Simplify: 39b8 - (-19b8)

What is the slope of the line that has the equation 4x + 2y = 12?

WARRIOR [948]

Answer:

The slope is -2

Step-by-step explanation:

convert to slope intercept form. the number or fraction by the x when in slope intercept form is the slope.

6 0

3 years ago

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Four points partition the directed line segment from A to B. • Point P partitions the directed line segment from A to B into a 3

Alecsey [184]

Answer:

S is closest to B.

Step-by-step explanation:

Given a directed line segment from point A to B.

Point P divides the line A to B in a ratio 3:4.

Point Q divides the line A to B in a ratio 4:3.

Point R divides the line A to B in a ratio 2:5.

Point S divides the line A to B in a ratio 5:2.

To find:

The point which is closest to the point B.

Solution:

Here, to find the point closest to B we need to find the distances PB, QB, RB and SB.

We can see the sum of ratio 3:4, 4:3, 2:5 and 5:2 is 7.

Let the distance between A and B be 7 units.

Now, the distances can be found easily.

$PB = \dfrac{4}{7}\times 7 = 4\ units$

$QB = \dfrac{3}{7}\times 7 = 3\ units$

$RB = \dfrac{5}{7}\times 7 = 5\ units$

$SB = \dfrac{2}{7}\times 7 = 2\ units$

The point which has the minimum distance from point B, will be nearest to B.

We can clearly observe that SB is the minimum distance.

Therefore, <em>S is closest to B</em>.

4 0

3 years ago

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The ratio of boys to girls in the school is 4:3 if there were 16 boys how many girls at in band?

larisa86 [58]

Answer:

12 girls

Step-by-step explanation:

16 divided by 4 is 4

Since the ratio is 4:3, that means that for every 4 boys, there are three girls.

3 x 4 is 12

Your answer is 12 girls.

7 0

3 years ago

Which representation of a transformation on a coordinate grid does not preserve congruence?

Alex17521 [72]

Answer:

B

Step-by-step explanation:

Consider all options:

A. Transformation with the rule

$(x,y)\rightarrow (x,-y)$

is a reflection across the x-axis.

Reflection across the x-axis preserves the congruence.

B. Transformation with the rule

$(x,y)\rightarrow \left(\dfrac{7}{8}x,\dfrac{7}{8}y\right)$

is a dilation with a scale factor of $\frac{7}{8}$ over the origin.

Dilation does not preserve the congruence as you get smaller figure.

C. Transformation with the rule

$(x,y)\rightarrow (x+6,y-4)$

is a translation 6 units to the right and 4 units down.

Translation 6 units to the right and 4 units down preserves the congruence.

D. Transformation with the rule

$(x,y)\rightarrow (y,-x)$

is a clockwise rotation by $90^{\circ}$ angle over the origin.

Clockwise rotation by $90^{\circ}$ angle over the origin preserves the congruence.

3 0

3 years ago

Ex 2.8<br> 3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1

harkovskaia [24]

$y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\
y''(0)=20\cdot0^3=0$

The value of the second derivative for $x=0$ is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of $5x^4$ is always positive for $x\in\mathbb{R}\setminus \{0\}$ . That means at $x=0$ there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval $[-2,1]$ .
The function $y$ is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.

$y_{max}=y(1)=1^5-3=-2$

4 0

3 years ago