Gina’s number is 2 more than Sara’s. The sum of their numbers is 68. What are their numbers?

Answer:

TRY 416in²

Step-by-step explanation:

front:

8×17=136÷2=68

same for the back

back = 68

side 1=

7×15=105

side 2=

8×7=56

bottom=

17×7=119

68+68+105+56+119=416

Answer:

7/9 is larger and the common denominator is 36.

to find the common denominator we have to take out LCM of denominator of both the fraction.

hope this answer helps you dear!

Addition Property of Equality is basically a complex way of saying add the same number to both sides.  In this problem we are trying to isolate x for it to be by itself so we must deal with -6.  Since we have -6 on one side we must use the "Addition Property of Equality" to add 6 to both sides which would cancel out the -6 and add 6 to 14.

Therefore, the option that best fits the description on what number we would have to use to get added in the equation would be option D, 6.

Answer: About 0.2 gallons

Step-by-step explanation: 4/18=0.2 repeating, so each person gets about 0.2 gallons.

Each of her friend will get 4 and a half gallons of juice.

Division is one of the four main arithmetical operations by which we find the equal distribution of something.

Given that, At Lara's party, 4 gallon of fruit punch are shared equally among 18 friend.

To find how much each of them got, we will divide total amount of punch  by total number friends

Amount of juice each of them gets, = 18/4 = 4.5

Hence,  Each of her friend will get 4 and a half gallons of juice.

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Answer:

3h

Step-by-step explanation:

Given function:

\(f(x) = 3x + 1\)

To find f(a + h), substitute x = a + h into f(x).

Similarly, to find f(a), substitute x = a into f(x).

Therefore:

\(\begin{aligned}\implies f(a+h)-f(a)&=[3(a+h)+1]-[3(a)+1]\\&=[3a+3h+1]-[3a+1]\\&=3a+3h+1-3a-1\\&=3a-3a+3h+1-1\\&=3h\end{aligned}\)

Answer:

-3/4

Step-by-step explanation:

The line passes through the two points which are A(1,1) and B(5,-2) . We know that the slope of the line passing through two points is ,

\(\implies Slope =\dfrac{y_2-y_1}{x_2-x_1}\\\\\implies Slope =\dfrac{ -2-1}{5-1}\\\\\implies Slope =\dfrac{-3}{4} \\\\\implies \underline{\underline{ Slope (m) =\dfrac{-3}{4}}}\)

Hence the slope of the line is -3/4 .

Answer:

No Solutions

Step-by-step explanation:

for |4x -3| + 10 < 2

|4x - 3| < -8

Not possible since absolute value is positive

6n because 5n +n =6 its probably wrong so hope its right??????

Answer: Arnav is 1.8m

Step-by-step explanation: I multiplied 1.5 by 0.20 and then added that answer to 1.5 and then I got 1.8

:D

Answer:

1.5 x 2= 3m its really just that easy.... it took me a while to learn this trick but it works for most things.

The production possibilities frontier (PPF) for a country is typically concave to the origin, meaning it is bowed outwards. This occurs because productive resources, such as land, labor, and physical capital, are not equally efficient in producing different goods or services.

The concave shape of the production possibilities frontier (PPF) reflects the concept of diminishing returns or increasing opportunity costs. As a country allocates more resources to the production of one good, it must sacrifice the production of other goods. However, as more resources are diverted towards a specific good, the additional output gained becomes smaller and smaller.
This occurs because not all productive resources are equally efficient in producing all goods or services. Some resources may be better suited for specific industries or have specialized skills. As a result, the PPF is bowed outwards, indicating that the opportunity cost of producing more of one good increases as the production of the other good is reduced.
In summary, the concave shape of the production possibilities frontier is a result of the varying efficiency and specialization of productive resources in different industries. This leads to increasing opportunity costs and the bowed-out nature of the PPF.

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Answer:

7 friends.....

Step-by-step explanation:

7÷2=3.5

a)The eigenvalues of A are λ1 = -4,  λ2 = -4,  λ3 = -4,  λ4 = -2

b)The orthonormal eigenbasis of matrix A is \($\begin{pmatrix}0&-1&0&0\\0&0&-1&0\\0&0&0&-1\\1&0&0&0\end{pmatrix}$\).

Given a symmetric matrix A = \($\begin{pmatrix}-4&0&0&-2\\0&-4&-2&0\\0&-2&-4&0\\-2&0&0&-4\end{pmatrix}$\).

Step 1: The eigenvalues of A is given by |A- λI| = 0

where I is the identity matrix of the same order as A.

|A- λI| = \($\begin{vmatrix}-4- λ&0&0&-2\\0&-4- λ&-2&0\\0&-2&-4- λ&0\\-2&0&0&-4- λ\end{vmatrix}$\)

Expanding the above determinant along the first column, we get:

|A- λI| = \($(-1)^1(-4- λ)\begin{vmatrix}-4- λ&-2&0\\-2&-4- λ&0\\0&0&-4- λ\end{vmatrix} + 2\begin{vmatrix}0&0&-2\\-4- λ&-4- λ&0\\-2&0&-4- λ\end{vmatrix}$\)

|A- λI| =\($(-1)^1(-4- λ)\begin{vmatrix}-4- λ&-2\\-2&-4- λ\end{vmatrix}(−4−λ)2 + 2(−2)\begin{vmatrix}-4- λ&-4- λ\\-2&-4- λ\end{vmatrix}(−4−λ)3|A- λI| \\= $(λ+4)^3(λ+2)$\)

Hence, the eigenvalues of A are

λ1 = -4,

λ2 = -4,

λ3 = -4,

λ4 = -2

Step 2: We need to find the eigenvectors of matrix A associated with each eigenvalue obtained in step 1.

By solving the equation Ax = λx, we can obtain the eigenvectors.

x1 = \($\begin{pmatrix}0\\0\\0\\1\end{pmatrix}$, \\x2 = $\begin{pmatrix}-1\\0\\0\\0\end{pmatrix}$, \\x3 = $\begin{pmatrix}0\\-1\\0\\0\end{pmatrix}$, \\x4 = $\begin{pmatrix}0\\0\\-1\\0\end{pmatrix}$\)

Now we have found the eigenvectors of matrix A associated with each eigenvalue obtained in step 1.

To obtain the orthonormal eigenbasis of A, we need to normalize these eigenvectors.

The eigenvectors of A form an orthonormal eigenbasis for A when they are normalized.

To normalize the eigenvectors, we need to divide each eigenvector by its corresponding length.

To obtain the lengths of each eigenvector, we use the formula;

\($||x|| = \sqrt{\sum_{i=1}^{n}x_i^2}$\)

where n is the order of the matrix.

Here n = 4 and ||x|| is the length of each eigenvector.

The length of eigenvector x1 is ||x1|| = 1

The length of eigenvector x2 is ||x2|| = 1

The length of eigenvector x3 is ||x3|| = 1

The length of eigenvector x4 is ||x4|| = 1

Hence, the orthonormal eigenbasis of matrix A is \($\begin{pmatrix}0&-1&0&0\\0&0&-1&0\\0&0&0&-1\\1&0&0&0\end{pmatrix}$\)

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Answer:

a

Step-by-step explanation:

The ladder makes an angle of 66.9° with the ground.

A right angled triangle is a triangle (has three sides and three angles) in which one of the angles measure 90°.

Trigonometric ratios is used to show the relationship between the sides of the right angled triangle and its angles.

The ladder is 15 ft long and the wall is 13.8 ft long. Let θ represent the angle that the ladder makes with the ground. Hence:

sinθ = 13.8/15

sinθ = 0.92

θ = 66.9°

Therefore the ladder makes an angle of 66.9° with the ground.

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Answer:

m<1 = 40°

m<2 = 118°

m<3 = 71°

Step-by-step explanation:

✔️m<2 = 180° - 62° (angles in a straight line/supplementary angles)

m<2 = 118°

✔️m<1 = 180° - (118° + 22°) (sum of ∆)

m<1 = 40°

✔️m<3 = 180 - (47 + 62) (sum of ∆)

m<3 = 71°

Answer:

slope is 3

Step-by-step explanation:

10,17

7,8

8-17=-9

7-10=-3

-9/-3=3

Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

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Answer:

17

Step-by-step explanation:

5x2=10

8 1/2x2=17

Two circles intersect at points A and B and have a common external tangent that is tangent to the circles at points T and U, M be the intersection of line AB and TU. If AB = 9 and BM = 3, then TU will be equal to 9.6.

In order to find the length of TU, We can use the Pythagorean theorem to find the length of TU. We know that AB = 9, and BM = 3, so the length of AM must be 6. We can then use the Pythagorean theorem to solve for TU:

TU = √(62 + 92) = √93 = 9.6.

Therefore, the length of TU is 9.6.

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Answer:

heyy i kno u

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer:

6( 3+1)

Step-by-step explanation:

18 + 6

Factor a 6 from each term

6*3 + 6*1

6( 3+1)

Answer: e

Step-by-step explanation:

Answer:

False.

Step-by-step explanation:

In translation, rotation and reflections there is no size change but in dilation the size of the pre-image changes.

So, it is false.

To find the range of the function f(x) = √x - 7, we need to consider the domain of the function, which is the set of all possible input values that we can use in the function. Since the square root of a number must be non-negative, the domain of this function is x ≥ 49.

Next, we need to evaluate the function for different values of x within the domain to see what values it produces. For example, if we plug in x = 49, we get f(49) = √49 - 7 = 7 - 7 = 0. If we plug in x = 50, we get f(50) = √50 - 7 = 7.236 - 7 = 0.236. As we can see, the function takes on both positive and negative values within its domain, so the range is all real numbers.

To represent this visually, we can plot the function on a graph and see how its values vary as the input x changes. We can use a graphing calculator or other graphing technology to do this. On a graph, the x-axis represents the input values (the domain of the function), and the y-axis represents the output values (the range of the function).

Here is a graph of the function f(x) = √x - 7:

[Insert graph here]

As we can see from the graph, the range of the function is all real numbers, indicated by the fact that the graph extends to both positive and negative infinity on the y-axis. This tells us that the range of the function is {y | y ∈ ℝ}.

An effective leader is able to balance and integrate both relationship-building and task-oriented aspects of leadership.

Effective leaders recognize that leadership is not solely about achieving tasks and goals; it also involves building and maintaining strong relationships with their team members.

They understand that establishing positive relationships is crucial for fostering trust, collaboration, and engagement within the team.

By prioritizing relationships, effective leaders create a supportive and inclusive work environment where individuals feel valued, heard, and motivated to contribute their best.

At the same time, effective leaders also understand the importance of accomplishing tasks and achieving organizational goals.

They possess the ability to set clear objectives, delegate responsibilities, and monitor progress to ensure that tasks are completed efficiently and effectively.

They are skilled at organizing resources, making decisions, and providing guidance to their team members, all while maintaining a focus on the desired outcomes.

The key to being an effective leader lies in the ability to balance and integrate both relationship-building and task-oriented aspects of leadership.

This means recognizing that strong relationships contribute to improved teamwork, communication, and employee satisfaction, which in turn enhance overall performance and productivity.

By acknowledging and valuing both dimensions, effective leaders create a harmonious work environment that fosters growth, success, and the well-being of both individuals and the organization as a whole.

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Answer:

D. 16

Step-by-step explanation:

32/2 = 16

Answer:

im not sure but i think the answer is 1,983.31

Step-by-step explanation:

Answer:

1022

Step-by-step explanation:

total of eggs

= 53 × 24

= 1272

the good eggs

= 1272 - 250

= 1022

The total number of members of the club will be 128 members.

It should be noted that the total number of members of the club will be:

= 25 + 38 + 32 + 24 + 9

= 128

Also, the histogram has been completed and attached.

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Answer:4 or -4

Step-by-step explanation: