Given:
The system of equations is,
[tex]\begin{gathered} 4x-3y=11\text{ . . . . . . (1)} \\ 2x-y=-8\text{ . . . . . .(2)} \end{gathered}[/tex]The objective is to solve the equations using the elimination method.
Explanation:
To solve the equations multiply the equation (2) by -3.
[tex]\begin{gathered} -3\lbrack2x-y=-8\rbrack \\ -6x+3y=+24\text{ . . . . (3)} \end{gathered}[/tex]On solving equations (1) and (3),
[tex]\begin{gathered} 4x-3y=11 \\ \frac{-6x+3y=24}{-2x=35} \end{gathered}[/tex]On further solving the above equation,
[tex]x=-\frac{35}{2}[/tex]Substitute the value of x in equation (2).
[tex]\begin{gathered} 2(-\frac{35}{2})-y=-8 \\ -35-y=-8 \\ -y=-8+35 \\ -y=27 \\ y=-27 \end{gathered}[/tex]Hence, the value of x is (-35/2) and the value of y is -27.
Jessa completed a 50-mile bicycle race in 4 hours. After the race, she realized that the air pressure in her tires was low, which slowed her down by an average of 2 miles per hour. She wants to solve theequation below to find r, her average speed in miles per hour with properly inflated tires,4(r - 2) = 50
Solve for x6m + 3= [tex] \frac{2x - 4}{2} [/tex]can you help me through it
The initial expression is:
[tex]6m+3=\frac{2x-4}{2}[/tex]To solve for x, we need to multiply both sides by 2, as:
[tex]\begin{gathered} (6m+3)\cdot2=\frac{2x-4}{2}\cdot2 \\ 12m´+6=2x-4 \end{gathered}[/tex]Adding 4 on both sides, we get:
[tex]\begin{gathered} 12m´+6+4=2x-4+4 \\ 12m+10=2x \end{gathered}[/tex]Dividing by 2 on both sides:
[tex]\begin{gathered} \frac{12m+10}{2}=\frac{2x}{2} \\ 6m+5=x \end{gathered}[/tex]Answer: x = 6m + 5
Given the function g(x) x2 + 10x + 20,determine the average rate of change of thefunction over the interval -9 < x < 0.
Step 1: Given the equation
[tex]g(x)=x^2+10x+20[/tex]Step 2: Evaluate g(-9).
[tex]\begin{gathered} g(-9)=(-9)^2+10(-9)+20 \\ =81-90+20=11 \end{gathered}[/tex]Step 3: Evaluate g(0)
[tex]\begin{gathered} g(0)=0^2+10(0)+20 \\ =20 \end{gathered}[/tex]Step 4: Given an interval [-9 , 0], the rate of change formula is
[tex]\begin{gathered} \text{Rate of change(R) = }\frac{g(0)-g(-9)}{0-(-9)} \\ \end{gathered}[/tex]Step 5: Substitute for the values of g(0) and g(-9)
[tex]\begin{gathered} R=\frac{20-11}{0+9} \\ =\frac{9}{9}=1 \end{gathered}[/tex]Therefore, the average rate of change for the function over the interval [-9,0] is 1
(07.02 MC)Factor completely 5ax² - 20x³ + 2a - 8x.O (a + 4x)(5x² + 2)O (a +4x)(5x² - 2)O (a-4x)(5x² + 2)O (a-4x)(5x² - 2)
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]5ax²\:-\:20x³\:+\:2a\:-\:8x[/tex]STEP 2: Factor the expression
[tex]\begin{gathered} Factor\text{ }out\text{ }5x^2\text{ }from\text{ }5x^2a-20x^3 \\ 5x^2(a-4x) \\ \\ Factor\text{ }out\text{ }2\text{ }from\text{ }2a-8x \\ 2(a-4x) \end{gathered}[/tex]STEP 3: combine the factors
[tex]\begin{gathered} =5x^2\left(a-4x\right)+2\left(a-4x\right) \\ \mathrm{Factor\:out\:common\:term\:}a-4x \\ =\left(a-4x\right)\left(5x^2+2\right) \end{gathered}[/tex]Hence, the factors are given as:
[tex]\left(a-4x\right)\left(5x^2+2\right)[/tex]
What are the coordinates of the image of B(5, -4) after it is reflected over the x-axis?
Answer:
Given that,
To find the coordinates of the image of B(5, -4) after it is reflected over the x-axis
Since the point is reflected over the x axis , hence the x coordinate is same and y coordinate will be opposite sign of the given point
The given point is B(5, -4)
The image of B(5, -4) after it is reflected over the x-axis is (5,4)
Answer is: (5,5)
can you help me with number 6 its says the point given in each table lie on a line find the slope of the line then graph the line
The coordinates of two points on the line can be represented as:
(x1, y1)=(-1, 3)
(x2, y2)=(2, -1)
Now, the slope of the line can be calculated as,
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ =\frac{-1-3}{2-(-1)} \\ =\frac{-4}{3} \end{gathered}[/tex]Therefore, the slope of the line is -4/3.
Now, plot the points on the graph and join them to obtain the line.
The graph of the line is given as:
Bob is washing windows at his house. He has a 16 ft. ladder and needs the ladder to reach 12 ft . up the side of the house. how far from the base of the house, to the nearest tenth of a foot, does the ladder need to placed ? use the diagram below to help you
We can draw the diagram as:
We have a right triangle and we have to find d.
We can write the Pythagorean theorem as:
[tex]\begin{gathered} d^2+12^2=16^2 \\ d^2=16^2-12^2 \\ d^2=256-144 \\ d^2=112 \\ d=\sqrt[]{112}\approx10.6 \end{gathered}[/tex]Answer: the distance from the base of the house to the ladder is 10.6 ft.
Identify the equation which has the roots 5 and 10.x2 + 15x - 50 = 0x2 + 15x + 50 = 0x2 - 15x + 50 = 0x2 - 15x - 50 = 0
The standard expression for a quadratic equation is expressed as:
[tex]y=ax^2+bx+c[/tex]If the roots of the equation is a and b, the factors of the equation will be (x-a) and (x-b)
If the roots of the equation is 5 and 10, hence the required factors will be (x - 5) and (x - 10)
Take the product of the factors to determine the required equation
[tex]\begin{gathered} f(x)=(x-5)(x-10) \\ f(x)=x(x)-10x-5x+50 \\ f(x)=x^2-15x+50 \end{gathered}[/tex]Hence the equation with the roots 5 and 10 is x^2 - 15x + 50 = 0
Reed is buying wood flooring for his rectangular kitchen. The dimensions of his kitchen are 12 feet by 10 5/12 feet. The cost of the wood flooring he likes is $3.90 per square foot.How much will the wood flooring cost to cover his kitchen floor?A$360.38B.$469.63С$487.50D$491.40
Given the area of a rectangle,
[tex]\begin{gathered} \text{Area of Rectangle=l}\times b \\ \end{gathered}[/tex][tex]\begin{gathered} \text{Length, l=12ft} \\ \text{Breadth, b= 10}\frac{5}{12}ft \end{gathered}[/tex][tex]\begin{gathered} \text{Area}=12\times10\frac{5}{12} \\ =12\times\frac{125}{12} \\ =125ft^2 \end{gathered}[/tex]If the cost of a square foot is $3.9, then the cost of 125 square ft will be
[tex]\begin{gathered} 125ft^2\times\text{ \$3.9} \\ =\text{ \$487.5} \end{gathered}[/tex]Hence, the cost to cover his kitchen floor is $487.5
Option C is the correct option
Which of the following describes the best fit function for this data?A)nonlinear, exponentialB)nonlinear, quadraticC)linear, quadraticD)linear, exponential
Answer:
The correct option is option A.
The best description for the given data is:
NONLINEAR, EXPONENTIAL
Explanation:
The graph is nonlinear because it's points are not in a straight line.
It is not a quadratic graph because it is not U-shaped, as a quadratic graph is expected to be.
Flying against the wind, an airplane travels 7210 kilometers in 7 hours. Flying with the wind, the same plane travels 4050 kilometers in 3 hours. What is the rate of the plane in still air and what is the rate of the wind?
Now we have 2 equations and 2 variables (va and vw). We can isolate a variable in one Equation and substitue in the other, as follow:
[tex]\begin{gathered} 7210=7v_a-7v_{w_{}_{}} \\ 4050=3v_a+3v_w \\ \text{Isolating va in the first equation: } \\ 7v_a=7210+7v_{w_{}} \\ v_a=\frac{7210+7v_{w_{}}}{7}=1030+v_{w_{}} \\ \text{Substituting in the second equation: } \\ 4050=3v_a+3v_w \\ 4050=3(1030+v_{w_{}})+3v_w \\ 4050=3090+3v_{w_{}}+3v_w \\ 4050=3090+6v_w \\ 4050-3090=6v_w \\ 960=6v_w \\ v_w=\frac{960}{6}=160\text{ km/h} \\ v_a=1030+v_{w_{}}=1030+160 \\ v_a=1190\text{ km/h} \end{gathered}[/tex]may you please help me out on both of them
uriah61706, this is the solution:
14. 45% of 600
0.45 * 600
270
15. Original price = $ 33.75
Discount = 17%
Discount = 0.17 * 33.75
Discount = 5.74
Candice will save $ 5.74
the slope of the line below is 0.8 .write the equation of the line in point slope form, using the coordinates of the labeled point. Do not use the parentheses on the y side.
Answer:
[tex]y+3=0.8(x+2)[/tex]Explanation:
Given that:
Slope of the line, m = 0.8
Point on the line = (-2, -3)
The point slope form of a line with slope m and passing through (a, b) is
[tex]y-b=m(x-a)[/tex]Substitute the given values into the formula.
[tex]\begin{gathered} y-(-3)=0.8(x-(-2)) \\ y+3=0.8(x+2) \end{gathered}[/tex]which is the required equation of line.
There are about 34 million gallons of water in Reservoir A and about 38 million gallons in Reservoir B. During a drought, Reservoir A loses about 0.8 million gallons per month and Reservoir B loses about 1.1 million gallons per month. After how many months with the reservoirs contain the same amount of water? Round your answer to the nearest whole month.
we have:
m = month
Reservoir A = 34 - 0.8m
Reservoir B = 38 - 1.1m
the expression is
[tex]\begin{gathered} 34-0.8m=38-1.1m \\ 34-0.8m+1.1m=38-1.1m+1.1m \\ 34+0.3m=38 \\ 34+0.3m-34=38-34 \\ 0.3m=4 \\ \frac{0.3m}{0.3}=\frac{4}{0.3} \\ m=13.3 \end{gathered}[/tex]answer: 13 months
Which set of equations has (5, 0) as its solution?A and BC and DB and DA and D
The solution is the point where 2 lines cross each other.
By looking at the graph we can see that equations A and B cross each at the coordinates (x,y) = (5,0)
So,
A and B
Simplify -34 + (-15) Y Х x f( f(x) VX X, ✓ (x) x SZT
The answer is
[tex]-34+(-15)=-34-15=-(34+15)=-49[/tex]-49
1. In 1910, the average level of CO, in the atmosphere was 300ppm. In 2005, it was380ppm. What is the percent change in atmospheric CO2?Answer:
We need to first find out the overall change in the CO concentration.
We'll have it to be: change = Current - Former = 380 - 300 = 80ppm
Percent change =
[tex]\begin{gathered} \frac{change}{\text{former}}\times100 \\ \frac{80}{300}\times100=26.67\text{ percent} \end{gathered}[/tex]Therefore, percent change = 26.67%
(8,-2)and(12,-6)1) put in slope intercept form2) solve the same points but in standard form
The slope intercept form: y = -x + 6
In standard form, we have: x + y = 6
Explanation:
1) The points: (8,-2)and(12,-6)
The slope intercept formula:
[tex]y\text{ = mx +c}[/tex]where m = slope and c = intercept
m = change in y/ change in x
[tex]\begin{gathered} m\text{ = }\frac{(-6-(-2))}{(12-8)} \\ m\text{ = }\frac{-6+2}{4}\text{ = -4/4} \\ m\text{ = -1} \end{gathered}[/tex]To get the intercept, insert the value of x and y using any of the points:
using point (8, -2) = (x, y)
y = -1x + c
-2 = -(8) + c
-2 = -8 + c
-2+8 = c
c = 6
y = -1(x) + 6
Equation of line with slope -1 and intercept 6
The slope intercept form: y = -x + 6
2) In standard form: Ax + By = C
In our derived equation, A = -1, B = 1 and c = 6
y + x = 6
x + y = 6
In standard form, we have: x + y = 6
the length of a ant fire is 30 millimeters. how long is the fire ant in centimetrs?
Since 1 centimiter = 10 milimiters
We have to divide lenght value by 10:
30 mm / 10 mm/cm = 30/10 = 3cm
The fire ant is 3 centimeters long.
determine the sloution by graphing y=3x-5
Step 1: Write out and number the system of equations
[tex]\begin{gathered} y=3x-5-------------------------(1) \\ y=3x+5-------------------------(2) \end{gathered}[/tex]Step 2: Graph equation 1 and equation 2
Stuck on this could you check and see if I am right?
It is given that principal is 250 dollar at 6 percent compounded.
a. Annually.
Use n=1
Use the formula for amount.
[tex]A=P(1+\frac{r}{n})^{nt}_{}[/tex]Substitute the values.
[tex]A=250(1+\frac{6}{100})^8=250(1.06)^8[/tex][tex]A=398.46dollar[/tex]For the interest , A=P+I.
Substitute the values,
[tex]398.46=250+I[/tex][tex]I=398.46-250=148.46dollar.[/tex]B. Quarterly.
Use n =4
Use the formula for amount.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex][tex]A=250(1+\frac{6}{100\times4})^{4\times8}=250(1+0.015)^{32}[/tex][tex]A=402.58dollar.[/tex]The interest is determined as A=P+I.
[tex]I=402.58-250=152.58\text{ dollar}[/tex]C. Monthly.
Use n =12
Use the amount formula.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Substitute the values.
[tex]A=250(1+\frac{6}{100\times12})^{12\times8}[/tex][tex]A=250(1+0.005)^{96}=403.54dollar[/tex]Hence the amount is 403.54 dollar.
For interest , A=P+I
Substitute the values and find I,
[tex]403.54-250=I[/tex][tex]I=153.54dollar.[/tex]Hence the interest earned is 153.54 dollar.
evaluate the expression for the given value of tue variable 3(n-10); n=3
Substitute n=3 into the given expression:
[tex]n=3\Rightarrow3(n-10)=3(3-10)=3(-7)=-21[/tex]Therefore, the value of the expression when n=3 is -21.
OOC 6. Find the Area - LEVEL 3 4 mm 2 mm 5 mm 3 mm 2 mm
Given data:
The given figure is shown.
The area of the given figure is,
[tex]\begin{gathered} A=(4\text{ mm)(2 mm)+}(3\text{ mm)(2 mm)} \\ =8mm^2+6mm^2 \\ =14mm^2 \end{gathered}[/tex]Thus, the area of the figure is 14 mm^2.
The difference between two numbers is 12. If one number is represented by x, the other number can be expressed as ______. The product of the numbers, P(x), expressed in the form P(x) = ax²+bx + c, is P(x) = ______
The difference between two numbers is 12. If one number is represented by x, the other number can be expressed as x - 12. The product of the numbers, P(x), expressed in the form P(x) = ax²+bx + c, is P(x) = x² - 12x
x*(x - 12)
x*x - x*12
x² - 12x
Which is the unit rate, k, in the proportional relationship y = kx shown in the table?
Given a table that represents the relation between (x) and (y):
We will find the unit rate (k) in the proportional relationship y = kx shown in the table
From the given equation:
[tex]\begin{gathered} y=kx \\ \\ k=\frac{y}{x} \end{gathered}[/tex]Choose the data of one raw to find (k)
so, from the first raw:
When x = -2, y = -1/2
[tex]k=\frac{-\frac{1}{2}}{-2}=\frac{1}{2\cdot2}=\frac{1}{4}[/tex]So, the answer will be k = 1/4
Find the measure of a complementary angle, a supplementary angle, and a vertical angle for the following measures. • m(
Lets start from the definitions:
Complementary (C) is the angle that, once you add it, the result will be 90°;
Suplementary (S) is the angle that, once you add it, the result will be 180°;
Vertical (V) is the oposite angle when two lines cross each other. They will be the same.
From this, we can calculate for the first angle (m(Complementary:[tex]C_A+23=90\rightarrow C_A=90-23=67\degree[/tex]Suplementary:[tex]S_A+23=180\rightarrow S_A=180-23=157\degree_{}[/tex]Vertical:[tex]V_A=23\degree[/tex]--------------------- And now, we calculate for the second angle -------------------------
Complementary:[tex]C_B+y=90\degree\rightarrow C_B=90\degree-y\degree[/tex]Suplementary:[tex]S_B+y=180\rightarrow S_B=180\degree-y\degree[/tex]Vertical:[tex]V_B=y\degree[/tex]Review 2 Three friends all live on the same street that runs west to east. Beth lives 4 blocks from Ann. Carol lives 2 blocks from Beth. If the street is represented by a number line and Ann's house is located at o, what are the possible locations for Carol's house? The possible locations for Carol's house are ato answers as needed)
1) Gathering the data
3 friends
Beth lives 4 blocks Ann
2) Let's sketch it
3) Let's do a number line
Since Ann's in position 0, and Beth is 4 blocks away, She might be at the right or at the left of Ann. Beth might be at point 4 or at the point -4. A for Carol 2 and -2.
Carol, can be always at halfway between Ann and Beth since She's only 2 blocks to the right or she can be 2 blocks to the left.
In the number line, The possible locations for Beth are point 4 and point -4 since 4 and -4 have the same absolute value, in comparison to zero. And Carol's place might be at point 2 or point -2.
Hans cell phone plan costs $200 to start. Then there is a $50 charge each month. Graph the cost of the cell phone plan over a period of two years
Solution
For this case we can create the following equation:
C = 200 + 50x
Where x = represent the number of months since the start
C= Total cost
We can create the graph and we got:
Which of the following correctly displays 3ū - 2517a.- 2532373ū-25253ū -25bd.3ū - 2537-2537Mark this and returnNextSubmit
The representation that correctly displays the relation is
This diagram corresponds to option D
Option D is correct
Question number 1 You are comparing the costs of producing jewelry at two different manufacturers. Company 1 charges $3.25 per piece of jewelry plus a $400 flat fee. Company 2 charges $2.50 per pair piece of jewelry plus a $600 flat fee. How many pieces of jewelry are produced when the total costs for both companies are equal? Company 1 = $3.25x + 400 Company 2 = $2.50x+600 Solve the following equation to determine when the costs are equal 3.25x + 400 = 2.50x + 600 X=1333.33 DOC x=173.91 x=34.78 C O x=266.67
The value of x at equal total cost is 266.67
Here, we want to solve the equation to get the x-value that shows the total costs for the two companies are equal
We proceed as follows;
[tex]\begin{gathered} 3.25x\text{ + 400 = 2.50x + 600} \\ 3.25x-2.50x\text{ = 600-400} \\ \\ 0.75x\text{ = 200} \\ \\ x\text{ = }\frac{200}{0.75} \\ x\text{ = 266.67} \end{gathered}[/tex]