The small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.
Similar triangles are triangles that have the same shape but can have different sizes. In this case, the shadow of the boy, the boy himself, and the light post form similar triangles.
Let h be the height of the light post, x be the distance between the boy and the light post, and s be the length of the shadow, we can use the following ratios -
(boy's height) / (boy's shadow) = (light post height) / (light post shadow)
i.e. (4 feet 6 inches) / (3 feet 4 inches) = (h) / (x)
Now, we can find the height of the light post by using the above equation and the given values of the boy's height and the shadow.
The small boy can measure the distance between him and the light post, and he can use this value in the above equation to determine the height of the light post. The equation is h/x = (4.5)/(3.33)
This is the ratio of the height of the light post and the distance between the boy and the light post, so h = (4.5 * x) / (3.33)
In this way, the small boy can use the mathematical reasoning of similar triangles and the concept of ratios to determine the height of the light post.
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Simplify 2h+3h^2−4g^4+5f^2+11g^4−4h+f^2
Answer:3h^2 + 7g^4 + 5f^2 - 4h - 4g^4
Step-by-step explanation:To simplify the expression 2h+3h^2−4g^4+5f^2+11g^4−4h+f^2, we can follow these steps:
Group together like terms:
2h + (-4h) = -2h
3h^2 + f^2 = 3h^2 + f^2
-4g^4 + 11g^4 = 7g^4
This gives us the expression: -2h + 3h^2 + 5f^2 + 7g^4
Combine the constants:
3h^2 + 5f^2 + 7g^4 = 3h^2 + f^2 + 7g^4
Combine the like terms:
-2h + 3h^2 + f^2 + 7g^4 = 3h^2 + f^2 + 7g^4 - 2h
So, the simplified expression is: 3h^2 + 7g^4 + 5f^2 - 4h
After simplifying, the expression we'll get, 2h+3h^2+7g^4+6f^2-4h.
To simplify these algebraic expressions, we need to group the like terms. Like terms can be defined as terms that contain the same variables raised to the same power. Only the numerical coefficients are different.
After grouping like terms, perform the required operations. Here we have two operations i.e addition and subtraction. So group the like terms which need to add and those which need to subtract.
For example, Here -4g^4+11g^4 are like terms and 5f^2+f^2 are like terms. So we'll subtract 4 from 11, we'll get 7 and the variable will remain the same that is g^4. Similarly, we'll add 5 and 1, we'll get 6 and the variable will remain the same that is f^2.
Other terms will remain as it is.
2h+3h^2+(-4g^4+11g^4)+(5f^2+f^2)-4h
2h+3h^2+7g^4+6f^2-4h
Therefore the answer is, 2h+3h^2+7g^4+6f^2-4h
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When Lisa runs, she takes 80 steps in 100 meters. How far has Lisa run when she has taken 2500 steps. Round to kilometers
Answer 0.000032 km
Step-by-step explanation: divide
on a certain hot summer day 128 people used the public swimming pool. the daily prices are $1.50 for children and $2.00 for adults. the receipts for admission totaled $223.00. How many children and how many adults swam at the public pool that day?
The number of children and adults that swam in the pool that day is given as follows:
Children: 66.Adults: 62.How to obtain the number of children and adults?The variables to the system of equations are given as follows:
Variable x: number of children.Variable y: number of adults.128 people used the public swimming pool, hence:
x + y = 128.
x = 128 - y.
The receipts for admission totaled $223.00, hence:
1.5x + 2y = 223.
We have that x = 128 - y, hence the number of adults is obtained as follows:
1.5(128 - y) + 2y = 223
0.5y = 31
y = 62.
Then the number of children is obtained as follows:
x = 128 - 62
x = 66.
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a culture of yeast doubles in size every 20 minutes. the size of the culture is now n0. find its size in 12 hours. how do you solve these problems? sugar is put in a large quantity of water and the mixture is stirred. after 2 minutes, 50% of the sugar has dissolved. how much longer will it take until 90% of the sugar has dissolved?
How much longer will it take until 90% of the sugar has dissolved can be obtained by the equation t = -(log(1-0.9))/(log(0.5)) + 2
1. To find the size of a yeast culture after 12 hours, you can use the formula: size = n0 * 2^(t/20), where t is the time in minutes. In this case, t = 12*60 = 720, so the size of the culture after 12 hours would be n0 * 2^(720/20) = n0 * 2^36.
2. To find how long it takes for 90% of the sugar to dissolve, you can use the formula: t = -(log(1-x))/(log(0.5)), where x is the percentage of sugar dissolved and t is the time in minutes. In this case, x = 0.9 and we know that 50% of the sugar has dissolved in 2 minutes, so we can find t by plugging in the values and solving for t: t = -(log(1-0.9))/(log(0.5)) + 2.
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A square has a diagonal that is 22 m long. What is the area of the square?
If necessary, round your answer to the nearest whole number.
Pre-Quiz th Percent - Item 35684 Guided Learning Practice A baseball team played 55 games this year. They won 33 games and lost 22 games. What percent of games did they lose? Po
The percentage of games they lose is 40%.
How do you calculate percentage in different ways?The most basic approach is to divide a number by the total and then multiply by 100. For example, if you have 10 out of a total of 25, you would divide 10 by 25 to get 0.4, and then multiply by 100 to get 40%.
Another way to calculate percentage is to use proportion. This involves setting up a proportion with the given numbers and the percent you want to find on one side and 100 on the other side. For example, if you have 10 out of 25 again and want to find the percent, you would set up the proportion 10/25 = x/100. Solve for x and you get 40%.
Another method is to use a percentage calculator. This is a simple tool that allows you to enter two numbers and it will automatically calculate the percentage for you.
Finally, if you need to calculate the difference between two percentages, you can subtract the smaller percentage from the larger one. For example, if you have 10 out of 25 and 15 out of 30, you would subtract 40% from 50% to get 10%.
All of these methods can help you calculate percentages quickly and easily.
Total number of games team played = 55 games
number of games they won = 33
number of games they lose = 22
The percentage of games they lose = 22/55 x 100 = 40%
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Need help 7-10 asap I’m stuck on these
7. To show that VRHK is a square, one can observe that the opposite sides of the quadrilateral, VR and HK, are equal in length and the two adjacent sides, RH and VK, are also equal in length.
8. For VRHK to be a square, z must equal √2, so that VC = 6√2 and
VR = 12.
9. The length of RK is 12√2
10. The length of VK is 12√2
Give difference between sides and diagonal of square?A square is a two-dimensional, regular geometric shape with four sides of equal length and four angles of 90 degrees. The sides of a square are the four straight lines that make up the shape. The length of each side is the same as the length of the other three sides.The diagonal of a square is a line segment that connects two opposite corners of the square. The diagonal is not a side of the square, as it does not run along the same line as the other sides. The diagonal of a square is always the same length, which is the square root of the sum of the squares of the sides. This is known as the Pythagorean Theorem.The sides of a square are all equal, while the diagonal of a square is not equal to any of the sides. The length of the sides of a square is always the same, regardless of the size of the square, while the length of the diagonal of a square varies with the size of the square. The diagonal of a square is always longer than any of the sides, since it is the hypotenuse of a right triangle.Solution:
8. We can solve this problem by using the Pythagorean Theorem. We know that the sides of a square are equal, so we can set up an equation using the theorem. VC = 6z, VR = 12, and we want the hypotenuse, VRHK, to be a square. VH² = VR² + RH² = 12√2.
VC = 6z = VH/2 = 12√2/2 = 6√2
6z = 6√2
z = √2
9. The length of RK' = s√2 =12√2
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Lin wrote this number sentence to solve a problem: 35+7-5 Which problem was Lin MOST LIKELY trying to solve?
There are 35 students in Mr. Ken's class. There are 7 students in his class who are sick today. How many students in his
class are not sick?
There are 35 students in Mr. Ken's class. During class, 7 more students join the class to watch a movie. How many
students are there in all?
There are 35 students in Mr. Ken's class. There are 7 classes in the school, each with the same number of students. How
many students are in the school?
There are 35 students in Mr. Ken's class. He made 7 groups for reading. He put an equal number of students in each
group. How many students are in each group?
Answer:
Step-by-step explanation:
BRO MY MATH TEACHER IS ON TO ME SOMEONE HELP A family camping in a national forest builds a temporary shelter with a tarp and a 6-foot pole. The bottom of the pole is even with the ground, and one corner is staked 10 feet from the bottom of the pole. What is the slope of the tarp from that corner to the top of the pole?
To find the slope of the tarp, we can use the concept of rise over run, which is the ratio of the vertical change (the rise) to the horizontal change (the run). In this case, the rise is the distance from the corner of the tarp to the top of the pole, and the run is the distance from the corner of the tarp to the bottom of the pole.
We can use the Pythagorean theorem to find the length of the hypotenuse of the right-angled triangle formed by the corner of the tarp, the bottom of the pole and the top of the pole.
The length of the hypotenuse is the distance from the corner of the tarp to the top of the pole and the length of the adjacent side is the distance from the corner of the tarp to the bottom of the pole.
We know that:
adjacent side = 10 ft
Hypotenuse = h
Applying the Pythagorean theorem:
h^2 = 10^2 + 6^2
h = √(10^2 + 6^2)
h = √(100 + 36) = √136 = 11.66 ft
Now we can calculate the slope:
slope = rise/run = (h-10) / 6
slope = (11.66-10) / 6 = 1.66/6 = 0.277
So the slope of the tarp from the corner to the top of the pole is 0.277 or approximately 0.28.
Name each angle in four ways. Then classify the angle as acute, right, obtuse, or straight
Classification of all the angles in four different ways along with name are:
1. ∠ABC, ∠CBA, ∠B, ∠1 and the name is right angle.
2. ∠DEF, ∠FED, ∠E, ∠2 and the name is obtuse angle.
3. ∠LMN, ∠NML, ∠M, ∠3 and the name is straight angle.
4. ∠XYZ, ∠ZYX, ∠Y, ∠4 and the name is acute angle.
5. ∠KLM, ∠MLK, ∠L, ∠5 and the name is acute angle.
6. ∠RST, ∠TSR, ∠S, ∠6 and the name is obtuse angle.
Figure is attached.
Classification of the all the angles in the attached figure in four different ways with their names are:
1. Different name of the angles : ∠ABC, ∠CBA, ∠B, ∠1 .
Measure of the angle is 90°, it is right angle.
2. Different name of the angles : ∠DEF, ∠FED, ∠E, ∠2
Measure of the angle is more than 90°, it is obtuse angle.
3. Different name of the angles : ∠LMN, ∠NML, ∠M, ∠3
Measure of the angle is 180°, it is straight angle.
4. Different name of the angles : ∠XYZ, ∠ZYX, ∠Y, ∠4
Measure of the angle is less than 90°, it is acute angle.
5. Different name of the angles : ∠KLM, ∠MLK, ∠L, ∠5
Measure of the angle is less than 90°, it is acute angle.
6. 2. Different name of the angles : ∠RST, ∠TSR, ∠S, ∠6
Measure of the angle is more than 90°, it is obtuse angle.
Therefore, as per the classification of the given angles different ways to represent them are:
1. ∠ABC, ∠CBA, ∠B, ∠1 , right angle.
2. ∠DEF, ∠FED, ∠E, ∠2 , obtuse angle.
3. ∠LMN, ∠NML, ∠M, ∠3 , straight angle.
4. ∠XYZ, ∠ZYX, ∠Y, ∠4, acute angle.
5. ∠KLM, ∠MLK, ∠L, ∠5 , acute angle.
6. ∠RST, ∠TSR, ∠S, ∠6 ,obtuse angle.
The above question is incomplete , the complete question is :
Name each angle in four ways. Then classify the angle as acute, right, obtuse, or straight.
Attached figure.
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a room has dimensions of 9.15 meters by 9.4 meters by 3.68 meters. what is the volume of the room in cm^3?
The room with the given dimensions has a volume of 316, 516, 800 cm^3.
The volume of a room is a measure of the amount of space inside it, and it is calculated by multiplying the length, width, and height of the room.
In this case, the room has dimensions of 9.15 meters by 9.4 meters by 3.68 meters.
To find the volume of the room in cm^3, we first need to convert the dimensions of the room from meters to centimeters.
1 meter is equal to 100 centimeters, so
9.15 meters is equivalent to 915 centimeters,
9.4 meters is equivalent to 940 centimeters,
and 3.68 meters is equivalent to 368 centimeters.
Once we have the dimensions in centimeters, we can calculate the volume by multiplying the length, width, and height:
915 cm x 940 cm x 368 cm = 316, 516, 800 cm^3.
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interpret the quote never confuse the size of your paycheck with the size of your talent
Note that the quote given above simply means that an employee or worker should never equate how much they earn to how much they are actually worth. This can take on different meanings depending on whether you want to assign a positive connotation to it or a negative one.
What is a quote in Literature?A quote is a verbatim reproduction of someone else's words that is generally surrounded by quotation marks and attributed to the original author or speaker.
Quoting implies paraphrasing someone else's remarks and citing the source. You must ensure the following when quoting a source:
The quoted content is surrounded by quotation marks or shown as a block quote.The original author is properly credited.The wording is exactly the same as the original.Learn more about Quotes:
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Solve the inequality + 6 > -3.
A x < -2
B x > -2
C x < 12
D x > 12
The solution to the inequality is (b) x > -2
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
4.5x + 6 > -3
Collect the like terms
So, we have the following representation
4.5x > - 3 - 6
Evaluate the like terms
This gives
4.5x > -9
Divide both sides by 4.5
x > -2
Hence, the solution is (b) x > -2
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A colony of 100 bacteria doubles in size every 60 hours what will the population be 189 hours from now
By evaluating an exponential equation, we will see that the population after 189 hours will be 888 bacteria.
What will be the population in 189 hours from now?We know that initially we have a total of 100 bacteria, and it doubles in size every 60 hours, then the population can be modeled with the exponential equation.
p(x) = 100*(2)^x
Where x is groups of 60 hours, we can rewrite:
x = t/60h
Where t is the amount of hours, and rewrite the equation as:
p(t) = 100*(2)^(t/60h)
The population in 189 hours from now willbe:
p(189 h) = 100*(2)^(198 h/60h) = 887.7
The population is 888 (where we rounded the value)
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Is the relation shown in the arrow diagram a function? (0,-2) (0,1) (1,2) (2,1) (3,4)
Answer: no, not a function
Step-by-step explanation: 0 is in the input twice, and if it were a function, it would only be there once. every input can only have one output
a 16 pound bag of kitty kibbles is . an -pound bag of feline flavor is . which statement about the unit prices is true?
If a 16 pound bag of Kitty Kibbles is $20.80 and 8-pound bag of Feline Flavor is $11.20 then the true statement about the unit price is (D) Kitty Kibbles has a lower unit price of $1.30/pound .
the cost of the 16 pound bag of Kitty Kibbles is = $20.80 ;
So , the cost of 1 pound bag of Kitty Kibbles is = $20.80/16
= $1.3 ;
the cost of 8 pound bag of Feline Flavor is = $11.20 ;
So , cost of 1 pound bag of Feline Flavor is = 11.20/8 ;
= $1.4 ;
on comparing both the unit prices , we get that the per unit cost of Kitty Kibbles is lower and the price is $1.3 ;
Therefore , the true statement is (D) Kitty Kibbles has a lower unit price of $1.30/pound .
The given question is incomplete , the complete question is
A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true ?
A. Feline Flavor has a lower unit price of $1.40/pound.
B. Feline Flavor has a lower unit price of $1.30/pound.
C. Kitty Kibbles has a lower unit price of $1.40/pound.
D. Kitty Kibbles has a lower unit price of $1.30/pound.
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CONNECTING CONCEPTS Find the value of x such that the quadrilateral is a parallelogram. Then find the perimeter of the parallelogram. Explain.
The value of 'x' must be 4 units such that the quadrilateral is a parallelogram and the perimeter of the parallelogram is 40 square units.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
We know the opposite sides of a parallelogram are equal.
Therefore, 3x - 1 = x² - 5 and 2x + 1 = x² - 7.
x² - 5 - 3x - 1 = 0.
x² - 3x - 4 = 0, solving for x we have x = 4.
And,
2x + 1 = x² - 7.
x² - 7 - 2x - 1 = 0.
x² - 2x - 8 = 0, solving for x we have x = 4
(Negative values are inadmissible).
The perimeter of the parallelogram is 2×(the sum of the opposite sides).
= 2(3x - 1 + 2x + 1).
= 2(5x).
= 2×5×4.
= 40 square units.
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there were x quarts of liquid in a con-tainer. first, 3 4 of the liquid in the container was removed. then another 1 2 quart was poured into the container. write an expression in terms of x for the number of quarts of liquid in the container at the end. then write another equivalent expres-sion.explain
The another equivalent expression of total liquid is (x+2)/4.
Expressions that perform similarly but differ in appearance are said to be equivalent expressions. When the same value for the variable is entered, two algebraic expressions that are equivalent will have the same result.
x quarts liquid in the container 3/4 part of liquid is removed
Then remaining liquid in container = X - [tex]\frac{3}{4}X[/tex]
Then remaining liquid in container = x/4quarts
Another 1/2 quart is poured into container
Then total liquid = [tex]X-\frac{3}{4}X+\frac{1}{2}[/tex] quarts
total liquid = [tex]\frac{X+2}{4}[/tex] quarts
So, then the another equivalent expression of total liquid is (x+2)/4.
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NUMber 5
If you eplain how you didi it I put you as brianliest
Answer:
y=1/2x+2
Step-by-step explanation:
given the 2 equations, you know the following:
when x=2, you get a value of 3, let's call it Y
same with the next equation: when x=6, Y = 5
so the slope will be the diff b/w ys and then divided by diff of x's
so 5-3=2 is the diff of y
6-2=4 is the diff of x
divide 2/4 = 1/2 so the slope is 1/2
then you know the equation would be something like y=1/2 x but then you need to decide the intercept
1/2 of x when x=6 is 3, but Y =5
so you know the intercept is 2..
so the linear f(x) would be y=1/2x+2
done
What is the value of x? enter your answer in the box. x = cm
The value of x in the given equation will be 2/5
From the data,
We have to determine the value of x.
The given equation is: 18x-16=-12x-4
For determining the value of x, we will first shift the like terms on one side of the equation.
So, for solving the value of x we will shift the terms containing x and the constant on both sides of the equation.
So, shifting -12x from the right-hand side of the equation to the left-hand side of the equation,
We will get it as:
18x+12x = -4+16
30x=12
Now for solving the value of x we will shift x from the left side of the equation to the right side of the equation.
So, the value of x will be = 12/30 = 2/5
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The correct question may be:
What is the value of x
18x-16=-12x-4
Enter your answer in the box.
1. In parallelogram ABCD, what is the relationship between angle a° and angle b°?
a° = b°
a° - b° = 180°
a° = -b°
a° + b° = 180°
2. In rectangle FGHK, FC = CH = 8. 5 cm. What is the area of rectangle FGHK?
8. 5cm
120cm
125. 5cm
15cm
3. In rectangle FGHK, FC = CH = 8. 5 cm. What is the length of GK?
8 cm
8. 5 cm
15. 5 cm
17 cm
4. In parallelogram EFGH, what is the relationship between angle e and angle g?
e° – g° = 180°
e° = -g°
e° = g°
e° + g° = 180°
1. In parallelogram ABCD, the sum of ∠a and ∠b is 180 degree. So the option d "a° + b° = 180°" is correct.
2. In rectangle FGHK, FC = CH = 8. 5 cm, then the area of rectangle FGHK is 120 square cm. So the option b is correct.
3. The length of GK is 17 cm because the length of all diagonal is same in rectangle. So the option d is correct.
4. In parallelogram EFGH, the sum of ∠e and ∠f is 180 degree. So the option d "a° + b° = 180°" is correct.
1. In parallelogram ABCD, ∠a and ∠b are adjacent to each other.
So, AB║DC.
Then we get ∠a and ∠b as subsequent interior angles, both of which need to be added.
So the sum of ∠a and ∠b is 180 degree.
a° + b° = 180°
2. In rectangle FGHK, FC = CH = 8. 5 cm.
From the diagram, FG = 8 cm
FH = FC + CH
FH = 8.5 + 8.5
FH = 17 cm
Using Pythagorean Theorem to find the value of GH.
FH^2 = FG^2 + GH^2
(17)^2 = (8)^2 + GH^2
289 = 64 + GH^2
Subtract 64 on both side, we get
GH^2 = 225
Taking square root on both side, we get
GH = 15 cm
The area of rectangle = FG × GH
The area of rectangle = 8 × 15
The area of rectangle = 120 square cm
3. In rectangle FGHK, FC = CH = 8. 5 cm.
So FH = FC + CH
FH = 8.5 + 8.5
FH = 17 cm
As, a rectangle is split into two congruent right triangles by a diagonal. The length of the rectangle's diagonals are all the same.
So GK = FH = 17 cm
4. In parallelogram EFGH, ∠e and ∠f are adjacent to each other.
So, EF║HG.
Then we get ∠e and ∠f as subsequent interior angles, both of which need to be added.
So the sum of ∠e and ∠f is 180 degree.
e° + f° = 180°
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how much money will it cost you to drive 100.0 miles if your car gets 25.70 miles per gallon and gas costs $3.309/gallon?
It will cost $12.87 for driving 100 miles.
Based on the given problem, we have identified the given information as follows:
25.70 miles per gallon100 miles as the distance traveled by car$3.309 as the cost of gasoline per gallonThen, we identify the unknown quantity which is the total cost of gasoline, and represent this as C. Now, this can be solved by using the formula
[tex]C = \frac{distance traveled by car}{25.70 miles per gallon} * Cost of gasoline per gallon[/tex]
By substituting the given to the variable given in the formula above, we have,
[tex]C = \frac{100}{25.70} * 3.309[/tex]
C = $ 12.87
The obtained value of C is $12.87, therefore, we can conclude that it costs 12.87 dollars for driving 100 miles.
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explain briefly how the statistic can be used to make inferences about the parameter to test the claim
In statistics, we use samples to make inferences about population
That is the great advantage of the whole role of distribution. Once you know a particular situation or experiment, that you can associate to one specific distribution and compute parameters, you can obtain from a relative smaller quantity of data and with good approximation, inferences about the whole population.
Statistical inference is the method of using data analysis to infer characteristics of a probability distribution.
Inferential statistics is the branch of statistics that uses sample statistics to estimate a population parameter or test a hypothesis about such a parameter.
statistics
Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
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What are two additional questions that would be meaningful to drill down into with this same dataset, given what you've seen so far?
The two additional questions that would be meaningful to drill down into with this same dataset is that What type of variation occurs within my variables? and What type of covariation occurs between my variables?.
The term data set is defined as a collection of related sets of information that is composed of separate elements but can be manipulated as a unit by a computer.
Here we need to find the two additional questions that would be meaningful to drill down into with this same dataset,
As per the definition we have know that the question that need to be asked over the data set are listed as follows:
They are type of variation occurs within my variables and the type of covariation occurs between my variables.
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pls solve this I will give Brainly
Answer:
42
Step-by-step explanation:
(2x + 3) = 7
7x7=49
note:the other 7 is from the exponent 2
49-7=42
(6n+ 3)(6n- 4) find each product
The product of the two expressions is equal to 36n²-6n-12
What Is Distributive Property?According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.
Given here: The expression (6n+ 3)(6n- 4)
Using the distributive property of multiplication we get
(6n+ 3)(6n- 4)
6n(6n-4)+3(6n-4)
Now arranging the like terms and again applying the distributive property we get
36n²-24n+18n-12
36n²-6n-12
Hence, The product of the two expressions is equal to 36n²-6n-12
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Name the true solution(s) to the equation. name the extraneous solution(s) to the equation.
The true solution to the equation [tex]\(x + 5 - \sqrt{x} = 3\)[/tex] is [tex]\(x = \frac{4}{9}\)[/tex], and there are no extraneous solutions.
To find the true solution(s) to the equation, we need to solve for x and check if the obtained solutions satisfy the original equation. The extraneous solution(s), if any, will be the solutions that do not satisfy the original equation.
To solve the equation, we can start by isolating one of the square root terms. Rearranging the equation, we have:
[tex]\sqrt{x + 5} = 3 + \sqrt{x}[/tex].
The equation can be evaluated as:
[tex]\sqrt{x + 5} - \sqrt{x} &= 3 \\(\sqrt{x + 5})^2 &= (3 + \sqrt{x})^2 \\x + 5 &= 9 + 6\sqrt{x} + x \\6\sqrt{x} &= -4 \\\sqrt{x} &= \frac{-2}{3} \\x &= \frac{4}{9}\end{align*}[/tex]
Therefore, the true solution to the equation [tex]\(x + 5 - \sqrt{x} = 3\)[/tex] is [tex]\(x = \frac{4}{9}\)[/tex], and there are no extraneous solutions.
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The complete question:
Solve the following equation and identify the true solution(s) as well as the extraneous solution(s):
[tex]\sqrt{x + 5} - \sqrt{x} = 3[/tex].
determine the dimensions of a rectangular solid (with a square base) of maximum volume if its surface area is 150 square inches.
The rectangular solid with the maximum volume would be a cube.
The surface area of a cube = 6A,
where A = the area of any one side
hence, the area of one side = 150/6 = 25 sq in.
The length of one face,
L = 25^0.5 = 5 in.
The volume, V of a cube = L^3.
Surface area
Surface area is the amount of space covering the outside of a three-dimensional shape.
volume
Volume is a three-dimensional quantity that is used to measure the capacity of a solid shape. It means the amount of three-dimensional space a closed figure can occupy is measured by its volume.
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question is in the picture below
Answer:
C
Step-by-step explanation:
The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?
Answer:110
Step-by-step explanation: Add 7 shingles every row you go up.
Row 1=75
2=82
3=89
4=96
5=103
6=110
Answer:
33
Step-by-step explanation:
it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!
STARTS AT 75
row one: 68
row two: 61
row three:54
row four: 47
row five: 40
row six: 33