what is the length of the dominant line in the time graph below? l leave your answer in simplest radical form.
Answers
Let's first calculate the lenght of the side of the rectangle.
[tex]l=\sqrt[]{8^2+5^2}=\sqrt[]{64+25}=\sqrt[]{89}[/tex]so we get that the dotted line is:
[tex]d=\sqrt[]{2^2+89}=\sqrt[]{93}[/tex]so the answer is square root of 93
Related Questions
Drew has a video game with five differentchallenges. He sets the timer to play his gamefor 10.75 minutes. He spends the same amountof time playing each challenge. How long doesDrew nlay the fifth challenge?
Answers
For each game, Drew spends 10.75 minutes, this means in total Drew spends
[tex]5\cdot10.75\text{ minutes}[/tex]this product gives
[tex]5\cdot10.75=53.75\text{ minutes}[/tex]then, in the fifth challenge Drew spends 53.75 minutes
3 * 10 ^ - 6 = 4.86 * 10 ^ - 4 in scientific way
Answers
Answer:
3*10=30
10^-6=1^-6. (10 raised to the power of-6)
therefore 3*1^-6=3
is equal to
4.86*10=48.6
10^-4=1^-4
therefore 48.6*1^-4=48.6
I need help with a math problem. I linked it below
Answers
According to the distributive property of multiplication:
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]Then,
[tex]\begin{gathered} -6(x+5)=12 \\ -6x-6\cdot5=12 \\ -6x-30=12 \end{gathered}[/tex]To find x, add 30 to both sides:
[tex]\begin{gathered} -6x-30+30=12+30 \\ -6x=42 \end{gathered}[/tex]And divide both sides by -6:
[tex]\begin{gathered} \frac{-6}{-6}x=\frac{42}{-6} \\ x=-7 \end{gathered}[/tex]Answer:
- 6x - 30 = 12
x = -7
Match the number with the correct description.
PLEASE HELP
Answers
Answer:
Answers on attached image
Step-by-step explanation:
Please help i need the answers for a test and how to work em out for the future
Answers
Given: The angles as shown in the image
[tex]\begin{gathered} m\angle DEY=105^0 \\ m\angle DEF=27x+3 \\ m\angle YEF=6x+3 \end{gathered}[/tex]To Determine: The measure of angle DEF
Solution
It can be observed that
[tex]\begin{gathered} m\angle DEY+m\angle YEF=m\angle DEF \\ Therefore \end{gathered}[/tex][tex]\begin{gathered} 105^0+6x+3=27x+3 \\ 105=27x-6x+3-3 \\ 105=21x \\ x=\frac{105}{21} \\ x=5 \end{gathered}[/tex][tex]\begin{gathered} m\angle DEF=21x+3 \\ =21(5)+3 \\ =105+3 \\ =108 \end{gathered}[/tex]Question 12
Given:
[tex]\begin{gathered} m\angle UIJ=x+43 \\ m\angle HIJ=66 \\ m\angle HIU=x+37 \end{gathered}[/tex]To Determine: The measure of angle HIU
Solution:
It can be observed that
[tex]m\angle UIJ+m\angle HIU=m\angle HIJ[/tex][tex]\begin{gathered} x+43+x+37=66^0 \\ Collect-like-terms \\ x+x+43^0+37^0=66^0 \\ 2x+80^0=66^0 \\ 2x=66^0-80^0 \\ 2x=-14^0 \\ x=-\frac{14^0}{2} \\ x=-7^0 \end{gathered}[/tex]Therefore, the measure of angle HIU would be
[tex]\begin{gathered} m\angle HIU=x+37^0 \\ m\angle HIU=-7+37^0 \\ m\angle HIU=30^0 \end{gathered}[/tex]Hence, the measure of angle HIU is 30⁰
A projectile is fired vertically upwards and can be modeled by the function h(t)= -16t to the second power+600t +225 during what time interval will the project I’ll be more than 4000 feet above the ground round your answer to the nearest hundredth
Answers
Given:
[tex]h(t)=-16t^2+600t+225[/tex]To find the time interval when the height is about more than 4000 feet:
Let us substitute,
[tex]\begin{gathered} h(t)\ge4000 \\ -16t^2+600t+225\ge4000 \\ -16t^2+600t+225-4000\ge0 \\ -16t^2+600t-3775\ge0 \end{gathered}[/tex]Using the quadratic formula,
Here, a= -16, b=600, and c= -3775
[tex]\begin{gathered} t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ =\frac{-600\pm\sqrt[]{600^2-4(-16)(-3775)}}{2(-16)} \\ =\frac{-600\pm\sqrt[]{360000^{}-241600}}{-32} \\ =\frac{-600\pm\sqrt[]{118400}}{-32} \\ =\frac{-600\pm40\sqrt[]{74}}{-32} \\ =\frac{-75\pm5\sqrt[]{74}}{-4} \\ t=\frac{-75+5\sqrt[]{74}}{-4},x=\frac{-75-5\sqrt[]{74}}{-4} \\ t=7.99709,t=29.5029 \end{gathered}[/tex]So, the interval is,
[tex]8.00\le\: t\le\: 29.50[/tex]0.27x4.42erterttwerutiyrteyruiti
Answers
Answer:
if need to solve
Step-by-step explanation:
1.1934
if it help let me know this
Can someone help out with a math prob?
pic of question below
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The polar equation of the curve with the given Cartesian equation is r = √7
How to convert polar equation to cartesian equationGiven the Cartesian equation: x² + y² = 7
The relationships between polar and cartesian equation :
x = r cosθ
y = r sinθ
Where r is the radius and θ is the angle
Put the values of x and y into the given cartesian equation:
(r cosθ)² + (r sinθ)² = 7
r²cos²θ + r²sin²θ = 7
r²(cos²θ + sin²θ) = 7
Since the trigonometric identity cos²θ + sin²θ = 1
r²(1) = 7
r² = 7
r = √7
Therefore, the polar equation for the represented curve is r = √7
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What is the measure of the base of the rectangle if the area of the triangle is 32 ft2 ?A) 8 ftB) 16 ft C) 32 ftD) 64 ft
Answers
Answer:
B) 16 ft
Explanation:
The area of a triangle is equal to
[tex]Area\text{ =}\frac{Base\times Height}{2}[/tex]We know that the area is 32 ft² and the height is 4 ft, so replacing these values, we get
[tex]32=\frac{\text{Base}\times4}{2}[/tex]Now, we can solve for the base. So multiply both sides by 2
[tex]\begin{gathered} 32\times2=\frac{\text{Base }\times4}{2}\times2 \\ 64=\text{Base }\times4 \end{gathered}[/tex]Then divide both sides by 4
[tex]\begin{gathered} \frac{64}{4}=\frac{Base\times4}{4} \\ 16=\text{Base} \end{gathered}[/tex]Therefore, the measure of the base is 16 ft
Which values are solutions to the inequality below? Check all that applySqrt x>=9Choices are:-2, 82, 32, 180, 99, 63
Answers
We notice the following:
[tex]\begin{gathered} \sqrt[]{x}\ge9\ge0 \\ \Rightarrow \\ x\ge81 \end{gathered}[/tex]Then, possible solutions of the inequality are all real numbers greater or equal than 81. From the given set of solution, those numbers that fullfill that requirement are:
[tex]82,\text{ 180 and 99}[/tex]$1750 is invested in an account earning 3.5% interest compounded annualy. How long will it need to be in an account to double?
Answers
Given :
[tex]\begin{gathered} P\text{ = \$ 1750} \\ R\text{ = 3.5 \%} \\ A\text{ = 2P} \\ A\text{ = 2}\times\text{ 1750 = \$ 3500} \end{gathered}[/tex]Amount is given as,
[tex]\begin{gathered} A\text{ = P( 1 + }\frac{R}{100})^T \\ 3500\text{ = 1750( 1 + }\frac{3.5}{100})^T \\ \text{( 1 + }\frac{3.5}{100})^T\text{ = }\frac{3500}{1720} \end{gathered}[/tex]Further,
[tex]\begin{gathered} \text{( 1 + }\frac{3.5}{100})^T\text{ = 2} \\ (\frac{103.5}{100})^T\text{ = }2 \\ (1.035)^T\text{ = 2} \end{gathered}[/tex]Taking log on both the sides,
[tex]\begin{gathered} \log (1.035)^T\text{ = log 2} \\ T\log (1.035)\text{ = log 2} \\ T\text{ = }\frac{\log \text{ 2}}{\log \text{ 1.035}} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} T\text{ = }\frac{0.3010}{0.0149} \\ T\text{ = 20.20 years }\approx\text{ 20 years} \end{gathered}[/tex]Thus the required time is 20 years.
Cost of a pen is two and half times the cost of a pencil. Express this situation as a
linear equation in two variables.
Answers
The equation to illustrate the cost of a pen is two and half times the cost of a pencil is C = 2.5p.
What is an equation?A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the cost of a pen is two and half times the cost of a pencil.
Let the pencil be represented as p.
Let the cost be represented as c.
The cost will be:
C = 2.5 × p
C = 2.5p
This illustrates the equation.
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Find the future value using the future value formula and a calculator in order to achieve $420,000 in 30 years at 6% interest compounded monthly
Answers
The present value of in order to achieve $420000 in 30 years at 6% interest compounded monthly is $69737.60
The future value = $420000
The time period = 30 years
The interest percentage = 6%
The interest is compounded monthly
A = [tex]P(1+\frac{i}{f})^{fn}[/tex]
Where A is the final value
P is principal amount
i is the interest rate
f frequency where compound interest is added
n is the time period
Substitute the values in the equation
420000 = P × [tex](1+\frac{0.06}{12} )^{(12)(30)[/tex]
420000 = P × 6.02
P = 420000 / 6.02
P = $69737.60
Hence, the present value of in order to achieve $420000 in 30 years at 6% interest compounded monthly is $69737.60
The complete question is:
Find the present value using the future value formula in order to achieve $420,000 in 30 years at 6% interest compounded monthly
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Given two functions f(x) and g(x):f(x) = 8x - 5,8(x) = 2x2 + 8Step 1 of 2 Form the composition f(g(x)).Answer 2 PointsKeypadKeyboard Shortcutsf(g(x)) =>Next
Answers
we have the functions
[tex]\begin{gathered} f(x)=8x-5 \\ g(x)=2x^2+8 \end{gathered}[/tex]Find out f(g(x))
Substitute the variable x in the function f(x) by the function g(x)
so
[tex]\begin{gathered} f\mleft(g\mleft(x\mright)\mright)=8(2x^2+8)-5 \\ f(g(x))=16x^2+64-5 \\ f(g(x))=16x^2+59 \end{gathered}[/tex]Find the 5th term of the arithmetic sequence -5x – 5, -123 – 8,- 19x – 11, ...Answer:Submit Answer
Answers
5x – 5, -123x – 8,
- 19x – 11, ...
Difference is =
rounded 425.652 to the hundredths place
Answers
Since the given number is 425.652
The hundredth digit is the 2nd number right at the decimal point
It is 5
To round to the nearest hundredth, we will look at the digit right to it
1. If it is 0, 1, 2, 3, or 4 we will ignore it and write the number without change except by canceling that digit
2. If it is 5, 6, 7, 8, or 9 we will cancel it and add the digit left to it 1
Since the right digit to the digit 5 is 2, then we will remove it and do not change the digit 5 (case 1), then
The number after rounding should be 425.65
The answer is 425.65
Find decimal notation for 100%
Answers
The decimal notation of percentage is the quotient of the percentage divided by 100.
So it follows that :
[tex]\frac{100\%}{100}=1[/tex]The answer is 1
Evaluate the expression shown: 30-3²-2+7
Answers
Answer:
=26
Step-by-step explanation:
30−32−2+7
=30−9−2+7
=21−2+7
=19+7
=26
what is the slope for the following points?(-1,1) and(3,3)
Answers
To find the slope for a line that connects the given points, use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are the given points.
Use:
(x1,y1) = (-1,1)
(x2,y2) = (3,3)
replace the values of the previous parameters in the formula for m:
[tex]m\text{ = }\frac{3-1}{3-(-1)}=\frac{2}{3+1}=\frac{2}{4}=\frac{1}{2}[/tex]Hence, the slope is 1/2
Write equation for graph ?
Answers
The equation for parabolic graphed function is y = [tex]-3x^{2} -24x-45[/tex].
What is parabola graph?
Parabola graph depicts a U-shaped curve drawn for a quadratic function. In Mathematics, a parabola is one of the conic sections, which is formed by the intersection of a right circular cone by a plane surface. It is a symmetrical plane U-shaped curve. A parabola graph whose equation is in the form of f(x) = ax2+bx+c is the standard form of a parabola.
The given graph has 2 intercept at x axis x = -3, x = -5
y = a (x+3) (x+5)
using the intercept (-4, 3)
3 = a (-4 +3)(-4+5)
3 = a (-1)(1)
a =-3
y = -3(x+3)(x+5)
y = -3 [x(x+5) +3(x+5)]
y = [tex]-3x^{2}-24x-45[/tex]
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1. The equations y = x2 + 6x + 8 and y = (x + 2)(x+4) both define thesame quadratic function.Without graphing, identify the x-intercepts and y-intercept of the graph.Explain how you know
Answers
Given the quadratic equation
[tex]y=x^2\text{ +6x + 8}[/tex](1) x-intercepts are -2 and -4 is the points that pass through the x-axis
when y = 0
[tex]\begin{gathered} y\text{ = 0 } \\ x^2\text{ + 6x + 8 = 0} \\ x^2+2x\text{ +4x +8 = 0} \\ (x\text{ + 2)(x +4)=0} \\ x\text{ +2 = 0 or x +4 =0} \\ x\text{ = -2 or x = -4} \end{gathered}[/tex](11) y-intercepts = 8 is the points that pass through the y axis when x = 0
[tex]\begin{gathered} y=x^2\text{ +6x +8} \\ \text{when x = 0} \\ y=0^2\text{ +6(0) +8} \\ \text{y = 8} \end{gathered}[/tex]
How do I solve it and what would be the answer
Answers
The quotient is x² + 4x + 3
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
Explanation:[tex](x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2)}[/tex][tex]\begin{gathered} x\text{ - 2 = 0} \\ x\text{ = 2} \\ \\ \text{coefficient of }x^3+2x^2\text{ - 5x - 6:} \\ 1\text{ 2 -5 -6} \\ \\ We\text{ will divide the coefficients by 2} \end{gathered}[/tex]Using synthetic division:
[tex]\begin{gathered} (x^3+2x^2\text{ - 5x - 6) }\div\text{ (x - 2) = }\frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}} \\ \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}\text{ = quotient + }\frac{remai\text{ nder}}{\text{divisor}} \\ \\ The\text{ coefficient of the quotient = 1 4 3} \\ \text{The last number is zero, so the remainder = 0} \end{gathered}[/tex][tex]\begin{gathered} \frac{(x^3+2x^2\text{ - 5x - 6)}}{\text{(x - 2)}}=1x^2\text{ + 4x + 3 + }\frac{0}{x\text{ - 2}} \\ \text{quotient }=\text{ }x^2\text{ + 4x + 3} \end{gathered}[/tex]For a (x - 2) to be a factor of x³ + 2x² - 5x - 6, it will not have a remainder when it is divided.
Since remainder = 0
Yes, (x - 2) is a factor of x³ + 2x² - 5x - 6
What is the slope of a line parallel to the line whose equation is 12x – 15y = 315.Fully simplify your answer.
Answers
Answer:
4/5
Explanation:
Definition: Two lines are parallel if they have the same slope.
Given the line:
[tex]12x-15y=315[/tex]Determine the slope of the given line by expressing it in the slope-intercept form (y=mx+b), where m is the slope:
[tex]\begin{gathered} 12x-15y=315 \\ \text{ Add 15y to both sides of the equation} \\ 12x-15y+15y=315+15y \\ 12x=315+15y \\ \text{ Subtract 315 from both sides:} \\ 12x-315=315-315+15y \\ 12x-315=15y \\ \text{ Divide all through by 15} \\ \frac{15y}{15}=\frac{12}{15}x-\frac{315}{15} \\ y=\frac{4}{5}x-21 \end{gathered}[/tex]• The slope of the line, m = 4/5.
Since the lines are parallel, they have the same slope.
Hence, the slope of a line parallel to the line whose equation is 12x – 15y = 315 is 4/5.
Find x.special 10A. 3B. 23√3- this is in fractionC. 6√3D. 3√3
Answers
First, we need to remember the cosine formula which is: cosine(theta)= adjacent/hypotenuse, now let's apply the formula to the triangle we have:
By using the formula we find that x=3√3 .
The answer is D.
HELP PLEASE!
Dave has a piggy bank which consists of dimes, nickels, and pennies. Dave has seven
more dimes than nickels and ten more pennies than nickels. If Dave has $3.52 in his piggy bank, how many of each coin does he have?
Answers
Dave has 17 nickels, 24 dimes and 27 pennies in his piggy bank.
According to the question,
We have the following information:
Dave has 7 more dimes than nickels and 10 more pennies than nickels.
Now, let's take the number of nickels to be x.
So,
Dimes = (x+7)
Pennies = (x+10)
Now, Dave has $3.52 in his piggy bank.
We will convert nickels, dimes and pennies into dollars.
We know that 1 nickel = 0.05 dollars, 1 dime = 0.1 dollars and 1 pennies = 0.01 dollars.
Now, we will convert the given numbers of nickel, dime and pennies into dollars.
x Nickels in dollars = $0.05x
(x+7) dimes in dollars = $0.1(x+7)
(x+10) pennies in dollars = $0.01(x+10)
Now, we will them.
0.05x + 0.1(x+7) + 0.01(x+10) = 3.52
0.05x + 0.1x + 0.7 + 0.01x + 0.1 = 3.52
0.16x + 0.8 = 3.52
0.16x = 3.52-0.8
0.16x = 2.72
x = 2.72/0.16
x = 17
Now, we have:
Number of nickels = 17
Number of dimes = (17+7)
Number of dimes = 24
Number of pennies = (17+10)
Number of pennies = 27
Hence, the number of nickels, dimes and pennies are 17, 24 and 27 respectively.
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George filled up his car with gas before embarking on a road trip across the country. The capacity of George's gas tank is 12 gallons and her car uses 2 gallons of gas for every hour driven. Make a table of values and then write an equation for G, in terms of t, representing the number of gallons of gas remaining in George's gas tank after t hours of driving.
Answers
Given that the capacity of George's gas tank is 12 gallons and her car uses 2 gallons of gas for every hour driven.
[tex]\begin{gathered} G_{\circ}=12 \\ m=-2 \end{gathered}[/tex]slope m is negative since the gas is reducing every hour.
Writing the equation for G, in terms of t, representing the number of gallons of gas remaining in George's gas tank after t hours of driving.
[tex]\begin{gathered} G=G_{\circ}+mt \\ G=12+(-2)t \\ G=12-2t \end{gathered}[/tex]The equation for G is;
[tex]G=12-2t[/tex]Calculating the number of gallons remaining in the tank after 0,1,2 and 3 hours, we have;
[tex]\begin{gathered} G=12-2t \\ at\text{ t=0}; \\ G_0=12-2(0)=12 \\ at\text{ t=1}; \\ G_1=12-2(1)=10 \\ at\text{ t=2}; \\ G_{2_{}}=12-2(2)=12-4=8 \\ at\text{ t=3;} \\ G_3=12-2(3)=12-6=6 \end{gathered}[/tex]Completing the table, we have;
Find the area and the perimeter of the following rhombus. round to the nearest whole number if needed.
Answers
ANSWER
[tex]\begin{gathered} A=572 \\ P=96 \end{gathered}[/tex]EXPLANATION
To find the area of the rhombus, we have to first find the length of the other diagonal.
We are given half one diagonal and the side length.
They form a right angle triangle with half the other diagonal. That is:
We can find x using Pythagoras theorem:
[tex]\begin{gathered} 24^2=x^2+16^2 \\ x^2=24^2-16^2=576-256 \\ x^2=320 \\ x=\sqrt[]{320} \\ x=17.89 \end{gathered}[/tex]This means that the length of the two diagonals is:
[tex]\begin{gathered} \Rightarrow2\cdot16=32 \\ \Rightarrow2\cdot17.89=35.78 \end{gathered}[/tex]The area of a rhombus is given as:
[tex]A=\frac{p\cdot q}{2}[/tex]where p and q are the lengths of the diagonal.
Therefore, the area of the rhombus is:
[tex]\begin{gathered} A=\frac{32\cdot35.78}{2} \\ A=572.48\approx572 \end{gathered}[/tex]The perimeter of a rhombus is given as:
[tex]P=4L[/tex]where L = length of side of the rhombus
Therefore, the perimeter of the rhombus is:
[tex]\begin{gathered} P=4\cdot24 \\ P=96 \end{gathered}[/tex]Transformations that preserve shape and size are called rigid motions. Find a definition of just the word rigid using the internet and write it below.
Answers
Simply put,
Rigid means not moving.
In transformations, rigid motions are transformations that preserve distance.
A rocket is shot off from a launcher. The accompanying table represents the height of the rocket at given times, where x is time, in seconds, and y is height, in feet. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest tenth. Using this equation, find the height, to the nearest foot, at a time of 3.8 seconds.
Answers
Given
The data can be modeled using a quadratic regression equation.
Using the general form of a quadratic equation:
[tex]y=ax^2\text{ + bx + c}[/tex]We should use a regression calculator to obtain the required coefficients. The graph of the equation is shown below:
The coefficients of the equation is:
[tex]\begin{gathered} a\text{ = -17.5 (nearest tenth)} \\ b\text{ = }249.0\text{ (nearest tenth)} \\ c\text{ = }-0.5 \end{gathered}[/tex]Hence, the regression equation is:
[tex]y=-17.5x^2\text{ + 249.0x -0.5}[/tex]We can find the height (y) at a time of 3.8 seconds by substitution:
[tex]\begin{gathered} y=-17.5(3.8)^2\text{ + 249}(3.8)\text{ - 0.5} \\ =\text{ }693 \end{gathered}[/tex]Hence, the height at time 3.8 seconds is 693 ft
Are the graphs of the equations parallel, perpendicular, or neither?x -3y = 6 and x - 3y = 9
Answers
The equation of a line in Slope-Intercept form, is:
[tex]y=mx+b[/tex]Where "m" is the slope of the line and "b" is the y-intercept.
By definition:
- The slopes of parallel lines are equal and the y-intercepts are different.
- The slopes of perpendicular lines are opposite reciprocals.
For this case you need to rewrite the equations given in the exercise in Slope-Intercept form by solving for "y".
- Line #1:
[tex]\begin{gathered} x-3y=6 \\ -3y=-x+6 \\ y=\frac{-x}{-3}+(\frac{6}{-3}) \\ \\ y=\frac{x}{3}-2 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m_1=\frac{1}{3} \\ \\ b_1=-2 \end{gathered}[/tex]- Line #2:
[tex]\begin{gathered} x-3y=9 \\ -3y=-x+9 \\ y=\frac{-x}{-3}+(\frac{9}{-3}) \\ \\ y=\frac{x}{3}-3 \end{gathered}[/tex]You can identify that:
[tex]\begin{gathered} m_2=\frac{1}{3} \\ \\ b_2=-3_{}_{} \end{gathered}[/tex]Therefore, since:
[tex]\begin{gathered} m_1=m_2 \\ b_1\ne b_2 \end{gathered}[/tex]You can conclude that: The graphs of the equation are parallel.