Answer: x= 4/9
Step-by-step explanation:
9x^2-16=0
9x^2 = 16
9x = 4
x= 4/9
a better understanding of how I can solve for 1/2d-3/4d+3f-2f
The simplified form of the given expression is, 1/4d + f.
What is simplified form of the expression?
To simplify an expression, create an equivalent expression without any terms that are similar.
The expression will then be rewritten using the fewest terms possible.
Mathematical operations can be made much simpler by using the right order of operations. Exponents, terms in parentheses, multiplication, division, addition, and finally subtraction are the correct order of operations.
Consider the given expression,
1/2d - 3/4d + 3f - 2f
Here the like terms are '1/2d and 3/4d' and '3f and 2f'.
To simplify the expression,
1/4d + f
Hence, the simplified form of the given expression is, 1/4d + f.
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The maker of an automobile advertises that it takes 11 seconds to accelerate from 25 kilometers per hour to 75 kilometers per hour. Assuming constant acceleration, compute the distance, in meters, the car travels during the 11 seconds. Round your answer to two decimal places. 168.06 m 152.78 m 305.56 m 76.39 m 32.73 m
The value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.
Explain the equation of motion?motion is shift in a body's orientation or position over time. Translation is defined as movement across a line or a curve. Rotation is a motion that modifies a body's orientation.Time t = 11 sec
Initial velocity u = 25 kmph
u = (25 × 1000)/(60 × 60) = 6.9 m/s
final velocity v = 75 kmph
v = (75 × 1000)/(60 × 60) = 20.83 m/s
From the first equation of motion;
v = u + at
Put the values;
20.83 = 6.9 + 11a
20.83 - 6.9 = 13a
11a = 13.93
a = 13.93 / 11
a = 1.26 m/s²
Thus, the value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.
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Describe fully the single transformation that takes shape P to shape Q.
Answer: Shape P is similar to shape Q, however, shape P, is smaller than shape Q.
A single transformation that takes shape P to shape Q is; a dilation by a scale factor of 3 with a center of dilation at .
Reasons:
The give figure shows;
The preimage figure = P
The image figure = Q
The image P is larger than the preimage Q, therefore, the figure, Q is a
dilation of the preimage P
(x₁, y₁) = A point on the preimage, P = (2, 3)
(x₂, y₂) = The corresponding point on the dilated image, Q = (4, 9)
k = The scale factor = 3
Therefore;
The center of dilation, (x₀, y₀) = (1, 0)
Therefore;
The single transformation that takes shape P to shape Q is a dilation by a scale factor of 3 with a center of dilation at (1, 0).
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Step-by-step explanation:
Jane bought 3 shirts and returned 2 pairs of pants. Her friend Laura bought 4 shirts and 3 pairs of pants. Jane’s bill was $5 and Laura’s bill was $120. Write a systems of equations to determine the cost of a shirt, s, and the cost of a pair of pants, p.
The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120
Define System of Equation
A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given,
Jane bought 3 shirts and returned 2 pairs of pants
Laura bought 4 shirt and 3 pairs of pants.
Let, s = cost of shirt
and, p = cost of a pair of pants
The equation for Jane is
3s - 2p = $5
Here, -ve sign because Jane returned 2 pairs of pants and then bill was $5.
Now, the equation for Laura is
4s + 3p = $120
Here, +ve sign because Laura bought 4 shirt and 3 pairs of pants and then bill was $120.
So, the system of equation we get
3s - 2p = $5
4s + 3p = $120
After solving simultaneously we get the values s = 15 and p = 20.
Now, if you want to cross check then put the values of s and p in equations and it should be equal to RHS value like this,
for 1st equation,
3 * 15 - 2 * 20 ⇒ 45 - 40 = 5 (which is correct)
for 2nd equation,
4 * 15 + 3 * 20 ⇒ 60 + 60 = 120 (which is correct)
Hence, The system of equations to determine the cost of a shirt and the cost of a pair of pants is 3s - 2p = $5 and 4s + 3p = $120.
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Will give big points
Answer: 6 and 7
Step-by-step explanation: The square root of 41 is 6.4. Since you multiply it by itself, it’s the nearest square root to 41.
Jacob makes lemonade to sell at a carnival. He makes 20 cups of lemonade in 120 minutes. Working at this rate, how many cups of lemonade can Jacob make in 1 hour?
Answer:
10 cups
Step-by-step explanation:
120minutes divided into 60minutes = 2 hours
20 divided by 2 = 10 cups
evaluate the integral by interpreting it in terms of areas. 0 36 − x2 dx −6
The value of the original integral is 42, as expected.
What must an answer about a indefinite integral of a function include?
A definite integral is an infinitesimal sum derived from a integrable function, that is, a function that exist for all value x within the range of integration.
To evaluate this integral, we can interpret it in terms of the area of a region. To do this, we can rewrite the integral as:
∫0 36 − x2 dx −6
= ∫0 36 x2 dx + ∫0 36 dx
= ∫x2 dx + ∫dx
The first integral on the right-hand side represents the area under the curve y = x^2 from x = 0 to x = 6.
The second integral on the right-hand side represents the area of the rectangle with base 6 and height 1, which is just 6.
Therefore, the original integral can be interpreted as the sum of the area under the curve y = x^2 from x = 0 to x = 6 and the area of the rectangle with base 6 and height 1. This area is equal to 36 + 6 = 42. Thus, the value of the original integral is 42.
We can also verify this result using the formula for the area under a curve:
∫x2 dx = (1/3) x3 + C
Substituting the limits of integration, we get:
∫0 6 x2 dx = (1/3) * 6^3 - (1/3) * 0^3
= (1/3) * 216
= 72
Therefore, The value of the original integral is 42, as expected.
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Need help understanding how to Solve EBF = 6x+4 and CBF = 7x-2 find EBF
The measure of angle EBF is 40 degrees
How to determine the measure of angle EBF?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
EBF = 6x + 4
CBF = 7x - 2
Also from the question, we understand that the measures of angle EBF and the measure of angle CBF are congruent
This can be represented mathematically as follows
EBF = CBF
Substitute the known values in the above equation, so, we have the following representation
6x + 4 = 7x - 2
Multiply through by 1
6x + 4 = 7x - 2
Collect the like terms
7x - 6x = 4 + 2
Evaluate the like terms
x = 6
Recall that
EBF = 6x + 4
Substitute the known values in the above equation, so, we have the following representation
EBF = 6 x 6 + 4
Evaluate
EBF = 40
Hence, the measure is 40 degrees
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Complete question
If the measures of angle EBF and the measure of angle CBF are congruent and EBF = 6x+4 and CBF = 7x-2 find EBF
Bruno Fruscalzo decided to start a small production facility in Sydney to sell gelato to the local restaurants. His local milk supplier charges $0.5 per kg of milk plus a $15 delivery fee (that is independent of the amount ordered). Bruno’s holding cost is $0.03 per kg per month. He needs 9250 kgs of milk per month.
a. Suppose Bruno orders 9750 kgs each time. What is his average inventory (kgs)? 4,875 kgs
(Round your answer to 1 decimal place.)
b. Suppose Bruno orders 6250 kgs each time. How many orders does he place with his supplier each year? 1.0 orders
c. How many kgs should Bruno order from his supplier with each order to minimize the sum of ordering and holding costs? 15 kgs
(Do not round intermediate calculations. Round your answer to 2 decimal places.)
d. If Bruno’s storage vessel can hold only 2000 kgs of milk, what would be Bruno’s annual ordering and holding costs?
(Do not round intermediate calculations. Round your answer to 2 decimal places.)
e. If Bruno’s storage vessel can hold only 5750 kgs of milk, what would be Bruno’s annual ordering and holding costs?
(Do not round intermediate calculations. Round your answer to 2 decimal places.)
f. Bruno’s supplier’s truck can carry 20,000 kgs of milk. The supplier does not want to deliver to more than 3 customers with each truck. Thus, the supplier requires a minimum order quantity of 6,500 kgs. If Bruno orders the minimum amount, what would be the sum of his annual ordering and holding costs? Assume he has a storage vessel large enough to hold 6,500 kgs.
(Round your answer to 3 decimal places.)
g. Bruno’s supplier offers a 4% discount when a customer orders a full truck, which is 20,000 kgs. Assume Bruno can store that quantity and the product will not spoil. If Bruno orders a full truck, what would be the inventory holding and ordering cost incurred per kg of milk? Assume the discount also applies to the holding cost.
1 decimal places required.
The cost of the milk from the supplier can be calculated as follows:
Cost of milk = (price per kg of milk) * (number of kg of milk) + delivery fee
= $0.5/kg * 9250 kg + $15
= $<<0.5*9250+15=4675>>4675
The holding cost of the milk can be calculated as follows:
Holding cost = (holding cost per kg per month) * (number of kg of milk)
= $0.03/kg/month * 9250 kg
= $<<0.03*9250=277.5>>277.5
Therefore, the total cost of the milk for Bruno's production facility is $4675 for the milk from the supplier and $277.5 for the holding cost, for a total of $4952.5.
please help asap! theres a picture below to help
The coefficient and constant in the system of linear equations are identified below
System of Linear EquationThe system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1.
In this question, we are given two equations to define the variables.
3x + 7y = 18 ...eq(i)
2x - 4y = 9 ..eq(ii)
In the equations above;
3 = The coefficient of x in the first equation7 = The coefficient of y in the first equation2 = The coefficient of x in the second equation-4 = The coefficient of y in the second equation18 = The constant in the first equation9 = The constant in the second equationLearn more on system of linear equation here;
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Rhett drove 50 miles East then 40 miles North. How many miles would Rhett have driven directly from the starting point to the end point? (Round to the nearest mile)
Answer:
[tex]\sqrt{4100}[/tex]
Step-by-step explanation:
Step 1 Substitute Using Pythagorean Theorem:
x = [tex]\sqrt{50^2+40^2}[/tex]
Step 2 Solve:
[tex]50^2=2500[/tex]
[tex]40^2=1600[/tex]
Therefore,
[tex]\sqrt{50^2+40^2}=\sqrt{4100}[/tex]
Which equation could represent the situation described and how long does it take for the bacteria to reach 16,000?
The equation to represent the given situation is [tex]500(2)^x=16000[/tex] after 5 hours. Therefore, option B is the correct answer.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, a bacteria has an initial population of 500 and is doubling every hour.
Let x be the number of hour bacteria population to reach 16,000
The bacteria reaches a population of 16,000 bacteria.
So, the equation is [tex]500(2)^x=16000[/tex]
⇒ [tex]2^x[/tex]=16000/500
⇒ [tex]2^x[/tex]=160/5
⇒ [tex]2^x=2^5[/tex]
⇒ x=5
Therefore, after 5 hours the bacteria population reaches 16,000.
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for each 7-subset of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, give the next largest 7-subset or indicate that the 7-subset is the last one in lexicographic order. (a) {1, 2, 3, 4, 5, 6, 7} (b) {2, 4, 5, 9, 11, 12, 13} (c) {2, 4, 5, 11, 12, 13, 14} (d) {2, 4, 5, 6, 11, 12, 14} (e) {7, 8, 10, 11, 12, 13, 14}
(a) {2, 3, 4, 5, 6, 7, 8}
(b) {2, 4, 5, 9, 11, 12, 14}
(c) No next largest 7-subset; this is the last one in lexicographic order.
(d) {2, 4, 5, 6, 11, 12, 13}
(e) No next largest 7-subset; this is the last one in lexicographic order.
What in math is a subset?If all of the items in a set A are also in a set B, then the sets A and B are subsets of one another. To put it another way, the set A is contained within the set B. A and B stand for the subset connection.
Subset example: What is it?For instance, if A represents the set of natural numbers and B represents the set of all whole numbers, then B is a subset of A since the set of whole numbers contains all natural numbers. This is how we may comprehend it: Natural numbers 1, 2, 3, and so on make up the set A. B = A collection of whole numbers, such as "0, 1, 2, 3,..."
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(d)
Most of the kinetic energy of the diver is transferred to the water.
How does this affect the thermal energy of the water?
Tick (✓) one box.
The thermal energy decreases.
The thermal energy stays the same.
The thermal energy increases.
Most of the kinetic energy of the water is transferred into the water, then the thermal energy will increase. Hence, option C is correct.
What is kinetic energy?Kinetic energy is the term used in physics to describe the force that a moving item has. It is described as the amount of effort necessary to accelerate anybody with a particular mass from rest to a given velocity. Except variations in speed, the body retains the kinetic energy it gains during acceleration.
The body uses exactly the same amount of energy when slowing down from its current rate to a state of rest. Formally, kinetic energy refers to any term in a system's Lagrangian that has a derivative with respect to time.
As per the given information in the question,
When the kinetic energy of the diver is transferred into the water, the thermal energy will increase.
The entity's thermal energy grows as the average kinetic energies of its particles rise. As a result, an object's thermal energy rises as its temperature does.
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Two hikers set out from camp. the first hikes 4 miles due west then turns 40° south and hikes 1.8 miles. second hikes 4 miles to East then turns 52° north toward North in Heights 1.8 miles which hiker is farther from the camp explain
Answer:
The second hiker is farther away from the visitor center as all things being equal cos 128 < cos 140
from distance^2 = 4^2 + 1.8^2 -- 2*4*1.8 cos (angle turned).
Step-by-step explanation:
brainliest pls
Answer:
The first hiker is the farthest from camp since 140° > 128°.
Step-by-step explanation:
The journeys of both hikers can be modelled as triangles (see attachment).
Even though they hike the same distance of 4 miles plus 1.8 miles, as the angles of their turns between the two legs of their journeys are different, the final distance they are from camp is also different.
The first hiker turns 40° south so the included angle of the triangle is 140°.
The second hiker turns 52° north, so the included angle of the triangle is 128°.
As 140° > 128°, the distance between the first hiker and camp is farther than the distance between the second hiker and camp.
To prove this, use the cosine rule to find the missing length of each triangle.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Cosine Rule} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
First hiker:
[tex]\implies c^2=4^2+1.8^2-2(4)(1.8) \cos 140^{\circ}[/tex]
[tex]\implies c^2=19.24-14.4\cos 140^{\circ}[/tex]
[tex]\implies c=\sqrt{19.24-14.4\cos 140^{\circ}}[/tex]
[tex]\implies c=5.501912393[/tex]
Second hiker:
[tex]\implies c^2=4^2+1.8^2-2(4)(1.8) \cos 128^{\circ}[/tex]
[tex]\implies c^2=19.24-14.4\cos 128^{\circ}[/tex]
[tex]\implies c=\sqrt{19.24-14.4\cos 128^{\circ}}[/tex]
[tex]\implies c=5.301464443[/tex]
As 5.50 > 5.30, this proves that the first hiker is farthest from the camp.
A satellite orbiting the earth uses radar to communicate with two control stations on the earth’s surface. The satellite’s orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth’s radius is 3,963 miles, answer the following questions. Round all answers to the nearest whole number.
1. Is there a right angle in the triangle shown by connecting the center of the earth, the satellite, and Station 1? How do you know? *Assume that the line connecting the satellite and Station 1 is tangent to the earth.
The number of miles that a signal sent from Station 1 to the satellite and then to Station 2 will have to travel is; 48135 miles
How to find the distance of separation?Let us first find the distance from Station 1 to the satellite:
Using trigonometric ratio, we have;
tan 8.7 = length of longest leg/length of shortest leg
Thus;
tan 8.7 = 3963/length of longest leg
Length of longest leg = 3963/tan8.7°
Length of longest leg = 3963/0.15302150298
Length of longest leg = 25,898 miles
Distance from Station 2 to satellite:
Using trigonometric ratio again, we have;
sin 8.7 = length of longest leg/ length of hypotenuse
sin 8.7 = 3963/length of hypotenuse
Length of hypotenuse =3963/ sin 8.7
Length of hypotenuse =3963/0.1526082024
Length of hypotenuse = 26, 200 miles
Thus, the difference is;
26200 - 3,963 = 22237 miles
Total distance will calculated as;
25898 miles + 22237 miles = 48135 miles
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The complete question is:
A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles.
How many miles will a signal sent from Station 1 to the satellite and then to Station 2 have to travel?
HELP PLEASEJG
Problem: What is the actual distance between two cities if it is drawn to scale of 1:3,000,000 and it is 3 cm on the map?
Answer:
distance between two cities will be 9 000 000 km
Answer:
Step-by-step explanation:Scale of a map is 1:3000000 i.e, 1cm on map =30km so distance of towns on map =3.5cm Actual distance = 3.5×30=105km
Can someone help me with making the x the subject of the formula100 point up for grabs pls helpppp I will make brainliest
y =xa+ b
y =xa− b
y =x + 2 divided by two
Answer:
x = [tex]\frac{y-b}{a}[/tex]
Step-by-step explanation:
y = xa + b ( subtract b from both sides )
y - b = xa ( isolate x by dividing both sides by a )
[tex]\frac{y-b}{a}[/tex] = x , that is
x = [tex]\frac{y-b}{a}[/tex]
-------------------------------------
y = xa - b ( add b to both sides )
y + b = xa ( isolate x by dividing both sides by a )
[tex]\frac{y+b}{a}[/tex] = x , that is
x = [tex]\frac{y+b}{a}[/tex]
--------------------------------------------
assuming you mean
y = [tex]\frac{x+2}{2}[/tex] ( multiply both sides by 2 to clear the fraction )
2y = x + 2 ( subtract 2 from both sides )
2y - 2 = x , that is
x = 2y - 2
What is the common ratio of the sequence below?
2/3, 1/6, 1/24, 1/96,…
1/9
1/4
4
9
2. Dottie needs to learn a total of 24 vocabulary words. She has learned 75% of the words.
How many of her vocabulary words did she learn so far?
A. 3
B. 6
C. 18
D. 21
A line has a slope of 1 and passes through the point (–3, –13)What is its equation in slope intercept form?
The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
The equation of the line is
y = x - 10.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The line has,
Slope = 1
Passes through = (-3, -13)
Now,
The equation of a line is given as,
y = mx + c
Put (-3, -13) = (x, y)
-13 = 1 x (-3) + c
-13 = -3 + c
c = -13 + 3
c = -10
Now,
The equation of the line.
y = 1x - 10
y = x - 10
Thus,
The equation of the line is
y = x - 10.
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! if f( n + 1) = f(n) + 2 and f(2) = 4 then f(4) =
explain
Answer: 8
Step-by-step explanation:
From our knowledge, we know two things.
f(n + 1) = f(n) + 2f(2) = 4From here, we can work out what f(3) is by substituting n as 2
f(2 + 1) = f(2) + 2
f(3) = 4 + 2 = 6
And we can work out f(4) by substituting n as 3
f(3 + 1) = f(3) + 2
f(4) = 6 + 2 = 8
Eventually, if you continue doing this, you will see a sequence forming where the next number is the previous number added by 2.
Which of the following is a factor of (x+y)3−(x3+y3)? · x2+y2+2xy · x2+y2−xy · xy2 · 3xy ·
We know that (D) 3xy is the factor of the given equation (x+y)³-(x³+y³) using the algebraic identity.
What is algebraic identity?An identity element, also known as a neutral element, in a binary operation on a set is a set element that, when the operation is applied, leaves each element of the set untouched.
In algebraic structures like groups and rings, this idea is applied.
The left side of the equation equals the right side of the equation in an algebraic identity.
As an illustration, (a+b)2 = a2+2ab+b2 is true for all values of and b.
So, we have the equation:
(x + y)³ - (x³ + y³)
Now, get factors as follows:
Use the algebraic identity: (a + b)³ = a³ + b³ + 3ab (a + b)
x³ + y³ + 3xy (x + y) - x³ - y³
Simplify one more step to obtain:
3xy (x + y)
Therefore, we know that (D) 3xy is the factor of the given equation (x+y)³-(x³+y³) using the algebraic identity.
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Correct question:
Which of the following is a factor of (x + y)3 - (x3 + y3 )
a. x² + y² + 2xy
b. x² + y² - xy
c. xy²
d. 3xy
solve by applying the counting principle.
A car dealership has five exterior color choices, six interior color choices, and two model choices. How many different ways could you choose a car?
There are 60 different ways could you choose a car and this can be determined by using arithmetic operations.
What are arithmetic operations?
For all real numbers, the four fundamental arithmetic operations in mathematics are: Finding the sum in addition ('+') Subtraction (Difference-finding; "-") Multiplication ("×") Finding the quotient in division ("÷").
Given :
A car dealership has five exterior color choices.
A car dealership has six interior color choices.
A car dealership has two model choices.
The following steps can be used to determine the different ways could you choose a car:
Multiply 5 and 6 that is multiply five exterior color choices and six interior color choices.
= 5 * 6
Multiply the above expression by 2 which is with two model choices.
= 30 * 2
Further, simplify the above expression.
= 60
Hence, There are 60 different ways could you choose a car.
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before agreeing to purchase a large order of polyethylene sheaths for a particular type of high-pressure oil-filled submarine power cable, a company wants to see conclusive evidence that the true standard deviation of sheath thickness is less than .05mm. what hypotheses should be tested? what are the type i and type ii errors?
Hypothesis is tested as H₀: σ = 0.05 mm versus H₁: σ < 0.05 mm.
The type I error occurs if we accept a shipment that should have been rejected .
A type II error occurs if we reject a shipment that should have been accepted.
Given that,
A corporation wants to see concrete proof that the genuine standard variation of sheath thickness is less than 0.05mm before committing to a significant order of polyethylene sheaths for a certain kind of high-pressure oil-filled submarine power line.
We have to find what theories need to be tested and what exactly are types I and ii errors.
We know that
H₀: σ = 0.05 mm
versus
H₁: σ < 0.05 mm.
In this context,
The type I error occurs if we accept a shipment that should have been rejected .
A type II error occurs if we reject a shipment that should have been accepted.
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how many solutions does 4(1/2x + 3) = 3x + 12 - x have?
please answer ASAP
Answer:
Infinite
Step-by-step explanation:
2x + 12 = 2x + 12
they both are equal
If 5 dollars can be exchanged for 7.7095 units of some foreign currency, how much of that currency can be obtained for 6 dollars?
If 5 dollars can be exchanged for 7.7095 units of some foreign currency, the unit of that currency that can be obtained for 6 dollars will be
How do we calculate how much currency can be obtained for 6 dollars?5 dollars can be exchanged for 7.7095 units. This means that 1 dollar equals to:
5 dollars / 5 = 7.7095 units / 5
1 dollar = 7.7095 units / 5
1 dollar = 1.5419 units.
Now, for 6 dollars, the foreign currency that can be obtained is:
= 6 * 1.5419 units
= 9.2514 units. Therefore, 9.2514 unit of the foreign currency can be obtained for 6 dollars.
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At the beginning of a population study, a city had 230,000 people. Each year since, the population has grown by 2.8%. Let t be the number of years since start of the study. Let y be the city's population. Write an exponential function showing the relationship between y and t.
Answer:
y = 0.028t + 230,000
Step-by-step explanation:
We know
t = number of years since the start of the study
y = be the city's population
Each year the population has grown by 2.8%, this is the slope
The city had 230,000 people, this is the y-intercept
2.8% = 0.028
The equation is y= mx + b
So, our equation in this case is
y = 0.028t + 230,000
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In the figure, quadrilaterals ABHI, BCDE, and EFGH are squares. Which statement can be concluded from the fact that the area of square ABHI plus the area of square BCDE is equal to the area of square EFGH?
The statement that can be concluded from the fact that the area of square ABHI plus the area of square BCDE is equal to the area of square EFGH is of:
D. BE² + BH² = EH².
How to obtain the areas?The area of a square of side length s is given by the side length squared, as follows:
A = s².
Hence the areas of each square on the image given at the end of the answer are given as follows:
Area of ABHI = AB² = BH² = HI² = AI² (all these side lengths are equal).Area of BCDE = BC² = CD² = DE² = EB².Area of EFGH = EH² = HG² = GF² = FE².Hence the correct statement regarding the areas is given as follows:
BE² + BH² = EH².
Meaning that statement D is correct.
Missing InformationThe problem is given by the image shown at the end of the answer.
More can be learned about the area of an square at https://brainly.com/question/25092270
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The vertices of a cube or cuboid is suppposed to be V, side is E and surface is F, then which of the following is the relation between them? Write it.
1) V+E+F=2
2)V+E-F=2
3) V-E+F=2
4)V-E-F=2
The relation between the vertices of a cube or cuboid is V, the side is E, and the surface, F is V - E + F = 2. Option 3) is the correct answer.
What is the relationship between the vertice, face and side of a cube or cuboid?The vertice, face, and side of a cube or cuboid are related by Euler's Theorem. This theorem states that the number of faces, vertices, and edges of any polyhedron are related by Euler's formula.
Euler's formula can be stated as:
F + V = E + 2.
or
F + V - E = 2
where,
F = equal to the number of faces,
V = equal to the number of vertices
E = equal to the number of edges.
Learn more about vertices on
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