Answer:
(4x -1 ) ( x +5 )
Step-by-step explanation:
4x2 + 19x-5
(4x ) ( x )
We need to get -5 The factors are -1 and 5 and 1 and -5
4*5 = 20
so the 5 will be on the outside We do this because we have +19 on the inside
(4x -1 ) ( x +5 )
Lets check
FOIL
4x^2 +20x -x -5 = 4x^2 +19x-5
Answer:
The factors are (4x-1)(x+5).
Step-by-step explanation:
4x^2+19x-5
Break the middle term:
First multiply the coefficient of first term by the constant.
4*5=20
Now find any two numbers whose product = 20 and whose sum is equal to the middle term.
20*1 = 20
20-1 = 19
Now break the middle term:
4x^2+20x-x-5
Now group the first two terms and last two terms:
(4x^2+20x)-(x+5)
Now take the common from each group.
4x(x+5)-1(x+5)
(4x-1)(x+5).
Thus the factors are (4x-1)(x+5).....
What is the volume of a sphere that has a radius of 9?
Answer:
V = 3053.63
Step-by-step explanation:
The volume of a sphere that has a radius of 9 is 3053.63.
V=4
3πr3=4
3·π·93≈3053.62806
Answer is provided in the image attached.
what is the area of the sector shown
Answer:
[tex] D.~ 34.2~cm^2 [/tex]
Step-by-step explanation:
An arc measure of 20 degrees corresponds to a central angle of 20 degrees.
Area of sector of circle
[tex] area = \dfrac{n}{360^\circ}\pi r^2 [/tex]
where n = central angle of circle, and r = radius
[tex] area = \dfrac{20^\circ}{360^\circ}\pi (14~cm)^2 [/tex]
[tex] area = \dfrac{1}{18}(3.14159)(196~cm^2) [/tex]
[tex] area = 34.2~cm^2 [/tex]
how does one do this? may someone teach me how to calculate and solve this problem please, thanks.
Answer:
x=1
Step-by-step explanation:
So we are talking about parabola functions.
All parabolas (even if they aren't functions) have their axis of symmetry going through their vertex.
For parabola functions, your axis of symmetry is x=a number.
The "a number" part will be the x-coordinate of the vertex.
The axis of symmetry is x=1.
Answer:
x=1
Step-by-step explanation:
The vertex of a parabola is the minimum or maximum of the parabola.
This is the line where the parabola makes a mirror image.
Assuming the equation for the parabola is ( since this is a function)
y= a(x-h)^2 +k
where (h,k) is the vertex
Then x=h is the axis of symmetry
y = a(x-1)^2+5
when we substitute the vertex into the equation
The axis of symmetry is x=1
Write the slope-intercept form of the equation that passes through the point (0,-3) and is perpendicular to the line y = 2x - 6
For this case we have that by definition, the equation of a line of the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cutoff point with the y axis
By definition, if two lines are perpendicular then the product of their slopes is -1.
We have the following line:
[tex]y = 2x-6[/tex]
Then[tex]m_ {1} = 2[/tex]
The slope of a perpendicular line will be:
[tex]m_ {1} * m_ {2} = - 1\\m_ {2} = \frac {-1} {m_ {1}}\\m_ {2} = - \frac {1} {2}[/tex]
Thus, the equation of the line will be:
[tex]y = - \frac {1} {2} x + b[/tex]
We substitute the given point and find "b":
[tex]-3 = - \frac {1} {2} (0) + b\\-3 = b[/tex]
Finally the equation is:
[tex]y = - \frac {1} {2} x-3[/tex]
Answer:
[tex]y = - \frac {1} {2} x-3[/tex]
Answer:
[tex]y=-\frac{1}{2}x -3[/tex]
Step-by-step explanation:
The slope-intercept form of the equation of a line has the following form:
[tex]y=mx + b[/tex]
Where m is the slope of the line and b is the intercept with the y axis
In this case we look for the equation of a line that is perpendicular to the line
[tex]y = 2x - 6[/tex].
By definition If we have the equation of a line of slope m then the slope of a perpendicular line will have a slope of [tex]-\frac{1}{m}[/tex]
In this case the slope of the line [tex]y = 2x - 6[/tex] is [tex]m=2[/tex]:
Then the slope of the line sought is: [tex]m=-\frac{1}{2}[/tex]
The intercept with the y axis is:
If we know a point [tex](x_1, y_1)[/tex] belonging to the searched line, then the constant b is:
[tex]b=y_1-mx_1[/tex] in this case the poin is: (0,-3)
Then:
[tex]b= -3 -(\frac{1}{2})(0)\\\\b=-3[/tex]
finally the equation of the line is:
[tex]y=-\frac{1}{2}x-3[/tex]
Helllllllppppp plzzzzzzzzz
Answer:
Hey, You have chosen the correct answer.
the correct answer is C.
Isabel is on a ride in an amusement park that Slidez the right or to the right and then it will rotate counterclockwise about its own center 60° every two seconds how many seconds pass before Isabel returns to her starting position
Final answer:
Isabel's ride rotates 60° every two seconds. It takes 6 intervals (360° divided by 60°) to make a full rotation. Multiplying 6 intervals by 2 seconds gives us 12 seconds for Isabel to return to the starting position.
Explanation:
To determine how many seconds will pass before Isabel returns to her starting position on the ride, we need to establish the total degrees of rotation that equate to a full circle, which is 360°. Since the ride rotates 60° every two seconds, we can calculate the number of two-second intervals required to complete a full 360° rotation.
Firstly, divide 360° by 60° to find the number of intervals:
360° / 60° = 6 intervals
Since each interval takes 2 seconds, multiply the number of intervals by 2 to find the total time:
6 intervals × 2 seconds/interval = 12 seconds.
Therefore, it will take Isabel 12 seconds to return to her starting position on the amusement park ride.
The perimeter of a bedroom is 88 feet. The ratio of the width to the length is 5:6. What are the dimensions of the bedroom?
Answer:
20 feet wide, 24 feet long
Step-by-step explanation:
Let x - width, y - length.
The perimeter is given by the formula:
P = 2*(width + length) or using x, y
P = 2*(x + y) = 88
x + y = 44
And we know that the ratio between the sides is 5/6:
x/y = 5/6. x is on top because the length is bigger than the width
x = 5y/6
Plug this in the first expression:
y + 5y/6 = 44. Muliply by 6
6y + 5y = 264
11y = 264
y = 264/11 = 24.
So x = 5(24)/6 = 20
Match the identities to their values taking these conditions into consideration sinx=sqrt2 /2 cosy=-1/2 angle x is in the first quadrant and angle y is in the second quadrant. Information provided in the picture. PLEASE HELP
Answer:
[tex]\boxed{\vphantom{\dfrac{\sqrt{2}}{2}}\quad \cos(x+y)\quad }\longleftrightarrow \boxed{\quad \dfrac{-(\sqrt{6}+\sqrt{2})}{4}\quad }[/tex]
[tex]\boxed{\vphantom{\dfrac{\sqrt{2}}{2}}\quad \sin(x+y)\quad }\longleftrightarrow \boxed{\quad\dfrac{\sqrt{6}-\sqrt{2}}{4}\quad }[/tex]
[tex]\boxed{\quad \tan(x+y)\quad }\longleftrightarrow \boxed{\quad\sqrt{3} -2\quad }[/tex]
[tex]\boxed{\vphantom{\sqrt{3}}\quad \tan(x-y)\quad }\longleftrightarrow \boxed{\quad-(2+\sqrt{3})\quad }[/tex]
Step-by-step explanation:
To find the values of the given trigonometric identities, we first need to find the values of cos x and sin y using the Pythagorean identity, sin²x + cos²x ≡ 1.
Given values:
[tex]\sin x = \dfrac{\sqrt{2}}{2}\qquad \textsf{Angle $x$ is in Quadrant I}\\\\\\\cos y=-\dfrac{1}{2}\qquad \textsf{Angle $y$ is in Quadrant II}[/tex]
Find cos(x):
[tex]\sin^2 x+\cos^2 x=1\\\\\\\left(\dfrac{\sqrt{2}}{2}\right)^2+\cos^2 x=1\\\\\\\dfrac{1}{2}+\cos^2 x=1\\\\\\\cos^2 x=1-\dfrac{1}{2}\\\\\\\cos^2 x=\dfrac{1}{2}\\\\\\\cos x=\pm \sqrt{\dfrac{1}{2}}\\\\\\\cos x=\pm \dfrac{\sqrt{2}}{2}[/tex]
As the cosine of an angle is positive in quadrant I, we take the positive square root:
[tex]\cos x=\dfrac{\sqrt{2}}{2}[/tex]
Find sin(y):
[tex]\sin^2 y + \cos^2 y = 1 \\\\\\ \sin^2 y + \left(-\dfrac{1}{2}\right)^2 = 1 \\\\\\ \sin^2 y + \dfrac{1}{4} = 1 \\\\\\ \sin^2 y = 1-\dfrac{1}{4} \\\\\\ \sin^2 y = \dfrac{3}{4} \\\\\\ \sin y =\pm \sqrt{ \dfrac{3}{4}} \\\\\\ \sin y = \pm \dfrac{\sqrt{3}}{2}[/tex]
As the sine of an angle is positive in quadrant II, we take the positive square root:
[tex]\sin y = \dfrac{\sqrt{3}}{2}[/tex]
The tangent of an angle is the ratio of the sine and cosine of that angle. Therefore:
[tex]\tan x=\dfrac{\sin x}{\cos x}=\dfrac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}=1[/tex]
[tex]\tan y=\dfrac{\sin y}{\cos y}=\dfrac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=-\sqrt{3}[/tex]
Now, we can use find the sum or difference of two angles by substituting the values of sin(x), cos(x), sin(y), cos(y), tan(x) and tan(y) into the corresponding formulas.
[tex]\dotfill[/tex]
cos(x + y)[tex]\cos(x+y)=\cos x \cos y - \sin x \sin y \\\\\\ \cos(x+y)=\left(\dfrac{\sqrt{2}}{2}\right) \left(-\dfrac{1}{2}\right) - \left(\dfrac{\sqrt{2}}{2}\right) \left(\dfrac{\sqrt{3}}{2}\right) \\\\\\ \cos(x+y)=-\dfrac{\sqrt{2}}{4} - \dfrac{\sqrt{6}}{4} \\\\\\ \cos(x+y)=\dfrac{-\sqrt{2}-\sqrt{6}}{4} \\\\\\ \cos(x+y)=\dfrac{-(\sqrt{2}+\sqrt{6})}{4} \\\\\\ \cos(x+y)=\dfrac{-(\sqrt{6}+\sqrt{2})}{4}[/tex]
[tex]\dotfill[/tex]
sin(x + y)[tex]\sin(x+y)=\sin x \cos y + \cos x \sin y \\\\\\\sin(x+y)=\left(\dfrac{\sqrt{2}}{2}\right) \left(-\dfrac{1}{2}\right) + \left(\dfrac{\sqrt{2}}{2}\right) \left(\dfrac{\sqrt{3}}{2}\right) \\\\\\\sin(x+y)=-\dfrac{\sqrt{2}}{4} + \dfrac{\sqrt{6}}{4} \\\\\\ \sin(x+y)=\dfrac{-\sqrt{2}+\sqrt{6}}{4} \\\\\\ \sin(x+y)=\dfrac{\sqrt{6}-\sqrt{2}}{4}[/tex]
[tex]\dotfill[/tex]
tan(x + y)[tex]\tan(x+y)=\dfrac{\tan x + \tan y}{1-\tan x \tan y} \\\\\\ \tan(x+y)=\dfrac{1 + (-\sqrt{3})}{1-(1) (-\sqrt{3})} \\\\\\ \tan(x+y)=\dfrac{1 -\sqrt{3}}{1+\sqrt{3}} \\\\\\ \tan(x+y)=\dfrac{(1 -\sqrt{3})(1 -\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})} \\\\\\ \tan(x+y)=\dfrac{1-2\sqrt{3}+3}{1-\sqrt{3}+\sqrt{3}-3} \\\\\\ \tan(x+y)=\dfrac{4-2\sqrt{3}}{-2} \\\\\\ \tan(x+y)=-2+\sqsrt{3} \\\\\\ \tan(x+y)=\sqrt{3} -2[/tex]
[tex]\dotfill[/tex]
tan(x - y)[tex]\tan(x-y)=\dfrac{\tan x - \tan y}{1+\tan x \tan y} \\\\\\\tan(x-y)=\dfrac{1 - (-\sqrt{3})}{1+(1) (-\sqrt{3})} \\\\\\\tan(x-y)=\dfrac{1 +\sqrt{3}}{1-\sqrt{3}} \\\\\\\tan(x-y)=\dfrac{(1 +\sqrt{3})(1 +\sqrt{3})}{(1-\sqrt{3})(1+\sqrt{3})} \\\\\\ \tan(x-y)=\dfrac{1+2\sqrt{3}+3}{1+\sqrt{3}-\sqrt{3}-3} \\\\\\ \tan(x-y)=\dfrac{4+2\sqrt{3}}{-2} \\\\\\ \tan(x-y)=-2-\sqrt{3}\\\\\\\tan(x-y)=-(2+\sqrt{3})[/tex]
Solve the equations to find the number and type of solutions
The equation 8 - 4x = 0 has
real solution(s).
DONE
Answer:
This has one real solution, x=4
Step-by-step explanation:
8 - 4x = 0
Add 4x to each side
8 - 4x+4x = 0+4x
8 =4x
Divide each side by 4
8/4 = 4x/4
2 =x
This has one real solution, x=4
Answer:
This equation has 1 real solution, x=2....
Step-by-step explanation:
8- 4x=0
Move 8 to the R.H.S
-4x=0-8
-4x=-8
Divide both sides by -4
-4x/-4 = -8/-4
x=2
Thus this equation has 1 real solution, x=2 ....
Rachel has been watching the number of alligators that live in her neighborhood. The number of alligators changes each week.
n f(n)
1 48
2 24
3 12
4 6
Which function best shows the relationship between n and f(n)?
f(n) = 48(0.5)^n − 1
f(n) = 48(0.5)^n
f(n) = 24(0.5)^n
f(n) = 96(0.5)^n − 1
Answer:
f(x) = 48(0.5)^n - 1 ⇒ 1st answer
Step-by-step explanation:
* Lets explain how to solve the problem
- The number of alligators changes each week
∵ The number in week 1 is 28
∵ The number in week 2 is 24
∵ The number in week 3 is 12
∵ The number in week 4 is 6
∴ The number of alligators is halved each week
∴ The number of alligators each week = half the number of alligators
of the previous week
- The number of alligators formed a geometric series in which the
first term is 48 and the constant ratio is 1/2
∵ Any term in the geometric series is Un = a r^(n - 1), where a is the
first term and r is the constant ratio
∴ f(n) = a r^(n - 1)
∵ a = 48 ⇒ The number of alligators in the first week
∵ r = 1/2 = 0.5
∴ f(x) = 48(0.5)^n - 1
the answer is f(x) = 48(0.5)^n - 1
1. Factor each of the following completely. Look carefully at the structure of each quadratic function and consider the best way to factor. Is there a GCF? Is it an example of a special case? SHOW YOUR WORK
Answer: 1) (x - 7)(x - 8)
2) 2x(2x-7)(x + 2)
3) (4x + 7)²
4) (9ab² - c³)(9ab² + c³)
Step-by-step explanation:
1) x² - 15x + 56 → use standard form for factoring
∧
-7 + -8 = -15
(x - 7) (x - 8)
************************************
2) 4x³ - 6x² - 28x → factor out the GCF (2x)
2x(2x² - 3x - 14) → factor using grouping
2x[2x² + 4x - 7x - 14]
2x[ 2x(x + 2) -7(x + 2)]
2x(2x - 7)(x + 2)
*************************************
3) 16x² + 56x + 49 → this is the sum of squares
√(16x²) = 4x √(49) = 7
(4x + 7)²
******************************************************
4) 81a²b⁴ - c⁶ → this is the difference of squares
√(81a²b⁴) = 9ab² √(c⁶) = c³
(9ab² - c³)(9ab² + c³)
How is the interquartile range calculated?
Minimum
Q1
Q1
Median
Median
Q3
Q3
Maximum
Maximum
Answer:
A
Step-by-step explanation:
The interquartile range is the difference between the upper quartile and the lower quartile, that is
interquartile range = [tex]Q_{3}[/tex] - [tex]Q_{1}[/tex]
The interquartile range (IQR) represents the spread of the middle 50 percent of a data set and is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). It also helps in identifying potential outliers in the data.
Explanation:The interquartile range (IQR) is a measure of statistical dispersion, which is the spread of the middle 50 percent of a data set. It is calculated by subtracting the first quartile (Q1) from the third quartile (Q3). To elaborate:
If, for example, Q1 is 2 and Q3 is 9, the IQR is calculated as 9 minus 2, resulting in an IQR of 7.
In addition to providing insight into the spread of the central portion of the data set, the IQR can also be used to identify potential outliers. These are values that fall more than 1.5 times the IQR above Q3 or below Q1.
children play a form of hopscotch called jumby. the pattern for the game is as given below.
Find the area of the pattern in simplest form.
Answer:
7t^2 + 21t
Step-by-step explanation:
You have 7 tiles of each t by t+3.
One tile has an area of
t * (t+3) = t^2 + 3t
So in total the area is
7* (t^2 + 3t)
7t^2 + 21t
plz help meh wit dis question but I need to show work.....
Answer:
5
Step-by-step explanation:
16+24
--------------
30-22
Complete the items on the top of the fraction bar
40
----------
30-22
Then the items under the fraction bar
40
------------
8
Then divide
5
Step-by-step explanation:
First of all, solve the numerator.
16+24=40
Secondly, solve the denominator:
30-22 = 8
So now the fraction appear like this :
[tex] \frac{40}{8} [/tex]
40/8 = 5
If 47400 dollars is invested at an interest rate of 7 percent per year, find the value of the investment at the end of 5 years for the following compounding methods, to the nearest cent.
(a) Annual: $______
(b) Semiannual: $ _____
(c) Monthly: $______
(d) Daily: $_______
Answer:
Part A) Annual [tex]\$66,480.95[/tex]
Part B) Semiannual [tex]\$66,862.38[/tex]
Part C) Monthly [tex]\$67,195.44[/tex]
Part D) Daily [tex]\$67,261.54[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
Part A)
Annual
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=1[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{1})^{1*5}[/tex]
[tex]A=47,400(1.07)^{5}[/tex]
[tex]A=\$66,480.95[/tex]
Part B)
Semiannual
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=2[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{2})^{2*5}[/tex]
[tex]A=47,400(1.035)^{10}[/tex]
[tex]A=\$66,862.38[/tex]
Part C)
Monthly
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=12[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{12})^{12*5}[/tex]
[tex]A=47,400(1.0058)^{60}[/tex]
[tex]A=\$67,195.44[/tex]
Part D)
Daily
in this problem we have
[tex]t=5\ years\\ P=\$47,400\\ r=0.07\\n=365[/tex]
substitute in the formula above
[tex]A=47,400(1+\frac{0.07}{365})^{365*5}[/tex]
[tex]A=47,400(1.0002)^{1,825}[/tex]
[tex]A=\$67,261.54[/tex]
The value of an investment of $47,400 at an interest rate of 7% per year was calculated at the end of 5 years for different compounding methods, reaching slightly different amounts, with the highest value obtained through daily compounding.
The value of the investment at the end of 5 years for different compounding methods would be:
(a) Annual: $62,899.68(b) Semiannual: $63,286.83(c) Monthly: $63,590.92(d) Daily: $63,609.29Evaluate the function rule for the given value. y = 15 • 3^x for x = –3
Answer:
5/9
Step-by-step explanation:
y = 15 • 3^x
Let x = -3
y = 15 • 3^(-3)
The negative means the exponent goes to the denominator
y = 15 * 1/3^3
= 15 * 1/27
=15/27
Divide the top and bottom by 3
=5/9
Consider the function represented by 9x+3y= 12 with x as the independent variable. How can this function be written using
function notation?
o AV=-=x+
o 0) = -3x+4
o Px) =-x+
o F) = - 3y+ 4
Answer:
f(x)=-3x+4
(can't see some of your choices)
Step-by-step explanation:
We want x to be independent means we want to write it so when we plug in numbers we can just choose what we want to plug in for x but y's value will depend on our choosing of x.
So we need to solve for y.
9x+3y=12
Subtract 9x on both sides
3y=-9x+12
Divide both sides by 3:
y=-3x+4
Replace y with f(x).
f(x)=-3x+4
Which linear function represents the line given by the point-slope equation y +7=-2/3(x + 6)
Answer:
y = -(2/3)*x - 11
Step-by-step explanation:
To convert a point-slop equation into a linear function, there are certain steps which have to be followed. The primary aim is to make y the subject of the equation. By making sure that y is on the left hand side of the equation and x is on the right hand side of the equation, our goal will be achieved. To do that, first of all do the cross multiplication. This will result in:
3(y+7) = -2(x+6).
Further simplification results in:
3y + 21 = -2x - 12.
Keeping the expression of y on the left hand side and moving the constant on the right hand side gives:
3y = -2x - 33.
Leaving y alone on the left hand side gives:
y = -(2/3)*x - 33/3.
Therefore, y = -(2/3)*x - 11!!!
A parallelogram has coordinates A(1,1), B(5,4), C(7,1), and D(3,-2) what are the coordinates of parallelogram A’BCD after 180 degree rotation about the origin and a translation 5 units to the right and 1 unit down ?
Answer:
The coordinates are (4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)
Step-by-step explanation:
* Lets revise some transformation
- If point (x , y) rotated about the origin by angle 180°
∴ Its image is (-x , -y)
- If the point (x , y) translated horizontally to the right by h units
∴ Its image is (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
∴ Its image is (x - h , y)
- If the point (x , y) translated vertically up by k units
∴ Its image is (x , y + k)
- If the point (x , y) translated vertically down by k units
∴ Its image is (x , y - k)
* Now lets solve the problem
∵ ABCD is a parallelogram
∵ Its vertices are A (1 , 1) , B (5 , 4) , C (7 , 1) , D (3 , -2)
∵ The parallelogram rotates about the origin by 180°
∵ The image of the point (x , y) after rotation 180° about the origin
is (-x , -y)
∴ The images of the vertices of the parallelograms are
(-1 , -1) , (-5 , -4) , (-7 , -1) , (-3 , 2)
∵ The parallelogram translate after the rotation 5 units to the right
and 1 unit down
∴ We will add each x-coordinates by 5 and subtract each
y-coordinates by 1
∴ A' = (-1 + 5 , -1 - 1) = (4 , -2)
∴ B' = (-5 + 5 , -4 - 1) = (0 , -5)
∴ C' = (-7 + 5 , -1 - 1) = (-2 , -2)
∴ D' = (-3 + 5 , 2 - 1) = (2 , 1)
* The coordinates of the parallelograms A'B'C'D' are:
(4 , -2) , (0 , -5) , (-2 , -2) , (2 , 1)
write a point slope equation for the line that has slope 3 and passes through the point (5,21). do not use parenthesis on the y side
Answer:
y - 21 = 3(x - 5)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
here m = 3 and (a, b) = (5, 21), hence
y - 21 = 3(x - 5) ← in point- slope form
The point slope form of an equation is y - y1 = m(x - x1). Substituting the given point (5,21) and slope 3 into the equation, we get y - 21 = 3(x - 5). To remove the parenthesis on the y side, we simplify the equation to be y = 3x + 6.
Explanation:The question asks for the writing of a point-slope equation of a line with a given slope of 3 that passes through a point (5,21). The point-slope form of an equation is generally denoted as:
y - y1 = m(x - x1)
Here, (x1, y1) = (5,21) and m (slope) = 3. Hence, substituting these values yields the equation:
y - 21 = 3(x - 5)
The asked equation without parenthesis on the y side would be:
y = 3x - 15 + 21
So, the final equation is:
y = 3x + 6
Learn more about Point-Slope Equationhttps://brainly.com/question/35491058
#SPJ11
A high school track is shaped as a rectangle with a half circle on either side . Jake plans on running four laps . How many meters will jake run ?
Answer:
[tex]1,207.6\ m[/tex]
Step-by-step explanation:
step 1
Find the perimeter of one lap
we know that
The perimeter of one lap is equal to the circumference of a complete circle (two half circles is equal to one circle) plus two times the length of 96 meters
so
[tex]P=\pi D+2(96)[/tex]
we have
[tex]D=35\ m[/tex]
[tex]\pi =3.14[/tex]
substitute
[tex]P=(3.14)(35)+2(96)[/tex]
[tex]P=301.9\ m[/tex]
step 2
Find the total meters of four laps
Multiply the perimeter of one lap by four
[tex]P=301.9(4)=1,207.6\ m[/tex]
Answer:
1207.6
Step-by-step explanation:
step 1
i got it right on the test
step 2
you get it right on the test
What is the midpoint of a line segment with the endpoints (-6, -3) and (9,-7)?
Answer: (1.5, -5)
Step-by-step explanation: a p e x
Which of the following numbers are less than 9/4?
Choose all that apply:
A= 11/4
B= 15/8
C= 2.201
Answer:
OPTION B.
OPTION C.
Step-by-step explanation:
In order to know which numbers are less than [tex]\frac{9}{4}[/tex], you can convert this fraction into a decimal number. To do this, you need to divide the numerator 9 by the denominator 4. Then:
[tex]\frac{9}{4}=2.25[/tex]
Now you need convert the fractions provided in the Options A and B into decimal numbers by applying the same procedure. This are:
Option A→ [tex]\frac{11}{4}=2.75[/tex] (It is not less than 2.25)
Option B→ [tex]\frac{15}{8}=1.875[/tex] (It is less than 2.25)
The number shown in Option C is already expressed in decimal form:
Option C→ [tex]2.201[/tex] (It is less than 2.25)
Whats the quotient for this?
Answer:
Step-by-step explanation:
Divide 4378 by 15
From 4378 lets take the first two digits for division:
43/ 15
We know that 43 does not come in table of 15
So we will take 15 *2 = 30
43-30 = 13
The quotient is 3 and the remainder is 13
Now take one more number which is 7 with 13
137/15.
Now 137 does not come in table of 15
15*9 = 135
135-137 = 2
It means quotient is 9 and remainder is 2
Now take one more number which is 8 with 2
28/15
28 does not come in table of 15
15*1 = 15
28-15 = 13/15
Now the quotient is 1 and remainder is 13
Hence, the quotient of 4,378 is 291 and remainder is 13 ....
The equations 3x-4y=-2, 4x-y=4, 3x+4y=2, and 4x+y=-4 are shown on a graph.
Which is the approximate solution for the system of equations 3x+4y=2 and 4x+y=-4?
A. (–1.4, 1.5)
B. (1.4, 1.5)
C. (0.9, –0.2)
D. (–0.9, –0.2)
i cant download the graph picture but please help.
Answer:
A (-1,4,1.5)
Step-by-step explanation:
Solve by graphing, the lines intersect near this point.
What is the equation of the graph below
Answer:
y=-(x-3)^2+2
Step-by-step explanation:
since the curve is convex up so the coefficient of x^2 is negative
and by substituting by the point 3 so y = 2
Answer:
B
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (3, 2), hence
y = a(x - 3)² + 2
If a > 0 then vertex is a minimum
If a < 0 then vertex os a maximum
From the graph the vertex is a maximum hence a < 0
let a = - 1, then
y = - (x - 3)² + 2 → B
The diagram represents three statements: p, q, and r. For what value is both p ∧ r true and q false?
2
4
5
9
Answer:
9
Step-by-step explanation:
From the diagram:
only p true in 8 cases;only q true in 7 cases;only r true in 6 cases;both p and q true, r false in 5 cases;both p and r true, q false in 9 cases;both q and r true, p false in 4 cases;all three p, q and r true in 2 cases.So, correct option is 9 cases.
Answer:
The correct option is 4. For value 9 both p ∧ r true and q false.
Step-by-step explanation:
The diagram represents three statements: p, q, and r.
We need to find the value for which p ∧ r is true and q false.
p ∧ r true mean the intersection of statement p and r. It other words p ∧ r true means p is true and r is also true.
From the given venn diagram it is clear that the intersection of p and r is
[tex]p\cap r=9+2=11[/tex]
p ∧ r true and q false means intersection of p and r but q is not included.
From the given figure it is clear that for value 2 all three statements are true. So, the value for which both p ∧ r true and q false is
[tex]11-2=9[/tex]
Therefore the correct option is 4.
Please help and explain
Answer: Option A
[tex]x=\frac{3+i}{2}[/tex] or [tex]x=\frac{3-i}{2}[/tex]
Step-by-step explanation:
Use the quadratic formula to find the zeros of the function.
For a function of the form
[tex]ax ^ 2 + bx + c = 0[/tex]
The quadratic formula is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
In this case the function is:
[tex]2x^2-6x+5=0[/tex]
So
[tex]a=2\\b=-6\\c=5[/tex]
Then using the quadratic formula we have that:
[tex]x=\frac{-(-6)\±\sqrt{(-6)^2-4(2)(5)}}{2(2)}[/tex]
[tex]x=\frac{6\±\sqrt{36-40}}{4}[/tex]
[tex]x=\frac{6\±\sqrt{-4}}{4}[/tex]
Remember that [tex]\sqrt{-1}=i[/tex]
[tex]x=\frac{6\±\sqrt{4}*\sqrt{-1}}{4}[/tex]
[tex]x=\frac{6\±\sqrt{4}i}{4}[/tex]
[tex]x=\frac{6\±2i}{4}[/tex]
[tex]x=\frac{3\±i}{2}[/tex]
[tex]x=\frac{3+i}{2}[/tex] or [tex]x=\frac{3-i}{2}[/tex]
Use the Quadratic Formula to solve the equation x2 - 4x = -7
The given quadratic equation x² - 4x = -7 is rearranged into standard form and then solved using the quadratic formula -b ± √(b² - 4ac) / (2a). The roots of the equation are realized from solving this formula.
Explanation:The subject of this problem is a quadratic equation in the form of ax²+bx+c = 0. The given equation is x² - 4x = -7, which can be rearranged into standard form as x² - 4x + 7 = 0. Thus, in this case, a=1, b=-4, and c=7.
The solutions or roots for this quadratic equation can be calculated using the quadratic formula, which is -b ± √(b² - 4ac) / (2a). Substituting the values of a, b, and c into the formula will give the roots of the given equation.
Doing that, we get: x = [4 ± √((-4)² - 4*1*7)] / (2*1)
The values that solve the equation are the roots of the quadratic equation.
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To solve the equation x^2 - 4x = -7 using the Quadratic Formula, we follow the steps of plugging the values of a, b, and c into the formula, evaluating the square root and simplifying to find the solutions.
Explanation:To solve the equation x2 - 4x = -7 using the Quadratic Formula, we first need to make sure the equation is in standard form, which is ax2 + bx + c = 0. In this case, a = 1, b = -4, and c = 7. Plugging these values into the Quadratic Formula, we get:
x = (-(-4) ± √((-4)2 - 4(1)(-7))) / (2(1))
x = (4 ± √(16 + 28))/2
x = (4 ± √44)/2
x = (4 ± 2√11)/2
x = 2 ± √11
So the solutions to the equation x2 - 4x = -7 are x = 2 + √11 and x = 2 - √11.
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What is the sum of entries a32 and b32 in A and B? (matrices)
Answer:
The correct answer is option D. 13
Step-by-step explanation:
From the figure we can see two matrices A and B
To find the sum of a₃₂ and b₃₂
From the given attached figure we get
a₃₂ means that the third row second column element in the matrix A
b₃₂ means that the third row second column element in the matrix B
a₃₂ = 4 and b₃₂ = 9
a₃₂ + b₃₂ = 4 + 9
= 13
The correct answer is option D. 13
[tex]A={\begin{bmatrix}a_{11}&a_{12}&\cdots &a_{1n}\\a_{21}&a_{22}&\cdots &a_{2n}\\\vdots &\vdots &\ddots &\vdots \\a_{m1}&a_{m2}&\cdots &a_{mn}\end{bmatrix}}[/tex]
So
[tex]a_{32}=4\\b_{32}=9\\\\a_{32}+b_{32}=4+9=13[/tex]