Answer:
[tex]y = - {10}^{x - 3} - 5[/tex]
Step-by-step explanation:
The parent exponential function given to us is
[tex]y = f(x)= {10}^{x} [/tex]
If this function is reflected over the x-axis, shifted right 3 units and down 5 units, then it becomes:
[tex]y = g(x) = - f(x - 3) - 5[/tex]
This implies that:
[tex]y = g(x) = - {10}^{x - 3} - 5[/tex]
where the negative multplier indicates reflection over x-axis, x-3, indicates shift to the right 3 units, and -5 indicates downward shift 5 units
What is the greatest area that you can make with a rectangle that has a perimeter of 24.
Answer:
Step-by-step explanation:
The greatest area of the rectangle with a perimeter of 24 units is in fact a square. So we take 24 units and divide by 4 to get a square of 6 units to a side. the area of that square is 6 units x 6 units = 36 square units
I NEED HELP ASAP WITH THE QUESTION
Equivalent expression for x + x + x + x + x is 5x and that of 18y - 12 are 6·3y - 6·2 and 6(3y - 2)
Step-by-step explanation:
Step 1: Find equivalent expression for x + x + x + x + x. It is 5x. Step 2: Find equivalent expressions for 18y - 12Equivalent expressions are 6·3y - 6·2 and 6(3y - 2)
5(-3x - 2) - (x - 3) = -4 (4x +5) + 13
Answer: No value for x
Step-by-step explanation:
Step 1: open the bracket
5(-3x - 2) - (x - 3) = -4 (4x +5) + 13
-15x + 10 - x +3= -16x - 20 +13
Step 2: combine like terms
-15x - x + 16x = -20 +13 -10 -3
-16× +16× = -20
0= -20
help! need asap! brainiest if right
Step-by-step explanation:
After the translation, rotation and reflection position of the image may differ but the side lengths, angle, orientation remains the same, so that the congruence is maintained, but in dilation the size of the image may get enlarged or reduced, so that congruence is not there.
Parallelograms are congruent when
Reflect across the y- axis and then translate 1 unit left.
Reflect across the y- axis then rotate 45° counterclockwise.
Translate 4 units up then rotate 180° counterclockwise
Parallelograms are non-congruent when
Translate 5 units right then dilate by a factor of 2
Rotate 90° clockwise then dilate by a factor of 6
Dilate by a factor of 3 then reflect across the x- axis
Why do you think George Washington wanted the us to avoid entangling alliances
Y=1/2+2 in standard form
Answer:
So Y would be 2 1/2, but in standard form it's 2.5
Step-by-step explanation:
So basically, you just have to add the numbers together. 2 + 1/2 = 2 1/2. 50 is half of 100, and this is 1/2 we're talking about. So we can change it to 2.5
You're welcome.
Answer:
y = 2.5
Step-by-step explanation:
[tex]y = \frac{1}{2} + 2[/tex]
[tex]( \frac{1}{2} = 0.5)[/tex]
[tex]y = 0.5 + 2[/tex]
[tex]y = 2.5[/tex]
A directed line segment on a gridded map shows the path of a hot air balloon from 1(0,0) to B(8,4). Each grid unit represents 1 mile. The balloon traveled at a constant speed of 20 miles per hour Point V divides line segment AB in the ratio 6 to 2.
a) What are the coordinates of point V? Round to the nearest tenth if necessary
b) Mary states that the distance from point A to point Vis 6 miles. What is Mary's mistake? What is the
correct distance? (Check)
Answer:
Step-by-step explanation:
There is a point V with ration 6 to 2, therefore we must find the coordinates of point V and the distance from A to V
According to the graph
[tex]c^{2}=x^{2}+y^{2}\\c^{2}=8^{2}+4^{2}\\c=\sqrt{64+16}=8.9.4\\sin\alpha =\frac{4}{8.94}[/tex]
α≅27°
V=2*8.94/6 (ratio 6:2)
V=2.98mile
[tex]sin27=\frac{y}{2.98}\\y=sin27*2.98=1.35\\cos27=\frac{x}{2.98}\\x=cos27*2.98=2.65[/tex]
coordinates of V = (2,65;1.35)
Distance from A to V
[tex]d_{AV}=2.98 miles[/tex]
finally
Mary's mistake is to take the 6 to 2 ratio as the distance traveled from the globe only in the x direction
An arc on a circle measures 125°. The measure of the central angle, in radians, is within which range? 0 to StartFraction pi Over 2 EndFraction radians StartFraction pi Over 2 EndFraction to π radians π to StartFraction 3 pi Over 2 EndFraction radians StartFraction 3 pi Over 2 EndFraction to 2π radians
Answer:
The answer is B or pi/2 to pi radians.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
The lifespans of meerkats in a particular zoo are normally distributed. The average meerkat lives 13.1 years; the
standard deviation is 1.5 years.
Use the empirical rule (68 – 95 - 99.7%) to estimate the probability of a meerkat living less than 14.6
years.
Using the Empirical Rule, it is found that there is a 84% probability of a meerkat living less than 14.6.
----------------------
The Empirical Rule states that in a normal distribution, 68% of the measures are within 1 standard deviation of the mean, 95% are within 2 standard deviations and 99.7% are within 3 standard deviations.----------------------
The mean is of 13.1 years, while the standard deviation is of 1.5 years.We have also consider that the normal distribution is symmetric, which means that 50% of the measures are above the mean and 50% are below.14.6 = 13.1 + 1.5, thus, one standard deviation above the mean.Of the 50% of the measures below the mean, all are below 14.6, while of the 50% above, 68% are below 14.6, thus:[tex]P = 50 + 0.68(50) = 50 + 34 = 84[/tex]
84% probability of a meerkat living less than 14.6.
A similar problem is given at https://brainly.com/question/13503878
To estimate the probability of a meerkat living less than 14.6 years, we can use the empirical rule which states that approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Explanation:To estimate the probability of a meerkat living less than 14.6 years, we can use the empirical rule which states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.
Given that the average lifespan is 13.1 years and the standard deviation is 1.5 years, we can calculate the z-score for 14.6 years using the formula:
z = (x - μ) / σ
where x is the value we want to find the probability for (14.6 years), μ is the mean (13.1 years), and σ is the standard deviation (1.5 years).
Substituting the values, we get:
z = (14.6 - 13.1) / 1.5 = 1.0
Now we can look up the probability corresponding to a z-score of 1.0 in a standard normal distribution table, which is approximately 0.8413. This means that the probability of a meerkat living less than 14.6 years is about 0.8413 or 84.13%.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ2
Solve 3x + k = cfor x.
Create a chart to show how to use the distributive property to simplify the expression: 7 (5x +
10) – 10x.
Answer:
25x + 70
Step-by-step explanation:
Step 1: Distribute
7 (5x + 10) - 10x
7*5x + 7*10 - 10x
35x + 70 - 10x
25x + 70
Answer: 25x + 70
Explain how to write the equations of vertical lines, and why they are written this way
1. Recall the vertical line equation.
2. Plug in the x that we know.
3. Write down the final equation
Pls mark me brainiest :)
Write an inequality to describe the relationship between -1 2/3 and -1/4.
Answer:
-14>-1 2/3
Step-by-step explanation:
Answer:
-14>-1 2/3
Step-by-step explanation:
(I NEED THIS ANSWERED QUICKLY! I WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWER!)
The coordinates of the vertices of quadrilateral ABCD are (7, -7), (4, -10), (1.5, -2.5), and (6, -3), respectively. If quadrilateral ABCD is rotated 180° counterclockwise about the origin, what are the coordinates of D’?
A. (6, 3)
B. (3, -6)
C. (-6, 3)
D. (-3, 6)
Answer:
D
Step-by-step explanation:
literlay just count
Answer:
i believe the answer is c
Step-by-step explanation:
In the isosceles triangle ABC, we have AB=AC=4. The altitude from B meets AC at H. If AH=3(HC) then determine BC.
In isosceles triangle ABC with AB=AC=4, and AH=3HC, the length of BC is [tex]\( \frac{4\sqrt{5}}{5} \)[/tex] units, determined using the Pythagorean Theorem and the given relationship between AH and HC.
In isosceles triangle ABC, let BH be the altitude from B to side AC. Given AB = AC = 4 and AH = [tex]3 \cdot[/tex] HC, we can use the Pythagorean Theorem in right triangle ABH:
[tex]\[ BH^2 + AH^2 = AB^2 \][/tex]
Substitute the given values:
[tex]\[ BH^2 + (3HC)^2 = 4^2 \][/tex]
Simplify:
[tex]\[ BH^2 + 9HC^2 = 16 \][/tex]
Since BH = HC in an isosceles triangle, substitute BH with HC:
[tex]\[ HC^2 + 9HC^2 = 16 \][/tex]
Combine like terms:
[tex]\[ 10HC^2 = 16 \][/tex]
Solve for HC :
[tex]\[ HC^2 = \frac{8}{5} \][/tex]
Now, use the Pythagorean Theorem in right triangle BHC:
[tex]\[ BC^2 = BH^2 + HC^2 \][/tex]
Substitute the known values:
[tex]\[ BC^2 = HC^2 + HC^2 \]\[ BC^2 = 2HC^2 \]\[ BC^2 = 2 \cdot \frac{8}{5} \]\[ BC^2 = \frac{16}{5} \][/tex]
Therefore, BC is the square root of [tex]\( \frac{16}{5} \)[/tex], which simplifies to [tex]\( \frac{4}{\sqrt{5}} \)[/tex] or [tex]\( \frac{4\sqrt{5}}{5} \)[/tex].
The length of BC in an isosceles triangle with sides AB=AC=4 and altitude BH, where AH=3(HC), is 2√2 units.
Explanation:To determine the length of BC in an isosceles triangle ABC with sides AB=AC=4 and altitude BH, where AH=3(HC), we can use the properties of similar triangles and the Pythagorean theorem.
Since the triangle is isosceles, the altitude BH will bisect the base AC at H, creating two right triangles ABH and CBH. We know that AH=3(HC), which can be expressed as AH=3x and HC=x for some value x. Therefore, AC = AH + HC = 3x + x = 4x.
Using the Pythagorean theorem (a² + b² = c²), in triangle ABH, we get:
AH² + BH² = AB²(3x)² + BH² = 4²9x² + BH² = 16And in triangle HBC, we have:
HC² + BH² = BC²x² + BH² = BC²Since we want to find BC, we first solve for BH from the first right triangle:
BH² = 16 - 9x²Substitute BH² into the second equation:
x² + (16 - 9x²) = BC²-8x² + 16 = BC²To find x, we use AC = 4x = 4, thus x = 1. Substituting x into the equation for BC, we get:
-8(1)² + 16 = BC²-8 + 16 = BC²BC² = 8BC = √8BC = 2√2 unitsIt costs $100 to rent the bowling alley, plus $4 per person. The cost for any number (n) of people can be found using the expression 100 + 4n. The cost for 20 people equals $ ___. (Input whole number only.)
Numerical Answers Expected!
Answer:$4 × 20 = 80 + 100 = 180
Step-by-step explanation:
$80 is how much it is for 20 people, then you add the $100 rent which equals 180
Answer:
180
Step-by-step explanation:
How do I find vertex
Answer:
Get the equation in the form y = ax2 + bx + c.
Calculate -b / 2a. This is the x-coordinate of the vertex.
To find the y-coordinate of the vertex, simply plug the value of -b / 2a into the equation for x and solve for y.
Step-by-step explanation:
find the recursive formula.
-28, -35, -42, -49, ...
Answer:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] - 7
Step-by-step explanation:
Note the common difference d between consecutive terms in the sequence, that is
d = - 35 - (- 28) = - 42 - (- 35) = - 49 - (- 42) = - 7
Thus to obtain a term in the sequence subtract 7 from the previous term
[tex]a_{n+1[/tex] = [tex]a_{n}[/tex] - 7 with a₁ = - 28
Write an equation for the nth term of the geometric sequences-3,6,-12,......
Answer:
Write an equation for the nth term of the geometric sequences-3,6,-12,....
an= ar∩-1
a= first term
r= common ratio
an= nth term
an= -3 x (-2) (-12-1)
an= -3 x (-2) (-13)
an= -3 x (-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)(-2)
an= -3 x -16384
nth term= 49152
Step-by-step explanation:
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue , 1 red , and 1 orange section is?
Hey there!
[tex]\large\boxed{25\%}[/tex]
Assuming that all the sections are the same size, there are four sections of equal size.
Blue would be one out of those four sections, so the probability is 1/4. In decimal form this is .25, and as a percent this is 25%.
Hope this helps!
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue , 1 red , and 1 orange section is 1/4.
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue, 1 red, and 1 orange section is 1/4 or 25%.
Total = 1+1+1+1 = 4
Number of blue =1
Therefore, probability =1/4
A new car is Purchased for 16200 dollars. The value of the car depreciates at 14.25% per year. What will the value of the car be, to the nearest cent,after 6 years?
Answer:
6,440.5
Step-by-step explanation:
So the car starts at 16,200. For the first part of the equation it's 16,200 × x raised to the y. X in this equation would be 1-.1425 = 0.8575. 16,200×(.8575)^y. Y is the number of years after you purchased the car. So, 16,200×(.8575)^6 and that equals 6,440.5
Answer:
$6440.5
Step-by-step explanation:
I hope this helps!
Two linear equations are shown.
What is the solution to the system of equations?
(7,4)
• (31)
• (s. *)
(9,7)
y=
1/3x + 2
4
5
6
x
y = 4/3x - 5
The solution to the system of equations is (7, 13/3).
We have Equations,
y= 1/3x + 2,
y= 4/3 x - 5
Solving above two equations we get
1/3 x + 2 = 4/ 3 x - 5
1/3 x - 4/3 x = -5 - 2
-3/3 x = -7
-x = -7
x = 7
and, y = 4/3(7) - 5 = 28/3-5 = 13/3
Thus, the solution of equation is (7, 13/3).
Learn more about Equation here:
https://brainly.com/question/29657983
#SPJ7
I WILL MARK BRINLIEST FOR CORRECT ANSWER, PLEASE HELP.
Answer:
f(-2) = 4
f(0.5)= 0
f(1)=1
Step-by-step explanation:
Norma has 9 pies to divide among 4 friends. How many pies will each friend receive if all of the pies must be used and can be divided into smaller parts?
Answer:
2 1/4
Step-by-step explanation:
What is (-7a^4bc^3)(5ab^4c^2)
Answer:=-35a^5b^5c^5
Step-by-step explanation:
Answer:
-35a^5b^5c^7
Step-by-step explanation:
Step 1: Distribute
(-7a^4bc^3)(5ab^4c^4)
(-7 * 5) * (a^4 * a) * (b * b^4) * (c^3 * c^4)
(-35) * (a^5) * (b^5) * (c^7)
-35a^5b^5c^7
Answer: -35a^5b^5c^7
Find the product.
4(−12)(−3)
Answer:
144
Step-by-step explanation:
Answer:
-12/3
Step-by-step explanation:
a regular hexagon is to be cut out of a circular sheet of metal that has a radius of 6 inches.
Approximately how many square centimeters of sheet will be left over a scraps?
A:32.9
B:93.5
C:113.1
D:126.2
Answer:
[tex]\large \boxed{\text{D. 126.2 cm}^{2}}[/tex]
Step-by-step explanation:
The area left over for scrap is the area of the circle minus the area of the hexagon.
1. Area of circle
The formula for the area of a circle is
A = πr²
A = π(6)² = 36π = 113.1 in²
2. Area of hexagon
A hexagon consists of six equilateral triangles, each of side a, and we can divide each of them into two right triangles.
So, we can calculate the area of one right triangle and multiply by 12.
The formula for the area of one triangle is
A = ½bh
(a) Height of a small triangle
Per the Pythagorean Theorem,
[tex]\begin{array}{rcr}h^{2} + 3^{2} & = & 6^{2}\\h^{2} + 9 & = & 36\\h^{2} & = & 27\\& = & 3\sqrt{3}\\\end{array}\\[/tex]
(b) Area of a small triangle
A = ½ bh = ½ × 3 × 3√3 = 4.5√3 in²
(c) Area of the hexagon
The hexagon contains 12 small triangles.
A = 12 × 4.5√ 3 = 54√3 ≈ 93.53 in²
3. Area of scrap
A ≈ 113.1 in² - 93.53 in² = 19.6 in²
[tex]A = \text{19.6 in}^{2} \times \left(\dfrac{\text{2.54 cm}}{\text{1 in}}\right )^{2} = \text{126.2 cm}^{2}\\\\\text{The area of the scrap is $\large \boxed{\textbf{126.2 cm}^{\mathbf{2}}}$}[/tex]
Choose the equation that represents this situation. Use p to represent the
price of an item and tto represent its total cost with gift wrapping.
A store adds a $5 fee to the price of each item that a customer wants to have
gift-wrapped
O A. p=t+5
O B. t= 5p
OC. t= p +5
O D. t+p=5
Answer:
(c)t=p+5
Step-by-step explanation:
total price= item price + gift wrapping cost (given)
gift wrapping cost is constant/unchanged= 5
total price= t
item price=p
therefore by derivation t=p+5 (option c)
Final answer:
The correct equation to represent the store's $5 gift wrapping fee added to the price of an item is C. t = p + 5, where p is the price of the item and t is the total cost with gift wrapping.
Explanation:
The question is asking to find an equation that shows the relationship between the price of an item, represented by p, and its total cost with gift wrapping, represented by t. Given that the store adds a $5 fee for gift wrapping, the correct equation needs to include the original price of the item and the additional gift wrapping fee. Therefore, the total cost t is equal to the price of the item p plus the $5 wrapping fee.
The correct equation representing this situation is C. t = p + 5.
This is because when you start with the initial price of an item p and add a fixed gift wrapping fee of $5, you get the total cost t. It is the sum of the two values: the price of the item plus the additional fixed fee for gift wrapping.
Write a verbal expression for 2n+7
Please help me figure this out explain it to me
Answer:
40yd
Step-by-step explanation:
area of total minus unshaded portion