The slope intercept form of the line for (-1,0) and (4,-5) is y = -x -1.
We know that,
Slope intercept form of a line is given by:-
y = mx + c
Where,
m is the slope of the line,
c is the y -intercept of the line and,
(x,y) is the ordered pair of each point on the line
We know that,
m = (-5-(-1))/(4 - 0) = (-5 +1)/4 = -4/4 = -1
Putting (-1,0) in the line, we get
0 = (-1)*(-1) + c
0 = 1 + c
c = -1
Hence, the equation of the line is given by:-
y = -1x -1 = -x - 1
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A group of hikers tracked how long it took to hike a 20-mile trail. They hiked 3.75 miles in 3 hours, 7.5 miles in 6 hours, and 12 miles in 8 hours.
Determine if the relationship between the hikers' distance and time is proportional.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 1.25 miles per hour.
Yes, it is proportional because the ratios for miles per hour are all equivalent to 0.8 miles per hour.
No, it is not proportional because 3.75 miles in 3 hours is not equivalent to 7.5 miles in 6 hours.
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.
Answer:
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.
Step-by-step explanation:
first lets find out how far they hiked per hour3.75 mi in 3 hourswe need to do 3.75÷3= and we get 1.25 mi an hour now we need to do the next oneit is 7.5 mi in 6 hoursso we are gonna do 7.5÷6=and we get 1.25 mi an hournow lets do the last one12 mi in 8 hourswe are gonna do 12÷9=and we get 1.5 mi in an hourso the 3 hours and 6 hour are proportional so it would be: No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.The correct relationship between the hikers distance and time is;
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.
What is Proportional?
Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
A group of hikers tracked how long it took to hike a 20-mile trail.
And, They hiked 3.75 miles in 3 hours, 7.5 miles in 6 hours, and 12 miles in 8 hours.
Now,
Find the proportional as;
For hiked 3.75 miles in 3 hours,
Proportional = 3.75 / 3
= 1.25
For hiked 7.5 miles in 6 hours,
Proportional = 7.5 / 6
= 1.25
For hiked 12 miles in 8 hours,
Proportional = 12 / 8
= 1.5
Thus, The correct relationship between the hikers distance and time is;
No, it is not proportional because 7.5 miles in 6 hours is not equivalent to 12 miles in 8 hours.
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Which function has the domain x greater-than-or-equal-to negative 11?
y = StartRoot x + 11 EndRoot + 5
y = StartRoot x minus 11 EndRoot + 5
y = StartRoot x + 5 EndRoot minus 11
y = StartRoot x + 5 EndRoot + 11
The function y= √(x+11) + 5 has Domain x≥-11 .
The Domain of the function is defined as the set of all possible values , that can be input in the function .
In the question;
it is given that
Option(a)
the function is ,
y = √(x + 11) + 5
the square root is defined only for x≥0,
So, we have x+11≥0
subtracting 11 from both the side , we get
x ≥ -11
hence Domain is x≥-11 .
Option(b)
the function is ,
y = √(x - 11) + 5
we have x-11≥0
Adding 11 to both the side , we get
x ≥ 11
hence Domain is x ≥ 11 .
Option(c)
the function is ,
y = √(x + 5) - 11
we have x+5≥0
subtracting 5 from both the side , we get
x ≥ -15
hence Domain is x ≥ -5 .
Option(d)
the function is ,
y = √(x + 5) + 11
we have x+5≥0
subtracting 5 from both the side , we get
x ≥ -15
hence Domain is x ≥ -5 .
From above we can see that only option(a) has Domain as x ≥ -11.
Therefore , the function y= √(x+11) + 5 has Domain x≥-11 , option(a) is correct .
The given question is incomplete , the complete question is
Which function has the domain x ≥ -11?
(a) y = √(x + 11) + 5
(b) y = √(x - 11) + 5
(c) y = √(x + 5) - 11
(d) y = √(x + 5) + 11
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Answer:
is a
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the graph of quadratic function g is shown on the grid. the coordinates of the x-intercepts, the y-intercepts, and the vertex are integers what is the maximum value of g? A) (0, - 8)B) (- 4,0)C) (- 3, 1)D) (- 2, 0)
SOLUTION:
Case: The minimum value from a graph
Given: Integer values of vertex and intercepts
Required: To find the maximum value of g
Method:
Tracing the maximum point and value from the graph. This is usually the point on the graph where y has its highest value
Final answer:
The maximum value is at (-3, 1)
You are in business and have a product that sells for $10 that 1000 people buy each month. You want to make a profit and wonder whether you should raise the price in increments of a dollar. For each dollar you raise the price, you lose 100 customers. How many dollars can you go up to maximize your profit, or should you go up at all?
Let:
P = Profit
n = Number of increments by $1
R = Revenue
The profit is given by:
[tex]\begin{gathered} P=10+1n \\ P=10+n \end{gathered}[/tex]Therefore, the revenue is:
[tex]R=(10+n)(1000-100n)[/tex]Expand the equation using the distributive property:
[tex]\begin{gathered} R=10000-1000n+1000n-100n^2 \\ R=-100n^2+10000 \end{gathered}[/tex]The maximum profit of this quadratic function is located at the vertex, we can find the vertex as follows:
[tex]\begin{gathered} V(h,k) \\ h=-\frac{b}{2a} \\ a=-100 \\ b=0 \\ k=R(h)=R(0)=10000 \end{gathered}[/tex]The vertex is (0,10000) in another words the maximum profit is achieve if you don't raise the price.
Enter your answer and show all the steps that you use to solve this problem in the space provided.
What is the value of x?
____________________________________________________________________________________________________________
The value of x is 71 degree .
What is isosceles triangle ?Triangles that have two sides at least equally spaced apart are said to be isosceles. As three-sided enclosed polygons with three sides, triangles are known to exist. Depending on the length of their sides, triangles can be categorized as equilateral, isosceles, or scalene.
The three interior angles of a triangle will always have a sum of 180°. A triangle cannot have an individual angle measure of 180°, because then the other two angles would not exist (180°+0°+0°).
So ,
x +x+38 = 180
2x = 180 -38
2x = 142
x = 71
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Danny says 4 < 6, so 204 < 216. Is his reasoning correct? Explain.
As given by the question
There are given that 4<6, so 204<216.
Now,
On the number line, 4 is less tha6 and 204 is also less than 216
Hence, the given reasoning is correct.
If s varies inversely as t and s = 8 when t = 5, find the equation that connects s and t.
We know that:
- s varies inversely as t
- s = 8 when t = 5
And we must find the equation that connects s and t
To find the equation that connects s and t we must use that
In this case, we can say that s = x and t = y. So, our equations would be
[tex]\begin{gathered} st=k \\ \text{ or,} \\ s=\frac{k}{t} \end{gathered}[/tex]Now, knowing that s = 8 when t = 5 we can replace the values in the first equation
[tex]8\cdot5=40[/tex]So, k = 40
Finally, replacing k = 40 in the second equation we obtain
[tex]s=\frac{40}{t}[/tex]ANSWER:
A) s = 40 / t
Steve works at lowes and gets a 10% commission for each appliance he sells. If he sells $5,680 worth of appliances this week, how much will he earn with a base of $1,500
10% commission means that Steve earns 10% of his sales. If he sells $5,680 worth of appliances this week, then he earns 10% of it, which is computed as follows:
[tex]5,680\cdot\frac{10}{100}=568\text{ \$}[/tex]Given that he has a base of $1,500, then he will earn $1,500 + $568 = $2068
which of the following are the solution to -8×2-8=-32?
Write the quadratic function in standard form.G(x) = x2 - 8x
Okay, here we have this:
Considering the provided quadratic function, we are going to rewrite in standard form, so we obtain the following:
So to rewrite the function in standard form we will complete the square:
[tex]\begin{gathered} x^2-8x \\ =x^2-8x+(-4)^2-(-4)^2 \\ =(x-4)^2-(-4)^2 \\ g(x)=(x-4)^2-16 \end{gathered}[/tex]And from this equation we get that the vertex is (4, -16)
Therefore the correct graph is the one in the upper right corner.
unit rate of 3/4 page in 2 minutes unit rate
Quantity 1
30
Unit 1
miles
Quantity 2
2.5
Unit 2
hours
= ?
Answer:
= 12 miles per hour
Showing Work
This is a fraction equal to
30 miles ÷ 2.5 hours
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 2.5
30 miles ÷ 2.5
2.5 hours ÷ 2.5
=
12 miles
1 hour
=
12 miles
hour
= 12 miles per hour
Choose the correct graph of the system of inequalities:y ≥ 5x - 4y < -2x + 3
Given:
The inequalities are,
[tex]\begin{gathered} y\ge5x-4 \\ y<-2x+3 \end{gathered}[/tex]To find:
The correct graphs.
Explanation:
Let us find the intercepts.
For the first inequality,
When x = 0, we get,
[tex]\begin{gathered} y=0-4 \\ y=-4 \end{gathered}[/tex]When y = 0, we get
[tex]\begin{gathered} 0=5x-4 \\ 5x=4 \\ x=0.8 \end{gathered}[/tex]So, the intercepts are
[tex](0.8,0),(0,-4)[/tex]For the second inequality,
When x = 0, we get,
[tex]\begin{gathered} y=0+3 \\ y=3 \end{gathered}[/tex]When y = 0, we get
[tex]\begin{gathered} 0=-2x+3 \\ -2x=-3 \\ x=1.5 \end{gathered}[/tex]So, the intercepts are
[tex](1.5,0),(0,3)[/tex]So, the graph becomes,
to get the paint color moss green, 2 parts violet paint mixed with 3 parts yellow paint. how many parts yellow paint should be mixed with 5 parts violet paint and **EXPLAIN THE ANSWER STEP BY STEP!**
Answer:
7.5 parts yellow
Step-by-step explanation:
The color moss green has violet and yellow paint mixed in the proportion 2 to 3. You want to know the number of parts of yellow paint that should be mixed with 5 parts of violet paint.
ProportionThe proportion can be written different ways. We like to put the unknown value in the numerator. (x is the number of parts of yellow paint)
yellow : violet = 3 : 2 = x : 5
Expressed as fractions, the proportion is ...
[tex]\dfrac{3}{2}=\dfrac{x}{5}\\\\5\times\dfrac{3}{2}=x\qquad\text{multiply by 5}\\\\\dfrac{15}{2}=x=7.5\qquad\text{simplify}[/tex]
7.5 parts yellow paint should be mixed with 5 parts violet paint.
__
Additional comment
If you kept the proportion as violet : yellow, then the unknown value would be in the denominator. The solution to that proportion requires another step. Here, we just needed to multiply by the denominator value to find the unknown.
An ice cream cone has a radius of 10 cm and a slant height of 12 cm what it is the surface area
Surface Area of a Right Circular Cone
Given a cone of radius R and slant height L, the surface area is calculated as follows:
[tex]A=\pi R(R+L)[/tex]We are given the following data:
R = 10 cm
L = 12 cm
Computing the surface area:
[tex]A=\pi *10\text{ cm}(10\text{ cm}+12\text{ cm})[/tex]Operating:
[tex]\begin{gathered} A=\pi *10\text{ cm}(22\text{ cm}) \\ A=220\pi\text{ }cm^2 \end{gathered}[/tex]This is the exact value. The approximate value can be obtained by substituting pi = 3.14:
A ≈ 690.8 square cm
If the m42 = 40, what is the m45?
Answer:
m5 = 140
Step-by-step explanation:
m1 = m2
m1 = 40
m5 + m1 = 180
m5 + 40 = 180
m5 = 140
Reason quantitatively. On a number line, the coordinate of point A is negative and the coordinate of point B is positive. a. When will the midpoint of line AB be positive?b. when will the midpoint of line AB be negative? c. when will the midpoint of line AB be zero?d. when will the distance from A to B be negative?
On a number line, the coordinate of point A is negative and the coordinate of point B is positive.
The mid point is defined as:
[tex]M=\frac{A+B}{2}[/tex]a. When will the midpoint of line AB be positive?
When B>A
b. when will the midpoint of line AB be negative?
When A>B
c. when will the midpoint of line AB be zero?
When:
[tex]\left|A\right|=\left|B\right|[/tex]d. when will the distance from A to B be negative?
Never the distance is not defined as negative by definition of distance.
The distance is a magnitude and for this reason not makes sense say negative distance because is always 0 or positive, if for example we find the distance from A to A is 0 since we are in the same point, but we never say we travel -200 m to reach a city for example.
4(m+5) + 5 > -3m - 2
Answer/Step-by-step explanation:
4(m+5) + 5 > -3m - 2
4m + 20 + 5 > -3m - 2
4m + 25 > -3m - 2
+3m +3m
--------------------------------
7m + 25 > -2
-25 -25
--------------------------------
7m > - 27
÷7 ÷7
----------------
-27
m > ---------
7
(-27/7), ∞)
I hope this helps!
Find the value of x. Round your answer to the nearest tenth. (One number after the decimal place)
We have the following:
We can calculate the value x by means of the Pythagorean theorem that says the following
[tex]h^2=a^2+b^2[/tex]In this case the value of the hypotenuse is x, we replace and we have
[tex]\begin{gathered} x^2=12.8^2+5.3^2 \\ x^2=163.84+28.09 \\ x=\sqrt[]{191.93} \\ x=13.85 \end{gathered}[/tex]The value of x is 13.85
Coach Matt is making dodgeball teams. He has 16 fifth gradets and 36 sixth graders. To be fair, Coach Matt wants there to be the same number of 5th graders and the same of the sixth graders on each team. Can coach Matt make a teams using all the 5th and 6th graders do the statement that explains why or why not .Here are the choices:1. No. 8 is a factor of 36 but not a factor of 162. Yes. 8 is a common factor of 16 and 363. No. 8 is a factor of 16,but not a factor of 264. Yes. 8 is the greatest common factor of 16 and 36
We are ask to choose a staement that explain why and why not, in other words, we are to choose the correct statements
The correct statements are;
No. 8 is a factor of 16 but ot 36
Solve for x. 32-8 = x-6 2 Enter your answer in the box.
Answer:
3x-8=2x-12
x-8=-12
x=-4
Step-by-step explanation:
Answer:
x = -4
Step-by-step explanation:
This question tests on the concept of solving algebraic equationsn, order of operations. (Brackets, × ÷ + -).
Steps below:
[tex] \frac{3x - 8}{2} = x - 6 \\ \frac{3x - 8}{2} (2) = 2(x - 6) \\ 3x - 8 = 2x - 12 \\ 3x - 2x - 8 = 2x - 2x - 12 \\ x - 8 = - 12 \\ x - 8 + 8 = - 12 + 8 \\ x = - 4[/tex]
72 is equal to 80% of a number n. write and solve an equation to find n. write the percent as a decimal
Answer:
n=90
Step-by-step explanation:
80% as a decimal is 0.80
0.80n = 72
n = 72/0.80
n = 90
look on the top and see a answer with apple)
have a nice night!
Gabriel has a coin jar full of nickles and pennies. There are tweleve more pennies than nickles. He has a total of $6.06. Are these statements true or false.
n = number of nickles
p = number of pennies
Therefore,
p = 12 + n
1 nickel = 0.05 dollars
1 penny = 0.01 dollars
Therefore,
[tex]\begin{gathered} n(0.05)+(12+n)0.01=\text{6}.06 \\ 0.05n+0.12+0.01n=6.06 \\ 0.06n+0.12=6.06 \\ \text{0}.06n=6.06-0.12 \\ 0.06n=5.94 \\ n=\frac{5.94}{0.06} \\ n=99 \end{gathered}[/tex]Therefore,
p = 12 + 99 = 111
n = 99
One linear equation for the sytem is p + 5n = 606 is true
The system has one solution is true.
Givin the triangle below which of the following equations correctly represents the relationship between a,b,c
The correct option is A. i.e., [tex]c^2 = a^2 + b^2 - 2ab cos (90)[/tex]°
Given,
From the figure:
The triangle which of the following equations correctly represents the relationship between a ,b, c
Now, According to the question:
The relationship between the three sides of a triangle ABC is:
[tex]c^2 = a^2 + b^2 - 2ab cos (90)[/tex]°
From the diagram,
The angle opposite to c is 90°
Thus, [tex]c^2 = a^2 + b^2 - 2ab cos (90)[/tex]
Hence, The correct option is A. i.e., [tex]c^2 = a^2 + b^2 - 2ab cos (90)[/tex]°
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In an investigation, Detective Cortez discovered a photograph that showed his number one suspect at the scene of the crime. To get a better look, he enlarged the picture by a scale factor of 8/1. If the original photo measured 4 inches by 3.6 inches, what were the dimensions of the enlargement?
The dimensions of the enlargement will be: 32 inches by 28.8 inches.
How do we get the new dimensions?The new dimensions can be gotten with the formula below:
Scale factor = Dimensions of new image / Dimensions of the original image.
Dimensions of new image = Scale factor × Dimensions of the original image
8 × 4 = 32 inches
8 × 3.6 = 28.8 inches.
Therefore, the new dimensions of the enlargement will be:
3 inches by 28.3 inches.
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Which of the following graphs has the smallest y-intercept and which graph would have the largest maximum as X moves towards 100?
Step 1
Given;
Step 2
[tex]\begin{gathered} y=1.3x \\ y-interecept\text{ is found when we set x=0} \\ y=1.3(0) \\ y-intercept=(0,0) \end{gathered}[/tex][tex]\begin{gathered} y=(1.3)^x \\ y=(1.3)^0 \\ y=1 \\ y-intercept=(0,1) \end{gathered}[/tex][tex]\begin{gathered} y=-0.8x+10 \\ y=-0.8(0)+10 \\ y=10 \\ y-intercept=(0,10) \end{gathered}[/tex][tex]\begin{gathered} y=10(0.8)^x \\ y=10(0.8)^0 \\ y=10 \\ y-intercept=(0,10) \end{gathered}[/tex]Thus,
[tex]y=1.3x\text{ has the smallest y-intercept}[/tex][tex][/tex]2. Use the following statement to answer the questions. Statement: If two angles are supplementary, then the angles are a linear pair.
(a) Write the inverse of the statement. Is the inverse true or false? Explain your reasoning.
(b) Write the converse of the statement. Is the converse true or false? Explain your reasoning.
(c) Write the contrapositive of the statement. Is the contrapositive true or false? Explain your reasoning.
Answer:
inverse is
- if two angles are not supplementary than the angles are not a linear pair. True because if they dont equal 180 they arent a linear pair
Converse is
- If two angles are a linear pair theyre supplementary
True because if theyre a linear pair they will always equal 180
Contrapositive is
- if two angles are not supplementary, they are not a linear pair
True because linear pairs always equal 180
May I please get help with this. For I have tried many times but still could not get the correct answer or how to recreate the dilation
a) From the graph,
shortest side length of original figure = 1/2 units
By dilating the original figure by 4, we would multiply each length by 4
Thus,
shortest side length of final figure = 1/2 x 4 = 2 units
b) shortest side length of the final figure = 4 x shortest side length of the original figure
c) A dilation with a positive scale factor greater than 1 gives an enlarged figure.Thus, the answer is False
d) After dilation, the original and final figures are similar. Thus, the answer is False
The display shows the favorite sport among 9th graders.
Bar graph shows student preferences for sports, with 16 students preferring baseball, 34 preferring basketball, 43 preferring football, 4 preferring soccer, and 3 preferring swimming.
Which of the following describes the data set?
Univariate and categorical
Univariate and numerical
Bivariate and categorical
Bivariate and numerical
The data-set for the favorite sport among 9th graders is classified as follows:
Univariate and categorical.
What are the classification of variables?The variables can be classified as categorical or numerical depending on the values that they assume as follows:
Categorical: The possible values assumed by the variable are labels, such as yes/no, good/bad, basketball, baseball, football, soccer and so on..Numerical: The values assumed by the variable are numbers.In this problem, the values assumed by the variable sport are:
Baseball, Basketball, Football, Soccer, Swimming.
Since these are names, the data-set is classified as categorical.
The only variable in this problem is the favorite sport of each student, that is, there is one variable, hence the student is classified as univariate.
Thus the correct option is the first one, given by:
Univariate and categorical.
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3 (a + b)solve ______= b for a c
First, apply distributive property:
[tex]\frac{3(a)\text{ + 3\lparen b\rparen}}{c}=b[/tex][tex]\frac{3a+3b}{c}=b[/tex][tex]3a+3b=bc[/tex][tex]3a\text{ = bc - 3b}[/tex]Common factor b
[tex]3a=b(c-3)[/tex][tex]a=\frac{b(c-3)}{3}[/tex]i need the first five terms and the 23 term thank you
we have the following:
[tex]a_n=\frac{11}{8}+\frac{1}{2}n[/tex]therefore, n = 23
[tex]\begin{gathered} a_{23}=\frac{11}{8}+\frac{1}{2}23 \\ a_{23}=\frac{11}{8}+\frac{23}{2} \\ a_{23}=\frac{11\cdot2+23\cdot8}{8\cdot2}=\frac{22+184}{16}=\frac{206}{16}=\frac{103}{8} \end{gathered}[/tex]the answer is 103/8
