Toni's grandmother is 3 years more than 6 times Toni's age. The sum of their ages in years is 87. Which equation can be used to find each of their ages?​

Answer:

√5 < 2.5 < 5

Step-by-step explanation:

√5= 2.23

therefore,

√5 < 2.5 < 5

Answer:

the surface area of the rectangular prism is 572cm².

Step-by-step explanation:

The surface area of a rectangular prism can be calculated using the formula 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height. Plugging in the values you provided, we get:

2 * 4cm * 15cm + 2 * 4cm * 14cm + 2 * 15cm * 14cm = 572 cm²

So the surface area of the rectangular prism is 572 square centimeters.

Answer:

idek and i dont ;like how this is working!

Step-by-step explanation:

Answer:

for 4, 10, 14 the gcf would be 2

Step-by-step explanation:

Answer:

Area of the figure = 224 yd²

Step-by-step explanation:

Area of Rectangle = Length × Width

Area of Δ = 1/2 (base × height)

Dividing the whole figure

Triangle 1:

1/2(12 × 14) = 168/2 = 84 yd²

Rectangle 1:

3 × 11 = 33 yd²

Rectangle 2:

7 × 9 = 63 yd²

Rectangle 3:

4 × 11 = 44 yd²

Adding all

Area of the figure = 84 +33 +63 + 44

Area of the figure = 224 yd²

Answer:

Total area = 224 yd²

Step-by-step explanation:

Make a sketch. See attachment

Total area =

area 1 + area 2 + area 3 + area 4 + area 5 + area 6 + area 7

15 + 84 + 42 + 32 + 7 + 28 + 16

Total area = 224 yd²

Answer:

The hospital gets \(2.75\:\rm{mg}\) of medicines from these three companies.

Step-by-step explanation:

Company A has \(1.3\) milligrams, which is \(0.9\) milligram more than Company C's.

If \(A,B,C\), are the medicines produced by Companies A,B,C, respectively,

then, \(A=1.3\:\rm{mg}\), and its expression is given as,

\(\begin{aligned}A&=0.9+C\\1.3&=0.9+C\\C&=1.3-0.9\\C&=0.4\:\rm{mg}\end{aligned}\)

Company A has \(1.3\) milligrams, which is twice the difference between the weight of Company B's supply and Company C's.

So, its expression is given as,

\(A=2(B-C)\\\)

Substituting values of \(A,C\), the expression becomes,

\(\begin{aligned}1.3&=2(B-0.4)\\0.65&=B-0.4\\B&=0.65+0.4\\B&=1.05\:\rm{mg}\end{aligned}\)

So, the hospital gets,

\(\begin{aligned}A+B+C&=1.3+0.4+1.05\\&=2.75\:\rm{mg}\end{aligned}\)

of medicines.

We are required to find the total milligrams if medicine the hospital can get from the three companies.

The total quantity of medicine the hospital can get from the three companies is 2.75 milligrams

There are there companies:

Company A

Company B

Company C

Company A = 1.3 milligrams

Company A is 0.9 milligrams more than Company C's

A = 0.9 + C

1.3 = 0.9 + C

1.3 - 0.9 = C

0.4 = C

C = 0.4 milligrams

Company A is also twice the difference between the weight of

Company B's supply and Company C's

A = 2(B - C)

1.3 = 2(B - 0.4)

1.3 = 2B - 0.8

1.3 + 0.8 = 2B

2.1 = 2B

Divide both sides by 2

B = 2.1/2

B = 1.05 milligrams

Therefore,

A + B + C

= 1.3 + 1.05 + 0.4

= 2.75 milligrams

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Answer:

isjsuzizwjskzkzuziziss

Answer:

e7eufthysostutrhrbdbdhdbdhrbt

======================================================

Explanation:

The triangle on the left has a = 8 as one of the legs, and c = 17 as the hypotenuse. Use the pythagorean theorem to find the missing side.

\(a^2+b^2 = c^2\\\\8^2+b^2 = 17^2\\\\64 + b^2 = 289\\\\b^2 = 289-64\\\\b^2 = 225\\\\b = \sqrt{225}\\\\b = 15\\\\\)

This is the height of the parallelogram as marked by the dashed line.

The base is 9 units across the bottom. We won't use 8 as the base because it's too short along the top.

area = base*height

area = 9*15

area = 135 square units

Answer: 245

Step-by-step explanation:

Answer:

The answer is D

Step-by-step explanation:

The sequence is decreasing as n increases and sequence converges to the value 0.

The given sequence is defined as aₙ = 1 / (7n + 3).

To determine if the sequence converges or diverges, we need to analyze its behavior as n approaches infinity.

As n increases, the denominator 7n + 3 also increases which means that the values of aₙ will get smaller and smaller, approaching zero as n becomes larger.

The sequence converges to the value 0.

The sequence is decreasing as n increases.

The sequence converges to the value 0.

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To find the area of the combined rectangles, we need the dimensions (length and width) of each rectangle. However, the provided text and numbers do not seem to correspond to a clear description of the rectangles or their dimensions. Could you please provide more specific information or clarify the question?

Answer:

Step-by-step explanation:

Range of the function is the set of y-values (output values) of the function on the graph.

Domain of the function is the set of x-values (input values) of the function.

Domain of the function : [-5, 4)

(including x = -5 and excluding x = 4)

Range : [-4, 2)

(Including y = -4 and excluding y = 2)

x - intercepts : x = -5, -2, 2

Average rate of change over the interval [0, 2]

= \(\frac{f(2)-f(0)}{2-0}\)

= \(\frac{0-(-4)}{2-0}\) [Since, f(2) = 0, f(0) = -4]

= 2

Right most interval where the graph is positive → [2, 4]

The key feature of a function include the intercepts and intervals of the function

(a) The range

The least y value on the graph is at y = -4, and the maximum is at y = 2, with an open circle.

So, the range is:

\(\mathbf{Range = [-4,2)}\)

(b) The domain

The least x value on the graph is at x = -5, and the maximum is at x = 4, with an open circle.

So, the domain is:

\(\mathbf{Domain = [-5,4)}\)

(c) The x-intercepts

This is the point where the graph crosses the x-axis.

So, we have:

\(\mathbf{x-intercept =-2 \ and\ 2}\)

(d) Average rate of change over [0,2]

From the graph, we have:

f(0) = -4

f(2) = 0

So, the average rate of change (m) is:

\(\mathbf{m = \frac{f(2) - f(0)}{2 - 0}}\)

\(\mathbf{m = \frac{0 - -4}{2 - 0}}\)

\(\mathbf{m = \frac{4}{2}}\)

\(\mathbf{m =2}\)

(d) The right-most interval where the graph is positive

The graph is positive from x = 2 to x = 4.

Hence, the right-most interval where the graph is positive is [2,4]

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Answer:

272,690,813          2,442,810              0.90

national population .      popullation change .      average annual percent change

Step-by-step explanation:

Answer:

Thus, option “c” 10% is correct.

Step-by-step explanation:

The percentage of students that like dubstep = 30%

The percentage of students that like trance music = 25%

The percentage of student that wants only house music = 20%

The percentage of students that like bot dubstep and trance = 15%

Now we have to find the percentage of students that like trance music but nor dubstep.

The percentage of students that like the trance music but nor dubstep = 100% - 30% – 25 % - 20% - 15%

The percentage of students that like trance music but nor dubstep = 10%

Thus, option “c” 10% is correct.

well, since we know that there are 180° in π radians, how many degrees will it be in 345°?

\(\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 345&x \end{array}\implies \cfrac{180}{345}~~ = ~~\cfrac{\pi }{x}\implies \cfrac{12}{23}~~ = ~~\cfrac{\pi }{x} \\\\\\ 12x=23\pi \implies x=\cfrac{23\pi }{12}\)

Answer:

its c

Step-by-step explanation:

C. R: (0, 400)

In mathematics, a rational function is any function that can be described by using a rational fraction, which is an algebraic fraction such that each the numerator and the denominator are polynomials. The coefficients of the polynomials need no longer be rational numbers; they'll be taken in any field k.

A rational function is one that can be written as a polynomial divided by a polynomial. for the reason that polynomials are defined everywhere, the domain of a rational feature is the set of all numbers except the zeros of the denominator. example 1. f(x) = x / (x - 3). The denominator has only one 0, x = 3.

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Answer:

a)

\begin{gathered} {5}^{2} = 25 \\ {6}^{2} = 36 \\ {7}^{2} = 49\end{gathered}

5

2

=25

6

2

=36

7

2

=49

Therefore:

25, 36 and 49

Answer:

A 4 side dice.

Step-by-step explanation:

Benjamin has 4 possible homerooms with the same probability. This means that every homeroom has a 1/4 = 0.25 (or 25%) probability of getting chosen.

You could emulate this situation with a 4 sided dice (are like little pyramids) where each side of the dice would represent the selection of one of the homerooms.

1. When we simplify sec² x + tan² xsec² x, the result obtained is sec⁴x

2. When we simplify (sec² x - 1) / sin² x, the result obtained is sec² x

3. When we simplify (1/sec² x) + (1/csc² x), the result obtained is 1

4. When we simplify (sec x / sin x) - (sin x / cos x), the result obtained is cot x

5. When we simplify (1 + sin x)(1 - sin x), the result obtained is cos² x

6.  When we simplify cos x + sin xtan x, the result obtained is sec x

We can simplify the trig identities as follow:

1. Simplification of sec² x + tan² xsec² x

sec² x + tan² xsec² x = sec² x(1 + tan² x)

Recall

sec² x = 1 + tan² x

Thus,

sec² x(1 + tan² x) = sec² x × sec² x

sec² x(1 + tan² x) = sec⁴x

Therefore, the simplified is written as

sec² x + tan² xsec² x = sec⁴x

2. Simplification of (sec² x - 1) / sin² x

(sec² x - 1) / sin² x

Recall,

sec² x - 1 = tan² x

Thus,

(sec² x - 1) / sin² x = tan² x / sin² x

Recall

tan² x = sin² x / cos² x

Thus,

tan² x / sin² x = (sin² x / cos² x) / sin² x

tan² x / sin² x = 1/ cos² x

Recall

1/ cos² x = sec² x

Therefore, the simplified expression is written as:

(sec² x - 1) / sin² x = sec² x

3. Simplification of (1/sec² x) + (1/csc² x)

(1/sec² x) + (1/csc² x)

Recall

sec² x = 1/cos² x

Thus,

cos² x = 1/sec² x

Also,

csc² x = 1/sin² x

Thus,

sin² x = 1/csc² x

Therefore, we have

(1/sec² x) + (1/csc² x) = cos² x + sin² x

Recall

cos² x + sin² x = 1

Thus, the simplified expression of (1/sec² x) + (1/csc² x) is:

(1/sec² x) + (1/csc² x)  = 1

4. Simplification of (sec x / sin x) - (sin x / cos x)

(sec x / sin x) - (sin x / cos x) = (sec xcos x - sinx sinx) / sinx cos x

Recall

sec x = 1/cos x

sinx sinx = sin² x

Thus,

(sec x / sin x) - (sin x / cos x) = [(cos x/cos x) - sin² x] / sinx cos x

(sec x / sin x) - (sin x / cos x) = [1 - sin² x] / sinx cos x

Recall

1  - sin² x = cos² x

Thus, we have

[1 - sin² x] / sinx cos x = [cos² x] / sinx cos x

[1 - sin² x] / sinx cos x = cos x / sin x

Recall

cos x / sin x = cot x

Thus, the simplified expression of (sec x / sin x) - (sin x / cos x) is:

(sec x / sin x) - (sin x / cos x) = cot x

5. Simplification of (1 + sin x)(1 - sin x)

(1 + sin x)(1 - sin x)

Clear bracket

1 - sin x + sin x - sin² x

1 - sin² x

Recall

1 - sin² x = cos² x

Thus, we have

(1 + sin x)(1 - sin x) = cos² x

6. Simplification of cos x + sin xtan x

cos x + sin xtan x

Recall

tan x = sin x / cos x

cos x + sin xtan x = cos x + sin x (sin x / cos x)

cos x + sin xtan x = cos x + (sin² x / cos x)

cos x + sin xtan x = (cos² x + sin² x) / cos x

Recall

cos² x + sin² x = 1

cos x + sin xtan x = 1 / cos x

1/cos x = sec x

Thus,

cos x + sin xtan x = sec x

The simplified expression of cos x + sin xtan x is sec x

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Answer:

B

Step-by-step explanation:

its B

To calculate the surface area of a rectangular prism, we need to find the area of each of its six faces and then add them up. In this case, the dimensions of the shape are:

Refer to the attachment below.

There are three pairs of faces on a rectangular prism:

8 cm × 3 cm = 24 cm²

Since there are two of these faces, the total area is:

2 × 24 = 48 cm²

8 cm × 6 cm = 48 cm²

Since there are two of these faces, the total area is:

2 × 48 = 96 cm²

3 cm × 6 cm = 18 cm²

Since there are two of these faces, the total area is:

2 × 18 = 36 cm²

Now, add up the areas of all six faces:

Surface Area = 48 + 96 + 36 = 180 cm²

So, the surface area of the rectangular prism is 180 cm².

________________________________________________________

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Answer: 2.333333...

Step-by-step explanation:

If we apply rise over run, we see that it rises 3.5 spaces, and runs 1.5, which means that   \(m = \frac{rise}{run} = \frac{3.5}{1.5} = 2.33333...\)

The solution is Option D.

The median of the data is A = 20 and the mean of the data is M = 22.7

The mean value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values.

Mean = Sum of Values / Number of Values

Given data ,

Let the mean of the data be represented as M

Let the median of the data be represented as A

Now , the equation will be

The list of donations is represented as set D

Set D = { 10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55 }

Now , the mean M is = 10 + 10 + 10 + 10 + 15 + 15 + 15 + 19 + 20 + 20 + 20 + 25 + 25 + 25 + 30 + 30 + 55 + 55 / 18

The mean M = 409 / 18

On simplifying the equation , we get

The mean M = 22.722

Now , the median of the data is A = 20

Hence , the mean is 22.7

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The median of 20 is the most accurate to use, since the data is skewed.

The most accurate measure of center to use in this case is the median of 20. This is because the data is skewed, with a few high-value donations (such as the two donations of 55 dollars) that pull the mean up. However, most of the donations are clustered around 10 to 20 dollars. As a result, the median, which is the middle value when the data is sorted in order, is a better representation of the "typical" donation amount.

In this case, the median is 20, which means that half of the donations were less than 20 dollars and half were more. This is a more accurate representation of the central tendency of the data than the mean of 22.7, which is influenced by the high-value donations. Therefore, the charity should use the median of 20 to accurately represent the typical donations received.

The capacity of the trophy that us 30 cm high is 0.4286 liter

An equation is an expression that shows how numbers and variables are linked together using mathematical operations such as addition, subtraction, multiplication and division.

7 cm height cup holds 100 ml. Therefore:

7 cm = 100 ml

For a 30 cm height trophy:

30 cm = 30 cm * 100 ml per 7 cm = 428.57 ml

1000 ml = 1 l

428.57 ml = 428.57 ml * 1 liter per 1000 ml = 0.4286 liter

The capacity of the trophy is 0.4286 liter

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Answer:

t = 8w + w/2

Step-by-step explanation:

Given that :

Weight of bird = w

Amount of water consumed = 8*w = 8w

Amount of food ate = 0.5*w = 1/2w

Hence, the combined weight of water and food (t) consumed by the humming bird :

t = amount of water consumed + amount of food ate

t = 8w + w/2

Answer:

option b

Because 3 can be taken out as a common number which is three vice versa off three the distributive property.

hope it helps ..if not you can reach out to me ....for better defination.

The value of median will be same.

Given:

The objective is to determine whether the median of a data set is same or not while ordering from greatest to least or least to greatest.

There are two possible data sets, which is even number of sets or odd number of sets.

If the number of sets (n) is even, consider two terms,

Then, the average of these two numbers will gives the median of the even sets.

If the number of sets (n) is odd, the median can be calculated as,

Hence, the value of median will be same, even if the order of the sets are arranged greatest to least or least to greatest.

Answer:

$ 6.375

Step-by-step explanation:

Cost of ticket = $7.50

Discount = 15%

Discount price  = 15/100 x 7.50 = 1.125

Cost of student ticket = $7.50 - 1.125 = $ 6.375

I hope im right!!