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:
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]
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.
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
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:
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.
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.
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?
How do you write 158.1 as a decimal
Step-by-step explanation:
1.581 × 10² like this ? : )
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
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]
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 :)
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
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
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
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
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]
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
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.
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.
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.
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 ♡♡♡♡♡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:
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
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.
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]
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!
Solve for X:
X/6-y/3=1
x = 6 + 2y
hope it 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