All categories

3 years ago

4. What is the axis of symmetry for h(x) = 19(x – 5)^2 + 6

Mathematics

1 answer:

tester [92]3 years ago

4 0

Answer:

x = 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

(h, k ) are the coordinates of the vertex and a is a multiplier

h(x) = 19(x - 5)² + 6 ← is in vertex form

with vertex (h, k ) = (5, 6 )

The axis of symmetry is a vertical line passing through the vertex

with equation x = 5

You might be interested in

Does anyone know how to do this (#2) PLZZZZ HELPPPPPPPP

timurjin [86]

Answer:

a.- slope= 36

Interpretation : The cable car travels 36 meter per minute

b.- y = 36x + 100

c.- 640 meters

Step-by-step explanation:

a.-

Find slope using the slope formula : $\frac{y2-y1}{x2-x1}$

Plug in the two given points: $\frac{1000-100}{25-0}$

Subtract the numbers : $\frac{900}{25}$

Reduce the fraction : 36

b.-

Using the given y-interspet (100) and the slope create an equation: y = 36x + 100

c.-

Using the equation you created plug in 15 for x to find the

distance: y = 36 (15) + 100

Multiply the numbers : y = 540 + 100

Add the numbers : y = 640

8 0

3 years ago

A geometric sequence is shown below.

mestny [16]

Answer:

An explicit representation for the nth term of the sequence:

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

It means, option (B) should be true.

Step-by-step explanation:

Given the geometric sequence

$-\frac{1}{2},\:-2,\:-8,\:-32,...$

A geometric sequence has a constant ratio, denoted by 'r', and is defined by

$f_n=f_1\cdot r^{n-1}$

Determining the common ratios of all the adjacent terms

$\frac{-2}{-\frac{1}{2}}=4,\:\quad \frac{-8}{-2}=4,\:\quad \frac{-32}{-8}=4$

As the ratio is the same, so

r = 4

Given that f₁ = -1/2

substituting r = 4, and f₁ = -1/2 in the nth term

$f_n=f_1\cdot r^{n-1}$

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

Thus, an explicit representation for the nth term of the sequence:

$f_n=-\frac{1}{2}\cdot \:4^{n-1}$

It means, option (B) should be true.

8 0

2 years ago

24% students in a clan were absent in a day .If 38 students were present ,what is the total strength in the clan

Lemur [1.5K]

Answer:

50 students

Step-by-step explanation:

24% students in a clan were absent in a day .

Hence, the Percentage of students present is calculated as:.

= 100 % - 24 %

= 76%

From the question, we know that:

If 38 students were present ,what is the total strength in the clan

The total strength of the clan = Total number of students. This is calculated as:

76% × x = 38 students.

76/100 × x = 38

76x /100 = 38

Cross Multiply

76x = 38 × 100

x = 3800/76

x = 50 students

5 0

3 years ago

Solve y-12/25=3 1/5. What number is y? A. 3 1/5 B. 3 17/25 C. 3 7/25 D. 4 17/25

kicyunya [14]

Answer:

Option c) y= $3\frac{17}{25}$ is correct

The value of y is 3 $\frac{17}{25}$

Step-by-step explanation:

Given equation is

$y-\frac{12}{25}=3\frac{1}{5}$

To solve the given equation for y

$y-\frac{12}{25}=3\frac{1}{5}$

$y-\frac{12}{25}=\frac{16}{5}$ (converting mixed fraction to normal fraction )

$y-\frac{16}{5}=\frac{12}{25}$

$y-\frac{(16\times 5)+12}{25}$ (taking LCM 25 )

$=\frac{80+12}{25}$ (adding the terms )

$y=\frac{92}{25}$ (now convert fraction into mixed fraction )

Therefore y= $3\frac{17}{25}$

Option c) y= $3\frac{17}{25}$ is correct

The value of y is 3 $\frac{17}{25}$

6 0

3 years ago

Determine if the set is a Pythagorean triple

balandron [24]

Answer:

Pythagorean Triples are sets of whole numbers for which the Pythagorean Theorem holds true. The most well-known triple is 3, 4, 5. This means that 3 and 4 are the lengths of the legs and 5 is the hypotenuse.

4 0

3 years ago