Quadratics are in the general form:
[tex]ax^2+bx+c[/tex]For completing the square, we use:
[tex](x+\frac{b}{2})^2=c+(\frac{b}{2})^2[/tex]Now, we have:
[tex]\begin{gathered} (x+\frac{12}{2})^2=-23+(\frac{12}{2})^2 \\ (x+6)^2=-23+(6)^2 \\ (x+6)^2=13 \end{gathered}[/tex]From here, we can easily solve for x with a little algebra. Shown below:
[tex]\begin{gathered} \sqrt[]{(x+6)^2}=\pm\sqrt[]{13} \\ x+6=\pm\sqrt[]{13} \\ x=-6\pm\sqrt[]{13} \end{gathered}[/tex]The answer(s) are:
[tex]\begin{gathered} x=-6+\sqrt[]{13} \\ x=-6-\sqrt[]{13} \end{gathered}[/tex]For further clarification
Form:
[tex](x+\frac{12}{2})^2=13[/tex]C is the depth in meters and f(x) is in grams of salt kilograms of sea water approximate the salinity to the nearest hundredth) when the depth is 797 meters
Using the function f(x) = 28.7 + 1.2log (x + 1) that models the salinity of the ocean to depths of 1000 meters the salinity to the nearest hundredth is 32.18 g/kg
How to find the salinity at the required depthThe salinity s calculated using the logarithmic function model
f(x) = 28.7 + 1.2log (x + 1)
given that f(x) is in grams of salt per kilogram of seawater and x is the depth in meters
for x = 797 meters
f(x) = 28.7 + 1.2log (x + 1)
f(x) = 28.7 + 1.2log (797 + 1)
f(x) = 28.7 + 1.2log (798)
f(x) = 28.7 + 1.2 * 2.902
f(x) = 28.7 + 3.4824
f(x) = 32.1824
f(x) = 32.18 (to the nearest hundredth)
Learn more about logarithm here:
https://brainly.com/question/29420555
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If ST = x + 4, TU = 10, and SU = 9x + 6, what is ST?
Given:
[tex]\begin{gathered} ST=x+4 \\ \\ TU=10 \\ \\ SU=9x+6 \end{gathered}[/tex]Find-:
The value of "x."
Explanation-:
The line of property
[tex]SU=ST+TU[/tex]Put the value is:
[tex]9x+6=x+4+10[/tex][tex]\begin{gathered} 9x+6=x+14 \\ \\ 9x-x=14-6 \\ \\ 8x=8 \\ \\ x=\frac{8}{8} \\ \\ x=1 \end{gathered}[/tex]So, the value of "x" is 1.
Solve and graph on a number line x - 2 > -5 and x - 2 < 4
ANSWER
Interval notation: (-3, 6)
Inequality form: -3 < x < 6
Number Line Graph:
EXPLANATION
[tex]\begin{gathered} x\text{ - 2 > - 5 OR x - 2 < 4} \\ x\text{ > - 5 + 2 OR x < 4 + 2} \\ x\text{ > -3 OR x < 6} \\ \end{gathered}[/tex]Hence, -3 < x < 6
Find the equation of a line that has the points (3,4) and (-6,5) . Write the answer in slope intercept form
For any line passing through the points (x1,y1) and (x2,y2), its slope is given by:
a = (y2 - y1)/(x2 - x1)
And its intercept is given by:
b = y1 - ax1 = y2 - ax2
And the equation of this line, in the slope-intercept form, is y = ax + b
Then, for a line passing through the points (3,4) and (-6,5), we have:
a = (5 - 4)/(-6 - 3) = -1/9
Then, the intercept is:
b = 4 + 3/9 = 13/3
Therefore, the equation of the line is given by:
y = -x/9 + 13/3
PLS HELP FOR BRAINLIEST
Answer:
the answer is
5 cupcakes and 8 muffins
5+8=13
2(5)+1.5(8)=22
write the following comparison as a ratio in simplest form using a fraction, a colon and the word to. _ 198 cents to 234 cents is?
Given data:
The expression for the kratio of 198 cents to 234 cents is,
[tex]\begin{gathered} \frac{198}{234}=\frac{18\times11}{18\times13} \\ =\frac{11}{13} \\ =11\colon13 \end{gathered}[/tex]Thus, the correct option is (d).
Formulas, walkthrough, something. I can't figure it out.
Answer:
[-16,16]U[20,+oo)
Step-by-step explanation:
1) x-16 ≥ 0
x ≥ 16
2) x-20 ≥ 0
x ≥ 20
3) x+16 ≥ 0
x ≥ -16
- 16. 16. 20
1) - - +. +
2) - - - +
3) - +. +. +
- +. - +
Solution : -16≤x≤ 16 ∨ x≥20
From a point on the North Rim of the Grand Canyon, the angle of depression to a pointon the South Rim is 2. From an aerial photo, it can be determined that the horizontaldistance between the two points is 10 miles. How many vertical feet is the South Rimbelow the North Rim (nearest whole foot).
Question:
Solution:
The situation of the given problem can be drawn in the following right triangle:
This problem can be solved by applying the trigonometric identities as this:
[tex]\tan(2^{\circ})=\frac{y}{10}[/tex]solving for y, this is equivalent to:
[tex]y\text{ = 10 tan\lparen2}^{\circ}\text{\rparen=0.349 miles}[/tex]now, 0.349 miles is equivalent to 1842.72 feet. Now, this number rounded to the nearest whole foot is equivalent to 1843.
Then, the correct answer is:
1843 feet.
what is the range of the giving relation {(9,1), (9,4) , (9,5) , (9,6)}
ANSWER
EXPLANATION
We are given the relation:
{(9, 1), (9, 4), (9, 5), (9, 6)}
The range of any set of points in
use distributive property to fill in the blanks (4×7) - (4×3) = ___ × (7-3)
Solve the equation for the indicated variable. (Leave ± in the answer as needed)
The given expression is:
[tex]h=td^2[/tex]Therefore,
[tex]td^2=h[/tex]Dividing both sides of the equation by t:
[tex]\frac{td^2}{t}=\frac{h}{t}[/tex]Hence,
[tex]d^2=\frac{h}{t}[/tex]Thus,
[tex]d=\sqrt{\frac{h}{t}}=\frac{\sqrt{h}}{\sqrt{t}}[/tex]To rationalize the equation by √t:
[tex]\begin{gathered} d=\frac{\sqrt{h}}{\sqrt{t}}\times\frac{\sqrt{t}}{\sqrt{t}}=\frac{\sqrt{ht}}{t} \\ d=\frac{\sqrt{ht}}{t} \end{gathered}[/tex]d =
convert the following fraction to a decimal 3 15/16 a 2,5472 b. 3.156 c. 3.0375 d. 4. 238
ANSWER:
3.9375
EXPLANATION:
Given:
[tex]3\frac{15}{16}[/tex]To convert this to decimal, first convert the fraction, 15/16 to decimal:
[tex]\frac{15}{16}=\text{ 0.9375}[/tex]Now add the 3 whole number to 0.9375:
[tex]3\text{ + 0.9375 = 3.9375}[/tex]f (x)=2^ x -10 and the domain of f(x) is the set of integers from 1 to 3which values are elements of the range of f(x) Select all that apply.a. -12b. -10c. -9d. -6e. -2
We have to find the range of the function f(x).
The definition of f(x) is:
[tex]f(x)=2^x-10[/tex]The domain of this function is defined as: D: {-1, 0, 1, 2, 3}, which represents all the integers from -1 to 3.
Then, we have to find the range by applying the function to each of the elements of the domain:
[tex]f(-1)=2^{-1}-10=\frac{1}{2}-10=-9.5[/tex][tex]f(0)=2^0-10=1-10=-9[/tex][tex]f(1)=2^1-10=2-10=-8[/tex][tex]f(2)=2^2-10=4-10=-6[/tex][tex]f(3)=2^3-10=8-10=-2[/tex]Then, the range of f(x) is R: {-9.5, -9, -8, -6, -2}.
Answer:
The options that apply from the list are -9, -6 and -2. [Options c, d and e]
Can you help Turn this equation to the other equation
3x-y=-27
x+2y=16
y=_x+_
y=_x+_
Answer:
y=3x+27
2y= x+16or,
or,y= x+16/2
891 to which closer to hundred
891 is closer to 900.
Consider the following:
800, 820, 840, 860, 880, 900
891 is found between 880 and 900
Thus, the hundred 891 is closer to is 900
Leah just accepted a job at a new company where she will make an annual salary of $65000. Leah was told that for each year she stays with the company, she will be given a salary raise of $2500. How much would Leah make as a salary after 6 years working for the company? What would be her salary after t years? Salary after 6 years: Salary after t years:
Explanation
Step 1
let s represents the salaray
let t represents the number of years she works.
she will make an annual salary of $65000. Leah was told that for each year she stays with the company, she will be given a salary raise of $2500
hence.
[tex]S=65000+2500t[/tex]and, we have the function for the salary:
for example, after 1 year
it means, t=1
replace
[tex]\begin{gathered} S=65000+2500t \\ S=65000+2500\cdot1 \\ S=65000+2500 \\ S=67500 \end{gathered}[/tex]so After 6 years
it is, when t= 6
[tex]\begin{gathered} S=65000+2500t \\ S=65000+2500\cdot6 \\ S=65000+15000 \\ S=80000 \end{gathered}[/tex]I hope this helps you
I do not understand the problem on how to to write an equation.
Given a line passes through the point (-4,6) and has a slope of 3
We will write the equation of the line in point-slope from
The formula of the point-slope form will be as follows:
[tex]y-k=m(x-h)[/tex]Where (h, k) is the point that lies on the line and (m) is the slope
From the given:
m = 3
h = -4
k = 6
Substitute into the formula
so, the answer will be:
[tex]y-6=3(x+4)[/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]Can you help me with number 14? Thank you I am having trouble with it.
To solve number 14, we will make use of the Law of Cosines, which states that:
[tex]=\sqrt[]{^2+^2^{}-2\cos}[/tex]As in our problem b = 15, c = 13 and A = 95°,we can replace these values in the formula and solve for a:
[tex]=\sqrt[]{15^2+13^2-2\cdot(15\cdot13)\cos 95}[/tex][tex]=\sqrt[]{15^2+13^2-390\cos 95}[/tex][tex]a\approx20.69[/tex]In our case, a is the segment BC.
Answer: 20.7
help me with this simple math18. look for this simple math riddle1+4=52+5=123+6=218+11=?I'm stuck here when 8+11
Given,
The mathematical expressions are
1+4=5
2+5=12
3+6=21
8+11=?
The pattern of the expression is,
[tex]\begin{gathered} 1+1\times4=5 \\ 2+2\times5=12 \\ 3+3\times6=21 \end{gathered}[/tex]Similarly,
[tex]8+8\times11=96[/tex]Hence, the value is 96.
what is 4/6 divided by 3/12 the qotient is..........
Answer:
2 2/3
Explanation:
If 4/6 is divided by 3/12, we write the mathematical expression as:
[tex]\frac{4}{6}\div\frac{3}{12}[/tex]To obtain the quotient, we follow the steps below:
Step 1: Change the division sign to multiplication and take the inverse of the fraction after the division sign.
[tex]\frac{4}{6}\times\frac{12}{3}[/tex]Step 2: Reduce the terms where possible.
[tex]\begin{gathered} =\frac{4}{1}\times\frac{2}{3} \\ =\frac{8}{3} \\ =2\frac{2}{3} \end{gathered}[/tex]The quotient is 2 2/3.
which of the following statements correctly compares the tow functions f(x) and g(x)?.
We have two functions and we have to find which statements are true.
They both have a maximum value of 1.
f(x) has a minimum and not a maximum, so this statement is not true.
The graphs of both functions cross the x-axis at 0.
f(x) does not cross the x-axis, so this statement is not true.
The graphs of both functions cross the y-axis at 1.
This is true for f(x).
For g(x), we have to calculate g(0) to find at which value of y the function cross the y-axis:
[tex]g(0)=-4\cdot0^2+1=0+1=1[/tex]This statement is true.
Function f(x) has a minimum value of 1 and function g(x) has a maximum value of 1.
This is true for f(x).
For g(x), the maximum value happens when x=0, because for all other values of x, the quadratic term becomes more negative.
In the previous statement we calculate g(0)=1, so 1 is the maximum value of g(x).
This statement is true.
They both have a minimum value of 1.
g(x) does not have a minimum value. This statement is not true.
Answer: The statement that are true:
- The graphs of both functions cross the y-axis at 1.
- Function f(x) has a minimum value of 1 and function g(x) has a maximum value of 1.
*DUE TODAY* ANSWER ASAP Olivia has read 40 pages of a 70 page book, 60 pages of an 85 page book and 43 of a 65 page book. What is the percentage of pages Olivia has not read? PLEASE GIVE ME A STEP BY STEP EXPLANATION PLEASE!
A triangle has angles that are 38º and 47º. Find the measure of the third angle. 177 ° 95° 133 °85 °
hello,
As we know, a triangule has 3 angles and the sum of them must be equal to 180º. So, let's calculate the question:
38 + 47 + x = 180
85 + x = 180
x = 180 - 85
x = 95º
after a raise Alex salary increased from 30000 anually to 31590 find the percent
intial value = 30,000
final value = 31,590
30,00 ( 1 + x) = 31,590
Solve for x ( increase in decimal form)
30,000+ 30,000x = 31,590
30,000x = 31,590-30,000
30,000x =1,590
x= 1,590/30,000
x= 0.053
Multiply by 100
0.053 x 100= 5.3%
I need help with the calculus portion of my ACT prep guide
The first thing we have to do is find the pascal coefficients of the triangle for this we use the following image
From our exercise we know that
[tex]\begin{gathered} (2x^3-3y)^3\to(a+b)^3 \\ a=2x^3 \\ b=-3y \end{gathered}[/tex]Then our coefficients of Pascal's triangle are 1 - 3 - 3 - 1
Using the right triangle we get:
[tex]1a^3+3a^2b+3ab^2+1b^3[/tex]We substitute the values of a and b in our new expression to find our solution
[tex]1(2x^3)^3+3(2x^3)^2(-3y)+3(2x^3)(-3y)^2+1(-3y)^3[/tex][tex]\begin{gathered} 8x^9+3(4x^6)^{}(-3y)+3(2x^3)(9y^2)^{}-27y^3 \\ 8x^9-36x^6y+54x^3y^2-27y^3 \end{gathered}[/tex]So the solution is:
[tex]8x^9-36x^6y+54x^3y^2-27y^3[/tex]Use a calculator to help answer the question, Show that the point (6,1) is equidistant from points (9,0) and (3,0).The distance from (6,1) to (9,0) and the distance from (6,1) to (3,0) are both [ ] . Thus, (6,1) is equidistant from the two points.
First find the distance from (3,0) to (6,1)
We will use the distance formula
d = sqrt( (x2-x1)^2 + ( y2-y1)^2)
= sqrt( ( 6-3)^2 + ( 1-0)^2)
= sqrt( 3^2 + 1^2)
= sqrt( 9+1)
= sqrt(10)
Now we can find the distance between ( 6,1) and (9,0)
We will use the distance formula
d = sqrt( (x2-x1)^2 + ( y2-y1)^2)
= sqrt( ( 9-6)^2 + (0-1)^2)
= sqrt( 3^2+ (-1)^2)
= sqrt( 9+1)
= sqrt(10)
The distance is sqrt(10)
[tex]\sqrt[]{10}[/tex]A polygon will be dilated on a coordinate grid to create a smaller polygon. The polygon is dilated usi Xthe origin as the center of dilation.Which rule could represent this dilation?
The rule for a dilation by a factor of k using the origin as the center of dilation, is:
[tex](x,y)\rightarrow(kx,ky)[/tex]In the options A and B, additions and substractions are involved. Then, they cannot be the rule of a dilation about the origin.
In the options C and D, we can see that both are dilations about the origin. The factor used in the option C is 5/4, while the factor used in the option D is 0.9.
Nevertheless, notice that 5/4 is greater than 1 and 0.9 is smaller than 1.
Then, the dilation from option C would produce a bigger polygon, while the dilation from option D will produce a smaller polygon.
Since the polygon must be a smaller one, then the rule that could represent this dilation is:
[tex](x,y)\rightarrow(0.9x,0.9y)[/tex]Which corresponds to option D.
Select all statements that must be true.
(Select all that apply)
Students selecting B are likely mistaking the range for
the IQR. Students selecting C are likely mistaking the
median for the IQR. Students selecting D are likely
mistaking the mean for the median. It may be possible
that the mean is 3.6 goals per game, but cannot be
determined from the box plot alone. Students selecting
F are likely mistaking Q1 for the minimum.
A. The interquartile range (IQR) is 1.2 goals per game.
B. The interquartile range (IQR) is 3.2 goals per game.
C. The interquartile range (IQR) is 3.6 goals per game.
The average goals scored per game are calculated for
20 soccer tournaments. The 20 averages are used to
create this box plot.
O O OOO
D. The mean is 3.6 goals per game.
E. The median is 3.6 goals per game.
E The minimum is 2.8 goals per game.
H
G. The maximum is 5.6 goals per game.
2
2.4 2.8 3.2 3.6
4
4.4
4.8
5.2 5.6
6
Average Number of Goals per
Game
The maximum = 5.6 goals per game
median = 3.6 goals per game
Interquartile range (IQR ) = 1.2 goals per games
Explanation:To solve this question, we need an illustration that identifies the part of the box and whiskers plot:
The minimum on the box and whiskers = 2.4 goals per game
The maximum = 5.6 goals per game
The median = the line in between the box
median = M on the image
median = 3.6 goals per game
upper quartile = Q3 = 4
lower quartile = Q1 = 2.8
The interquartile range = IQR
[tex]\begin{gathered} \text{IQR = Q}_3-Q_1 \\ \text{IQR = }4\text{ - 2.8} \\ \text{IQR = 1.2} \end{gathered}[/tex]Interquartile range (IQR ) = 1.2 goals per games
[tex]\begin{gathered} \text{Mean = average of the data set} \\ \text{Mean = }\frac{su\text{m of the numbers}}{nu\text{mber of the data set}} \\ \text{Mean = }\frac{2.4\text{ + }2.8+3.6+4+5.6}{5} \\ \text{Mean = 18.4/5} \\ \text{Mean = 3.68} \end{gathered}[/tex]The mean is 3.68 goals per game
I am in alternative school I am a 12th grader I dropped out Beginning 10th grade then came back to school 12th grade I have applied math I have no clue what I'm doing I'm scared for my finals in May I need help
we have the expression
4÷5×6+7×55
Remember that
Applying PEMDAS
P ----> Parentheses first
E -----> Exponents (Powers and Square Roots, etc.)
MD ----> Multiplication and Division (left-to-right)
AS ----> Addition and Subtraction (left-to-right)
so
step 1
Multiplication and Division (left-to-right)
5x6=30
7x55=385
substitute in the given expression
4÷30+385
step 2
Multiplication and Division (left-to-right)
4÷30=0.13
substitute
0.13+385
step 3
Addition and Subtraction (left-to-right)
0.13+385=385.13
therefore
the answer is 385.13