Find the axis of symmetry for this parabola:
y = -4x2 - 8x - 7

Answer:

here

Step-by-step explanation:

The distance between the earth and the moon is approximately 384000 km. To Do: Express the distance in meters in exponential notation. Therefore the answer is 3.84 × 10 8 m.

Answer:

Hope this helps ;) don't forget to rate this answer !

Step-by-step explanation:

To write a polynomial function of least degree with rational coefficients that has the given roots, we can use the factor theorem. The factor theorem states that if r is a root of a polynomial function P(x), then x - r is a factor of P(x).

In this case, the roots of the polynomial are x = -2 and x = 10. We can use the factor theorem to write a polynomial function that has these roots as follows:

P(x) = (x + 2)(x - 10)

This polynomial function has degree 2, which is the least degree possible, and all of its coefficients are rational numbers. It has roots x = -2 and x = 10, as required.

The answer of the given question , the  ordered pair represents the point labeled H is   (-1/2, 5/4).

A graph is  visual representation of data, which typically displays  relationship between two or more variable. Graphs are commonly used to present complex information and  an easy-to-understand manner. They allow us  quickly and easily identify patterns, trends, and relationships in data that might not be able to apparent from simply looking at raw numbers.

The origin is at (0,0), and point H is located to the left one-half unit and up one and one-fourth units from the origin.

Since the x-axis starts at negative 2, with tick marks every one-fourth unit up to positive 2, we can count the units from the origin to the left to find the x-coordinate of point H.

Starting from 0 and moving left by 1/4 unit 2 times, we get -1/2. Therefore, the x-coordinate of point H is -1/2.

Similarly, since the y-axis starts at negative 2, with tick marks every one-fourth unit up to positive 2, we can count the units from the origin upwards to find the y-coordinate of point H.

Starting from 0 and moving up by 1/4 unit 5 times, we get 5/4. Therefore, the y-coordinate of point H is 5/4.

Hence, the ordered pair that represents the point labeled H is (-1/2, 5/4).

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Answer:

b

Step-by-step explanation:

b

The simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

We can write the simplified form of the given expression using the exponent rule as -

{aˣ/aⁿ} = {aˣ a⁻ⁿ} = {aˣ ⁻ ⁿ}

Given is the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\)

We can simplify the expression as -

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (27)^{\frac{1}{2} \times \frac{2}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 27^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = (3)^{3}^{\frac{1}{3} }\)

\($(27^{\frac{1}{2} }) ^{\frac{2}{3} } = 3\)

Therefore, the simplified expression for \($(27^{\frac{1}{2} }) ^{\frac{2}{3} }\) is equal to 3.

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In 2021 a 30-second commercial during the Super Bowl cost $5.6 million and the CPI was approximately 271.4. Assuming that price changes are simply due to inflation, when the CPI was 33.4 the estimated cost of a 30-second commercial during the first Super Bowl in 1967 would be approximately $68,900.

To calculate the cost of the 30-second commercial during the first Super Bowl in 1967, we can use the concept of inflation and the Consumer Price Index (CPI).

The CPI measures the average price change of a basket of goods and services over time. By comparing the CPI values of two different years, we can estimate the relative increase in prices due to inflation.

Given data:

Cost of a 30-second commercial in 2021 = $5.6 million

CPI in 2021 = 271.4

CPI in 1967 = 33.4

To calculate the cost in 1967, we need to adjust the 2021 cost for inflation using the CPI ratio:

Cost in 1967 = (Cost in 2021) * (CPI in 1967 / CPI in 2021)

Cost in 1967 = ($5.6 million) * (33.4 / 271.4)

Cost in 1967 ≈ $0.689 million

To round the cost to the nearest hundred dollars, we can multiply the cost by 100 and round it to the nearest whole number:

Cost in 1967 ≈ $68,900

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"the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, the sum of two numbers is twenty-six the difference between five is more than the larger number and twice the smaller number' into a variable expression.

Since x represents the smaller of the two numbers,

Thus the larger number will be 26 - x

The expression asked above will be:

=> 5 + larger number - 2 * smaller number

=> 5 + 26 - x - 2 * x

=> 31 -3x

therefore,  "the difference between five more than the larger number and twice the smaller number' can be written as the expression 31 -3x.

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Answer:

804.25

Step-by-step explanation:

See image below:)

Answer: 3/4

Step-by-step explanation:

Both 81 and 108 are divisible by 27

Answer:

Step-by-step explanation:

The area of the shaded region of the rectangle is approximately 573.92 square feet.

The figure in the image is that of a rectangle with a semi-circle inscribed in it.

The area of rectangle is expressed as:

Area = Length × Width

The area of semi-circle is expressed as:

Area = 1/2 × πr²

To determine the area of the shaded region, we simply subtract the area of the semi-circle from the area of the rectangle.

Area of shaded region = area of rectangle - area of semi-circle

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

From the image:

Length = 40 ft

Width = 20 ft

Radius r = 12 ft

Plug the values into the above formula:

Area of shaded region = ( Length × Width ) - ( 1/2 × πr² )

Area of shaded region = ( 40 × 20 ) - ( 1/2 × 3.14 × 12² )

Area of shaded region = ( 800 ) - ( 226.08 )

Area of shaded region = 573.92 ft²

Therefore, the area is approximately 573.92 square feet.

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The mean is approximately 9, the median is 9, the mode is 8, and the range is 7.

To find the mean, we add up all the numbers in the data set and divide by the total number of numbers:

Mean = (7 + 6 + 8 + 12 + 9 + 13 + 8) / 7 = 63 / 7 ≈ 9

So the mean is approximately 9.

To find the median, we need to arrange the numbers in order from smallest to largest:

6, 7, 8, 8, 9, 12, 13

Since there are an odd number of values in the data set, the median is the middle value, which is 9.

To find the mode, we need to look for the value that occurs most frequently in the data set. In this case, 8 occurs twice, which is more than any other value, so the mode is 8.

To find the range, we need to subtract the smallest value from the largest value:

Range = largest value - smallest value = 13 - 6 = 7

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The required domain of the function If g(x) = f(-2x) is [-16, 8] in interval notation.

The domain of g(x) is the set of all x for which the function g(x) is defined. If g(x) = f(-2x), then the domain of g(x) is the same as the domain of -2x, subject to the restriction that f(x) is defined for the corresponding values of x.

In interval notation, the domain of -2x is (-∞, ∞).

However, since f(x) is defined only on the interval [-8, 4], the domain of g(x) must be restricted to values of x that correspond to values of -2x within the interval [-8, 4].

To find the corresponding values of x, we need to solve the equation -2x = t for x, where t is a number in the interval [-8, 4].

Solving for x, we get x = -t/2. So, the domain of g(x) is the set of all x such that -t/2 is in the interval [-8, 4], or equivalently, t is in the interval [-16, 8]. In interval notation, this is [-16, 8].

So, the domain of g(x) is [-16, 8] in interval notation.

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Answer:

\(X=6.67ft/s\)

Step-by-step explanation:

From the question we are told that:

Height of pole \(H_p=15\)

Height  of man \(h_m=6ft\)

Speed of Man \(\triangle a =4ft/s\)

Distance from pole \(d=35ft\)

Let

Distance from pole to man=a

Distance from man to shadow =b

Therefore

 \(\frac{a+b}{15}=\frac{b}{6}\)

 \(6a+6b=15y\)

 \(2a=3b\)

Generally the equation for change in velocity is mathematically given by

 \(2(\triangle a)=3(\triangle b )\)

 \(2*4=3(\triangle b)\)

 \(\triangle a=\frac{8}{3}\)

Since

The speed of the shadow is given as

 \(X=\triangle b+\triangle a\)

 \(X=4+8/3\)

 \(X=6.67ft/s\)

Let's make another angle y

Where y= 51° (corresponding angles )

and x+y= 180°. ( linear pair )

x+51°= 180° (y=51°)

x=180°-51°

x= 129°

So the value of x is 129°

Hope you got your answer !

Answer:

129°

Step-by-step explanation:

x and 51° are corresponding angles, therefore their sum is 180°

so x= 180° -51°= 129°

Answer:

X= 7

Step-by-step explanation:

Answer:

-12

Step-by-step explanation:

(-3)4

-3*4

-12

Elaborate ur question about - 34

Answer:

No, you cannot cross multiply when adding fractions. Cross multiply only when you need to determine if one fraction is greater than another

Step-by-step explanation:

The scenario is an observational study, done by the teacher.

The correct option is (B)

Firstly,  A type of study in which individuals are observed or certain outcomes are measured. No attempt is made to affect the outcome.

Survey is defined as the act of examining a process or questioning a selected sample of individuals to obtain data about a service, product, or process.

Experimental research, also called experimentation, is research conducted using a scientific approach using two or more variables.

If we look at the question, the teacher was trying to do the observational study. By observing the students answer.

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Using Proportion the table value is,

Cheese   Number of Pizzas

3 pounds          8

18 pounds        48

22.5 pounds    60

27 pounds        72

What is a proportion?

A percentage is created when two ratios are equal to one another. We write proportions to construct equivalent ratios and to resolve unclear values. a comparison of two integers and their proportions. According to the law of proportion, two sets of given numbers are said to be directly proportional to one another if they grow or shrink in the same ratio.

We have,

3 pounds bag of cheese makes 8 pizzas.

This means,

3 pounds = 8 pizzas

1 pound = 8/3 pizzas

Now,

1 pound = 8/3 pizzas

Multiply 18 on both sides.

18 pounds = 18 x 8/3

18 pounds = 48 pizzas

1 pound = 8/3 pizzas

Multiply 22.5 on both sides.

22.5 pounds = 22.5 x 8/3

22.5 pounds = 60 pizzas

1 pound = 8/3 pizzas

Multiply 27 on both sides.

27 pounds = 27 x 8/3

27 pounds = 72 pizzas

Thus,

The number of Pizzas for 3 pounds is 8.

The number of Pizzas for 18 pounds is 48.

The number of Pizzas for 22.5 pounds is 60.

The number of Pizzas for 27 pounds is 71.

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Answer:

Air conditioners are rated by the number of British Thermal Units (BTU) of heat they can remove per hour. Another common rating term for air conditioning size is the "ton," which is 12,000 BTU per hour.

Each air conditioner has an energy-efficiency rating that lists how many BTUs per hour are removed or “pulled out” for each watt of power it draws.

The efficiency rating for room conditioners is the Energy Efficiency Ratio, or EER.

The efficiency rating for central air conditioners, is the Seasonal Energy Efficiency Ratio, or SEER.

These ratings are posted on an Energy Guide Label, which must be conspicuously attached to all new air conditioners. Energy Star-labeled appliances mean that they have high EER and SEER ratings

The total amount the man had = 52,200 rupees. Out of this, he gave 21,750 rupees to his son, 13,050 rupees to his daughter, and 17,400 rupees to his wife , the total amount given away by the man = 21,750 + 13,050 + 17,400 = 52,200 rupees.

A man gave 5/12 of his money to his son, 3/7 of the remainder to his daughter, and the remaining to his wife. If his wife gets Rs. 8,700, what is the total amount?

The given problem can be solved using the concept of ratios and fractions. Let us solve the problem step-by-step.Assume the man had x rupees with him.The man gave 5/12 of his money to his son.

The remaining amount left with the man = x - 5x/12= (12x/12) - (5x/12) = (7x/12)The man gave 3/7 of the remainder to his daughter.'

Amount left with the man after giving it to his son = (7x/12)The amount given to the daughter = (3/7) x (7x/12)= (3x/4)The remaining amount left with the man = (7x/12) - (3x/4)= (7x/12) - (9x/12) = - (2x/12) = - (x/6) (As the man has given more money than what he had with him).

Therefore, the daughter's amount is (3x/4) and the remaining amount left with the man is (x/6).The man gave all the remaining amount to his wife.

Therefore, the amount given to the wife is (x/6) = 8700Let us find the value of x.x/6 = 8700 x = 6 x 8700 = 52,200

Therefore, the man had 52,200 rupees with him.He gave 5/12 of his money to his son. Therefore, the amount given to his son is (5/12) x 52,200 = 21,750 rupees.

The remaining amount left with the man = (7/12) x 52,200 = 30,450 rupees.He gave 3/7 of the remainder to his daughter. Therefore, the amount given to his daughter is (3/7) x 30,450 = 13,050 rupees.

The amount left with the man = (4/7) x 30,450 = 17,400 rupees.The man gave 17,400 rupees to his wife.
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d. True. The sum of four 50° angles is 200°, so they can compose a 200° angle.

what is a geometric sequence?

A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed constant called the common ratio. The common ratio is denoted by the letter r.

The general formula for a geometric sequence is:a₁, a₁r, a₁r², a₁r³, ...

a. False. The sum of a 20° angle and a 70° angle is 90°, so they can compose a 90° angle.

b. False. The sum of three 50° angles is 150°, so they cannot compose an angle that measures 350⁰.

c. False. The sum of a 15° angle and a 60° angle is 75°, so they can compose an angle that measures 75°.

Therefore, d. True. The sum of four 50° angles is 200°, so they can compose a 200° angle.

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Answer:

B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The size of the angle between AH and the plane ABCD is approximately 74.4°, rounded to one decimal place.

To find the size of the angle between AH and the plane ABCD in the given cuboid, we can use the concept of three-dimensional geometry.

First, let's consider the right triangle BCA. The given angle BCA is 48°, and we know that the length of AB is 7.3 cm. Using trigonometric functions, we can find the length of BC:

BC = AB * sin(BCA)

BC = 7.3 * sin(48°)

BC ≈ 5.429 cm

Now, let's look at the right triangle BAH. The length of AH is given as 8.1 cm. We can find the length of BH by subtracting BC from AB:

BH = AB - BC

BH ≈ 7.3 - 5.429

BH ≈ 1.871 cm

Next, let's consider the right triangle ABH. We want to find the angle BAH, which is the complement of the angle between AH and the plane ABCD. We can use the cosine function to find the angle BAH:

cos(BAH) = BH / AH

cos(BAH) ≈ 1.871 / 8.1

BAH ≈ arccos(1.871 / 8.1)

BAH ≈ 74.4°

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Answer:

x = sqrt(11)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the sides and c is the hypotenuse

x^2 +(sqrt(5))^2 = 4^2

x^2 +5 = 16

x^2 =16-5

x^2 = 11

Taking the square root of each side

x = sqrt(11)

Answer:

\((x+5)^2+(y-2)^2=36\)

Step-by-step explanation:

The equation of a circle is \((x-h)^2+(y-k)^2=r^2\) where \((h,k)\) is the center and \(r\) is the radius, thus:

\((x-h)^2+(y-k)^2=r^2\\(x-(-5))^2+(y-2)^2=6^2\\(x+5)^2+(y-2)^2=36\)

This means that our equation for the given circle is \((x+5)^2+(y-2)^2=36\)

Answer:

-36

-3y

Step-by-step explanation:

F

Answer:

(4,-7)

Step-by-step explanation:

y=4x-9

y+3=x

y=4(y+3)-9

y=4y+12+9

y=4y+21

y-4y=21

-3y=21

y=-7

Now use y to find x

y+3=x

-7+3=4

x=4