To expand (2x + 4) (3x^2 + 5x + 7), draw a rectangle with six regions, multiply the terms in each region and add them together. The final expanded form is 6x^3 + 22x^2 + 34x + 28.
To expand the polynomial expression (2x + 4) (3x2 + 5x + 7), we will use the rectangle (or area) method. This involves drawing a rectangle divided into six regions, each representing a product of a term from the first binomial and a term from the second trinomial.
First, draw a 2x3 rectangle, with the dimensions representing the two terms in the first binomial and the three terms in the second trinomial.
Label the length of the rectangle with the three terms from the second trinomial, 3x2, 5x, and 7.
Label the width of the rectangle with the two terms from the first binomial, 2x and 4.
Fill in each of the six regions by multiplying the term at the end of the row by the term at the top of the column. For example, the top-left region would be 2x multiplied by 3x2, giving 6x3.
Continue filling in the other five regions: 2x times 5x is 10x2, 2x times 7 is 14x, 4 times 3x2 is 12x2, 4 times 5x is 20x, and 4 times 7 is 28.
Combine like terms to get the final expanded form: 6x3 + 22x2 + 34x + 28.
Find the distance between (3,4) and (-5,7)
Answer:
(x+7, y-3)
Step-by-step explanation:
7 units to the right and 3 units down
write the equation of each line in point slope form.then graph the line
Slope -1/2, y-intercept 2
Answer:
[tex]y - 3 = - \frac{1}{2}(x + 2)[/tex]
Explanation:
I chose the coordinate of [-2, 3], and according to the Point-Slope Formula, y - y₁ = m(x - x₁), all the negative symbols give the OPPOSITE terms of what they really are, so be EXTREMELY careful inserting this coordinate into the formula with their CORRECT signs:
I am joyous to assist you anytime.
** It does not matter which coordinate you choose, as long as it falls on the line.
Write 500,000 in expanded form
Answer:
500,000
Expanded forms can be written like a sentence or stacked for readability as they are here.
Expanded Notation Form:
500,000
+ 0
+ 0
+ 0
+ 0
+ 0
Expanded Factors Form:
5 × 100,000
+ 0 × 10,000
+ 0 × 1,000
+ 0 × 100
+ 0 × 10
+ 0 × 1
Expanded Exponential Form:
5 × 105
+ 0 × 104
+ 0 × 103
+ 0 × 102
+ 0 × 101
+ 0 × 100
Word Form:
five hundred thousand
Step-by-step explanation:
Answers above..
3x² -2 = ab
express x as the subject of formula
Answer:
x = ± [tex]\sqrt{\frac{ab+2}{3} }[/tex]
Step-by-step explanation:
Given
3x² - 2 = ab ( isolate the x² term by adding 2 to both sides )
3x² = ab + 2 ( divide both sides by 3 )
x² = [tex]\sqrt{\frac{ab+2}{3} }[/tex] ( take the square root of both sides )
x = ± [tex]\sqrt{\frac{ab+2}{3} }[/tex]
Answer:
x = √ [(ab + 2)/ 3]
Step-by-step explanation:
3x^2 - 2 = ab
3x^2 = ab + 2
x^2 = (ab + 2)/ 3
x = √ [(ab + 2)/ 3]
Q. Saline IV fluid bags cost $64.20 for 24, 1000 ml bags from one supplier. A new supplier sells 500 ml bags for $2 each
The hospital uses about 10,000, 1000 ml bags each month. Nurses report that about half of the bags are more than half
full when they are discarded. If you are going to use only one supplier, which size bag provides the best deal, and how
much will you save each month? Compare the cost of the new supplier to the current one.
Answer:
The 1000 ml bags, over $3000
Step-by-step explanation:
First, determine how many bags you need from each vendor. Then find the cost per bag with each vendor. Remember, the bags are reported to be only half full when discarded, therefore you need the equivalent of 5,000 1,000 ml bags and 5,000 500ml bags.
Answer:100ml bag is 3000
Step-by-step explanation:
If r is seven more than the square of l , then r =
A) l2 + 7
B) l7 + 2
C) (l + 2)7
D) (l + 7)2
Maria gave the casheir $50.00 to pay for three shirts. The casheir gave her back $8.75 in change. Each shirt cost the same amount. What is the cost in dollars and cents for each shirt?
Answer:
$13.75
Step-by-step explanation:
First figure out how much she paid, by taking the change from the $50
50 - 8.75 = 41.25
She paid $41.25 dollars on three tee-shirts.
Now take how much she spent and divide it on the number of items (tee-shirts) to figure how much each one cost.
41.25 divided by 3 = 13.75
$13.75
Each Tee-shirt cost $13.75
Final answer:
To find the cost of each shirt, subtract the change given from the total amount paid and then divide by the number of shirts purchased.
Explanation:
In this scenario, Maria paid $50.00 for three shirts and received $8.75 in change. To find the cost of each shirt, we subtract the change from the total amount she gave. $50.00 - $8.75 = $41.25. Since she bought three shirts, we divide $41.25 by 3 to find the cost of each shirt. The cost of each shirt is $13.75.
Gary says that 3 - 1 1/3 will be more than 2, since 3 – 1 is 2. Draw a picture to prove that Gary is wrong.
Answer:
It makes 5/3 it is less than two!
Step-by-step explanation:
Topic: Fractions and Mixed Numbers
You have to remember the concept of fractions, let's represent by cake diagrams, it says that Gary says that 3, let's say it's 3 cakes, as the fractions are represented in terms of thirds, let's draw the cakes each one divided in 3.
and the statement says that taking away 1 and 1/3 it will make more than 2.
As you can see in the picture below, we take away 1 cake and we will take away another third of a second cake represented by the brown region of the cakes. it means that the yellow region is what's left after taking the 1 and 1/3. as you can see it doesn't make two, makes less than two exactly 5/3.
PS: Try and do it mathematically now!
Write two inequalities using a number pairs using the symbols < or >
5 and -11
Answer:
5 <-11
Step-by-step explanation:
5 is greater than -11
6
5
4
3
2
1
0
-1
-2
-3
-5
-6
-7
-8
-9
-10
-11
The inequalities created from the number pair 5 and -11 are '5 > -11' and '-11 < 5'. These represent that 5 is greater than -11 and that -11 is less than 5.
Explanation:To write two inequalities using the number pairs 5 and -11 with the symbols < and >, we consider the numeric value and sign of the numbers. We know that any positive number is always greater than a negative number. This gives us the first inequality: 5 > -11
Now, if we want to write an inequality using <, then we swap the order of numbers. Thus: -11 < 5
These statements tell us that 5 is greater than -11 and -11 is less than 5, which demonstrates how to use < and > inequalities with numbers.
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This equation graphed is?
Graph the following points:
(-2, -3)
(-1, -2)
(0, -1)
(1, cuberoot{2} -2}
(7, 0)
emade
There are 666 students
going to a trivia
competition. If each school
van can hold 6 students,
how many vans will they
need?
Answer:
666 divided by 6 is 111. So, they would need 111 vans.
PLEASE HELP! ILL MARK BRAINLIEST
Describe how the graph of y= x2 can be transformed to the graph of the given equation.
y = (x - 15)^2
Shift the graph of y = x2 right 15 units.
Shift the graph of y = x2 left 15 units.
Shift the graph of y = x2 down 15 units.
Shift the graph of y = x2 up 15 units.
Answer:
A,shift the graph of y =x2 right 15 units
Step-by-step explanation:
The new equation is subtracting 15 from the value of x.
When you subtract a number from x, the graph moves to the right by the number you subtract.
x-15, shifts the graph right 15 units.
The answer is: Shift the graph of y = x2 right 15 units.
The measure of one of the small angles of a right triangle is 15 less than twice the measure of the other small angle. Find the measure of both angles
Answer:
35° and 55°
Step-by-step explanation:
The sum of the angles of a right rectagle is 180°, with a right angle of 90°.
The tell us that A = 2B-15, so:
180° = 90° + A + B
180° = 90° + 2B - 15 + B
180° - 90° + 15 = 2B + B
105° = 3B
B = 105°/3 = 35°
Now, let's find A:
A = 180° - 90° - 35° = 55°
Using the properties of a right triangle and setting up an equation based on the relationship between the two small angles, we find that the angles measure 35 degrees and 55 degrees, respectively.
To solve the problem involving the angles of a right triangle, we recall that the sum of the angles in any triangle is 180 degrees. In a right triangle, one angle is always 90 degrees, which leaves a total of 90 degrees to be shared between the other two angles.
If we let x represent the measure of one of the small angles, then the problem tells us that the other angle is 2x - 15 degrees.
Therefore, we can set up the following equation to solve for x:
x + (2x - 15) + 90 = 180
Combining like terms gives us:
3x - 15 + 90 = 180
3x + 75 = 180
Now, we subtract 75 from both sides of the equation:
3x = 105
Finally, we divide by 3 to find the measure of x:
x = 35
Having found that one of the small angles measures 35 degrees, we can now find the other small angle:
2x - 15 = 2(35) - 15
= 70 - 15
= 55 degrees.
So, the two small angles of the right triangle are 35 degrees and 55 degrees.
Create a set of numbers with five different values that have a mean of 50.
Answer 15 20 10 2.5 7.5
Find the percent of each number.
1. 32% of 60 =
Answer:
Step-by-step explanation:
Answer:
19.2
Step-by-step explanation:
What’s the answer to
(x+y+ 3)(x+y-4)
The answer is [tex]x^2 + 2xy + y^2 - x - y - 12[/tex]
How many times greater is 1 kilogram than 1 microgram?
A. 10^9
B. 10^-9
C. 1/10^9
D. 10^8
Final answer:
1 kilogram is 10^9 times greater than 1 microgram because 1 kg equals 1000 grams, and there are 10⁶ micrograms in a gram, equating to 10⁹ µg/kg.So,option A.10⁹ is correct.
Explanation:
To determine how many times greater 1 kilogram is than 1 microgram, we need to understand the metric prefixes and their corresponding values. Knowing that 'micro' denotes 10⁻⁶, we can establish that 1 microgram (µg) equals 10⁻⁶grams (g). Since 1 kilogram (kg) equals 1000 grams, we then convert kilograms to micrograms by multiplying by 10⁶:
1 kg = 1000 g x 10⁶ µg/g = 10⁹ µg.
Thus, 1 kilogram is 10⁹ times greater than 1 microgram, which corresponds to option A.
Which point is not on the graph of the function y = x + 5?
(2, 7)
(6, 11)
(220, 225)
(10, 5)
Answer:
(10, 5 )
Step-by-step explanation:
To determine which points lie on the graph or not.
Substitute the x- coordinate of the point into the equation and if the value agrees with the y- coordinate of the point then the point is on the graph.
(2, 7 )
y = 2 + 5 = 7 ← True thus point is on the graph
(6, 11 )
y = 6 + 5 = 11 ← True thus point is on the graph
(220, 225 )
y = 220 + 5 = 225 ← True thus point is on the graph
(10, 5 )
y = 10 + 5 = 15 ≠ 5 ← Point is not on the graph
What is the limit of the function?
limx→∞f(x)=−4x^9−3x^3+2x−11
[tex]\bf \lim\limits_{x\to \infty}~-4x^9-3x^3+2x-11 \\\\\\ \lim\limits_{x\to \infty}~-4x^9~~+~~\lim\limits_{x\to \infty}~-3x^3~~+~~\lim\limits_{x\to \infty}~2x~~+~~\lim\limits_{x\to \infty}~-11[/tex]
for any positive value of "x" as it races off towards ∞, our first limit of -4x⁹ will give us a rather large negative value, our second limit of -3x³ will also give us a large negative value and both will combine to produce an even larger negative value.
our third limit of 2x will give us a positive value, however a much smaller than its previous siblings, and our last limit is just a fixed of -11, not moving at all.
since the negative values are moving faster than the positive ones, and thus overwhelming the positive ones, the limit will increasingly be racing towards -∞.
The limit of the function, [tex]\lim_{n \to \infty} f(x)= -4x^2 - 3x^3+2x - 11[/tex] is - ∞.
Here, given function is,
f(x)=−4x^9−3x^3+2x−11
We have to find the value of [tex]\lim_{n \to \infty} f(x)= -4x^2 - 3x^3+2x - 11[/tex].
What is limit of function?
Limit of function means the value towards which a function moves when the value of independent variable moves to infinity.
Now,
[tex]\lim_{n \to \infty} f(x)= -4x^2 - 3x^3+2x - 11[/tex]
[tex]\lim_{n \to \infty} f(x)= \lim_{n \to \infty} (-4x^2) - \lim_{n \to \infty} (3x^3) + \lim_{n \to \infty} 2x - \lim_{n \to \infty} 11[/tex]
[tex]\lim_{n \to \infty} f(x)= -[/tex]∞
Here, limit of [tex]-4x^{2}[/tex] is -∞, limit of [tex]-3x^{3}[/tex] is -∞ and limit of 2x is ∞.
For any positive value of x as it races off towards ∞ but here we find the limits as, -∞.
Since the negative values are moving faster than positive.
Hence, the limit will be towards -∞.
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combine the like terms
1.4b-[tex]3b^{2}[/tex]+4c-[tex]2b^{2}[/tex]+c
Answer:
If your asking us to just combine like terms it would be -3b^2-2b^2+1.4b+4c+c
but if your asking us to answer the question it would be -5b^2+1.4b+5c
Hope I helped :)
Example 2: A Real World Example
Maria decides to take a walk along Central Avenue to purchase a book at the bookstore. On her way, she passes the
Furry Friends Pet Shop and goes in to look for a new leash for her dog. Furry Friends Pet Shop is seven blocks west of the
bookstore. She leaves Furry Friends Pet Shop and walks toward the bookstore to look at some books. After she leaves
the bookstore, she heads east for seven blocks and stops at Ray's Pet Shop to see if she can find a new leash at a better
price. Which location, if any, is the farthest from Maria while she is at the bookstore?
Determine an appropriate scale, and model the situation on the number line below.
HHHHHHHH
Explain your answer. What does zero represent in the situation?
Answer:
Both pet stores are an equal distance away from the book store.
East and West are opposites and she has to go 7 in each direction (from the bookstore) to reach each pet store
Is this statement true or false?
According to the graph, during periods of recession, the number of people in poverty increases.
True
False
Answer: The Statement is true
Step-by-step explanation: the lines in the graph are constantly parallel to each other, showing that when one increases, so does the other
Answer:
The given statement is true.
Step-by-step explanation:
We are given the following graph in the picture:
On the x-axis years are shown from 1959 to 2005.
The y axis shows the poverty rate and the number of people in poverty.
The blue strips in the graph are the recession time.
Now, for each blue strip, we could see the line for poverty rate and the number of people in poverty increases. There is an upward trend in the line in the blue strip.
In other words we could say that the slope increases for all the blue strips which actually represents that the number of people in poverty increases in recession.
Thus, the given statement is true.
at 8 a.m. the temperature was -14 degrees by noon the tempature was 12 degrees. Find the change did it rise or drop?
What is 9/45 simplified
Answer:
5
Step-by-step explanation:
[tex]\text{Hello there!}\\\\\text{We are simplifying the fraction:}\,\frac{9}{45}\\\\\text{Both 9 and 45 is divisible by 9, so we'll divide both sides by 9}\\\\\text{Divide:}\\\\\frac{9\div9}{45\div9}=\frac{1}{5}\\\\\boxed{\text{Answer:}\frac{1}{5}}}[/tex]
What is negative 5 5/6–2 3/5
Answer:
the answer is -8 13/30
Step-by-step explanation:
Solve the system of equations. y = x ^ 2 - 3x + 6 y = 2x + 6
Answer:
the answer is A.
Step-by-step explanation:
The values of the system of equations y=[tex]x^{2}[/tex]-3x+6, y=2x+6 is (0,6),(5,16).
What is equation?Equation is relationship between two or more variables that are expressed in equal to form.Equations of two variables look like ax+by=c.It may be linear equation, quadratic equation,cubic equation.
How to solve the equation?We have been given two equations as y=[tex]x^{2}[/tex]-3x+6 and y=2x+6 and we are required to solve the equations for the value of x.
Putting the value of y from second equation in first equation.
2x+6=[tex]x^{2}[/tex]-3x+6
Cancellng 6 from both sides.
[tex]x^{2}[/tex]-5x=0
x(x-5)=0
x=0,x-5=0
x=0,x=5
Putting the values of x in second equation to get the value of y.
y=2x+6
y=2(5)+6
=10+6
y=16
y=2x+6
y=2*0+6
=6
Points will be (0,6),(5,16).
Hence the values of the system of equations y=[tex]x^{2}[/tex]-3x+6, y=2x+6 is (0,6),(5,16).
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what values of y will make the expression true? 10 - y = y - 10
Answer:
y = 10
Step-by-step explanation:
Given
10 - y = y - 10 ( subtract y from both sides )
10 - 2y = - 10 ( subtract 10 from both sides )
- 2y = - 20 ( divide both sides by - 2 )
y = 10
At a stock exchange there were a total of 10,000 shares sold in one day. Stock A had four times as many
shares sold as Stock B. The number of shares sold for Stock C was equal to the sum of the numbers of
shares sold for Stock A and Stock B. How many shares of each stock were sold?
shares of Stock A were sold,
were sold.
shares of Stock B were sold, and
shares of Stock
What’s the answer
Answer:
Share sold by Stock A = 4000, Stock B = 1000 and Stock C = 5000
Step-by-step explanation:
Total sold sold = 10000
i.e. [tex]A + B + C = 10000[/tex] ....(1)
Shares sold by stock A = 4 × Shares sold by stock B
i.e. [tex]A = 4B[/tex] ....(2)
Shares sold by stock C = Shares sold by stock A + Shares sold by stock B
i.e. [tex]C = A + B[/tex] ....(3)
substituting value of [tex]A[/tex] from (2) in (3) we get
[tex]C = 4B + B = 5B[/tex] ....(4)
substituting value of [tex]A[/tex] and [tex]C[/tex] from (2) and (4) in (1) we get
[tex]4B + B + 5B = 10000\\10B = 10000\\B = 1000[/tex]
[tex]A = 4B = 4*1000 = 4000[/tex]
[tex]C = 5B = 5*1000 = 5000[/tex]
About how much does the plant grow?
4
2 1/2
3
2
Hey!
------------------------------------------------
[tex]\large\boxed{The~plant~grew~2\frac{1}{2}~feet!}[/tex]
------------------------------------------------
Steps To Solve:
~Find common denominators
6/7 = 54/63
2/9 = 14/63
~Turn into improper fractions
1 54/63 = 117/63
4 14/63 = 266/63
~Subtract.
266/63 - 117/63 = 149/63
~Turn into mixed number
149/63 = 2 23/63
~Round
2 23/63 ≈ 2 1/2
Answer:
2 1/2
Step-by-step explanation:
because 4 2/9 － 1 6/7 equal to 2 half which equal to 2 1/2
Put these numbers in order from least to greatest
1.82, 1.6, 1 4/5
Answer:
1.6, 1 4/5 (1.8), 1.82
Step-by-step explanation:
Answer:
1.6;1 4/5;1.82