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2 years ago

Name: -

Mathematics

1 answer:

Luden [163]2 years ago

7 0

Answer:

Step-by-step explanation:

Distance=400+200=600km

diplacement=x 200-0km=200km

total distance travelled=400+400=800km

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What value of y makes the 2 triangles congruent by SSS?

aleksandrvk [35]

The triangle was just flipped so the missing side is going to equal 36, so...
2y+20= 36
(Subtract 20 from each side to isolate the 2y)
2y= 16
(Divide each side by 2 to isolate the variable)

ANSWER:
y= 8

8 0

3 years ago

Which of the following numbers is a multiple of 6? A. 106 B. 333 C. 424 D. 882

brilliants [131]

882 is a multiple of 6. if you multiply 6 by 147, you get 882.

4 0

3 years ago

Find the equation, (f(x) = a(x - h)2 + k), for a parabola containing point (2, -1) and having (4, -3) as a vertex. What is the s

Nataliya [291]

Answer:

$f(x)=\frac{1}{2}x^2-4x+5$

Step-by-step explanation:

A parabola is written in the form

$f(x)=a((x-h)^2+k)$ (1)

where:

$h$ is the x-coordinate of the vertex of the parabola

$ak$ is the y-coordinate of the vertex of the parabola

$a$ is a scale factor

For the parabola in the problem, we know that the vertex has coordinates (4,-3), so we have:

$h=4$ (2)

$ak=-3$

From this last equation, we get that $a=\frac{-3}{k}$ (3)

Substituting (2) and (3) into (1) we get the new expression:

$f(x)=-\frac{3}{k}((x-4)^2+k) = -\frac{3}{k}(x-4)^2 -3$ (4)

We also know that the parabola contains the point (2,-1), so we can substitute

x = 2

f(x) = -1

Into eq.(4) and find the value of k:

$-1=-\frac{3}{k}(2-4)^2-3\\-1=-\frac{3}{k}\cdot 4 -3\\2=-\frac{12}{k}\\k=-\frac{12}{2}=-6$

So we also get:

$a=-\frac{3}{k}=-\frac{3}{-6}=\frac{1}{2}$

So the equation of the parabola is:

$f(x)=\frac{1}{2}((x-4)^2 -6)$ (5)

Now we want to rewrite it in the standard form, i.e. in the form

$f(x)=ax^2+bx+c$

To do that, we simply rewrite (5) expliciting the various terms, we find:

$f(x)=\frac{1}{2}((x^2-8x+16)-6)=\frac{1}{2}(x^2-8x+10)=\frac{1}{2}x^2-4x+5$

6 0

3 years ago

How do you solve (Arc)QPT if <QZT = 120

yuradex [85]

By definition, the arc length is given by:
arc = R * theta * ((2 * pi) / 360)
Where,
theta: angle in degrees
R: radio
We have then:
(Arc) QPT if <QZT = 120:
theta = 360-120 = 240 degrees
R = 13.5 units
Substituting values we have:
(Arc) QPT = R * theta * ((2 * pi) / 360)
(Arc) QPT = (13.5) * (240) * ((2 * pi) / 360)
(Arc) QPT = 56.55 units
Answer:
(Arc) QPT = 56.55 units

7 0

3 years ago

The decimal d is formed by writing in succession all the positive integers in increasing order after the decimal point; that is,

Maksim231197 [3]

Answer:

Step-by-step explanation:

We are given that a decimal number d

d=0.12345678...

Where d is formed by writing in succession all the positive integers in increasing order after decimal point.

We have to find the 100th digit of d to the right of the decimal point.

Place of first digit 1 after decimal=Tenth

Place of second digit 2 after decimal=Hundredth

Place of third digit 3 after decimal=Thousandth

Therefore, 100th digit of d to the right of the decimal point=2

5 0

3 years ago