The system of equation are:
[tex]\begin{gathered} 3x+2y=17 \\ 4x+6y=26 \end{gathered}[/tex]to solve this problem we can solve the second equation for x so:
[tex]\begin{gathered} 4x=26-6y \\ x=6.5-1.5y \end{gathered}[/tex]Now we can replace x in the firt equation so:
[tex]3(6.5-1.5y)+2y=17[/tex]and we can solve for y so:
[tex]\begin{gathered} 19.5-4.5y+2y=17 \\ 19.5-17=2.5y \\ 2.5=2.5y \\ \frac{2.5}{2.5}=1=y \end{gathered}[/tex]Now we replace the value of y in the secon equation so:
[tex]\begin{gathered} x=6.5-1.5(1) \\ x=5 \end{gathered}[/tex]So the solution as a ordered pair is:
[tex](x,y)\to(5,1)[/tex]Exam Content
Question 25
Approximately how many years would it take money to grow from $5,000 to $10,000 if it could earn 6% interest?
It would take 16.66 years to grow from $5,000 to $10,000 if it could earn 6% interest.
Time it would take money to grow from $5,000 to $10,000
The prinicipal amount is $ 5000
The total amount is $ 10000
The rate of interest is 6%
Interest = Amount - principal
interest = 10000 - 5000 = 5000
By putting the simple interest formula
SI = prt/100
where p is the principal, r is the rate of interest and t is the time period
SI = 5000 x 6% x t/100
5000 = 5000 x 6 x t / 100
5000 x 100= 5000 x 6 x t
t = 100/6
t = 16.66
Therefore, it would take 16.66 years to grow from $5,000 to $10,000 if it could earn 6% interest.
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Write an equation of each circle described below. Show work! (Hint: find the coordinates of the center first)Given a circle with (5, 1) and (3,-1) as the endpoints of the diameter.(x − B1)² + (y - B2)² = (B3)²B1=B2=B3=Blank 1:Blank 2:Blank 3:Submit
Given:
It is given that a circle is represented by two end points (5,1) and (3,-1).
Find:
we have to find the equation of the circle, radius and center of the circle using end points.
Explanation:
The circle represented by two end points (5,1) and (3,-1) is drawn as
The diameter of the circle is
[tex]d=\sqrt{(5-3)^2+(1-(-1))^2}=\sqrt{4+4}=\sqrt{8}=2\sqrt{2}[/tex]Therefore radius of the circle is
[tex]B3=\frac{d}{2}=\frac{2\sqrt{2}}{2}=\sqrt{2}[/tex]The center of the circle is
[tex](B1,B2)=(\frac{5+3}{2},\frac{1-1}{2})=(\frac{8}{2},\frac{0}{2})=(4,0)[/tex]Therefore, the equation of the circle is
[tex](x-4)^2+(y-0)^2=(\sqrt{2})^2[/tex]where,
[tex]\begin{gathered} B1=4 \\ B2=0 \\ B3=\sqrt{2} \end{gathered}[/tex]What is the greatest common factor of 28y^2 and 49y^2?A. 196y^2B. 7y^2C. 21y^2D. 7y
the value is 7 and keep the y^2
so is
[tex]7y^2[/tex]The table shows the numbers of ships that visited a port in the past 5 years. Identify a polynomial function for thenumber of ships in thousands that visited the port in a given year.
The function is f(x) = 1.3x^2 + 0.1X
HELP PLEASEEEEE!!!!!!
A rational number that is between -0.45 and -0.46 is -0.455.
What is the rational number?The values given are negative decimal numbers. A decimal is a method that is used to write non-integers. An example of a decimal is 0.48. A negative number is a number whose value is less than one.
A rational number is a number that can be expressed as a fraction of two integers
Examples of rational numbers are 2 , -0.455.
-0.455 can be expressed as an integer of -0.22750 and 0.22750.
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3. (02.04 MC)
Choose the equation that represents a line that passes through points (-6, 4) and (2, 0).
The answer to the question is here
Which of the following sets does the number 12 over five belong to
The given figure is
12/5 = 2.4
Firstly, let us define the terms.
whole numbers are set of natural number including zero. It does not include decimals. Thus, 12/5 is not a whole number
Integers are are the set of whole numbers including all the negative natural numbers. It does not include fractions. Thus, 12/5 is not a whole number
Rational numbers is a set of fractions where the denominators and numerators are integers. Since 5 and 12 are integers, 12/5 is a rational number
Irrational numbers are numbers that numbers that cannot be written on the number line. They include square root of 2, pi. etc. Thus, 12/5 is not an irrational number
Real numbers is the set of all rational and irrational numbers. Thus, 12/5 is a real number
Therefore, the correct options are
How many values does the expression 6+(x+3)^2 have?
The solution of a quadratic equation is imaginary.
What are the solutions of a quadratic function?
A quadratic equation with real or complex coefficients has two solutions, called roots.
These two solutions may or may not be distinct, and they may or may not be real.
The solution of the given quadratic function is calculated as follows;
6 + (x + 3)² = 0
subtract 6 from both sides of the equation;
6 + (x + 3)² - 6 = 0 - 6
(x + 3)² = - 6
take square root of both sides
x + 3 = √-6
x + 3 = 6i
x = 6i - 3
Thus, the solution of a quadratic equation can be determined solving for the value of unknown in the equation.
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Suppose that there are two types of tickets to a show: advance and same day. Advance tickets cost 30 and the same day tickets cost 20. For one performance there were 60 tickets sold in all and the total amount paid for them was $1600. How many tickets of each type were sold
Let A be the number of advance tickets sold and S be the total number of same-day tickets sold. The total amount of tickets is A+S, then:
[tex]A+S=60[/tex]The total earnings for A advanced tickets is 30A, while the total earnings for selling S same-day tickets is 20S. Then, the total amount of money for selling A advanced tickets and S same-day tickets, is 30A+20S, then:
[tex]30A+20S=1600[/tex]Solve the system of equations to find the total amount of tickets of each type that were sold. To do so, isolate A from the first equation and then substitute the resulting expression in the second one:
[tex]\begin{gathered} A+S=60 \\ \Rightarrow A=60-S \end{gathered}[/tex][tex]\begin{gathered} 30A+20S=1600 \\ \Rightarrow30(60-S)+20S=1600 \end{gathered}[/tex]Solve for S:
[tex]\begin{gathered} \Rightarrow1800-30S+20S=1600 \\ \Rightarrow1800-10S=1600 \\ \Rightarrow-10S=1600-1800 \\ \Rightarrow-10S=-200 \\ \Rightarrow S=-\frac{200}{-10} \\ \therefore S=20 \end{gathered}[/tex]Substitute S=20 into the expression for A:
[tex]\begin{gathered} A=60-S \\ =60-20 \\ =40 \end{gathered}[/tex]Then, the solution for this system is:
[tex]\begin{gathered} A=40 \\ S=20 \end{gathered}[/tex]if you run 5/6 of a mile in 1/12 of how hour how much is that
The entire miles that the person runs in 1 hour is 10 miles
What is a fraction?A fraction simply means the numbers that's expressed as a/b where a = numerator and b = denominator.
In this case, the person runs 5/6 of a mile in 1/12 of an hour.
The number of miles for the entire run will be the division of the fractions given. This will be illustrated as:
= 5/6 ÷ 1/12
= 5/6 × 12
= 5 × 2
= 10 miles
The entire race is 10 miles.
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Please help me and explain to me these questions step by step. Thank youQuestion 8: Use simple interest
Given:
Amount Nicole borrowed = $1100
Annual interest rate = 7%
Duration = 6 months
Let the amount of interest be x
The amount after t years can be calculated using the formula:
[tex]\text{Amount = }P(1\text{ }+\text{ rt)}[/tex]The interest that she would pay can be calculated using the formula:
[tex]\text{Interest = Amount - Principal}[/tex]The amount after 6 months is:
[tex]\begin{gathered} \text{Amount = 1100(1 + 007 }\times\frac{6}{12}) \\ =\text{ 1138.5} \end{gathered}[/tex]Hence, the interest:
[tex]\begin{gathered} \text{Interest = 1138.5 - 1100} \\ =\text{ 38.5} \end{gathered}[/tex]Answer: $38.5
For one of the meals eaten duringthe field trip to Williamsburg, VA,WHMS will be charged $115.50 foradults to eat and $712.50 forstudents to eat WHMS will leave a10% tip. How much money willWHMS leave for the tip
The total amount the WHMS would be charged for adults and students to eat is
115.5 + 712.5 = $828
We were told that WHMS will leave a 10% tip. Recall that percentage is expressed in terms of 100. This means that the amount of money that WHMS will leave for the tip is
10/100 * 828 = $82.8
WHMS would leave $82.8 for the tip
Looking to receive help on the following practice question thank you.
use the definition of sec and write it in terms of cos
[tex]r=4\cdot\frac{1}{\cos \theta}[/tex]multiply both sides by cos
[tex]r\cos \theta=4[/tex]then we know that r*cos is equal to x in the cartesian
[tex]x=4[/tex]laws exponents multiplication band power to a power simplifymake it small steps please the smallest you canbare minimum of steps
Answer:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)=-12r^6s^{-4}[/tex]Explanation:
Given the expression:
[tex](4r^4s^{-2})(-3rs^{-3})(rs)[/tex]This can be rearranged using law of multiplication (That multiplication is cummutative) to become:
[tex](4)(-3)(r^4rr)(s^{-2}s^{-3}s)[/tex]This becomes, using the law of exponents:
[tex]-12r^{4+1+1}s^{-2-3+1}[/tex]and finally, we have:
[tex]-12r^6s^{-4}[/tex]What does 10 represent in 10/6
10/6
This is a fraction, in a fraction the bottom number represents the denominator and the top number represents the numerator.
So, in this case, 10 represents the numerator.
need help with this problem answer in a quick and clear response
Answer:
A system of inequalities with parallel boundaries doesn't have a solution when the regions for each inequality don't intersect. This region depends on the sign of inequality, so the signs of inequality determine if the system has solutions.
Identify the leading coefficient, degree and end behavior. write the number of the LC and degree
Given
[tex]P(x)=-4x^4-3x^3+x^2+4[/tex]Solution
The LC is -4
End behavior is determined by the degree of the polynomial and the leading coefficient (LC).
TThe degree of this polynomial is the greatest exponent is
[tex]\begin{gathered} x\rightarrow\infty\text{ then P\lparen x\rparen} \\ p(\infty)=-4(\infty)^4-3(\infty)^3+\infty^2+4 \\ p(\infty)=-4\infty^4-3\infty^3+\infty^2+4 \\ P(\infty)=-\infty \\ \end{gathered}[/tex][tex]\begin{gathered} x\rightarrow-\infty \\ p(-\infty)=-4(-\infty)^4-3(-\infty)^3+(-\infty)^2+4 \\ P(-\infty)=-4\infty^4+3\infty^3+\infty^2+4 \\ P(-\infty)=-\infty \end{gathered}[/tex]The degree is even and the leading coefficient is negative.
The final answer
How many megagrams(Mg) are there in 3.6 tons?[ ? ] MgMass in MgEnter
Step 1
Given;
[tex]3.6\text{tons}[/tex]Required; To find how many megagrams(Mg) are in 3.6 tonnes
Step 2
Find how many megagrams(Mg) are in 3.6 tonnes
[tex]\begin{gathered} 1\text{ tonne=1000000}g \\ 1\text{ megagram=1}000000g \end{gathered}[/tex]Therefore,
[tex]1\text{ tonne = 1 megagram}[/tex][tex]\frac{1\text{ tonne}}{3.6\text{ tonnes}}=\frac{1\text{ megagram}}{x\text{ megagram}}[/tex][tex]\begin{gathered} x\text{ megagram(1 tonne)=1 megagram(3.6 tonnes)} \\ \frac{x\text{ megagram}(1\text{ tonne)}}{1\text{ tonne}}\text{=}\frac{\text{1 megagram(3.6 tonnes)}}{1\text{ tonne}} \\ x=\text{ 3.6 megagrams} \\ x=3.6Mg \end{gathered}[/tex]
Find all critical points of the function f(x) = x^3 + 5x^2 - 7x - 3.The critical point(s) is(are) =
We are given:
[tex]f(x)=x^3+5x^2-7x-3[/tex]Now, we know that in order to determine the critical points we derivate and the derivative is then equal to 0, that is:
[tex]f^{\prime}(x)=3x^2-10x-7=0[/tex]Now, we solve for x, that is:
[tex]3x^2+10x-7=0\Rightarrow x=\frac{-(10)\pm\sqrt[]{(10)^2-4(3)(-7)}}{2(3)}[/tex][tex]\Rightarrow\begin{cases}x=-\frac{5+\sqrt[]{46}}{3}\Rightarrow x\approx-3.9 \\ \\ x=\frac{-5+\sqrt[]{46}}{3}\Rightarrow x\approx0.6\end{cases}[/tex]So, the critical points of the function are:
[tex]\begin{cases}x=-\frac{5+\sqrt[]{46}}{3} \\ \\ x=\frac{-5+\sqrt[]{46}}{3}\end{cases}[/tex]Now, we determine the y-components of the points, that is:
[tex]\begin{cases}f(-\frac{5+\sqrt[]{46}}{3})=(-\frac{5+\sqrt[]{46}}{3})^3+5(-\frac{5+\sqrt[]{46}}{3})^2-7(-\frac{5+\sqrt[]{46}}{3})-3\Rightarrow f(-\frac{5+\sqrt[]{46}}{3})=41.03608735 \\ \\ f(\frac{-5+\sqrt[]{46}}{3})=(\frac{-5+\sqrt[]{46}}{3})^3+5(\frac{-5+\sqrt[]{46}}{3})^2-7(\frac{-5+\sqrt[]{46}}{3})-3\Rightarrow f(\frac{-5+\sqrt[]{46}}{3})=-5.184235498\end{cases}[/tex]So, the two critical points are:
[tex](-\frac{5+\sqrt[]{46}}{3},41.03608735)[/tex]and:
[tex](\frac{-5+\sqrt[]{46}}{3},-5.184235498)[/tex]This can be seing as follows:
у = -3х5х + y = 14i need help finding the matrix of this
3x + y = 0
5x + y = 14
[tex]\Delta\text{ = }\begin{bmatrix}{3} & 1{} & \\ {5} & 1{} & {} \\ {} & {} & {}\end{bmatrix}\text{ = (3 x 1) - (5 x 1) = 3 - 5 = -2}[/tex][tex]undefined[/tex]
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Is there a relationship between the distance and the sum? Is there a relationship between the distance and the difference?
A 5-column table with 3 rows. Column 1 is labeled a with entries 1, 4, negative 6. Column 2 is labeled b with entries 2, negative 1, negative 3. Column 3 is labeled a + b with entries 3, 3, negative 9. Column 4 is labeled a minus b with entries negative 1, 5, negative 3. Column 5 is labeled Distance with entries 1 unit, 5 units, 3 units.
Which describes the relationship between the distance and the difference?
The distance is always the opposite of the difference.
The distance is exactly the difference.
The distance is the absolute value of the difference.
The distance is not related to difference.
The third option that is the distance is the absolute value of the difference describes the relationship between distance and difference.
We know that the distance between two points is the difference of those two values.
But as the distance between two points can never be negative, we will write the absolute value of the difference as the distance between the two points.
Here we can see that,
a - b = -1 when distance = 1
a - b = 5 when distance = 5
a - b = 3 when distance = 3
Hence, the relationship between difference and distance is described by the third option.
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determine the point and slope that were used to write each linear equation in point slope form
The slope-point form is:
[tex]y-y_0=m(x-x_0)[/tex]where (x0,y0) is a point in the line and m is the slope.
A) If the equation is written in slope-point form, we have:
[tex]y-0=2(x-5)[/tex]Then, the point is (5,0) and the slope is m=2.
Answer: Point = (5,0)
Slope = 2
B)
[tex]\begin{gathered} y+3=5x \\ y-(-3)=5(x-0) \end{gathered}[/tex]Answer: Point (0,-3)
Slope = 5
calculate the surface area of a hollow cylinder which is closed at one end if the base radius is 3.5 cm and the height is 8 cm
Answer:
A=2πrh+2πr2=2·π·3.5·8+2·π·3.52≈252.89821cm²
The surface area is 214.305cm².
What is surface area?The surface area is the area of the outer covering of the object.
It is given that radius, r=3.5 cm, and height, h=8 cm.
The surface area of the given object will be the sum of curved surface area and the area of the bottom, which is circle.
Surface Area = Curved Surface Area + Area of bottom circle
=2πrh+πr²
=2π(3.5)(8)+π(3.5)²
=56π+12.25π
=68.25π
Substitute π=3.14 to determine the surface area.
Surface Area = 68.25(3.14)
=214.305
So, the surface area will be 214.305cm².
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The total fixed costs of producing a product is $36,000 and the variable cost is $124 per item. If the company believes they can sell 1,800 items at $170 each, what is thebreak-even point?667 items695 items705 items783 itemsNone of these choices are correct.
3450 turns to degrees and 3450 turns to radians.
We will have the following:
*First: We know that 1 turn will be equal to 360°. So:
[tex]3450\cdot360=1242000[/tex]So, 3450 turns equal to 1 242 000 degrees.
*Second: We have that the expression to convert degrees to radians is:
[tex]d\cdot\frac{\pi}{180}=r[/tex]Here d represents degrees and r radians. So, we replace the number of degrees and solve for radians:
[tex](1242000)\cdot\frac{\pi}{180}=6900\pi[/tex]So, 3450 turns are 6900pi radians.
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
Eddie brought his DVD set to the secondhand store to sell he was paid for all three DVDs in the set before he left Eddie used $15.70 of his earnings to purchase a pair of headphones had $2.30 remaining which equation can you use to find the amount of money Eddie received for each DVD
15.70(d-3)=2.30
3d-15.70=2.30
15.70d-3=2.30
3(d-15.70)=2.30
answer reflects:
3 dvds sold for d price - cost of headphones and a remaining $2.30
What are the solutions to the equation (x-3)(x+5)=-15
Hence, the solutions of the equation is [tex]x = 0, -2[/tex].
What is the equation?
A mathematical statement that shows that two mathematical expressions are equal.
Here given expression is
[tex](x-3)(x+5)=-15\\\\x^2+5x-3x-15=-15\\\\x^2+5x-3x=0\\\\x^2+2x=0\\\\x(x+2)=0\\\\x=0,-2[/tex]
Hence, the solutions of the equation is [tex]x = 0, -2[/tex].
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Which of the following could be the areas of the three squares below? A. 12ft^2, 16ft^2, 20ft^2B. 10ft^2, 18ft^2, 30ft^2C. 4ft^2, 5ft^2, 12ft^2D. 8ft^2, 16ft^2, 24ft^2i have to show work too :(
The correct option is D
8ft^2, 16ft^2, 24ft^2 could be the three areas of the given squares
Explanation:To know the area of the three squares, we need to know the side length of each square. This can be done by applying Pythagorean rule on the right-angle triangle formed in the middle.
The square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides (legs).
The area of a square is the square of its side length.
Taking the square roots of each of the given options, which ever option has Pythagorean triple is the correct option.
A.
[tex]2\sqrt[]{3},4,2\sqrt[]{5}[/tex]This is NOT a Pythagorean triple.
B.
[tex]\sqrt[]{10},3\sqrt[]{2},\sqrt[]{30}[/tex]This is NOT a Pythagorean triple.
C.
[tex]2,\sqrt[]{5},2\sqrt[]{3}[/tex]This is NOT a Pythagorean triple
D.
[tex]2\sqrt[]{2},4,2\sqrt[]{6}[/tex]This is a Pythagorean triple.
CHECK[tex]\begin{gathered} (2\sqrt[]{2})^2+4^2=(2\sqrt[]{6})^2 \\ 8+16=24 \\ 24=24 \end{gathered}[/tex]Select the correct answer from each drop-down menu.Glven: W(-1, 1), X(3, 4), Y(6, 0), and Z(2, -3) are the vertices of quadrilateral WXYZ.Prove: WXYZis a square.
ANSWER
all four sides have a length of 5
EXPLANATION
The distance between two points (x₁, y₁) and (x₂, y₂) is,
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]Let's find the distance between each pair of points, WX, XY, YX, and WZ,
[tex]WX=\sqrt{(3-(-1))^2+(4-1)^2}=\sqrt{(3+1)^2+(4-1)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]XY=\sqrt{(6-3)^2+(0-4)^2}=\sqrt{(3)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex][tex]YZ=\sqrt{(2-6)^2+(-3-0)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=5[/tex][tex]WZ=\sqrt{(2-(-1))^2+(-3-1)^2}=\sqrt{(2+1)^2+(-4)^2}=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5[/tex]Hence, using the distance formula we found that all four sides have a length of 5.
the difference between 58% of a number and 39% of the same number is 247. what is 62% of that number
Answer
62% of the number = 806
Explanation
We are told that that the difference between 58% of a number and 39% of the same number is 247.
We are then asked to compute 62% of the number.
Let the number be x.
From the first statement,
58% of x = 0.58 × x = 0.58x
39% of x = 0.39 × x = 0.39x
The difference between them is 247
0.58x - 0.39x = 247
0.19x = 247
Divide both sides by 0.19
(0.19x/0.19) = (247/0.19)
x = 1300
So, we can now calculate 62% of the number
62% of x = 0.62 × x = 0.62 × 1300 = 806
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