[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 12x^4\cdot -\cfrac{5}{6x^3y^2}\implies -\cfrac{12\cdot 5\cdot x^4}{6x^3y^2}\implies -\cfrac{12}{6}\cdot \cfrac{5}{1}\cdot \cfrac{x^4}{x^3y^2}\implies -2\cdot 5\cdot \cfrac{x^4x^{-3}}{y^2} \\\\\\ -10\cdot \cfrac{x^{4-3}}{y^2}\implies -10\cdot \cfrac{x}{y^2}\implies -\cfrac{10x}{y^2}[/tex]
pleass answer the following
The picture is blurry I could help but I can’t really see it
PLEASE ANSWER ASAP
Solve graphically the system of linear equations:
x+2y=4
−2x+5y=10
The system of linear equations, \(x + 2y = 4\) and \(-2x + 5y = 10\), was solved graphically. The lines intersect at (2, 1), yielding the solution \(x = 2\) and \(y = 1\).
To solve the system of linear equations graphically, we'll plot the lines corresponding to each equation and find their point of intersection, which represents the solution to the system.
Let's rearrange the equations to be in slope-intercept form (\(y = mx + b\)) for ease of graphing:
a. \(x + 2y = 4\)
\[ 2y = -x + 4 \]
\[ y = -\frac{1}{2}x + 2 \]
b. \(-2x + 5y = 10\)
\[ 5y = 2x + 10 \]
\[ y = \frac{2}{5}x + 2 \]
Now, we'll plot these lines on the graph:
The graph shows that the two lines intersect at the point \((2, 1)\). Therefore, the solution to the system of linear equations is \(x = 2\) and \(y = 1\).
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Can anyone find what A = ______ m square?
Answer:
B. 16pi
Step-by-step explanation:
Lets input our radius int the formula. pi*4^2. 4^2 is 16 so the answer is 16pi.
Which two blue rectangles have the same total area as the red rectangle
D is the correct answer
Answer: D
Hope this Helps!
maureen purchased a watch for a sale price of $24. the price was 20% off its original price.which expression computes the original price of the watch? (answer choices A. $24 x 0.20 B. $24 x (1 - 0.20) C. $24 ÷ (1 - 0.20) D. $24 ÷ 0.20)
A might be the answer because 20%of 24 = 4.8 and 24×0.20 give you 4.8
if f(x)=3x+5/x, what is f9a+2)
A. 3(a+2)+8/a+2
B. 3(f(a))+5/f(a)+2
C. 3a+5/a+2
Answer:
b
Step-by-step explanation:
For this case we have a function of the form [tex]y = f (x)[/tex], where:
[tex]f (x) = 3x + \frac {5} {x}[/tex]
You want to find the value of the function to:
[tex]x = a + 2[/tex]
That is to say:
[tex]f (a + 2) = 3 (a + 2) + \frac {5} {a + 2}[/tex]
Rewriting we have:
[tex]f (a + 2) = 3a + 6 + \frac {5} {a + 2}[/tex]
ANswer:
[tex]f (a + 2) = 3 (a + 2) + \frac {5} {a + 2}[/tex]
Is the following shape a right triangle? How do you know?
Answer:
Yes
Step-by-step explanation:
A has a right angle because A on the triangle is turned at a 90 degree angle.
Answer:
B) Yes , two sides are perpendicular and side length fir the Pythagorean theorem.
Step-by-step explanation:
Given : A triangle on the graph.
To find : Is the following shape a right triangle? How do you know.
Solution : We have given that
A triangle ABC We need to explain is it right triangle or not.
Right triangle : A triangle which have two sides perpendicular or one of the angle is 90 degree.
We can see from the graph side AB and AC are perpendicular to each other.
Therefore, B) Yes , two sides are perpendicular and side length fir the Pythagorean theorem.
solve for x (-3+5) - (6x-8)
Answer:
-6x +10
Step-by-step explanation:
(-3+5) - (6x-8)
We cannot solve since there is no equals sign, we can only simplify
Combine the -3 and the 5 in the parentheses
(2) - (6x-8)
2 - (6x-8)
Distribute the minus sign
2 -6x +8
-6x +10
What is the slope of the line that passes through point (3,2) and point (6,11)?
Answer: 3
The work is shown in the attached sheet! :)
Answer:
slope is 3
Step-by-step explanation:
What is the denominator of the fraction 4/7
A denominator is the number that a fraction is being divided by, or the number below the line is a fraction. In this case the denominator is 7.
Answer:
7
Step-by-step explanation:
It’s the bottom number
A triangular pyramid has a height of 18 yards and a base with an area of 330 square yards. What is the volume of the pyramid?
A. 660 yd
B. 2,970 yd
C. 1,980 yd
D. 5,940 yd
Final answer:
The volume of the triangular pyramid is calculated using the formula V = 1/3 × base area × height. With a base area of 330 square yards and height of 18 yards, the volume is found to be 1,980 cubic yards. Therefore, the correct answer is C.
Explanation:
The volume of a triangular pyramid can be calculated using the formula V = 1/3 × base area × height. Given that the base area is 330 square yards and the height of the pyramid is 18 yards, we can calculate the volume by substituting these values into the formula: V = 1/3 × 330 × 18 = 1980 cubic yards. Therefore, the correct answer is C. 1,980 yd³.
The volume of the triangular pyramid is 1,980 cubic yards, making the correct answer option C.
To find the volume of the triangular pyramid, we first need to determine the area of the base triangle. Since the base has an area of 330 square yards, we can use the formula for the area of a triangle, which is 1/2 * base * height. Let's denote the base of the triangle as b and the height as h. We can rearrange the formula to solve for b:
[tex]\[ 330 = \frac{1}{2} \times b \times h \][/tex]
Given that the height of the pyramid is 18 yards, we can plug this value in and solve for the base:
[tex]\[ 330 = \frac{1}{2} \times b \times 18 \][/tex]
330 = 9b
[tex]\[ b = \frac{330}{9} \][/tex]
b = 36.67
Now, we have the base length of the triangle. Next, we can calculate the volume of the pyramid using the formula for the volume of a pyramid, which is [tex]\( \frac{1}{3} \times base\ area \times height \)[/tex]. Let's denote the volume as V:
[tex]\[ V = \frac{1}{3} \times 330 \times 18 \][/tex]
V = 1980
So, the volume of the pyramid is 1980 cubic yards. Therefore, the correct answer is option C: 1,980 yd.
Plz help i need it!!
Answer: c) 19,807
Step-by-step explanation:
[tex]A=A_o\cdot e^{kt}\\\\\bullet A_o\text{ is the initial population}\\\bullet \text{k is the rate of decrease}\\\bullet \text{t is the number of years after 2010}\\\\A=22,000\cdot e{(-0.021)(5)}\\.\ =22,000\cdot e^{-0.105}\\.\ =19,807[/tex]
Where is the location of the vertex of the parabola on a coordinate grid y=x^2+2x+1
Answer:
(-1,0)
Step-by-step explanation:
Convert the equation to vertex form which becomes y=(x+1)^2+0
Then we can see the vertex in the form (h,k) in y=a(x-h)^2+k
[tex](-1,0)[/tex]
Explication pas à pas:
Convertir l'équation en forme de sommet qui devient [tex]y = (x + 1) ^ 2 + 0[/tex]
Ensuite, nous pouvons voir le sommet sous la forme (h, k) dan
[tex]y = a (xh) ^ 2 + k[/tex]
What is the distance on a number line between 17 and −9.
the distance between them is 26
Can someone help me Solve these problems :(((
1.x+ 20 = -32
2.w+10=25
3.7.2 + b = 12
4.5.3 + s = 15
5.p + (-25) = -10
6.m + (-1.6) = -4.8
x=-52
w=15
b=4.8
s=9.7
p=15
m=3.2
Q1.
[tex]x + 20 = - 32[/tex]
Add -20 to both sides of the equation.
[tex]x + 20 - 20 = - 32 - 20[/tex]
Simplify
[tex]x = - 52[/tex]
Q2.
[tex]w + 10 = 25[/tex]
Add -10 to both sides of the equation.
[tex]w + 10 - 10 = 25 - 10[/tex]
[tex]w = 15[/tex]
Q3.
[tex]7.2 + b = 12[/tex]
Add -7.2 to both sides of the equation.
[tex] - 7.2 + 7.2 + b = 12 - 7.2[/tex]
[tex]b = 4.8[/tex]
Q4.
[tex]5.3 + s = 15[/tex]
Add -5.3 to both sides to get,
[tex]s + 5.3 - 5.3 = 15 - 5.3[/tex]
Simplify:
[tex]s = 9.7[/tex]
Q5.
[tex]p + ( - 25) = - 10[/tex]
Add 25 to both sides,
[tex]p - 25 + 25 = - 10 + 25[/tex]
[tex]p = 15[/tex]
Q6.
[tex]m + - 1.6 = -4.8[/tex]
Add 1.6 to both sides of the equation;
[tex]m + - 1.6 + 1.6 = - 4.8 + 1.6[/tex]
[tex]m = - 3.2[/tex]
Please help I have school in 20 mins and I have a lot of homework I never finished
Answer: The correct answer is H.
Step-by-step explanation: The first step is to calculate how much he is going to pay 28% on. The difference between $3,775 and $3,523 = $252.
The formula to calculate his total taxes = .28 x $252 + $699.65.
$70.56 + $699.65 = $770.21, which is the total federal taxes that he needs to pay.
Next, to determine the amount he will receive you need to subtract the taxes from his gross income. $3,775 - $769.65 = $3,004.79 Net Income
Answer:
h
Step-by-step explanation:
which of the following properties is ALWAYS TRUE for a parallelogram?
Answer:
all sides are parallel to the other,has four sides
Step-by-step explanation:
Write a polynomial expression that represents the area of the trapezoid [a= 1/2h(b1+b2)]
Answer:
1/2*(x+1)[(6x+5)+(4x+7)}
Step-by-step explanation:
The area of a trapezoid can be expressed as a polynomial using the formula a = 1/2h(b1+b2), where 'a' is the area, 'h' is the height, and 'b1' and 'b2' are the base lengths. If h=x, b1=y, and b2=z, then the polynomial expression for the area is a=0.5xz(y+z).
Explanation:The area of a trapezoid can be expressed in the form of a polynomial by using the formula a = 1/2h(b1+b2), where 'a' represents the area, 'h' is the height of the trapezoid, and 'b1' and 'b2' are the lengths of the parallel sides. Expressing this as a polynomial expression, we could have variables in place of the height and side lengths, depending on the specific trapezoid. For example, if h = x, b1 = y, and b2 = z, then the polynomial expression for the area of the trapezoid becomes a = 0.5xz(y+z).
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Solve for r. 13 = r (34 - 2) show your work
Answer:
For the (), it is 32. r = 13.
Step-by-step explanation:
32 - 13 = 19.
Thomas has an album that holds 600 baseball cards each page of the album holds 6 cards. If 45% of the album is empty, how many pages are filled with baseball cards
Answer:
55 pages
Step-by-step explanation:
Knowing that the book holds 600 cards and 6 cards/page, we can tell that there are 100 pages.
From that, we know that 45% are empty, which means 55% of all of the pages have cards.
55% of 100 is 55. Therefore, 55 pages have baseball cards.
Final answer:
To find out how many pages of Thomas's album are filled with baseball cards, we first calculate the number of filled card slots and then divide by the number of slots per page, resulting in 55 filled pages.
Explanation:
Thomas has an album that holds 600 baseball cards, and each page of the album holds 6 cards. If 45% of the album is empty, we first calculate how many cards are in the filled portion of the album, and then determine how many pages are filled with baseball cards.
First, find 45% of 600 to determine the number of empty slots: 0.45 × 600 = 270. Therefore, there are 270 empty slots for baseball cards. To find the number of filled slots, subtract this number from the total capacity: 600 - 270 = 330 filled slots.
Since each page holds 6 cards, to find out how many pages are filled, divide the number of filled slots by the number of slots per page: 330 ÷ 6 = 55. Therefore, Thomas has filled 55 pages with baseball cards.
then
rue?
6. Use the coordinates to prove the most
precise classification for the
quadrilateral.
A(-3,1), B(0,5), C(4,2), D(1,-2)
Answer:
Square
Step-by-step explanation:
You can use the distance formula from one point to another to find that the side lengths are all equals.
You can also graph it and see that it is a triangle.
With these coordinates, this shape is most likely a square. You can also tell from the distance between each point as they are equal. Graphing calculator: Desmos.com
If the sum of two congruent lengths equal the length of a third side,then the triangle created is isosceles. Is this a true statement?
Answer:
No; statement is FALSE.
Step-by-step explanation:
If two congruent (equal length) sides of a triangle sum up to the length of the third side, we have a flat (2-dimensional) figure that is NOT a triangle. So this statement is FALSE.
Jules add a border around his mirror. The mirror is shaped like a triangle each side is 35 cm long how long is the border
Answer:
The border is 105 cm long
Step-by-step explanation:
The length of the border of the mirror is 105 cm.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
The mirror is in the shape of a triangle.
Each side of the triangle.
Now,
The perimeter of the mirror.
= 3 x side
= 3 x 35 cm
= 105 cm
Thus,
The length of the border is 105 cm.
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Whats the square root of 42???
Answer:
6.48074069841
Step-by-step explanation:
We can enter this on a calculator or can be estimated
Which exponential function has an initial value of 2? f(x) = 2(3x) f(x) = 3(2x)
Answer:
X=2 F=6 This works for both equations. Hope this helps!
Step-by-step explanation:
Answer:
The exponential function [tex]f(x)=2(3^x)[/tex] has an initial value of 2. The correct option is 1.
Step-by-step explanation:
The general form of an exponential function is
[tex]g(x)=ab^x[/tex]
Where, a is initial value and b is growth or decay factor.
In option 1, the given function is
[tex]f(x)=2(3^x)[/tex]
Here, the initial value is 2 and growth factor is 3. Therefore the correct option is 1.
In option 2, the given function is
[tex]f(x)=3(2^x)[/tex]
Here, the initial value is 3 and growth factor is 2. Therefore option 2 is incorrect.
help with this question please
ty
4(2x-5) is the answer
answer: 4(2x - 5)
explanation: if you don’t know how to factor gcf, look it up. But you need to find the gcf of 8 and 20 which is 4. Then you just get your answer. Sorry this is hard to explain but a tip is to distribute and check to see that it matches the original problem to find out if your answer is right. I will do that for this. 4(2x - 5) I use distributive property here meaning I distribute the 4 to both terms. 4 times 2x is 8x. 4 times negative 5 is negative 20. That leaves me with the original equation 8x - 20 so the answer is correct.
How much of the purchase will they have to borrow
Answer:
They will have to borrow $ 31,211
(23% of the purchase price)
Step-by-step explanation:
Total price : $135,700
Down payment: 20% of total price
Closing costs : 3% of total price
The Colburns will have to borrow 23% of the total price.
0.23*$135,700 = $ 31,211
X=-42 what slope if a line is perpendicular to it and what slope of the line is parallel
Answer:
Parallel is undefined
Perpendicular is 0
Step-by-step explanation:
The line x = -42 is a vertical line through the x-axis. As such its slope is undefined. All parallel lines have the same slope and will also be undefined. Perpendicular lines will be lines horizontal through the y-axis. This means the slope of any perpendicular line to it will be 0.
find the value of y when x equals 0 , -3x-9y=36
Answer:
-3x - 9y = 36
If x = 0
Step-by-step explanation:
1. Plug 0 to x:
-3(0) - 9y = 36
2. Simplify
0 - 9y = 36
3. Cross out the 0 to make the question faster to solve, which now you are left with:
-9y = 36
4. Divide both sides by -9:
-9y/-9 = 36/-9
5. Simplify:
y = -4 <--------Answer
Hope this Helped!!!!!
~Shane
The value of y when x equals 0 in the equation -3x - 9y = 36 is -4.
To find the value of y when x equals 0 in the equation -3x - 9y = 36, we can simply substitute 0 for x and solve for y.
Substituting 0 for x, the equation becomes:
-3(0) - 9y = 36
This simplifies to:
-9y = 36
Dividing both sides of the equation by -9, we get:
y = 36 / -9
This gives us:
y = -4
Therefore, the value of y when x equals 0 is -4.
17........................
Answer:
Step-by-step explanation:
First, add 3 to both sides:
-5 = -6∛(x²)
Next, divide both sides by -6, to isolate ∛(x²):
5/6 = ∛(x²)
Eliminate the radical by cubing both sides:
5³
---- = x²
6³
Finally, take the square root of both sides. This will isolate x. There will be two roots: one +, the other -.
x = ±√(5³/6³)
This simplifies to: ± (5/6)∛(5/6).
Answer:
a. [tex]0.76,-0.76[/tex]
Step-by-step explanation:
The given equation is;
[tex]-8=-3-6\sqrt[3]{x^2}[/tex]
Add 3 to both sides of the equation to get;
[tex]-8+3=-3+3-6\sqrt[3]{x^2}[/tex]
[tex]\Rightarrow -5=-6\sqrt[3]{x^2}[/tex]
Divide both sides by -6.
[tex]\Rightarrow \frac{-5}{-6}=\sqrt[3]{x^2}[/tex]
[tex]\Rightarrow \frac{5}{6}=\sqrt[3]{x^2}[/tex]
Cube both sides of the equation;
[tex]\Rightarrow (\frac{5}{6})^3=x^2[/tex]
[tex]\Rightarrow \frac{125}{216}=x^2[/tex]
Take square root of both sides
[tex]\pm \sqrt{\frac{125}{216}}=x[/tex]
[tex]\pm 0.76=x[/tex]
[tex]\therefore x=0.76,-0.76[/tex]