what does 6+9 equal all together

Answer:

Step-by-step explanation:

Sum of -3a 2 b 2 , –52 a 2 b 2 , 4a 2 b 2 , 23 a 2 b 2=

(-3a 2 b 2)+( –52 a 2 b 2)+ (4a 2 b 2)+(23 a 2 b 2)=

-3a 2 b 2 –52 a 2 b 2 +4a 2 b 2 +23 a 2 b 2=.-28a 2 b 2 is the answer

Explanation

Step 1

if ABCD is a square then, the segment AB must be perpendicular to segment BC

it means,( if two lines are perpendicular, the product of the slopes is -1)

Step 2

find the slope of segment AB

Let P1(2,1) P2(4,4)

Step 3

replace in equation (1) to find the slope of side BC

slope2= slope of side BC

I hope this helps you

Answer:

∠A=123°.

Step-by-step explanation:

From the given figure it is clear the CD and CE are two tangent lines on circle with center A.

Radius is perpendicular to the tangent at the point of tangency.

\(\angle ADC=90^{\circ}\)

\(\angle AEC=90^{\circ}\)

Smaller arc DE = (5x-2)°

It means central angle DAE is (5x-2)°.

\(\angle DAE=(5x-2)^{\circ}\)

Now, ADCE is a quadrilateral and sum of all angles of a quadrilateral is 360 degrees.

\(\angle ADC+\angle DCE+\angle AEC+\angle DAE=360^{\circ}\)

\(90^{\circ}+(2x+7)^{\circ}+90^{\circ}+(5x-2)^{\circ}=360^{\circ}\)

\((7x+5)^{\circ}+180^{\circ}=360^{\circ}\)

\((7x+5)^{\circ}=360^{\circ}-180^{\circ}\)

\((7x+5)^{\circ}=180^{\circ}\)

\(7x+5=180\)

\(7x=175\)

\(x=25\)

The value of x is 25.

\(\angle A=5x-2=5(25)-2=125-2=123^{\circ}\)

Therefore, the measure of ∠A is 123°.

Thus we only take the positive root:x = 27/8 = 3.375Answer: 3.375 feet.

The problem states that a rectangular garden that measures 50 feet wide and 45 feet long is enclosed by a uniform width of x feet paved path. To solve the problem,

we can use the formula of the combined area of the garden and the paved path and equate it to 2646 square feet. The combined area is computed by adding the area of the garden and the area of the paved path.

Garden area:Length of garden = 45 ftWidth of garden = 50 ftArea of garden = Length x Width= 45 x 50= 2250 square feet

Paved path:

If the garden has a uniform width of x feet paved path, then the width of the paved path would be x + 2x + x= 4x. The width is multiplied by 2 because there are two widths surrounding the garden.

Length of paved path = length of garden + 2 (width of paved path)= 45 + 2 (4x)= 8x + 45Width of paved path = width of garden + 2 (width of paved path)= 50 + 2 (4x)= 8x + 50

The area of the paved path is computed by subtracting the area of the garden from the combined area.Area of paved path = Combined area - Garden area2646 square feet

= (8x + 45) (8x + 50) - 2250= 64x² + 760x + 675

We then solve for the value of x by factoring the quadratic equation.2646 square feet = 64x² + 760x + 6752646 - 2646

= 64x² + 760x + 675 - 264664x² + 760x - 1971

= 0(8x - 27) (8x + 73) = 0

The value of x cannot be negative,

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Answer:

67

Step-by-step explanation:

Subsitute both given values into the equation then continue to simplify the equation

3(4(-2)+5(3)) -2(7(-2)-3(3))

3(-8+15) -2(-14-9)

3(7) -2(-23)

21 +46

67

Answer:

price of vegetables= regular price-discount

p=r-discount

Step-by-step explanation:

discount = regular price- price of vegetables

discount= r-p

OR

price of vegetables= regular price-discount

p=r-discount

percentage discount

[(original price- discounted price)/original price]*100= percent discount

Answer:

P = r - 8

Step-by-step explanation:

Got it correct.

Answer:

it's 63

please mark brainliest❤

Step-by-step explanation:

8×4=32

3×7=21

2×5=10

32+21+10=63

The probability density function of Z = X + Y can be determined by finding the CDF and then differentiating it to obtain the PDF.

To find the probability density function (PDF) of the random variable Z = X + Y, we need to determine the cumulative distribution function (CDF) of Z and then differentiate it to obtain the PDF.

First, let's find the cumulative distribution function (CDF) of Z:

FZ(z) = P(Z ≤ z) = P(X + Y ≤ z)

To find this probability, we can integrate the joint probability density function over the region where X + Y is less than or equal to z:

FZ(z) = ∫∫R fX,Y(x, y) dx dy

Where R is the region defined by 0 ≤ x ≤ y ≤ 1.

Integrating the joint PDF over this region, we get:

FZ(z) = ∫∫R 2(x + y) dx dy

To evaluate this integral, we split it into two parts:

FZ(z) = ∫[0, z] ∫[x, 1] 2(x + y) dy dx + ∫[z, 1] ∫[0, 1] 2(x + y) dy dx

After evaluating these integrals, we obtain the expression for the CDF of Z.

Finally, to find the PDF of Z, we differentiate the CDF with respect to z:

fZ(z) = d/dz FZ(z)

By differentiating the obtained CDF expression, we can find the PDF of Z.

Therefore, the probability density function of Z = X + Y can be determined by finding the CDF and then differentiating it to obtain the PDF.

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The similar triangles in the question, with proportional sides indicates;

4. The proportion that must be true is the option G

G. 4/6 = 7/x

Similar triangles are triangles are triangles that have the same shape but may have different sizes.

The possible triangles in the question includes two triangles with specified side lengths AB = 6 inches, AC = 7 inches, DE = 4 inches, DF = x inches

The definition of similar triangles indicates that we get;

DE/AB = EF/BC

DF/AC = DE/AB

DF/AC = EF/BC

Therefore;

(x/7) = 4/6

The correct option which indicates the proportion that must be true, therefore is option G

G. 4/6 = x/7

Part of the question includes two triangles, please see attached diagram created with MS Excel

The possible proportions, from which to select the proportion that must be true are;

F (7/x) = (4/6)

G 4/6 = x/7

H 6/4 = x/7

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Answer:

21/428 or 0.04 906542056074...

Step-by-step explanation:

the range of values of y for which the binomial expression 5y - 7 is in the interval (-5, 13) is:

2/5 < y < 4

To find the range of values of y that satisfy this condition, we can set up an inequality:

-5 < 5y - 7 < 13

Adding 7 to all parts of the inequality, we get:

2 < 5y < 20

Dividing by 5, we get:

2/5 < y < 4

Therefore, the range of values of y for which the binomial expression 5y - 7 is in the interval (-5, 13) is:

2/5 < y < 4
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Exact value of the definite integral is 320. Comparing the results: Exact value of the definite integral = 320, Trapezoidal Rule approximation (n = 4) = 340, Simpson's Rule approximation (n = 4) ≈ 246.6667.

What is trapezoid?

A trapezoid is a quadrilateral (a polygon with four sides) that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs.

To approximate the value of the definite integral ∫[0, 4] 5x * x^2 dx using the Trapezoidal Rule and Simpson's Rule, we need to specify the value of n, which represents the number of subintervals.

Let's calculate the approximations using n = 4 for both methods:

Trapezoidal Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using the Trapezoidal Rule is given by:

\(T_4 = (h/2) * [f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4)]\)

Plugging in the values:

\(T_4 = (1/2) * [f(0) + 2f(1) + 2f(2) + 2f(3) + f(4)]\\\\= (1/2) * [5(0)(0^2) + 2(5)(1)(1^2) + 2(5)(2)(2^2) + 2(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/2) * [0 + 10 + 80 + 270 + 320]\\\\= (1/2) * 680\\\\= 340\)

Simpson's Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using Simpson's Rule is given by:

\(S_4 = (h/3) * [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4)]\)

Plugging in the values:

\(S_4 = (1/3) * [f(0) + 4f(1) + 2f(2) + 4f(3) + f(4)]\\\\= (1/3) * [5(0)(0^2) + 4(5)(1)(1^2) + 2(5)(2)(2^2) + 4(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/3) * [0 + 20 + 40 + 360 + 320]\\\\= (1/3) * 740\\\\= 246.6667\)

Exact value of the definite integral:

∫[0, 4] 5x * \(x^2\) dx = [(5/4) * \(x^4\)] evaluated from 0 to 4

\(= (5/4) * 4^4 - (5/4) * 0^4\\\\= (5/4) * 256 - (5/4) * 0\\\\= 320 - 0\\\\= 320\)

Comparing the results:

Exact value of the definite integral = 320

Trapezoidal Rule approximation (n = 4) = 340

Simpson's Rule approximation (n = 4) ≈ 246.6667

As we can see, the Trapezoidal Rule approximation is slightly greater than the exact value, while Simpson's Rule approximation is less than the exact value.

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Answer:

C.  3

Step-by-step explanation:

Perpendicular lines have slopes that are negative inverses of the other.

This inverse of -1/3 is -3.  The negative of -3 is 3.

The slope of the perpendicular line is 3.

Answer:

x=1

Step-by-step explanation:

it is

Answer:

Check out the graph

Answer: 5 & 12

Step-by-step explanation: The formula for the Pythagorean theorem is a^2 + b^2 = c^2. So if 5^2 + 12^ = 13^, 5 & 12 must be the side lengths that form the right angle.

The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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Answer: A, 3 B, 2 C, 6

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

The supremum of the set A does not exist (it is negative infinity), and the infimum of the set A is 1.

To define the supremum and infimum of the set A, we first need to determine the properties of the set.

The set A is defined as A = {(x-3)/(x-2) ∈ R : x < 0}.

To find the supremum (also known as the least upper bound) of A, we need to find the smallest value that is greater than or equal to all the elements of A. In other words, we are looking for the least upper bound of the set A.

Let's analyze the elements of A:

For x < 0, the expression (x-3)/(x-2) can take on different values depending on the value of x. We need to find the maximum value that this expression can reach for all x < 0.

As x approaches 0 from the left side, (x-3)/(x-2) approaches negative infinity. Therefore, there is no finite supremum for the set A.

Next, let's find the infimum (also known as the greatest lower bound) of A. We need to find the largest value that is less than or equal to all the elements of A. In other words, we are looking for the greatest lower bound of the set A.

Again, analyzing the elements of A:

As x approaches negative infinity, (x-3)/(x-2) approaches 1. Therefore, the infimum of the set A is 1.

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Answer:

a=

1/0

Step-by-step explanation:

The perpendicular line has an equation of y + 7 = -1/7(x - 3)

The equation is given as

y = 7x + 14

Also, from the question

The point is given as

Point = (3, -7)

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 7

This means that the slope of y = 7x + 14 is 7

Perpendicular lines have their slopes to be opposite reciprocals

This means that the other line has a slope of -1/7

The equation of the perpendicular lines is then calculated as

y = m(x - x₁) +y₁

Where

m = -1/7

(x₁, y₁) = (3, -7)

So, we have

y = -1/7(x - 3) - 7

Evaluate

y = -1/7(x - 3) - 7

Add 7 to both sides

y + 7 = -1/7(x - 3)

Hence, the equation of the perpendicular line is y + 7 = -1/7(x - 3)

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Answer:

C. Public colleges are cheaper for in-state residents.

Step-by-step explanation:

Answer:

1. When adding you just add the numbers from the same space so

3  7

10 45

2. Same as adding but the opposite

2  1  2

3  1  6

1  2  1

Step-by-step explanation:

The average mean of all 40% of all adults in increase p-hats will be approximately 0.4.

If 40% of all adults in Ohio support the increase, this means that the population proportion is p = 0.4. We can use this value to calculate the mean of the sampling distribution of p-hat, which is given by the formula:

mean of p-hat = p

That is, the mean of the sampling distribution of p-hat is equal to the population proportion. In this case, the mean of the sampling distribution of p-hat is:

mean of p-hat = p = 0.4

So, if we take all possible samples of the same size from the population and calculate the proportion of adults who support the increase in each sample, the average mean of all those proportions (p-hats) will be approximately 0.4.

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The probability of being dealt a card that helps improve your hand is approximately 0.7083 or 70.83%.

To determine the probability of being dealt a card that helps you, we need to consider two factors: the number of favorable cards remaining in the deck and the total number of cards remaining.

At the beginning of the game, a standard deck of 52 cards is used. After the initial deal, you and the dealer have each received two cards, so there are 52 - 4 = 48 cards remaining in the deck.

To determine the favorable cards that can improve your hand, we need to consider the possible outcomes. In this case, you have a four and a jack, and you're looking to improve your hand. Let's analyze the possibilities:

To improve your hand to a better total without exceeding 21, you would want to draw a card between 5 and 9, inclusive. In this case, you know that the dealer's one visible card is a five, so there are three more fives left in the deck. Additionally, there are four cards each of 6, 7, 8, and 9, making a total of 16 favorable cards for improving your hand.

Lastly, if you're hoping to improve your hand to a total of 20, you would need an ace, 2, 3, or 6. As we assumed earlier, there are three aces remaining, and there are four cards each of 2, 3, and 6. So there are a total of 3 + 4 + 4 + 4 = 15 favorable cards for achieving a total of 20.

In total, the number of favorable cards for improving your hand is 3 (blackjack) + 16 (improve to a better total) + 15 (improve to a total of 20) = 34.

To calculate the probability, we divide the number of favorable cards by the total number of cards remaining in the deck:

Probability = Number of Favorable Cards / Total Number of Cards Remaining

Probability = 34 / 48

Simplifying the fraction, the probability is 17 / 24 or approximately 0.7083 (rounded to four decimal places).

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Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path. This is formalized by using the →(if-then) and ∧(logical and) operators.

Given information and corresponding atomic propositions:

We need to formalize the given statements in terms of atomic propositions r, b, and w, which are defined as follows:

r: Rabbits have been seen in the area.

b: Berries are ripe along the path.

w: Walking on the path is safe.

Now, let us formalize each of the given statements in terms of these atomic propositions:

a) Berries are ripe along the path, but rabbits have not been seen in the area.

b: Rabbits have not been seen in the area, and walking on the path is safe, but berries are ripe along the path.

c: If berries are ripe along the path, then walking is safe if and only if rabbits have not been seen in the area.

d: It is not safe to walk along the path, but rabbits have not been seen in the area, and the berries along the path are ripe.

e) For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

Walking is not safe on the path whenever rabbits have been seen in the area, and berries are ripe along the path.

The formalizations in terms of atomic propositions are:

a) b ∧ ¬r.b) ¬r ∧ w ∧

b.c) (b → w) ∧ (¬r → w).

d) ¬w ∧ ¬r ∧

b.e) (¬r ∧ ¬b) → w.b ∧

Berries are ripe along the path, but rabbits have not been seen in the area.

This is formalized by using the ∧(logical and) operator.

(¬r ∧ ¬b) → w: It means For walking on the path to be safe, it is necessary but not sufficient that berries not be ripe along the path and for rabbits not to have been seen in the area.

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Answer:

35

Step-by-step explanation:

The angle is reflected.