Pls help!! Solve and graph the inequalities

Find the 52nd term of the given arithmetic sequence-30, -38, -46, -54...

torisob [31]

The sequence is given to be:

$-30,-38,-46,-54...$

The nth term of an arithmetic sequence is calculated using the formula:

$a_n=a_1+(n-1)d$

where a₁ is the first term, n is the number of terms, and d is the common difference.

From the given sequence, the following parameters can be gotten:

$\begin{gathered} a_1=-30 \\ d=-38-(-30)=-8 \end{gathered}$

Therefore, the parameters can be substituted into the formula to find the 52nd term:

$\begin{gathered} n=52 \\ \therefore \\ a_{52}=-30+(52-1)(-8) \\ a_{52}=-30+51(-8)=-30-408 \\ a_{52}=-438 \end{gathered}$

The 52nd term is -438.

8 0

1 year ago

Tony is mailing packages. Each small package costs him $2.80 to send. Each large package costs him $3.60. How much will it cost

Natasha_Volkova [10]

Answer:

The answer is $33.6

Step-by-step explanation:

Each small package costs him $2.80

3 small packages will cost him 3 x $2.80 = $8.4

Each large package costs him $3.60

7 large packages will cost 7 x $3.60 = $25.2

Cost to send 3 small packages and 7 large packages = $8.4 + $25.2

= $33.6

6 0

3 years ago

Sin x= 1.5 value of x

alina1380 [7]

Answer:

x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z

or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z

Step-by-step explanation:

Solve for x:

sin(x) = 1.5

1.5 = 3/2:

sin(x) = 3/2

Take the inverse sine of both sides:

Answer: x = π - sin^(-1)(3/2) + 2 π n_1 for n_1 element Z

or x = 2 π n_2 + sin^(-1)(3/2) for n_2 element Z

3 0

3 years ago

1. Given points A(3, -5) and B(19, -1), find the coordinates of point C that sit 3/8 of the way along line AB, closer to A than

zaharov [31]

1. C(x, y) = (7.3, –3.9)

2. C(x, y) = (17, –1.5)

Solution:

Question 1:

Let the points are A(3, –5) and B(19, –1).

C is the point that on the segment AB in the fraction $\frac{3}{8}$ .

Point divides segment in the ratio formula:

$$C(x, y)=\left(\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n}\right)$

Here, $x_1=3, y_1=-5, x_2=19, y_2=-1$ and m = 3, n = 8

$$C(x, y)=\left(\frac{3\times19+8\times3}{3+8} , \frac{3\times(-1)+8\times(-5)}{3+8}\right)$

$$=\left(\frac{57+24}{11} , \frac{-3-40}{11}\right)$

$$=\left(\frac{81}{11} , \frac{-43}{11}\right)$

C(x, y) = (7.3, –3.9)

Question 2:

Let the points are A(3, –5) and B(19, –1).

C is the point that on the segment AB in the fraction $\frac{3}{8}$ .

Point divides segment in the ratio formula:

$$C(x, y)=\left(\frac{mx_2+nx_1}{m+n} , \frac{my_2+ny_1}{m+n}\right)$

Here, $x_1=3, y_1=-5, x_2=19, y_2=-1$ and m = 7, n = 1

$$C(x, y)=\left(\frac{7\times19+1\times3}{7+1} , \frac{7\times(-1)+1\times(-5)}{7+1}\right)$

$$=\left(\frac{133+3}{8} , \frac{-7-5}{8}\right)$

$$=\left(\frac{136}{8} , \frac{-12}{8}\right)$

C(x, y) = (17, –1.5)

8 0

3 years ago

Please help I’m on a test “Given the triangle below, what is the longest side length?”

Mkey [24]

~11.31

Pythagorean Theorem because it is a right triangle.

7 0

3 years ago