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3 years ago

Please Help!!! Determine the intercepts of the line that corresponds to the following table of values.

Mathematics

1 answer:

Orlov [11]3 years ago

6 0

Answer:

y-intercept is (0,30); x-intercept is (52.5,0).

Step-by-step explanation:

Note that as x increases by 7 from -35 to -28, y decreases by 4 from 18 to 14. Thus, the slope of this line is

m = rise / run = -4/7.

Let's find the equation of the line. Start with the slope-intercept form:

y = mx + b. Use the slope m = -4/7 and the point (-28, 14) to find b:

14 = -(4/7)(28) + b, or

14 = -16 + b. Then b = 30, and the equation of the line in slope-intercept form is y = (-4/7)x + 30. The y-intercept is (0, 30).

Find the x-intercept by setting y=0 and solving the resulting equation for x:

y = (-4/7)x + 30 becomes (4/7)x = 30, and x = (7/4)(30) = 214, or 52.5.

The x-intercept is thus (52.5, 0).

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Verify cot x sec^4x=cotx +2tanx +tan^3x

Tanzania [10]

Answer:

See explanation

Step-by-step explanation:

We want to verify that:

$\cot(x) \: { \sec}^{4} x = \cot(x) + 2 \tan(x) + { \tan}^{3} x$

Verifying from left, we have

$\cot(x) \: { \sec}^{4} x = \cot(x) \: ( 1 + { \tan}^{2} x )^{2}$

Expand the perfect square in the right:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: ( 1 + { 2\tan}^{2} x + { \tan}^{4} x)$

We expand to get:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + \cot(x){ 2\tan}^{2} x +\cot(x) { \tan}^{4} x$

We simplify to get:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + 2 \frac{ \cos(x) }{\sin(x) ) } \times \frac{{ \sin}^{2} x}{{ \cos}^{2} x} +\frac{ \cos(x) }{\sin(x) ) } \times \frac{{ \sin}^{4} x}{{ \cos}^{4} x}$

Cancel common factors:

$\cot(x) \: { \sec}^{4} x = \cot(x) \: + 2 \frac{{ \sin}x}{{ \cos}x} +\frac{{ \sin}^{3} x}{{ \cos}^{3} x}$

This finally gives:

$\cot(x) \: { \sec}^{4} x = \cot(x) + 2 \tan(x) + { \tan}^{3} x$

3 0

3 years ago

Which problem is solved using this model? 15÷15 3÷115 3÷15 15÷15 https://static.k12.com/nextgen_media/assets/1503272-MAT

Pie

Answer:

As the model is shown below.

As per model a thing is divided into five parts.There are three things and each one of them is being divided into five equal parts.

The value of fifth part of each of them is 1/5.

If we consider each part of a thing as one,

So, total number of parts = 15

Total thing=3

So, the answer of the above model is 3÷ 15.

Out of all the options which are 15÷15 , 3÷115 , 3÷15, 15÷15 →3÷15 is correct.

5 0

2 years ago

Tanya runs diagonally across a rectangular field that has a length of 40 yards and a width of 30 yards. How far did Tanya run?

Yuliya22 [10]

Tanya run 50 yards across the diagonal of the rectangular field.

<u>Step-by-step explanation</u>:

Step 1 :

Length of the rectangular field = 40 yards
width of the rectangular field = 30 yards

Step 2 :

Measure of the diagonal = √(length^2 + width^2 )

Step 3 :

Diagonal = √(40^2 + 30^2 )

= √(1600 + 900)

= √2500

= ±50

Step 4 :

Since distance cannot be negative, The measure of diagonal = 50 yards.

∴ Tanya runs diagonally across a rectangular field is 50 yards.

4 0

3 years ago

The two-way table represents data from a survey asking schoolchildren whether they are attending a summer camp, taking swimming

amm1812

The joint relative frequency values are the top-left four squares, or the intersection of 2 variables, divided by the total number in the bottom-right corner, which is 96.

Find the intersection of Camp and Swimming lessons. The number is 42. Divide this number by 96:
42 ÷ 96 = 43.75%

Best answer is 44%

7 0

3 years ago

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What are line plots with fractions

GREYUIT [131]

Line plots are like for rounding them or put them in order fracton

3 0

3 years ago