Answer:
Step-by-step explanation:
a) 3x^2-12x-11=3*x^2-3*2*2*x+3*4-23=3*(x^2-2*2x+2^2)-23=3*(x-2)^2-23
so a= -2 ,b= -23
b) x1=[12+V(12^2-4*3* -11)]/6=12/6+V(144+132)/6=2+2/6V69=2+1/3V69=
2+V69/9=2+V23/3
c=2, d= 23/3
a) The value of a and b from the expression are -2 and -23 respectively.
b) The value of c and d are 2 and 23/3 respectively'
a) Given the quadratic function [tex]3x^2-12x-11[/tex], writing the equation in the form [tex]3(x+a)^2+b[/tex] using the completing the square method.
[tex]3x^2-12x-11=0\\x^2-\frac{12}{3}x-\frac{11}{3} =0\\x^2-4x-\frac{11}{3} =0\\(x^2-4x+4)-4-\frac{11}{3}=0\\(x-2)^2-\frac{23}{3} =0\\3(x-2)^2-23=0[/tex]
Compare the result with [tex]3(x+a)^2+b[/tex];
a = -2
b = -23
Hence the value of a and b from the expression are -2 and -23 respectively.
b) Given the quadratic equation [tex]3x^2-12x-11=0[/tex] using the general formula to factorize the equation;
[tex]x=\frac{-b\pm \sqrt{b^2-4ac} }{2a} \\x=\frac{-(-12)\pm \sqrt{(-12)^2-4(3)(-11)} }{2(3)} \\x=\frac{12\pm \sqrt{144+132} }{6} \\x=\frac{12\pm\sqrt{276} }{6} \\x=2\pm\sqrt{\frac{276}{36} }\\x=2\pm\sqrt{\frac{23}{3} } }[/tex]
Compared with c ± √d, the value of c and d are 2 and 23/3 respectively.
Learn more on quadratic functions here: https://brainly.com/question/17895228
Hi can any one please help me I really need help please help me I need help
Answer:
1(a)1,030,000+0.13x
(b)$1,030,026
2. (a)Base and Index
(b)See Explanation
Ste-by-Step Explanation
(a)Total Amount to be paid to the four actors
=500,000+(300,000+0.02x)+(150,000+0.03x)+(80,000+0.08x)
Collect like terms
=500,000+300,000+150,000+80,000+0.02x+0.03x+0.08x
[tex]\text{Total Amount Paid= }1,030,000+0.13x[/tex]
(b)When x=200
[tex]\text{Total Amount Paid= }1,030,000+0.13(200)\\=1,030,000+26\\=$1,030,026[/tex]
Question 2
(a)The two parts of a power are the base and index.
Take, for example, the expression: [tex]a^b\\[/tex]
[tex]a$ is the base\\b is the index[/tex]
Another example using numbers is: [tex]10^3[/tex]
In this case:
[tex]10$ is the base\\3 is the index[/tex]
(b)Like terms are terms that have the same letter/variable attached to them.
For example, the following pairs are like terms
8x and 3x4y and -9y6pq and pq3 and 3These, however, are not like terms
3 and 3y4x and 4yThe U.S. Census reports Native Americans by Group of answer choices one tribe only or in combination with another tribe plus in combination with any other race. one tribe only, one tribe only or in combination with another tribe, and one tribe only or in combination with another tribe plus in combination with any other race. one tribe only. one tribe only or in combination with another tribe. one tribe only and one tribe only or in combination with another tribe
Answer:
one tribe only or in combination with another tribe plus in combination with any other race.
Step-by-step explanation:
United States Census Bureau (USCB) is the governmental agency saddled with the responsibility of providing data about the citizens of America and her economy. The Census Bureau was founded on the 1st of July, 1902 and has its headquarter in Suitland, Maryland, United States of America.
The U.S. Census reports Native Americans by one tribe only or in combination with another tribe plus in combination with any other race.
Native Americans are the indigenous people (citizens) of the United States of America and they are also known as the American Indians. The Census Bureau reports them by one tribe only such as Cherokee, Apache, Hopi, Chinook etc or in combination with another tribe such as Aleuts, Tlingit, Chenega, etc plus in combination with any other race such as Black Americans, Asian Americans, White Americans, Native Hawaiian etc.
2 Points
What is the measure of ZE, in degrees?
Answer:
B. 84 deg
Step-by-step explanation:
Sides DE and FE are congruent since they both have the same length.
That makes angles D and F congruent.
m<D = m<F = 48
The sum of the measures of the angles of a triangle equals 180 deg.
m<E + m<D + m<F = 180
m<E + 48 + 48 = 180
m<E = 84
If f(x) = X over 2+8, what is f(x) when X equals 10?
Answer:
[tex] \boxed{\huge{\sf f(x) = 1}} [/tex]
Given:
[tex] \sf f(x) = \frac{x}{2 + 8} [/tex]
To Find:
[tex] \sf f(x) \: when \: \bold{x} = 10[/tex]
Step-by-step explanation:
[tex] \sf Evaluate \: f(x) = \frac{x}{2 + 8} \: where \: \bold{x} = 10 : \\ \sf \implies f(x) = \frac{x}{2 + 8} = \frac{10}{2 + 8} \\ \\ \sf 2 + 8 = 10 : \\ \sf \implies f(x) = \frac{10}{ \boxed{\sf 10}} \\ \\ \sf \frac{ \cancel{\sf 10}}{ \cancel{\sf 10}} = 1 : \\ \sf \implies f(x) = 1[/tex]
Find the median, divide it by 3 20, 82, 39, 23, 20, 60, 64.
Answer:
by using formula of median you can do it.
Answer:
put the numbers in order
20,20,23,39,60,64,82
Find the number in the middle
39 is in the middle because there is 3 numbers on each side so it is the median.
Divide by 3.
39 / 3 = 13
Hope this helps
Step-by-step explanation:
The expression (1/23) ^1000 is closest to what integer?
HELP QUICK PLS
Answer:
The expression is close to 0Step-by-step explanation:
Given the expression [tex](\frac{1}{23} )^{1000} \\[/tex], for us to know the closest integer, the following step must be carried out;
[tex](\frac{1}{23} )^{1000} \\=\frac{1^{1000} }{23^{1000} } \\= \frac{1}{23^{1000}} \\= \frac{1}{5.34 * 10^{1361} }} \\= 1.87*10^{-1362}[/tex]
The value gotten is a very small value which is close to 0
Melinda sold packages of gourmet coffee, x, and pastries, y, at a school fundraiser. The packages of coffee sold for $6 each and pastries sold for $4 each. At the end of the fundraiser, she had sold 2 more packages of coffee than pastries and made $72 in total sales for the fundraiser. Create and graph system of linear equations that model this situation.
Answer:
Please find the attached graph
Melinda sold 8 packages of coffee and 6 packages of pastries
Step-by-step explanation:
The parameters given are;
Number of Packages of coffee = x
Number of Packages of pastries = y
Price of each package of coffee = $6
Price of each package of coffee = $4
Number of packages of packages of coffee sold = 2 more than packages of packages pastries sold
x = 2 + y
y = x - 2................(1)
Sum of money made in the fundraiser = $72
∴ x × $6 + y × $4 = $72
y = ($72 - x × $6)/$4 = 18 - 3/2·x
y = 18 - 3/2·x.........(2)
The solution is
x - 2 = 18 - 3/2·x
x + 3/2 = 18 + 2 = 20
5/2·x = 20
x = 2/5×20 = 8
y = x - 2 = 8 - 2 = 6
This is the answer from plato/edmentum.
The equation of a circle is given below. ( x + 8 3 ) 2 + y 2 = 1 (x+ 3 8 ) 2 +y 2 =1left parenthesis, x, plus, start fraction, 8, divided by, 3, end fraction, right parenthesis, squared, plus, y, squared, equals, 1 What is its center? ( (left parenthesis , ,comma ) )right parenthesis What is its radius? If necessary, round your answer to two decimal places. units
Answer:
The center is (-8/3,0) and the radius is 1
Step-by-step explanation:
(x+8/3)^2 + y^2 = 1
We know the equation of a circle is given by
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
Rewriting
(x- -8/3)^2 + (y-0)^2 = 1^2
The center is (-8/3,0) and the radius is 1
NEED HELP ASAP!! RESPOND AS QUICK AS POSSIBLE!!!
Answer:
d
Step-by-step explanation:
Write as an expression: Twice the product of the squares of x and y Thanks! -Jamie
Answer: [tex]2(xy )^{2}[/tex] the same thing as 2([tex]x^{2} y^{2}[/tex])
Step-by-step explanation:
You multiply 2 by x times y squared.
John is filling a bathtub that is 12 inches deep. He notices that it takes two minutes to fill the tub with three inches of water. He estimates it will take 10 more minutes for the water to reach the top of the tub if it continues at the same rate. Is he correct?
Answer:
No
Step-by-step explanation:
2 = 3 inches
2x5=10
10 = 3x5 of 15 inches
so no and it would take 8 minutes to fill up the tub
Find the volume of the cylinder
Answer:
see below
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
We know the radius is 9 and the height is 20
V = pi ( 9)^2 ( 20)
V = 1620 pi
If we approximate pi by 3.14
V =5086.80 cm^3
If we approximate pi by pi button
V =5089.3800099 cm^3
Answer:
V=5089.380099cm^3
Step-by-step explanation:
V=πr^2h
V=π(9)^2(20)
V=π(9)^2(20)
V=5089.380099cm^3
According to the Insurance Institute of America, a family of four spends between $400 and $3,800 per year on all types of insurance. Suppose the money spent is uniformly distributed between these amounts. If we select a family at random, what is the probability they spend less than $2,000 per year on insurance per year? (Round your answer to 4 decimal places.)
Answer:
0.471
Step-by-step explanation:
Calculation for the probability that they spend less than $2,000 per year on insurance per year
First step is to find the base
Base =$2,000-$400
=$1,600
Second step is to find the probability using this formula
P=1/b+a×base
Where,
b represents $3,800
a represents $400
base represents $1,600
Let plug in the formula
P=1/$3,800-$400×$1,600
Hence,
P=1×$1,600/$3,800-$400
P=$1,600/$3,400
P=0.471
Therefore the probability that they spend less than $2,000 per year on insurance per year will be 0.471
Write the equation of the line that passes through (1,5) and (-2, 14) in slope-intercept form
Answer:
y = -3x + 8
Step-by-step explanation:
(1, 5) ; (-2, 14)
[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\=\frac{14-5}{-2-1}\\\\=\frac{9}{-3}\\\\=-3[/tex]
m = -3 ; (1 , 5)
Equation: [tex]y-y_{1}=m(x-x_{1})[/tex]
y - 5 = (-3)(x - 1)
y - 5 = -3x + 3
y = -3x + 3 + 5
y = -3x + 8
In this activity, you will use equations to represent this proportional relationship: Olivia is making bead bracelets for her friends. She can make 3 bracelets in 15 minutes. Find the constant of proportionality in terms of minutes per bracelet.
Answer:
If she makes 3 bracelets in 15 minutes the constant of proportionality is 15/3 = 5 minutes per bracelet.
Answer:
5 minutes
Step-by-step explanation:
Did she can make 3 bracelets in 15 minutes then you have to divide 15/3 to get the number of minutes she can make one bracket. Therefore your answer would be 5 minutes per bracelet.
Hope this helps!
H(x)=4x-2;find h(-9)
Answer: h(-9)=4*(-9)-2=-36-2=-38
-38 is ur answer
Answer:-38
Step-by-step explanation:h(x) =4x -2
H(-9)
substitute for x using -9
H(-9) =4x -2
4(-9) -2
-36-2
H(-9) =-38
Solve each system by the addition method.
x + 2y = -1
5x - 4y = 16
Put your answer in ordered pair (x, y) DECIMAL form.
Answer:
(x, y) = (2, -1.5)
Step-by-step explanation:
x + 2y = -1
5x - 4y = 16
<=>
(2)x + (2)2y = (2)(-1)
5x - 4y = 16
<=>
2x + 4y = -2
5x - 4y = 16
<=>
7x = 14
<=>
x = 2
(*)x + 2y = -1
=> 2 + 2y = -1
=> 2y = -3
=> y = -1.5
=> (x, y) = (2, -1.5)
Divide a24 − a18 + a12 by a6. What is the quotient? A. a4 − a3 + a2 B. a18 − a12 + a6 C. a18 + a12 − a6 D. a30 − a24 + a18
Answer:
A
Step-by-step explanation:
Find the point-slope equation for the line that passes through the points (-8,-32) and (3,1). Use the first point in your equation.
Hey there! :)
Answer:
y + 32 = 3(x + 8)
Step-by-step explanation:
Begin by finding the slope of the line using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Plug in the coordinates of the points into the equation:
[tex]m = \frac{1 - (-32)}{3 - (-8)}[/tex]
Simplify:
[tex]m = \frac{33}{11}[/tex]
m = 3.
Point-slope form is:
y-y₁=m(x-x₁)
Plug in the coordinates of the first point, as well as the slope:
y - (-32) = 3(x - (-8)
y + 32 = 3(x + 8)
Answer: y+32=3(x+8)
Step-by-step explanation:
First you need to find the slope.The slope is the change in y divided by the change in x values.
-32 - 1 = -33
-8 - 3 = -11
-33/-11 = 3 the slope is 3
and in point-slope form is like y-b= m(x-a) where b is a y coordinate and a is the x coordinate.
it could be like y-1=3(x-3) or y+32= 3(x+8)
Jon recently drove to visit his parents who live 528 miles away. On his way there his average speed was 14 miles per hour faster than on his way home (he ran into some bad weather). If Jon spent a total of 22 hours driving, find the two rates.
Answer:
speed while going = 42, while returning home = 28
Step-by-step explanation:
let his speed on the way to his parents house is (x)
then his speed while returning is x - 14
Time = Distance / speed
528 / x + 528 / x -14 = 22
multiplying the denominator ...
528x + 528x +7392 = 22x^2 +14x
1056x + 7392 = 22x^2 + 308x
0 = 22x^2 -748x -7392
"dividing by 22"
0 = x^2 -34x-336
0 = (x+8) (x-42)
x must be 42
finally jon's speed while back home is 42 - 14 = 28
Find the surface area of the prism.
Help please
Answer:
256 in ^2
Step-by-step explanation:
The area of the base B = 12*5 = 60 in ^2
The height is 14 inches
The perimeter of the base is
2 ( l+w) =2 ( 12+5) = 2 ( 17) = 34
The surface area is = 2B + Ph = 2 * 60 + 34*4
= 120 + 136
=256
What is true about the domain and range of the function?
The graph of the function f(x) = (x +2)(x + 6) is shown
below.
у
6
The domain is all real numbers, and the range is all
real numbers greater than or equal to 4.
O The domain is all real numbers greater than or equal to
4, and the range is all real numbers.
O The domain is all real numbers such that -65x3-2,
and the range is all real numbers greater than or equal
to-4.
The domain is all real numbers greater than or equal to
4, and the range is all real numbers such that -63x3
-2.
4
N
-6 -4 +2
4
6
х
N
-2-
-4
6t
Answer:
The correct option is;
The domain is all real numbers and the range is all real numbers greater than or equal to -4
Step-by-step explanation:
A function defines an output given an input and the set of all the possible inputs to a function is the domain of a function such that there is an output, such that the domain is the set of x values which are points on the curve of the function
The set of outputs that are produced from a given input is the range of a function
The given function is f(x) = (x + 2)(x + 6)
From the curve we see that the minimum y-coordinate, f(x), value is at -4, which is the lower bound of the range, while the x-coordinate values, the domain can be seen extending past the graph sheet which from the expression for the function also (f(x) = (x + 2)(x + 6)) indicates that the x values is the set of all real numbers (on the number line)
Therefore, the correct option is;
The domain is all real numbers and the range is all real numbers greater than or equal to -4.
Answer:
The domain is all real numbers and the range is all real numbers greater than or equal to -4
Step-by-step explanation:
what is the solution to this equation x/5=30
Answer:
x= 150
Step-by-step explanation:
X/5 = 30
x = 5×30
x= 150
Answer:
150
Step-by-step explanation:
[tex]\frac{x}{5}[/tex] = 30
→ Multiply both sides by 5 to isolate x
x = 150
The temperatures of Charleston, South Carolina on May 3rd are recorded in the table below. Determine the equation that models this data.
Answer:
Ok, the first step to see the behavior of this data is doing a graph of it,
So we can see that it looks like an reversed V. (at the bottom of the answer you can see the graph)
Then, we can model this with a piecewise function like:
For the first part we can take the two pairs:
if 11 am is our t = 0h
(0, 85) and (6, 93)
then the linear equation
y = a*t + b
a = (93 - 85)/(6 -0) = 8/6.
and b = 85.
then the linear equation is:
y = (8/6)*t + 85. for 0h ≤ t ≤ 6h
The second part of this equation can be modeled with the points
(6, 93) and (11, 84)
then we have:
y = s*t + c
s = (84 - 93)/(11 - 6) = -7/5
and we can find the value of c as:
93 = (-7/5)*6 + c
93 + (7/5)*6 = 101.4
then this second part is:
y = (-7/5)*t + 101.4 for 6 ≤ t ≤ 11h
then, in conclusion we have:
y = (8/6)*t + 85. for 0h ≤ t ≤ 6h
f(x) =
y = (-7/5)*t + 101.4 for 6 ≤ t ≤ 11h
Answer:
y=7.496sin(0.3243x+0.315)+73.489
Step-by-step explanation:
simply put the data into a graph and graph each equation to see if its matched
what is the method and answer for brainliest
Equal steps mean each number is the same distance from the previous one
From -2 to 28 is 28 units
There are 4 spaces between the numbers
28/4 = 7
Each number is in increase of 7
-2 + 7 = 5
5+7 = 12
12+7 = 19
19+7 = 26
The third number would be 12
What is the result of substituting for y in the bottom equation?
y = x + 3
y= x2 + 2x-4
A. x+ 3 = x2 + 2x - 4
B. X+ 3 = x2
C. y= (x+3)2 + 2(x + 3) - 4
D. y= x2 + 2x - 4 - (x+3)
Answer:
(A)[tex]x + 3= x^2 + 2x-4[/tex]
Step-by-step explanation:
Given the equations:
[tex]y = x + 3\\y= x^2 + 2x-4[/tex]
Substitution simply means replacing the variable y in the second equation with its equivalent x+3 from the first equation.
Substitution of y into [tex]y=x^2 + 2x-4[/tex] gives us:
[tex]x + 3= x^2 + 2x-4[/tex]
The correct option is A.
The numbers -1/5 and -5 are 'negative reciprocals.' True or False?
Answer:
False
Step-by-step explanation:
The negative reciprocal of -1/5 would be 5, and the negative reciprocal of -5 is 1/5. A way to double-check is all negative reciprocals add to -1.
-1/5 + -5= -5 1/5
Hope this helps and you understand negative reciprocals more for future problems ahead.
Given: In ΔBLU, LE ⟂ BU , and BL ≅ UL Prove: ΔBEL ≅ ΔUEL STATEMENT REASON 1. LE⟂ BU and BL ≅ UL 1. Given 2. LE ≅ LE 2. Reflexive Property 3. ΔBEL ≅ ΔUEL 3. _______________ Which of the following choices will complete the reasoning for statement #3? A SSA B AAA C HL D None of these choices are correct.
Answer:
I think it is C
Step-by-step explanation:
You own a comic book store. When you order comic books for your store to sell, you get 18 comic books per bundle. How many comic books would you have to sell if you ordered 7 bundles?
Answer:
the answer is 126
Step-by-step explanation:
beacuse if you sell 7 bundles for every one you get 18 so 18+18+18+18+18+18+18=126
Answer:
126 books
Step-by-step explanation:
There are 18 books per bundle and 7 bundles
So you would multiply 7 with 18 and get your answer of 126 books to sell
Trey is running for president of the chess club, and he received 8 votes. There are 80 members in the club. What percentage of the club members voted for Trey?
Answer:10
Step-by-step explanation:
8/80=1/10*100=10