Solve the system of equations using the elimination method. Note that the method of elimination may be referred to as the addition method. (If there is no solution, enter NO SOLUTION.)0.2x + 0.7y = 2.20.9x − 0.2y = 3.2(x, y) =
To solve the system of equations
[tex]\begin{gathered} 0.2x+0.7y=2.2 \\ 0.9x-0.2y=3.2 \end{gathered}[/tex]we need to make the coefficients of one of the variables opposite, that is, they need to have the same value with different sign; let's do this with the y variable, so let's multiply the second equation by 0.7 and the first equation by 0.2; then we have:
[tex]\begin{gathered} 0.04x+0.14y=0.44 \\ 0.63x-0.14y=2.24 \end{gathered}[/tex]Now we add the equations and solve the resulting equation for x:
[tex]\begin{gathered} 0.04x+0.14y+0.63x-0.14y=0.44+2.24 \\ 1.64x=2.68 \\ x=\frac{2.68}{0.67} \\ x=4 \end{gathered}[/tex]Now that we have the value of x we plug it in one of the original equations and solve for y:
[tex]\begin{gathered} 0.2(4)+0.7y=2.2 \\ 0.8+0.7y=2.2 \\ 0.7y=2.2-0.8 \\ 0.7y=1.4 \\ y=\frac{1.4}{0.7} \\ y=2 \end{gathered}[/tex]Therefore, the solution of the system of equation is (4,2)
Subtracting algorithm
Using subtracting algorithm, we have 69,000 - 42,547 = 26,453 and 152,681 - 34,820 = 117,861.
According to the question,
We have the following expressions:
_ _ , 0 0 0
-4 2, _ _ _
_________
2 6 , 4 5 3
Now, we will first solve this.
The spaces has to be filed with the digits from 0 to 9 and in both the questions, no digit has to be repeated.
Now, we will solve it from the right hand side.
(Note that we will solve each row that is we will solve vertically.)
0 is given, then we have blank, and in result we have 3.
It is clear that no number can be subtracted from 0. So, we have to regroup it from other digits. So, it will be 10.
Now, 10-3 = 7
So, this blank will be 7.
Now, come to next one.
We have 0 and a blank and then 5 in the result.
Now, it should be 9 because 1 was taken away from it.
So, 9-5 = 4
This blank has to be filled with 4.
Now, we will solve next one.
We have 0, a blank and then 4 in the result.
Now, this 0 will make 9.
9-4 = 5
This blank has to be filled with 5.
Now, we have a blank, 2 and 6 in the result.
1 has been carried from this digit.
So, we have:
6+2+1 = 9
This blank has to be filled with 9.
Next, we have a blank, 4 and 2 in the result.
4+2 = 6
This has to be filled with 6.
Now, we will solve the second question like this.
_ 5 2, 6 8 1
- _ 4, _ _ _
__________
1 1 7, 8 6 1
Now, moving from right to left vertically:
We have 1, a blank and 1 in the result.
1-1 = 0
Blank = 0
We have 8, a blank and 6 in the result.
8-6 = 2
Blank = 2
We have 6, a blank and 8 in the result.
Now, 8 can not be subtracted from 6. So, it has to be 16.
16-8 = 8
Blank = 8
Now, next one is complete.
So, we have next one.
We have 5, a blank and 1 in the result.
We will subtract 1 from 4 because 1 was carried away from 5.
4-1 = 3
Blank = 3
Now, we have a blank and 1 in the result.
Blank = 1
Hence, the answers would be 69,000 - 42,547 = 26,453 and 152,681 - 34,820 = 117,861.
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Triangle MNO has its vertices at the following coordinates:M(2, 2) N(-1,3) O(1,5)Give the coordinates of the image triangle M'N'O' after a 90° counterclockwise rotation about the origin.
The counter clockwise rotation of any point X(x,y) about origin results in change of coordinates as,
[tex]X(x,y)\rightarrow X^{\prime}(-y,x)[/tex]Determine the coordinates of the vertices of the triangle M'N'O'.
[tex]M(2,2)\rightarrow M^{\prime}(-2,2)[/tex][tex]N(-1,3)\rightarrow(-3,-1)[/tex][tex]O(1,5)\rightarrow(-5,1)[/tex]So coordinates of triangle M'N'O' are;
M'(-2,2)
N'(-3,-1)
O'(-5,1)
Find S13 of the arithmetic sequence below.
1/4, 1/2, 3/4, 1, …
Sum of arithmetic progression is given as 91/4
What is arithmetic progression?
An arithmetic sequence or progression is defined as a sequence of numbers in which for every pair of consecutive terms, the second number is obtained by adding a fixed number to the first one.
What is Sum of arithmetic progression?
The sum of the first n terms can be calculated if the first term, common difference and the total terms are known. The formula for the arithmetic progression sum is explained below:
Consider an AP consisting “n” terms.
Sn = n/2[2a + (n − 1) × d]
Given, a = 1/4, n = 13
d = 1/2-1/4 = 1/4
formula for sum is given by
Sn = n/2[2a+(n-1)d]
Substitute the values, we get
S13 = 13/2[2(1/4)+12(1/4)]
=13/2(1/2+3)
=13/2(7/2)
=91/4
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Devonte is growing a rose. Today the rose is 5 cm high. The rose grow$ 1.5 cm per day. Write a linear equation that represents the helght of the rose (y) after (2) days. How tall will the rose be after 20 days?
The equation of a line in slope-intercept form, is:
[tex]y=mx+b[/tex]Where m represents the slope of the line (rate of change), and b represents the y-intercept of the line (initial value).
Since the rose grows 1.5 cm per day, then the rate of change is 1.5:
[tex]m=1.5[/tex]Since today the rose is 5cm high, then the initial value is 5:
[tex]b=5[/tex]Then, the height of the rose after x days is:
[tex]y=1.5x+5[/tex]To find the height of the rose after 20 days, substitute x=20:
[tex]\begin{gathered} y=1.5(20)+5 \\ =30+5 \\ =35 \end{gathered}[/tex]Then, the height of the rose after 20 days is 35 cm.
Ben has a collection of 15 coins and quarters and dimes there's seven quarters in the collection. describe ratio that compares the coins that compare the whole coin collection part of it then write the ratio and at least two different ways
Since the collection contains quarters and dimes, we are going to compare the whole collection to the quarters (7),
We can represent a ratio, like:
15:7 or 15/7
Draw a graph, and label and scale both axes. Plot the points (-2, 3) and (1, -5), clearly labeling them.
Answer:
Explanation:
First, we draw the graph, label the x and y-axis. Then we plot the points given.
To plot the point (-2, 3), we first move to units to the left from the origin and the 3 units up as sketched below
Similarly for (1, -5), we have
We moved one unit to the right and 5 units down.
To find the slope, we take the vertical distance and the horizontal distance and then the slope will be
slope vertical distance / horizontal distance
Therefore the slope is
[tex]Slope=-\frac{8}{3}[/tex]
A set of 12 data points is given above. Which of thefollowing is true of these data?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given data
[tex]\lbrace14.9,21.1,21.2,8.4,14.5,5.9,7.6,10.0,4.8,3.2,28.7,29.5\rbrace[/tex]STEP 2: Find the mean ofthe data
[tex]\begin{gathered} The\:arithemtic\:mean\:\left(average\right)\:is\:the\:sum\:of\:the\:values\:in\:the\:set\:divided\:by\:the\:number\:of\:elements\:in\:that\:set. \\ \mathrm{If\:our\:data\:set\:contains\:the\:values\:}a_1,\:\ldots \:,\:a_n\mathrm{\:\left(n\:elements\right)\:then\:the\:average}=\frac{1}{n}\sum _{i=1}^na_i\: \\ Sum=169.8 \\ n=12 \\ mean=\frac{169.8}{12} \\ mean=14.15 \end{gathered}[/tex]STEP 3: Find the median
[tex]\begin{gathered} \mathrm{The\:median\:is\:the\:value\:separating\:the\:higher\:half\:of\:the\:data\:set,\:from\:the\:lower\:half.} \\ \:the\:number\:of\:terms\:is\:odd,\:then\:the\:median\:is\:the\:middle\:element\:of\:the\:sorted\:set \\ If\:the\:number\:of\:terms\:\:is\:even,\:then\:the\:median\:is\:the\:arithmetic\:mean\:of\:the\:two\:middle\:elements\:of\:the\:sorted\:set \\ \\ \mathrm{Arrange\:the\:terms\:in\:ascending\:order} \\ 3.2,\:4.8,\:5.9,\:7.6,\:8.4,\:10,\:14.5,\:14.9,\:21.1,\:21.2,\:28.7,\:29.5 \\ median=12.25 \end{gathered}[/tex]Hence, it can be seen here that the mean is larger than median.
STEP 4: Find the Interquartile range
[tex]\begin{gathered} The\:interquartile\:range\:is\:the\:difference\:of\:the\:first\:and\:third\:quartiles \\ First\text{ Quartile}=6.75 \\ Third\text{ quartile}=21.15 \\ IQR=14.4 \end{gathered}[/tex]STEP 5: Find the standard deviation
[tex]\begin{gathered} \mathrm{The\:standard\:deviation,\:}\sigma \left(X\right)\mathrm{,\:is\:the\:square\:root\:of\:the\:variance:\quad }\sigma \left(X\right)=\sqrt{\frac{\sum _{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1}} \\ Standard\text{ deviation}=9.11836 \end{gathered}[/tex]Hence, it can be seen from above that the interquartile range is larger than the standard deviation.
STEP 6: Find the range
[tex]\begin{gathered} \mathrm{The\:range\:of\:the\:data\:is\:the\:difference\:between\:the\:maximum\:and\:the\:minimum\:of\:the\:data\:set} \\ Minimum=3.2 \\ Maximum=29.5 \\ Range=26.3 \end{gathered}[/tex]STEP 7: Fnd the variance
[tex]\begin{gathered} \mathrm{The\:sample\:variance\:measures\:how\:much\:the\:data\:is\:spread\:out\:in\:the\:sample.} \\ \mathrm{For\:a\:data\:set\:}x_1,\:\ldots \:,\:x_n\mathrm{\:\left(n\:elements\right)\:with\:an\:average}\:\bar{x}\mathrm{,\:}Var\left(X\right)=\sum _{i=1}^n\frac{\left(x_i-\bar{x}\right)^2}{n-1} \\ Variance=83.14454 \end{gathered}[/tex]Hence, it can be seen that the range is not larger than the variance.
Therefore, the answer is I and II only.
Solve the following system of inequalities graphically on the set of axes below. State the coordinates of a point in the solution set.y ≥ 3x - 6y < -2x - 1LABEL ALL COORDINATESAnswer
Answer:
(-3, 2)
Explanation:
Given the system of inequalities:
[tex]\begin{gathered} y\ge3x-6 \\ y<-2x-1 \end{gathered}[/tex]To solve the inequalities graphically, follow the steps below:
Inequality 1
First, find the equation of the boundary line.
[tex]y=3x-6[/tex]Next, determine the intercepts to draw the boundary line.
[tex]\begin{gathered} \text{When }x=0,y=3(0)-6=-6\implies(0,-6) \\ \text{When y}=0,0=3x-6\implies3x=6\implies x=2\implies(2,0) \end{gathered}[/tex]Join the points (0,-6) and (2,0) using a solid line.
Finally, determine the required half-plane using the origin test.
[tex]\begin{gathered} At\text{ (0,0)} \\ y\ge3x-6\implies0\ge-6(T\text{rue)} \end{gathered}[/tex]The side that contains the point (0,0) is the required half-plane.
The graph showing the first inequality is given below:
Inequality 2
First, find the equation of the boundary line.
[tex]y=-2x-1[/tex]Next, determine the intercepts to draw the boundary line.
[tex]\begin{gathered} \text{When }x=0,y=-2(0)-1=-1\implies(0,-1) \\ \text{When y}=0,0=-2x-1\implies-2x=1\implies x=-0.5\implies(-0.5,0) \end{gathered}[/tex]Join the points (0,-1) and (-0.5,0) using a broken line.
Finally, determine the required half-plane using the origin test.
[tex]\begin{gathered} At\text{ (0,0)} \\ y<2x-1\implies0<-1(False\text{)} \end{gathered}[/tex]The side that DOES NOT contain the point (0,0) is the required half-plane.
The graph of the system of inequalities is given below:
A point in the solution set is (-3, 2).
Henry had a batting average of 0.341 last season (out of 1000 at-bats, he had 341 hits). Given that thisbatting average will stay the same this year, answer the following questions,What is the probabilitythat his first hit willoccur within his first 5at-bats? Answer choice. 0.654. 0.765. 0.821. 0.876
The probability of a successful batting is 0.341; we need to find the probability of at least 1 hit within the first 5 at-bats; thus,
[tex]P(Hit)=1-P(NoHit)[/tex]Therefore, we need to calculate the probability of not hitting the ball within the first 5 at-bats.
The binomial distribution states that
[tex]\begin{gathered} P(X=k)=(nBinomialk)p^k(1-p)^{n-k} \\ n\rightarrow\text{ total number of trials} \\ k\rightarrow\text{ number of successful trials} \\ p\rightarrow\text{ probability of a successful trial} \end{gathered}[/tex]Thus, in our case,
[tex]P(k=0)=(5Binomial0)(0.341)^0(0.659)^5=1*1*0.124287...[/tex]Then,
[tex]P(Hit)=1-0.124287...\approx0.876[/tex]Therefore, the answer is 0.876A store is having a sale to celebrate President’s Day. Every item in the store is advertised as one- fourth off the original price. If an item is marked with a sale price of , what was its original price?
If the discount is one fourth off, it means the discount is 1/4 = 25% of the original price, so the final price will be 75% or 3/4 of the original price.
In order to find the original price, we just need to divide the final price by 3/4, this way we "remove" the discount.
For example, if the sale price is $75, the original price would be:
[tex]\text{original price}=\frac{75}{\frac{3}{4}}=75\cdot\frac{4}{3}=25\cdot4=100[/tex]So for a sale price of $75, the original price would be $100.
In general, for a discount of x%, the original price (given the sale price) can be calculated as:
[tex]\text{original price}=\frac{\text{sale price}}{1-\frac{x}{100}}[/tex]Money in a particular savings account increases by 6% after a year. How much money will be in the account after one year if the initial amount is $125?
Select from the drop-down menus to correctly complete each statement.
The opposite of −358 is on the
Choose...
side of zero on a number line as −358. The opposite of 429is on the
Choose...
side of zero on a number line as 429.
The opposite of −3 5/8 is on the opposite side of zero on a number line as −3 5/8 . The opposite of 4 2/9 is on the opposite side of zero on a number line as 4 2/9 .
What is a number line?A number line is a type of graph with a graduated straight line which contains both positive and negative numbers that are typically placed at equal intervals along its length.
What are opposites?In Mathematics, opposites simply refers to numbers that are located on opposite sides of zero (0) on any number line. Additionally, opposites generally have the same distance from zero (0) on any given number line.
In conclusion, -3 5/8 is a number that is located on the opposite side of zero (0) on a number line while 4 2/9 is a number that is also located on the opposite side of zero (0) on a number line.
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Complete Question:
Select from the drop-down menus to correctly complete each statement. The opposite of −3 5/8 is on the ______ side of zero on a number line as −3 5/8 . The opposite of 4 2/9 is on the ______ side of zero on a number line as 4 2/9 .
Write it in reduced form as a ratio of polynomials p(x)/q(x)
We are given the following expression
[tex]\frac{x^2}{x-5}-\frac{8}{x-2}[/tex]Let us re-write the expression as a ratio of polynomials p(x)/q(x)
First of all, find the least common multiple (LCM) of the denominators.
The LCM of the denominators is given by
[tex](x-5)(x-2)[/tex]Now, adjust the fractions based on the LCM
[tex]\begin{gathered} \frac{x^2}{x-5}\times\frac{(x-2)}{(x-2)}=\frac{x^2(x-2)}{(x-5)(x-2)} \\ \frac{8^{}}{x-2}\times\frac{(x-5)}{(x-5)}=\frac{8(x-5)}{(x-2)(x-5)} \end{gathered}[/tex]So, the expression becomes
[tex]\frac{x^2(x-2)}{(x-5)(x-2)}-\frac{8(x-5)}{(x-2)(x-5)}[/tex]Now, apply the fraction rule
[tex]\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}[/tex][tex]\frac{x^2(x-2)}{(x-5)(x-2)}-\frac{8(x-5)}{(x-2)(x-5)}=\frac{x^2(x-2)-8(x-5)}{(x-5)(x-2)}[/tex]Finally, expand the products in the numerator
[tex]\frac{x^2(x-2)-8(x-5)}{(x-5)(x-2)}=\frac{x^3-2x^2-8x+40}{(x-5)(x-2)}[/tex]Therefore, the given expression as a ratio of polynomials p(x)/q(x) is
[tex]\frac{x^3-2x^2-8x+40}{(x-5)(x-2)}[/tex]a large community college has professors and lectures. total number of facility members is 228. the school reported that they had five professors for every 14 lectures. how many of each type of faculty member does the community college employee?
a large community college has professors and lectures. total number of facility members is 228. the school reported that they had five professors for every 14 lectures. how many of each type of faculty member does the community college employee?
Let
x -----> number of professors
y ----> number of lectures
we have that
x+y=228
x=228-y -------> equation A
x/y=5/14
x=(5/14)y ------> equation B
equate equation A and equation B
228-y=(5/14)y
solve for y
(5/14)y+y=228
(19/14)y=228
y=228*14/19
y=168
Find the value of x
x=228-168=60
therefore
number of professors is 60number of lectures is 168when you do the graph part can you write on my picture, please?
Given that y = x + 3
Find the value of y when x = 1, 2, 3, 4, 5, and 6
For x = 1
y = 1 + 3
y = 4
For x = 2
y = 2 + 3
y = 5
For x = 3
y = 3 + 3
y = 6
For x = 4
y = 4 + 3
y = 7
For x = 5
y = 5 + 3
y = 8
For x = 6
y = 6 + 3
y = 9
Hence, the table can be filled as follows
x y
1 4
2 5
3 6
4 7
5 8
6 9
The next thing is to graph it on a graph
1. A jar contains 5 red marbles numbered 1 to 5 and 6 blue marbles numbered 1 to 6. A marble is drawn at random from the jar. Find the probability that the marble is blue or odd-numbered.
We will use the following formula:
[tex]P(A\cup B)=P(A)+P(B)-P(A\cap B).[/tex]First, we compute the probability that we get a blue marble:
[tex]P(\text{Blue)}=\frac{6}{5+6}=\frac{6}{11}\text{.}[/tex]Now, we compute the probability of getting an odd-numbered marble:
[tex]P(\text{odd-num)}=\frac{6}{11}\text{.}[/tex]Finally, the probability that we draw a blue and odd-numbered marble is:
[tex]P(\text{blue and odd)=}\frac{3}{11}.[/tex]Answer: The probability that the marble is blue or odd-numbered is:
[tex]\begin{gathered} P(\text{blue or odd)=P(blue)+P(odd-num)-P(blue and odd)=}\frac{6}{11}+\frac{6}{11}-\frac{3}{11}=\frac{9}{11}. \\ P(\text{blue or odd)}=\frac{9}{11}\text{.} \end{gathered}[/tex]What is the reference angle for 289°? A. 71° B. 19° C. 11° D. 89°
Given:
Angle θ=289°.
For angles from 270° to 360°, the reference angle can be calculated by subtracting the given angle from 360° .
The reference angle of θ can be calculated as:
[tex]\begin{gathered} 360\degree-\theta=360\degree-289\degree \\ =71\degree \end{gathered}[/tex]Therefore, reference angle of 289° is 71°.
For questions 5&6 find F -1(x), the inverse of F(x)
To find the inverse function, we can follow the next steps:
First Function1. Replace x with y as follows:
[tex]y=3x+7\Rightarrow x=3y+7[/tex]2. Solve the resulting equation for y. Subtract 7 from both sides of the equation:
[tex]x-7=3y+7-7\Rightarrow x-7=3y[/tex]3. Divide both sides of the equation by 3:
[tex]\frac{(x-7)}{3}=\frac{3}{3}y\Rightarrow y=\frac{(x-7)}{3}=\frac{1}{3}(x-7)=\frac{x}{3}-\frac{7}{3}[/tex]Second FunctionWe need to repeat the process to obtain the inverse of this function:
1. Replace x with y:
[tex]y=8x\Rightarrow x=8y[/tex]2. Solve for y. Divide both sides by 8:
[tex]\frac{x}{8}=\frac{8}{8}y\Rightarrow y=\frac{x}{8}[/tex]In summary, we have that the inverse functions are:
For function
[tex]y=3x+7[/tex]The inverse function is:
[tex]y=F^{-1}^{}(x)=\frac{(x-7)}{3}[/tex]And, for the function
[tex]y=8x[/tex]The inverse function is:
[tex]y=f^{-1}(x)=\frac{1}{8}x[/tex]Josh's grocery bill is $56.00 and the sales tax in his state is 7% how much extra does he have to pay? I assume 125?
Given:
Josh's grocery bill is $56.00
The sales tax in his state is 7%
[tex]\begin{gathered} \text{Extra money he have to pay=56}\times\frac{7}{100} \\ \text{Extra money he have to pay=}\frac{392}{100} \\ \text{Extra money he have to pay= \$3.92} \end{gathered}[/tex]On total Josh has to pay $59.92
Josh has to pay extra money as tax is $3.92
find 2x:3y if x:y = 2:5
4 : 15
Explanation:[tex]\begin{gathered} \text{x : y = 2: 5} \\ \frac{x}{y}\text{ = }\frac{2}{5} \\ \\ 2x\text{ : 3y = ?} \end{gathered}[/tex][tex]\begin{gathered} 2x\colon\text{ 3y = }\frac{2x}{3y} \\ 2x\colon3y\text{ = }\frac{2}{3}\times\frac{x}{y} \end{gathered}[/tex][tex]\begin{gathered} \text{substitute for x/y in 2x:3y} \\ \frac{2}{3}\times\frac{x}{y}\text{ =}\frac{2}{3}\times\frac{2}{5} \\ =\text{ }\frac{4}{15} \\ \\ \text{Hence, 2x:3y = }\frac{4}{15} \\ or \\ 4\colon15 \end{gathered}[/tex]Find the x-coordinate for the point of intersection by using the equations method of solving. Show all the work. f (x)=2x+6g(x)= -3x+1
y = 2x + 6
y = -3x + 1
Equality
2x + 6 = -3x + 1 6 is in the left side and is positive so we substract 6 in both sides
2x +6 - 6 = -3x + 1 - 6
Simplify
2x = -3x - 5
Add -3x in both sides
2x + 3x = -3x + 3x - 5
Simplify
5x = -5
2x + 3x = 1 - 6
5x = -5
x = -5/5
This is the x-coordinate
x = -1
need help with this problem, find the length of the darkened arc. C is the center of the circle
Notice that the central angle measures 138 degrees, We have a property of the circle that says that the measure of a central angle is equal to the arc between its sides.
Therefore, the arc measures 138 degrees
A school bus with the football team left Jefferson HighSchool and drove at an average speed of 48 mph. A schoolbus with the cheerleading squad left 2 hours later and wasable to catch up to the football team after 6 hours. Whatwas the speed of the bus carrying the school's cheerleadingsquad?
Given data
A school bus with the football team from Jefferson High School drove at an average speed of 48mph
Another school bus with the cheerleading squad left 2 hours later and caught with the football team after 6 hours.
Required
To find the speed of the bus carrying the Cheerleading squad.
Step 1
Determine the distance the bus carrying the football team had travelled in the first 2 hours
Speed is given as
[tex]\begin{gathered} \text{speed =}\frac{dis\tan ce}{time} \\ \text{where sp}eed\text{ = 48mph} \\ \text{time = 2 hours} \\ \text{distance = sp}eed\text{ x time} \\ \text{distance = 48 x 2 =96miles} \end{gathered}[/tex]Step 2
Determine of the distance covered by the bus with the football team in the next 6 hours and find the total distance in 8 hours
[tex]\begin{gathered} \text{Distance = sp}eed\text{ }\times\text{ time} \\ where \\ \text{speed = 48mph} \\ \text{time = 6 hours} \\ \text{Distance = 48 }\times\text{ 6 = 288 miles} \end{gathered}[/tex]The total distance in 8 hours covered by the bus = 288 + 96 = 384miles
Step 3
Determine the speed of the bus carrying the Cheerleaders
The total distance to be covered by the Cheerleaders is 384 miles
The total time of their journey to catch with the bus carrying the Football team is 6hours
Hence the speed of the bus required is given as
[tex]\begin{gathered} \text{Speed = }\frac{dis\tan ce}{time} \\ \text{speed = }\frac{384}{6} \\ \text{speed = 64mph} \end{gathered}[/tex]Therefore, the speed of the bus carrying the school's Cheerleaders squad is 64mph
What is the equation of the line that passes through points (1,-19) and (-2,-7)?
This problem is about linear equations. We need to find the equation of the line w
EFG IS dilated with scale factor of 4 to create triangle E’F’G’ the measure of angle F’ is 53 degrees what is the measurement of angle F
The measurement of ∠ F = 53 °.
Given,
Triangle EFG is dilated with a scale factor of 4 to create Δ E ' F ' G ' .
The measure of ∠ F ' is 53 °.
To find the measurement of angle F.
We know that a dilation creates similar figures i.e. it preserves the measure of angles.
Therefore, if Triangle EFG is dilated to form Δ E ' F ' G ', then the measure of ∠ F' = measure of ∠ F [Corresponding angles remains same]
⇒ The measure of ∠ F' = measure of ∠ F = 53 °
Hence, The measurement of ∠ F = 53 °.
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AB has endpoint A(-3,-5) and midpoint M(2,-1).Find the coordinate (x,y) of B.
By definition, the formula to find a Midpoint is:
[tex]M=(\frac{x_1+x_2}{2}+\frac{y_2-y_1}{2})[/tex]Where the coordinates of the first point are:
[tex](x_1,y_1)[/tex]And the coordinates of the second point is:
[tex](x_2,y_2)[/tex]Let be the coordinates of the Midpoint:
[tex](x_M,y_M)[/tex]In this case, knowing coordinates of the point A and the Midpoint, you can set up the following equations:
- Equation 1:
[tex]x_M=\frac{x_A+x_B}{2}[/tex]- Equation 2:
[tex]y_M=\frac{y_A+y_B}{2}[/tex]Choose the Equation 1, substiutute values and solve for x-coordinate of the endpoint B:
[tex]\begin{gathered} x_M=\frac{x_A+x_B}{2} \\ \\ 2=\frac{-3+x_B}{2} \\ \\ (2)(2)=-3+x_B \\ 4+3=x_B \\ x_B=7 \end{gathered}[/tex]Now choose the Equation 2 and solve for the y-coordinate of the point B:
[tex]\begin{gathered} y_M=\frac{y_A+y_B}{2} \\ \\ -1=\frac{-5+y_B}{2} \\ \\ (-1)(2)=-5+y_B \\ -2+5=y_B \\ y_B=3 \end{gathered}[/tex]Therefore, the coordinates of P are:
[tex]B(7,3)[/tex]For each ordered pair, determine whether it is a solution to 4x - 5y = -13.Is it a solution?x$(x, y)YesNo(-7, -3)(3, -4)OO(-2, 1)oO(6, 7)0
The equation is 4x - 5y = -13.
Substitute -7 for x and -3 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-7)-5\cdot(-3)=-13 \\ -28+15=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation so point (-7,-3) is solution of equation.
Substitute 3 for x and -4 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot3-5\cdot(-4)=-13 \\ 12+20=-13 \\ 32\ne-13 \end{gathered}[/tex]The ordered pair not satisfy the equation. So point (3,-4) is not a solution of the equation.
Substitute -2 for x and 1 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot(-2)-5\cdot1=-13 \\ -8-5=-13 \\ -13=-13 \end{gathered}[/tex]The ordered pair satisfy the equation. So point (-2,1) is solution of equation.
Substitute 6 for x and 7 for y in the equation to check whether ordered pair is solution of the equation.
[tex]\begin{gathered} 4\cdot6-5\cdot7=-13 \\ 24-35=-13 \\ -11\ne-13 \end{gathered}[/tex]The orderedpair not satisfy the equation. So point (6,7) is not a solution of the equation.
Angel Corporation produces calculators selling for $25.99. Its unit cost is $18.95. Assuming a fixed cost of $80,960, what is the breakeven point in units?
The breakeven point is 11,500, meaning that if the sell that number of units, the profit will be zero.
How to get the breakeven point?
Here we know that the unit price is $25.99, so if they sell x units, the revenue is
R(x) = $25.99*x
And the cost per unit is $18.95, plus a fixed cost of $80,960
Then the cost of x units is:
C(x) = $80,960 + $18.95*x
The breakeven point is the value of x such that the cost is equal to the revenue, so we need to solve:
$25.99*x = $80,960 + $18.95*x
$25.99*x - $18.95*x = $80,960
$7.04*x = $80,960
x = $80,960/%7.04 = 11,500
Learn more about cost and revenue:
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at the casino Robert has currently lost 72$ he plays another game during which he loses 35$ find the total amount of money Robert has lost
we know that
Robert has currently lost 72$
he plays another game during which he loses 35$
to find out the total money Robert has lost, adds the amount 1 plus the amount 2
so
72+35=$107