Answer: H(x)=4(x-9)^2-17
Step-by-step explanation:
what is 475.53 minus 67.37
Which expression is equivalent to (4g^3h^2k^4)^3/8g^3h^2 - (h^5k^3)^5
Given expression:[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}-\left(h^5k^3\right)^5[/tex]
[tex]\left(4g^3h^2k^4\right)^3:\quad 2^6g^9h^6k^{12}[/tex]
[tex]8:\quad 2^3[/tex]
[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}=\frac{2^6g^9h^6k^{12}}{2^3g^3h^2}[/tex]
[tex]=2^3g^6h^4k^{12}[/tex]
[tex]\left(h^5k^3\right)^5=h^{25}k^{15}[/tex]
[tex]\frac{\left(4g^3h^2k^4\right)^3}{8g^3h^2}-\left(h^5k^3\right)^5=2^3g^6h^4k^{12}-h^{25}k^{15}[/tex]
[tex]=8g^6h^4k^{12}-h^{25}k^{15}[/tex]
Therefore, correct option is 4th option [tex]8g^6h^4k^{12}-h^{25}k^{15}[/tex].
Answer:
ANSWER IS D
Step-by-step explanation:
Find the midpoint of segment below
He ratio of the lengths of the corresponding sides of two rectangles is 8:3. the area of the larger rectangle is 320 ft2. what is the area of the smaller rectangle? 120 ft2 30 ft2 90 ft2 45 ft2
What can you say about the nature of any other zeros of the quadratic equation ax^2+bx+c=0 , which has one complex zero? Explain your answer.
which of the diagram below represents the statement. if it is an insect then it has wings
Geoffrey wrote the following paragraph proof showing that rectangles are parallelograms with congruent diagonals.
According to the given information, quadrilateral RECT is a rectangle. By the definition of a rectangle, all four angles measure 90°. Segment ER is parallel to segment CT and segment EC is parallel to segment RT by the Converse of the Same-Side Interior Angles Theorem. Quadrilateral RECT is then a parallelogram by definition of a parallelogram. Now, construct diagonals ET and CR. Because RECT is a parallelogram, opposite sides are congruent. Therefore, one can say that segment ER is congruent to segment CT. Segment TR is congruent to itself by the Reflexive Property of Equality. The _______________ says triangle ERT is congruent to triangle CTR. And because corresponding parts of congruent triangles are congruent (CPCTC), diagonals ET and CR are congruent.
Which of the following completes the proof?
A (ASA) Theorem
B (HL) Theorem
C (SAS) Theorem
D (SSS) Theorem
The answer is (SAS) Theorem. Because we know triangle ERT is congruent to triangle CTR, it has the sides ( C& E and R&T, and the angle T&R).
Hope its correct.
A first grader measures 1 meter high how much bigger is a first grader compared to the height of a book
To solve this problem, we would be needing the actual height or size of the book which is not given in the problem. However for the sake of calculation let us assume that the average height of a book is 8.5 inches.
Then the next step we have to do is to convert the height of the first grader from units of meter to units of inches. We know that:
1 meter = 39.37 inches
Therefore the height of the first grader is 39.37 inches.
Taking the ratio with the bigger number in the numerator (height of the 1st grader / height of the book):
ratio = 39.37 inches / 8.5 inches
ratio = 4.63
Therefore this means that the first grader is about 4.63 times taller than the book.
Line PQ has endpoints at P (-2,3) and Q (4,1). The center of dilation is (-1,4) and the scale factor is 2. What are the coordinates of the endpoints of P'Q'?
Which number sentence below matches this word problem?
Jen and Marcus got 15 miles up river before they ran out of gas. They floated 9 miles back down river before they reached the shore. How far did they get? A.15 - 6 = 9
B. 9 + 15 = 24 C.15 - 9 = 6
D. 135 9 = 15
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
Jen and Marcus got 15 miles up river before they ran out of gas. They floated 9 miles back down river before they reached the shore
so, distance they travel before they ran out of gas = 15 miles
distance they floated back down river = 9 miles
So, they are at
[tex]15-9\\\\=6\ miles[/tex]
Hence, They are 6 miles far.
Therefore, Option 'C' is correct.
a machine fills 150 bottles of water every 8 minutes. How many minutes will it take this machine to fill 675 bottles?
Find the area of the circle. Leave your answer in terms of pi diameter is 4.1 m
Answer:
Area of the circle will be (4.20 [tex]\pi[/tex])
Step-by-step explanation:
We have to find the area of the circle with diameter given is 4.10 m.
Since radius of a circle is represented by [tex](\frac{diameter}{2})[/tex]
Therefore, radius of the circle = [tex](\frac{4.1}{2})[/tex] = 2.05 m
Formula of the area of a circle is A = [tex]\pi r^{2}[/tex]
So area of the circle with radius 2.05 m will be
A = [tex]\pi (2.5)^{2}[/tex]
= 4.20 [tex]\pi[/tex]
Area of the circle will be (4.20 [tex]\pi[/tex])
Find the exact value of tan (arcsin (two fifths)). For full credit, explain your reasoning.
[tex]\rm tan\theta = \dfrac{2}{\sqrt{21} }[/tex]
Step-by-step explanation:
Given :
[tex]\rm sin^-^1(\dfrac{2}{5})=\theta[/tex]
Calculation :
[tex]\rm sin\theta = \dfrac{perpendicular}{hypotenuse}[/tex]
According to Pythagorean theorem,
[tex]a^2+b^2=c^2[/tex]
here a = 2, c = 5. Then,
[tex]2^2+b^2=5^2[/tex]
[tex]b^2=25-4=21[/tex]
[tex]b=\pm\sqrt{21}[/tex]
Nothing is given in the question so we take positive
[tex]b = \sqrt{21}[/tex]
Therefore,
[tex]\rm tan\theta=\dfrac{perpendicular}{base}[/tex]
[tex]\rm tan\theta = \dfrac{2}{\sqrt{21} }[/tex]
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Identify an equation in standard form for an ellipse with its center at the origin, a vertex at (9, 0), and a co-vertex at (0, 1).
One of the acute angles of a right triangle is 50° and its hypotenuse is 7 inches. find the lengths of its legs to the nearest tenth of an inch.
Final answer:
To determine the lengths of the legs of a right triangle with a hypotenuse of 7 inches and an acute angle of 50°, we use the trigonometric functions cosine and sine. The adjacent leg (A) is approximately 4.5 inches and the opposite leg (B) is approximately 5.4 inches, both to the nearest tenth.
Explanation:
The student asked: "What are the lengths of the legs of a right triangle if one of the acute angles is 50° and the hypotenuse is 7 inches?"
To find the lengths of the legs of a right triangle, we can use trigonometry. The cosine of an angle in a right triangle is equal to the adjacent leg divided by the hypotenuse, and the sine of an angle is equal the opposite leg divided by the hypotenuse.
Since we know the hypotenuse (7 inches) and one acute angle (50°), we can find:
the length of the opposite leg (leg B) using sine (sin(50°) = leg B / 7 inches).
By solving these equations:
leg A = cos(50°) × 7 inches
leg B = sin(50°) × 7 inches
After calculating, we find:
leg A ≈ 4.5 inches (to the nearest tenth)
leg B ≈ 5.4 inches (to the nearest tenth)
In four to five sentences, explain some of the factors that cause shifts in supply and demand and what the effects of these shifts are.
Answer:
Sample Response: Shifts in supply and demand occur when the amount of goods available increases or decreases, or when the demand for a particular good increases or decreases. Shifts in supply can happen when consumers change their spending habits, when competitors produce similar goods, or when the availability of labor or resources changes. Shifts in demand occur when the price changes or when the number of people trying to buy the good changes. It can also happen when people's tastes change.
If two cylinders are similar and the ratio between the lengths of their edges is 4:3 what is the ratio of their volumes
Answer:
64:27
Step-by-step explanation:
Maria needs $2.35 to buy a magazine. The only money she has is a jar of nickels and dimes. Write an equation in standard form for the different amounts of nickels x and dimes y she could use. Show your work :)
can anyone help me calculate AC, AD, and EC?
AC = sqrt(56^2 + 33^2) = 65cm
EC = sqrt(65^2 - 16^2) = 63 cm
to find AD 33-25 = 8
8^2 + 56^2 = AD^2
64 + 3136=3200^2
square root (3200) = 56.5685 round off to 56.6cm
John received $0.76 change from a purchase in the drugstore. if he received eight coins, and five of the coins are the same denomination, how many quarters did he receive?
5 nickels , 2 quarters, and 1 pennies = 8 coins.
he received 2 quarters
(08.02)How many solutions are there for the system of equations shown on the graph?
No solution
One solution
Two solutions
Infinitely many solutions
Answer:
The system of equations has no solution
Step-by-step explanation:
We have to find the number of solutions of system of equations shown in the graph.
Since, the number of solutions of system of equations is that point of thew graph on which the graph of two equations meet.
Since, we can see from the graph the two lines are parallel
Hence, they can never meet.
Hence, the system of equations has no solution.
Hence, first option is correct.
Solve for t: 35t + 70 (7-t) = 385
a segment is divided into two parts having lengths in the ratio of 5:3. if the difference between the lengths of the parts is 6 " find the length of the longest part
The length of the longest part is 15 units.
The length of the longest part in a segment divided into parts in the ratio of 5:3 with a difference of 6 units is 15 units.
The length of the longest part is 15 units.
Let the lengths of the two parts be 5x and 3x.Since the difference between them is 6, we can set up the equation 5x - 3x = 6.Solving for x gives x = 3, so the longest part is 5x = 5 * 3 = 15 units.The photo printed has length of 6 imams width of 4. A smaller picture is printed the ratio of the new picture to the size of the first picture is 1.5 to 2. What's the length and width of the new picture?
The new picture will have a length of 4.5 inches and a width of 3 inches.
There is asking about the size of a scaled-down photo in comparison to the original photo that has a length of 6 inches and a width of 4 inches. Given the ratio of the new picture to the size of the first picture is 1.5 to 2, we need to calculate the new dimensions.
The scale factor from the original to the new photo is 1.5 / 2, which simplifies to 0.75. Thus, we multiply the original dimensions by 0.75 to find the dimensions of the new picture:
Length of new picture = 6 inches * 0.75 = 4.5 inches
Width of new picture = 4 inches * 0.75 = 3 inches
The minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let v
represent the wind speed.
The absolute value equation that represents the minimum and maximum speeds of a Category 1 hurricane is |v - 84.5| ≤ 10.5, where v is the wind speed.
Explanation:To write an absolute value equation that represents the minimum and maximum speeds of a Category 1 hurricane, you will center it around the average of the two, which is (74 + 95) / 2 = 84.5 mph. The difference between the maximum speed and the average speed is 95 - 84.5 = 10.5 mph. Thus, the absolute value equation to represent the wind speeds of this hurricane category is |v - 84.5| ≤ 10.5, where v represents the wind speed.
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An absolute value equation representing the minimum and maximum sustained wind speeds of a Category 1 hurricane can be written as |v - 84.5| = 10.5, where v is the wind speed in miles per hour. This equation indicates that the wind speed can deviate by 10.5 mph above or below 84.5 mph, encompassing the range of 74 to 95 mph.
Explanation:To represent the minimum and maximum sustained wind speeds of a Category 1 hurricane using an absolute value equation, we can use the variable v to stand for the wind speed. The absolute value of a number represents its distance from zero regardless of direction, which in the context of wind speed means how much the speed differs from a certain value.
For instance, if the center value is the average of the minimum and maximum speeds, that would be (74 + 95) / 2 = 84.5 miles per hour. Therefore, the absolute value equation that represents the wind speeds that form the boundaries of Category 1 could be written as |v - 84.5| = 10.5. This equation means that the Category 1 wind speed, v, can be 10.5 miles per hour above or below 84.5 miles per hour, which corresponds to the range between 74 and 95 miles per hour.
However, there usually isn't just one single absolute value equation to represent this range. Another approach could involve setting two absolute value inequalities that represent the minimum and maximum separately, such as |v - 74| ≥ 0 for the minimum speed and |v - 95| ≤ 0 for the maximum speed.
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How many pints of blood does a person have for every 14 pounds of body weight?
Answer:
[tex]1[/tex] units.
Step-by-step explanation:
Here body weight is 14 pounds =[tex]\frac{14}{2.205}[/tex] kg =[tex]6.35[/tex] kg (∵ 1 kg ≈ 2.205 ponds ).
Normally, 75 ml of blood needs, if the body weight is 1 kg. Therefore total amount of blood for the body weight 14 pounds [tex](6.35 kg) = 6.35*75 ml=476.25 ml[/tex] [tex]=.47625 l[/tex] and we know that 1 litter of blood =2.11338 point of blood.
Hence total amount of blood = [tex]0.47625*2.11338[/tex] points =[tex]1.006497[/tex] units≈ [tex]1[/tex] units.
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If y varies directly with x and y = 15 when x = 5, what is the value of k?
y = kx
15 = k5
k = 15/5
k = 3
What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expected values. Thank you!
Answer with explanation:
⇒A game will be fair , if there is equal chance of winning and losing.
→The game would be fair , if
Landing on Blue sector gives 3.5 points.
Then the, Expected value will be
[tex]E(x_{i})=x_{i} \times P(x_{i})\\\\E(x)=x_{1} \times P(x_{1})+x_{2} \times P(x_{2})+x_{3} \times P(x_{3})+x_{4} \times P(x_{4})\\\\E(x)=-1 *\frac{2}{7}+(0) *\frac{2}{7}+(1) *\frac{2}{7}+(3.5) *\frac{1}{7}\\\\E(x)=(3.5) *\frac{1}{7}\\\\E(x)=0.50[/tex]
→→By Assigning, Blue sector =3.5 points, the game will become fair, Gives, E(x)=0.50.
A game is considered fair if the expected value for all players is zero, balancing the potential wins and losses over the long run. By adjusting winnings and losses so that the sum of the expected values of all outcomes is zero, and recalculating these expected values, we can prove the fairness of the game.
Explanation:To make a game fair using expected values, one must ensure that the expected value for all players is zero, meaning that there's no advantage or disadvantage to playing the game in the long run. The expected value is calculated by multiplying the value of each possible outcome by its probability and summing these products.
Let's consider the card and coin flipping game and determine its fairness. The expected value (EV) for this game can be expressed as:
EV(face card and heads) = P(face card) * P(heads) * winnings from face card and headsEV(face card and tails) = P(face card) * P(tails) * winnings from face card and tailsEV(non-face card) = P(non-face card) * (P(heads) + P(tails)) * loss from non-face cardTo avoir long-term loss, the sum of the expected values for all outcomes should be zero. If the current values do not result in a fair game, we can adjust the winnings and losses such that the expected value is balanced. By recalculating these probabilities with new values, we can verify if the game is fair or not.
The given measurements may or may not determine a triangle. If not, then state that no triangle is formed. If a triangle is formed, then use the Law of Sines to solve the triangle, if it is possible, or state that the Law of Sines cannot be used. B = 137°, c = 9, b = 14
Final answer:
Explanation of units for trigonometric functions and how to apply the Law of Sines in triangle problems.
Explanation:
The units for sine, cosine, and tangent must be dimensionless. These trigonometric functions relate angles to side lengths in a triangle.
The Law of Sines can be used to solve triangles when you have a known angle and the opposite side length. It states that the ratio of the length of a side to the sine of its opposite angle is constant.
When given measurements may or may not form a triangle, you can apply the Law of Sines to determine if a triangle can be solved. If not, it means no triangle can be formed.