Answer:
Speed = Distance ÷ Time
time = distance ÷ speed
Step-by-step explanation:
248 ÷ 55 * 60 = 270.54 minutes
What is the distance between points (7, -4) and (7, 9)?
Answer:
13Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (7, -4) and (7, 9). Substitute:
[tex]d=\sqrt{(7-7)^2+(9-(-4))^2}=\sqrt{0+13^2}=\sqrt{13^2}=13[/tex]
Used [tex]\sqrt{a^2}=a[/tex]
Math sequences number patterns
Answer:
see explanation
Step-by-step explanation:
(a)
Note the squared value in column 3 which is the square of 1 more than the row number, that is
row 2 → (2 + 1)² →3²
row 3 → (3 + 1)² → 4²
Find the square root of 676 = 26 → (25 + 1)² = 26²
Hence the row number is 25
(b)
The pattern in column 1 is [ row number × (row number + 2 ) + 1 ]
row number is n then n(n + 2) + 1 = n² + 2n + 1
Explain how to determine the number of square feet required to cover your rectangular garden that has a length of 10 feet and a width of 8 feet?
Answer:
Multiply the length and the width of the shape together to get the area of the square or rectangle in square feet.
10 multiplied by 8 equals 80 square feet
Step-by-step explanation:
Got a 100 on it.
Final answer:
To cover a rectangular garden measuring 10 feet by 8 feet, multiply the length by the width to get an area of 80 square feet, which is the amount of material needed.
Explanation:
Calculating the Area of a Rectangular Garden
To determine the number of square feet required to cover your rectangular garden, you need to calculate the area of the garden. The area of a rectangle is found by multiplying the length by the width. In this case, the garden has a length of 10 feet and a width of 8 feet.
Steps to Calculate the Area
Measure the length and width of the garden using a measuring tape.
Multiply the length by the width to get the area in square feet: 10 feet (length) × 8 feet (width) = 80 square feet.
Therefore, you would need 80 square feet of material to cover the entire garden.
Write x^3/2 in radical form
Answer:
Step-by-step explanation:
I think you meant x^(3/2). This breaks down in at least two ways:
[x^3]^(1/2), or √(x^3)m or √x³), or
[x^(1/2)]^3 = (√x)^3
To write [tex]x^{3/2}[/tex] in radical form, rewrite it as (√x)³or √(x³). This utilizes the relationship between fractional exponents and radicals.
To write [tex]x^{3/2}[/tex] in radical form, we can use the relationship between exponents and radicals. In general, the expression [tex]x^{a/b}[/tex] can be written in radical form as the b-th root of x raised to the power 'a'. So, applying this rule to the given expression.
[tex]x^{3/2}[/tex]
Step-by-Step Explanation:
Rewrite the exponent 3/2 as a fraction where the numerator is the power and the denominator is the index of the root.So, [tex]x^{3/2}[/tex] can be written as the square root of x raised to the power of 3.This translates to: (√x)³ or equivalently, [tex](x^{3})^{1/2}[/tex] which means the square root of x cubed.Therefore, the radical form of [tex]x^{3/2}[/tex] is √x³ or (√x)³.
15 points please answer asap
The answer is:
The area of this figure is 946 square inches.
Why?We can see that the figure is composed by two rectangles with diferrent dimensions, so, to calculate the area of the entire figure.
So,
For the first rectangle, we have:
[tex]Base=7in\\Height=28in[/tex]
The area will be:
[tex]Area=Base*Height=7in*28in=196in^{2}[/tex]
For the second rectangle, we have:
[tex]Base=25in\\Height=30in[/tex]
The area will be:
[tex]Area=Base*Height=30in*25in=750in^{2}[/tex]
Now, calculating the area of the entire figure, we have:
[tex]TotalArea=FirstRectangleArea+SecondRectangleArea\\\\TotalArea=196in^{2}+750in^{2}=946in^{2}[/tex]
Have a nice day!
Find the surface area of the pyramid shown to the nearest whole number get brainlists
Answer
914 m^2 to the nearest whole number.
Step-by-step explanation:
The area of the hexagonal base is made up of 6 congruent triangles so its area = 6* 1/2 base* height
= 6 * 1/2 * 12 * 6√3
= 216-√3 m^2.
The area of each slanting triangle = 6 * 15 m^2 so the lateral area of the pyramid
= 6*6*15= 540 m^2
Total surface area = 540 + 216√3
= 914.12 m^2.
hope this helps
and to make it simpler its C or 914.12
Hello anyone can do this? Please put answer in points(x,y)
Answer:
Check the attached graph
Step-by-step explanation:
Given that slope of the line is m = 1
And the line passes through the point (-3,5).
Now we need to graph the line using above information. So begin by graphing the point (-3,5).
Slope means rise/run
Then slope = 1 means rise/run=1=1/1
means move point 1 unit up then 1 unit right
then new point is at (-2,6).
Now draw a line joining both points to get the final graph.
TIMED HURRY PLS!
Maria determined that these expressions are equivalent expressions using the values of x=3 and x=7. Which statements are true? Check all that apply.
Answer:
We have the following equations:
5 + 3x - 2 and x + 2(x+1) + 1
Before checking the statements. Let's solve the syste of equations:
5 + 3x - 2 = x + 2(x+1) + 1
5 + 3x - 2 = x + 2x+2 + 1
3x + 3 = 3x + 3
Both equations are equivalent. Now, let's judge the statements:
1. The expressions are only equivalent when evaluated with odd values.
Given that the both expression are the same, the expressions are equivalent for ALL values.
Therefore, the statement IS FALSE ❌
2. The expressions are only equivalent for x=3 and x=7.
Given that the both expression are the same, the expressions are equivalent for ALL values, not only x=3 and x=7.
Therefore, the statement IS FALSE ❌
3. The expressions should have been evaluated with one odd value and one even value.
If two expressions are equivalent, they should be equivalent for ALL values. Sometimes, evaluating just one odd and one even value isn't enough. That's why the best approach is to solve the system of equations.
Therefore, the statement IS FALSE ❌
4. The expressions have equivalent values when x=6.
Given that the both expression are the same, the expressions are equivalent for x=6 (And all the real values too).
Therefore, the statement IS TRUE ✅
5. When x=0, the first expression has a value of 3 and the second expression has a value of 4.
Given that BOTH expressions are equvalent, they have the same value when x=0, which is 3.
Therefore, the statement IS FALSE ❌
6. The expressions have equivalent values for any value of x.
Given that the both expression are the same, the expressions are equivalent for ALL values of x.
Therefore, the statement IS TRUE ✅
7. When x=10, both expressions have a value of 33
Given that the both expression are the same, the expressions are equivalent for ALL values of x. That's why when x=0, both expressions have a value of 33.
Therefore, the statement IS TRUE ✅
Answer:
D,F,G
Step-by-step explanation:
It Makes Sense.
HELP PLZ
What is the shape of the following cross section????
Answer:
Triangle
Step-by-step explanation:
Look at the shape of the red part
The shape of the triangle is the cross-section part of the given figure. Thus, option A is correct.
How to find the shape inscribed in a square?The cross-section part of the given figure could be the shape fro the inscribed figure.
Here we can see that the three-dimensional figure inscribed in the square is a cone.
The right circular cone is the cone in which the line joining peak of the cone to the center of the base of the circle is perpendicular to the surface of its base.
But for the plane of the square, the triangle is the cross-section part of the given figure.
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Which is the correct letter answer of the value of the log equation?
Answer:
The value of the single logarithm is -11 ⇒ answer B
Step-by-step explanation:
* Lets revise the rule of the logarithmic functions
# ㏒ a + ㏒ b = ㏒ ab
# ㏒ a - ㏒ b = ㏒ a/b
# ㏒ a^n = n ㏒ a
# ㏒ 1 = 0
* Now lets solve the problem
∵ [tex]log_{b}(\frac{A^{5}C^{2}}{D^{6}})[/tex]
- Change the single logarithm to an expression by change the
multiplication to addition and the division to subtraction
∵ [tex]log_{b}A^{5}=5log_{b}A[/tex]
∵ [tex]log_{b}C^{2}=2log_{b}C[/tex]
∵ [tex]log_{b}D^{6}=6log_{b}D[/tex]
∴ The single logarithm = [tex]5log_{b}A+2log_{b}C-6log_{b}D[/tex]
* Now lets substitute the values
∵ [tex]log_{b}A=3;===log_{b}C=2;===log_{b}D=5[/tex]
- Substitute the values into the expression
∴ The value = 5(3) + 2(2) - 6(5) = 15 + 4 - 30 = -11
* The value of the single logarithm is -11
A 2-pound bottle of barbecue sauce costs $22.40. What is the price per ounce
Answer:
The answer is $0.69. This is because there are 32 ounces in the bottle, and $22.08/32=0.69, or $0.69.
Step-by-step explanation:
Find f/g for the functions provided. 10 points Help needed.
ANSWER
[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]
EXPLANATION
The given functions are
[tex]f(x) = {x}^{3} - 27[/tex]
and
[tex]g(x) = 3x - 9[/tex]
[tex]( \frac{f}{g} )(x) = \frac{f(x)}{g(x)} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{ {x}^{3} - 27}{3x - 9} [/tex]
[tex]( \frac{f}{g} )(x) = \frac{ (x - 3)( {x}^{2} + 3x + 9) }{3(x -3 )} [/tex]
Cancel the common factors,
[tex]( \frac{f}{g} )(x) = \frac{ {x}^{2} + 3x + 9 }{3} [/tex]
OR
[tex]( \frac{f}{g} )(x) = \frac{1}{3} ( {x}^{2} + 3x + 9)[/tex]
What is the discriminant of 3x2 + 6x = 2?
Answer: x = 1/6 or 1.6667
Steps3x * 2 + 6x = 2
Multiply the numbers: 3 * 2 = 6
6x + 6x = 2
Add similar elements: 6x + 6x = 12x
12x = 2
Divide both sides by 12
12x / 12 = 2 / 12
Simplify
x = 1/6
Answer: The required discriminant of the given quadratic equation is 60.
Step-by-step explanation: We are given to find the discriminant of the following quadratic equation :
[tex]3x^2+6x=2\\\\\Rightarrow 3x^2+6x-2=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]
We know that
the discriminant of a quadratic equation [tex]ax^2+bx+c=0,~a\neq 0[/tex] is given by
[tex]D=b^2-4ac.[/tex]
For the given equation (i), we have
a = 3, b = 6 and c = -2.
Therefore, the discriminant of the given equation will be
[tex]D=b^2-4ac=6^2-4\times3\times(-2)=36+24=60.[/tex]
Thus, the required discriminant of the given quadratic equation is 60.
Solve this system of equations by elimination:
8x+9y=48
12x+5y=21
Answer:
Let's solve your system of equations by elimination.
8x+9y=48;12x+5y=21
Steps:
Multiply the first equation by 5,and multiply the second equation by -9.
5(8x+9y=48)
−9(12x+5y=21)
Becomes:
40x+45y=240
−108x−45y=−189
Add these equations to eliminate y:
−68x=51
Then solve−68x=51for x:
−68x /−68 = 51 /−68 (Divide both sides by -68)
x= −3 /4
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
8x+9y=48
Substitute
−3 /4
8x+9y=48:
8( −3 /4 )+9y=48
9y−6=48 (Simplify both sides of the equation)
9y−6+6=48+6 (Add 6 to both sides)
9y=54
9y /9 = 54 /9 (Divide both sides by 9) y=6
Answer: x= −3 /4 and y=6
Hope This Helps! Have A Nice Day!!
which point lies outside the circle with equation (x - 2) + (y + 3) = 4 (1, -4 ) ( 0, -3 ) ( 2, 0 ) (2, -4 )
Answer:
The point (2,0) is outside the circle
Step-by-step explanation:
we have
[tex](x-2)^{2}+(y+3)^{2}=4[/tex]
[tex](x-2)^{2}+(y+3)^{2}=2^{2}[/tex]
This is the equation of a circle with center at (2,-3) and radius equal to 2 units
Using a graphing tool
Plot the circle and the given points and verify if the point lie outside the circle
we have
[tex](1, -4 ),(0, -3),(2, 0),(2,-4)[/tex]
so
The point (2,0) is outside the circle
see the attached figure
The sixth grade chorus has a boy to girl ratio of 3:8 which of the following ratios is equivalent to this ratio?
A) 15 boys to 55 girls
B) 55 boys to 15 girls
C) 40 boys to 15 girls
D) 15 boys to 40 girls
The ratio in option (D), 15 boys to 40 girls is equivalent to 3 : 8.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
The given ratio of boy to girls is 3 : 8.
To find the equivalent ratio to 3:8.
Solve with the help of option,
(A)
15 boys to 55 girls.
The ratio 15 : 55 = 3 : 11
(B)
55 boys to 15 girls,
The ratio 55 : 15 = 11 : 3.
(C)
40 boys to 15 girls,
The ratio 40 : 15 = 8 : 3
(D)
15 boys to 40 girls,
The ratio 15 : 40 = 3 : 8.
The ratio of 15 boys to 40 girls is 3:8.
Hence, the correct option is (D).
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Consider the following formula used to estimate the height, h, of a seedling after w weeks since planting: h = (1/5)w + (8/5). Which of the following represents the formula that could be used to find the number of weeks since planting using the height, h, of the seedling?
A. w = 5h - (8/5)
B. w = 5h - 8
C. w = h/5 - 8
D. w = h/5 - 8/5
[tex]\bf h=\cfrac{1}{5}w+\cfrac{8}{5}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{5}}{5(h)=5\left( \cfrac{1}{5}w+\cfrac{8}{5} \right)}\implies 5h=w+8\implies 5h-8=w[/tex]
The equation that can be used to find the number of weeks since planting is (b) w = 5h - 8
How to determine the equation of the number of weeks?The equation is given as:
h = (1/5)w + (8/5)
Multiply through by 5
5h = w + 8
Subtract 8 from both sides
5h - 8 = w
Make w the subject
w = 5h - 8
Hence, the equation that can be used to find the number of weeks since planting is (b) w = 5h - 8
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can a triangle have sides with the given lengths? 2ft, 7ft, 12ft
Answer:yes
Step-by-step explanation:
2+7=9
12+2=14
12+7=19
Answer:
No
Step-by-step explanation:
the sum of two sides has to be greater than the third side
2+7=9 9 isn't greater than 12
Which shapes can the composite figure be divided into to find the area?
a rectangle and a triangle
a rectangle and two triangles
a trapezoid and a rectangle
a trapezoid and two triangles
Answer:
a rectangle with two triangles.
Step-by-step explanation:
this way you will be able to find the area of the rectangle then add it to the area of the two triangles.
Answer:
the correct answer is b
Step-by-step explanation:
At a local pizza place, the cost of a large cheese pizza is $13.99. Each additional topping is $1.25. You order a large pizza, and it cost $16.49. Describe the pizza you ordered.
what is the remainder in the synthetic division problem
Answer:
C
Step-by-step explanation:
1 | 4 6 - 2
4 10
------------------
4 10 8 ← remainder
Answer:
Option C
Step-by-step explanation:
Given is a division in synthetic
We have to find the remainder
The divisor is x-1 and dividend is [tex]4x^2+6x-2[/tex]
By synthetic division we get the following:
1) 4 6 -2\\
4 10\\
----------------------\\
4 10 8=R
Thus remainder is 8
what are the zeros of the function f(x) = x^2 + 2x- 8 / x^2 - 2x - 8
Answer:
x=-4 and x=2
Step-by-step explanation:
You are given the function
[tex]f(x)=\dfrac{x^2+2x-8}{x^2-2x-8}[/tex]
The zeros of the function are those value of x, for which [tex]f(x)=0[/tex]
First, find x for which function is undefined
[tex]x^2-2x-8\neq0\\ \\x^2-4x+2x-8\neq 0\\ \\x(x-4)+2(x-4)\neq 0\\ \\(x-4)(x+2)\neq 0\\ \\x\neq 4\text{ and }x\neq -2[/tex]
Now find points at which f(x)=0:
[tex]f(x)=0\Rightarrow x^2+2x-8=0\\ \\x^2+4x-2x-8=0\\ \\x(x+4)-2(x+4)=0\\ \\(x-2)(x+4)=0\\ \\x=2\text{ or }x=-4[/tex]
For both these values (x=-4 and x=2) function f(x) is defined, then x=-4 and x=2 are zeros of the function.
Final answer:
To find the zeros of the given function, set the numerator equal to zero and solve for x. The zeros are x = -4 and x = 2.
Explanation:
We can notice that both the numerator and denominator share the same factors (x² - 2x - 8). This means that f(x) is undefined where the denominator is zero.
Therefore, the zeros of the function f(x) = x² + 2x - 8 / x² - 2x - 8 can be found by setting the numerator equal to zero and solving for x.
By factoring the numerator and denominator, it becomes easier to identify the zeros.
x² - 2x - 8 = 0
Factoring the expression:
(x - 4)(x + 2) = 0
Therefore, the zeros of the function f(x) are x = 4 and x = -2.
If a data set has many outliers, which measure of central tendency would be the BEST to use?
A) mean
B) median
C) mode
D) range
Mode could work but I believe the best answer would be median.
Answer:
median
Step-by-step explanation:
Median is correct. One extreme outlier can "drag" the mean up or down, while it would have little or no effect on the median.
Select all expressions that are equivalent to 6x+1-(3x-1)
where are the expressions ?
Answer:
3x + 2
Step-by-step explanation:
Least to greatest 3/10, 0.222, 3/5, 0.53
The answer is .22222..., 3/10, .53, and 3/5.
Hope this helps!
Hello there!
The numbers in order from least to greatest are:
0.2222, 3/10, 0.53, 3/5
Start by turning all the numbers into either decimals. To do this, take the two fractions, 3/5 and 3/10 and divide them out.
3 divided by 5 = 0.6
3 divided by 10 = 0.3
Now let's look at our numbers again.
0.3, 0.222, 0.6, 0.53.
We know that 2 is less than 3, and 3 is less than 5, and 5 is less than 6, so lets rearrange the numbers into that order.
0.2222, 0.3, 0.53, 0.6
Now, convert any fractions that were converted into decimals back into their original forms.
0.2222, 3/10, 0.53, 3/5
This is your final answer. I hope this helps and have a great day!
Rectangle 1 has length x and width y. Rectangle 2 is made by multiplying each dimension of Rectangle 1 by a
factor of k, where k>0.
(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?
(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
(c) Write a paragraph proof to show that the area of Rectangle 2 is k2 times the area of Rectangle 1.
Answer:
a) yes they are similar
b)Proved below
c)Proved below
Step-by-step explanation:
a) rectangle 1 and 2 are similar by definition of similar rectangles.
Definition of similar rectangles states that two rectangles are similar if they have same shape but different sizes. The ratio between their corresponding sides are same, in this case as rectangle 2 is made by multiplying each dimension of Rectangle 1 by a
factor of k, where k>0 thus providing same proportion in length of different corresponding sides of two rectangles hence rectangle 1 and 2 are similar.
b) Perimeter of rectangle 1, P1= s1+ s2+ s3 + s4
As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore
Perimeter of rectangle 2, P2= k.s1+ k.s2+ k.s3 + k.s4
Taking k common
= k(s1+ s2+ s3 + s4)
Substituting P1 in above expression
P2 =k(P1)
Hence the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.
c) Area of rectangle 1, A1= 2(s1)(s2)
As each side of rectangle 2 is formed by multiplying each dimension of Rectangle 1 by k, therefore
Area of rectangle 2, A2= 2(k.s1)(k.s2)
= 2k^2(s1)(s2)
= k^2 [2(s1)(s2)]
Substituting A1 in above expression
A2 = k^2(A1)
Hence the area of Rectangle 2 is k2 times the area of Rectangle 1 !
A water tank is a cylinder with radius 40 cm and depth 150 m
150 cm
40 cm
It is filled at the rate of 0.2 litres per second.
1 litre = 1000 cm3
Does it take longer than 1 hour to fill the tank?
3.142×40^2×150=753,982.237
if1sec =0.2litres
what about 753.982=
753.982×1/0.2
=22.80
To determine if filling a tank takes longer than an hour, calculate the tank's volume, convert it to liters, and then divide by the fill rate. With a 240π liter capacity and a 0.2 L/s fill rate, it takes approximately 1.05 hours, thus longer than 1 hour.
To determine if it takes longer than 1 hour to fill a water tank with a radius of 40 cm and depth of 150 cm at a rate of 0.2 liters per second, we first calculate the volume of the tank and then the total time required to fill it at the given rate.
Step 1: Calculate the Volume of the Tank
Volume of a cylinder = πr²h, where r is the radius and h is the height.
Here, r = 40 cm and h = 150 cm.
Volume = π(40²)(150) = π(1600)(150) = 240000π cm³.
Step 2: Convert the Volume to Liters
Since 1 liter = 1000 cm³, the volume in liters = 240000π / 1000 = 240π liters.
Step 3: Calculate the Filling Time
Time = volume / rate = 240π / 0.2 = 1200π seconds.
To convert to hours, divide by 3600 (the number of seconds in an hour).
Total time in hours = 1200π / 3600 = π/3 hours, which is approximately 1.05 hours.
Since it takes approximately 1.05 hours to fill the tank, it does take longer than 1 hour to fill the tank.
What is a solution for both equations y=x+3 and -2x+y=1
Answer:
(2, 5)
Step-by-step explanation:
Given the 2 equations
y = x + 3 → (1)
- 2x + y = 1 → (2)
Substitute y = x + 3 into (2)
- 2x + x + 3 = 1
- x + 3 = 1 ( subtract 3 from both sides )
- x = - 2 ( multiply both sides by - 1 )
x = 2
Substitute x = 2 into (1) for corresponding value of y
y = 2 + 3 = 5
Solution is (2, 5)
Answer: y=5, x=2
Step-by-step explanation:
If a product is normally retails for $40 and we give you a six dollar discount what percentage is your discount are we giving you
Answer:
The discount is 15% because 6/40 = 0.15 and a percent is multiplied by 100 so the answer is 15%.
To find the percentage discount, subtract the discount amount from the original price and divide by the original price, then multiply by 100.
Explanation:To find the percentage discount, we need to calculate the amount of the discount first. The discount is given as $6, so we subtract $6 from the original price of $40 to get $34. To find the percentage, we divide the discount amount by the original price and multiply by 100. In this case, the discount percentage would be (6/40) * 100 = 15%.
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Write an expression to represent:
Three more than the product of two and a number xxx.
Answer:
(2x)+3
Step-by-step explanation:
I'm sure most of you just want the answer, but if you want me to educate you, keep reading!!
The product of two and a number x can be written as 2x.
Three more than something means that we add 3 to it.
If we add 3 to 2x, we have 3+2x.
So in conclusion, the answer would be (2x)+3.
Hope this helps! :)
The final value will be 2x+3
How to find the expression?Firstly,
The product of two and a number x can be written as 2x.Three more than something means that we add 3 to it.∴If we add 3 to 2x, we have 3+2x.
So the answer would be (2x)+3.
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