Answer:
10√7
Step-by-step explanation:
[tex]4 \sqrt{7} + 3 \times 2 \sqrt{7} \\ 4 \sqrt{7} + 6 \sqrt{7} \\ 10 \sqrt{7} [/tex]
Answer:
10√7
Step-by-step explanation:
To combine the radicals, you must have the same number under both radicands. Luckily, you can simplify one of the radicands. This is done by separating the radicand (√28) into its common factors (√4 x √7) and taking the square root of one of the factors (√4 = 2).
4√7 + 3√28 <---- Original expression
4√7 + 3(√4 x √7) <---- Expand √28
4√7 + (3 x 2)√7 <----- Take √4
4√7 + 6√7 <---- Multiply coefficients
10√7 <---- Add both terms
the diameter of a cone is 1.5 meters, the height is 1.5 times the radius, what is the volume?
Answer:
.66 cu. meters
Step-by-step explanation:
volume for cone is V=1/3 x TT x r^2 x height
TT (pi) is 3.14
radius is 1/2 of diameter (1/2 x 1.5 = .75 )
height is 1.5 x radius (1.5 x .75 = 1.125)
V= 1/3 x 3.14 x .75^2 x 1.125
V= .66 cu. meters
PLEASE HELP ASAP!!
The graph below is the solution for which set of inequalities?
1) x-2y ≤ 4
x+y ≤ 5
x ≥ 0
y ≥ 0
2) 3x-y ≤ 12
2x+y ≤ 10
x ≥ 0
y ≥ 0
3) 2x-y ≤ 8
x+y ≤ 5
x ≥ 0
y ≥ 0
4) x+y ≤ 5
x+y ≤ 4
x ≥ 0
y ≥ 0
Answer:
Hi,
Step-by-step explanation:
x>=0
y>=0
x+y-5<=0 line passing through (0,5) and (5,0) with (0,0) in minus region
2x-y-8<=0 line passing trough (0,-8) and (4,0) with (0,0) in minus region
Answer C
Keisha pumped 6 gallons of water into her pool each minute for 48 minutes what was the total change in the amount of water in the pool
The total change in the amount of water in the pool is 288 gallons.
What is Volume?Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.
Here, Rate of water pumped into her pool = 6 gallons / minute.
Total Duration = 48 minutes
Total amount of water = Rate X Time
= 6 X 48
= 288 gallons
Thus, the total change in the amount of water in the pool is 288 gallons.
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Prove that the two circles shown below are similar. (10 points)
Circle C is shown with a center at negative 3, 1 and a radius of 4. Circle E is shown with a center of 4, 9 and a radius of 3.
Both circle C and circle E are similar to each other but the radii are different.
What is a circle?It is the center of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Circle C is shown with a center at (negative 3, 1) and a radius of 4.
Circle E is shown with a center of (4, 9) and a radius of 3.
There is only one parameter in the circle which is radius or diameter.
Then both circle C and circle E are similar to each other but the radii are different.
As shown in the graph.
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[tex]y=1-sqrt(1-2/x)[/tex]
make x the subject
[tex]~~~~~~~~y = 1- \sqrt{ 1- \dfrac 2x}\\\\\\\implies \sqrt{ 1- \dfrac 2x} = 1 - y\\\\\\\implies 1 - \dfrac 2x = (1 -y)^2~~~~~~~~~~~~~;[\text{Square on both sides}]\\\\\\\implies \dfrac 2x = 1-(1-y)^2\\\\\\\implies \dfrac{1}{x} = \dfrac{1-(1-2y+y^2)}{2}\\\\\\\implies x = \dfrac{2}{1-1+2y-y^2}\\\\\\\implies x = \dfrac{2}{2y-y^2}\\\\\\\implies x = -\dfrac{2}{y(y-2)}~~~~~~~~~~~~~~~~~;[y\neq 0,~ y \neq 2]\\[/tex]
28.4.2 Test (CST): Transformations, Congruence, and Similarities, Part 2
Quadrilateral RUST has a vertex at R (1,5).
T
S
What are the coordinates of R'after the translation (x, y) → (x+1, y-1),
Answer:
R'(2,4)
Step-by-step explanation:
When doing translations you subtract or add within the coordinates like a normal problem.
If it helps you, write it as seperate equations like:
1-1 and 5-1
Hope that helps ✓
Help me to answer this math please
The water consumption based on the information for three months will be 22267m³.
How to calculate the values?The total water consumption for the three months will be:
= 7219 + 7390 + 7658
= 22267m³
In conclusion, the information simply wants you to add the values of the water given.
Therefore, the water consumption based on the information for three months will be 22267m³.
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How long did she take for the total distance?
Dana has covered 15 miles on her bike. She covered the first 9 miles at 3 miles an hour and the remaining distance at 2 miles an hour.
Please help ffast and thanks!
Answer:
6 h
Step-by-step explanation:
The relation between time, speed, and distance is ...
time = distance / speed
The total time for the two segments of her ride will be the sum of the times for each of the segments.
__
first 9 milest1 = (9 miles)/(3 mi/h) = 3 h
last 6 milesAfter riding 9 miles of the 15-mile distance, Dana had 15 -9 = 6 miles to go.
t2 = (6 miles)/(2 mi/h) = 3 h
total timeThe total time required for the distance of 15 miles is ...
t1 +t2 = (3 h) +(3 h) = 6 h
It took 6 hours for Dana to cover the distance.
The Chesapeake Bay holds about 18 trillion gallons of water. The bay covers 4,480 square miles or 2,867,200 acres. Each acre can hold 750,000 oysters. Each oyster can filter 50 gallons of water each day. Can there be enough oysters to filter the whole Chesapeake Bay in one day? How is this number impacted by the bay's conditions?
There are enough oysters to filter the whole Chesapeake Bay in one day.
The numbers can be affected by the water temperature and the cleanliness of the water.
Are there enough oysters?The total number of water that can be filtered by the oysters is a function of the total amount of oysters in the bay and the quantity of water they can filter.
Total amount of water they can filter = oysters per acre x total acre x total gallons they can filter each day
(2.9 x[tex]10^{6}[/tex]) x (7.5 x [tex]10^{5}[/tex]) x (5 x 10) = 1.0875 x [tex]10^{14}[/tex]
The gallons of water in the bay in standard form = 1.8 x [tex]10^{13}[/tex]
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Identify the equation of direct variation given that y varies directly with x.
y is 15 when x is 11.
The equation of direct variation given that y varies directly with x.
y is 15 when x is 11 will be [tex]y = \dfrac{15}{11} x[/tex].
What is proportionality?The proportional relationship between x and y can be written symbolically as
[tex]x \propto y[/tex]
That middle sign is called the sign of proportionality.
Variation: Direct from y to x:
[tex]x \propto y[/tex]
y = 15, x= 11
Write the equation
[tex]x \propto y[/tex]
Express as an equation
[tex]y = kx[/tex]
Where k is the constant of variation
Substitute
y = kx
15 = 11k
Solve for k
k = 15/11
Substitute in [tex]y = kx[/tex]
[tex]y = \dfrac{15}{11} x[/tex]
Thus, the equation of direct variation given that y varies directly with x.
y is 15 when x is 11 will be [tex]y = \dfrac{15}{11} x[/tex].
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Wyatt analyzed the data from his science experiment and found that the MAD was greater than the IQR.
What does this tell you about the variability of the data?
A: The middle 50% of the data is
spread out more than the
average variation.
B: The average variation is spread
out more than the middle 50%
of the data.
C: The average of the data is closer to the
least value than it is to the greatest
value.
D: The average of the data is closer to the
greatest value than it is to the least value.
Answer:
C: The average of the data is a closer to the least value than it is to the greatest value
A Circular pie with a diameter of 10” Is cut into six equal pieces. What is the surface area of two slices of pie?
To solve this question, let's find the surface area of the entire pie and then divide it by 6 for each slice.
The area of a circle is pi*r^2. We are given the diameter, so divide that by 2 to get the radius.
Now that you have the area, divide by 6. That is the area of each slice. The problem asks for the area of 2 slices though, so multiply that by 2.
3. Given: AABC, ADEF, and FEL CE
A
6
What is a correct sequence of similarity transformations that shows AABC~ ADEF?
A. a rotation of 180 degrees about point E followed by a horizontal translation
B. a counterclockwise rotation of 90 degrees about point E followed by a horizontal translation
C. a rotation of 180 degrees about point E followed by a dilation with a scale factor of 2 centered at point E
D. a counterclockwise rotation of 90 degrees about point E followed by a dilation with a scale factor of 2 centered
at point E
A correct sequence of similarity transformations that shows AABC~ ADEF is that D. a counterclockwise rotation of 90 degrees about point E followed by dilation with a scale factor of 2 centered at point E.
What is similarity transformation?A similarity transformation refers to a geometric similarity, or to a matrix transformation that results in a similarity.
In this case, the correct sequence of similarity transformations that shows AABC~ ADEF is that a counterclockwise rotation of 90 degrees about point E followed by dilation with a scale factor of 2 centered at point E.
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If 8n = 128, n equals:
Answer:
8n is the same as 8 times a number.
That means...
Continuation:
[tex]8 * n = 128[/tex]
[tex]128 \div 8 = n[/tex]
[tex]128 \div 8 = 16[/tex]
Therefore, n is 16.
A pyramid and a cone are both 12 centimeters tall and have the same
volume. What statement must be true about the two solids?
AA
OA. The horizontal cross-sections of the prisms at the same height
must have the same area.
OB. The vertical cross-sections of the prisms at the same width must
have the same area.
C. The area of the cross-sections of the prisms are multiples of each
other.
D. The cross-sections of the prisms are the same shape.
Answer:
The horizontal cross-sections of the prisms at the same height must have the same area.
Step-by-step explanation:
A pyramid and a cone are both 12 centimeters tall and have the same volume.... What is the volume?
Volume is the quantification of the three-dimensional space a substance occupies.
We have to determine the true statement, and it is
The horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.
The horizontal cross-sections of the prisms at the same height must have the same area thus the correct option is A.
What is the volume?A pyramid and a cone are both 12 centimeters tall and have the same volume, we know that Volume is the quantification of the three-dimensional space a substance occupies.
We have to determine the true statement, and it is the horizontal cross-sections of the prisms at the same height must have the same area cone and given pyramid are looks like same in two-dimensional.
If we cross-section the figures at the same height, it won't get the same shape but we should get the same area, as the area of the cross-section will be proportional to the base area, and the base area of both figures are the same.
Thus, the correct option is A.
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Without using the formula, work out the gradient of the graph shown.
Reason:
Start at the y intercept (0,4) which is where the red line crosses the y axis.
Then move up 2 units, and to the right 1 unit to arrive at (1, 6) which is another point on this red line.
The motion of "up 2, right 1" means:
rise = 2run = 1gradient = slope = rise/run = 2/1 = 2Feel free to use any other two points you prefer and you should get the same result. For instance, you could have started at the x intercept (-2,0) and did the "up 2, right 1" motion to arrive at (-1, 2).
Which statement about the angles in the figure is true?
m/3+m/5= 180°
m/7+m/10 = 180°
m/8+m/9 = 90°
m/1+m/8= 90°
The true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°
Determining the measures of anglesFrom the question, we are to determine the statement that is true about the angles in the given figure
In the given diagram, we can observe that
m∠3 + m∠8 + m∠9 + m∠10 = 180° (Sum of angles in a triangle)
Also,
m∠3 = m∠1 (Vertically opposite angles)
m∠9 + m∠10 = 90° (Vertically opposite angles)
∴ m∠1 + m∠8 + 90° = 180°
m∠1 + m∠8 = 90°
Hence, the true statement about the angles in the figure is m∠1 + m∠8 = 90°. The correct option is the last option m∠1 + m∠8 = 90°
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Pls Help :(((
If a^x=b^y=c^z is a system of exponential expression where b^2=ac
Prove that 1/x + 1/z = 2/y
[tex]\text{Let,}\\\\~~~~~~~a^x =b^y = c^z = k\\\\\text{So,}\\ \\a = k^{\dfrac 1x}\\\\b=k^{\tfrac 1y}\\\\\ c = k^{\tfrac1z}\\\\\text{Now, given that,}\\\\~~~~~~~~~b^2 = ac\\\\\implies \left( k^\tfrac 1y \right)^2 = k^{\tfrac 1x} \cdot k^{\tfrac 1z}\\\\\implies k^{\tfrac 2y} = k^{\tfrac 1x + \tfrac 1z} ~~~~~~~~~~;[a^m \cdot a^n = a^{m+n}]\\\\\implies \dfrac 2y = \dfrac 1x + \dfrac 1z\\\\\implies \dfrac 1x + \dfrac 1z = \dfrac 2y \\\\\text{Proved.}[/tex]
A rectangular swimming pool is 30 cm wide and 40 cm in length. Find the total area and perimeter of the swimming pool.
Answer:
Area: 1,200 square centimeters. Perimeter: 140 centimeters.
Step-by-step explanation:
Since you have to multiply the length and width in order to find the area, multiply 30 and 40 together and you can find 1,200. Next, to find the perimeter you have to add all the lengths of the rectangular swimming pool, which will result in 140 centimeters.
Which of the following transformations will result in an image that maps onto itself?
A. rotate 180 degrees counterclockwise and then reflect across the y-axis
B. reflect across the y-axis and then reflect again across the y-axis
C. rotate 90 degrees counterclockwise and then rotate 270 clockwise
D. reflect across the y-axis and then reflect across the x-axis
If we reflect across the y-axis and then reflect again across the y-axis , it will give result an image that maps onto itself , Option B is the right answer.
What are the rules of Transformations ?The reflection of the point (x,y) across the x-axis is the point (x,-y), across the y-axis is the point (-x,y). , across the line is the point (y, x)
The 90 degree counterclockwise rotation of a point (x, y) is the point (-y, x)
The 180 degree counterclockwise rotation of a point (x, y) is the point (-x, -y)
The 270 degree clockwise rotation of a point (x, y) is the point (-y, x)
Therefore on application of these rules
For Case A
The point will be (-y , x)
For Case B
The point will be (x,y)
Therefore Option B is the answer.
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MATH!!! find the volume of the pyramid. pleaseee answer correctly and tell me how you got your answer.
The area of polygons formulas to V=2.56m^2
We have to determine,
The volume of the pyramid.
What is the volume of the pyramid?The volume of a pyramid is found using the formula,
V = (1/3) Bh
where 'B' is the base area and 'h' is the height of the pyramid.
hight =2.4m
base=1.4+1.8
base=3.2m
V = (1/3) (3.2)(2.4)
V=2.56m^2
As we know the base of a pyramid is any polygon,
we can apply the area of polygons formulas to find 'B.
V=2.56m^2.
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what is the median and mean amount of sugar? pictures attached
Answer:
Step-by-step explanation:
mean is found by adding the numbers and dividing the sum by the number while the median is the middle value of the list ordered in an ascending order
what adds to -288 and adds to -41?
Answer: -329 sorry if i'm not right
Graph the inequality p < - 8. Also ignore my dirty iPad
Step-by-step explanation:
it is just a line covering all values smaller than -8 (that means left of -8).
so, it is a line starting at -8 and going all the way to the left (to the arrow on the left). and you make an empty (hollow) dot at -8, because the value -8 is not included (otherwise it would be p <= -8, and it would be a filled dot at -8).
Alesha has $25. She spent $4 on lunch and $3 for a book everyday. How many days could Alesha use the money for?
Please explain with steps tysm!
Part A: In your own words, describe the relationship between the temperature of the city and the number of ice cream cones sold. (5 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate slope and y-intercept. (5 points)
Part A: The amount of ice cream increases as the temperature increases. Part B: the slope is 2 and the y-intercept will be 5.
What is the slope of a line which passes through points ( p,q) and (x,y)?Its slope would be:
[tex]m = \dfrac{y-q}{x-p}[/tex]
Part A: The relationship between the temperature of the city and the number of ice cream cones sold.
From the graph, the dots on the graph increase in the up-right direction.
Thus, The amount of ice cream increases as the temperature increases.
Part B: The line of best fit
First, if we draw a line through the points
we select any 2 points on the line:
( p,q) and (x,y) as (15, 35) and (0, 5).
The slope (m) is:
[tex]m = \dfrac{y-q}{x-p}[/tex]
[tex]m = \dfrac{5 - 35}{0-15}\\\\m = 2[/tex]
So, the line of best fit is:
y = mx + c
y = 2(x - 0) + 5
y = 2x + 5
The y-intercept will be when x = 0
y = 2x + 5
y = 0 + 5
y = 5
Thus, the slope is 2 and the y-intercept will be 5.
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Wren recorded an outside temperature of –2°F at 8 a.m. When she checked the temperature again, it was 4°F at 12:00 p.m. If x represents the time and y represents the temperature in degrees Fahrenheit, what is the slope of the line through these two data points?
Answer:
Answer
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Assuming the time changes at a constant rate, the equation for this is linear (so has the equation y=mx +c)
8am = -2
9am = -0.5
10am = 1.0
11am = 2.5
12pm = 4
m = change in each value or the slope , for this it is m=1.5
c = the y intercept, we find this by: when x=8 y must = 1.5 , which it isn't , y has to = -2 . So c = -3.5
The equation then is: y= 1.5*x - 3.5
The gradient/slope/m value is 1.5. The answer is 1.5
What is 2x^2+3x-9? i need help finding this answer
(2x−3)(x+3)
HAVE A NICE DAY!
Answer:
x=3/2 or x=-3
Step-by-step explanation:
first off equate the equation to zero
2x²+3x-9=0
then using factorisation method multiply 2 and -9 to get -18.
factors of -18 include +6 and -3
2x²+6x-3x-9=0
then factorise it
2x(x+3)-3(x+3)
(2x-3)(x+3)=0
2x=3 x+3=0
x=3/2 or -3
Find CD.
A) 5
B) 28
C) 56
D) 96
Answer:
C) 56
Step-by-step explanation:
. What is the length of BC¯¯?
2. What is the length of AC¯¯?
3. What is the length of AD
Please help me with this
Answer:
42
Step-by-step explanation:
6 times 7 is 42