In the given right triangle, where the length of one side is a = 7 and the length of another side is x (unknown), the task is to determine the value of tan θ. The provided answer choices are √49 - 22/7, √49 - 2/7, and √49 - 2.
Explanation:
To determine the value of tan θ, we need to use the definition of the tangent function, which is equal to the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the opposite side is a and the adjacent side is x. Therefore, tan θ = a/x.
Given that a = 7, we can substitute this value into the expression: tan θ = 7/x.
From the answer choices, we can simplify each expression to determine the correct value.
The expression √49 - 22/7 can be simplified as √27/7, which is not equal to 7/x.
The expression √49 - 2/7 can be simplified as √47/7, which is also not equal to 7/x.
The expression √49 - 2 can be simplified as √47, which is not equal to 7/x.
None of the provided answer choices is equal to the expression 7/x, which means we cannot determine the exact value of tan θ without knowing the length of the other side (x)
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4 kilograms of almonds cost $34. how much does it cost for kilograms of almonds?
The cost of kilograms of almonds is $8.5 if 4 kilograms of almonds cost $34.
According to the questions,
4 kilograms of almonds cost $34. In order to find one kilograms of almonds only if we divide 34 by 4.
= [tex]\frac{34}{4}[/tex] = 8.5
Hence, the cost of kilograms of almonds is $8.5 if 4 kilograms of almonds cost $34.
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For decades, hoax artists have been going out into grain fields to make crop circles like the one shown below. Though many people believed these crop circles to be the work of aliens we now know that these designs were made by people with very simple tools and some geometric knowledge. To make each circle, one person stands stationary in a field holding a rope of a specific length, while another person holds the other end of the rope. The second person circles the first and uses a wooden plank to bend the grain stalks until all the grain in that circle lies flat against the ground. Then they both move to make other circles. The result is often very beautiful, especially when seen from the air. Along with the image below, Use your knowledge of the unit circle and radian measure of angles to answer the following questions. [Note: When the questions ask you to consider circles and their angle in relation to the main circle, the question is referring to the location of the center of each circle.]
a. Consider circles 1 through 6. If these circles are equally spaced around the main circle, and circle 1 is at 0°, what is the direction (in degrees) of each of these circles in relation to the main circle?
b. Consider circles 7 through 12. If circle 7 is at 45°, what is the radian measure of each of these circles in relation to the main circle? Explain how you know these values.
c. If the center of circle 3 is 100 feet away from the main circle, what are the coordinates of the center of circle 3 (the origin is at the center of the main circle)? Use these coordinates to prove that the distance from the centers of circle 3 and the main circle are 100 feet apart.
d. After creating the design, the designers want to inspect their work. They start at 0° and walk all the way around the design almost two times and stop at circle 12. How many radians did they cover during their inspection?
e. Consider circles 5 and 6. In relation to the main circles, do the center points of circles 5 and 6 have even or odd symmetry? Why?
a. circle 2 = 60°
circle 3 = 120°
circle 4 = 180°
circle 5 = 240°
circle 6 = 300°
b. circle 8 = 15°
circle 9 = 75°
circle 10 = 155°
circle 11 = 215°
circle 12 = 265°
How to determine the valuesFrom the information given, we have that;
There are six major circles
Six minor circles
a. There are 6 circles at a point
Note that angles at a point sum up to 360 degrees
Now, let's divide their sum by the six parts
= [tex]\frac{360}{6}[/tex]
= [tex]60[/tex] degrees
Then, circle 1
= 0 × 60
= 0
Circle 2
= 1 × 60
= 60°
Circle 3
= 2 × 60
= 120°
Circle 4
= 3 × 60
= 180°
Circle 5
= 4 × 60
= 240°
Circle 6
= 5 × 60
= 300°
b. We have that each of these circles ( circle 7 - 12) radian measure is
= main circle - [tex]\frac{\pi }{12}[/tex]
The relative position or direction of circle 7 - 12 to their corresponding main circles ( 1 - 6) are all the same, we then have;
For circles 8
= 60° - 45°
= 15°
Circle 9
= 120° - 45°
= 75°
Circle 10
= 180° - 45°
= 155°
Circle 11
= 240° - 45°
= 215°
Circle 12
= 300° - 45°
= 265°
They share the relationship of radian of circle 7 - 12 corresponding to circles 6 - 12 minus π/12
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Please help me solve the answers
The modal and mean mark of the frequency distribution is 5 and 4.83 respectively.
Mean and modeMode refers to a mark which reoccurs most in a frequency distribution.
Modal mark = 5The total number of students who wrote the test = 2 + 3 + 4 + 6 + 10 + 4 + 3 + 2 + 1 + 1
= 36 students
Mean mark = Total mark / Total students
= (2×1) + (3×2) + (4×3) + (6×4) + (10×5) + (4×6) + (3×7) + (2×8) + (1×9) + (1×10) / 36
= (2+6+12+24+50+24+21+16+9+10 / 36
= 174/36
= 4.83333333333333
Approximately,
Mean mark = 4.83
If 25% of students failed,
Number of students who failed = 25% of 36
= 25/100 × 36
= 0.25 × 36
= 9 students.
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The slope in the simplest form
How many different 2 digit numbers are there with the following property: the tenth digit is greater that the units digit?
Answer:
45 numbers
Step-by-step explanation:
The 10-digit numbers are from 10-99. We can manually analyze each tenth digit and see if we can find a pattern from it. First, 10-19 ~ 10 is the only number in the sequence where the tenth digit is greater than the unit digit (because 1 > 0). In every other case, 1 is less than or equal to the unit digit.
Next, 20-29 ~ 20 and 21 are the two numbers where the tenth digit is greater than the unit digit
30-39 ~ 30, 31, 32 follow the property
40-49 ~ 40, 41, 42, 43 follow the property
We can keep going, but we can see that there is a pattern. The number of numbers that correspond with the property for each set of 10 numbers is equal to the value of the tenth digit. We see that for the 40s, there are 4 numbers. For the 20s, on the other hand, there are 2 numbers. This pattern carries through:
50-59 ~ 5 numbers, 60-69 ~ 6 numbers, 70-79 ~ 7 numbers, 80-89 ~ 8 numbers, 90-99 ~ 9 numbers
We need to find how many 2-digit numbers total follow the property. We can just add our results together to get our answer:
1+2+3+4+5+6+7+8+9=45
If you select 25 in the top values list, access displays _____ in the query results.
If you select 25 in the Top Values list, Access displays the top 25 records in the query results.
How to find Access Query Results?Queries are excellent tools in Microsoft Excel to show information from related tables in a single result set, as the results that you pull from queries aren’t limited to a single table.
The way to create a simple query using the wizard is as follows;
Click the “Query Wizard” button in the “Queries” group on the “Create” tab in the Ribbon. In the “New Query” dialog box that appears, you can see the ways in which you can create queries. Select the “Simple Query Wizard” choice.Click “OK” to begin.Now, If you select 25 in the top values list, access displays the top 25 records in the query results.
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Pmlease helppp tyyyy
Answer:
Step-by-step explanation:
Solving quadratic equation using formula:5x² - 6x - 2 = 0
a = Coefficient of x² = 5
b = coefficient of x = -6
c = constant = -2
Discriminant = D = b² - 4ac
= (-6)² - 4 * 5 * (-2)
= 36 + 40
= 76 > 0
So, the quadratic equation has two distinct real roots.
[tex]\sf \boxed{\bf x = \dfrac{-b \± \sqrt{D}}{2a}}\\\\[/tex]
[tex]\sf = \dfrac{-[-6] \± \sqrt{76}}{2*5}\\\\= \dfrac{6 \±8.7}{10}\\\\=\dfrac{6+8.7}{10} \ ; \ or \ x =\dfrac{6-8.7}{10}\\\\=\dfrac{14.7}{10} \ ; \ or \ x = \dfrac{-2.7}{10}[/tex]
x = 1.47 or x = -0.27
Answer: x = 1.5 or (-0.3)
b) x² + 3x = 40
x² + 3x - 40= 0
We can solve the quadratic equation using factor method.
Sum = 3
Product = -40
Factors = 8 , (-5)
When we add, 8 + (-5) = 3 , we get 5and when we multiply 8 *(-5) = -40, we get -(-40).
Rewrite the middle term of the quadratic equation using the factors.
x² + 8x - 5x - 40 = 0
x(x + 8) - 5(x + 8)= 0
(x + 8) (x - 5) = 0
x + 8 = 0 or x - 5 = 0
x = -8 or x = 5
Answer : x = -8 , 5
what is the value of x
find the value of f
Answer:
x = 20°
f = 40°
Step-by-step explanation:
4x + 5x = 180°
because a straight line is 180°
so 9x = 180°
1x = 180 ÷ 9
1x = 20
all angles in a triangle add together is 180°
so 7x + f = 180°
1x = 20
7x = 20 × 7
7x = 140°
f = 180° - 140 °
f = 40°
Answer:
x = 20 , f = 40
Step-by-step explanation:
4x and 5x are a linear pair and sum to 180° , then
4x + 5x = 180
9x = 180 ( divide both sides by 9 )
x = 20
then
5x = 5 × 20 = 100° and 3x = 3 × 20 = 60°
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
5x is an exterior angle of the triangle , then
f + 3x = 5x , that is
f + 60 = 100 ( subtract 60 from both sides )
f = 40
There are federal excise taxes on the retail price when purchasing fishing equipment. the taxes are intended to help pay for parks and conservation. what is the federal excise tax rate if there is an excise tax of $17.50 on a fishing rod and reel that has a retail price of $175?
Using proportions, it is found that the federal tax rate is of 10%.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The tax rate is the proportion that $17.50 is of $175, hence:
r = 17.50/175 = 0.1 = 10%.
The federal tax rate is of 10%.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2022, tysm for the help!
Answer:
C. Best models this relationship
Step-by-step explanation:
Answer:
C: y=1/3x
Step-by-step explanation:
I'll set up an equation for this.
When x = 6, y needs to be 2.
--> 2 = 6 times ___
since 6 times 1/3 is 2, ___ is 1/3.
Now we know that 1/3 is the slope. In a complete equation, this will be shown as y = 1/3 x.
This can be proven by reinserting the value of x and y.
2 = 1/3 (6)
Since this equation works, we can be sure that C: y=1/3 x is correct.
For 3, 5, Are the triangles similar? If so, state the similarity and the postulate or theorem that justifies your answer.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).The graph represents the piecewise function:
The definition of the piecewise function is given as follows:
[tex]f(x) = x + 3, -3 \leq x < 1[/tex].[tex]f(x) = 5, -1 \leq x \leq 1[/tex].What is a piecewise function?A piecewise function is a function that has different definitions, depending on the input.
Researching this problem on the internet, for x equal or greater than -3 and less than -1, the function is a line with a slope of 1 that goes through (-3,0), hence the definition is found as follows:
y = x + b
0 = -3 + b
b = 3
Then:
[tex]f(x) = x + 3, -3 \leq x < 1[/tex].
For x between -1 and 1, inclusive, the function is constant at 5, hence the definition is:
[tex]f(x) = 5, -1 \leq x \leq 1[/tex].
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ABC Corporation recently issued an IPO. Shortly thereafter it decides it wants to buy back some of its shares. What time frame restrictions would ABC face in order to buy back their own stock
The time restriction faced by ABC Corporation for it to buy back its newly issued shares is 4 weeks
What is share buyback?
Share buyback means that the company would repurchase its own shares in the stock market by paying investors holding the shares, then reduce its number of shares outstanding by the number of shares bought back.
The shares repurchased are known as Treasury stocks, which are held until the company decides to reissue them or cancel them.
The restriction placed on a company before it can repurchase its shares is that the shares must be in issue 4 weeks, in other words, the new issued shares through Initial Public Offer(IPO) must be existence for 4 weeks before being repurchased by the company after having issued an IPO.
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What are the first five terms in the
recursive sequence defined by the
following?
The first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}
Recursive functionGiven the nth term of a recursive expression shown below
an =an-1 - 1.4
where
an-1 is the preceding term
a1 is the first term
an is the nth term
an-1 is
Given the following
a1 = 0
For the second term a2
a2 = 0 - 1.4
a2 = -1.4
For the third term a3
a3 = -1.4 - 1.4
a3 = -2.8
For the fourth term a4
a4 = -2.8 - 1.4
a4 = -4.2
For the fifth term a2
a5 = -4.2 - 1.4
a5 = -5.6
Hence the first five terms of the sequence are {0, -1.4, -2.8, -4.2, -5.6}
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La suma de un número con su mitad es igual a 75. ¿Cuál es ese número?
Doy corona porfis
Considerando la definición de una ecuación, el número desconocido es 50.
Definición de ecuaciónUna ecuación es la igualdad existente entre dos expresiones algebraicas conectadas a través del signo de igualdad en la que figuran uno o varios valores desconocidos, llamadas incógnitas, además de ciertos datos conocidos.
Los miembros de una ecuación son cada una de las expresiones que aparecen a ambos lados del signo igual.
Número desconocidoEn este caso, "La suma de un número con su mitad es igual a 75" puede ser expresado mediante una ecuación, donde consideras que "x" es la incógnita, que representa el número desconocido.
Teniendo en cuenta que la mitad de un número se calcula dividiendo el número por 2, entonces la ecuación queda expresada como:
x + x÷2= 75
O lo que es lo mismo
x + [tex]\frac{1}{2}[/tex]x= 75
Resolviendo:
[tex]\frac{3}{2}[/tex]x= 75
x= 75 ÷[tex]\frac{3}{2}[/tex]
x= 75×[tex]\frac{2}{3}[/tex]
x=50
Finalmente, el número desconocido es 50.
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PLEASE BELP IM ACTUALLY REALLY STUCK
Answer: 4
Step-by-step explanation:
Slope is rise over run (up over sideways) from two points.
The two points shown are (0,4) and (-2,-4).
By counting, you can find the slope, which is 8/2 = 4.
Find the measure of each numbered angle.
Answer: [tex]m\angle 1=82^{\circ}, m\angle 2=128^{\circ}[/tex]
Step-by-step explanation:
By the same-side interior angles theorem,
[tex]m\angle 1=180^{\circ}-98^{\circ}=82^{\circ}\\\\m\angle 2=180^{\circ}-52^{\circ}=128^{\circ}[/tex]
In a recent baseball season, Ron was hit by pitches 19 times in 596 plate appearances during the regular season. Assume that the probability that Ron gets hit by a pitch is the same in the playoffs as it is during the regular season. In the first playoff series, Ron has 22 plate appearances. What is the probability that Ron will get hit by a pitch exactly once
The probability that Ron will get by a pitch exactly once is 0.351912.
Given that out of 596 plate appearance Ron was hit 19 times from pitches.
We have to find the probability that ron was hit by pitches in 22 plate appearances.
The value of probability lies between 0 and 1. The formula of calculating proabability is number of items/ total items.
We can find the required probability through binomial distribution which is
n[tex]C_{r}p^{r} (1-p)^{n-r}[/tex] where n is the number of trials and r is the successes.
Probability that Ron will be hit =19/596
=0.031
Probability that Ron will get hit by a pitch exactly once =P(X=1)
=[tex]22C_{1}(0.031)^{1} (1-0.031)^{21}[/tex]
=22!/1!21!*0.031*[tex](0.969)^{21}[/tex]
=22*0.031*0.516
=22*0.015996
=0.351912
Hence the probability that Ron will get hit by a pitch exactly once is 0.35.
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Beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey bars. If Beth places the swings at point D, how could she prove that point D is equidistant from the jungle gym and monkey bars?
If segment DC bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
If segment DC bisects segment AB, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
If segment AD bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
If segment AD bisects segment AB, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.
Option A is correct. If segment DC bisects segment AB, then point D is equidistant from points A and B because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects. This can be obtained using perpendicular bisector theorem.
What is perpendicular bisector theorem ?Perpendicular bisector theorem : In a plane, if we choose a point, say D, on the perpendicular bisector,say PQ, drawn from segment, say AB, then the point D is equidistant from the endpoints, that is A and B, of the segment.
That is, perpendicular bisector PQ of line segment AB is the line with Q = 90° and Q is the midpoint of AB ⇒ AQ = BQ. A point on PQ say D is equidistant from A and B ⇒AD and BD.
Thus in the given question we can use perpendicular bisector theorem.
Here DC is the perpendicular bisector of the line segment AB and therefore AD and BD are equal.
Hence it is clear that Option A is correct.
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The density of a certain material is such that it weighs 5 ounces per gallon of volume what is the density in pounds per cubic meter
The density in pounds per cubic meter is 83 pounds per cubic metre.
How to find density?The density is mass of a unit volume of a material substance.
In other words, density is the ratio between mass and volume or mass per unit .
Therefore, density can be represented mathematically as follows:
density = mass / volume
Hence,
mass = 5 ounces
5 ounces = 0.3125 pounds
1 gallon = 0.00378541 pounds
Therefore,
density = 0.3125 / 0.00378541
density = 82.5538052681
density = 83 pounds per cubic metre.
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A square has a side length of 10 inches. Congruent isosceles right triangles are cut off each corner so that the resulting octagon has equal side lengths. How many inches are in the length of one side of the octagon
The length of the side of the octagon is 4.142 inches.
We can find the length of the sides of the octagon as follows:Let the length of the congruent sides of the isosceles triangle be x.
The hypotenuse of the triangle is given by:
√x+x = √2x
This is also the length of the sides of the octagon. It is given that the sides of the octagon are equal.
It is also given that the length of the square side is 10 inches.
This means that:
x + √2x + x = 10
2x + √2x = 10
(2 + √2)x = 10
(2 + 1.414)x = 10
3.414x = 10
x = 10/3.414
x = 2.929 inches.
The side of the octagon is given by:
√2 × 2.929 = 4.142 inches
Therefore, we have found that the length of the sides of the octagon is 4.142 inches.
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Instructions: Find the missing length indicated.
400
144
X
The missing side of a right triangle x is 24 units.
How to find side of a right angle triangle?A right triangle has one of its angles as 90 degrees. The side of a right angle triangle can be found using trigonometric ratios.
The side x can be found using similar triangle ratios,
Hence,
x / 400 = 144 / x
cross multiply
x × x = 400 × 144
x² = 57600
square root both sides
√x² = √57600
x = 240
Therefore, the value of x in the right triangle is 240 units.
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Total area=
Help me please thanks so much
The surface area of the parallelpiped is equal to 800 square units.
What is the surface area of a parallelpiped?
The surface area of the parallelpiped seen in the picture is equal to the sum of the areas of its six faces, which are combination of areas of quadrilaterals and triangles. There are four parallelograms and two squares. Thus, the surface area of the solid is:
A = 2 · 8 · 20 + 2 · 7 · 20 + 2 · 10²
A = 800
The surface area of the parallelpiped is equal to 800 square units.
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All the events in the sample space that are not part of the specified event are called _____. Group of answer choices joint events the complement of the event simple events independent events
All the events in the sample space that are not part of the specified event are called Complement of Event.
Complement of event:
The complement of an event is the subset of outcomes in the sample space that are not in the event. A complement is itself an event. The complement of an event A is denoted as A c A^c Ac or A′. An event and its complement are mutually exclusive and exhaustive.
Two events are said to be complementary when one event occurs if and only if the other does not. The probabilities of two complimentary events add up to 1. For example, rolling a 5 or greater and rolling a 4 or less on a die are complementary events, because a roll is 5 or greater if and only if it is not 4 or less.
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If the price of gas started at $2.56 per gallon and increased at a rate of 4% per year, after how many years will the price of gasoline per gallon reach or exceed $5?
The price of gas is modeled by f(x) = 2.56(1.04)x.
Use logarithms to find the answer to the question.
Answer: 18 years
Work Shown:
[tex]f(\text{x}) = 2.56(1.04)^\text{x}\\\\5 = 2.56(1.04)^\text{x}\\\\5/2.56 = (1.04)^\text{x}\\\\1.953125 = (1.04)^\text{x}\\\\\log(1.953125) = \log(1.04^\text{x})\\\\\log(1.953125) = \text{x}*\log(1.04)\\\\\text{x} = \frac{\log(1.953125)}{\log(1.04)}\\\\\text{x} \approx 17.0682937693249\\\\[/tex]
The steps above show f(x) replaced with 5. Then you'd use logarithms to isolate the variable x. The relevant useful log rule is [tex]\log(A^B) = B\log(A)[/tex] so we can pull down the exponent.
From here it seems your teacher wants you to round up to the nearest integer.
If we plugged in x = 17, then f(x) = 4.99 which is one cent too small.
While x = 18 leads to f(x) = 5.19
Therefore, x = 18 has the price reach or exceed $5
I forgot how to do this, I need an explanation to find the answer
Answer:
23.53
Step-by-step explanation:
OK so we got sin 52°=0.8 and the cos 52°=0.6
but we need tan 52° because we don't want to spend our time on calculating hypothenuse so
[tex] \frac{ \sin(52) }{ \cos(52) } = 1.3 = \tan(52) [/tex]
so
[tex]1.3 = \frac{x}{18.1} = = = > x = 23.53[/tex]
The mean number of goals a netball team scores
per match in the first 9 matches of a competition
is 4.
a) How many goals does the team score in total in
the first 9 matches of the competition?
b) If the team scores 3 goals in their next match,
what would their mean number of goals after 10
matches be?
The goals does the team score in total in the first 9 matches of the competition is 36 and their mean number of goals after 10 matches is 3.9.
What is the total goals scored by the team in 9 matches ?Given that the mean number of goals a netball team scores per match in the first 9 matches of a competition is 4.
Thus the average of the goals in 9 matches is 4.
Total number of goals is = 9*4 = 36 goals .
What is the mean number of goals after 10 matches ?Given that the team scores 3 goals in their next match .
Thus the total number of goals scored in 10 matches is 36 + 3 = 39 goals,
Required mean = Total goals / 10 matches .
∴ Required mean = 39/10 = 3.9 .
Therefore, the goals does the team score in total in the first 9 matches of the competition is 36 and their mean number of goals after 10 matches is 3.9.
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The sum of the reciprocal of a positive number and the reciprocal of 3 more than the number is
7/10. Find the number.
Write an equation with the following characteristics:
1. It uses x to represent the number.
2. It uses the information as it is given above.
3. It can be solved to answer the question.
Equation:
The number is:
Answer:
[tex]\sf Equation: \quad \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]
The number is 2.
Step-by-step explanation:
The reciprocal of a number is simply 1 divided by the number.
The reciprocal of a fraction is where the numerator and denominator are swapped (so the fraction is turned upside down).
Let x be the positive number.
The reciprocal of the positive number x:
[tex]\sf \implies \dfrac{1}{x}[/tex]
The reciprocal of 3 more than the number x:
[tex]\sf \implies \dfrac{1}{x+3}[/tex]
The sum of the reciprocal of a positive number and the reciprocal of 3 more than the number is 7/10:
[tex]\implies \sf \dfrac{1}{x}+\dfrac{1}{x+3}=\dfrac{7}{10}[/tex]
To solve, make the denominators of the two fractions on the left side the same by multiplying them.
Multiply the numerator of the first fraction by the denominator of the second fraction to get the new numerator of the first fraction.
Multiply the numerator of the second fraction by the denominator of the first fraction to get the new numerator of the second fraction.
[tex]\implies \sf \dfrac{1(x+3)}{x(x+3)}+\dfrac{1(x)}{(x+3)(x)}=\dfrac{7}{10}[/tex]
[tex]\implies \sf \dfrac{x+3}{x(x+3)}+\dfrac{x}{x(x+3)}=\dfrac{7}{10}[/tex]
Add the numerators and keep the denominator so that there is now one fraction:
[tex]\implies \sf \dfrac{2x+3}{x(x+3)}=\dfrac{7}{10}[/tex]
Cross multiply:
[tex]\implies \sf 10(2x+3)=7x(x+3)[/tex]
Expand:
[tex]\implies \sf 20x+30=7x^2+21x[/tex]
Rearrange so the equation is equal to zero:
[tex]\implies \sf 7x^2+x-30=0[/tex]
Split the middle term:
[tex]\implies \sf 7x^2+15x-14x-30=0[/tex]
Factor the first two terms and last two terms separately:
[tex]\implies \sf x(7x+15)-2(7x+15)=0[/tex]
Factor out the common term (7x + 15):
[tex]\implies \sf (x-2)(7x+15)=0[/tex]
Apply the zero product property:
[tex]\sf (x-2)=0 \implies x=2[/tex]
[tex]\sf (7x+15)=0 \implies x=-\dfrac{15}{7}[/tex]
As x is a positive number, x = 2.
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Help me please!! Thanks so much
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