The common difference of the arithmetic sequence is:
4
Step-by-step explanation:We kn ow that if the first term of an arithmetic sequence is a and d is the common difference of the sequence then the nth term of the sequence is given by the formula:
[tex]a_n=a+(n-1)d[/tex]
Here we are given:
[tex]a=-3[/tex]
and
[tex]a_15=53\\\\i.e.\\\\a+(15-1)d=53\\\\i.e.\\\\a+14d=53[/tex]
Now using the value of a we have:
[tex]-3+14d=53\\\\i.e.\\\\14d=56\\\\i.e.\\\\d=4[/tex]
if the parent function is 3 square root x, describe the translation of the function y=3 square root x-4 +3
Answer:
Step-by-step explanation:
Four units to the rights and three units up from ^3 square x.
help!!!
All rectangles can also be classified as which of the following? Select all that apply. r
rhombus
square
parallelogram
trapezoid
quadrilateral
Answer:
All rectangles can also be classified as which of the following? Select all that apply. r
rhombus
square
parallelogram
trapezoid
quadrilateral
Step-by-step explanation:
In plane geometry, a rectangle is a parallelogram.
Parallelogram: its opposite sides are parallel, it can also be a square, or a rhombus.
In Euclidean geometry, a quadrilateral is a polygon that has four sides and four vertices.
The answer is: Rhombus, square, parallelogram, and quadrilateral.
Would you expect a scatterplot comparing speed of a car in time it takes to drive 10 miles to show a positive association a negative association or no association explain you’re thinking
61/100in word form,decimal
What is the value of y?
Answer:
57
Step-by-step explanation:
Ap3x
Write the equation of the line passing through (−1, 0) and (0, −3).
The equation of the line passing through (-1, 0) and (0, -3) is y = -3x - 3, where -3 is the slope, and -3 is also the y-intercept.
The equation of a line can be written in slope-intercept form as y = mx + b, where m is the slope of the line, and b is the y-intercept. To find the slope m, we can use the two points given; the slope is the change in y over the change in x, which is (-3 - 0)/(0 - (-1)) = -3/1 = -3. With the slope found, and knowing that the line passes through the point (0, -3), we can say the y-intercept b is -3. The equation of the line through the points (-1, 0) and (0, -3) is y = -3x - 3.
Jerome went on a hike. He climbed three-fourths of a mile in two-thirds of an hour. What was his hiking speed in miles per hour?
Final answer:
Jerome's hiking speed was calculated by dividing the distance he hiked, three-fourths of a mile, by the time it took him, two-thirds of an hour. This yielded a hiking speed of 1.125 miles per hour.
Explanation:
To calculate Jerome's hiking speed in miles per hour, we need to divide the distance he hiked by the time it took him. Jerome hiked three-fourths of a mile in two-thirds of an hour. To find the speed, we use the formula:
Speed = Distance ÷ Time
Speed = ¾ mile ÷ ⅓ hour
To divide fractions, we multiply by the reciprocal of the denominator:
Speed = ¾ × ⅔ = 3/4 × 3/2 = 9/8
This fraction simplifies to 1⅛ (1.125) miles per hour. So, Jerome's hiking speed was 1.125 miles per hour.
It is important to remember that when we talk about speed, we are referring to the distance traveled over a certain period of time regardless of the direction of travel.
The function f is such that f(x)=4x-1 find f^-1(x)
Which equation represents the line that passes through (–6, 7) and (–3, 6)? y = –x + 9 y = –x + 5 y = –3x – 11y y = –3x + 25
Step [tex]1[/tex]
Find the slope of the line
we know that
the formula to calculate the slope between two points is equal to
[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]
Let
[tex]A(-6,7)\\B(-3,6)[/tex]
substitute the values
[tex]m=\frac{(6-7)}{(-3+6)}[/tex]
[tex]m=\frac{(-1)}{(3)}[/tex]
[tex]m=-1/3[/tex]
Step [tex]2[/tex]
with the slope m and the point [tex]A(-6,7)[/tex] find the equation of the line
we know that
the equation of the line in the point-slope form is equal to
[tex]y-y1=m*(x-x1)[/tex]
substitute the values
[tex]y-7=(-1/3)*(x+6)[/tex]
[tex]y=(-1/3)x-2+7[/tex]
[tex]y=(-1/3)x+5[/tex]
therefore
the answer is
[tex]y=(-1/3)x+5[/tex]
witch one of these is correct
In the number 35.3816, the underlined three is __________ the other three.
The rule of thumb in filmmaking is that you must shoot at least 3 minutes of film for every minute in a movies “final cut”. A 30 minute roll of film cost $250. How much will film cost to make a 90 minute movie?
Please explain how to do this problem! I can’t figure it out!
Dr. Silas studies a culture of bacteria under a microscope. The function b(t)=50(1.4)^t represents the number of bacteria t hours after Dr. Silas begins her study.
a) What is the y-intercept of the function? What does this mean in the context of the problem?
b) Is this exponential growth or decay? How do you know?
c) How many bacteria would there be 5 hours after Dr. Silas began her study?
Please show all your work!
The function relates to a bacteria count that starts at 50, grows exponentially due to the base of the exponent being greater than 1, and is projected to reach approximately 192 bacteria after 5 hours.
Explanation:a) The y-intercept of the function is the value of the function when t = 0. For the function [tex]b(t)=50(1.4)^t[/tex], if you substitute 0 for t, you get [tex]50(1.4)^0[/tex] which simplifies to 50. Consequently, the y-intercept is 50 which in context, means the study started with 50 bacteria.
b) This function represents exponential growth. We know this because the base of the exponent (1.4) is greater than 1. If the base had been less than 1, it would represent exponential decay.
c) To determine the number of bacteria 5 hours into the study, we need to substitute 5 for t in the formula.
Hence, [tex]b(5)=50(1.4)^5 = approximately 192.2.[/tex] The number of bacteria cannot be in fractions, thus we consider this as approximately 192.
Learn more about Exponential Growth here:https://brainly.com/question/12490064
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Rosalie earns extra money by working as a babysitter over the weekend. She charges $10 to drive to the home and an additional $8 per hour.
You want to apply a fertilizer to your lawn. The directions on the bottle call for mixing 3 ounces of fertilizer with 2 gallons of water. Your sprayer holds 5 gallons. To completely fill the sprayer with a proper mixture, how many ounces of fertilizer must you use?
A. 61⁄5
B. 52⁄3
C. 71⁄2
D. 31⁄3
Answer: 5 2/3
Step-by-step explanation:
If 20% of a class takes a car to school and 48% takes the bus and 8% ride their bikes to school and there are 825 in the school what percent of students use another method to travel to school
suppose that a pair of 7 sided dice is tossed. What is the expected value of the sum?
The expected value of the sum when rolling a pair of 7-sided dice is 8.
Explanation:When rolling a pair of 7-sided dice, each die has numbers 1 through 7 on its faces. To find the expected value of the sum, we need to calculate the average of all possible sums.
The first die can have 7 possible outcomes, and for each outcome, the second die can also have 7 possible outcomes. This gives us a total of 7*7=49 possible outcomes. The sums of these outcomes range from 2 (1+1) to 14 (7+7).
To find the expected value, we multiply each sum by its probability and sum them up. Since each sum has an equal probability of occurring (1/49), we can simplify the calculation:
Expected value = (2*1/49) + (3*1/49) + (4*1/49) + ... + (14*1/49) = 8
Therefore, the expected value of the sum when rolling a pair of 7-sided dice is 8.
A box of 20 Crunchy Munchy cookies costs $2.50 and a box of 40 Crunchy Munchy cookies costs $4.00. One quart of milk costs $1.50. Which of the following is a better bargain?
What is the simplified form of the expression? x8 2y10 5x5
Four consecutive even integers add to obtain 324
if h(x)=(f o g) (x) and h(x)=√x+5, find g(x) if f(x)=√x+2
we are given
[tex]h(x)=(fog)(x)[/tex]
we can write it as
[tex]h(x)=f(g(x))[/tex]
[tex]f(x)=\sqrt{x+2}[/tex]
now, we can replace x as g(x)
[tex]f(g(x))=\sqrt{g(x)+2}[/tex]
[tex]h(x)=\sqrt{g(x)+2}[/tex]
[tex]h(x)=\sqrt{x+5}[/tex]
now, we can equate them
[tex]\sqrt{x+5}=\sqrt{g(x)+2}[/tex]
now, we can solve for g(x)
Take square both sides
[tex](\sqrt{x+5})^2=(\sqrt{g(x)+2})^2[/tex]
[tex]x+5=g(x)+2[/tex]
now, we can solve for g(x)
Subtract both sides by 2
[tex]x+5-2=g(x)+2-2[/tex]
[tex]x+3=g(x)[/tex]
[tex]g(x)=x+3[/tex].............Answer
on a map, each centimeter represents 45 kilometers. two towns are 135 kilometers apart. what is the distance between the towns on the map
what is r divided by 8
how many books can you get in a storage bin that is 4 feet high and 9 feet long and 11 feet wide
the segments shown below could form a triangle ac=9. cb=8. ba=17
No, the triangle can not form.
What is Triangle inequality?The sum of any two sides of a triangle is greater than the third side.
Given:
ac=9. cb=8. ba=17
The question is attached below.
We know each triangle satisfy the triangle inequality which state that the sum of the two shorter sides must exceed the length of the third side.
But ,9+8=17 which equal to the third side .
So, these segments do not form a triangle.
Learn more about triangle inequality here:
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Mr. Clark claims that he has a coin that is weighted so that the probability of heads is 40%. To test this, his students flip the coin 200 times and calculate the relative frequency of heads and tails.
Outcome Heads Tails
Relative frequency 0.38 0.62
Select from the drop-down menus to correctly complete each statement.
The relative frequency of heads is
40%.
Mr. Clark's claim about the theoretical probability is likely to be
.
This means that the theoretical probability of tails is most likely
for this coin.
What is the approximate distance between the points (-5, 1) and (-2, 3) on a coordinate grid? A.7.81 units B.3.61 units C.2.23 units D.3.32 units
Answer:
3.61
Step-by-step explanation:
Janice used a 16-inch dowel and a 21-inch dowel to build a kite what is the perimeter of her kite
A trapezoid has an area of 15 square feet. If the bases are 4 feet and 6 feet , what is the height of the trapezoid? Hurry Big test tomorrow this the last one
Final answer:
The height of the trapezoid is 3 feet.
Explanation:
To find the height of a trapezoid with given bases and area, you can use the formula for the area of a trapezoid, which is the average of the two bases multiplied by the height. The formula is as follows:
Area = ½ × (base1 + base2) × height
Given that the area of the trapezoid is 15 square feet and the two bases are 4 feet and 6 feet, the formula becomes:
15 = ½ × (4 + 6) × height
This simplifies to:
15 = ½ × 10 × height
Therefore, we can calculate the height by dividing the area by 5 (which is half of 10):
height = 15 ÷ 5 = 3 feet
So, the height of the trapezoid is 3 feet.
0.5cm=1.5m. 36m tall. Find the scale factor.
Final answer:
To find the model height for an object that is 36 m tall using the given scale of 0.5 cm equals 1.5 m, we establish a proportion, which yields a model height of 12 cm, representing the scale factor as 1 cm : 3 m.
Explanation:
The question asks to find the scale factor given that 0.5 cm on a model equals 1.5 m in real life, and an object's real-life height is 36 meters. First, understand that the scale factor is the ratio of the model's size to the actual size. For this scenario, the given scale is 0.5 cm = 1.5 m. To find the model height for an object that is 36 m tall, we use this scale.
Set up a proportion based on the given scale: 0.5 cm/1.5 m = x cm/36 m. Simplifying the ratio to its smallest form, we get 1 cm = 3 m. Therefore, using cross multiplication, we find the height of the model as x = 0.5 cm * (36 m / 1.5 m).
Calculating gives x = 12 cm. Hence, the scale factor, when considering the model's size to the actual size, is represented as 1 cm : 3 m, and the actual model height is 12 cm for the 36 m tall object.