Answer: The factor of the above function is (2x + 3) (3x + 4)
We are given the below function
[tex]6x^2\text{ + 17x + 12}[/tex]This function can be factor using factorization method
The co-efficient of x^2 = 6
Multiply 6 by 12 to get the constant of the function
12 x 6 = 72
Next, find the factors of 72
Factors of 72 : 1 and 72, 2 and 36, 6 and 12, 9 and 8, 3 and 24
The only factor that will give us 17 when add and give us 72 when multiply is 8 and 9
The new equation becomes
[tex]\begin{gathered} 6x^2\text{ + 17x + 12} \\ 6x^2\text{ + 8x + 9x + 12} \\ \text{Factor out 2}x \\ 2x(3x\text{ + 4) + 3(3x + 4)} \\ (2x\text{ + 3) (3x + 4)} \end{gathered}[/tex]The factor of the above function is (2x + 3) (3x + 4)
please try to answer quickly my brainly app keeps crashing
From the figure, the radius of the sphere is:
[tex]r=1\text{ in}[/tex]The volume of the sphere is given by the formula:
[tex]V=\frac{4}{3}\pi r³[/tex]Using the value of the radius:
[tex]\begin{gathered} V=\frac{4}{3}\pi(1)³ \\ \\ \therefore V=\frac{4\pi}{3}\text{ in^^b3} \end{gathered}[/tex]Approximating to the nearest cubic inch:
[tex]\therefore V\approx4\text{ in^^b3}[/tex]ther
What is the name of the decimal number?7.1seventy-one seven and one hundredthsseven and one tenth seventeen
Answer:
seven and one-tenth.
Explanation:
To name decimal number, we first name the values before the decimal point, in this case, seven
Then, we add an and that corresponds to the decimal point
Finally, we say the number after the decimal point and the place of this number, in this case, one-tenth.
Therefore, the name of the decimal number 7.1 is:
seven and one-tenth.
Help me out please I don’t understand what I’m doing
Since we have the value for selling each shirt, the earnings that came from the hats sold and the total earnings we can complete equation using a linear equation in which the cost of each shirt will represent the slope and the y-intercept will be the earnings that came from the hats, like this:
[tex]5x+40=125[/tex]then clear the equation for x in order to find how many shirts were sold
[tex]\begin{gathered} 5x=125-40 \\ 5x=85 \\ x=17 \end{gathered}[/tex]In the circle below, if AB is a diameter, find the measure of arc AB.
A circle has 360°
since the diameter cuts in half the circle
The measure of the arc of half the circle (semicircle) measure arcAB is
[tex]AB=\frac{360}{2}[/tex][tex]AB=180[/tex]AB=180°
Then correct answer is
option a
Which of the following correctly represents the movement on the number line for the calculation 21 - (- 15) + (- 30) ?
a- left right left
b-right left left
c- right left right
d-right right left
It is the movement on the number line is right right left
The option (d) is correct .
Given,
The movement on the number line for the calculation
21 - (- 15) + (- 30)
To find the which of the following correctly represents the movement of calculation?
Now, According to the question:
21 - (- 15) + (- 30)
21 + 15 - 30 = 6
right right left
Hence, It is the movement on the number line is right right left
The option (d) is correct.
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we need to seat 200 people. A table holds 8 people How Many tables do we need ?
Kyah, this is the solution to the exercise:
People = 200
Capacity of each table = 8 people
In consequence, we need:
Number of tables = People/Capacity of each table
Replacing by the values we know:
Number of tables = 200/8
Number of tables = 25
help meeeeeeeeee pleaseee !!!!!
The values of the composition of the functions are:
(f o g)(x) = -x³ - x + 1
(g o f)(x) = -x³ - x - 1
How to Determine the Composition of a Function?To find the value of the composition of a given function, the inner function is first evaluated, then the output of the inner function is then replaced into the outer function and simplified.
Given the functions:
f(x) = x³ + x + 1g(x) = -x(f o g)(x) = f(g(x))
Substitute -x for x into the function f(x) = x³ + x + 1:
f(g(x) = (-x)³ + (-x) + 1
f(g(x) = -x³ - x + 1
(g o f)(x) = g(f(x))
Substitute x³ + x + 1 for x into the function g(x) = -x:
g(f(x)) = -(x³ + x + 1)
g(f(x)) = -x³ - x - 1
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The half life of titanium - 44 , a radioactive isotope, is 63 years. If a substance starts out with 1000 kg of titanium- 44( round all the answers to the nearest hundredth of a kilogram or year) A) how much titanium- 44 will remain after 441 years ? B) how long will it be before there is only 1 kg of titanium- 44 ?
a)
Every 63 years, the amount of titanium halves.
441 years later means how many halving?
441/63 = 7 halving
We start off with 1000 and do 7 halving to get the amount of Titanium-44 after 441 years.
[tex]\begin{gathered} 1000(\frac{1}{2})^7 \\ =7.8125 \end{gathered}[/tex]after 441 years, the amount of titanium remaining would be 7.8125 kg
b)
Let's find the point where the remaining titanium would be 1 kg.
That would be:
[tex]1=1000(\frac{1}{2})^t[/tex]t is the time we are looking for. We can solve this using Ln(natural log):
[tex]\begin{gathered} 1=1000(\frac{1}{2})^t \\ 0.001=\frac{1}{2}^t \\ ln(0.001)=\ln (\frac{1}{2}^t) \\ \\ t=\frac{\ln (0.001)}{\ln (\frac{1}{2})} \\ t=9.965 \end{gathered}[/tex]There is basically 9.965 halving. That would make the years approximately:
9.965 * 63 (half life) = 627.795 years (approx)
estimate the product by rounding to the nearest ten: 28×51×76
To estimate each number by rounding it to the nearest ten, we will look at the unit digit,
If it is less than 5, then we replace it by 0 and keep the ten-digit as it
If it is 5 or more, then we will replace it by 0 and add the ten-digit by 1
Let us do that with every number
28, the unit digit is 8 which is greater than 5, then replace it by 0 and add 2 by 1
28 rounded to 30
51, the unit digit is 1 which is less than 5, then replace it by 0
51 rounded to 50
76, the unit digit is 6 which is greater than 5, then replace it by 0 and add 7 by 1
76 rounded to 80
Now let us multiply them
[tex]28\times51\times76=30\times50\times80=120,000[/tex]The product of the given numbers is 120,000
Just give me the answer please, my device is at 10%
Solve for x
We can use sine
[tex]\begin{gathered} \sin 48^0=\frac{x}{17} \\ \text{Cross multiply} \\ x=17\times\sin 48^0 \\ x\text{ =17}\times0.7431448 \\ x=12.6\text{ } \end{gathered}[/tex]help meeeeeeeeeeeeeeeeeeeeeee
Given m//n find the value of x and y (5x+1)° (6x-10)° (y°)
To find the value of x, use the vertical angle theorem.
Vertical angles are congruent.
Thus we have:
6x - 10 = 5x + 1
Solve for x.
6x - 10 = 5x + 1
Add 10 to both sides:
6x - 10 + 10 = 5x + 1 + 10
6x = 5x + 11
Subtract 5x from both sides:
6x - 5x = 5x - 5x + 11
x = 11
To find the value of y, use corresponding angles thoerem.
When two parallel lines are crossed by a transversal, the angles in matching corners are correponding angles.
Corresponding angles are congruent.
Thus, we have:
y = 6x - 10
Substitiute x for 11:
y = 6(11) - 10
y = 66 - 10
y = 56°
ANSWER:
x = 11, y = 56°
What is the the measure and length of arc MC
As given by the question
There are given that the measuring circle.
Now,
From the given circle, the length of the MN is 28 units, because the half of the length of the MN is 14. So just multiply by 2 into half of the given value.
Hence, the length of MN is 28 units.
Now,
For the measure of MN:
The measurement of the angle MN is 74 degrees.
Hence, a measure of arc MN is 74 degrees. and the length of segment MN is 28 units.
Use the Pythagorean Theorem to find x, in simplest radical form. 20
The Pythagorean theorem states that the sum of the squares of the two sides of a right angle is equal to the square of the hypotenuse (longest side).
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where }c\text{ is the hypotenuse, and }a\text{ and }b\text{ are the other two sides of a right triangle.} \end{gathered}[/tex]Given: c = 20, a = 8, and b = x. Find x.
[tex]\begin{gathered} a^2+b^2=c^2 \\ (8)^2+(x)^2=(20)^2 \\ 8^2+x^2=20^2^{} \\ 64+x^2=400 \\ x^2=400-64 \\ x^2=336 \\ \sqrt{x^2}=\sqrt[]{336} \\ x=\sqrt[]{16\cdot21} \\ x=4\sqrt{21}\text{ (final answer)} \end{gathered}[/tex]I need answers to 6a and 6b. This is for my homework :,)
The system of equations has 3 cases
1. y = ax + b, y = ax + c
Since the coefficient of x and y are the same, and the y-intercepts are different, then
The two lines are parallel
2. y = ax + b, y = dx + c
Since the 2 lines have different coefficients of x, then
The two lines are intersected
3. y = ax + b, y = ax + b
Since the two lines have equal coefficients of x and equal y-intercepted, then
The two lines are coincide (same line)
6. a)
Since the system of equations is
[tex]\begin{gathered} y=2x+3 \\ y=12x-2 \end{gathered}[/tex]The coefficients of x not equal
Then from case 2 above
The two lines are intersected
6.b
Since the system of equations is
[tex]\begin{gathered} y=13x+2 \\ y=13x-2 \end{gathered}[/tex]The coefficients of x are equal
The y-interceptes not equal
Then from case 1 above
The two lines are parallel
which statement is true and why? & why not the others?
For this problem, we have three circles with different radii. We need to determine which circles are similar and point out the reason for our statement.
Every circle has the same shape, the only thing that sets them apart is the radii. Since we can represent the relationship between the radii as fractions, then all circles are similar. Due to this, the only correct option is the second one. "Circle 1 is similar to both circle 2 and circle 3".
Solve these: state whether there is no solution, one solution specify it , or infinitely many Solutions.
Step 1:
Write the two systems of equations
y = 3x = 2
3x = y - 3
Step 2:
Substitute y from the first equation into the second equation
[tex]\begin{gathered} 3x\text{ = y - 3} \\ 3x\text{ = 3x + 2 - 3} \\ 3x\text{ - 3x = 2 - 3} \\ 0\text{ = 2 - 3} \\ 2\text{ = 3} \end{gathered}[/tex]Final answer
NO SOLUTION
5|x +1| + 7 = 38
Solve for x
Answer: No solutions
Step-by-step explanation:
[tex]5|x+1|+7=-38\\\\5|x+1|=-45\\\\|x+1|=-9[/tex]
However, as absolute value is non-negative, there are no solutions.
Give the point-slope form of the equation of the line that is perpendicular to y= -4x/5+10 and contains P(5,6)
You have to write the equation of a line perpendicular to
[tex]y=-\frac{4}{5}x+10[/tex]That crosses the point (5, 6)
A caracteristic of a line permendicular to another one is that its slope pf the perpendicular line is the negative inverse of the slope of the first line.
So for example if you have two lines:
1_ y=mx+b
and
2_ y=nx+c
And both lines are perpendicular, the slope of the second one will be the negative inverse of the slope of the first one, that is:
[tex]n=-\frac{1}{m}[/tex]The slope of the given line is m=-4/5
The negative inverse is
[tex]-(\frac{1}{-\frac{4}{5}})=-(-\frac{5}{4})=\frac{5}{4}[/tex]Now that you know the slope of the perpendicular line, use it along with the given point (5, 6)
in the slope-point formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-6=\frac{5}{4}(x-5) \end{gathered}[/tex]Describe where the function has a hole and how you found your answer.
Step 1:
Write the function
[tex]f(x)\text{ = }\frac{x^2+\text{ 7x + 10}}{x^2\text{ + 9x + 20}}\text{ }[/tex]Step 2:
Factorize both the numerator and the denominator.
[tex]\begin{gathered} f(x)\text{ = }\frac{x^2\text{ + 2x + 5x + 10}}{x^2\text{ + 4x + 5x + 20}} \\ f(x)\text{ = }\frac{x(x\text{ + 2) + 5(x + 2)}}{x(x\text{ + 4) + 5 (x + 4)}} \\ f(x)\text{ = }\frac{(x\text{ + 5)(x +2)}}{(x\text{ + 5)(x + 4)}} \end{gathered}[/tex]Step 3:
A hole is a common factor between the numerator and the denominator.
Hole: x + 5 = 0
x = -5
Final answer
Hole is -5
9. ¿Cuál es el equivalente
fraccionario
de 0.2666 ...?
Answer:
4/15
Step-by-step explanation:
4/15 = 0.26666666...
Mr. Hanes places the names of four of his students, Joe, Sofia, Hayden, and Bonita, on slips of paper. From these, he intends to randomly select two students to represent his class at the robotics convention. He draws the name of the first student, sets it aside, then draws the name of the second student. Whats the probability he draws he draws Sofia then joe?
Given:
Total student = 4
Joe, Sofia, Hayden, and Bonita.
Find-:
Probability he draws Sofia then Joe.
Explanation-:
Probability: Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
The formula of probability:
[tex]P(A)=\frac{\text{ Number of favorable outcomes to A}}{\text{ Total number of possible outcomes}}[/tex]For Sofia.
Total number of possible outcomes = 4
Favorable outcomes for Sofia = 1
So probability for Sofia :
[tex]P(S)=\frac{1}{4}[/tex]After the first student set it aside.
For Joe.
Total number of possible outcomes = 3
A favorable outcome for Joe = 1
So probability for Joe.
[tex]P(J)=\frac{1}{3}[/tex]So probability for Sofia then joe is:
[tex]\begin{gathered} P=\frac{1}{4}\times\frac{1}{3} \\ \\ P=\frac{1}{12} \end{gathered}[/tex]
Mr. McFall uses 2% cups of peanuts for every 1/2 cup of chocolate chips in a mixture. Enter the number of cups of peanuts for every 1 cup of chocolate chips. Remember to reduce.
To solve this problem I'll use proportions.
2 1/8 cups ------------------------ 1/2 cup of chocolate.
x ----------------------- 1 cup od chocolate chips
x = (1*2 1/8) / 1/2
x = 17/8 / 2
x = 4 % cups of peanuts
What is the distance between A(5,-2) and B(-2,4)?
Answer:
[tex]\sqrt{85}[/tex]
Step-by-step explanation:
Let's use the distance formula to solve for the distance between the two given points!
d = [tex]\sqrt{(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 }[/tex]
Now, we input the points:
(5-(-2) + (-2-4)
(which will equal...)
(7) + (-6)
Now we input the solutions we got here to the distance formula:
[tex]d =\sqrt{(7)^2 + (-6)^2[/tex]
(we simplify....)
[tex]7^2 = 49\\(-6)^2 = 36[/tex]
input these solutions into the distance formula again...
[tex]\sqrt{49 + 36} = \sqrt{85}[/tex]
85 is not a number that can be square rooted properly, nor does it have any perfect squares available to divide equally.
Therefore, we conclude that the distance between A(5, -2) and B(-2,4) is [tex]\sqrt{85}[/tex].
Write the equation for a parabola with a focus at (1,-4) and a directrix at x= 2.x=?
The basic form of the equation is;
4p (x- h)= (y - k)²
where (h, k) is the vertex and p is the distance from the vertex to either of its directrix or the focus
But, focus is = (1, -4) adn directrix = 2
So, the perpendicular point is :
(1.5 , -4)
p = -0.5
Putting all the values into the formula
4p (x- h)= (y - k)²
4(-0.5)(x - 1.5) = (y - (-4)²
simplify
-2(x - 1.5) = (y + 4)²
-2(x - 1.5) = y² + 8y + 16
Divide through the equation by -2
x - 1.5 = (-1/2) y² - 4y - 8
Add 1.5 to both-side of the equation
[tex]x\text{ = -}\frac{1}{2}y^2-4y\text{ - 8 + 1.5}[/tex][tex]x=-\frac{1}{2}y^2-4y\text{ - 6.5}[/tex]Dylan invested $93,000 in an account paying an interest rate of 3% compoundedquarterly. Assuming no deposits or withdrawals are made, how much money, to thenearest cent, would be in the account after 17 years?
The formula to calculate compound interest is given to be:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
[tex]\begin{gathered} A=\text{ final amount} \\ P=\text{ initial amount (principal)} \\ r=\text{ interest rate} \\ n=\text{ number of times interest applied per time period} \\ t=\text{ number of time period elapsed} \end{gathered}[/tex]The following parameters are given in the question:
[tex]\begin{gathered} P=93000 \\ r=\frac{3}{100}=0.03 \\ n=4(quarterly) \\ t=17\text{ years} \end{gathered}[/tex]We can substitute these values into the formula to calculate the final amount as follows:
[tex]A=93000(1+\frac{0.03}{4})^{4\times17}[/tex]Solving, we get:
[tex]\begin{gathered} A=93000\times1.0075^{68} \\ A=154,577.64 \end{gathered}[/tex]The amount after 17 years is $154,577.64
Dave jogs 8 feet per second. Give each rate in miles per hour.
Answer:
Step-by-step explanation:
first find seconds in an hour
60(seconds in a minute) *60(minutes in an hour) = 3600 seconds in an hour
then multiply 8 by 3600 to see how many feet per hour
28,800
we need miles so there are 5280 feet in a mile
28800/5280 is 5.45454545 or 5.455 miles per hour
Kareem wants to attend a college that will cost $13.800 for the first year. His uncle gave him a special gift of 3000 to use toward the cost. Kareem plans to attend the college in 3 years. How much must Kareem save each month to have enough for the year cost?
Kareem needs to save $13,800 in total
He already got $3000 from his uncle.
Thus, he needs $13,800 - $3000 = $10,800 more
He will need to save up $10,800 in 3 years, that is 3 x 12 = 36 months
To find the amount he must save each month, we will divide $10,800 by 36:
[tex]\frac{10,800}{36}=\$300[/tex]Answer$3001 ptsQuestion 7Mike reads 5 pages an hour. The independent variable is time. What is the dependentvariable?O the number of pagesthe number of hoursO the number of books
We are given that Mike reads 5 pages an hour. This is the quotient of pages with respect to time. In this case, the time is the independent variable and the number of pages is the dependent variable since the number of pages depends on the time interval that is considered.
rectangle rstw has diagonals RT and SW that intersect at Z. If RZ= 5x+8 and SW= 11x-3 find the value of x.
Answer:
19
Explanation:
We know that the diagonals of a rectangle are always equal, therefore RT = SW.
So if RZ = 5x + 8 and SW = 11x - 3, lets's go ahead and find x as shown below;
[tex]\begin{gathered} 2(5x+8)=11x-3 \\ 10x+16=11x-3 \\ 16+3=11x-10x \\ 19=x \\ \therefore x=19 \end{gathered}[/tex]