Since we multiplied 3 to each side of the equation of 3x + y = 9, the new equation 9x + 3y = 27 pertains to the same equation. This means that the graph of 3x + y = 9 and 9x + 3y = 27 are the same.
Thus, the intersection of 2x + 4y = 8 and 3x + y = 9 is the same as the intersection of 2x + 4y = 8 and 9x + 3y = 27.
Therefore, the solution of 2x + 4y = 8 and 9x + 3y = 27 is the same solution as the first system of linear equation.
Bismark Tractor put a markup of 26% on cost on a part for which it paid $350. Find the markup
From the question
Percentage markup = 26%
Selling price(SP) = $350
To find the Markup
The formula below will be used
[tex]\text{ \%Markup }=\frac{SP-CP}{CP}-100\text{\%}[/tex]Since Cost price(CP) is not given
Hence, substitute given values to find CP
[tex]26=\frac{350-CP}{CP}\times100[/tex]Solve for CP
Cross multiply
[tex]26CP=100(350-CP)[/tex]Expand the bracket
[tex]26CP=35000-100CP[/tex]Collect like terms
[tex]\begin{gathered} 26CP+100CP=35000 \\ 126CP=35000 \end{gathered}[/tex]Divide both sides by 126
[tex]\begin{gathered} \frac{126CP}{126}=\frac{35000}{126} \\ CP=\text{ \$}277.78 \end{gathered}[/tex]Hence the cost price is $277.78
To find Markup the formula below will be used
[tex]\text{Markup }=SP-CP[/tex]Hence,
[tex]\begin{gathered} \text{Markup }=\text{ \$}350-\text{ \$}277.78 \\ \text{Markup }=\text{ \$}72.22 \end{gathered}[/tex]Therefore, the markup is $72.22
A) What was the change of annual sales between the first year 2013, and the 2019 year’s (b) What is the average rate of change in sales for the 2019 year beginning in 2013?_____billion dollars per year
Given:
Sales in 2013 = 36.44 billions of dollars
Sales in 2019 = 38.16 billions of dollars
(a) Change of annual sales between 2013 and 2019
The change of annual sales between 2013 and 2019 is the difference between the annual sales in 2019 and the annual sales in 2013:
[tex]\text{change of annual sales = sales in 2019 - sales in 2013}[/tex]Substituting the given values:
[tex]\begin{gathered} \text{change of annual sales = 38.16 - 36.44 } \\ =\text{ }1.72 \end{gathered}[/tex]Hence, the change of annual sales is 1.72 billions dollars
(b) The average rate of change in sales for the 2019 year begining in 2013:
The average rate of change can be calculated using the formula:
[tex]\begin{gathered} \text{Average rate of change = }\frac{sales\text{ in 2019 - sales in 2013}}{2019\text{ - 2013}} \\ =\text{ }\frac{1.72\text{ }}{6}\text{ } \\ =\text{ 0.287 billion dollars per year} \end{gathered}[/tex]Hence, the average rate of change in sales for the 2019 year begining in 2013 is 0.287 billion dollars per year
Find two different sets of coins that each make 120% of a dollar, where no type of coin is in both sets
First we have to find how much is the 120% of a dollar so we can made a rue of 3
[tex]\begin{gathered} 1\to100 \\ x\to120 \end{gathered}[/tex]and the equation will be:
[tex]x=\frac{1\cdot120}{100}=1.20[/tex]So to have 1.20 dollars we can have:
option 1: 1 coin of 1 dollar and two dimes
option 2: 1 coin of a dollar and 4 coins of 5 cents.
translate the phrase into mathematical symbols. the square of 5 in mathematical symbols
Solution:
Given:
The square of 5.
The square of a number is the result of multiplying the number by itself.
The word square is usually equivalent to raising a number to the power of 2.
For example:
[tex]The\text{ square of 4 is }4^2[/tex]Therefore, the square of 5 is:
[tex]5^2[/tex]Answer:
[tex] {5}^{2} [/tex]
Or, if you can enter symbols from clavier only, this is 5^2
write the equation in
Write equation form
A circle centered in (0,0) have for equation
(X-h)^ 2 + (Y-k) ^2 = R^2,. R= 10
h=k= 0
Then equation is
X^2 + Y^2 = 10^2 = 100
The length of Ryan's room was decreased by 7ft. The original length was 29ft. What is the percent decrease
A sweater is $43. it is on sale for 20% off. what is the final price?
sweater: $43
sale 20% off
final price ?
[tex]43-(43\cdot0.2)=34.4[/tex]the final price is 34.4
Consider a picnic. if you want to buy enough hot dogs and buns without having any leftovers, you need to balance the number of packages of buns (which usually contain 8 buns) with the number of packages of hot dogs (which usually contain 10 dogs). you would get 5 and 4 packages. Now you need to feed at least 500 people. If you want to feed everyone, but still have equal numbers of buns and hot dogs, what is the minimum number of packages of buns and hot dogs you need, respectively?Hint: you determined that you can make 40 servings from five packages of buns and four packages of hot dogs without anything left over. This means that you can also make 80, 120, 160, and so forth, servings without anything left over. These numbers are called multiples of 40.
We are given information about how many buns and dogs are contained in each package and are asked which is the minimum number of packages needed.
By using the hint given to us, we know that we need 5 packages of buns and 4 packages of hot dogs to feed 40 people, therefore, let's use multiples of 40 to get closer to the magic number of 500, as follows:
[tex]\begin{gathered} 40\cdot12=480,\text{ which is the closest we can get to 500 using multiples of 40} \\ Therefore,\text{ }in\text{ }order\text{ }to\text{ }feed\text{ }480\text{ }people\text{ }we\text{ }need: \\ 5\cdot12=60\text{ }packages\text{ }of\text{ }buns \\ 4\cdot12=48\text{ }packages\text{ }of\text{ }hot\text{ }dogs \\ \end{gathered}[/tex]Now, we have already fed 480 people, we need at least 20 more, but remember that we don't want to have any leftovers and we want the same number of buns and dogs, therefore, we can't feed exactly 500, we have to feed 520, which means we have to go over another multiple of 40, by buying 5 more packages of buns and 4 more packages of hot dogs.
Therefore, the correct answer is 65 packages of buns and 52 packages of hotdogs:
[tex]\begin{gathered} 60+5=65\text{ }packages\text{ }of\text{ }buns \\ 48+4=52\text{ }packages\text{ }of\text{ }hotdogs \end{gathered}[/tex]
Farmers often plant crops in circular areas because one of the most efficient watering systems for crops provides water in a circular area. Passengers in airplanes often notice the distinct circular patterns as they fly over land used for farming. A photographer takes an aerial photo of a field on which a circular crop area has been planted. He prints the photo out and notes that 2 centimeters of length in the photo corresponds to 100 meters in actual length. a. What is the scale factor of the actual farm to the photo? If the dimensions of the entire photo are 25 cm by 20 cm, what are the actual dimensions of the rectangular land area in meters captured by the photo? If the area of the rectangular photo is 5 cm', what is the actual area of the rectangular area in square meters?
It is given that 2 centimeters of length in the photo correspond to 100 meters in actual length.
a. What is the scale factor of the actual farm to the photo?
The scale factor is given by
[tex]SF=\frac{model\: length}{actual\: length}[/tex]Jessica is going for a walk. She takes 3 hours to walk 7.5 miles. What is her speed?
Solution:
Speed, s, can be calculated using the formula;
[tex]\begin{gathered} s=\frac{d}{t} \\ \\ \text{ Where;} \\ d=distance,t=time \end{gathered}[/tex]Thus;
[tex]\begin{gathered} d=7.5miles,t=3hours \\ \\ s=\frac{7.5miles}{3hours} \\ \\ s=25\frac{miles}{hour} \end{gathered}[/tex]ANSWER: Her speed is 25 miles per hour.
Question 1 Evaluate the expression below. Then explain why you chose to evaluate it in the order that you did. -21 ÷ (1/3) ÷ (-7) × 5 ÷( -2/3 ) × 2
To evaluate this expression:
-21 ÷ (1/3) ÷ (-7) × 5 ÷( -2/3) × 2 [1]
We need to remember the PEMDAS procedure:
First, solve parentheses, then exponents; then, multiplications, divisions, and finally additions and subtractions.
However, in this case, we will start to solve this expression from the left to the right (in the order the operations started, that is, from left to right):
-21 ÷ (1/3) ÷ (-7) × 5 ÷( -2/3) × 2
First step:
-21 / 1/3 = -21 * 3 = -63
-63 ÷ -7 = 9
We multiply this result by 5:
9 x 5 = 45
45 ÷ (-2/3) = 45 x -(3/2) = -135/2
(-135/2) * 2 = -135
We chose to evaluate this way because it was the order in which appeared each operation, that is, from left to right.
This is a way of evaluating this expression.
If lines m and n are parallel, which of these is true?(A)1 and 2 are supplementary angles(B)1 and 6 are corresponding angles(C)3 and 5 are alternate interior angles(D)4 and 6 are consecutive interior angles(E)5 and 8 are congruent angles(F)6 and 7 are supplementary angles(G)1 and 7 are alternate exterior angles
Answer:
A, D, and E.
Explanation:
Definitions:
• Two angles are said to be ,supplementary, if they ,add up to 180 degrees.
,• Two angles are said to be ,congruent if their measures are equal.
,•
If lines m and n are parallel lines, the following statements are true:
0. 1 and 2 are supplementary angles
,1. 4 and 6 are consecutive interior angles
,2. 5 and 8 are congruent angles
When you write a number between 0 and 1 inscientific notation, the exponent of the power of10 will be
If the number is between 0 and 1, and we are writing it in scientific notation, the exponent of the power of 10 is going to be smaller than 0 (that is a negative number for the exponent)
This is because the number of powers of ten are going to be part of a denominator.
For example, the number 0.001 which is between zero and 1 , can be written as:
1 divided by 1000. Notice then the 1000 value is in the denominator. powers of 10 in the denominator are represented always with negative exponents when written in scientific notation.
Anotther example is shown below:
[tex]0.0005=\frac{5}{10000}=\frac{5}{10^4}=5\, \, 10^{=4}[/tex]Again, the exponent of the power 10 will be a negative integer number in scientific notation.
suppose observe distance of a golf ball travel when the clubhead speed was 100 miles per hour was 265 yards what is the residual
Answer
a) Predicted distance covered by the golfball for a club-head speed of 100 mph = 260.8 yards
b) Residual of the observed value of 265 yards is 4.2 yards.
Explanation
We have been given a relation that relates the club-head speed in miles per hour, x, to the distance covered by the golf ball in yards, y.
y = 2.8333x - 22.4967
a) We are then asked to find the distance covered by the golf ball for a club-head speed of 100 miles per hour.
That is, we need to find y when x = 100
y = 2.8333x - 22.4967
y = 2.8333 (100) - 22.4967
y = 283.33 - 22.4967
y = 260.8333 yards = 260.8 yards to the nearest tenth.
b) We are then told that the actual distance covered by the golfball for a club-head speed of 100 miles per hour is 265 yards.
We are then asked to find the residual of the observed value.
The residual of an observed value is the difference between the observed value and the predicted value of the quantity of interest.
For this question,
Observed value = 265 yards
Predicted or estimated value = 260.8 yards
Residual = (Observed value) - (Predicted value)
Residual = 265 - 260.8
Residual = 4.2 yards
Hope this Helps!!!
Determine if f(x) = - (x ^ 3)/6 - 6/(x ^ 2) is a polynomial functionIf it is, and the leading coefficient . If not , state why .
Given function is:
[tex]f(x)=-\frac{x^3}{6}-\frac{6}{x^2}\ldots(1)[/tex]A polynomial is an algebraic expression that involves only positive integer exponents for the variables.
A polynomial function is of the form:
[tex]p(x)=a_nx^n_{}+a_{n-1}x^{n-1}+a_{n-2}x^{n-2}+\cdots+a_0[/tex]Solving equation (1)
[tex]\begin{gathered} f(x)=-\frac{x^3}{6}-\frac{6}{x^2} \\ =-\frac{x^5+36}{6x^2} \\ =-\frac{x^{-2}(x^5+36)}{6} \end{gathered}[/tex]We can see that the function has a negative exponent.
The given function is not a polynomial function.
Evaluate the piecewise function at the given values of the independent variableFind A B C
Based on the piecewise function, we have two conditions: if x is equal to 5 and not equal to 5.
Since the given value of x in the question is 3, let's use the first condition that states x is not equal to 5.
[tex]h(x)=\frac{x^2-25}{x-5}[/tex]Let's plug in x = 3 in the function above.
[tex]h(3)=\frac{3^2-25}{3-5}[/tex]Then, simplify.
[tex]\begin{gathered} h(3)=\frac{9-25}{-2} \\ h(3)=\frac{-16}{-2} \\ h(3)=8 \end{gathered}[/tex]Therefore, h(3) = 8.
Similary, for B, since the given value of x is 0, which is not equal to 5 still, let's use the first condition and plug in x = 0.
[tex]\begin{gathered} h(x)=\frac{x^2-25}{x-5} \\ h(0)=\frac{0^2-25}{0-5} \\ h(0)=\frac{-25}{-5} \\ h(0)=5 \end{gathered}[/tex]Hence, h(0) = 5.
Lastly, for C, the given value of x is 5. With that, we shall use the second condition.
[tex]\begin{gathered} h(x)=4 \\ h(5)=4 \end{gathered}[/tex]Therefore, h(5) = 4.
Is (5,4) a solution to this system of linear equation
We have the following system of equations:
[tex]\begin{gathered} y=x-1\text{ (1)} \\ y=-x+5\text{ (2)} \end{gathered}[/tex]To see if (5,4) is a solution, we must substitute x=5 or y=4 into the two equations:
[tex]\begin{gathered} (1)4=5-1 \\ 4=4\text{ TRUE} \\ (2)\text{ } \\ 4=-5+5 \\ 4=0\text{ FALSE} \end{gathered}[/tex]Therefore (5,4) is NOT a solution to this system of linear equations.
A salesperson earns commission on the sales that she makes each mouth.The sales person earns 5% commissions on the first $5,000 she has in sales. The sales person Earns 7.5% commissions on the amount of her sales that are greater than $5,000. The sales person Earns $1,375 in last month.How much money in dollars did she have in sales last month?
We have that we can represent the total sales with the following expression:
[tex]\text{total sales=ssales with 5\% comission + sales with 7\% comission}_{}[/tex]Now, we have that the sales person earns 5% comission on the first $5000, this is equivalent to:
[tex]5000\cdot(0.05)=250[/tex]then, if the salesperson earns $1375 in comissions, we have the following equations:
[tex]\begin{gathered} \text{7.5\% comission = total comissions-5\% comissions} \\ \Rightarrow\text{ 7.5\% comission = 1375-250=1125} \end{gathered}[/tex]we have that the sales with 7.5% comissions got the salesperson $1125, then, we have the following:
[tex]\text{sales with 7.5\% = }\frac{7.5\text{ \% comission}}{7.5\text{ \%}}=\frac{1125}{0.075}=15000[/tex]therefore, the salesperson had 15000+5000=$20000 in sales to earn $1375 in comissions
Find the volume of this cone. Leave the answer in terms of π.A. 48π cubic cmB. 150.72π cubic cmC. 1,728π cubic cmD. 2,000π cubic cm
Explanation
Given that the height of the cone is 4cm and that the diameter of the cone is 12cm. Therefore, we can find the volume of the cone below.
[tex]volume=\frac{1}{3}\pi r^2h=\frac{1}{3}\pi(\frac{12}{2})^2(4)=\frac{\pi\times36\times4}{3}=48\pi[/tex]Answer: Option A
Consider the equation, where p is a real number coefficient. - (pc - 2) = 9 What is the value of x in the equation? 3 P O r = O = 25 OI= 29
Question 2 of 10 The graphs below have the same shape. What is the equation of the blue graph? f(x) = x2 g(x) = 2 foy 6 -5 g(x) = O A. g(x) = (x - 5)2
Notice that both graphs have the same shape, but the blue curve is the red one after a translation to the right.
In general, given a function h(x), a translation in the x-axis direction is given by the formula
[tex]\begin{gathered} h(x)\to h(x-a) \\ a>0\to\text{ a units to the right} \\ a<0\to\text{ a units to the left} \end{gathered}[/tex]In our case, notice that the vertex of the parabola (0,0) transforms into (5,0)
[tex]\begin{gathered} (0,0)\to)=(5,0)=(5+0,0) \\ \Rightarrow g(x)=f(x-5) \end{gathered}[/tex]Then,
[tex]\Rightarrow g(x)=(x-5)^2[/tex]The answer is g(x)=(x-5)^2
A probability experiment consists of rolling a fair 15-sided die. Find the probability of the event below.rolling a number divisible by 5The probability is a(Type an integer or decimal rounded to three decimal places as needed.)
Since the dice is a fair one we know that we have the same probability for each side to come up. That means that each number has a probability of 1/15 to appear.
Now we need to find the probability of finding a number that is divisible by 5. The numbers in the dice are 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15. The numbers that are divisible by 5 are 5,10 and 15. Then the probability we are looking for is the sum of each probability, then we have:
[tex]P=\frac{1}{15}+\frac{1}{15}+\frac{1}{15}=\frac{3}{15}=\frac{1}{5}=0.2[/tex]Therefore the probability is 0.2.
-13, 97, -1003, 9997Arithmetic Neither Geometric
Given data:
The given terms are -13, 97,-1003, 9997.
As the terms have alternatively positive negative signs, so they can't be in AP.
The expression for the common ratio is,
[tex]\begin{gathered} \frac{97}{-13}=\frac{-1003}{97} \\ 97^2=1003\times13 \\ 9409\ne13039 \end{gathered}[/tex]Thus, the above series is neither in Arithematic progression nor in Geometric progression.
48. Which is the graph of the solution set of|2x - 1| < 9 ?A. H-5 -4 -3 -2 -1 0 1 2 3 45B.-5 -4 -3 -2 -1 0 1 2 3 4 5C. +-5 -4 -3 -2 -1 01 2 3 4 5D.HH-5 -4 -3 -2 -1 0 1 2 3 4 572-- لا
We have to find the representation of the solution set of the inequality:
[tex]|2x-1|<9[/tex]We can divide this inequality into two, as the absolute value function is like a piecewise function.
We can calculate it in the case that 2x-1 is negative. Then, we can solve it as:
[tex]\begin{gathered} -(2x-1)<9 \\ -2x+1<9 \\ -2x<9-1 \\ -2x<8 \\ x>\frac{8}{-2} \\ x>-4 \end{gathered}[/tex]When 2x-1 is positive, we can solve it as:
[tex]\begin{gathered} 2x-1<9 \\ 2x<9+1 \\ 2x<10 \\ x<\frac{10}{2} \\ x<5 \end{gathered}[/tex]Then, if we combine the two results, the solution set is -4 < x <5 and it represented as Option C.
Answer: Option C.
8x + 8 > -64 and -7 - 8x>-79
In order to find the solution of this system of inequations, let's isolate the variable x in each inequation:
[tex]\begin{gathered} 8x+8>-64 \\ 8x>-64-8 \\ 8x>-72 \\ x>-\frac{72}{8} \\ x>-9 \\ \\ -7-8x>-79 \\ -8x>-79+7 \\ -8x>-72 \\ 8x<72 \\ x<\frac{72}{8} \\ x<9 \end{gathered}[/tex]We have that x > -9 and x < 9, so the solution is the interval -9 < x < 9.
Other notations for this answer are:
[tex]\begin{gathered} \text{set-builder notation: }\mleft\lbrace x\mright|-9A percent can also be written as a _________
Answer:
Decimal Fraction.
Explanation:
If we have 25%, we can write it as:
[tex]\begin{gathered} 25\%=\frac{25}{100} \\ =0.25 \end{gathered}[/tex]A percent can also be written as a Decimal Fraction.
What is the absolute difference between the sum of the multiples of two from 1 and 100, inclusive, and the sum of the multiples of three from 1 and 100, inclusive?
Answer
The absolute difference between the sum of the multiples of two from 1 and 100, inclusive, and the sum of the multiples of three from 1 and 100, inclusive = 867
Explanation
To solve this, we need to first find the sum of multiples of 2 from 1 to 100 inclusive and find the sum of multiples of 3 from 1 to 100 inclusive. These set of numbers, form an arithmetic progression because all the terms have the same common difference
To do that, we need to note that the sum of an arithmetic progression is given as
[tex]\text{Sum = }\frac{n}{2}\lbrack2a+(n-1)d\rbrack[/tex]a = First term
n = number of terms
d = common difference
For the multiples of 2
a = 2
n = 50
d = 2
[tex]\begin{gathered} \text{Sum = }\frac{n}{2}\lbrack2a+(n-1)d\rbrack \\ \text{Sum = }\frac{50}{2}\lbrack2(2)+(49-1)(2)\rbrack \\ =\frac{50}{2}\lbrack4+(48\times2)\rbrack \\ =\frac{50}{2}\lbrack4+96\rbrack \\ =\frac{50}{2}(102) \\ =2550 \end{gathered}[/tex]For the multiples of 3
a = 3
n = 33
d = 3
[tex]\begin{gathered} \text{Sum = }\frac{n}{2}\lbrack2a+(n-1)d\rbrack \\ \text{Sum }=\frac{33}{2}\lbrack2(3)+(33-1)(3)\rbrack \\ =\frac{33}{2}\lbrack6+(32\times3)\rbrack \\ =\frac{33}{2}\lbrack6+96\rbrack \\ =\frac{33}{2}(102) \\ =1683 \end{gathered}[/tex]So,
The absolute difference = |(Sum of multiples of two from 1 to 100 incusive) - (Sum of multiples of three from 1 to 100 incusive)
= |2550 - 1683|
= 867
Hope this Helps!!!
The data display below shows the distribution of quiz scores for Ms. Engels first period math class.
Step 1: Check direction of the tail of the distribu
write an equation for the following circle in standard form based on the information given: center (-4,1) radius:3 please show steps to get it done
We are asked to write the equation for the circle in standard form based on the information below.
center = (-4, 1)
radius = 3
Recall that the equation of the circle in standard form is given by
[tex](x-h)^2+(y-k)^2=r^2[/tex]Where (h, k) are the coordinates of the center and r is the radius.
Substituting the coordinates of the center and value of the radius we get
[tex]\begin{gathered} (x-(-4))^2+(y-1)^2=(3)^2 \\ (x+4)^2+(y-1)^2=9 \end{gathered}[/tex]Therefore, the equation of the given circle is
[tex](x+4)^2+(y-1)^2=9[/tex]Express the confidence interval 50.8% ± 6.2% in interval form.Answer using decimals rounded to three places, not as percentages.
Okay, here we have this:
Considering the provided confidence interval, we are going to express it in interval form, so we obtain the following:
So we will first convert the given confidence interval from percent to decimal:
Confidence interval=50.8% ± 6.2%
Confidence interval=50.8/100 ± 6.2/100
Confidence interval=0.508 ± 0.062
Now let's convert it to interval form, where the smaller endpoint will be the result of taking the minus operation, and the larger endpoint will be the result of taking the plus operation:
Confidence interval= (0.508 - 0.062, 0.508 + 0.062)
Confidence interval= (0.446, 0.57)
Finally we obtain that the confidence interval in interval form is (0.446, 0.57).