The expression as a power is 2^10 and 2^9
What is index form?Index form of a number can be defined as the number that is written in the form of an exponential expression.
It is also described as a single number that is raised to another variable or number.
It is important to note the following index forms with base of 2, we have;
2^1 = 22^2 = 42^3 = 82^4 = 162^5 = 322^6 = 64We have the expression as;
8•2^7
Substitute the values
2^3 . 2^7
Add the powers
2^3 + 7
2^10
16•32
Substitute the values
2^4 . 2^5
Add the powers
2^ 4 + 5
2^9
The expression is written as; 2^ 10 and 2^9
Hence, the values are 2^10 and 2^9
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48 - (3 c+4)=4(c+5)+3 c=???
Answer in multiple forms depending on what needed
Answer:
c = 3
Step-by-step explanation:
48- (3c+4)=4(c+5)+3
48-3c-4=4(c+5)+3 Distributed the - sign
48 -3c -4= 4c+20 +3 Distributed the 4
44-3c =4c+23 Combined like terms
21-3c=4c Subtract 23 from both sides
21=7c Add 3c to both sides
3=c
Simplify 5^3 x 5 please
Answer:
5^4
Step-by-step explanation:
5^3x5
5x5x5x5
5^4
Hopes this helps please mark brainliest
The simplified form of the expression, 5³.5 will be 625.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
It is given that the expression is, 5³.5
=5³.5
The base should remain constant and the exponents added when multiplying like bases. Keep the base constant when raising a base with power to another power, and multiply the exponents instead. Keep the base constant and deduct the exponents in the denominator and numerator when dividing like bases.
Apply the law of exponent as
xᵃ × xᵇ = xᵃ⁺ᵇ
=5³⁺¹
=5⁴
=5x5x5x5
=625
Thus, the simplified form of the expression, 5³.5 will be 625.
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Help Need ASAP
Paula makes purses. The materials cost $2.25 per purse. She sells them for $5.00 each. Paula wants to invest $5000 for some new equipment. Which of these could be used to determine x, the number of purses Paula must sell to pay for the new equipment?
Responses
5.00x - 2.25x = 5000
5.00x + 2.25x = 5000
5.00x = 5000
2.25x = 5000
The equation that represents the number of purses Paula must sell to pay for the new equipment is 5.00x = 5000.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, Paula makes purses and the materials cost $2.25 per purse.
She sells them for $5.00 each now she wants to invest $5000 in some new equipment and we are assuming the no. of purses to be x.
Here the equation 5.00x - 2.25x = 5000 represents Paula's profit.
The equation that represents the no. of purses she must sell to pay for the new equipment is 5.00x = 5000.
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Answer: 5.00x - 2.25x = 5000
Step-by-step explanation:
If tan 8 = 3 and 8 lies in the second quadrant. Use a Pythagorean identity to find
the exact value of cos 6.
The exact value of Cosθ is -1/√10 .
In the question ,
it is given that ,
the value of tanθ = 3/1 ,
that means the perpendicular = 3x
and the base of the triangle is = 1x,
So ,By Pythagoras Theorem
hypotnuse² = perpendicular² + base²
hypotnuse² = (3x)² + (1x)²
hypotnuse² = 9x² + 1x²
hypotnuse² = 10x²
hypotnuse = (√10)x
So , Cosθ = base / hypotnuse
Cosθ = 1x/(√10)x
Cosθ = 1/√10
Since , [tex]\theta[/tex] lies in the second quadrant ,
and in second quadrant Cos is negative ,
So , Cosθ = -1/√10
Therefore , The exact value of Cosθ is -1/√10 .
The given question is incomplete , the complete question is
If Tanθ = 3 , θ lies in the second quadrant. Use a Pythagorean identity to find the exact value of Cosθ ?
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$6000 are invested in a bank account at an interest rate of 6 percent per year.
Find the amount in the bank after 11 years if interest is compounded annually.
Find the amount in the bank after 11 years if interest is compounded quarterly.
Find the amount in the bank after 11 years if interest is compounded monthly.
Finally, find the amount in the bank after 11 years if interest is compounded continuously.
The value after 11 years with annual compounding is $11,389.79
The value after 11 years with quarterly compounding is $11,552
The value after 11 years with monthly compounding is $11,589.68
The value after 11 years with continous compounding is $70,080.78.
What is the future value?When an amount is compounded annually, it increases in value once a year. When an amount is compounded quarterly, it increases in value four times a year. When an amount is compounded monthly, it increases in value twelve times a year. When an amount is compounded continuously, it increases continuously over the investment period.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate - annual rate / number of compounding m = number of compoundingN = number of yearsValue after 11 years with annual compounding: $6,000 x (1.06)^11 = $11,389.79
Value after 11 years with quarterly compounding: $6,000 x (1 + 0.06 /4)^(11 x 4) = $11,552
Value after 11 years with monthly compounding: $6,000 x (1 + 0.06 /12)^(11 x 12) = $11,589.68
The formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rateValue after 11 years: 6,000 x (2.718^0.06) x 11 = $70,080.78
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What is the largest multiple of 30 which is less than 520?
The largest multiple of 30 that is less than the number, 520, can be found to be 510.
How to find the multiple?To find the largest multiple that 30 has, which is also less than 520, first find the number of times that 30 can go into 520:
= 520 / 30
= 17.333
Then use this number to find the largest multiple below 520 by rounding 17.33 downwards to 17.
The multiple of 30 that is the largest and below 520 is then:
= 30 x Rounded down result of division of 520
= 30 x 17
= 510
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the length of a rectangle is 2 feet more than the width. Find the minimum dimensions if the perimeter is more than 16 feet and the length and width are integers.
Answer:
L = 6 feet ; W = 4 feet
Step-by-step explanation:
l = 2 + w
perimeter/2 = 8
l + w > 8
2 + w + w > 8
2 + 2w > 8
2w > 8-2
2w > 6
2/2 w > 6/2
w > 3
smallest integer > 3 = 4
W= 4
L = 4 + 2 = 6
Find the values of x and y.
Answer: The correct answer is x = 50
Step-by-step explanation:
The sum of angles in a triangle = 180 degrees
This is a right-angled triangle, so one of the angles is 90 degrees + x +y
Therefore: 90 + y + x = 180
Substitute the variables:
90 + 40 + x = 180
130 + x =180
Subtract 130 from each side:
(-130) 130 + x =180 (-130)
x = 50
Select the correct answer from each drop-down menu. Using the image below, select the best answer from each pull-down to complete the statements. The measure of ∠FED is ? °. ∠CBD and ∠ ? are complementary angles. Please help. thank you
The value of ∠FED is 120° and ∠CBD is complementary to ∠FDE
What are complementary angles?Complementary angles are two angles that sum up to 90°
For example 60° and 30° are complementary.
Either angle is called the complement of the other angle.
∠FED, ∠FDE and ∠DFE are in a triangle.
so,
∠FED + ∠FDE + ∠DFE = 180°
16x - 8 + 2x + 9 + 35 = 180 ( sum of angles in a triangle)
18x +36 = 180
18x = 180 - 36
18x = 144
x = 144/18
x = 8
so ∠FED = 16x - 8
Substitute x = 8 into the equation above we have
16(8) - 8 = 128 - 8 = 120°
∠FDE = 2x + 9
∠FDE = 2(8) + 9 = 25°
∠BED = 6x + 12
∠BED = 6(8) + 12
∠BED = 48 + 12
∠BED = 60°
∠CBD = -2x + 81
∠CBD = -2(8) + 81
∠CBD = 65°
so since ∠CBD = 65° and 90 - 65 = 25°
∠CBD is complementary to ∠FDE
In conclusion, ∠FED is 120° and ∠CBD is complementary to ∠FDE
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A school is arranging a field trip to the zoo. The school spends 643.34 dollars on passes for 36 students and 2 teachers. The school also spends 339.48 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
$
40 POINTS
By taking some simple quotients, we will see that the cost per student is:
$26.36
How much money was spent on a pass and lunch for each student?First, we know that the school spends $643.34 on passes for 38 people, then the cost of each pass is given by the quotient:
p = $643.34/38 = $16.93
Then there is also lunch for the 36 students, which costed $339.48, then the cost in lunch per student is.
l = $339.48/36 = $9.43
The total cost per student is:
$16.93 + $9.43 = $26.36
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Please help me find the slope on the lined graphed below??
Answer:
2/3
Step-by-step explanation:
The gradient is found by doing rise/run. If you go to a point on the line you can then rise 2 squares and run 3 to the right. This means that the gradient is 2/3. It is not negative as the line is going up.
Please Help 2
Find (fxg)(x) if f(x)=x2+2+4 and g (x)=x-2
Answer:
x³ - 8
Step-by-step explanation:
A business started the year with a net worth of $4,873. During the first six months of the year, the business
recovered and increased its net worth to a value of $15,866. Find the average monthly increase in net worth for the 6-month period.
The average monthly increase in net worth for the 6-month period is $1832.16.
Given:
A business started the year with a net worth of $4,873. During the first six months of the year, the business recovered and increased its net worth to a value of $15,866.
Six months net worth = 15,866 - 4873
= 10,993
Average monthly increase in net worth = six month net worth / 6
= 10,993/6
= $1832.16.
Therefore The average monthly increase in net worth for the 6-month period is $1832.16.
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I NEED HEEEEELP!!
There are 5 cockroaches crawling on each square meter of the front of this building. How many cockroaches are crawling on the front of the building?
Please, show your work and explain. TYSM!! ^^
There are 855 cockroaches crawling on the front of the building
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
The population density is given as:
Population density = total animals / area occupied
Given that, the population density of the cockroaches is 5 cockroaches per square meter.
The area of the building = area of triangle + area of square
Area of building = (1/2) * (24 - 9)(12) + (9 * 9) = 90 + 81 = 171 m²
Population density = total animals / area occupied
5 cockroaches per square meter = Total cockroaches / 171 m²
Total cockroaches = 855
There are 855 cockroaches
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Write an equation of the line that is PARALLEL to 12x - 4y = 4 and through the point (-9,-2).
Answer:
y=3x+25
Step-by-step explanation:
we need start by making slope intercept form
lets move the 12x after moving it we get
-4y=-12x+4 we need to remove the - 4 from the y so we need to divide the whole equation by - 4
we get y=3x-1
now we can create an equation to get the parallel line
y+2=3(x+9) now distribute
y+2=3x+27 and subtract the two
y=3x+25
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, what was the change in the altitude of the missile?
The required change in height of the missile is 16100 feet.
Given that,
A missile was fired from a submarine from 200 feet below sea level. If the missile reached a height of 15900 feet before exploding, the change in the altitude of the missile is to be determined.
Change in defined as when the object is in one state but after a certain period of time, the state of the object changes is called change of the state.
here,
The height attained by the missile above sea level is 15900 feet.
The height attained by the missile below the seal level is 200 feet.
Change in height = 15900- (-200) = 15900 + 200 = 16100.
Thus, the required a change in height of the missile is 16100 feet.
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Use the order of operations to simplify this expression (1/4 + 7/8)x 1/2
Order of operation to simplify this expression as follows:
[tex]((1\div4+7\div 8)\times 1)\div 2[/tex]
⇒ [tex]((0.25+7\div 8)\times 1)\div 2[/tex]
⇒ [tex]((0.25+0.875)\times 1)\div2[/tex]
⇒ [tex](1.125\times 1)\div2[/tex]
⇒ [tex]1.125\div 2[/tex]
⇒ [tex]0.5625[/tex]
What is order of operation?
The best way to solve an expression is from left to right if all the operations are the same (for instance, only addition, only subtraction, only multiplication, or only division). However, we must adhere to the order of operations for expressions including several operations.
The rule that dictates how to solve an expression involving numerous operations is known as the order of operations.
PEMDAS can help you remember that sequence. In PEMDAS, each letter denotes a mathematical operation.
Given Expression is ; [tex]((1\div4+7\div 8)\times 1)\div 2[/tex]
Firstly we calculate the highest priority between(+,-, x, and [tex]\div[/tex])
Here, division is the highest priority ,
[tex]((0.25+7\div 8)\times 1)\div 2[/tex]
[tex]((0.25+0.875)\times 1)\div2[/tex]
and then we solve parathesis,
[tex](1.125\times 1)\div2[/tex]
now we do multiply,
[tex]1.125\div 2[/tex]
and the final answer will be [tex]0.5625[/tex]
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The diameter of a semicircle is 4 yards. What is the semicircle's perimeter?
Use 3.14 for x.
d=4 yd
The diameter of a semicircle is 4 yards. The perimeter for a semicircle having a diameter of 4 yards is 10.28 yards.
The perimeter of a shape is the distance of the path or boundary that surrounds the shape.
The formula for the perimeter of a semicircle is πr + 2r
π(pie)=3.14
r(radius)=2 yards (∴ radius=1/2diameter)
∴ the perimeter of a semicircle = πr + 2r
= 3.14×2+2×2
=10.28 yards.
∴ The perimeter of a semicircle with a diameter of 4 yards is 10.28 yards.
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y5 • y14 =
A. 2y19
B. y60
C. y19
D. 2y60
ALGEBRA
For how many values of x is h(x) = 0? Justify you answer.
Answer:
the answer for x when h(x) is 2.9
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
How to solve: 24 - (5 + 3)^2 + 4 × 2^3 step by step.
The value of the exponent given as 24 - (5 + 3)^2 + 4 × 2^3 is -8.
What is an exponent?An exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
In this case, the value given will be expressed thus:
= 24 - (5 + 3)^2 + 4 × 2^3
= 24 - (8)² + 4 × 8
= 24 - 64 + 32
= -8
The value is -8.
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Fine the slope of the line and use rise/run to fill in the blanks
Answer: Rise is 5 and run is 1 and now that is equal 5
Step-by-step explanation:
Solve the system by back substitution.
- 2x - 4y - z- 3w = -5
-2y - 12z - 4w = - 16
5z +5w=10
4w =12
Answer:
y=8 x=-19.5
Step-by-step explanation:
Start from the bottom equation and work your way upSolve the fourth equation for w-5w=-15-5w/(-5)=-15/(-5)w = 3 Then use that value of w to plug into the third equation. Notice we're going backwards or up the chain of equations. After w is replaced, solve for zz+w = 2z+3 = 2z+3-3 = 2-3z = -1 Now use z = -1 and w = 3 to plug into the second equation. Solve for y-2y-12z-4w = -16-2y-12(-1)-4(3) = -16-2y+12-12 = -16-2y = -16-2y/(-2) = -16/(-2)y = 8
Use y = 8, z = -1, w = 3 to plug into the first equation. Solve for x:
2x+4y+z+3w=12x+4(8)+(-1)+3(3)=12x+32-1+9=12x+40=12x+40-40=1-402x=-392x/2=-39/2x = -39/2 The value of x as a fraction is x = -39/2The value of x in decimal form is x = -19.5
A bus ticket used to cost $2.50
Today, 1 bus ticket costs $2.75
The increase in cost is?
The percent increase is?
Dave’s Furniture Store is having a 35% off sale on tables. Robert paid $195 for a table that was on sale. What was the original price of the table?
Answer:
557.143
Step-by-step explanation:
195 / 35% = 557.14
Select the two values of x that are roots of this equation. 2x^2 + 7x + 6 = 0  A. x = –2  B.   C. x = –4  D. x = –3
The root of the quadratic equation is 2x² + 7x + 6 is x = -2 and x = -3 / 2.
How to find the roots of an equation?The roots of a quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation.
The equation to find the roots, is a quadratic equation.
Hence,
2x² + 7x + 6
2x² + 3x + 4x + 6
x(2x + 3) + 2(2x + 3)
Hence,
(x + 2)(2x + 3) = 0
Therefore,
x + 2 = 0 or 2x + 3 = 0
x = -2 or x = -3 / 2
The roots of the equation is x = -2 and x = -3 / 2
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Helpi really need this
Answer:
The height of the flagpole is about 25.6 feet.
Step-by-step explanation:
The figure is omitted--please sketch it.
Put your calculator in degree mode.
Let h be the height of the flagpole.
[tex] \tan(52) = \frac{h}{20} [/tex]
[tex]h = 20 \tan(52) = 25.6[/tex]
Find the slope using points: (0, - 3) and (- 4, 2)
Answer:
-5/4
Step-by-step explanation:
slope
[tex]\frac{y2-y1}{x2-x1}\\\\ \frac{2-(-3)}{-4-0}=\frac{5}{-4}\\ \\slope = \frac{-5}{4}[/tex]
Find the coordinates of the point which divide the lines joining the following pairs of points in the given ratio
a. (5,8) and (-1,3) 2:3
b.(4,7) and (3,-2) 4:5
The coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio 2:3 is (8,4).
Using the section formula, if a point (x,y) divides the line joining the points (x₁, y₁) and (x₂, y₂) in the ratio m:n, then
(x,y)=( (mx₂+nx₁)/m+n , (my₂+ny₁)/m+n )
Let the points be A(5,8) and B(-1, 3). Let a point P(x,y) divides AB in the ratio 2:3
Therefore, we have
P(x,y)=((2(-1) + 3x5)/(2+3) , (2(3) + 3x8)/(2+3))
P(x,y)=(2.6,6)
Hence,the coordinates of the point which divide the lines joining the pairs of points (5,8) and (-1,3) in the given ratio 2:3 is (8,4).
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