The distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.
What is a plane?
A plane is a flat surface on which a straight line joining any two points on it would wholly lie.
Given equations are
[tex]4x-5y+z=16[/tex]
[tex]8x-10y+2z=2[/tex]
The distance between two planes is given by the formula:
[tex]D=\dfrac{|d_2-d_1|}{\sqrt{a^2+b^2+c^2}}[/tex]
Here from equations
[tex]4x-5y+z=16[/tex]
[tex]8x-10y+2z=2[/tex]
We can also write the equation [tex]8x-10y+2z=2[/tex] as:
[tex]4x-5y+z=1[/tex]
So now the two equations are:
[tex]4x-5y+z=16[/tex]
[tex]4x-5y+z=1[/tex]
here a=4 b=-5 c =1 and d1=16 d2=1
Putting the values in the equation.
[tex]D=\dfrac{|-16+1|}{\sqrt{4^2+(-5)^2+(10^2)}}[/tex]
[tex]D=2.34[/tex]
Hence the distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.
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How do I Factorise X^2 - 25
To Factorize Something:
⇒ means to put it into the simplest terms that when multiplied
together transforms into the original form
Let's Solve:
[tex]x^2-25=(x+5)(x-5)[/tex]
Let's Check:
[tex](x+5)(x-5)=x*x+(-5)x+5x-25=x^2-5x+5x-25=x^2-25[/tex]
Answer: (x+5)(x-5)
Hope that helps!
Answer:
(x + 5)(x - 5)
Step-by-step explanation:
[tex]x^2-25[/tex]
[tex]=x^2-5^2[/tex]
[tex]x^2-5^2=\left(x+5\right)\left(x-5\right)[/tex]
[tex]=\left(x+5\right)\left(x-5\right)[/tex]
can someone please tell me how many cups is 7/2 pints??
Answer:
8
Step-by-step explanation:
This net will be folded to form a prism.
A net of a rectangular prism. From top to bottom, the rectangles are labeled B, D, E, F. The left side is labeled A and the right side is labeled C.
Which pairs of faces will be opposite one another when the prism is created? Check all that apply.
D and F
A and C
A and B
B and F
B and E
B and C
E and F
A and F
Mark this and return
The opposite faces are D and F, A and C, and B and E. Then the correct options are A, B, and E.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
This net will be folded to form a prism.
A net of a rectangular prism.
From top to bottom, the rectangles are labeled B, D, E, and F.
The left side is labeled A and the right side is labeled C.
Then the pairs of faces will be opposite one another when the prism is created will be
BD, DE, EF, FB, AD, DC, CF, FA, AB, BC, BE, and EA all are the adjacent side faces.
AC, BE, and DF are the opposite faces.
Then the correct options are A, B, and E.
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-3(7+6t)
Can you tell me the answer
Answer: -21 + -18t
Step-by-step explanation:
-3(7+6t)
-3 x 7= -21
-3 x 6t= 18t
Give the general solution in degrees and radians. 9) 8cosØ = 4
Hi Student!
The first step that we need to take before solving this problem is understand what we need to do and what information we are given to do that. So first they are asking for us to determine the solution (or find theta) in both degrees and radians. The information that is given to us is the equation [tex]8* cos (\theta) = 4[/tex].
After completing the initial step, the next step is to actually start solving the equation for the unknown which in this case is theta or the angle.
Divide both sides by 8
[tex]8* cos (\theta) = 4[/tex][tex]\frac{8* cos (\theta)}{8} = \frac{4}{8}[/tex][tex]cos (\theta) = \frac{1}{2}[/tex][tex]cos (\theta) = 0.5[/tex]Multiply by the inverse of cos
[tex]cos^{-1}(cos (\theta)) = cos^{-1}(0.5)[/tex][tex]\theta = cos^{-1}(0.5)[/tex][tex]\theta = 60[/tex]After solving for the unknown or theta, we were able to determine that the solution for our equation is 60 degrees. Now we can move onto the final step which is to convert our answer to radians to complete the final part of the problem statement.
We can convert from degrees to radians by multiplying by π/180 which would get rid of degrees and give us radians.
Plug in the values
[tex]degrees*\frac{\pi }{180\ degrees}[/tex][tex]60\ degrees*\frac{\pi }{180\ degrees}[/tex]Simplify the expression
[tex]\frac{\pi\ *\ 60\ degrees }{180\ degrees}[/tex][tex]\frac{\pi}{3}[/tex]Therefore, our final answer is that our solution in degrees is 60 degrees and our solution in radians is π/3.
Which statements are true about a histogram with one-minute increments representing the data? select three options. a histogram will show that the mean time is approximately equal to the median time of 7.5 minutes. the histogram will have a shape that is left-skewed. the histogram will show that the mean time is greater than the median time of 7.4 minutes. the shape of the histogram can be approximated with a normal curve. the histogram will show that most of the data is centered between 6 minutes and 9 minutes.
If a histogram has one-minute increments representing the data, we will see that:
A histogram will show that the mean time is approximately equal to the median time of 7.5 minutesThe shape of the histogram can be approximated with a normal curve.The histogram will show that most of the data is centered between 6 minutes and 9 minutes.What will the histogram show?If there are is a histogram which has one-minute increments to represent the data, the shape will be that of a normal curve thanks to most data being between the 6 and 9 minute mark.
The fact that the histogram will have a normal curve means that the mean will be approximately equal to the median because the mean and median are usually equal for normal distributions.
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Answer:
If a histogram has one-minute increments representing the data, we will see that:
A histogram will show that the mean time is approximately equal to the median time of 7.5 minutes
The shape of the histogram can be approximated with a normal curve.
The histogram will show that most of the data is centered between 6 minutes and 9 minutes.
Step-by-step explanation:
Zoe is decorating the outside of a box in the shape of a triangular prism. The figure
below shows a net for the box.
15 ft
12 ft
12 ft
17 ft
13.89 ft
13.89 ft
What is the surface area of the box, in square feet, that Zoe
decorates?
The surface area of the box, in square feet, that Zoe decorates is 430.35 square feet
The surface area of the boxTo determine the surface area from the net of the box, we simply calculate the area of each shape.
From the given figure, we have the following shapes and dimensions:
Rectangles: 15 ft by 12 ft and 13.89 ft by 15 ftTriangle: Base = 12 ft and Height= 7 ftThe area is then calculated using:
Area = Areas of the rectangle + Area of the triangle
So, we have:
Area = 15 * 12 + 13.89 * 15 + 0.5 * 12 * 7
Evaluate the sum of products
Area = 430.35
Hence, the surface area of the box, in square feet, that Zoe decorates is 430.35 square feet
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Answer:577.35 square feet
Step-by-step explanation:
♀️
f(x) = ax³ + 2x² + bx + c. Given that f(0) = f, f(1) = 4 and f(-2) = 8, find the value of a, b and c.
Answer:
a = -1/6
b = 7/6
c = 1
Step-by-step explanation:
[tex]f(x)=ax^3+2x^2+bx+c\\\\f(0)=a(0)^3+2(0)^2+b(0)+c\\\\1=c[/tex]
[tex]f(1)=a(1)^3+2(1)^2+b(1)+1\\\\4=a+2+b+1\\\\4=a+b+3\\\\1=a+b\\\\1-b=a[/tex]
[tex]f(-2)=(1-b)(-2)^3+2(-2)^2+b(-2)+1\\\\8=-8+8b+8-2b+1\\\\8=6b+1\\\\7=6b\\\\\frac{7}{6}=b[/tex]
[tex]1-b=a\\\\1-\frac{7}{6}=a\\ \\-\frac{1}{6}=a[/tex]
So, the true equation would be [tex]f(x)=-\frac{1}{6}x^3+2x^2+\frac{7}{6}x+1[/tex] if you substitute the coefficients and the constant.
Lottie buys a pack of 50 cans of lemonade.
She pays £17 for the cans.
Lottie sell 32 of the cans for 50p each.
She sells the remaining cans for 20p each.
Work out Lottie's percentage profit.
Give your answer correct to three significant figures.
15.3%
In Order:1) Lotte buys 50 cans for £17.
2) Sells 32 cans for 50 penny each.
3) Sells remaining for 20 penny each.
Solve:Total cost for 32 cans:
price of each can × total cans
50 penny × 32
1600 penny
Remaining Cans : 50 - 32 = 18 cans
Total cost of this 18 cans:
20 penny × 18
360 penny
[tex]\boxed{\bf 100 \ penny \ (p) = 1 \ pound \ ( \sf \£ )}[/tex]
Total Gained : 1600 + 360 = 1960 pence ≈ £19.6
Profit : selling price - cost price : 19.6 - 17 = £2.6
Profit In percentage:
[tex]\sf \dfrac{(selling \ price - cost \ price)\ x \ 100}{cost \ price}[/tex]
[tex]\rightarrow \sf \dfrac{2.6\ x \ 100}{17}[/tex]
[tex]\rightarrow \sf 15.294 \%[/tex]
[tex]\rightarrow \sf 15.3 \% \ \ (rounded \ to \ nearest \ three \ significant \ figure)[/tex]
Lottie's percentage profit based on the provided information is 15.29%
How can the percent be found?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Per cent refers to one hundred percent.
The cost will be £17 according to the question
Total amount generated are;
32 cans * £0.50=£16
18 cans * £0.20=£3.60
Then the total will be £16 + £3.60 = £19.60
Profit = amount generated- cost
=£19.60 - £17
= £2.60
The percentage profit:
[tex]= \frac{2.60}{17} * 100 \\\\=[/tex]
15.29%
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Help me on this please!
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &25\\ r=rate\to 300\%\to \frac{300}{100}\dotfill &3\\ t=\textit{elapsed time}\dotfill &x\\ \end{cases} \\\\\\ A=25(1 + 3)^{x}\implies A=25(4)^x~\hfill f(x)=25(4)^x[/tex]
4 is really 1 + 3, namely the growth rate is 300/100 or 300%.
so the quantity today, is 300% more than yesterday, so whatever it was yesterday plus three times that much, so the quantity is 4 times as large as yesterday's.
earth makes one full rotation on its axis in a day how long does it take for it to rotate 150 degrees
Earth rotates one full rotation a day
360° in 3600sSo
It rotates 1° in
3600/360=10sIt rotates 150° in
150(10)1500sThe rectangular prism below has a base area of 44.3 units2 and a volume of 221.5
a
units. Find its height.
[tex]base \: area = 44.3 \: {units}^{2} [/tex]
[tex]volume = 221.5 \: {units}^{3} [/tex]
To find:the height of the given rectangular prism.
Solution:[tex]volume= base \: area \times height[/tex]
[tex]height = \frac{volume}{base \: area} [/tex]
[tex]height = \frac{221.5}{44.3} [/tex]
[tex]height = 5 \: units[/tex]
Therefore, the height of the given rectangular prism is 5 units.
The value of height of rectangular prism is,
⇒ h = 5 units
What is mean by Rectangle?A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
Given that;
The rectangular prism below has a base area of 44.3 units² and a volume of 221.5 units³.
Since, The volume of rectangular prism is,
⇒ V = Base area x height
⇒ 221.5 = 44.3 × h
⇒ h = 221.5 / 44.3
⇒ h = 5 units
Thus, The value of height of rectangular prism is,
⇒ h = 5 units
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CL 1-146. Solve for the variable(s) in each triangle below. a. 15,20, and 15.
The variable(s) in each triangle below 9, 12 and 16.
What is Area of Triangle?The basic formula to find the area of a triangle is, area of triangle = 1/2 (b × h); where 'b' is the base and 'h' is the height of the triangle.
Let the base of the triangle be 15.
So, the area is:
Area= 1/2*b*h
= 1/2*15*20
= 150.
Let the base of the triangle be 25.
So, the area is:
Area= 1/2*b*h
150= 1/2*25*h
= 300/25
h =12
Now, using Pythagoras Theorem
15²= h²+x²
15²=12²+x²
225-144= x²
x²= 81
x=±9
Now, x+y=25
y=16
Thus , values are 9,12 and 16.
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HELPPPP HURRY!!!!!!!!!
Describe one way you could graph the equation: y = 4x + 1,?
Answer:
Start at (0,1) and then go up 4 spaces over 1 to the left and repeat going up 4 over 1. To complete the graph by getting it to go behind the y intercept of (0,1) you go from the y intercept down 4 over 1 to the right and repeat going down 4 over 1.
For plotting a line, we need to plot points [tex](0,1)[/tex] and [tex](\frac{-1}{4},0)[/tex] on the cartesian plane and join them to form a line.
What is plotting a line?For plotting a line, we only need two points to graph a line. With that idea, we take advantage of the two “convenient” points which can easily be solved algebraically from the equation of the line; namely, the x-intercept (x,0) and y-intercept (0,y).
[tex]y = 4x + 1\\\\Put\ x = 0 \\y = 1\\we\ get\ (0,1)\ as\ a\ point\ lying\ on\ the\ line. \\\\Put\ y = 0 \\x = \frac{-1}{4} \\we\ get\ (\frac{-1}{4} ,0)\ as\ a\ point\ lying\ on\ the\ line. \\[/tex]
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2. Find the coordinate of A(-4, 6) after it has been rotated 90 degrees counterclockwise, reflected over the x-axis, and dilated by a scale factor of 2.
The new coordinates of A is (-12,8)
What is Dilation ?To dilate something in the coordinate plane, multiply each coordinate by the scale factor. This is called mapping.
For any dilation the mapping will be (x,y) → (kx,ky).
Convert the point (x, y) to (-y, x) in order to rotate 90 degrees counter clockwise.
The given point is A(-4 ,6) ,after it has been rotated the new coordinates are A(-6,-4)
After reflecting it over x axis the new coordinated will be (-6,4)
Then dilating it with a scale factor of 2
The new coordinates of A is (-12,8)
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I don't know pls help
Answer:
125
Step-by-step explanation:
JIK is congruent to MIL so they both equal 55. 360-55=305-55=250. now MIJ and LIK are gonna be equal so you can divide 250 by 2 which gives you 125. if you add them up it equals 360, a full circle! pls give me brainliest!
A survey was given to a random sample of 45 residents of a town to determine
whether they support a new plan to raise taxes in order to increase education
spending. of those surveyed, 9 respondents said they were in favor of the plan. at the
95% confidence level, what is the margin of error for this survey expressed as a
proportion to the nearest thousandth?.
Using the z-distribution, it is found that the margin of error for the 95% confidence interval is of 0.117.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The sample size and the estimate are given as follows:
[tex]n = 45, \pi = \frac{9}{45} = 0.2[/tex]
Hence the margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]M = 1.96\sqrt{\frac{0.2(0.8)}{45}}[/tex]
M = 0.117.
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PLease Help its a math problem !!! Which statement is true based on the table below?
Answer:
slope of f(x) is 3Step-by-step explanation:
Slope of f(x) :
m = 4 - 1 / -2 + 3m = 3/1m = 3CorrectY-intercept of g(x) :
when x = 0y-intercept is 1Wrongg(x) is an exponential function ⇒ Wrongf(x) is a linear function ⇒ Wrong
The 1st option is correct.
WILL MARK BRAINIEST
The average of the first three numbers were was six the average of the next 7 numbers was 19 what was the overall average of the 10 numbers
Answer:
3 1 4 7 9 3 8
Step-by-step explanation:
The two data sets shown below are almost identical. Which of the following
statements are true? (Select TWO)
Data Set 1: 32 41 51 63 66 71
Data Set 2: 32, 41, 51, 3 66, 71
The range of Data Set 2 is smaller than the range of Data Set 1.
The median of Data Set 2 is exactly 30 less than the median of Data Set 1.
The mean of Data Set 2 is exactly 10 less than the mean of Data Set 1.
The standard deviation of Data Set 2 is larger than the standard deviation of Data Set 1.
Based on the calculations, the two (2) statements which are true are:
The mean of Data Set 2 is exactly 10 less than the mean of Data Set 1.Option D.How to calculate the range?Mathematically, range can be calculated by using this formula;
Range = Highest number - Lowest number
Range 1 = 71 - 32
Range 1 = 39.
Range 2 = 71 - 3
Range 2 = 68.
Therefore, the range of Data Set 2 is not smaller than the range of Data Set 1.
How to calculate the mean?Mathematically, the mean for these data sets would be calculated by using this formula:
Mean = [F(x)]/n
For the total number of Data Set 1, we have:
F(x) = 32 + 41 + 51 + 63 + 66 + 71
F(x) = 324.
Substituting the parameters into the formula, we have:
Mean = [F(x)]/n
Mean 1 = [324]/6
Mean 1 = 54.
For the total number of Data Set 2, we have:
F(x) = 32 + 41 + 51 + 3 + 66 + 71
F(x) = 324.
Substituting the parameters into the formula, we have:
Mean 2 = [264]/6
Mean 2 = 44.
Difference = Mean 1 - Mean 2
Difference = 54 - 44
Difference = 10.
Therefore, the mean of Data Set 2 is exactly 10 less than the mean of Data Set 1.
For the standard deviation of Data Set 1, we have:
SD₁ = √(1/n × ∑(xi - u₁)²)
SD₁ = √(1/5 × ∑(32 - 54)² + 1/5 × ∑(41 - 54)² + 1/5 × ∑(51 - 54)² + 1/5 × ∑(63 - 54)² + 1/5 × ∑(66 - 54)² + 1/5 × ∑(71 - 54)²)
SD₁ = 15.34.
For the standard deviation of Data Set 2, we have:
SD₂ = √(1/n × ∑(xi - u₂)²)
SD₂ = √(1/5 × ∑(32 - 44)² + 1/5 × ∑(41 - 44)² + 1/5 × ∑(51 - 44)² + 1/5 × ∑(3 - 44)² + 1/5 × ∑(66 - 44)² + 1/5 × ∑(71 - 44)²)
SD₂ = 24.88.
Therefore, the standard deviation of Data Set 2 is larger than the standard deviation of Data Set 1.
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i will give you 100 points HELp
Answer:
CD ≈ 26.0 cm
Step-by-step explanation:
using the sine ratio in right triangle ABD
sin35° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{AB}{BD}[/tex] = [tex]\frac{12}{BD}[/tex] ( multiply both sides by BD )
BD × sin35° = 12 ( divide both sides by sin35° )
BD = [tex]\frac{12}{sin35}[/tex] ≈ 20.92 cm
using the sine rule in Δ BCD
[tex]\frac{BD}{sinC}[/tex] = [tex]\frac{CD}{sinB}[/tex] , that is
[tex]\frac{20.92}{sin52}[/tex] = [tex]\frac{CD}{sin102}[/tex] ( cross- multiply )
CD × sin52° = 20.92 × sin102° ( divide both sides by sin52° )
CD = [tex]\frac{20.92sin102}{sin52}[/tex] ≈ 26.0 cm ( to 3 significant figures )
Answer:
CD = 26.0 cm (3 sf)
Step-by-step explanation:
Sine Rule for side lengths
[tex]\sf \dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
Find length BD:
[tex]\implies \sf \dfrac{AB}{\sin ADB}=\dfrac{BD}{\sin BAD}[/tex]
[tex]\implies \sf \dfrac{12}{\sin 35^{\circ}}=\dfrac{BD}{\sin 90^{\circ}}[/tex]
[tex]\implies \sf BD=\dfrac{12\sin 90^{\circ}}{\sin 35^{\circ}}[/tex]
[tex]\implies \sf BD=20.92136155...cm[/tex]
Find length CD:
[tex]\implies \sf \dfrac{BD}{\sin BCD}=\dfrac{CD}{\sin DBC}[/tex]
[tex]\implies \sf \dfrac{20.921...}{\sin 52^{\circ}}=\dfrac{CD}{\sin 102^{\circ}}[/tex]
[tex]\implies \sf CD=\dfrac{20.921...\sin 102^{\circ}}{\sin 52^{\circ}}[/tex]
[tex]\implies \sf CD=25.96941667...cm[/tex]
Therefore, CD = 26.0 cm (3 sf)
HELPHELEHEPELEHELPEGELPE
Answer: A= 68 square centimeters
Step-by-step explanation:
A= [tex]B^{1}[/tex] +[tex]B^{2}[/tex]/2 x h
6+11=17
17/2=8.5
8.5 x 8= 68
PLEASE HELP!
Before you answer:
-No spam (Will be reported)
-No incorrect answers (Will be reported)
-Correct answers and explanations will be mark as BRAINLIEST
Answer:
Step-by-step explanation:
Sphere:1) a) r = 7 cm
[tex]\sf \boxed{\text{Volume of sphere=$\dfrac{4}{3}\pi r^3$}}[/tex]
[tex]\sf =\dfrac{4}{3}*3.14*7*7*7\\\\= 1436 \ cm^3[/tex]
[tex]\sf \boxed{\text{\bf Surface area of sphere = $4\pi r^2$}}[/tex]
= 4*3.14 * 7 * 7
= 615.44 cm²
b) r= 8.4 cm
[tex]Volume = \dfrac{4}{3}\pi r^3[/tex]
[tex]\sf =\dfrac{4}{3}*\dfrac{22}{7}*8.4*8.4*8.4\\\\= 2483.7 \ cm^3[/tex]
Surface area = 4*3.14*8.4*8.4
= 887.04 cm²
Hemisphere:a) r = 6 cm
[tex]\sf \boxed{\text{\bf Volume of hemisphere =$\dfrac{2}{3} \pi r^3$}}[/tex]
[tex]\sf =\dfrac{2}{3}*3.14*6*6*6\\\\= 452.16 \ cm^3[/tex]
[tex]\sf \boxed{\text{\bf Surface area of hemisphere=3 \pi r^2}}[/tex][tex]\sf \boxed{\text{\bf Surface area of hemisphere = $3 \pi r^2$}}[/tex]
= 3 * 3.14 * 6 * 6
= 339.12 cm²
a cylindrical pipe is 36 ft long and has a volume of 100ft. find its approximate diameter to the nearest hundredth of a foot
Answer:
0.940
Step-by-step explanation:
100 = 36 x pi x r^2
now divide both sides by 36pi
r^2 = 0.88419412...
then square root both sides
r = 0.94031597...
The children at Farmfield School are collecting money for charity.
Their target is to collect £360
So far they have collected £57.73
How much more money do they need to reach their target?
f(x)=(x+3)^2 -8 how many real solutions?
Answer:
2 real solutions
Step-by-step explanation:
[tex]f(x)=(x+3)^2-8\\\\0=(x+3)^2-8\\\\8=(x+3)^2\\\\\pm\sqrt{8}=x+3\\\\x=-3\pm\sqrt{8}[/tex]
Therefore, the function set at [tex]f(x)=0[/tex] has two real solutions (x-intercepts).
You can also check the discriminant of the function by expanding it:
[tex](x+3)^2-8=x^2+6x+9-8=x^2+6x+1\\\\b^2-4ac=6^2-4(1)(1)=36-4=32 > 0[/tex]
Since it's greater than 0, there's two real solutions
Calculate the distance between the pairs of coordinates, and classify them according to the distance between them.
(3, 4) and (2, 1)
(3, 7) and (5, 2)
(5, -2) and (3, 3)
(-2, 3) and (1, 2)
(-4, -2) and (-3, 1)
(4, -1) and (-1, 1)
Answer:
the first one is 3
second. is -5/2
third is 5/-2
fourth is -1/3
fifth is 3
sixth is 0/-5
Answer:
Square Root of 10: (3, 4) and (2,1)
(-4,-2) and (-3, 1)
(-2, 3) and (1,2)
Square Root of 29:
(3,7) and (5,2)
(5, -2) and (3,3)
(4,-1) and (-1,1)
Step-by-step explanation: Just took the test
PLS ANSWER WITH EXPLANATION!!!!!!! 50 points and brainliest for best answer!!!!1
Theresa uses a unique box in the shape of a trapezoidal prism for her specialty candles. The area of the base of the box for the smaller candle is 125 cm2 and the box is 12 cm tall. The box used for the larger candle has a base whose area is 160% that of the smaller box, and it is 6 centimeters taller.
What percent of the volume of the smaller box is the volume of the larger box?
Answer:
Answer:
82cm
Step-by-step explanation:
The volume of the larger box is 240% that of the volume of the smaller box.
What is an equation?
An equation is an expression that shows the relationship between two or more numbers and variables
Volume of smaller box = area of base * height = 125 cm² * 12 cm = 1500 cm³
Volume of larger box = area of base * height = (1.6 * 125 cm²) * (12 + 6) cm = 3600 cm³
Ratio of volume = 3600/1500 = 2.4 = 240%
The volume of the larger box is 240% that of the volume of the smaller box.
Volume of the smaller box
Area of base ×Height125(12)1400cm³Area of base of larger box
160% of 1251.6×125200cm²Volume
200(6)1200cm³Percentage
1400/1200×100116.67%A motorist travels 122 km before his first stop. If he had 10% of his journey to complete at this point, how long was the total ride
Answer:
233km
Step-by-step explanation:
An athlete completes one round of a circular track of diameter 200 m in 40 s what will be the distance covered and displacement at the end of 2 min 20s
Answer:
700π m ~ 2199 m
Step-by-step explanation:
diameter = d = 200 m
2 min 20s = 140 s
1 round / 40 s
140 = 40 * 3 + 20
so the athlete will cover 3 round and half
1 round = d * π
covered = c = 3 * 200 * π + 200/2 * π = 700 * π
