Please help this is he and I’m so confused

Step-by-step explanation:

To find the x-intercepts of the quadratic function f(x) = x^2 + 6x - 27, we need to set f(x) equal to zero and solve for x.

So we have:

f(x) = 0

x^2 + 6x - 27 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

Where a = 1, b = 6, and c = -27.

Substituting these values into the quadratic formula, we get:

x = (-6 ± sqrt(6^2 - 4(1)(-27))) / 2(1)

x = (-6 ± sqrt(180)) / 2

x = (-6 ± 6sqrt(5)) / 2

x = -3 ± 3sqrt(5)

So the x-intercepts of the quadratic function are approximately -10.16 and 4.16.

The variation constant is 22 and the equation of variation where y varies inversely as x is y = 22/x.

When two variables, y and x, are inversely proportional, it means that as one variable increases, the other variable decreases proportionally, and vice versa. Mathematically, this can be expressed as:

y = k/x

where k is the variation constant. To find k, we can use the given information that "y = 11 when x = 2". Substituting these values into the inverse variation equation above, we get:

11 = k/2

Multiplying both sides by 2, we get:

k = 22

So, the variation constant is 22.

Now, we can write the equation of variation as:

y = 22/x

This means that as x increases, y decreases proportionally. For example, if x doubles to 4, y would be halved to 5.5, keeping the product (xy) constant.

Learn more about variation constant here: https://brainly.com/question/25215474.

#SPJ11

Jackie needs to pour 2/9of a quart of water from the first bottle to the second bottle to make them have the same amount of water.

Two or more expressions with an Equal sign is called as Equation.

Let us assume that we transfer an amount "x" from the first bottle to the second bottle.

This means that the first bottle will have 1-x quarts of water, while the second bottle will have 5/9 + x quarts of water.

Now, we want to find the value of "x" that makes both bottles have the same amount of water.

We can set up an equation:

1-x = 5/9 + x

We can then solve for "x" by adding "x" to both sides and subtracting 5/9 from both sides:

1 - 5/9 = 2x

4/9 = 2x

x = 2/9

Hence, Jackie needs to pour 2/9 of a quart of water from the first bottle to the second bottle to make them have the same amount of water.

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ1

The value of x from the exponential equation is x = 1/2

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

16ˣ = 4

On simplifying , we get

From the laws of exponents , we get mᵃ×mᵇ = mᵃ⁺ᵇ

So , 16ˣ = 4

when x = 1/2

16^(1/2) = 4

On further simplification , we get

√16 = 4

4 = 4

Therefore , the value of x is 1/2

Hence , the exponential equation is solved and the value of x = 1/2

To learn more about exponents click :

https://brainly.com/question/28966438

#SPJ9

The volume of the small can is  25.12 inches cube.

Mrs. Roberts' dog, Rover, loves to eat peanuts. A large can of peanuts has a diameter of 4 inches and a height of 6 inches. The small can that she plans to purchase has the same diameter but is 1/3 of the height of the large can.

Therefore, the approximate volume of the small can can be found as follows:

Hence,

volume of the small can = πr²h

where

Therefore,

r = 4 / 2 = 2 inches

h = 1 / 3 (6) = 2 inches

Hence,

volume of the small can = 3.14 × 2² × 2

volume of the small can = 3.14 × 4 × 2

volume of the small can = 3.14 × 8

volume of the small can = 25.12 inches cube

learn more on volume here: https://brainly.com/question/18123686

#SPJ1

Answer: $89

Step-by-step explanation:

to find average add up all numbers and divide by how many there are

so, do

(125+110+95+80+70+54)/6

which equals 89

All sides of the given rhombus measure 5 cm respectively.

A rhombus is a quadrilateral with four equal-length sides in planar Euclidean geometry.

The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths.

Quadrilaterals having four congruent sides are called squares.

Squares are rhombuses by definition since they are quadrilaterals with four congruent sides.

So, consider the following values: AC = 8 cm, BD = 6 cm, OD = OB = 3 cm, and OA = OC = 4 cm.

Now,

OB² + OC² = BC²

3²+ 4² = BC²

9 + 16 = BC²

25 = BC²

5 = BC

A rhombus has an equal number of sides.

Therefore, all sides of the given rhombus measure 5 cm respectively.

Know more about the rhombus here:

https://brainly.com/question/88523

#SPJ9

(3x²+18x)/(7x+21)  is the  simplified answer of  (x+6)/(3x+9)-:(7)/(9x)+42.

To divide the given expressions, we need to first simplify the expressions as much as possible and then use the rule for dividing fractions. The rule for dividing fractions is to multiply the first fraction by the reciprocal of the second fraction.

Simplifying the expressions:

(x+6)/(3x+9) = (x+6)/(3(x+3)) = (x+6)/3(x+3)

(7)/(9x) = 7/9x

Now, using the rule for dividing fractions:

((x+6)/3(x+3)) ÷ (7/9x) = ((x+6)/3(x+3)) * (9x/7)

= (9x(x+6))/(3(x+3)*7)

= (3x(x+6))/(x+3)*7

= (3x²+18x)/(7x+21)

To know more about reciprocal click on below link:

https://brainly.com/question/18634761#

#SPJ11

Answer:

1.  c

2. b

3.  a

Step-by-step explanation:

Surface Area of a cylinder = 2πrh + 2πr²

1.  2(3.14)(5)(11) + 2(3.14)(5)² = 502.4

2. 2(3.14)(6)(10) + 2(3.14)(6)² = 602.88

3.  2(3.14)(2)(12) + 2(3.14)(2)² = 175.84

The area of the isosceles trapezoid with base lengths 2ft and 5ft and leg lengths 2.5ft will be 8.75ft

Isosceles trapezoid, also known as isosceles trapezium, is defined as a convex quadrilateral, which mainly consists of a line of symmetry that bisects one pair of the opposite side, it is also know that the base angles are of equal measure. It has parallel bases with the legs also being of the equal measure, on the other hand the opposite angles of the isosceles trapezoid are supplementary, which makes it a cyclic quadrilateral.

Area of an Isosceles Trapezoid = [(a+b)h]/2 square units,

when we put these values in the formula, we get:

Area = [(2+5)2.5]/2

Area = (7 × 2.5)/2

Area = 17.5/2

Area = 8.75ft²

therefore, we know that the area of the isosceles trapezoid with base lengths 2ft and 5ft and leg lengths 2.5ft will be 8.75ft

To learn more about area, click here:

brainly.com/question/27683633

#SPJ1

The simplified expression is  [tex]12u^8[/tex].

What is simplification?

Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.

Here the given expression is ,

=> [tex]-2u^5(-6u^3)[/tex]

Now simplifying the expression,

=> [tex]-2\times -6 \times u^5 \times u^3[/tex]

=> 12[tex]u^{5+3}[/tex]

=> [tex]12u^8[/tex]

Hence the simplified expression is  [tex]12u^8[/tex].

To learn more about Simplification refer the below link

https://brainly.com/question/20373987

#SPJ1

The correct interval for the area of triangle PQR is 2 <= A < 4.

To find the correct interval for the area of triangle PQR, we first need to calculate the area using the given points. We can do this by using the formula for the area of a triangle in three dimensions:

A = (1/2) * sqrt((x2*y3 - x3*y2)^2 + (x3*y1 - x1*y3)^2 + (x1*y2 - x2*y1)^2)

Plugging in the given points for P, Q, and R, we get:

A = (1/2) * sqrt((1*3 - 3*0)^2 + (3*0 - 0*1)^2 + (0*0 - 1*3)^2)

Simplifying, we get:

A = (1/2) * sqrt(9 + 9)

A = (1/2) * sqrt(18)

A = (1/2) * 3 * sqrt(2)

A = (3/2) * sqrt(2)

A = 2.12

Therefore, the correct interval for the area of triangle PQR is 2 <= A < 4. The correct answer is option b. 2 <= A < 4.

Learn more about formula for the area

brainly.com/question/1398431

#SPJ11

Answer:

The formula for calculating the amount of money in an account with continuous compounding is:

A = Pe^(rt)

Where:

A = the amount of money in the account after t years

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

t = the time (in years)

Substituting the given values into the formula, we get:

A = 7500e^(0.0158)

A ≈ $9,071.21

Therefore, to the nearest hundred dollars, there would be $9,100 in the account after 8 years.

Step-by-step explanation:

The correct equation for the sentence is: 24 = 31.4n - 8.4.

Twenty-four is equal to 31.4 times a number plus a negative 8.4 multiplied by the proper equation, which is:

24 = 31.4n - 8.4

This formula can be rewritten as follows:

31.4n = 24 + 8.4

And after being distilled:

31.4n = 32.4

Finally, by multiplying both sides by 31.4, we can find the value of n:

n = 32.4/31.4

Thus, the following is the proper equation for the phrase:

24 = 31.4n - 8.4.

To know more about Equation visit:

https://brainly.com/question/29657988

#SPJ1

The percent increase of the puppy's weight is 25%

A puppy weighed 28 ounces on Monday

It gained 7 ounces in one week

Total weight is = 28 + 7

= 35

The percent increase can be calculated as follows

= 35/28

= 1.25

= 1.25-1

= 0.25 × 100

= 25%

Hence the percent increase of the puppy's weight is 25%

Read more on percent increase here

https://brainly.com/question/20066775

#SPJ1

Answer:120

Step-by-step explanation:

Answer:

A) $8

B) 4+2x

Step-by-step explanation:

If it costs $2 for every mile driven, and Huoa rides for 2 miles, then you multiply 2×2=4. Then you add another $4 for the $4 the driver charges for just getting in, so 4+4=8

Another way to do that is to use the equation that's the answer for part B. As you don't know the number of miles, you substitute that unknown number for x.

4+2x

The x represents the number of miles

The 2 represents the amount charged for each mile

The 4 represents the flat fee for getting into the car

If you plug 2 (for the 2 miles driven) into the equation you get:

4+2(2)

4+4

8

Answer:

335.6511628

Step-by-step explanation:

Ux258-336=168

U-336=0.6511628

U=336.6511628

To prove that \[ A^{n}=\left[\begin{array}{ccc} a^{n} & n a^{n-1} & \frac{n(n-1)}{2}a^{n-2} \end{array}\right], we will use mathematical induction.

Base case: For \( n=1 \), \( A^{1}=A \). This is true since
\[ A=\left[\begin{array}{ccc} a & 1 & 0 \\ 0 & a & 1 \\ 0 & 0 & a \end{array}\right] \]
which matches the left side of our equation.

Inductive step: Assume that the statement is true for some \( n=k \), i.e.
\[ A^{k}=\left[\begin{array}{ccc} a^{k} & ka^{k-1} & \frac{k(k-1)}{2}a^{k-2} \end{array}\right] \]
We will now show that it is true for \( n=k+1 \).
\[ A^{k+1}=A^{k}\cdot A \]

We substitute the induction hypothesis into this equation and get:
\[ A^{k+1}=\left[\begin{array}{ccc} a^{k} & ka^{k-1} & \frac{k(k-1)}{2}a^{k-2} \end{array}\right]\cdot \left[\begin{array}{ccc} a & 1 & 0 \\ 0 & a & 1 \\ 0 & 0 & a \end{array}\right] \]

Calculating the matrix product yields:
\[ A^{k+1}=\left[\begin{array}{ccc} a^{k+1} & (k+1)a^{k} & \frac{(k+1)k}{2}a^{k-1} \end{array}\right] \]
which matches the left side of our equation, completing the proof.

Learn more about  completing the proof

brainly.com/question/30920773

#SPJ11

The side x is 30 miles

The unknown side is 346 yards

The sine rule, also known as the law of sines, is a formula that relates the sides and angles of a non-right triangle (a triangle that does not have a 90-degree angle). The sine rule states that the ratio of the length of a side of a triangle to the sine of the opposite angle is the same for all three sides of the triangle.

1) Using the sine rule;

x/sin 65 = 32/sin75

xsin75 = 32sin65

x = 32sin65/sin75

x = 30 miles

2) The angle = π/3 = 180/3 = 60 degrees

Using the cosine rule;

c^2 = (200)^2 + (400)^2 - (2 * 200 * 400) cos 60

c^2 = 200,000 - 80,000

c = 346 yards

Learn more about cosine rule:https://brainly.com/question/28716982

#SPJ1

The coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

Dilation is the process of resizing or transforming an object. It is a transformation that makes the objects smaller or larger with the help of the given scale factor. The new figure obtained after dilation is called the image and the original image is called the pre-image.

here, we have,

From the given graph, triangle ABC have A(1, 3), B(7, 1) and (1, 1).

Triangle ABC is enlarged with a scale factor of -2 and the origin of the Centre to give triangle A'B'C'.

Now, A(1, 3) → -2(1, 3)→A'(-2, -6)

B(7, 1) → -2(7, 1) → B'(-14, -2)

C(1, 1) → -2(1, 1) → C'(-2, -2)

Therefore, the coordinates of the triangle A'B'C' are A'(-2, -6), B'(-14, -2) and C'(-2, -2).

To learn more about the dilation visit:

brainly.com/question/13176891.

#SPJ1

Answer:

The answer is  3

Answer:

Option d: Side OP is congruent to side RS.

To prove that ΔNOP ≅ ΔQRS by ASA, we need to show that:

1. ∠N ≅ ∠Q (given)

2. Side NP ≅ Side QS (given)

3. Side OP ≅ Side RS (additional information needed)

Hence, option d is the correct answer.

The simplified expression is (3y-7)/(y^2-35)/3.

To simplify the given expression, we need to find the least common denominator (LCD) of the two fractions. The LCD of (y-5) and (y+7) is (y-5)(y+7).
Next, we need to multiply each fraction by the LCD in order to get the same denominator for both fractions.
(2)/(y-5) * (y+7)/(y+7) + (7)/(y+7) * (y-5)/(y-5)
= (2y+14)/(y^2-35) + (7y-35)/(y^2-35)

Now, we can combine the two fractions since they have the same denominator.
(2y+14+7y-35)/(y^2-35)
= (9y-21)/(y^2-35)
Finally, we can simplify the fraction by factoring out a 3 from the numerator.
= (3)(3y-7)/(y^2-35)
= (3y-7)/(y^2-35)/3
You can read more about least common denominator  at https://brainly.com/question/19249494

#SPJ11

The answer would be 51,998

The final simplified expression turns out to be "-8x^2 + 6x - 6"

To perform the addition or subtraction and simplify the expression, we need to combine like terms and simplify the expression. First, we need to subtract the second expression from the first one:

x^2 + x − 2 - (9x^2 − 5x + 4)

Next, we need to distribute the negative sign to each term in the second expression:

x^2 + x − 2 - 9x^2 + 5x - 4

Now we can combine like terms:

-8x^2 + 6x - 6

This is the simplified expression. Therefore, the answer is:

-8x^2 + 6x - 6

Know more about simplified expression here:

https://brainly.com/question/18077352

#SPJ11

A $900 item on the sale of 20% discount the

Money off: $180

Amt. of tax: $50.40

Money paid: $770.40

Final price: $770.40

what is discount ?

A discount is a reduction in the price of an item or service, often offered as a promotion or incentive to encourage customers to make a purchase. The discount is usually expressed as a percentage of the original price and represents the amount of money that the customer can save on the purchase.

For example:

Percentage discount: a certain percentage of the original price is deducted from the selling price. For example, a 20% discount on a $100 item would reduce the price to $80.

According to the question:
To calculate the final price of the item with sales tax, we can follow these steps:

Calculate the amount of money off by multiplying the original price by the discount percentage:

Money off = 0.20 x $900 = $180.

Calculate the price after the discount by subtracting the money off from the original price:

Price after discount = $900 - $180 = $720.

Calculate the amount of sales tax by multiplying the price after discount by the tax rate:

Amount of tax = 0.07 x $720 = $50.40.

Calculate the money paid by adding the price after discount and the amount of tax:

Money paid = $720 + $50.40 = $770.40.

Therefore, the final price with 7% sales tax is $770.40.

To know more about discount visit:
https://brainly.com/question/29124624
#SPJ1

The mean, median and mode of the prices that the bags of flour are sold at are:

To find the mean, we add up all the prices and divide by the total number of prices:

Mean:

= (1.45 + 1.55 + 1.90 + 1.95 + 1.45) / 5

= 1.66

To find the median, we need to arrange the prices in order from lowest to highest:

1.45, 1.45, 1.55, 1.90, 1.95

There are five prices, so the median is the middle value, which is 1.55.

To find the mode, we need to look for the price that appears most frequently in the data set. In this case, there are two prices that appear twice, 1.45 and 1.55. So there is no unique mode for this data set.

Find out more on mean at https://brainly.com/question/14532771

#SPJ1

Answer: 2

Step-by-step explanation:

Answer and Explanation: The only even number that is not a composite number is 2. All even numbers are defined as numbers that are divisible by, or have a divisor of, 2.

Answer:

The answer to your question is, 2

Step-by-step explanation:

The reason why that is our answer is because, 2 can either be multiplied and divided but 2 NUMBERS.

Such as the following:

2 / 1 = 2.

1 x 2 = 2.

What is a composite number?

A composite number are numbers that have more than two factors like the number 2:

2 / 1 = 2.

1 x 2 = 2.

Thus the answer to your problem is, 2

The coordinates (x,y) to sketch the graph is mentioned below. (b) The intercepts of the graph represent the situations where one of the items is not purchased.

A graph is a visual representation of data that shows the relationship between variables. It consists of a set of points or vertices, connected by lines or curves called edges or arcs. Graphs are commonly used in mathematics, statistics, and other fields to display information in a way that is easy to understand and interpret.

a) To sketch the graph, we can create a table of values for the equation 5x + 3y = 30:

Bags of Popcorn (x) Drinks (y) Total Cost

0                                          10          30

1                                          8          30

2                                          6          30

3                                          4          30

4                                          2          30

6                                          0          30

Then we can plot the points from the table on a graph with the number of bags of popcorn on the x-axis and the number of drinks on the y-axis. Connecting the points gives us a line that represents all possible combinations of bags of popcorn and drinks that cost $30.

b) The intercepts of the graph represent the situations where one of the items is not purchased. The x-intercept (0,10) represents the situation where no bags of popcorn are purchased, so all $30 is spent on 10 drinks. The y-intercept (6,0) represents the situation where no drinks are purchased, so all $30 is spent on 6 bags of popcorn. The slope of the line represents the rate at which the cost of one item changes relative to the cost of the other item. In this case, the slope is -5/3, which means that for each bag of popcorn purchased, the cost of drinks decreases by $5/3.

To know more about cost visit:

https://brainly.com/question/19075809

#SPJ1