Final answer:
The expanded form of the algebraic expression (2x + 1)(3x - 8) is 6x² - 13x - 8.
Explanation:
To expand the algebraic expression (2x + 1)(3x - 8), we'll use the distributive property, which states that a(b + c) = ab + ac. First, we multiply 2x by each term in the second parentheses (3x and -8), and then we multiply 1 by each term in the second parentheses. Let's do this step by step:
Multiply 2x by 3x to get 6x².Multiply 2x by -8 to get -16x.Multiply 1 by 3x to get 3x.Multiply 1 by -8 to get -8.Now, we combine these terms:
6x² - 16x + 3x - 8
Simplify by combining like terms:
6x² - 13x - 8
Therefore, the expanded form of (2x + 1)(3x - 8) is 6x² - 13x - 8.
the larger of two numbers is 7 less than three times the smaller number. if the sum of the numbers is 61, find the numbers
Let X = the large #
Y = the small #
We have 2 unknowns, therefore we need 2 equations to solve for them:
X + Y = 61
X = 3Y - 7
Using the substitution method we get:
X + Y = 61 original equation
(3Y - 7) + Y = 61 substituting for X
4Y - 7 = 61 combine like terms
4Y - 7 + 7 = 61 + 7 add 7 to both sides
4Y = 68 simplify
4Y/4 = 68/4 divide both sides by 4
Y = 17 solve for Y
X + Y = 61 original equation
X + 17 = 61 replace Y with 17
X + 17 - 17 = 61 - 17 subtract 17 from both sides
X = 44 solve for X
Check your answer:
X + Y = 61 X = 3Y - 7
44 + 17 = 61 44 = 3(17) - 7
61 = 61 check! 44 = 51 - 7
44 = 44 check!
Therefore, the larger #(X) = 44 and the smaller #(Y)= 17.
If 80 is decreased by 30%, what is the new amount?
Answer:
The answer is 56.. hope I helped thanks and bye.
Twice a number decreased by 8 is 2 less than half the number. What is the number?
Answer:
4
Step-by-step explanation:
with th information given we can express the equation:
[tex]2x-8=\frac{x}{2} -2[/tex]
where [tex]x[/tex] is the unknown number.
to clear for [tex]x[/tex] first we multiply the equation by 2, to eliminate the fraction:
[tex]2(2x-8=\frac{x}{2}-2 )\\4x-16=x-4[/tex]
moving all terms with [tex]x[/tex] to the left:
[tex]4x-x-16=-4\\3x-16=-4[/tex]
and adding +16 to each side:
[tex]3x-16+16=-4+16\\3x=12[/tex]
and finally, dividing by 3
[tex]x=\frac{12}{4} =4[/tex]
the number is 4.
When Jose and Sean were 5 years old Jose was 1 1/2 inches taller than Sean then Jose grew at an average of 2 3/4 inches per year until he was 13 years old.jose was 63 inches tall when he was 13 years old. How tall was Sean when he was 5 years old
Sean's height when he was 5 years old is given as follows:
39.5 inches.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation shown as follows:
y = mx + b
The coefficients m and b have the meaning presented as follows:
m is the slope of the function, representing the increase/decrease in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, representing the numeric value of the function when the input variable x has a value of 0. On a graph, it is the value of y when the graph of the function crosses or touches the y-axis.Jose grew at an average of 2 3/4 inches per year, hence the slope is given as follows:
m = 2.75.
Thus:
J(x) = 2.75x + b.
Jose was 63 inches tall when he was 13 years old(8 years after he was 5 years old), hence the intercept b is given as follows:
63 = 2.75(8) + b
b = 63 - 2.75 x 8
b = 41 inches.
When Jose and Sean were 5 years old Jose was 1 1/2 inches taller than Sean, hence Sean's height is given as follows:
41 - 1.5 = 39.5 inches.
More can be learned about linear functions at https://brainly.com/question/15602982
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Solve the following equation then place the correct number in the box provided 3(2x+5)> 2(x+6)
The answer is actually x ≥ -3/4
Tell whether the two quantities vary directly. Explain your reasoning. The cafeteria provides three meals per day.
Answer:
The cafeteria provides three meals per day.
Reason 1
Yes, they vary directly
As number of days increases ,Total number of meals i.e
1st day ⇒ 3
2nd day⇒6
3 rd day⇒9
4th day⇒12
......................
.........................
increases.
Total number of Meals = k×Number of days
But there is another possibility also
Reason 2
1 st day ⇒ 3
2nd day ⇒3
3rd day⇒ 3
.....................
.....................
As you can see from the above expression On each day number of meals is
constant.
So we can say that ,
On each Day=Constant amount of meal=3
So, there is no Proportionality between Days and Meal.
Please help me and let me know if number a is wrong or not
its kinda upside down
Identify the slope of the line shown in the graph below
a
slope = 5
b
slope = undefined
c
slope = 0
d
slope = 1
e graph shows the altitude of a helicopter over time.
A graph measuring altitude and time. A line runs through coordinates (0, 10,000) and (15, 4000) and shows a decrease in altitude as time increases
What is the slope of the line and what does it mean in this situation?
The slope is –2000 . This means that the helicopter descends 2000 ft each minute.
The slope is –400 . This means that the helicopter descends 400 ft each minute.
The slope is 400. This means that the helicopter ascends 400 ft each minute.
The slope is 2000. This means that the helicopter ascends 2000 ft each minute.
Let
x-------> the time
y-------> the altitude of a helicopter
Step 1
Find the slope of the line
we know that
the slope m of the line between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
we have
[tex](x1,y1)=(0,10,000)\\(x2,y2)=(15,4,000)[/tex]
substitute in the formula
[tex]m=\frac{(4,000-10,000)}{(15-0)}[/tex]
[tex]m=\frac{(-6,000)}{(15)}[/tex]
[tex]m=-400\frac{feet}{minute}[/tex]
therefore
the answer is the option
The slope is [tex]-400[/tex] . This means that the helicopter descends [tex]400[/tex] ft each minute.
Answer:
-400
Step-by-step explanation:
Round 146.56 to the nearest tenth.
Because the 6 in the hundredths place is bigger than 5( the maximum) the tenths place will automatically round up to the next following number. The answer will be 146.6
Jackie had $135 to spent at the mall she spent 29% of the money on a dress. Jackie spent $_ on the dress ?
Jackie spent $39.15 on the dress.
Just the two circled ones please- unit rates. Also can someone explain how they got the answer? I am having trouble with these two
4.
In both cases divide the number of laps by the number of minutes to find the unit rate in laps per minute.
30 laps in 12 minutes: (30 laps)/(12 minutes) = 2.5 laps/minute
120 laps in 48 minutes: (120 laps)/(48 minutes) = 2.5 laps per minute
The rates are equivalent.
6.
I can't see the dimensions of the picture.
Do this:
Do these two divisions.
Divide the width by the length of the poster and of the picture.
Poster: (60 inches)/(100 inches) = 0.6
Picture: (width of picture)/(length of picture) = ?
If the second division also equals 0.6, then the ratios are equivalent.
A washer and a dryer cost 634 dollars combined. The washer cost 66 dollars less than the dryer. What is the cost of the dryer?
Steps to Solve:
1. 634 / 2 = 317
2. 317 + 66 = 383
Answer:
A = $383
Notes:
Read the question, this problem is not that hard to solve!
Sal washed 5 cars in 50 minutes unit rate
it took him 10 minutes to wash each car
What’s the place value of 3 in 167.43
Note the place values:
1 : hundred
6 : tens
7 : ones
.
4 : tenths
3 : hundredths
Look at the place value for 3. It is in the hundredths value, therefore, Hundredths is your answer
~Rise Above the Ordinary
Quadrilateral RSTU has vertices R(1,3), S(4,1), T(1,-3) and U(-2,-1). Is it true or false that this is a rectangle because the diagonals are congruent and the sides RS and ST are perpendicular?
Given vertices ofQuadrilateral RSTU as R(1,3), S(4,1), T(1,-3) and U(-2,-1).
We need to check if diagonals are congruent.
The coordinates of verticales diagonal RT are R(1,3) and T(1,-3).
The coordinates of verticales diagonal SU are S(4,1), and U(-2,-1),
By applying distance formula:
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
RT = [tex]=\sqrt{\left(1-1\right)^2+\left(-3-3\right)^2}[/tex]=[tex]\sqrt{36}[/tex]
RT = 6
SU [tex]=\sqrt{\left(-2-4\right)^2+\left(-1-1\right)^2}[/tex].
[tex]=2\sqrt{10}[/tex].
Diagonal RT is not congruent to Diagonal SU.
Therefore, Quadrilateral RSTU is not a rectangle because the diagonals are not congruent.
So, it is False.
Final answer:
The quadrilateral RSTU is not a rectangle due to not having all right angles, making it a parallelogram.
Explanation:
The given quadrilateral RSTU is not a rectangle. To determine if it's a rectangle, we need to check if all angles are right angles, which is not the case here even if the diagonals are congruent and RS and ST are perpendicular.
Since the angles are not all right angles, the shape formed is a parallelogram. A rectangle must have all angles as right angles, so these conditions do not define a rectangle.
which equation is in slope intercept form and represents a line with slope 3 through the point (9,-4)?
Answer:
y = 3x - 23
Step-by-step explanation:
y + 4 = 3(x - 9)
y + 4 = 3x - 27
y = 3x - 23
which is the graph of linear inequality 2y>X-2
[tex]2y > x-2\qquad|:2\\\\y > \dfrac{1}{2}x-1[/tex]
for < or > line is - - - - - - - -
for ≤ or ≥ line is _________
for < or ≤ shaded below the line
for > or ≥ shaded above the line
Therefore your answer is the third graph.
Answer:
Option C. is the correct option.
Step-by-step explanation:
The given inequality is 2y > x - 2
1). As we know on a graph > (greater than) sign reflects the shaded part above the line
and < (less than) tells about the shaded region below the line.
2). If there is a sign of equality ≥ or ≤ then the line is denoted by a solid line in the graph.
When signs are in the form of > or < only then line will be in the dotted form.
By these rules we can easily say shaded area above the dotted line represents the solution area of the inequality 2y > x - 2.
Therefore, option C is the answer.
name 5 consecutive integers where the middle one is 0
-52, -37, 0, 23, 67
Any numbers would work as long as their in correct order, and 0 is the middle number. Remeber that with negatives, ordering is different!
How can you use a number line to compare any two numbers
no. you many not .....
You can use a number to compare two numbers by figuring out which one is least and which one is greater or if something is positive or negative.
y=5 horizontal or vertical? x=3 horizontal or vertical?
Y= vertical & x= horizontal
y=vertical and x=horizontal
Hope this helps ^_^
Please Help <3 Please Help <3
Hey, there! For this question, we can just start by plugging in the known values. [tex](f + g)(x)[/tex] can be rewritten as [tex](\frac{x}{2} - 3 + 3x^2 + x - 6)(x)[/tex].
Combine like terms: [tex](\frac{x}{2} + x - 3 - 6 + 3x^2)(x)[/tex]
If you add x to [tex]\frac{x}{2}[/tex], x will become [tex]\frac{2x}{2}[/tex], which means that x/2 + x = 3/2x.
--> [tex](\frac{3}{2}x - 9 + 3x^2)(x)[/tex]
If you rearrange this, then your answer will be option b. Hope this helps.
f(x) = [tex]\frac{x}{2}[/tex] - 3
+ g(x) = 3x² + x - 6
f(x) + g(x) = 3x² + [tex]\frac{x}{2}[/tex] + x -3 - 6
= 3x² + [tex]\frac{3}{2}x[/tex] - 9
Answer: B
what's 5÷251? could someone help me?
well 251 cannot go into 5 as a whole number because its way bigger than 5 so, it will be a decimal.
Your answer is
5/251 = 0.01992031872
Riley has a piece of yarn that is 6 1 2 ft long. She wants to cut the yarn into sections that are each 1 4 ft long. How many sections will the yarn be cut into?
Answer: The yarn will be cut into 26 sections.
Step-by-step explanation:
Since we have given that
Length of piece of yarn = [tex]6\dfrac{1}{2}=\dfrac{13}{2}\ feet[/tex]
Length of section = [tex]\dfrac{1}{4}\ feet[/tex]
We need to find the number of sections that will be cut into:
So, the number of sections would be
[tex]\dfrac{13}{2}\div \dfrac{1}{4}\\\\=\dfrac{13}{2}\times \dfrac{4}{1}\\\\=13\times 2\\\\=26[/tex]
Hence, the yarn will be cut into 26 sections.
Find the coordinates of the midpoint of the segment with the given endpoints A(1,2) and B(3,6).
midpoint = (2, 4 )
using the midpoint formula
midpoint = [ [tex]\frac{1}{2}[/tex] (1 + 3 ), [tex]\frac{1}{2}[/tex] (2 + 6 )] = (2, 4)
The midpoint of the line segment with given endpoints A(1,2) and B(3,6) can be found using the formula for a midpoint, which is ((x1+x2)/2, (y1+y2)/2). Substituting the coordinates of points A and B into this formula gives us the midpoint coordinates as (2,4). So the midpoint is (2,4).
Explanation:The question is asking for the midpoint of the line segment with given endpoints A(1,2) and B(3,6). We can calculate this using the formula for the midpoint of a segment, which is ((x1+x2)/2, (y1+y2)/2). In this case:
x1 = 1 (the x-coordinate of point A) y1 = 2 (the y-coordinate of point A) x2 = 3 (the x-coordinate of point B) y2 = 6 (the y-coordinate of point B)
Substituting these values into the formula gives us the midpoint = ((1+3)/2, (2+6)/2) = (2,4). Therefore, the coordinates of the midpoint of the segment with the given endpoints A(1,2) and B(3,6) are (2, 4).
Learn more about Midpoint here:https://brainly.com/question/28224145
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Simplify. 7square toot 32-6square root 72
[tex]7\sqrt{32}-6\sqrt{72}=7\sqrt{16\cdot2}-6\sqrt{36\cdot2}\\\\=7\cdot\sqrt{16}\cdot\sqrt2-6\cdot\sqrt{36}\cdot\sqrt2\\\\=7\cdot4\cdot\sqrt2-6\cdot6\cdot\sqrt2=28\sqrt2-36\sqrt2\\\\=-8\sqrt2[/tex]
[tex]Used:\\\\\sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}[/tex]
How do I write a fraction in the simplest form
Ask if the numerator and denominator can be divided by the same number, which is called a common factor.
See if at least one number in the fraction is a prime number.
Simply just find the least common factor between the numerator and the denominator of the fraction, For example, 2/4, you know that between the two numbers, they both share the same common factor, 2, so divide 2 on the top and the bottom, and then your final answer would be 1/2. However, if there seems to be no common factor between the numerator and the denominator for a fraction, do not simplify it any more. You cannot have a decimal as a numerator or a denominator. For example, 3/5 has no common factor so you do not have to simplify it as it is already at its most simplest form.
Hope you found this helpful:)
Ugh this is bothering me
Simplify completely
(h12h4)3
Answer:
it is not h^48. I just took the test and its h^24!
Step-by-step explanation:
Are 5/6 and -4.713 on the same side or the opposite side of zero ?
Evaluate 6 • 3 ÷ start root 9 end root – 1.
A. 2
B. 3
C. 5
D. 6
6 * 3 / sqrt9
Using PEMDAS, solve SQRT first.
6 * 3 / 3
Using PEMDAS, solve 6 * 3.
18 / 3
Solve.
6.
Your answer is 6.
Answer:
It's 5 for connexus students, I did it already.
Step-by-step explanation: