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2 years ago

Luke can paint 91 portraits in 7 weeks.

Mathematics

2 answers:

dimulka [17.4K]2 years ago

8 0

91 divided by 7 is 13. so he can paint 13 in 1 week. 13 x 4 equals 52 so he can paint 52 portraits in 4 weeks.

GarryVolchara [31]2 years ago

8 0

he can paint ( 4 / 7 ) * 91 paintings in 4 weeks

4 / 7 = 0.57142857142

0.57142857142 * 91 = 52 paintings in 4 weeks

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What is the slope of the line of (1,0) and (-1,-3)

Alinara [238K]

Slope formula: m = $\frac{(y2-y1)}{(x2-x1)}$ (Knowing that m represents the slope)

Substitute (1,0) for (x1,y1), and (-1,-3) for (x2,y2)

Slope of the line of (1,0) and (-1,-3) is:

m = $\frac{(-3-0)}{(-1-1)}$ = $\frac{-3}{-2}$ = $\frac{3}{2}$

(Simplify)

Slope of the line of (1,0) and (-1,-3) is $\frac{3}{2}$

6 0

3 years ago

Suppose that we don't have a formula for g ( x ) g(x) but we know that g ( 1 ) = − 1 g(1)=-1 and g ' ( x ) = √ x 2 + 15 g′(x)=x2

dezoksy [38]

Answer:

g(0.9) ≈ -2.6

g(1.1) ≈ 0.6

For 1.1 the estimation is a bit too high and for 0.9 it is too low.

Step-by-step explanation:

For values of x near 1 we can estimate g(x) with t(x) = g'(1) (x-1) + g(1). Note that g'(1) = 1²+15 = 16, and for values near one g'(x) is increasing because x² is increasing for positive values. This means that the tangent line t(x) will be above the graph of g, and the estimates we will make are a bit too big for values at the right of 1, like 1.1, and they will be too low for values at the left like 0.9.

For 0.9, we estimate

g(0.9) ≈ 16* (-0.1) -1 = -2.6

g(1.1) ≈ 16* 0.1 -1 = 0.6

4 0

3 years ago

Given the sequence in the table below, determine the sigma notation of the sum for term 4 through term 15. N an 1 4 2 −12 3 36 t

Rzqust [24]

By applying basic property of Geometric progression we can say that sum of 15 terms of a sequence whose first three terms are 5, -10 and 2 is $\sum_{n=4}^{15} 5(-2)^{n-1}$$$

<h3>What is sequence ?</h3>

Sequence is collection of numbers with some pattern .

Given sequence

$a_{1}=5\\\\a_{2}=-10\\\\\\a_{3}=20$

We can see that

$\frac{a_1}{a_2}=\frac{-10}{5}=-2\\$

and

$\frac{a_2}{a_3}=\frac{20}{-10}=-2\\$

Hence we can say that given sequence is Geometric progression whose first term is 5 and common ratio is -2

Now $n^{th}$ term of this Geometric progression can be written as

$T_{n}= 5\times(-2)^{n-1}$

So summation of 15 terms can be written as

$\sum_{n=4}^{15} T_{n}\\\\$\\$\sum_{n=4}^{15} 5(-2)^{n-1}$$$

By applying basic property of Geometric progression we can say that sum of 15 terms of a sequence whose first three terms are 5, -10 and 2 is $\sum_{n=4}^{15} 5(-2)^{n-1}$$$

To learn more about Geometric progression visit : brainly.com/question/14320920

8 0

3 years ago

Aljan and Bella are both driving from Cleveland to Chicago. Aljan leaves at

Natalija [7]

Answer:

Bella will pass Ajjan after 4h and they will have travelled 260 miles.

Step-by-step explanation:

In order to calculate the number of hours, "x", that it'll take for Bella to pass Aljan, we need to find the value of "x" that makes both equations equal. Therefore,

$60*x + 20 = 65*x\\65*x - 60*x = 20\\5*x = 20\\x = \frac{20}{5} = 4$

In order to calculate the distance they traveled, we must use this value for "x" in any of the equations, as done below:

$y = 65*4\\y = 260$

Bella will pass Ajjan after 4h and they will have travelled 260 miles.

4 0

3 years ago

The sum of 2 numbers is 38. one number is 10 more than the other.

son4ous [18]

Answer:

24, 14

Step-by-step explanation:

x + y = 38

x = 10 + y

You can substitute (10+y) into the top equation where the x is.

10 + y + y = 38

10 + 2y = 38

2y = 28

y = 14

Now plug 14 in for y in either equation to get x

x = 10 + 14

x = 24

8 0

3 years ago