Answer:
√3·5x
Step-by-step explanation:
√(75x²) = √75·√x²
or =√3√25√x² Recognize that both 25 and x² are perfect squares.
or =√3·5x
Which equation represents a circle with a center at (-3,-5) and a radius of 6 units?
(x – 3)2 + (y – 5)2 = 6
(x – 3)2 + (y-5)2 = 36
(x + 3)2 + (y + 5)2 = 6
(x + 3)2 + (y + 5)2 = 36
va
Answer: (x+3)2 + (y+5)2 =36
Step-by-step explanation:
Answer:
d
Step-by-step explanation:
A restaurant is offering a new buffet with six types of sandwiches, four sides, and five desserts. If customers are allowed to select one sandwich, one side, and one dessert, how many meal combinations are possible?
Answer:
240
Step-by-step explanation:
Multiply everything together. 6*4*5 is 240.
Carlo rode his bike from his house to his friend Kevin’s house from there he rode to a video game store then he Road 3.2 km from the video game store back to his house that it was in the grid so the path Carlo trouble how many kilometers deCarlo ride his bike
Answer: 13.7
Step-by-step explanation:
The total distance Carlo travelled form his house to Kelvin's house to the game store and back to his house is 13.7 km.
How to calculate distance from the graph?Using the distance formula, we can caulate the distance he rode from his house to Kelvin's house and then to the video game store.
Therefore,
d = √(y₂ - y₁)²+(x₂- x₁)²
Hence,
(0, 0)(2.5, 6)
Distance from his house to Kelvin's house = √(6- 0)²+(2.5 - 0)²
Distance from his house to Kelvin's house = √36 + 6.25 = 6.5 km
Therefore,
(2.5, 6)(2.5, 2)
Distance from Kelvin's house to game store = √(2- 6)²+(2-5 - 2.5)²
Distance from Kelvin's house to game store = √16 = 4 km
Hence,
Total distance travelled = 6.5 + 4 + 3.2 = 13.7 km
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You are making an open box from a rectangular sheet of cardboard by cutting squares of equal length from each corner and folding up the sides. The dimensions of the sheet of cardboard are 15 inches by 12 inches. Write a polynomial that represents the total volume of the open box.
Answer:
[tex]V(x) = 4x^3 - 54x^2 + 180x[/tex]
Step-by-step explanation:
We are given the following in the question:
A rectangular piece of cardboard of side 15 inches by 12 inches is cut in such that a square is cut from each corner.
Let x be the side of this square cut. When it was folded to make the box.
The height of box =
[tex]x\text{ inches}[/tex]
The length becomes
[tex](15-2x)\text{ inches}[/tex]
The width becomes
[tex](12-2x)\text{ inches}[/tex]
Volume of box =
[tex]V =l\times w\times h[/tex]
Putting values, we get
[tex]V(x) = (15-2x)(12-2x)x\\V(x) = (180-30x-24x+4x^2)(x)\\V(x) = (4x^2 - 54x + 180)(x)\\V(x) = 4x^3 - 54x^2 + 180x[/tex]
is the required polynomial for volume of box formed.
A shipping container in the shape of a rectangular solid must have a volume of 84 cubic meters. The client tells the manufacturer that, because of the contents, the length of the container must be one meter longer than the width, and the height must be one meter greater than twice the width. What should the dimensions of the container be?
Answer:
The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.
Step-by-step explanation:
Let the width of rectangular solid be x
We are given that the length of the container must be one meter longer than the width
So, Length of solid = x+1
We are also given that height must be one meter greater than twice the width
So, Height of solid = 2x+1
So, Volume of solid = [tex]Length \times Width \times height[/tex]
Volume of solid = [tex](x+1) \times x \times (2x+1)[/tex]
Volume of solid =[tex](x^2+x)(2x+1)[/tex]
Volume of solid =[tex]2x^3+x^2+2x^2+x=2x^3+3x^2+x[/tex]
We are given that a rectangular solid must have a volume of 84 cubic meters
So, [tex]2x^3+3x^2+x=84\\2x^3+3x^2+x-84=0\\(x-3)(2x^2+9x-28)=0\\[/tex]
On equating
x-3=0
x=3
So, Length of solid = x+1=3+1 = 4 feet
Height of solid = 2x+1 =2(3)+1=7 feet
Width of solid = 3 feet
Hence The Length , width and height of solid are 4 feet , 3 feet and 7 feet respectively.
The volume of a rectangular solid shipping container = 84 cubic meters
The width of the container = 3m
The length of the container = (x + 1) = (3+1) = 4m
The height of the container = (2x + 1) = (2 x 3 + 1) = 7m
Given:
The volume of a rectangular solid shipping container = 84 cubic meters
Let: The width of the container be x
The length of the container must be one meter longer than the width.
So, The length of the container be (x + 1)
The height must be one meter greater than twice the width.
So, The height of the container be (2x + 1)
To find the dimensions of the container
The Volume of the container = Length x Width x Height
[tex]84=x(x+1)(2x+1)[/tex]
[tex]84=(x^{2} +x)(2x+1)[/tex]
[tex]84=2x^{3} +3x^{2} +x[/tex]
[tex]2x^{3} +3x^{2} +x-84=0\\(x-3)(2x^{2} +9x+28)=0\\x-3=0\\x=3[/tex]
So, The width of the container = 3m
The length of the container = (x + 1) = (3+1) = 4m
The height of the container = (2x + 1) = (2 x 3 + 1) = 7m
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Angle C is inscribed in circle O. AB is a diameter of circle O. What is the radius of circle O?
Answer:
6.5 units
Step-by-step explanation:
In circle with center O, AB is diameter.
[tex] \therefore m\angle ACB = 90°\\[/tex]
(Angle inscribed in a semicircle)
[tex] \therefore \: in\: \triangle ABC, \:AB \: is\: hypotenuse \\[/tex]
By Pythagorean theorem:
[tex]AB = \sqrt{ {12}^{2} + {5}^{2} } \\ = \sqrt{144 + 25} \\ = \sqrt{169} \\ AB \: = 13 \\ r = \frac{13}{2} = 6.5 \: units[/tex]
What is the proof for this equation?
3x+27=2y+32
I will give brainliest!!!!!! Thx
Mr. and Mrs. Chavez close on a 30 year home loan for $250,000. The monthly payment with no points is $1,580, but if they buy a point it is $1,560. What might you infer if Mr. and Mrs. Chavez choose not to buy a point?
a.
They plan to sell the house at the end of 5 years.
b.
They plan to sell the house at the end of 10 years.
c.
They plan to sell the house at the end of 15 years.
d.
They plan to stay in the house at least 30 years.
Answer: A
Answer: A
Step-by-step explanation:
Simplify an expression for the area of the rectangle.
Answer:
39.6x +26.4
Step-by-step explanation:
The area of a rectangle is given by
A = l*w
A = 13.2 * (3x+2)
Distribute
39.6x +26.4
Euclid’s root beer mug is shaped basically like a cylinder that is eight inches tall with a radius of three inches. Aristotle’s root beer glass is shaped basically like a cone that is 18 inches tall with a diameter of four inches. Which vessel holds the most root beer?
The Euclid's mug holds the most root beer.
Step-by-step explanation:
Euclid's mug :
Height = 8 inches
Radius = 3 inches
Volume = π(r x r) h
= (3.14) (9) 8
= 226.08 cubic inches
Aristotle's mug:
Height = 18 inches
Diameter = 4 inches
Radius = 2 inches
Volume = (1/3) π(r x r) h
= (1/3) (3.14) (4) 18
= 37.68 cubic inches
The Euclid's mug holds the most root beer.
Type the expression that results from the following series of steps:
start with y, subtract 4, then times 9.
Start with y: [tex]y[/tex]
Subtract 4: [tex]y-4[/tex]
Multiply by 9: [tex]9(y-4)=9y-36[/tex]
Answer:
[tex]9(y - 4) \\ = 9y - 36[/tex]
Step-by-step explanation:
[tex]start \: \: \: \: \: \: \: \: \: \: = y \\ subtract \: = y - 4 \\ times \: \: 9 \: \: \: = 9(y - 4) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 9y - 36[/tex]
Which of the following lines best fits the data shown in the scatter plot
Answer:
Im pretty sure its A
Step-by-step explanation:
Therefore, the option (A) is the correct answer.
What is the scatter plot?
Scatter plots are the graphs that present the relationship between two variables in a data-set. It represents data points on a two-dimensional plane or on a Cartesian system.
As per the given information, the correct graph is in option (A) because in this graph it is moving upward with respect to the line of curve.
Hence, the option (A) is the correct answer.
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Pedro is building a playground in the shape of a right triangle he wants to know the area of the playground to help him decide how sand to buy what are the dimensions of the rectangle
Answer:
Amount of sand=Area of triangle(ABC)=1/2*AB*BC
Dimension of rectangle as length=BC and breadth=AB
Step-by-step explanation:
Given:
Pedro building a playground in shape of right angled triangle.
To Find:
How much sand he need to buy
And if playground changed to rectangle what will be the dimensions.
Solution:
Consider a ΔABC be the play ground vertex of playground,
And AB and BC be the sides making right angle.
The sand required to fill ground will be the amount of are covered by the ABC triangle.
So,
Area Of triangle(ABC)=1/2* base* height
Here base will be BC and height =AB
Therefore Area of Triangle(ABC)=1/2*BC*AB
Depending on the lengths of base and height amount of sand will be decided.
Now,
For Rectangle dimensions,
We know that if same sized triangles composes each other forms a rectangle.
It requires two triangle to form one rectangle as follows
(Refer the attachment)
Same sized Triangle ACD is imposed on it to from rectangle ABCD.
So dimension for rectangle will be same as the triangle
Dimension=length and breadth
i.e. length=base of triangle=BC
Breadth=Height of triangle=AB
i.e Breadth =AB.
What is the equation of the line that passes through the point (6,-5)(6,−5) and has a slope of -\frac{3}{2}−
2
3
The equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex] is y+5 = -3/2(x+6).
What is the Point-slope form?The equation of the straight line has its slope and given point.
If we have a non-vertical line that passes through any point(x1, y1) has gradient m. then general point (x, y) must satisfy the equation
y-y₁ = m(x-x₁)
Which is the required equation of a line in a point-slope form.
WE need to find the equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex].
Given: m=-3/2 and x_1 = -6 and y_1 =-5
So the required equation of a line in a point-slope form;
y+5 = -3/2(x+6)
Hence, The equation of the line that passes through the point (6,-5)and has a slope of [tex]-\dfrac{3}{2}[/tex] is y+5 = -3/2(x+6).
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The equation of the line that passes through the point (6, -5) and has a slope of -3/2 is y = -3/2x + 4.
Explanation:To find the equation of the line, we can use the point-slope form of a linear equation, which is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. In this case, the point is (6, -5) and the slope is -3/2. Plugging these values into the equation, we get y - (-5) = -3/2(x - 6), which simplifies to y + 5 = -3/2(x - 6).
Expanding the equation further, we get y + 5 = -3/2x + 9. To isolate y, we can subtract 5 from both sides of the equation, resulting in y = -3/2x + 4. Therefore, the equation of the line that passes through the point (6, -5) and has a slope of -3/2 is y = -3/2x + 4.
margot used 1/2 pounds of turkey to make 2/3 liters of turkey chill. If margots recipe is for 1 liter of turkey chill,how many pounds of turkey will she need to make 4 times the recipe
Answer:
2 pounds of turkey?
Step-by-step explanation:
Margot will therefore need 3 pounds of turkey to make 4 liters of her turkey chili.
To find out how many pounds of turkey Margot will need to make 4 times her turkey chili recipe for 1 liter, we first identify the amount needed for 1 liter based on the given ratio, and then multiply that amount by 4.
Margot uses 1/2 pounds of turkey for 2/3 liters of turkey chili. If we need to find out the amount for 1 liter, we can set up a proportion:
1/2 pounds turkey / (2/3 liters) = x pounds turkey / 1 liter
We cross multiply to solve for x:
(1/2) * 1 = x * (2/3)
Now we solve for x:
x = (1/2) * (3/2)
x = 3/4 pounds of turkey for 1 liter of chili
For 4 liters of chili (4 times the recipe), we would multiply:
4 * (3/4 pounds) = 3 pounds of turkey
8) An ultimate frisbee team has to order jerseys, shorts, and hats. They have a budget of $1350 to
spend on $50 jerseys, $20 shorts, and $15 hats. They want to buy 40 items in preparation for the
oncoming season and must order as many jerseys as shorts and hats combined. How many of
each item should they order? Write a system of equations to help you solve this problem.
Answer:
Step-by-step explanation:
By using j, s ,h to represent the number of jerseys,shorts and hats respectively.
System of Equations:
j + s + h = 40
j = s + h
50j + 20s + 15h = 1350
(s + h) + s + h = 40
2s + 2h = 40
s + h = 20
s = 20 – h
50[(20 – h) + h] + 20(20 – h) + 15h = 1350
50(20) + 400 – 20h + 15h = 1350
1400 – 5h = 1350
5h = 50h
h = 10
s = 20 – 10
s = 10
j = 10 + 10
j = 20
20 jerseys, 10 shorts, 10 hats
They order 20 jerseys, 10 shorts, 10 hats
What is system of equation?A system of equations, also known as a set of simultaneous or equation system, is a finite set of equations for which we sought the common solutions.
According to the question
By using j, s ,h to represent the number of jerseys ,shorts and hats respectively.
System of Equations:
j + s + h = 40. . . . . Equation (1)
j = s + h. . . . . . .Equation (2)
50j + 20s + 15h = 1350 . . . . . . Equation (3)
By putting the value of j = s + h in equation (1)
(s + h) + s + h = 40
2s + 2h = 40
s + h = 20
s = 20 – h. . . . . . . .Equation (4)
By putting the value of j = s + h and s = 20 - h in equation (3) we get
50[(20 – h) + h] + 20(20 – h) + 15h = 1350
50(20) + 400 – 20h + 15h = 1350
1400 – 5h = 1350
5h = 50h
h = 10
s = 20 – 10
s = 10
j = 10 + 10
j = 20
Hence , 20 jerseys, 10 shorts, 10 hats
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Let x^2+17x=-5 What values make an equivalent number sentences after completing the square? (Do not simply your answers)
Answer:
[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]
Step-by-step explanation:
Given the expression:
[TeX] x^2+17x=-5 [/TeX]
To complete the square,
First Step: Identify the Coefficient of x.
Coefficient of x=17
Second Step: Divide the coefficient of x by 2.
Third Step: Square your result from the second step.
This gives:
[TeX] (\frac{17}{2})^{2}[/TeX]
Fourth Step: Add your result to both sides if the equation.
[TeX] x^2+17x+(\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]
Fifth Step:Express the left hand side as a square
[TeX] (x+\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]
Sixth Step:Simplify the Right Hand Side
[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]
These are the values that make an equivalent number sentence.
Find the Perimeter of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
9514 1404 393
Answer:
43.1
Step-by-step explanation:
The perimeter is the sum of the lengths of the two straight edges, each of which is 9 units long, and the circumference of the full circle of diameter 8 units. The circumference is pi times the diameter.
P = 2(9) +8π = 18 +25.13
P ≈ 43.1 . . . units
The perimeter of the combination of a rectangle and two semicircles is found by adding the straight sides of the rectangle and the circumference of the resulting full circle formed by the semicircles. In this case, it's 43.1 units.
To find the perimeter of the combined shape consisting of a rectangle and two semicircles, we need to consider the lengths of the straight parts as well as the circumference of the circles. The perimeter is the sum of the lengths of the straight sides of the rectangle, each of which is 9 units long, and the circumference of the full circle with a diameter of 8 units.
Using the formula for the circumference of a circle (C = πd) where d is the diameter, the circumference of the full circle would be 8π. So, the total perimeter of the shape is:
P = 2*(9) + 8π
That gives us:
P = 18 + 25.13 approximately
So, P ≈ 43.1. . . units
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Explain how to rewrite the equation -2x - 6y = 18 in slope-intercept form.
Answer:
y = -1/3x -3
Step-by-step explanation:
-2x - 6y = 18
We want to solve for y since the slope intercept form is y =mx+b where m is the slope and b is the y intercept
Add 2x to each side
-2x-6y +2x = 2x+18
-6y = 2x+18
Divide each side by -6
-6y/-6 = 2x/-6 + 18/-6
y = -1/3x -3
This is in slope intercept form with the slope -1/3 and the y intercept -3
Answer:
[tex]y = - \frac{x }{ 3} - 3[/tex]
Step-by-step explanation:
-2x - y = 18
Add 2x to both sides.
-6y = 2x + 18
divide both sides by -6.
[tex]y = \frac{2x + 18}{ - 6} [/tex]
divide 2x + 18 by 6
[tex]y = - \frac{x }{ 3} - 3[/tex]
Nathan needs some paint for his bedroom. He finds two cans of white paint, four cans of green paint and three cans of pink paint in his garage. If he chooses a can of paint without looking at the color, what is the chance that he will paint his bedroom pink
Answer:
3/9 or 33.33%
Step-by-step explanation:
there are 9 total cans and 3 pink cans. So, that'd be 3/9 or 33.33%
hope this helps!
Answer:
1/3
Step-by-step explanation:
Lena‘s observed that in the last 12 issues of rise over run weekly 384o out of950 pages contain an advertisement what is the probability that the next page she turns to will contain an advertisement
Answer:
Probability thay the next page she turns to will have an advert = 0.4042
Step-by-step explanation:
In the last 12 issues of the magazine, 384 out of 950 pages contain an advertisement.
We now need to find the probability that the next page has an advertisement.
Probability of an event
= n(of that event) ÷ n(total sample spaces)
n(of the event of an advert) = number of pages with adverts in those issues = 384
n(total sample spaces) = total number of pages = 950
Probability that the next page or any page at all will have an advert = (384/950) = 0.4042
Hope this Helps!!!
What is 12 divided by 220
Answer:
0.0545454545455
Step-by-step explanation:
Solve -x^2-9x-20=0 with the quadratic formula
plz help!
Answer:
a = -1 b = -9 c = -20
x1 = [--9 +- (sq root -9^2 - 4 * -1 * -20)] / 2 * -1
x1 = 9 +sq root (81 - 80) / -2
x1 = [9 + 1 ] / -2
x1 = -5
x2 = 9 -sq root (81 - 80) / -2
x2 = 8 / -2
x2 = -4
Step-by-step explanation:
what is domain and range
Answer:
the domain is anything with the x-axis and range the y-axis
Answer:
Domain- is the set of all possible x-values or "input" for the function that gets you to the "output" or y-values. Range- is the difference between the highest and the lowest values.
Step-by-step explanation:
The scale of Miguel's dollhouse is 1in.=2 2/7ft. If the pants of the military uniform of the father in the dollhouse are 1 2/5 inches long, how long would the pants be in real life?
Answer:
3 1/5 ft
Step-by-step explanation:
We can set up a proportion:
[tex]\frac{1}{2\frac{2}{7} } =\frac{1\frac{2}{5} }{x}[/tex] , where x is how long the pants are in real life
Cross multiply:
x = (2 2/7) * (1 2/5)
It's easier if we have improper fractions, so convert the mixed numbers into improper fractions:
2 2/7 = 16/7
1 2/5 = 7/5
Now, put these back in:
x = (16/7) * (7/5) = 16/5 = 3 1/5
Thus, in real life, the pants would be 3 1/5 ft long.
Hope this helps!
Answer:
3⅕ ft
Step-by-step explanation:
1 in --> 2 2/7 ft
2 2/7 = 16/7
1 2/5 in = 7/5 in
7/5 × 16/7 = 16/5 ft
3 1/5 ft
What is the value of t?
John is icing 30 cupcakes. He spreads mint icing on 1/5 of the cupcakes and chocolate icing on 1/2 of the remaining cupcakes. How many cupcakes will get chocolate frosting?
Answer: 12 cupcakes will get chocolate frosting
Step-by-step explanation: John started with 30 cupcakes and spresd mint icing on 1/5 of these. That means he did the following
Mint icing = 30 x 1/5
Mint icing = 6
That leaves him with a total of 30 minus 6 cupcakes which equals 24 cupcakes.
Next he spreads chocolate icing on half of the remaining, that is half of 24. That means he did the following;
Chocolate icing = 24 x 1/2
Chocolate icing = 12
Therefore 12 cupcakes will get chocolate frosting
Simplify.
Remove all perfect squares from inside the square root.
Assume x is positive.
\sqrt{20x^8}
Answer:
[tex]2x^4\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{20x^8}[/tex] = [tex]\sqrt{4*5*(x^4)^2}[/tex] = [tex]2x^4\sqrt{5}[/tex]
The solution of the equation after remove all perfect squares from inside the square root is,
⇒ 2x⁴√5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ √20x⁸
Now, We can simplify and remove all perfect squares from inside the square root as;
⇒ √20x⁸
⇒ √2 × 2 × 5 × (x⁴)²
⇒ 2x⁴√5
Thus, The solution of the equation after remove all perfect squares from inside the square root is,
⇒ 2x⁴√5
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Evaluate Loga√44+ Log a√275- Log 11a
They all have base 10
Answer:
[tex]log(10a)[/tex]
Step-by-step explanation:
[tex]log(a\sqrt{44})+log(a \sqrt275)-log(11a)[/tex]
We can simplify this using these log laws:
[tex]log(a)+log(b)=log(ab)\\log(a)-log(b)=log(\frac{a}{b})[/tex]
[tex]log(\frac{a^2\sqrt{44} \sqrt{275}}{11a})[/tex]
We also have laws to simplify square roots
[tex]\sqrt{a}*\sqrt{b} = \sqrt{ab}[/tex]
So this becomes
[tex]log(\frac{a^2\sqrt{12100}}{11a})[/tex]
[tex]\sqrt{12100} = 110[/tex]
so this becomes
[tex]log(\frac{110a^2}{11a})=log(10a)[/tex]
The function below describes the number of students who enrolled at a university, where f(t) represents the number of students and t represents the time in years.
Initially,_____ students enroll at the university. Every______ , the number of students who enroll at the university increases by a factor of______ .
Answer:
18,500 , 1 , 1.03
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.
f(t) =18,500(1.03)^t
1st blank:
19,055
1.03
3
18,500
2nd blank:
t years
2 years
3 years
1 year
3rd blank:
19,055
3
18,500
1.03
My answer:
Given that: f(t) =18,500*[tex]1.03^{t}[/tex]
1st blank:
Initial value when t = 0, so we have:
f(0) =18,500*[tex]1.03^{0}[/tex]
[tex]f(0) =18,500(1)\\ f(0) =18,500[/tex]
So we choose D for 1st blank
2nd and 3rd blank:
Because it's an exponential function f(t) =18,500*[tex]1.03^{t}[/tex] , with every value of t increment f(t) increase by a factor of 1.03 . So Every 1 year the number of students who enroll at the university increases by a factor of 1.03
=> 2nd blank: 1
=> 3rd blank: 1.03
Hope it will find you well.
Answer:
The first blank this is 18,500. Second blank is 1. The third blank is 1.03. hope this helps
Step-by-step explanation: