Given:
A quadratic equation is:
[tex]3x^2+9x-2=0[/tex]Find-:
The roots of the quadratic equation
Explanation-:
Use quadratic formula:
[tex]ax^2+bx+c=0[/tex]Roots of the equation,
[tex]x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]The roots of the given equation are:
[tex]3x^2+9x-2=0[/tex][tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ \\ x_{1,2}=\frac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)} \\ \\ x_{1,2}=\frac{-9\pm\sqrt{81-(-24)}}{6} \\ \\ x_{1,2}=\frac{-9\pm\sqrt{81+24}}{6} \\ \\ x_{1,2}=\frac{-9\pm\sqrt{105}}{6} \end{gathered}[/tex]The roots of a quadratic equation are:
[tex]\begin{gathered} x_{1,2}=\frac{-9\pm\sqrt{105}}{6} \\ \\ x_1=\frac{-9+\sqrt{105}}{6},x_2=\frac{-9-\sqrt{105}}{6} \end{gathered}[/tex][tex]\begin{gathered} x_1=\frac{-9+\sqrt{105}}{6},x_2=\frac{-9-\sqrt{105}}{6} \\ \\ x_1=0.2078,x_2=-3.2078 \end{gathered}[/tex]The roots of a quadratic equation are 0.2078 and -3.2078.
8. (07.01 MC)If the sin 60º = 13, then which statement is true? =2cos 30º =V3, because the cosine and sine are complements523cos 120º =2because the cosine and sine are supplementscos 30º = 0, because the cosine and sine are complementscos 120º = 0, because the cosine and sine are supplements
Note that if the angles are complementary with each other, the sine and cosine are the same.
From the problem, sin 60 = √3/2, the complement of 60 degrees is 30,
so cos 30 is the same as sin 60.
The best answer is Choice A
10 ydFind the surface area of the closed hemisphere.Enter your answer in terms of A and rounded to thenearest tenth.The surface area is ]# yd? or approximatelyyd?
We have the following:
[tex]A=2\cdot\pi\cdot r^2[/tex]we have that the radius is half the diameter, therefore
[tex]\begin{gathered} r=\frac{d}{2}=\frac{10}{2} \\ r=5 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} A=2\cdot\pi\cdot5^2 \\ A=50\pi\cong157 \end{gathered}[/tex]The surface area is 50*pi yd^2 or approximately 157 yd^2
Need help with relationship between measures of two given angles
Note that in the picture we are asked about the angles QRW and RWQ. This two angles are part of the the same triangle. So we can ignore the rest of the image and focus only on the triangle that contains both. We have the following
Using this information, we can see that the measure of the three sides of the triangle are different. This means that the triangle is a scalene triangle. This type of triangles have the property that the measure of each angle is different from the other. So, we know that the measure of angles QRW and RWQ are different.
To dig deeper in the problem, we will use the sines law for triangle, which states the following. If we have a triangle of the form
Then, we have the following
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]In this case, we have c=45 and a=47, so we have
[tex]\frac{\sin A}{47}=\frac{\sin C}{45}[/tex]where A is the angle RWQ and C is the angle QRW, if we multiply both sides by 45, we get
[tex]\sin C=\frac{45}{47}\cdot\sin A[/tex]In this case, we have that 45/47 < 1. Since angles A and C are less than 180° degrees, the sine of this angles is a positive number, so we have that
[tex]\sin C=\frac{45}{47}\cdot\sin A<\sin A[/tex]Note also that angles A and C should have a measure less than 90°. Over this interval, the sine function is an increasing function, which means that if sin(C)So we have that the measure of angle QRW is less than the measure of angle RWQ.
#WT 10, 4). 47-3, -1), and Y-5. 11) classify A#XY by its sides ae: Vanhem
Answer:
Isosceles triangle
Explanation:
An isosceles triangle is one in which two side lengths are congruent while the third is not.
Looking at the triangle given we see that the two side lengths WY and WX are the same; therefore, the triangle is isosceles.
Solve the following equation for x.x^2−47=17List your answers separated by a comma, not using a ± sign and do not include x= in your answer.Question 2 options:3, 5-9, 9-8, 8-30, 0
ANSWER :
The values of x are -8 and 8
EXPLANATION :
From the problem, we have the equation :
[tex]x^2-47=17[/tex]Add 47 to both sides :
[tex]\begin{gathered} x^2-47+47=17+47 \\ x^2=64 \end{gathered}[/tex]Take the square root of both sides :
[tex]\begin{gathered} \sqrt{x^2}=\sqrt{64} \\ x=\pm8 \end{gathered}[/tex]Determine the domain and range of the function shown below. Assume the entire function is shown. Domain: Range:
The function is made of the following ordered pairs:
(-1,-3) (1, -5) (2, 3) (3, 6) (5, 6) (7, -1)
The first coordinate of the ordered pairs is the input value and the second coordinate is the output value of the function.
The domain is the set of all the input values as shown below:
Domain: {-1, 1, 2, 3, 5, 7}
Range: {-3, -5, 3, 6, -1}
Sorting the values of the range.
Range: {-5, -3, -1, 3, 6}
Choose the best selection for thequadrilateral with vertices at thefollowing points:(4,0), (8,0), (4,-4), (8,-4)Hint: Start by graphing the points.Distance Formula: d= (x2 – x1)2 + (y2 - y1)2A. RectangleB. SquareC. RhombusD. Trapezoid
We are given coordinates of four points and we are asked to find the best selection of the shape.
In order to know what shape this is, we simply graph all the points and see what shape we get.
Using a graphing calculator, the points make up the following shape:
Now that we have the shape, we know that it can either be a Rectangle or a Square.
If the shape is a rectangle, the lengths x and y are not equal. If the shape is a square, lengths x and y are equal.
In order to find x and y, we use the distance formula given to us as:
[tex]\begin{gathered} |d|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where,} \\ (x_2,y_2)\to\text{ Second point} \\ (x_1,y_1)\to\text{ First point} \end{gathered}[/tex]Now let us find x and y.
x:
The points that make up the length x are:
(4, 0), and (4, -4)
Therefore, length x can be gotten as:
[tex]\begin{gathered} x_2=4,y_2=0,x_1=4,y_1=-4 \\ |x|=\sqrt[]{(4-4)^2+(0--4)^2} \\ |x|=\sqrt[]{4^2} \\ \\ \therefore|x|=4 \end{gathered}[/tex]Now we find y.
y:
The points that make up the length y are:
(4, 0) and (8, 0)
Therefore, length y can be gotten as:
[tex]\begin{gathered} x_2=4,y_2=0,x_1=4,y_1=-4 \\ |x|=\sqrt[]{(4-4)^2+(0--4)^2} \\ |x|=\sqrt[]{4^2} \\ \\ \therefore|x|=4 \end{gathered}[/tex]Jane is a software saleswoman. Her base salary is $1500, and she makes an additional $110 for every copy of English isFun she sells.Let P represent her total pay (in dollars), and let N represent the number of copies of English is Fun she sells. Write anequation relating P to N. Then use this equation to find her total pay if she sells 29 copies of English is Fun.
You know that "P" represents her total pay (in dollars) and "N" represents the number of copies of English is Fun Jane sales.
According to the information given in the exercise, Jane makes $110 for every copy of English is Fun, then you can set up the following expression for this:
[tex](110)(N)=110N[/tex]Knowing that her base salary is $1500, you can conclude that her total pay "P" will be the sum of her base salary and the amount of money she makes for every copy she sells. Based on this, you can write the following equation relateion "P" to "N":
[tex]P=1500+110N[/tex]If Jane sales 29 copies of English is Fun, then:
[tex]N=29[/tex]Substituting this value into the equation and evaluating, you get:
[tex]\begin{gathered} P=1500+(110)(29) \\ P=1500+3190 \\ P=4690 \end{gathered}[/tex]The answers
- Equation:
[tex]P=1500+110N[/tex]- Solution:
[tex]P=4690[/tex]Her total pay if she sells 29 copies of English is Fun, is $4690
Find the total amount in the compound interest account $10000 is compounded semiannually at a rate of 11% for 20 years. (Round to the nearest cent.)
The compound interest formula is:
[tex]A=P(1+\frac{r}{m})^{mt}\begin{cases}A=amount \\ P=initialValue \\ r=interest \\ m=\#timesCompounedPerYear \\ t=years\end{cases}[/tex]Therefore:
[tex]A=(10000)(1+\frac{0.11}{1})^{20}=80623.12[/tex]A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 95% pure antifreeze. In order to obtain 50 gallons of a mixture that contains 75% pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer:
See below
Step-by-step explanation:
Final amount of pure antifreeze = .75 (50)
amount of 70 % that is pure antifreeze = .70 x
amount of 95 % that is pure antifreeze = .95 (50-x)
ingredients in = ingredients out
.70x + .95 (50-x) = .75 (50)
x = 40 gal this is the amount of 70 %
then 95 % = 50 - 40 = 10 gal
O GEOMETRY Perimeter involving rectangles and circles A training field is formed by joining a rectangle and two semicircles, as shown below. The rectangle is 88 m long and 67 m wide. What is the length of a training track running around the field? (Use the value 3.14 for π, and do not round your answer. Be sure to include the correct unit in your answer.) 88 m 1 67 m 1 0 m X m² S m³ 1/5 ?
Step 1
to know the full distance for the track running we need to add twilce the length of the rectangle to the perimeter of the circel, so
so
a) find the circumference of the circle , it is given by
[tex]\begin{gathered} C=\text{ }\pi d\text{ } \\ where\text{ d is the diameter} \end{gathered}[/tex]hence
[tex]\begin{gathered} let\text{ d=67 m} \\ so \\ C=\pi *67\text{ m=210.38 m} \end{gathered}[/tex]finally, add twice the length of the rectangle, so
[tex]\begin{gathered} traininin\text{ track = 210.38+\lparen2*88\rparen=210.38+176} \\ traininin\text{ track = 386.38} \end{gathered}[/tex]therefore, the answer is
[tex]386.38\text{ m}[/tex]I hope this helps you
16 a.)Vivian approximated the square root of 15. What is the value of the square root of 15 to the nearest whole number? Show or explain how you got your answer.
ANSWER
3.872
EXPLANATION
Given:
A number 15
Desired Outcome:
Square root of the number
Square root of 15
Step 1:
Starting on the right, we'll put a bar above the digits to match them together.
Step 2:
Find a number that when multiplied by itself produces a result that is less than or equal to 15 and close to 15. So the answer is three. Using 3 as the divisor, we get 3 as the quotient (same as the divisor), and 6 as the remainder.
Step 3:
Enter the divisor twice with a blank on the right. Choose the largest possible digit to fill in the blank, which will become the new digit in the quotient, so that the resultant product is less than or equal to the dividend when the new divisor is multiplied by the new quotient. Divide the leftover and write it down. Repeat this method until you get the desired number of decimal places.
Hence, the square root of 15 is 3.872
Find the number that belongsin the green boc
the value for green box is 7.61
It can be calculated using sine law
first we need to know the angle opposite of 5
using sine law
Write the point-slope form of an equation of the line that passes through (4, -3) and (2, 1).
Oa y-4-2
(x+3)
Oby+3=-2 (x-4)
OC y-3= -2(x-4)
y+3= =(x-4)
The point-slope form that passes through (4, -3) and (2, 1) is y+3 is −2(x−4). A slope of a line is the change in y coordinate with respect to the change in x coordinate.
How to calculate Point-slope form ?The slope of the line and any points on the line determine the point-slope form of a line. When given a point on the line and the slope, the form's purpose is to describe the equation of the entire line.
The slope of a line passing through the two points P=(x1,y1) and Q=(x2,y2) is given by m = y2−y1 / x2−x1
We have that x1=4, y1=−3, x2=2, y2=1.
Plug the given values into the formula for slope: m = (1)−(−3)/(2)−(4)
=4−2 =−2.
Now, the y-intercept is b=y1−m⋅x1 (or b=y2−m⋅x2, the result is the same).
b=−3−(−2)⋅(4)=5.
Finally, the equation of the line can be written in the form y=mx+b.
y=−2x+5.
The slope of the line is m=−2.
The equation of the line in the slope-intercept form is y=−2x+5.
The equation of the line in the point-slope form is y+3=−2(x−4).
The equation of the line in the point-slope form is y−1=−2(x−2).
The general equation of the line is 2x+y−5=0.
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In the game of Monopoly, a player is sent to jail if he or she rolls doubles with a pair of dice 3 times in a row.What is the probability of rolling doubles on a single turn? (Enter your probability as a fraction.) _______What is the probability of rolling doubles 3 times in succession? (Enter your probability as a fraction.) _______
The probability of rolling doubles on a single turn is the number of favorable cases over the number of total cases, the favorable cases are those when you get a double, the number of total cases is the number of total possible outcomes.
Now, the number of total possible outcomes is
[tex]6\times6=36.[/tex]The number of favorable cases is
[tex]6.[/tex]Therefore, the probability of rolling doubles is:
[tex]\frac{6}{36}=\frac{1}{6}\text{.}[/tex]Now, the probability of rolling double 3 times in succession is the product of rolling a double in a single turn, therefore:
[tex]P=\frac{1}{6}\times\frac{1}{6}\times\frac{1}{6}=\frac{1}{216}.[/tex]Answer:
The probability of rolling doubles on a single turn is:
[tex]\frac{1}{6}\text{.}[/tex]The probability of rolling doubles 3 times in succession is:
[tex]\frac{1}{216}\text{.}[/tex]22. [-/2 Points]DETAILS OSELEMALG1 1.4.325.Translate to an algebraic expression, but do not simplify.the quotient of -4 and the sum of a and b†
Given:
The quotient of -4 and the sum of a and b.
Required:
To translate to an algebraic expression.
Explanation:
The sum of a and b is
[tex]a+b[/tex]The quotient of -4 and the sum of a and b is
[tex]\frac{-4}{a+b}[/tex]Final Answer:
[tex]-\frac{4}{a+b}[/tex]If a number is raised to a power of 2, it is A. CubbedB. Powered C. Squared
If we raise a number to a power of 2, we can represent the result graphically as shown below (where n is the number to be raised to a power of 2)
This is a square of side equal to n.
Therefore, the answer is option C, squared.
May you solve the system of linear equations by graphingm?
We shall begin by plotting the graph of the equations given which are;
[tex]\begin{gathered} y=\frac{1}{3}x+6 \\ y=-\frac{2}{3}x+3 \end{gathered}[/tex]The black line shows the graph of y = [1/3]x + 6
The red line shows the graph of y = [-2/3]x + 3
The solution to these system of equations is at the point (-3, 5)
Simplify the following expression. 7m+7(4m+2)
Given the expression:
7m + 7(4m + 2)
Use distributive property to expand the parenthesis:
= 7m + 7*4m + 7*2
= 7m + 28m + 14
Sum up like terms:
= 35m + 14
ANSWER:
35m + 14
mrs corwin has a contractor install a new quarter circle window in her house like shown at right. what is the area of the window? use 3.14 pi. round to the nearest tenth
The area of a circle is given by:
[tex]A=\pi r^2[/tex]Since it is a quarter of the circle, the area is:
[tex]\begin{gathered} A=\frac{\pi r^2_{}}{4} \\ where \\ r=7 \\ \pi=3.14 \\ so\colon \\ A=\frac{(3.14)(7^2)}{4} \\ A\approx38.5in^2 \end{gathered}[/tex]For the experiment, determine the two given events are independent. The answers are guessed on a twenty-question multiple-choice test. The events are "the first question is correct" and "the second answer is correct". Are the two events independent or not independent?
Two events are independent when one of the events happen and the result does not affect on the result for the second event.
In this case if we have multiple-choice answers on the test the probability of having the correct answer for both of them is the same, however if we get the first one correct it does not mean that we will have the second answer correct.
For this reason the events are independent.
Construct a Venn diagram where U={a,b,c,d,e,f,g}, A={b,d,f,g}, and B={b}.Move each of the lettered points to an appropriate region on the Venn diagram.
Explanation:
Given the universal set, U and subsets A and B as follows:
• U={a,b,c,d,e,f,g}
,• A={b,d,f,g}
,• B={b}
Answer:
The Venn diagram representing the sets is given below:
Note:
• The ,letter b is common to both A and B,, so we put it in the intersection of both sets.
,• The ,letters a, c, and e do not belong to either A or B,, so we place it outside of the two sets.
What is the equation of the line of best fit for the following data? Round theslope and y-intercept of the line to three decimal places.ху2258.7.109111113
Answer:
Explanation:
The equation o
What is thX= ら*e coefficient of the term x³y5 in the expansion of the binomial expression (2x − y)³?
The coefficient of the term x²y in the binomial expansion of (2x − y)³ is -12.
The expression (2x − y)³ can be simplified as
8x³−12x²y+6xy²−y³ .
Thus the coefficient of the binomial expansion is -12.
Of the use of the binomial theorem, it is possible to determine the expanded value of either formula with the form (x + y)ⁿ.
The values of (x + y)², (x + y)³, and (a + b + c)² can be easily determined by adding the integers algebraically in accordance with the exponent value.
The binomial theorem was first mentioned by a well-known Greek mathematician by the name of Euclid in the fourth century BC.
According to the binomial theorem, which represents it as a sum of terms using distinct exponents of the variables x and y, the algebraic statement (x + y)ⁿ can be expanded. A coefficient, or numerical value, is assigned to each word in a binomial expansion.
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Suppose Albers Elementary School has 26 teachers and Bothel Elementary School has 14 teachers. If thetotal number of teachers at Albers and Bothel combined is 27, how many teachers teach at both schools
Given:
Albers Elementary School has 26 teachers
Bothel Elementary School has 14 teachers
And the total number of teachers at Albers and Bothel combined is 27
Note, there a number of teachers working at both schools
We will let the following:
The number of teachers at Albers = x
The number of teachers at Bothel = y
The number of teachers at both = z
So, we can write the following system of equations:
x + z = 26 ⇒ (1)
y + z = 14 ⇒ (2)
x + y + z = 27 ⇒ (3)
Solving the system of equations to find x, y, and z
From (1) ⇒ x = 26 - z
From (2) ⇒ y = 14 - z
Substitute with (x) and (y) into equation (3)
[tex]\begin{gathered} (26-z)+(14-z)+z=27 \\ -z-z+z=27-14-26 \\ -z=-13 \\ z=13 \end{gathered}[/tex]So, the answer will be
The number of teachers teach at both schools = 13
*only do question 14*diagrams are not drawn to scale. i only care about the answers & the steps you did to get the answers.don’t be slow pls (:
∠KU and ∠LE are vertically opposite angles, which means that they are congruent, so that:
[tex]\angle KU=\angle LE=60º[/tex]∠LUE and ∠LKE intersect the same arc mLE, which means that they are congruent:
[tex]\angle\text{LUE}=\angle\text{LKE}=32º[/tex]∠KU and the vertex angle marked in blue are supplementary angles, which means that they add up to 180º:
[tex]\begin{gathered} 60+x=180º \\ x=180-60 \\ x=120º \end{gathered}[/tex]Knowing two of the three angles of the upper triangle, you can calculate the measure of the missing one, ∠ULK:
[tex]\begin{gathered} 32+120+\angle\text{ULK}=180 \\ 152+\angle\text{ULK}=180 \\ \angle\text{ULK}=180-152 \\ \angle\text{ULK}=28º \end{gathered}[/tex]∠ULK and ∠UEK intercept the same arc mKU, so they are congruent:
[tex]\angle\text{ULK}=\angle\text{UEK}=28º[/tex]Type the correct answer in each box. Spell all words correctly.
Two triangles are graphed in an x y plane. The vertices are as follows: first: A (negative 6, 2), B (negative 2, 6), and C (negative 4, 2); second: A prime (negative 6, negative 2), B (negative 2, negative 6), and C (negative 4, negative 2). A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a . When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, vertex of ∆A″B″C″ will have the same coordinates as B′.
Part A: Transformation which mapped ABC to A′B′C′; reflection along x-axis.
Part B: The coordinate of B" is the same as the coordinate of B'.
What is referred as the term transformation?A transformation is a broad term for four major methods of changing the form and/or position of the a point, line, as well as geometric figure. The Pre-Image is the original shape of a object, and the Image for under transformation is the final shape as well as position of the object.For the given question;
The coordinates are-
∆ABC; A(-6, 2), B(-2, 6), C(-4, 2).
∆A′B′C; A'(-6, - 2), B (-2, -6), C (-4, -2).
A) We are now told that ABC was transformed into
∆A′B′C. We can see from the coordinates that merely the y coordinate sign modified after the transformation.
As a result, the transformation which mapped ABC to A′B′C′ is a reflection along the x-axis.
B) A′B′C′ is now reflected all across line x = -2 to form A′′B′′C′′. Because the line x = -2 is vertical as well as the coordinate of B' in A′B′C′ has had an x - coordinate of -2,
Thus, the coordinate of B" is the same as the coordinate of B'.
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i have the first answer but keep getting the second one wrong please help!!
Kenyan = k
$3.50 per pound
Sri Lankan = s
$5.60 per pound
6lbs of blend
$28.35
s+k = 6
3.50k + 5.60s = 28.35
where:
k = lbs of kenyan
s = lbs of Sri Lankan
Solve the system
s+k = 6
3.50k + 5.60s = 28.35
solve the first equation for s:
s = 6-k
Replace in the second equation:
3.50k + 5.60 (6-k) = 28.35
3.50k + 5.60(6)+ 5.60(-k) = 28.35
3.50k + 33.6 - 5.60k = 28.35
3.50k - 5.60k = 28.35-33.6
-2.1k= -5.25
k= -5.25/-2.1
k= 2.5 lbs
Replace k on any equation and solve for s
s+k= 6
s+ 2.5 = 6
s= 6-2.5
s= 3.5 lbs
A store makes a profit of $25 on each watch it sells. What solution setwill represent how many watches the store must sell to make a profitof at least $375?US
Here, the variable is the number of watches.
The profit on each watch it sells is, $25.
The least profit to be made is, $375.
Let x be the number of watches, Then we have, the total profit as,
[tex]25x[/tex]This profit should be atleast 375, therefore, we have,
[tex]\begin{gathered} 25x\ge375 \\ \frac{25x}{25}\ge\frac{375}{25} \\ x\ge15 \end{gathered}[/tex]I am having a little bit of trouble on this (help)
Answer:
D
Step-by-step explanation:
We should use ratio.
AB is 5
DE is 10
AB/DE = 1/2
BC is 12 and EF is 24
BC/EF=1/2
AC is 13 and DF is 26
AC/DF= 1/2
So we can write the equation like D choice.