Diego is thinking of two positive numbers. He says, “If we triple the first number and double the second number, the sum is 34.”
Write an equation that represents this clue. Then, find two possible pairs of numbers Diego could be thinking of.
Diego then says, “If we take half of the first number and double the second, the sum is 14.”
Write an equation that could represent this description.
What are Diego’s two numbers? Explain or show how you know. A coordinate plane is given here, in case helpful.
The equation that represent the situation is as follows;
3x + 2y = 34
1 / 2x + 2y = 14
The two number Diego is thinking of are 8 and 5.
How to use equation to represent a problem?He is thinking of two positive numbers.
If we triple the first number and double the second number, the sum is 34.
If we take half of the first number and double the second, the sum is 14.
Therefore, the equation that can be used to solve the situation is as follows:
let
x = first number
y = second number
3x + 2y = 34
1 / 2x + 2y = 14
Therefore,
3x + 2y = 34
1 / 2x + 2y = 14
5 / 2 x = 20
5x = 40
x = 40 / 5
x = 8
3(8) + 2y = 34
2y = 34 - 24
2y = 10
y = 10 / 2
y = 5
Therefore, the two numbers are 8 and 5.
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8.4m^9n^5 divided by 2.1m^3n^5
Answer: [tex]4m^{6}[/tex]
Step-by-step explanation:
[tex]\frac{8.4m^{9} n^{5} }{2.1m^{3}n^{5}}[/tex]
Dividing exponents is the same as subtracting the exponents, so
[tex]\frac{m^{9}}{m^{3}} =m^{9-3}=m^{6}[/tex]
[tex]\frac{n^{5}}{n^{5}} =n^{5-5}=n^{0}=1[/tex]
So now our equation looks like
[tex]\frac{8.4m^{6}}{2.1}[/tex]
Now we can divide the numbers
8.4/2.1 = 4
So your final answer is [tex]4m^{6}[/tex]
mary has scored 78 , 60 , 82 , 94 , and 88 on her previous fice tests . What score does she need on her next test so that her average ( mean ) is 80 ?
Mary has scored 78, 60, 82, 94, and 88 on her previous fice tests.
What score does she need on her next test so that her average (mean) is 80?
Let x be the next test score
Recall that the mean is given by
[tex]mean=\frac{\text{sum of test scores}}{total\text{ numbers of tests}}[/tex]We have the following information,
mean = 80
sum of test scores = 78 + 60 + 82 + 94 + 88 + x = 402 + x
total number of tests = 6
So, let us substitute these values into the above formula
[tex]\begin{gathered} mean=\frac{\text{sum of test scores}}{total\text{ numbers of tests}} \\ 80=\frac{402+x}{6} \\ 6\times80=402+x \\ 480=402+x \\ 480-402=x \\ 78=x \\ x=78 \end{gathered}[/tex]Therefore, Mary need to score 78 on her next test so that her mean is 80
On a unit circle, the terminal point of theta is (1/2,square root 3/2). what is theta
Given the terminal point of Θ:
[tex](\frac{1}{2},\frac{\sqrt[]{3}}{2})[/tex]Let's find the value of Θ.
In polar coordinates, we have the points as
[tex]P=(R,\theta)[/tex]Where:
R is the radius and Θ is the angle.
We know in rectangular coordinates, we have:
x = R * cosΘ
Y = R * sinΘ
Thus, to find the value of Θ, we have:
[tex]\sin \theta=\frac{\sqrt[]{3}}{2}[/tex]Solve for Θ.
[tex]\begin{gathered} \\ \text{sin}\theta=\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Take the inverse cosine of both sides:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{\sqrt[]{3}}{2}) \\ \\ \theta=\frac{\pi}{3} \end{gathered}[/tex]ANSWER:
[tex]C.\text{ }\frac{\pi}{3}radians[/tex]Alyssa's algebra test score was 8 points lower than Jennifer's. The total of their two tests was 180. What did each girl receive?
Based on the equation, each girl received the following Algebra test scores:
Alyssa's = 86 pointsJennifer's = 94 points.What is an equation?An equation is a mathematical expression that claims that two values are equivalent.
Equations use the equation symbol (=) to illustrate the equality of two or more expressions.
Algebraically, let Alyssa's algebra test score = x
Let Jennifer's test score = x + 8
The total of their two tests = 180
x + x + 8 = 180
2x + 8 = 180
2x = 180 - 8
2x = 172
x = 86 (172/2)
Alyssa's test score = 8 points lower
Shareable points = 172 (180 - 8)
Each received 86 points from the shareable points
Alyssa's test score = 86 points
Jennifer's test score = 94 points
Check:
86 + 94 = 180
94 = 8 points greater than 86
Thus, using an equation, we can conclude that Alyssa scored 86 points on the Alegra test, which is 8 points less than Jennifer's 94 points.
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Josh wants to make the lamp purple.
He will use dye to make the plastic purple.
Josh will mix red dye with green dye and blue dye in the ratio 9:3:15 to make
purple dye.
Josh uses 30 litres of green dye.
(b) How many litres of purple dye will Josh make with the 30 litres of green dye?
Show a check of your working.
(5)
Answer:
Step-by-step explanation:
since 30 liters is ten times 3 liters, you must mulitply all of the amounts of dye liters (not green because we know its 30) by 10. this would make a ratio of 90:30:150. Now, add them all up to equal 270 liters of purple dye in total.
Find Point F so that angle ABC is = to angle DEF
Answer
(5, 2)
Step-by-step explanation
Point D in triangle DEF is the equivalent to point A in ABC. Similarly, E is the equivalent to B. In consequence, F is the equivalent to C.
We can obtain points D and E by translating points A and B 6 units to the right and 4 units up.
Translation 6 units to the right and 4 units up transforms the point (x, y) into (x+6, y+4). Applying this rule to point C:
C(-1, -2) → (-1+6, -2+4) → F(5, 2)
What is the probability that a randomly selected Shopper is a man given that he shops at Home Depot? Round the answer to the nearest hundredth of a percent.
Out of all the 500 people, how many are Men, shopping at Home Depot?
See the cell crossing "Men" row and "Home Depot" column.
it is 37
Hence, probability of shopper being a men who shops at Home Depot is:
37/500
In decimal:
0.074
In percentage:
7.40%Shay's net pay is $575.50 biweekly. If her gross annual income is$17,500, how much is deducted from each paycheck?a. $153.67b. $2,537c. $97.58d. $3,688
a. $157.67
Explanation:
>> net income (total amount without the taxes etc...)
. biweekly = $575.50
. per month = $575.50 * 2 = $1,151 (~since it happens 2 times per month)
. per year = $1,151 * 12 = $13,812
>> gross income (total amount with the taxes etc...)
. per year = $17,500
>> amount deducted (~going to taxes etc...)
. per year = $17,500 - $13,812 = $3,688
. per month = $3,688 / 12 =~ $307.33
. per paycheck = $307.33 / 2 =~ $153.67
find the number of units of grain that are to be produced to maximize the profit if…
we need to make revenue-cost and then maximize
[tex]\begin{gathered} R(x)-C(x) \\ (97x-2x^2)-(2x^2+49x+6) \end{gathered}[/tex]simplify
[tex]\begin{gathered} =97x-2x^2-\mleft(2x^2+49x+6\mright) \\ =97x-2x^2-2x^2-49x-6 \\ =-2x^2-2x^2+97x-49x-6 \\ =-4x^2+97x-49x-6 \\ =-4x^2+48x-6 \end{gathered}[/tex]now, to maximize, we need to find the derivate and make it equal to 0
[tex]\begin{gathered} \frac{d}{dx}(-4x^2+48x-6)=0 \\ -8x+48=0 \\ -8x=-48 \\ \frac{-8x}{-8}=\frac{-48}{-8} \\ x=6 \end{gathered}[/tex]so, the maximum profit is at x = 6
What is anequation of the line that passes through the points (-4, -1) and(6, -1)?
We are given the following two points
[tex](-4,-1)\text{and }(6,-1)[/tex]We are asked to find the equation of the line that passes through these points.
Recall that the equation of the line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
The slope of the line is given by
[tex]m=\frac{y_2−y_1}{ x_2−x_1}[/tex][tex]\text{where}(x_1,y_1)=(-4,-1)\text{and}(x_2,y_2)=(6,-1)[/tex]Let us substitute the given values into the slope formula
[tex]m=\frac{-1-(-1)}{6-(-4)}=\frac{-1+1}{6+4}=\frac{0}{10}=0[/tex]So, the slope of the equation is 0
The equation of the line becomes
[tex]y=0x+b[/tex]Now let us find the y-intercept (b)
Choose any one point from the given two points
Let choose (-4, -1) and substitute it into the above equation
[tex]\begin{gathered} y=0x+b \\ -1=0(-4)+b \\ -1=0+b \\ b=-1 \end{gathered}[/tex]Therefore, the equation of the line in slope-intercept form is
[tex]y=-1[/tex]Note that this equation has 0 slope that is why mx part becomes 0
the sugar sweet company is going to transport its sugar to market. it will cost $3250 to rent trucks, and it will cost andl additional $125 for each ton of sugar transported.let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. write and equation relating C to S and then graph your equation.
The variables are
C: total cost ($)
S: amount of sugar (tons)
The equation that relates these two variables is;
C = 3250 + 125S
The graph of the equation is:
where C is the dependent variable, and S is the independent variable
which of the following are point-slope equations of the line going through (-2,-2) and (2,1) check all that apply
The Point-Slope form of the equation of a line is:
[tex]y_{}-y_1=m(x-x_1)_{}[/tex]Where "m" is the slope of the line and this is a point on the line:
[tex](x_1,y_1)[/tex]You can find the slope of a line using this formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In this case, knowing that this line passes through these points:
[tex](-2,-2);\mleft(2,1\mright)[/tex]You can set up that:
[tex]\begin{gathered} y_2=-2 \\ y_1=1 \\ x_2=-2 \\ x_1=2 \end{gathered}[/tex]Substituting values into the formula and evaluating, you get:
[tex]m=\frac{-2-1}{-2-2}=\frac{-3}{-4}=\frac{3}{4}[/tex]Knowing the slope and coordinates of two points on the line, you can set up these two equations for this line:
1. First equation:
[tex]\begin{gathered} y-(-2)=\frac{3}{4}(x-(-2)) \\ \\ y+2=\frac{3}{4}(x+2) \end{gathered}[/tex]2. Second equation:
[tex]y-1=\frac{3}{4}(x-2)[/tex]The answers are: Option A and Option B.
A. Find f(1/2 pie)
B. Find the all values x when f(x)=0. Use a comma to separate each value.
C. Fine the range. Write it in Interval notation.
Answer:
A. [tex]f(\frac{1}{2}\pi)=2[/tex]
B. [tex]x=-2\pi, -\pi, 0, \pi, 2\pi[/tex]
C. [tex][-2, 2][/tex]
Step-by-step explanation:
A:
Since we want to find: [tex]f(\frac{1}{2}\pi)[/tex], all we do is go that that x-value on the function and then go either up or down until we find where the y-value is at that x-value, because [tex]f(\frac{1}{2}\pi)[/tex] is just another way of expressing "the y-value of the function f, at [tex]x=\frac{1}{2}\pi[/tex]
In this case it turns out that the y-value is two, which you can verify by going to that x-value and finding where the y-value is at that point.
So: [tex]f(\frac{1}{2}\pi)=2[/tex]
B.
To find all the x-values such that: [tex]f(x)=0[/tex], we just need to find where the graph crosses the x-axis, also known as an x-intercept. This is because at an x-intercept, the y-value will be equal to zero.
Looking at the graph you can see that these x-intercepts occur at: [tex]x=-2\pi, -\pi, 0, \pi, 2\pi[/tex]
in general you'll notice that all the values are actually separated by a value of pi, so the general formula for a zero in this equation is likely going to be: [tex]x=\pi n\text{ where n is an integer}[/tex], since trigonometric functions are periodic, they repeat.
C.
Looking at the graph you'll notice the value is increasing, then decreasing, then increasing... and so on.
The max value it reaches is two, and the min value it reaches is negative two.
The range of a function is the y-values that the function can output, considering all the possible inputs, or the domain.
In this case no matter the input we can only output values between -2 and 2.
In this interval notation, we use brackets, since the minimum and maximum possible values are included in the range, since the function does output 2 and -2, it doesn't just "approach" it.
So we get a range of: [tex][-2, 2][/tex]
how much accumulated interest should the investor expect at the end of 10 years?
Answer:
The correct option is D
The accumulated interest after 10 years is $2,125.00
Explanation:
We have the following parameters:
Principal (P) = $2,500
Rate (R) = 8.5%
Time (T) = 10 years
To calculate the interest after 10 years, we use the formula:
[tex]A=\frac{PRT}{100}[/tex][tex]\begin{gathered} A=\frac{2500\times8.5\times10}{100} \\ \\ =2125 \end{gathered}[/tex]The interest is $2,125
Write this absolute value function as a piecewise function. y= 2|x|-3
A function can be written as piecewise function if it changes its behaviour ( increasing or decreasing ) about a point.
[tex]\begin{gathered} Thefunctionf\mleft(x\mright)=y=|x|changesitsbehaviourat|x|=0ie,x=0. \\ y=|x|=x,ifx<0=-x,ifx>0 \\ |x|=a\Rightarrow x=\pm a \end{gathered}[/tex]Here Here,
The given function is : y = 2|x| - 3
Here,
The function will change its behaviour when
| x | = 0
=> x = 0
Now,
If x < 0 , then ;
=> y = 2[–(x)] – 3
=> y = –2x – 3
=> y = – 2x – 3
If x ≥ 0 , then ;
=> y = 2(x) – 3
=> y = 2x – 3
=> y = 2x -3
Hence ,
y = – 2x – 3 , if x < 0
y = 2x - 3 , if x ≥ 0
[tex]f(x)=\begin{cases}-2x-3\text{ , if x < }0 \\ \\ 2x-3\text{ , if x }\ge0\end{cases}[/tex]Liz bought seven liters of orange juice for a party. About how many quarts of juice did she buy?
Let's make a conversion:
[tex]7l\times\frac{1.05669qt}{1l}=7.39683qt\approx7.40qt[/tex]She bought about 7.39683qt
Liz bought 7.396817 quarts of orange juice for a party.
What are Quarts?The liquid quart in the United States is a measure of fluid volume equal to one-fourth of a gallon, two pints, or four cups. The liquid quart is not to be confused with the dry quart (US) or the imperial quart, which are two distinct units.
Multiply the volume by the conversion ratio to transform a liter measurement into a quart measurement.
Since each liter equals 1.056688 quarts, you may use the following easy formula to convert:
quarts = liters × 1.056688
The volume in quarts is equal to the liters multiplied by 1.056688.
We have been given that Liz bought seven liters of orange juice for a party.
We have to convert 7 liters to quarts using the formula above.
7 L = (7 × 1.056688) = 7.396817 qt
Thus, she bought 7.396817 quarts of orange juice for a party.
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Write a function g(x), the translation of... that has a horizontal asymptote at y=2 and..
we have that
Vertical asymptote at x=3
so
The denominator could be (x-3)
Horizontal asymptote at y=2
so
Degree on Top is Equal to the Bottom
The numerator could be equal to 2x and the leading coefficient of the denominator is 1
therefore
[tex]g(x)=\frac{2x}{(x-3)}[/tex]Solve using proportions.
Andrew is on a low-carbohydrate diet. If his diet book tells him that an 8-oz serving of pineapple contains 19.2 g of carbohydrate,
how many grams of carbohydrate does a 5-oz serving contain?
Using proportions we know that a 5-oz serving contains 12g of carbohydrates.
What are proportions?A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls, and 0.25 are males (by dividing 1 by 4).
So, the carbohydrates in a 5-oz serving:
Now, calculate as follows:
8:19.2g = 5:xg8/19.2 = 5/xg8xg = 19.2(5)8xg = 96xg = 96/8x = 12gTherefore, using proportions we know that a 5-oz serving contains 12g of carbohydrates.
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2+2+13-2/35? please help
Answer: 16.94285714
Step-by-step explanation: 2/35 is 0.05714285714. 13+2+2 = 17.
17- 0.05714285714 is 16.94285714.
1) The table represents the relationship between a length measured in meters and th same length measured in kilometers. a. Complete the table. meters kilometers 1,000 1 3,500 500 b. Write an equation for converting the number of meters to kilometers. 75 1 X
Explanation:
1)
1 kilometer is equal to 1000 meters:
1 km = 1000 m
So,
1m = 1/1,000 km
To complete the table, we can use the rule of three:
a) 1,000 m?
1m - 1/1,000 km
1,000m - x
x = 1/1000 * 1,000 = 1 km
As we can see, we only have to divide the measure in meters by 1000.
b) 3,500 m = 3,500/1,000 = 3.5 km
c) 500 m = 500/1,000 = 0.5 km
d) 75 m = 75/1,000 = 3/40 km = 0.075 km
e) 1 m = 1/1000 = 0.001 km
f) x = x/1,000 = 0.001x km
2)
The relation is:
Y = 0.001x
Where x is the measure in km and x in meter.
(1 2/7-3/14)/8/15trying to remember how to do this
We will write it as a fraction in ordet to solve, that is:
[tex]\frac{(1\frac{2}{7}-\frac{3}{14})}{(\frac{8}{15})}[/tex]We then operate as follows:
[tex]\frac{((\frac{7}{7}+\frac{2}{7})-\frac{3}{14})}{(\frac{8}{15})}\Rightarrow\frac{(\frac{9}{7}-\frac{3}{14})}{(\frac{8}{15})}\Rightarrow\frac{(\frac{15}{14})}{(\frac{8}{15})}\Rightarrow\frac{15\cdot15}{14\cdot8}\Rightarrow\frac{225}{112}[/tex]We have this, since 1 integer will be equal as a numerator divided by a denominator with equal values. Examples 1 = 2/2, 1 = 45/45, ...
.......................
we have that
Part c)
the probability is equal to
P=0.14+0.27+0.58
P=0.99because is the sum of
x=1, x=2 and x=3
Part D
the probability is
P=0.01+0.14+0.27
P=0.42because is less than or equal 2
1. Graph the system of equations.2. What are all the values for x for which f(x)=g(x)?
Solution:
Given the system of equations:
[tex]\begin{gathered} f(x)=-x^2+6x-4 \\ g(x)=|x-3|-1 \end{gathered}[/tex]1) The graphs of the system of equations are as shown below:
2) Values of x for which
[tex]f(x)=g(x)[/tex]From the graph of the system of equations, the points at which the graph functions cut or intersect each other, give the solution of the system of equations.
Thus, in the graph of the system of equations, the functions intersect each other at the point (1,1) and (5,1) as shown below:
Thus, the values of x for which f(x) = g(x) are
[tex]\begin{gathered} x=1,\text{ } \\ x=5 \end{gathered}[/tex]Been struggling on this for days, some help would be appreciated.
Answer:
-b plus or minus square root of b square - 4ac
divided by 2a
where by a is the first term
b is the second term
c is the third term
Step-by-step explanation:
a = 1
b = -5
c = 4
x = 4 & 1
31. Find the circumference.
a. 18.84 in
b. 36 in
c. 9 in
I need help with these please you don't need to write the explanation you could write the answers
is it 3, right?
3.- B, angle 1 and angle 8
2.- It's incomplete, Number two it's incomplete I think I need a picture of this problem.
2 .- 4, letter J
Done, bye
what are three consecutive integers that add to 40
Answer:
12 1/3 + 13 1/3 + 14 1/3 = 40
Step-by-step explanation:
Here we will use algebra to find three consecutive integers whose sum is 40. We start by assigning X to the first integer. Since they are consecutive, it means that the 2nd number will be X + 1 and the 3rd number will be X + 2 and they should all add up to 40. Therefore, you can write the equation as follows:
2y-4=3y-5 How Many solutions have?
Answer:
one solution
Step-by-step explanation:
solve it.
2y-4=3y-5
-y=-1
y=1
Identify the transformation from ABC to A'B'C' .(x+4, y+8)(x-4, 4-8)(x+8, y+4)(x-8, y-4)
When you locate the coordinates of A it is (-4, 1)
Locate the coordinates of A', it is : (4, 5)
This implies, 8 was added to the x coordinate and 4 was added to the y-coordinate
Hence, the transformation is;
(x + 8, y+4)