Answer:
y = 4x + 5 and y = 4x - 5Step-by-step explanation:
(1) y = 4x + 5 and (2) y = 4x - 5
substitute (1) to (2):
4x + 5 = 4x - 5 subtract 4x from both sides
5 = -5 FALSE (no solution)
(1) y = 4x + 5 and (2) 2y = 8x + 10
substitute (1) to (2):
2(4x + 5) = 8x + 10 divide both sides by 2
4x + 5 = 4x + 5 subtract 4x from both sides
5 = 5 TRUE (infinitely many solutions)
(1) y = 4x + 5 and (2) y = x + 5
substitute (1) to (2):
4x + 5 = x + 5 subtract 5 from both sides
4x = x subtract x from both sides
3x = 0 divide both sides by 3
x = 0
Put it to (2):
y = 0 + 5 = 5
One solution (0, 5)
(1) y = 4x + 5 and (2) y = 8x + 10
substitute (1) to (2):
4x + 5 = 8x + 10 subtract 5 from both sides
4x = 8x + 5 subtract 8x from both sides
-4x = 5 divide both sides by (-4)
x = -1.25
Put it to (1):
y = 4(-1.25) + 5 = -5 + 5 = 0
One solution (-1.25, 0)
Boston Terriers weigh up to 25 lb suppose a puppy of this breed weighs 15 pounds write and solve an inequality to show how much more the dog could probably white show the work
Answer:
15+x<_25
Step-by-step explanation:
however much weight the puppy gains (x) can not be greater than 25 but can be equal to 25
Answer:
[tex]15+x\leq 25[/tex]
So, [tex]x\leq 10[/tex]
Step-by-step explanation:
Boston Terriers weigh up to 25 lb.
Suppose a puppy of this breed weighs 15 pounds.
Let the puppy can weigh 'x' pounds more.
So, [tex]x=25-15=10[/tex]
But as it is given the maximum weight can be 25 pounds, so the puppy can weigh a maximum of 10 pounds more.
Given by :
[tex]15+x\leq 25[/tex]
So, [tex]x\leq 10[/tex]
It’s Choose More than one answer Just to let you know ..and can someone please help ..please
Answer:
Step-by-step explanation:
Answer x = 0
1 < 0 and 13<0
Rationalize the denominator and simplify
12/√7+2
Answer:
The answer is 4√7 - 8
Step-by-step explanation:
12/√7+2
Rationalize the denominator
=12/7+2 * √7-2/√7-2
=12√7-24/7-4
=12√7-24/3
By taking common from numerator we get
=12(√7-2)/3
=4√7-8
Answer:
The answer is 4√7 - 8
Step-by-step explanation:
Positive integer A has 2 different prime factors: p and q (p<q) such that A = pq. Positive integer B is greater than A and the quotient A^2/B is an integer. How many possible values of B are there? PLEASE GIVE AN EXPLANATION WITH YOUR ANSWER!
Answer:
4
Step-by-step explanation:
The integer A^2 will have 9 divisors:
1, p, q, p^2, pq, q^2, p^2q, pq^2, p^2q^2
Of these, the last 4 are greater than A. Hence there will be these 4 values of B.
Answer:
it removed body waste like and instructions
What makes a trapezoid an isosceles trapezoid?
A. Its legs are congruent.
B. its bases are congruent
C. Its opposite angles are congruent.
D. Its diagonals bisect each other
Answer:
A. Its legs are congruent.
Step-by-step explanation:
It is a parallelogram if ...
the bases are congruent,opposite angles are congruent, orthe diagonals bisect each other.Alexis took an elevator one floor down from the lobby of her office building to the parking garage. Then she took the elevator back up 5 floors to her office. She described her movement with this expression: 1+5 What was Alexis’ error? She should have used –1 for moving below the lobby. She should have used –5 for moving up 5 floors. She should have used –1 for her movement down and –5 for her movement up. She should have started at zero and then added 6.
Answer:
Her mistake was that she should have used –1 for moving below the lobby.
Step-by-step explanation:
Lets denote the lobby as Floor zero (0)
- if you go up, you add a positive value to this quantity.
- if you go down, you add a negative value to this quantity.
Lets assume that moving through each floor is equivalent to advancing one unit
* She first took an elevator one floor down
(-1)
Then she took the elevator back up 5 floors to her office
(+5)
Her movement is described by the expression
(-1) + (5)
Her mistake was that she should have used –1 for moving below the lobby.
Answer:
A
Step-by-step explanation:
What is the solution to the equation
Answer:
The solution of given equation 5(x - 6) = 2(x + 3) is given by,
x = 12
Step-by-step explanation:
It is given that,
5(x - 6) = 2(x + 3)
To find the solution of given equation
5(x - 6) = 2(x + 3)
5x - (5 * 6) = 2x + (2 * 3)
5x - 30 = 2x + 6
5x - 2x = 6 + 30
3x = 36
x = 36/3
x = 12
Therefore the solution of given equation is,
x = 12
A line has a slope of 1/4 and passes through point (0.4,-1/2). What is the value of the y-intercept?
Answer: The value of the y-intercept is [tex]-\frac{3}{5}[/tex]
Step-by-step explanation:
The equation of the line in Slope-intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
In this case we know that the line passes through point [tex](0.4,-\frac{1}{2})[/tex] and has a slope of [tex]\frac{1}{4}[/tex]. Then we can substitute the following values into [tex]y=mx+b[/tex]:
[tex]x=0.4\\\\y=-\frac{1}{2}\\\\m=\frac{1}{4}[/tex]
Then:
[tex]-\frac{1}{2}=\frac{1}{4}(0.4)+b[/tex]
And finally, we must solve for "b":
[tex]-\frac{1}{2}=\frac{1}{4}(0.4)+b\\\\-\frac{1}{2}-\frac{1}{10}=b\\\\b=-\frac{3}{5}[/tex]
For this case we have that by definition, the slope-intersection equation of a line is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
y: It is the cut point with the "y" axis
They tell us as data that:
[tex]m = \frac {1} {4}[/tex]
So, the equation is:
[tex]y = \frac {1} {4} x + b[/tex]
We substitute the given point to find "b":
[tex]- \frac {1} {2} = \frac {1} {4} (0.4) + b\\- \frac {1} {2} = \frac {0.4} {4} + b\\b = - \frac {1} {2} - \frac {0.4} {4}\\b = -0.5-0.1\\b = -0.6[/tex]
Thus, the cut point with the y axis is -0.6
Answer:
[tex]b = -0.6[/tex]
Over which interval is the graph of f(x)= -x^2 +3x+ 8 increasingly
Answer:
x<1.5
Step-by-step explanation:
The equation is
[tex]f(x)=-x^2+3x+8[/tex]
Use a graphing tool to find the vertex of the parabola.When you get the vertex from the graph, you can now write the increase as ; all x-values less than the x-value of the vertex value in the graph
From the graph, the vertex is at (1.5,10.25), the parabola opens down with maximum value y=10.25
The interval of increase is x<1.5
Answer:
[tex]x \geq \frac{3}{2}[/tex]
Step-by-step explanation:
First, the first derivative of the function is computed to distinguish which interval is increasing.
[tex]f'(x) = -2\cdot x + 3[/tex]
An interval is increasing only if slope is increasing as long as x increases. Then, it is quite evident that curve is increasing for:
[tex]x \geq \frac{3}{2}[/tex]
The base of a 11 foot ladder is 2 feet from a building . If the ladder reaches the flat root , how tall is the building ?
Using the Pythagorean theorem with the length of the ladder as the hypotenuse and the base distance as one side, we calculate the height of the building to be approximately 10.82 feet.
Explanation:The student's question can be solved using the principles of the Pythagorean theorem, which relates the lengths of the sides of a right triangle.
In this scenario, the ladder, the building, and the ground form a right triangle.
The ladder serves as the hypotenuse, the height of the building is the opposite side, and the distance from the ladder's base to the building is the adjacent side.
To find the height of the building, we can set up the equation using the Pythagorean theorem as follows:
a2 + b2 = c2
where a is the distance from the base of the ladder to the building (2 feet), b is the height of the building, and c is the length of the ladder (11 feet).
Plugging in the values we have:
22 + b2 = 112,4 + b2 = 121,b2 = 121 - 4,b2 = 117.
Therefore, the height of the building is:
b = √117 ≈ 10.82 feet.
The building is approximately 10.82 feet tall.
Identify the linear term in the function of y = 2x2 − 5x − 12
Answer:
The linear term is -5x
Step-by-step explanation:
The linear term is the term that has the degree equal to 1.
The given function is
y = 2x^2 − 5x − 12
here 2x^2 = quadratic term i.e having degree 2
-5x = linear term i.e having degree 1
-12 = constant
so, The linear term is -5x
Multiply each pair of factors. Type the product in
the space provided
(6 + 3i)(6 - 3i) =
[tex]\bf \stackrel{\textit{difference of squares}}{(6+3i)(6-3i)}\implies (6)^2-(3i)^2\implies \stackrel{\textit{recall }i^2=-1}{36-(3^2 i^2)}\implies 36-(9\cdot -1) \\\\\\ 36+9\implies 45[/tex]
Step-by-step explanation:
6*6 - 6*3i + 6*3i -3i*3i
36-18i+18i-9i^2
36-9(-1)= 36+9= 45
1. y = sin? (In x). Find dy
Show your work. en nuov vlomia
A.
sin (In x2)
х
cos? (In x)
c. sin (In x) cos(Inx)
D.
2 sin (In x) cos(In x)
E. None of the above.
Answer:
dy/dx= cos(ln(x))/x
Step-by-step explanation:
y=sin(ln(x)) given
We have to use chain rule to differentiate!
Let u=ln(x) then du/dx=1/x
So we have
if y=sin(ln(x)) then y=sin(u) and dy/dx=dy/du * du/dx=cos(u) *1/x
where again u=ln(x) so
dy/dx=cos(ln(x)) *1/x
dy/dx=cos(ln(x))/x
I hope I have the right intepretation because I do see a ? in between sin and (ln(x)) .
find the slope of the line that contains the following points. r(-2, 4), s(6, -2)
Finding the slope using two points:
The formula for slope is
[tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
In this case...
[tex]y_{2} =-2\\y_{1} =4\\x_{2} =6\\x_{1} =-2[/tex]
^^^Plug these numbers into the formula for slope...
[tex]\frac{-2 - 4}{6 - (-2)}[/tex]
[tex]\frac{-6}{8}[/tex]
^^^Can be further simplified to...
[tex]\frac{-3}{4}[/tex]
^^^This is your slope
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
[tex]{\displaystage\boxed{\frac{-3}{4}}[/tex]
Step-by-step explanation:
Slope formula:
↓
[tex]\displaystyle\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\displaystage y_2=(-2)\\\displaystage y_1=4\\\displaystage x_2=6\\\displaystage x_1=(-2)\\[/tex]
[tex]\displaystage \frac{-2-4}{6-(-2)}=\frac{-6}{8}=\frac{-6\div2}{8\div2}=\frac{-3}{4}[/tex]
-3/4 is the correct answer.
I hope this helps you, and have a wonderful day!
This triangle below has an area of 24 units squared. Find the missing side.
b*h/2 is the formula for area
8*h= 24
24*2= 48
48/8= 6
6 is the height/ missing side
The value of x for the given right angle triangle such that its area is 24 units² will be 8.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle.
The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.
As per the given triangle,
The area of right angle triangle = (1/2)8 × x
(1/2)8 × x = 24
x = 24/4 = 8
Hence "The value of x for the given right angle triangle such that its area is 24 units² will be 8".
For more about triangles,
https://brainly.com/question/2773823
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whats the exanded expression for -7(k-3)
Answer:
-7k+21
Step-by-step explanation:
Distributive Property:
↓
[tex]A(B+C)=AB+AC[/tex]
A=-7, B=K, and C=3
-7k+7*3
Multiply by the numbers from left to right to find the answer.
7*3=21
-7k+21 is the correct answer.
Which of the following are solutions to | x+3 = 4x - 7? Check all that apply.
Answer:
x=5/4, 3/10
Answer:B. x=10/3
Step-by-step explanation:
A P E X
Which equation represents a line that passes through (–9, –3) and has a slope of –6?
Answer:
y + 3 = -6(x + 9) - point-slope formy = -6x - 57 - slope-intercept formStep-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
========================================
We have the slope m = -6 and the point (-9, -3).
Substitute:
[tex]y-(-3)=-6(x-(-9))\\\\y+3=-6(x+9)[/tex]
Convert to the slope-intercept form (y = mx + b):
[tex]y+3=-6(x+9)[/tex] use the distributive property
[tex]y+3=-6x-54[/tex] subtract 3 from both sides
[tex]y=-6x-57[/tex]
what is 9+5x-6+2x ???
ANSWER:
7x + 3
let us break the problem into two smaller equations that match-
5x + 2x = 7x
9 - 6 = 3
this leaves you with 7x + 3.
4. Simplify the following expression: (2/5+4/3)/(3/5)
A. 3/14
B. 75/131
C. 26/9
D. 11/144
Answer: [tex]\bold{C.\quad \dfrac{26}{9}}}[/tex]
Step-by-step explanation:
[tex]\bigg(\dfrac{2}{5}+\dfrac{4}{3}\bigg)\div\dfrac{3}{5}\\\\\\\text{According to PEMDAS, the parenthesis must be performed first.}\\\\\bigg[\dfrac{2}{5}\bigg(\dfrac{3}{3}\bigg)+\dfrac{4}{3}\bigg(\dfrac{5}{5}\bigg)\bigg]\div\dfrac{3}{5}\\\\\\\bigg(\dfrac{6}{15}+\dfrac{20}{15}\bigg)\div\dfrac{3}{5}\\\\\\\dfrac{26}{15}\div\dfrac{3}{5}\\\\\\\text{Dividing by a fraction is multiplying by its reciprocal.}\\\dfrac{26}{15}\times\dfrac{5}{3}\\\\\\\text{Simplify.}\\\dfrac{26}{3}\times\dfrac{1}{3}[/tex]
[tex]=\large\boxed{\dfrac{26}{9}}[/tex]
Clara solved the equation 7/3x = −2/3 as shown → 7/3x( 3/7 ) = −2/3 ( 3/7 ) x = −14 What is Clara’s error?
Answer:
The solution is -2/7 not –14.
Answer:
its D
Step-by-step explanation:
Let f(x)=x^2-5x-36.
Enter the x-intercepts of the quadratic function in the boxes.
x= and x=
please help
Answer:
9 and -4
Step-by-step explanation:
Find two numbers that multiply to be -36 and add to be -5.
That is -9 and 4.
So the factored form of x^2-5x-36 is (x-9)(x+4)
So the x-intercepts are 9 and -4
For his long distance phone service, bill pays a $7 monthly fee plus 7 cents per minute. Last month, bill’s long distance bill was $18.27. For how many minutes was bill billed?
Answer:
161 minutes
Step-by-step explanation:
$1827-$7=$11.27
$11.27/.07=161
Answer:
161 minutes
Step-by-step explanation:
Bill pays a monthly fee for his long distance phone service = $7.00
and call charges per minute = 7 cents
1 dollar = 100 cents
Therefore 7 cents = [tex]\frac{7}{100}[/tex] = $0.07
Last month, Bill's long distance bill was $18.27.
Let Bill used the phone service for x minutes
The equation for his uses in minutes :
7.00 +(0.07x) = 18.27
0.07x = 18.27 - 7.00
0.07x = 11.27
x = [tex]\frac{11.27}{0.07}[/tex]
x = 161 minutes
Bill was billed for 161 minutes.
9) Out of the 15 friends that I have, the
proportion of blonds to brunettes is 6 to 9.
Which of the following statements is false?
a) The ratio of the number of
friends to brunettes is 15 to 9
b) The ratio of brunettes to blonds
is 6 to 9
c) The ratio of blonds to the
number of friends is 6 to 15
d) The ratio of brunettes to the
number of friends is 9:15
The answer is b because the ratio is blondes to brunettes.
Follow below steps;
The student asked which statement about the proportions of blonds and brunettes among their 15 friends is false. Given that the proportion of blonds to brunettes is 6 to 9, let's evaluate the options:
Option a) The ratio of the number of friends to brunettes is 15 to 9. This statement is true since there are 15 friends in total and 9 of them are brunettes.
Option b) The ratio of brunettes to blonds is 6 to 9. This statement is false because the proportion of blonds to brunettes is 6 to 9, so the ratio of brunettes to blonds should be 9 to 6.
Option c) The ratio of blonds to the number of friends is 6 to 15. This statement is true because there are 6 blonds out of 15 friends.
Option d) The ratio of brunettes to the number of friends is 9:15. This statement is also true because there are 9 brunettes out of 15 friends.
Therefore, option b is the false statement as the ratio of brunettes to blonds is incorrectly stated as 6 to 9 instead of the correct ratio 9 to 6.
Self-Check
Practice Exercise 4
News cameras take an overhead picture of a part of a crowd at an outdoor event. Journalists then count the number of people in the picture and use the sample to estimate the total number of people in the crowd. This process is an example of
Answer:
cluster system
Step-by-step explanation: For edgunity
This process is an example of cluster system.
The following information should be considered:
A cluster refers to a group of inter-connected computers where it work together for support applications and middleware (e.g. databases). In a cluster, each & every computer is known to be a “node”.learn more: https://brainly.com/question/4804019?referrer=searchResults
The equation c = 6.5h represents the cost, c, of renting a bicycle for h hours. The table below can be used to show the same information.
Cost for Renting Bicycles
Number of Hours (h)
0
2
4
6
Cost (c)
If Francesca rents a bicycle for 2 hours and Phil rents a bicycle for 6 hours, how much more does Phil pay?
Answer:
$26
Step-by-step explanation:
To find your answer, simply plug in Francesca's time and Phil's time to your cost equation.
Francesca can be represented by the following equation:
[tex]c=6.5(2)\\c=13[/tex]
Phil can be represented by the following equation:
[tex]c=6.5(6)\\c=39[/tex]
As such, Francesca pays $13 and Phil pays $39. Next, since you want to find how much more Phil paid, all you have to do is subtract 13 from 39. That will give you $26.
Kelly shares 3 candy bars equally between her 5 friends. What fraction of a candy bar does each friend receive?
A- three fifths candy bar
B- one third candy bar
C- five thirds candy bar
D- one fifth candy bar
Answer:
three fifths candy bar
Step-by-step explanation:
3/1 ÷ 5/1
3/1 × 1/5 = 3/5
Answer:
3 fiths of a candy bar
Step-by-step explanation:
A angle measures 83 degrees what is its supplement?
Answer:
<2 = 97
Step-by-step explanation:
Definition: Supplementary angles are 2 or more angles with the same vertex that add up to 180o
Solution
<1 = 83
<2 = ?
Total = 180o
<1 + <2 = 180 Substitute for angle 1
83 + <2 = 180 Subtract 83 from both sides.
83 - 83 + <2 = 180 - 83 Do the subtraction
<2 = 97 degrees
The supplement of an 83-degree angle is the angle that adds up to 180 degrees with it. By subtracting 83 from 180, we find that the supplement of the angle is 97 degrees.
Explanation:The question is asking for the supplement of an angle that measures 83 degrees. In geometry, the supplement of an angle is the angle that, when added to the original angle, equals 180 degrees. To find the supplement of an 83-degree angle, you subtract 83 from 180.
Step-by-step solution:
Start with the total measure of a straight line, which is 180 degrees.Subtract the given angle from 180 degrees: 180 - 83 = 97 degrees.The supplement of an 83-degree angle is therefore 97 degrees.On the first of each month, Shelly runs a 5k race. She keeps track of her times to track her progress. Her time in minutes is recorded in the table:
Jan 40.55 July 35.38
Feb 41.51 Aug 37.48
Mar 42.01 Sept 40.87
Apr 38.76 Oct 48.32
May 36.32 Nov 41.59
June 34.28 Dec 42.71
Determine the difference between the mean of the data, including the outlier and excluding the outlier. Round to the hundredths place.
39.98
39.22
0.76
1.21
Answer:
0.76
Step-by-step explanation:
The mean of the data including the outlier is:
Mean = (40.55 + 41.51 + 42.01 + 38.76 + 36.32 + 34.28 + 35.38 + 37.48 + 40.87 + 48.32 + 41.59 + 42.71)/12 = 39.98 seconds.
In this case, the outlier comes to be the data: 48.32. If we don't consider that data point, the mean equals:
Mean = (40.55 + 41.51 + 42.01 + 38.76 + 36.32 + 34.28 + 35.38 + 37.48 + 40.87 + 41.59 + 42.71)/11 = 39.22
The difference is: 39.98 - 39.22 = 0.76
Answer:
C . 0.76
Step-by-step explanation:
We are given that on the first of each month , Shelly runs a 5 k race. She keeps track of her times to track her progress. Her time in minutes is recorded in the table:
Jan 40.55 Feb 41.51
March 42.01 Apr 38.76
May 36.32 June 34.28
July 35.38 Aug 37.48
Sept 40.87 Oct 48.32
Nov 41.59 Dec 42.71
We have to find the difference between the mean of the data , including the outlier and excluding the outlier
Outlier: That observation which is different from other observations.
The outlier in the given observations is 48.32 because is different from other observations.
Mean of the data including the outlier
Mean =[tex]\frac{Sum \;of\;observations}{Total\;number\;of\;observations}[/tex]
Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+48.32+41.59+42.71}{12}[/tex]
Mean=[tex]\frac{479.78}{12}[/tex]
Mean=39.982
Mean of the data excluding the outlier
Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+41.59+42.71}{11}
Mean=[tex]\frac{431.46}{11}[/tex]
Mean=39.224
Difference between mean of the data including the outlier and excluding the outlier=39.982-39.224=0.758
Difference between mean of the data including the outlier and excluding the outlier=0.76
Answer Answer:
Step-by-step explanation:
We are given that on the first of each month , Shelly runs a 5 k race. She keeps track of her times to track her progress. Her time in minutes is recorded in the table:
Jan 40.55 Feb 41.51
March 42.01 Apr 38.76
May 36.32 June 34.28
July 35.38 Aug 37.48
Sept 40.87 Oct 48.32
Nov 41.59 Dec 42.71
We have to find the difference between the mean of the data , including the outlier and excluding the outlier
Outlier: That observation which is different from other observations.
The outlier in the given observations is 48.32 because is different from other observations.
Mean of the data including the outlier
Mean =[tex]\frac{Sum \;of\;observations}{Total\;number\;of\;observations}[/tex]
Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+48.32+41.59+42.71}{12}[/tex]
Mean=[tex]\frac{479.78}{12}[/tex]
Mean=39.982
Mean of the data excluding the outlier
Mean=[tex]\frac{40.55+41.51+42.01+38.76+36.32+34.28+35.38+37.48+40.87+41.59+42.71}{11}
Mean=[tex]\frac{431.46}{11}[/tex]
Mean=39.224
Difference between mean of the data including the outlier and excluding the outlier=39.982-39.224=0.758
Difference between mean of the data including the outlier and excluding the outlier=0.76
Answer :C . 0.76