Given
f(x)=3x2+7x and g(x)=2x2-x-1, find (f+g)(x).

Answer:

5.   m < 1 = 72 degrees.

6.    m < 1 = 80 degrees.

Step-by-step explanation:

5. < 1 = 72 degrees.

If we draw a line through the point of < 1,  We see that  We have have 2 angles  of 40 and 32 ( alternate angles).

6.  By the same reasoning m < 1 = 60 + 20

= 80 degrees.

Answer:

1/36

Step-by-step explanation:

3(1/3)=3/3=1

2*3=6

(1/6)^2=(1/6)(1/6)=1/36

Answer:

Step-by-step explanation:

1 - 25 (a+b)^2 = 1 - 5² (a+b)²

= 1 - (5*[a + b) ]²                    { [tex]a^{m} *a^{n}  = a^{m+n}[/tex] }

= 1 - (5a +5b)²

= (1 + 5a +5b) (1 - [5a + 5b])      { a² - b² = (a + b)(a - b)   }

=(1 + 5a +5b) (1- 5a - 5b)

Answer: 54678 years

Step-by-step explanation:

This can be solved by the following equation:

[tex]N_{t}=N_{o}e^{-\lambda t}[/tex] (1)

Where:

[tex]N_{t}=54\%=0.54[/tex] is the quantity of atoms of carbon-14 left after time [tex]t[/tex]

[tex]N_{o}=1[/tex] is the initial quantity of atoms of C-14 in the mammal hide

[tex]\lambda[/tex] is the rate constant for carbon-14 radioactive decay

[tex]t[/tex] is the time elapsed

On the other hand, [tex]\lambda[/tex] has a relation with the half life [tex]h[/tex] of the C-14, which is [tex]5730 years[/tex]:

[tex]\lambda=\frac{ln(2)}{h}=\frac{ln(2)}{5730 years}=1.21(10)^{-4} years^{-1}=0.000121 years^{-1}[/tex] (2)

Substituting (2) in (1):

[tex]0.54=1e^{-(0.000121 years^{-1}) t}[/tex] (3)

Applying natural logarithm on both sides of the equation:

[tex]ln(0.54)=ln(1e^{-(0.000121 years^{-1}) t})[/tex] (4)

[tex]-0.616=-(0.000121 years^{-1}) t[/tex] (5)

Isolating [tex]t[/tex]:

[tex]t=\frac{-0.616}{-0.000121 years^{-1}}[/tex] (6)

[tex]t=54677.68 years \approx 54678 years[/tex] (7)  This is the age of the mammal hide

The age of the mammal hide to the nearest year is approximately 11,239 years.

To find the age of the mammal hide with 37% of its original amount of C-14 remaining, we can use the decay formula for a substance undergoing exponential decay, which is described by the equation N(t) = N0(1/2)t/T, where N(t) is the remaining amount of substance, N0 is the original amount of substance, t is the time that has elapsed, and T is the half-life of the substance.

In this case, the half-life of C-14 is 5,730 years. Since we know the remaining amount of C-14 is 37% of the original amount, we can set up the equation 0.37 = (1/2)t/5730. To solve for t, we take the natural logarithm of both sides:

ln(0.37) = ln((1/2)t/5730)

ln(0.37) = (t/5730) * ln(1/2)

t = (ln(0.37)/ln(1/2)) * 5730

When we compute the value for t, we get the age of the mammal hide. By performing this calculation, we find that t is approximately 11,239 years. This is the estimated age of the mammal hide to the nearest year.

Answer:

Carrie read at a rate of 21 2/3 pages per hour

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Time Ms. Graves gave her class to read = 18 minutes

Number of pages Carrie read in 18 minutes = 6 1/2 pages

2. At what rate, in pages per hour, did Carrie read?

Rate = Number of pages/Time given

For getting the exact rate per hour, we should use the Rule of Three Simple, this way:

Number of pages in 60 minutes * 18 = 6 1/2 * 60

Number of pages in 60 minutes = (6.5 * 60)/18

Number of pages in 60 minutes = 390/18 = 21.67 or 21 2/3

Carrie read at a rate of 21 2/3 pages per hour

Answer:

y+1=5(x+2)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1)=5(x-(-2))

y+1=5(x+2)

Answer:

If today is Saturday, the probability that tomorrow is Sunday.

Step-by-step explanation:

Step-by-step explanation:

|h-3|<5

This implies that

h-3<5 or h-3<-5

h<5+3 or h<-5+3

h<8 or h<-2

Hence the solution set is {h:h<-2 or h<8 }

Therefore the number line in the picture shows the solution set for |h-3|<5

The inequality |h-3|<5 means that h is a numerical value between -2 and 8. A number line representing this solution set would be marked between these two values.

The inequality |h-3|<5 represents all numbers that are less than 5 units from 3 on the number line. It leads to two simple inequalities. When we remove the absolute value we get -5 < h-3 < 5, which simplifies to -2 < h < 8. So the number line that shows the solution set will have a line drawn between -2 and 8, indicating all the numbers between these two values satisfy the inequality.

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I am not sure if i understand that 3600 is the cost of all the bikes they have bought in total, but they would have to sell 31 bikes to break even.

Answer: The answer is 5.2 (rounded to the nearest tenth)

Actual Answer: 5.19615242

Hope this helps!

Answer:

its the square root of 27 to the power of 2

Step-by-step explanation: hope this helps

Answer:

The wingspan of 26 atlas moths are 286 inches.

Step-by-step explanation:

Given:

An Atlas moth has a wingspan of 11 inches.

Now, to find the wingspan of 26 atlas moths.

So, we use unitary method:

As given an atlas wingspan has 11 inches.

Then for wingspan of 26 atlas we multiply it by 11 inches:

⇒  [tex]26\times 11\ inches[/tex]

[tex]=286\ inches.[/tex]

Therefore, the wingspan of 26 atlas moths are 286 inches.

Final answer:

To find the total wingspan of 26 Atlas moths, multiply the wingspan of one moth, 11 inches, by 26, resulting in a total of 286 inches.

Explanation:

The question involves simple multiplication to determine the total wingspan of 26 Atlas moths. If one Atlas moth has a wingspan of 11 inches, then the wingspan of 26 Atlas moths can be found by multiplying 11 inches by 26.

Step-by-step calculation:

Determine the wingspan of one Atlas moth, which is already given as 11 inches.

Multiply the wingspan of one moth by the total number of moths: 11 inches * 26 = 286 inches.

Therefore, the total wingspan of 26 Atlas moths is 286 inches.

Answer:

see the prime factors

Step-by-step explanation:

24= 6*4=3*2*2*2

=2*3*4

Answer:

No

Step-by-step explanation:

First off, the number 4 is not a prime number and the prime factorization of a number has to consist of all prime numbers. 2*3*4 does result in 24 but 4 is not prime because a prime number is a whole number with exactly two factors, itself and 1. 4 has more than two factors; the factors of 4 are 1, 2, and 4 so 4 isn't prime.

2*2*2*3 is the prime factorization of 24 because when you break down 24 into prime numbers, the results are 2*2*2*3.

24=2*12(here, we broke the number 24 into two factors 2 and 12. it doesn't matter which factors you break the number into because you still get the same result.)

2*12=2*2*6(we broke the number 12 into 2*6 because 12 isn't prime. we have to break each number into prime numbers.)

2*2*6=2*2*2*3(finally, we broke down 6 because it is the only number left that is not prime. 2*3=6 and 2 and 3 are prime so we break down 6 into 2*3)

Now you have the prime factorization of 24!

24=2*2*2*3

The answer is 25.12 exactly

Answer:

linear

Step-by-step explanation:

This graph is linear

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

How I got that answer:

The vertex is the lowest point of parabolas that open upward.

(h,k) = vertex

(h,k) = (-3,-1)

h = -3

k = -1

For each of the answer choices, a = 1.

The general template of a quadratic in vertex form is

y = a(x-h)^2 + k

Plug a = 1, h = -3, k = -1 into that equation. Simplify.

y = a(x-h)^2 + k

y = 1(x-(-3))^2 + (-1)

y = (x+3)^2 - 1

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola. The provided equations have vertices at different points. You must match the vertex of your graph with the correct equation.

In order to find the equation of the graph in vertex form, we need to locate the vertex on the graph. The vertex form of a quadratic equation is y = a(x - h)² + k, where (h,k) is the vertex of the parabola.

Considering the options provided:

However, without a graph or specific vertex provided, we won't be able to define the equation of the graph precisely in vertex form. You need to match the vertex of your graph to one of the above options.

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When a triangle is translated, the resulting triangle will be congruent to the original triangle.

The congruency statement is ABCD = ZYXW

From the complete question, corresponding points are:

This means that:

Hence, the congruency statement is ABCD = ZYXW

Read more about congruency at:

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Final answer:

To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. Plug in the given values of the lengths of the legs EF and EG, and solve the equation to find the length of GF.

Explanation:

To find the length of line segment GF in a right triangle EFG, you can use the Pythagorean theorem. According to the Pythagorean theorem, the sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse. In this case, the hypotenuse is line segment GF. Let's label the length of EF as x, and the length of EG as y.

Using the Pythagorean theorem, we can set up the following equation: x^2 + y^2 = GF^2.

Plugging in the given values, x = 9.4 and y = 6.8, we get: 9.4^2 + 6.8^2 = GF^2. Solving this equation will give us the length of line segment GF.

155-45=110

3850÷110=385 bicycles

Answer:

35

Step-by-step explanation:

3850/(155-45)

3850/110

35

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Answer:The reasonable time for the base ball to land on the ground is 5 seconds

Step-by-step explanation:

To get the time we will differentiate

h(t) = -16t2 + 80t + 224, w.r.t t

dh(t)/dt= 0

-32t +80=0

32t=80

t=80/32

t= 2.5 seconds This is the time the base ball has been in the air

The reasonable time for it to take the baseball to land on the ground is T= 2×t

T= 2×2.5

T=5 seconds

Answer:

all work is shown and pictured

Answer:

The equation of the line is 2 x +3 y = 15.

Step-by-step explanation:

Here the given points are ( -3, 7) & ( 3, 3) -

Equation of a line whose points are given such that

[tex]x_{1}, y_{1}[/tex] ) & ( [tex]x_{2}, y_{2}[/tex] )-

 y - [tex]y_{1}[/tex]   =  [tex]\frac{ y_{2} - y_{1} }{ x_{2} - x_{1} }[/tex]   ( x - [tex]x_{1}[/tex]  )

i.e.  y - 7= [tex]\frac{3 - 7}{3 - (-3)}[/tex]  ( x- (-3))

      y - 7 =  [tex]\frac{-4}{3 + 3}[/tex] ( x + 3 )

      y - 7= [tex]- \frac{2}{3}[/tex]  ( x + 3 )

      3 ( y - 7)  =  - 2 ( x + 3)

      3 y -21 = -2 x - 6

      2 x + 3 y = 21 - 6

      2 x + 3 y = 15

Hence the equation of the required line whose passes trough the points ( - 3, 7) & ( 3, 3)  is 2 x + 3 y = 15.

Answer:

You're not giving enough details about the figure

Answer:

The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)

Step-by-step explanation:

we have

[tex]f(x)=2x^{2}+3x-5[/tex]

This is a vertical parabola open upward (the leading coefficient is positive)

The vertex is a minimum

The coordinates of the vertex is the point (h,k)

step 1

Find the vertex of the quadratic function

Factor the leading coefficient 2

[tex]f(x)=2(x^{2}+\frac{3}{2}x)-5[/tex]

Complete the square

[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-5-\frac{9}{8}[/tex]

[tex]f(x)=2(x^{2}+\frac{3}{2}x+\frac{9}{16})-\frac{49}{8}[/tex]

Rewrite as perfect squares

[tex]f(x)=2(x+\frac{3}{4})^{2}-\frac{49}{8}[/tex]

The vertex is the point (-\frac{3}{4},-\frac{49}{8})

step 2

Find the x-intercepts (values of x when the value of f(x) is equal to zero)

For f(x)=0

[tex]2(x+\frac{3}{4})^{2}-\frac{49}{8}=0[/tex]

[tex]2(x+\frac{3}{4})^{2}=\frac{49}{8}[/tex]

[tex](x+\frac{3}{4})^{2}=\frac{49}{16}[/tex]

take the square root both sides

[tex]x+\frac{3}{4}=\pm\frac{7}{4}[/tex]

[tex]x=-\frac{3}{4}\pm\frac{7}{4}[/tex]

[tex]x_1=-\frac{3}{4}+\frac{7}{4}=1[/tex]

[tex]x_2=-\frac{3}{4}-\frac{7}{4}=-2.5[/tex]

therefore

The function f(x) is negative in the interval (-2.5,1)

The function f(x) is positive in the interval (-≠,-2.5) ∪ (1,∞)

see the attached figure to better understand the problem

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Solution:

Given that area of mirror is 225 square inches

[tex]width = 13\frac{3}{4} \text{ inches }[/tex]

Converting the above mixed fraction we get,

[tex]width = 13\frac{3}{4} = \frac{13 \times 4 + 3}{4} = \frac{55}{4} \text{ inches }[/tex]

Let us find the length of mirror

The area of mirror is given as:

area of mirror = length x width

Substituting the given values,

[tex]225 = length \times \frac{55}{4}\\\\length = 225 \times \frac{4}{55}\\\\length = 225 \times 0.0727\\\\length = 16.36[/tex]

Thus length of mirror is 16.36 inches

Will the mirror fit in a space that is 15 inches by 16 inches?

NO. The mirror will not fit in a space that is 15 inches by 16 inches

Because length of mirror is 16.36 inches whereas the given space is 15 inches long

16.36 > 15 so the length of mirror will not fit inside the space

Also width of mirror is [tex]\frac{55}{4} = 13.75[/tex] inches which is less than the given space whose width is 16 inches

13.75 < 16 so the width of mirror will not fit inside the space

Answer:

C : 40%

Step-by-step explanation:

20 ÷ 50 = 0.40 also to solve just divide the smaller number from the greater number in order to be able to get the correct percentage.

Answer:

Step-by-step explanation

is / of = % / 100.....proportion formula

20 is what percent of 50...

20 / 50 = x / 100

cross multiply

50x = 2000

x = 2000/50

x = 40.......so 20 is 40% of 50

The fir trees are 9 meters tall and the pine trees are 12 meters tall

Solution:

Let f be the height of one fir tree

Let p be the height of one pine tree

Given that combined height of one fir tree and one pine tree is 21 meters

So we get,

height of one fir tree + height of one pine tree = 21

f + p = 21 ----- eqn 1

Also given that height of 4 fir trees stacked on top of each other is 24 meters taller than one pine tree

height of 4 fir trees stacked on top of each other  = 24 + height of one pine tree

4f = 24 + p ---- eqn 2

Let us solve eqn 1 and eqn 2 to find values of "f and "p"

From eqn 1,

f = 21 - p ----- eqn 3

Substitute eqn 3 in eqn 2

4(21 - p) = 24 + p

84 - 4p = 24 + p

-4p - p = 24 - 84

-5p = - 60

Substitute p = 12 in eqn 3

f = 21 - 12 = 9

Summarizing the results:

height of one fir tree = 9 meters

height of one pine tree = 12 meters

The rate at which the vehicle can travel is 6 miles per gallon

Solution:

Given that experimental vehicle is able to travel [tex]\frac{3}{8}[/tex] mile on [tex]\frac{1}{16}[/tex] gallon of water

To find: Rate at which the vehicle can travel, in miles per gallon of water

distance traveled in miles = [tex]\frac{3}{8} \text{ miles }[/tex]

gallon of water = [tex]\frac{1}{16} \text{ gallons }[/tex]

Miles per gallon is given as:

[tex]\text{ miles per gallon }=\frac{\text{ distance traveled in miles}}{\text{gallon of water }}[/tex]

Substituting the given value we get,

[tex]\rightarrow \frac{\frac{3}{8}}{\frac{1}{16}}\\\\\rightarrow \frac{3}{8} \times \frac{16}{1}\\\\\rightarrow 3 \times 2 = 6[/tex]

So the rate at which the vehicle can travel, in miles per gallon of water is 6 miles per gallon

Answer:

Step-by-step explanation:

x = 60

ΔMAD ≅ Δ SUN

So corresponding parts of congruent triangle are congruent.

∠MDA = ∠NSU

Answer:

x = 90

Step-by-step explanation:

Remember you have to post complete questions in order to get good and exact answers. So here I'll assume a diagram shown below. From the statement. we know that:

△MAD ≅ △SUN

This implies that triangle MAD is congruent to triangle SUN meaning that corresponding sides and angles measure the same. In other words:

∠M = ∠S

∠A = ∠U

∠D = ∠N

And:

MA = SU

AD = UN

MD = SN

So, from the figure:

∠S = ∠M = 30°

As the sum of internal angles of every triangle measures 180°, then:

∠S + ∠U + ∠N  = 180°

And:

∠U = x°

So:

30° + x° + 60°  = 180°

x° = |80° - 30° - 60°

x° =  90°

So:

x = 90

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