 is x^3 - 1.
Finall we have 1/2 of this:
= 1/2(x^3 - 1) or we could write it as (x^3 - 1) / 2.
Answer:
[tex]\frac{x^3-1}{2}[/tex]
Step-by-step explanation:
We must follow what the statement asks us, starting from the last thing and going forward from there.
A number cubed: [tex]x^3[/tex]
The difference of a number cubed and one: [tex]x^3-1[/tex]
And finally:
one-half of the difference of a number cubed and one, this would be one half of the expression we already found:
[tex]\frac{x^3-1}{2}[/tex]
The lines shown below are parallel. If the green line has a slope of --, what is
the slope of the red line?
Answer: the answer would be -1/11
Step-by-step explanation: the reason being the slope of the green is a negative slope because it is going down ward not upwards therefore it is negative and because the the lines are parallel they are equal so the slope of both lines are -1/11
Factor completely. 81x^4 − 1
The expression 81x⁴ - 1 can be factored completely by identifying it as a difference of squares. First, factor it into (9x² + 1)(9x² - 1) and then further factor (9x² - 1) into (3x + 1)(3x - 1). The final factored form is (9x² + 1)(3x + 1)(3x - 1).
We are given the expression 81x⁴ - 1 and need to factor it completely. This is a difference of squares, which can be written as:
81x⁴ - 1 = (9x²)² - 1²The difference of squares formula is a²- b² = (a + b)(a - b). Applying this formula, we get:
(9x²)² - 1² = (9x² + 1)(9x² - 1)Next, notice that 9x²- 1 is also a difference of squares:
9x² - 1 = (3x)²- 12Again using the difference of squares formula, we get:
(3x)² - 1 = (3x + 1)(3x - 1)Putting everything together, the complete factorization of 81x⁴ - 1 is:
81x⁴ - 1 = (9x² + 1)(3x + 1)(3x - 1)gerard’s baby brother spends 7/8 of his day sleeping. How many hours does his baby brother sleep? i
[tex] \frac{7}{8} \times 24 = 21 \\ [/tex]
You multiply 7/8 to the number of hours in a day which 24
Gerard's baby brother sleeps for 7/8 of the day, which equals 21 hours when calculated (7/8 * 24 hours).
Explanation:Gerard's baby brother spends 7/8 of his day sleeping.
To calculate how many hours this is, we need to know how many hours there are in a full day.
A full day has 24 hours. So, we multiply 7/8 by 24 to find out the total hours spent sleeping.
Here's the step-by-step calculation:
Multiply the fraction of the day spent sleeping (7/8) by the total number of hours in a day (24).7/8 * 24 = 21 hours.Therefore, Gerard's baby brother sleeps for 21 hours a day.
Which shows the correct substitution of the values a,b and c from the equation 1=-2x+3x^2+1
Answer:
a = 3 , b = -2 , c = 0
Step-by-step explanation:
The given equation is:
1 = -2x + 3x^2 + 1
To find the correct substitution values of a, b and c. We need to convert t into the standard form first.
Standard form of a Quadratic equation is written as:
ax^2 + bx + c = 0 (where a is not equal to zero)
Converting the given equation into its standard form:
1 = -2x + 3x^2 + 1
-2x + 3x^2 + 1 - 1 = 0
3x^2 - 2x + 0 = 0
OR 3x^2 - 2x = 0
According to the equation
a = 3 , b = -2 , c = 0
Slope-intercept form of the equation for the line?
Answer:
[tex]\large\boxed{y=-\dfrac{3}{10}x+\dfrac{1}{2}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
b - y-intercept
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points from the graph (-5, 2) and (5, -1).
Substitute:
[tex]m=\dfrac{-1-2}{5-(-5)}=\dfrac{-3}{10}=-\dfrac{3}{10}[/tex]
We have the equation in form:
[tex]y=-\dfrac{3}{10}x+b[/tex]
Put the coordinates of the point (5, -1) to the equation:
[tex]-1=-\dfrac{3}{10}(5)+b[/tex]
[tex]-1=-\dfrac{3}{2}+b[/tex]
[tex]-\dfrac{2}{2}=-\dfrac{3}{2}+b[/tex] add 3/2 to both sides
[tex]\dfrac{1}{2}=b\to b=\dfrac{1}{2}[/tex]
Consider this equation: 2x + 2 = 11 - x
Now consider the equation written as: 3x + 2 = 11
Which of the following is the correct property of equality that justifies rewriting the equation?
Answer: Addition property of equality
Step-by-step explanation: You added the x to the other side, which is clearly using addition. Hope this help!
A shipping company charges $6 to ship a package that weighs up to 1 pound and $2 for each additional pound or portion of
a pound. Which equation represents this situation?
Of(x) = 8+2[x-1, where x > 0
Of(x) = 6+2Lx-1), where x > 0
O (x) = 6+2[x+1), where x > 0
Of(x) = 6+2x+1), where x > 0
Answer:
6 + 2[x - 1) , where x > 0. I think.
Answer:
f(x) = 6+2Lx-1), where x > 0
Step-by-step explanation:
To answer this you need to understand two things, variables and constants, the constant price of the shipping is $6 so that is a constant, now the company would charge you with $2 for every fraction or pound extra over the one pound that you are charged for the $6, so your variable is the weight of the package, and this will be expressed by X
So the function would look like this:
[tex]f(x)= 6+ 2(x-1) when x > 0[/tex]
If the weight of your package is less than oneyou´d just pay the 6 bucks, since when the weight is bigger than 1 pound you would pay 2 extra bucks, you just need yo know how many extra buck you´ll pay that´s why it´s expressed with the Lx-1)
Find the difference:
[tex] \sqrt[ {8ab}^{3} ]{{ac}^{2} } - \sqrt[ {14ab}^{3} ]{ {ac}^{2} } [/tex]
Answer: The difference cannot be found because the indices of the radicals are not the same.
Step-by-step explanation:
To find the difference you need to subtract the radicals. But it is important ot remember the following: To make the subtraction of radicals, the indices and the radicand must be the same.
In this case you have these radicals:
[tex]\sqrt[ {8ab}^{3} ]{{ac}^{2} }- \sqrt[ {14ab}^{3}]{{ac}^{2} }[/tex]
You can observe that the radicands are the same, but their indices are not the same.
Therefore, since the indices are different you cannot subtract these radicals.
PLEASE HELP PLEASE
Tricia has the same number of nickels and dimes in her pocket. The coins total $3.60. How many of each coin does she have?
A) 12 nickels and 12 dimes
B) 24 nickels and 24 dimes
C) 36 nickels and 36 dimes
D) 48 nickels and 48 dimes
Answer:
B
Step-by-step explanation:
Find out the total value of each option and see which one gives a total of $3.60
For A, 12 nickels + 12 dimes = 12 x $0.05 + 12 x $0.10 = $1.80 ≠ $3.60
For B, 24 nickels + 24 dimes = 24 x $0.05 + 24 x $0.10 = $3.60 (correct)
For C, 36 nickels + 36 dimes = 36 x $0.05 + 36 x $0.10 = $5.40 ≠ $3.60
For D, 48 nickels + 48 dimes = 48 x $0.05 + 48 x $0.10 = $7.20 ≠ $3.60
Answer:
For my opinion, the best option it B.
Choose the required figure.
A right triangle circumscribed about a circle:
Answer:I think that in this problem you need a right angle with a circle in it
71, 92, 94, 93, 98, 85, 66, 70, 68, 93, 87, 71, 85, 52, 61, 62, 85, 69, 95, 79
Calculate the mean for the data list above.
ОА. 82
ОВ. 78.8
Ос. 93
Op. 87
To find the mean you must add all the numbers together then divide the sum by the total amount of numbers in the data set
71 + 92 + 94 + 93 + 98 + 85 + 66 + 70 + 68 + 93 + 87 + 71 + 85 + 52 + 61 + 62 + 85 + 69 + 95 + 79 = 1576
There are at total of 20 numbers in this data set so you must divide 1576 by 20
1576 / 20 = 78.8
Hope this helped!
~Just a girl in love with Shawn Mendes
what is the value of x?
Answer:
A. 68°
Step-by-step explanation:
sum of angles inside a triangle = 180°
75 + 37 + x = 180
x = 180 - 75 - 37
= 68°
The sum of angles inside a triangle is 180°. so option is A. 68°.
What is the angle sum property?The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.
Given angles are; 75 and 37.
The sum of angles inside a triangle = 180°
75 + 37 + x = 180
x = 180 - 75 - 37
x = 68°
Learn more about the triangles;
https://brainly.com/question/2773823
#SPJ2
The given line passes through the points (-4,-3) and (4,1) what is the equation in point-slop
e form, of the line that is perpendicular to the given line and passes through the point (-4,3)?
let's bear in mind that perpendicular lines have negative reciprocal slopes...... hmmmm what's the slope of the given line anyway?
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-3)}{4-(-4)}\implies \cfrac{1+3}{4+4}\implies \cfrac{4}{8}\implies \cfrac{1}{2} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{\cfrac{1}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{2}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{2}{1}\implies -2}}[/tex]
so, we're really looking for a line whose slope is -2 and runs through (-4 , 3)
[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{-3})~\hspace{10em} slope = m\implies -2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-3)=-2[x-(-4)] \implies y+3=-2(x+4) \\\\\\ y+3=-2x-8\implies y=-2x-11[/tex]
2 arcs of a circle are congruent if and only if their Associated chords are perpendicular
This is False
That is because the Arcs can only be congruent if the Chords are also Congruent
Answer:
FALSE
Step-by-step explanation:
f(-5) if f(x)=|x+1|
Answer:
The answer is 6.
Step-by-step explanation:
Plug in: f(-5)=|-5+1|
Because this an absolute problem -5 is positive within |x|
so therefore f(-5)= |6|
Which graph represents a function with direct variation?
Answer:
The graph that represent direct variation in the attached figure
Step-by-step explanation:
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
The graph that represent direct variation in the attached figure
Answer:
option d
Step-by-step explanation:
Order these values given in scientific notation from least to greatest.
1.49 x 10^5
1.05 x 10^-6
3.81 x 10^8
2.44 x 10^-9
3.75 X 10^4
Answer:
2.44x10^-9
1.05x10^-6
3.75x10^4
1.49x10^5
3.81x10^8
Final answer:
Values in scientific notation are ordered by their exponent values. First, compare the sign and size of the exponents, and then compare the coefficients if necessary. The ordered values from least to greatest are: 2.44 x 10^-9, 1.05 x 10^-6, 3.75 x 10^4, 1.49 x 10^5, 3.81 x 10^8.
Explanation:
To order the given values in scientific notation from least to greatest, we look at the exponent to determine their relative sizes. The values with negative exponents will be smaller than those with positive exponents, and among those with the same sign exponents, the one with the smaller absolute value of exponent is smaller. Then we compare the coefficients if necessary, that is if the exponents are the same.
[tex]2.44 x 10^-9[/tex]
[tex]1.05 x 10^-6[/tex]
[tex]3.75 x 10^4[/tex]
[tex]1.49 x 10^5[/tex]
[tex]3.81 x 10^8[/tex]
Given f(x) = 17-X^2what is the average rate of change in f(x) over the interval [1, 5]?
Answer:
-6
Step-by-step explanation:
The formula for finding the rate of change is:
[tex]Rate\ of\ change=\frac{f(b)-f(a)}{b-a}[/tex]
The interval is [1,5]
So, a = 1 and b=5
[tex]f(1) = 17 - (1)^2\\ =17-1\\=16\\f(5) = 17-(5)^2\\=17-25\\=-8[/tex]
Putting in the values
[tex]Rate\ of\ change = \frac{f(5)-f(1)}{5-1} \\=\frac{-8-16}{5-1}\\= \frac{-24}{4}\\ =-6[/tex]
The average rate of change is -6 ..
Answer:
-6
Step-by-step explanation:
Which of the following is the point-slope form of the line?
Answer:
A
Step-by-step explanation:
We can see that the slope is positive, which means that the x-term must be positive.
If you expand and simply both equations into the form y = mx + b, you will find that m is positive for A and negative for B, hence A is the correct answer.
Use substitution to write an equivalent quadratic equation.
(3x + 2)2 + 7 (3x + 2) – 8 = 0
-
u2 + 74 - 8 = 0, where u = (3x + 2)2
u2 + 7u - 8 = 0, where u = 3x + 2
u2 + 70 - 8 = 0, where u = 7(3x + 2)
lu² +4-8=0
What’s the answer?
For this case we can make a change of variable, to obtain a quadratic equation of the form:
[tex]ax ^ 2 + bx + c = 0[/tex]
Making the change:[tex]u = 3x + 2[/tex]
Substituting the change we have:
[tex]u ^ 2 + 7u-8 = 0[/tex]
Thus, the correct option is:[tex]u ^ 2 + 7u-8 = 0[/tex]where [tex]u = 3x + 2[/tex]
Answer:
Option B
Answer:
second option: [tex]u^{2}+7u-8=0[/tex]
Step-by-step explanation:
We have the equation given:
[tex](3x+2)^{2}+7(3x+2)-8=0[/tex]
We can replace the variable in the quardatic equation.
So,
[tex]Putting\\u=3x+2[/tex]
Putting u in place of 3x+2 will give us:
[tex](u)^{2}+7(u)-8=0[/tex]
So the answer is:
[tex]u^{2}+7u-8=0[/tex]
So, the second option is correct ..
there 240 students in the middle school band. The band director is dividing the students into groups of 10. Into how many groups will the band director divide the students?
Answer:
Step-by-step explanation:
1 group = 10 students
x group = 240 students.
1/x = 10/240 Cross multiply
10x = 240 Divide by 10
10x/10=240/10 Do the division
x = 24
What is the vertex of the graph of g(x) = |x – 8| + 6? A (6, 8) B (8, 6) C (6, –8) D (–8, 6)
its (8,6)
to get your x, you set what's in the absolute value to 0
so
x-8=0
then subtract 8 on both sides to get
x=8
then your y is just the number to the right of the absolute value so
y=6
Answer: Option B
(8, 6)
Step-by-step explanation:
By definition, for an absolute value function of the form
[tex]f (x) = | x-h | + k[/tex]
the vertex of f(x) will always be at the point
(h, k)
In this case we have the function of value ansoluto:
[tex]g(x) = |x - 8| + 6[/tex]
Therefore in this case
[tex]h=8\\k=6[/tex]
Finally the vertex of the function g(x) is: (8, 6)
The answer is the option B
Billy is helping to make pizzas for a school function. He's made 25 pizzas so far. His principal asked him to make at least 30 pizzas but no more than 75. Solve the compound inequality and interpret the solution.
30 ≤ x + 25 ≤ 75
Answer: Number of pizzas would be less than 5 but not more than 50.
Step-by-step explanation:
Since we have given that
Number of pizzas so far = 25
His principal asked him to make at least 30 pizzas but no more than 75.
According to question, we have
30 ≤ x + 25 ≤ 75
First we subtract 25 from both the sides:
[tex]30-25\leq x \leq 75-25\\\\=5\leq x\leq 50[/tex]
Hence, number of pizzas would be less than 5 but not more than 50.
The solution to the compound inequality is 5 x 50.
The compound inequality given is 30 x 25 75, where x represents the number of additional pizzas Billy needs to make to satisfy the principal's request. To solve for x, we need to isolate x in the inequality.
First, we subtract 25 from all parts of the compound inequality to shift the 25 pizzas already made to the other side of the inequality. This gives us:
30 - 25 x + 25 - 25 75 - 25
Simplifying the inequality, we get:
5 x 50
This means that Billy needs to make at least 5 more pizzas to reach the minimum requirement of 30 pizzas (since 25 + 5 = 30) and no more than 50 additional pizzas to not exceed the maximum allowed number of 75 pizzas (since 25 + 50 = 75).
Therefore, the number of additional pizzas Billy should make is any integer value between 5 and 50, inclusive. This ensures that the total number of pizzas made will be within the principal's specified range of 30 to 75 pizzas."
Which expresión is equivalente to (4g3 h2 k4)3
Answer: [tex]\bold{64g^9h^6k^{12}}[/tex]
Step-by-step explanation:
[tex]\text{Apply the product rule:} (a^b)^c=a^{b*c}\\\\(4g^3h^2k^4)^3\\\\=4^{(1*3)}g^{(3*3)}h^{(2*3)}k^{(4*3)}\\\\=4^3g^9h^6k^{12}\\\\=64g^9h^6k^{12}[/tex]
Maria has three red dresses, 2 white dresses, and one blue dress . What is the probability she will wear a blue dress at her party?
Answer:
1/6
Step-by-step explanation:
there are 6 dresses altogether and 1 blue dress.
Answer:
[tex]\frac{1}{6}[/tex]
Step-by-step explanation:
We have been given that Maria has three red dresses, 2 white dresses, and one blue dress. We are asked to find the probability that Maria will wear a blue dress at her party.
[tex]\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}[/tex]
We know that number of blue dresses is 1, so number of favorable outcomes is 1.
Total dresses = 3 Red dresses + 2 White dresses + 1 Blue dress = 6 dresses.
[tex]\text{Probability that Maria will wear a blue dress at her party}=\frac{1}{6}[/tex]
Therefore, our required probability is [tex]\frac{1}{6}[/tex].
Determine the range of the function graphed above.
A. [4,∞)
B. [-4,0]
C. [0,4]
D. (-∞,4]
Answer:
D. (-∞,4]
Step-by-step explanation:
The range is the y values
The lowest y values is negative infinity
The highest y values is 4
( - inf, 4]
We use the parentheses since we cannot get to negative infinity, the bracket since we reach 4
6a - 5b when a = -3 and b = 4
Given.
6a - 5b
Plug in values.
6(-3) - 5(4) =
-18 - 20 =
-38
For this case we have the following expression:
[tex]6a-5b[/tex]
We must evaluate the expression when:
[tex]a = -3\\b = 4[/tex]
Then, replacing the values we have:[tex]6 (-3) -5 (4)[/tex]
Taking into account that according to the law of the signs of multiplication, it is fulfilled that:
[tex]+ * - = -[/tex]
So:
[tex]-18-20 =[/tex]
Equal signs are added and the same sign is placed:
-38
Answer:
-38
A license plate consists of three letters followed by
three digits. How many license plates are possible if
no letter may be repeated?
Answer: 15,600,000
Step-by-step explanation:
26 x 25 x 24 =15,600 combinations of letter with no repeats
10 x 10 x 10 = 1000 with repeating numbers
15,600 x 1000 = 15,600,000
The total number of possible license plates is 26*25*24*10*9*8.
The number of possible license plates with no repeated letters can be calculated by multiplying the number of choices for each position. Since no letter can be repeated, the choices for the first position would be 26 letters, then 25, and then 24 for the three positions. For the digits, there are 10 choices for each position.
So, the total number of possible license plates would be 26*25*24*10*9*8.
7s+4m+2l=24
5s+3m+6l=30
3s+7m+10l
Answer:
486 - 160l
Step-by-step explanation:
m = 90 - 32l
s = -48 + 18l
l = stationary
Combine like-terms, evaluate, then you will arrive at this crazy answer.