René Descartes provided the first systematic link between Euclidean geometry and algebra.
What is Geometry?This branch of mathematics involves the study of object shape, their spatial relationship and that of their surrounding space.
René Descartes is referred to as the father of analytic geometry due to him establishing the relationship between Euclidean geometry and algebra.
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What is the slope of the line?
Answer:
3/1
Step-by-step explanation:
left one and three up
For the following exercises, determine whether each of the following relations is a function.
1. y = 2x + 8
Answer:
The relation y=2x+8 is a function because the two different output values of the function have the one unique input value.
Step-by-step explanation:
The given relation is y=2x+8.
It is required to determine the relation is a function.
This solution can be obtained by using the concept of function. First write the given relation y=2x+8 and determine whether the given relation is a function.
Step 1 of 1
The given relation is y=2x+8.
This relation shows that the two different output values of the function have one unique input value and this relation is a linear function.
Hence, the relation is a function.
Please help me it’s trig!!!!!!!
The measure of angle of ∠BAM (θ) will be 9°. Then the correct option is D.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
ABCD is a rectangle with AB = 3BC.
And M is the mid-point of BC.
2BM = BC
Then the tangent of angle of ∠BAM (θ) will be
tan θ = (BM) / (AB)
tan θ = (BM) / (3BC)
tan θ = (BM) / (3 × 2BC)
tan θ = 1/6
θ = tan⁻¹ (1/6)
θ = 9.46°
θ ≅ 9°
Then the correct option is D.
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how do i multiply 42 x 60 and round to the nearst hunderends
Writing Exercises
84. Using your own words, explain the difference between a monomial, a binomial, and a trinomial.
Answer: a monomial has one term, binomial has 2 terms, and trinomial has 3.
Step-by-step explanation:
using a bit of greek and latin roots, we can observe that all 3 terms have the same suffix of nomial in them. From this, we know that mono means one, bino means two, and tri means 3. Fun fact, there's also polynomial (if you did or didn't know), which is multiple terms more than 3.
Which of these shapes is congruent to the given shape? a quadrilateral, tilting right, plotted on a grid. a. a quadrilateral plotted on a grid across 4 units. b. a quadrilateral, tilting right, plotted on a grid. c. a vertical quadrilateral plotted on a grid. d. a quadrilateral, tilting left, plotted on a grid. e. a quadrilateral, tilting left, plotted on a grid.
Option D is correct.
Figures are missing in the question.
The images below shows the missing figures of question.
Solution:For congruent figures, we need the same shape, same area, and inverse direction.
Congruent figures have congruency. That seems simple enough, but congruent figures need not be turned the same way or face the same direction to be congruent.
In the case of geometric figures, line segments with the same length are congruent and angle with the same measure are congruent.
In elementary geometry the word congruent is often used as follows. The word equal is often used in place of congruent for these objects.
In this sense, two plane figures are congruent implies that their corresponding characteristics are "congruent" or "equal" including not just their corresponding sides and angles, but also their corresponding diagonals, perimeters, and areas.
The figure in option D satisfies all these conditions. Hence, Option D is correct.
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look at image please answer both
6. The system of equations has no solution.
7. B. Tables - 15 lbs, chairs - 3.5 lbs.
How to Find the Solution to the System of Equations?The values of x and y that makes two equations equal is the solution of a system of equations.
6. 3x + 4y = 12 --> eqn. 1
y = 3 - 3/4x --> eqn. 2
Substitute y = (3 - 3/4x) into eqn. 1 to find x:
3x + 4(3 - 3/4x) = 12
3x + 12 - 3x = 12
12 = 12 [unable to solve further for x]
This means that the system of equations has no solution.
7. t = tables
c = chairs
3t + 5c = 62.5 --> eqn. 1
3t + 2c = 52 --> eqn. 2
Subtract
3c = 10.5
c = 3.5 [chairs]
Substitute c = 3.5 into eqn. 2
3t + 2(3.5) = 52
3t + 7 = 52
3t = 52 - 7
3t = 45
t = 15 [table]
Therefore, the answer is: B. Tables - 15 lbs, chairs - 3.5 lbs.
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john and Tyrone each go for a morning jog before work. John's jogging pace is represented by' the equation y=5x where y is the the number of miles he jogs, and x is the number is the number of hours he jogs. Tyrones pace is given by the graph. Choose the statement that correctly compares their unit rates.
Answer:
The answer is B. Tyrone's unit rate is 1 more mile per hour then John’s unit rate.
Step-by-step explanation:
First of all at the bottom is what the graph and the answer options are.
Hope this helped! :D
please assist me on this question
Answer:
x = 175 units
Step-by-step explanation:
x is to (49 + 576) as 49 is to x
x/ 625 = 49/x cross multiply
x^2 = 30625
x=175
Answer:
x = 175 units
Step-by-step explanation:
x is to (49 + 576) as 49 is to x
x/ 625 = 49/x cross multiply
x^2 = 30625
x=175
HOPE THIS HELPS LOVE -3-
Landon is lying in the grass looking at the top of a tree that is 200 m away. The angle of elevation between Landon's head and the top of
the tree is 36 degrees.
What is the height of the tree?
O 145 m
O 275 m
O 118 m
162 m
200 m
The height of the tree which is the opposite side of the right triangle is 145 meters.
How to find height when given angle of elevation?The angle of elevation is 36 degrees.
The situation forms a right angle triangle.
Therefore,
base of the triangle = 200 m
Hence, using trigonometric ratios,
tan 36 = opposite / adjacent
tan 36 = x / 200
x = 200 tan 36
x = 200 × 0.726542528
x = 145.308505601
x = 145.31 m
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list the 8 numbers between 4 and 40 in a sequence of 10 numbers a common difference
Answer:
8, 12, 16, 20, 24, 28, 32, 36
Step-by-step explanation:
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
a₁ is the first term and d the common difference
given a₁ = 4 and a₁₀= 40 , then
4 + 9d = 40 ( subtract 4 from both sides )
9d = 36 ( divide both sides by 9 )
d = 4
add d to each term to obtain the next term
4 + 4 = 8
8 + 4 = 12
12 + 4 = 16
16 + 4 = 20
20 + 4 = 24
24 + 4 = 28
28 + 4 = 32
32 + 4 = 36
the 8 terms between 4 and 40 are
8, 12, 16, 20, 24, 28, 32, 36
please help its due soon! :(
Which statement describes the end behavior of this function?
f(x) = log(x − 2)
A.
As the value of x decreases, the value of f(x) moves toward positive infinity.
B.
As the value of x increases, the value of f(x) moves toward positive infinity.
C.
As the value of x increases, the value of f(x) moves toward negative infinity.
D.
As the value of x decreases, the value of f(x) moves toward a constant.
Answer:
So, the correct answer is that as x gets bigger, f(x) moves towards positive infinity.
Noise levels at 5 volcanoes were measured in decibels yielding the following data: 108,133,140,129,136 1. Construct the 98% confidence interval for the mean noise level at such locations. Assume the population is approximately normal.
2. Calculate the sample standard deviation for the given sample data. 3. Find the critical value that should be used in constructing the confidence interval.
The confidence interval or the mean noise level is (108.17,150.23) and sample standard deviation is 12.52.
Given noise levels:108,133,140,129,136. and confidence level 98%.
We have to find the confidence level and the sample standard deviation of the given data.
Confidence level=98%.
n=5
Sample standard deviation=[tex]\sqrt{(x-x bar)^{2} /n-1}[/tex]
=[tex]\sqrt{626.8/4}[/tex]
=[tex]\sqrt{156.7}[/tex]
=12.52
critical t value at 98% confidence level with degree of freedom(5-1) is 3.747
Standard error= critical t*s/[tex]\sqrt{n}[/tex]
Standard error is the difference between the real values and calculated values.
=3.747*12.52/[tex]\sqrt{5}[/tex]
=46.91/2.23
=21.03
Upper confidence interval=Mean +standard error
=129.2+21.03
=150.23
Lower confidence interval=Mean - standard error
=129.2-21.03
=108.17
Hence the confidence interval is (108.17,150.23) ,sample standard deviation is 12.52 and critical t value is 3.747.
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someone help me with this pleaseeeeeeeeeeeeee
Answer:
[a] 11 feet
[b] 7 feet
[c] 10 feet
Step-by-step explanation:
See attached. We will pull different details from the graph and information given to solve the different problems,
Answer:
See below
Step-by-step explanation:
Using the equation (instead of the graph....my answer got deleted for using the graph instead of the equation)
When the ball leaves fingers x = 0 :
a) -1/25 ( 0-10)^2 + 11 = 7 ft
b) max height will be at - b/2a
-1/25 ( x^2 -20x +100 ) + 11 <====expand
-1/25 x^2 + 4/5x +7 a = -1/25 b= 4/5
then - b/2a = - 4/5 / (2* -1/25) = 10=x
sub in this value of x into the equation to find max height = 11ft
c) when x = 15
-1/25 ( 15-10)^2 + 11 = 10 ft
Which of the following functions cannot be odd?
Polynomials
Rationals
Trigonometric
Exponential
Step-by-step explanation:
Exponential can't be odd, because any exponential function has a range that isn't defined for all reals
If a linear function contains the pairs (5,7) and (9,11), which pairs should have the reciprocal function to this one?
Please choose an answer.
a.
(7.5) and (11.9)
b.
(5.7) and (11.9)
c.
(5.7) and (9.11)
d.
(7.5) and (9.11)
The new coordinates will be ( 7,5) and (11,9) , Option A is the correct answer.
What is a Reciprocal Function ?The reciprocal function is the inverse of the function, such that 1/ f(x) is the reciprocal of f(x).
The given linear function has pairs of points
(5,7) and (9,11)
The reciprocal of this will be
interchanging of the coordinates
Therefore the new coordinates will be
( 7,5) and (11,9)
Option A is the correct answer.
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URGENT NEED ANSWER NOWWWWW!!!!!!WORTH 27 POINTS!!!
Black Diamond Ski Resort charges $25 for ski rental and $10 an hour to ski. Bunny Hill Ski Resort charges $50 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same.
a.10x+25=5x+50
b.10x-25=5x-50
c.10x+50=5x+25
d.10x-50=5x-25
Answer:
A
Step-by-step explanation:
because for black diamond its 10x+25
and for bunny hill its 5x+50
Which of the expressions below are equal to 8x² + 30x + 18?
Select all that apply.
A) (4x + 3) (2x + 6)
B) 6x² + 20x + 2x² + 10x + 18
C) 2(4x² + 15x + 9)
D) 4(2x² + 7x + 4)
Answer:
A, C, and D
Step-by-step explanation:
A) (4x + 3) (2x + 6) is equal to 8x² + 30x + 18 because when you multiply two binomials, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, (4x + 3) (2x + 6) can be rewritten as (4x)(2x) + (4x)(6) + (3)(2x) + (3)(6). This can further be simplified to 8x² + 24x + 18.
C) 2(4x² + 15x + 9) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 2(4x² + 15x + 9) can be rewritten as 2(4x²) + 2(15x) + 2(9). This can further be simplified to 8x² + 30x + 18.
D) 4(2x² + 7x + 4) is equal to 8x² + 30x + 18 because when you multiply a number by a binomial, you use the distributive property. The distributive property states that for any numbers a, b, and c, a(b + c) = ab + ac. So, 4(2x² + 7x + 4) can be rewritten as 4(2x²) + 4(7x) + 4(4). This can further be simplified to 8x² + 28x + 16.
12. A girl walks 3/4 of the way home in 18 minutes.
At the same rate, she can walk the rest of the
way home in how many minutes?
conplete the sentences below for the numbers 16,-9, and -15
Step-by-step explanation:
1. The number to the right of 0 is 16.
2. The number that is the least is -15.
3. -15 is smaller than 0 than -9 is.
A game of chance has a spinner with five equal-sized sections, The results of 625 spins are shown below. For which color is the difference between the theoretical probability and experimental probability greatest? Explain.
The color that has the greatest difference between the theoretical and experimental probability is yellow.
Which color has the greatest difference?Theoretical probability of each color = number of color in each section / total number of sections
1/5 = 0.2
Experimental probability is based on the result of an experiment that has been carried out multiples times
Experimental probability
Experimental probability of choosing orange = 118 / 625 = 0.19
Difference = 0.2 - 0.19 = 0.01
Experimental probability of choosing purple = 137 / 625 = 0.22
Difference 0.22 - 0.2 = 0.02
Experimental probability of choosing brown = 122 / 625 = 0.20
0.2 - 0.2 = 0
Experimental probability of choosing yellow = 106 / 625 = 0.17
0.20 - 0.1696 = 0.0304
Experimental probability of choosing green = 142 / 625 = 0.23
0.2272 - 0.20 = 0.0272
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What is the LCM of 20 ,8 ,4?
Answer:
Least common multiple (LCM) of 20, 8, 4 is 40.
LCM(20, 8, 4) = 40
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
Answer:
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
Of the songs in Brianna's music library, 1/3 are rock songs. Of the rock songs, 7/10 feature a guitar solo. What fraction of the songs in Brianna's music library are rock songs that feature a guitar solo?
Answer:
7/30 of her music library
Step-by-step explanation:
We are looking for 7/10 of 1/3. In this case this "of" means we will multiply the two fractions. To multiply fractions, we multiply
top × top
and
bottom × bottom
1/3 × 7/10
is 1×7 on top, and
3×10 on the bottom.
= (1×7)/(3×10)
= 7/30
7/30 cannot be simplified, so that is the answer.
please answer this question with steps
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - ( [tex]\frac{5}{2}[/tex] a² + [tex]\frac{3}{2}[/tex] a³ + [tex]\frac{a}{3}[/tex] - [tex]\frac{6}{5}[/tex] ) ← distribute parenthesis by - 1
= [tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] - [tex]\frac{5}{2}[/tex] a² - [tex]\frac{3}{2}[/tex] a³ - [tex]\frac{a}{3}[/tex] + [tex]\frac{6}{5}[/tex] ← collect like terms
= ([tex]\frac{1}{3}[/tex] a³ - [tex]\frac{3}{2}[/tex] a³ ) + (-[tex]\frac{3}{4}[/tex] a² - [tex]\frac{5}{2}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{5}{2}[/tex] + [tex]\frac{6}{5}[/tex] ) ← change to common denominators
= ([tex]\frac{2}{6}[/tex] a³ - [tex]\frac{9}{6}[/tex] a³ ) + (- [tex]\frac{3}{4}[/tex] a² - [tex]\frac{10}{4}[/tex] a² ) - [tex]\frac{a}{3}[/tex] + (- [tex]\frac{25}{10}[/tex] + [tex]\frac{12}{10}[/tex] ) ← simplify
= - [tex]\frac{7}{6}[/tex] a³ - [tex]\frac{13}{4}[/tex] a² - [tex]\frac{1}{3}[/tex] a - [tex]\frac{13}{10}[/tex]
Answer:
Step-by-step explanation:
[tex]\sf \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\left[\dfrac{5}{2}a^2+\dfrac{3}{2}a^3+\dfrac{a}{3}-\dfrac{6}{5}\right]=[/tex]
[tex]\sf = \dfrac{1}{3}a^3-\dfrac{3}{4}a^2-\dfrac{5}{2}-\dfrac{5}{2}a^2-\dfrac{3}{2}a^3-\dfrac{a}{3}+\dfrac{6}{5}\\\\\\( Combine \ like \ terms)\\\\= \dfrac{1}{3}a^3 -\dfrac{3}{2}a^3 -\dfrac{3}{4}a^2-\dfrac{5}{2}a^2-\dfrac{a}{3}-\dfrac{5}{2}+\dfrac{6}{5}\\\\=\left[\dfrac{1*2}{3*2}-\dfrac{3*3}{2*3}\right]a^3 + \left[-\dfrac{3}{4}-\dfrac{5*2}{2*2}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{5*5}{2*5}+\dfrac{6*2}{5*2}\right]\\\\\\[/tex]
[tex]\sf ==\left[\dfrac{2}{6}-\dfrac{9}{6}\right]a^3+\left[-\dfrac{3}{4}-\dfrac{10}{4}\right]a^2-\dfrac{a}{3}+\left[-\dfrac{25}{10}+\dfrac{12}{10}\right]\\\\=\dfrac{2-9}{6}a^3+\dfrac{(-3-10)}{4}a^2-\dfrac{a}{3}+\dfrac{(-25+12)}{15}\\\\[/tex]
[tex]\sf = \dfrac{-7}{6}a^3+ \dfrac{(-13)}{4}a^2-\dfrac{a}{3}+\dfrac{(-13)}{15}\\\\=-\dfrac{7}{6}a^3-\dfrac{13}{4}a^2-\dfrac{a}{3}-\dfrac{13}{15}[/tex]
The rocket that will return the rock and soil samples to Earth cannot lift off if the total weight of the samples from the rovers exceeds 530 pounds. What is the probability that the total weight of the samples will exceed 530 pounds? Group of answer choices
Binomial distribution will be used to know the probability that the total weight of the samples will exceed 530 pounds.
It is given that the rocket that will return the rock and soil samples to Earth cannot lift off if the total weight of the samples from the rovers exceeds 530 pounds.
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability q = 1 − p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.
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Determine whether the given relation is an implicit solution to the given differential equation. Assume that the relationship does define y implicitly as a function x and use implicit differentiation.
x^2-sin (x+y)=1 ,dy/dx=2 x sec(x+y) - 1
We cannot express the function [tex]x^{2} -sin(x+y)=1[/tex] in y=f(x) form it has an implicit function.
Given function [tex]x^{2} -sin(x+y)=1[/tex] and dy/dx=2x sec(x+y)-1
A relation is said to be an implicit solution of a differential equation involving x,y and derivatives of y with respect to x if defined explicit solution. In other words the function which cannot be written as y=f(x).
Function is a relationship between two or more variables which have one value for each value of x.
We have to first differentiate the function with respect to x.
[tex]x^{2} -sin(x+y)=1[/tex]
2x-cos(x+y)(1+dy/dx)=0
2x-cos(x+y)+cos(x+y)dy/dx=0
cos(x+y) dy/dx=cos(x+y)-2x
dy/dx={cos(x+y)-2x}/cos(x+y)
dy/dx=cos(x+y)/cos(x+y)-2x/cos(x+y)
dy/dx=1-2x cos(x+y)
The given solution is incorrect.
when we solve the function to collect the variable y in one side we cannot be able to do that.
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is 7 1/5•49 7/5 equivalent to 49 2/10 • 7 1/5
We can calculated each one out :
7 1/5 x 49 7/5 = 36/5 x 252 / 5 = 9072 / 25
49 2/10 x 7 1/5 = 980 / 10 x 36/5 = 35280 / 50 = 3528 / 5
or a much simpler way is that because both multiplication has 7 1/5 so we only have to compare the other terms, and since 49 7/5 is not equal to 49 2/10 these are not equal. and i didnt notice that till now.
Find the area of all the letters!!!!
The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of the given letters
J = 0.5 × 8 ft × 6 ft = 24 ft²
K = 8ft × 9ft = 72 ft²
L = 6ft × 9ft = 54 ft²
M = 10ft × 9ft = 90ft²
N = 0.5 × 8 ft × 6 ft = 24 ft²
U = 0.5 × 16 yd × 15 yd = 120 yds²
V = 0.5 × 16 yd × 15 yd = 120 yds²
W = 16 yd × 16 yd = 256 yds²
V = 0.5 × 16 yd × 15 yd = 120 yds²
X = 0.5 × 16 yd × 15 yd = 120 yds²
A = 5 in × 10 in = 50 in²
B = 10 in × 12 in = 120 in²
C = 5 in × 12 in = 60 in²
D = 5 in × 10 in = 50 in²
E = 5 in × 12 in = 60 in²
F = 10 in × 12 in = 120 in²
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when you go to another country you might need to exchange United States Dollars for the local countries currency. For example if you go to south korea, you can get 780 Won for $1.00. How many dollars would I expect to get if I exchanged 98,000 Won.