Answer:
The values of h and k are 9 and -8, respectively
Step-by-step explanation:
This is how to determine the values of h and k
The vertex of the function g(x) is located at (9, –8)
The vertex of a function is represented as:
Vertex = (h,k)
This means that:
(h,k) = (9,-8)
By comparison, we have:
h = 9 and k = -8
So, the values of h and k are 9 and -8, respectively
Which x value is in the domain of the function f(x)=2cot(3x)+4?A. pi/4B. pi/3C. piD. 2pi
Solution:
Given:
[tex]f(x)=2cot(3x)+4[/tex]The domain of the function is;
[tex]\frac{\pi }{3}nHence, the x-value that is in the domain of the function is;[tex]\begin{gathered} any\text{ value that is not a multiple of }\frac{\pi}{3} \\ \\ Hence,\text{ } \\ \frac{\pi}{3},\pi,2\pi\text{ will be multiples of 3x and will make the function undefined.} \\ \\ Therefore,\text{ the x-value in the domain is }\frac{\pi}{4}\text{ because putting x = }\frac{\pi}{4}\text{ makes the function defined} \end{gathered}[/tex]Therefore, OPTION A is correct.
The equation of the line is y=_. The slope indicates that the temperature decreases by 3.5 F for each 1000 foot increase in altitude
The slope of the function is m = -3.5, which indicates that the temperature decreases by 3.5 degrees for each 1000 feet increase in elevation.
The temperature at Sea level is 87 °F
What is the slope of a function?The slope of a straight line function is the ratio of the rise to the run of the function.
Parts of the question that appear missing includes; The slope and the temperature at Sea level is required.
A point on the table of the graph is that at 4 feet, the temperature is 73 °F
The rate at which the the temperature changes = -3.5 °F per 1,000 feet
The slope of the equation is therefore;
y - 73 = -3.5·(x - 4)
y = -3.5·x + 14 + 73 = -3.5·x + 87
y = -3.5·x + 87
The equation of the the line of the temperature above Sea level is an equation of a straight line, which is of the form; y = m·x + c
Where;
m = The slope of the function
By comparison, the slope of the equation of the line the function is; m = -3.5
The temperature at Sea level, which is the y-intercept is found at the point where x = 0, which gives;
y = -3.5 × 0 + 87 = 87
The temperature at Sea level is 87 °F
The slope of line of the graph of the function, m = -3.5
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Find the equation of a line with given slope and containing the given point. Write the equation in slope-intercept form. M= -2, point ( 2,1 )Y=
The equation of a line in slope-intercept form is;
[tex]y=mx+b[/tex]For the given information, that is the slope and a point on the line, we now have;
[tex]\begin{gathered} (x,y)=(2,1) \\ m=-2 \\ y=mx+b\text{ now becomes;} \\ 1=-2(2)+b \\ 1=-4+b \\ \text{Add 4 to both sides} \\ 1+4=-4+4+b \\ 5=b \\ \text{Now that we have }\det er\min ed\text{ the value of b,} \\ We\text{ can substitute for m and b as follows; } \\ y=mx+b\text{ becomes;} \\ y=-2x+5 \end{gathered}[/tex]ANSWER:
The equation of the line therefore is;
[tex]y=-2x+5[/tex]Answer:
y = -2x + 5
Step-by-step explanation:
Pre-SolvingWe are given that a line contains the point (2,1) and a slope (m) of -2.
We want to write the equation of this line in slope-intercept form, which is y=mx+b, where m is the slope and b is the value of y at the y-intercept.
Since we are already given the slope of the line, we can plug that value into the equation.
Replace m with -2.
y = -2x + b
Now, we need to solve for b.
As the line passes through (2,1), we can use those values to help solve for b.
Substitute 2 as x and 1 as y.
1 = -2(2) + b
Multiply.
1 = -4 + b
Add 4 to both sides.
5 = b
Substitute 5 as b.
y = -2x + 5
Writing an equation in slope intercept form for the line passing through each pair of point . (0, 3) and ( 1, -2)
Data:
• Point ,A( 0, 3 )
,• Point ,B( 1, -2 )
,• Equation in slope-intercept form:
[tex]y=mx+b[/tex]Procedure:
0. Finding the slope ( ,m ,):
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{-2-3}{1-0}=\frac{-5}{1}[/tex][tex]m=-5[/tex]2. Finding the intersection with y-axis ( b ) using point A:
[tex]\begin{gathered} y=mx+b \\ 3=(-5)\cdot0+b \\ b=3 \end{gathered}[/tex]Answer:
[tex]y=-5x+3[/tex]Summary:
0. We found the slope of the equation ( ,m ,)
,1. We found the intersection with the ,y-axis ,( ,b ,)
,2. We displayed the values in the correct position of the equation.
use the diagrams to answer the following questions Number 8
In a cyclic quadrilateral opposite sides add up to 180:
Therefore:
[tex]\begin{gathered} x+82=180 \\ solve_{\text{ }}for_{\text{ }}x: \\ x=180-82 \\ x=98^{\circ} \end{gathered}[/tex]Answer:
∠x = 98
hi how do i solvle this word problem?An office building worth $1 million when completed in 2010 is being depreciated linearly over 40 years. What was the book value of the building in 2012? What will it be in 2025? (Assume the scrap value is $0.)2012 $ 2025 $
Answer:
2012: $950,000
2025: $625,000
Explanation:
Since the scrap value is $0, the amount depreciated each year is equal to the initial worth of the building divided by the number of years, so
[tex]\frac{1,000,000}{40}=25,000[/tex]It means that each year the worth of the building decreases by $25,000
Then, 2012 is 2 years after 2010, so the book value of the building in 2012 is:
$1,000,000 - 2($25,000) = $950,000
In the same way, 2025 is 15 years after 2010, so the book value is
$1,000,000 - 15($25,000) = $625,000
Therefore, the answers are
2012: $950,000
2025: $625,000
Which graph was created using a table of values calculated from the equation y=(2/5)^x+1
Usually, an important point to verify the graph is the point:
[tex](0,f(0))[/tex]It's when the function touches the y-graph, then, let's evaluate the function at x = 0
[tex]\begin{gathered} y=\left(\frac{2}{5}\right)^{x+1}\text{ , \lparen x =0\rparen} \\ \\ y=\left(\frac{2}{5}\right)^{0+1} \\ \\ y=\left(\frac{2}{5}\right)^1 \\ \\ y=\frac{2}{5}=0.4 \end{gathered}[/tex]Therefore the point should be
[tex](0,0.4)[/tex]Therefore any graph that does not include that point is not correct!
We can also eliminate all graph that shows a crescent curve, but, in fact, only the point we calculated can eliminate all graphs and gives us the correct answer:
)) Rick has decided to examine his checking account statements. The account balance was $2,010 last month, and 50% less this month. What is the account balance this month?
The account balance this month is $4020
Let the account balance this month = x
From the question, we have
The account balance was $2,010 last month.
∴x* 50%= $2,010
⇒x* 50/100= $2,010
⇒x* 1/2= $2,010
⇒x = $4020
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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if x-1/x = 20, then x =
Given
[tex]\frac{x-1}{x}=20[/tex]Solution
[tex]\begin{gathered} \frac{x-1}{x}=\frac{20}{1} \\ \text{cross multiply} \\ 1(x-1)=20(x)_{} \\ we\text{ have} \\ x-1=20x \\ \text{collect the like terms} \\ -1=20x-x \\ -1=19x \\ \text{rewrite} \\ 19x=-1 \\ \text{Divide both sides by 19} \\ \frac{19x}{19}=-\frac{1}{19} \\ \\ x=-\frac{1}{19} \end{gathered}[/tex]The final answer
[tex]x=-\frac{1}{19}[/tex]Jakayla is thinking of a number. The number includes the digits 3,7 and 8 and rounds to 700 when rounding to the nearest hundred. what number could Jakayla be thinking of?
According to given data we have numbers 3,7,8
So the possible numbers starting from 7 are 738 and 783.
But the nearest to 700 is 738.
So Jakayla is thinking about 738
Two angles are complementary to each other. One angle measures 23°, and the other angle measures (6x − 20)°. Determine the value of x.
Answer:
15.5
Step-by-step explanation:
23-20=3
6x-3=90
3-90=93
93÷6=15.5
Answer:
14.5
Step-by-step explanation:
i got it right on the test
Solve the system by substitution. 9y = x - 4x + y = -35 Submit Answer
Let:
[tex]\begin{gathered} 9y=x\text{ (1)} \\ -4x+y=-35\text{ (2)} \end{gathered}[/tex]Replace (1) into (2):
[tex]\begin{gathered} -4(9y)+y=-35 \\ -36y+y=-35 \\ -35y=-35 \\ y=1 \\ \text{ Replace y into (1)} \\ x=9(1) \\ x=9 \end{gathered}[/tex]I need help with the third question where it says segment addition
ANSWER
EXPLANATION
We have that the line EG = 71.
We are given that
EF = 8x - 17
and
FG = 5x - 3
We see from the diagram that:
EF + FG
a/b = c/d is equivalent to b/a = d/c. in other words, if two fractions are in proportion, their _____ are also in proportion
If two fractions are in proportion, their inverse ratio are also in proportion.
Proportion:
Proportion means an equation in which two ratios are set equal to each other.
Given,
a/b = c/d is equivalent to b/a = d/c. in other words, if two fractions are in proportion, their _____ are also in proportion.
Here we need to fill the blank with the correct answer.
According to Invertendo Property,
For the four numbers a, b, c, d,
Consider if a : b = c : d, then b : a = d : c; which means
if two ratios are equal, then their inverse ratios are also equal.
It can be written as,
If a : b :: c : d then b : a :: d : c.
Then it can be written as,
=> a : b :: c : d
⟹ a/b= c/d
When take the inverse, then we get,
⟹ b/a= d/c
Which implies the following,
⟹ b : a :: d : c
Therefore, the answer is inverse ratio.
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Simplify -7(-5+3x)-4x
Solution:
Given:
[tex]-7(-5+3x)-4x[/tex]Expanding the bracket,
[tex]\begin{gathered} -7(-5+3x)-4x \\ (-7)(-5)+(-7)(3x)-4x \\ 35-21x-4x \end{gathered}[/tex]Simplifying further,
[tex]35-21x-4x=35-25x[/tex]Therefore, the solution is;
[tex]-7(-5+3x)-4x=35-25x[/tex]Consider the following polynomial function.f(x) = (x+4)²(x - 2)5(x - 1)Step 2 of 3: Find the x-intercept(s) at which f crosses the axis. Express the intercept(s) as ordered pair(s).AnswerCorrectSelect the number of x-intercept(s) at which f crosses the axis.
Given the function:
[tex]f\mleft(x\mright)=(x+4)^2\left(x-2\right)^5(x-1\rparen[/tex]The x-intercept iswhen y =0, so:
[tex]\begin{gathered} x+4=0 \\ x+4-4=0-4 \\ x=-4 \\ \end{gathered}[/tex]And
[tex]\begin{gathered} x-2=0 \\ x-2+2=0+2 \\ x=2 \end{gathered}[/tex]And
[tex]\begin{gathered} x-1=0 \\ x-1+1=0+1 \\ x=1 \end{gathered}[/tex]Therefore, the x-intercepts are:
(-4, 0), (2, 0) and (1, 0)
Answer:
(-4, 0), (2, 0) and (1, 0)
A math teacher said that 18 out of 25 students passed the test. What percent of the students did NOT pass the test?can you please show me the work for this?
Given:
A math teacher said that 18 out of 25 students passed the test.
So,
Total number of students = 25 student
Number of students who passed the test = 18
Number of students who did not pass the test = 25 - 18 = 7
So, the percent of the students who did NOT pass the test =
[tex]\frac{7}{25}\times100=28\%[/tex]So, the answer will be 28%
If reciangle ABCD is in quadrant II, and rotated 270 degrees counterciockwise around the origin, then what quadrant will rectangle A'B'C'D' be in ? Quadrant l Quadrant II Quadrant lll Quadrant IV
Quadrant IV.
1) Let's Draw this to give us a better idea.
In a 270º CCW Rotation, the rule is every coordinate to be translated
(x.y) ---(y,-x)
2) Let's give to our quadrilateral
A(-2,3) ---- A'(3,2)
B(-4, 3) -----B'(3,4)
C(-6, 4) -----C' (4,6)
D( -8, 4) ---- D' (4, 8)
And so forth
So Quadrant IV is the answer.
Which inequality represents all values of x for which the product below is defined?A.x 0B.x 6C.x -3D.x 6
Solution
Step 1:
Write the expression:
[tex]\sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}}[/tex]Step 2:
[tex]\begin{gathered} Apply\text{ the rule below:} \\ \sqrt{a}\text{ . }\sqrt{b}\text{ = }\sqrt{ab} \end{gathered}[/tex]Step 3:
[tex]\begin{gathered} \sqrt{x\text{ - 6}}\text{ . }\sqrt{x\text{ + 3}} \\ \\ \sqrt{(x-6)(x+3)} \\ \\ For\text{ the function to be defined} \\ (x\text{ - 6\rparen\lparen x + 3\rparen }\ge\text{ 0} \end{gathered}[/tex]Step 4:
[tex]x\le \:-3\quad \mathrm{or}\quad \:x\ge \:6\:[/tex]Final answer
[tex]\begin{gathered} Option\text{ D } \\ x\text{ }\ge\text{ 6} \end{gathered}[/tex]I need answers fast
What else would need to be congruent to show that ASTU = AJKL by SAS?
7
R
Glven:
STK
ZSE
S
A. TU. KL
B. TU = JL
C. SU - KL
D. SU JL
Given:
[tex]STU\cong JKL[/tex]Therefore by the SAS theorem::
[tex]\begin{gathered} ST\cong JK \\ \angle S\cong\angle J \\ SU\cong JL \end{gathered}[/tex]Answer: D.
Evaluate the expression xy - 3x when x = 4 and y = 5
Answer:
xy - 3x = 8
when x = 4 and y = 5
Explanation:
Given the expression
xy - 3x
When x = 4 and y = 5, the equation becomes
(4)(5) - 3(4)
= 20 - 12
= 8
Solve the inequality -2d < 5
Answer:
d> -5/2
Step-by-step explanation:
-2d<5
divide both sides by -2
d>-5/2
Answer:
d > - [tex]\frac{5}{2}[/tex]
Step-by-step explanation:
- 2d < 5
divide both sides by - 2, reversing the symbol as a result of dividing by a negative quantity.
d > [tex]\frac{5}{2}[/tex] or d > 2.5
Line t is graphed in the xy-plane. Line t does not have a y-intercept. Which of the following equations couldrepresent a line parallel to line t?
when a graph doesn't have a y intercept it means that its y value is zero.
The constants in the equations are all intercepts. The only equation whose y is zero and has no constant ( intercept ) is x = 2
Thus, the solution to the question is x = 2 ( because y=o at this point and it has no constant )
What are 2 numbers that are exactly the same are said to be?
When two numbers are exactly the same, we say that they're equal. Is denoted by the sign '='
Find the slope vx and the distance Ay for this pair of coordinates. (-2,-4) (3,-1) Change in y Change in x
The slope and the distance of two points (a,b), (c,d) is given by
[tex]\begin{gathered} m\text{ = }\frac{d-b}{c-a} \\ d=\sqrt[]{\mleft(c-a\mright)^2+(d-b)^2} \end{gathered}[/tex]Replacing our original points, we have
[tex]\begin{gathered} m=\frac{-1-(-4)}{3-(-2)}=\frac{-1+4}{3+2} \\ m=\frac{3}{5} \\ d=\sqrt[]{(3-\mleft(-2)\mright)^2+(-1}-(-4))^2 \\ d=\sqrt[]{5^2+3^2} \\ d=5.83 \end{gathered}[/tex]The price to mail a letter at the post office is $0.51 for the first ounce, and $0.20 for each additional ounce. Stephanie paid $1.31 to mail her letter. How much did the letter weigh?A. 7 ounces B.6 ouncesC.4 ounces D.5 ounces
The cost of sending mail is given as $0.51 for the first ounce and then every ounce after that costs $0.20.
For each letter, the cost would be expressed as;
[tex]\begin{gathered} C=0.51+0.20x \\ \text{Where x is the weight in ounces} \\ \text{For Stephanie's letter,} \\ 1.31=0.51+0.20x \\ \text{Subtract 0.51 from both sides} \\ 1.31-0.51=0.51-0.51+0.20x \\ 0.8=0.20x \\ \text{Divide both sides by 0.20} \\ \frac{0.8}{0.2}=x \\ 4=x \\ \text{Note that she paid \$0.51 for the first ounce} \\ \text{This means she paid for 1 ounce plus another 4 ounces} \\ \text{Stephanie's letter weighs 5 ounces} \end{gathered}[/tex]Therefore, Stephanie's letter weighs 5 ounces.
The correct answer is option D
f(x) = 2x + 4 and g(x) = -8f(x). = What equation shows the correct rule for the function g? O g(x) = -4x O g(x) = -4x + 4 = g(x) = -8x - 32 O g(x) = -4x - 32 – -
The given functions are
[tex]\begin{gathered} f(x)=\frac{1}{2}x+4 \\ g(x)=-8f(x) \end{gathered}[/tex]Multiply f by -8 to get g
[tex]\begin{gathered} g(x)=-8(\frac{1}{2}x+4) \\ g(x)=-8(\frac{1}{2}x)+(-8)(4) \\ g(x)=-4x+(-32) \\ g(x)=-4x-32 \end{gathered}[/tex]The correct answer is D
In your own words describe an exponential function. Are there restrictions on the domain why or why not? Are exponential and logarithmic function inverse. why or why not?(this is all one question, from the same page i just am on my laptop so cant provide picture)
Answer:
An exponential function is a mathematical function, which is used in many real-world situations. It is mainly used to find the exponential decay or exponential growth or to compute investments, model populations, and so on. In this article, you will learn about exponential function formulas, rules, properties, graphs, derivatives, exponential series, and examples.
An example of an exponential formula is given below as
[tex]y=ab^x[/tex]The following figure represents the graph of exponents of x. It can be seen that as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, for x > 1, the value of y = fn(x) increases for increasing values of (n).
Are there restrictions on the domain why or why not?
For any exponential function, f(x) = ab^x, the domain is the set of all real numbers. For any exponential function, f(x) = ab^x, the range is the set of real numbers above or below the horizontal asymptote, y = d, but does not include d, the value of the asymptote.
Hence,
The domain of exponential functions is equal to all real numbers since we have no restrictions with the values that x can take.
Are exponential and logarithmic function inverse. why or why not?
Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = a^x is x = a^y. The logarithmic function y = logx base a is defined to be equivalent to the exponential equation x = a^y
Hence,
Exponential functions and logarithmic functions are inverses of each other
I am confused on my geometry test review and need help.
4/3 = ? /12
Multiply both-side of the equation by 12
4/3 x12 = ?
48 / 3 = ?
16 = ?
WX = 16
Is A= {9000, 5, 8, 119} a finite set?
ANSWER
Yes, it is.
EXPLANATION
A finite set is a set that contains a finite number of elements. That is, the number of elements in a finite set are countable.
The set given is:
A = {9000, 5, 8, 119}
There are 4 elements in this set and hence, it is countable.
According to the definition of a finite set, this set is a finite set.