For this case we must find the solutions of the following equation:
[tex]4x ^ 2-x + 9 = 0[/tex]
We apply the cudratic formula:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
Where:
[tex]a = 4\\b = -1\\c = 9[/tex]
Substituting:
[tex]x = \frac {- (- 1) \pm \sqrt {(- 1) ^ 2-4 (4) (9)}} {2 (4)}\\x = \frac {1 \pm \sqrt {1-144}} {8}\\x = \frac {1 \pm \sqrt {-143}} {8}[/tex]
Thus, the complex roots are:
[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]
Answer:
[tex]x_ {1} = \frac {1 + i \sqrt {143}} {8}\\x_ {2} = \frac {1-i \sqrt {143}} {8}[/tex]
Simplify remove all perfect squares from inside the square root 125
Answer:
[tex]5\sqrt{5}[/tex]
Step-by-step explanation:
We start by factoring 125 and look for a perfect square:
125= 5*5*5=[tex]5^{2} *5[/tex].
This allow us to simplify the radical:
[tex]\sqrt{125} = \sqrt{5^{2} *5}[/tex]
So we have:
[tex]\sqrt{5^{2} *5} =5\sqrt{5}[/tex]
You paint 1/2 wall in 1/4 hour. At that rate how long will it take you to paint one wall?
Answer:
1/2 hr.
Step-by-step explanation:
Make a whole number of the wall. In this case, multiply by 2:
1/2 x 2 = 2
Because you multiplied 2 to the wall, you must also multiply 2 to the hours:
1/4 x 2 = 2/4
Remember to simplify:
(2/4)/(2/2) = 1/2
It will take you 1/2 hr to paint one wall.
~
30 minutes
A quarter of an hour is 15 minutes, because 60÷4=15.
So, this means that half of a wall equals to 15 minutes.
If you painted half of a wall, you have another half remaining.
Therefore, 2×15=30
30 minutes is the answere
Two roads that cross at right angles are used as coordinate axes for a map. A library is
located at point L.
Use the drop-down menus to complete the statements about the location of the library.
The library is located at point (_,_).
The library is __
miles from Road X and __
miles from Road Y.
Answer:
Part 1) The library is located at point (3.25,-1.5)
Part 2) The library is 1.5 miles from Road X
Part 3) The library is 3.25 miles from Road Y
Step-by-step explanation:
step 1
Find the coordinates of the library
we know that
Observing the graph
The length of each square in the graph is 0.5 miles
so
The coordinates of point L are (3.25,-1.5)
therefore
The library is located at point (3.25,-1.5)
step 2
Find the distance of the library from road X
we know that
The distance of point L from road X is the perpendicular distance of point L to the Road X
The perpendicular distance is the absolute value of the y-coordinate of point L
therefore
The library is 1.5 miles from Road X
step 3
Find the distance of the library from road Y
we know that
The distance of point L from road Y is the perpendicular distance of point L to the Road Y
The perpendicular distance is the absolute value of the x-coordinate of point L
therefore
The library is 3.25 miles from Road Y
URGENT HELP MEEEEE!!!:D
Answer: C: 3rd degree polynomial wit 3 terms.
Step-by-step explanation: The polynomial has 3 terms and the highest degree is 3.
C. Third degree polynomial with three terms.
Terms are, by definition, the number of nonzero coefficients for powers of x. In this case, there are 3 nonzero coefficients (3 terms) because [tex]-1=-1x^0[/tex]. For example, [tex]2x^3[/tex] has one term, but [tex]0[/tex] has 0 terms.
The degree of a polynomial is the highest power involved in the expression. In this case, it's [tex]4x^3[/tex], so the degree is 3.
What is the simplified expression for 4^4 x 4^3/4^5
Could Triangle JKL be congruent to Triangle XYZ? Explain.
Answer:
Im pretty sure its C
Step-by-step explanation:
because when u line up the the right angles u see the hypotenuse and leg of another triangle is the same
The given triangles are not congruent since the hypotenuse of one triangle is equal to the length of leg of another triangle.
What is congruency?Congruent triangles are triangles having both the same shape and the same size.Types of congruencies are SSS, SAS, AAS, ASA, RHS.How to find whether ΔJKL and ΔXYZ are congruent?For two triangles two be congruent, we need to check the the equality of corresponding sides and angles.Here the hypotenuse of ΔJKL is 10 units and one side(not the hypotenuse) of ΔXYZ is 10So the corresponding sides of the triangles are not equal.
So the triangles are not congruent.
So, option C is correct.
Find more about "Congruency" here: brainly.com/question/2938476
#SPJ2
if sin(x-3)° / cos(2x+6) = 1, then the value of X is
Answer:
x = 29° + n·120° . . . or . . . 261° +n·360° . . . . for any integer n
Step-by-step explanation:
Multiplying by the denominator, the equation becomes ...
sin((x -3)°) = cos((2x+6)°)
The sine and cosine are equal when ...
(x -3) + (2x +6) = 90 + n·360 . . . . . for any integer n
3x +3 = 90 + n·360 . . . . . . . . . collect terms
x +1 = 30 +n·120 . . . . . . . . . . . .divide by 3
x = 29 + n·120 . . . . . . . . . . . . . . subtract 1
__
The sine and cosine are also equal when ...
(x -3) -(2x +6) = 90 + n·360
-x -9 = 90 +n·360
x = -99 -n·360
Since n can be any integer, this can also be written as ...
x = 261 + n·360
Possible values of x include {29, 149, 261, 269} +n·360 for any integer n.
_____
The graph shows solutions to sin(x-3)-cos(2x+6)=0, which has the same solutions as the given equation.
Which statement is true about the equations –3x + 4y = 12 and 1/4x – 1/3y = 1?
A. The system of the equations has exactly one solution at (–8, 3).
B. The system of the equations has exactly one solution at (–4, 3).
C. The system of the equations has no solution; the two lines are parallel.
D. The system of the equations has an infinite number of solutions represented by either equation.
Answer:
Option C. The system of the equations has no solution; the two lines are parallel.
Step-by-step explanation:
we have
-3x+4y=12 -----> equation A
(1/4)x-(1/3)y=1 ----> equation B
Multiply equation B by -12 both sides
-12*[(1/4)x-(1/3)y]=1*(-12)
-3x+4y=-12 ----> equation C
Compare equation A and equation C
The lines are parallel , but the y-intercepts are different
therefore
The system has no solution
What is the equation that passes through (4, 3) and (2, -1)?
Y = 2x - 5
y = 4x -13
y = 6x+4
y = 1/2 x -2
Answer:
y = 2x - 5
Step-by-step explanation:
We are to find the equation of line the line which passes through the points (4, 3) and (2, -1).
Finding the slope:
Slope = [tex]\frac{3-(-1)}{4-2} =2[/tex]
Substituting the coordinates of one of the given points and slope in the standard form of an equation to find the y intercept.
[tex]y=mx+c[/tex]
[tex] -1 = 2 (2) + c \\\\ c = - 5 [/tex]
So the equation of the line would be [tex]y=2x-5[/tex]
Answer: first option.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope of the line and "b" is the y-intercept.
To find "m", we need to substitute the coordinates of the points (4, 3) and (2, -1) into this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We can identify that:
[tex]y_2=-1\\y_1=3\\x_2=2\\x_1=4[/tex]
Then:
[tex]m=\frac{-1-3}{2-4}\\\\m=2[/tex]
To find "b" we must substitute the slope and one of the given points into [tex]y=mx+b[/tex] and solve for "b". Then, this is:
[tex]3=2(4)+b\\\\3-8=b\\\\b=-5[/tex]
Therefore, the equation of this line is:
[tex]y=2x-5[/tex]
A die rolled. The set of equally likely outcomes is {1,2,3,4,5,6}. Find the probability of rolling an odd number.
Answer:
3/6 or 50%
Step-by-step explanation:
The probability of rolling an odd number from the dice numbered, {1,2,3,4,5,6} is 3/6.
6 numbers in all.
3 odd numbers.
3 even numbers.
Therefore, 3/6 or 50%.
If WZYX is equal to PMLN describes two quadrilaterals, which other statement is also true? I NEED THIS ANSWER ASAP
A.WXYZ equal to LMNP
B.WXYZ equal to NPML
C.WXYZ equal to PNLM
D.WXYZ equal to MLNP
Answer:
C.WXYZ equal to PNLM
Step-by-step explanation:
Look at the given statement, WZYX is equal to PMLN.
WZYX is equal to PMLN. W corresponds to P.
WZYX is equal to PMLN. Z corresponds to M.
WZYX is equal to PMLN. Y corresponds to L.
WZYX is equal to PMLN. X corresponds to N
Now look in the choices. The letters must correspond like they do above.
W must correspond to P.
WXYZ equal to P...
X must correspond to N.
WXYZ equal to PN...
Y must correspond to L.
WXYZ equal to PNL...
Z must correspond to M.
WXYZ equal to PNLM
Answer: C.WXYZ equal to PNLM
Answer: C.WXYZ equal to PNLM
Two forces of 7 newtons and 11 newtons act on a body at an angle of 60° to each other. Find the magnitude of the resultant force to the nearest whole number.
Answer:
16 N
Step-by-step explanation:
If the 7 N force is at 0°, and the 11 N force is at 60°, then the components of the resultant force are:
Fₓ = 7 cos 0° + 11 cos 60° = 12.5
Fᵧ = 7 sin 0° + 11 sin 60° ≈ 9.53
The magnitude of the resultant force is:
F = √(Fₓ² + Fᵧ²)
F ≈ 15.7
Rounded to the nearest whole number, the magnitude is 16 N.
How many roots does the polynomial function, y = (x + 4)(x-2)(x+7) have?
A. 3
B. 1
C. 2
D. A
Answer:
A. 3Step-by-step explanation:
The polynomial y = (x + 4)(x - 2)(x + 7) has 3 roots.
y = 0 ⇒ (x + 4)(x - 2)(x + 7) = 0 ⇔ x + 4 = 0 ∨ x - 2 = 0 ∨ x + 7 = 0
x + 4 = 0 subtract 4 from both sides
x = -4
x - 2 = 0 add 2 to both sides
x = 2
x + 7 = 0 subtract 7 from both sides
x = -7
The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots: -4, 2, and -7.A. 3
The polynomial function y = (x + 4)(x - 2)(x + 7) has three distinct roots, which can be found by setting y to zero and solving for the values of x that make the function equal to zero. When you set y to zero, the equation becomes 0 = (x + 4)(x - 2)(x + 7), and the roots are x = -4, x = 2, and x = -7. Hence, the correct answer to the question of how many roots the polynomial function has is:
A. 3
Help me with question 4 and 5
if kevin makes c toys in m minutes, how many toys can he make per hour
Answer:
[tex]\frac{60c}{m}[/tex]
Step-by-step explanation:
We can use the unity rule to solve this problem.
Number of toys made in m minutes = c
Number of toys made in 1 minute = [tex]\frac{c}{m}[/tex]
Number of toys made in 60 minutes = [tex]\frac{c}{m} \times 60 = \frac{60c}{m}[/tex]
Since 60 minutes = 1 hours, we can write:
Number of toys made in 1 hour = [tex]\frac{60c}{m}[/tex]
Therefore, we can say that Kevin makes [tex]\frac{60c}{m}[/tex] toys per an hour.
Find the value of Z in the picture
Answer:
172°
Step-by-step explanation:
Connect the center of the circle with two endpoints of the chord. You'll get the isosceles triangle with the angles adjacent to the base of
[tex]94^{\circ}-90^{\circ}=4^{\circ}[/tex]
Then the angle between two congruent sided (two radii of the circle) is
[tex]180^{\circ}-2\cdot 4^{\circ}=172^{\circ}[/tex]
This angle is central angle subtended on the arc z, so the measure of z is 172°.
Answer: OPTION B.
Step-by-step explanation:
It is important to remember that:
[tex]Tangent\ chord\ angle=\frac{1}{2}(Intercepted\ arc)[/tex]
We can identify in the figure that 94° is the measure of a tangent chord angle. Then, we can find "x":
[tex]94\°=\frac{1}{2}x\\\\(2)(94\°)=x\\\\x=188\°[/tex]
Since there are 360° in a circle, we can subtract 360° and the value of "x" to find the value of "z". Then we get:
[tex]z=360\°-x\\\\z=360\°-188\°\\\\z=172\°[/tex]
How would you do number 12 and 15?
Answer:
[tex]x_1=x_2=-\dfrac{2}{3}[/tex]
Step-by-step explanation:
For the quadratic equation [tex]ax^2+bx+c=0[/tex] the discriminant is defined as
[tex]D=b^2-4ac[/tex]
and the quadratic formula for the roots gives us two roots:
[tex]x_1=\dfrac{-b-\sqrt{D}}{2a}[/tex]
and
[tex]x_2=\dfrac{-b+\sqrt{D}}{2a}[/tex]
For the equation [tex]9x^2 +12x+4=0[/tex] use quadratic formula to find roots:
[tex]D=12^2-4\cdot 9\cdot 4=144-144=0[/tex]
So,
[tex]x_1=x_2=\dfrac{-12\pm \sqrt{0}}{2\cdot 9}=-\dfrac{12}{18}=-\dfrac{2}{3}[/tex]
AB || CD. Find the measure of
Step-by-step explanation:
solve the equation:
5x-10=4x+20
Answer:
The correct answer is option B. 140
Step-by-step explanation:
From the figure we can see that,
AB ║ CD
To find the value of x
From the figure we can see that,
<CFE = <BEF [Alternate interior angles are equal]
4x + 20 = 5x - 10
5x - 4x = 20 + 10
x = 30
To find the measure of <BEF
m<BEF = 5x - 10
= (5*30) - 10
= 150 - 10
= 140°
Therefore the correct answer is option B. 140
intersecting lines that are formed as a right angle are defined as?
Answer:
Perpendicular
Step-by-step explanation:
Definition of perpendicular lines:
Lines that intersect forming a right angle are perpendicular lines.
Answer:
Perpendicular
Step-by-step explanation:
wh as t is a prime numbers
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers
Step-by-step explanation:
Final answer:
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. Prime numbers have many interesting properties and applications in mathematics.
Explanation:
A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. In other words, it is a number that is only divisible by 1 and itself.
For example, the numbers 2, 3, 5, and 7 are prime numbers because they have no divisors other than 1 and themselves. On the other hand, the number 4 is not prime because it is divisible by 1, 2, and 4.
Prime numbers have many interesting properties and applications in mathematics, including their role in number theory and cryptography.
Find all the real zeros of the function y = -5x -7
Answer:
-7/5 if your function really is f(x)=-5x-7
Step-by-step explanation:
The zeros of an expression are the numbers you can plug into that expression that will make that expression 0.
So what value of x will make the expression
-5x-7=0.
You don't have to this by observation. We can just solve it and see.
-5x-7=0
Add 7 on both sides:
-5x. =7
Divide both sides by -5:
x. =7/-5
x. =-7/5
So -7/5 will make the expression equal to 0.
Let's test this:
-5x-7 when x=-7/5
-5(-7/5)-7
7-7
0
So it does indeed.
Suppose y varies directly as x, and y=2 when x=4. Which of the following statements is true?
Answer:
constant of variation = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Given y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 2 when x = 4
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{2}{4}[/tex] = [tex]\frac{1}{2}[/tex]
Answer:
The constant of variation is 1/2.
Step-by-step explanation:
y = kx where k is the constant of variation.
So k = y/x = 2/4 = 1/2.
The length of a rectangular is 7/10 ft .and the width is 1/5ft what is the perimeter
[tex]\huge\boxed{1 \frac{4}{5}\ \text{ft}}[/tex]
Explanation:Change [tex]\frac{1}{5}[/tex] so that is has a common denominator. [tex]\frac{1*2}{5*2}=\frac{2}{10}[/tex]
Make an equation. [tex]\frac{7+7+2+2}{10}[/tex]
Add. [tex]\frac{14+4}{10}[/tex]
Add. [tex]\frac{18}{10}[/tex]
Divide both sides by 2. [tex]\frac{9}{5}[/tex]
Convert to a mixed number. [tex]1 \frac{4}{5}[/tex]
Answer:
1 4/5 ft.
Step-by-step explanation:
Change 7/10 into 70
Change 1/5 into 20
( It will be easier to find perimeter this way )
Formula: P=2(l+w)
P=2(l+w)=2·(70+20)=180
Then, you change the 180 back into a fraction to get 1 4/5.
One-third of Sharon's land has
farm animals. One-fifth of the farm
animals are chickens. Which
model shows what fraction of
Sharon's land has chickens?
Which of the following ordered pairs represents a solution to the linear
inequality y > 2x - 3?
O A. (3,2)
O B. (9,12)
O C. (4,4)
O D. (2,5)
Answer:
O D. (2,5)
Step-by-step explanation:
y > 2x - 3
Substitute the points into the inequality and see if it is true
(3,2)
2 > 2(3) - 3
2> 6-3
2>3 False
(9,12)
12 > 2(9) - 3
12> 18-3
12>15 False
(4,4)
4 > 2(4) - 3
4> 8-3
4>5 False
(2,5)
5 > 2(2) - 3
5> 4-3
5>1 True
Answer:D
Step-by-step explanation:
if angle a is 60° and angle c is 30°what is the measurement of angle b ?
Answer:
m∠B = 90°
Step-by-step explanation:
Note that the figure given to you is a triangle, which has 3 angles, and the total measurement of 3 angles is = 180°.
Let m∠B = x
m∠A = 60°
m∠C = 30°
Set the equation:
m∠A + m∠B + m∠C = 180°
Plug in the corresponding numbers to the corresponding variables:
60 + x + 30 = 180
Isolate the variable, x. Combine like terms:
x + (60 + 30) = 180
x + (90) = 180
Isolate the variable, x. Subtract 90 from both sides:
x + 90 (-90) = 180 (-90)
x = 180 - 90
x = 90
m∠B = 90°
A girls' track team must run 3 miles on the first day of practice and 6 miles every day after that. The boys' team must run 5 miles every day of practice. The coach will order new javelins at the end of the day that each girl's total mileage surpasses each boy's. How many total miles will each girl have run by the time the coach orders the new equipment?
Answer:
The 4th day so 21 miles the girls would have to run
Step-by-step explanation:
Answer:
Each girl would have ran a total of 21 miles and boys would have ran a total of 20 miles by the end of the fourth day before the couch order new javelins.
Step-by-step explanation:
Girls track team
First day of practice=3 miles
Days afterwards= 6 miles
Boys track team
Everyday= 5 miles
coach will order new javelins at the end of the day that each girl's total mileage surpasses each boy's.
First day
Each girl total mileage= 3 miles
Each boy total mileage= 5 miles
Second day
Each girl total mileage= 3miles+6miles=9 miles
Each boy total mileage=5 miles+5 miles= 10 miles
Third day
Each girl total mileage= 3+6+6=15 miles
Each boy total mileage=5+5+5=15 miles
Fourth day
Each girl today mileage= 3+6+6+6=21 miles
Each boy total mileage=5+5+5+5= 20 miles
Difference=girls-boys
=21-20= 1 mile
The fourth day is the day each girl's total mileage(21 miles) surpasses each boy's total mileage(20 miles) with a total of 1 mile
The sales of a certain product after an initial release can be found by the equation
S = 16V 3t +25, where s represents the total sales (in thousands) and t represents
the time in weeks after release.
Make a table of values, graph the function and use the graph to estimate the sales
7 weeks after release.
A about $98
B about $98,000
C about $1,225,000
D about $20,000
Answer:
B about $98,000
Step-by-step explanation:
The equation that models the sales of the product after an initial release is:
[tex]S = 16 \sqrt{3t} + 25[/tex]
where s represents the total sales (in thousands) and t represents
the time in weeks after release.
The table and graph is shown in the attachment.
From the graph we estimate the sales
7 weeks after release to be about 98 thousands dollars.
The correct choice is B.
30 POINTS!!
Test the residuals of two other points to determine how well the line of best fit models the data.
Answer:
the line of best feet passes through three poin
Step-by-step explanation:
1st three points are green, yellow and red
2nd three point are green yellow and upward green
Final answer:
The outlier with a large residual indicates it does not fit the line of best fit, and removing it can improve the model's accuracy. After recalculating without the outlier, a stronger correlation coefficient of 0.9121 suggests that the line of best fit models the data better.
Explanation:
Understanding Residuals and Outliers in Linear Regression
In the context of linear regression, a residual is the difference between the observed value of the dependent variable (y) and the predicted value (ý) provided by the regression model. We are testing the residuals to determine how closely the regression line models the actual data points. If a residual is larger than twice the standard deviation (in this case, greater than 32.8 or less than -32.8), the corresponding data point is considered an outlier. The single large outlier identified with a grade of 65 on the third exam and 175 on the final exam has a substantial residual of 35, indicating that this data point does not fit well with the line of best fit. This outlier can significantly affect the regression line's slope and y-intercept.
Outliers can have a significant impact on the best-fit line, potentially skewing the results and affecting predictions. To assess the outlier's influence, we can remove it and re-calculate the best-fit line and correlation coefficient. If the coefficient is closer to 1 or -1 and the sum of squared errors (SSE) is lower after re-calculating, this indicates a better fit. In this case, the line of best fit without the outlier provides a correlation coefficient of 0.9121, suggesting a stronger linear relationship between the third exam and final exam scores after removing the outlier.
Find the volume of the oblique rectangular prism with length 8cm, width 7cm, and height 9cm.
Final answer:
The volume of the oblique rectangular prism is calculated using the length, width, and height. The formula V = l times w times h gives a volume of 504 cubic centimeters.
Explanation:
To find the volume of an oblique rectangular prism, we use the same formula as for a right rectangular prism because the volume is not affected by the obliquity of the sides. The formula for the volume (V) is the product of the length (l), width (w), and height (h). So, using the provided dimensions:
V =l times w times h = 8 cm times 7 cm times 9 c
Now, let's calculate:
V = 8 times 7 times 9 = 504 cm
Therefore, the volume of the oblique rectangular prism is 504 cubic centimeters.