Answer:
a= 2, b= 3, c= 7
Step-by-step explanation:
Given the quadratic equation:
2x² + 3x +7 =0Quadratic equation in general form is:
ax² + bx + c = 0Comparing the two above we can get following coefficients:
a= 2
b= 3
c= 7
A= 4
B= 12
C= 9
Theese are correct
select the two values of x that are roots of this equation 2x^2 + 7x + 6=0
A. X=-3
B. X=-3/2
C. X=-4
D. X=-2
Answer:
x = -2 or x = -3/2 thus B. & D. are the answer
Step-by-step explanation:
Solve for x:
2 x^2 + 7 x + 6 = 0
Hint: | Factor the left hand side.
The left hand side factors into a product with two terms:
(x + 2) (2 x + 3) = 0
Hint: | Find the roots of each term in the product separately.
Split into two equations:
x + 2 = 0 or 2 x + 3 = 0
Hint: | Look at the first equation: Solve for x.
Subtract 2 from both sides:
x = -2 or 2 x + 3 = 0
Hint: | Look at the second equation: Isolate terms with x to the left hand side.
Subtract 3 from both sides:
x = -2 or 2 x = -3
Hint: | Solve for x.
Divide both sides by 2:
Answer: x = -2 or x = -3/2
Answer:
B and D
Step-by-step explanation:
Given
2x² + 7x + 6 = 0
To factorise the quadratic
Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 2 × 6 = 12 and sum = + 7
The factors are + 4 and + 3
Use these factors to split the x- term
2x² + 4x + 3x + 6 = 0 ( factor the first/second and third/fourth terms )
2x(x + 2) + 3(x + 2) = 0 ← factor out (x + 2) from each term
(x + 2)(2x + 3) = 0
Equate each factor to zero and solve for x
x + 2 = 0 → x = - 2 → D
2x + 3 = 0 ⇒ 2x = - 3 ⇒ x = - [tex]\frac{3}{2}[/tex] → B
A parking garage charges $22.50 for the first hour and $2.50 for each additional hour. Write and solve an equation to find how many hours you can park in the garage for $30. Use "x" to represent the number of hours.
Final answer:
To park for $30 in a parking garage that charges $22.50 for the first hour and $2.50 for each additional hour, you can park for 4.2 hours.
Explanation:
The parking garage charges $22.50 for the first hour and $2.50 for each additional hour. Let's use 'x' to represent the number of hours. To find how many hours you can park for $30, we need to write and solve the equation.
Total cost equation:
$22.50 + $2.50(x-1) = $30
$22.50 + $2.50x - $2.50 = $30
$2.50x = $10.50
x = 4.2 hours
Therefore, you can park for 4.2 hours for $30 in the garage.
| x-3 | < x-3
can someone give a step by step process on how to do this?
Answer:
There are no solutions to the inequality.
Step-by-step explanation:
|x - 3| < x – 3
1. Separate the inequality into two separate ones.
(1) x – 3 < x – 3
(2) x – 3 < -(x – 3)
2. Solve each equation separately
(a) Equation (1)
[tex]\begin{array}{rcl}x - 3 & < & x - 3\\x & < & x\\\end{array}\\\text{This is impossible. No solutions exist.}[/tex]
(b) Equation (2)
[tex]\begin{array}{rcl}x - 3 & < & -(x - 3)\\x - 3 & < & -x + 3\\x & <& -x + 6\\2x & < & 6\\x & < & 3\\\end{array}\\\text{This is impossible. No solutions exist}[/tex]
For example, if x = 0, we get
|0 - 3| < 0 - 3 or
3 < -3
The manufacturer of a new product developed the following expression to predict the monthly profit, in thousands of dollars, from sales of t
product when it is sold at a unit price of x dollars.
-0.5x2 + 221 – 224
What is represented by the zero(s) of the expression?
A.
the unit price(s) when the profit is equal to 0
B.
the unit price(s) when profit is greatest
c.
the profit when the unit price is equal to 0
OD.
the profit when the unit price is greatest
Reset
Next
Answer:
A. The answer is our unit prices when our profit is 0
Step-by-step explanation:
The zeros are the x-intercepts, when the curve passes through the x-axis.
I'm going to call our function P
P(x)=-0.5x^2+221x-224 is equal to 0 (our profit is equal to 0) when x (the unit price is such and such)
The answer is our unit prices when our profit is 0
The expression represents the monthly profit from sales of a product at a given unit price. The zero(s) of the expression represent the unit price(s) when the profit is equal to 0.
Explanation:The expression -0.5x^2 + 221x - 224 represents the monthly profit, in thousands of dollars, from sales of a product when it is sold at a unit price of x dollars.
The zero(s) of the expression are the unit price(s) when the profit is equal to 0. To find the zero(s), we need to set the expression equal to 0 and solve for x.
-0.5x^2 + 221x - 224 = 0We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.The zero(s) of the expression will give us the unit price(s) at which the profit is equal to 0.Learn more about Quadratic equations here:https://brainly.com/question/30098550
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what is the value of x?
Answer:
x = 3Step-by-step explanation:
∠QRT and ∠SRT are supplementary angles,
therefore m∠QRT + m∠SRT = 180°.
(45x)° + m∠SRT = 180° subtract (45x)° from both sides
m∠SRT = 180° - (45x)°
We know: the sum of the measures of the angles of the triangle is equal to 180 °. Therefore we have the equation:
(180 - 45x) + (57 + x) + 25x = 180 combine like terms
(-45x + x + 25x) + (180 + 57) = 180
-19x + 237 = 180 subtract 237 from both sides
-19x = -57 divide both sides by (-19)
x = 3
What is the simplified form of the following expression?
Oo oo
Answer:
[tex]\frac{\sqrt[3]{100x}}{5}[/tex]
Step-by-step explanation:
we have
[tex]\sqrt[3]{\frac{4x}{5}}[/tex]
Multiply inside by [tex]\frac{25}{25}[/tex]
so
[tex]\sqrt[3]{\frac{4x*25}{5*25}}[/tex]
[tex]\sqrt[3]{\frac{100x}{125}}[/tex]
Remember that
[tex]\sqrt[3]{125}=5[/tex]
substitute
[tex]\sqrt[3]{\frac{100x}{125}}=\frac{\sqrt[3]{100x}}{\sqrt[3]{125}}=\frac{\sqrt[3]{100x}}{5}[/tex]
PLEASE HELP ME! 8 POINTS!
Answer:
720/1681
Step-by-step explanation:
First quadrant so everything is positive for a trig function of just the angle. I would suggest just drawing a right triangle using tan(x)=40/9 (opp/adj). Find the hypotenuse which is sqrt(40^2+9^2)=sqrt(1600+81)=sqrt(1681)=41. So sin(x)=40/41 and cos(x)=9/41.
Therefore sin(2x)=2sin(x)cos(x)=2(40/41)(9/41)=720/1681
HELLLLLLPPPPPP!!!!!!!!!
Answer:
A
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= 3x² - 2x + 4 - (5x² + 6x - 8) ← distribute parenthesis by - 1
= 3x² - 2x + 4 - 5x² - 6x + 8 ← collect like terms
= - 2x² - 8x + 12 → A
in a concert hall, 250 seats out of 300 were occupied. to the nearest thousand, what part of the hall was not occupied?
Answer: 0.167 is the part of the hall that was not occupied. Or 16.7 %
Step-by-step explanation:
300-250=50 this is the number of seats not occupied since 250 is the amount occupied.
So, 50/300=5/30 which can be converted to a number which is 0.1666666667. It says to round to the thousandths place, which is the 3rd number. That is 0.167
Answer:
0.167 part of the hall was not occupied
Step-by-step explanation:
Given :In a concert hall, 250 seats out of 300 were occupied.
To Find :To the nearest thousand, what part of the hall was not occupied?
Solution:
Total seats = 300
Occupied seats = 250
Unoccupied seats = 300-250 = 50
So, The part of the hall was not occupied = [tex]\frac{\text{unoccupied seats}}{\text{total seats}}[/tex]
= [tex]\frac{50}{300}[/tex]
= [tex]0.167[/tex]
Hence 0.167 part of the hall was not occupied
For what values of y does 125=(1/25)^y-1
[tex]125 = \frac{1}{125} {}^{y - 1} \\ 125 = ( {5}^{ - 2} ) {}^{y - 1} \\ \\ {5}^{3} = {5}^{2 - 2y} \\ 3 = 2 - 2y \\ - 0.5 = y[/tex]
Answer:
The answer is [tex]y=-0.5[/tex]
Step-by-step explanation:
In order to determine the "y" value, we have to change the way of we see the equation.
In these cases, when the variable is in the exponent and it is possible to make two exponents in each side of the equation, we have to equal bases and then we have to make other equation between the exponents of both sides.
So,
[tex]125=(\frac{1}{25})^y^-^1\\(5)^3=(5^-^2)^y^-^1\\(5)^3=(5)^-^2^*^y^+^2\\[/tex]
Then, we have to make an equation between the exponents of both sides:
[tex]3=-2*y+2\\2*y=2-3\\2*y=-1\\y=\frac{-1}{2}=-0.5\\ y=-0.5[/tex]
Finally, the value of "y" is -0.5
which is the greatest common factor of 24 and 60
Aloha! My name is Zalgo and I am here to be of assistance to you today. The GCF (Greatest Common Factor) of 14 and 60 would be 12. To the GCF of 24, you need to multiply 2^3 by 3. In order to get the GCF of 60, you need to multiply 2^2 by 3 times 5.
I hope that this info helps! :P
"Stay Brainly and stay proud!" - Zalgo
(By the way, do you think you could mark me as Brainliest? I'd greatly appreciate it! Mahalo! XT)
The greatest common factor of 24 and 60 is 12.
What is the greatest common factor of 24 and 60?To get the greatest common factor, we will list the factors of each number and find the largest one that they have in common.
The factors of 24 are:
1, 2, 3, 4, 6, 8, 12, and 24.
The factors of 60 are:
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
The largest factor that 24 and 60 have in common is 12.
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1. Two lines, A and B, are represented by the following equations: Line A: 2x + y = 6 Line B: x + y = 4 Which statement is true about the solution to the set of equations? (4 points) It is (2, 2). There are infinitely many solutions. It is (4, 0). There is no solution.
Answer:
It is (2, 2).
Step-by-step explanation:
A gym charges a one-time fee of $75 to join,plus membership dues of $25 per month. Which equation represents the total cost,c, of belonging to the gym for m months
A) C=25m-75
B) C=25m+75
C) C=75m+25
D) C=75m-25
Answer:
the answer is B
Step-by-step explanation:
75 is a one time payment. 25 is the amount that you will pay permonth
Answer:
C=25m+75
Step-by-step explanation:
Which is the graph of f(x) = 5(2)x?
A is the answer. (0,5) (2,20)
Step-by-step explanation:
This is the correct graph on Desmos, the other user forgot to add x as an exponent.
(0,5) (2,20)
In a singing competition, there are
150 participants. At the end of each
round, 40% of the participants are
eliminated. How many participants
are left after n rounds?
Answer:
150(.40)^n is your equation
Step-by-step explanation:
Answer:
[tex]=150\cdot{0.4^n}[/tex]
Step-by-step explanation:
Let n be the number of rounds. Lets look at n=1 which is round one. Therefore if 40% of the contestants are eliminated then we can write an expression of the number of contestants eliminated:
[tex]=150\cdot{0.4}[/tex]
For round two, n=2:
[tex]=150\cdot{0.4)\cdot{0.4}=150\cdot{0.4^2}[/tex]
Therefore for the n number of rounds:
[tex]=150\cdot{0.4^n}[/tex]
Which expression is equivalent to (x + 2)(3x – 3)?
Multiply the two brackets together
(x+2)(3x-3)
x(3x)*(-3)(x)+2(3x)(2*-3)
3x^2-3x+6x-6
3x^2+3x-6
Answer is : 3x^2+3x-6
Answer
A. x5y3
Step-by-step explanation:
If you repeat the perpendicular line segment construction twice using paper folding, you can construct:
A.the midpoint of a line segment.
B.an angle congruent to a given angle.
C.a parallel to a line through a point not on the line.
D.an angle bisector.
Final answer:
By repeating the perpendicular line segment construction twice using paper folding, one can effectively find the midpoint of a line segment, demonstrating the application of geometric principles and theorems related to perpendicular constructions.
Explanation:
If you repeat the perpendicular line segment construction twice using paper folding, you can construct the midpoint of a line segment. This is based on the principle that constructing perpendiculars at the ends of a given line segment and then erecting a third perpendicular midway between them will intercept the line segment at its midpoint. This is affirmed by the theorems that explain the geometrical properties and relationships of constructing perpendicular lines and their midpoints.
To elucidate, let's take a line segment AB of a certain length, and fold the paper to construct a perpendicular line at point A. Next, repeat the same action at point B. Now, fold the paper to find the midpoint of AB, and erect a perpendicular line at this midpoint. This results in the third perpendicular intersecting AB exactly at its midpoint, demonstrating that this method is effective for finding the midpoint of a line segment, thereby validating option A.
You can construct: The midpoint of a line segment.
The correct option is (A).
Paper folding constructions can be used to create geometric shapes and lines based on certain properties. Let's break down each of the given options and see if they can be achieved by repeating the perpendicular line segment construction twice:
A. The midpoint of a line segment: Yes, this can be achieved. Folding a line segment in half will give you its midpoint. By repeating the perpendicular line segment construction twice, you fold the line segment once to find a point equidistant from both endpoints (which is the midpoint), and folding it again should confirm that the resulting point is indeed the midpoint.
B. An angle congruent to a given angle: No, this cannot be achieved. The perpendicular line segment construction does not involve creating or manipulating angles, so it cannot be used to construct an angle congruent to a given angle.
C. A parallel to a line through a point not on the line: No, this cannot be achieved. The perpendicular line segment construction does not involve creating parallel lines.
D. An angle bisector: No, this cannot be achieved. Again, the perpendicular line segment construction does not involve manipulating angles, so it cannot be used to construct an angle bisector.
Therefore, the correct option is:
A. The midpoint of a line segment.
Anthony is making A collage for his art class my picking Shapes randomly. He has five squares, two triangles, two ovals, and four circles. find p( circle is chosen first)
I am not sure but I think the probability of a circle being chosen first is 4/13
because 13 is the amount of shapes in total, and 4 is the amount of circles. I hope you found this helpful.
Answer:
The answer is [tex]\frac{4}{13}[/tex].
Step-by-step explanation:
There are five squares, two triangles, two ovals, and four circles.
So, total shapes are = [tex]5+2+2+4=13[/tex]
The probability that the first chosen shape will be a circle is given by :
[tex]\frac{possible outcomes}{total number of outcomes}[/tex]
= [tex]\frac{4}{13}[/tex]
Note: 4 because any 1 out of 4 can be selected.
(29 PTS) Explain how the Quotient of Powers Property was used to simplify this expression. 3^4/9 = 3^2
A/ By simplifying 9 to 32 to make both powers base three and adding the exponents
B. By simplifying 9 to 32 to make both powers base three and subtracting the exponents
C. By finding the quotient of the bases to be 1/3 and simplifying the expression
D. By finding the quotient of the bases to be 1/3 and cancelling common factors
Answer:
B. By simplifying 9 to [tex]3^{2}[/tex] to make both powers base three and subtracting the exponents
Step-by-step explanation:
When you have a division the quotient of powers property states that the exponents should be substracted, and by simplifying 9 to [tex]3^{2}[/tex] you end up with an equation like this:
[tex]\frac{3^{4} }{3^{2} }[/tex]=[tex]3^{2}[/tex]
Then you just have to substract the exponent from the denominator from the numerator´s exponent, which would be:
4-2=2
and the resultant equation would be:
[tex]3^{2} =3^{2}[/tex]
The Quotient of Powers Property allows you to subtract exponents when dividing expressions with the same base. The expression 3^4/9 simplifies to 3^2 because 9 can be expressed as 3^2, therefore their exponents are subtracted (4-2=2).
Explanation:In this question, the Quotient of Powers Property is used. This property states that to divide where the base remains the same, you subtract the exponents. In the expression 3^4/9 = 3^2, we know that 9 can be expressed as 3^2.
Therefore, it becomes 3^4/3^2. According to the Quotient of Powers Property, we subtract the exponent of the denominator from the exponent of the numerator (4-2=2). Hence the expression simplifies to 3^2. The correct choice is B: By simplifying 9 to 3^2 to make both powers base three and subtracting the exponents.
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Help me pleasee , timed
Answer:
The second alternative is correct
Step-by-step explanation:
We have been given the expression;
[tex](x^{27}y)^{\frac{1}{3}}[/tex]
The above expression can be re-written as;
[tex](x^{27})^{\frac{1}{3}}*y^{\frac{1}{3}}\\\\(x^{27})^{\frac{1}{3}}=x^{27*\frac{1}{3}}=x^{9}[/tex]
On the other hand;
[tex]y^{\frac{1}{3}}=\sqrt[3]{y}[/tex]
Therefore, we have;
[tex]x^{9}\sqrt[3]{y}[/tex]
Answer:
Option 2: [tex]x^{9}(\sqrt[3]{y})[/tex]
Step-by-step explanation:
Given
[tex](x^{27}y )^{\frac{1}{3} }[/tex]
The exponent power will be multiplied with the powers inside the bracket
So,
[tex](x^{27 * \frac{1}{3}} y^{\frac{1}{3}})[/tex]
[tex]= x^{\frac{27}{3}} y^{\frac{1}{3} }[/tex]
[tex]= x^{9} y^{\frac{1}{3}}[/tex]
Writing in radical form will give us:
[tex]x^{9}(\sqrt[3]{y})[/tex]
So,
Option 2 is the correct answer ..
6. The ratio of red ribbons to green ribbons is 4 to 6. If
there are a total of 30 red ribbons, then how many green
ribbons are there?
Answer:
45
Step-by-step explanation:
The 4 part of the ratio represents 30 red ribbons
Divide 30 by 4 to find the value of one part of the ratio
30 ÷ 4 = 7.5, hence
6 × 7.5 = 45 ← number of green ribbons
The range of the following relation R {(3, -5), (1, 2), (-1, -4), (-1, 2)} is (1 point)
{-4, -5, 2, 2)
{-1, 1, 3)
{-1,-1,1,3)
{-5, -4,2)
Answer:
{-5,-4,2}
Step-by-step explanation:
The domain is the inputs and the range is the outputs
The outputs are the y values
{ -5,2,-4,2}
We only list them once and in order from smallest to largest
{-5,-4,2}
Please answer now and please explain thank you
Hello There!
The answer would be the first one.
This is saying that Tom can not save exactly 50.25 but he must save more than that
Vertical? Obtuse? Straight or acute
Answer:
D. Acute
Step-by-step explanation:
This is an acute angle because the angle is less then 90 degrees.
<FOA is an Acute angle (D).
How I know...
Acute angles are angles are below 90 degrees (aka LESS then a right angle)
Hope this helped!
~Just a girl in love with Shawn Mendes
what are the coterminal angles for an angle of 5 pi over 3 radians
ANSWER
[tex] \frac{5\pi}{3} + 2\pi \: n[/tex]
EXPLANATION
Coterminal angles are angles that have the same terminal side in standard position.
We want find all angles that are coterminal with
[tex] \frac{5\pi}{3} \: \: radians[/tex]
We add or subtract multiples of 2π radians to this angle to obtain all angles that are coterminal with this angle.
The coterminal angles are:
[tex] \frac{5\pi}{3} + 2\pi \: n[/tex]
where n is an integer.
Answer:
-7 Pi/3, -Pi/3, 11 Pi/3
Step-by-step explanation:
8. Let f(x) = x 2 + 3x − 12 what is the average rate of change from x = 3 and x = 5?
[tex]\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\[-0.35em] \rule{34em}{0.25pt}\\\\ f(x)= x^2+3x-12\qquad \begin{cases} x_1=3\\ x_2=5 \end{cases}\implies \cfrac{f(5)-f(3)}{5-3} \\\\\\ \cfrac{[(5)^2+3(5)-12]~~-~~[(3)^2+3(3)-12]}{2}\implies \cfrac{[25+3]~~-~~[9-3]}{2} \\\\\\ \cfrac{28-6}{2}\implies \cfrac{22}{2}\implies 11[/tex]
1. You have a piece of land where you want to grow a garden. You only
have 20 yards of fencing to surround the garden. Work through the steps
below to figure out the maximum space you can create to grow plants.
A) you decide to make the width 3 yards.
Length: _____ yards
Area: _____ square yards
find the area of the smaller sector (please help me(
Answer:
27
Step-by-step explanation:
What is the answer to 4 • 4.
Answer:
16
Step-by-step explanation:
4 groups of 4 is 16:
[tex]\left\begin{array}{cccc}*&*&*&*\*&*&*&*&*\*&*&*&*&*\*&*&*&*&*\end{array}\right[/tex]
the first quartile of a data set is 72, and the third quartile is 92. Which of these values in the data set is an outlier ?
A. 61
B. 121
C. 101
D. 41
Answer: Option D
D. 41
Step-by-step explanation:
A value [tex]x_i[/tex] is considered an outlier if
[tex]x_i> Q_3 + 1.5IQR[/tex]
or
[tex]x_i <Q_1 - 1.5IQR[/tex]
Where
[tex]Q_3[/tex] is the third quartile
[tex]Q_1[/tex] is the first quartile
IQR is the interquartile range.
[tex]IQR = Q_3-Q_1[/tex]
In this case:
[tex]Q_3=92\\Q_1=72[/tex]
So
[tex]IQR = 92-72 =20[/tex]
[tex]Q_3 + 1.5IQR = 92 + 1.5*20 = 122[/tex]
[tex]Q_1 - 1.5IQR=72-1.5*20=42[/tex]
Then the outlier values will be all those greater than 122 or less than 42
Therefore the answer is the option D.