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The vertex form of our quadratic equation is:

y = (x - 5)^2 - 4

A quadratic equation with a vertex (h, k) and a leading coefficient a is:

y = a*(x - h)^2 + k

We know that the quadratic function has roots of 3 and 7, then if the leading coefficient is a, we can write:

f(x) = a*(x - 3)*(x - 7)

We also know that it passes through the point (1, 12), then:

12 = a*(1 - 3)*(1 - 7)

12 = a*(-2)*(-6)

12 = a*12

12/12 = a

1 = a

Then the quadratic is:

y = (x - 3)*(x - 7)

Expanding that we get:

y = x^2 - 3x - 7x + 21

y = x^2 - 10x + 21

The x-value of the vertex is halfway between the two roots:

x' = (3 + 7)/2 = 5

So evaluating in x = 5 we get:

y = (5)2 - 10*5 + 21

y = 25 - 50 + 21 = -4

The vertex is (5, -4), then the vertex form is:

y = (x - 5)^2 - 4

The correct option is the last one.

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Answer:

f(x) = (x − 5)2 − 4

Step-by-step explanation:

i got it right on my quiz

The largest number is -1

What is number ?

An arithmetic value known as a number is used to represent a quantity and do calculations. Numbers are represented by written symbols, such as "3," which are referred to as numerals. A number system is a method of writing that uses logically ordered digits or symbols to represent numbers.

An item in mathematics used for measurement, labeling, and counting is a number. The prime numbers 1, 2, 3, 4, and so forth are the original examples. Number words can be used to represent numbers in language.

Let the 4 consecutive integers are

x

x+1

x+2

x+3

x + (x+1) + (x+2) + (x+3) = -10

4x + 6 = -10

4x = -16

x = -4

The 4 consecutive integers are -4 , -3 , -2 , -1

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Answer:

4×side

Step-by-step explanation:

i hope this helps

There are three parameter-passing modes in C++: by value, by pointer, and by reference.

Now, According to the question:

There are three parameter-passing modes in C++: by value, by pointer, and by reference.

What are the three main parameters?

The three main parameters assessed when calculating the Human Development Index of a place are:

A. Economic parameters.

B. Health parameters.

C. Education parameters.

D. Linguistic parameters.

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Answer:

The answer is 5

Step-by-step explanation:

length(Hypotenuse) = 13m

height(opposite) = 12m

ground(adjacent) = ?

using the formula

Hyp² = oppo² + Adj²

13² = 12² + Adj²

Adj² = 13² – 12²

Adj² = 169 – 144

Adj² = 25

Adj = √25

Adj = 5

:- the distance of the foot of the ladder from the bottoms wall is 5

i hope this helps

If you're not motivated, it would take you approximately nine months; however, if you are and can dedicate an hour or two every day to studying, it would only take you about six months.

6 Unknown Methods for Quickly Mastering Algebra

You may probably self-study Math rather simply as if you were in college with all the free materials available online, including lectures, syllabi, ebooks, and MOOCS. You can go at your own pace, which is the finest part. It's common for algebra to be challenging because we mistakenly think we're learning new material when, in reality, we're just applying language to specific concepts that we already know to be true.

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The vertex of the graph of f(x) = 2x² + 8x - 3 is (-2, -11). It lies in the third quadrant.

Therefore the answer is (-2, -11).

Simplifying the given graph to the form f(x) = a(x - h)² + k

f(x) = 2x² + 8x - 3

f(x) = 2×(x² + 4x) - 3

f(x) = 2×(x² + 4x + 4) - 3 - 2×4

f(x) = 2×(x + 2)² - 11

So f(x) = 2x² + 8x - 3 is symmetrical about the line x = -2. At x = -2, y = -11.

Therefore, the vertex of the graph is (-2, -11).

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = 2x² + 8x - 3?"

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There are five ways to find if two triangles are congruent: SSS, SAS, ASA, AAS and HL.

1. SSS (side, side, side)-If three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

2. SAS (side, angle, side) -If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.

3. ASA (angle, side, angle)-If two angles and the included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

4. AAS (angle, angle, side)-If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

5. HL (hypotenuse, leg)

This one applies only to right angle triangles

From the figure,

HL stands for "Hypotenuse, Leg" (the longest side of a right-angled triangle is called the "hypotenuse", the other two sides are called "legs")

It means we have two right-angled triangles with

It doesn't matter which leg since the triangles could be rotated.

For example: From fig(2)

is congruent to fig(3)

If the hypotenuse and one leg of one right-angled triangle are equal to the corresponding hypotenuse and leg of another right-angled triangle, the two triangles are congruent.

The additional information need to know in order to prove the two triangles congruent using HL is the hypotenuses to be congruent.

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Answer:

Flax: 80 acres

Sunflowers: 160 acres

Step-by-step explanation:

Let's

x = acres of flax

y = acres of sunflowers

We have the equations:

x + y = 240

y = x + 80

Let's do it in standard form

x + y = 240

x - y = -80

2x = 160

x = 80 acres

Now put 80 back in the equation to find sunflowers

80 + y = 240

y = 160 acres

So, 80 acres of flax and 160 acres of sunflowers!

The value of x =68

We know that x+22 = 90 because the sum of the two angles is a vertical angle to the right angle and vertical angles are equal.

x+22 =90

Subtract 22 from each side

x+22-22 = 90-22

x =68

In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown.

"How do you find value of x?

Generally, the algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. To find the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to find the result.

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Answer: 68

Step-by-step explanation:

Provided the correct answer after places 34 as the answer.

Answer:

To find the percentage of bad apples, we need to divide the number of bad apples by the total number of apples and then multiply by 100%. In this case, there were 24 apples in total and 6 of them were bad, so the percentage of bad apples is 6/24 * 100% = 25%. Rounded to the nearest number, this is equal to 25%.

The total surface area​ of a cylinder are 1187.35 cm sq.

Suppose that the radius of considered right circular cylinder be 'r' units.

And let its height be 'h' units.

Then, its volume is given as:

[tex]V = \pi r^2 h \: \rm unit^3[/tex]

We are given the curved surface area and volume of a cylinder are 880 CM^2 and 3080 cm^3 respectively.

A = 880

V = 3080

Curved surface area of cylinder = 2πrh

880 = 2π x r x h

rh = 880/ 2π

Volume of cylinder = πr x r x h

3080 =  πr x r x h

rh =   3080 / πr

Substitue the values;

880/ 2π = 3080 / πr

440/π = 3080 / πr

r  = 3080 / 440

r = 7

Now, rh = 880/ 2π

h = 20.01

The total  surface area​ = 2πr(r + h)

= 2π x  7(7 + 20.01)

= 1187.35 cm sq.

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The survey reports that 80%, percent actively observed mammals = 0.4246

Given that,

The 2011 national survey of fishing, hunting, and wildlife-associated recreation, there were over 71 million wildlife watchers in the us.

The survey reports that 80%, percent actively.

A simple random sample of only 500 wildlife watchers.

Following are the solution to the given question:

By using the approximation of normal for the proportions so, the values:  

P ( p⁻ < p ) = P ( Z < ( p⁻ - p ) / [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]

So,

P ( 0.79 < p⁻ < 0.81 ) = P ( p⁻ < 0.81 ) - P ( p⁻ < 0.79 )

= P ( Z < (0.81-0.80) / [tex]\sqrt{\frac{0.80(1-0.80)}{500} }[/tex] ) - P ( Z < (0.79-0.80) / [tex]\sqrt{\frac{0.80(1-0.80)}{500} }[/tex] )

=  P ( Z < 0.56 ) - P ( Z < -0.56 )

= 0.7123 - 0.2877 (using the Z table )

P ( 0.79 < p⁻ < 0.81 ) = 0.4246

Therefore,

The survey reports that 80%, percent actively observed mammals = 0.4246

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Step-by-step explanation:

Gabby is an editor. She needs to review a textbook with 398 pages. She plans to review 9 pages each day for the next 31 days. She works out that she will have 279 pages left to review after that. Does that sound about right?

398 - ( 9 * 31) = 119 pages left

No, because Gabby will only have 119 pages left after reading 9 pages a day for 31 days. 279 pages is an overestimate.

Each side is 1.55 miles in the fence.

What is fence?

A structure meant to delineate a boundary or prevent escape or intrusion. Particularly: a boundary line or immaterial barrier made of posts, wire, or boards.

Given:

Alex is building a fence in the shape of an equal sided hexagon the total amount of fence available to him is 15 kilometers.

Since, Hexagon has six sides and each side is equal.

So there is 2.5 kilometer to fence each side.

Now to convert kilometer into miles.

Since

1 kilometer = 0.621371 miles

So,

2.5 kilometers = 1.55343 miles

Hence, each side is 1.55 miles in the fence.

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Simplification of the given numbers  (1.1)^ 10000 or 1000 gives

(1.1)^ 10000 is larger number than 1000.

As given in the question,

Given two numbers are:

(1.1)^ 10000  and 1000

Simplify the numbers to get the larger number we have,

Apply Binomial theorem in the expression   (1.1)^ 10000

( a + b )ⁿ = ⁿC₀aⁿb⁰ + ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b² +.....+ ⁿCₙa⁰bⁿ

(1.1)¹⁰⁰⁰⁰

= ( 1 + 0.1)¹⁰⁰⁰⁰

Here a = 1, b = 0.1 and n= 10000

( 1 + 0.1)¹⁰⁰⁰⁰

=¹⁰⁰⁰⁰C₀1¹⁰⁰⁰⁰(0.1)⁰ + ¹⁰⁰⁰⁰C₁1¹⁰⁰⁰⁰⁻¹(0.1)¹ + ¹⁰⁰⁰⁰C₂1¹⁰⁰⁰⁰⁻²(0.1)² +..........+ ¹⁰⁰⁰⁰C₁₀₀₀₀1⁰(0.1)¹⁰⁰⁰⁰

= 1 + 1000+......

= 1001+ ....

> 1000

Therefore, from the given numbers (1.1)^ 10000 or 1000 the larger number is (1.1)^ 10000 compare to 1000.

The above question is incomplete , the complete question is :

Which number is larger (1.1)^ 10000 or 1000?

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The value of c in the given convex polygon is 2°

What is the sum of interior angles of a convex polygon?

If a convex polygon has n sides, then its interior angle sum is given by the following equation: S = (n −2) × 180°

According to the given question:

Number of sides in the given polygon n = 5

Therefore, sum of interior angles of the polygon S = (n -2 ) x 180°

S = (5 -2) x 180°

S = 3 x 180°

S = 540°

Now to find the value of c we can simply add all the interior angles given in the figure and equate it to S

Hence,

136° + 119° + 147° + 48° + 45c = 540°

                            450° + 45c = 540°

                                        45c = 90°

                                            c = 2°

So the value of c is 2°

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Answer:

B.) 13

C.) 0.6

Step-by-step explanation:

The order of operations to evaluate these expressions is as follows:

Parentheses

Exponents

Multiplication/Division

Addition/Subtraction

So, for B.)

[tex]9^\frac{1}{2}+\sqrt{25}-8\div2+3^2[/tex]

This can be rewritten as
[tex]9^\frac{1}{2}+25^\frac{1}{2}-8\div2+3^2[/tex]

Since there are no parentheses, evaluate the exponents first:

[tex]3+5-8\div2+9[/tex]

Next, there are no multiplication steps, but there is one division:

[tex]3+5-4+9[/tex]

To finish, evaluate from left to right:

[tex]3+5-4+9\\8-4+9\\4+9\\13[/tex]

Follow the same pattern for C.)

[tex](\frac{1}{2})(\frac{3}{5})(2^3-6)[/tex]

This expression can be rewritten as

[tex](1\div2)(3\div5)(2^3-6)[/tex]

First, evaluate the expressions in the individual parentheses, keeping in mind the expression [tex](2^3-6)[/tex] must be evaluated following the same pattern (evaluate the exponent before subtracting six):

[tex](.5)(.6)(8-6)\\(.5)(.6)(2)[/tex]

To finish, evaluate from left to right:

[tex](.3)(2)\\.6[/tex]

Hope that helps!

Answer:

(y, x )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x )

The nth formula of any mathematical expression represents the general formula for the given sequence or series.

Therefore, the nth formula is used to represents the mathematical sequence or series in standard form.

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Answer:

hi this is so simple you know use

formula to solve

Answer:

[tex] \frac{2}{5} [/tex]

Step-by-step explanation:

[(5^-1×3^-1)÷6^-1]

[tex] = (\frac{1}{5} \times \frac{1}{3}) \div \frac{1}{6} [/tex]

[tex] = \frac{1}{15} \div \frac{1}{6} [/tex]

[tex] = \frac{1}{15} \times 6[/tex]

[tex] = \frac{1}{3 \times 5} \times 3 \times 2[/tex]

[tex] = \frac{3 \times 2}{3 \times 5} [/tex]

[tex] = \frac{2}{5} [/tex]

mark as brainliest pls i need it

The unique set of 3 prime numbers for which the sum of the numbers is 44 are {2, 5, 37}, {2, 11, 31}, {2, 13, 29} and {2, 19, 23}.

Prime numbers are the numbers in the set of natural numbers for which 1 and the number itself are the only factors of it.

The numbers which are not prime are called composite numbers.

We have to find the set of 3 prime numbers which on adding yields 44.

Now 44 is a composite number and also an even number.

We also know that adding two odd numbers as well as adding two even numbers always gives the even number.

2 is the only even prime number.

So if we take this set which is not including 2, then by adding odd + odd + odd gives the odd number.

But the answer we needed is 44, which is even.

So this set always contain 2 as one of the prime number.

So by adding the other two prime numbers, we must get 42.

Thus we got,

{2, 5, 37}  = 2 + 5 + 37 = 44

{2, 11, 31} = 2 + 11 + 31 = 44

{2, 13, 29} = 2 + 13 + 29 = 44

{2, 19, 23} = 2 + 19 + 23 = 44

Hence the unique 3 set of prime numbers are  {2, 5, 37}, {2, 11, 31}, {2, 13, 29} and {2, 19, 23} for which the sum is 44.

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Answer:

A,-10p+4q

Step-by-step explanation:

-2(5p-2q)

-2*5p+(-2*-2q)

-10p+4q

Answer:

[tex] - 10p + 4q[/tex]

is the answer. A

r stands for the Pearson correlation coefficient, which measures the strength and direction of the linear relationship between two variables. p stands for the critical value for the correlation coefficient, which is used to determine the significance of the correlation coefficient.

The Pearson correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a perfect negative linear relationship, 0 indicates no linear relationship, and 1 indicates a perfect positive linear relationship. The correlation coefficient is a good way to determine the strength of the relationship between two variables.The critical value for the correlation coefficient (p) is used to determine the significance of the correlation. It is determined by the sample size, the number of variables being correlated, and the level of significance. The lower the P value, the more significant the correlation is. If the P value is below the chosen level of significance, then the correlation is considered statistically significant.In conclusion, r is the Pearson correlation coefficient and p is the critical value for the correlation coefficient. R measures the strength and direction of the linear relationship between two variables, while P indicates the significance of the correlation. Both measures are important when assessing the relationship between two variables.

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The root of the graph of f(x) =(x - 5)3(x + 2)2 touches the x-axis at -2,5

(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.

(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.

Given: Function f(x) is (x - 5)3(x + 2)2

If a curve touches the x-axis then f(x) = 0

⇒ (x - 5)3(x + 2)2 = 0.

But if ab = 0 ⇒ either a = 0 or b = 0 or both zero.

⇒ (x - 5)3 = 0 and (x + 2)2 = 0

⇒ (x - 5) = 0 and x + 2 = 0

⇒ x = 5 and x = - 2.

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Yes , the given statement a binomial can have degree three is true.

As given in the question,

Binomial can have degree three is a true statement explain in a following way:

Therefore, binomial may have degree 3 is a true statement.

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There are 2 terms in this mathematical expression. One multiplication sign act as an operator of two numbers.

It is a mathematical statement express the relationship between two or more terms along with mathematical symbols. Terms can be numbers, variables with or without coefficient. symbols can be addition sign, multiplication sign, division and subtraction sign, equal or inequal sign etc. Beside this we have many other operator or symbols to state the mathematical expression.

In the above question, we have 2 numbers along with a symbol. We notice that 4 and 5 are two numbers multiplied here as there is a multiplication sign between them.

4 x 5 denotes an expression which state that 4 is multiplied by 5 and the result will be 20.

hence, we have 2 terms and one operator.

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The possible product is:

2 * 5 = 10

1 * 10 = 10

In mathematics, multiplication is a process of combining numbers and finding the product. It is denoted by the symbol "x" or "*". There are different ways to perform multiplication, such as using a multiplication table, using a calculator, or using the standard algorithm. The standard algorithm is a systematic method for performing multiplication that involves multiplying the digits in the ones, tens, and so on place value columns, and then carrying and regrouping as necessary.

To find all the possible products that can be obtained by multiplying some combination of the numbers 2, 3, 5, and 7 that result in a product of 10. Here are the two possible products that can be obtained by multiplying these numbers:

2 * 5 = 10

1 * 10 = 10

The possible products that result in a product of 10 are 2 * 5 and 1 * 10.

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