All categories

3 years ago

HELP WITH MATH PLEASE

Mathematics

1 answer:

sergey [27]3 years ago

7 0

Answer:

1) (-3,-2)

2) x=-3

Step-by-step explanation:

1) The vertex of a parabola is the turning point that is the minimum or maximum of the graph, based on the shape of the parabola. In this case, the vertex is the minimum. By looking at the coordinate points, we can tell that the minimum value where the graph changes the direction is at (-3,-2).

2) The line of symmetry is the line on the graph that cuts the shape exactly in half. This means that if you were to fold the graph along this line, the two sides would be identical. All parabolas have a line of symmetry and it always matches the vertex. The equation for the line of symmetry will be x= whatever the x-value of the vertex is. So, for this graph, the line of symmetry is x=-3.

You might be interested in

The time required for a skilled worker to produce x shirts is given by the function T(x) = 4x + 2, where T is measured in hours.

solong [7]

Answer:

A. $1,110

B. 50 units.

Step-by-step explanation:

A. Substitute $x=18$ into the function $T(x)=4x+2$ for calculate the time in hours required for the worker to produce 18 units:

$T(18)=4(18)+2=74$

Now you need to substitute $T=74$ into the function $S(T)=15T$ to calculate the amount in dollars she will be paid for 74 hours:

$S(74)=15(74)=1,110$

She will be paid $1,110.

B. To calculate the number of units that the worker needs to produce to be paid $3,030 , you need to substitute $S(T)=3,030$ into the function $S(T)=15T$ and solve for T (to find the number of hours she requires to work to be paid $3,030)

$3,030=15T\\\\T=\frac{3,030}{15}\\\\T=202$

Now, substitute $T(x)=202$ into $T(x)=4x+2$ and solve for x, to calculate the number of units she produces in 202 hours:

$202=4x+2\\\\202-2=4x\\\\x=\frac{200}{4}\\\\x=50$

She would need to produce 50 units to be paid $3,030

5 0

3 years ago

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

REMOVE the outlier from the data, and then do the following: Round answers to the nearest

tresset_1 [31]

Answer:

outliar is23

Step-by-step explanation:

7 0

3 years ago

Determine the holes, vertical asymptotes, and horizontal asymptotes of the rational function y=3x^2+10x-8/x^2+7x+12

kompoz [17]

There would be a hole when x = -4.

If you factor both the top and the bottom, you will see that the factor (x + 4) is in both the numerator and denominator. Therefore, the would be a hole when x = -4 because that would also make the denominator 0.

8 0

3 years ago

What percentage is .0019951

ICE Princess25 [194]

The most exact answer would be 0.19951% but the approximate answer would be 0.2%.

8 0

3 years ago

Read 2 more answers