Answers
a. Using properties of exponents, the value of the expression is 10⁰
b. The equation has no solution
What are properties of exponents?a. Properties of exponents are mathematical rules that allow us to simplify and manipulate expressions involving exponents. These properties help us perform operations such as multiplication, division, and raising to a power more efficiently.
In the given problem, we have to solve and simplify using properties of exponents.
Given that; [tex]\frac{10^-^3}{10^-^3}[/tex];
we can apply quotient rule when dividing exponents here;
[tex]\frac{10^-^3}{10^-^3} = 10^-^3 ^+^3 = 10^0[/tex]
The answer is 10⁰
b. To simply the equation, we just need to use basic mathematical operation to find the value of x.
3x - 2x + 4 = 5x - 4x - 8
Simplify;
x + 4 = x - 8
Collect like terms
x - x = -8 - 4
0 = -12
No solution
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Related Questions
if the r-value, or correlation coefficient, of a data set is 0.854, what is the coefficient of determination to three decimal places?
Answers
(0.854)² = 0.729316. To three decimal places, this would be 0.729.
Answer with explanation:
Coefficient of determination(r²), is defined as, how well the data values are associated with each other when Regression line is drawn. In regression analysis, the coefficient of determination measures , how well the regression predictions approximate the real data points, means it measures the closeness between two variables.The Value of r², lies between 0 to 1. If value of r²=1, it shows ,regression line that is data values are Perfectly associated with each other.
If ,r²=0, it means there is no variation between two variables.There is 0% variation between two variables.
→Coefficient of Variation=[Correlation coefficient]²
=r²
=(0.854)²
=0.854 × 0.854
=0.729316
=0.730(Approx)
The state capitol building in Baton Rouge, Louisiana, is 450 feet tall. Ella’s scale model of the building uses the scale 25 feet = 10 inches. How tall is Ella’s model? 18 inches 180 inches 1,125 inches 425 inches
Answers
[tex] \frac{450}{x} [/tex] = [tex] \frac{25}{10} [/tex]
Notice the feet (450 and 25) are lined up next to each other, and the inches (x and 10) are lined up as well. Next, we solve by cross multiplying and dividing. 450 times 10 gives us 4500. Then, we divide by the remaining number,25. 4500/25 equals 180. So, Ella's model is 180 inches tall.
What is the solution of the system? Use either the substitution method or the elimination method. 4x + 2y = 104x + 2y = 10 x − y = 13x − y = 13
There is no solution.
(3.5, −1)
(6, −7)
(−7.5, 2)
Answers
x-y=13 Equation 2
Solving by substitution method.
Isolate x from equation 2.
x=y+13
Substitute value of x in equation 1
4(y+13)+2y=10
4y+52+2y=10
6y+52=10
6y=-42
y=-7
Now substitute value of y in x=y+13
x=-7+13
x=6
Answer: (6,-7)
What is 20 percent of 60
Answers
20 percent of 60 we can setup like this.
.20*60=x
x=12
Hope this helps. Questions please just ask. Thank you
1\5*60=
12
you multiply 1\5*60\1 to get the answer 12
Amount Saved = Original Price x Discount % / 100. So,
Amount Saved = 60 x 20 / 100
Amount Saved = 1200 / 100
Amount Saved = $12 (answer)
What if mac bought8pack of toy boats and then he gave his friend 3boats? If mac has 13 boats now,how many boats were in each pack?
Answers
We have 8 packs of toy boats, meaning there are a specific amount of toy boats per pack, so we have to multiply 8 by a variable, x. Considering this is the total, too, we should let this sit at the end of the equation (=8x). Mac gave his friend 3 toy boats, meaning we will be subtracting 3 from our equation, but this will be on the other side of the equation with 8x (-3). We also have a current total of 13 toy boats after Mac gave away 3 boats, meaning that 13 will have to sit alone (+13).
With this information, let's set up an equation. With what we have, the equation will look like this:
8x - 3 = 13
Now all we have to do is solve for x. To start this off, we should add 3 to both sides to isolate the variable.
8x = 13 + 3; simplify.
8x = 16; All that is left is to divide both sides by 8 and we will have figured out how many toy boats were in each pack.
8x / 8 = x; 16 / 8 = 2.
We are left with our answer, x = 2. That being said, there were 2 toy boats per pack.
I hope this helps!
This semicircle has a diameter of 5 meters.
What is the area of this figure?
Use 3.14 to for pi.
Enter your answer as a decimal in the box. Round your answer to the nearest hundredth.
Answers
[tex]A_sc = \frac{1}{2} \pi r^2 [/tex]
r is the radius, and we are given the diameter. Radius is half the diameter, so it's 2.5m. Let's plug that into the formula (using 3.14 as an estimation for pi):
[tex]A_t = \frac{1}{2}(3.14)(2.5)^2 = 9.81m^2 [/tex]
So, the area of this semicircle is 9.81m².
420% of what number is 26,565
Answers
to check u can multipley 6325 by 420% u get 26565
Cameron has clear container in the shape of a cube.Each egde 9 centimeters long.He found the volume of the container in cubic centimeters by multiplying the egde length by itself 3 times.What is the volume of the container in the cubic
Answers
Write the resultant if the 2 vectors as an ordered pair.
<5, -2> and <0,0>
Answers
Step 1. Find z1 by adding x1^2 and y1^2.
z1= 5^2 + 0^2 = 5
Step 2. Find z2 by adding x2^2 and y2^2.
z2= -2^2 + 0^2 = 2
Step 3. Find c.
5^2 + 2^2 = c^2
c=square root of 29
c=5.39
The final answer is 5.39.
A rectangle 7 feet longer than it is wide find the dimensions of the rectangle if its area is one 198 sq ft.
Answers
l=w+7
w(w+7)=198
w^2+7w-198=0
(w-11)(w+18)=0
w=11 or -18
w=11 and l=18
A data set contains three points, and two of the residuals are -10 and -20. What is the third residual?
Answers
The residuals of any data set should get added to zero. If there are three residuals (say A, B, and C) in any data set, then it could be written as A + B + C = 0.
Given are the two residuals -10 and -20 out of three point in a particular data set.
Let's assume A = -10 and B = -20, so that we could find third value C of the given data set.
We know A + B + C = 0
(-10) + (-20) + C = 0
(-30) + C = 0
C = 30
It means that third residual must be 30.
Hence, the final answer is 30.
Answer:
30
Step-by-step explanation:
do anyone know how to solve this? need the answer fast.
Answers
.. (x +4)/(2x -5) = -3
.. x +4 = -3(2x -5)
.. 7x = 11
.. x = 11/7
The desired value is
.. (3/11)*g^-1(-3)
.. = (3/11)*(11/7)
.. = 3/7
[tex] \frac{3}{11} g^{-1}(-3) = \frac{3}{7}[/tex]
Which expression is equivalent to 1/4(2−5x+6) ?
Please answer fast!
Answers
The equivalent expression for the given expression is 2-5x/8.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
The given expression is 1/4(2-5x+6).
The equivalent expression is
1/4(8-5x)
=8/4 -5x/8
= 2-5x/8
Therefore, the equivalent expression is 2-5x/8.
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To find the equivalent expression to 1/4(2−5x+6), distribute 1/4 to each term inside the parentheses to get 1/2 - 5/4x + 3/2.
To simplify the expression 1/4(2−5x+6), you need to distribute the 1/4 to each term inside the parentheses:
1/4 * 2 = 1/21/4 * (-5x) = -5/4x1/4 * 6 = 3/2Putting it all together, the equivalent expression is 1/2 - 5/4x + 3/2.
how many times does a person blink in 1.5 min
Answers
Find the balance in the account after the given period.
$4,200 deposit earning 4.2% compounded monthly, after 2 years. Use the direction in the pic plz.
Answers
[tex]A=4200(1+ \frac{0.042}{12})^1^2^*^2 \\ = 4200(1+0.0035)^2^4 \\ = 4200(1.0035)^2^4 \\ = 4567.37[/tex]
A triangle and a rectangle are drawn. The triangle's base is equal to the rectangle's length. The triangle's height is equal to the rectangle's width. Which sentence is true?
A.)exactly 1 of these rectangle's can fit inside this triangle.
B.)2 of these rectangles can fit inside this triangle
C.)exactly 1 of these triangle's can fit inside this rectangle
D.)2 of these triangles can fit inside this rectangle
Answers
Exactly 1 of these triangles can fit inside this rectangle.
Explanation:The sentence that is true is exactly 1 of these triangles can fit inside this rectangle. To understand why, let's analyze the dimensions of the triangle and the rectangle. Suppose the base of the triangle is 4 units and the height is 3 units. If the length of the rectangle is also 4 units and the width is 3 units, the triangle will perfectly fit inside the rectangle. However, if the length or width of the rectangle is different from the corresponding dimensions of the triangle, it will not be possible to fit the triangle inside the rectangle without overlapping.
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Explain how you would use a number line to find to find the absolute value of-12
Answers
The absolute value of -12 is 12 and we can find it on the number line by going 24 times right from -12.
What is absolute value?The absolute value or modulus of a real number x, and we know that modulas always gives a positive number.
How to determine absolute value?The number which is given in the question is -12 and we have to find the absolute value of this number. To find out the absolute value we have to put this number in modulas.
I -12 I =it will give us 12
to make -12 to 12 we need to first take it to 0 by adding 12 and then from 0 to 12 by adding another 12. We have added 24 to-12 to reach 12.
In this way we can find the absolute value of -12 on number line.
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A news anchorman can read 7.5 lines in 0.5 minutes. How many lines can he read in 8.5 minutes? Round the answer to the nearest tenth, if necessary.
A. 15.0 lines B. 127.5 lines
C. 31.9 lines D. 2.7 lines
Answers
what is 9,750,000,000 in scientific notation
Answers
So, when doing this kind of notation (scientific notation), this is pretty much like braking down the number,and trying to make it more simple.
[tex]\boxed{9,750,000,000} \ in \ scientific \ notation... \\ \\ \Longrightarrow\boxed{\boxed{9.75*10^9}} \Longleftarrow[/tex]
I hope this helps you! :)
Ramona is asked to draw a tree using a scale of 1 inch:3 meters.She draws a 4-inch tree.How tall is the tree?
Answers
what is the inverse of the conditional statement? If a polygon the has five angles, then it is a Pentagon
Answers
Answer: The inverse f the given statement is
"If a polygon is not a Pentagon, then it does not have five sides".
Step-by-step explanation: We are given to write the inverse of the following conditional statement:
"If a polygon the has five angles, then it is a Pentagon".
INVERSE of a conditional statement :
If the conditional statement is
"If p, then q",
then its inverse statement is given by
"If not q, then not p".
Therefore, the inverse of the given statement is
"If a polygon is not a Pentagon, then it does not have five sides".
Answer:
It is Option C If a polygon does not have five angles then it is not a pentagon.
Step-by-step explanation:
beer Bottles are filled so that they contain an average of 475 ml of beer in each bottle. Suppose that the amount of beer in a bottle is normally distributed with a standard deviation of 8 ml.
Answers
We use the normal distribution density function f(z) to find the probability of a specific range of values.
Z= ((X-μ)/σ)
μ = 475σ = 8
a) X< 470 ml
P[X<470] = P[Z<(470-475)/8] = P[Z<(470-475)/8] = P[Z<-0.625] = 0.2659
b) 6 pack with a mean of less than 470ml
Z = ((X-μ)/(σ/√n))
Z = (470-475)/(8/√6)
P [Z<-1.53] = 0.063
c) 12 pack with a mean of less than 470ml
Z = ((X-μ)/(σ/√n))
Z = (470-475)/(8/√12)
P [Z<-2.165] = 0.0152
Renee is making a scale diagram of her mp3 player. The length of her scale drawing is 8 inches, and the width is 14 inches. The actual length of the mp3 player is 4 centimeters, and the width is 7 centimeters. what is the scale factor?
Answers
Explanation:
The scale factor is the ratio between the scale drawing measures and the actual measures.
scale drawing length 8 inches
scale factor = ratio = -------------------------------- = --------------- = 2
actual length 4 inches
Also,
scale drawing width 14 inches
scale factor = ratio = ----------------------------- = --------------- = 2
actual width 7 inces
As seen the scale factor is 2.
The scale factor is 1:2 or 1/2.
To determine the scale factor between the actual dimensions and the scale drawing, divide the actual length and width by the corresponding values in the scale drawing dimensions. In this case, the scale factor is 1:2 or 1/2.
To find the scale factor:
Calculate the ratio of the actual length to the scale length: 4 cm / 8 in = 0.5Calculate the ratio of the actual width to the scale width: 7 cm / 14 in = 0.5Since both ratios are the same, the scale factor is 1:2 or 1/2.A rectangular prism has a length of 3 1/2 inches, a width of 3 1/2 inches, and a height of 7 inches. Danny has a storage container for the prism that has a volume of 90 cubic inches.
What is the difference in volume between the prism and the storage container?
PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!
Answers
length x width x height. So for the prism you multiply 3 1/2 x 3 1/2 x 7. Which gives you the answer of 85.75, or rounded it’ll give you 86.
Now to find the difference you subtract the volume of the prism from the container which will give you your final answer
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What is the period of the function f(x) shown in the graph?
Answers
In this case we have that the period will be given by:
T = ((3/4) pi) - ((- 1/4) pi)
T = ((3/4) pi) + ((1/4) pi)
T = ((3 + 1/4) pi)
T = ((4/4) pi)
T = pi
Answer:
the period of the function f(x) shown in the graph is
T = pi
A pair of running shoes costs five dollars more than a pair of regular tennis shoes .. the total cost for both is one 115 $ What is the price of the regular tennis shoes?
Answers
$55 for the pair of Regular
What is the volume of a right circular cylinder with a radius of 4 m and a height of 4 m?
Answers
V = ((pi) * (r ^ 2)) * (h)
Where,
r: radio
h: height.
We have then:
V = ((pi) * ((4) ^ 2)) * (4)
V = 64 * pi m^3
Answer:
The volume of a right circular cylinder is
V = 64 * pi m^3
the length of bill's backyard swimming pool is 60 ft longer than the width if the pool. The surface area of the water is 1600 square ft. What is the width of the pool?
Answers
Surface Area of water = A = 1600[tex]ft^{2}[/tex]
Length of the swimming pool = L = 60[tex]ft[/tex] + W
Width of the swimming pool = W =?
Since,
Area = Length * Width
A = L * W
Therefore,
1600 = (60 + W) * W
1600 = 60W + W*W
=> [tex]W^{2} + 60W - 1600 = 0[/tex]
In the above equation(in terms of quadratic formula),
a = 1
b = 60
c = -1600
x = W
Use,
x(for positive) = [tex]x =\frac{ -b + \sqrt{ b^{2} - 4*a*c } }{2*a} [/tex]
Plug-in the values you would get:
x = (-60 + 100) / 2
x = 20 --- (1)
x(for negative) = [tex]x =\frac{ -b - \sqrt{ b^{2} - 4*a*c } }{2*a} [/tex]
Plug-in the values you would get:
x = (-60 - 100) / 2
x = -80 --- (2)
Since x = W = Width, and width CANNOT be negative, therefore, the correct answer is (1):
Ans: Width = 20ft
To find the width of Bill's rectangular pool, set up an equation with 'x' as the width, resulting in x(x + 60) = 1600. Solving this quadratic equation, the width of the pool is found to be 20 feet.
The question asks us to determine the width of Bill's backyard swimming pool given that the pool's length is 60 feet longer than its width and the surface area of the water is 1600 square feet. To solve this, we can set up an equation where the width of the pool is x feet and the length is x + 60 feet. Because surface area is found by multiplying the length by the width for a rectangular object, our equation is x(x + 60) = 1600.
Now, solve for x:
x^2 + 60x = 1600x^2 + 60x - 1600 = 0We can solve this quadratic equation by factoring or using the quadratic formula. In this case, the equation factors nicely:
(x + 80)(x - 20) = 0Setting each factor equal to zero gives us:
x + 80 = 0 or x - 20 = 0x = -80 or x = 20Since a negative width doesn't make sense for a physical object, we discard x = -80 and the width of the pool is 20 feet.
Solve the following equation for x: 6(4x+5)= 3(x+8)+3. Round to the nearest hundredth.
Answers
24x + 30 = 3x + 24 + 3
24x + 30 = 3x + 27
24x - 3x = 27 - 30
21x = - 3
x = -3/21
x = - 0.143 <==
6(4x+5)=3(x+8)+3
Distribute.
24x+30=3x+24+3
24x+30=3x+27
Subtract 30 on both sides.
24x= 3x-3
Subtract 3x on both sides.
21x=3
Divide both sides by 21.
x=0.142857... the question said hundredth so:
x=0.143
I hope this helps!
~kaikers
if triangle rst is an acute angle then m