Final answer:
The expression 5ac+10ab-2c²-4bc is factored by first taking out the common factor of 2, and then grouping terms to extract 'a' from the first two and 'c' from the last two terms to get 2(a(5c + 5b) - c(c + 2b)).
Explanation:
To factor the expression 5ac+10ab-2c²-4bc, we look for common factors in each term. Observing the coefficients, we see that each term is divisible by 2. Also, we can factor out variable 'a' from the first two terms and variable 'c' from the last two terms. The factored expression is:
2a(5c + 5b) - 2c(c + 2b).
We can then extract the common factor 2 from both parts to get:
2(a(5c + 5b) - c(c + 2b)).
This is the fully factored form of the given expression.
Need help with this?
x= -2 hope this help do you need to show your steps?
Step 1. Separate terms with roots from terms without roots
[tex]\sqrt{x+3}=5 - 4[/tex]
Step 2. Simplify 5 - 4 to 1
[tex]\sqrt{x+3} =1[/tex]
Step 3. Square both sides
[tex]x + 3 = 1[/tex]
Step 4. Subtract 3 from both side
[tex]x = 1 - 3[/tex]
Step 5. Simplify 1 - 3 to -2
[tex]x = -2[/tex]
How to express exponential equation, 3^c = 27 , as a logarithmic equation
If you consider the logarithm base 3 of both sides, you have
[tex] \log_3(3^c) = \log_3(27) [/tex]
You can use a rule of logarithms that allow you to turn exponents into multiplicative factors:
[tex] \log_a(b^c) = c\log_a(b) [/tex]
So the equation becomes
[tex] c\log_3(3)=\log_3(27) [/tex]
Now, by definition, you have
[tex] \log_a(b)=c \iff a^c=b [/tex]
So, you have
[tex] \log_3(3)=x \iff 3^x=3 \iff x = 1,\quad \log_3(27)=y \iff 3^y=27\iff y=3 [/tex]
So, the equation becomes
[tex] 1\cdot c = 3 \iff c=3 [/tex]
[tex]log_{3}[/tex]27 = c
using the law of logs : [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
given [tex]3^{c}[/tex] = 27 then
[tex]log_{3}[/tex] 27 = c
5(2x-1)/3 -4 =11 what does x =
Solve for x by simplifying both sides of the equation, then isolating the variable.
x = 5
To solve the equation 5(2x-1)/3 - 4 = 11 for x, you need to isolate the term containing x on one side and perform basic algebraic operations to find that x = 5.
Explanation:The mathematical equation in question is 5(2x-1)/3 - 4 = 11, which you can solve to find the value of x. First off, you should isolate the term including x on one side to simplify the equation. Multiply both sides by 3 to get rid of the division by 3. The equation then becomes: 5(2x-1) - 4*3 = 11*3, which simplifies to 5(2x-1) - 12 = 33. Then, add 12 to both sides to isolate the term containing x on one side: 5(2x-1) = 45. Next, divide both side by 5 so the equation becomes: 2x-1 = 9. Finally, add 1 then divide by 2 to solve for x, and you get x = 5.
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need help asap, will mark brainlyist!!!!!!!
A. y = -x³ leading coefficient is negative
B. y = x³ + 1 leading coefficient is positive
C. y = x² leading coefficient is positive
D. y = (x-1)³ leading coefficient is positive
Answer: B, C, D
Holly bought blank CD's and spent $34.57.What is that amount rounded to the nearest dollar?.
Answer:
$35
Step-by-step explanation:
Rounding to the nearest dollar which would be 4 so in that case you would use the 5 in .57 and because 5 is a large number it would make the 4 into a five thus making it $35. Hope this helped :)
What is the y-intercept of 6x+ 12y= 60?
A. 5
B. 10
C .60
What is the slope of the line that contains the points (1, −1) and (−2, 8)?
A. −3
B. 7 over 3 negative
C. 1 over 3 negative
Compare using an inequality symbol 54.045 and 54.405
The two of the given numbers 54.045 and 54.405 can be compared using the inequality as 54.045 < 54.405.
Given two numbers 54.045 and 54.405. If the two numbers are plotted on the graph as shown below, it can be clearly seen that 54.045 comes before 54.405 on positive axis.
Therefore, 54.045 is smaller than 54.405. So ‘<’ smaller than inequality symbol will be used in between 54.045 and 54.405.
Hence, the correct representation of the comparison is 54.045 < 54.405.
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K is the midpoint of segment HL . H has coordinates (1, -7 ) , and K has coordinates(-9, 3 ). Find the coordinates of other end point L.
The coordinates of the other endpoint L are (-19, 13).
If K is the midpoint of segment HL, we can use the midpoint formula to find the coordinates of point L.
The midpoint formula states that if you have the coordinates of two endpoints of a line segment and the coordinates of the midpoint, you can find the missing endpoint.
Let's denote the coordinates of point L as (x, y).
The midpoint formula is:
Midpoint =[tex]\(\left(\frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2}\right)\)[/tex]
Given:
Coordinates of K = (-9, 3)
Coordinates of H = (1, -7)
Let (x, y) be the coordinates of point L.
Using the midpoint formula for x-coordinates:
[tex]\(\frac{{1 + x}}{2} = -9\)[/tex]
Solving for x:
[tex]\(1 + x = -18\)[/tex]
[tex]\(x = -19\)[/tex]
Using the midpoint formula for y-coordinates:
[tex]\(\frac{{-7 + y}}{2} = 3\)[/tex]
Solving for y:
[tex]\(-7 + y = 6\)[/tex]
[tex]\(y = 13\)[/tex]
Therefore, the coordinates of the other endpoint L are (-19, 13).
how many patients in the hospital were at least 60 years old? 55 45 115 70
i looked it up and i may be wrong but i think its 45
Answer:
I think it is 55 because it said how many people were at least 60 so i added the last two columns together.
Step-by-step explanation:
What is 3 2/5⋅2 1/3 ?
A. 5 2/15
B. 6 2/15
C. 7 14/15
D. 8 1/15
let's firstly, convert the mixed fractions to improper, and then multiply.
[tex]\bf \stackrel{mixed}{3\frac{2}{5}}\implies \cfrac{3\cdot 5+2}{5}\implies \stackrel{improper}{\cfrac{17}{5}}~\hfill \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{17}{5}\cdot \cfrac{7}{3}\implies \cfrac{17\cdot 7}{5\cdot 3}\implies \cfrac{119}{15}\implies 7\frac{14}{15}[/tex]
This is a procedure to multiply mixed numbers. Then multiply the fractions and simplify the resulting fraction into a mixed number.
Explanation:The problem asked here is a multiplication problem with mixed numbers. First, let's convert 3 2/5 and 2 1/3 to improper fractions. For 3 2/5, multiply 5 (the denominator) and 3 (the whole number), then add 2 (the numerator). We get 17/5. For 2 1/3, multiply 3 (the denominator) and 2 (the whole number), then add 1 (the numerator). We get 7/3.
Now let's multiply the fractions. The resulting fraction is (17/5) x (7/3) = 119/15. This simplifies to 7 14/15.
So, 3 2/5 multiplied by 2 1/3 equals 7 14/15.
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What are the domain and range of each relation?
Drag the answer into the box to match each relation.
Answers:
The domain of the graph is {-3, -1, 1, 4}. The range of the graph is {-4, -1, 1, 4}
The domain of the set of ordered pairs is {-4, -3, 1}. The range of the set of ordered pairs is {1, 3, 4}
====================================================
Recall that the domain is the set of allowed x values. All we do is list the unique x coordinates of each point which are -3, -1, 1 and 4. The range is the set of y values so we just list the unique y coordinates of each point which are -4, -1, 1 and 4.
The same will happen with the other problem as well. The set of points listed is pretty much identical to the first problem, but the points haven't been graphed, but instead their coordinates have been listed out. The first coordinate is the x coordinate. The second coordinate is the y coordinate. Each point is in the form (x,y).
The domain of the graph is {-3, -1, 1, 4}. The range of the graph is {-4, -1, 1, 4}
The domain of the set of ordered pairs is {-4, -3, 1}. The range of the set of ordered pairs is {1, 3, 4}
====================================================
Recall that the domain is the set of allowed x values. All we do is list the unique x coordinates of each point which are -3, -1, 1 and 4. The range is the set of y values so we just list the unique y coordinates of each point which are -4, -1, 1 and 4.
The same will happen with the other problem as well. The set of points listed is pretty much identical to the first problem, but the points haven't been graphed, but instead their coordinates have been listed out. The first coordinate is the x coordinate. The second coordinate is the y coordinate. Each point is in the form (x,y
Please help asap 27 pts
[tex]-7k < 63\qquad|\text{change the signs}\\\\7k > -63\qquad|\text{divide both sides by 7}\\\\k >-9\\\\Answer:\ c)\ k > -9.[/tex]
what is y=8/5(x-9)+16 in slope intercept form
y = 8/5( x - 9 ) + 16
8/5 = 1.6
y = 1.6x - 14.4 + 16
y = 1.6x + 1.6
The slope is therefore 1.6 and
The y-intercept is 1.6
GEOMETRY HELP , thank you doe helping me , the question is in the below
The answer to your problem is Substitution (A) due to y being 4.
There were 70 birds in a tree. One year later, the number oIn 2013, there were 70 birds in a tree. One year later, the number of birds decreased by 30%. How many birds were in the tree in 2014?F birds decreased by 30%. How many birds were in the tree in 2014?
Julio cubes a number and then takes the cube root of the result.He ends up with 20.What number did julio start with
Julio initially started with the number 20, because cubing the number and then taking the cube root returns the original number.
If Julio cubes a number and then takes the cube root of the result, and ends up with 20, then the number he started with is also 20. This is because the cube of a number n is n
to the power of 3 (n³), and the cube root of a number is the inverse operation, which will return the original number. In symbolic form, if n is cubed to get n³, then taking the cube root of n³ will return n. Since Julio ends up with 20, the number he started with must have been 20.
The expression below represents the number of bacteria in a petri dish after t hours. Interpret the meaning of the expression.
The answer is B) The initial number of bacteria is 57, and the growth rate is 31% per hour.
The expression shown is an exponential expression. An exponential expression usually takes the form [tex]ab^{x}[/tex], as this one does. A represents the initial value, in this case-the initial number of bacteria. B represents the growth rate. When it is an increasing growth rate, it will begin with 1, because it will have everything it had before, plus the percent increase, the decimal portion. In this case, a=57, and b=0.31.
Hope this makes sense!
How do you solve 3/2x-4=16
[tex]\frac{3}{2}x[/tex] - 4 = 16
[tex]\frac{3}{2}x[/tex] = 20 added 4 to both sides
3x = 40 multiplied both sides by 2
x = [tex]\frac{40}{3}[/tex] divided both sides by 3
Answer: x = [tex]\frac{40}{3}[/tex]
Given f(x) = ax – b, what is f-1(x)?
A) x+b/a
B) 1/ax-b
C) 1/ax+b
ANSWER
The correct answer is A
[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]
EXPLANATION
Given [tex]f(x)=ax-b[/tex].
We can find the inverse by taking the steps.
1. Let [tex]y=ax-b[/tex]
2. Interchange x and y
[tex]x=ay-b[/tex]
3. Make y the subject
[tex]x+b=ay[/tex]
[tex]\frac{x+b}{a}=y[/tex]
The new function we got now is the inverse of f(x)
[tex]f^{-1}(x)=\frac{x+b}{a}[/tex]
x + b/a Replace f(x) with y, interchange x and y and solve for y.
Find the x-coordinate where the graph of the function f(x) = e(–sinx) has a slope of 0
pie
pie/4
pie/2
none of these
[tex]y = e^{-sin(x)}[/tex]
[tex]y' = -e^{-sin(x)}(cos(x))[/tex]
[tex]0 = -e^{-sin(x)}(cos(x))[/tex]
When is cos (x) = 0? at 90° (aka π/2)
Answer: [tex]\frac{\pi}{2}[/tex]
Answer: Hello there!
We have the function f(x) = exp(-sin(x)) and we want to see in wich point the slope is 0.
This is equivalent to see when f'(x) = 0
where f'(x) is the derivative of f(x)
Then the first step is derivate the function f(x)
if we have a function of the form g(h(x)), his derivate is:
g'(h(x))*h'(x)
In our case, g(x) = exp(x) and h(x) = - sin(x)
then f'(x) = exp(-sin(x))*(-cos(x))
Now we know that exp(-sin(x)) is never equal to 0, then we need to se when the cosine is equal to zero.
cos(90°) = 0, and 90° is equivalent to pi/2
Then f'(pi/2) = exp(-sin(pi/2))*(-cos(pi/2)) = 0
this means that the function f(x) has a slope of 0 in the point x = pi/2
would the correct answer be 4? photo attached.
The answer is B. 2
Hope it helps
In bluepoint, the average low temperature for January was 40F. The average low in February was 27%F lower. What was the average low in February?
There are 21 groups of 3 in a room. How many people are there. I need an equation
Which angles shown in the drawing are supplementary
Distance between 2 airports = 1,450 miles. Average speed of airplane = 350 mph. Travel time by bus after arrival at airport = 20 minutes. Total travel time = hours.
Divide total miles between airports by the airplane's speed to find the time it took to travel by plane:
1450 miles / 350 mph = 4.142 hours = 4 hours 9 minutes
Then add the time the bus traveled:
4 hours 9 minutes + 20 minutes = 4 hours 29 minutes
Answer:
4 hours and 29 mins
Step-by-step explanation:
What is the equation and the solution to 136 divided by 3
A web designer charges a $200 fee plus $50 per hour to build a website. Which equation represents the total cost, y, to a customer based on the number of hours, x, it takes to buld the website? A. y = 50x − 200 B. y = 250x C. y = 200x + 50 D. y = 50x + 200
D. y = 50x + 200 is your answer
can i please get help with this question?
The answer is 3.88888888889
The answer is 35/9
You first would remove the parentheses
Next you see that there is a subtraction symbol and a negative symbol right beside each other. You cant have 2 negatives side by side, so you change the symbol to addition
The problem then looks like this: 5/9 + 3 1/3
To make the problem easier you change the mixed number (3 1/3) to an improper fraction which is 10/3
Because its 5/9 + 10/3 you multiply 10 and 3 and get 30, and you keep the LCD (least common denominator) which is 9
Finally you add 5 + 30 = 35 and have 9 as your denominator
35/9 or 3 8/9
Which two units of measure below are longer than a meter?
centimeter
kilometer
millimeter
heptometer
Please help me with this question
For this question, you simply take the x value from the given chart and plug it into the equation, then if the outcome makes sense based on the chart then you use another value of x and plug the second value in and if that also makes sense then you continue plugging in all the x values from the chart until all of them match. There is only one chart which contain the correct table of values.
To start of, let’s plug in the x values from graph 1, the first two values seems to be correct. However, in the third value, it does not match, therefore the first option is in correct.
Moving on to the second option, we could already determine that this table of values is incorrect because the very first x value does not match.
Moving onto the third table of values, we determine that all of the x values are in accordance with the y-values, therefore this option is correct.
Answer: Third option