Select the correct answer.
Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina?

A.
The equation that represents this situation is t − 3 = 18. Tina is 21.
B.
The equation that represents this situation is t + 3 = 18. Tina is 15.
C.
The equation that represents this situation is 3 − t = 18. Tina is 21.
D.
The equation that represents this situation is -3 − t = 18. Tina is 15.

This equation has infinitely many solutions.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Here, we have

Given: 3x+4y = -10...(1),

y = -3/4x - 5/2....(2)

We solve this linear equation and we get

We multiply equation (2) by 4 and we get

4y + 3x = -5(2)

4y + 3x = -10

Hence, this equation has infinitely many solutions.

To learn more about the linear equation from the given link

https://brainly.com/question/2030026

#SPJ1

Answer:

2744m^3

Step-by-step explanation:

14*14*14=2744m^3

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

For more such questions on triangle

https://brainly.com/question/28470545

#SPJ8

\(\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}\)

C. 4.

Answer:

\(b = 2\sqrt{2}\\\\a=4\)

Step-by-step explanation:

\(b = 2\sqrt{2}\\a = \sqrt{b^2+(2\sqrt{2})^2} = \sqrt{8+8}=\sqrt{16}=4\)

Answer:

1-(n+6)                       (n+6)-1

Step-by-step

i just got it right on study island

Answer:

C: a < θ < 90%

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Find unit rate (since it starts at 0,0)

at 45 seconds  it is 900 bottles

             900 bottles / 45 seconds = 20 bottle / sec

20 bottles / sec * 80 sec = 1600 bottles

Answer: y= 1700 (1- .0325) ^15= 1700(.9675) ^15=1700(.60920660)= 1035.65 km Hope this helps!

Step-by-step explanation:To calculate the area of the forest after 5 years, we need to use the formula:

A = A0 * (1 - r/100)^t

PLEASE MARK BRAINLIST

Answer:

Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:

tan(1) = 2tan(1/2) / (1 - tan^2(1/2))

To find tan(1/2), we can use the half-angle formula for tangent:

tan(1/2) = sin(1) / (1 + cos(1))

We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:

tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)

Again, we cannot simplify this expression any further without a calculator.

For the second expression, we are asked to find the value of:

tan(arctan(6/4))

By definition, tan(arctan(x)) = x for all x, so we have:

tan(arctan(6/4)) = 6/4 = 3/2

Therefore, the exact value of the expression tan(6/4) is 3/2.

Answer:

8/3

Step-by-step explanation:

Because all 4 angles are congruent, the sides are proportional.

the scale factor is 5/30 = 1/6.

meaning x = 16(1/6)=8/3.

Answer:

\(h_{max}=5.5\)

Step-by-step explanation:

Given

\(h = -0.1(d + 1)(d - 12)\)

Solving (a): The graph

To do this, we plot h on the vertical axis and d on the horizontal

See attachment for graph

Solving (b): The maximum of h

From the attached graph, h has the maximum value when:

\(d = 4.225\)

So, the maximum of h is:

\(h_{max}=5.5\)

Answer:

1. True

2. True

3. False

4. True

5. False

6. True

7. Jesus.

The theoretical probability of spinning red is given as follows:

1/3.

The parameters that are needed to calculate a probability are listed as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

For the spinner in this problem, 2 out of 6 regions are red, hence the theoretical probability is given as follows:

2/6 = 1/3.

Learn more about the concept of probability at https://brainly.com/question/24756209

#SPJ1

Vertex: (1, -36); intercepts: x = 7, -5 (option D)

Given:

To find:

the vertex and the x-intercepts

i) Vertex is given as (h, k). To determine the vertex, we will apply the formula:

Vertex (h, k): (1, -36)

ii) x-intercept is the value of x when y = 0. To determine x-intercept, we will substitute y with 0. Then solve for x

Answer:

4/5 is the slope

Answer:

(-5,-4) or (-4, -5)

Step-by-step explanation:

The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.

The formula for population variance uses the division of (sum of squared deviations) by the total number of elements in the population, while the formula for sample variance uses the division of (sum of squared deviations) by the sample size minus one.

The formula for population variance is given by:

σ² = (1/N) * ∑(X - μ)²,

where N is the total number of elements in the population, X is an individual value in the population, and μ is the mean of the population.

s²= (1/(n-1)) * ∑(X - m)²,

where n is the sample size and m is the mean of the sample.

Learn more about variance on:

brainly.com/question/15858152

#SPJ1

Ok, so

We want to justify the fact that triangle PQR is similar to triangle STU.

First, let me draw the situation here below:

If you notice, both angles of each triangle are equal. We can also see that the sides of triangles PQR and STU should have a ratio.

This is:

If we replace:

With this, we can affirm that there's a dilation scale factor of 2. This means that the bigger figure is two times bigger than the smaler one. Therefore, the triangles PQR and STU are similar.

Both triangles are similar because their corresponding angles are congruent and the corresponding sides are in proportion.

The box plots provide visual representations of the distribution of salaries at two companies, Company A and Company B. To compare the ranges and medians of the data sets, we examine the characteristics of each box plot.

The range of a data set represents the difference between the maximum and minimum values. Looking at the box plots, we can determine that the range of Company A's salaries is larger than the range of Company B's salaries.

This can be inferred by observing the lengths of the whiskers, where the whiskers in Company A's box plot extend further in both the upper and lower directions compared to Company B's box plot.

The median of a data set represents the middle value when the data is arranged in ascending or descending order. Comparing the medians of the two box plots, we can determine that the median of Company A's salaries is higher than the median of Company B's salaries.

This is evident by comparing the positions of the medians within the boxes. In Company A's box plot, the median is closer to the upper quartile, indicating a higher median salary, while in Company B's box plot, the median is closer to the lower quartile, suggesting a lower median salary.

In summary, the range of salaries at Company A is larger than that of Company B, indicating a wider spread of salary values. Additionally, the median salary at Company A is higher than the median salary at Company B, suggesting a higher central tendency or midpoint in the distribution of salaries.

For more such questions distribution

https://brainly.com/question/30331609

#SPJ8

The limit of the sum (6xi-3)/n as n approaches infinity is 9, which means that as the number of subintervals in the interval [0,3] becomes larger and larger, the sum of the values (6xi-3)/n approaches 9.

The limit is a concept in mathematics that helps us understand what happens as a function or a sequence approaches a certain value.

In this particular problem, we are looking at the limit of a sum of values as the number of subintervals in the interval [0,3] approaches infinity.

The interval [0,3] is divided into n equal subintervals and a number xi is chosen arbitrarily in the ith subinterval. We then look at the sum of the values (6xi-3)/n for all n subintervals.

Mathematically, we can write this sum as:

S = (6xi-3)/n for i = 1, 2, ..., n

And the limit of S as n approaches infinity can be written as:

lim n -> infinity S = lim n -> infinity (6xi-3)/n

Now, we use the concept of a Riemann Sum to evaluate the limit of this sum. A Riemann Sum is a way of approximating the area under a curve by breaking it down into rectangles and summing their areas.

In our case, we can think of the sum S as a Riemann Sum for the function f(x) = 6x-3 over the interval [0,3]. As n approaches infinity, the width of the subintervals approaches 0, and the sum S approaches the definite integral of f(x) over [0,3].

Using the fundamental theorem of calculus, we can find the definite integral of f(x) over [0,3] as:

∫f(x)dx = 6x^2/2 - 3x evaluated from 0 to 3

And this value is 9, so the limit of S as n approaches infinity is 9.

To know more about limit here.

https://brainly.com/question/17019350

#SPJ4

Answer:

x=

Step-by-step explanation:

⅔x= 7x-1

2/3x=6

multiply both sides by 3/2

(3/2)(2/3x)= 6×3/2

x=

Answer:

I think the answer is.. .

Step-by-step explanation:

(b)

The company's March expected cash receipts from current and prior credit sales are $97,660.

The cash receipts represent the receipts from cash sales and the cash collections from credit sales.

Each period's cash receipts depend on the company's cash collection history based on estimated collections from credit customers.

Cash sales percent = 30% of sales

Credit sales percent = 70% of sales (100% - 30%)

Collections on credit:

The month of sales = 25%

The second month = 55%

The third month = 15%

                               January    February    March

Project Sales:        $74,000    $99,000  $109,000

Credit Sales:         $51,800     $69,300   $76,300

Cash receipts:

Cash sales (30%) $22,200     $29,700   $32,700

Collections on credit:

1st month (25%)      12,950         17,325     19,075

2nd month (55%)                       28,490     38,115

3rd month (15%)                                           7,770

Total cash receipts in March                 $97,660

Thus, the company's March expected cash receipts from current and prior credit sales are $97,660.

Learn more about the credit collection history at https://brainly.com/question/20714255

#SPJ1

Answer:5(3+1); 20

Step-by-step explanation:

5x3 is 15 and 5x1 is 5 which is equivalent to 15+5, then add to get 20.

The input (x) that satisfies the condition of being multiplied by 6 and then Subtracted by 80 to give the same value as the output is 16.

The input as "x." According to the given information, the input (x) is multiplied by 6 and then subtracted by 80, resulting in the output. In mathematical terms, this can be expressed as:

Output = (6 * x) - 80

The problem states that the input and output are the same. Therefore, we can set up the equation:

x = (6 * x) - 80

To solve for x, we'll rearrange the equation and isolate the variable:

x - 6 * x = -80

Combine like terms:

-5 * x = -80

Divide both sides by -5:

x = (-80) / (-5)

Simplifying the division:

x = 16

Hence, the input (x) that satisfies the condition of being multiplied by 6 and then subtracted by 80 to give the same value as the output is 16.

For more questions on Subtracted .

https://brainly.com/question/31129970

#SPJ8

-x+2y=0

To find the slope we have to express the equation in slope-intercept form:

y= mx+b

Where:

m= slope

b= y- intercept

So, we have to solve for y:

-x+2y=0

2y= x

y= 1/2x

m= 1/2

Slope is 1/2

Answer: -3.7

Step-by-step explanation:

Step 4 is wrong 6.1 - 9.8 = -3.7

Answer:

3*3*3=27 is the rights answer

3x6=18(move 1 to the left/replace the 0)

3x1=3

Answer:

2kg for 1.97 is indeed the best option