could someone please help me really quickly?
[tex]6x^2 +17x -3\\\\=6x^2 +18x-x-3\\ \\=6x(x+3)-(x+3)\\ \\=(x+3)(6x-1)\\\\\text{The length and width of the rectangle are}~ (6x-1)~ \text{and}~ (x+3)[/tex]
Answer:
[tex]\textsf{length}=6x - 1[/tex]
[tex]\textsf{width}=x+3[/tex]
Step-by-step explanation:
Area of a rectangle = length × width
Given area: [tex]A=6x^2+17x-3[/tex]
Therefore, [tex]6x^2+17x-3=\sf length \cdot width[/tex]
To find the length and width, we need to factorize the given expression for area.
To factor a quadratic in the form [tex]ax^2+bx+c[/tex]
Find 2 two numbers (d and e) that multiply to ac and sum to bRewrite b as the sum of these 2 numbers: d + e = bFactorize the first two terms and the last two terms separately, then factor out the comment term.[tex]6x^2+17x-3 \implies a=6, b=17, c=-3[/tex]
[tex]ac=6 \cdot -3=-18[/tex]
[tex]d+e=17[/tex]
So we are looking for a pair of numbers that multiply to -18 and sum to 17.
Factors of 18: 1, 2, 3, 6, 9, 18
Therefore, the two numbers (d and e) that multiply to -18 and sum to 17 are:
18 and -1
Rewrite [tex]17x[/tex] as [tex]+18x-x[/tex]:
[tex]\implies 6x^2+18x-x-3[/tex]
Factor first two terms and last two terms separately:
[tex]\implies 6x(x+3)-1(x+3)[/tex]
Factor out common term [tex](x+3)[/tex]:
[tex]\implies (6x-1)(x+3)[/tex]
As length > width,
[tex]\textsf{length}=6x - 1[/tex]
[tex]\textsf{width}=x+3[/tex]
Hexagon BCDEFG is shown below. Each square on the grid is a unit square. What is the area of the
hexagon in square units?
Answer:
B. 100 units
Step-by-step explanation:
What I did was I couunted the lines at the bottum and since it was 10 then I counted up and that was 10 so you would do 10x10 get 100 units.
what amount is closest to a quart 100 milliliters or 500 milliliters or one liter or 10 liters
Answer:
1 liter
Step-by-step explanation:
100 milliliters = 0.10566882 quarts
500 milliliters = 0.52834411 quarts
1 liter = 1.05668821 quarts
10 liters = 10.5668821 quarts
______________________________
From this, we can see that 1 liter is closest to a quart.
hope this helps!
which of the following value, when multiplied by 2/3, results in a product that is greater than 2/3
a. 2/3
b 3/2
c 3/4
d 4/4
Answer:
b
Step-by-step explanation:
2/3 * 2/3 = 4/9
2/3 * 3/2 = 1
2/3 * 3/4 = 1/2
2/3 * 4/4 = 2/3
How do you write 158.1 as a decimal
Step-by-step explanation:
1.581 × 10² like this ? : )
Please help on math.
Answer:
832.5²
Step-by-step explanation:
Base x height ÷ 2 is the formula to find a triangles area.
45 x 37= 1665 then 1665 ÷ 2 = 832.5 dont forget to add the ²
Answer:
832.5²
Step-by-step explanation:
11 + ( − 11 ) = 0 whats the answer?
Answer:
0
Step-by-step explanation:
uhhh it already solved and also, its the answer because if theres like a "+-" you can just convert it to "-" so then it will be
11 - 11
11 - 11 = 0
Answer:
0
Step-by-step explanation:
as + and then - is - so 11- 11 = 0
2/7+1/7+1/7= answer plss
Answer:
2÷7+1÷7+1÷7 = 0.57142857142
Answer:
[tex]\frac{4}{7}[/tex]
Step-by-step explanation:
[tex]\frac{2}{7}[/tex] + [tex]\frac{1}{7}[/tex] + [tex]\frac{1}{7}[/tex]
= [tex]\frac{2+1+1}{7}[/tex]
= [tex]\frac{4}{7}[/tex]
for the function f, use compisition of functions to show that f^-1 is a given.
let f(x)=(1+x)/x show that f^-1(x)=1/x-1
Step-by-step explanation:
If we have f(x) and it's inverse, and we compose them
we will get
[tex]f {}^{ - 1} (f(x) = x[/tex]
So here we compose
[tex]( \frac{1}{ \frac{1 + x}{x} - 1} )[/tex]
[tex]( \frac{1}{ \frac{1}{x} + 1 - 1} [/tex]
[tex] \frac{1}{ \frac{1}{x} } [/tex]
[tex]x [/tex]
So the composition is x, so they are inverses.
Determine whether 2x+2y= -6 is a function?
Answer:
It's a function because when you simplify it becomes y=-x-3. the only reason it wouldn't be a function would be if the equation were to be x = a random number that is not a variable. The equation would not pass the vertical line test which is the requirement to see if an equation is a function.
Simply put, it's a function.
2 Which equation represents the relationship
shown in the table below?
(8.5A)
9
AW
3
4
5
10
7
16
11
28
22
Ay
A y = 6x + 3
B y = 3x - 5
C y = (x - 5
D y = 3x + 3
Answer:
3x - 5 fits the equation perfectly
Step-by-step explanation:
if we put the following value in X we get,
x processing y
3. 3*3 - 5. 4
5. 3*5 - 5. 10
7. 3*7 -5. 16
9. 3*9 - 5. 22
11. 3*11 - 5. 28
NO LINKS!!
The Odd Man Out!
PART 2:
For each set of figures below, three are similar (meaning that they are related through a sequence of transformations including dilation), and one is an exception. Find the exception in each set of figures and answer the questions for each set.
Answer:
a. exception: C; obtuse angle with a different measure
b. corresponding angles are congruent; corresponding sides are proportional
c. corresponding angles are congruent among the similar triangles; they are not congruent when the triangles are not similar
d. corresponding sides are porportional; they are not proportional when the triangles are not similar
Step-by-step explanation:
As you know, similar triangles have congruent corresponding angles, and proportional corresponding sides. This gives them the same shape, but they may be of differenent sizes.
__
a.Figure C appears to have a larger smallest angle and a smaller largest angle than the rest of the figures. Its long side relative to its second-longest side appears to be shorter, consistent with a smaller largest angle.
__
b.The similar triangles have congruent corresponding angles and proportional corresponding sides.
__
c.See (b) regarding similar triangles. Non-similar triangles have different angles.
__
d.See (b) regarding similar triangles. Non-similar triangles have different side proportions.
Show all work pls and thank :-)
Answer:
-a^3 -3a^2
Step-by-step explanation:
(fg) (x) = x^2 (x-3)
= x^3 - 3x^2
(fg) (-a) = (-a)^3 -3 (-a)^2
= -a^3 -3a^2
There are approximately 8,441 people per square mile in Phoenix. If Phoenix is 964 square miles,
approximately how many people live in Phoenix.
Answer: 8,137,124
Step-by-step explanation:
You can find the answer by multiplying the number of people by the number of sq miles.
8441 * 964
The rectangle has an area of 36 square meters and a base of 35 meters. Find the width.
Answer:
About 1.03m
Step-by-step explanation:
A=36
L=35
w=A/L=36/35 which is about 1.03m
i need help pls could you answer this?
Find the mean, median and mode of this data. Round to the nearest dollar if necessary.
Step-by-step explanation:
Median: 35000
Mean: 383333.33333333 (round it)
Mode: 10000, 20000, 30000, 40000, 200000, 2000000 (all the numbers)
find the amount of hydrogen in a liter of acid rain that has a pH of 5.5 math
To calculate hydronium concentration from pH, type on you calculator
10 to the power of negative pH value
10^-5.5 = 3•10^6 mol/L
Since there are 3 hydrogens in every hydronium molecule,
There are 9 • 10^6 hydrogens in that liter of acid.
True or false? Show steps
Answer:
TRUE
Step-by-step explanation:
Consider
[tex] log_{ \sqrt{x} }( {x}^{k} ) [/tex]
[tex] log_{ \sqrt{x} }( {( \sqrt{x} }^{2})^{k} ) [/tex]
[tex] log_{ \sqrt{x} }{( \sqrt{x})^{2k} } ) [/tex]
we know that
[tex] log( {a}^{b} ) = b log(a) [/tex]
===
[tex]2k (log_{ \sqrt{x} }( \sqrt{x} ) )[/tex]
Also we know that
[tex] log_{a}(a) = 1[/tex]
===
[tex]2k( log_{ \sqrt{x} }( \sqrt{x} ) = 2k \times 1 = 2k[/tex]
Hence
[tex] log_{ \sqrt{x} }( {x}^{k} ) = 2k[/tex]
Therefore it TRUE
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is
prime". Let B be the event "the outcome is a divisor of 3". Find P(A|B).
Answer:
P(A|B) = 0.5
Step-by-step explanation:
A: set of prime numbers ={1,2,3}
B: set of divisors of 3 ={1,3}
P(A)=P(1)+P(2)+P(3)= 0.1+0.1+0.3 =0.5
P(B)=P(1)+P(3)=0.1+0.3=0.4
P(A|B) means: probability of A knowing that B
In other words we have to find the probability that a prime outcome occurs knowing that it is a divisor of 3
Its formula is given by:
P(A|B) = P(AintersectionB) /P(B)
A intersection B: outcome is prime and a divisor of 3 at the same time. (common elements between sets A and B)
A int B= {1,3}
P(AintB)= P(A)xP(B) = 0.5x0.4=0.2
Now back to the formula:
P(A|B) =P(AintB) / P(B)
=0.2/0.4=0.5
HOPE THIS HELPS :)
Amazon pays an annual dividend of $4.40 per share. On Tuesday it closed at $550 per share. This
was up $6.50 per share from the previous day (Monday's close).
than
A.What was the yield (percent) on Tuesday? Round to tenth of a percent
B.At what price did it close on Monday?
C.What was the percent change from Tuesday to Monday?
D.What was the yield on Monday?
Determine each feature of the graph of the given function.
2x + 8
f(x) =
x² + x
x - 12
[tex]x=\frac{1+4f-\sqrt{16f^{2}+8f+25 } }{2}[/tex]
why is l-8l>l2l even though -8,2
Answer:
the absolute value of (-8) is 8 and the absolute value of (2) is 2
so l-8l>l2l
Step-by-step explanation:
Espanol
The area of a rectangle is 35 yd?, and the length of the rectangle is 3 yd more than twice the width. Find the dimensions of the rectangle.
DO
Answer: 7/2 yards by 10 yards
Step-by-step explanation:
Solve 3 log 2x = 4. Round to the nearest thousandth if necessary.
5
2.783
10.772
best answer of this equation is 10.772
Answer: 10.772
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
exact form:
x= 10 4/3
--------- (its a fraction)
2
decimal form: 10.77217345....
after that round to the nearest thousandth.
Which inequality describes the graph?
y ≥ 1/2x – 2
y < 1/2x – 2
y ≤1/2 x – 2
y >1/2 x – 2
[tex]y < \frac{1}{2} x - 2 \\ [/tex]
Have a great day ♡♡♡♡♡Identify the trinomial that is a perfect square.
A. 9x2 + 30x + 16
B. 16x2 + 20x + 9
C. 36x2 + 60x + 25
D. 4x2 + 30x + 25
Answer:
Option C, [tex]36x^2 + 60x + 25[/tex]
Step-by-step explanation:
Step 1: Determine the perfect square
According to online, "When an expression has the general form a²+2ab+b², then we can factor it as (a+b)². For example, x²+10x+25 can be factored as (x+5)². This method is based on the pattern (a+b)²=a²+2ab+b², which can be verified by expanding the parentheses in (a+b)(a+b)"
The only one that seems to work is Option C so lets factor it.
[tex]36x^2 + 60x + 25[/tex]
[tex](6x + 5)(6x + 5)[/tex]
[tex](6x + 5)^2[/tex]
Yup! We can see that Option C would give us a perfect square
Answer: Option C, [tex]36x^2 + 60x + 25[/tex]
Solve for X:
X/6-y/3=1
x = 6 + 2y
hope it helps...!!!
Which answer best describes the shape of this distribution?
bell-shaped
skewed left
uniform
skewed right
Answer:
Skewed right
Step-by-step explanation:
There is a 'tail' towards the right.
Find a polynomial of least possible degree having the graph shown
f(x)=0
The polynomial of least possible degree having the graph as given is; f(x) = x³-8x²+x +42.
Polynomial of least possible degreeIt follows from the graph that the roots of the polynomial are; -2, 3 and 7.
On this note, the factors of such polynomial are;
Hence; (x+2)(x-3)(x-7) = f(x)
f(x) = x³-8x²+x +42Read more on polynomials;
https://brainly.com/question/2833285
Gretchen made a paper cone to hold a gift for a friend. The paper cone was 15 inches high and had a radius of 2 inches. Find the volume of the paper cone to the nearest tenth. Use 3.14 for π.
Answer
91.67inch^3
Step-by-step explanation:
The volume of a cone can be calculated using below formula
V= 1/3 π.r^2h
Where h= height of the cone
r= radius of the cone
V= volume of the cone
Given :
height= 11 inches
radius= 5 inches
π= 3.14
Then substitute into the formula we have
V= 1/3 × 3.14× 5^2 ×11
V= 91.67inch^3
Therefore volume of the cone is 91.67inch^3