Answer:
$8
Step-by-step explanation:
A group of tourists spends $156 to rent snorkels and fins.
They rented 15 snorkels and 18 pairs of fins.
Renting a snorkel costs four times as much as renting a pair of fins.
Let us assume that the rental cost of a pair of fins is x, so the rental cost of snorkel will be 4x.
Then total cost of 15 snorkels and 18 pairs of fins will be,
[tex]=15(4x)+18x[/tex]
[tex]=60x+18x[/tex]
[tex]=78x[/tex]
But it is given as $156, so
[tex]\Rightarrow 78x=156[/tex]
[tex]\Rightarrow x=2[/tex]
Therefore, the rental cost of a pair of fins is $2 and cost of snorkel is [tex]2\times 4=\$8[/tex]
basketball goal 10 ft high casts a shadow 36 ft long. Find the elevation to the sun
Answer:
angle of elevation to the sun is 15.52°
Step-by-step explanation:
basketball goal 10 ft high casts a shadow 36 ft long
This forms a right angle triangle. the diagram is attached below
We need to find out angle A
We know opposite side = 10ft and adjacent side = 36 ft
We use tan formula
[tex]tan(A) = \frac{opposite}{adjacent}[/tex]
[tex]tan(A) = \frac{10}{36}[/tex]
To find A we move tan to the other side, it becomes tan^-1
[tex]A =tan^{-1}(\frac{10}{36})[/tex]
A = 15.52
So angle of elevation to the sun is 15.52°
Your class field trip is to a museum that charges $4 for adults and $2 for students. If cost $60 for 27 tickets for your class, the teacher, and chaperones. How many adult tickets were purchased? How many student tickets were purchased?
Answer:
3 adults and 24 students
Step-by-step explanation:
We can set-up a system of equations to find the number of adults. We know students and adults attended. We will let s be the number of students and a be the number of adults. Since 27 tickets were purchased, then s+a=27.
We also know they were purchased for $60 and adult tickets cost $4 and student tickets cost $2. We can write 2s+4a=60.
We will solve by substituting one equation into the other. We start by solving the first equation for c. s+a=27 becomes s=27-a.
Now we substitute s=27-a into 2s+4a=60. Simplify and isolate the variable a.
2s+4a=60
2(27-a)+4a=60
54-2a+4a=60
54+2a=60
54-54+2a=60-54
2a=6
a=3
This means that 3 adults attended and 24 students attended since 3+24=27.
Please help im so dumb...uwu
Answer:
127
Step-by-step explanation:
We can use the Exterior Angle of a Triangle theorem to find x. It states that the exterior angle of a triangle is equal to the sum of the two opposite interior angles.
We will start with x+5. It is equal to 79 +____ an angle we don't know yet. But we do know that the angle____ and x equals 180 because they form a straight line. Therefore the unknown angle must be 180-x.
So we will set x+5=79+180-x. We will combine like terms, use inverse operations, and isolate.
x+5=79+180-x
x+5=259-x
x+x+5=259-x+x
2x+5=259
2x+5-5=259-5
2x=254
x=127
Answer:
127
Step-by-Step Explanation:
I already did this on edginuety :)
What is the radical form of each of the given expressions?
What is the radical form of each of the given expressions?
6 1/5
6 7/5
6 1/6
7 1/2
7 5/2
6 9/2
Answer:
[tex]6^{\frac{1}{5} }=\sqrt[5]{6}[/tex]
[tex]6^{\frac{7}{5} }=\sqrt[5]{6^7}[/tex]
[tex]6^{\frac{1}{6} }=\sqrt[6]{6}[/tex]
[tex]7^{\frac{1}{2} }=\sqrt[2]{7}[/tex]
[tex]7^{\frac{5}{2} }=\sqrt[2]{7^5}[/tex]
[tex]6^{\frac{9}{2} }=\sqrt[2]{6^9}[/tex]
Step-by-step explanation:
A radical is the root operation for n roots such as square root or cuberoot in the form [tex]\sqrt[n]{x}[/tex]. A fraction exponent [tex]x^{m/n}[/tex] can be converted to the radical form.
[tex]6^{\frac{1}{5} }=\sqrt[5]{6}[/tex]
[tex]6^{\frac{7}{5} }=\sqrt[5]{6^7}[/tex]
[tex]6^{\frac{1}{6} }=\sqrt[6]{6}[/tex]
[tex]7^{\frac{1}{2} }=\sqrt[2]{7}[/tex]
[tex]7^{\frac{5}{2} }=\sqrt[2]{7^5}[/tex]
[tex]6^{\frac{9}{2} }=\sqrt[2]{6^9}[/tex]
Define a function that transforms the parent root function with a horizontal compression by a factor of 5 and a downward shift of 10 units.
Answer:
[tex]f(x)=\sqrt[n]{5x}-10[/tex]
Step-by-step explanation:
Compression of a function (in graph) occurs when the coefficient of the function (the number in front of [tex]x[/tex]) increases from 1. e.g. 2, 3, 4, 5 etc.Expansion is when this same value is a fraction, e.g. [tex]\frac{1}{3} ,\frac{1}{5}[/tex] etc.Vertical shift upwards is when there is a positive number added to the original function and vertical shift downwards is when there is a negative number added to the original function.Parent root function is given by:
[tex]f(x)=\sqrt[n]{x}[/tex]
According to rules,
Compression would be achieved by multiplying the [tex]x[/tex] by 5. So, we would have [tex]\sqrt[n]{5x}[/tex]Downward vertical shift would be achieved by adding a [tex]-10[/tex] to the function.So, [tex]\sqrt[n]{x}-10[/tex]Combining these 2 transformation gives us the function:
[tex]f(x)=\sqrt[n]{5x} -10[/tex]
Answer choice A is right.
Answer:
A. f(x)= n√5x-10
Kaitlyn completed a bike race. The length of the race was 11 1/4 miles, and Kaitlyn averages 7 1/2 miles each hour. How long did it take Kaitlyn to finish the race? Show your work, and be sure to include the correct units in your answer.
Answer:
It took Kaitlyn 13.25 hours to complete the race.
Step-by-step explanation:
1. Take the number of miles and the average speed per mile
2. Multiply the distance by the speed; 11 1/4 x 7 1/2
4. Solve; 13 1/4 hours
5. Convert into decimals; 13.25 hours
Need help please thanks
Answer:
x-intercept = 3 ; y-intercept = -5
Step-by-step explanation:
Lets rearrange the equation into the form y = mx + b:
5x - 3y = 15
-3y = 15 - 5x
Divide by -3:
y = 5x/3 - 5
Here we know that b (-5) is the y-intercept, and we can find the x-intercept by starting at the y-intercept and using the slope till we get the x-intercept. Or you can set y = 0 and solve for x, either way you get x-intercept = 3.
This equation is in standard form, if you put it into slope-intercept form, you will be able to graph it. Once you graph it you will be able to find the intercepts.
5x - 3y = 15
-3y = -5x + 15
y = 5/3x - 5
X-Intercept: (3,0)
Y-Intercept: (0, -5)
Natasha is starting a house cleaning business. She purchased cleaning supplies and charged the same amount for each pool cleaned. -126 + 30x The expression represents the profit Natasha has earned from cleaning houses. How much money does she charge to clean a house? 30??
Answer:
Natasha charges $30 per house
Step-by-step explanation:
Profit = -126 + 30x
The cost of the cleaning supplies is 126
and the cost per house is 30
x = the number of houses cleaned.
HELP Can you determine the third angle measure in a triangle, if you know the other two angles?
Answer:
yes; you can just remember that all the angles on a triangle equal 180 so just add the two angles, subtract from 180 to get your last angle degrees.
There are more inches on a football field (100 yards) than there are centimeters on a 28 meter basketball court true or false
Answer:
The given statement is True
Step-by-step explanation:
WE have to find out that which one has more no of inches
so now we have
100 yards football field
28 meter basketball court
Total no of inches in one yard = 36 inches
Total no of inches in 100 yard = 36 * 100
= 3600 inches
Now total no of inches in one meter = 39.3701 inches
Total no of inches in 28 meter = 28 * 39.3701
=1102.3628 inches
So we can see that 1102.3628 is smaller than 3600
So It can also be seen that football field has more inches then a basketball court
So the given statement is True
Answer:
The given statement is true.
Step-by-step explanation:
First we will apply conversions to given terms:
1 yard has = 36 inches
So, 100 yards has = [tex]36\times100=3600[/tex] inches.
1 meter = 100 cm
So, 28 meters has = [tex]28\times100=2800[/tex] cm
So, now upon comparing we can see that 3600 is greater than 2800.
Therefore, the inches in a 100 yard field are greater than the cm in a 28 meter basketball court.
The statement given here is true.
help me with these math questions.
graph A
no x-intercept
no y-intercept
H.A is y = 5
V. A. is x = 0
*****************************************
Answer: [tex]\frac{150}{31}[/tex]
Step by step explanation:
log₆(5x + 6) - log₆(x - 4) = 2
log₆[tex](\frac{5x+6}{x-4})[/tex] = 2
[tex](\frac{5x+6}{x-4})[/tex] = 6²
[tex](\frac{5x+6}{x-4})[/tex] = 36
5x + 6 = 36(x - 4)
5x + 6 = 36x - 144
6 = 31x - 144
150 = 31x
[tex]\frac{150}{31}[/tex] = x
**********************************************************
Answers:
a. (-1, -5)b. upc. x = -1d. [tex]\frac{-2+\sqrt{15}}{3} and\frac{-2-\sqrt{15}}{3}[/tex]e. -2f. see attachmentg. domain (-∞, ∞) range [-5, ∞)Explanation:
f(x) = 3x² + 6x - 2
a=3 b=6 c=-2
x = [tex]\frac{-b}{2a} =\frac{-6}{2(3)} = \frac{-6}{6} = -1[/tex]
Axis Of Symmetry: x = -1
f(-1) = 3(-1)² + 6(-1) - 2
= 3 - 6 - 2
= -5
Vertex: (-1, -5)
x = [tex]\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}[/tex]
= [tex]\frac{-6+/-\sqrt{6^{2}-4(3)(-2)}}{2(3)}[/tex]
= [tex]\frac{-6+/-\sqrt{36+24}}{6}[/tex]
= [tex]\frac{-6+/-\sqrt{60}}{6}[/tex]
= [tex]\frac{-6+/-2\sqrt{15}}{6}[/tex]
= [tex]\frac{-2+/-\sqrt{15}}{3}[/tex]
x-intercepts: [tex]\frac{-2+/-\sqrt{15}}{3}[/tex]
What do you know to be true about the values of A and B
Answer with explanation:
There are two triangles.We will use angle sum property to get the correct Inequality.
In Triangle 1
→x° + a° + 75°=180°
→x° + a°= -75°+180°
→x° + a°= 105°
In triangle 2
→y° + b° + 60°=180°
→y°+b°=180°-60°
→y°+b°=120°
As there are four different variables ,and only two equations.So,we can't determine the value of , a and ,b.
Option D: Can't be Determined
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
What is the inverse of h?
Answer:
a
Step-by-step explanation:
Answer: D
Step-by-step explanation:
Inverse is when you swap the x's and y's and solve for "y":
y = 6x + 1
swap: x = 6y + 1
solve: x - 1 = 6y
[tex]\dfrac{1}{6}(x-1)=y[/tex]
Which expression has a solution of 56, if r = 8?
6r
7r
8r
9r
The required expression that has a solution of 56 is 7r. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
In order to determine the expression that has a solution of 56 when r = 8, lets inverse the expression, to determine the exact expression,
Now,
Let the constant value be x,
xr = 56
Put x = 8
8x=56
x = 56/8
x = 7
So the expression can be given as 7r = 56
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Use the diagram and the Pythagorean Theorem to find the EXACT area of square ABCD
A) 23
B) 24
C) 25
D) 26
What is the division property of exponents?
[tex]\dfrac{a^b}{a^c}=a^{(b-c)}[/tex]
Step-by-step explanation:An exponent represents repeated multiplication. For example, ...
... x^3 = x·x·x
... x^2 = x·x
If we divide these, the x's in the denominator cancel an equal number in the numerator:
... (x·x·x)/(x·x) = x
If we represent the repeated multiplication using exponents, we can represent the cancellation by subtraction:
... (x^3)/(x^2) = x^(3-2) = x^1 = x
Once we have this idea in mind that division can be done by subtracting denominator exponents, we can use it regardless of the magnitude or sign of the exponents involved.
Triangles ?ABC and ?DEF are similar. Find the lengths of the sides of ?DEF, if AB=2 cm, BC=3 cm, CA=4 cm, DE=1.5 cm.
The lengths of the sides of triangle DEF are DE = 0.75 cm, EF = 1.125 cm, and DF = 1.5 cm.
Explanation:Triangles ABC and DEF are similar, which means their corresponding angles are equal. In similar triangles, the ratio of the lengths of corresponding sides is constant. To find the lengths of the sides of DEF, we can use the ratio of the corresponding sides of ABC and DEF.
Let x be the length of DE in triangle DEF. Since DE corresponds to AB, we have the ratio x/2 = 1.5/4, which simplifies to x = 0.75 cm. Similarly, for EF corresponding to BC, y/3 = 1.5/4, giving y = 1.125 cm. Finally, for DF corresponding to CA, z/4 = 1.5/4, yielding z = 1.5 cm.
Therefore, the lengths of the sides of triangle DEF are DE = 0.75 cm, EF = 1.125 cm, and DF = 1.5 cm. This result is consistent with the idea that in similar triangles, the ratio of corresponding sides remains constant.
The calculation involved setting up and solving simple proportions based on the given lengths of the sides of triangle ABC and using them to find the lengths of the sides of triangle DEF.
Help me please!! Algebra two!
Answer:
a. -2, odd; -1, odd; 1, odd; 2, odd
b. [tex](x+2)(x+1)(x-1)(x-2)[/tex]
c. even likely degree 4
Step-by-step explanation:
A polynomial graph has several features we look for to determine the equations.
The zeros of the function are the x-intercepts. If the x-intercepts touch but do not cross then the intercepts have an even multiplicity like 2, 4, 6, etc. If the x-intercepts cross over then they have an odd multiplicity. Degree is the exponent or multiplicity of each zero. Therefore if we know the multiplicity of each zero we can add them together to find or make an educated guess for the degree of the entire polynomial. The shape of the graph tells us what type of polynomial. Odd degrees have a backwards S shape. Even degrees have a W shape. The shape can even tell us the if the equation has a positive or negative leading coefficient. Upside down W or an M shape is negative. While a sideways S shape is negative.In this graph, there are four real zeros: -2,-1,1,2
We can write them in intercept or factored form as (x-2), (x-1), (x+1) and (x+2).
Because the graph crosses the x-axis at -2, it's multiplicity is odd likely 1. This is the same for each of the zeros or x-intercepts.
The graph a W shape and facing upwards so it has a positive leading coefficient with an even degree.
This means the function has a degree of 4 or higher with the degree being even.
helpppppppppppppppp pleaseeeeeeeeeeee
Answer:
48, 11, and 90 from top to bottom
Step-by-step explanation:
Hi! You again!
so for every adult, there are 6 children
8+8+8+8+8, or 8x6, is 48
15+15+15+15+15+15, or 15x6 is 90
and the middle is where it's a bit tricky, since we have to divide instead of multiply.
we're trying to find out what times 6 is 66.
11+11+11+11+11+11 is 66.
Answer:
8-48
11-66
15-90
Step-by-step explanation:
make a table start from 1 and work your way down.
'' HOT PIZZA''is offering 20% disscount on all its pizzas. Ali orders a pizza for the reduced price of ?5.60 what was the origanal pizza?
Final answer:
To find the original price of a pizza before a 20% discount that resulted in a final price of £5.60, divide the final price by 0.8. The original price is calculated to be £7.00.
Explanation:
The question involves determining the original price of a pizza before a 20% discount was applied, given that the reduced price after the discount is £5.60.
To calculate the original price, we can use the formula for finding the original price when the final price and discount rate are known.
Let's denote the original price as OP. Since a 20% discount was applied, the pizza sold for 80% of its original price. The equation representing this situation is:
0.8 × OP = £5.60
Now, we divide the reduced price by 0.8 to find the original price:
OP = £5.60 / 0.8
OP = £7.00
Thus, the original price of the pizza was £7.00 before the 20% discount was applied.
David earned a gross pay of $160 for one week. He worked 20 hours. What is his hourly wage?
Answer:
8
Step-by-step explanation:
160 divided by 20 hours = 8.
David has a 8 hourly wage.
Your answer would be $8. 20hrs divided into $160=$8
Hope this helps....
At the county fair, two hot dogs and an ice cream cone cost $2.50. Two slices of pizza and an ice cream cone cost $3.50. What is the total cost of one hot dog, one slice of pizza and one ice cream cone at the county fair?
Answer:
The total cost of one hot dog, one slice of pizza and one ice cream cone at the county fair is $3.
Step-by-step explanation:
Let us assume that the cost of the one hot dogs be x.
Let us assume that the cost of the one ice cream cone be y.
Let us assume that the cost of the one silce of pizza be z.
As given
At the county fair, two hot dogs and an ice cream cone cost $2.50.
Than the equation becomes
2x + y = 2.50
Two slices of pizza and an ice cream cone cost $3.50.
2z + y = 3.50
Than two equations are
2x + y = 2.50 and 2z + y = 3.50
Adding the both above equation.
2x + y + 2z + y = 2.50 + 3.50
2x + 2z + 2y = 6
[tex]x + y + z = \frac{6}{2}[/tex]
x + y + z = 3
Therefore the total cost of one hot dog, one slice of pizza and one ice cream cone at the county fair is $3.
A cell phone package charges $39 even if 0 minutes are used during the month. Each additional minute of talk time adds $0.07. What is the total cost if you talked on the phone for 10 hours during the month?
using the formal y = mx + b
Answer:
total cost = $ 81
Step-by-step explanation:
It is given that the fixed cost is $ 39
and the cost per minute is $0.07
Let us assume the number of minutes used be x
we have
total cost = cost per minute × number of minutes used + fixed cost
we plug the given values, so we have
[tex]total cost = 0.07 x+39[/tex]
we need to find the total cost for 10 hours used
x= 10 hours = 10(60) minutes = 600 minutes
so we have total cost for x= 600 minutes
[tex]total cost = 0.07(600)+39[/tex]
[tex]total cost =42+39 = 81[/tex]
hence the total cost = $ 81
50 points if you can help me !
A student says that the function
f(x)-=(1/0.5)^x is an exponential decay function. Explain the students error
Answer:
The base is greater than 1, making it an exponential growth function.
Step-by-step explanation:
The student's mistake is that an exponential decay function can only have the base as less than 1, but because 1/0.5 = 2, it's an exponential growth function.
Answer:
Step-by-step explanation:
f(x)=(1/0.5)^x
Lets simplify what is in the parentheses
1 / .5 = 2
f(x)=(2)^x
Since 2 > 1
This function grows
please help ill give brainliest
Answer:
[tex]m=\frac{-10}{4}[/tex], [tex]\frac{-5}{4}=m+\frac{-15}{4}[/tex] and [tex]m+2=-0.5[/tex]
Step-by-step explanation:
We solve for m in the equation to find the value.
[tex]\frac{3}{4}+m=\frac{-7}{4} \\\frac{3}{4}-\frac{3}{4}+m=\frac{-7}{4}-\frac{3}{4}\\m=\frac{-10}{4}[/tex]
We now look for expressions which are [tex]m=\frac{-10}{4}=-2.5[/tex] or whose expressions solve to the same.
The following are equivalent [tex]m=\frac{-10}{4}[/tex], [tex]\frac{-5}{4}=m+\frac{-15}{4}[/tex] and [tex]m+2=-0.5[/tex].
Before she rides her bike, Saima warms up for 12 minutes. On Tuesday, Saima rode her bike for 52 miles. If it takes Saima 6 minutes to ride each mile, how long did it take for Saima to warm up and ride her bike on Tuesday?
Answer:
324 minutes or 5 hours 24 minutes
Step-by-step explanation:
On Tuesday, Saima rode her bike for 52 miles. If it takes Saima 6 minutes to ride each mile, then it takes her
[tex]52\cdot 6=312[/tex]
minutes to ride all 52 miles.
Before she rides her bike, Saima warms up for 12 minutes.
Therefore, it takes Saima
[tex]12+312=324[/tex]
minutes to warm up and ride her bike on Tuesday.
Step-by-step explanation:
On Tuesday, Saima rode her bike for 52 miles. If it takes Saima 6 minutes to ride each mile, then it takes her
minutes to ride all 52 miles.
Before she rides her bike, Saima warms up for 12 minutes.
Therefore, it takes Saima
minutes to warm up and ride her bike on Tuesday.
75 points to the first person who helps
The dot plot below shows the number of different types of trees in Sean's garden:
A straight line is shown with 4 equidistant marks. The first mark is labeled Redbud, the second mark is labeled Magnolia, the third mark is labeled Snowbell, and the fourth mark is labeled Maple. The first mark has 2 dots, the second mark has 3 dots, the third mark has 1 dot, and the fourth mark has 4 dots. Below the line is written Number of Trees.
Which table shows the data displayed in the dot plot?
Garden Trees Number
Redbud 4
Magnolia 1
Snowbell 3
Maple 2
Garden Trees Number
Redbud 1
Magnolia 2
Snowbell 0
Maple 3
Garden Trees Number
Redbud 2
Magnolia 5
Snowbell 6
Maple 10
Garden Trees Number
Redbud 2
Magnolia 3
Snowbell 1
Maple 4
Answer:
Garden Trees Number
Redbud 2
Magnolia 3
Snowbell 1
Maple 4
Step-by-step explanation:
If the first mark is labeled Redbud and has 2 dots then it has 2 trees.
If the second mark is labeled Mangolia and has 3 dots then it has 3 trees.
If the third mark is labeled Snowbell and has 1 dot then it has 1 tree.
If the fourth mark is labeled Maple and has 4 dots then it has 4 trees.
Answer:
D
Step-by-step explanation:
which of the following could be the graph of y=x^2-2
Answer:
3rd one for lesson: Translations of the Square Root Function
Step-by-step explanation:
It should be a parabola that opens upward and is shifted 2 units downward.
The graph of the quadratic function y = x² - 2 typically looks like.
The graph of the quadratic function y = x² - 2 is a parabola. Specifically, it's a upward-opening parabola because the coefficient of the x² term (which is 1) is positive.
- The vertex of the parabola is at the point (0, -2).
- The parabola opens upward, so it does not intersect or cross the x-axis.
- It reaches its minimum value at the vertex, which is -2.
The graph that represents an upward-opening parabola with a vertex at (0, -2) and does not intersect the x-axis. It should be a parabola that opens upward and is shifted 2 units downward.
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The sum of two numbers is 61 . The larger number is5 more than the smaller number. What are the numbers?
Answer: 33 and 28
Step-by-step explanation:
so, all we know is ? + ? = 61
if the larger number is 5 more than the smaller number, we can assume that..
33 + 28 = 61
The mean distance ran by all four of them is 30.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is that sum of two numbers is 61 . The larger number is 5 more than the smaller number.
We can write the equations as -
x + y = 61 .... Eq{ 1 }
y = x + 5 .... Eq{ 2 }
Now, we can write -
x + y = 61
x + x + 5 = 61
2x = 56
x = 28
and
y = 33
Therefore, the mean distance ran by all four of them is 30.
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A triangular table top has a base that is twice as long as its height. If the area of the table surface is 324 square inches, what is the value of the height and the base?
Answer:
Height is 18 inches.
Base is 36 inches.
Step-by-step explanation:
Let the base of the triangular table top be x inches.
The height will be [tex]\frac{1}{2}[/tex]x inches.
The area of the triangular table top is 324 inches²
Area of a triangle = [tex]\frac{1}{2}[/tex] × Base × Height
342 inches² = [tex]\frac{1}{2}[/tex] × x × [tex]\frac{1}{2}[/tex]x
[tex]\frac{x^2}{4}[/tex] = 324
Finding the square root on both sides gives;
[tex]\frac{x}{2}[/tex] = 18
Therefore x (the base) = 36 inches
And [tex]\frac{1}{2}[/tex] (the height) = 18 inches.
Final answer:
The height of the triangular table top is 18 inches, and the base is 36 inches, using the formula for the area of a triangle and given that the base is twice the height with an area of 324 square inches.
Explanation:
The question requires finding the height and base of a triangular table top given that the area is 324 square inches and the base is twice as long as the height. To find these dimensions, we can use the formula for the area of a triangle, which is Area (A) = [tex]\frac{1}{2}[/tex] × base (b) × height (h). Given that the base is twice the height, we can express the base as 2h.
Now, we can set up the equation using the given area: 324 = [tex]\frac{1}{2}[/tex] × 2h × h. Simplifying gives us 324 = h², so the height (h) would be the square root of 324, which is 18 inches. The base (2h) is therefore 36 inches. So, the dimensions of the tabletop are a base of 36 inches and a height of 18 inches.