Answer: 5 units
Step-by-step explanation:
What is 6 multiplied by 8
Answer:
48
Step-by-step explanation:
Step 1: Convert words into an expression
What is 6 multiplied by 8
6 * 8
Step 2: Multiply
6 * 8
48
Answer: 48
what is the expression in simplified form (-9√2)(4√6)
A. -5√8
B. -72√3
C. -36√8
D. -72√2
Answer: -72√3
Step-by-step explanation:
(-9√2)(4√6)
−9√2*4√6
-9*4√2*6
-9*4√12
-9*4*2√3
-72√3
Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)
- Cutiepatutie ☺❀❤
Final answer:
To simplify (-9√2)(4√6), we multiply numerical coefficients (-9) and (4), and the square roots √2 and √6, simplifying to get -72√3 which is option B.
Explanation:
To simplify the expression (-9√2)(4√6), we need to follow the rules of algebraic multiplication for square roots. Here are the steps to simplify the expression:
Multiply the numerical coefficients together: (-9) × (4) = -36.Multiply the square roots together: √2 × √6 = √(2×6) = √12.Now, we simplify √12 by breaking it down into its prime factors: √(4×3) = √4 × √3 = 2√3.Combine the results: -36 × 2√3 = -72√3 which is our final simplified form.The correct option from the given choices is thus B. -72√3.
The boat is going 10 miles per hour in still water it takes 2 hours to go downstream and 3 hours to go upstream. What’s the speed of the current and distance of the trip?
Answer:
2 mph24 miles one-way; 48 miles round tripStep-by-step explanation:
Let c represent the speed of the current. The travel time is inversely proportional to the travel speed. In one direction the current speed is added to the boat speed; in the other direction, it is subtracted. You can write the relation ...
(10 +c)/(10 -c) = 3/2
2(10 +c) = 3(10 -c) . . . . . . "cross multiply"
20 +2c = 30 -3c . . . . . . . eliminate parentheses
5c = 10 . . . . . . . . . . . . . . . add 3c -20
c = 2 . . . . . . . . . . . . . . . . . divide by 5
The speed of the current is 2 miles per hour.
__
The speed downstream is then (10 +2) = 12 miles per hour. The travel time in that direction is 2 hours, so the distance covered is ...
(12 mi/h)(2 h) = 24 mi
The one-way distance of the trip is 24 miles.
Mary and her friends set out to sea on their annual fishing trip. Their distance from the shore in miles, y, increases by 3 miles each hour, x. write an equation to model this relationship.
y=3x
y=3/2x
y=x+3
y=2x
y=x-4
y=x+5
Answer:
y=3x
Step-by-step explanation:
If y is the total distance from the shore and it increases by 3 miles every hour, then by plugging in the amount of hours that have passed into x we will find the distance they have traveled. For example, if they have been out for 5 hours then you would do y=3(5) which would be 15 miles from the shore.
The correct equation to represent the relationship between Mary's distance from shore and time is y=3x. This is a linear equation, with 3 representing the rate of increase in distance for each time unit (each hour).
Explanation:In this case, Mary is moving at a constant rate, which means we are dealing with a linear relationship. The problem states that her distance from shore, y, increases by 3 miles for each hour, x. Therefore, the correct equation to model this scenario would be y=3x.
This is an equation of a line where 3 is the slope, signifying the change in distance for each time unit (in this case, an hour), and x is the time in hours. So, as time increases, the distance from the shore also increases at a rate of 3 miles per hour.
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How did the graph of f(x) = x^2 and g(x) = 3/4 x^2 relate?
g(x) = [tex]\frac{3}{4} f(x)[/tex] or g(x) is 3/4 times of f(x) , F(x) and g(x) have common solution or intersecting point in the graph parabola at x=0 i.e. in origin and x = [tex]\frac {4}{3}[/tex].
Step-by-step explanation:
We have a function f(x) = [tex]x^{2}[/tex] and another function , g(x) = [tex]\frac{3}{4} x^{2}[/tex]. In the graph of y = [tex]x^{2}[/tex] , the point (0, 0) is called the vertex. The vertex is the minimum point in a parabola that opens upward. In a parabola that opens downward, the vertex is the maximum point.
Graphing y = (x - h)2 + k , where h = 0 & k = 0
Function g(x) can be formed with compression in function f(x) by a factor of 3/4 , i.e. g(x) = [tex]\frac{3}{4} f(x)[/tex] or g(x) is 3/4 times of f(x).Domain and range of f(x) and g(x) are same ! Although structure of both functions is same the only difference is g(x) is compressed vertically by a factor 3/4. Both are graph of a parabola with vertex at (0,0). Also, F(x) and g(x) have common solution or intersecting point at x=0 i.e. in origin.
What is the center of a circle whose equation is x2 + y2 – 12x - 2y + 12 = 0?
(-12, -2)
O (-6, -1)
(6, 1)
O (12, 2)
Solution:
Given equation of circle is:
[tex]x^{2} +y^{2} -12x-2y+12=0[/tex]
Move the constant to other side
[tex]x^{2} +y^{2} -12x-2y = -12[/tex]
Group the equation
[tex](x^{2} -12x)+(y^{2}-2y)=-12[/tex]
Add 36 and 1 from both sides
[tex](x^{2} -12x +36)+(y^{2}-2y + 1)=-12 + 36 + 1\\\\(x^{2} -12x + 36)+(y^{2}-2y + 1)= 25[/tex]
Which is simplified as:
[tex](x - 6)^2 + (y-1)^2 = 25[/tex] --------- eqn 1
The equation of circle is given as:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where, r is radius and (h, k) is center
Compare eqn 1 with above general equation
(h, k) = (6, 1)
Thus the center of a circle is (6, 1)
Answer:
the center the circle is (6,1)
Step-by-step explanation:
78/17 round to the nearest 10
Answer:
0
Step-by-step explanation:
78/17 gives 4.588
In rounding up numbers, 1 to 4 is rounded up to zero, while numbers 5 to 9 will be rounded up to 1.
In the question above, we are asked to round up to the nearest 10. And then 78/17 gives 4.588
This number is between 0 and 10.
The whole number there is 4. Therefore, 4 will be rounded up to Zero.
If the question and us to round up to the nearest whole number, as we have 4.588
The number before the whole number 4 is 5 (the tenth digit), and then 5 will be rounded up to 1. That 1 will hence be added to 4.
4+1= 5. To nearest whole number, it is 5 but to nearest ten, it is 0
For what integer value of x is 4x – 2 >17 and 3x +5<24 ?
Help me please !!
Answer:
The integer values of x are 5 and 6
Step-by-step explanation:
we have
Inequality A
[tex]4x-2>17[/tex]
solve for x
adds 2 both sides
[tex]4x>19[/tex]
divide by 4 both sides
[tex]x> 4.75[/tex]
solution A is the interval (4.75,∞)
Inequality B
[tex]3x+5<24[/tex]
solve for x
subtract 5 both sides
[tex]3x<19[/tex]
divide by 3 both sides
[tex]x<6.33[/tex]
solution B is the interval (-∞,6.33)
The solution of the inequality A and the inequality B is
(4.75,∞) ∩ (-∞,6.33)=(4.75,6.33)
The integer values of x are 5 and 6
Final answer:
The integer value of x for which both inequalities 4x - 2 > 17 and 3x + 5 < 24 are true is x = 5.
Explanation:
To find the integer value of x for which the inequalities 4x – 2 > 17 and 3x + 5 < 24 are both true, we solve each inequality step by step.
For the first inequality, 4x – 2 > 17, add 2 to both sides to get 4x > 19. Then divide by 4 to isolate x, yielding x > 4.75.For the second inequality, 3x + 5 < 24, subtract 5 from both sides to get 3x < 19. Then divide by 3 to isolate x, resulting in x < 6.3333.Both inequalities must be true, so we need to find the interval where x > 4.75 and x < 6.3333. Since x must be an integer, the only integer within this range is x = 5.Complete the statement. Round to the nearest tenth if necessary. 3 km per minute = __ mi per hour?
3 km per minute is approximately equal to 111.8 miles per hour.
To convert 3 km per minute to miles per hour, we can use the conversion factors:
1 kilometer = 0.621371 miles 1 hour = 60 minutes
First, let's convert 3 km per minute to km per hour:
3 km/min * 60 min/hour = 180 km/hour
Now, let's convert km per hour to miles per hour:
180 km/hour * 0.621371 miles/km = 111.84757 miles/hour
Rounding to the nearest tenth, we get:
3 km per minute is approximately equal to 111.8 miles per hour.
can someone answer 8-11 please
Answer:
7.9
4.2
9.3
17.8
Step-by-step explanation:
8. √63
the square of 8 is 64 √63 is close to 64 so we can say it's 7.9 approximately
9. √18
the square of 4 is 16, √18 is greater than 16 so we can say it's 4.2 approximately
10. √87
the square of 9 is 81, √87 is greater than 81 so we can say the value of it is approximately 9.3
11. √319
the square of 18 is 324, √319 is smaller than 324 so we can say it's 17.8
How many cubic meters of material are there in a conical pile of dirt that has radius 11 meters and height 6 meters? Use 3.14 for pi.
The volume of a conical pile of dirt with an 11-meter radius and a 6-meter height is approximately 754.24 cubic meters.
The question is asking for help in calculating the volume of a conical pile of dirt.
The formula for finding the volume of a cone is [tex]V = (1/3) \pi r^2h[/tex], where V is the volume, r is the radius, and h is the height of the cone.
Substituting the given values, the radius r is 11 meters, the height h is 6 meters, and using 3.14 for
π, the calculation would be -
V = (1/3) * 3.14 * 112 * 6.
To find the volume: V = (1/3) * 3.14 * 121 * 6
= 3.14 * 40.333333 * 6
= 754.24 cubic meters.
So, there are approximately 754.24 cubic meters of material in the conical pile of dirt.
what are some equivalent expressions for :
120.5y + 80.5y + 65.5y
Answer:
266.5y
Step-by-step explanation:
120.5y+80.5y+65.5y
201y+65.5y
266.5y
Brandon had $500. He spent 47% of his money on a tablet computer. How much did his computer cost?
Answer:
453
Step-by-step explanation:
Since Brandon spent 47 % of his money you Will subtract 500-47.
x+1+2/x add the two radical expressions
Answer:
[tex]\frac{ \sqrt{ {x}^{2} + x} + 2}{ \sqrt{x} } [/tex]
Step-by-step explanation:
If you are talking about radical expressions, then the two equations should be something like
[tex] \sqrt{x + 1} + \frac{2}{ \sqrt{x} } [/tex]
Assuming this is the intended expression, then:
[tex] \frac{ \sqrt{x \times } \sqrt{x + 1} + 2}{ \sqrt{x} } [/tex]
We then simplify by collecting LCM to obtain:
[tex]\frac{ \sqrt{ {x}^{2} + x} + 2}{ \sqrt{x} } [/tex]
Andre says that 10x + 11 and 5x + 11 are equivalent because they both equal 16 when x is 1. do you agree with Andre?
Answer: No
Step-by-step explanation:
10x + 11 when x= 1 is equal to 21
While 5x + 11, when x=1 is equal to 16
A farm is 350 acres .72% of the farm is suitable for farming. How many acres can be used to farm?
Answer:
252
Step-by-step explanation:
Multiply 350 by the decimal form of 72%. To find the decimal form of 72%, divide 72 by 100 or move every number two places to the right:
72/100 = 0.72
Then multiply 350 by 0.72:
350 x 0.72 = 252
I hope this helps!
please help me i need help
Step-by-step explanation:
(a)
[tex] In\: \triangle ABC \& \triangle DEF \\\\
\frac {AB} {DE} = \frac {40} {48} = \frac {5} {6}...(1)\\\\
\angle ABC \cong \angle DEF... (each\: 90°)...(2)\\\\
\frac {BC} {EF} = \frac {30} {36} = \frac {5} {6}...(3)\\\\[/tex]
From equations (1), (2) & (3)
[tex] \triangle ABC \sim \triangle DEF[/tex]
(By SAS Postulate)
Hence both of the triangles are similar.
(b)
Prism DEF will have greater volume, because length of its sides are larger than that of prism ABC.
6/5 = 1.2 times greater.
What is 60% of 76???
Answer:
45.6
Step-by-step explanation:
0.60 x 76 = 45.6
Answer:45.6
Step-by-step explanation:
60/100*76
0.6*76
45.6
The measure of an angle is 63.7°. What is the measure of its supplementary angle?
Answer:
116.3
Step-by-step explanation:
Supplementary angles add to 180
One angle is 63.7, the other is x
63.7+x = 180
Subtract 63.7 from each side
63.7-63.7+x = 180-63.7
x = 116.3
terry sees this offer : reburfished phone 35% off now only £78 , how much was the phone before the discount
write an equation that is parallel to 3x-2y=14 and passes through point (-6,-11)
y = ([tex]\frac{3}{2}[/tex])x -2 is the equation of the required line
Step-by-step explanation:
Step 1 :
Equation of the given line is 3x-2y=14
Re writing this in the form y = mx + c , we have
-2y = -3x +14
y = ([tex]\frac{3}{2}[/tex])x - 7
The co efficient of x , m is the slope of the line. So for the given line the slope is [tex]\frac{3}{2}[/tex]
Step 2 :
We have to find equation of a line which is parallel to this line. All parallel lines will have the same slope. Hence the required line has a slope of [tex]\frac{3}{2}[/tex].
Step 3 :
Equation of line with slope m and passing through a point ([tex]x_{1} ,y_{1}[/tex]) is
(y-[tex]y_{1}[/tex]) = m((x-[tex]x_{1}[/tex])
So equation of line passing through (-6,-11) and with a slope of [tex]\frac{3}{2}[/tex] is
(y-(-11)) = [tex]\frac{3}{2}[/tex] ( x - (-6))
y + 11 = [tex]\frac{3}{2}[/tex] ( x + 6)
y = ([tex]\frac{3}{2}[/tex])x + 9 - 11
y = ([tex]\frac{3}{2}[/tex])x -2
Step 4 :
Answer :
y = ([tex]\frac{3}{2}[/tex])x -2 is the required equation
The given equation has the slope 3/2 after converting to the slope-intercept form. Because parallel lines share the same slope, the equation for the line parallel to the given line, passing through the point (-6,-11), is found to be y = (3/2)x - 9 using the point-slope form.
Explanation:To find an equation that is parallel to a given equation, we must first find the slope of the given line. The equation provided is in the form Ax + By = C. To convert this into slope-intercept form (y = mx + b), where m is the slope, we rearrange the equation to get y = (3/2)x - 7. Therefore, the slope of the given line is 3/2.
Parallel lines share the same slope, the equation of the line parallel to the given one that passes through point (-6,-11) will also have the slope 3/2. We stick this and our point into the point-slope form of a line (y - y1 = m(x - x1)) to get: y + 11 = 3/2(x + 6). Simplifying, we get y = (3/2)x - 9 which is the equation of the line parallel to the given equation that passes through the point (-6,-11).
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Jane is considering a 7/23 balloon mortgage with an interest rate of 4.15% to
purchase a house for $197,000. What will be her monthly payment for the first
7 years of the balloon mortgage?
O A. $945.98
O B. $933.64
O c. $900.00
O D. $957.62
Answer:
957.62
Step-by-step explanation:
Given the house price, P=$197,000, [tex]n=12\times 30=360, i=0.0415/12[/tex], the monthly payments, M, can be calculated as:
[tex]M=P[\frac{i(1+i)^n}{(1+i)^{360}-1}]\\\\M=[\frac{\frac{0.0415}{12}(1+\frac{0.0415}{12})^360}{(1+\frac{0.0415}{12})^{360}-1}]\\\\M=957.62[/tex]
Hence, the monthly payment of the baloon mortgage is $957.62
Which of the following numbers could be added to 3/14 to make a sum greater than 1/2
Answer:
x > 2/7
Step-by-step explanation:
Step 1: Make an inequality
3/14 + x > 1/2
Step 2: Solve for x
3/14 + x - 3/14 > 1/2 - 3/14
x > 2/7
Answer: x > 2/7
Find the volume of the cone
Enter and exact answer in terms of pi or use 3.14 for pi and round your answer to the nearest hundredth
Answer:
Find 6.75% of 260
Step-by-step explanation:
Hi
To find the volume of a cone, you use the formula 1/3πr²h, substituting in the radius for r and the height for h. For an example cone with a radius of 4 and a height of 9, the volume would be 48π or approximately 150.72 after rounding to the nearest hundredth.
Explanation:The student is asked to find the volume of a cone. The formula to find the volume of a cone is 1/3πr²h, where r is the radius of the base of the cone and h is the height of the cone.
If the student is given the radius and the height, they would just need to substitute the values into the formula. For example, if the radius of the cone is 4 and the height is 9, the volume would be 1/3 * π * (4)² * 9 = 48π. If the student prefers a decimal approximation, they can substitute pi with 3.14 to get 150.72, rounded to the nearest hundredth.
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Graph the image of triangle ABC after a reflection across the x-axis. The vertices of the image will be called A” B” , and C” .
For the graph, the image of triangle ABC after a reflection across the x-axis, the vertices of the image will be called A” B” , and C” are respectively, (-3, 4), (-3, 1), (-1, 1)
What is "reflection about the axis" ?Reflection about the axis is a transformation in geometry where a figure is flipped across a line or plane, producing a mirror image of the original figure. The line or plane across which the figure is reflected is called the axis of reflection.
Given that,
A graph, having triangle ABC
The reflection points, A', B', C' = ?
All the vertices and their mirror image will be at equal distance from the x-axis
So, y-coordinate will be equal in magnitude but different in sign for all the vertices and their mirror image
x-axis is axis of reflection,
there will be no change in x-coordinates
So, x-coordinates will be same in magnitude and in sign as well
Now, Mirror image points can be written as,
A' = (-3, 4)
B' = (-3, 1)
C' = (-1, 1)
Hence, the points are (-3, 4), (-3, 1), (-1, 1)
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What is the equation of the line that passes through the point (-4, 4) and has a
slope of -3
Answer:
[tex]y=-3x+4[/tex]
solve for x: picture included
Answer:
9
Step-by-step explanation:
because diameter never change or if it is radius the first half is 9 so, the second half would be 9 too.
so, x=9
Write a sequence that has two geometric means between -6 and 2/9
Translate this sentence into an equation. 48 is the product of Greg’s score and 3. Use the variable g to represent Greg’s score
Answer:
G x 3 = 48
Step-by-step explanation:
let G be Greg's score
And product means multiplication.
so G x 3 = 48.
finding Greg's score means 3g = 48.
g = 48/3
g = 16.
Simplify this algebraic expression completely 9x-6(x+4)
Answer:
3x - 24
Step-by-step explanation:
9x - 6x - 24
3x - 24