The Distributive Property holds as both sides of the given equality are equal.
Distributive PropertyThe distributive property means that the outer time of the expression multiplies each of the inner terms of the expression. Then, these terms may be combined, if they contain like-terms.
The left-hand side of the expression is given as follows:
2/5(4/3 - 1/3).
Applying the distributive property, it is found that:
2/5 x 4/3 = 8/15.2/5 x 1/3 = 2/15.Subtracting them, it is found that:
2/5(4/3 - 1/3) = 8/15 - 2/15 = 6/15 = 2/5. (as both 6 and 15 are divided by 3).
Precedence of operationsThe right-hand side of the expression is:
2/5 x 4/3 - 2/5 x 1/3
Multiplication takes precedence over subtraction, hence:
2/5 x 4/3 - 2/5 x 1/3 = 8/15 - 2/15
Same denominator, hence the numerators can be subtracted as follows:
8/15 - 2/15 = 6/15 = 2/5. (as both 6 and 15 are divided by 3).
Both sides of the expression have the same value, hence the distributive property holds for this problem.
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At the fast food restaurant, an order of fries costs $0.94 and a drink costs $1.04. Howmuch would it cost to get 3 orders of fries and 2 drinks? How much would it cost toget f orders of fries and d drinks?
Determine the total cost for 3 order of fries and 2 drinks.
[tex]\begin{gathered} T=3\cdot0.94+2\cdot1.04 \\ =2.82+2.08 \\ =4.9 \end{gathered}[/tex]Determine the expression for f orders of fries and d drinks.
[tex]\begin{gathered} T=f\cdot0.94+d\cdot1.04 \\ =0.94f+1.04d \end{gathered}[/tex]So cost of 3 order of fries and 2 drinks is $4.9.
The cost order for f orders of fries and d drinks is 0.94f + 1.04d.
Devon is 30 years old than his son, Milan. The sum of both their ages is 56. Using the variables d and m to represent the ages of Devon and Milan, respectively, write a system of equations to describe this situation. Enter the equations below, separated by a comma.How old is Devon?
Let's set d as the age of Davon and m as the age of Milan.
Devon is 30 years old than his son Milan, it is represented by the equation:
[tex]d=m+30\text{ Equation (1)}[/tex]The sum of both ages is 56, the equation that represents the situation is:
[tex]d+m=56\text{ Equation (2)}[/tex]To find Devon's age, in equation 1, solve for m in terms of d:
[tex]m=d-30[/tex]Now, replace in equation 2 and solve for d:
[tex]\begin{gathered} d+(d-30)=56 \\ 2d-30=56 \\ 2d=56+30 \\ 2d=86 \\ d=\frac{86}{2} \\ d=43 \end{gathered}[/tex]Devon is 43 years old.
41 increased by 4 is what number ?
The statement
41 increased by 4
The word increase mean adding to the given number 41
Hence,
The statement can be expressed as
[tex]41+4[/tex]Simplifying the result gives
[tex]41+4=45[/tex]Therefore, the answer is
[tex]45[/tex]Point X is (3, -6). Wgich point is 10 units away from Point X
If we find the point X on the plane we can see the following:
Notice that the point D and the point X are 10 units apart with respect the x-axis, therefore, the point that is 10 units away from X is point D
Explain how to find the point equidistant from all three vertices in the given triangle. Choose the correct answer below. A. Find the intersection of the perpendicular bisectors of each side of the triangle B. Find the intersection of all of the midsegments of the triangle, C. Find the intersection of the angle bisectors of each angle of the triangle, D. Find the midpoint of the line segment that bisects Angle B.
ANSWER:
The correct option is the following:
C. Find the intersection of the angle bisectors of each angle of the triangle,
EXPLANATION:
The point that equidistant is the point at which the three bisectors of the internal angles of the triangle intersect, and it is the center of the circumference inscribed in the triangle and equidistant from its three sides.
IMPORTANT NOTE:
Any point on the bisector of an angle of a triangle equidistant from the sides that define that angle.
Jo borrowed $3800 for 8 months from a bank at 5.5% a. how much interest did jo pay the bank for the us of it's money?b. how much did he pay total?
Let's begin by listing out the given information:
Loan (p) = $3,800
Time (t) = 8 months = 8/12 year
Interest rate (r) = 5.5%
a)
We calculate it thus:
[tex]\begin{gathered} I=\frac{p\times r\times t}{100} \\ I=\frac{3800\times5.5\times\frac{8}{12}}{100}=139.33 \\ I=\text{\$}139.33 \end{gathered}[/tex]b)
The amount paid in total is:
[tex]\begin{gathered} A=p+I \\ A=3800+139.33=3939.33 \\ A=\text{\$}3939.33 \end{gathered}[/tex]suppose that you have a savings account with 8500 in it. it pays 7% interest compound as shown below. find the value for the next 4 years
We want find the compound interest annualy for 4 years, $8500, at 7%'
The formula for the compound amount over one year is;
[tex]A=P(1+\frac{r}{100})[/tex]1st year:
[tex]\begin{gathered} A=8500(1+0.07) \\ A=\text{ \$9095} \end{gathered}[/tex]2nd year:
[tex]\begin{gathered} A=9095(1.07) \\ A=\text{ \$9731.65} \end{gathered}[/tex]3rd year:
[tex]\begin{gathered} A=9731.65(1.07) \\ A=\text{ \$10412.87} \end{gathered}[/tex]4th year:
[tex]\begin{gathered} A=10412.87(1.07) \\ A=\text{ \$11141.77} \end{gathered}[/tex]Write a SITUATION that can be represented with this graph. Not an equation.
We need to think of something that will cool down 10 degrees in 5 hours to be more realistic. You may say that this graph describes the temperature profile of a fermentation broth after it is heated to 82 degrees is left on the tank to cool down to room temperature.
9×6 can u help me with this
You have to multiply the numbers:
9x6 =54
Multiply is the same as adding the number 6 times
9+9+9+9+9+9 =54
I NEED HELP ASAP Which of these data sets could best be displayed on a dot plot?721, 722, 722, 723, 724, 724, 724, 725, 727, 728, 73016, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 971.3, 1.9, 2.5, 2.7, 2.7, 3.5, 4.8, 5.3, 7.9, 9.00.012, 0.078, 0.093, 0.147, 0.187
Take into account that dop plots are usefull for small or moderate sized data sets, and also they are suefull for data with big gaps.
Based on the previous description, you can conclude that the best option for a dot plot is:
16, 29, 31, 37, 44, 49, 58, 63, 69, 70, 83, 97
in comparisson with the other data sets, the elements of the rest of data sets are closer to each other.
Here are the numbers of times 13 people ate out last month.5, 3, 4, 6, 3, 4, 5, 6, 4, 7, 3, 7, 6Find the modes of this data set.If there is more than one mode, write them separated by commas.If there is no mode, click on "No mode."No modeX?.
The mode is the number that appears most or occurs most frequently. Therefore, the mode of the data set below can be calculated below
[tex]5,3,4,6,3,4,5,6,4,7,3,7,6[/tex]Let's rearrange the data
[tex]3,3,3,4,4,4,5,5,6,6,6,7,7[/tex]The mode will be
[tex]\mleft\lbrace3,4,6\mright\rbrace[/tex]the ratio of men to woman working for a company is 5 to 4. if there is 225 employees total how many women work for the company
Given:
The ratio of men to women = 5: 4
Total number of employees = 225
The total ratio is:
[tex]\begin{gathered} =\text{ 5 + 4} \\ =\text{ 9} \end{gathered}[/tex]The number of women is the ratio of women to the total ratio times the number of employees
[tex]\begin{gathered} =\frac{4}{9}\times225 \\ =\text{ 100} \end{gathered}[/tex]Answer:
100 women
Help please!!!!!!!!!!!!!!!!!!!!!!!!!Which is the best buy?a. $18.09 for 9 bottles of juiceb. $22.33 for 11 bottles of juice
Answer:
The correct option is option a.
$18.08 for 9 bottles is the better buy.
Explanation:
The best buy is the item with the lesser price tag.
Let us chech which of the given items has the lesser price tag.
a. $18.08 for 9 bottles of juice
Let us find how much one bottle costs.
1 bottle = 18.08/9
= 2.01
1 bottle of juice costs $2.01 approximately
b. $22.23 for 11 bottles of juice
1 bottle = 22.23/11
= 2.03
1 bottle of juice costs $2.03 approximately.
Comparing these prices per bottle of juice, we realise that the one with $18.08 for 9 bottles is the better buy.
3. State whether each sequence is arithmetic or geometric, and then find the explicit and recursive formulas for each sequence.Formulas:
A sequence is called arithmetic if the difference between two consecutives is a constant
In the first case we see a constant difference of 5
every two consecutives have difference of 5, for example 20-15, 30-25 and so on.
In the second case we see the division between two consecutives is a constant . That is called a GEOMETRIC sequence.
the constant in this case is 18/6 =3
lets return to the 1st case find the explicit
An = Ao +(n-1) d
An means the n term in the sucession
Ao means the first term
d means the constant
with that in mind we replace the values obtained
An= 5 + (n-1) •5
now for the recursive
a1= 5
An = An-1 + 5
Now lets go to the second part, the geometric sequence. Just is needed to replace the values in the ABOVE RIGHT formula
so then
An = A1 •(3)^(n-1)
An = 2• (3)^(n-1)
there are 12 questionsI got 7 right what did I make?
there are 12 questions
I got 7 right
the easiest way to solve this is by using a rule of three
Step 1
Let
[tex]12\text{ questiones }\Rightarrow100\text{ percent}[/tex]then
[tex]7\text{ questions }\Rightarrow x\text{ percent}[/tex]Step 2
do the relation and solver for x
[tex]\begin{gathered} \frac{12}{100}=\frac{7}{x} \\ 12\cdot x=100\cdot7 \\ 12\cdot x=700 \\ x=\frac{700}{12} \\ x=58.33 \\ \end{gathered}[/tex]so, you did the 58.33 %
What is the measure of the exterior angle of the triangle? A. 23°B. 149°C. 180°D. 31°
Solution
The diagram below will be of help
From the image above
We know that the sum of angle in a triangle is 180 degrees
That is
[tex]\begin{gathered} 63+86+y=180 \\ 149+y=180 \\ y=180-149 \\ y=31^{\circ} \end{gathered}[/tex]Now, to find x
We also know that the sum of angle in a straight line is 180 degrees
That is
[tex]y+x=180[/tex]We now solve for x
[tex]\begin{gathered} x=180-y \\ x=180-31 \\ x=149^{\circ} \end{gathered}[/tex]Therefore, the value of x = 149 degrees
Option B
PMark for Review 1 Harold spent the summer working at a diner. He now pays for a monthly subscription to a magazine. The equation y -35x + 180 can be used to represent this situation, where y is the amount of money Harold has remaining after x months of paying for his monthly magazine subscription. Which statement best describes the amount of money Harold has, given this equation? - A) Harold started with $35 and he spends $180 per month on his magazine subscription. B) Harold started with $180 and he gets paid $35 per month. C) Harold started with owed $180 for magazines and he continues to spends $35 per month on his magazine subscription. D) Harold started with $180 and he spends $35 per month on his magazine subscription.
the option D is the correct answer
the equation is
y = 35x +180
that means he started with 180 $ and his monthly subscription is 35 $.
Ramon has assets that sum up to $253,000. He has liabilities that sum up to $216,345. what is his net worth?
Net worth is equal to total assets minus total liabilities (debt).
So,
Total Assets = 253000
Total Liabilities = 216345
Hence,
Net Worth = 253000 - 216345 = $36,655
Put the following equation of a line into slope-intercept form, simplifying allfractions.2x + 8y = 24
For each ordered pair, determine whether it is a solution to 3x + 5y=-17. Is it a solution? X 6 ? No (-8,3) (-4, -1) (6, 7) (7,2)
Determine whether is a solution for:
[tex]\begin{gathered} 3x+5y=-17 \\ To\text{ determine if it's a solution, we can isolate y and see if the statement} \\ is\text{ true:} \\ 5y=-17-3x \\ y=-\frac{17}{5}-\frac{3}{5}x \end{gathered}[/tex]For, x=-8, y has to be 3:
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(-8) \\ y=\frac{7}{5}=1.4 \end{gathered}[/tex](-8, 3) is not a solution for the equation.
For x=-4, y has to be -1:
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(-4) \\ y=-1 \end{gathered}[/tex](-4, -1) is a solution for the equation.
For x=6, y has to be -7:
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(6) \\ y=-7 \end{gathered}[/tex](6, -7) is a solution for the equation.
For x=7, y has to be 2
[tex]\begin{gathered} y=-\frac{17}{5}-\frac{3}{5}(7) \\ y=-\frac{38}{5}=-7.6 \end{gathered}[/tex](7, 2) is not a solution for the equation.
The scatter plot shows the median household income x in thousands of dollars, and the number of adults per 1,000 people with bachelors degree y of 50 U.S states. The line y=4.08x+63.13 is a good fit for this data
So,
The line:
[tex]y=4.08x+63.13[/tex]Is a good fit of the data given.
To predict the number of bachelor's degrees in Mississippi, we replace x by 40.6 and operate:
[tex]\begin{gathered} y=4.08(40.6)+63.13 \\ y=228.778 \end{gathered}[/tex]The number of bachelor's degrees per 1000 people when x=40.6 median income, is predicted as 228.778.
Calculate the area of the right triangle that has the following coordinates:
A: (-2,-1)
B: (1, 1)
C: (3,-2)
You must show all calculations to earn any credit. I suggest that you sketch this
triangle on graph paper so that the visual can help you.
The area of right triangle is [tex]\frac{1}{15}[/tex].
The given coordinates are [tex](-2,-1), (1, 1), (3,-2)[/tex].
We have to find the area of right triangle.
To find the area we first draw the graph using that coordinate.
The graph of the coordinate is
To find the area we use the formula
[tex]\angle ABC=\frac{1}{2}(|AB|)(|AC|)[/tex]
We first find the value of [tex](|AB|)[/tex] and [tex](|AC|)[/tex].
e coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]B[/tex] is [tex](1,1)[/tex].
The slope of [tex](|AB|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AB|)=\frac{1-(-1)}{1-(-2)}[/tex]
The slope of [tex](|AB|)=\frac{1+1}{1+2}[/tex]
The slope of [tex](|AB|)=\frac{2}{3}[/tex]
The coordinate of [tex]A[/tex] is [tex](-2,-1)[/tex] and [tex]C[/tex] is [tex](3,-2)[/tex].
The slope of [tex](|AC|)=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
The slope of [tex](|AC|)=\frac{(-2)-(-1)}{3-(-2)}[/tex]
The slope of [tex](|AC|)=\frac{-2+1}{3+2}[/tex]
The slope of [tex](|AC|)=-\frac{1}{5}[/tex]
Now finding the area of right triangle by putting the values.
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times(-\frac{1}{5})[/tex]
Area can't be negative so
[tex]\angle ABC=\frac{1}{2}\times\frac{2}{3} \times\frac{1}{5}\\\angle ABC=\frac{2}{30}\\\angle ABC=\frac{1}{15}[/tex]
Hence, the area of right triangle is [tex]\frac{1}{15}[/tex].
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find the zeros algebraically: f(x)=x^4-8x^3+5x^2+14x
The given equation is:
x^4-8x^3+5x^2+14x
In this question, we have to find the zeros algebraically. Hence, we need to find the values of x that satisfy the equation.
Note: The roots (values of x) are equal to the power of the equation. Therefore, the given equation will have 4 roots
Therefore,
x^4-8x^3+5x^2+14x = 0
or
x(x^3-8x^2+5x+14) = 0
=> x = 0 and x^3-8x^2+5x+14 = 0
Therefore, the first root is x = 0.
Now,
x^3-8x^2+5x+14 = 0
To simplify that, try putting different values of x (starting from 1 and -1). The value that makes both sides equal to zero would be the solution.
Let's start with (1):
For x = 1
(1)^3 - 8(1)^2 + 5(1) + 14 = 0
1 -8(1) + 5 + 14 = 0
-1 -8 +5 + 14 = 0
- 9 + 19 = 0
10 = 0
It is false, therefore, x = 1 is not the solution.
For x = -1
(-1)^3 - 8(-1)^2 + 5(-1) + 14 = 0
-1 -8(1) - 5 + 14 = 0
-1 -8 -5 + 14 = 0
- 14 + 14 = 0
0 = 0
hence, x = -1 is the second solution.
If x = -1 is the solution, (x + 1) should be the factor of x^3-8x^2+5x+14. Therefore, the whole equation can be divided by factor
x^3-8x^2+5x+14 / (x+1). = x^2 - 9x + 14. (using division)
Now, let's find the roots of x^2 - 9x + 14
x^2 - 9x + 14 = 0
x^2 - 7x - 2x + 14 = 0
x(x - 7) - 2 (x - 7) = 0
(x - 7) (x - 2) = 0
or
x - 7 = 0. and x - 2 = 0
x = 7 and x = 2
Therefore, the zeros of the given equation are, 0, -1, 2 and 7.
Quadrilateral MNOP is dilated by a scale factor of % to create quadrilateral M'N'O'P. The perimeter of quadrilateral MNOP is x units. What is the perimeter in units of quadrilateral M'N'O'P'? A. x units B. ( V2 x units COM X units D. 8/7 x units
If the perimeter of the quadrilateral MNOP is x
And a scale factor of a dilated image is
[tex]\frac{7}{8}[/tex]If the perimeter of M'N'O'P' = y
Then
[tex]\text{scale factor = }\frac{perimeter\text{ of y}}{perimeter\text{ of x}}\text{ = }\frac{7}{8}[/tex]Cross multiplying,
[tex]perimeterofy=M^{\prime}N^{\prime}O^{\prime}P^{\prime}=\frac{7}{8}\text{ x units}[/tex]The perimeter of M'N'O'P' = 7/8 x units
Option A is correct
I really need help make sure that your answer is 7th grade appropriate
Examples:
1. Five increased by four times a number
[tex]5+4n[/tex]where n is the number
2.The product of 4, and a number decreased by 7
[tex]4(n-7)[/tex]Derivative of ln(x)cos(x)
The derivative of the given expression ln(x)cos(x) can be written as (cos(x))/x - sin(x)ln(x).
What is derivative?
In mathematics, the derivative of a function of a real variable measures how sensitive the function's value (or output value) is to variations in its argument (input value). The derivative is the fundamental tool in calculus. A measure of how quickly an object's position changes over time is its velocity, which is the derivative of that object's position with respect to time.
We can solve this derivation using multiplication property of derivatives:
i.e. [tex]\frac{d}{dx}(uv) = u\frac{dv}{dx} + y \frac{du}{dx}[/tex]
In the given question, lets consider ln(x) as u and cos(x) as v
putting the values from question.
[tex]\frac{d}{dx}(ln(x)cos(x)) = ln(x)\frac{d(cos(x))}{dx} + cos(x) \frac{d(ln(x))}{dx}[/tex]
[tex]= ln(x)(-sin(x)) + cos(x)(\frac{1}{x})[/tex]
= (cos(x))/x - sin(x)ln(x)
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Which steps show how to use the distributive property to evaluate 9 - 32? A. 9(32) = 9(30 + 2) = 9.30 + 9 - 2 = 270 + 18 = 288 0 B. 9(32) = 9(30 + 2) = 9 - 30 + 30 - 2 = 270 + 60 = 330 OC. 9(32) = 9(30 + 2) = 9.30 – 9.2 = 270 – 18 = 252 O D. 9(32) = 9(30 + 2) = 9.30 + 2 = 270 + 2 = 272
to find the distribution of
[tex]9\cdot32[/tex]rewrite 32 as an addition
[tex]32=30+2[/tex]rewrite the product
[tex]9\cdot(30+2)[/tex]distribute the 9
[tex]\begin{gathered} 9\cdot30=270 \\ 9\cdot2=18 \\ \\ 9\cdot(30+2)=9\cdot30+9\cdot2 \\ 9\cdot(30+2)=270+18 \\ 9\cdot32=288 \end{gathered}[/tex]In shop, you make a table. The sides of the table measure 36" and 18". If the diagonal of the table measures 43", is the table "square"? (In construction, the term "square" just means the table has right angles at the corners.)
We are given the following information:
Table sides = 36 inches & 18 inches
Diagonal of table = 43 inches
We are to find out if the table is "square" (that is if the table follows the Pythagoras theorem). We will check this below:
[tex]\begin{gathered} \text{The Pythagoras Theorem is given by:} \\ c^2=a^2+b^2 \\ c=43in,b=36in,a=18in \\ \text{Substituting we have:} \\ 43^2=18^2+36^2 \\ 1849=324+1296 \\ 1849=1620 \\ \Rightarrow1849\ne1620 \\ \\ \therefore\text{ The table is not ''square''} \end{gathered}[/tex]Therefore, the table is not "square" (it does not have right angles at the corners)
Yesterday, Alan had k baseball cards. Today, he gave 19 away. Using k, write an expression for the number of cards Alan has left.
Answer:
k-19
Step-by-step explanation:
If Alan had k baseball card and gave 19 away then he would have 19 less then k
Answer:
K - 19= X
Step-by-step explanation:
I hope this helps!
Animal is a bird Can fly Tiger Penguin ✓ ✓ Robin ✓ Snail Sparrow ✓ ✓ Pelican ✓ ✓ ✓ Bat Let event A = The animal is a bird. Let event B = The animal can fly. Which outcomes are in A and 8? O A. (robin, sparrow.pelican) B. (penguin, robin, sparrow, pelican) c. robin, sparrow, pelican, bat) D. (penguin, robin, sparrow. pelican, bat)
Outcome that are in A and B simply means both outcome must be achieved.
Therefore,
[tex]\begin{gathered} \text{Animal can fly and Animal is bird both exist in } \\ A\text{. }\mleft\lbrace\text{Robbin, sparrow, pelican}\mright\rbrace \end{gathered}[/tex]