Answer:
x = -3, 2
Step-by-step explanation:
[tex]log_6(x+1)+log_6x=1 \\ \\ log_6 \{x(x+1) \} = 1 \\ \\ x(x + 1) = {6}^{1} \\ \\ {x}^{2} + x = 6 \\ \\ {x}^{2} + x - 6 = 0 \\ \\ {x}^{2} + 3x - 2x - 6 = 0 \\ \\ x(x + 3) - 2(x + 3) = 0 \\ \\ (x + 3)(x - 2) = 0 \\ \\ x + 3 = 0 \: \: or \: \: x - 2 = 0 \\ \\ x = - 3 \: \: or \: \: x = 2 \\ \\ x = - 3, \: \: 2[/tex]
What is f(-3) for the function f(x) = -5x - 7?
Need this now will mark you brainliest!!!
Answer:
f ( x ) = 8
Step-by-step explanation:
Step 1:
f ( x ) = - 5x - 7 Function
Step 2:
f ( - 3 ) = - 5 ( - 3 ) - 7 Input x
Step 3:
f ( - 3 ) = 15 - 7 Multiply
Answer:
f ( - 3 ) = 8 Subtract
Hope This Helps :)
Solve for b.
Ab + c = d
B= (d-c)/a
B= a + c/d
B= a/c-d
Answer:
B
Step-by-step explanation:
just took this test
Solve the inequality 8y - 3(y - 2)< 2y + 4(2y + 4) write solution in interval notation
Answer: y>-2
Step-by-step explanation:
8y-3(y-2) < 2y+4(2y+4)
8y-3y+6 < 2y+8y+16
6-16<2y+8y-8y+3y
-10<5y
y>-2
Answer:
(−∞,−2)
Step-by-step explanation:
Start by simplifying each side as much as possible by distributing and combining like terms to get
8y−3(y−2)8y−3y+65y+6>2y+4(2y+4)>2y+8y+16>10y+16
Subtract 10y from both sides to collect the variables on the left, then subtract 6 from both sides to collect all the constants on the right.
5y+65y+6−10y−5y+6−5y+6−6−5y>10y+16>10y+16−10y>16>16−6>10
Divide each side by −5 to solve for y. Since −5<0, the inequality changes direction.
−5y−5y−5y>10<10−5<−2
In interval notation, we write this as (−∞,−2).
Andre rode his bike at a constant speed. He rode 1 mile in 5 minutes. Which of these equations represents the amount of time t (in minutes) that it takes him to ride a distance of d miles?
Answer:
5minutes and the the distance is 1miles
Answer:
t=5d
Step-by-step explanation:
Given that Andre rode his bike at a constant speed.
Number of miles driven = 1 mile
Time taken to drive 1 mile = 5 minutes.
Then speed can be calculated using formula:
Speed = Distance / Time
Now we have to find the amount of time t (in minutes) taken by him to right distance d so we can again use same formula.
Speed = Distance / Time
or
Time = Distance / Speed
Plug the given values
t = 5d
Hence find answer will be equation t=5d.
PLEASE HELP
At Bulk candy, gummy bears cost $5 for 7 ounces. You LOVE gummy bears. You fill up the bag and the
weight comes in at 24.5 ounces. How much do you owe? (no tax)
Answer:
17.50
Step-by-step explanation:
7*3 is 21 and 7/2 is 3.7 so its 5*3 (15) plus 2.50, so 17.50
Hope this helped!
pls if u answer ill give brainliest :))) PLSS
When evaluting an expression, is it easier to combine terms first or substitute values first?
Answer:
Substitute values first
Combine like terms 3y2 + 3(4y2 - 2)
Step-by-step explanation:
[tex]3y {}^{2} + 3(4y {}^{2} - 2) \\ \\ {3y}^{2} + 12 {y}^{2} - 6 \\ 15 {y}^{2} - 6[/tex]
Answer:
15y² - 6
Step-by-step explanation:
3y2 + 3(4y2 - 2)
Distribute: 3y² + 12y² - 6
Add like terms: 15y² - 6
I hope this helped, please mark Brainliest, thank you!
whats 2+2? geng geng geng geng geng
Answer:
4
Step-by-step explanation:
Answer:
the answer is 4 geng geng geng geng
psdt: thanks for the points
Step-by-step explanation:
have a good night ^-^
What is -15 = x/-0.5
Solve for X
Answer:
7.5
Step-by-step explanation:
you need to get the X alone so you multiply both sides by -0.5.
that leaves you with x=7.5
Michael owns dogs, hamsters and fish in the ratio 2:3:6
If he has 6 hamsters, how many pets does he have?
Answer:
11
Step-by-step explanation:
I think you just add the ratios together.
which number is IRRATIONAL
because when you look for the root of ninety, it gives you a result that is not a natural or Rational number, but a completely Irrational number.
the result is 9.4868329
Step-by-step explanation:Irrational numbersare numbers that cannot be expressed as the ratio of two whole numbers. This is opposed to rational numbers, like 2, 7, one-fifth and -13/9, which can be, and are, expressed as the ratio of two whole numbers.
hope this help!!
Answer:
c)
Step-by-step explanation:
Since sqrt(90) is an irrational number, by definition it cannot be represented as a ratio of two integers.
Given y = sin(2x - π) + 1, find the (a) derivative, (b) equation of the tangent line at x = π/2, (c) equation of the normal line at x = π/2.
Answer:
(a) [tex]y'= 2cos(2x - \pi)[/tex]
(b) [tex]y=2x - \pi + 1[/tex]
(c) [tex]y=-\frac{x}{2} +\frac{\pi + 4}{4}[/tex]
Step-by-step explanation:
[tex]y=sin(2x-\pi)+1[/tex]
Part (a)Find the derivative of this function by using the chain rule and the power rule.
We know that the derivative of sinx = cosx. Find the derivative of this entire function first, [tex]sin(2x-\pi)+1[/tex], then multiply this by the derivative of the inside function, [tex]2x-\pi[/tex].
[tex]\frac{d}{dx}(sin(2x-\pi)+1)[/tex]Use the chain rule to find the derivative of sin(2x - π) + 1, which is cos(2x - π), then multiply this by the derivative of (2x - π). The derivative of π is 0, because it is a constant. The derivative of 2x is 2 based on the Power Rule.
[tex]cos(2x-\pi) \times 2[/tex]Simplify this expression.
[tex]2cos(2x - \pi)[/tex]This is the derivative of [tex]y=sin(2x-\pi)+1[/tex]; therefore, we can write:
[tex]y'= 2cos(2x - \pi)[/tex] Part (b)In order to find the equation of the tangent line at [tex]x=\frac{\pi}{2}[/tex], we will need to find the slope of the tangent line and the x- and y- coordinates (we already know the x- cord).
The steps to finding the equation of the tangent line at a certain are:
Plug into y' to find the slope of the tangent line.Plug into y to find the (x, y) coordinates.Use point-slope to write our equation in slope-intercept form.We know that y' = 2cos(2x - π). Let's plug x = π/2 into this equation for x to find the slope of the tangent line.
[tex]y'(\frac{\pi}{2} ) = 2cos(2(\frac{\pi}{2})-\pi)[/tex]Simplify inside the parentheses.
[tex]y'(\frac{\pi}{2} ) = 2cos(\frac{2\pi}{2}-\pi)[/tex] [tex]y'(\frac{\pi}{2} ) = 2cos(\pi - \pi)[/tex] [tex]y'(\frac{\pi}{2} ) = 2cos(0)[/tex] [tex]y'(\frac{\pi}{2} ) = 2[/tex]Now we know that the slope of the tangent line is 2.
Let's plug x = π/2 into the original function, y.
[tex]y(\frac{\pi}{2})=sin(2(\frac{\pi}{2})-\pi)+1[/tex]Simplify inside the parentheses.
[tex]y(\frac{\pi}{2})=sin(0)+1[/tex] [tex]y(\frac{\pi}{2})= 0+1[/tex] [tex]y(\frac{\pi}{2})=1[/tex]This tells us that the y-value, when x = π/2, equals 1. Our coordinates that we can use are (π/2, 1).
Now we can use point-slope form to write an equation for the tangent line to y at x = π/2.
Point-slope equation:
[tex]y-y_1=m(x-x_1)[/tex]We have [tex](x_1, \ y_1)[/tex], which are the x- and y- coordinates, and [tex]m[/tex], which is the slope of the tangent line.
Substitute these values into the equation:
[tex]y-(1)=2(x-(\frac{\pi}{2}))[/tex]Distribute 2 inside the parentheses.
[tex]y-1=2x-\frac{2 \pi}{2}[/tex]Add 1 to both sides of the equation.
[tex]y=2x-\frac{2\pi}{2} + 1[/tex] [tex]y=2x - \pi + 1[/tex]This is the equation of the tangent line of [tex]y=sin(2x-\pi)+1[/tex] at [tex]x=\frac{\pi}{2}[/tex].
Part (c)In order to find the equation of the normal line at x = π/2, we can use the information that the tangent line is perpendicular to the normal line.
This information is helpful because this means that their slopes are opposite reciprocals.
Let's use the point-slope equation again, but instead of m = 2, m will be the opposite reciprocal of 2 ⇒ -1/2. We will still use the same coordinate points.
[tex]m=-\frac{1}{2} \ \ \ \ \ \ (\frac{\pi}{2}, \ 1)[/tex] [tex]y-(1) = -\frac{1}{2}(x - (\frac{\pi}{2} ))[/tex]Distribute -1/2 inside the parentheses.
[tex]y-1=-\frac{1}{2}x + \frac{\pi}{4}[/tex]Add 1 to both sides of the equation.
[tex]y=-\frac{1}{2}x + \frac{\pi}{4}+1[/tex] [tex]y=-\frac{1}{2}x + \frac{\pi}{4} + \frac{4}{4}[/tex] [tex]y=-\frac{1}{2}x + \frac{\pi+4}{4}[/tex]You can leave it written as this, or write it as:
[tex]y=-\frac{x}{2} +\frac{\pi + 4}{4}[/tex]This is the equation of the normal line of [tex]y=sin(2x-\pi)+1[/tex] at [tex]x=\frac{\pi}{2}[/tex].
Find the smallest number which is exactly divisible
by 15 20 and 30
Answer:
60
Step-by-step explanation:
The smallest number that is divisible by 15, 20 , and 30, must have the needed factors of each of these numbers:
15 = 3 * 5
20 = 2 * 2 * 5
30 = 2 * 3 * 5
Then the minimum common factor must have the following factors to satisfy the divisibility of all of the numbers above:
2 * 2 * 3 * 5 = 60
What division problem can be represented using the number line?
A number line going from 0 to StartFraction 10 Over 3 EndFraction in increments of one-third. An arrow goes from 0 to five-thirds and from five-thirds to StartFraction 10 Over 3 EndFraction.
StartFraction 10 Over 3 EndFraction divided by five-thirds
Five-thirds divided by StartFraction 10 Over 3 EndFraction
2 divided by five-thirds
2 divided by StartFraction 10 Over 3 EndFraction
Answer:
It's the first answer.
Step-by-step explanation:
Answer:
The Answer is A
Step-by-step explanation:
Determine the solution set of (3x - 5)2 = 36.
{-1/3, 11/3}
{11/3}
{-6, 6}
Answer:
[tex]the \: solution \: set \:is \to \{{-6, 6} \}[/tex]
Given the following formula, solve for t v= u + at
A t= a(v+a)
b t= a(v-u)
c t=v-u/a
d t=v+a/a
Answer:
rc
Step-by-step explanation:
rc
Which weighs more: a watermelon that weighs 7.5 kilograms or a baby that weighs 12 pounds? Explain your reasoning. (Note: 1 pound is about 0.45 kilograms and 1 kilogram is about 2.2 pounds.)
Answer:
The watermelon.. I think
Step-by-step explanation:
Multiply 7.5 times 2.2 and you get 16.5, which is greater than 12. Please correct me if wrong on this because everybody makes mistakes.
Look at the factors of 24 and 32.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 32: 1, 2, 4, 8, 16, 32
The GCE of 24 and 32 is
Answer: 8
Step-by-step explanation:
Answer:
8
Step-by-step explanation:
Solve for x (2x-8) (9x-10)
Answer
x+3=17
Step-by-step explanation:
Answer: 18x2 -92x+ 80
Step-by-step explanation:
is the expression 32/-8 undefined? If not find the quotient.
Answer:
the quotient is 4
Step-by-step explanation:
Given a right triangle as shown below estimate the length of the missing side to the nearest tenth of a centimeter
Answer:
C. 19.4
Step-by-step explanation:
c=a2+b2−−−−−−√
a=162+112−−−−−−−−√
c=256+121−−−−−−−−√
c=377−−−√
c=19.4165
sal recorded the outdoor temperature as -4°F at 7:30 am . at noon , it was 22°F . sal said the temperature changed by 18°F because 22-4=18. Is sal right or wrong .
Answer:
Sal is wrong, correct answer is 26°FStep-by-step explanation:
Initial temperature = -4°FTemperature at noon = 22°FTemperature change:
22 - (-4) = 22 + 4 = 26°FSal is wrong as the difference should be calculated as subtraction of the two values and absolute value of the result should be taken as the answer
Answer:
Sal was wrong as the change of temperature is 26°F
Step-by-step explanation:
recorded temperature at 7:30 A.M. = -4°F
at noon = 22°F
change of temperature = 22 - (-4) = 26°F
therefore, Sal was wrong as the change of temperature is 26°F
Point A is located on the coordinate planet (3,-6) Point B is directly across the x-axis from point A and is the same distance from the x-axis as point A
What are the coordinates of point B?
Answer:
(3,6)
Step-by-step explanation: it is a reflection across the x-axis which is positive (3,6)
Ok
Put -9,-4, and -10 in order from least to greatest. You can use the number line to help.
-2
-10
0
4
6
-8
2
8
-6
10
-10
Answer:
X=5.086
Step-by-step explanation:
432.34 on the number line, converted to negotiable /85 decimal places, divided by the sum of 432.34/85:
X=5.086
Edit: Gime branlies
A new truck costing $60,000 with a residual value of $6,000
An accountant who is currently earning $42,380 annually expects a 6.5% raise. What is the amount of the
expected raise?
Answer:
$2754.70
Step-by-step explanation:
What is the coefficient of the third term in this expression? a^2+3c^3+6b^3
Answer: The coefficient is 3c
Step-by-step explanation:
Write an equation in standard form for the line, where the points (-2, -1) and (0, 4) are on the line
Answer:
An equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
Step-by-step explanation:
Given the points
(-2, -1) and (0, 4)The slope between two points
[tex]\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-2,\:-1\right),\:\left(x_2,\:y_2\right)=\left(0,\:4\right)[/tex]
[tex]m=\frac{4-\left(-1\right)}{0-\left(-2\right)}[/tex]
[tex]m=\frac{5}{2}[/tex]
Writing the equation in point-slope form
As the point-slope form of the line equation is defined by
[tex]y-y_1=m\left(x-x_1\right)[/tex]
Putting the point (-2, -1) and the slope m=1 in the line equation
[tex]y-\left(-1\right)=\frac{5}{2}\left(x-\left(-2\right)\right)[/tex]
[tex]y+1=\frac{5}{2}\left(x+2\right)[/tex]
[tex]y=\frac{5}{2}x+4[/tex]
Writing the equation in the standard form form
As we know that the equation in the standard form is
[tex]Ax+By=C[/tex]
where x and y are variables and A, B and C are constants
so
[tex]y=\frac{5}{2}x+4[/tex]
[tex]\frac{5}{2}x-y=-4[/tex]
Therefore, an equation in standard form for the line is:
[tex]\frac{5}{2}x-y=-4[/tex]
The school Library was building a new one-room addition. the architects drawing shown below uses the scale 1/8 in = 1ft
Dimensions: 2 1/4 and 3 3/16
Using the dimensions indicated on the drawing, what is the total area of the new room?
Answer:
the total are is 459
Step-by-step explanation:
3 3/16 divided by 1/8 = 25 1/2 or 25.5
2 1/4 divided by 1/8 = 18
so 18 x 25.5 = 459
hope this helps
The total area of the new room is 459.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
WE are given that school Library was building a new one-room addition. the architects drawing shown below uses the scale 1/8 in = 1ft
Dimensions: 2 1/4 and 3 3/16
Therefore,
3 3/16 divided by 1/8 = 51/2 or 25.5
2 1/4 divided by 1/8 = 18
Thus we have the area
= 18 x 25.5
Area = 459
The total area of the new room is 459.
Learn more about scale factor here:
https://brainly.com/question/11178083
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When a rate is simplifed so that it has a denominator of 1 unit, it is called a(n) ___________ rate.
Answer:
called unit rate .
Step-by-step explanation:
