What is the surface area of this square pyramid with a base length of 3 inches and a slant height of 7 inches?
Answers
Answer:
Step-by-step explanation:
To find the surface area of a square pyramid, we need to add the area of the base to the sum of the areas of the four triangular faces.
The area of the base of the pyramid is:
Area of square base = (base length)^2
Area of square base = 3^2
Area of square base = 9 square inches
To find the area of each triangular face, we need to first find the length of each side. Since the base is a square, all sides are equal to 3 inches. The slant height is given as 7 inches, which is the height of each triangular face.
Using the Pythagorean theorem, we can find the length of each side of the triangular face:
(side length)^2 + (height)^2 = (slant height)^2
(side length)^2 + 7^2 = 7^2
(side length)^2 = 7^2 - 7^2
(side length)^2 = 24.5
side length ≈ 4.95
The area of each triangular face is:
Area of triangular face = (1/2) × (base length) × (height)
Area of triangular face = (1/2) × 3 × 7
Area of triangular face = 10.5 square inches
Therefore, the total surface area of the square pyramid is:
Total surface area = Area of base + Sum of areas of four triangular faces
Total surface area = 9 + 4(10.5)
Total surface area = 42 square inches
Hence, the surface area of this square pyramid is 42 square inches.
Related Questions
QUESTIONLinda bought a 10-roll package of toilet paper for$10.25,"tax included. How much did the towels cosťper roll?A) * $10.25.B) $1:03C)..-$1.10D) $1.25
Answers
We have the following:
To calculate the unit price we must calculate the amount of total money spent for the total number of package of toilet paper purchased
\(p=\frac{10.25}{10}=1.025\cong1.03\)Therefore, the answer is the option B
Use the given conditions to determine the number of possible triangles.
first side length: 5 feet
second side length: 8 feet
third side length: 15 feet
Do the given conditions create a unique triangle, more than one triangle, or no triangle?
1-no triangle
2-unique triangle
3-more than one triangle
Answers
According to triangle inequality theorem, there is no triangle using the given length.
What is the triangle inequality theorem?
This theorem merely states that the third side of a triangle cannot be smaller than the total of the first two sides. You will have a valid triangle if this holds true for each of the three possible combinations. To confirm that the triangle is feasible, you will need to go through each of these combinations one at a time. Theorem a+b > c, a+c > b, and b+c > a can alternatively be thought of as an inequality. The triangle has sides of lengths a, b, and c.
We can find the conditions by using triangle inequality theorem.
Here given the sides
Let, a = 5feet b = 8feet c = 15feet
So the sum of a+b > c ,a+c > b and b+c > a
But here the sum of a and c is less than b
Hence it does not form any triangle.
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Which of the following terms best describes each of the two points marked with dots in the ellipse below?
Answers
Answer:
Focus.
Step-by-step explanation:
.
Answer:
The correct answer is D. Focus.
Step-by-step explanation:
A) What is the magnitude of the electric force on charge A in (Figure 1) ?
1.0 nC A 1 cm 1.0 nC 4.0 nC 1 cm
B)What is the direction of the net electric force on charge B in the figure? (up or down)
Answers
A) Magnitude of the electric force on charge A is approximately 3.596 × 10⁻² N.
B) Net electric force on charge B will be in the downward direction.
How to calculate the both parts of the qustion?A) To calculate the magnitude of the electric force on charge A, we can use Coulomb's Law:
F = (k * q1 * q2) / r²
where:
- F is the magnitude of the electric force
- k is the electrostatic constant, which is approximately 8.99 × 10⁹ N m²/C²
- q1 and q2 are the magnitudes of the charges (in this case, q1 = 1.0 nC and q2 = 4.0 nC)
- r is the distance between the charges (1 cm, which should be converted to meters: 1 cm = 0.01 m)
Now, plug in the values and solve for F:
F = (8.99 × 10⁹ N m²/C² * 1.0 × 10⁻⁹ C * 4.0 × 10⁻⁹ C) / (0.01 m)²
F ≈ 3.596 × 10⁻² N
The magnitude of the electric force on charge A is approximately 3.596 × 10⁻² N.
B) To determine the direction of the net electric force on charge B, we need to analyze the forces between charge B and charges A and C.
Since both charges A and C are positive and have the same magnitude (1.0 nC), they will both repel charge B. The forces between charges A and B, and B and C will be equal and opposite. Thus, the net electric force on charge B will cancel out horizontally.
However, the vertical component of the force between charge B and charge C will not be canceled out.
Since charge C is positive and has a higher magnitude (4.0 nC) than charge A, it will exert a stronger electric force on charge B. Therefore, the net electric force on charge B will be in the downward direction.
Learn more about Coulomb's Law.
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Logarithms and stuff, please help
Answers
Answer:
\(\displaystyle t=-25\log\left(\frac{20}{30}\right)\)
Step-by-step explanation:
Logarithms
The model that predicts the percentage of voters (V) as a function of the number of years (t) is:
\(V(t)=100-30\cdot e^{-0.04t}\)
It's required to find in how many years the value of V will be V=80%. The equation to solve is:
\(100-30\cdot e^{-0.04t}=80\)
Subtracting 100:
\(-30\cdot e^{-0.04t}=80-100=-20\)
Dividing by -30:
\(\displaystyle e^{-0.04t}=\frac{20}{30}\)
Applying logs:
\(\displaystyle \log( e^{-0.04t})=\log\left(\frac{20}{30}\right)\)
For logs property:
\(\displaystyle -0.04t\log(e)=\log\left(\frac{20}{30}\right)\)
log(e)=1. Solving for t:
\(\displaystyle t=\frac{\log\left(\frac{20}{30}\right)}{-0.04}\)
Since 0.04=1/25:
\(\boxed{\displaystyle t=-25\log\left(\frac{20}{30}\right)}\)
Which equation represents the graph of Charli's line? A. y= -3/4x-3. B. Y= 3/4x- 4. C. y = -4/3x- 4. D. y= 4/3x- 3. LOOK AT THE PHOTO PLZZ
Answers
a major credit card company has determined that customers charge between $300 and $1500 per month. the monthly amount charged is uniformly distributed. find the standard deviation of the monthly amount charged. (round to four decimal places if needed)
Answers
The standard deviation of the monthly amount charged is 346.41
Step 1: Identify the values of a and b, where [a , b] is the interval over which the continuous uniform distribution is defined.
Since it takes between 300 and 1500 minutes to be seated at the restaurant, we have:
a = 300
b = 1500
Step 2: Calculate the variance using the formula Var(x) = \(\frac{(b-a)^{2} }{12}\)
Using the formula for the variance and the values identified in step 1
(a = 300 , b = 1500), we have:
Var(x) = \(\frac{(b-a)^{2} }{12}\)
= \(\frac{(1500 - 300)^{2} }{12}\)
= 1440000/12
= 120,000
the variance is 120,000
Step 3: Calculate the standard deviation by taking the square root of the variance. σ = \(\sqrt{Var(x)}\)
The standard deviation is the square root of the result from step 2 (variance = 120,000)
σ = \(\sqrt{Var(x)}\)
σ = \(\sqrt{120000}\)
= 346.41
The standard deviation of the monthly amount charged is 346.41
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I just need level two and three solved please
Answers
Answer:
intercepts: (0, 5/2) or (-5, 0)arbitrary point: (7, 6)Step-by-step explanation:
You want two methods of choosing points on the line with slope 1/2 through A(-1, 2).
InterceptsWriting the equation in standard form, we can find the x- and y-intercepts. To get there, we can start from point-slope form:
y -k = m(x -h) . . . . . . line with slope m through point (h, k)
y -2 = 1/2(x -(-1)) . . . . . using given slope and point
2y -4 = x +1 . . . . . . . . . . multiply by 2
x -2y = -5 . . . . . . . . . . . . add -1 -2y
Setting x=0 tells us the y-intercept is ...
0 -2y = -5
y = -5/-2 = 5/2
So, the y-intercept is (0, 5/2).
Setting y=0 tells us the x-intercept is ...
x -2(0) = -5
x = -5
So, the x-intercept is (-5, 0).
Arbitrary pointIt will be convenient to choose an arbitrary y-value to find another point on the line. We can pick y = 6, for example, Then the corresponding x-value is ...
x -2y = -5
x = -5 +2y = -5 +2(6) = 7
Another point on the line is (7, 6).
__
Additional comment
If we were to choose an arbitrary value for x, we would want it to be odd, so the corresponding y-value would be an integer. We chose to pick an arbitrary value of y so we didn't have to worry about how to make the x-value an integer.
<95141404393>
Please help I will give brainliest and a lot of points :)
Answers
The inequality shaded in the graph is given as follows:
y ≥ 5x/2 + 3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:
b = 3.
When x increases by 2, y increases by 5, hence the slope m is given as follows:
m = 5/2.
Then the equation of the line is given as follows:
y = 5x/2 + 3.
The line is a solid line, and values above it are plotted, hence the inequality is given as follows:
y ≥ 5x/2 + 3.
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help. at this point ill give you head for help
Answers
A bag of balloons which are either green or purple. There are 15 green balloons for each purple balloon. How many green balloons are in the bag?.
Answers
Answer:
1
Step-by-step explanation:
if they said a bag maybe green or purple and 15 except for 1 is purple and 1 is green
Element X is a radioactive isotope such that every 3 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 410 grams, how much of the element would remain after 10 years, to the nearest whole number?
Answers
Answer:Y=41
Step-by-step explanation:
2x + 4 help me please lol
Answers
Answer:
2(x+2)
Step-by-step explanation:
The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 72% of the carbon-14 expected in living matter, when did the tree die?
Answers
Answer:
t =2654.01465 year
Step-by-step explanation:
Given that the half-life of carbon-14 is 5600 years and if a piece of charcoal made from the wood of a tree shows only 72% of the carbon-14 expected in living matter.
we know
\(y=a(b)^{t/h}\)
where y= final amount
a= initial amount
b= growth/decay
t= time elapsed
h= half time
plugging the values we get
\(0.72 =(\frac{1}{2})^{t/5600}\\\)
taking log on both side
log 0.72 = t/5600 log(1/2)
solving we get t =2654.01465 year
6x6x6x6
How would you write the following expression in exponential form?
Answers
Answer:
6 to the power of 4 6˄4
Step-by-step explanation:
you’re multiplying 6 four times (6x6x6x6)
Ryan is riding on a bike course that is 80 miles long. So far, he has ridden 56 miles of the course. What percentage of the course has Ryan ridden so far?
Answers
Hi :)
To find percentage, divide 56 by 80 and multiply by 100
To remember this, know that since 56 is of 80, of/number x 100 56/80 x 100
You should get something like 70, which happens to be your answer, 70%
Hope this helps,
Jeron
P.S (brainliest? only if i helped)
Which of the following numbers is closest to 12? O A. V145 B. 7147 C. V 142 D. V 146 . V
Answers
Answer: C
Step-by-step explanation:
Answer:
145
Step-by-step explanation:
12x12=144 and the closest number to 144 is 145
26 is 6 more than k. Solve for K.
Answers
Answer:
k = 20
Step-by-step explanation:
simplify both sides of the equation, then isolate the variable.
hope it helps you!:))
Ms. Gonzales is investing $17000 at an annual interest rate of 6%
compounded continuously. How much money will be in the account after
16 years? Round your answer to the nearest hundredth (two decimal
places).
Answers
Answer:
44398.84
Step-by-step explanation:
17,000e^(0.06)(16)
it helps to use a desmos scientific calculator
ing the Equation of a Line from a Table
What is the equation of the line with points represented in What can you conclude about the line represented in
the table?
the table? Select all that apply.
x
-8
4
8
y
6
-3
-6
Using either slope-intercept or point-slope forms will
result in different equations.
O Using either slope-intercept or point-slope forms will
result in the same equation.
3
The slope is
The slope is
4
3
The y-intercept is 2.
The y-intercept is 0.
Done
Answers
The equation is: y = -3/4x (in slope-intercept form) or y + 3 = -3/4(x - 4) (in point-slope form).
The correct statements are:
Using either slope-intercept or point-slope forms will result in different equations.The slope is -3/4.The y-intercept is 0.How to Write the Equation of a Line?The slope-intercept form is expressed as y = mx + b [m is the slope, b is the y-intercept].
The point-slope form is expressed as y - b = m(x - a) [(a, b) is a point on the line, while m is the slope of the line].
Given the table:
x | y
-8 6
4 -3
8 -6
Use two points, (-8, 6) and (4, -3), to find the slope:
Slope (m) = change in y / change in x = (-3 - 6) / (4 - (-8))
m = -9/12
m = -3/4
To find the y-intercept, substitute (x, y) = (4, -3) and m = -3/4 into y = mx + b:
-3 = -3/4(4) + b
-3 = -3 + b
-3 + 3 = b
b = 0
To write the equation in slope-intercept form, substitute m = -3/4 and b = 0 into y = mx + b:
y = -3/4x - 0
y = -3/4x
To write the equation in point-slope form, substitute m = -3/4 and (a, b) = (4, -3) into y - b = m(x - a):
y + 3 = -3/4(x - 4).
Therefore, we can conclude that:
Using either slope-intercept or point-slope forms will result in different equations.The slope is -3/4.The y-intercept is 0.Learn more about the equation of a line on:
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Hilaria borrowed $8,000 from her grandfather to pay for college. Four years later, she paid him back the $8,000, plus $1,600 interest. What was the rate of simple interest (as a percent)?
Answers
The rate of simple interest is 0.05, which is equivalent to 5% when expressed as a percentage.
To calculate the rate of simple interest, we can use the formula:
Interest = Principal * Rate * Time
Given that Hilaria borrowed $8,000 and paid back $1,600 in interest after four years, we can set up the equation:
$1,600 = $8,000 * Rate * 4
Divide both sides of the equation by $8,000 * 4
$1,600 / ($8,000 * 4) = Rate
Simplifying the equation: 0.05 = Rate
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13. Six friends will stay at a cabin in the woods this weekend.
The distance to the cabin is 148.5 miles. Each person will
drive one sixth of the distance. How far will each person
drive?
Answers
Answer:
Each person will drive 24.75 miles far.
Step-by-step explanation:
each person will drive = 1/6 of 148.5
or, each person will drive = 148.5/6
so, each person will drive = 24.75 miles.
i19-1 practice question seven
Answers
Answer:
D
Step-by-step explanation:
Write the equation of a line with a slope of 4 and a y-intercept of −3.
Answers
Answer: y=4x-2
Step-by-step explanation:
Slope-intercept form: y=ax+b, where a is the slope and b is the y-intercept.
Given: slope is 4, and y-intercept is -3
y=ax+b
y=4x+(-3)
y=4x-3
Hope this helps!! :)
Please let me know if you have any question
x = -5
y = -6
What is the solution set?
Answers
Answer:
I believe that it is x=9
Step-by-step explanation:
sorry if im wrong im not 100% sure
y =-0.011x + 40.604
What is the slope
Answers
WILL GIVE BRAINLIEST, please hurry!!!
Amanda estimates that the product of a fraction and a decimal is 7. Which expression could represent the fraction and the decimal?
A. 2/5 x 3.5
B. 1/3 x 7.02
C. 3/5 x 7.1
D. 6/7 x 8.42
Answers
Answer:
D
Step-by-step explanation:
Determine the value of A
Answers
Check the picture below.
\(\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{9}\\ a=\stackrel{adjacent}{4\sqrt{2}}\\ o=\stackrel{opposite}{a} \end{cases} \\\\\\ (9)^2= (4\sqrt{2})^2 + (a)^2\implies 81=4^2(2)+a^2\implies 81=32+a^2 \\\\\\ 49=a^2\implies \sqrt{49}=a\implies \boxed{7=a}\)
Which aspects of a four-hour shopping trip can be expected to vary inversely? A) the total distance walked and the number of steps taken B) the total number of stores visited and the average time spent in each store C) the total amount spent on shirts and the average cost per shirt D) the time it takes to walk from one store to another and the distance between the two stores E) the average wait time to make a purchase and the number of cashiers working in a store F) the number of customers paying by cash and the total number of customers SELECT ALL THAT APPLY
Answers
Answer:
The correct option is;
E) The average wait time to make payment and the number of cashiers working in a store
Step-by-step explanation:
An inversely proportional relationship is a relationship between two variables one where the increase in the magnitude one variable leads to the reduction in the magnitude of a second variable written mathematically as follows;
y ∝ 1/x
Therefore, given that as the number of cashiers at a store increases, the number of customers attended to per unit time by all the cashiers together increases, and the number of wait time observed by a customer to pay for the goods bought decreases.
Answer:
B.) The total number of stores visited and the average time spent in each store
E.) The average wait time to make a purchase and the number of cashiers working in a store
Step-by-step explanation:
It is correct I just took the test :)
how many roots does f (x) = 2x3 + x2 - 7x + 1 have
Answers
The equation would have three roots.
How many roots?The highest power term in a cubic equation is a variable raised to the third power, making it a polynomial equation of degree three. A cubic equation's general form is as follows:
Ax3 + Bx2 + Cx+ D = 0
There can be one, two, or three real roots in a cubic equation. Complex roots, which come in pairs called complex conjugates, are possible for cubic equations. The equation still has three roots in this instance, although they could not be true roots.
The roots of the equation are;
x1 = -2.19682
x2 = 0.14684
x3 = 1.54998
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