Answers
The equation for the graph sketched below is given as y = -3(3)^x
Exponential equationThe standard form of an exponential equation is given as y = ab^x
Using the coordinate points on the graph (-1, 1) and (0, -3)
The equivalent equations are;
1 = ab^-1
-3 = ab^0
From equation2;
a= -3
Substitute into equation 1;
1 = ab^-1
1 = 3b^-1
1 =3/b
b =3
Determine the equation
y = ab^x
y = -3(3)^x
This gives the required exponential equation
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Related Questions
Divide: (u² - 3u - 5) ÷ (u+3).
Answers
Answer:
u - 6 + 13/u+3
Step-by-step explanation:
Have a good day :)
Please answer question 5 and 6.
5.Given the functions f(x)=-2x + 4 and g(x) = 2x- 8, find the value of x for which f(x) = g(x).
6.Graph the function.
Answers
By graphing both equations and finding where the graphs intercept, we can see that the solution for the system is x = 3.
For which value of x both functions give the same output?Here we have the functions:
f(x) = -2x +4
g(x) = 2x - 8
We want to find the value of x such that:
f(x) = g(x).
If we graph the two functions, we just need to identify the x-value of the point where the functions intercept.
The graph can be seen in the image below.
There we can see that the graphs intercept at (3, -2), meaning that the solution of:
f(x) = g(x) is x = 3.
Which is the same thing that if we write:
f(x) = g(x)
-2x + 4 = 2x - 8
4x = 12
x = 12/4 = 3
x = 3
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Determine the distance between A(-3, 4) and B(2, -4).
Answers
5 units
Explanation
Step 1
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1_{})^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Let
P1=A(-3,4)
P2=B(2,-4)
Step 2
put the values into the equation
[tex]\begin{gathered} \text{distance}=\sqrt[]{(-4-4)^2+(2-(-3))^2} \\ \text{distance}=\sqrt[]{(0)^2+(2+3)^2} \\ \text{distance}=\sqrt[]{(0)^2+(5)^2} \\ \text{distance}=\sqrt[]{(25} \\ \text{distance}=5 \end{gathered}[/tex]Please help I’ll mark you as brainliest if correct!
Answers
The value of a in the magic square is 25
The value of b in the magic square is 3
The value of c in the magic square is 14
The value of d in the magic square is 7
What are the missing values?The mathematical operations that would be used to determine the missing numbers are addition and subtraction. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of determining the difference of two or more numbers.
According to the information provided in the question, all rows, diagonals and columns add to the same number. Thus, the first step is to determine the sum of all the squares.
The three squares of the diagonal from left to right has all the complete numbers.
Sum of the the squares = 5 + 16 + 27 = 48
a = 48 - 18 - 5 = 25
b = 48 - 18 - 27 = 3
c = 48 - 29 - 5 = 14
d = 48 - 27 - 14 = 7
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Jackie deposited $500 in an account for 10 years at 6% interest.How much money did she earn?
Answers
After 10 years, the money dis she earn is $800 with the interest of 6%.
Interest:
Interest is the amount for a particular principal amount of money at some rate of interest.
Given,
Jackie deposited $500 in an account for 10 years at 6% interest.
Here we need to find the money did she earned.
We know that, the interest for the amount is 6%.
So, the amount after 10 years is,
=> 500 x (6/100) x 10
=> 30 x 10
=> 300
Therefore, the interest amount is 300.
So, the total amount she will receive after 10 years is,
=> 500 + 300
=> 800
Therefore, she will earn $800 after 10 years.
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A retailer owes a wholesaler $300,000 due in 45 days. If the payment is 15 days late, there is a 1% penalty charge. Since the bill isn't due immediately, the retailer can invest the $300,000 in a certificate of deposit and make money on the interest. The retailer has two options: a 45-day certificate of deposit (CD) earning 6% per year simple interest or a 60-day certificate earning 7% per year simple interest.
Answers
A 45-day certificate of deposit (CD) earning 6% per year simple interest. Simple interest and precise simple interest are the two types of simple interest. $2250 is simple interest for the 6% interest.
What is simple interest ?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest is the amount repaid for using borrowed funds over a predetermined amount of time.
Simple interest=p*n*r
=300000*6/100*45/365
=2250
Ordinary simple interest and precise simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest.
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For the triangle shown, find the length AD. (Assume u = 17, v = 17, ∠x = 25°, and ∠y = 25°
Answers
Using the law of Sines, the length of side AD, |AD|, is 7.44
Calculating lengthFrom the question, we are to determine the length of side AD
From the given information, we have that
u = 17 and v = 17
Then,
ΔBCD is an isosceles triangle
∴ m ∠DBC = m ∠ BCD
m ∠DBC = x = 25°
∴ m ∠BCD = 25°
Also,
m ∠BCA = ∠y + m ∠BCD
m ∠BCA = 25° + 25°
m ∠BCA = 50°
Now, we will determine the measure of ∠CAD.
m ∠CAD + m ∠DBC + m ∠BCA = 180° (Sum of angles in a triangle)
m ∠CAD + 25° + 50° = 180°
m ∠CAD = 180° - 25° - 50°
m ∠CAD = 105°
Now,
From law of Sines, we can write that
|AD| / sin DCA = |DC| / sin CAD
|AD| / sin y = u / sin CAD
|AD| / sin 25° = 17 / sin 105°
|AD| = (17 × sin 25°) / sin 105°
|AD| = 7.43795
|AD| ≈ 7.44
Thus,
Length AD is 7.44
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thank u plssssssss do it
Answers
Answer:
63
Step-by-step explanation:
23 + 94 = 117
180 degrees ( sum of all angles in a triangle)
180 - 117 = 63
i need help with question 17
Answers
Answer:
[tex]42[/tex]Step-by-step explanation:
To find the median of a stem and leaf plot, use the equation:
[tex]\begin{gathered} median=\frac{n+1}{2} \\ where, \\ n=\text{ number of data} \end{gathered}[/tex]Therefore, for the given plot, there are 16 elements.
[tex]\begin{gathered} \text{ median=}\frac{16+1}{2} \\ \text{ median=8.5} \end{gathered}[/tex]When there are two middle values, the median is the mean of these two values:
[tex]\begin{gathered} \frac{3+1}{2}=2 \\ \text{ Hence, the median is 42.} \end{gathered}[/tex]Can someone please help with this
Answers
Answer:
x = 8
y = 8
Step-by-step explanation:
The two equations are:
x + y = 16 (1)
x = y (2)
Since x = y substitute for y in terms of x in (1):
x + x = 16
2x = 16
2x/2 = 16/2
x = 8
y = 8
The numerator of a rational number is 4 less than its denominator. If I is added to both its numerator and denominator, it becomes 2/3 Find the rational number.
Answers
The required rational number is 7/11.
let the denominator be x.
and since we are given that the numerator of a rational number is 4 less than its denominator, the numerator will be x-4.
working on the given condition, i.e. If I is added to both its numerator and denominator, it becomes 2/3
(x-4+1)/(x+1) = 2/3
further solving it by cross multiplication we get,
3(x-4+1)=2(x+1)
=> 3(x-3)=2x+2
=> 3x-9=2x+2
=> 3x-2x=9+2
=> x=11
=> x= 11 (denominator)
we know the numerator is 4 less than the denominator i.e.
11-4=7
thus the required fraction will be 7/11.
What are rational numbers?
A rational number is-" one that can be stated mathematically as the ratio or fraction p/q of two integers, p and q, which must both be non-zero".
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4) A done relevant a bomb witha velocity of 20m/s horizotally from a hieght of 50m the ground clculate time
Answers
The time taken for the bomb to fall to the ground is 2.5 sec.
What is a projectile motion?In this case, the bomb is moving like a projectile and has projectile motion.A body can only move in a projectile motion when it is affected by gravity. A body moving as a projectile is a projectile motion.We model a particle as having zero acceleration (and thus constant velocity) when it is projected horizontally.The particle in this instance has a zero initial velocity and a constant downward vertical acceleration of g.Given:
Height (h) = 50 m
Horizontal velocity(u) = 20 m/s
Time (t) =?
We use, h = ut to determine the time
50 = 20 × t
Divide both sides by 20,
t = 50 / 20
t = 5/2 s ≅ 2.5 sec
Thus, the bomb will take 2.5 sec to land on the ground.
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The complete question is: "A bomb is projected horizontally downward from a height of 50m with a velocity of 20m/s. Calculate the time taken for the bomb to fall to the ground."
a ferry charges $40 for each car and $8.50 for each person in the car. Does this situation represent a function?
Answers
Yes, This situation represent a function.
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The cost of each car = $40
The cost of each person = $8.50
Let the number of car = x
The number of persons in a car = z
Then, Total cost of car = $40x
Total cost of persons in car = $8.50z
So, Total cost (y) = $40x + $8.50z
Thus, The function for this situation is;
y = $40x $8.50z
Clearly, This is a linear function with three variable.
Thus, This situation represent a function.
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One Serving of pancakes takes 2/3 cups of milk how many cups of milk with 24 servings for pancakes required
Answers
Answer:
Step-by-step explanation:
Given that:-
Since, Serving of 1 pancakes takes 2/3 cups of milk
Hence, serving of 24 pancakes takes (2/3)*24
=48/3
=16
So that; 16 cups of milk are required for serving of 24 pancakes.
Answer:
16 cups of milk
Step-by-step explanation:
Make a proportion
[tex]\frac{serrvings}{cups of milk}[/tex] = [tex]\frac{servings }{cups of milk}[/tex]
[tex]\frac{1}{\frac{2}{3} }[/tex] = [tex]\frac{24}{x}[/tex] cross multiply and solve
1x = [tex]\frac{2}{3}[/tex][tex](\frac{24}{1})[/tex] 1x is the same a x. 24 is the same as [tex]\frac{24}{1}[/tex]
x = [tex]\frac{48}{3}[/tex]
x = 16
2(4x-3)-8-2x=4
someone please help me with this, fast
Answers
....................... .x=3
if f(x)=-5, what is x?
Answers
Answer:
x is any real number from -infinity to infinity.
Check all the angles that are congruent to angle 5.
Answers
The angles congruent to ∠5 are as follows:
∠8∠1∠4∠9∠12How to find angles in parallel lines?According to the diagram, line l, m and n are parallel lines.
Therefore, when parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertical opposite angle etc.
Hence, the angles that are congruent to ∠5 can be solved as follows:
∠5 ≅ ∠8 (vertically opposite angles)
Vertically opposite angles are congruent.
∠5 ≅ ∠1 (corresponding angles)
Corresponding angles are congruent.
∠5 ≅ ∠4 (alternate angles)
Alternate angles are congruent.
∠5 ≅ ∠9 (corresponding angles)
∠5 ≅ ∠12 (alternate exterior angles)
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Write an equation for the quadratic graphed below:
x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2)
Answers
The equation for the quadratic graphed as x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2) can be written as y = -1/2 (x+3)(x+1)
Which of these equations is quadratic?An equation of the second degree, or one with at least one squared term, is a quadratic equation. The equation in standard form is written as ax2 + bx + c = 0, where a, b, and c are numerical coefficients that are constants, and x is an unknown variable.
The initial constant, “a,” cannot be 0, and this is an unbreakable rule.
How do you translate a graph into some equation?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.
Thereafter draw a sloping triangle connecting the two spots you find on the line.
If the x intercepts are -3 and -1, then the factored form is y = a(x + 3)(x + 1). In order to find "a", we plug in the data point (x, y) of (0, -2) so:
-2 = a(0+3)(0+1)
-2 = 4a
a = -1/2
So the equation can be written as y = -1/2 (x+3)(x+1)
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For
f(x) = 3x and g(x) = x4 + 2, find the following.
(b)(g ∘ f)(x)
Answers
Let f(x) = 5x²-2 and let g(x) = 3x + 1. Find (f + g)(2).
(f+g)(2)= (Simplify your answer.)
Answers
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:(f+g)(x) = 5x² + 3x - 1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f(x) = 5 {x}^{2} - 2[/tex]
and
[tex]\qquad \tt \rightarrow \: g(x) = 3x + 1[/tex]
We need to find : (f + g) (x) = ?
[tex]\qquad \tt \rightarrow \: (f + g)(x) = f(x) + g(x)[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} - 2 + 3x + 1[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} + 3x - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Find the median 6, 13, 15, 9, 6, 11, 14
Answers
The median of a set of numbers is the number that appears in the middle after arranging the set of numbers in ascending or descending order
Step 1:Arrange the given values in ascending order.
Step 2. Find the number of observations in the given set of data. It is denoted by n.
Step 3. If n is odd, the median equals the [(n+1)/2]th observation.
The set of numbers given in the question are
[tex]6,13,15,9,6,11,14[/tex]By rearranging the numbers in ascending order, we will have
[tex]6,6,9,11,13,14,15[/tex]The numbers are 7 in number that is
[tex]N=7[/tex]Since the value of N is an odd number, then the median will be calculated using the formula below
[tex]\begin{gathered} \text{Median}=\frac{(n+1)}{2}th \\ \text{Median}=\frac{7+1}{2}th\text{ number} \\ \text{Median}=\frac{8}{2}th\text{ number} \\ \operatorname{median}=4th\text{ number} \end{gathered}[/tex]The 4th number after arranging the set of numbers is
[tex]=11[/tex]Hence,
The median of the set of numbers in the question = 11
f(x) = x + 3g(x) = 2x2 - 4Find (f ·g)(x)
Answers
SOLUTION
f(x) = x + 3
[tex]undefined[/tex]are y=5x-4 and y=-5x+5 parallel or perpendicular
Answers
Answer:
Perpendicular
Step-by-step explanation:
It js seems right. i did one very similar and the awnser was Perpendicular
The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data, using 7 classes.
Answers
Answer:
Step-by-step explanation:
The ages of the signers of the Declaration of Independence are shown. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a grouped frequency distribution and a cumulative frequency distribution for the data using 7 classes. Limits Boundaries 27-33 26.5-33.5 7 41 54 47 40 39 35 50 37 49 42 70 32 44 52 39 50 40 30 34 69 39 45 33 42 44 63 60 27 42 34 50 42 52 38 36 45 35 43 48 46 31 27 55 63 46 33 60 62 35 46 45 34 53 50 50 34-40 33.5-40.5 14 41-47 40.5-47.5 15 48-54 11 47.5-54.5 54.5-61.5 55-61 3 62-68 61.5-68.5 3 69-75 68.5-75.5 55
the graph of g(x) = (x + 2)2 is a translation of the graph of f(x) ___ by ___ units
Answers
The provided translated function, f(x), shifts left by two units on the horizontal axis.
Describe translation.One type of transformation is translation. Both the scaling calculation and the compression calculation are performed using it. This approach wouldn't change the object's form or shape.
The given graph equation for the translation, as per the query, is g(x) = (x + 2)²
The translation of the given quadratic function is: y = g(x) = (x + 2)²
Consequently, the parent function is written as y = g(x) = x2.
Additionally, the vertex should be known when graphing the translated function:
a(x - h)2 + k = y = g(x);
where the parent function is (0, 0) and the vertex values are (h, k).
(h, k) = is the vertex for the function that is provided (-2, 0)
This information causes the translation function to move the graph two units to the left.
Horizontal translation is the name given to the translation.
As a result, the given function, f(x), shifts horizontally, or left, by 2 units.
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what is the slope of the line?
Answers
Answer:
slope :
[tex] \dfrac{y2 -y1}{x2 - x1} [/tex][tex] \dfrac{3 - 1}{0 - 1} [/tex][tex] \dfrac{2}{ - 1} [/tex][tex] - 2[/tex]Correct option - F
slove using elimination10x + 8 y = 20 10 x + 2 y = -10
Answers
we have
10x + 8 y = 20 ------> equation A
10 x + 2 y = -10 ------> equation B
Multiply equation A by -1 both sides
so
-10x-8y=-20 -----> new equation A
Adds new equation A and equation B
\
--------------------
-8y+2y=-20-10
-6y=-30
y=5
Find the value of x
substitute the value of y in equation A or equation B or new equation A
10x + 8(5) = 20
10x+40=20
10x=20-40
10x=-20
x=-2
therefore
the solution is the ordered pair (-2,5)Donna bought a desk on sale for $343. This price was 35% of the original price.
Answers
The original price for the desk is $980.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.
Given:
Sale price = 343
price was 35% of the original price.
let the original price be x
35% of x = 343
35 / 100 * x = 343
x= 343 * 100/ 35
x=980
Hence, the original price of the desk was $980.
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highest common factor of 106 and 104
Answers
The Greatest Common Factor (GCF) for 104 and 106, notation GCF(104,106), is 2.
Given that,
The numbers 106 and 104.
We have to find the greatest common factor of 106 and 104.
The greatest commo factor is nothing but the greatest common factor, which is the product of two or more numbers, is the largest number (GCF). By dividing them by the largest number, a natural number is produced (factor).There are a few factors that both share once all the number's factors have been identified. The common factor with the highest number among the others is said to be the greatest common factor. The GCF is often referred to as the highest common factor (HCF)
The factors of 104 are 1,2,4,8,13,26,52,104;
The factors of 106 are 1,2,53,106.
Therefore, as we can see, the Greatest Common Factor or Divisor is 2, because it is the greatest number that divides evenly into all of them.
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Help giving 100 points!!
Answers
slope is -3!!
Given the coordinates of two points on the line, use the slope formula to determine the slope of the line. The slope formula is the quotient of the difference in y-values and the difference in x-values.