Answer:
In short, 0 is the only number such that for any number x, x + 0 = x. ... So, the reason that any number to the zero power is one is because any number to the zero power is just the product of no numbers at all, which is the multiplicative identity, 1
Answer:The zero exponent rule states that any term with an exponent of zero is equal to one. This lesson will go into the rule in more detail, explaining how it works and giving some examples. There will also be a quiz to test your knowledge.
The zero exponent rule is one of the rules that will help you simplify exponents. Let's first define some terms as they relate to exponents. When you have a number or variable raised to a power, the number (or variable) is called the base, while the superscript number is called the exponent, or power.
Usually, you'll see this written with the base being a normal-size number (or letter, if you're working with a variable). The exponent will be in a slightly smaller font, raised a little up above and to the right of the base. However, in some formats, like this one, you'll see the base, a mark called a caret that looks like an inverted V, and then the exponent. So if you have a base of 2 and an exponent of 3, we'll write that out here as 2^3 = 8.
Now that you know the terms, let's go back to the zero exponent rule. The zero exponent rule basically says that any base with an exponent of zero is equal to one. For example:
x^0 = 1
Msr walkers class set up an online fund with a goal to raise 1280
Answer: is brainly broken for u too??
Step-by-step explanation:
Edwin works at a fast-food restaurant. Every Tuesday, he helps unload a delivery truck. This
table shows how many boxes of hamburger buns and how many boxes of potatoes he
unloaded last Tuesday,
What is the weight of each box?
Answer:
Each box of buns weighs 18 pounds and each box of potatoes weighs 35 pounds
Step-by-step explanation:
Let's say each bun box weighs b pounds and each potato box weighs p pounds. For each box of buns, we add b pounds. Therefore, for 40 boxes of buns, we add 40 * b pounds. Similarly, for 35 boxes of potatoes, we add 35 * p pounds.
For Tuesday, the total weight of the buns boxes is equal to 40 * b. The total weight of the potato boxes is equal to 35 * p. Adding these two together, we get the total weight of the boxes to be equal to
40 * b + 35 * p = 1945
For Friday, we can apply similar techniques to get
60 * b + 70 * p = 3530
We therefore have the two equations
40 * b + 35 * p = 1945
60 * b + 70 * p = 3530
One way to solve this would be to convert this into a matrix and use Guass-Jordan Elimination. With the amount of bun boxes representing the first column, the amount of potato boxes representing the second, and the total weight of each day representing the third, we have
[tex]\left[\begin{array}{ccc}40&35&1945\\60&70&3530\end{array}\right][/tex]
One thing that we can do here is multiply the first row by -2 and add it to the second. That way, there would be a 0 in the 2nd column in the 2nd row, making an equation of the form
something * b = something else, enabling us to solve for b.
We thus have
[tex]\left[\begin{array}{ccc}40&35&1945\\(-40*2+60)&(-35*2+70)&(-1945*2 +3530)\end{array}\right] = \left[\begin{array}{ccc}40&35&1945\\-20&0&-360\end{array}\right][/tex]
Therefore, we can say that
-20 * b = -360
divide both sides by 20 to isolate b
b = 18
Therefore, each box of bunds weighs 18 pounds. Plugging that into an equation, we have
40 * b + 35 * p = 1945
40 * 18 + 35 * p = 1945
720 + 35 * p = 1945
subtract 720 from both sides to isolate the p and its coefficient
1225 = 35 * p
divide both sides by 35 to isolate p
p = 35
Therefore, each box of potatoes weighs 35 pounds
Cody is a lifeguard and spots a drowning child 40 meters along the shore and 70 meters from the shore to the child. Cody runs along the shore for a while and then jumps into the water and swims from there directly to the child. Cody can run at a rate of 4 meters per second and swim at a rate of 1.1 meters per second. How far along the shore should Cody run before jumping into the water in order to save the child? Round your answer to three decimal places.
Answer:
Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.Thus,
Step-by-step explanation:
Consider the diagram below.
In this case we need to minimize the time it takes Cody to save the child.
Total time to save the child (T) = Time taken along the shore (A) + Time taken from the shore (B)
The formula to compute time is:
[tex]time=\frac{distance}{speed}[/tex]
Compute the time taken along the shore as follows:
[tex]A=\frac{x}{4}[/tex]
Compute the time taken from the shore as follows:
[tex]B=\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]
Then the total time taken to save the child is:
[tex]T=\frac{x}{4}+\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}[/tex]
Differentiate T with respect to x as follows:
[tex]\frac{dT}{dx}=\frac{d}{dx}[\frac{x}{4}]+\frac{d}{dx}[\frac{\sqrt{70^{2}+(40-x)^{2}}}{1.1}][/tex]
[tex]=\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}[/tex]
Equate the derivative to 0 to compute the value of x as follows:
[tex]\frac{dT}{dx}=0[/tex]
[tex]\frac{1}{4}-\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=0\\\\\frac{1}{1.1}\cdot \frac{(40-x)}{\sqrt{70^{2}+(40-x)^{2}}}=\frac{1}{4}\\\\4\cdot (40-x)=1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\\\\\{4\cdot (40-x)\}^{2}=\{1.1\cdot [\sqrt{70^{2}+(40-x)^{2}}]\}^{2}\\\\16\cdot (40-x)^{2}=1.21\cdot [70^{2}+(40-x)^{2}}]\\\\16\cdot (40-x)^{2}-1.21\cdot (40-x)^{2}=5929\\\\14.79\cdot (40-x)^{2}=5929\\\\(40-x)^{2}=400.88\\\\40-x\approx 20.022\\\\x\approx 40-20.022\\\\x\approx 19.978[/tex]
Thus, Cody should run approximately 19.978 meters along the shore before jumping into the water in order to save the child.
Quina is cooking fish for a group of travelers quina has 78 huge fish and each fish can feed 3 travelers. how many travelers can Quina feed?
Answer:
234 people
Step-by-step explanation:
1 fish = 3 people
Multiply each side by 78
1*78 = 3 *78
78 fish = 234 people
Answer:
234 traveling people
Step-by-step explanation:
78 times 3 equals 234
Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs. Enter your answer as an addition equation, like this: 42+(-53)=-11
Answer:
2.75 cups of sugar
Step-by-step explanation:
Hello!
To find the total amount of sugar Dante needs we need to add the amount need for each recipe
Cookie recipe needs 1.5 cups
Brownie recipe needs 1.25 cups
1.5 + 1.25 = 2.75 cups of sugar
The answer is 2.75 cups of sugar
Hope this helps!
Answer:
the answer is 1.5+1.25=1.75
Step-by-step explanation:
i just added them together
your welcome ( it also depends on how many times he uses the recipes)
What the correct answer now
Answer:
527.52 m²
Step-by-step explanation:
The surface area (A) of the cone is calculated as
A = area of base + curved area
= πr² + πrl ( r is the radius and l the slant height )
= 3.14 × 7² + 3.14 × 7 × 17
= 3.14 × 49 + 3.14 × 119
= 3.14(49 + 119)
= 3.14 × 168
= 527.52 m²
Solve without calculator log54 base 10
Step-by-step explanation:
log54 = log(2×3³)
= log2 + log3³
= log2 + 3log3
A beach is 7.3 miles wide and 30 miles long. If one inch of rain falls on this beach, how many cubic feet of rain fell in this area? Hint: convert units to feet first.
Answer:
Step-by-step explanation:
volume=7.3×1760×3×30×1760×3×1/12=73×176×90×440=508780800 ft³
Answer:
508,780,800 ft³ of rain
Step-by-step explanation:
In order to do the computation, we need to express all the given lengths in feet.
recall that 1 mile = 5280 feet
hence,
width = 7.3 miles = 7.3 x 5280 = 38,544 feet
length = 30 miles = 30 x 5280 = 158,400 feet
also recall that 1 inch = 1/12 feet
hence,
depth of rainfall = 1 inch = 1/12 feet
Volume of rain = width of beach x length of beach x depth of rainfall
= 38,544 x 158,400 x (1/12)
= 508,780,800 ft³ of rain
Please help!!! Find the length of MK
Answer:
HK = 42
HM = 23
MK = ??
23 + MK = 42
MK = 19
^^^ so you're correct :)
Let me know if this helps!
Find the area. Round to the nearest tenth.
6 ft
3 ft
12.16 ft
9.16 ft
Answer:
100.5 ft^2
Step-by-step explanation:
First find the area of the rectangle
A = l*w
A = 12.16 * 6
A =72.96 ft^2
Then find the area of the triangle
A = 1/2 bh
The base is 12 ft - 6ft = 6ft
The height is 9.16 ft
A = 1/2 ( 9.16) * 6
A = 27.48 ft^2
Add them together
27.48+72.96
100.44 ft^2
Round to the nearest tenth
100.5 ft^2
Answer:
[tex]\huge \boxed{\mathrm{100.4 \ ft^2 }}[/tex]
Step-by-step explanation:
To find the area of the shape, we can add the area of the rectangle with the area of the triangle.
Area of rectangle :
base × height
6 ft × 12.16 ft
72.96 ft²
Area of triangle :
base × height × 1/2
(12 ft - 6 ft) × 9.16 ft × 1/2
6ft × 9.16 ft × 1/2
27.48 ft²
Adding the areas.
72.96 ft² + 27.48 ft²
100.44 ft²
≈ 100.4 ft² (rounded to nearest tenth)
Which property is shown in the matrix addition below?
5
-1
0
5
-7
0.4
0
-7
0
0.4
+
+
+
6.2
-8.5
-9.9
6.2
-9.9
-8.5
12
0
2
12
0
2
inverse property
identity property
commutative property
associative property
Help please!
Answer:
associative property
The solution is, property is shown in the matrix addition below is
associative property.
Here, we have,
The property shown in the given matrix addition is associative property.
Let's define associative property first,
The Associative Property of Addition for Matrices states :
Let A , B and C be m×n matrices .
Then, (A+B)+C=A+(B+C) .
Associative Law of Addition of Matrix:
Matrix addition is associative. This says that, if A, B and C are Three matrices of the same order such that the matrices B + C, A + (B + C), A + B, (A + B) + C are defined then A + (B + C) = (A + B) + C.
Since P and Q are of the same order and pij = qij then, P = Q.
Here, from the given information,
we get, A , B and C be 4×1 matrices,
and, (A+B)+C=A+(B+C)
So, The solution is, property is shown in the matrix addition below is
associative property.
To learn more on matrix click:
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What is the value of this expression when c = -4 and d = 10?
Answer:
[tex]\Large \boxed{\mathrm{\bold{B. \ 9}}}[/tex]
Step-by-step explanation:
Plug in c = -4 and d = 10 for the expression.
1/4(-4³ + 10²)
Evaluate the expression.
1/4(-64 + 100)
1/4(36)
36/4 = 9
Answer:
[tex]\huge\boxed{B. \ \ 9}[/tex]
Step-by-step explanation:
1/4 (c³ + d²)
Given that c = -4 and d = 10
1/4 ( -4³ + 10²)
1/4 ( -64+100)
1/4 ( 36 )
=> 9
BRAINLIEST
HOW CAN POSTULATES AND THEOREMS RELATING TO SIMILAR AND CONGRUENT ANGLES BE USED TO WRITE A PROOF?
Answer:
How can postulates and theorems relating to similar and congruent triangles be used to write a proof? If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar. ... If the three sets of corresponding sides of two triangles are in proportion, the triangles are similar.
Step-by-step explanation:
Hope this helps :D good luck!!
You land a job as an police officer. Your salary for the 1st year is $43,125. You will receive a 7% increase every year. How much will your salary be at the start of year six?
Answer:
Salary after 5 year(A) = $60,485 (Approx)
Step-by-step explanation:
Given:
Staring salary(P) = $43,125
Growth rate(r) = 7%
Number of year (n) = (6-1) = 5
Find:
Salary after 5 year(A)
Computation:
[tex]A=P(1+r)^n \\\\ A = 43125(1+0.07)^5 \\\\ A = 60485[/tex]
Salary after 5 year(A) = $60,485 (Approx)
If x^a=y^b=z^c and y^2=zx ,show that :. 1 by a + 1 by c = 2 by b.
Answer:
1/a + 1/c = 2/b
Step-by-step explanation:
.......................
The distance of planet Mercury from the Sun is approximately 5.8. 107 kilometers, and the distance of planet Venus from the Sun is 1.1. 10 kilometers. About how many more kilometers is the
distance of Venus from the Sun than the distance of Mercury from the Sun?
Answer:
I would say about 5 times but I am not sure so if it is wrong am sorry.
A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total admission revenue, not including sales tax, and had a total of 450 guests. The system of equations below can be used to model the number of guests that were children, x, and the number of guests that were adults, y.
Answer:
Answer on Edmentum! :)
Step-by-step explanation:
Hope this helps!
The number of children were 172 and number of adults were 278.
What is linear equation?An equation that makes a straight line when it is graphed.
Given that, A local museum charges $25 per adult and $12 per child for admission fees. At the end of a day, the museum made $9,014 in total admission revenue, not including sales tax, and had a total of 450 guests
According to question,
12x+25y = 9014
x+y = 450
Solving using elimination method, we get,
x = 172 and y = 278
Hence, The number of children were 172 and number of adults were 278.
For more references on linear equation, click;
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which of the following statements must be true about this diagram ? check ALL that apply
Answer:
Check A, B and DStep-by-step explanation:
A. m∠4 = 180° - m∠3
m∠1 = 180° - (m∠3 + m∠2)
m∠3 < m∠3 + m∠2 ⇒ m∠4 >m∠1
B. m∠4 = 180° - m∠3
m∠2 = 180° - (m∠3 + m∠1)
m∠3 < m∠3 + m∠1 ⇒ m∠4 >m∠2
C. Not necessarily {could be but not always}
D. m∠4 = 180° - m∠3
m∠1 + m∠2 + m∠3 = 180° ⇒ m∠1 + m∠2 = 180° - m∠3 = m∠4
E. m∠3 = m∠1 + m∠2 only if m∠3 = 90°
F. Not necessarily. {Could be but also could not be. In the picture is, but we don't know if the diagram is accurate or just approximate.}
does it matter in what order we divide our our prime factors explain
Answer:
No, it does not matter.
Step-by-step explanation:
In prime factorization there is only one way to be factored. Once these numbers are broken down, into prime numbers you will get the same result no matter what list of prime numbers you use and what order you use them in.
Factor completely x3 + 8x2 − 3x − 24. (x − 8)(x2 − 3) (x + 8)(x2 + 3) (x − 8)(x2 + 3) (x + 8)(x2 − 3)
Answer:
(x + 8) (x² - 3)
Step-by-step explanation:
Given:
x³ + 8x² - 3x - 24
Find:
Factors
Computation:
x³ + 8x² - 3x - 24
x²(x + 8) -3(x + 8)
(x + 8) (x² - 3)
Factor of the given equation is (x + 8) (x² - 3)
Answer:
(x + 8) (x² - 3)
Step-by-step explanation:
Ethan bought 4 packages of pencils. After he gave 8 pencils to his friends, he had 40 pencils
left over. How many pencils were in each package? Use the drop-down menus to solve the
problem arithmetically and algebraically.
Answer:
12
Step-by-step explanation:
Because you add 8 to the 40 which is 48 then divide equaling 12
Answer:
12
Step-by-step explanation:
40+8=48
48/4=12
What is the solution for 5x-9 is less than or equal to 21
Answer:
Step-by-step explanation:
5x - 9 <= 21
5x <=30
x <= 6
A geometric series has a common ratio of (-2) and the first term is 3.
Show that the sum of the first eight positive terms of the series is 65 535.
Answer:
see explanation
Step-by-step explanation:
The sum to n terms of a geometric series is
[tex]S_{n}[/tex] = [tex]\frac{a_{1}(r^{n}-1) }{r-1}[/tex]
where a₁ is the first term and r the common ratio
Given a₁ = 3 and r = - 2 , then
3 × - 2 = - 6
- 6 × -2 = 12
12 × - 2 = - 24
- 24 × - 2 = 48
48 × - 2 = - 96
- 96 × - 2 = 192
The positive terms are in a geometric progression
3, 12, 48, 192, ....
with a₁ = 3 and r = 12 ÷ 3 = 48 ÷ 12 = 4 , then
S₈ = [tex]\frac{3(4^{8}-1) }{4-1}[/tex] = [tex]\frac{3(65536-1)}{3}[/tex] = 65536 - 1 = 65535
the area of a parallelogram is 48cm².if the two adjacent sides are 8cm and 6cm, find the length of its diagonal .
Answer:
10cm
Step-by-step explanation:
Assuming the shape is a rectangle since it's already stated that it's a parallelogram, and the area is stated, we can use the Pythagorean theorem to find the length
[tex]a^{2} +b^2=c^2[/tex], where c will be the length
isolate c
[tex]c^2=a^2+b^2[/tex]
[tex]c=\sqrt{a^2+b^2}[/tex]
substitute for a and b
[tex]c=\sqrt{8^2+6^2}[/tex]
[tex]c=\sqrt{64+36}[/tex]
[tex]c=\sqrt{100}[/tex]
[tex]c=10[/tex]
2 divided by 3 + 2 divedes by 3 +3 divided by 3 =?
Answer:
1/5
Step-by-step explanation:
1/5
2/3+3/3+4/3
=2/5*3/6
= 1/5
I'm not sure.
Answer:
The answer should be 0.022
whats the factored form of 6x 2 - 8x - 8 = 0
Answer:
2(x -2)² = 0
Step-by-step explanation:
2(x² - 4x - 4) = 0
2(x -2)² = 0
x = 2
Answer:
[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]
The factored form of [tex]6x^2-8x-8=0[/tex] is [tex]2(3x-2)(x+2)=0[/tex]
Step-by-step explanation:
[tex]6x^2-8x-8=0[/tex]
The way the quadratic equation was given, we can't have a factored form in the format: [tex](ax-b)(cx+d)[/tex]
First, divide both sides by 2
[tex]3x^2-4x-4=0[/tex]
Now, it is about thinking. From the equation, we will get something in the format: [tex](ax-b)(cx+d)[/tex]
Let's expand this: [tex](ax-b)(cx+d) = acx^2+adx-bcx-bd[/tex]
From here, we can give some values for those variables, based on the quadratic equation [tex]3x^2-4x-4=0[/tex]:
[tex](3x-b)(x+d) = 3\cdot 1\cdot x^2+3dx-b\cdot 1 \cdot x-bd= \boxed{3x^2+3dx-bx-bd}[/tex]
Once we want the middle term to be -4 and bd to be 4, we can easily evaluate the other variables.
[tex](3x-2)(x+2) = 3\cdot 1\cdot x^2+3(2)x-(2)\cdot 1 \cdot x-(2)(2)= \boxed{3x^2+6x-4x-4}[/tex]
Therefore,
[tex](3x-2)(x+2)=3x^2-4x-4[/tex]
But we are not ready yet!
This is the factored form of [tex]3x^2-4x-4=0[/tex], to get the factored form of the problem equation, just multiply the factored form we got by 2.
[tex]2(3x-2)(x+2)=6x^2-8x-8[/tex]
PLEASE ANSWER QUICKLY ASAP
ANSWER QUESTION A
Answer:
2934.46692
Step-by-step explanation:
if you need to round it,
hundrenths: 2,934.47
tenths: 2,934.5
Thousandths: 2,934.467
Hope this helps!
1. Why is f(x)=(3x+13)2+89 not the vertex form of f(x)=9x2+2x+1? 2. What is the vertex of the parabola with the equation y=(x−2)2+10?
Answer:
Step-by-step explanation: u hv 2 make a table for x and y and put in #'s like 1,2,3,4 so u get 1 side of the parabola. x-1, y-11/x-2,y-11/x-3,y-11/x-4,y-14; here u c that u have 2 y's=11 so the points between are the Vertex Points of (2,10)
X has a coefficient, the vertext is (2,10)
pls help me asap!!!!!!!!
Answer:
Center: (9,3)
Radius: 9 units
Step-by-step explanation:
[tex]x^{2} -y^{2} -18x-6y+9=0[/tex]
[tex]x^{2} -18x+81+y^{2} -6y+9=-9+81+9[/tex]
[tex](x-9)^{2} +(y-3)^{2} =81[/tex]
Center: (9,3)
[tex]r^{2} =81[/tex] → [tex]r=9[/tex]
Radius : 9 units
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OAmalOHopeO
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A classroom floor has an area of
(30x^3 + 8x^2, with a width of 2x feet.
What is the length of the floor?
Answer:
15x² + 4x feet
Step-by-step explanation:
We need to calculate (30x³ + 8x²) / 2x.
(30x³ + 8x²) / 2x
= 30x³ / 2x + 8x² / 2x
= 15x² + 4x