please help asap! ----------------------------

Answer: 7.7 miles

Step-by-step explanation:

2.5x + 5.75 = 25 (x = each mile traveled)

2.5x = 25 - 5.75

2.5x = 19.25

x = 7.7 miles

Given:

Prime numbers can be expressed as a sum and difference of 2 prime numbers.

To find:

The prime numbers that can be expressed as a sum and difference of 2 prime numbers.

Solution:

Prime numbers are the positive integers which are greater than 1, divisible by only 1 and itself.

Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19,... .

Only 2 is the even prime number.

The sum and difference of two odd integers is always an even number. So, we need to take one even prime number and one odd prime number to add and subtract the numbers to get a prime number.

[tex]2+3=5[/tex]

[tex]7-2=5[/tex]

Therefore, 5 is the only prime number that can be expressed as a sum and difference of 2 prime numbers.

From online research, the article is;

As days get shorter and colder in the autumn, chlorophyll molecules break down. Leaves quickly lose their green color. Some leaves begin to look yellow or orange because they still contain pigments called carotenoids. One such pigment, carotene, gives carrots their bright-orange color.

But red is special. This brilliant color appears only because the leaves of some plants, including maples, actually produce new pigments, called anthocyanins.

That’s a strange thing for a plant to do without a reason, says Bill Hoch of the University of Wisconsin in Madison. Why? Because it takes a lot of energy to make anthocyanins.

Why red?

To figure out the purpose of the red pigment, Hoch and his coworkers bred mutant plants that can’t make anthocyanins and compared them with plants that do make anthocyanins. They found that plants that can make red pigments continue to absorb nutrients from their leaves long after the mutant plants have stopped.

This study and others suggest that anthocyanins work like a sunscreen. When chlorophyll breaks down, a plant’s leaves become vulnerable to the sun’s harsh rays. By turning red, plants protect themselves from sun damage. They can continue to take nutrients out of their dying leaves. These reserves help the plants stay healthy through the winter.

The more anthocyanins a plant produces, the redder its leaves become. This explains why colors vary from year to year, and even from tree to tree. Stressful conditions, such as drought and disease, often make a season redder.

Now, Hoch is breeding plants for a new set of experiments. He wants to find out whether turning red helps plants survive cold weather.

“There’s a clear correlation between environments that get colder in the fall and the amount of red produced,” he says. “Red maples turn bright red in Wisconsin. In Florida, they don’t turn nearly as bright.”

More protection

Elsewhere, scientists are looking at anthocyanins in other ways. A recent study in Greece, for instance, found that as leaves grow redder, insects eat them less. On the basis of this observation, some scientists argue that red pigments defend a plant against bugs.

Leaves may turn red in the autumn to protect themselves from the sun’s ultraviolet rays.

J. Miller

Hoch rejects that theory, but Lee thinks that it might make sense. He points out that red leaves contain less nitrogen than green ones do. “It may actually be that insects avoid red leaves because they’re less nutritious,” Lee says.

However, “it’s pretty confusing at this point,” Lee admits. “People debate back and forth.”

To settle the debate, scientists will need to look at more species under more conditions, Lee says. So, he’s now researching leafy plants rather than trees. He’s especially interested in tropical plants, whose leaves turn red when they’re young rather than old.

Answer:

As seen in the Explanation, different people have given reasons why bright red leaves in the fall help protect the trees in the winter. Thus, there is sufficient evidence to conclude that bright red leaves in the fall help protect the trees in the winter.

Step-by-step explanation:

From the article, we can see that Hoch and his coworkers carried out an experiment on mutants and they discovered that plants that can make red pigments tend to continue absorbing nutrients from their leaves a long time after the mutant plants have stopped.

This study and other believe that plants make anthocyanins which acts as a kind of sunscreen to the plants. They also discovered that by the plants turning red, they protect themselves from sun damage

Also, we see that some scientists in Greece found out that as leaves grow redder, insects eat them less and they argued that red pigments defend a plant against bugs and as such Leaves may turn red in the autumn to protect themselves from the sun’s ultraviolet rays.

My Answer: One study said that anthocyanins are pigments that make leaves turn red. And some trees don’t absorb as many nutrients as trees with red leaves. That particular study focused on trees that don’t produce anthocyanins. So i believe there's some evidence, but not a definitive conclusion.

Edmentum Answer: There’s some evidence, but not a definitive conclusion. One study focused on trees that don’t produce anthocyanins. Anthocyanins are pigments that make leaves turn red. The study said that these trees don’t absorb as many nutrients as trees with red leaves.

Another study found that insects are generally not inclined to eat red leaves on trees. There seems to be a trend that suggests that red leaves are important for the trees’ survival in the fall. This trend needs to be validated by conducting more tests.

Step-by-step explanation:

Paraphrased

Answer:

In picture

Step-by-step explanation:

Brainliest please ~

Answer: y = [tex]\frac{5}{3}x +5[/tex]

Step-by-step explanation:

This is how you find the slope: [tex]slope=\frac{rise}{run}=\frac{y1-y2}{x1-x2}[/tex]

Find two coordinate points. Let's use (-3,0) and (0,5). Based on this, we know that y1 is 0, y2 is 5, x1 is -3, and x2 is 0. Plug these into the formula:

[tex]\frac{0-5}{-3+0} =\frac{-5}{-3} =\frac{5}{3}[/tex]

So, the slope is [tex]\frac{5}{3}[/tex]

The y intercept is where the line hits the y graph. We can see that the y intercept is 5 (or (0,5))

Slope intercept form: y = mx + b, m = slope, b = y intercept

Plug everything in:

y = [tex]\frac{5}{3}x +5[/tex]

Answer:

2m^3n^3

Step-by-step explanation:

Let us start with the number parts

36 , 2 and 4

2 is common here as it can divide all

The smallest m factor is m^3 so it is common for all

The smallest n factor is n^3 which is also common for all

So, we have the greatest common factor as;

2 * m^3 * n^3 = 2m^3n^3

18 - (-f) = 91

Subtracting a negative value changes to addition:

18 + f = 91

Subtract 18 from both sides:

F = 73

Answer:

f = 73

Step-by-step explanation:

Solve for f

18 - ( - f ) = 91

18 + f = 91

18 - 18 + f = 91 - 18

f = 73

Answer:

LK = 38

Step-by-step explanation:

MN is the midsegment, and the midsegment is the average length of the top and bottom, so:

[tex]\frac{18 + LK}{2} =28[/tex]

solve for LK:

[tex]18+LK=56\\\\LK=38[/tex]

Answer:

(0,6) and (3,1)

Step-by-step explanation:

The equation is already in slope intercept form.

y = mx + b

Since the y-intercept is '6', the first point would be (0, 6).

-----------------------------------

We can move three units to the right and 5 units down to get our second point, (3,1).

Note that slope is rise over run.

(0 + 3, 6 - 5) - > (3, 1).

The points would be (0,6) and (3,1). After plotting, you would draw a continuous line through them.

Hope this helps.

Answer:

The answer is 90cm

Step-by-step explanation:

Hello,

Lateral area = (3+3+3+3)*6=4*3*612*6=72 (cm²)

Bases area= 2*3²=18 (cm²)

Total area= 72+18=90 (cm²)

Answer:

991

Step-by-step explanation:

We are looking for a number that is one more than a multiple of 9(denoted by the 9k) and is a three digit number. We can start by looking for 3-digit number divisible by 9 which are close to 1,000, since that is the next number larger than the largest three-digit number. We can tell that 999 is divisible by 9 because when divided it does not leave a remainder(you can also figure this out with divisibility tricks). We add one to get 1,000. This is not a three-digit number,  so we need to look for a smaller multiple of 9. Subtracting 9 from 999, we get the next largest multiple of 9. We can add 1, and this time, the number, 991, is a three digit number, and the largest that can be in the form 9k + 1.

Step-by-step explanation:

Hello,

Let's say a the  first term and r the ratio  of the G.P.

[tex]u_1=a=81\\u_2=a*r\\u_3=a*r^2\\u_4=a*r^3\\\\\dfrac{u_4}{u_1} =\dfrac{a*r^3}{a} =r^3=\dfrac{24}{81} =\dfrac{8}{27} \\\\r=\sqrt[3]{\dfrac{8}{27} } \\\\\boxed{r=\dfrac{2}{3}}\\[/tex]

Answer:

8x +120= 400

Step-by-step explanation:

Let the number of hours Max worked over the summer be x.

Assuming that he had $0 in his bank at the start of summer,

Total savings= 8(number of hours) +120

400= 8x +120

8x +120= 400

To find the value of x, first bring all the constants to one side of the equation.

8x= 400 -120

Simplify:

8x= 280

Divide both sides by 8:

x= 280 ÷8

x= 35

∴ Max worked for 35 hours over the summer.

Answer:

8 m

-----------------Work--------------

2*3 = 6

Ratio

2*4 = 8

(a) ∠AEC = ∠CFD, by transitive property of equality

(b) ∠CDE = 108°, ∠DCB = 108°, ∠ABC = 108°,∠EAB = 144°, ∠AED = 72°

The reason the above values are correct is as follows:

(a) The given parameters are;

Figure ABCDE is a pentagon

The sides AE is parallel to side CD

Line EC is parallel to side BC

The point of intersection of the extension off side ED and BC = Point F

∠ABC = ∠CDE

Required:

To show that ∠AEC = ∠CFD

Method:

Draw the pentagon ABCDE and include the added construction

Analyze the drawing

Solution:

∠ECF and ∠ABC are corresponding angles between parallel lines EC ║BC

∴ ∠ECF ≅ ∠ABC by corresponding angles formed by parallel lines are congruent

∠ECF = ∠ABC by definition of congruency

∠ABC = ∠CDE = ∠ECF by transitive property

∠ECD ≅ ∠AEC by alternate angles formed between parallel lines having a common transversal

∠ECD = ∠AEC by definition of congruency

∠ECF = ∠FCD + ∠ECD by angle addition postulate

∠CDE = ∠FCD + ∠CFD by exterior angle theorem

From ∠CDE = ∠ECF above, we have;

∠ECF = ∠FCD + ∠ECD = ∠FCD + ∠CFD

∴ ∠ECD = ∠CFD by addition property

∠ECD = ∠AEC, therefore;

∠AEC = ∠CFD, by transitive property

(b) Given that ΔEDC and ΔDFC are both isosceles triangles, with sides;

ED = DC, and DF = FC;

Let r represent ∠CFD, we have;

∠FCD = ∠CDF by base angles of isosceles triangle ΔDFC

∠ECD = ∠CED by base angles of isosceles triangle ΔEDC

∠AEG = ∠CDE by corresponding angles formed by parallel lines having a common transversal

∠AEC = ∠ECD by alternate angles

∴ ∠AEG + ∠AEC + ∠CED = 180° Sum of angles on a straight line

∠CDE = ∠CFD + ∠FCD

∠CDE + ∠CDF = 180° (linear pair angles)

∴ ∠AEG + ∠CDF = 180° by transitive property

∠AEC + ∠CED = ∠CDF by transitive property

∠AEC = ∠ECD = ∠CED = ∠CFD = r

∴ ∠CFD + ∠CFD = ∠CDF

2·r = ∠CDF

∠CDE = ∠FCD + ∠CFD

∠FCD = ∠CDF = 2·r

∴ ∠CDE = 2·r + r = 3·r

∠CDE = 3·r

The angles of the pentagon are;

∠CDE + ∠DCB + ∠ABC + ∠EAB + ∠AED = 540° sum of angles in a pentagon

∠DCB = 180° - ∠FCD

∠DCB = 180° - 2·r

∠ABC = ∠CDE = 3·r

∠EAB = ∠CEH corresponding angles

∠CEH = 180 - ∠AEC

∴ ∠EAB = 180° - ∠AEC

∴ ∠EAB = 180° - r

∠AED = ∠AEC + ∠CED = r + r = 2·r

∠AED = 2·r

Therefore, we have;

3·r + 180° - 2·r + 3·r + 180° - r + 2·r = 540°

5·r + 360° = 540°

r = (540° - 360°)/5 = 36°

r = 36°

∠CDE = 3 × 36° = 108°

∠DCB = 180° - 2×36° = 108°

∠ABC = 3 × 36° = 108°

∠EAB = 180° - 36° = 144°

∠AED = 2 × 36° = 72°

Learn more about geometry word problems here:

https://brainly.com/question/9873001

https://brainly.com/question/16810496

Answer:

{5, 6, 7}

Step-by-step explanation:

When we have a given relation, the domain is the set of inputs, and the range as the set of the outputs.

so for a function f(x), and a domain {a. b. c}

The range is:

{f(a), f(b), f(c)}

In this case, we have:

f(x) = x + 6

and the domain is {-1, 0, 1}

Then the range is:

{ f(-1), f(0), f(1) }

{-1 + 6, 0 + 6, 1 + 6}

{5, 6, 7}

The correct option is the third one.

Answer:

D

Step-by-step explanation:

Look for the intersection point of the two graphs

Another way:

You can just substitute each pair in both equations and u will find that d is the correct answer

Answer:

22 people were born in the uk  (66 ÷ 360) × 120=22

Step-by-step explanation:

Using the pie chart, the fraction of people born in the UK, is: 7/30.

A pie chart is a graphical representation used to describe the composition of a data using degrees or percentages.

84° is given as the number of people that were born in the UK.

That's about: 84/360 × 120 = 28 people.

28 out of 120 people would give us a fraction of: 28/120 = 7/30.

Learn more about pie chart on:

https://brainly.com/question/26851221

#SPJ2

Answer:

D

Step-by-step explanation:

It can't be C and B since it doesn't have two parts, and if it was uniform it would have another part attached to the bottom. Moreover, it can't be A since it isn't positively skewed or negatively skewed, so it must be D.

The shape of this distribution is Unimodal symmetric.

Option D is the correct answer.

A histogram is a representation of the distribution of data with intervals.

We have,

In statistics, a distribution is considered unimodal symmetric if it has a single mode or peak and is symmetric around that mode.

This means that the data is evenly distributed on both sides of the mode and is equally likely to occur on either side.

A common example of a unimodal symmetric distribution is the normal distribution, also known as the Gaussian distribution or bell curve.

Thus, the shape of this distribution is Unimodal symmetric.

Learn more about histograms here:

brainly.com/question/16819077

#SPJ7

Answer:

y < -7

Step-by-step explanation:

You balance it like a normal equation:

8y + 3 > 15y + 52

8y + 3 (-8y) > 15y + 52 (-8y)

3 (-52) > 7y + 52 (-52)

-49 (÷7) > 7y (÷7)

y < -7

Answer:

  12

Step-by-step explanation:

3/4 = 9/12

7/6 = 14/12

12 is a suitable common denominator for these fractions.

__

4 = 2·2

6 = 2·3

The common denominator must include all these factors (and no more than necessary), so must be ...

  LCD = 2·2·3 = 12

Answer:

mine ended june 9th but i got summer school for 2 classes lol

School ended the 15 of June but I'm in summer school rn it ends this Friday

Answer:

9 : 7

Step-by-step explanation:

Given

4.5 : 3 [tex]\frac{1}{2}[/tex] ( multiply both parts by 2 to clear the fractions )

= 9 : 7

Answer:

8050 m²

Step-by-step explanation:

We can divide the diagram up into two components: a rectangle with a width of 60 m and a height of 80 m, and a triangle with a base of 130 m (190 - 60) and a height of 50 m (80 - 30).

The area of the rectangle:

A = lw

A = 60 m (80 m)

A = 4800 m²

The area of the triangle:

A = 1/2 b*h

A = 1/2 (130 m) (50 m)

A = 1/2 (6500 m²)

A = 3250 m²

Now, we can add the areas of the two separate components:

A = 4800 m² + 3250 m²

A = 8050 m²

Answer:

[tex]{ \tt{y \: \alpha \: {x}^{3} }} \\ { \tt{y = k {x}^{3} }} \\ { \bf{k \: is \: a \: proportionality \: constant}} \\ { \tt{1512 = (k \times {6}^{3}) }} \\ { \tt{k = 7}} \\ { \boxed{ \bf{y = 7 {x}^{3} }}}[/tex]

Step-by-step explanation:

If the volume of a cubical room is 2700 cm³ .

l³=2700

l=3 (100)⅓

Step-by-step explanation:

[tex]here \: is \: your \: solution : - \\ \\ GIVEN \: \: -:- \\ \\ = > \: area \: of \: circle \: = 616 \: m {}^{2} \\ \\ \ = > pi = 22 \div 7 \\ \\ = > we \: need \: to \: find \: radius \: \\ \\ = > area \: of \: circle \: = \pi \: r {}^{2} \\ \\ = > \: \pi \: r {}^{2} = 616 \: m {}^{2} \\ \\ = > \: r {}^{2} \times (22 \div 7) = 616 \\ \\ = > \: r {}^{2} =( 616 \times 7) \div 22 \\ \\ = > \: r { }^{2} = 4312 \div 22 \\ \\ = > r {}^{2} = 196 \\ \\ = > \: r = \sqrt{196} \\ \\ = > \: r = 14 \: \: \: (ANSWER✓✓✓) \\ \\ HOPE \: IT \: HELPS \: YOU \: (◕ᴗ◕✿)[/tex]