Answer:
x =7
Step-by-step explanation:
Remark
A geometric sequence always has terms that are separated by a common ratio. For example 3 9 27 81 243 .... Each term is multiplied by a common number and the term before it. In this case the common term is 3. To get the next term after 9, you multiply 9 by 3.To get the common ratio divide the second term by the first and then the third term by the secondEquation
(x + 2)/(x - 4) = (3x + 6)/ (x + 2)
Solution
I would begin this problem by taking out the common factor on the top right term. You'll see why in a second.
(x + 2)/(x - 4) = 3(x + 2)/ (x + 2) Notice the two binomials on the right cancel.
(x + 2)/(x - 4) = 3/1 Cross multiply(x + 2)*1 = 3*(x - 4) Remove the brackets on the right.x + 2 = 3x - 12 Add 12 on both sides.x + 2 + 12 = 3x - 12 + 12 Simplifyx + 14 = 3x Subtract x from both sides14 = 3x - x2x = 14 Divide by 2x = 14/2x = 7Alice planted some corn in the back yard and measures it’s height regularly. The last time she checked, the stalks were 60 inches tall. Now they are 72 inches tall. What is the percent of increase in the height of the stalks?
The percentage increase in the height of the corn stalks is 20%. This was calculated by subtracting the old height from the new height, dividing by the old height, and then multiplying by 100.
Explanation:The question is asking about the percentage increase in the height of the corn stalks that Alice planted. The stalks were previously 60 inches tall and now, they are 72 inches tall.
The formula to calculate the percentage increase is:
[(New Value - Old Value) / Old Value] x 100%
Substituting the given values into the formula, we get
[ (72 - 60) / 60 ] x 100%
This simplifies to [12/60] x 100%, which equals to 20%.
Therefore, there has been a 20% increase in the height of the corn stalks.
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ab is tangent to circle o at b. find the length of the radius r fur ab=5 and ao=8.6
Look at the picture.
We must use the Pythagorean theorem:
[tex]AB^2+OB^2=AO^2\\\\5^2+r^2=8.6^2\\\\25+r^2=73.96\qquad\text{subtract 25 from both sides]\\\\r^2=48.96\to r=\sqrt{48.96}\\\\\boxed{r\approx7}[/tex]
Answer: The radius is equal 7.Tabitha walked 13.5 miles in 3 hours. at that speed how many miles will she wallk in seven hours?
Answer: 31.5 miles
Step-by-step explanation: know how many miles tabitha walked per hour, which is 4.5 miles. then multiply 13.5 x 2, and add 4.5 to receive your answer - 31.5.
Answer:
Step-by-step explanation: The answer is 31.5 miles. The way I got it is by multiplying 13.5 by 2 because that will be 6 hours already. That gives me 27. Then you divide 13.5 to get how much she walk for just 1 hour which is 4.5. When you add that to 27, you get 31.5. Hope this helps!!!!!
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What is the simplified form of the rational expression below? 6x^2-54/5x^2+15x
The simplified form of the rational expression 6x^2-54/5x^2+15x is 6(x - 3)/5x. This was achieved by factoring the original expressions, cancelling out common terms, and applying the difference of squares formula.
Explanation:The subject here is the simplification of a rational expression. First, let's factor the numerator (6x^2 - 54) and the denominator (5x^2 + 15x). The common factor in the numerator is 6 and in the denominator is 5x. After factoring we get:
6x^2 - 54 = 6(x^2 - 9)
5x^2 + 15x = 5x(x + 3)
Now, we can use the property a^2 - b^2 = (a + b)(a - b) to further simplify x^2 - 9 to (x - 3)(x + 3). This gives our new numerator as 6(x - 3)(x + 3).
The denominator 5x(x + 3) remains the same. Therefore, the simplified form of the rational expression is 6(x - 3)(x + 3)/5x(x + 3). The (x + 3) terms can be cancelled out leaving us with the final simplified rational expression of:
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l-15l __ l15l is it <> or =?
|a| = a for a ≥ 0
|a| = -a for a < 0
|-15| = -(-15) = 15
|15| = 15
Therefore |-15| =|15|What is the y intercept of the line with the equation y=2x+8
Answer:
in the point slop form y=2x+8
the slope is 2
the y intercept is 8
The slope-intercept form of line:
y = mx + b
m - slope
b - y-intercept
We have y = 2x + 8. Therefore:
slope m = 2
y-intercept b = 8
Answer: y-intercept = 8.21 3/5 is what percent of 40
Answer:
21.6 is 54% of 40.
Step-by-step explanation:
21.6 ÷ 40 = 0.54 = 54%
Method 1:
[tex]21\dfrac{3}{5}=\dfrac{21\cdot5+3}{5}=\dfrac{108}{5}\\\\\\\\\begin{array}{ccc}40&-&100\%\\\dfrac{108}{5}&-&p\%\end{array}\qquad\text{cross multiply}\\\\\\\\40p=\dfrac{108}{5}\cdot100\\\\40p=108\cdot20\\\\40p=2160\qquad\text{divide both sides by 40}\\\\\boxed{p=54}[/tex]
Answer: 21 3/4 is 54% of 40.Method 2:
[tex]\dfrac{\frac{108}{5}}{40}\cdot100\%=\dfrac{108}{5}\cdot\dfrac{1}{4}\cdot10\%=\dfrac{108}{2}\%=54\%[/tex]
Answer: 21 3/4 is 54% of 40.10$ for 4 cans of soup ratio and unit rate
one gallon is equal to about 3.785 liters .what is the greatest number of whole liters of water u could pour into a one-gallon container without it overflowing ? explain your answer
We know that there are about 3.785 liters in 1 gallon. From here we could pour 3 whole liters into a one-gallon container without overflowing since 3 < 3.285 liters. But if we try to pour the next whole liter( 4 liters) it would be too much since 4 is greater then 3.785 liters. So the answer is 3 liters.
Hope this helps. <3
Which of the following is the equation of a circle whose center is at the origin and whose diameter has end (-1,2) and (1,-2)
Answer:
x² + y² = 5
Step-by-step explanation:
The circle with center (h, k) and radius r has equation ...
... (x -h)² + (y -k)² = r²
You can find r² using the Pythagorean theorem or the distance formula, or you can simply calculate what it needs to be to make one or the other of the points lie on the circle.
For (h, k) = (0, 0), the equation is ...
... (x -0)² + (y -0)² = r²
Using (-1, 2) for (x, y), we can find r² as ...
... (-1 -0)² + (2 -0)² = r² = 1 + 4 = 5
Then the circle equation is ...
... x² + y² = 5
What is the seventh term of the sequence 2, 3, 4 1/2 …?
Answer:
22 25/32
Step-by-step explanation:
well you just dividde the number in half and add the half and continue this and that's the seventh term. please be grateful it took me five minutes to do this
The seventh term of this sequence is 34.17875
Given : Each consecutive term is calculated by adding the half of preceding term to the preceding term.
Like : 2 + 1/2 (2) = 2 + 1 = 3
3 + 1/2 (3) = 3 + 3 / 2 = 3 + 1.5 = 4.5 or 4 1/2
4.5 + 1/2 ( 4.5 ) = 6.75
Similarly :
6.75 + 1/2 (6.75) = 10.125
10.125 + 1/2 (10.125) = 15.1875
15.1875 + 1/2 (15.1875) = 22.78125
22.78125 + 1/2 (22.78125) = 34.17875
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3r-34r+80 please factor this
Answer:
(3r-10) (r+8)
Step-by-step explanation:
3r-34r+80
The first step is to combine like terms
3r - 34r
is -31r
-31r+80
We cannot factor since 31 is a prime number and 80 is not a multiple of 31
If you mean
3r^2-34r+80
(3r-10) (r+8)
A Youth chorus of 30 members. There are 14 boys in the chorus. What is the ratio of boys to girls in the simplest form?
A: 7/15
B: 8/15
C: 7/8
D: 8/7
Answer:
C PLEASE GIVE BRAINLIEST
Step-by-step explanation:
30 - 14 = 16girls
ratio is : 14/16 = 7/8
Answer:
C
Step-by-step explanation:
I took the test
If a wave has a wavelength of 9 meters and a period of 0.006, what is the velocity of the wave ?
Answer:
Divide 9 by 0.006 you should get 1500
Step-by-step explanation:
Answer:
0.054
Step-by-step explanation:
Velocity = wavelength times frequency
= 9 * 0.006
= 0.054
What is the length of if ?
8 in.
8.75 in.
10.25 in.
14 in.
Answer:
Diagram attached
AJ = 8.75 in.
Step-by-step explanation:
Since triangles HBA & HKJ are similar,
BH/AH = KH/JH
3 in /5.25 in = 8 in /JH
JH = 14 in
JA = JH - AH = JH - 5.25 in = 8.75 in
HJ = 14 in.
AJ = 14 in - 5.25 in
AJ = 8.75 in.
A 30m tall building casts a shadow. the distance from top of the building to the top of the shadow is 36m. Find the lengths of the shadow
Final answer:
Using the Pythagorean theorem, the length of the shadow cast by a 30m tall building, with a diagonal distance of 36m from the top of the building to the top of the shadow, is calculated to be approximately 19.9 meters.
Explanation:
To find the length of the shadow cast by a 30m tall building, we can use the Pythagorean theorem. This theorem relates the lengths of the sides of a right triangle. Here, the building and its shadow form the two legs of a right triangle, and the line from the top of the building to the top of the shadow is the hypotenuse.
Let's denote:
The height of the building (opposite side) as O = 30m
The length of the shadow (adjacent side) as A
The distance from the top of the building to the top of the shadow (hypotenuse) as H = 36m
According to the Pythagorean theorem, we have:
O2 + A2 = H2
Plugging in the known values, we get:
302 + A2 = 362
900 + A2 = 1296
A2 = 1296 - 900
A2 = 396
A = √396
A ≈ 19.9m (rounded to one decimal place)
Therefore, the length of the shadow is approximately 19.9 meters.
Find the coordinates of the midpoint for segment HX if is H(7, 10) and X (5, -8)
Answer:
(6,1)
Step-by-step explanation:
I used the Midpoint Formula.
The manager of a store orders model railroad sets that cost $390 and sells them for $429. What is the mark-up, as a percentage?
Answer:
10%
Step-by-step explanation:
We have been given that the manager of a store orders model railroad sets that cost $390 and sells them for $429.
We will use markup % formula for our given problem.
[tex]\text{Markup percentage}=\frac{\text{Selling price- Cost}}{\text{Cost}}\times 100[/tex]
[tex]\text{Markup percentage}=\frac{429-390}{390}\times 100[/tex]
[tex]\text{Markup percentage}=\frac{39}{390}\times 100[/tex]
[tex]\text{Markup percentage}=\frac{1}{10}\times 100[/tex]
[tex]\text{Markup percentage}=10[/tex]
Therefore, markup is 10% of cost.
The current temperature in Smalltown is 20°F. This is 6 degrease less than twice the temperature that it was six hours ago. What was the temperature in Smalltown six hours ago?
Answer:
The temperature six hours ago was 13 °F
Step-by-step explanation:
Six hours ago the temperature was x degrees.
The temperature now is "6 degrees less than twice the temperature that it was six hours ago."
The temperature now is 2x - 6.
The temperature now is 20 deg.
2x - 6 = 20
2x = 26
x = 13
Answer: The temperature six hours ago was 13 °F.
Miss Johnson drives to work everyday when she left for work one day the automator mileage gauge on her car read 38643.8 when she returned to her house at the end of the day the automator red 38 points 668.6 if she didn't drive anywhere else during the day but to work and back how many miles is it from her house to her work explain how you got your answer
Answer:
Distance from her house to her work = 12.4 Miles
Step-by-step explanation:
Given :-
==> Automator mileage gauge read 38643.8 Miles before she left to work.
==> Automator mileage gauge read 38668.6 Miles after she came home from work.
==> She didn't drive anywhere else during the day. home to work & work to home.
Car driven during the day = 38668.6 - 38643.8
= 24.8 Miles
Let the distance from home to work be X
*It is assumed that Distance from home to work = Distance from work to home
So, Distance from work to home = X
Total distance driven during the day = Distance from home to work + Distance from work to home
Total distance driven during the day = X + X
24.8 = 2X
24.8 ÷ 2 = X
12.4 = X
Distance from her house to her work = 12.4 Miles
Answer: I think the answer is 24.8
Step-by-step explanation:
6691 ÷28. solved by long divison
To calculate 6691 divided by 28 using long division, divide each set of numbers step by step to arrive at a quotient of 238 with a remainder of 27, resulting in a decimal of approximately 238.96 when rounded.
The question involves the process of long division which is a method used in arithmetic. The student is trying to divide 6691 by 28:
Divide 66 by 28, which goes 2 times. Write 2 above the division bar, to the right of the first quotient place.
Multiply 2 by 28, which is 56, and subtract that from 66 to get a remainder of 10. Bring down the next digit, 9, to make 109.
Divide 109 by 28, which goes 3 times. Write 3 on the division bar. Multiply 3 by 28 (equals 84) and subtract from 109 to get 25.
Bring down the next digit, 1, to make 251. Divide this by 28, which goes 8 times. Eight times 28 is 224. Subtract this from 251 to get 27.
27 is less than 28, so the division process stops here. The answer up to this point is 238, with a remainder of 27.
The long division calculation of 6691 divided by 28 is 238 with a remainder of 27 or as a decimal, 238.96.
Write -3/4x-6 in standard form using integers
A. -3x+4y=-24
B. 3x+4y=24
C. 3x+4y=-24
D. 3x+4y=-6
Answer:
[tex]3x+4y=-24[/tex]
Therefore, option C is correct.
Step-by-step explanation:
We have been given the equation:
[tex]y=\frac{-3x}{4}-6[/[/tex]
We will take LCM 4 on right hand side of the above equation:
[tex]y=\frac{-3x-24}{4}[/tex]
Now, we will multiply the 4 in denominator on right hand side to the y in left hand side pof the equation we get:
[tex]4y=-3x-24[/tex]
After rearranging the terms we get:
[tex]3x+4y=-24[/tex]
Therefore, option C is correct.
Given: △AKL, AK=9 m∠K=90°, m∠A=60° Find: The perimeter of △AKL The area of △ AKL
Answer:
Perimeter of ΔAKL is, [tex]27 +9 \sqrt{3}[/tex] units.
Area of ΔAKL is, [tex]\frac{81\sqrt{3} }{2}[/tex] square units
Step-by-step explanation:
Given: In ΔAKL , AK = 9 units , [tex]m\angle K = 90^{\circ}[/tex] and [tex]m\angle A= 60^{\circ}[/tex].
In ΔAKL
[tex]\tan (A) = \frac{KL}{AK}[/tex]
Substitute the value AK = 9 units and [tex]m\angle A =60^{\circ}[/tex] to solve for KL ;
[tex]\tan(60^{\circ}) = \frac{KL}{9}[/tex]
[tex]\sqrt{3} = \frac{KL}{9}[/tex]
⇒[tex]KL = 9\sqrt{3} units[/tex]
In right angle ΔAKL,
Using Pythagoras theorem;
[tex]AL^2 = AK^2+KL^2[/tex] ......[1]
Substitute AK = 9 units and [tex]KL =9\sqrt{3} units[/tex] in [1] to solve for AL;
[tex]AL^2 = 9^2+(9\sqrt{3})^2[/tex]
[tex]AL^2 = 81+(81 \cdot 3)[/tex]
[tex]AL^2 = 81+243 = 324[/tex]
[tex]AL = \sqrt{324} = 18 units[/tex]
Perimeter of triangle is the sum of all the sides.
Perimeter of triangle AKL = AK +KL +AL = [tex]9 + 9\sqrt{3} + 18 = 27 +9 \sqrt{3}[/tex] units.
Formula for Area of right angle triangle is given by:
[tex]A = \frac{1}{2} Base \times Height[/tex]
Area of triangle AKL= [tex]\frac{1}{2} (9\sqrt{3}) \times (9)[/tex]
= [tex]\frac{81\sqrt{3} }{2}[/tex] square units
Final answer:
The perimeter of triangle AKL is approximately 29.09 m, and the area is 20.25 m², calculated using the properties of a 30°-60°-90° right triangle.
Explanation:
To find the perimeter of △AKL, we need to determine the lengths of all three sides. We know that AK = 9 m, ∠K = 90° (which makes △AKL a right triangle), and ∠A = 60°. Because the angles in a triangle add up to 180°, ∠L must be 30° (180° - 90° - 60°). In a 30°-60°-90° right triangle, the lengths of the sides are in the ratio 1:√3:2. Thus, if AK is the side opposite the 60° angle, AL must be half of AK, and KL must be AK times √3.
Therefore, AL = ½ × 9 m = 4.5 m, and KL = √3 × 9 m ≈ 15.59 m. The perimeter is the sum of AK, AL, and KL: 9 m + 4.5 m + 15.59 m ≈ 29.09 m.
The area of △AKL can be found using the formula for the area of a right triangle, which is ½ × base × height. AK and AL can serve as the base and height, respectively, so the area A is ½ × 9 m × 4.5 m = 20.25 m².
Find the greatest common factor of the following monomials 22a^5, 8a
What is Y=6x-6 and -3x-3y=-24
System of substitution
Answer:
x = 2
y = 6
Step-by-step explanation:
y= 6x - 6
-3x- 3y= -24
to find the value of x:
- 3x - 3 (6x - 6)= -24
- 3x - 18x + 18= -24
-21x + 18 = -24
-21x= -42
x = 2
Now, to find the value of y:
(substitute x into the equation)
y = 6 x - 6
y = 6 (2) - 6
y = 12 - 6
y = 6
A store owner bought a pair of headphones fo$150. He wanted to sell them for a profit of 30%. What price would he have to mark the headphones in order to make a profit?
Answer:
180
Step-by-step explanation:
30% of 150 = 30
because
30% of 15 = 3
30 + 150 = 180
Answer:
Step-by-step explanation:150+30=180
Classify the sequence (an) =(1,16,31,46,...) as arithmetic, geometric, or neither. If there is not enough information to classify the sequence, choose not enough information.
Harper knows he is 50 yards from the school. The map on his phone show that the school is 3/4 inches from current location. How far is Harper from home if map shows the distance as 3 inches
Answer: 200 yards
Step-by-step explanation:
So if 3/4 inches on the map is equal to 50 yards then you could divide the 3 inch distance from him to his home by 3/4 and then multiply that answer by 50. So 3 ÷ 3/4 = 4. 4 * 50 = 200. He is 200 yards from his home.
Answer:
Harper is 200 yards away home.Step-by-step explanation:
To solve this problem, we use the rule of three, if 50 yards represents 3/4 inches, how many yards would represent 3 inches?
[tex]x=3in\frac{50yd}{\frac{3}{4}in } =3\frac{200}{3}yd=200yd[/tex]
So, 3 inches represents 200 yards, that means Harper is 200 yards away home.
Remember that the rule of three is just about using the ratio that the problem already gave.
Therefore, the answer is 200 yards.
Please try to answer `#7 7.
Answer:
#7 is 3,150 tickets
Step-by-step explanation:
You multiply 126 and 25 together to get 3,150, because if each of the 126 students have to sell 25 tickets, that means you have to use multiplication.
HELP WITH MATH!! Look at the graph. What are the first four terms of the arithmetic sequence?
Answer:
a=9
b=4
v=69
Step-by-step explanation: