The line of equation (y + 3x = 10) passes through all the points in the given table.
What are equations?The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.So, the equation will be:
Points:
x=0,1,2,3 y=10,7,4,1We know that when x = 0, then y = 10 and when we will increase x = 1, then y will decrease to y = 7.
The decrease in y is the difference of 3 (10 - 7 = 3)Then, y + 3x = 10 can be the equation.
Lets, 's check:
When x = 0:
y + 3x = 10y = 10 - 3(0)y = 10When x = 1:
y + 3x = 10y = 10 - 3(1)y = 7
When x = 2:
When x = 3:
y + 3x = 10y = 10 - 3(3)y = 1Since all the values of x and y are in proportion now, (y + 3x = 10) is the equation.
Therefore, the line of equation (y + 3x = 10) passes through all the points in the given table.
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If you bought a stock last year for a price of $90 and it is gone down 13% since then how much is the stock worth now to the nearest cent
The stock worth is $78.3
Given,
Bought a stock last year for a price of $90
And, price gone down is 13%
To find how much is the stock worth?
No, According to the question
Firstly, find the 13% of 90 i.e.,
= 13/100 x90
= $11.7
Stock worth is
= 90 - 11.7
= 78.3
Hence, The stock worth is $78.3
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A cookie jar contains 8 oatmeal, 7 peanut butter and 10 sugar cookies. What is theprobability that Ivan will pull a peanut butter cookie from the jar, eats it, then pulls asugar cookie from the jar?A. 17/49B.7/60C. 17/600D. 7/600
Answer:
B. 7/60
Explanation:
Given;
Number of oatmeal cookies = 8
Number of peanut butter cookies = 7
Number of sugar cookies = 10
Total number of cookies = 8 + 7 + 10 = 25
So the probability of Ivan pulling a peanut butter cookie from the jar can be determined as seen below;
[tex]\begin{gathered} P(\text{peanut butter cookie) }=\frac{\text{ number of peanut butter cookies}}{\text{Total number of cookies}} \\ P(\text{peanut butter cookie) }=\frac{7}{25} \end{gathered}[/tex]So if Ivan ate the peanut butter cookie he pulled (he did not replace it), it means that the total number of cookies will be 24, so the probability of pulling a sugar cookie from the jar will now be;
[tex]\begin{gathered} P(sugar\text{ cookie) }=\frac{\text{ number of sugar cookies}}{\text{Total number of cookies}} \\ P(sugar\text{ cookie) }=\frac{10}{24}=\frac{5}{12} \end{gathered}[/tex]So we can determine the probability that Ivan will pull a peanut butter cookie from the jar, eats it, then pulls a sugar cookie from the jar by multiplying the above probabilities;
[tex]P(peanut,sugar)=\frac{7}{25}\times\frac{5}{12}=\frac{7}{5}\times\frac{1}{12}=\frac{7}{60}[/tex]Therefore, the probability is 7/60
$11,335 is invested, part at 9% and the rest at 6%. If the interest earned from the amount invested at 9% exceeds the interest earned from the amount invested at 6% by $865.35, how much is invested at each rate?
The amount that was invested at 9% is $10303 , and at 6% is $1032 .
In the question ,
it is given that
total amount invested is $11335 .
let the amount invested at 9% be "x" .
so , the interest earned from 9% part is 0.09x
and let the amount invested at 6% be "y" .
the interest earned from 6% part is 0.06y
So , the equation is x + y = 11335 .
x = 11335 - y
Also given that interest earned from 9% amount exceeds the interest earned from 6% by $865.35 .
So , according to the question
0.09x = 0.06y + 865.35
On substituting x = 11335 - y in the above equation , we get
0.09(11335 - y) = 0.06y + 865.35
1020.15 - 0.09y = 0.06y + 865.35
0.09y + 0.06y = 1020.15 - 865.35
0.15y = 154.8
y = 154.8/0.15
y = 1032
and x = 11335 - 1032
x = 10303
Therefore , The amount that was invested at 9% is $10303 , and at 6% is $1032 .
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Draw the graph of the line that is perpendicular to Y= 4X +1 and goes through the point (2, 3)
Given:
[tex]\begin{gathered} y=4x+1 \\ \text{ point }(2,3) \end{gathered}[/tex]To find:
Draw a graph of a line that is perpendicular to the given line and passing through a given point.
Explanation:
As we know that relation between two slopes of perpendicular slopes of lines:
[tex]m_1.m_2=-1[/tex]Slope of given line y = 4x + 1 is:
[tex]m_2=4[/tex]So, the slope of line perpendicular to given line is:
[tex]m_2=-\frac{1}{4}[/tex]Also, so line equation that is perpendicular to given line is:
[tex]y=-\frac{1}{4}x+c...........(i)[/tex]Also, the required line is passing thorugh given point (2, 3), i.e.,
[tex]\begin{gathered} 3=-\frac{1}{4}(2)+c \\ c=3+\frac{1}{2} \\ c=\frac{7}{2} \end{gathered}[/tex]So, line equation that is perpendicular to given line is:
[tex]y=-\frac{1}{4}x+\frac{7}{2}[/tex]The required graph of line is:
Hi hope you are well!!I have a question: When Debbie baby-sits she charges $5 to go the house plus $8 for every hour she is there. The expression 5+8h gives the amount in dollars she charges. How much will she charge to baby-sit for 5 hours? Please help me with this questionHave a nice day,Thanks
5 + 8h
h= number of hours
Replace h by 5 and solve
5 + 8(5)
5 +40
45
She will charge $45
For the line that passes through Y(3,0), parallel to DJ with D(-3,1) and J(3,3), complete the following: Find the slope. Write an equation in point-slope form. Graph the line.Slope:Point-slope form:
I am going to graph the situation on an external graphing utility and show you the answer, it will take a
minute, stay with me.
[tex]m\text{ = }\frac{rise\text{ }}{\text{run}}=\frac{change\text{ in y}}{\text{change in x}}=\frac{3}{1}=3[/tex][tex]y\text{ = mx+b}\rightarrow\text{ b =-1}[/tex]So the equation of the line is.
[tex]y\text{ =3x -1}[/tex][tex]y\text{ -1 = m(3-0)}[/tex]Which of the following are roots of the polynomial function?Check all that apply.F(x) = x3 + 3x2 - 9x+5A. 1 - 13B. 3 - 2C. 1D. 1. 13E. 3 + 2F. -5
we have
F(x) = x3 + 3x2 - 9x+5
solve by graphing
using a graphing tool
the figure in the attached image
REmember that the zeros
please wait a minute
the roots are -5 and 1
therefore
answer option C and F
consider triangle 1 and triangle 2for which value of Q would the two triangles be similar - 136 -105 -75-31
Given:
If the given triangles are similar.
The corresponding angles should be congruent.
Both triangles have the same angle 105 degrees.
The second angle is 31 degrees and q.
[tex]q=31^o[/tex]If triangles are similar then the value of q is 31 degrees.
At a point 125 feet from the base of a building, the angle of elevation to the third floor is 22°. What is the height of the third floor?A 53.9 feetB 14,124 feetC. 50.5 feetD. 333.3 feet
From the problem statement, we can draw the triangle shows below:
H is the height of the building we will solve for.
Shown below >>>
[tex]\begin{gathered} \tan 22=\frac{H}{125} \\ H=125\tan 22 \\ H=50.5\text{ f}eet \end{gathered}[/tex]AnswerCPlease help with this problem my son is having problems showing his work an understanding how. Solve x2 – 6x = 16 using the quadratic formula method. Show your work. Then describe the solution.
Solution
We are given the quadratic equation
[tex]x^2-6x=16[/tex]We want to solve by using the quadratic formula method
Note: Given a quadratic equation
[tex]ax^2+bx+c=0[/tex]The formula method is given
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From
[tex]\begin{gathered} x^2-6x=16 \\ x^2-6x-16=0 \\ \text{Comparing with the general form of a quadratic equation} \\ a=1 \\ b=-6 \\ c=-16 \end{gathered}[/tex]Substituting the parameters intot the quadratic formula
and
Therefore,
[tex]x=8,-2[/tex]The table below shows the average price of a Miami Marlins baseball ticket between 2006 and 2021.
By evaluating the equation in x = 2040, we can estimate the price to be $1507.7.
How to evaluate the equation?To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12. If we know the value of our variables, we can replace the variables with their values and then evaluate the expression.
Given that,
We know that the equation:
y = 1.83*x - 2225.5
Models the relationship between the year, x, and the average ticket price of a Miami Marlins baseball ticket.
We know that this relationship works for the years 2006 to 2021, but can be used to estimate the price for years after and before that.
if we use x = 2040
we will get
y = 1.83*2040 - 2225.5 = 1507.7
Hence, The price will be 1507.7, in dollars, of a game in the year 2040.
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Which of the following sets of ordered pairs represents a function?
A.
{ (0, -2), (-27, -13), (-10, -5), (-27, -12) }
B.
{ (-7, -14), (-9, -18), (-5, -10), (-6, -12) }
C.
{ (1, -1), (1, -27), (1, -26), (1, -17) }
D.
{ (81, 1), (81, -1), (83, 4), (86, 6) }
Answer: B
Step-by-step explanation:
For the set of ordered pairs to be a function, each x-value has to correspond to only one y-value.
In option A, the x-value of -27 corresponds to both -13 and -12.
In option C, the x-value of 1 corresponds to -1, -27, -26, and -17.
In option D, the x-value of 81 corresponds to both 1 and -1.
(2.4 × 10^3) × (3 × 10^n) = 7.2 × 10^9
Answer:
n = 6
Step-by-step explanation:
(2.4 × 10^3) × (3 × 10^n) = 7.2 × 10^9
First lets solve the parentheses:
(2.4 × 1000) × ( 3 × 10^n) = (7.2 × 1000000000)
2.4 × 1000 = 2400 so...
2400 × (3 × 10^n ) = 7200000000
Next lets divide:
7200000000/2400 = 3000000
So now we have...
(3 × 10^n ) = 3000000
Even though we just divided we have to divide again so...
3000000/3 = 1000000
then to get the answer of n we have to figure out how many times to the power of 10 do we get 1000000.
one easy but time consuming way is
dividing it by ten till you get to one and you would get the same answer. You choose to do that way then that works for your.
There are also other way to figure that out but your teacher teaches you an easier way to figure it out.
Select all statements that are true about equilateral triangle ABC.
To determine statements that are correct, we proceed as follows:
Step 1: We recall the definition of an "equilateral" triangle
An equilateral triangle is one which"
- has all its sides equal to each other
- has all its internal angles equal to 60 degrees each
From the above definition, it can be concluded that
(A) Angles B and C are 60 degrees is a true statement
Step 2: We solve the triangle for x, as follows:
Now, consider the left right-triangle:
Now, we apply the sine trigonometric ratio to obtain the value of x,
[tex]undefined[/tex]Evaluate the expression.If x=12, y=8, and z=3x3 + y + z3
We need to find the value of
[tex]x^3+y+z^3[/tex]Where x = 12, y = 8, and z = 3
Substitute these values in the expression above
[tex](12)^3+8+(3)^3[/tex]12^3 = 1728
3^3 = 27
Then
[tex]1728\text{ + 8 + 27 = 1763}[/tex]The value of the given expression is 1763
Where do the graph shifted if the function changes from Y=x^2 to Y=(x+h)^2
The independent variable x is shifted (x + h). This is a value of h units to the right since it is the sum to the variable x.
So, the graph to find where the graph shift, we need to find the difference between these two values:
[tex](x+h)^2-x^2=x^2+2hx+h^2-x^2=2hx+h^2[/tex]Then, the graph is shifted
[tex]2hx+h^2[/tex]Box #1 options is: A.true B.false
Box #2 options are: A.true B.false
Box #3 options are: A.enough B.not enough
Answers:
falsetruenot enough=======================================================
Explanation:
Let's say the claim is [tex]\text{x}^2 \ge \text{x}[/tex] true for any real number x. It certainly works for things like x = 5 and x = 27.
A counter-example to show this isn't true is to use x = 0.5
So,
[tex]\text{x}^2 \ge \text{x}\\\\0.5^2 \ge 0.5\\\\0.25 \ge 0.5\\\\[/tex]
The last statement is false, which thereby proves the original claim doesn't work for x = 0.5; by extension, the overall claim of that inequality working for any real number is false.
As you can see, all we need is one counter-example to contradict the claim to prove it false.
Unfortunately one single example is not enough evidence to prove a claim true. Think of it like saying "it's much easier to knock down a sand castle than to build it up".
Instead, we need to use a set of clearly laid out statements and reasons based on previously established theorems.
23. At a company employing 140 people, 40% of the employees took the bus to work,and 5 % lived close enough to walk. The others drove cars. How many employeesdrive cars to work?Answer
Since the total percent of the employees is 100%
Since 40% of them took the bus
Since 5% walk
Add them and subtract the sum from 100% to get the percentage of who take the car
[tex]\begin{gathered} 40+5=45 \\ 100-45=55 \end{gathered}[/tex]Then 55% of the employees use cars
Since the total number of employees is 140, then
Let us find 55% of 140
Change 55% to a number by divide it by 100, then multiply it by 140
[tex]\begin{gathered} N=\frac{55}{100}\times140 \\ N=77 \end{gathered}[/tex]There are 77 employees who use cars
What is the 100th term of the arithmetic sequence below? 2x, 3x + 4, 13x - 1
We are given an arithmetic progression and are requested to find the 100th term of the progression. We need to find the value of x from the question by equating differences.
[tex]\begin{gathered} T_2-T_1=T_3-T_2 \\ 3x+4-2x=13x-1-(3x+4)=13x-1-3x-4 \\ x+4=10x-5 \\ \text{Collecting like terms gives us:} \\ 10x-x=4+5 \\ 9x=9 \\ x=1 \end{gathered}[/tex]Now we will find the actual value of our terms.
[tex]\begin{gathered} T_1=a=2(1)=2 \\ T_2=3(1)+4=7 \\ T_3=13(1)-1=12 \\ \text{Therefore,} \\ \text{ d = }T_2-T_1=T_3-T_2 \\ d=7-2=12-7=5 \end{gathered}[/tex]Common difference, d = 5
Lastly, we employ our AP formula to find the 100th term.
[tex]\begin{gathered} Tn=a+(n-1)d \\ T_{100}=2+(100-1)5 \\ T_{100}=2+(99)5=497 \end{gathered}[/tex]The 100th term is 497
Graph the following equation:(y + 4) = 2(x - 2)Step 1 of 3: Find a point on the line and the slope of the line.
Given:
The equation of line is,
[tex]y+4=2(x-2)[/tex]Find the slope of equation,
[tex]\begin{gathered} y+4=2(x-2) \\ y+4=2x-4 \\ y=2x-8 \\ \text{slope= 2} \end{gathered}[/tex]Find the points on line,
[tex]\begin{gathered} \text{For x=0,} \\ y=2x-8 \\ y=-8 \\ (x,y)=(0,-8) \\ \text{for x=4,} \\ y=2x-8 \\ y=2(4)-8 \\ y=0 \\ (x,y)=(4,0) \\ \text{For x=2} \\ y=2x-8 \\ y=2(2)-8=-4 \\ (x,y)=(2,-4) \\ \text{For }x=5 \\ y=2x-8 \\ y=2(5)-8=2 \\ (x,y)=(5,2) \end{gathered}[/tex]The graph of equation of line is,
Question 10 of 10
Question 10
▸
Find the Error One cleaning solution uses 1 part vinegar with 2 parts water. Another cleaning solution uses 2 parts vinegar with 3 parts water
A student says that these mixtures are equivalent because, in each solution, there is one more part of water than vinegar. Find the error and
correct it.
In the first cleaning solution, the ratio of vinegar to water is
however, has a ratio of
Need help with this question?
Check Answer
The ratios
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The second solution.
equivalent
Done and
The error is that there is no proportional relationship between the ratios which is corrected and can be described as a linear relationship with the help of the equation y = m + 1.
What is the proportional relationship?Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportional relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant.So, the ratios we have:
1:2 and 2:3.Then, performing:
1/2 = 0.52/3 = 0.67Hence, ratios of 1:2 and 2:3 are not equal.
Therefore, the error is that the relationship between the given ratios is not proportional.
As can be seen, each ratio has a difference of 1, that is:
2 - 1 = 13 - 2 = 1Therefore, when one variable changes by 1, the other variable only changes by a constant value (y = x = c).
It can therefore be described as a linear relationship, and the constant is 1.The equation has the following form:
y = x + 1Where y stands for the water solution and x for the vinegar component.
Therefore, the error is that there is no proportional relationship between the ratios which is corrected and can be described as a linear relationship with the help of the equation y = m + 1.
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I can't find the last mark can someone help please
Step-by-step explanation:
right, M = ((xa + xb)/2, (ya + yb)/2) = (3.5, 3.5)
the line through O and M (I assume we need the slope-intercept form) is in general
y = ax + b
"a" is the slope, "b" is the y-intercept (the y-value when x = 0).
the slope is the ratio (y coordinate change / x coordinate change) when going from one point on the line to another.
so, our 2 points : (0, 0) and (3.5, 3.5).
x changes by +3.5 (from 0 to 3.5).
y changes by +3.5 (from 0 to 3.5).
so, the slope "a" is +3.5/+3.5 = 1.
the point (0, 0) gives us "b" (the y-value when x = 0) directly : 0.
so, the line equation is
y = x
3. Given x=2 and y=-3, evaluate the expression given below 2x - 3xy - 2y? A) -28 B) 28 C) 8 D) 44
Given:-
x=2,y=-3
[tex]2x-3xy-2y\text{?}[/tex]To find evalute the given expression,
[tex]2x-3xy-2y[/tex]
Subtitute the x and y value in above equation,
[tex]\begin{gathered} 2(2)-3(2)(-3)-2(-3) \\ =4-(6\times-3)+6 \\ =4-(-18)+6_{} \\ =4+18+6 \\ =28 \end{gathered}[/tex]So the required value is 28.
So the correct option B.
A website recorded the number of referrals it received from social media websites over a 10-year period. The results can be modeled by g = 2500(150), where is the year and SSRinterpret the values of a and & in this situation.a represents the number of referrals after 9 years, represents the growth factor of the number of referrals each yeara represents the number of referrals it received at the start of the model; &represents the decay factor of the number of referralsa represents the number of referrals after 9 years; b represents the decay factor of the number of referrals sach yeara represents the number of referrals it received at the start of the model & represents the growth factor of the number offWhat is the annual percent increase?The annual percent increase is %.
Given
[tex]y=2500(1.50)^t[/tex]Find
Interpret the values of a and b , also annual percent increase
Explanation
As the general form of growth exponential function is in the form of
[tex]\begin{gathered} y=ab^t \\ \end{gathered}[/tex]where a is the inital value
t is the time
b= 1+r = where r is the rate of growth
so , in given situation
a represents the number of referrals it received at the start of the model; and b represents the growth factor of the number of referrals
option 4 is the correct one.
now we have to find the annual percent increase
for this we have to find the final referrels after 1 years.
for this put t = 2in given equation
[tex]\begin{gathered} y=2500(1.50)^2 \\ y=5625 \end{gathered}[/tex]annual percent increase =
[tex]\begin{gathered} \frac{5625-2500}{2500}\times100 \\ \\ \frac{3125}{2500}\times100 \\ \\ 125\% \end{gathered}[/tex]Final Answer
Therefore , the correct option is d .
the annual percent increase is 125%
find the slope of the line passing through the points (-5,4) and (3,-3)
P1 = (-5, 4)
P2 = (3, -3)
Formula
[tex]\text{slope = }\frac{(y2\text{ - y1)}}{(x2\text{ - x1)}}[/tex]Substitution
[tex]\begin{gathered} \text{ slope = }\frac{(-3-4)}{(3\text{ + 5)}} \\ \text{ slope = }\frac{-7}{8} \end{gathered}[/tex]Result
[tex]\text{ slope = }\frac{-7}{8}[/tex]What is the answer to 3/8 + 7 5/8
Given the Addition:
[tex]\frac{3}{8}+7\frac{5}{8}[/tex]You can find the sum as follows:
1. Covert the Mixed Number to an Improper Fraction:
- Multiply the Whole Number part by the denominator of the fraction.
- Add the result to the numerator.
- The denominator does not change.
Then:
[tex]7\frac{5}{8}=\frac{5+(7\cdot8)}{8}=\frac{5+56}{8}=\frac{61}{8}[/tex]2. Rewrite the Addition:
[tex]=\frac{3}{8}+\frac{61}{8}[/tex]3. Since the denominators are equal, you only need to add the numerators:
[tex]=\frac{3+61}{8}=\frac{64}{8}[/tex]4. Simplifying the fraction, you get:
[tex]=8[/tex]Hence, the answer is:
[tex]=8[/tex]An item is regularly priced at $35. Lena bought it on sale for 20% off the regular price. How much did Lena pay?
An item is regularly priced at $35.
Cost price of item = $35
Lena bought it on sale for 20% off the regular price
i.e. 20% of 35 is off in the item of cost $35
So, The amount Leena will paid = $35- 20% of 35
[tex]\begin{gathered} \text{Amount L}eena\text{ will pay =}35-20\text{ \%of35} \\ \text{Amount L}eena\text{ will pay}=35-\frac{20\times35}{100} \\ \text{Amount L}eena\text{ will pay}=35-7 \\ \text{Amount L}eena\text{ will pay}=28\text{ dollars} \end{gathered}[/tex]So, Leena will pay $28
Answer: $28
will give brainlist
The table shows a proportional relationship.
Workout (hours) 1 2 3
Calories Burned 320 640 960
Create a description in words for the table.
The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
The number of hours working out is dependent on the number of calories burned. For every 320-hour workout, there is 1 calorie burned, and for every 640-hour workout, there are 2 calories burned.
The number of calories burned is dependent on the number of hours working out. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
The number of calories burned is dependent on the number of hours working out. For every 320-hour workout, there is 1 calorie burned, and for every 640-hour workout, there are 2 calories burned.
The description for the table in word will be A. The number of hours working out is dependent on the number of calories burned. For a one-hour workout, there are 320 calories burned, and for a two-hour workout, there are 640 calories burned.
What is a proportional relationship?Proportional connections are those in which the ratios of two variables are equal. Another way to think about them is that one variable in a proportional relationship is always a constant value multiplied by the other. This is known as the "constant of proportionality."
In this case, the table shows a proportional relationship between workout and calories burned. In 1 hour, 320 calories are burned.
In conclusion, the correct option is A.
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LM is the midsegment of Trapeziod RSXY. may you please help me find what LM is?
Step 1: Problem
Mid-point of a Trapezoid
Step 2: Concept
[tex]LM\text{ = }\frac{RS+\text{ YX}}{2}[/tex]Step 3: Method
RS = 4.1
YX = 8.2
[tex]\begin{gathered} LM\text{ = }\frac{4.1\text{ + 8.2}}{2} \\ LM\text{ = }\frac{12.3}{2} \\ LM\text{ = 6.15} \end{gathered}[/tex]Step 4: Final answer
LM = 6.15
which of the relationships below represents a function with the same rate of change of the function y= -4x + 2
Given data:
The given equation of the line is y= -4x + 2.
Substitute 0 for x in the given equation.
[tex]\begin{gathered} y=-4(0)+2 \\ =2 \end{gathered}[/tex]Substitute 1 for x in the given equation.
[tex]\begin{gathered} y=-4(1)+2 \\ =-2 \end{gathered}[/tex]Thus, option (D) is correct.