explanation:
The sides of a cube are squares, and they are covered by the respective sides of the cubes covering that side of the big cube. If we can show that a sqaure cannot be descomposed in squares of different sides, then we are done.
We cover the bottom side of that square with the bottom side of smaller squares. Above each square there is at least one square. Those squares have different heights, and they can have more or less (but not equal) height than the square they have below.
There is one square, lets call it A, that has minimum height among the squares that cover the bottom line, a bigger sqaure cannot fit above A because it would overlap with A's neighbours, so the selected square, lets call it B, should have less height than A itself.
There should be a 'hole' between B and at least one of A's neighbours, this hole is a rectangle with height equal to B's height. Since we cant use squares of similar sizes, we need at least 2 squares covering the 'hole', or a big sqaure that will form another hole above B, making this problem inifnite. If we use 2 or more squares, those sqaures height's combined should be at least equal than the height of B. Lets call C the small square that is next to B and above A in the 'hole'. C has even less height than B (otherwise, C would form the 'hole' above B as we described before). There are 2 possibilities:
C has similar size than the difference between A and BC has smaller size than the difference between A and BIf the second case would be true, next to C and above A there should be another 'hole', making this problem infinite. Assuming the first case is true, then C would fit perfectly above A and between B and A's neighborhood. Leaving a small rectangle above it that was part of the original hole.
That small rectangle has base length similar than the sides of C, so it cant be covered by a single square. The small sqaure you would use to cover that rectangle that is above to C and next to B, lets call it D, would leave another 'hole' above C and between D and A's neighborhood.
As you can see, this problem recursively forces you to use smaller and smaller squares, to a never end. You cant cover a sqaure with a finite number of squares and, as a result, you cant cover a cube with finite cubes.
If you have a lowest score of 21 and a range of 47, your highest score will be:________
Answer: 68
Step-by-step explanation:
range=47 lowest score = 21 let highest score =x
Range=highest score - lowest score
47 = x - 21
x = 47 + 21
x = 68
Therefore the highest score is 68
The highest score is 68.
Range = Highest Score - Lowest Score
In this case,
the lowest score is 21 and
the range is 47.
So, we can rearrange the formula to solve for the highest score:
Highest Score = Range + Lowest Score
Substituting in the given values:
Highest Score = 47 + 21
Thus, the highest score will be 68.
The scale model of a rectangular garden is 1.5 ft by 4 ft. The scale model is enlarged by a scale factor of 7 to create the actual garden. What is the area of the actual garden
Answer:
The Area of the actual garden is 294 square feet.
Step-by-step explanation:
The scale model of a rectangular garden is 1.5 ft by 4 ft.
Length of scale model=1.5 ft
Breath of scale model=4 ft
The scale model is enlarged by a scale factor of 7 to create the actual garden.
It means that the dimension of the garden are multiplied with the scale factor to find the actual dimension.
Hence,
Length of actual garden=[tex]1.5\times 7= 10.5\ ft[/tex]
Breath of actual garden=[tex]4\times 7 = 28\ ft[/tex]
Now Area of garden can be calculated by multiplying length and breadth.
Framing the equation we get;
Area of actual garden=[tex]10.5\ ft \times 28\ ft = 294\ ft^2[/tex]
Hence, area of the actual garden is 294 square feet.
Answer:294 took test
Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,900 at 4.29%. He knows he has the option of beginning repayment of the loan in 4.5 years. He also knows that during this non-payment time, interest will accrue at 4.29%.
Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.
To calculate the interest that Rich will accrue during the 4.5-year nonpayment period on his federal unsubsidized student loan, we can use the formula for simple interest:
Interest = Principal (loan amount) x Rate x Time
Where:
Principal (loan amount) = $7,900
Rate = 4.29% (0.0429 as a decimal)
Time = 4.5 years
Now, plug these values into the formula:
Interest = $7,900 x 0.0429 x 4.5
Interest = $7,900 x 0.19205
Interest ≈ $1,518.45
So, Rich will accrue approximately $1,518.45 in interest during the 4.5-year nonpayment period on his federal unsubsidized student loan.
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Rich has been approved for a federal unsubsidized student loan and wants to know the interest that will accrue during his 4.5 years as a freshman in college. Calculating the interest using the formula, the total accrued interest is $1,146.75.
Explanation:Rich is attending a 4-year college and has been approved for a 10-year federal unsubsidized student loan of $7,900 at an interest rate of 4.29%. During his 4 years as a freshman, he has the option to start repaying the loan after 4.5 years. However, interest will continue to accrue at a rate of 4.29% during this non-payment period.
To calculate the interest that will accrue during the 4.5 years, we can use the formula:
Interest Accrued = Principal x Interest Rate x Time
Substituting the values, we get:
Interest Accrued = $7,900 x 0.0429 x 4.5 = $1,146.75
Therefore, the interest that will accrue during the non-payment time is $1,146.75.
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Match the square root with its perfect square: 1 . √4 1 2 . √144 2 3 . √9 3 4 . √121 4 5 . √64 5 6 . √169 6 7 . √100 7 8 . √25 8 9 . √1 9 10 . √36 10 11 . √81 11 12 . √16 12 13 . √49 13
Answer:
√1 1
√4 2
√9 3
√16 4
√25 5
√36 6
√49 7
√64 8
√81 9
√100 10
√121 11
√144 12
√169 13
Step-by-step explanation:
1. = 49
2. = 169
3. = 81
4. = 100
5. = 441
6. = 36
I just finished the assignment, trust me.
7600 people were surveyed about their favorite type of milkshake what percentage of the people like vanilla how many of the people like chocolate how many of the total people like vanilla or strawberry
Answer:
Lack of information
Step-by-step explanation:
I can't find what percent or whatever information about the flavour,so I guess you need to give more information. If you give me more information, I will try to reply in the comments.
Hope this helps!!! ;)
A 20 kg sphere is at the origin and a 10 kg sphere is at x = 20 cm. At what position on the x-axis could you place a small mass such that the net gravitational force on it due to the spheres is zero?
Step-by-step explanation:
Let the small mass be m and position on x axis be y.
A 20 kg sphere is at the origin.
Distance to 20 kg mass = y
A 10 kg sphere is at x = 20 cm
Distance to 10 kg sphere = 20 - y
We have forces between them are equal
We have gravitational force
[tex]F=\frac{GMm}{r^2}[/tex]
Where G = 6.67 x 10⁻¹¹ N m²/kg²
M = Mass of body 1
M = Mass of body 2
r = Distance between them
Here we have
[tex]\frac{G\times 20\times m}{y^2}=\frac{G\times 10\times m}{(20-y)^2}\\\\800-80y+2y^2=y^2\\\\y^2-80y+800=0\\\\y=68.28cm\texttt{ or }y=11.72cm[/tex]
So the small mass should be placed at x = 11.72 cm or x = 68.28 cm
The positions on the x-axis obtained using quadratic equation such that net gravitational force is zero are 68.28 and 11.72 cm respectively.
Recall the force of universal gravitational attraction :
[tex] \frac{Gm_{1}m_{2}}{r^{2}}[/tex]Sphere 1 :
Mass = 20 kg Distance of 20kg sphere = dSphere 2 :
Mass = 10kgDistance of 10kg sphere = 20 - dGravitational force ; sphere 1 :
[tex] \frac{G \times 20 \times m_{2}}{d^{2}}[/tex] --(1)Gravitational force ; sphere 2 :
[tex] \frac{G \times 10 \times m_{2}}{(20 - d)^{2}}[/tex] - - (2)Equate (1) and (2)
[tex] \frac{G \times 20 \times m_{2}}{d^{2}} = \frac{G \times 10 \times m_{2}}{(20 - d)^{2}} [/tex]
[tex] 20(20 - d)^{2} = 10 \times d^{2} [tex]
20(400 - 40d + d²) = 10d²
8000 - 800d + 20d² = 10d²
10d² - 800d + 8000 = 0
Divide through by 10
d² - 80d + 800 = 0
Using a quadratic equation solver :
d = 68.28 cm or d = 11.72 cm
The possible positions are 68.28 cm and 11.72 cm
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What additional information will allow you to prove the triangles congruent by the HL Theorem?A. A = EB. bce= 90C. ac = dcD. ac=bd
Answer:
C) AC=DC
Step-by-step explanation:
In the figure of question attached below:
In Δ ACB and Δ DCE, AB and DE are hypotenuse respectively.
According to HL theorem:
"If hypotenuse and one leg of right angle triangle is congruent to Hypotenuse and one leg of other right angle triangle then triangles are congruent"
According to above statement if AB and DE are hypotenuse of Δ ACB and Δ DCE respectively then either
AC = DC (leg)
BC = EC (leg)
In order to prove congruence of triangles using HL theorem, AC must be equal to DC.
So option C is correct.
Answer:
C ) AC=DC
Step-by-step explanation:
edge 2021
Susan has 5 more pennies than dimes, three times more nickels than dimes and 4 less quarters than pennies. If Susan has 7 dimes, what is the total value of her money?
Sketch the graph of the given function. Then state the function’s domain and range. f(x)= 1/2(5)^x+3
Answer:
Graph of the following function is attached with the answer.
Domain : ( - ∞ , + ∞ )
Range : ( 3 , + ∞ )
Step-by-step explanation:
[tex]f(x)=\frac{1}{2}x^{2}+3[/tex]
Domain of any quadratic equation is from negative infinity to positive infinity under no restrictions.
So, Domain : ( - ∞ , + ∞ )
The Range of any function can be calculated easily if there is just one term with variable. The method to find Range by that method is explained with the example as follows:
Range of x : ( - ∞ , + ∞ )Range of [tex]\textrm{x}^{2}[/tex] : [ 0 , + ∞ ) as every square number is more than or equal to zero.Range of [tex]\frac{1}{2}\textrm{x}^{2}[/tex] : [ 0 , + ∞ ) as 0/2 = 0 and ∞/2 = ∞.Range of [tex]\frac{1}{2}\textrm{x}^{2}+3[/tex] : [ 3 , + ∞ ) as 0 + 3 = 3 and ∞ + 3 = ∞.Therefore the Range of [tex]\mathbf{f(x)\boldsymbol=\frac{1}{2}x^{2}\boldsymbol+3}[/tex] is [ 3 , + ∞ )
(NOTE : [a,b] means all the numbers between 'a' and 'b' including 'a' and 'b'.
(a,b) means all the numbers between 'a' and 'b' excluding 'a' and 'b'.
(a,b] means all the numbers between 'a' and 'b' including only 'b' not 'a'.
[a,b) means all the numbers between 'a' and 'b' including only 'a' not 'b'.
{a,b} means only 'a' and 'b'.
{a,b] or (a,b} doesn't mean anything. )
math question in the attached text
Answer:
A 1.44 cm cubed
Step-by-step explanation:
Just multiply all the numbers to get the area of the block
Answer:
A 1.44 cm cubed
Step-by-step explanation:
In an arcade game, a 0.13 kg disk is shot across a frictionless horizontal surface by being compressed against a spring and then released. The spring has a spring constant of 242 N/m and is compressed from its equilibrium position by 5.2 cm. What is the magnitude of the spring force on the disk at the moment it is released?
Answer:
12.584 N
Step-by-step explanation:
To solve this problem you need to use Hokke's law, this is a physics lar which states the force (F) you need to compress a spring for some distance (x) can be easily calculated with the equation F=kx. The constant k (the stiffness of the spring) is the value of 242 N/m and x is the distance 5.2 cm = 0.052 m. So if you multiply 242 N/m by 0.052 m you will obtain 12.584 N, which is the necessary force to compress the spring 5.2 cm. The mass of the spring is a nonrelevant data in this problem.
Your grandmother always has a jar of cookies on her counter. One day while you are visiting, you eat 555 cookies from the jar. In the equation below, ccc is the number of cookies remaining in the jar and bbb is the number of cookies in the jar before your visit.
Answer:
For 1 How does grandma have so many cookies??? For 2 if i eat 555 cookies then imma have diabetes. and for 3 there really is no way to find this out. The only way to find out how many cookies there is now it to see how much cookies there were before and you cant do that without seeing how much is in there now. Its a catch 22.
Step-by-step explanation:
Ann increased the quantities of all the ingredients in a recipe by 60\%60%60, percent. She used 808080 grams (\text{g})(g)left parenthesis, start text, g, end text, right parenthesis of cheese. How much cheese did the recipe require?
Answer:
50 grams
Step-by-step explanation:
Let the amount of cheese required by the recipe be "x"
Ann increased 60% from original amount and then used up 80 grams. Thus:
Original, increased by 60%, became 80
This translated to algebraic equation would be:
x + 0.6x = 80
Note: 60% = 60/100 = 0.6
So we can solve the above equation for "x" and get our answer. Shown below:
[tex]x + 0.6x = 80\\1.6x=80\\x=\frac{80}{1.6}\\x=50[/tex]
Hence,
the recipe required 50 grams of cheese
If an integer n is to be selected at random from the integers 1 to 100, inclusive, what is the probability that n(n 1) will be divisible by 4
Answer:
Step-by-step explanation:
total integers=100 (1,2,3,...,98,99,100)
numbers divisible by 4 =25 (4,8,12,...,96,100)
P=25/100=1/4
Here are the records of two different sequences (A,B ) of a coin tossed eight times. A: T H H H H H H H B: H T T H T H H T If you know for sure that the coin is fair, are these two sequences equally probable outcomes or, if they are not, which sequences is more probable than the other?"
Answer: Sequence B is more probable than A.
Step-by-step explanation:
This two sequences are not equally probable. Sequence B is more probable than A due to the equal chances of getting head (H) and a tail (T). The probability of getting a head is equal to the probability of getting a tail which is 4/8 i.e 0.5
The sequence A is less probable because the head(H) occur more than tail (T). The probability of head occurring is almost a sure event i.e 1 which is not feasible.
Can someone please write the equation of hyperbola with vertices (0, -5) and (0, 5) and co-vertices (-2, 0) and (2, 0)?
Thank you so much!
Answer:
y^2/25 -x^2/4 = 1
Step-by-step explanation:
The equation can be written as ...
y^2/a^2 -x^2/b^2 = 1
where the vertices are at (0, ±a) and the co-vertices are at (±b, 0). Filling in the given values (a=5, b=2) gives the equation shown above.
On July 31, Oscar checked out of the Sandy Beach hotel after spending four nights. The cost of the room was $76.90 per night. He wrote a check to pay for his four-night stay. What was the total amount of his check?
Answer:
$307.60
Step-by-step explanation:
multiple $76.90 by the 4 nights he stayed. $76.90×4
Answer:
76.00
Step-by-step explanation:
Let A be a set with a partial order R. For each a∈A, let Sa= {x∈A: xRa}. Let F={Sa: a∈A}. Then F is a subset of P(A) and thus may be partially ordered by ⊆, inclusion.
a) Show that if aRb, then Sa ⊆ Sb.
b) Show that if Sa ⊆ Sa, then aRb.
c) Show that if B⊆A, and x is the least upper bound for B, then Sx is the least upper bound for {Sb:b∈B}
Answer:
See proofs below
Step-by-step explanation:
a) Suppose that aRb. Let y∈Sa , then y∈A and yRa. We have that yRa and aRb. Since R is a partial order, R is a transitive relation, therefore yRa and aRb imply that yRb. Now, y∈A and yRb, thus y∈Sb. This reasoning applies for all y∈Sa that is, for all y∈Sa, y∈Sb, threrefore Sa⊆Sb.
b) Suppose that Sa⊆Sb. Since R is a partial order, R is a reflexive relation then aRa. Thus, a∈Sa. The inclusion Sa⊆Sb implies that a∈Sb, then aRb.
c) Denote this set by S={Sb:b∈B}. We will prove that supS=Sx with x=supB.
First, Sx is an upper bound of S: let Sb∈S. Then b∈B and since x=supB, x is an upper bound of B, then bRx. Then b∈Sx. Now, for all y∈Sb, yRb and bRx, then by transitivity yRx, thus y∈Sx. Therefore Sb⊆Sx for all Sb∈S, which means that Sx is an upper bound of S (remember that the order between sets is inclusion).
Now, let's prove that Sx is the least upper bound of S. Let Sc⊆A be another upper bound of S (in the set F). We will prove that Sx⊆T.
Because Sc is an upper bound, Sb⊆Sc for all b∈B. Thus, if y∈Sb for some b, then y∈Sc. That is, if yRb then yRc. In particular, bRb then bRc for all b∈B. Thus c is a upper bound of B. Byt x=supB, then xRc. Now, for all z∈Sx, zRx and xRc, which again, by transitivity, implies that z∈Sc. Therefore Sx⊆Sc and Sx=sup S.
In a partial order set, if aRb, then Sa ⊆ Sb. If Sa ⊆ Sb, then aRb. If B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}.
Explanation:a) To show that if aRb, then Sa ⊆ Sb, we need to prove that if x ∈ Sa, then x ∈ Sb. Since x ∈ Sa, that means xRa holds. And since aRb, we can conclude that xRb holds as well. Therefore, x ∈ Sb, which implies that Sa ⊆ Sb.
b) To show that if Sa ⊆ Sb, then aRb, we need to prove that if aRb does not hold, then Sa ⊆ Sb does not hold. If aRb does not hold, it means that b is not in Sa. However, if Sa ⊆ Sb, it implies that every element in Sa is also in Sb. Hence, we arrive at a contradiction, which proves that if Sa ⊆ Sb, then aRb.
c) To show that if B ⊆ A and x is the least upper bound for B, then Sx is the least upper bound for {Sb : b ∈ B}, we need to prove that Sx is an upper bound for {Sb : b ∈ B} and that it is the least upper bound. Since x is the least upper bound for B, this means that every element of B is contained in Sx. Therefore, Sx is an upper bound for {Sb : b ∈ B}. Additionally, if there exists an upper bound U for {Sb : b ∈ B}, then every element of {Sb : b ∈ B} must be contained in U. Since Sb is a subset of Sa for every b ∈ B, it follows that every element of Sa is contained in U. Therefore, Sa ⊆ U for every a ∈ A. In particular, Sx ⊆ U, which proves that Sx is the least upper bound for {Sb : b ∈ B}.
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2. Jenna Ford purchased a compact stereo that regularly sells for $229.99 at a markdown rate of 53%. In California, where Jenna lives, the sales tax rate on this item is 7%. Find the final price of the item.
Answer:
$115.67
Step-by-step explanation:
given that the markdown rate is 53%, that means that the markdown is 53% of the original price, or,
markdown = 53% of $229.99 = 0.53 x 229.99 = $121.89
sale price before tax = Original Price - Markdown
= 229.99 - 121.89
= $108.10
sales tax = 7% of sale price before tax
= 0.07 x 108.10
= $7.57
Final price = price before tax + tax
= 108.1 + 7.57
= $115.67
The measures of one acute angle in a right triangle is four times the measure of the other acute
angle. Write and solve a system of equations to find the measures of the acute angles.
Help with this exercise
[tex]A_2[/tex] = 18°
[tex]A_3[/tex] = 4(18°) = 72°
Step-by-step explanation:Given:
One angle in the triangle is 90°One angle that isn't 90° is 4 times larger than another angle that isn't 90°Angles:
[tex]A_1[/tex] = 90°
[tex]A_2[/tex] = x
[tex]A_3[/tex] = 4x
Solution Pathway:
Under the rules for any triangle, a triangle's interior angles must add up to 180°. Using this, we can set up the equation:
sum of the interior angles = 180°90° + x + 4x = 180°Now let's solve for x.
90 +x + 4x = 18090 + 5x = 1805x = 90x = 18°Now that we know x is 18°, lets plug this value into the two unknown acute angles.
[tex]A_2[/tex] = 18°[tex]A_3[/tex] = 4(18°) = 72°Answer:
72 degrees and 18 degrees.
Step-by-step explanation:
If the 2 angles are x and y, we have the system:
x + y = 90 (as it is a right triangle)
x = 4y (given).
Substitute x =- 4y in the first equation:
4y + y = 90
5y = 90
y = 18.
So x + 18 = 90
x = 90 - 18
x = 72.
Jake, a varsity swimmer, is training for his upcoming season and needs to accelerate his post-exercise recovery rates. He trains intensely for 2 hours, 5 days a week. If he weighs 155-lb (70.45 kg), which of the following nutritional strategies would BEST replenish his glycogen stores?
Answer:
high glycemic carb with some protein
Step-by-step explanation:
Food like white bread made from dextrose supplement and chocolate milk that contains some protein for muscle repair.
Due to the spongelike characteristic of the muscle would make it soak up glucose from high glycemic carb.
please answer soon Which expression is equivalent to − 7 x + 6 ( x − 8 2 ) − 2 ( x + 3 ) + 10 ? A. − 3 x + 40 B. − 15 x − 20 C. − 3 x − 20 D. 15 x + 40
Multiply the parenthesis by 6:
-7x+6x-492-2(x+3)+10
Multiply the parenthesis by -2:
-7x+6x-492-2x-6+10
Calculate the sum of similar terms:
-3x-492-6+10
Calculate the sum or difference:
-3x-488
£980 is divided between Caroline, Sarah & Gavyn so that Caroline gets twice as much as Sarah, and Sarah gets three times as much as Gavyn. How much does Sarah get?
Sarah has received £ 294
Solution:
Given that £980 is divided between Caroline, Sarah & Gavyn
Let "c" be the amount received by caroline
Let "s" be the amount received by sarah
Let "g" be the amount received by gavyn
Caroline gets twice as much as Sarah
amount received by caroline = twice as much as Sarah
amount received by caroline = 2(amount received by sarah)
c = 2s ---- eqn 1
Sarah gets three times as much as Gavyn
amount received by sarah = three times as much as Gavyn
amount received by sarah = 3(amount received by gavyn)
s = 3g ------- eqn 2
Given that total amount is 980
c + s + g = 980 --- eqn 3
Let us solve eqn 1, 2, 3 to get values of "c" "s" "g"
From eqn 2,
[tex]g = \frac{s}{3}[/tex] --- eqn 4
Substitute eqn 1 and eqn 4 in eqn 3
[tex]2s + s + \frac{s}{3} = 980\\\\\frac{6s + 3s + s}{3} = 980\\\\6s + 3s + s = 980 \times 3\\\\10s = 2940\\\\s = 294[/tex]
Thus sarah has received £ 294
Final answer:
To solve for the amount Sarah receives, set up ratios based on the information provided and solve the resulting equation. The total amount divided among them is £980, which when divided by the total parts (10) gives Gavyn's share as £98. Sarah's share is three times Gavyn's share, resulting in £294.
Explanation:
The problem described is a classic division in ratio mathematics question where £980 is being divided among Caroline, Sarah, and Gavyn following certain rules.
According to the problem, Caroline receives twice the amount that Sarah receives and Sarah receives triple the amount that Gavyn receives.
We can set up the following ratios: C = 2S and S = 3G, where C stands for Caroline's amount, S for Sarah's, and G for Gavyn's. If we denote Gavyn's amount as G, then Sarah's amount is 3G and Caroline's is 2 × 3G which is 6G.
To find the value of G, we can write the equation G + 3G + 6G = £980 or 10G = £980. Solving for G gives us G = £98.
Therefore, Sarah, receiving three times as much as Gavyn, gets 3 × £98 = £294.
Find the m∠p.
pls and thanks <3
Answer:
36°
Step-by-step explanation:
Like your other question, the angles of the triangle must add up to 180. The tangent line is perpendicular to the center, so the angle must be 90°.
90° + 54° + 36° = 180°
write a verbal phrase to describe f > -4
I would say it as "the letter F is greater than negative four."
21. What is the exact volume of a sphere whose diameter is 14 cm? Show your work.
Answer:
The exact volume of a sphere is [tex]V=1437cm^3[/tex]
Step-by-step explanation:
Given that the diameter of a sphere is 14cm.
That is d=14
First find the radius of the sphere with diameter
[tex]r=\frac{d}{2}[/tex]
[tex]r=\frac{14}{2}[/tex]
Therefore r=7cm
Now to find the volume of the sphere:
[tex]V=\frac{4}{3}\pi r^3cm^3[/tex]
[tex]V=\frac{4}{3}\frac{22}{7}(7)^3[/tex] (here[tex]\pi=\frac{22}{7}[/tex] and r=7)
[tex]V=\frac{4}{3}(22)(7)^2[/tex]
[tex]V=\frac{4}{3}(22)(49)[/tex]
[tex]V=\frac{4}{3}(1078)[/tex]
[tex]V=\frac{4312}{3}[/tex]
[tex]V=1437.33cm^3[/tex]
Therefore the volume of the given sphere is [tex]V=1437.33cm^3[/tex]
The exact volume of a sphere is [tex]V=1437cm^3[/tex]
The function f(x) = 6x + 8 represents the distance run by a cheetah in miles. The function g(x) = x − 2 represents the time the cheetah ran in hours. Solve (f/g)(3), and interpret the answer.
a. 26; the cheetah's rate in miles per hour
b. 26; the number of cheetahs
c. 1/26 ; the cheetah's rate in miles per hour
d. 1/26 ; the number of cheetahs
Option a. 26; the cheetah's rate in miles per hour is the correct answer.
Step-by-step explanation:
Given
[tex]f(x) = 6x+8\\g(x) = x-2[/tex]
As the function f is in miles and function g is is hours, and we are dividing the function f by function g so the new unit will be:
miles/hour = miles per hour
Now
[tex]\frac{f}{g}(x)= \frac{f(x)}{g(x)}\\\frac{f}{g}(x) = \frac{6x+8}{x-2}[/tex]
We have to find (f/g)(3) so putting 3 in place of x
[tex]\frac{f}{g}(x) = \frac{6(3)+8}{-2}\\= \frac{18+8}{1}\\= 26[/tex]
Hence,
Option a. 26; the cheetah's rate in miles per hour is the correct answer.
Keywords: Functions, function operations
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Three pounds of dried cherries cost $15.90, 5 pounds of dried cherries cost $26.50, and 9 pounds of dried cherries cost $47.70. Which equation gives the total cost y of x pounds of dried cherries?
Final answer:
The equation that gives the total cost of x pounds of dried cherries is y = (10.60/2)x.
Explanation:
Let's create a table to represent the given information:
Pounds of Dried Cherries (x)Total Cost (y)315.90526.50947.70
To find an equation that gives the total cost of x pounds of dried cherries, we need to find a pattern in the data. From the table, we can see that as the pounds of dried cherries increase, the total cost also increases. This suggests a linear relationship between pounds and cost.
Now, let's analyze the changes in cost for each additional pound of dried cherries:
From 3 to 5 pounds: The cost increased by $26.50 - $15.90 = $10.60.From 5 to 9 pounds: The cost increased by $47.70 - $26.50 = $21.20.Based on these changes, the cost increased by $10.60 for every 2 additional pounds of dried cherries. Therefore, the equation that gives the total cost y of x pounds of dried cherries is:
y = (10.60/2)x
Which of the following is the simple interest paid on a loan of $354 at 6% for six months?
$10.62
$10.26
$12.47
$12.74
Answer: interest at the end of 6 months is $10.62
Step-by-step explanation:
The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 6 months = 6/12 = 0.5 years
P = $354
R = 6%
Therefore
I = (354 × 6 × 0.5)/100
I = 1062/100
I = 10.62
What is the measure of a°?
Answer:
The correct answer is C. 129.
Step-by-step explanation:
Let's recall that the Inscribed Quadrilateral Theorem states that a quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary.
In the case of the inscribed quadrilateral ABCD in the graph attached, we have that:
m∠C= 51°, therefore its supplementary angle, ∠A, should be the difference between 180° and m∠C.
m∠C= 180° - m∠A
Replacing with the real values:
51 = 180 - m∠A
m∠A = 129°
The correct answer is C. 129.