The given function is
[tex]y=4^{x+8}[/tex]The domain of the function would be all real numbers.
But the range would be all real numbers greater than zero because the function approximates to y = 0 but it doesn't go through.
Hence, the answer is the first option.Cindy and Cora are going to a movie. Cindy forgot her money and is going to pay Cora back later. The cost of the two tickets is $16.50 and a bucket of popcorn is $3.66. What is the total cost that Cora will pay for two tickets and one bucket of popcorn?
Answer: I think 10.08
$16.50 and a bucket of popcorn is $3.66
$16.50 + $3.66 = 20.16
20.16/2= 10.08
I need help please. I can’t do this I’m so lost!
To solve for the angles in a parallel line:
For a pair of parallel lines:
Corresponding Angles are equal m<1 = m<5 = 143°
Alternate Interior Angles are equal m<4 = m<6
Alternate Exterior Angles are equal m<2 = m<8
Consecutive Interior Angles add up to 180° m<3 + m<6 = 180
... then the lines are Parallel
[tex]\begin{gathered} m<5+m<6=180 \\ 143+m<6=180 \\ m<6=180-143 \\ m<6=37^0 \end{gathered}[/tex]Therefore the consecutive interior angles add up to 180
[tex]\begin{gathered} m<3+m<6=180 \\ m<3+37=180 \\ m<3=180-37 \\ m<3=143^0 \end{gathered}[/tex]Therefore the consecutive interior angles add up to 180
[tex]\begin{gathered} m<3+m<2=180 \\ 143+m<2=180 \\ m<2=180-143 \\ m<2=37^0 \end{gathered}[/tex]Hence the corresponding angle for m<3 = 143° and m<2 = 37°
A worker assembles 5.4 products per hour. At this rate how many products will she assemble in a year if she works 40 hours per week and gets two weeks of vacation each year? (Assume no holidays.) A) 432 products B) 2,700 products C) 5,400 products O D) 10,800 products
we have:
5.4 products per hour
1 year = 52 weeks
40 hours -----> 1 week
x hours -------> 50 weeks
[tex]\begin{gathered} x\times1=40\times52 \\ x=2000 \end{gathered}[/tex]she works 2080 hours per year
then,
5.4 products ----> 1 hour
y products -------> 2000 hours
[tex]\begin{gathered} y\times1=5.4\times2000 \\ y=10800 \end{gathered}[/tex]answer: D. 10,800 products
0) is Po= 9, and the population after 7 weeks is P7 = 51. Find an explicit formula for the beetle population after n weeks. Pn how many weeks will it take to reach beetle population 129
The time it will take to reach population of 129 is 20 weeks
What is Arithmetic progression?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms. An arithmetic progression with a common difference of 2 is found, for instance, in the numbers 5, 7, 9, 11, 13, and 15.
Arithmetic progression with the first term of 9.
The common difference is:
51-9/7 = 42/7 = 6.
6 beetles are added each week.
The general formula after n weeks is
Pn = 9 + 6n.
It will reach 129 when
Pn = 129,
129 = 9 + 6n
129 - 9 = 6n
120 = 6n
n = 120/6
n = 20
Hence, It will take 20weeks to reach beetle population 129
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Raven goes to the salon to get a $50 haircut and has a coupon for 15% off. What will be the cost of her hair cut after the discount from her coupon?
Cost of hair = $50 - discount
discount = 15% of $50
[tex]\begin{gathered} =\text{ }\frac{15}{100}\text{ x 50} \\ =\text{ }\frac{750}{100} \\ \text{Discount = \$7,5} \end{gathered}[/tex]Therefore,
Cost of haircut = $50 - $7.5
= $42.5
Use the above (rounded) slope and y-value to write the equation of the tangent line to the graph of f(x)at x=3. Write your answer in mx+b format.
In order to calculate the slope of f(x) at x = 3, we can use the formula below:
[tex]m=\frac{f(x+h)-f(x)}{h}[/tex]For x = 3 and h = 0.001, we have:
[tex]\begin{gathered} m=\frac{f(3.001)-f(3)}{0.001} \\ f(3.001)=4.8\cdot3.001^2-4.6\cdot3.001=43.2288048-13.8046=29.4242048 \\ f(3)=4.8\cdot3^2-4.6\cdot3=43.2-13.8=29.4 \\ m=\frac{29.4242048-29.4}{0.001}=\frac{0.0242048}{0.001}=24.2 \end{gathered}[/tex]The value of f(3), as calculated above, is 29.4.
The tangent line has a slope of m = 24.2 and it passes through the point (3, 29.4), so let's calculate the value of b:
[tex]\begin{gathered} y=mx+b \\ 29.4=24.2\cdot3+b \\ 29.4=72.6+b \\ b=29.4-72.6 \\ b=-43.2 \end{gathered}[/tex]Therefore the equation of the tangent line is y = 24.2x - 43.2.
Tomas is leaving a tip of 18% of his original bill. If the amount of the tip is $2.34, what is the amount of the original bill? Do not place a dollar sign as it will not be needed for this question.
Explanation
We are given the following information:
• Tomas is leaving a tip of 18% of his original bill.
,• The amount of his tip is $2.34.
We are required to determine the amount of the original bill.
This can be calculated as:
[tex]\begin{gathered} Tip=18\%\text{ }of\text{ }Original\text{ }bill \\ 2.34=18\%\times Original\text{ }bill \\ 2.34=0.18\times Original\text{ }bill \\ Original\text{ }bill=\frac{2.34}{0.18}=13 \end{gathered}[/tex]Hence, the amount of the original bill is $13.
in the design a regular hexagon is inscribed in a circle point q will map onto which point after a 120 degree clockwise rotation around the center
Given a regular hexagon
At first we should know that, the angle of rotation between any two consecutive two points will be 360/6 = 60
So,
So, the point q after rotation of 120 degree clockwise will be point S
The answer is option A. Point S
What is the domain of the function y = 2 StartRoot x minus 5 EndRoot?
x greater-than-or-equal-to negative 5
x greater-than-or-equal-to 2
x greater-than-or-equal-to 5
The domain of the function given; y = 2 StartRoot x minus 5 EndRoot is; x greater-than-or-equal-to 5.
What is the domain of the function given; y = 2√(x -5)?It follows from the task content that the domain of the square root function is to be determined.
Recall, that the domain of a function involving square roots includes all values of x except those which render the expression in the square root less than 0.
Hence, the domain of.the function given is;
x - 5 ≥ 0.
x ≥ 5.
Ultimately, the domain of the function is all values of x greater than or equal to; 5.
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what is the first step when you do 3(19c+4)=12
3(19c + 4) = 12
1st step multiply the bracket (19c + 4) by 3
3(19c + 4) = 3(19c) + 3(4)
3(19c + 4) = 57c + 12
57c + 12 = 12
2nd step subtract 12 from both sides
57c + 12 - 12 = 12 - 12
57c = 0
3rd step divide both sides by 57 to find c
[tex]\frac{57c}{57}=\frac{0}{57}[/tex]c = 0
According to historical records, the highest price for regular gas in Florida over the last ten years was just under $4.06 write an inequality to represent Florida's gas prices over the last ten years
We know that the regular gas over the last ten years was just under $4.06.
Also, it's important to keep in mind that the price must be more than zero.
Therefore, based on the given information, the inequality is
[tex]0The value of a truck bought new for $32,000 decreases 16.5%each year. Write an exponential function, and graph the function.Use the graph to predict when the value will fall to $3000.
The exponential decay function can be written as :
[tex]f(t)=P(1-r)^t[/tex]where P = initial amount
r = rate of decay (decreasing value)
t = time in years
From the problem, we have :
P = $32,000
r = 16.5% or 0.165
The function will be :
[tex]\begin{gathered} f(t)=32000(1-0.165)^t \\ f(t)=32000(0.835)^t \end{gathered}[/tex]Using desmos, the graph of the function will be :
Then use the graph to predict when the value will fall to $3000
That will be :
in about 13 years, the value will fall to $3000
ANSWER :
The function is :
[tex]f(t)=32000(0.835)^t[/tex]The value will fall to $3000 in about 13 years.
1. There were 330 people at a play. the admission price was $3 for adults and $1 for children. the admission receipts were $650. how many adults and how many children attended? A) Children: 170, Adults: 60B) Children: 30, Adults: 300C) Children: 160, Adults: 170D) Children: 170, Adults: 160
Explanation
Step 1
Set the equations
let x represents the number of adults attended
let y represents the number of children attended
so
There were 330 people at a play:
it means the sum of adults and children is 330
[tex]x+y=330\Rightarrow equation(1)[/tex]and
if the admission price for $3 for adults, the money from the adult tickets is
[tex]3x[/tex]and $1 for children
[tex]1y[/tex]admission receipts were $650,hence
[tex]\begin{gathered} 3x+y=650\Rightarrow equation(2) \\ \end{gathered}[/tex]Step 2
solve the equations
[tex]\begin{gathered} x+y=330\Rightarrow equation(1) \\ 3x+y=650\Rightarrow equation(2) \\ \end{gathered}[/tex]a) isolate y in equation (1) and replace in equation (2)
[tex]\begin{gathered} x+y=330\Rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=330-y \\ x=330-y \\ \text{Now , replace in equation (2)} \\ 3x+y=650\Rightarrow equation(2) \\ 3(330-y)+y=650 \\ 990-3y+y=650 \\ 990-2y=650 \\ \text{subtract 990 in both sides} \\ 990-2y-990=650-990 \\ -2y=-340 \\ divide\text{ both sides by -2} \\ \frac{-2y}{-2}=\frac{-340}{-2} \\ y=170 \end{gathered}[/tex]therefore
170 childrend attended
b) now, to find x, replace the y value in equation (1)
[tex]\begin{gathered} x+y=330\Rightarrow equation(1) \\ x+170=330 \\ \text{subtract 170 in both sides} \\ x+170-170=330-170 \\ x=160 \end{gathered}[/tex]Therefore,
160 adults attended
so, the answer is
[tex]D)\text{Children:}170\text{ , Adults :160}[/tex]I hope this helps you
Hi I need help sketching the graphIts a domain and function
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
y = - 5 + √x
Step 02:
Domain:
x ≥ 0
[0 , oo)
Graph:
x-intercept = 25
(25 , 0)
y-intercept = -5
(0 , -5)
That is the full solution.
The graph below shows Carlos’s speed on his trip to school. Which segment on the graph shows Carlos’s speed decreasing most rapidly? A. Segment CB. Segment EC. Segment FD. Segment I
Explanation
In the graph we can see different speeds Carlos used on his way to school, subdivided into different segments.
The segment on the graph that depicts Carlos's speed decreasing the most rapidly is given by the segment with the steepest look. By steepest look, this implies that the segment rises of falls sharply, in a form that is almost perpendicular.
Therefore, the right segment will be
Answer: Segment E
Construct parametric equations describing the graph of the line passing through the following points.(20, -14) and (12, -12)If y = 1-5, find the parametric equation for x,
ANSWER :
x = -4t - 16
EXPLANATION :
From the problem, we have the points :
[tex](20,-14)\quad and\quad(12,-12)[/tex]Solve for the equation of the line using two-point formula :
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]That will be :
[tex]\begin{gathered} y-(-14)=\frac{-12-(-14)}{12-20}(x-20) \\ y+14=\frac{2}{-8}(x-20) \\ y+14=-\frac{1}{4}(x-20) \\ y+14=-\frac{1}{4}x+5 \\ y=-\frac{1}{4}x+5-14 \\ y=-\frac{1}{4}x-9 \end{gathered}[/tex]Next is to substitute the given paremetric equation for y :
[tex]y=t-5[/tex]That will be :
[tex]\begin{gathered} y=-\frac{1}{4}x-9 \\ y=t-5 \\ t-5=-\frac{1}{4}x-9 \\ t-5+9=-\frac{1}{4}x \\ t+4=-\frac{1}{4}x \\ 4t+16=-x \\ x=-4t-16 \end{gathered}[/tex]Describe all numbers x that are at a distance of 4 from the number 7.Express this using absolute value notation.
SOLUTION:
Step 1:
In this question, we are given the following:
Describe all numbers x that are at a distance of 4 from the number 7.
Express this using absolute value notation.
Step 2:
The details of the solution are as follows:
Given:
Number x at a distance of 4 from the number 7.
Calculation:
The given statement is the numbers x are at a distance of 4 from the
number 7;
The number x at a distance of 4 is:
[tex]y\text{ = }\lvert{x}\rvert\text{ + 4}[/tex]x at a distance of 4 from the number 7;
[tex]y\text{ = }\lvert x-7\text{ }\rvert\text{ + 4}[/tex]CONCLUSION:
Thus, the absolue value equation is:
[tex]y\text{ = }\lvert{x-7}\rvert\text{ + 4}[/tex]Find the standard form of the equation of the circle having the following properties:Center at the originContaining the point (-5,4)Type the standard form of the equation of this circle.
Equation of a circle in standard form:
[tex](x-h)^2+(y-k)^2=r^2[/tex](h,k) is the center of the circle
r is the radius
For the given circle:
Use the center and the given point to find the radius: the radius is the distance from the center to any point in the circumference.
Distance between two points:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]\begin{gathered} (0,0) \\ (-5,4) \\ \\ r=\sqrt[]{(-5-0)^2+(4-0)^2} \\ r=\sqrt[]{(-5)^2+4^2} \\ r=\sqrt[]{25+16} \\ r=\sqrt[]{41} \end{gathered}[/tex]Use the center (0,0) (the origin) and the rafius to write the equation of the circle:
[tex]\begin{gathered} (x-0)^2+(y-0)^2=(\sqrt[]{41})^2 \\ \\ x^2+y^2=41 \end{gathered}[/tex]Then, the equation of the given circle in standard form is:[tex]x^2+y^2=41[/tex]Elmer is checking the distance between two landmarks on a map. The map uses a scale in which 2 inches equals 100 feet. If the actual distance between the landmarks is 7300 feet, how far is it between the landmarks on the map, in inches? Your answer can be exact or rounded to two decimal places. label optional
are the two triagles similar?if yes, complete the similarity statment.select all that apply
Answer:
The triangles are similar.
[tex]\Delta BAC\text{ \textasciitilde }\Delta YXZ\text{ by SSS similarity}[/tex]Explanation:
Given the triangles in the attached image;
we want to confirm if they are similar.
Let us compare the ratio of corresponding sides of the triangles.
For them to be similar the ratio of the corresponding sides of the triangles must be equal.
[tex]\frac{AB}{XY}=\frac{BC}{YZ}=\frac{AC}{XZ}[/tex]substituting the values in the figure;
[tex]\frac{AB}{XY}=\frac{18}{24}=\frac{3}{4}[/tex][tex]\frac{BC}{YZ}=\frac{27}{36}=\frac{3}{4}[/tex][tex]\frac{AC}{XZ}=\frac{33}{44}=\frac{3}{4}[/tex]The ratio of the corresponding sides are equal.
Therefore, the triangles are similar.
[tex]\Delta BAC\text{ \textasciitilde }\Delta YXZ\text{ by SSS similarity}[/tex]Options for the first box: 9.51, 9.75, 9.67, 9.59Options for the second box: 9.91, 9.99, 9.75, 9.83
We know that
• The mean is 9.75 meters per second.
,• The standard deviation is 0.08 meters per second.
According to the empirical rule, 95% of the data falls into 2 standard deviations below and above the mean, so we just have to subtract and add the standard deviation twice.
[tex]\begin{gathered} \bar{x}+2\sigma \\ \bar{x}-2\sigma \end{gathered}[/tex]Using the given information, we have
[tex]\begin{gathered} 9.75+2(0.08)=9.75+0.16=9.91 \\ 9.75-2(0.08)=9.75-0.16=9.59 \end{gathered}[/tex]Therefore, her next measurement will fall between the values of 9.59 and 9.91 meters per second.[tex]9.59A metallurgist has one alloy containing 43% aluminum and another containing 63% aluminum. How many pounds of each alloy must he use to make 43 pounds of a third alloy containing 49% aluminum? (Round to two decimal places if necessary.)
We will need a weight of 30.1 pounds of alloy having 43% aluminium and 12.9 pounds of alloy with 63% aluminium to make a 43 pounds of alloy containing 49% aluminium.
Let The weight(in pounds ) of first alloy be x.
So, The weight(in pounds ) of second alloy will be 43-x.
Now, we can generate the typical mixture in a linear equation as
0.43(x) + 0.63 (43-x) = 0.49(43)
0.43(x) + 0.63 (43) - 0.63(x) = 0.49(43)
0.63(43) - 0.49 (43) = 0.63(x)-0.43(x)
0.43(63-49)= (0.63-0.43)x
0.43(14)=0.2x
x = 30.1 pounds
So, We can say that we will need a weight of 30.1 pounds of the alloy with 43% aluminium and 12.9 pounds of alloy with 63% aluminium.
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3) cos X 2 37 12 35 35 B) ما را با را 35 12 C 35 D) 12
We get that
[tex]\cos x=\frac{35}{37}[/tex]Suppose your friend is trying to answer the following question:"How many centimeters are in 4.7 meters?"Your friend knows there are 100 cm in 1 m, exactly. Yet, when they solve the problem, they got an incorrect answer of "0.047 cm." Explain what they may have done wrong and how you could help them fix their mistake.
we know that
1 m=100 cm
so
to convert 4.7 meters to cm
Multiply 4.7 by 100
4.7*100=470 cm
Your friend instead of multiplying 4.7 by 100, divide 4.7 by 100
Select the correct answer from each drop menu Short answers only and this time also not a test
The parent function f(x) has a horizontal asymptote located at:
[tex]y=0[/tex]Since g(x) has the horizontal asymptote located at:
[tex]y=3[/tex]We can conclude that g(x) is the result of translate f(x) 3 units up, therefore:
[tex]g(x)=\frac{1}{x}+3[/tex]Answer:
k = 3
i got it wrong twice ( c and b are incorrect)
You have to closely look at the values and figure out a pattern.
If you look at the right-hand column, you can see a pattern of powers of 3.
3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
But the "power" doesn't correspond with nth term.
For example, when we have the power of "1", it is "2nd term", a_2.
Also, when we have the power of "3", it is the "4th term", a_4.
Hence,
the pattern suggests us that
the power is "1 less than" the nth term. In other words, the formula can be "a_(n-1) to the power 3" to incorporate this.
Looking at the choices,
A is correct.
what is 3/5 as an equation or fraction?
Given,
[tex]\frac{3}{5}[/tex]In algebra, an equation is a mathematical statement consisting of an equal symbol between two algebraic expression
In the given, there is no equal symbol
Then the given value looks like a fraction format
so,
[tex]\frac{3}{5}[/tex]Is a fraction
A group of 45 people attened a ball game.There were twice as many children as adults in the group, Set up a system of equations that represents the numbers of adults and children who attened the game and solve the system to find the number of children who were in the groupe as many children as adults in the group. set up a system of equations that represents the number of adults and children who attened the game and solve the system to find the number of children who were in the group
A system of equations representing the number of adults and children attending the game is x + 2x = 45, and the number of children who were in the group is 30.
What is an equation?An equation is a mathematical statement showing that two mathematical expressions are equal or equivalent.
Equations are represented using the equation sign (=).
The total number of people who attended the game = 45
Let the number of children, who were twice as many as adults, C = 2x
Let the number of adults, who attended the game, A = x
Therefore, the total number of attendees, T = x + 2x = 45
x + 2x = 45
3x = 45
x = 15
C = 2x
= 2(15)
= 30
Check:
x + 2x = 45
Substitute x with 15
15 + 2(15) = 45
15 + 30 = 45
45 = 45
Thus, from the system of equations, we can conclude that 30 children attended the game, which is twice the number of adults.
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4 in 3.2 in 7.5 in x x = [x] inches.
7.5in then 4in together next is 3.2in x and find
7.5" + 4" +3.2"x
Berto's age is x years. Rico's age is four times Berto's age.
In 10 years' time Rico's age will be twice Berto's age.
Use this information to write an equation in x.
Solve your equation to find Berto's present age.
The equation is 4x+10 = 2x+20 and value of x is 5.
What is equation?
Equation, a statement of equality between two expressions made up of variables and/or numbers. In essence, equations are questions, and the development of mathematics has been driven by attempts to find systematic answers to those questions. Equations range in complexity from simple algebraic equations (involving only addition or multiplication) to differential equations, exponential equations (involving exponential expressions), and integral equations.
Here Berto's age is x years. then
Rico's age = 4 times of Berto's age
=> Rico's age = 4x.
In 10 years then Berto's age = x+10, then ,
Rico's age +10 = 2(x+10)
now put Rico's age = 4x then,
=> 4x+10 = 2x+20
=>4x-2x=20-10
=>2x=10
=> x= 5
Hence the equation is 4x+10 = 2x+20 and value of x is 5.
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