We have
[tex]\begin{gathered} 2x-6y=8\text{ (1)} \\ 5x-4y=31\text{ (2)} \end{gathered}[/tex]we must solve the system of equations
First, we will solve for x the first equation
[tex]\begin{gathered} 2x-6y=8 \\ 2x=8+6y \\ x=\frac{8}{2}+\frac{6}{2}y \\ x=4+3y \end{gathered}[/tex]Then, we must replace the value of x in the second equation
[tex]\begin{gathered} 5(4+3y)-4y=31 \\ 20+15y-4y=31 \\ 11y=11 \\ y=\frac{11}{11} \\ y=1 \end{gathered}[/tex]Finally, we replace the value of y in the equation that we solved for x
[tex]\begin{gathered} x=4+3(1) \\ x=4+3 \\ x=7 \end{gathered}[/tex]So, the correct ordered pair is (7, 1)
A 1. Which of the following is equivalent to 37g - 11g? a. (37 - 11)g b. (37 - 11) +g c.(37 - 11) + g2 d. (37 - 11)9
From 37g - 11g we can factorize g. It yields
[tex]37g-11g=(37-11)g[/tex]Hence, the aswer is a.
Solve theses equations by elimination y= 3/2x -10 and -2x -4y =-8
SOLUTION
We want to solve the question with elimination method
[tex]\begin{gathered} y=\frac{3}{2}x-10.\text{ . . . . . . equation 1} \\ -2x-4y=-8\text{ . . . . . . . equation 2} \\ multiply\text{ equation 1 by 2, so as to remove the fraction } \\ 2\times y=(2\times\frac{3}{2}x)-(2\times10) \\ 2y=3x-20 \\ re-arranging\text{ we have } \\ -3x+2y=-20 \end{gathered}[/tex]So our paired equation becomes
[tex]\begin{gathered} -3x+2y=-20 \\ -2x-4y=-8 \end{gathered}[/tex]To eliminate y, multiply the upper equation by 4 and the lower by 2, we have
[tex]\begin{gathered} 4(-3x+2y=-20) \\ 2(-2x-4y=-8) \\ -12x+8y=-80 \\ -4x-8y=-16 \\ we\text{ have } \\ (-12x-4x)+(8y-8y)+(-80-16) \\ -16x+0=-96 \\ -16x=-96 \\ x=\frac{-96}{-16} \\ x=6 \end{gathered}[/tex]So put x for 6 into the second equation, we have
[tex]\begin{gathered} -2x-4y=-8 \\ -2(6)-4y=-8 \\ -12-4y=-8 \\ -4y=-8+12 \\ -4y=4 \\ y=\frac{4}{-4} \\ y=-1 \end{gathered}[/tex]Hence x = 6 and y = -1
The graph is shown below
Hence the point of intersection is (6, -1)
[tex]y = 3x + 19 \\ y = 5x + 33[/tex]how do you solve this with substitution?
We have the next system of equations:
[tex]\begin{gathered} y=3x+19\text{ (eq. 1)} \\ y=5x+33\text{ (eq. 2) } \end{gathered}[/tex]Substituting y = 3x + 19 into the second equation, and solving for x:
[tex]\begin{gathered} 3x+19=5x+33 \\ 3x+19-3x-33=5x+33-3x-33 \\ -14=2x \\ \frac{-14}{2}=\frac{2x}{2} \\ -7=x \end{gathered}[/tex]Substituting x = -7 into the first equation:
[tex]\begin{gathered} y=3(-7)+19 \\ y=-21+19 \\ y=-2 \end{gathered}[/tex]The solution is (-7, -2)
Questions 12-14: The box below shows some of the steps of multiplying twopolynomials. Use this picture for the next THREE questions.+8x26x46x2-8x+3x18x3-24x2-64x16+22x2
In the red block will be the product of 6x^2 times +8 so:
[tex]6x^2\cdot8=48x^2[/tex]In the blue block will be the product of -8x and x^2
[tex]x^2\cdot(-8x)=-8x^3[/tex]and in the yellow block will be the product of 2 and 3x so:
[tex]3x\cdot2=6x[/tex]Write a quadratic equation that has two imaginary solutions
We are asked to determine a quadratic equation that has two imaginary solutions. Let's suppose that the solution of the equation is the following:
[tex]x=\pm i[/tex]This means that the two imaginary solutions are "i" and "-i". Now, we use the following:
[tex]\pm i=\sqrt[]{-1}[/tex]Substituting we get:
[tex]x=\sqrt[]{-1}[/tex]Squaring both sides:
[tex]x^2=-1[/tex]Now, we add 1 to both sides:
[tex]x^2+1=0[/tex]And thus we have obtained a quadratic equation with two imaginary solutions.
#1 An airplane rises at an angle of 14° with the ground. Find, to the nearest 10 feet, the distance it has flown when it has covered a horizontal distance of 1500 feet.
The airplane rises at an angle of 14° with respect to the ground.
You have to find the distances (diagonal) that it frew if it covered a horizontal distance of 1500 feet.
The distance flew by the place with respect to the horizontal ground and the height the plane is at after traveling 1500 feet form a right triangle. Where x represents the hypothenuse of the triangle. To determine its measure, you have to use the trigonometric relations
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypohtenuse} \\ \cos \theta=\frac{adjacent}{hypothenuse} \\ \tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]Given that θ=14° and we know that the adjacent side to the angle measures 1500 feet, using the cosine we can determine the length of x as:
[tex]\begin{gathered} \cos 14=\frac{1500}{x} \\ x\cos 14=1500 \\ x=\frac{1500}{\cos 14} \\ x=1545.92ft \end{gathered}[/tex]The distance flew by the airplane is 1545.92ft
Craig earns $2.50 per hour plus $3.50 for each haircut he gives.He worked 7 hours and gave 4 haircuts. How much did he earn?a. $31.50b. $168c. $46d. $17.50
Craig earns $2.50 per hour plus $3.50 for each hair cut he gives.
He worked for 7 hours.
In hour basis, he earned
[tex]2.50\times7=17.5[/tex]He gave 4 hair cuts.
For 4 haircuts, he earned
[tex]3.50\times4=14[/tex]So, he total earned
[tex]17.5+14=31.5[/tex]Hence, the correct option is (A).
Please help:What is the mean of the data set?108, 305, 252, 113, 191Enter your answer in the box. __
Solution
- The formula for finding the mean of a dataset is
[tex]\begin{gathered} \bar{x}=\sum_{i=1}^n\frac{x_i}{n}=\frac{x_1+x_2+x_3+x__4+...+x_n}{n} \\ where, \\ x_i=\text{ The individual data points} \\ n=\text{ The number of data points in the data set} \\ \bar{x}=\text{ The mean} \end{gathered}[/tex]- The dataset given is:
108, 305, 252, 113, 191
- Thus, we can infer that:
[tex]\begin{gathered} x_1=108,x_2=305,x_3=252,x_4=113,x_5=191 \\ \\ \text{ The number of datapoints is }n=5 \end{gathered}[/tex]- Now, we can proceed to find the mean of the dataset as follows:
[tex]\begin{gathered} \bar{x}=\frac{108+305+252+113+191}{5} \\ \\ \therefore\bar{x}=193.8 \end{gathered}[/tex]Final Answer
The mean of the dataset is 193.8
Given: triangle ABC is an equilateral triangle. L, M, and N are the midpoints of AC, CB, and AB respectively. Prove: LMNB is a rhombus
Given:
∆ABC is an equilateral triangle, hence, all the three sides have the same length.
L, M, N are the midpoints of AC, CB, and AB. Hence, for instance, the distance between segment CM and MB are equal, by definition of midpoint.
Prove: LMNB is a rhombus.
Statement → Proof
1. ∆ABC is an equilateral triangle. → Given
2. Segment AB ≅ Segment AC ≅ Segment BC → Definition of an Equilateral Triangle
3. 1/2AB ≅ 1/2AC ≅ 1/2BC → Division Property of Equality
4. M and L are midpoints of BC and AC respectively. → Given
5. 1/2AB = Segment ML. → Midpoint Theorem
6. 1/2BC = Segment MB → Definition of Midpoint
7. Segment ML = Segment MB → Transitive Property of Equality using Statement 5 and 6
8. L and N are midpoints of AC and AB respectively. → Given
9. 1/2BC = Segment LN → Midpoint Theorem
10. 1/2AB = Segment BN → Definition of Midpoint
11. Segment LN = Segment BN → Transitive Property of Equality using Statement 9 and 10
12. Segment ML = Segment BN → Transitive Property of Equality using Statement 5 and 10
11. Segment MB = Segment LN → Transitive Property of Equality using Statement 6 and 9
13. Segment LN = Segment BN = Segment ML = Segment MB → Substitution Property of Equality using Statement 11 and 12
14. LMNB is a rhombus. → Definition of a rhombus.
One of the properties of a rhombus is that all 4 sides are equal in length.
Can someone pls help me with my homework I have to go to sleep so pls be fast
Okay, here we have this:
Let's calculate the slope (using the points: (2, 58.5) and (4, 107.5)):
m=(107.5-58.5)/(4-2)=49/2=24.5
Finally we obtain that the slope is 24.5, so this means that option III is incorrect.
And considering that the y intercept represents the value of y when x equals 0 (0 tickets sold), If a person does not buy any ticket, they should not pay anything, this means that the option IV isn't right.
So, finally we are only left with option I and II let's check them:
Replacing in function:
Total value = (number of tickets * cost per ticket) + service charge
2 Tickets:
58.5=(2*24.5)+9.5
58.5=49+9.5
58.5=58.5
4 Tickets:
107.5=(4*24.5)+9.5
107.5=98+9.5
107.5=107.5
8 Tickets:
205.5=(8*24.5)+9.5
205.5=196+9.5
205.5=205.5
12 Tickets:
303.5=(12*24.5)+9.5
303.5=294+9.5
303.5=303.5
20 Tickets:
499.5=(20*24.5)+9.5
499.5=490+9.5
499.5=499.5
Finally we obtain that the correct answer is the option A. Statements I and III.
AISD estimates that it will need 280000 in 8 years to replace the computers in the computer labs at their high schools. if AISD establishes a sinking fund by making fixed monthly payments in to an account paying 6% compounded monthly how much should each payment be
The initial amount of money that must be spend to replace the computers is P = $280,000. The period of time expected to replace all the computers is t = 8 years = 96 months. The interest rate is r = 6%.
Then, the monthly payment A is given by the formula:
[tex]\begin{gathered} A=P\frac{r(1+r)^t}{(1+r)^t-1} \\ A=280,000\cdot\frac{0.06\cdot(1+0.06)^{96}}{(1+0.06)^{96}-1} \\ A=\text{ \$16,862.74} \end{gathered}[/tex]12. The PRODUCT of six and a number increased by 2, translates to ? *6 +x+26x + 2O 6-8-2
Call the unknown number x.
The product of six and a number, would be written as 6x.
The product of six and a number increased by 2, would be written as 6x+2.
Type the correct answer in each box. Use numerals instead of wordsFind the value of each decimal model and then find the sum
To find the decimal values you have to count the number of shaded squares and divide it by the total number of squares in the grid.
Left value:
The grid is 10 x 10, which means that it is divided into 100 squares.
There are 23 shaded squares in the grid, so you can determine the decimal value as follows:
[tex]\frac{nº\text{shaded squares}}{total\text{ number of squares}}=\frac{23}{100}=0.23[/tex]Right value:
The grid is 10 x 10, so it is divided into 100 squares.
The number of shaded squares is 62. Divide 62 by 100 to determine the decimal value:
[tex]\frac{nº\text{shaded squares}}{total\text{ number of sqaures}}=\frac{62}{100}=0.62[/tex]Now what is left to do is to add both decimal values:
[tex]0.23+0.62=0.85[/tex]What are the first five terms of the arithmetic sequence defined explicitly by the formula an=1/8+2/3n
Answer:
D
Step-by-step explanation:
Given the formula of the arithmetic sequence, to find the first 5 terms, you just have to substitute n=1, n=2, n=2, n=4, and n=5.
Then, for the 1st term:
[tex]\begin{gathered} a_n=\frac{1}{8}+\frac{2}{3}n \\ a_1=\frac{1}{8}+\frac{2}{3}(1) \\ a_1=\frac{19}{24} \end{gathered}[/tex]2nd term:
[tex]\begin{gathered} a_2=\frac{1}{8}+\frac{2}{3}(2) \\ a_2=\frac{35}{24} \end{gathered}[/tex]There is no need to find the other 3 because there is no other sequence that has the first two terms as D.
After being discounted 10%, a weather radio sells for $62.96. Find the original price. (Round your answer to the nearest cent.)&Enter a number.$
Let the original price be x.
The discount is 10% of original price. So discount is,
[tex]\frac{10}{100}\cdot x=0.1x[/tex]The selling price after 10% discout is,
[tex]x-0.1x=0.9x[/tex]The selling price price is $62.96. So equation is,
[tex]\begin{gathered} 0.9x=62.96 \\ x=\frac{62.96}{0.9} \\ =69.955 \\ \approx69.96 \end{gathered}[/tex]So original price is 69.96.
Answer: 69.96
5) . Write theequation of a line in slope-intercept form.
Explanation
Given the two points
[tex]\begin{gathered} (x_1,y_1)=(-2,4) \\ (x_2,y_2)=(-1,1) \end{gathered}[/tex]The rise and run of the line is given as;
[tex]m=\frac{\text{rise}}{run}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-4}{-1-(-2)}=-\frac{3}{1}=-3^{}_{}[/tex]Recall, the equation of a line in slope-intercept form is given as;
[tex]y=mx+c[/tex]Since we know the value of m, we can find the value of c by using one of the points above.
When x=-2, y= 4. Therefore;
[tex]\begin{gathered} 4=-3(-2)+c \\ 4=6+c \\ c=4-6 \\ c=-2 \end{gathered}[/tex]We then insert m and c into the slope-intercept equation.
Answer:
[tex]y=-3x-2[/tex]Draw a sketch of f(x)= (x+4)^2-5. Plot the point for the vertex, and label the coordinate as a maximum or minimum, and draw & write the equation for the axis of symmetry.
Answer: The vertex is (-4,-5) and the axis of symmetry is x=-4.
Explanation:
Given:
f(x)=(x+4)^2-5
The graph for the given equation is:
The point for the vertex is at (-4,-5) and it is also the minimum coordinate.
To find the axis of symmetry, we rewrite first the equation y=(x+4)^2-5 in the form y=ax^2 +bx +c.
So,
[tex]\begin{gathered} y=(x+4)^2-5 \\ y=x^2+8x\text{ +16 -5} \\ y=x^2+8x\text{ +1}1 \end{gathered}[/tex]Let:
a=1, b=8, c =11
The formula for the axis of symmetry is:
[tex]x=\frac{-b}{2a}[/tex]We plug in what we know.
[tex]\begin{gathered} x=\frac{-b}{2a} \\ =\frac{-8}{2(1)} \\ =\frac{-8}{2} \\ x=-4 \end{gathered}[/tex]The axis of symmetry is x=-4.
Therefore, the vertex is (-4,-5) and the axis of symmetry is x=-4.
Kyle is a secretory. She earns $12.38 per hout. She worked 2 hours last week. What is her straight fine pay
Answer:
Her pay is;
[tex]\text{ \$24.7}6[/tex]Explanation:
Given that;
She earns $12.38 per hour
and She worked 2 hours last week.
Her pay can be calculated as;
[tex]\text{Total pay}=Rate\times time[/tex]Substituting the given values;
[tex]\begin{gathered} \text{Pay}=\text{ \$12.38}\times2 \\ \text{Pay}=\text{ \$24.76} \end{gathered}[/tex]Her pay is;
[tex]\text{ \$24.7}6[/tex]find the values of the variables X and Y in the given parallelogram
In the given parallelogram
From the property of diagonals of Parallelogram
The diagonals are bisect each other into equal parts
So, according to the figure
length 2x= length of y
2x=y
Similarly for the second diagonal,
length y+4=length3x
y+4=3x
Simplify the both equation by substitution method,
In substitution method, substitute the value of any one varibale and put into the another equation and simplify
[tex]\begin{gathered} 2x=y \\ y=2x \\ \text{Substitute the value of y into the other equation} \\ y+4=3x \\ 2x+4=3x \\ 3x-2x=4 \\ x=4 \end{gathered}[/tex]Now substitute the value of x=4 into the first equation and simplify for y
[tex]\begin{gathered} x=4 \\ 2x=y \\ 2(4)=y \\ y=8 \end{gathered}[/tex]So the value of varriables x = 4 and y=8
Answer : A) x=4, y=8
I went from my house to a playground, 300metres away in 10 minutes. I ran back andreached in 2 minutes. What was my averagespeed?
Average speed= total distance / total time
Distance 1 = 300 meters
Distance 2 = 300 meters (back)
Total distance = 300m+300m = 600 meters
Time 1= 10 minutes
Time 2 = 2 minutes
Total Time = 10min+2min=12 minutes
Average speed= 600 meters / 12 minutes = 50 meters/minute
in the right triangle ABC, if m < C = 90 and sun A = 3/5, cos B is
Given a right angle triangle ABC:
[tex]\begin{gathered} m\angle C=90 \\ \sin A=\frac{3}{5} \end{gathered}[/tex]As the measure of angle C = 90
so, the sum of the angles A and B = 90
So, angles A and B are complementary angles
so,
[tex]\begin{gathered} \sin A=\cos B \\ \\ \cos B=\sin A=\frac{3}{5} \end{gathered}[/tex]so, the answer will be cos B = 3/5
a financial advisor estimates that a company's profits follow the equation.
The equation that represent the profit is given by:
[tex]y=1000\cdot2^x[/tex]So in 3 years there are 36 months so the equation will be:
[tex]\begin{gathered} y=1000\cdot2^{36} \\ y=68^{},719,476,736,000 \end{gathered}[/tex]So is option A) it don't have sence because the profits are to great.
уA 5-digit PIN number is selected. What it the probability that there are no repeated digits?hoThe probability that no numbers are repeated isWrite your answer in decimal form, rounded to the nearest thousandth.Check Answer
Since there are 5 choices and there are 10 possible digits for each digit of the PIN( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
The total value possible 5 pins are 10⁵ = 100000
Using permutation, since 5 numbers are selected without repetition:
[tex]\frac{n!}{(n-k)!}=\frac{10!}{(10-5)!}=30240[/tex]The probability that no numbers are repeated is= 30240/ 100000
≈ 0.302
7. Which digital construction tool would help youdetermine whether point C or point D is the midpoint ofsegment AB?A. Angle bisectorB. Perpendicular bisectorC. Perpendicular lineD. Parallel line
The digital construction tool that would help determine wherer point C or point D is the midpoint of segment AB would be a Perpendicular Bisector. [Option B]
Since a bisector would divide the segment in two identical parts and the perpendicular line would mark the exact point in which the segment is being divided.
T x 3/4 for t = 8/9
repalce t=8/9
[tex]\begin{gathered} \frac{8}{9}\times\frac{3}{4} \\ \\ \frac{24}{36}=\frac{2}{3} \end{gathered}[/tex]the result is 2/3
If lines l, m, and n are parallel,AE is perpendicular to l, AC = 10, CD = 14, andAF = 6, what is the length of DG ? Give your answer as a decimal.
Using the properties of parallel line and similar triangle we calculate the length of the side DG to be 19.4 units .
In triangle ACF by using the properties of Pythagoras Theorem we can say that
AC² = FA² + CF²
Given:
AC = 10 , FA = 6
∴10² = 6² + CF²
or, CF = 8 units.
Now in triangles ΔACF and triangle ΔADG
CF is parallel to DG , therefore the two triangles are similar.
therefore we can say that using the properties of similar triangle we will use the ratio of the sides to find the given side.
AC/AD=CF/DG
or, 10/24 = 8 / DG
or, DG = 192 /10
or, DG = 19.2 units
Triangles that share the same form but differ in size are said to be similar. All equilateral triangles and squares with equal sides serve as examples of related items.
In other words, two similar triangles have similar sides that are proportionately equal and similar angles that are congruent.
Hence the length of the side is 19.2 units.
To learn more about parallel lines visit:
https://brainly.com/question/29042593
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a country with an area of 326 square miles has a population of 6846 residents which rate best represents the relationship between the population of the country in the area of the country
To answer this question, we need to remember the concept of rate. A rate is a result of comparing two different quantities, numbers. It is also a ratio - the result of dividing two numbers. In this case, we have two different quantities (or numbers):
1. Square miles that indicate the measurement of area. In this case, 326 square miles or 326 mi².
2. Population. In this case, we have 6846 residents.
In general, we can express the relationship if we divide the population by the area of the county, as the question suggests. Then, we have:
[tex]rate=\frac{Population}{Area}\Rightarrow rate=\frac{6846\text{residents}}{326mi^2}\Rightarrow rate=21\frac{residents}{mi^2}[/tex]Therefore, the rate that best represents the relationship between the population of the county and the area of the county is 21 residents per square mile (option C).
Larry can spend at most $2800 to renovate his home. One roll of wallpaper costs $35, and one can of paint costs $40. He needs at least 20 rolls of wallpaper and at least 30 cans of paint. Identify the graph that shows all possible combinations of wallpaper and paint that he can buy. Also, identify two possible combinations.
Answer:
[tex]D[/tex]Explanation:
Here, we want to identify the correct graph and the possible combinations
Let the number of rolls of wallpaper be x and the number of cans of paints be y
The total amount needed is at most $2,800
That means:
[tex]35x\text{ + 40y}\leq\text{ 2,800}[/tex]He needs at least 20 rolls of wallpaper:
[tex]x\text{ }\ge\text{ 20}[/tex]He also needs at least 30 cans of paint:
[tex]y\text{ }\ge\text{ 30}[/tex]Now, we have to plot the graph of the given inequalities on the same axes
We have the image of the plot as follows:
Now, let us select the correct answer choice
The correct answer choice lies within the small triangle (where the three inequalities overlap)
All the points within the small triangle are right answers
The correct answer choice here is thus D
What is the equation of the line that is perpendicular tothe given line and passes through the point (2, 6)?108(2.6)6x = 2O x = 62-10 -8 6 -22O y = 2O y = 62468 10X1-8-4)(8.4)68-10Oh
The line in the graph is horzontal and slope of a horizontal line is 0.
Determine the slope of perpendicular line as product of slope of perpendicular line is -1.
[tex]\begin{gathered} m=-\frac{1}{0} \\ =\text{undefined} \end{gathered}[/tex]The slope is undefined means line is vertical and passing through the point (2,6). So equation of line is,
[tex]x=2[/tex]Answer: x = 2
Find the surface area of a cylinder with a base diameter of 6 in and a height of 9 in. Write your answer in terms of II, and be sure to include the correct unit.
The surface area of a cylinder (S) with radius "r" and height "h" is:
[tex]S=2*\pi *r^2+2*\pi *r*h[/tex]Also, radius = diameter/2
Given:
r = 6/2 = 3 in
h = 9 in
Substitute the values in the equation and find S:
[tex]\begin{gathered} S=2\pi *3^2+2\pi *3*9 \\ S=2\pi *9+2\pi *27 \\ S=18\pi+54\pi \\ S=72\pi\text{ in}^2 \end{gathered}[/tex]Answer: The surface area is 72π in².