solve the equation for t.

1/2 t +8 = 5/2 t - 10​

"Dr. Paul Opler states, "I have some information on butterfly weights but not exact weights for the largest and smallest butterflies. However, I can make pretty good guesses. I have weights ranging from 0.3 gram for a large swallowtail to 0.04 gram for a small butterfly called the elf."

from the intern3t

Answer:

It would most likely 0.02 - 0.03 because if u think about it there wings don't weight more than about 0.1  and if the wings can hold up the body of the butterfly then i would assume that it would weight between 0.02 - 0.03.

Step-by-step explanation:

Answer:

x = 17

Step-by-step explanation:

Since the triangles are similar then corresponding angles are congruent.

∠ I = ∠P ← substitute values and solve for x

3x + 4 = 72 - x ( add x to both sides )

4x + 4 = 72 ( subtract 4 from both sides )

4x = 68 ( divide both sides by 4 )

x = 17

Answer:

4

Step-by-step explanation:

The first thing you need to do is find the geometric mean between 2 and 6.

That is the ratio that they hypotenuse of the largest triangle is divided into.

altitude^2 = 2* 6

altitude^2 = 12

altitude = sqrt(12)

altitude = 2 sqrt(3)

Now use Pythagorus to find x

x^2 = 2^2 + altitude^2

x^2 = 2^2 + 12

x^2 = 4 + 12

x^2 = 16

x = 4

Answer:

Step-by-step explanation:

= 12.50

12.50

13,5 = 18

To solve the problem, Connie can use the concept of proportion by setting up an equation with the given ratios.

By cross-multiplying and solving for x, the cost of 18 boxes of cereal can be determined.

To solve this problem, Connie can use the concept of proportion.

A proportion is an equation that states that two ratios are equal.

In this case, the ratio of the cost of 5 boxes of cereal to the number of boxes is equal to the ratio of the cost of 18 boxes of cereal to the number of boxes.

Let's set up the proportion:

5 boxes / $12.50 = 18 boxes / x

To solve for x, we can cross-multiply:

5x = 18 * $12.50

Now, divide both sides by 5 to isolate x:

x = (18 * $12.50) / 5

Calculate the value of x to find the cost of 18 boxes of cereal.

Answer:

The length of the painting, including the frame.

Step-by-step explanation:

We are given that a painting includes a frame of a fixed width around the painting and the total area of the painting is represented by the expression:

[tex](4+2x)(9+2x)[/tex]

We are to determine what does [tex](9+2x)[/tex] represent.

(9+2x) represents the length of the painting, including the frame because [tex](4+2x)(9+2x)[/tex] is the area of the painting including the frame. The longer side [tex](9+2x)[/tex] represents the length.

Answer:

huh

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]\dfrac{2}{3}(n-6)=5n-43\qquad\text{multiply both sides by 3}\\\\2(n-6)=15n-129\qquad\text{use the distributive property}\\\\2n-12=15n-129\qquad\text{add 12 to both sides}\\\\2n=15n-117\qquad\text{subtract}\ 15n\ \text{from both sides}\\\\-13n=-117\qquad\text{divide both sides by (-13)}\\\\n=9[/tex]

The equation 2/3(n-6) = 5n - 43 is solved by distributing, combining like terms, and isolating the variable n to find that n = 9.

To solve the equation 2/3(n-6) = 5n - 43, first distribute the 2/3 across the parentheses: 2/3n - 2/3  6 = 5n - 43. This simplifies to 2/3n - 4 = 5n - 43. Next, add 4 to both sides to get 2/3n = 5n - 39. Multiply everything by 3 to clear the fraction: 2n = 15n - 117. Now, we will subtract 15n from both sides to get -13n = -117. Finally, divide by -13 to find n: n = 9. This is the value of n that solves the original equation.

Answer:

The equation of the circle is (x + 3)² + (y + 5)² = 36

Step-by-step explanation:

* Lets revise the standard form of the equation of the circle

- The center-radius form of the circle equation is in the format  

  (x – h)² + (y – k)² = r², where the center is the point (h, k) and  

  the radius is r.  

- This form of the equation is helpful, because you can easily find  

  the center and the radius.

* Now lets solve the problem

∵ The center of the circle is (-3 , -5)

∵ The center of the circle in the equation is (h , k)

∴ h = -3

∴ k = -5

∴ The equation of the circle is (x - -3)² + (y - -5)² = r²

∴ The equation is (x + 3)² + (y + 5)² = r²

* Now lets find the value of r²

∵ The length of the radius of the circle is 6 units

∴ r = 6

∴ r² = (6)² = 36

∴ The equation of the circle is (x + 3)² + (y + 5)² = 36

Answer:

∠6 = 80°

Step-by-step explanation:

∠5 and ∠6 form a straight angle and are supplementary, hence

∠5 + ∠6 = 180 ← ∠5 = 100° ( given ), hence

100 + ∠6 = 180 ( subtract 100 from both sides )

∠6 = 80°

Answer:

The ball hits the ground after 7.6 sec.

Step-by-step explanation:

Realize that h = 0 when the rocket hits the ground.  Thus, we set h(t) = y = to 0 and solve for time (t):

y = 0 = h(t) = -16t^2 + 113t + 65.

Application of the quadratic formula is the easiest approach here.  Note that a = -16, b = 113 and c = 65.

The discriminant is b^2-4ac, or, in this case, 113^2 - 4(-16)(65) = 16929.

Because the discriminant is positive, we confirm that this equation has two real, unequal roots.

The time values are as follows:

     -113 ± √16929

t =  --------------------- =  -17.11/ (-32) sec, which we must reject                                  

          -32                    

                                     because time in

                                        this situation may not be (-).

The other root is:

 -113 ± √16929            

t =  --------------------- =  7.6 sec

          -32

The ball hits the ground after 7.6 sec.

The equation that fits this pattern is: [tex]\[ \text{Total Cost} = 3 \times (\text{Number of Days}) + 2 \][/tex]

The table depicts a linear relationship between the number of days a movie is rented and its total cost.

To identify the equation used to create this table, we can observe that each additional day increases the total cost by a constant amount.

Considering the initial cost and the rate of increase, we can formulate the equation. In this case, the initial cost appears to be $2, and for each additional day beyond the first, the cost increases by $3.

Therefore, the equation that fits this pattern is:

[tex]\[ \text{Total Cost} = 3 \times (\text{Number of Days}) + 2 \][/tex]

This equation represents a constant rate of increase of $3 per day, plus the initial cost of $2.

Thus, it accurately models the relationship between the number of days and the total cost.

The probable question may be:

The total cost of renting a movie for different numbers of days is shown in the table.

Which equation was used to create this table?

| Number of Days | Total Cost |

|----------------|------------|

| 1              | $5         |

| 2              | $8         |

| 3              | $11        |

| 4              | $14        |

| 5              | $17        |

Answer:

309 Cm.

Step-by-step explanation:

Since the dimensions of the Large Jewelry Box is tripled, and all the sides are only added together, the answer of the question is simply the Surface Area of the Small Jewelry Box x 3.

103 x 3 OR 103 + 103 + 103 = 309.

_______________________________________

100 + 100 + 100 = 300

3 + 3 + 3 = 9

300 + 9 = 309.

The correct answer is A. Hundreds. I hope this helps : )

A is the correct answer

Answer:

a. 18 cm

Step-by-step explanation:

We are given that a circle has an area of 324π cm2. We are required to determine its radius. The formula for the area of a circle with radius r units is;

[tex]A=pi*r*r[/tex]

We plug in the area given and solve for r;

[tex]324pi=pi*r^{2}\\\\r^{2}=324\\\\r=18[/tex]

The radius of the circle is 18 cm

Answer:

a. 18 cm

Step-by-step explanation:

Area of a circle is given by: A=πr²

where r is the radius and A the area.

therefore we substitute A with the value for the area in the question.

324π=πr²

cancelling the factor π on both sides gives: 324=r²

√324=r

r=18cm

Answer:

Step-by-step explanation:

3x+2(x-9)=8x+x-14

3x+2-9x=8x+x-14

add3xand-9x

-6x+2=8X+x-14

8X +X=9X

-6X+2=9X-14

+6X to both sides

2=3x-14

subtract 2 on both sides

3x/-12

the answer is -8

Answer:

The actual answer is 1!

Step-by-step explanation

Answer:

Step-by-step explanation:

[tex]\bold{Q4}\\\text{We have}\\\text{two right triangles with legs a = 4m and b = 7m}\\\text{three rectangles}\ 7m\ \times 38m,\ 8.06m\ \times\ 38m\ \text{and}\ 4m\ \times\ 38m\\\\\text{The formula of an area of a right triangle:}\\\\A=\dfrac{ab}{2}\\\\\text{substitute:}\\\\A_1=\dfrac{(4)(7)}{2}=\dfrac{28}{2}=14\ m^2\\\\\text{The formula of an area of a rectangle}\ l\ \times w:\\\\A=lw\\\\\text{substitute:}\\\\A_2=(7)(38)=266\ m^2\\A_3=(8.06)(38)=306.28\ m^2\\A_4=(4)(38)=152\ m^2\\\\\text{The Surface Area:}[/tex]

[tex]S.A.=2A_1+A_2+A_3+A_4\\\\S.A.=2(14)+266+306.28+152=752.28\ m^2[/tex]

[tex]\bold{Q11}\\(look\ at\ the\ picture)\\\\\text{The formula of a volume of a pyramid:}\\\\V=\dfrac{1}{3}BH\\\\B-\text{area of a base}\\H-\text{height}\\\\\text{In the base we have the square. The formula of an area of a square with side a:}\\\\A=a^2\\\\\text{We have}\ a=12ft.\ \text{Substitute:}\\\\B=12^2=144\ ft^2\\\\\text{For}\ H\ \text{we need use the Pythagorean theorem:}\\\\H^2+6^2=10^2\\\\H^2+36=100\qquad\text{subtract 36 from both sides}\\\\H^2=64\to H=\sqrt{64}\\\\H=8\ m[/tex]

[tex]\text{Substitute:}\\\\V=\dfrac{1}{3}(144)(8)=(48)(8)=384\ ft^3[/tex]

To find out how much Jennifer has saved, you start by tripling the amount Matthew has saved, which is $81. Then you subtract $26 from the result to get $217. Therefore, Jennifer has saved $217.

From the problems statement, we can model Jennifer's savings using the mathematical model, where Jennifer's savings is equal to triple Matthew's savings minus $26. Given that Matthew’s savings amount to $81, we can multiply Matthew's savings by three, which equals $243. Then, to find Jennifer's savings, we subtract $26 from $243 resulting in $217. Therefore, Jennifer has $217 saved.

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Answer:

Direct Variation

Step-by-step explanation:

The relationship between two variables such that y = kx if k is a nonzero number. Also, as one quantity increases, the second quantity increases or as one quantity decreases, the second quantity decreases. Therefore ac=5 is a direct variation

Answer:

The ratio is 15:13 (15 boys to 13 girls).

There are 28 students in all

13/28 of the students are girls.

Step-by-step explanation:

For the ratio, you simply need to put the information on the correct side of the colon [:]. The total amount of students is calculated by adding the numbers together. Finally, the fraction of girls in the class is found by adding the number of girls above the number of total students.

Answer:

Given:

Number of girls in class = 13

Number of boys in class = 15

Ratio of boys to girls,

[tex]\frac{Number\:of\:boys}{Number\:of\:girls}=\frac{15}{13}[/tex]

Ratio = 15 : 13

⇒ Total number of student = 13 + 15 = 28

Fraction of students are girls = [tex]\frac{13}{28}[/tex]

Answer:

D ans

Step-by-step explanation:

equation of circle=(x-h)^2+(y-k)^2=r^2

Answer:

(x+3)2 + (y + 5)2 = 16

Step-by-step explanation:

Final answer:

To find the probability that Ricardo will have a quiz on Tuesday, Thursday, or Friday, we add the individual probabilities for each of those days, resulting in a total probability of 60%.

Explanation:

Probability is a measure of the likelihood of an event occurring. To find the probability that Ricardo will have a quiz on Tuesday, Thursday, or Friday, we add the individual probabilities for each of those days.

Probability of having a quiz on Tuesday = 0.2

Probability of having a quiz on Thursday = 0.1

Probability of having a quiz on Friday = 0.3

Total probability = Probability on Tuesday + Probability on Thursday + Probability on Friday = 0.2 + 0.1 + 0.3 = 0.6. Expressing this as a percentage, we get 60%.

Answer:

[tex]\large\boxed{x=\dfrac{-3+\sqrt{40+10\sqrt{10}}}{2}}[/tex]

Step-by-step explanation:

[tex]2\log x=3-2\log(x+3)\\\\Domain:\ x>0\ \wedge\ x+3>0\to x>-3\\\\D:x>0\\============================\\2\log x=3-2\log(x+3)\qquad\text{add}\ 2\log(x+3)\ \text{to both sides}\\\\2\log x+2\log(x+3)=3\qquad\text{divide both sides by 2}\\\\\log x+\log(x+3)=\dfrac{3}{2}\qquad\text{use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log\bigg(x(x+3)\bigg)=\dfrac{3}{2}\qquad\text{use the de}\text{finition of a logarithm}\\\\x(x+3)=10^\frac{3}{2}\qquad\text{use the distributive property}[/tex]

[tex]x^2+3x=10^{1\frac{1}{2}}\\\\x^2+3x=10^{1+\frac{1}{2}}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\x^2+3x=10\cdot10^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\x^2+3x=10\sqrt{10}\qquad\text{subtract}\ 10\sqrt{10}\ \text{from both sides}\\\\x^2+3x-10\sqrt{10}=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=3,\ c=-10\sqrt{10}\\\\b^2-4ac=3^2-4(1)(-10\sqrt{10})=9+40\sqrt{10}\\\\x=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2(1)}=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2}\\\\x=\dfrac{-3-\sqrt{10+10\sqrt{10}}}{2}\notin D[/tex]

The length of the rectangle is 6 units.

To find the length of the side of a square using area, find the square root of the area.

Side = √206 = 14.35 feet.

Answer:12.66667

Step-by-step explanation:

Answer:

Average = (sum of numbers) ÷ (the amount of numbers)

a = (12 + 13 + 13) ÷ 3

a = 38/3 = 12.6...

The scale factor used for the dilation from N to N' is 1/3. The midpoint between the points (-8, 5) and (2, -2) is (-3, 1.5).

To find the scale factor used to dilate point N(6, -3) to N'(2, -1), we compare the coordinates directly since the transformation scales both the x and y components equally.

Using the x-coordinates (6 to 2), the scale factor can be calculated as the ratio of N' to N, which is 2/6 or 1/3.

Similarly, using the y-coordinates (-3 to -1), we would also arrive at a scale factor of 1/3, confirming our result.

To find the midpoint between two points, (-8, 5) and (2, -2), we use the midpoint formula ((x1 + x2)/2, (y1 + y2)/2).

Substituting the relevant coordinates, the midpoint is calculated as ((-8 + 2)/2, (5 + (-2))/2) which simplifies to (-3, 1.5).

Therefore, the midpoint is (-3, 1.5).

To determine the scale factor used for the dilation of point N to N', you must find the ratio of the image coordinates to the pre-image coordinates. Since the dilation is defined by N(6, -3) transforming to N'(2, -1), you calculate the scale factor as follows:
For the x-coordinates:
The pre-image, N, has an x-coordinate of 6, and the image, N', has an x-coordinate of 2. Therefore, the scale factor in the x-direction is:
\[ \text{Scale factor}_x = \frac{N'_{x}}{N_{x}} = \frac{2}{6} = \frac{1}{3} \]
Now for the y-coordinates:
The pre-image, N, has a y-coordinate of -3, and the image, N', has a y-coordinate of -1. So the scale factor in the y-direction is:
\[ \text{Scale factor}_y = \frac{N'_{y}}{N_{y}} = \frac{-1}{-3} = \frac{1}{3} \]
The x and y scale factors are equivalent, which suggests uniform scaling. Thus, the scale factor used in the dilation is \(\frac{1}{3}\).
To find the midpoint between two points, you calculate the average of the x-coordinates and the y-coordinates separately. Let's find this midpoint for the points (-8, 5) and (2, -2):
For the x-coordinates:
The average of the x-coordinates of the two points is:
\[ \text{Midpoint}_x = \frac{(-8) + 2}{2} = \frac{-6}{2} = -3 \]
For the y-coordinates:
The average of the y-coordinates of the two points is:
\[ \text{Midpoint}_y = \frac{5 + (-2)}{2} = \frac{3}{2} = 1.5 \]
So, the midpoint between the points (-8, 5) and (2, -2) is (-3, 1.5).

Answer: 830.7 per square mile.

Step-by-step explanation:

The formula for population density is Number of people divided by total area.

11,547 divided by 13.9 is 830.7.

Hope this helps!

The population density of Covington, Georgia is calculated by dividing the total population (11,547 people) by the total area (13.9 square miles). The result is approximately 830.79 people per square mile.

The population density of a place is calculated by dividing the total population by the total area. In this case, Covington, Georgia, has a total population of 11,547 people and a total area of 13.9 square miles. Thus, to determine the population density, we will use the following formula: Population Density = Total Population / Total area.

By substituting our given numbers into this formula, we would get: Population Density = 11,547 / 13.9. This calculation results in a population density of approximately 830.79 people per square mile for Covington, Georgia.

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Answer:

-68 could  be a potential outlier, but other than that, the data seems pretty steady.

The association between the altitude and the temperature is the higher up in the atmosphere you are, the colder it gets.

Answer:

Step-by-step explanation

I don't know if you are asking for a formula but Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

Answer:

x = 30517578124/29296875

Step-by-step explanation:

Solve for x:

3125 = 3 x + 1/9765625

Put each term in 3 x + 1/9765625 over the common denominator 9765625: 3 x + 1/9765625 = (29296875 x)/9765625 + 1/9765625:

3125 = (29296875 x)/9765625 + 1/9765625

(29296875 x)/9765625 + 1/9765625 = (29296875 x + 1)/9765625:

3125 = (29296875 x + 1)/9765625

3125 = (29296875 x + 1)/9765625 is equivalent to (29296875 x + 1)/9765625 = 3125:

(29296875 x + 1)/9765625 = 3125

Multiply both sides of (29296875 x + 1)/9765625 = 3125 by 9765625:

(9765625 (29296875 x + 1))/9765625 = 9765625×3125

(9765625 (29296875 x + 1))/9765625 = 9765625/9765625×(29296875 x + 1) = 29296875 x + 1:

29296875 x + 1 = 9765625×3125

9765625×3125 = 30517578125:

29296875 x + 1 = 30517578125

Subtract 1 from both sides:

29296875 x + (1 - 1) = 30517578125 - 1

1 - 1 = 0:

29296875 x = 30517578125 - 1

30517578125 - 1 = 30517578124:

29296875 x = 30517578124

Divide both sides of 29296875 x = 30517578124 by 29296875:

(29296875 x)/29296875 = 30517578124/29296875

29296875/29296875 = 1:

Answer:  x = 30517578124/29296875

For this case:

We rewrite the equation as:

[tex]5 ^ {- 10 + 3x} = 3.125[/tex]

We find ln on both sides of the equation to remove the exponent variable:

[tex]ln (5 ^ {- 10 + 3x}) = ln (3,125)[/tex]

Applying properties of logarithm we have:

[tex](-10 + 3x) ln (5) = ln (3.125)[/tex]

We apply distributive property:

[tex]-10ln (5) + 3xln (5) = ln (3,125)[/tex]

We clear the value of "x":

[tex]3xln (5) = ln (3,125) + 10ln (5)\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10ln (5)} {3ln (5)}\\x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}[/tex]

ANswer:

[tex]x = \frac {ln (3.125)} {3ln (5)} + \frac {10} {3}[/tex]