find if one or neither

Finding the vertex of the quadratic functions, the correct statement is:

Function 1 has the larger maximum at (4, 1).

A quadratic equation is modeled by:

\(y = ax^2 + bx + c\)

The vertex is given by:

\((x_v, y_v)\)

In which:

Considering the coefficient a, we have that:

For function 1, we have that:

f(x) = -x² + 8x - 15.

Hence the coefficients are a = -1, b = 8, c = -15, and the vertex is:

For function 2, we have that:

f(x) = -x² + 2x - 3.

Hence the coefficients are a = -1, b = 2, c = -3, and the vertex is:

1 > -2, hence the correct statement is:

Function 1 has the larger maximum at (4, 1).

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Answer:

\(\frac{5}{14}\)

Step-by-step explanation:

It's important to note here that fractions are just another way of representing division.

Therefore, \(\frac{\frac{1}{4}}{\frac{7}{10}}\) is the same thing as \(\frac{1}{4} \div \frac{7}{10}\).

To divide two fractions, we multiply by the reciprocal.

\(\frac{1}{4} \cdot \frac{10}{7}\)

We can now multiply the numerators and denominators.

\(1\cdot 10 = 10\\7 \cdot 4 = 28\\\\\frac{10}{28}\)

We can simplify this fraction by dividing both the numerator and denominator by 2.

\(10\div 2 = 5\\28 \div 2 = 14\)

So, \(\frac{5}{14}\).

Hope this helped!

Answer:

S=2000n+100000

Step-by-step explanation:

Since Nicole will have a salary of $110000 after working 5 years for the company, we know that S = 110000 when n = 5.  

         Find the slope using the two points.

           110000 - 100000            10000

   m =  ------------------------     =      ----------   =   2000

                       5-0                            2

The slope shows how much the salary increases each year, which is the same thing as saying that Nicole got a raise of $2000 every year.

The inverse tangent of 0.9 is approximately 42.0 degrees.

Therefore, the correct answer is option C: 42.0⁰.

The inverse tangent, also known as arctangent, is a trigonometric function that gives the angle whose tangent is a given number. In this case, we want to find the inverse tangent of 0.9.

Using a calculator or reference table, we can find that the inverse tangent of 0.9 is approximately 42.0 degrees.

To understand why this is the case, we can consider the definition of the tangent function. The tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle in a right triangle. The inverse tangent function reverses this relationship, giving us the angle when we know the tangent value.

In the case of 0.9, we can imagine a right triangle where the length of the side opposite the angle is 0.9 and the length of the side adjacent to the angle is 1. The inverse tangent of 0.9 tells us the angle that satisfies this relationship.

So, the inverse tangent of 0.9 is approximately 42.0 degrees.

Therefore, the correct answer is option C: 42.0⁰.

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\( {73.33ft}^{3} \)

Step-by-step explanation:

\(v = \pi {r}^{2} \frac{h}{3} \)

\(\pi {r}^{2} = {22ft}^{2} \)

\(v = 22 \times \frac{10}{3} \)

\(v = 22 \times 3.33\)

\(v = {73.33ft}^{3} \)

Using the Normal Z-distribution and the values from the Z-table, We can calculate that 12.5% can be expected to score between 70 and 90 according to the value of the mean and standard deviation provided.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it.

mean =100

standard deviation =60

70≤ x ≤ 90

70 - 100 ≤ x - 100 ≤ 90 -100

-0.5 ≤  Z ≤ -0.167

P = 0.125(From Z-Table)

Required percentage  = 12.5%

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The correct question is:

certain standardized math exams have a mean of 100 and a standard deviation of 60. of a sample of 36 students who take this exam, what percent could you expect to score between 70 and 90?

=πr^2h

=π(5)^2*11

=25*11π

=275π yd^3

Answer:

110 cards were sold on Mother's Day

Step-by-step explanation:

Bob's gift shop sold 20% of all the cards sold on Mother's Day.

Let the number of cards sold on Mother's day be m

Bob sold 20% of m or 0.2m

We know that 0.2m is 22, so now we can solve for m

110 cards were sold on mothers day

Note

We know that 0.2 is 1/5, so instead of dividing each side by 0.2, we could have multiplied both sides by 5

-Chetan K

Answer:

half of the area

Step-by-step explanation:

i am not sure

Answer:

b

Step-by-step explanation

One way to simplify variables with many levels (or decimal places) when creating a frequency distribution is to organize the data into class intervals (option B).

By grouping the data into intervals, the frequency distribution becomes more manageable and easier to interpret. This process involves dividing the range of values into distinct intervals or categories and then counting the number of observations falling within each interval. Class intervals provide a summary of the data by grouping similar values together, reducing the complexity of individual levels or decimal places.

This simplification technique is particularly useful when dealing with large datasets or continuous variables that have numerous levels or decimal values, allowing for a clearer representation and analysis of the data.

Option B holds true.

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Answer:

25

Step-by-step explanation:

Since they were born on consecutive years, their ages are 4 consecutive whole numbers. Let the lowest age be x. Then the other ages are x + 1, x + 2, and x + 3.

Now we add the 4 expressions and set the sum equal to 94.

x + x + 1 + x + 2 + x + 3 = 94

4x + 6 = 94

4x = 88

x = 22

The youngest one is 22.

The oldest one is

x + 3 = 22 + 3 = 25

Answer: 25

Answer:

q

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

Its 12 x 4. Which is 48

Answer: 4

Step-by-step explanation:

Alice ride her bicycle in 1 day for a distance of 4 miles.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Given that,

Alice rode her bicycle the same number of miles every day for 17 days.

Let x be the number of miles that Alice rode for 1 day.

She rode x miles for 17 days.

Total number of miles that she rode in 17 days = 68 miles

So, we have,

17x = 68

Dividing both sides by 17,

x = 4

Hence the number of miles Alice rode in 1 day is 4 miles.

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Reason: The line goes downhill when moving to the right, and when we're between x = -1 and x = 1. You can think of it like a roller coaster.

Answer:

9.625

Step-by-step explanation:

(3 1/2) x (2 3/4) = 9.625

Answer:

.........................

The four basic properties of exponents are the negative exponent property, the product of powers property, the quotient of powers property, and the power of a power property.

The properties of exponents are a set of rules that allow us to simplify terms that contain exponents.

Negative exponent property states that when a negative exponent is present, the base and the exponent are switched and the sign of the exponent is changed. For example,  x-2 = 1/x2.

The product of powers property states that when two terms with the same base are multiplied, the exponents are added together. For example, x3 x4 = x7.

The quotient of powers property states that when two terms with the same base are divided, the exponents are subtracted. For example, x6/x2 = x4.

The power of a power property states that when a term with an exponent is raised to another power, the exponents are multiplied. For example, (x3)2 = x6.

These properties can be used to simplify expressions that contain exponents. For example, the expression (−2m−2????4) 3 can be simplified using the power of a power property by multiplying the exponents. The expression simplifies to −2m−6????12.

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Answer:

The answer is 3y - 10x - 27

Answer:

y = x + 2

Step-by-step explanation:

As the equation of a line is in the form y = mx + c:

Step 1 - Calculate the y intercept

This can be done by looking at the y coordinate where x = 0:

y = mx + c

In the picture, the y intercept is 2 so:

y = mx + 2

Step 2 - Calculate the slope

This can be calculated by:

\(\frac{\text{change in y}}{\text{change in x}}\)

Get two sets of coordinates:

(0, 2) and (2, 4)

Calculate the changes by subtracting from one another:

\(\frac{4 - 2}{2 - 0} \\\frac{2}{2}\\=1\)

So the gradient is 1, meaning the equation of the line is:

\(y = 1x + 2 \\\text{or}\\y = x + 2\)

Hope this helps!

The equation is represented as follows:

p^2 + 2pq + q^2 = 1

The Hardy-Weinberg equation is a mathematical formula used in genetics to predict the frequency of genetic traits in a population. The equation is named after the scientists G. H. Hardy and W. Weinberg, who independently developed it in 1908 and 1909, respectively.

The equation states that the frequency of a genetic trait in a population will remain constant over time as long as certain conditions are met. These conditions are:

No mutations occur in the gene responsible for the trait

There is no natural selection for or against the trait

There is random mating within the population

The population size is large

The Hardy-Weinberg equation can be used to calculate the frequency of the dominant and recessive alleles (versions of a gene) in a population, and the probability of different genotypes (the combination of alleles an individual has) and phenotypes (the physical expression of the trait) within that population.

Where p is the frequency of the dominant allele, q is the frequency of the recessive allele, and p^2 represents the proportion of homozygous dominant individuals, 2pq represents the proportion of heterozygous individuals and q^2 represents the proportion of homozygous recessive individuals.

The Hardy-Weinberg equation is a useful tool for understanding how genetic traits are inherited and how they change over time. It is widely used in population genetics, evolutionary biology and medical genetics.

It is also important to notice that the Hardy-Weinberg equilibrium is a theoretical concept that is rarely met in real populations due to the existence of genetic drift, migration, mutation, nonrandom mating and natural selection.

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Answer:

\(f(-1)=-11\\f(0)=16\\f(2)=22\)

Step-by-step explanation:

\(\displaystyle f(-1)=3(-1)-8=-3-8=-11\\f(0)=3(0)+16=16\\f(2)=3(2)+16=6+16=22\)

Answer:

Step-by-step explanation:

\(Opposite = r\\Hypotenuse = 13\\\alpha = 34\\Using SOHCAHTOA\\Sin \alpha = \frac{opp}{hyp} \\Sin 34 = \frac{r}{13} \\0.559 = \frac{r}{13} \\Cross \: Multiply\\r = 0.559\times 13\\r = 7.267\\r = 7.27\)

Answer:

The Coefficient to 5 + 9y is 9

Step-by-step explanation:

The leading term in a polynomial is the term with the highest degree.

9y

The leading coefficient in a polynomial is the coefficient of the leading term.

9

espero que esto ayude, y que tengas una buena noche

Answer:

-2

Step-by-step explanation:

you answer the brackets first then add 9 then add 8

⇒ Let x be treated as any real number

⇒Meaning x can be a positive number or x can be a negative number.

⇒ The square root of x can be defined ONLY if x is a non negative number, ∀ x>0 the square root is defined

For this notation \(\sqrt{+x}\) there exist a certain real number ..It is defined.

Let x now be a negative number.

\(\sqrt{-x}\)

⇒For any negative number under the square root the result is an undefined number,

⇒ x and -x are all treated as VALUES (x) but NOT for all values (x) now you will find a defined number as an output.

⇒ As a conclusion for non negative x under a square root you get a defined value

⇒But for an negative number under a square root you get an undefined number as an output.

⇒Square root x may not be defined for some values x BECAUSE X CAN BE NEGATIVE..

4/3 cups of margarine will he need to make 4 batches of dog biscuits.

A fraction is a piece of the entire. The number is shown as a quotient in mathematics, in which the numerator and denominator are split. Both are integers in a straightforward fraction. The numerator, as well as the denominator of a complex fraction, as well as the denominator of a complex portion, is a fraction.

Zero, a positive natural number, or an unsigned negative integer are all examples of integers. The inverses of corresponding positive numbers, which are additive, are the negative numbers. The blackboard bold math b Z or boldface Z is a common way to represent the set of integers in mathematical terminology.

There are four batches of dog biscuits.

Making a batch requires 1/3 cup of margarine.

As we can see that for 1 batch of dog biscuits required 1/3 cup of margarine.

So to make 4 batches of dog biscuits:

= (1/3)*4

= 4/3

4/3 cups of margarine will he need to make 4 batches of dog biscuits.

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Answer:

127

Step-by-step explanation:

The angles are supplementary angles which means they add to 180

x+53 = 180

Subtract 53 from each side

x = 180-53

x=127

Answer:$111.27    hope this helped

Step-by-step explanation:

Answer:

Step-by-step explanation: