Answer:
36
Step-by-step explanation:
30% as a decimal is 0.30, take that and multiply it by 120 to find 30% of 120
120 × 0.30 = 36
Write an exponential function in the form of y=ab^x that goes through points (0,6) and (2,96)
Final answer:
The exponential function that goes through the points (0,6) and (2,96) is y = 6 * 4^x, where 6 is the initial value (a) and 4 is the base growth rate (b).
Explanation:
The student is asking for an exponential function in the form y = ab^x that passes through the points (0,6) and (2,96).
To find this function, we must determine the values of 'a' and 'b'. Since the function passes through the point (0,6), if we substitute x = 0, we get y = a * b^0. Since any number raised to the power of 0 is 1, it simplifies to y = a. Therefore, a = 6.
Next, we substitute the second point (2,96) into the original equation with our known value for 'a': 96 = 6 * b^2. To solve for 'b', we divide both sides of the equation by 6, resulting in 16 = b^2. Finding the positive square root of 16 gives us b = 4.
Therefore, the exponential function is y = 6 * 4^x.
The exponential function that goes through the points [tex]\((0, 6)\)[/tex] and [tex]\((2, 96)\)[/tex] is [tex]y = 6 \times 4^x[/tex]
To find the exponential function in the form [tex]\( y = ab^x \)[/tex] that goes through the points [tex]\((0, 6)\)[/tex] and [tex]\((2, 96)\)[/tex], we need to determine the values of [tex]\(a\)[/tex] and [tex]\(b\)[/tex].
1. Use the point [tex]\((0, 6)\)[/tex]
When [tex]\( x = 0 \), \( y = 6 \).[/tex]
[tex]\[6 = ab^0\][/tex]
Since [tex]\( b^0 = 1 \)[/tex]
[tex]\[6 = a \times 1\][/tex]
Therefore, [tex]\( a = 6 \).[/tex]
2. Use the point [tex]\((2, 96)\)[/tex]
When [tex]\( x = 2 \), \( y = 96 \)[/tex]
[tex]\[96 = 6b^2\][/tex]
Solving for [tex]\( b^2 \)[/tex]
[tex]\[b^2 = \frac{96}{6} = 16\][/tex]
Taking the square root of both sides:
[tex]\[b = 4\][/tex]
Thus, the exponential function is:
[tex]\[y = 6 \times 4^x\][/tex]
To verify, we can check both points:
For [tex]\((0, 6)\)[/tex]
[tex]\[y = 6 \times 4^0 = 6 \times 1 = 6\][/tex]
For [tex]\((2, 96)\)[/tex]
[tex]\[y = 6 \times 4^2 = 6 \times 16 = 96\][/tex]
what is the answer to 6 more than the product of five and a number decreased by one
How many soution does this system have ?
Y=3/4x-5
-3x+4y=-20
Answer:
There is no solution
Step-by-step explanation:
1. y = 3/4x - 5
2. -3x + 4y = -20
-3x + 4(3/4x - 5) = -20
-3x + 3x - 20 = - 20
-20 = -20
Determine and state an equation of the line perpendicular to 5x-4y=10nand passing through point (5,12).
Answer:
4x + 5y = 80
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 5x - 4y = 10 into this form
Subtract 5x from both sides
- 4y = - 5x + 10 ( divide all terms by - 4 )
y = [tex]\frac{5}{4}[/tex] x + [tex]\frac{5}{2}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{5}{4}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{4} }[/tex] = - [tex]\frac{4}{5}[/tex], thus
y = - [tex]\frac{4}{5}[/tex] x + c ← is the partial equation
To find c substitute (5, 12) into the partial equation
12 = - 4 + c ⇒ c = 12 + 4 = 16
y = - [tex]\frac{4}{5}[/tex] x + 16 ← in slope- intercept form
Multiply through by 5
5y = - 4x + 80 ( add 4x to both sides )
4x + 5y = 80 ← in standard form
The equation of line perpendicular to [tex]5x-4y=10[/tex] and passing through the point (5,12) is [tex]y=-\frac{4}{5}+16[/tex]
The line given in the problem is in Standard Form. The standard form of a linear equation is: [tex]Ax+By=C[/tex]
Where, if at all possible, A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.
[tex]5x-4y=10[/tex]
The slope of an equation in standard form is: [tex]m=-\frac{A}{B}[/tex]. Substituting the values from the equation in the problem gives:
[tex]m=-\frac{5}{(-4)} =\frac{5}{4}[/tex]
Let's call the slope of the line perpendicular to this line [tex]m_{p}[/tex] . The slope of a perpendicular line is:
[tex]m_{p} =-\frac{1}{m} =-\frac{4}{5}[/tex]
We can now use the point-slope formula to find the equation of the line. The point-slope formula states: [tex](y-y_{1})=m(x-x_{1})[/tex]
[tex]y-12=-\frac{4}{5} (x-5)[/tex]
[tex]5(y-12)=-4(x-5)\\5y-60=-4x+20\\5y=-4x+80\\y=-\frac{4}{5}x+16[/tex]
Therefore, the equation of line perpendicular to [tex]5x-4y=10[/tex] and passing through the point (5,12) is [tex]y=-\frac{4}{5}+16[/tex]
For more information:
https://brainly.com/question/10723884
True or False: If you shift one of the lines incorrectly and the other correctly, you will receive credit for the correctly shifted line. True
Final answer:
In logic and truth tables, shifting one line correctly while the other is shifted incorrectly will result in credit for the correctly shifted line.
Explanation:
True or False: If you shift one of the lines incorrectly and the other correctly, you will receive credit for the correctly shifted line. True
The statement is true in the context of logic and truth tables. When dealing with truth tables and logical operations, if one line is shifted correctly and the other incorrectly, credit is given for the line that was correctly shifted.
Order the numbers from greatest to least.
332 233 323
Answer:
Step-by-step explanation:
332 323 233
Answer:
233, 323, 332.
Step-by-step explanation:
Starting from 200 and count by 10 (200, 210, 220, 230.) 233 is the smallest number, repeat with each number.
What is the value of x?
30
45
(3x)
55
-20
Answer:45 Degrees
Step-by-step explanation:
3x+x= 180
4x=180
x=45 Degrees.
Bobby drives his truck at a rate of 50 to 60 miles per hour.
a. Approximately how far can Bobby drive in 2, 3, 4, and 5 hours?
b. Bobby plans to take an 8-hour trip, which will include a 1-hour stop for
lunch. What is a reasonable distance for Bobby to drive?
a. 2 hours = 100 to 120m
3 hrs = 150 to 180m
4 hrs = 200 to 240m
5 hrs = 250 to 300m
b. 400 to 480 miles
Bobby can drive between 50 times the number of hours and 60 times the number of hours depending on the drive duration. For an 8-hour trip with a 1-hour lunch stop, he drives for 7 hours, covering between 350 and 420 miles.
Explanation:a) Bobby's driving speed varies between 50 to 60 miles per hour. Therefore:
If he drives for 2 hours, at the minimum speed he can cover 50*2=100 miles, and at the maximum speed, he can cover 60*2=120 miles.If he drives for 3 hours, the range is between 50*3=150 miles and 60*3=180 miles.If he drives for 4 hours, the range is between 50*4=200 miles and 60*4=240 miles.And if he drives for 5 hours, the range is between 50*5=250 miles and 60*5=300 miles.b) For an 8-hour trip with a 1-hour stop for lunch, Bobby will effectively be driving for 7 hours. So, the minimum distance he could cover is 50*7=350 miles and the maximum distance is 60*7=420 miles.
Learn more about Distance Calculation here:https://brainly.com/question/34212393
#SPJ3
Wendy is deciding which summer job she should take.The two different pay options she may choose from are either $62 per day or $304 per week.Which is the best deal for Wendy?
Answer:
$62 per day
Step-by-step explanation:
$62 a day equals $434 a week witch turns out to be $22,568 a year
$304 a week equals $15,808 a year
6 less than the product of 8 and a
number n is 34
Answer:
8n-6 = 34
Step-by-step explanation:
6 less than the product of 8 and a number n is 34
less than means subtract from the next thing
-6
product means multiply
8n
Now we have 8n-6
is means equals
8n-6 = 34
the value of n is 5.
Step-by-step explanation:
Given,
6 less than the product of 8 and a number n is 34
To find the value of n
According to the problem,
n×8 - 6 = 34
or, 8n = 34+6
or, 8n = 40
or, n = 40÷8
or, n= 5
Hence, the value of n is 5.
25% of the students attended the school dance. if 32 attended the dance, how many students are there in all?
Answer:
128 students in total
Step-by-step explanation:
25/100 = 1/4
1/4 = 32/ x
1 x 32
Answer:
your answer is A
Step-by-step explanation:
32 *4=128
4*25=100%
The coefficient of 9(14)P is
09
14
126
Answer:
126
Step-by-step explanation:
The coefficient of 9(14)P = 9*14 = 126
what is the product of (2X+ Y) (5x-4+3)
Product is 10x² - 2x - y + 5xy
Step-by-step explanation:
Step 1: Find the product. Use distributive property.(2x + y)(5x - 4 + 3) = 10x² - 8x + 6x + 5xy - 4y + 3y
= 10x² - 2x - y + 5xy
Hope this will help u..✌✌
What is a proportional equation
Answer:
it is when the x and y intercept coordinates are changed by the same factor.
Step-by-step explanation:
The perimeter of a triangle below is 58 units. Find the value y
Answer:
1
Step-by-step explanation:
The solution set for -18 < 5x - 3 is _____.
3 > x
-3 > x
3 < x
-3 < x
Answer:
-3 < x
Step-by-step explanation:
add the negative 3 to the other side
you get: -15 < 5x
divide by 5 on both sides
you get: -3 < x
that's the answer
write an equation of the circle with center 6.-9) and radius 10!
The equation of the given circle is [tex](x-6)^{2}+(y+9)^{2}=100.[/tex]
Step-by-step explanation:
Step 1:
The equation of a circle with its center at (h, k) and a radius of r is given by
[tex](x-h)^{2}+(y-k)^{2}=r^{2}.[/tex]
The h value is the x coordinate and the k value is the y coordinates, so (h, k) is (6, -9).
The radius is given as 10 so [tex]r =10[/tex] and [tex]r^{2} = 100.[/tex]
Step 2:
By substituting the values we know, we get
[tex](x-h)^{2}+(y-k)^{2}=r^{2} = (x-6)^{2}+(y-(-9))^{2}=10^{2}.[/tex]
So the equation of the given circle is
[tex](x-6)^{2}+(y+9)^{2}=100.[/tex]
In Practing Partial Products Multiplictaion What im Going to do to 65 × 32 ?
Answer:
2080
Step-by-step explanation:
Step 1: Multiply
65 × 32
60*30 + 60*2 + 5*30 + 5*2
1800 + 120 + 150 + 10
2080
Answer: 2080
Answer:
2080
Step-by-step explanation:
The product of four and a number
Answer:
1+4x
Step-by-step explanation:
88+(-39)
show how you got the answer please
Answer:
49
Step-by-step explanation:
88+(-39) is the same as 88-39 given the distributive property, so 88-39=49
The histogram shows the time Mr. Lopez’s students spent studying for the final exam.Which statement is correct about the time Mr.Lopez's students spent studying for the final exam
Answer:
Most students spent an hour or less studying for the exam.
Step-by-step explanation:
Answer:
C on edge 2020
Most students spent an hour or less studying for the exam.
Step-by-step explanation:
I just took the assignment. Hope this helps!
The measure of an angle is 32°. What is the measure of its supplementary angle?
Which expressions are equivalent to 5 x-15? Select three options.
5 (x + 15)
5 (x-3)
4 x + 3 y-15- 3 y + x
-7 y-6 x- 8 y + x
-20 - 3 x + 5 + 8 x
PLSSS help my teacher already thinks i'm going crazy!
Answer:
[tex]b) 5 (x-3)\\c) 4 x + 3 y-15- 3 y + x\\e) -20 - 3 x + 5 + 8 x[/tex]
Step-by-step explanation:
We are given the following expression in the question:
[tex]5x-15[/tex]
a)
[tex]5 (x + 15)\\=5(x) + 5(15)\\=5x + 75[/tex]
which is not equivalent to the given expression.
b)
[tex]5 (x-3)\\=5(x)-3(5)\\=5x-15[/tex]
which is equivalent to the given expression
c)
[tex]4 x + 3 y-15- 3 y + x\\=4x+x+3y-3y-15\\=5x-15\\=5(x-3)[/tex]
which is equivalent to the given expression.
d)
[tex]-7 y-6 x- 8 y + x\\=-7y-8y-6x+x\\=-15y-5x\\=-5(x+3y)[/tex]
which is not equivalent to the given expression.
e)
[tex]-20 - 3 x + 5 + 8 x\\=-3x+8x-20+5\\=5x-15[/tex]
which is equivalent to the given expression.
Which of the following describes a pattern in the table
Im not sure it depends on the pattern? lol
The pattern described in the table is the value of b is 5 times the value of a.
What is a pattern?A pattern is defined as a sequence of repeating objects, shapes or numbers. We can relate a pattern to any type of event or object. A pattern has a rule that tells us which objects belong to the pattern and which objects do not belong to the pattern.
Given is a table,
a - 0 1 2 3 4
b - 0 5 10 15 20,
We can see, that the values in the b row are 5, 10, 15, 20 they are the multiple of 5
And values in row a, are 1, 2, 3, 4, we can see they are the numbers which are related to row b, in a way that, values in b are 5 times the value of a,
1 × 5 = 5
2 × 5 = 10
3 × 5 = 15
4 × 5 = 20
5 × 5 = 25
Therefore, we can say that the numbers in b are 5 times the corresponding value of the a,
Hence, the pattern described in the table is the value of b is 5 times the value of a.
Learn more about patterns, click;
https://brainly.com/question/23136125
#SPJ6
The complete question is :
Which rule describes the pattern in the table?
a 0 1 2 3 4
b 0 5 10 15 20
The value of b is 5 times the value of a.
The value of b is 5 less than the value of a.
The value of b is 5 more than the value of a.
The value of a is 5 times the value of b.
Factor the quadratic expression completely.
-7x^2-24x-9=
Answer:
[tex] - 7 {x}^{2} - 24 - 9 \\ - 7 {x}^{2} - 21x - 3x - 9 \\ - 7x(x + 3) - 3(x + 3) \\ ( - 7x - 3)(x + 3)[/tex]
Mischa wrote, “Anderson has ten trading cards. He gives some to Desai.” This describes a possible context for the expression x minus 10. Which explains the accuracy of what Mischa wrote?
Answer:
It is inaccurate. Her words translate to 10 minus x
Step-by-step explanation
she minuses x and gives it to desai
It is not correct. Her words translate to 10 minus x
Given that,
Mischa wrote, “Anderson has ten trading cards. He gives some to Desai.”Information regarding context:Since anderson does have 10 trading cards, So here the context should be that it minuses x and then it provides to the desai.The given context mentioned in the question is wrong.Learn more about the expression here: https://brainly.com/question/13947055?referrer=searchResults
what is the answer to 8x27383922
Answer:
219071376
Step-by-step explanation:
Answer:
219071376. Hope this helps :)
Help with #15, please show all work, will mark brainliest!
Measure of ∠B is 110°
Step-by-step explanation:
Step 1: Find ∠B of the parallelogram.In a parallelogram, opposite angles are equal.
⇒ ∠B = ∠D
⇒ ∠B = (5x + 10)°
Step 2: Use theorems of quadrilaterals to form equations to find x and y.Now, angles in a parallelogram are equal to 360°.
⇒ ∠A + ∠B + ∠C + ∠D = 360°
⇒ (3x + y)° + (5x + 10)° + (5y + 20)° + (5x + 10)° = 360°
⇒ 13x + 6y + 40° = 360°
⇒ 13x + 6y = 320° ------ (1)
Also, adjacent angles in a parallelogram are supplementary.
⇒ ∠A + ∠D = 180°
⇒ (3x + y)° + (5x + 10)° = 180°
⇒ 8x + y = 170° ----------- (2)
Step 3: Solve the 2 equations to find x and y.13x + 6y = 320
48x + 6y = 1020 (After multiplying eq. 2 with 6 to make coefficients equal)
Subtract (2) from (1)
⇒ -35x = -700
∴ x = 20
⇒ (5x + 10)° = 100 + 10 = 110°
Answer:
110°
Step-by-step explanation:
Angle A = Angle C
3x + y = 5y + 20
3x = 4y + 20
Angle C + Angle D = 180
5y + 20 + 5x + 10 = 180
5x + 5y = 150
x + y = 30
x = 30 - y
3(30 - y) = 4y + 20
90 - 3y = 4y + 20
7y = 70
y = 10
x = 30 - 10
x = 20
Angle B = Angle D
= 5(20) + 10
= 110°
Can someone please help me ?
Answer:
The first picture will have a solution a (3,4)
The second will have no solutions
The third picture will have a solution at (-4,-3)
Step-by-step explanation:
The solution is when the lines intersect you can tell in the first and third picture when they will and the second picture has parrell lines meaning they will never intersect
Given the point A(-3,-2) and B(6, 1), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1.
Answer:
P: (3,0)
Step-by-step explanation:
AB = (9,3)
⅔(9,3) = (6,2)
(-3,-2) + (6,2) = (3,0)
the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1 is (3,0).
What is the ratio formula for line segment?P=(mx2+nx1/m+n,my2+ny1/m+n).
The formula can be derived by constructing two similar right triangles, as shown below. Their hypotenuses are along the line segment and are in the ratio m : n m:n m:n.
Here, given that,
Given the point A(-3,-2) and B(6, 1),
Let, (x.y) is the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1.
Using the formula we get,
(x,y) = (nx1 + mx2)/(m + n) , (ny1 + my2)/(m + n)
P=(3,0)
hence, the coordinates of the point P on directed line segment AB that partitions AB in the ratio 2:1 is (3,0).
To learn more on ratio formula for line segment click:
https://brainly.com/question/19339816
#SPJ3