One number is 5 more than 3 times another number.the sum of the numbers is 45. find the numbers
Answer:
35 and 10
Step-by-step explanation:
Let m and n be the numbers
m is 5 more than 3 times n can be written as
m = 3n + 5 ... (1)
Sum of numbers is 45 so m + n = 45 .or
m = 45 - n ... (2)
Equating RHS of (1) and (2) gives us
3n + 5 = 45 - n
Collecting like terms
3n + n = 45 -5
4n = 40
n = 10
Therefore m = 45-10 = 35
Quick Check
In (1) substitute for m and n,
LHS is m = 35
RHS = 3 * 10 + 5 = 35
f(x) = 5x³ – 2r²
g(x) 3r -7
Answer:
-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9-9Question 17 of 25
how many solutions does the following system of equations have?
y=5/2x+2
2y=5x+4
a. zero
b. one
c.infinitely many
d. two
Answer:
c
Step-by-step explanation:
y = [tex]\frac{5}{2}[/tex] x + 2 → (1)
2y = 5x + 4 ( divide through by 2 )
y = [tex]\frac{5}{2}[/tex] x + 2 → (2)
the 2 equations are the same and will have infinitely many solutions
Select the correct answer. Which system of equations is represented by this graph? A graph has two diagonal curves. A curve declines through (negative 1, 5), and (2 point 3, negative 5). A curve declines through (negative 5, negative 2) and (2 point 3, negative 5). Both curves intersect at (2 point 3, negative 5). A. B. C. D.
The system of equations represented by the attached graph is y = (x + 3)^2 - 2 and y = -x + 1
How to determine the system of equations?This question will be answered using the attached graph
The curve
The curve is a quadratic function, and it has the following features:
Vertex, (h, k) = (-3, -2)
Point (x, y) = (-1, 2)
A quadratic function is represented as:
y = a(x - h)^2 + k
So, we have:
y = a(x + 3)^2 - 2
Substitute (x, y) = (-1, 2)
2 = a(-1 + 3)^2 - 2
This gives
2 = 4a-2
Solve for a
a = 1
Substitute a = 1 in y = a(x + 3)^2 - 2
y = (x + 3)^2 - 2
The line
The line is a linear function, and it has the following features:
Point (x1, y1) = (-1, 2)
Point (x2, y2) = (-6, 7)
The linear function is calculated as:
y = (y2 - y1)/(x2 - x1) *(x- x1) + y1
So, we have:
y = (7 -2)/(-6 +1) *(x + 1) + 2
Evaluate the quotient
y = -1(x + 1) + 2
Expand
y = -x -1 + 2
y = -x + 1
Hence, the system of equations represented by the attached graph is y = (x + 3)^2 - 2 and y = -x + 1
Read more about system of equations at:
https://brainly.com/question/18888202
#SPJ1
31. Lefties Find the sample size needed to estimate the percentage of California residents who are left-handed. Use a margin of error of three percentage points, and use a confidence level of 99%. a. Assume that pn and qn are unknown. b. Assume that based on prior studies, about 10% of Californians are left-handed. c. How do the results from parts (a) and (b) change if the entire United States is used instead of California
a. The required sample size when pn and qn are unknown then n = 1844
b. The required sample size when about 10% of Californians are left-handed is n = 664
c. There would have been no effect on parts a and b if entire US has been chosen
According to statement
a. No estimate of proportion is given so we will assume:
{p} = {q} = 0.5
For 99% confidence, z = 2.576
E = 0.03
Hence, Required sample size
n = (0.5)*(0.5)*(2.576/0.03)^2
n = 1844
b. {p} = 0.10
{q} = 1 - {p}
{q} = 1 - 0.10
{q} = 0.90
For 99% confidence, z = 2.576
E = 0.03
Hence, Required sample size n = (0.1)*(0.9)*(2.576/0.03)^2 = 664
c. There would have been no effect on parts a and b if entire US has been chosen because minimum sample size required is not dependent on population size.
Learn more about PERCENTAGE here https://brainly.com/question/24304697
#SPJ4
On a coordinate plane, 2 trapezoids are shown. Trapezoid M O N P has points (negative 5, 4), (negative 2, 5), (negative 2, 2), and (negative 5, 3). Trapezoid C D E F has points (3, negative 5), (4, negative 5), (5, negative 2), (2, negative 2).
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. Which congruency statement applies to the trapezoids?
CDEF ≅ NPOM
CDEF ≅ MNPO
CDEF ≅ NMOP
CDEF ≅ MOPN
A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal. The correct option is C.
What is a Trapezoid?A trapezoid is a quadrilateral which is having a pair of opposite sides as parallel and the length of the parallel sides is not equal.
Trapezoid CDEF was reflected across the x-axis followed by a 90° rotation about the origin to create the other trapezoid shown on the graph. The congruency statement that applies to the trapezoids is CDEF ≅ NMOP.
Hence, the correct option is C.
Learn more about Trapezoid:
https://brainly.com/question/8643562
#SPJ1
When 1,2504 is written in its simplest radical form, which value remains under the radical?
O 10
O 6
O 5
02
The value that remains under the radical is 2
How to determine the value under the radical?The correct expression in the question is:
1250^4
This can be rewritten as:
[tex]\sqrt[4]{1250}[/tex]
Express 1250 as product
[tex]\sqrt[4]{(2 * 5^4)}[/tex]
Expand the expression
[tex]\sqrt[4]{2} * \sqrt[4]{5^4}[/tex]
Simplify
[tex]\sqrt[4]{2} * 5[/tex]
Evaluate the product
[tex]5\sqrt[4]{2}[/tex]
Hence, the value that remains under the radical is 2
Read more about radical expressions at:
https://brainly.com/question/3008670
#SPJ1
At a football match, there were 250 more men than women. The number of children was twice the number of women and the number of men was twice the number of women and children combined. How many people were at the match.
Answer:
450 people were at the match
Step-by-step explanation:
So let's make equation :
W = women
M = Men
C = Children
First equation :
M = W + 250
Second equation :
C = 2W
Third equation :
M = 2(W+C)
Let's substitute the second equation into the third :
M = 2(W + 2W)
M = 2W + 4W
M = 6W
Let's substitute this equation into the first one :
6W = W + 250
5W = 250
W = 50
Now we know that that there were 50 women at the match and can substitute this value for the first equation and then the second :
M = 50 + 250
M = 300
This means that there must have been 300 men at the match.
C = 2(50)
C = 100
This means that there must have been 100 children at the match.
Adding all values together gives us :
50 + 300 + 100 =
450 people were at the match
Hope this helped and have a good day
HELPPPPPPP PLEASEEEEEEE
Find the solutions of the quadratic equation:
Answer:
Answer A is correct
Step-by-step explanation:
Let us use completing square method for this.
[tex]x^{2} -5x -10=0\\\\x^{2} -5x=10\\\\x^{2} -5x+\frac{25}{4}=10+ \frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{10*4}{1*4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40}{4} +\frac{25}{4}\\\\ (x+\frac{5}{2}) ^{2} =\frac{40+25}{4} \\\\(x+\frac{5}{2}) ^{2} =\frac{65}{4} \\\\(x+\frac{5}{2}) = \±\sqrt{\frac{65}{2} }\\\\(x+\frac{5}{2}) =\±\frac{\sqrt{65}}{4}\\\\x=\±\frac{\sqrt{65}}{4}-\frac{5}{2}[/tex]
∴ [tex]x=-\frac{5}{2} \±\frac{\sqrt{65}}{4}[/tex]
Which graph represents an exponential function?
The first graph is the exponential function.
What is exponential function?The exponential function serves as the positive-valued function with respect to real variable. and the values denoted as X which is exponential is all real numbers.
Analyzing the first graph, moving down the graph, we can see that x value increases.
Learn more about exponential function at:
https://brainly.com/question/12394974
#SPJ1
Answer:
First Graph
Step-by-step explanation:
Edge
help me please im in a rush
Answer:
390 m^2
Step-by-step explanation:
So let's start by finding the surface area of the two triangles on the side. Generally the area of a triangle can be calculated as: [tex]\frac{1}{2}bh[/tex]. but since there is two of them, we can calculate the area of both of them by simply canceling out the 1/2 to a 1. So the area of both triangles are 12 m * 5m as given in the diagram. This gives you 60m^2 area for both triangles on the side
Now let's calculate the rectangle on the top. It has a width and length of 13 and 11 m. So multiply these together to get: 143 m^2
Now let's calculate the rectangle that's on the bottom, it has the dimensions 11 and 12m and multiplying these together gets you: 132 m^2\
Now calculate the rectangle all the way in the back, it has the dimensions 5 and 11m, multiplying these together gets you 55 m^2.
Now add all these together: 60m^2 + 143m^2 + 132m^2 + 55m^2 = 390m^2
Two systems of equations are shown:
System A System B
6x + y = 2 2x − 3y = −10
−x − y = −3 −x − y = −3
Which of the following statements is correct about the two systems of equations?
The value of x for System B will be 4 less than the value of x for System A because the coefficient of x in the first equation of System B is 4 less than the coefficient of x in the first equation of System A.
They will have the same solution because the first equations of both the systems have the same graph.
They will have the same solution because the first equation of System B is obtained by adding the first equation of System A to 4 times the second equation of System A.
The value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical.
The correct statement is that the value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. Option D
How to determine the right statement
6x + y = 2 2x − 3y = −10 System A
-x − y = −3 −x − y = −3 System B
Let;s solve for x and y in system A
6x + y = 2
Make 'y' the subject
y = 2-6x
Substitute in the other equation
-x -y = -3
-x - (2-6x) = -3
-x -2+6x = -3
Collect like terms
5x = -3+2
x = -1/5
Substitute in y = 2-6x to find 'y'
y = 2- 6(-1/5)
y = 2+ 6/5
y = [tex]\frac{10+ 6}{5}[/tex]
y = 16/5
For system B
-x-y = -3
Make y subject, we have
-x + 3 = y
y = -x + 3
Substitute in the other equation, we have
2x − 3y = −10
2x - 3(-x+3) = -10
2x + 3x -9 = -10
Collect like terms
5x -9 = -10
5x = -10 + 9
x = 1/5
Substitute into y = -x + 3 to find 'y'
y = -(1) + 3
y = 2
Thus, the correct statement is that the value of x for System A will be equal to the value of y for System B because the first equation of System B is obtained by adding −4 to the first equation of System A and the second equations are identical. Option D
Learn more about simultaneous equations here:
https://brainly.com/question/16863577
#SPJ1
which inequality represents all values of x for which the quotient below is defined? sqrt 7x^2 / sqrt3x
Answer:
The Answer is x>0
Given the domain {-2, 1, 5}, what is the range for the relation 4x + y = 3?
Answer:
Step-by-step explanation:
Domain is the set of all possible inputs (x) for the function f(x)
The range is the set of all possible values for that domain
This function is 4x + y = 3 which can be re-written as y = 3-4x
Plug in each of the domain values and you will get the range
For -2 : y = 3-4(-2) = 3 + 8 = 11
For 1: y = 3-4(1) = -1
For 5: y = 3-4(5) = -17
So range is {-17, -1, 11}
5 Quick algebra 1 questions for 50 points!
Only answer if you know all 5, Tysm! :)
The equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
How to determine the equations?When a linear equation is represented as:
Ax + By = C
The slope (m) is:
m = -A/B
When the linear equation is represented as:
y = mx + c
The slope is m
A line perpendicular to a linear equation that has a slope of m would have a slope of -1/m
Using the above highlights, the equations of the lines are:
6. y = -2x + 5; (2, 7)
The slope is:
m = -2
The perpendicular slope is:
n = 1/2
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/2(x - 2) + 7
Evaluate
y = 1/2x - 1 + 7
This gives
y = 1/2x + 6
7. y = -5; (11, 15)
The slope is:
m = 0
The perpendicular slope is:
n = 1/0 = undefined
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 15
8. Graph ; (-12, 10)
The slope is:
m = (y2 - y1)/(x2 - x1)
Using the points on the graph, we have:
m = (2 - 3)/(3 - 4)
m = 1
The perpendicular slope is:
n = -1
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = -1(x + 12) + 10
y = -x - 12 + 10
Evaluate
y = -x - 2
9. y = -1/6x + 1; (-2, -9)
The slope is:
m = -1/6
The perpendicular slope is:
n = 6
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 6(x + 2) - 9
Evaluate
y = 6x + 12 - 9
This gives
y = 6x + 3
10. 6x + 2y = 14; (12, 0)
The slope is:
m = -6/2
m = -3
The perpendicular slope is:
n = 1/3
The equation of the perpendicular line is:
y = n(x - x1) + y1
This gives
y = 1/3(x - 12) + 0
Evaluate
y = 1/3x - 4
Hence, the equations of the perpendicular lines are: y = 1/2x + 6, y = 15, y = -x - 2, y = 6x + 3 and y = 1/3x - 4
Read more about linear equations at:
https://brainly.com/question/13763238
#SPJ1
How many units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$
56 units are in the sum of the lengths of the three altitudes in a triangle with sides $7,$ $24,$ and $25$
Properties of triangles are:
A triangle has three sides and three angles.
The sum of the angles of a triangle is always 180 degrees.
The exterior angles of a triangle always add up to 360 degrees.
The sum of consecutive interior and exterior angle is supplementary.
How to solve?Given:
Height: ha = 7
Height: hb = 24
Height: hc = 25
Sum to sides is:
25 +7 + 24 =56 units.
Learn more about Triangles:
https://brainly.com/question/4313883
#SPJ4
for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).
Answer:
k = 18=========
GivenLine 13x - ky + 7 = 0Line 2Passing through the points (4, 3) and (5, - 3)To findThe value of k, if the lines are perpendicularSolutionWe know the perpendicular lines have opposite reciprocal slopes, that is the product of their slopes is - 1.
Find the slope of line 1 by converting the equation into slope-intercept from standard form:
Info:
standard form is ⇒ ax + by + c = 0, slope - intercept form is ⇒ y = mx + b, where m is the slope3x - ky + 7 = 0ky = 3x + 7y = (3/k)x + 7/kIts slope is 3/k.
Find the slope of line 2, using the slope formula:
m = (y₂ - y₁)/(x₂ - x₁) = (-3 - 3)/(5 - 4) = - 6/1 = - 6We have both the slopes now. Find their product:
(3/k)*(- 6) = - 1- 18/k = - 1k = 18So when k is 18, the lines are perpendicular.
Sam runs 36 km in 2.5 hours, how many km does he run per hour
Answer:
Sarah runs at 14.4km/h
Step-by-step explanation:
36km = 2.5 hours
/ = per or divide
36km/2.5hours = 36 divided by 2.5 = 14.4km/h
Which of the following is a valid exclusion for the algebraic fraction 8ab^2x/4a^2b - 8ab^2
A. a=/ 0, b =/ 0, a = / b
B. a = / 0, b =/ 0
C. a =/ 0, b =/ 0, a = / 2b
D. b = / 0, a = / b
The valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b
How to determine the valid exclusion?The expression is given as:
8ab^2x/4a^2b - 8ab^2
Set the denominator to 0
4a^2b - 8ab^2 = 0
Divide through by 4ab
a - 2b = 0
Add 2b to both sides
a = 2b
Hence, the valid exclusion of the algebraic fraction is (c) a =0, b =0, a =2b
Read more about algebraic fraction at:
https://brainly.com/question/4344214
#SPJ1
What is the solution to the system of equations?
y = 2/3x + 3
x =-2
[-2, -15/2 ]
[-2, 5/3]
(-2, 11/6
(-2, 13/3)
Answer:
(- 2, [tex]\frac{5}{3}[/tex] )
Step-by-step explanation:
y = [tex]\frac{2}{3}[/tex] x + 3 → (1)
x = - 2
substitute x = - 2 into (1)
y = [tex]\frac{2}{3}[/tex] × - 2 + 3 = - [tex]\frac{4}{3}[/tex] + [tex]\frac{9}{3}[/tex] = [tex]\frac{5}{3}[/tex]
solution is (- 2, [tex]\frac{5}{3}[/tex] )
Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
3. 72,162
Answer:
The greatest common factor of 72 and 162 is 18.
Step-by-step explanation:
In my opinion, one of the easier ways to find the greatest common factor of two numbers is to get the prime factors of both and multiply the common ones. The prime factorization of 72 is 2*2*2*3*3, and the prime factorization of 162 is 2*3*3*3*3 (you can make a factor tree for both of these numbers to verify this). The common primes factors for both of these numbers are 2, 3, and 3 (both 72 and 162 have one 2 and at least two 3s). 2*3*3 is 18, which is the greatest common factor.
Question 1 of 5
Select the correct answer.
Which function has a domain of (-♾, ♾)and a range of (-♾, 4)?
PLEASE HELP
A: f(x) = -x^2 + 4
B: f(x) = 2^x +4
C: f(x) = -4x
D: f(x) = x + 4
Answer: A
Step-by-step explanation:
A) Correct. [tex]x^2 \geq 0 \implies -x^2 \leq 0[/tex]
B) Wrong. [tex]2^x > 0[/tex], so the range is [tex](4, \infty)[/tex]
C) Wrong. Linear functions have a range of all real numbers.
D) Wrong. Same logic as C.
what is y? i am having trouble figuring out what y is
Answer:
[tex]\sf \boxed{\bf y =5\sqrt{22}}[/tex]
Step-by-step explanation:
45° - 45° - 90° triangle:The ratio of sides of 45 - 45 - 90 triangle is a : a : a√2.
a is the side opposite to 45°.
From the figure, a = 5√11
The side opposite to 90° is a√2.
y = a√2
[tex]\sf = 5\sqrt{11} * \sqrt{2}\\\\ = 5*\sqrt{11*2}\\\\ = 5\sqrt{22}[/tex]
Please help me to find the value of x and y . As fast as possible....
Answer:
Step-by-step explanation:
Answer:
y = 40°
z = 140°
x = 100°
Information:
(i) Sum of interior angles of a triangle sum ups to 180°
(ii) On a straight line, the angles sum up to 180°
(iii) One exterior angle is equal to two opposite interior angles.
Solve for zHere the exterior angle theorem applies.
∠z = 120° + 20°
∠z = 140°
Solve for yFind the angle C. Here angles lie on a straight line.
∠? + 120° = 180°
∠? = 180° - 120° = 60°
80°, 60° and y are interior angles of a triangle.
y + 80°+ 60° = 180°
y = 180° - 140°
y = 40°
Solve for x∠? = 40° (vertically opposite angle)
Now,
y + x + 40° = 180°
40° + x + 40° = 180°
x = 100°
What is the answer to the question below
The distance between the two given points coordinates is; Option C: √85
How to find the distance between two coordinates?Formula for the distance between two coordinates is;
d = √((x₂ - x₁)² + (y₂ - y₁)²)
We are given the coordinates as;
(-2, 3) and (5, -3). Thus;
d = √((-2 - 5)² + (-3 - 3)²)
d = √(49 + 36)
d = √85
Read more about distance between two coordinates at; https://brainly.com/question/7243416
#SPJ1
Consider the following figure. (Note that the figure is not drawn to scale.) G 52° 56° 69° I 56° H Order the side lengths FG, GI, FH, GH, and IH from least to greatest. HELP NOW!!!!!
The order of the side lengths from least to greatest is; GH< IH< FG< GI< FH.
What is the order of the side lengths from least to greatest?As with other closed geometric figures, the shortest side length is opposite the smallest angle measure while the longest side length, is opposite the greatest angle measure.
Hence, it follows from the statement above that the order of side lengths is; GH< IH< FG< GI< FH.
Read more on angle measures and side lengths;
https://brainly.com/question/23272269
#SPJ1
Geometry question I need help with the true or false
Answer:
See below
Step-by-step explanation:
SAS says the two triangles are congruent
so side 6x-4 = 3x+8 then x = 4
x= 4 true
x = 3 false ( because we just found it = 4)
Pythag theorem says QT
(6x-4)^2 = QT^2 + 12^2
( 6(4)-4)^2 = 12 ^2 + QT^2
400 -144 = QT^2
QT = 16 true
what type of polynomial is -3
Answer:
a monomial, a constant
Step-by-step explanation:
It has only 1 term, so it's a monomial.
Also, the term is a constant.
What are the zeros of this function?
A. X=2 and x=-4
B. x=0 and x=4
C. X=0 and x=2
D. X=0 and x=-4
Answer:
The answer is B: x = 0 and x = 4
Step-by-step explanation:
The zeroes of a function are the x-intercepts, or the x values of the points that are on the x-axis. (The x-axis is the numbered horizontal line.)
One of the zeroes passes through the origin, which is (0,0). The other point is right before the number 5 on the x axis, which means that the point is (0, 4). If you look at the x-values of the ordered pairs of the zeroes, that's the answer.
(x, y)
Please help me figure out where they all belong to
The values of the trigonometric functions are
[tex]sin \theta = \frac{12}{13}[/tex]
[tex]cos \theta = \frac{5}{13}[/tex]
[tex]tan \theta = \frac{12}{5}[/tex]
[tex]cot\theta = \frac{5}{12}[/tex]
[tex]csc\theta = \frac{13}{12}[/tex]
Trigonometric functionsFrom the question, we are to determine the values of the given trigonometric functions
From the given information,
[tex]sec \theta =\frac{13}{5}[/tex]
∴ [tex]\frac{1}{cos \theta} =\frac{13}{5}[/tex]
[tex]cos \theta = \frac{5}{13}[/tex]
Thus,
Adjacent = 5
Hypotenuse = 13
Opposite = ?
Using the Pythagorean theorem
|Opp|² = |Hyp|² - |Adj|²
|Opp|² = 13² - 5²
|Opp|² = 169 - 25
|Opp|² = 144
|Opp| = √144
|Opp| = 12
∴ Opposite = 12
Thus,
By using SOH CAH TOA
[tex]sin \theta = \frac{12}{13}[/tex]
[tex]tan \theta = \frac{12}{5}[/tex]
[tex]cot\theta = \frac{1}{tan\theta}[/tex]
∴ [tex]cot\theta = \frac{5}{12}[/tex]
[tex]csc\theta = \frac{1}{sin\theta}[/tex]
∴ [tex]csc\theta = \frac{13}{12}[/tex]
Hence, the values of the trigonometric functions are
[tex]sin \theta = \frac{12}{13}[/tex]
[tex]cos \theta = \frac{5}{13}[/tex]
[tex]tan \theta = \frac{12}{5}[/tex]
[tex]cot\theta = \frac{5}{12}[/tex]
[tex]csc\theta = \frac{13}{12}[/tex]
Learn more on Trigonometric functions here: https://brainly.com/question/13276558
#SPJ1