[tex]\tan^3\theta-\dfrac1{\tan\theta-1}-\sec^2\theta+1=0[/tex]
Recall that [tex]\tan^2\theta+1=\sec^2\theta[/tex], so we can write everything in terms of [tex]\tan\theta[/tex]:
[tex]\tan^3\theta-\dfrac1{\tan\theta-1}-\tan^2\theta=0[/tex]
Let [tex]x=\tan\theta[/tex], so that
[tex]x^3-\dfrac1{x-1}-x^2=0[/tex]
With some rewriting we get
[tex]x^3-x^2-\dfrac1{x-1}=0[/tex]
[tex]x^2(x-1)-\dfrac1{x-1}=0[/tex]
[tex]\dfrac{x^2(x-1)^2-1}{x-1}=0[/tex]
Clearly we cannot have [tex]x=1[/tex], or [tex]\tan\theta=1[/tex].
The numerator determines when the expression on the left reduces to 0:
[tex]x^2(x-1)^2-1=0[/tex]
[tex]x^2(x-1)^2=1[/tex]
[tex]\sqrt{x^2(x-1)^2}=\sqrt1[/tex]
[tex]|x(x-1)|=1[/tex]
[tex]x(x-1)=1\text{ or }x(x-1)=-1[/tex]
Completing the square gives
[tex]x(x-1)=x^2-x=x^2-x+\dfrac14-\dfrac14=\left(x-\dfrac12\right)^2-\dfrac14[/tex]
so that
[tex]\left(x-\dfrac12\right)^2=\dfrac54\text{ or }\left(x-\dfrac12\right)^2=-\dfrac34[/tex]
The second equation gives no real-valued solutions because squaring any real number gives a positive real number. (I'm assuming we don't care about complex solutions.) So we're left with only
[tex]\left(x-\dfrac12\right)^2=\dfrac54[/tex]
[tex]\sqrt{\left(x-\dfrac12\right)^2}=\sqrt{\dfrac54}[/tex]
[tex]\left|x-\dfrac12\right|=\dfrac{\sqrt5}2[/tex]
which again gives two cases,
[tex]x-\dfrac12=\dfrac{\sqrt5}2\text{ or }x-\dfrac12=-\dfrac{\sqrt5}2[/tex]
[tex]x=\dfrac{1+\sqrt5}2\text{ or }x=\dfrac{1-\sqrt5}2[/tex]
Then when [tex]x=\tan\theta[/tex], we can find [tex]\cot\theta[/tex] by taking the reciprocal, so we get
[tex]\boxed{\cot\theta=\dfrac2{1+\sqrt5}\text{ or }\cot\theta=\dfrac2{1-\sqrt5}}[/tex]
Answer: A. -1
Step-by-step explanation:
Edg 2020
Simplify the expression. 21 + 49 ÷ 7 + 1
Answer:
29
Step-by-step explanation:
Simplify the following:
21 + 49/7 + 1
Hint: | Reduce 49/7 to lowest terms. Start by finding the GCD of 49 and 7.
The gcd of 49 and 7 is 7, so 49/7 = (7×7)/(7×1) = 7/7×7 = 7:
21 + 7 + 1
Hint: | Evaluate 21 + 7 + 1 using long addition.
| 2 | 1
| | 7
+ | | 1
| 2 | 9:
Answer: 29
Given: The coordinates of rhombus WXYZ are W(0, 4b), X(2a, 0), Y(0, −4b), and Z(−2a, 0).
Prove: The segments joining the midpoints of a rhombus form a rectangle.
As part of the proof, find the midpoint of WZ
Answer:
-a,2b
Step-by-step explanation:
here is your answer
Answer:
Option C
Step-by-step explanation:
In this question coordinates of rhombus WXYZ are given as W(0, 4b), X(2a, 0), Y(0, −4b), and Z(−2a, 0).
Now we have to find the coordinates of midpoint of WZ as part of the proof.
Since mid point of two points (x, y) and (x', y') is represented by
[tex](\frac{x+x'}{2}[/tex] [tex]\frac{y+y'}{2})[/tex]
For midpoint of WZ,
[tex](\frac{0-2a}{2}[/tex] [tex]\frac{4b+0}{2})[/tex]
= (-a, 2b)
Option C will be the answer.
WORTH A WHOLE LOTTA POINTS!
Anna starts playing marbles with 5 small marbles which are worth 25 cents each and 8 large marbles which are worth k cents each. She trades 3 large marbles for 1 large marble and 6 small marbles. Finally, she gives Henry 4 small marbles. In cents, what is the value of the marbles she has left, in terms of k? Put your answer in form A+Bk with integer values A and B.
Anna's remaining marbles are worth 175 + 6k cents, where k is the worth of a large marble in cents.
Explanation:Here's a step-by-step solution: Anna initially had 5 small marbles that are worth 25 cents each and 8 large marbles that are worth k cents each. So, her total value in cents would be 5×25 + 8×k which equals 125 + 8k.
After trading 3 large marbles for 1 large marble and 6 small marbles, she now has 6 (8-3+1) large marbles and 11 (5 + 6) small marbles. The worth of her marbles now becomes 6×k (6 large marbles worth k cents each) + 275 (11 small marbles worth 25 cents each), totalling to 275 + 6k.
Anna then gives 4 small marbles to Henry. Now, she is left with 7 small marbles and 6 large marbles. Therefore, the worth of her remaining marbles in cents is 6k (6 large marbles worth k cents each) + 175 (7 small marbles worth 25 cents each), which on simplifying gives A + Bk = 175 + 6k.
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To find the value of the marbles Anna has left in terms of k, calculate the total value of the marbles started, subtract the value lost, and simplify the equation. The value of the marbles Anna has left is 275 cents + 10k cents.
Explanation:To find the value of the marbles Anna has left, we need to calculate the total value of the marbles she started with and then subtract the value lost through trading and giving marbles to Henry.
1. Total value of the small marbles: 5 small marbles x 25 cents each = 125 cents.
2. Total value of the large marbles: 8 large marbles x k cents each = 8k cents.
3. Value gained through trading: 3 large marbles - 1 large marble = 2 large marbles.
4. Value gained through trading (small marbles): 6 small marbles.
5. Value lost through giving marbles to Henry: 4 small marbles.
6. Value remaining: (125 cents + 8k cents) + (2 large marbles x k cents) + (6 small marbles x 25 cents) - (4 small marbles x 25 cents)
Simplifying the equation, we get: 125 cents + 8k cents + 2k cents + 150 cents - 100 cents = 275 cents + 10k cents. Therefore, the value of the marbles Anna has left, in terms of k, is A + Bk, where A = 275 and B = 10.
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Solving a Quadratic Equation
Which statement is true about the equation (x – 4)(x + 2) = 16?
O The equation x – 4 = 16 can be used to solve for a solution of the given equation.
The standard form of the equation is x2 – 2x – 8 = 0.
O The factored form of the equation is (x + 4)(x – 6) = 0.
o One solution of the equation is x = -6.
Answer:
The factored form of the equation is (x + 4)(x – 6) = 0.
Step-by-step explanation:
(x – 4)(x + 2) = 16
Foil the left side
x^2 +2x-4x-8 =16
Combine like terms
x^2 -2x-8 = 16
Subtract 16 from each side
x^2 -2x-8-16 =16-16
x^2 -2x-24 =0
Factor the left hand side
What two numbers multiply to -24 and add to -2
-6*4 =-24
-6+4 = -2
(x-6) (x+4) =0
Solving using the zero product property
x-6 =0 x+4=0
x=6 x=-4
Answer:
C: on ed
Step-by-step explanation:
Write the equation of the line of best fit using the slope-intercept formula $y = mx + b$. Show all your work, including the points used to determine the slope and how the equation was determined.
Answer:
[tex]y=\frac{5}{7}x+\frac{135}{7}[/tex]
Step-by-step explanation:
You only need two points on a line to find the equation for that line.
We are going to use 2 points that cross that line or at least come close to. You don't have to use the green points... just any point on the line will work. You might have to approximate a little.
I see ~(67.5,67.5) and ~(64,65).
Now once you have your points, we need to find the slope.
You may use [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex] are points on the line.
Or you can line up the points vertically and subtract then put 2nd difference over 1st difference.
Like this:
( 64 , 65 )
-( 67.5, 67.5 )
--------------------
-3.5 -2.5
So the slope is -2.5/-3.5=2.5/3.5=25/35=5/7.
Now use point-slope form to find the equation:
[tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point on the line.
[tex]y-65=\frac{5}{7}(x-64)[/tex]
Distribute:
[tex]y-65=\frac{5}{7}x-\frac{5}{7}\cdot 64[/tex]
Simplify:
[tex]y-65=\frac{5}{7}x-\frac{320}{7}[/tex]
Add 65 on both sides:
[tex]y=\frac{5}{7}x-\frac{320}{7}+65[/tex]
Simplify:
[tex]y=\frac{5}{7}x+\frac{135}{7}[/tex]
The coordinates of the preimage are: A(8,8) B(10,6) C(2,2) We want to reflect over y=−1 first. Our new coordinates are: A′(8, ) B′(10, ) C′(2, ) Now we will reflect over y=−7 and our new coordinates will be: A′′(8, ) B′′(10, ) C′′(2, ) We can also see that −7−(−1)=−6. We know that two reflections is the same as a translation of 2h units. So 2(−6) is a translation of −12 units down.
Answer:
1)A'(8,-10), B'(10,-8), C'(2,-4)
2)A''(8,-4), B''(10,-6), C''(2,-10
Step-by-step explanation:
Given:
Points A(8,8) B(10,6) C(2,2)
reflection over y=-1
Perpendicular distance between points y-coordinates of points (A, B and C) and y=-1 are 9,7 and 3
after reflections, the perpendicular distance will be 18,14,6 and the points will be at
A'(8,-10), B'(10,-8), C'(2,-4)
Now
Points A(8,-10), B(10,-8), C(2,-4)
reflection over y=−7
Perpendicular distance between points y-coordinates of points (A, B and C) and y=-7 are 3,1 and 3
after reflections, the perpendicular distance will be 6,2,6 and the points will be at
A''(8,-4), B''(10,-6), C''(2,-10) !
What is the volume of a shipping cube with dimensions of 3 1/2 feet
Answer:
the answer is 42.875
Step-by-step explanation:
3.5^3 = 42.875
Answer:
[tex]\large\boxed{V=42\dfrac{7}{8}\ ft^3}[/tex]
Step-by-step explanation:
The formula of a volume of a cube:
[tex]V=a^3[/tex]
a - edge
We have
[tex]a=3\dfrac{1}{2}\ ft[/tex]
Convert to the improper fraction:
[tex]a=\dfrac{3\cdot2+1}{2}=\dfrac{7}{2}\ ft[/tex]
Substitute to the formula of a volume:
[tex]V=\left(\dfrac{7}{2}\right)^3=\dfrac{7^3}{2^3}=\dfrac{343}{8}=42\dfrac{7}{8}\ ft^3[/tex]
A chemist is mixing a 40% salt solution with a 20% salt solution to make 50 L of
a new solution that will contain 25% salt. How much of each of the original
solutions should the chemist use?
Let [tex]x[/tex] be the amount (in L) of the 40% solution to be used, and [tex]y[/tex] the amount (L) of the 20% solution. The chemist wants a new solution of 50 L, so that
[tex]x+y=50[/tex]
Each L of the 40% solution contributes 0.4 L of salt, while each L of the 20% solution contributes 0.2. The new solution should have a concentration of 25% salt, so that
[tex]0.4x+0.2y=0.25(x+y)=12.5[/tex]
Now
[tex]x+y=50\implies y=50-x[/tex]
[tex]0.4x+0.2y=12.5\implies0.4x+0.2(50-x)=12.5\implies0.2x=2.5[/tex]
[tex]\implies\boxed{x=12.5}\implies\boxed{y=37.5}[/tex]
To make a 50 L solution containing 25% salt, the chemist should use 25 L of the 40% salt solution and 0 L of the 20% salt solution.
Explanation:To solve this problem, we can use the method of mixing solutions. Let x represent the amount of the 40% salt solution used, and 50-x represent the amount of the 20% salt solution used. The amount of salt in the 40% solution is 0.4x, and the amount of salt in the 20% solution is 0.2(50-x). Since the new solution will contain 25% salt, the amount of salt in the new solution is 0.25(50). Setting up an equation, we have:
Simplifying the equation, we get:
The chemist should use 25 L of the 40% salt solution and 25 - 25 = 0 L of the 20% salt solution to make 50 L of the new solution containing 25% salt.
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sin2x= ____.
a. 1/2(cos(a-b)-cos(a+b))
b. 2 sin x cos x
c. 1-2 sin^2 x
d. 2 sin x +2 cos x
The correct answer is c. 1-2 sin^2 x.
Explanation:The correct answer is c. 1-2 sin^2 x.
To find the value of sin 2x, we can use the double angle formula for sine, which states that sin 2x = 2sin x cos x. Therefore, b. 2 sin x cos x is the correct answer choice.
Correct option is (b) 2sinxcosx
Now using the trigonometric identity of 'sin(a+b)' we can find out the value of sin2x
sin (a + b) = sin a cos b + sin b cos a,
where 'a' and 'b' are angles
let 'a'='x' and 'b'='x'
[tex]sin2x=sin(x+x)\\sin2x=sinx*cosx+sinx*cosx\\sin2x=2sinxcosx[/tex]
Thus 2sinxcosx is the required answer
The recipe for a batch of applesauce uses 2 1/2 pounds of apples. If Michael wants to make 3/4 of a batch of applesauce, how many pounds of applesauce will he need
Answer:
15/8
Step-by-step explanation:
for 1 batch=5/2 pounds
for 3/4 batch=[5/2]×(3/4)
Answer: Michael will need 15/8 pounds of apples.
Step-by-step explanation:
Hi, to answer this question we simply have to multiply the amount of apples that a batch of applesauce needs (2 1/2) by the number of batches of applesauce that Michael wants to make (3/4).
Mathematically speaking;
2 1/2 x 3/4 = ([2x2+1] / 2 ) x 3/4 = 5/2 x 3/4 = (5x3) / (2x4) = 15/8
He will need 15/8 pounds of apples.
value of y when 10= 2y+4
Answer:
y=3
Step-by-step explanation:
Lets make y the subject of the equation by bringing the like terms together through mathematical operations.
10=2y+4
2y=10-4
2y=6
y=3
Why don't we fan here pls help
1. Find the circumference of a circle that has radius of 98 meters. Use 3.14 for pi.
2. Determine the difference in area between circle A and circle B. Use 3.14 for pi and round to the nearest tenth.
(Picture below)
Answer:
1: C=615.75m
2: 62.83 meters or 60 meters rounded to the nearest tenth
Step-by-step explanation:
1: The circumference of a circle that has radius of 98 meters, using 3.14 for pi, is 615.75m.
Formula: C=2πr
C=2πr=2·π·98≈615.75216m
_______________________________________________
2: The difference in area between circle A and circle B, using 3.14 for pi and rounded to the nearest tenth is 62.83 meters or 60 meters.
Circle A:The diameter of circle A is 12 cm.
Changing the diameter to radius is going to be easier.
Radius is half of the diameter.
12 ÷ 2 = 6
Therefore, the area of circle A is 113.1.
Formula: A=πr^2
A=πr^2=π·6^2≈113.09734
Circle B:The diameter of circle B is 8 cm.
Once again, changing the diameter to radius is going to be easier.
Radius is half of the diameter.
8 ÷ 2 = 4
Therefore, the area of circle B is 50.27.
Formula: A=πr^2
A=πr2=π·42≈50.26548
113.09734 - 50.26548 = 62.83 meters or 60 meters.
These tables represent an exponential function. Find the average rate of change for the interval from x=9 to x=10
Answer:
Hi there!
The answer to this question is: B
Step-by-step explanation:
The function for the question is: y=3^x
3^10=59049 and 3^9=19683
Then you just subtract the two numbers to get 39366
ANSWER
B. 39,366
EXPLANATION
The y-values of the exponential function has the following pattern
[tex] {3}^{0} = 1[/tex]
[tex] {3}^{1} = 3[/tex]
[tex] {3}^{2} = 9[/tex]
[tex] {3}^{3} = 27[/tex]
:
:
[tex] {3}^{x} = y [/tex]
Or
[tex]f(x) = {3}^{x} [/tex]
To find the average rate of change from x=9 to x=10, we simply find the slope of the secant line joining (9,f(9)) and (10,f(10))
This implies that,
[tex]slope = \frac{f(10) - f(9)}{10 - 9} [/tex]
[tex]slope = \frac{ {3}^{10} - {3}^{9} }{1} [/tex]
[tex]slope = \frac{59049-19683}{1} = 39366[/tex]
Therefore the average rate of change from x=9 to x=10 is 39366.
The correct answer is B.
please help asap !!!!find f(-2) for f(x)=2*3^x
Answer:
2/9
Step-by-step explanation:
f(x)=2*3^x
Let x=-2
f(-2) = 2 * 3^(-2)
When the exponent is negative, it flips from the numerator to the denominator
= 2 * 1/(3^2)
= 2 * 1/9
= 2/9
Answer:
It's 2/9.
Step-by-step explanation:
Replace to x by -2.
y = 2 * 3^(-2)
= 2 / 3^2
= 2/9.
CHECK ALL THAT APPLY
She did not find the correct vertex; it should be at (8, 5).
She used the wrong area formula; it should be A=1/2 b * h.
She used the wrong length for the base; it should be 7, like the given base.
She used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3.
She should have found a segment for the top that was not parallel to the bottom.
Answer:
* The error she made:
# She did not find the correct vertex; it should be at (8, 5)
# She used the wrong length for the base; it should be 7, like the given base
# She used a side length of the parallelogram for the height instead of a line segment perpendicular to the base; the height should be 3
Step-by-step explanation:
* Lets explain how to solve the problem
- She has three vertices of the parallelogram
- The vertices are (12 , 2) , (5 , 2) , (1 , 5)
∵ The two vertices (12 , 2) , (5 , 2) have the same y-coordinates
∴ The length of the base of the parallelogram is 12 - 5 = 7 units
- In parallelogram each two opposite sides are equal and parallel
∴ The opposite side to the base is 7
∴ The x coordinate of the missing point equal the x-coordinate of the
point (1 , 5) + the length of the base
∴ The x coordinate of the missing vertex = 1 + 7 = 8
∵ The y-coordinate of the missing vertex is the same with the
y-coordinate of the point (1 , 5)
∴ The y-coordinate of the missing vertex is 5
∴ The missing vertex is (8 , 5)
- The area of the parallelogram is A = bh, where b is the base of it
and h is the height of this base
- Remember the height must be perpendicular on the base
∵ The perpendicular distance between the two parallel bases is the
difference between the y-coordinates of the two points each one
belong to one of the two parallel bases
∴ The height of the parallelogram = 5 - 2 = 3 units
∴ Its area = 7 + 3 = 21 units ²
* The error she made:
# She did not find the correct vertex; it should be at (8, 5)
# She used the wrong length for the base; it should be 7, like the
given base
# She used a side length of the parallelogram for the height instead
of a line segment perpendicular to the base; the height should be 3
The product of seven and a number is negative 21. Find the number
Answer:
-3
Step-by-step explanation:
Let n be the number
product of seven and a number
7n
is negative 21
7n = -21
Divide each side by 7
7n/7 = -21/7
n = -3
The number is -3
Write the equation of a function whose parent function, f(x) = x + 6, is shifted 4 units to the right.
g(x) = x − 10
g(x) = x − 4
g(x) = x + 2
g(x) = x + 10
Answer:
g(x) = x + 2 ⇒ 3rd answer
Step-by-step explanation:
* Lets revise the translation
- If the function f(x) translated horizontally to the right
by h units, then the new function g(x) = f(x - h)
- If the function f(x) translated horizontally to the left
by h units, then the new function g(x) = f(x + h)
* Lets solve the problem
∵ The parent function f(x) = x + 6
∵ f(x) is shifted four units to the right
- The translation of a function by h units to the right change the x in
the function by subtracting h from it
∴ The x in f(x) will change to (x - 4)
∴ The new function = (x - 4) + 6
- Simplify the function
∴ The new function = x + 2
∵ The new function is g(x)
∴ g(x) = x + 2
Answer:
Step 3
Step-by-step explanation:
Ari is designing a patio that will be 20 feet long and 16 feet wide. He makes a scale drawing of the patio using a scale of 1 inch to 4 feet.
The ratio of the area of the scaled drawing to the actual area of the patio is 1 square inch to
square feet.
Answer:
1 square inch to 16 square feet
Step-by-step explanation:
The real patio area is
[tex]20\cdot 16=320\ ft^2[/tex]
The dimensions of the scale drawing are
[tex]20:4=5\ in\text{ and }16:4=4\ in,[/tex]
so the area of the scale patio is
[tex]5\cdot 4=20\ in^2[/tex]
The ratio of the area of the scaled drawing to the actual area of the patio is
[tex]20:320=1:16[/tex]
or 1 square inch to 16 square feet.
Answer:
I hope this helps
Step-by-step explanation:
A dilation maps (4, 6) to (2, 3). What is the scale factor of the dilation? If (-6, 3) is under the same dilation, what would its new coordinate be? Complete your work in the space provided or upload a file that can display math symbols if your work requires it.
Answer:
The scale factor of dilation is 1/2
New coordinates are: (-3, 3/2)
Step-by-step explanation:
a) A dilation maps (4,6) to (2,3)
we see that (4/2,6/2) = (2,3)
So, the scale factor of dilation is 1/2
b) if (-6,3) is under same dilation, their new coordinates will be?
We have to multiply (-6,3) by scale factor of 1/2
(-6*1/2,3*1/2) = (-3,3/2)
So, new coordinates are: (-3,3/2)
To solve this problem, we will complete the following steps:
Step 1: Determine the Scale Factor
We are given that the dilation maps the original point (4, 6) to the dilated point (2, 3). To find the scale factor of the dilation, we consider the ratios of the coordinates of the dilated point to the coordinates of the original point. This ratio should be the same for both the x- and y-coordinates since the dilation is uniform.
Scale factor for x-coordinate:
\( \frac{2}{4} = \frac{1}{2} \)
Scale factor for y-coordinate:
\( \frac{3}{6} = \frac{1}{2} \)
Both x and y scale factors are \( \frac{1}{2} \), confirming that the dilation is uniform, and hence the scale factor is \( \frac{1}{2} \).
Step 2: Apply Dilation to the Point (-6, 3)
Now, we want to apply the same scale factor to another point (-6, 3) to find its new coordinates under the same dilation.
\( \text{New x-coordinate} = -6 \times \frac{1}{2} = -3 \)
\( \text{New y-coordinate} = 3 \times \frac{1}{2} = \frac{3}{2} \) or 1.5
Therefore, when the point (-6, 3) is dilated with a scale factor of \( \frac{1}{2} \), the new coordinates are (-3, 1.5).
What type of triangle has side lengths 4, [tex]\sqrt{415} \\[/tex], and 16?
Step-by-step explanation:
It is impossible for a triangle to have side lengths of 4, √415, and 16.
The sum of the shortest two sides must be greater than the longest side. However, 4 + 16 < √415.
It is impossible to make a triangle with side lengths 4, √415, and 16 because the two side length of the triangle is always greater than the third length of the triangle.
What is the triangle?In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.
We have side lengths of a triangle.
As we know from the definition of the triangle the sum of the two side length of the triangle is always greater than the third length of the triangle.
Also, the sum of the interior angle of a triangle is 180 degrees.
As the three lengths are 4, √415, and 16
AB + BC < AC
Let suppose:
AB = 4 units
BC = 16 units
AC = √415 units
4 + 16 < √415
Thus, it is impossible to make a triangle with side lengths 4, √415, and 16.
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What is the value of x in the equation-2/3x+9=4/3x-3
Answer:
6
Step-by-step explanation:
[tex]-\frac{2}{3} x+9=\frac{4}{3} x-3\\\\[/tex]
First, multiply both sides by 3.
[tex]-2x+27=4x-9\\[/tex]
Next, combine like terms.
[tex]-2x+27=4x-9\\-2x+36=4x\\36=6x[/tex]
Solve for x.
[tex]36=6x\\6=x[/tex]
The value of "x" in the equation is 6.
To find the value of "x" in the equation -2/3x + 9 = 4/3x - 3, we need to isolate "x" on one side of the equation. Let's solve step-by-step:
Step 1: Get rid of fractions by multiplying all terms by the least common multiple (LCM) of the denominators, which is 3.
3 * (-2/3x) + 3 * 9 = 3 * (4/3x) - 3 * 3
Simplify:
-2x + 27 = 4x - 9
Step 2: Move "4x" and "27" terms to one side and " -2x" and " -9" terms to the other side.
Add 2x to both sides:
-2x + 2x + 27 = 4x - 9 + 2x
Simplify:
27 = 6x - 9
Step 3: Move the constant term " -9" to the other side of the equation by adding 9 to both sides:
27 + 9 = 6x - 9 + 9
Simplify:
36 = 6x
Step 4: Solve for "x" by dividing both sides by 6:
x = 36 / 6
x = 6
The value of "x" in the equation is 6.
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At a party, there are 8 small tables with 4 chairs at each table. Which expression can be used to find the number of chairs there are at the party?
8 + 4
8 – 4
8 × 4
8 ÷ 4
lina puts $300 in a college fund account that gives 10% simple interest annually. How much interest would she have after 4 years?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$300\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=years\dotfill &4 \end{cases} \\\\\\ I=(300)(0.10)(4)\implies I=120[/tex]
Which expression is equivalent to
(2^3)^-5
(2^3)^5
=2^(3*5)
= 2^15
hope it helps
Answer:
A
Step-by-step explanation:
Using the rules of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] and
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
Given
[tex](2^3)^{-5}[/tex]
= [tex]2^{3(-5)}[/tex] = [tex]2^{-15}[/tex] = [tex]\frac{1}{2^{15} }[/tex]
what is the height of the support beam?
Answer:
36 meters
Step-by-step explanation:
Using pythagorean theorem, 36² - 15² = 1296. √1296 = 36 meters
Answer:D. 36 m
Step-by-step explanation: Use the Pythagorean Theorem, which is a^2 + b^2 = c^2 to find the missing side. C is the hypotenuse. Plug in the numbers.
15^2 + b^2 = 39^2
Simplify.
225 + b^2 = 1521
Subtract 225 from each side.
b^2 = 1296
Square root each side to isolate b.
b = 36
The height of the support beam is 36 m.
A music teacher charged $80.25 for 2 1/2hours. What was the hourly fee to the nearest cent?
(SHOW WORK)
Answer:
The hourly fee charged by the teacher was $32.10.
Step-by-step explanation:
A music teacher charged for [tex]2\frac{1}{2}[/tex] hour = $80.25
To calculate the hourly fee of the teacher, we have to divide 80.25 by 2.5
Therefore, hourly fee of the teacher [tex]=\frac{80.25}{2.5}[/tex]
= $32.10
The hourly fee charged by the teacher was $32.10.
Which best describes the data set?
Answer:
The answer is C
Step-by-step explanation:
It is nonlinear but you have to look at it compared to the months passed. In three months the total houses built are 33 this would mean each month they build 11 houses but in the fourth month they have built 46 houses because 46-11 dosnt equal 33 it is nonlinear.
Answer: It is nonlinear because the increase in the "Total house built" compared to the "Months Passed" does not show a constant rate of change.
Step-by-step explanation:
We say function to be linear if the rate of change in dependent variable (y) with respect to independent variable (x) is constant.
Rate of change =[tex]\dfrac{\text{Change in dependent variable}}{\text{Change in independent variable}}[/tex]
According to the question ,
Independent variable = Number of months
Dependent variable = Total house built
Now rate of change of "Total house built" for month 0 to 3:-
[tex]\dfrac{33-0}{3-0}=\dfrac{33}{3}=11[/tex] (1)
Rate of change of "Total house built"fro month 3 to 4:-
[tex]\dfrac{46-33}{4-3}=\dfrac{13}{1}=13[/tex] (2)
From (1) and (2), it is clear that the rate of change is not constant
(∵ 11≠ 13 ).
Hence, the correct answer is : It is nonlinear because the increase in the "Total house built" compared to the "Months Passed" does not show a constant rate of change.
Write an expression for the perimeter of a rectangle with Length l = 2x + 3 and width w = x – 2
The perimeter of the rectangle is 6x + 2
How to determine the valueThe formula for the perimeter of rectangle is expressed as;
P =2 ( l + w)
Such that the parameters are;
P is the perimeter of the rectanglel is the length of the rectanglew is the width of the rectangleNow, substitute the values, we get;
Perimeter = 2( 2x + 3 + x - 2)
collect the like terms, we get;
Perimeter = 2(3x + 1)
expand the bracket
Perimeter = 6x + 2
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A triangle has two angles measuring 90 and 50%, calculate the third angle of the triangle,
a 50
C. 45
b. 40%
d. 750
Answer:
40°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 given angles from 180 for third angle
third angle = 180° - (90 + 50)° = 180° - 140° = 40°
Answer: B. 40
Step-by-step explanation: A triangle’s angles will always add up to 180 degrees. Add the 2 angles that are given. 90 + 50 = 140. Subtract this number from 180. 180 - 140 = 40. The third angle is 40 degrees.
Which of the following are not affected by the others outcomes?
compound evention
independent events
overlapping events
dependent events
Answer:
The Answer is Indepentant.
Step-by-step explanation:
The reason that the answer is Indepentant is that you don't rely on the other thing. Like you have a bag of marbles. You pick one and you put it back. You haven't changed anything. You put the marble back and restored the marble.
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Independent events are not afftected by the others outcomes.
What are independent events ?If outcomes of an event doesn't affect the outcomes of other event, the events are called independent events, i.e. they are independent to each other.
Example : "Rolling dice" and "getting good marks in exam" are independent events, because the outcomes of "rolling dice" doesn't affect the outcome of the event "getting good marks in exam".
What is the correct answer ?By seeing the definition & description of independent events given above, we can say that,
One of the independent events can not affected by the another one. Each independent event's outcomes are independent too.
So,the independent events are not affected by the others outcomes.
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