Two horses are ready to return to their barn after a long workout session at the track. The horses are at coordinates H(1,10) and z(10, 1). Their barns are located in the same building, which is at coordinates B(-3,-9). Each unit/grid on the coordinate plane represents 100 meters. Which horse is closer to the barn? Justify your answer.
If f(x) = 3x – 2 and g(x) = 6 – 4x, find f(x) + g(x). A. 7 + 4x B. 4 – x C. –x – 4 D. –4 – 7x
Solve the following system of equations algebraically. 2x = 5y + 8. 3x + 2y = 31
(4.4*10^6)*(3.9*10^4)
Scientific notation please help and explain
Simplify.
3 square root of -27n^27
A. 3n^3
B. -3n^3
C. -3n^9
Using technology, we found that Juan’s investment account can be modeled by the function, c(x)=3x2-2x+10, in thousands of dollars. What was Juan’s initial investment?
A)$5
B)$10
C)$5,000
D)$10,000
Answer:
D) $10,000.
Step-by-step explanation:
We have been given a function [tex]c(x)=3x^2-2x+10[/tex], which represents Juan’s investment account in thousands of dollars. We are asked to find Juan's initial investment.
To find Juan's initial investment, we will substitute [tex]x=0[/tex] in our given function.
[tex]c(0)=3(0)^2-2(0)+10[/tex]
[tex]c(0)=3*0-0+10[/tex]
[tex]c(0)=10[/tex]
Since the function gives Juan's investment in thousands of dollars, so Juan's initial investment would be [tex]10\times \$1,000=\$10,000[/tex], therefore, option D is the correct choice.
How much money will be in a bank account after 9 years if $7 is deposited at an interest rate of 5% compounded annually?
how to find the midpoint using coordinates A(-1,5), B(2,-3)
Consider the function given by the graph. What are these values?
f(–2 ) =
f(0) =
f(4) =
The values of the function f(x) for the given graph are approximately -7, -18, and -29.
Explanation:The values of the function f(x) for the given graph can be found by looking at the corresponding points on the graph.
For f(-2), we look at the point on the graph where x = -2. From the graph, we can see that f(-2) is approximately -7.
Similarly, for f(0), we look at the point on the graph where x = 0. From the graph, we can see that f(0) is approximately -18.
For f(4), we look at the point on the graph where x = 4. From the graph, we can see that f(4) is approximately -29.
f(-2) = -1
- f(0) = 3
- f(4) = 0
The values of the function at different points on the graph can be found by looking at the corresponding coordinates on the graph.
To find f(-2), we look for the point on the graph where x = -2. From the graph, it appears that the y-coordinate of this point is -1. Therefore, f(-2) = -1.
To find f(0), we look for the point on the graph where x = 0. From the graph, it appears that the y-coordinate of this point is 3. Therefore, f(0) = 3.
To find f(4), we look for the point on the graph where x = 4. From the graph, it appears that the y-coordinate of this point is 0. Therefore, f(4) = 0.
It is important to note that the given information about the arrows and points (0,3) to (-6,0) and (0,1) to (6,-2) is unrelated to finding the values of the function at the given points. These arrows and points might represent something else in the context of the graph, but they do not affect the calculations of f(-2), f(0), and f(4).
Find the measure of each interior angle
Decagon in which the measures of each interior angles are x + 5, x + 10, x + 20, x + 30, x + 35, x + 40, x + 60, x + 70, x + 80, and x + 90
To find each interior angle of a decagon given as expressions with x, we sum the expressions and set equal to 1440 degrees, the total sum of interior angles. Solving for x, we find x=100 and then substitute to find each angle.
To find the measure of each interior angle of a decagon where the angles are given as expressions involving x, we must use the fact that the sum of interior angles in a polygon is (n-2)180 degrees, where n is the number of sides in the polygon. For a decagon, which has 10 sides, the sum would be (10-2)180 = 1440 degrees.
x + 5 + x + 10 + x + 20 + x + 30 + x + 35 + x + 40 + x + 60 + x + 70 + x + 80 + x + 90 = 1440
Combining like terms, we find that:
10x + 5 + 10 + 20 + 30 + 35 + 40 + 60 + 70 + 80 + 90 = 1440
10x + 440 = 1440
10x = 1440 - 440
10x = 1000
x = 100
Once x is found, we substitute back into each angle expression to find the measure of each interior angle:
x + 5 = 105 degrees
x + 10 = 110 degrees
x + 20 = 120 degrees
x + 30 = 130 degrees
x + 35 = 135 degrees
x + 40 = 140 degrees
x + 60 = 160 degrees
x + 70 = 170 degrees
x + 80 = 180 degrees
x + 90 = 190 degrees
Identify the domain of the exponential function shown in the following graph: y=10x
The adams family is remodeling their family room. the room measures 14 feet by 20 feet, and the contractor wants $35 per square foot to remodel it. how much will it cost to remodel?
Answer:
It would cost $9800 to remodel the room.
Step-by-step explanation:
The Adams family is remodeling their family room.
Length of the room = 20 feet
Width of the room = 14 feet
To get area of the room we use the formula
Area = Length × Width
A = 20 × 14 = 280 feet²
The contractor wants $35 per square foot to remodel it.
So it would cost = 280 × 35 = $9800
It would cost $9800 to remodel the room.
Mr. Brown owned a house, which he rented for $60 a month. The house was assessed at $9000. In 1975 the rate of taxation was increased from $25 to $28 per $1000 assessed valuation. By what amount should the monthly rent have been raised to absorb the increase in that year's taxes?
A 12 foot rope is cut into two pieces so that one piece is 3 feet less than twice the length of the other piece. how long is each piece?
12 feet long
1st piece = x
2nd piece = 2x-3
3x-3 =12
3x=15
x = 5
1st piece = 5 feet
2nd piece = 2*5=10-3=7 feet
Find the range of the data. Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88 A) 22
B)24
C)28
D)23
Answer:
Option B - 24
Step-by-step explanation:
Given : Scores: 81, 79, 80, 88, 72, 96, 86, 73, 79, 88
To find : The range of the data?
Solution :
Range is defined as the difference between the smallest and the largest element of the data.
First we arrange the data into ascending order:
72,73,79,79,80,81,86,88,88,96
The smallest number is 72
The largest number is 96
The range of the data = largest number - smallest number
The range of the data = 96 - 72
The range of the data = 24
Therefore, Option B is correct.
Which set of numbers can represent the side lengths, in centimeters, of a right triangle?
Answer:
Any set of numbers that fit in Pythagoras theorem will represent that set.
Step-by-step explanation:
Though options are not given, but there is a standard way to get such combinations of number.
As it is a right triangle, we have to work on Pythagoras theorem.
The sum of squares of two other sides is equal to square of the hypotenuse.
Like : [tex]3^{2} +4^{2} =5^{2}[/tex]
Given: AC is the hypotenuse and BD is the altitude of △ABC. AD=27, CD=40, AB=e, BD=j, and BC=h
Find the value of e
How the literal devil am i supposed to do this, legit i've tried for hours first answer gets Brainliest
What is the area of the trapezoid?
There exists a similarity transformation that maps ΔABC to ΔA′B′C′. The measure of angle A is 68°, and the measure of angle B is 46°. What is the measure of angle C in degrees?
The measure of angle C in triangle ABC is 66 degrees, calculated by subtracting the sum of angles A and B from 180 degrees.
The measure of angle C can be determined by using the fact that the sum of angles in any triangle is always 180 degrees. Given that the measure of angle A is 68° and the measure of angle B is 46°, we can calculate the measure of angle C as follows:
C = 180° - A - B
C = 180° - 68° - 46°
C = 180° - 114°
C = 66°
Thus, the measure of angle C in ΔABC is 66 degrees.
What is the slope of the line that contains the points (9, –4) and (1, –5)?
The slope of the line that contains the given point is the rise/run, which is: 1/8.
How to Find the Slope of a Line?The slope of a line = rise / run = change in y / change in x.
Given the points on a line as (9, –4) and (1, –5):
Change in y = (-4 -(-5) = 1
Change in x = (9 - 1) = 8
Slope of the line = change in y/change in x = 1/8.
Learn more about the slope of a line on:
https://brainly.com/question/3493733
#SPJ2
Using a calculator and the formula above, calculate the APR. Choose the correct answer.
Betty Buyer has a short term note at 16% interest per year.
To the nearest tenth, APR =
15.9
17.2
16.6
%.
Complete the statements about the key features of the graph of f(x) = x5 – 9x3. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.
Choose all of the zeroes of f(x).
–3 with multiplicity 1
3 with multiplicity 1
0 with multiplicity 1
0 with multiplicity 3
3 with multiplicity 0
The end behavior of f(x) has the same end behavior of [tex]x^3[/tex] and all the zeroes of f(x) wiil be: -3 with multiplicity 1, 3 with multiplicity 1, 0 with multiplicity 3.
Given :
[tex]f(x) = x^5-9x^3[/tex] --- (1)
The value of x at which f(x) becomes zero can be determine by eqaution the equation (1) to zero.
[tex]x^5-9x^3=0[/tex]
[tex]x^3(x^2-9)=0[/tex]
[tex]x^3(x-3)(x+3)=0[/tex]
Therefore, all the zeroes of f(x) will be:
-3 with multiplicity 1,
3 with multiplicity 1,
0 with multiplicity 3.
The end behavior of f(x) has the same end behavior of [tex]x^3[/tex]. As x goes to negative infinity, f(x) goes to negative infinity, and as x goes to positive infinity, f(x) goes to positive infinity.The graph of f(x) is attached below.
For more information, refer the link given below:
https://brainly.com/question/24153248
Which number produces a rational number when added to 0.42?
Amy purchased 17 pencils and 18 pens for a fund-raiser at school and spent $61.50. Jocelyn purchased 10 pencils and 21 pens and spent $57. How much does each pencil cost?
In the above figure, find the measure of angle AEB + the measure of angle CED.
A. 75
B. 93
C. 112
D. 140
Find the least common multiple of 8c4 and 6c2 .
If a triangle is equilateral then it has 3 congruent angles proof
Allow ABC to be an
equilateral triangle so AB = AC = BC. Let X be the midpoint of BC, AX is the
median of BC, and BX = CX. Look at triangles BAX and CAX. Obviously, AX = AX since
AB = AC and BX = CX, subsequently by SSS Congruence Test, we have that
triangles BAX and CAX are congruent. Therefore, corresponding angles are
congruent so <ABX = <ACX. Because <ABX and <ABC are the same angle,
they are obviously congruent, and then <ABX = <ABC. Likewise, <ACX and
<ACB are the same angles so <ACX = <ACB. Then, <ABC = <ACB. Please
note that <ABC = <B and <ACB = <C. Therefore, <B = <C.
At present, disregard AX and let Y be the midpoint of AC.
Then BY is the median of AC. Then AY = CY. Evidently, BY = BY. Because AB = BC, we see that triangles ABY
and CBY are congruent by SSS. Then corresponding sames are congruent so <BAY
= <BCY. Since <BAY and <BAC are the same angles then <BAY =
<BAC. Similarly, <BCY = <BCA since they are the same angles. Then
<BAC = <BCA. Note that <BAC = <A and <BCA = <C. Therefore,
<A = <C.
Thus, <A = <C = <B. So all the angles are congruent.
Angle 1 and angle 2 form a linear pair. if m angle 2 = 67. what is m angle 1
Final answer:
The measure of angle 1 can be found by using the fact that angle 1 and angle 2 form a linear pair. By setting up an equation and solving, we find that angle 1 measures 113 degrees.
Explanation:
To find the measure of angle 1, we need to understand that angle 1 and angle 2 form a linear pair. A linear pair of angles is formed when two adjacent angles are supplementary, meaning they add up to 180 degrees. So, angle 1 + angle 2 = 180 degrees. Given that angle 2 measures 67 degrees, we can substitute this value into the equation to find angle 1: angle 1 + 67 degrees = 180 degrees. Solving for angle 1, we get angle 1 = 180 degrees - 67 degrees = 113 degrees.
Create a list of the odd numbers between 1 and n (include 1 as well as n -- if it's odd-- in the list). Associate the list with the variable odds.
The depth of the water at the end of a pier changes periodically along with the movement of tides. On a particular day, low tides occur at 12:00 am and 12:30 pm, with a depth of 2.5 m, while high tides occur at 6:15 am and 6:45 pm, with a depth of 5.5 m. Let t = 0 be 12:00 am. Write a cosine model, d = acos(bt) + k, for the depth as a function of time. This amplitude is meters. a =
Answers:
1.5, -1.5, 12.5, 4pi/25, 4, D
Step-by-step explanation:
Answer:
1.5 meters
a = -1.5
12.5 hours
b = 4 pi/25
k = 4 meters
last option is D
Step-by-step explanation:
edg 23'