Please help me simplify this expression!!

Answer:

Answer is D; x=1

Step-by-step explanation:

Subtract 7 on bth sides

Divide by 6 on both sides

Add 3 on both sides

Answer:

73 cm (Estimated)

Step-by-step explanation:

Let's use hero's formula to solve this.

=> 1/2(14 + 11 + 18) = S

=> 1/2(43) = S

=> S = 21.5

√s(s - a)(s - b)(s - c)

=> √21.5(21.5 - 14)(21.5 - 11)(21.5 - 18)

=> √21.5 x 7.5 x 9.5 x 3.5

=> 73.2226911551 = Area of triangle

=> 73 cm² (Estimated)

Hoped this helped.

Answer:

y = 3x + 1

Step-by-step explanation:

As you can see the y-intercept is at the number 1

and for the slope, if u do rise over run or y/x you get....

3/1 = 3

So the slope is 3

Hope this helped!

Answer:

The median for Set A is greater than the median

for Set B.

Step-by-step explanation:

From the boxplot attached, we can deduce the following :

Median (vertical line in between the box on a boxplot).

Median, set A = 30

Median, set B = 29

Range = (Maximum - Minimum. Value)

Set A :

Maximum = 35 ; Minimum = 21

Range = 35 - 21 = 14

Set B :

Maximum = 37 ; Minimum = 24

Range = 37 - 34 = 3

Hence, from the options, the only correct statement is The median for Set A is greater than the median for Set B.

Answer:

A. y is all real numbers.

Step-by-step explanation:

The range is the possible values that y can take

In this graph y goes from negative infinity to infinity so y can be all real numbers

Step-by-step explanation:

- 22 = -8u + 6(u-7)

-22 = -8u + 6u - 42

8u - 6u = 22 - 42

2u = -20

u = -20/2

u = -10

Answer:

Step-by-step explanation:

\( \mathrm{ - 22 = - 8u + 6(u - 7)}\)

Distribute 6 through the parentheses

⇒\( \mathsf{ - 22 = -8u + 6u - 42}\)

Collect like terms

⇒\( \mathrm{ - 22 = - 2u - 42}\)

Swap the sides of the equation

⇒\( \mathrm{ -2u - 42 = - 22}\)

Move constant to R.H.S and change it's sign

⇒\( \mathrm{ - 2u = - 22 + 42}\)

Calculate

⇒\( \mathrm{ - 2u = 20}\)

Divide both sides of the equation by -2

⇒\( \mathrm{ \frac{ - 2u}{ - 2} = \frac{20}{ - 2} }\)

Calculate

⇒\( \mathrm{u = - 10}\)

Hope I helped!

Best regards!

The data in the table of values can be used to find the line of best fit after plotting the graph

a. Please find attached the graph of the data showing the next two points on the table, which are (9, 9.8), (7, 11)

b. Linear correlation

c. Please find attached the graph of the data showing the line of best fit created with MS Excel

A line of best fit is a line that passes through a set of scatter plot, which most precisely reflects the relationship between the points.

a. Please find attached the graph of the data in the table, including the plot of the next two points (9, 9.8), and (7, 11), created with MS Excel

b. The type of correlation on the graph which consists of a straight line that is drawn across the points such that the distance between the line and the points on the graph is minimized, is a linear correlation.

c) The line of best fit, can be obtained adding the Trendline chart element on MS Excel, which can be obtained as follows;

Please find attached the graph of the Number of hours sleep to the Age of the children, showing the line of best fit, created with MS Excel

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Answer:

(A) - V=11.8098 cm^3, The actual volume of a bouncy ball is less than the  estimation.

(B) -\(m=\rho V \Rightarrow w=mg\)

(C) - Yes, the \(A_{paper}\geq SA_{box}\)

Step-by-step explanation:

Given the three part question.

(A) - Given that 1000 bouncy balls fill a box (dimensions: 27cm by 27cm by 16.2cm) in its entirety. Estimate the volume of one bouncy ball.

(B) - Describe a method in which you could find the weight of one bouncy ball

(C) - Given a square piece of wrapping paper (24 by 24 in), is this enough to cover the entire box?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Part (A):

(1) - Compute the volume of the box

\(\boxed{\left\begin{array}{ccc}\text{\underline{Volume of a Box:}}\\\\V=l\times w\times h\end{array}\right}\)

\(V_{tot.}=l\times w\times h\\\\\Longrightarrow V_{tot.}=27\times 27\times 16.2\\\\\therefore \boxed{V_{tot.}=11809.8 \ cm^3}\)

(2) - Use the volume we just found to estimate the volume of one bouncy ball

\(\boxed{\left\begin{array}{ccc}\text{\underline{Volume of One Bouncy Ball:}}\\\\V_{1 \ ball}=\frac{V_{tot.}}{1000} \end{array}\right}\)

\(V_{1 \ ball}=\frac{V_{tot.}}{1000}\\\\\Longrightarrow V_{1 \ ball}=\frac{11809.8}{1000} \\\\\therefore \boxed{V_{1 \ ball} \approx 11.8098 \ cm^3}\)

Thus, the estimated volume of one ball is found. Now, is this the actual volume of one ball? No, the actual volume of 1 ball would be less than the value we just computed. This is because there is space left between each ball. I have attached an image for you to visualize.

Part (B):

One way you could find the weight of one balls is by find the ball's mass using the following formula. You would have to look up the density of the bouncy ball's material.

\(mass=density\times volume \rightarrow \boxed{m=\rho V}\)

Then using the value you find for mass you could then use the following formula to determine 1 ball's weight.

\(weight=mass \times gravity \rightarrow \boxed{w=mg}\)

Part (C):

(1) - Compute the surface area of the box

\(\boxed{\left\begin{array}{ccc}\text{\underline{Surface Area of a Rectangular Box:}}\\\\SA=2(wl+hl+hw)\end{array}\right}\)

\(SA_{box}=2(wl+hl+hw)\\\\\Longrightarrow SA_{box}=2((16.2)(27)+(27)(27)+(27)(16.2))\\\\\Longrightarrow SA_{box}=2(437.4+729+437.4)\\\\\Longrightarrow SA_{box}=2(1603.8)\\\\\therefore \boxed{SA_{box}=3207.6 \ cm^2}\)

(2) - Compute the surface area of the square piece of wrapping paper

\(\boxed{\left\begin{array}{ccc}\text{\underline{ Area of a Square:}}\\\\A=s^2\end{array}\right}\)

\(A_{paper}=s^2\\\\\Longrightarrow A_{paper}=(24)^2\\\\\therefore \boxed{A_{paper}=576 \ in^2}\)

(3) - The surface area of the box and wrapping paper are in different units. So, we must do a unit conversion

\(\boxed{1 \ cm^2 =0.155 \ in^2}\)

\(\frac{3207.6 \ cm^2}{1} \times \frac{0.155 \ in^2}{1 \ cm^2}=\boxed{497.178 \ in^2} =SA_{box}\)

(4) - The wrapping paper will completely cover the box if \(A_{paper}\geq SA_{box}\)

\(576 \ in^2\geq 497.178 \ in^2 \therefore \text{The wrapping paper will cover the box}\)

Thus, all parts have been answered.

20 milliliters is equal to 1.352037 tablespoons. To convert any amount of milliliters to tablespoons, simply divide the volume in milliliters by 14.7867648.

A milliliter (mL) is a unit of volume in the metric system. It is equal to one cubic centimeter (cc). One tablespoon (tbsp) is equal to 14.7867648 milliliters (mL). To convert 20mL to tablespoons, we can use the formula:

Tablespoons = milliliters ÷ 14.7867648

To calculate the number of tablespoons, we divide 20 by 14.7867648.

Tablespoons = 20 ÷ 14.7867648

Tablespoons = 1.352037

Therefore, 20 milliliters is equal to 1.352037 tablespoons. To convert any amount of milliliters to tablespoons, simply divide the volume in milliliters by 14.7867648.

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The expected time for activities, use the formula for expected value and multiply the time for each activity by its probability. Therefore, the expected time for these activities is 2.8 hours.

To calculate the expected time for activities, we can use the formula for expected value.

The expected value is calculated by multiplying the time for each activity by its probability of occurrence, and then summing up these values. The formula for expected value is: Expected Value = (Time1 * Probability1) + (Time2 * Probability2) + ... + (TimeN * ProbabilityN) Here's a step-by-step example:

1. List all the activities and their corresponding times and probabilities.

2. Multiply the time for each activity by its probability.

3. Sum up the values obtained in step 2.

For example, let's say we have two activities: Activity 1: Time = 2 hours, Probability = 0.6 Activity 2: Time = 4 hours, Probability = 0.4 Using the formula, we calculate the expected time as follows: Expected Time = (2 hours * 0.6) + (4 hours * 0.4) = 1.2 hours + 1.6 hours = 2.8 hours

Therefore, the expected time for these activities is 2.8 hours.

Here full question is not provided  but the full answer given above.

Remember, this is just one example, and you can use the same formula for any number of activities with their respective times and probabilities. In summary, to calculate the expected time for activities, use the formula for expected value and multiply the time for each activity by its probability. Then, sum up these values to get the expected time.

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The complete steps are

A matrix that is produced by flipping every row and column in the original matrix.

When a matrix is transposed, its rows become columns and its columns become rows. It is especially useful in applications where the inverse and adjoint of matrices must be obtained.

Given:

AX + B = C

Step 1 : AX = C - B

and, Step 2: x = (C- B)/ A

which is the transposition of the Matrix.

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Given the matrix equation:

AX + B = C

Outline the steps for solving this equation.

Step 1:

Step 2:

DONE

Answer:

Step 1: B. Add the opposite of B to both sides

Step 2: D. Multiply both sides by the inverse of A

Answer:

1/2

Step-by-step explanation:

The red markings is not clear but I think the larger one is triangle DEF, if not, then the answer is 2

Answer:

1/2

Step-by-step explanation:

The dude above said if the big triangle is not DEF then it's two, but the big triangle is DEF therefore it is: 1/2.

Answer: d. No, because the study was not taken from a random sample of scholarship athletes.

Step-by-step explanation:

Since the study only focuses on basketball players, the sample may not be representative of all scholarship athletes in the university. This can cause bias in the results and make it difficult to generalize the findings to the larger population of scholarship athletes. Therefore, the university administration should not fully trust the results of this study.

The smallest number a such that A + BB is regular for all B > a can be determined by finding the eigenvalues of the matrix A. The value of a will be greater than or equal to the largest eigenvalue of A.

A matrix A is regular if it is non-singular, meaning it has a non-zero determinant. We can consider the expression A + BB as a sum of two matrices. To ensure A + BB is regular for all B > a, we need to find the smallest value of a such that A + BB remains non-singular. One way to check for singularity is by examining the eigenvalues of the matrix A. If the eigenvalues of A are all positive, it means that A is positive definite and A + BB will remain non-singular for all B. In this case, the smallest number a can be taken as zero. However, if A has negative eigenvalues, we need to choose a value of a greater than or equal to the absolute value of the largest eigenvalue of A. This ensures that A + BB remains non-singular for all B > a.

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The most appropriate choice for area of rectangle will be given by-

Difference between area of rectangle 2 and area of rectangle 3 is the largest.

Difference is 25.92 \(cm^2\)

What is area of rectangle?

Area of rectangle is the total space taken by the rectangle.

If l is the length of the rectangle and b is the breadth of the rectangle, then area of rectangle is given by

Area of rectangle = \(l \times b\)

Here,

Area of rectangle 1 = 60.81 \(cm^2\)

Area of rectangle 2 = 61.44 \(cm^2\)

Area of rectangle 3 = 35.52 \(cm^2\)

Area of rectangle 4 = 47.88 \(cm^2\)

Difference between Area of rectangle 1 and rectangle 2 =

                                                                                             (61.44 - 60.81)\(cm^2\)

                                                                                            = 0.63 \(cm^2\)

Difference between Area of rectangle 1 and rectangle 3 =

                                                                                            (60.81 - 35.52)\(cm^2\)

                                                                                             = 25.29 \(cm^2\)

Difference between Area of rectangle 1 and rectangle 4 =

                                                                                             (60.81 - 47.88)\(cm^2\)

                                                                                            = 12.93 \(cm^2\)

Difference between Area of rectangle 2 and rectangle 3 =

                                                                                             (61.44 - 35.52)\(cm^2\)

                                                                                            = 25.92 \(cm^2\)

Difference between Area of rectangle 2 and rectangle 4 =

                                                                                            (61.44 - 47.88) \(cm^2\)

                                                                                            = 13.56 \(cm^2\)

Difference between Area of rectangle 3 and rectangle 4 =

                                                                                           (47.88 - 35.52) \(cm^2\)

                                                                                            = 12.36 \(cm^2\)

Difference between area of rectangle 2 and area of rectangle 3 is the largest.

Difference is 25.92 \(cm^2\)

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Answer: ∠1 = 90°

Step-by-step explanation:

      There are a few steps we will take to solve this problem. In each step, I will write an equation to help us solve, then use inverse operations to solve.

      First, we will use the exterior angles theorem to find the measurement of ∠3 (this will help us solve for ∠2, then for ∠1).

89° = 51° + ∠3

∠3 = 38°

      Next, we will find the measurement of ∠2 since we know ∠2 plus ∠3 is 90 degrees, as shown by the perpendicular lines and the box.

90° = ∠3 + ∠2

90° = 38° + ∠2

∠2 = 52°

      Lastly, we will solve for ∠1. We know that there are 180 degrees in a triangle.

180° = 38° + ∠1 + ∠2

180° = 38° + ∠1 + 52°

180° = 90° + ∠1

∠1 = 90°

Answer:

90

Step-by-step explanation:

I started by finding angle 5

180 - 89 = 91  Supplemental angles

Then I found angle 3

The sum of the interior angles of a triangle is 180

180-89-91 = 38

Angle2 and 3 are complementary angles

90- 38 =52

the sum of the interior angles of a triangle is 180

Angle 1

180 - 52 - 38 = 90

There are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

To find the number of acres in a lot, you can use the following formula:

Number of acres = (length in feet) x (width in feet) / 43,560

First, convert the length and width from miles to feet. There are 5,280 feet in a mile, so:

Length in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet
Width in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet

Next, plug these values into the formula:

Number of acres = (2,640 feet) x (2,640 feet) / 43,560 = 174,240,000 / 43,560 = 160 acres

Therefore, there are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

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Answer:

Sam is 24 years old and his mother is 48 years old.

Step-by-step explanation:

Equations

Let's call

x   = Sam's current age

Since Sam's mother is twice as old as Sam:

2x = Sam's mother current age

x + 12 = Sam's age in 12 years

2x - 12 = Sam's mother age 12 years ago

These two last expressions are equal:

x + 12 = 2x - 12

Subtracting x and adding 12:

x = 24

2x = 48

Sam is 24 years old and his mother is 48 years old.

Sam, is 24 years old. His mom is 48 years old.

Since the two hexagons are similar, their corresponding sides are in the same ratio as the scale factor.

Let x be the length of a side of the smaller hexagon, then the corresponding length of a side of the larger hexagon can be expressed as (3/7)x.

The area of a hexagon can be calculated using the formula: A = (3√3/2)s², where s is the length of a side.

Since the area of the smaller hexagon is 18 m², we can solve for x as follows:

18 = (3√3/2)x²

x² = 12/√3

x = 2√3

Now we can calculate the area of the larger hexagon:

Area of the larger hexagon = (3√3/2)(3/7x)² = (3√3/2)(3/7(2√3))² = 54/49 m²

Finally, we can calculate the volume of the larger hexagon, assuming it is a regular hexagonal prism:

Volume of the larger hexagon = Area of hexagon x Height

The height of the hexagonal prism is the same as the length of the side of the larger hexagon, which is (3/7)x:

Volume of the larger hexagon = (54/49) x (3/7)x = 54/343 x² ≈ 0.212 x²

Substituting the value of x, we get:

Volume of the larger hexagon ≈ 0.212 x (2√3)² = 1.272 m³

Therefore, the volume of the larger hexagon is approximately 1.272 m³.

Well, I'm not sure if it's correct but I got 42.

I got this by doing something along the lines of:

1) 18/x = 3/7

2) Cross multiply

3) 3x = 126

4) Divide both sides by 3

5) x = 42

The false principle of Agile Development is D - Complexity is essential to development processes.

What is Agile Development?

Teams use the iterative agile development methodology for software development. Cross-functional, self-organized teams frequently adapt projects by analyzing the environment and user requirements.

The principle of Agile Development that is NOT correct is - "Complexity is essential to development processes".

In fact, Agile Development principles emphasize simplicity and minimizing complexity wherever possible.

This is because complexity can lead to a slower development process, difficulty in making changes, and increased risk of errors or bugs.

The other three principles listed are accurate principles of Agile Development.

Therefore, the incorrect option is D.

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Answer:

-2x-4

Step-by-step explanation:

We have to combine like terms in this expression. So, only -3 and -1 can be combined, and the same thing applies to 2x and -4x. If we add -3 and -1 as it says in the expression, that is -4. If we add 2x and -4x which is also in the expression, it is -2x. We can combine these two resulting terms to simplify the expression. The answer is -2x-4.

Answer: the correct answer is D and E

Step-by-step explanation:

6(x-2) > 15

6x - 12 > 15

6x > 27

x > 27/6

Hope it helps!

Answer:

x>4.5

Step-by-step explanation:

6(x-2)>15

We do this is as if it were an equation:

6(x-2)>15

Expand the brackets:

6x-12>15

Add 12 to both sides:

6x-12+12>15+12

Simplify:

6x>37

Now we divide both sides by 6:

6x÷6>37÷6

x > 4.5

If we put 5 into the original equation as it is more than 4.5, we get:

6(5-2)>15

We can simplify the brackets or expand first:

Simplifying the brackets first:

6(3)>15

18>15 ✅

Expanding first:

6(5-2)>15

30-12>15

18>15 ✅

Hey there :)

Please check the attached image for answer with explanation.

\(Benjemin360 :)\)

Integrate by parts to find some useful recurrences relating Iₙ and Jₙ.

\(\displaystyle I_n = \int_{-\pi}^\pi x^n \cos(x) \, dx = uv \bigg|_{x=-\pi}^{x=\pi} - \int_{-\pi}^\pi v\, du \\\\ \implies I_n = -n \int_{-\pi}^\pi x^{n-1} \sin(x) \, dx \\\\ \implies I_n = -n J_{n-1}\)

where u = xⁿ and dv = cos(x) dx.

\(\displaystyle J_n = \int_{-\pi}^\pi x^n \sin(x) \, dx = uv \bigg|_{x=-\pi}^{x=\pi} + \int_{-\pi}^\pi v\, du \\\\ \implies J_n = \pi^n - (-\pi)^n + n \int_{-\pi}^\pi x^{n-1} \cos(x) \, dx \\\\ \implies J_n = \pi^n - (-\pi)^n + n I_{n-1}\)

The integrals for n = 0 are trivial:

\(\displaystyle I_0 = \int_{-\pi}^\pi \cos(x) \, dx = \sin(\pi) - \sin(-\pi) = 0\)

\(\displaystyle J_0 = \int_{-\pi}^\pi \sin(x) \, dx = -\cos(\pi) - (-\cos(-\pi)) = 0\)

Now, the integral we're interested in is

\(\displaystyle \int_{-\pi}^\pi x^n f(x) \cos(x) \, dx\)

but we know f(x) is quadratic, and we want to find its coefficients a, b, and c such that

\(\displaystyle \int_{-\pi}^\pi x^n (ax^2+bx+c) \cos(x) \, dx\)

But this is simply

\(\displaystyle \int_{-\pi}^\pi (ax^{n+2}+bx^{n+1}+cx^n) \cos(x) \, dx = aI_{n+2} + bI_{n+1} + cI_n\)

Using the recurrences above and the initial values we've computed, we find

• I₁ = -J₀ = 0

• J₁ = π - (-π) + I₀ = 2π

• I₂ = -2 J₁ = -4π

• J₂ = π² - (-π)² + 2 I₁ = 0

• I₃ = -3 J₂ = 0

• J₃ = π³ - (-π)³ + 3 I₂ = 2π³ - 12π

• I₄ = -4 J₃ = -8π³ + 48π

When n = 0, the integral we care about is

\(aI_2 + bI_1 + cI_0 = -4\pi a + 0 + 0 = 4\pi \implies a = -1\)

When n = 1,

\(aI_3 + bI_2 + cI_1 = 0 - 4\pi b + 0 = 4\pi \implies b = -1\)

When n = 2,

\(aI_4 + bI_3 + cI_2 = (48\pi - 8\pi^3)a + 0 - 4\pi c = 4\pi \implies c = 2\pi^2 - 13\)

so that

\(f(x) = \boxed{-x^2 - x + 2\pi^2 - 13}\)

The other rotation that can be used to achieve the transformation is; C: 270° counterclockwise

What is the rotation used?

From the coordinates of XYZ transformed to coordinates of triangle X'Y'Z', we can see that the transformation pattern is;

(x, y) -----> (-y, x)

Now, this pattern of transformation occurs when;

There is a 90° clockwise rotation. However, the other rotation that can be used to achieve this is a 270° counterclockwise rotation

Answer: Triangle XYZ can be rotated 90° counterclockwise using the origin as the center of rotation to create triangle X’Y’Z’. To obtain the original triangle XYZ, we need to rotate the triangle X'Y'Z' by 90° clockwise using the origin as the center of rotation. This means that rotating the triangle X'Y'Z' by 90° clockwise is the same as rotating triangle XYZ by 90° counterclockwise, so the answer is 90° clockwise.

Answer:

8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

When n = 1:

n² + 7 = 1² + 7 = 8

When n = 2:

n² + 7 = 2² + 7 = 11

When n = 3:

n² + 7 = 3² + 7 = 16

When n = 4:

n² + 7 = 4² + 7 = 23

When n = 5:

n² + 7 = 5² + 7 = 32

When n = 6:

n² + 7 = 6² + 7 = 43

Therefore, the first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Answer:

When n = 1, n² + 7 = 1² + 7 = 8

When n = 2, n² + 7 = 2² + 7 = 11

When n = 3, n² + 7 = 3² + 7 = 16

When n = 4, n² + 7 = 4² + 7 = 23

When n = 5, n² + 7 = 5² + 7 = 32

When n = 6, n² + 7 = 6² + 7 = 43

The first 6 terms of n² + 7 are 8, 11, 16, 23, 32, and 43.

Step-by-step explanation:

ᓚᘏᗢ

hope u have a good day man

Answer:

$2.71 + 4j = $6.75

j = $1.01

Step-by-step explanation:

$2.71 + 4j = $6.75

4j = 6.75 - 2.71 = 4.04

j = 4.04/4 = $1.01

Answer:

$6.75 = $2.71 + 4j

j = $1.01

Step-by-step explanation:

The total amount of money Ava spent was $6.75. We can make this one side of an equation.

The other side of the equation can be what Ava bought for that $6.75. We know that she bought $2.71 of oranges and 4 juice bottles, so we can add these on the other sides of the equation.

\(\$6.75 = \$2.71 + 4j\)

To solve this equation for \(j\), we can first subtract $2.71 from both sides.

\(\textrm{ } \ \$6.75 = \$2.71 + 4j\\\underline{-\$2.71} \ \ \ \ \underline{-\$2.71 \ \ \ \ }\)

  \(\$4.04 = 4j\)

Finally, we can divide both sides by 4.

\(\$4.04 = 4j\\\overline{\ \ \ 4\ \ \,} \ \ \ \ \overline{\: 4 \:}\)

\(\$1.01 = j\)

\(\boxed{j = \$1.01}\)

answer: she can buy 10 tube of paints

Answer:

\(\boxed {t = -1}\)

Step-by-step explanation:

Solve for the value of \(t\):

\(5t + 16 = 6 - 5t\)

-Take \(5t\) and add to \(5t\):

\(5t + 16 + 5t = 6 - 5t + 5t\)

\(10t + 16 = 6\)

-Subtract \(16\) to both sides:

\(10t + 16 - 16 = 6 - 16\)

\(10t = -10\)

-Divide both sides by \(10\):

\(\frac{10t}{10} = \frac{-10}{10}\)

\(\boxed {t = -1}\)

So, the value of \(t\) is \(-1\).