Can someone please explain this for me I’m
Not sure of the steps. See photo above
Answers
[tex]\bf \cfrac{x^8}{x^{14}}\implies x^8x^{-14}\implies x^{8-14}\implies x^{-6}\implies \stackrel{\textit{using the power rule}}{-6x^{-7}\implies \cfrac{-6}{x^7}}[/tex]
Question 1:
We have the following expression:
[tex]4x ^ {-4}[/tex]
By definition of power properties we have to:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then, rewriting the expression:
[tex]\frac {4} {x ^ 4}[/tex]
ANswer:
[tex]\frac {4} {x ^ 4}[/tex]
Question 2:
For this case we have the following expression:
[tex]\frac {x ^ 8} {x ^ {14}} =[/tex]
By definition of power properties of the same base we have:
[tex]x ^ n * x ^ m = x ^ {n + m}[/tex]
Then, we can rewrite the denominator of the expression as:
[tex]\frac {x ^ 8} {x ^ 8 * x ^ 6} =[/tex]
Simplifying terms of the numerator and denominator:
[tex]\frac {1} {x ^ 6}[/tex]
ANswer:
[tex]\frac {1} {x ^ 6}[/tex]
Related Questions
6 = 3x - 9
x + 4 < 1
x/2 + 3 = -5
Answers
Answer:
see explanation
Step-by-step explanation:
1
6 = 3x - 9 ( add 9 to both sides )
15 = 3x ( divide both sides by 3 )
5 = x
2
x + 4 < 1 ( subtract 4 from both sides )
x < - 3
3
[tex]\frac{x}{2}[/tex] + 3 = - 5
Multiply terms on both sides by 2
x + 6 = - 10 ( subtract 6 from both sides )
x = - 16
Find the tan θ when sin θ= -cos θ and θ is in quadrant IV
Answers
Answer:
Step-by-step explanation:
sin θ= - cos θ
if : cos θ ≠ 0
you have : tan θ = -1
tan θ = - tan π/4
tan θ = tan(- π/4 )
θ = - π/4 +kπ k ∈ Z
calculate: k when θ is in quadrant IV : 3π /2 ≤ θ ≤2π
3π /2 ≤ - π/4 +kπ ≤2π
add π/4: 3π /2 + π/4 ≤ - π/4 +kπ+π/4 ≤2π +π/4
7π/4 ≤ kπ ≤9π/4
7/4 ≤ k ≤9/4
1.75 ≤ k ≤ 2.25
k ∈ Z : k =2
so : θ = - π/4 +2π
θ = 7π/4
θ = 7(180°)/4 = 315°
Which pair of points will determine a line
parallel to the x-axis?
(1) (2,3), (2,-5)
(2) (5, 4), (-1, 4)
(3) (2, 2), (-1, -1)
(4) (3, 4), (6,2)
Please help I don’t get it I’m stuck:(
Answers
Answer:
2) (5,4) and (-1,4)
These have the same y so this line will be horizontal making it parallel to the x-axis.
Step-by-step explanation:
All horizontal lines are parallel to each other. The x-axis is horizontal. So we are looking for a horizontal line. On a horizontal line, all the y-coordinates are the same; their equation is in the form y=a number after all.
Anyways we looking for a pair of points with the same y-coordinate.
1) (2,3) and (2,-5)
These have the same x-coordinate so this line is vertical. This would actually be perpendicular to the line given.
2) (5,4) and (-1,4)
These have the same y so this line will be horizontal making it parallel to the x-axis.
3) (2,2) and (-1,-1)
y's aren't the same so not horizontal
x's aren't the same so not vertical
4) (3,4) and (6,2)
y's aren't the same so not horizontal
x's aren't the same so not vertical
For a pair of points to be parallel to the x-axis, the points have to consist the same x-coordinates.
In this case, only (1) (2,3), (2,-5) have the same x-coordinates.
Therefore, the answer is (1) (2,3), (2,-5).
Hope it helps!
What are the solutions to the equation 3(x-4)^2=27
Answers
Answer:
x=1, x=7
Step-by-step explanation:
Firstly, you can simplify by dividing both sides by 3, which will make the equation easier to simplify:
(x-4)^2=9
Next, you can take the square root of each side, which will cancel the square, and make the 9 even easier to work with:
(x-4)=(± )3
*Note the (± ) sign, this is because there is a positive and negative answer*
After this, you will basically have two equations:
(x-4)=3
and
(x-4)=-3
You are going to solve both to get both answers, but lets start with the positive first:
x-4=3 Add 4 to both sides to get an x= equation
x=7
And it's the same thing for the negative:
x-4=-3 Add 4 to both sides to get an x= equation
x=1
Hope this helps
Final answer:
To solve the equation 3(x-4)²=27, divide by 3 to get (x-4)²=9, then take the square root to find the solutions x=7 and x=1.
Explanation:
When we're tasked with solving a quadratic equation, such as 3(x-4)²=27, we first need to get it into the standard form of a quadratic equation, which is ax² + bx + c = 0. To do so in this case, we can divide both sides of the equation by 3 to isolate the squared term, yielding (x-4)²= 9. We then take the square root of both sides, giving us x - 4 =3. Solving for x results in two solutions: x = 4 + 3 and x = 4 - 3, which simplifies to x = 7 and x = 1 respectively. These are the solutions to the given equation.
To verify these solutions, you can substitute them back into the original equation to ensure that they satisfy the equation, which in this case, they will. This critical step confirms the accuracy of our solutions.
Which solid has six faces, four lateral faces, two bases, eight vertices, and 12 edges?
square pyramid
triangular prism
rectangular prism
triangular pyramid
Answers
Rectangular prism: 6 faces (4 lateral, 2 bases), 8 vertices, 12 edges, meeting all criteria specified.
let's break down the characteristics of each of the options provided:
1. **Square Pyramid**:
- Faces: A square pyramid has five faces. It has a square base and four triangular faces.
- Vertices: A square pyramid has five vertices.
- Edges: A square pyramid has eight edges (the base square has four edges, and each triangular face has one edge).
2. **Triangular Prism**:
- Faces: A triangular prism has five faces. It has two triangular bases and three rectangular lateral faces.
- Vertices: A triangular prism has six vertices.
- Edges: A triangular prism has nine edges (three on each base triangle and three connecting the lateral faces).
3. **Rectangular Prism**:
- Faces: A rectangular prism has six faces. It has two rectangular bases and four rectangular lateral faces.
- Vertices: A rectangular prism has eight vertices.
- Edges: A rectangular prism has 12 edges (four on each base rectangle and four connecting the lateral faces).
4. **Triangular Pyramid**:
- Faces: A triangular pyramid has four faces. It has a triangular base and three triangular lateral faces.
- Vertices: A triangular pyramid has four vertices.
- Edges: A triangular pyramid has six edges (three on the base triangle and three connecting the lateral faces).
Given the characteristics you provided: six faces, four lateral faces, two bases, eight vertices, and 12 edges, we can eliminate the options of square pyramid and triangular pyramid because they don't fit all the criteria.
Now let's look at the remaining options:
- **Triangular Prism** has five faces, six vertices, and nine edges. It doesn't match the given criteria.
- **Rectangular Prism** has six faces (two bases and four lateral faces), eight vertices, and 12 edges, which perfectly matches all the provided characteristics.
Therefore, the correct answer is the **Rectangular Prism**.
NEED HELP ASAP (RADICALS)
Order from least to greatest:
[tex]\sqrt{9}[/tex]
-6[tex]\sqrt{5}[/tex]
5[tex]\sqrt{3}[/tex]
-5[tex]\sqrt{6}[/tex]
Answers
According to the rational root theorem what are all the potential rational roots of f(x)=9x^4-2x^2-3x+4
Answers
Answer:
+/- 1, [tex]\frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9}[/tex] ....
Step-by-step explanation:
The Rational root theorem states that If f(x) is a Polynomial with integer coefficients and if there exist a rational root of the form p/q then p is the factor of the constant term of the function and q is the factor of the leading coefficient of the function
Given: f(x)= 9x^4-2x^2-3x+4
Factors of q (leading coefficient) are: +/-9, +/-3, +/-1
Factors of p (constant term) are: +/-4 , +/-2, +/- 1
According to the theorem we write the roots in p/q form:
Therefore,
p/q =+/- 1, [tex]\frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9}[/tex] ....
What is the value of b in the equation below?
5^6/5^2=a^b
3
4
5
8
Answers
Answer:
b=4
Step-by-step explanation:
subtract the exponents
6-2=4
The value of b is 4.
What is exponent ?Exponent is a mathematical method to express large numbers in power form. It will describe how many times a number multiplied by itself.
Example : 7⁵ , where the number 7 multiplied 5 times by itself.
What is the required value of b ?Given, 5⁶/5² = 5ᵇ
We know that, in exponent, if [tex]a^{m}=a^{n}[/tex], then m=n
Here, 5⁶/5² = 5ᵇ
⇒ [tex]5^{6-2} =5^{b}[/tex]
⇒ [tex]5^{4} =5^{b}[/tex]
∴ By the above rule, b = 4
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What is a requirement of supplementary angles?
Answers
Answer:
Two Angles are Supplementary when they add up to 180 degrees.
Step-by-step explanation:
Notice that together they make a straight angle.
Cecilia correctly solved this inequality.
3x > 102
X> 34
Which graph matches the inequality?
28 29 30 31 32 33 34 35 36 37 38 39 40
28 29 30 31 32 33 34 35 36 37 38 39 40
Answers
The graph of the inequality x > 34 is graphed
What is an inequality?An inequality is an expression that shows the non equal comparison of two or more numbers and variables.
Given the inequality:
3x > 102
Divide the inequality by 3:
x > 34
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which function results after applying the sequence of transformations to f(x) = x^5
Answers
This is the final function f(x) = (-2(x-2))^5 after a horizontal shrink, reflection, and shift.
To determine which function results after applying a given sequence of transformations to the original function f(x) = x^5, we need to apply each transformation in the correct order. Transformations affect the graph and the function's formula. Here is how you would apply the transformations in the correct order:
f(2x): Multiply the independent variable by 2, which shrinks the graph horizontally by half. The function becomes f(x) = (2x)^5.
f(-2x): Negate the independent variable x, which flips the graph across the y-axis. The function becomes f(x) = (-2x)^5.
f(-2x-2): Subtract 2 from the result of -2x. This is incorrect as the sequence of operations should reflect transformations applied directly to the independent variable x. Instead, it should be f(x-2) after step (ii), which translates the graph to the right by 2 units.
If we were to correct the third operation and apply the transformations properly, the resulting function after applying a horizontal shrink, reflection across the y-axis, and horizontal shift would be f(x) = (-2(x-2))^5.
Solve sin2∅=sin∅ on the interval 0≤x< 2[tex]\pi[/tex] .
a. 0,[tex]\frac{\pi }{3}[/tex]
b. 0, [tex]\pi[/tex], [tex]\frac{\pi }{3}[/tex], [tex]\frac{5\pi }{3}[/tex]
c. 0, [tex]\pi[/tex], [tex]\frac{2\pi }{3}[/tex],[tex]\frac{4\pi }{3}[/tex]
d. [tex]\frac{3\pi }{2}[/tex], [tex]\frac{\pi }{2}[/tex],[tex]\frac{\pi }{6}[/tex], [tex]\frac{5\pi }{6}[/tex]
Answers
Answer:
[tex]\large\boxed{b.\ 0,\ \pi,\ \dfrac{\pi}{3},\ \dfrac{5\pi}{3}}[/tex]
Step-by-step explanation:
[tex]\text{Use}\ \sin2x=2\sin x\cos x\\\\\sin2\O=\sin\O\\\\2\sin\O\cos\O=\sin\O\qquad\text{subtract}\ \sin\O\ \text{from both sides}\\\\2\sin\O\cos\O-\sin\O=0\qquad\text{distribute}\\\\\sin\O(2\cos\O-1)=0\iff\sin\O=0\ \vee\ 2\cos\O-1=0[/tex]
[tex]\sin\O=0\iff\O=0\ \vee\ \O=\pi\\\\2\cos\O-1=0\qquad\text{add 1 to both sides}\\\\2\cos\O=1\qquad\text{divide both sides by 2}\\\\\cos\O=\dfrac{1}{2}\iff\O=\dfrac{\pi}{3}\ \vee\ \O=\dfrac{5\pi}{3}[/tex]
Caleb took his sled to the top of the hill. The snow was pure and white. He jumped on the sled and whizzed down the hill. He was so excited. Winter was his favorite season. He went down the hill three times. Each time he traveled ninety feet. How far did he travel on his sled?
Help summer Homework
Answers
He traveled 270 feet. (90 yards)
Jacob is calculating the amount of time it takes a rocket to get to the moom
Answers
Answer:
16 hours
Step-by-step explanation:
Speed=distance/time
Let S be speed, D be distance, and t be time.
Let's solve the speed equation for t since we are looking for time, t.
[tex]S=\frac{D}{t}[/tex]
Multiply both sides by t:
[tex]St=D[/tex]
Divide both sides by S:
[tex]t=\frac{D}{S}[/tex]
So our distance is 239000 and our speed is 250 so plug them in:
[tex]t=\frac{239000}{250}[/tex]
Putting into the calculator now:
t=956 minutes (I knew this was in minutes because the speed was 250 miles per minute)
We need to convert this to hours. 60 minutes=1 hour.
60 minutes=1 hour
956 minutes=x hours
You can setup a proportion if you don't know you just need to take 956 and divide it by 60. Like so:
[tex]\frac{60}{956}=\frac{1}{x}[/tex]
Cross multiply:
[tex]60x=956(1)[/tex]
[tex]60x=956[/tex]
Divide both sides by 60:
[tex]x=\frac{956}{60}[/tex]
Putting into calculator now:
x=15.9333333333333 which mean we have almost 16 hours
Which inequality is not true? -7/8 > -0.50 -7/8 < -0.60 -7/8 < -1/4 -7/8 > -15/16
Answers
help !! I can’t find the answer
Answers
Answer:
385/pi
Step-by-step explanation:
Circumference is given by
C= pi * d where d is the diameter
385 = pi *d
Divide each side by pi
385/pi = pi * d/pi
385/pi = d
Which angle is coternal with 130 degrees?
Answers
Answer:
- 230°
Step-by-step explanation:
A coterminal angle is the given angle ± 360n ( where n is an integer )
Given 130°
Then a coterminal angle = 130° - 360° = - 230°
OR 130° + 360° = 490°
A normal distribution has a mean of 50 and standard deviation of 5. Which value produces a negative z-score?
Answers
Answer:
[tex]x\:<\:50[/tex].
Step-by-step explanation:
The z-score for a normal distribution is calculated using the formula:
[tex]Z=\frac{x-\mu}{\sigma}[/tex].
From the question, the distribution has a mean of 50.
[tex]\implies \mu=50[/tex] and the standard deviation is [tex]\sigma=5[/tex].
For a z-score to be negative, then, [tex]\frac{x-\mu}{\sigma}\:<\:0[/tex].
[tex]\frac{x-50}{5}\:<\:0[/tex].
[tex]x-50\:<\:0\times 5[/tex].
[tex]x-50\:<\:0[/tex].
[tex]x\:<\:0+50[/tex].
[tex]\therefore x\:<\:50[/tex].
Any value less than 50 will produce a negative z-score
A translation is shown on the grid below.
Which are true statements about the translation?
1 The sides of the image and preimage are congruent.
2 The image is turned 90 degrees.
3 The angles in the image are different from the angles in the pre-image
4 The image is a slide of the preimage.
5 The image has a different shape than the pre-image
6 Each point has moved in a different direction.
7 Each point has moved the same number of units.
Answers
Answer:
The correct options are 1, 4 and 7.
Step-by-step explanation:
From the given figure it is clear that the vertices of preimage are A(-4,2), B(-4,-2) and C(-1,-2).
The vertices of image are A'(1,5), B'(1,1) and C'(4,1).
The relation between vertices of preimage and image is defined by the rule
[tex](x,y)\rightarrow (x+5,y+3)[/tex]
It means the figure ABC translated 5 units right and 3 units up.
Translations a rigid transformation. It means the size and shape of image and preimage are same.
We can say that,
(a) The sides of the image and preimage are congruent.
(b) The angles in the image and angles in the pre-image are same.
(c) The image is a slide of the preimage.
(d) The image and pre-image have same shape.
(e) Each point has moved in same direction.
(f) Each point has moved the same number of units.
Therefore the correct options are 1, 4 and 7.
plzzz hurry up and help me if A+B=45
prove that
(1+tanA)(1+tanB)=2
Answers
Answer:
see explanation
Step-by-step explanation:
If A +B = 45° then tan(A+B) = tan45° = 1
Expanding (1 + tanA)(1 + tanB)
= 1 + tanA + tanB + tanAtanB → (1)
Using the Addition formula for tan(A + B)
tan(A+B) = [tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = 1 ← from above
Hence
tanA + tanB = 1 - tanAtanB ( add tanAtanB to both sides )
tanA + tanB + tanAtanB = 1 ( add 1 to both sides )
1 + tanA + tanB + tanAtanB = 2
Then from (1)
(1 + tanA)(1 + tanB) = 2 ⇒ proven
Solve the following system using the elimination method: 2x-4y=2 -4x+6y=-4
Answers
Answer:
(1, 0)
Step-by-step explanation:
Given the 2 equations
2x - 4y = 2 → (1)
- 4x + 6y = - 4 → (2)
Multiplying (1) by 2 and adding to (2) will eliminate the x- term
4x - 8y = 4 → (3)
Add (2) and (3) term by term
(- 4x + 4x) + (6y - 8y) = (- 4 + 4), simplifying gives
- 2y = 0 ⇒ y = 0
Substitute y = 0 in (1) or (2)
Substituting in (1) gives
2x - 0 = 2, that is
2x = 2 ( divide both sides by 2 )
x = 1
Solution is (1, 0 )
The first number in a sequence is 8. If each number in the sequence is 10 less than three times the previous number, then what will the fourth term be?
Answers
The fourth term of the arithmetic series is 38.
Given that, the first number in arithmetic series (a)=8 and common difference (d) =10.
What is the nth term of the arithmetic series?The nth term of the arithmetic series is [tex]a_{n} =a+(n-1) \times d[/tex].
Now, the fourth term= [tex]a_{4} =8+(4-1) \times 10[/tex]
=8+30=38
Therefore, the fourth term of the arithmetic series is 38.
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The Outlanders Club keeps track of the mean and median ages of its members. The ages of the six members are 26, 18, 42, 22, 38,
and 34. Which will increase more, the mean or the median, when a new member who is 65 years old joins?
Answers
You have to first put the numbers in order
18,22,26,34,39,42
To find the median you have to find the number that’s in the middle and since there are two of them, you have to find the average of them
26+34=60
60/2=30
Median is 30
To find the mean, you have to add everything together and then divide it by 6.
18+22+26+34+39+42=181
181/6= 30.17
Now you have to add the 65
18,22,26,34,39,42,65
The middle number is 34
Median=34
18+22+26+34+39+42+65=246
246/7=35.14
Now you just have to subtract
new median-old median
34-30=4
New mean-old mean
35.14-30.17=4.97
So the mean will increase more
Solve 2x-3/5=x+6 ASAP
Answers
Answer:
Problem 1: [tex]\frac{2x-3}{5}=x+6[/tex] gives x=-11
Problem 2: [tex]2x-\frac{3}{5}=x+6[/tex] gives x=33/5
Step-by-step explanation:
I will do it both ways:
Problem 1:
[tex]\frac{2x-3}{5}=x+6[/tex]
I don't like the fraction so I'm going to clear by multiplying both sides by 5:
[tex]2x-3=5(x+6)[/tex]
Distribute:
[tex]2x-3=5x+30[/tex]
Subtract 2x on both sides:
[tex]-3=3x+30[/tex]
Subtract 30 on both sides:
[tex]-33=3x[/tex]
Divide both sides by 3:
[tex]-11=x[/tex]
Problem 2:
[tex]2x-\frac{3}{5}=x+6[/tex]
Clear the fraction by multiplying both sides by 5:
[tex]5(2x-\frac{3}{5})=5(x+6)[/tex]
Distribute:
[tex]10x-3=5x+30[/tex]
Subtract 5x on both sides:
[tex]5x-3=30[/tex]
Add 3 on both sides:
[tex]5x=33[/tex]
Divide both sides by 5:
[tex]x=\frac{33}{5}[/tex]
For this case we must solve the following equation:
[tex]\frac {2x-3} {5} = x + 6[/tex]
Multiplying by 5 on both sides we have:
[tex]2x-3 = 5 (x + 6)\\2x-3 = 5x + 30[/tex]
We add 3 to both sides of the equation:
[tex]2x = 5x + 30 + 3\\2x = 5x + 33[/tex]
Subtracting 5x on both sides:
[tex]2x-5x = 33\\-3x = 33[/tex]
Dividing between -3 on both sides:
[tex]x = \frac {33} {- 3}\\x = -11[/tex]
Answer:
-11
Which expression will help you find the surface area of this right triangular prism? Select all the apply
Answers
To find the surface area of a right triangular prism, we have to calculate the area of all its faces, which include the two triangular bases and the three rectangular faces.
1. **Triangular Bases:** If the right triangle base has sides of lengths `a`, `b`, where `b` is the base and `a` is the height of the triangle, then the area of one triangular base will be given by the formula:
\[\text{Area of one triangular base} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times a \times b.\]
Since there are two identical triangular bases, we multiply this area by 2:
\[\text{Total area of triangular bases} = 2 \times \left( \frac{1}{2} \times a \times b \right) = a \times b.\]
2. **Rectangular Faces:** The three rectangular sides include two rectangles that are formed by the sides of the triangle (`a` and `b`) with the height (`h`) of the prism and one rectangle that is the width of the base `b` and the height of the prism. The areas of these rectangles will be:
- Rectangle with side `a` and height `h`: \[a \times h.\]
- Rectangle with base `b` and height `h`: \[b \times h.\]
- Rectangle with the side corresponding to the hypotenuse `c` of the base triangle and height `h`: \[c \times h.\]
Therefore, the total area of the three rectangles is the sum of the areas:
\[\text{Total area of rectangular faces} = a \times h + b \times h + c \times h = h \times (a + b + c).\]
Putting it all together, the formula for the total surface area (SA) of the right triangular prism is:
\[ SA = a \times b + h \times (a + b + c).\]
So, the expression that will help you find the surface area of a right triangular prism is the sum of the areas of the two triangles and the three rectangles as given by this formula.
A square image has a side length of 7 cm on a computer monitor. It is projected on a screen using an LCD projector. When projected, 1 cm of the image on the monitor represents 8 cm on the screen. Find the perimeter of the square in the projection.
answers are 392, 224, 448
Answers
Answer:
The perimeter of the square in the projection is [tex]224\ cm[/tex]
Step-by-step explanation:
we know that
1 cm of the image on the monitor represents 8 cm on the screen
so
using proportion
Find out how much represent on the screen 7 cm on a computer monitor
Let
x ----> the length side of the square image on the screen
[tex]\frac{1}{8}\frac{monitor}{screen} =\frac{7}{x}\frac{monitor}{screen} \\ \\x=8*7\\ \\x=56\ cm[/tex]
Find the perimeter of the image on the screen
the perimeter of a square is equal to
[tex]P=4b[/tex]
[tex]b=56\ cm[/tex]
substitute
[tex]P=4(56)=224\ cm[/tex]
Answer:
224cm
Step-by-step explanation:
The scale factor of the dilation is 8, so a 1 cm by 1 cm square on the monitor represents a 8 cm by 8 cm
square on the screen.
The figure shows two squares. The larger square has a side of 56 centimeters. The smaller square has a side of 7 centimeters. The sides of the larger square are parallel to the sides of the smaller one.
The side length of the square in the projection is the product of the side length of the preimage and the scale factor.
h=7(8)
cm
Simplify.
h=56
cm
The perimeter of the square is
P=4(56)
cm
Simplify.
P=224
cm
Therefore, the perimeter of the square in the projection is 224
cm.
Shirley is drawing triangles that have the same area. the base of each triangle inversely with the heigh. what are the possible base and height of a second triangle if the first triangles base is 12 and its height is 8.
select one:
a. 120 and 80
b. 10 and 10
c. 60 and 36
b. 16 and 6
Answers
Answer:
A
Step-by-step explanation:
they're proportional
Answer: the answer is A
Step-by-step explanation:
have a good day
- 18
A scientist rolls two balls A and B down two different ramps. Ball A rolls 4 meters in the 1st second, 9 meters in the 2nd second, 14
meters in the 3rd second, and so on. Ball B rolls 3.5 meters in the 1st second, 6.5 meters in the 2nd second, 9.5 meters in the 3rd
second, and so on. How many meters would each ball roll in 10 seconds?
Select one
a. A: 49 m: B: 305 m
b. A: 54 m; B: 33.5 m
CA: 59 m: B: 36.5 m
d. A: 85 m: B: 72 m
Answers
Answer:
a. A. 49m B 30.5 m
Step-by-step explanation:
If I have understood the question correctly:
Ball A:
After each second the total distance travelled increases by 5 meters.
Ball A: after 10 seconds it has rolled 4 + (10-1) * 5 = 49m
Ball B: after 10 seconds it has rolled 3.5 + (10-1)* 3 = 30.5 m.
Answer:
Option A. A: 49 m: B: 30.5 m
Step-by-step explanation:
Ball A rolls 4 meters in the 1st second, 9 meters in the 2nd second, 14 meters in the 3rd second, and so on.
We can see that after each second the total distance traveled by ball increases by 5 meters.
So, we can solve this as an arithmetic sequence that is [tex]a+(n-1)d[/tex]
For ball A, a = 4 n = 10 d = 5
Ball B rolls 3.5 meters in the 1st second, 6.5 meters in the 2nd second, 9.5 meters in the 3rd second, and so on.
For ball B, a = 3.5 n = 10 d = 3
For ball A:
After 10 seconds, the distance will be [tex]4+(10-1)5[/tex]
= [tex]4+45[/tex] = 49 meters
For ball B:
After 10 seconds, distance covered will be [tex]3.5+(10-1)3[/tex]
= [tex]3.5+27[/tex] = 30.5 meters.
Hence, the answer is option A.
Cindy bought a car for $21,330. A few years later, she sold the car for $19,700. Find the percent of change in the value.
Answers
well, the difference is 21330 - 19700 = 1630.
now, if we take 21330 as the 100%, what is 1630 off of it in percentage?
[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 21330&100\\ 1630&x \end{array}\implies \cfrac{21330}{1630}=\cfrac{100}{x}\implies \cfrac{2133}{163}=\cfrac{100}{x} \\\\\\ 2133x = 16300\implies x=\cfrac{16300}{2133}\implies x \approx 7.64[/tex]
Answer:
Change in the price of the car was 7.64%
Step-by-step explanation:
Cindy bought a car for $21330.
After few years she sold the car for $19700.
Net loss she suffered = Selling price - Cost price
= 21330 - 19700
= $1630
Now the percent change in the value will be = [tex]\frac{\text{Difference in the price}}{\text{Cost price of the car}}\times 100[/tex]
= [tex]\frac{1630}{21330}\times 100[/tex]
= 7.64%
Therefore, change in the price of the car was 7.64%
You have a total of $1760 to invest. Account A pays 7% annual interest and account B pays 4% annual interest. How much should you invest in each account if you would like the investment to earn $ 95 at the end of one year? Let A represent the amount of money invested in the account that earns 7% annual interest and let B represent the amount of money invested in the account that earns 4% annual interest. Complete the system of linear equations to solve the problem.
Answers
Answer:
You should invest $820 in account A and $940 in account B
Step-by-step explanation:
* Lets use the system of linear equations to solve the problem
- Simple Interest Equation I = Prt , Where:
# P = Invested Amount
# I = Interest Amount
# r = Rate of Interest per year in decimal; r = R/100
# t = Time Period involved in months or years
* Lets solve the problem
- The total money invested is $1760
- Account A pays 7% annual interest
- Account B pays 4% annual interest
- Let A represent the amount of money invested in the account A
- Let B represent the amount of money invested in the account B
- You would like to earn $ 95 at the end of one year
∴ The interest from both accounts at the end of one year is $95
- Lets write the equations
# Account A :
∵ Account A has $A invested
∴ P = $A
∵ Account A pays 7% annual interest
∴ r = 7/100 = 0.07
∵ t = 1 year
∵ I = Prt
∴ I = A(0.07)(1) = 0.07A
# Account B :
∵ Account B has $B invested
∴ P = $B
∵ Account A pays 4% annual interest
∴ r = 4/100 = 0.04
∵ t = 1 year
∵ I = Prt
∴ I = B(0.04)(1) = 0.04B
- The total amount of interest from both accounts at the end of one
year is $95
∴ I from A + I from B = 95
∴ 0.07A + 0.04B = 95 ⇒ multiply both sides by 100
∴ 7A + 4B = 9500 ⇒ (1)
- The total money to invest in both accounts is $1760
∵ Account A has $A invested
∵ Account B has $B invested
∴ A + B = 1760 ⇒ (2)
* Lets solve the system of equations to find the amount of money
invested in each account
- Multiply equation (2) by -4 to eliminate B
∵ A + B = 1760 ⇒ × -4
∴ -4A - 4B = -7040 ⇒ (3)
- Add equation (1) and (3)
∵ 7A + 4B = 9500 ⇒ (1)
∵ -4A - 4B = -7040 ⇒ (3)
∴ 7A - 4A = 9500 - 7040
∴ 3A = 2460 ⇒ divide both side by 3
∴ A = 820
- Substitute the value of A in equation (1) or (2)
∵ A + B = 1760 ⇒ (2)
∴ 820 + B = 1760 ⇒ subtract 820 from both sides
∴ B = 940
- From all above
* You should invest $820 in account A and $940 in account B