a) The mistake that mara made in step 3 is that; she didn't apply the basic rule of logarithm which should have given the expression log 3^x = x log 3
b) The mistake that mara made in step 4 is that; you must eradicate the log at the same time and as such it should be x log 3 = 3log 3
c) The mistake she made throughout is not applying the basic rule of logarithm.
How to solve Exponential Equations using logarithm?
She is trying to solve the exponential function 7 x 3^x = 189 with the following steps;
Step 1. 7 x 3^x = 189
Step; 2. 3^x = 27; This step is correct because she got it by using division property of equality to divide both sides by 7.
Step 3; log^3 (^3) = log^27; This step is incorrect because from basic rules of logarithm, we know that; log 3^x = x log 3
Step 4. xlog^33=9; This is incorrect because you cannot remove the log on one side of the equation without doing the same on the second side. Thus, what she she should have had here is;
x log 3 = 3log 3
Step 5. x * 1 = 9; This is wrong because dividing both sides by log 4 gives; x = 3
Step 6. x = 9; This is wrong because x = 3
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Complete question is;
Mara solved an exponential equation by using logarithms. This is her work.
1. 7 x 3^x = 189
2. 3^x = 27
3. log^3 (^3) = log^27
4. xlog^33=9
5. x * 1 = 9
6. x = 9
Review Mara's work in steps 3 and 4. (Hint: There is one mistake in those steps.)
a. Be sure to explain what she did and why it was correct or incorrect for Step 3.
b. Be sure to explain what she did and why it was correct or incorrect for Step 4.
c. Provide Mara with feedback on what the mistake was and how to fix it.
Sort the order of the electron holding capacity of the energy levels starting from the nucleus.
Below is a sequence of events. Place them in the order they should occur, number 1 being the first item. Select the step number from the drop down next to each item.
Items to order:
1.
Can hold a maximum of 18 electrons.
2.
Can hold a maximum of eight electrons.
3.
Can hold a maximum of 32 electrons.
4.
Can hold a maximum of two electrons.
The order of the energy levels starting from the highest is:
3. Can hold a maximum of 32 electrons
1. Can hold a maximum of 18 electrons.
2. Can hold a maximum of eight electrons.
4. Can hold a maximum of two electrons.
Energy levels and electron holding capacityWhen a shell gets bigger, it can retain more electrons, and has greater electron energies the further it is from the nucleus.
Two electrons can fit in the first shell, which is closest to the nucleus. Eight electrons can fit in the second shell. 18 electrons can fit in the third shell then 32 electrons can fit inside of the last shell.
The shell that can contain 32 electrons has the highest energy level
Following this relationship, it shows that the arrangement is done using the number of electrons to arrive at 3, 1, 2,and 4
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Rewrite the equation in standard form from vertex form: y = -4(x - 3)² + 6
The equation of the parabola, in standard form is ______________
y = -4x²+24x-30 is the standard form of parabola whose equation is y = -4(x - 3)² + 6
What is Parabola?Parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped.
The given equation is y = -4(x - 3)² + 6.
We need to write this equation as standard form of parabola.
the equation of a parabola in standard form is.
y=ax² +bx+c
The given equation should be expanded y = -4(x - 3)² + 6.
y = -4(x²+9-6x)+6
Now apply distributive property
y = -4x²-36+24x+6
y = -4x²+24x+6-36
y = -4x²+24x-30
Hence y = -4x²+24x-30 is the standard form of parabola whose equation is y = -4(x - 3)² + 6
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Find the equation of the line
Answer:
[tex]y= \frac 12 x -3\\y=0.5x -3[/tex]
Depending if you can imput fractions, or decimal numbers.
Step-by-step explanation:
The slope can easily calculated as [tex]m=\frac{\Delta y}{\Delta x} = \frac {0-(-3)}{6-0} = \frac 36 = \frac12[/tex]
The y intercept can be easily read from the graph as and is -3
The ratio of teachers to students on a field trip is 2:13. If there are 132 more students than adults on the field trip, how many adults are there and how many students are there?
There are 284 number of students and 152 number of adults.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given,
The ratio of teachers to students on a field trip is 2:13
Let x be the number of adults
If there are 132 more students than adults on the field trip, then 132+x
To find the number of adults and number of students formulate a equation as below
2/13=(x+132)/x
Apply cross multiplication
2x=13(x+132)
Apply distributive law on RHS
2x=13x+1716
11x=1716
Divide both sides by 11
x=152
x+132=152+132=284
Hence there are 284 number of students and 152 number of adults.
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Solve 5x² + 1 = 51 by finding square roots.
x = 50, -50
x = √10,-√10
x = 10, −10
x = √50,-√√/50
Answer:
x = √10,-√10
explanation:
5x2 + 1 = 51
you would carry the +1 to the other side making it
5x2=51-1
which is 5x2=50
this equation above can then be turned into
x2=50÷5
which goes on to form the equation
x2=10
this can then be turned into x=the square root of ten
and since it is know that when an equation is x2 whether it is negative or positive it would result in the same answer
but yeah I'm not smart or whatever but I hope this helps
not too sure it's correct though
Write an equation of the line that passes through each pair of points.(5, −2), (7, −1)
[tex](\stackrel{x_1}{5}~,~\stackrel{y_1}{-2})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{(-2)}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{5}}} \implies \cfrac{-1 +2}{2} \implies \cfrac{ 1 }{ 2 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ \cfrac{1 }{ 2 }}(x-\stackrel{x_1}{5}) \implies y +2 = \cfrac{1 }{ 2 } ( x -5) \\\\\\ y+2=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }\implies y=\cfrac{1 }{ 2 }x-\cfrac{5 }{ 2 }-2\implies {\Large \begin{array}{llll} y=\cfrac{1 }{ 2 }x-\cfrac{9}{2} \end{array}}[/tex]
Answer:
y=1/2x-9/2
Step-by-step explanation:
First you want to find the slope by doing -2-(-1)/5-7
Therefore the slope is 1/2
Next you want to add in any set of points, either (5, -2) or (7, -1)
Substitute the x- point in place of x and the y in place of y in y=1/2x+b
Once you do this you should get -2=1/2(5)+b
You should get -2=2 1/2+b
Then subtract 2 1/2 from -2
You should get -4 1/2
Once you have the slope and y- intercept you can put together your problem
y=1/2x-4 1/2
don't forget to convert, y=1/2x-9/2
Hope this helps
Write an inequality for the statement: negative one half is a minimum of the product of a number and negative five sixths.
N × (-5/6) ≥ -1/2 is the inequality for the statement
How to write an inequality for the statement?
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value e.g 5 < 6, x ≥ 2, etc.
Given the statement: negative one half is a minimum of the product of a number and negative five sixths.
This statement can also be written as the product of a number and negative five sixths is greater than or equal to negative one half
Let N represent the number. Thus, the inequality of the statement is:
N × (-5/6) ≥ -1/2
Note: The symbol ≥ is pronounced as greater than or equal to
Therefore, the inequality for the statement is N × (-5/6) ≥ -1/2
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Jason watched a caterpillar move 10 feet in 2 minutes. Jason says that the caterpillar's unit rate is 0.2 feet per minute, Is Json correct? Explain.
Differentiate the function with respect to x.
The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]
Given,
In the question:
The function is:
f(x) = [tex]x^4(5x^4+4)[/tex]
Differentiate the function with respect to x.
Now, According to the question:
f(x) = [tex]x^4(5x^4+4)[/tex]
Expand the expression:
f(x) = [tex]5x^8+4x^4[/tex]
Calculate the derivative
f'(x) = [tex]\frac{d}{dx}(5x^8+4x^4)[/tex]
f'(x) = [tex]\frac{d}{dx}(5x^8)+\frac{d}{dx} (4x^4)[/tex]
Isolate Coefficients
f'(x) = 5 x [tex]\frac{d}{dx}(x^8)+4 \frac{d}{dx} (x^4)[/tex]
Apply the power rule
f'(x) = 5x [tex]8x^7+4[/tex] x[tex]4x^3[/tex]
f'(x) = [tex]40x^7 + 16x^3[/tex]
Hence, The function is differentiate w.r.t. x get the answer is [tex]40x^7 + 16x^3[/tex]
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A car dealership increased the price of a certain car by 13%. The original price was $39,400.
Answer:
find the increased dollar amount by finding the percentage amount first:
$ 39,400 * .13
= $ 5,122
then take $ 5,122 and add it to the original price
$ 39,400 + $ 5,122 = $ 44,522 (new price)
Step-by-step explanation:
what is (18x45) divided by 8
The solution for (18x45) divided by 8 = 101.25
Simplify (18x45) divided by 8
Step 1: Rewrite the equation in mathematical terms
we have:
[tex]\frac{18 x 45}{8}[/tex]= [tex]\frac{810}{8}[/tex]
= 101.25
Therefore, the solution for (18x45) divided by 8 = 101.25
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A rectangular-prism-shaped toy chest is 2 \text { m}2 m2, start text, space, m, end text by 1 \text { m}1 m1, start text, space, m, end text by 1 \text { m}1 m1, start text, space, m, end text.
A shipping crate is packed with 181818 of these toy chests. There is no extra space in the crate.
What is the volume of the crate?
The volume of the crate if there is no extra space in the crate is 36m³.
How calculate the volume?From the information illustrated, the prism is 2m by 1m by 1m abd the shipping crate is packed with 18 of these.
In this case, the volume will be:
= Length × Width × Height
= 2 × 1 × 1
= 2m³
Since there are 18 crates, the total volume will be:
= 2m³ × 18
= 36m³
The volume is 36m³.
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Complete question
A rectangular-prism-shaped toy chest is 2m by 1m by 1m. A shipping crate is packed with 18 of these toy chests. There is no extra space in the crate. What is the volume of the crate?
Hey can someone please explain this to me I’m a bit confused. Thank you I appreciate it!
The area of given figure is 93mm².
Pat randomly chooses marbles from an urn without replacement. The urn originally contained 55 red marbles, 30 white marbles, and 15 blue marbles. What is the probability that Pat’s second pick will be a blue marble given that the first pick was a red marble?
The probability that Pat’s second pick will be a blue marble is the fracion 5/3 considering choosing marbles without replacement.
Probability of an event without replacementProbability of an event without replacement simply means once an item is drawn, then we do not replace it back to the sample space before drawing a second item.
For the fact that a red marble was first drawn without replacement with the probability of 55/100, given that there are 55 red marbles and a total of 100 marbles in the Urn.
Hence, there will be 99 samples left for the second draw to be made.
The probability that the second pick will be a blue marble = 15/99.
Therefore, the probability that the second pick is a blue marble after the first pick without replacement is the fraction 5/33 reduced to its lowest term from 15/99.
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Find the equation of the line passing through (1, 5) and parallel to y = 3x – 1.
=====================================================
Explanation:
The equation y = 3x-1 is in slope-intercept form y = mx+b
m = 3 = slopeb = -1 = y interceptParallel lines have equal slopes, but different y intercepts.
The answer will also have a slope of m = 3.
Plug that slope value, and the coordinates of the given point [tex](x_1,y_1) = (1,5)[/tex] , into the point-slope formula below.
Solve for y.
[tex]y - y_1 = m(x - x_1)\\\\y - 5 = 3(x - 1)\\\\y - 5 = 3x - 3\\\\y = 3x - 3+5\\\\y = 3x + 2\\\\[/tex]
That's how we arrive at the answer of y = 3x+2
As a check, plugging x = 1 into that answer should get us y = 5.
It confirms that the point (1,5) is on this line.
Year No. of cars sold
in (hundreds)
2000 45
2002 51
2004 53
2006 60
2008 77
A car manufacturer's sales figures for 2000 to 2008 are shown in the table. Estimate the average rate of change in the number of cars the manufacturer sold between 2002 and 2006.
A.
450 cars per year
B.
225 cars per year
C.
2,900 cars per year
D.
600 cars per year
Answer: In photo below
You're Welcome :)
The average rate of change in the number of cars the manufacturer sold between 2002 and 2006 is B. 225 cars per year.
What is the average rate of change?The average rate of change shows the slope line over the stated interval.
We can find the average rate of change by dividing the change in y-values by the change in x-values.
Year No. of cars sold
in (hundreds)
2000 45
2002 51
2004 53
2006 60
2008 77
The total number of cars sold between 2002 and 2006 = 16,400
The number of cars sold in 2002 = 5,100
The number of cars sold in 2006 = 6,000
The increase in car sold between 2002 and 2006 = 900 (6,000 - 5,100)
OR:
Increase in the number of cars sold in 2004 = 200 (5,300 - 5,100)
Increase in the number of cars sold in 2006 = 700 (6,000 - 5,300)
Total change in y-values = 900 (6,000 - 5,100)
Total change in x-values = 4 (2006 - 200)2
Average rate of change = 225 (900/4)
Thus, we can conclude that for 4 years, car sales increased on, average, by 225 each year.
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A number c divided by 3 is greater than -20
The solution of the given statement will be inequality c > -60.
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
We have been given the statement "number c divided by 3 is greater than -20".
As per the given statement, we can represent this algebraic form with inequality as:
⇒ c / 3 > -20
Inequality by multiplying both sides of the inequality by 3:
⇒ 3 × c / 3 > 3 × -20
⇒ c > -60
Thus, the solution of the given statement will be inequality c > -60.
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The question seems to be incomplete the correct question would be
Find the solution if a number c divided by 3 is greater than -20.
Raina, Trey, and Deandre have a total of $145 in their wallets. Raina has $10 more than Trey. Deandre has 3 times what Raina has. How much do they have in their wallets?
Trey, Raina, and Deandre have $21,$31, and $93 in their wallets respectively.
From the question the sum of the money in their wallets is:
Raina + Trey +Deandre=$145
R + T + D =$145................(i)
Raina has $10 more than Trey= ($10 + T)
Deandre has 3 times more Raina =3($10 + T)
substituting the values of Raina and Deandre in Eqn (i) we have
R + T + D =$145
($10 + T) + T +{3$(10 + T)}=$145
$10 +T +T+ $30 + 3T =$145
5T +$40 = $145
5T = $145 - $40
5T = $105
T = $105/5
T = $21
i.e Trey = $21
Raina has $10 more than Trey= ($10 + T)
i.e = ($10 + $21)
Raina =$31
Deandre has 3 times more Raina =3($10 + T)
=3($10 + $21)
=$30 +$63
Deandre =$93
Therefore the total sum of money in thier wallet is:
Raina + Trey +Deandre=$145
$31 + $21 + $93= $145
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Given the coordinate, perform the following transformation and give the new coordinates.
12. Reflect (2, 3) over the x axis: (
13. Reflect (7, -2) over the y axis: (
14. Rotate (4, 5) 90° about the origin: (
15. Rotate (-3, -2) 270° about the origin:
16. Reflect (17, -23) over the line y=x.
The reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).
What is a reflection?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when they are all equally spaced apart from one another.
The reflection of the point (2,3) over the x-axis is calculated as,
(2,3) ⇒ (2,-3)
The reflection of the point (7,-2) over the y-axis is calculated as,
(7,-2) ⇒ (-7,-2)
Therefore, the reflection of the point (2,3) over the x-axis is (2,-3). The reflection of the point (7,-2) over the y-axis is (-7,-2).
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What is the product of 1.45 and 0.34 rounded off to one decimal place
Answer: 0.5
Step-by-step explanation:
1.45*0.34 = 0.493
Rounded to the tenth place is 0.5
The weight of substance X is halved per minute. In the beginning, the weight of substance X is 5kg.
(a) Find the weight of substance X after 4 minutes.
(b) After how many minutes will the weight of substance X first go below 0.5kg?
Please give your answer as an integer.
EMERGENCY PLEASE HELPPPP
Answer:
a: 0.3125kg
b: 4
Step-by-step explanation:
for a we simply calculate 5 * 0.5 ^ 4.
we then see that the weight after 4 minutes is smaller than 0.5kg, but if we go back to 3 minutes (by multiplying our solution to a by 2), giving us 0.625kg, which is now bigger than 0.5kg. meaning 4 minutes is the first whole amount that will give us a weight smaller than 0.5kg.
determine the midpoint of the line segment connecting (6,-5) and (-1,-6)
The midpoint of the line joining (6,-5) and (-1,-6) is (-5/2,-11/2).
How to determine the midpoint of the line joining two points (a,b) and (p,q)?
To get the midpoint of the line joining two points (a,b) and (p,q), we first have to add the x coordinates of two points and divide it by 2. So the midpoint's x coordinate will be (a+p)/2 . Similarly, we have to do the same with y. Then the midpoint of the line joining two points (a,b) and (p,q) will be [(a+p)/2,(b+q)/2}.
To get the midpoint of (6,-5) and (-1,-6) , first, we have to add the x coordinates and divide it by 2 . And have to do the same with y.
so, the midpoint will be [(6+(-5)]/2,[-5+(-6)]/2.
Hence ans will be ,(-5/2,-11/2)
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Write the number in 2 equivalent
forms as a fraction, decimal, or
percent.
20
20
What is the equivalent percent?
Step-by-step explanation:
Percentage means to be out of 100 . So, 20% is equivalent of being 20100 . That evaluates out to 0.20 . Removing the unnecessary 0 at the end gives us the decimal 0.2 , which is the correct answer.
Let's play a game where I flip a coin. If the coin lands on Heads you win a $1, if it lands on Tails you lose a $1. I flip a coin 8 times and here is the results Tails Tails Tails Tails Tails Tails Tails Tails So you lost 8 times in a row and thus lose $8.00.
Part1: Would you like to continue this game. Why or why not.
Part 2: Calculate the P-value of getting 8 tails in a row assuming the coin is fair. Is it a big number or small?
Part 3: Based on the P-value you got above what would you conclude about your initial hypothesis that the coin is fair.
Using the z-distribution to test the hypothesis, it is found that:
1. You would not like to continue the game, as in each trial you are losing.
2. The p-value is of 0.0023.
3. The low p-value means that there is enough evidence to conclude that the coin is biased.
What are the hypothesis tested?At the null hypothesis, it is tested if there is not enough evidence that the coin is biased, that is, the proportion of heads is of 0.5, hence:
[tex]H_0: p = 0.5[/tex]
At the alternative hypothesis, it is tested if there is enough evidence that the coin is biased, that is, it has a proportion of heads lower than 0.5, hence:
[tex]H_1: p_1 < 0.5[/tex]
What is the test statistic?The test statistic is given by the equation as follows:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which the variables are listed and explained as follows:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.The values of these parameters are given as follows:
[tex]\overline{p} = \frac{0}{8} = 0, n = 8, p = 0.5[/tex]
Hence the test statistic is:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0 - 0.5}{\sqrt{\frac{0.5(0.5)}{8}}}[/tex]
z = -2.83.
P-value and conclusionUsing a z-distribution calculator, and considering a left-tailed test, as we are testing if the proportion is less than a value, with z = -2.83, the p-value is of 0.0023.
Since this p-value is less than the standard significance level of 0.05, it means that there is enough evidence to conclude that the coin is biased towards tails.
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QUESTION 1
1 POINT
To study whether there is a correlation between regular exercise and sleep, a researcher randomly selected 100 people who
exercise regularly and 100 people who do not exercise regularly, and compared how many hours they sleep at night, on
average.
Is the study observational or experimental? If it is an experiment, what is the controlled factor?
Select the correct answer below:
The study is an experiment. The controlled factor is the amount of sleep.
O The study is an experiment. The controlled factor is the amount of exercise.
The study is an observational study.
O The study is an experiment. The controlled factor is the survey.
Since the researcher randomly selected 100 people who exercise regularly and 100 people who do not exercise regularly, and compared how many hours they sleep at night, on average: C. the study is an observational study.
What is an observational study?An observational study can be defined as a type of scientific study in which a researcher observes and measures the effect of a diagnostic test, risk factors, and specific treatments on individuals without intervening, manipulating, altering, or changing those who are or aren't exposed to it (controlled conditions).
In Science, a controlled variable must always be held constant and unchanged in an experiment in order to prevent it from affecting or influencing the result, which is not applicable to this research.
In conclusion, we can logically deduce that this research is an observational study because people (participants) were chosen through an appropriate process, however, no attempt was made to control any aspect of the people (participants), even though the variable of interest (exercise) was recorded for one of the group.
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For the functions f(x)=2x4+2x3−x2+2x+3 and g(x)=x+1 find (fg)(x) and (fg)(−4)
The value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.
What is polynomial?A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.
Given function is f(x) = 2x⁴ + 2x³− x²+ 2x + 3
The value of the function is calculated as,
f(x) = 2x⁴ + 2x³− x²+ 2x + 3
(fg)(x) = (2x⁴ + 2x³− x²+ 2x + 3)(x+1)
(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)
The value of (fg)(x) is calculated as,
(fg)(x) = (2x⁵ + 2x⁴ + x³ + x ² +5x +3)
(fg)(-4) = (2(-4)⁵ + 2(-4)⁴ + (-4)³ + (-4)² +5x-4 +3)
(fg)(-4) = -2048 +1024-64+16-20+3
(fg)(-4) = -1089
Therefore, the value of the function (fg(x) is 2x⁵ + 2x⁴ + x³ + x ² +5x +3 and the value of f(g)(-4) is -1089.
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Can you write 6 x 10^5 x 0.08 in scientific notation.
Please.
4.8 × 10^4
Step-by-step explanation:= 4.8 × 10^4 {scientific notation}= 4.8e4 {scientific e notation}= 48 × 103 {engineering notation - thousand; prefix kilo- (k)}= 4.8 × 104 {standard form}4 {Order of Magnitude - for scientific and standard forms}= 48000 {real number}= forty-eight thousand {word form}At Happy Tails Animal Boarding, cat food and dog food is purchased weekly, Last week, Karen purchased 6 bags of cat food and 9 bags of dog food for a total of 117$. This week, she purchased 4 bags of cat food and 7 bags of dog food for a total of 87$.
Assuming the prices for cat and dog food have not changed over the past two weeks, find and solve the system of equations which can be used to determine the cost of a bag of cat food, c, and the cost of a bag of dog food, d.
c=cost of a bag of cat food
d=cost of a bag of dog food
Write Two Equation
?
?
One bag of cat food costs $6 and one bag of dog food costs $9.
What is system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
The problem states that c equals the cost of bag of cat food and d equals the cost of bag of dog food.
Last week she paid $117 for 6 bags of cat food and 9 bags of dog food.
Therefore, the equation becomes,
6c + 9d = 117 ..(1)
This week she paid $87 for 4 bags of cat food and 7 bags of dog food.
Therefore, the equation becomes,
4c + 7d = 87 ..(2)
Now to solve the system of equations
To solve the first equation for c.
6c + 9d = 117
6c = 117 - 9d
[tex]c = \frac{117}{6}-\frac{9d}{6}[/tex]
Plug value of c in equation (2).
[tex]4(\frac{117}{6}-\frac{9d}{6}) +7d = 87\\78 - 6d + 7d = 87\\d = 87-78\\d = 9[/tex]
Plug d = 9 in equation (1)
6c + 9(d) = 117
6c + 9(9) = 117
6c + 81 = 117
6c = 117 - 81
6c = 36
c = 6
Hence, one bag of cat food costs $6 and one bag of dog food costs $9.
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You have a loan for $1000 at 7.65 APR 100 of the loan is due each month and there is a penalty of 2% on the original amount were not paid If you do not pay anything on that loan during the year and assuming there is no compounding how much will you owe in total
If you do not pay anything on that loan during the year and assuming there is no compounding, the total sum owing is $1,216.50.
What does a loan simply mean?When money is given to someone else with the knowledge that it would be returned with interest, it is referred to as a loan. . Lenders will consider a borrower's income, credit rating, and level of debt before deciding to grant a loan.
Money borrowed from a bank or other financial organization is known as a loan. The borrower consents to repay the loan's principal plus interest. There are many different kinds of loans, such as auto loans, student loans, and mortgages.
The amount is 1000(1 + 0.0765), or 1000 x 1.0765, or 1,076.50.
Punishment equals 12(0.02 x 1000) = 12(20) = 240.
The total sum owing is $1,216.50 (1,076.50 plus 240).
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The base of a triangle is one half of its height. If the area of the triangle is 196 square millimeters,
find its base and height.
Step-by-step explanation:
the area of a triangle is
base × height / 2
in our case
base × height / 2 = 196 mm²
base × height = 392
base = height / 2
so, using that in our main equation :
(height / 2) × height = 392
height² = 784
height = sqrt(784) = 28 mm
base = height / 2 = 28/2 = 14 mm