In a certain arithmetic sequence, a5=12 and a6=16. What is a1?

Answer:(15,0)

Step-by-step explanation:

The Vertex is : (-6, -30)

The X-intercepts are : Approximately (-10.89, 0) and (-1.11, 0)

The Y-intercept is : (0, 6)

The Axis of symmetry is : x = -6

The functions Domain: is All real numbers

The Range is : All real numbers greater than or equal to -30.

To sketch the graph of the quadratic function \(f(x) = x^2 + 12x + 6,\) we can start by identifying the vertex, x-intercepts, y-intercept, axis of symmetry, domain, and range.

To find the vertex, we can use the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in standard form\((ax^2 + bx + c).\)

In this case, a = 1, b = 12, and c = 6.

Applying the formula, we get x = -12/(2 \(\times\) 1) = -6.

To find the y-coordinate of the vertex, we substitute this x-value into the equation:\(f(-6) = (-6)^2 + 12(-6) + 6 = 36 - 72 + 6 = -30.\)

So, the vertex is (-6, -30).

To determine the x-intercepts, we set f(x) = 0 and solve for x. In this case, we need to solve the quadratic equation \(x^2 + 12x + 6 = 0.\)

Using factoring, completing the square, or the quadratic formula, we find that the solutions are not rational.

Let's approximate them using decimal values: x ≈ -10.89 and x ≈ -1.11. Therefore, the x-intercepts are approximately (-10.89, 0) and (-1.11, 0).

The y-intercept is obtained by substituting x = 0 into the equation: \(f(0) = 0^2 + 12(0) + 6 = 6.\)

Thus, the y-intercept is (0, 6).

The axis of symmetry is the vertical line that passes through the vertex. In this case, it is the line x = -6.

The domain of the function is all real numbers since there are no restrictions on the possible input values of x.

To determine the range, we can observe that the coefficient of the \(x^2\) term is positive (1), indicating that the parabola opens upward.

Therefore, the minimum point of the parabola occurs at the vertex, (-6, -30).

As a result, the range of the function is all real numbers greater than or equal to -30.

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By using the concept of mathematical expression, it is obtained that

(62−42)×3 is represented by  3 times the difference between 62 and 42

First option is correct

What is mathematical expression?

A mathematical expression consist of numbers connected with addition, subtraction, multiplication and division.

Here the given  mathematical expression is (62−42)×3

Here, the signs shown are subtraction and multiplication. So the concept of difference and times will be used here

(62−42)×3  means whole of (62 - 42) is multiplied with 3

So, this is 3 times the difference between 62 and 42

First option is correct

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Correct Question

Which phrase represents this expression?

(62−42)×3

a) 3 times the difference of 62 and 42

b) 3 times the difference of 42 and 62

c) The difference of 62 and the product of 3 times 42

d) The difference of the product of 3 times 42 and 62

Answer:

As by the picture, qp is the correct answer.

Step-by-step explanation:

Both are multiplication and in multiplication you can swap the factors and get the same answer every time.

Answer:

your answer will be Isosceles trapezoid

Step-by-step explanation:

^_^

Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions

The inverse of a function is a function that can reverse into another function.

If we have function f and g, and f f(x) = y, then g is the inverse of f if and only if g(y) = x

Also, if f is a function f⁻¹ is the inverse of x and ff⁻¹(x) = f⁻¹f(x) = x

Given the functions m(x) = x³ - 5 and n(x) = ∛(x + 5)

If m(x) and n(x) are inverse, then m(n(x)) = n(m(x)) = x

So, we proceed as follows

m(x) = x³ - 5

m(n(x)) = (∛(x + 5))³ - 5

m(n(x)) = x + 5 - 5

m(n(x)) = x + 0

m(n(x)) = x

Also,

n(x) = ∛(x + 5)

n(m(x)) = ∛(x³ - 5 + 5)

n(m(x)) = ∛(x³ - 0)

n(m(x)) = ∛(x³)

n(m(x)) = x

Since m(n(x)) = n(m(x)) = x, then m(x) and n(x) are inverse functions

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The area of the smaller rectangle (KLMN) is 16.

Since rectangles ABCD and KLMN are similar, their corresponding sides are proportional.

Let's assume the length of side AB in rectangle ABCD is x, and the length of side KL in rectangle KLMN is y.

We can set up the proportion:

(x/y) = (20/16)

To find the area of the smaller rectangle, we need to determine the ratio of their areas.

Since the area of a rectangle is given by the product of its length and width, the ratio of the areas will be equal to the square of the ratio of their sides:

(Area of ABCD)/(Area of KLMN) = (x²)/(y²)

We are given that the area of ABCD is 25, so we have:

25/(Area of KLMN) = (x²)/(y²)

To find the area of KLMN, we need to substitute the values of x and y from the proportion:

25/(Area of KLMN) = (20/16)²

Simplifying the right side:

25/(Area of KLMN) = (5/4)²

25/(Area of KLMN) = 25/16

Cross-multiplying:

25 × 16 = 25 × (Area of KLMN)

400 = 25 × (Area of KLMN)

Dividing both sides by 25:

16 = Area of KLMN

Therefore, the area of the smaller rectangle (KLMN) is 16.

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By answering the above question, we may state that Hence, neither expressions French nor German are spoken by nearly 97.7% of the world's population.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.

In the image you included, a pie chart illustrating the distribution of the global languages spoken by the entire population can be seen.

We need to figure out what portion of the world's population does not speak either French or German in order to respond to your query.

Around 1.2% of the world's population speaks French, according to the pie chart, and 1.1% speaks German, according to the same data.

Hence, it is possible to determine the proportion of people on Earth who do not speak either French or German as follows:

German: 1.1%; French: 1.2%; 100% = 97.7%

Hence, neither French nor German are spoken by nearly 97.7% of the world's population.

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The experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible and 1 indicates that it is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In other words, it is the ratio of the number of desired outcomes to the total number of outcomes.

The frequency of card 6 is 7 and the frequency of card K is 12. However, the card K is also counted in the total count for JQK, so we need to subtract 2 from the frequency of K to get the actual count of K.

Actual count of K = 12 - 2 = 10

Total count of 6 and K = 7 + 10 = 17

The experimental probability of drawing a K or 6 is the frequency of drawing K or 6 divided by the total number of draws:

Experimental probability = (frequency of K or 6) / (total number of draws)

Experimental probability = 17 / 100

Therefore, the experimental probability that the card selected was a K or 6 is 17/100 or 0.17.

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Answer:

2 2/9 yards or 20/9 yards

Step-by-step explanation:

Slimy went 4 times as much as Speedy did so that means 5/9 x 4 yards which is the same thing as 5 x 4/9 so 5 x 4/9 equals 20/9 or 2 2/9 so Slimy crawled 2 2/9 yards.

The top of the slide is 52.3 ft above the water level.

A triangle is said to be right-angled if one of its angles is exactly 90 degrees. The total of the other two angles is 90 degrees. Perpendicular and the triangle's base are the sides that make up the right angle. The longest of the three sides, the third side is known as the hypotenuse.

Given, A water slide at an amusement park is 85 ft long and is inclined at an angle of 52 degrees with the horizontal.

The water slide forms a right triangle with the ground and the height we want to find. The angle between the ground and the slide is 52 degrees, which means that the angle between the slide and the height we want to find is 90 - 52 = 38 degrees.

We can use the sine function to find the height:

sin(38) = opposite/hypotenuse

where the opposite side is the height we want to find, and the hypotenuse is the length of the slide.

Substituting the values we know, we get:

sin(38) = h/85

Solving for h, we get:

h = 85 * sin(38) ≈ 52.3 ft

Therefore, the top of the slide is approximately 52.3 ft above the water level.

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Answer: 70 cats

Step-by-step explanation:

add 2+7 = 9
90/9 = 10
multiply 2x10 = 20 dogs
10x7= 70 cats.

Answer:

840

Step-by-step explanation:

Since the order matters, we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

\(P_{(n,x)} = \frac{n!}{(n-x)!}\)

In this question:

The first seat is Jose's.

The remaining four are organized among the other 7 members. So

\(P_{(7,4)} = \frac{7!}{(7-4)!} = 840\)

So the correct answer is:

840

Answer:

The answer is B on Edge 2020

Step-by-step explanation:

I did the Exam

Answer:

Step-by-step explanation:

The measure of each inscribed angle at T and S is 72.5 degrees, and the sum of their measures is: 145 degrees

What is inscribed angle ?

An inscribed angle is an angle formed by two chords of a circle that have a common endpoint on the circle. The vertex of the inscribed angle is on the circle, and the sides of the angle intersect the circle at two distinct points.

There are some important properties of inscribed angles:

According to the question:
If the inscribed angles of T and S intercept the same arc, then they must be equal in measure. Let's call the measure of each angle x.

Since the sum of the measures of the angles in a triangle is 180 degrees, we can set up an equation to find the measure of the third angle in triangle TSY:

x + x + measure of angle YTS = 180 degrees

Simplifying the equation, we get:

2x + measure of angle YTS = 180 degrees

But we know that the measure of angle YTS is equal to half the measure of arc YZ, since it is an inscribed angle intercepting the same arc. So:

measure of angle YTS = 1/2 * measure of arc YZ = 1/2 * 70 degrees = 35 degrees

Substituting this value into our equation, we get:

2x + 35 degrees = 180 degrees

Solving for x, we get:

2x = 145 degrees

x = 72.5 degrees

Therefore, the measure of each inscribed angle at T and S is 72.5 degrees, and the sum of their measures is:

72.5 degrees + 72.5 degrees = 145 degrees

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Answer:

Option c

Step-by-step explanation:

3/4 multiplied by 16/5

3/4×16/5

12/5

Option c is correct

The product between 3/4 and 16/5

Answer:

4. x = 11

5. x = -13

Step-by-step explanation:

4.   3x + 7 = 5x - 15

           -7           -7

3x = 5x - 22

-5x   -5x

-2x = -22

-2x/-2 = -22/-2

x = 11

5. 3(2x - 5) = 9x + 24

6x - 15 = 9x + 24

    +15          +15

6x = 9x + 39

-9x   -9x

-3x = 39

-3x/-3 = 39/-3

x = -13

Hope this helps, have a great day:)

The following answers are given as:

2.1)

2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.

2.2)

8 teaspoons of vinegar are needed for  20 teaspoons of olive oil.

2.3)

There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.

2.4)

There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

6 teaspoons of vinegar = 15 teaspoons of olive oil.

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 2 on both sides.

2 teaspoons of vinegar = 5 teaspoons of olive oil.

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 8 on both sides.

8 teaspoons of vinegar = 20 teaspoons of olive oil.

Now,

Total number of teaspoons = 42

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 12 on both sides.

12 teaspoons of vinegar = 30 teaspoons of olive oil.

12 + 30 = 42 teaspoons

Now,

1 teaspoon of vinegar = 5/2 teaspoons of olive oil.

Multiply 4 on both sides.

4 teaspoons of vinegar = 10 teaspoons of olive oil.

4 + 10 = 14 teaspoons

Thus,

2 teaspoons of vinegar are needed for 5 teaspoons of olive oil.

8 teaspoons of vinegar are needed for  20 teaspoons of olive oil.

There are 12 teaspoons of vinegar and 30 teaspoons of olive oil in the 42 teaspoons of salad.

There are 4 teaspoons of vinegar and 10 teaspoons of olive oil in the 14 teaspoons of salad.

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Answer:b

Step-by-step explanation:

jfdjiodkskskdkdkdekdikwodwiosisisis=g

Answer

parallel lines go strait and never intersect

Step-by-step explanation:

Answer:

15/100

Step-by-step explanation:

6/40 = 3/20

3 x 5 = 15

5 x 20 = 100

To prove that the triangles are congruent by ASA, the statement and reason could be used as part of the proof is option (A) ∠FGH ≅ ∠KGJ because vertical angles are congruent.

Here we have two triangle FHG and KJG,

The sides HF and the side JK are parallel

The length of the side of the HG and the length of the side JG are equal

HG ≅ JG

According to the ASA property of congruent, if the two angle and one side of the triangle are equal to the two angle and one side of the other triangle, then the both triangles are congruent

Here we have to prove that angle FHG and angle KJG are vertical angles

Here the vertical angles are congruent

Therefore, the statement that can be the part of proof is option (a) angle FGH ≅ angle KGJ because vertical angles are congruent.

I have solved the question in general, as the given question is incomplete

The complete question is:

Given: HF || JK; HG ≅ JG

Prove: FHG ≅ KJG

To prove that the triangles are congruent by ASA, which statement and reason could be used as part of the proof?

a) FGH ≅ KGJ because vertical angles are congruent.

b) JKG ≅ HFG because vertical angles are congruent.

c) FHG ≅ JKG because right angles are congruent.

d) HFG ≅ KJG because alternate interior angles are congruent.

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Answer:

9y+2

Step-by-step explanation:

You divide everything by 3

27y/3= 9y

6/3=2

Then add

9y+2

Hope this is helpful!

Answer:

9y + 2

Step-by-step explanation:

cuz 1/3(27) = 9y

and 1/3(6) = 2

add them and equals 9y + 2

G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. preconditions: x

x(x + 1)/2 = O(x^2)

The pseudocode segment given has two nested for loops. The outer loop is iterating over the variable x, while the inner loop is iterating over variable i. G count the maximum number of operations that the next pseudocode segment might possibly complete. Assume that the likelihood of all potential data sets is equal. Each loop iteration is increasing the variable z by 1. In total, this will result in x*(x+1) / 2 operations being performed. This is equal to O(x^2), which is the worst-case number of operations.

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Answer:

A

Step-by-step explanation: if u read closely and think about it hard enough youll see

14.

Answer:

The solution to the equation is;

Explanation:

Given the equation;

To solve, let us expand the bracket;

Simplifying and collecting the like terms;

subtract 49 from both sides;

divide both sides by -1;

Therefore, the solution to the equation is;

Answer:

x=11 degrees

Step-by-step explanation:

First what you would do is add 6x and 5x-7 to get 11x-7 degrees. Then you double that by using opposite angles theorem to get 22x-14 as the answer of two angles. Next you double 7x-11 to get 14x-22 by using the same theorem as the last one. then you do 14x-22+22x-14=360 degrees then you get your final answer of x=11 degrees

Answer:

\(\boxed{\textsf{y = 3}}\)

Step-by-step explanation:

\(\textsf{We are asked to solve for y.}\)

\(\textsf{We should begin by \underline{simplifying} the equation.}\)

\(\textsf{First, begin by dividing 750 from \underline{both sides} of the equation.}\\\)

\(\Large\underline{\textsf{Divide:}}\)

\(\mathtt{\frac{162000}{750} = \frac{750 \times 6^y}{750} .}\)

\(\mathtt{216=6^y}\)

\(\Large\underline{\textsf{Continue Dividing By 6:}}\)

\(\mathtt{\frac{216}{6} = 36 (^{y-1})}\)

\(\mathtt{\frac{36}{6} = 6 (^{y-2} )}\)

\(\Large\underline{\textsf{Identify y:}}\)

\(\mathtt{6^1 = 6. \ 6^{1+2} = 216. \ (6^3)}\)

\(\boxed{\textsf{y = 3}}\)

Answer: 7.8

Explanation: 8.9 - 2.9 = 6.0 + 1.8 = 7.8

Answer:

37.5

Step-by-step explanation:

16/46 = 20/(20+x)

or, 16(20+x) = 46×20

or, 320 + 16x = 920

or, 16x = 600

or, x = 600/16

x = 37.5

The expanded and simplified form of the expression (x + 5)(x - 1) is  x² - x + 5x - 5.

Given the expression in the question;

(x + 5)(x - 1)

To expand and simplify the expression (x+5)(x-1),

we use the distributive property:

(x + 5)(x - 1)

x(x - 1) + 5(x - 1)

Now we can simplify each term by using the distributive property again:

x(x - 1) = x² - x

5(x - 1) = 5x - 5

Putting these terms back together, we have:

(x+5)(x-1) = x² - x + 5x - 5

Combining like terms, we get:

(x+5)(x-1) = x² + 4x - 5

Therefore, (x+5)(x-1) simplifies to the quadratic expression x² + 4x - 5.

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