Given that
[tex]\begin{gathered} (\frac{5n^6}{m^{-3}n^2})^2 \\ \text{According to the law of indies,} \\ (\frac{a}{b})^2\text{ = }\frac{(a)^2}{(b)^2} \\ (\frac{5n^6}{m^{-3}n^2})\text{ = }\frac{(5n^6)^2}{(m^{-3}n^2)^2} \\ \text{According to the law of indicies again,} \\ (a^x)^y=a^{x\cdot y} \\ =\text{ }\frac{(5n^{6\text{ x 2}})}{(m^{-3\cdot2}n^{2\cdot2})} \\ =\text{ }\frac{5n^{12}}{(m^{-6}n^4)} \\ \text{According to the law of indices} \\ x^{-1}\text{ = }\frac{1}{x} \\ =5^{}n^{12}\cdot n^{-4}\cdot m^6 \\ =5n^{12\text{ - 4}}m^6 \\ =5n^8m^6 \end{gathered}[/tex]7a + 6 =34 what is the for a
Answer:
a = 4.
Step-by-step explanation:
7a + 6 =34
7a + 6 - 6 = 34 - 6
7a = 28
a = 28/7
a = 4.
which expression is equivalent to 4 sqrt 6/3 sqrt 2
12 sqrt 27/2
4 sqrt 24/2
12 sqrt 55296/2
12 sqrt 177147/3
The provided expression is equivalent to the expression mentioned in option (C) is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
The number expression is:
[tex]= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} }[/tex]
After applying the integer exponent property:
[tex]= \dfrac{\sqrt[4]{6} }{\sqrt[3]{2} } \times\dfrac{\sqrt[3]{2^2} }{\sqrt[3]{2^2} }[/tex] (rationalization)
[tex]= \dfrac{\sqrt[4]{6} \times\sqrt[3]{2}}{2 }[/tex]
= [tex]\rm \dfrac{\sqrt[12]{55296} }{2}[/tex]
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
Thus, the provided expression is equivalent to the expression mentioned in option (C) is correct.
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A financier plans to invest up to $500,000 in two projects. Project A yields a return of 10% on the investment where Project B yields a return of 15% on the investment. Because the invesemtns in project B is risker than the invesments in project A, the finaniced has decided that the invesment in projcect B should not exceed 40% of the total investment. How much should she invest in each project in order to maximize the retirn on her invesment? what is the maximum return?
She needs to invest $[tex]300,000\\[/tex] in project A and $[tex]200,000[/tex] in project B in order to maximize the return on her investment.
$[tex]500,000[/tex] is allotted for two projects Project A yields a return of [tex]10%[/tex]% and Project B yields a return of [tex]15%[/tex]% Investments in project B are riskier than investments in project A Investments in B should not exceed [tex]40%[/tex]% of the total invest How much money needs to invest in each project in order to maximize the return on the investment?What is the maximum return?Since a financier has $[tex]500,000[/tex] which she needs to invest in two projects named A and B
Out of the two projects A and B, project B is giving higher rate of return on the investment so maximum investment needs to be done on the project B
Hence in project B total percentage of investment will be [tex]40%[/tex]% which is also given it needs not to exceed more than [tex]40[/tex]%
Hence the investment amount on the project B is [tex]40[/tex]% of $[tex]500,000[/tex]
which is [tex](0.4)*$500,000[/tex] which is equal to $[tex]200,000[/tex] which is an investment in project B
Now the investment in project A will be $[tex]500,000[/tex]-$[tex]200,000[/tex]=$[tex]300,000[/tex]
Hence she needs to invest $[tex]300,000[/tex] in project A and $[tex]200,000[/tex] in project B.
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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select ALL of the measurement pairs that could be the dimensions of Rectangle B.
a
80 cm by 20 cm
b
18 cm by 4.5 cm
c
6 cm by 1.5 cm
d
10 cm by 2 cm
e
13 cm by 4 cm
The measurements pairs that could be the dimensions of Rectangle B are: 80 cm by 20 cm
18 cm by 4.5 cm
6 cm by 1.5 cm
What are the dimensions?A scaled copy is a copy of an image in which the dimensions of the initial image is multiplied by the same number. A scaled copy can either be a smaller version of the original image or a larger version of original image.
Is 80 cm by 20 cm the dimensions of Rectangle B:
80 / 12 = 6.7
20 / 3 = 6.7
The ratio of the lengths and widths are the same. Thus, the dimensions might the for Rectangle B.
Is 18 cm by 4. 5 cm the dimensions of Rectangle B:
18 / 12 = 1.5
4.5 / 3 = 1.5
The ratio of the lengths and widths are the same. Thus, the dimensions might the for Rectangle B.
Is 6 cm by 1.5 cm the dimensions of Rectangle B:
6 / 12 = 0.5
1.5 / 3 = 0.5
The ratio of the lengths and widths are the same. Thus, the dimensions might the for Rectangle B.
Is 10 cm by 2 cm the dimensions of Rectangle B:
10 / 12 = 0.83
2/ 3 = 0.67
The ratio of the lengths and widths is not the same. Thus, the dimensions cannot be for Rectangle B.
Is 13 cm by 4 cm the dimensions of Rectangle B:
13 / 12 = 1.08
4/ 3 = 1.33
The ratio of the lengths and widths is not the same. Thus, the dimensions cannot be for Rectangle B.
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What is the value of g(-4)?
The value of g(-4) from the function is 1
What is a function?A function can be defined as a law, rule or theorem that asserts or explains the relationship between two variables in an equation or expression.
These variables are called;
The dependent variableThe independent variableGiven the functions as;
g(x) = [tex]\sqrt[3]{x + 5}[/tex] when x ≤ -4g(x) = - x²+ 11 when x > -4To determine g(-4), we can see that the first function of g(x) would be used.
We have;
g(-4) = [tex]\sqrt[3]{x + 5}[/tex]
Substitute the value of x as - 4, we have;
g(-4 = [tex]\sqrt[3]{-4 + 5}[/tex]
g(-4) = ∛1
Find the cube root
g(-4) = 1
Hence, the value is 1
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If Flannery wants to make 48 cups ofpunch, how much water will she need?A 12 cB 24 cC 36 cD 48 c
From the given table 4 cups of punch need 3 cups of water
Then we can use the ratio method to solve the question
Punch: Water = 4: 3
Since we need 48 cups of punch, then
Punch: Water
4. 3
48. x
By using cross multiplication
[tex]\begin{gathered} 4\times x=48\times3 \\ 4x=144 \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} \frac{4x}{4}=\frac{144}{4} \\ x=36 \end{gathered}[/tex]To make 48 cups of punch you need 36 cups of water
The answer is C
calcula correctamente cada una de las ecuaciones de la recta.
pasa por los puntos a(4,-6) y b(-5,3)
The equation of straight line of the points is given as y = -x - 2
Equation of Straight LineTo solve this problem, we simply need to find the equation of straight line which can be done by finding the slope of the line and then intercept of the line.
In the given points;
A = (4, -6)B = (-5, 3)The formula of slope of a line is given as
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Substituting the values into the equation;
[tex]m = \frac{3 - (-6)}{-5 - 4} \\m = \frac{9}{-9} \\m = -1[/tex]
The slope of the line is equal to 1.
Let's find the intercept of the line
[tex]y = mx + c[/tex]
Taking point A;
[tex]y = mx + c\\-6 = -1(4) + c\\-6 = -4 + c\\c = -2[/tex]
The equation of the line is y = -x - 2
Translation: Find the equation of a straight line from two point A(4, -6) and B(-5, 3).
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Two families purchased lunch at a hotdog cart. The Cortez family paid $18.00 for 4 hot dogs and 4 drinks. The Lee famliy paid $20.00 for 5 hot dogs and 3 drinks.
What is the price, in dollars, of a hot dog?
Answer:
it would be 4.5 or 4.50 for the Cortez and the Lees payed 4 dollars
Step-by-step explanation:
what is the new side length of a in the actual figure
Answer:
Context? You need to have some information or a picture.
Step-by-step explanation:
Solve the equation for x. 2x+y=7
Answer:
b)
Step-by-step explanation:
2x+y=7
2x=7-y
x=(7-y)/2
Answer: B
Step-by-step explanation:
n
Solve the system of two linear inequalities graphically.3x + 5y < 30Lx23Step 1 of 3: Graph the solution set of the first linear inequality.AnswerThe line will be drawn once all required data is provided and will update whenever a value is updated. The regions will be added once the line is drawnEnable Zoom/PanChoose the type of boundary line:veSolid (-) O Dashed (...)Enter two points on the boundary line:D10Select the region you wish to be shaded:
Given:
[tex]\begin{gathered} 3x+5y<30 \\ x\ge3 \end{gathered}[/tex]Find-: Graph of inequality.
Sol:
Graph of inequality.
[tex]3x+5y<30[/tex]Inequality.
[tex]x\ge3[/tex]Graph is:
Graph of both inequality is:
please help with this question
The function for the area as a function of s, the sidel enght, is:
h(s) = ( (√3)/4 + 1)*s²
Which function gives the total area of the figure?Here we know that for an equilateral triangle of side length s, the area is:
f(s) = (√3)*s²/4
And for a square of side length s the area is:
g(S) = s²
in this case we have a figure that is composed of these two simpler figures, so the total area of our figure will be equal to the sum between the area of the equilateral triangle of side length s and the square of side length s, so we get:
h(s) = f(s) + g(s) = (√3)*s²/4 + s² = ( (√3)/4 + 1)*s²
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1) how do i put these in order (least to greatest)
-1/5, 0.25, -1.5, -1 1/4
2 ) how do i put these in order (least to greatest)
-0.76, -3/4, 7/10, 1.7
Answer:
-1.5,-1 1/4, -1/5, 0.25
-.76,-3/4,7/10, 1.7
the math team is planning a bake sale to raise money for a trip. They want to raise a total of $6 are are selling cookies for $2.00 each and cupcakes for $3.00 each write an equation to represent the situation & find the intercepts
Answer: Two cupcakes, unless it wants both, then I'd assume 2 cookies, one cupcake.
Step-by-step explanation:
Two cupcakes; 3 + 3 / 3 x 2 = 6
Cookies and cupcakes; 2 + 3 + 2 = 7
If 10 workers take eight hours to sew a stores order of pants, then how long would 15 workers take to sew the stores order of pants? Assume all workers work at the same steady rate and all the pants are the same. Part A.) Is the proportion 8hours/10 workers = Xhours/15 workers appropriate for solving the sewing problem why or why not? Part B.) explain how to reason about multiplication and division with quantities to solve the sewing problem
According to the given data we have the following proportion:
8hours/10 workers = Xhours/15 workers
A) The above proportion is not appropiate for solving the problem.
Since, the relationship between the number of workers and the time taken for sewing is an inverse relation:
The above proportion is just a direcly proportional relation.
B). As I stated above the relationship between the number of workers and the time taken for sewing is an inverse relation, hence, if the number of workers doubles then the number of time taken reduces to half.
So, since 15=10*15/10
therefore, time taken for 15 workers to sew pants is:
8/ 15/10 = 8* 10/15
=5 1/3 hours.
The time taken for 15 workers to sew pants is 5 1/3 hours.
help ne
-photos attached!!
Translate the triangle 4 units right and 3 units down. What are the coordinates of the image
-4-3-2
K
4
3
-2
O
2
234x
The coordinates are J'(_,_)K’(_,_)and L’(_,_)
Answer:
J': (3, 6)
K': (3, 4)
L': (0, 4)
Step-by-step explanation:
When we translate a point 4 units right, the x-coordinate of the point increases by 4 units, the y-coordinate remains the same
When a point is translated 3 units down, the y coordinate increases by 3 units, the x-coordinate remains the same
When you translate by 4 units right and 3 units down both x and y coordinates increase by 4 and 3 respectively
So when we apply this translation to the triangle, every point on that triangle, (x, y) changes to (x + 4, y + 3)
If we take the vertices of the triangle we see that the 3 vertices are
J(-1, 3) K(-1, 1) and L(-4, 1)
After applying the translation:
J(-1, 3) ==> J'(-1 + 4, 3 + 3) ==> J'(3, 6)
K(-1, 1) ==> K'(-1 + 4, 1 + 3) ==> K'(3, 4)
L(-4, 1) ==> L'(-4 + 4, 1 + 3) ==> L'(0, 4)
Stephen curry plays for the golden gate warriors and touts a 90% free throw shooting record. If he shot 20 free throws in a game, approximately how many did he miss.
Student solved the case without assistance
The slope is For 3 and 4, find the slope of the line that passes through the given points. 3. (0, 10) and (24, 6) 4. (0,6) and (20, 14)
3. The slope of the line through the points (0, 10) & (24, 6) is [tex]\frac{1}{4}[/tex]
4. The slope of the line through the points (0, 6) & (20, 14) is [tex]\frac{2}{5}[/tex]
What is meant by slope?The slope of a line indicates its steepness. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). The slope of a line, or a section of a line connecting two points, is a measure of its steepness.
Or. A line's slope is the ratio of how much y increases as x increases by some amount. The slope-intercept form of an equation is when the equation of a line is written in the form y = mx + b. The slope of the line is given by m. And b is the value of b in the y-intercept point (0, b).
How are the slopes calculated?
3. We know that , slope = m
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex](x_{1}, y_{1})=(0, 10)\\\\(x_{2}, y_{2})=(24, 16)[/tex]
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m= \frac{16- 10}{24 -0}\\\\m= \frac{6}{24}\\\\m=\frac{1}{4}[/tex]
4. We know that , slope = m
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex](x_{1}, y_{1})=(0, 6)\\\\(x_{2}, y_{2})=(20, 14)[/tex]
[tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m= \frac{14- 6}{20 -0}\\\\m= \frac{8}{20}\\\\m=\frac{2}{5}[/tex]
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A rectangular park is w ft wide. The park is 25 ft longer than its wide.Record your answer to each using Algebra.
What is the length of a fence (inculding the gates) that was built around the park
The length of the fence (including the gates) that was built around the park is (4w + 50) feet.
Here, we are given that a rectangular park is w ft wide and the park is 25 ft longer than its wide.
Thus, the length of the park = (w + 25) ft
Now, the park has to be fenced along all of its sides. Thus, we need to find the perimeter of the rectangular park.
The perimeter of a rectangle is given as-
2( length + breadth)
Thus, here, the perimeter will be-
2( w + 25 + w )
= 2( 2w + 25 )
= 4w + 50
Thus, the length of the fence (including the gates) that was built around the park is (4w + 50) feet.
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. A farmer ships oranges in wooden crates. Suppose each orange weighs the same amount. The total weight of a crate filled with g oranges is 24.5 pounds. Write an equation that represents the relationship between the weight of the crate and the number of oranges it contains.
The equation that represents the relationship between the weight and number of oranges is [tex]w[/tex]·[tex]g=24.5[/tex]
What is an equation?
An equation is a formula which represents the equality between two expression.
We are given each orange weight the same.
Let the weight of one orange be [tex]w[/tex].
Also we are given that there are [tex]g[/tex] oranges in the crate
Also the weight of the crate is 24.5 pounds
Now the equation representing the relationship between weight and number can be given by
[tex]w[/tex]·[tex]g=24.5[/tex]
Hence the equation representing the relationship between weight and number can be given by [tex]w[/tex]·[tex]g=24.5[/tex]
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The two parallelograms are similar. Find the degree measure of the angle. Explain your reasoning.
Answer:
3. ∠A = 110°
4. ∠H = 70°
5. ∠D = 70°
6. ∠F = 70°
Step-by-step explanation:
In a parallelogram, adjacent angles are supplementary (sum to 180°).
⇒ ∠A + ∠B = 180°
⇒ ∠A + 70° = 180°
⇒ ∠A = 110°
In a parallelogram, opposite angles are congruent.
⇒ ∠C = ∠A = 110°
⇒ ∠D = ∠B = 70°
If two parallelograms are similar, their corresponding interior angles are congruent.
⇒ ∠A = ∠E = 110°
⇒ ∠B = ∠F = 70°
⇒ ∠C = ∠G = 110°
⇒ ∠D = ∠H = 70°
ordered pair
-5x-4y=3
3x+10y=-17
The ordered pair of the solution of the equations -5x-4y=3 and 3x+10y=-17 is (1,-2).
The provided equations are,
Equation 1,
-5x-4y=3
Equation 2,
3x+10y=-17
Both the equations are linear equations is two variables,
We can use substitution method to solve these two equations,
From equation 1 we get,
-5x-4y=3
y = (-5x-3)/4
Now, substituting the value of y in equation 2,
we get,
3x+10( (-5x-3)/4)=-17
Solving and simplifying,
12x-50x-30 = -68
-38x = -38
x = 1,
Now, substituting x = 1 in equation 2,
we get,
3(1)+10y=-17
10y = -20
y = -2.
So, the ordered pair is (1,-2).
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In one serving of oatmeal, the ratio of the number of ounces of oats to the number of ounces of dried fruit is 4 to 7.
how many ounces of oats and dried fruit are needed for different numbers of servings.
The number of ounces of oats and dried fruit are needed for different numbers of servings are as follows:
2 servings = 8 ounces of oats and 14 ounces of dried fruit.6 servings = 24 ounces of oats and 48 ounces of dried fruit.7 servings = 28 ounces of oats and 49 ounces of dried fruit.What is a ratio?A ratio can be defined as a mathematical expression that's used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
In this scenario, we know that the ratio of the number of ounces of oats (O) in one serving to the number of ounces of dried fruit (D) in one serving is equal to 4 to 7.
For 2 servings, the ratio would be given by:
O:D = 2 × 4 : 2 × 7 = 8:14
Therefore, we have 8 ounces of oats and 14 ounces of dried fruit.
For 6 servings, the ratio would be given by:
O:D = 6 × 4 : 6 × 7 = 24:48
Therefore, we have 24 ounces of oats and 48 ounces of dried fruit.
For 7 servings, the ratio would be given by:
O:D = 7 × 4 : 7 × 7 = 28:49
Therefore, we have 28 ounces of oats and 49 ounces of dried fruit.
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Imagine you are a restaurant owner. Your opening inventory is $60,000. Your purchases are $40,000. Your closing inventory is $30,000. What is your Food Cost?
The Food cost pf your restaurant would be $70,000
In this question, we have been given an opening inventory is $60,000, purchases = $40,000 and closing inventory is $30,000
We need to find the cost of food.
We know that the formula for food cost:
Food cost = Opening Inventory + Purchases - Ending Inventory
Food cost = $60,000 + $40,000 - $30,000
Food cost = $1,00,000 - $30,000
Food cost = $70,000
Therefore, the Food cost pf your restaurant would be $70,000
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988 x 6.2
show your work
On a sunny day, a 3-foot red kangaroo casts a shadow that is 5 feet long. the shadow of a nearby eucalyptus tree is 7 feet long. find the height of the tree.
Answer: 5 feet
Step-by-step explanation:
The kangaroo added 2 feet of length to the shadow, therefore adding 2 feet of length of the 5 foot tree.
7-2=5
( sorry if it's confusing ^^ )
katlin bought 14 pencils, it costs her $3.50. how much did each pencil cost?
Answer: 0.25$ or a quarter
Step-by-step explanation:
Katlin bought 14 pencils, which cost her $3.50. So all you have to do is divide the amount ($) by the number of pencils.
3.50/14 = 0.25$
3.50 divided by 14
Each pencil cost a quarter
The distance from the earth to the sun is 1.5 extend eight KM and the distance from Mars to the sun is 2.2 8 X 10 eight KM what is the distance between earth and mars expressed in scientific notation
The distance between the Earth and the Sun is 1.5 extend eight kilometers, and the distance between Mars and the Sun is 2.2 8 X 10 eight kilometers. The scientific notation for the distance between Earth and Mars is 3.78 x 10^8 km.
How to find a distance?The length of the line connecting two points is the distance between them. If the two points are on the same horizontal or vertical line, the distance can be calculated by subtracting the non-identical coordinates.
Distance is defined as an object's total movement without regard for direction. Distance can be defined as how much ground an object has covered regardless of its starting or ending point.
Given,
The distance between Earth and Sun = 1.5 x 10^8 km
The distance between Sun and Mars = 2.28 x 10^8 km
Therefore the distance between Earth and Mars =
(1.5 x 10^8 + 2.28 x 10^8) km
= (1.5 + 2.28) x 10^8 km
= 3.78 x 10^8 km (Ans)
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Find the perimeter and the area of the figure.(assume right angles and parallel sides except we’re obviously otherwise)Simplify your answer and round to the nearest TENTH.
Given:
The length of the parallel sides,
a=17.4 m
b=44.1 m
The height, h=23.5 m
The measurements of the other two sides are,
c=27.5m and d=26.6m.
To find the area of the trapezium:
Using the formula,
[tex]\begin{gathered} A=\frac{1}{2}\times(a+b)\times h_{} \\ =\frac{1}{2}\times(17.4+44.1)\times23.5 \\ =\frac{1}{2}\times61.5\times23.5 \\ =722.625\text{ square meters} \end{gathered}[/tex]Hence, the area of the figure is 722.6 sq. m (rounded to the nearest tenth).
To find the perimeter of the trapezium:
[tex]\begin{gathered} P=a+b+c+d \\ =17.4+44.1+27.5+26.6 \\ =115.6\text{ m} \end{gathered}[/tex]Hence, the perimeter of the figure is 115.6 m.
8a) The formula V = Bh/3
shows how to
find the volume of a pyramid where V is
volume, B is Base Area and h is height. Solve
for B.
Answer:
B = 3V/h
Step-by-step explanation:
The formula V = Bh/3 shows how to find the volume of a pyramid where V is volume, B is Base Area and h is height. Solve for B.
V = Bh/3
multiply both sides by 3:
3(V) = 3(Bh/3)
3V = Bh
divide both sides by h:
3V/h = Bh/h
B = 3V/h
