Answer:
(3x + 1)²
Step-by-step explanation:
Given
9x² + 6x + 1 ← is a perfect square of the form
(ax + b)² = a²x² + 2abx + b²
Compare like terms to find a and b
a²x² = 9x² ⇒ a² = 9 ⇒ a = [tex]\sqrt{9}[/tex] = 3
b² = 1 ⇒ b = [tex]\sqrt{1}[/tex] = 1
and 2ab = 2 × 3 × 1 = 6
Thus
9x² + 6x + 1 = (3x + 1)²
Answer:
(3x + 1)^2
Step-by-step explanation:
The first and last terms are perfect squares. From its structure, this is a perfect square trinomial.
All of the symbols in the expression 9x2 + 6x + 1 are positive, so use the rule for the square of the sum of two terms.
In the given expression, a2 = 9x2 and b2 = 1, so a = 3x and b = 1.
2ab = 2(3x)
= 6x
This result matches the middle term in the polynomial expression, 6x, so apply the rule for the square of the sum of two terms.
The expression 9x2 + 6x + 1 is equal to (3x + 1)2.
An elm tree is 3 and one-half times as tall as an apple tree. The apple tree is 10 and two-thirds feet tall. How tall is the elm tree?
Answer:
The elm tree is 40 5/6 inches tall
Step-by-step explanation:
Let
Tallness of the apple tree = x
Tallness of the elm tree= 3 1/2x
Apple tree = 10 2/3 feet tall
Elm tree = 3 1/2x
Where x= 10 2/3
Elm = 3 1/2 (10 2/3)
= 7/2(35/3)
= 7*35 / 2*3
= 245 / 6
= 40 5/6 inches tall
The elm tree is 40 5/6 inches tall
Ms. Rothrock loves to go shopping with Ms. Cluver and Mrs. Gosch. When they went to Target Ms. Rothrock bought shirts and jeans. Each shirt cost $13 and each pair of jeans cost $15. Ms. Rothrock decided to buy 4 shirts. She spent $82. How many pairs of jeans did she buy?
Answer:
She bought 2 pairs of jeans
Step-by-step explanation:
$82- $13-$13-$13-$13=$30
$15*2=$30
$30=$30
she bought 2 pairs of jeans
Use graphing technology to find the range of the function f(x)=x2 +6x+9
Answer:
See below.
Step-by-step explanation:
Refer to the graph.
The range of a graph is the span of y-values it covers.
From the graph, we can see that the span of y-values is all values greater than or equal to 0.
Therefore, our range is, in interval notation:
[tex][0,\infty)[/tex]
Note that we use brackets with the 0 because 0 is included in our range.
In set notation, this is:
[tex]\{y|y\in\mathbb{R},y\geq 0\}[/tex]
Rewrite the equation so that it does not have fractions 2/3x-4=5/6
Answer:
.6x - 4 = .83
Step-by-step explanation:
prove that points (2a,4a), (2a,6a), and (2a +√3a,5a) are the vertices of an equilateral triangle of side
Answer:
Let A (2a, 4a)
B(2a, 6a)
C (2a + sqrt (3a), 5a)
Side AC:
[tex]\sqrt{(2a+\sqrt{3a}-2a)^2+(5a-4a)^2 }=\sqrt{3a+a^2}[/tex]
Side BC:
[tex]\sqrt{(2a+\sqrt{3a}-2a)^2+(5a-6a)^2 }=\sqrt{3a+a^2}[/tex]
Hence AC = BC
It is an isoceles triangle.
Side AB:
[tex]\sqrt{(2a-2a)^2+(6a-4a)^2 }=\sqrt{2a^2}=2a[/tex]
It proves that the triangle is NOT an equilateral triangle.
1x + 2 = Ox + 5
Solve the equation.
Answer:
x =-3
Step-by-step explanation:
1x + 2 = 0x + 5
hence 0x simplifies x
1x-0x = 2-5
x = -3
How many times does 9 go into 4,590
Plz help
Answer:
510
Step-by-step explanation:
4,590/9=510
Question 7. Ezequiel's Biology marks are 8.3, 6.8 and 9.4 out of 10. His final grade in Biology is the mean of these three marks a Calculate Ezequiel's final grade in Biology. Ezequiel wrote the three marks correct to the nearest unit to find his final grade in Biology.
Answer:
Ezequiel's final grade is 8
Step-by-step explanation:
The average (mean) of Ezequiel's grade is:
[tex]\frac{(8.3+6.8+9.4)}{3} \approx 8.16666[/tex]
which rounded to the nearest unit is 8.
Answer:
It would be 8 :)
Step-by-step explanation:
nearest thousand of 9082 please answer fast
Answer: 9,000
Step-by-step explanation:
estimate the equation 12+ 19.61
QUESTION:
QUESTION:estimate the equation 12+19.61.
QUESTION:estimate the equation 12+19.61.Answer:
QUESTION:estimate the equation 12+19.61.Answer:12+19.61 =31.61.
Marlena places a square rug on her living room floor, which is also a square. What area of her floor is NOT covered by the rug? A. 9 ft2 C. 63 ft2 B. 12 ft2 D. 81 ft2
Answer:B - 12ft2
Step-by-step explanation:
is -3 a whole number
Answer:
No it is not -3 is an integers
Answer:
no: -3 is an integer
Step-by-step explanation:
given the midpoint and one endpoint find the other endpoint. Endpoint (2,-9) Midpoint (-2,-1)
A) (4,8)
B) (-4,-8)
C) (-6,7)
D) (6,-7)
Answer:
Step-by-step explanation:
(x + 2)/2 = -2
x + 2 = -4
x = -6
(y + (-9))/2 = -1
y - 9 = -2
y = 7
(-6, 7)
answer is C
[tex](W^{8} )^{8}[/tex]
Answer:
w^64Step-by-step explanation:
[tex]\left(w^8\right)^8\\[/tex]
[tex]\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc}[/tex]
[tex]\left(w^8\right)^8=w^{8\times\:8}\\=w^6^4[/tex]
Evaluate 5w-w/x when w=6 and x=2
Answer:
27
Step-by-step explanation:
5×6-(6/2)
=30-3
=27
Answer:
[tex] 27[/tex]
Step-by-step explanation:
[tex]5w - \frac{w}{x} = \frac{5w}{1} - \frac{w}{x} = \frac{5(6)}{1} - \frac{6}{2} = 30 - 3 = 27[/tex]
or
[tex] \frac{5(6) }{1} - \frac{6}{2} = \frac{30}{1} - \frac{6}{2} = \frac{60 - 6}{2} = \frac{54}{2} [/tex]
6.88888888889 as a fraction
Answer:
62/9
Step-by-step explanation:
.88888888 is 8/9
Multiply 9*6 to get the whole amount
9*6 = 54
Add 8 because that's the fractional amount.
54 + 8 = 62
So 62/9 will give you 6.8888888889
If the relationships below are given in the form (input, output), which pairing always describes a function?
Answer: B
(height of a building in feet, height of the building in inches)
evaluate the expression 32^((3)/(5))
Answer:
8
Step-by-step explanation:
3/5=0.6
32^0.6=8
Ans.8
Angle F and angle G are complementary . The measure of angle F is three times the measure of angle G. What is the measure of each angle?
Answer:
[tex]g[/tex] = 22.5°
[tex]f[/tex] = 67.5°
Step-by-step explanation:
Let’s create a system of equations for [tex]f[/tex] and [tex]g[/tex].
Complementary angles are two angles that add up to 90°, so [tex]f+g=90[/tex]
Also, [tex]f[/tex] is thrice of g: [tex]f=3g[/tex]
We can now substitute [tex]3g[/tex] in [tex]f+g=90[/tex] for [tex]f[/tex].
[tex]3g + g = 90\\\\4g = 90\\\\g=22.5[/tex]
Now, we can find [tex]f[/tex] by substituting [tex]g[/tex] into either equation.
[tex]f + 22.5 = 90\\\\f = 90-22.5\\\\f = 67.5[/tex]
Hope this helped!
Which exponential equation correctly rewrites this logarithmic equation?
Answer:c
Step-by-step explanation:
This is how it should be when you are representing an exponential equation to a logarithmic equation
[tex]y=a^{x}[/tex]→log y base a =x
therefore the answer is c
The exponential equation which rewrites the logarithmic equation is given by 6ˣ = 18
What is Logarithm?The power to which a number must be increased in order to obtain another number is known as the logarithm. A power is the opposite of a logarithm. In other words, if we subtract an exponentiation from a number by taking its logarithm
The properties of Logarithm are :
log A + log B = log AB
log A − log B = log A/B
log Aⁿ = n log A
Given data ,
Let the logarithmic equation be represented as A
Now , the value of A is
log₆ 18 = x
From the properties of logarithm , we get
log Aⁿ = n log A
On simplifying , we get
6ˣ = 18
where the value of x = 1.61314
Hence , the exponential equation is 6ˣ = 18
To learn more about logarithm click :
https://brainly.com/question/12049968
#SPJ2
Powers of 10 with positive exponents are:
less than 1
greater than 1
Answer:
greater than 1
Step-by-step explanation:
Answer:
greater than 1
Step-by-step explanation:
Measure of arc JKM= ??
Answer:
180°
Step-by-step explanation:
JM is the diameter of the circle with center L.
[tex] \huge \red{ \boxed{\therefore m\widehat{(JKM)} = 180\degree}} \\ [/tex]
round 5.1234 to the nearest thousandths
Distribute: -3 (2x-4)
Answer:
24
Step-by-step explanation:
2x-4= -8×-3= 24
When you look at the P.E.M.D.A.S. method you have to do what's in the PERENTESSE first so that means 2x-4 is the first thing that I are solving and you get -8 now you have to multiply -8 by -3 then you get 24
Estimate the solution to the system of equations.
You can use the interactive graph below to find the solution.
y= -2x - 5
y = 2x - 2
Choose 1 answer:
Answer:
C.
x = -3/4
y = -3 1/2
Step-by-step explanation:
We can graph the systems of inequalities to find our answer. Where the 2 graphs intersect will be our solution point.
What is f(a) in the given function 6x-5
Answer:
f(a) = 6a -5
Step-by-step explanation:
Assuming your function is ...
f(x) = 6x -5
The expression f(a) means you replace x with 'a' everywhere in the above function definition:
f(a) = 6a -5
The sum of two numbers is 21.
The second number is six times the first number. Work out the two numbers
Answer:
3 and 18
Step-by-step explanation:
let x be the first number
let 6x be the second number
x + 6x = 21
7x=21
x=21/7
x=3
second number =6x
second number 6x3= 21
Simplify the expression where possible. (picture below)
Answer:
1/ [tex]x^{-8}[/tex]
Step-by-step explanation:
when there is two powers the correct method to solve is to multiply them so
4 * -2 = -8
It cost Paisley $9.20 to send 92 text messages. How much would it cost to send 110 text messages?
Answer:
$11
Step-by-step explanation:
92=$9.20
100?
920/100x110/92
After this you will get 11 dollars.
That is the amount to send 110 text messages.
The cost to send 110 text messages is $11.
Given that, it cost Paisley $9.20 to send 92 text messages.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the cost to send 110 text messages be x.
Now, 9.20:92::x:110
⇒ 9.20×110=92×x
⇒ 92x=1012
⇒ x=1012/92
⇒ x=$11
Hence, the cost to send 110 text messages is $11.
To learn more about the proportions visit:
https://brainly.com/question/7096655.
#SPJ3
Use the work below to simplify the expression –5 + b + 2a2 – 3b + 4. 1. Identify like terms: –5 and 4 b and –3b 2. Combine like terms: –5 + 4 = –1 b – 3b = –2b 3. Simplify the expression: What is the expression in its simplest form?
Answer:
the answer will be 2a2 – 2b – 1 because he simplified the expression en He He simplified it and then substracted tb from the y interecept.hop e yall are doing great dsorry for that my laptop ins broken and my keyboardletters are fadded so i cant see well but the asnswer is correct.triust me.
Step-by-step explanation:
The expression in its simplified form is 2a² - 2b -1 .
What is an algebraic expression?In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression.
The given expression is -5 + b +2a²-3b + 4.
Simplify the expression as follows:
-5 + b +2a²-3b + 4
= 2a² - 2b -1
Hence, the expression in its simplified form is 2a² - 2b -1 .
Learn more about the algebraic expressions:
https://brainly.com/question/953809
#SPJ5