- 2x
f(x)= x +4,
4x - 7
XS-10
- 10 X2
20. Use the piecewise function to evaluate points f(-1), f(2), and f(12).
O A. f(-1) = 3, f(2) = 1, and f(12) = 41
B. f(-1) = 3, f(2) = 6, and f(12) = 41
O C. f(-1) = 2. f(2) = 1, and |(12) = 41
D. f(-1) = 2. f(2) = 6, and f(12) = 41

Answer:

Applies are £0.50 each and bananas £0.80 each.

Step-by-step explanation:

Represent the numbers of apples and bananas by a and b respectively.

Then:

5a + 4b = £5.70, and:

4a + 2b = £3.60

Let's solve this system using elimination by addition/subtraction.  Multiply the 2nd equation by -2, obtaining the equivalent system

5a + 4b = £5.70

-8a  - 4b = -£7.20

--------------------------

-3a         =  -£1.50

Dividing both sides by -3, we get £0.50.  Apples are £0.50 apiece.

How much are bananas per piece?  Use the first equation; substitute £0.50 for a:

5(£0.50) + 4b = £5.70, or

                  4b = £3.20.  Then b = £0.80.

Applies are £0.50 each and bananas £0.80 each.

Answer:

Step-by-step explanation:

find the slope

[tex]\frac{4-8}{-5-(-3)} =\frac{-4}{-2} \\\\slope=2\\y=mx+b\\y=2x+b\\[/tex]

take a coordinate to fill in

[tex](-5,4)\\y=-5\\x=4\\-5=2(4)+b\\-5=8+b-8 -8\\-13=b\\[/tex]

this means that the equation is y=2x-13

and if you add m and b

you get :-11

I HOPE THIS HELPS

Answer:

7/2

Step-by-step explanation:

Let $A = (-3,8)$ and $B = (-5,4)$. The midpoint of $\overline{AB}$ is $\left( \frac{(-3) + (-5)}{2}, \frac{8 + 4}{2} \right) = (-4,6)$.

The slope of $\overline{AB}$ is $\frac{8 - 4}{(-3) - (-5)} = 2$, so the slope of the perpendicular bisector of $\overline{AB}$ is $-\frac{1}{2}$. Therefore, the equation of the perpendicular bisector is given by

\[y - 6 = -\frac{1}{2} (x + 4).\]Isolating $y,$ we find

\[y = -\frac{1}{2} x + 4.\]

Answer:

a) [tex]cos(\alpha)=-\frac{3}{5}\\[/tex]

b)  [tex]\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

c) [tex]\frac{4+3\sqrt{3} }{10}\\[/tex]

d)  [tex]\alpha\approx 53.1^o[/tex]

Step-by-step explanation:

a) The problem tells us that angle [tex]\alpha[/tex] is in the second quadrant. We know that in that quadrant the cosine is negative.

We can use the Pythagorean identity:

[tex]tan^2(\alpha)+1=sec^2(\alpha)\\(-\frac{4}{3})^2 +1=sec^2(\alpha)\\sec^2(\alpha)=\frac{16}{9} +1\\sec^2(\alpha)=\frac{25}{9} \\sec(\alpha) =+/- \frac{5}{3}\\cos(\alpha)=+/- \frac{3}{5}[/tex]

Where we have used that the secant of an angle is the reciprocal of the cos of the angle.

Since we know that the cosine must be negative because the angle is in the second quadrant, then we take the negative answer:

[tex]cos(\alpha)=-\frac{3}{5}[/tex]

b) This angle is in the first quadrant (where the sine function is positive. They give us the value of the cosine of the angle, so we can use the Pythagorean identity to find the value of the sine of that angle:

[tex]cos (\beta)=\frac{1}{2} \\\\sin^2(\beta)=1-cos^2(\beta)\\sin^2(\beta)=1-\frac{1}{4} \\\\sin^2(\beta)=\frac{3}{4} \\sin(\beta)=+/- \frac{\sqrt{3} }{2} \\sin(\beta)= \frac{\sqrt{3} }{2}[/tex]

where we took the positive value, since we know that the angle is in the first quadrant.

c) We can now find [tex]sin(\alpha -\beta)[/tex] by using the identity:

[tex]sin(\alpha -\beta)=sin(\alpha)\,cos(\beta)-cos(\alpha)\,sin(\beta)\\[/tex]

Notice that we need to find [tex]sin(\alpha)[/tex], which we do via the Pythagorean identity and knowing the value of the cosine found in part a) above:

[tex]sin(\alpha)=\sqrt{1-cos^2(\alpha)} \\sin(\alpha)=\sqrt{1-\frac{9}{25} )} \\sin(\alpha)=\sqrt{\frac{16}{25} )} \\sin(\alpha)=\frac{4}{5}[/tex]

Then:

[tex]sin(\alpha -\beta)=\frac{4}{5}\,\frac{1}{2} -(-\frac{3}{5}) \,\frac{\sqrt{3} }{2} \\sin(\alpha -\beta)=\frac{2}{5}+\frac{3\sqrt{3} }{10}=\frac{4+3\sqrt{3} }{10}[/tex]

d)

Since [tex]sin(\alpha)=\frac{4}{5}[/tex]

then  [tex]\alpha=arcsin(\frac{4}{5} )\approx 53.1^o[/tex]

Answer:

Domain { -1,3,5}

Step-by-step explanation:

The domain is the input to the function

Domain { -1,3,5}

Answer:

D

Step-by-step explanation:

4x^4+3x^2-3x^3-3x+1

Step-by-step explanation:

19/20 in decimal form is 0.95

Answer:

0.95

Step-by-step explanation:

19 ÷ 20

Divide.

= 0.95

Why am I just finding this?

Answer:

C. -3

Step-by-step explanation:

Plugging both of those points into the slope formula gets you a slope of -3.

Answer:

segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI  

Step-by-step explanation:

In the picture attached, the triangles are shown.

After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG  and segment EI. More specifically:

Answer:

segment FG = one half segment FI, segment FH = one half segment FE, and segment HG = one half segment EI; ΔHFG ~ ΔEFI  

Step-by-step explanation:

In the picture attached, the triangles are shown.

After the dilation and reflection, there is proportionality between segment FG and segment FI, segment FH and segment FE, and segment HG  and segment EI. More specifically:

FG = 1/2*FI

FH = 1/2*FE

HG = 1/2*EI

This answer is right! took the test on FLVS and confirmed it :)

Answer:

I think it's D because the line AC looks like it is splitting the rectangle in half. I think this is right since the angles are congruent. (Angle BAC and Angle ACD)

there are 53 children in the family gathering

Answer:

C = 53

Step-by-step explanation:

WHAT WE KNOW

m + w + c =100

2w - 2 = m

6 + w + m = c

-------------------------

FIND C

Answer:

The found values are:

A = 1/3

B = -8/3

Step-by-step explanation:

We know that general equation is given by:

y = mx + c

where m is the slope and c is a constant.

x + 3y = -5

y = -(1/3)x - 1/3(5)

Slop of the equation is -(1/3). As parallel line have same slope substitute it in the first equation:

Ax + By = 3

By = -Ax - 3

By = (1/3)x - 3

Hence, A = 1/3

Substitute point (-7,2) into the equation:

B(2) = (1/3)(-7) -3

B(2) = -7/3 - 3

B(2) = -16/3

B = -16/6

B = -8/3

Answer:

19.625 cm^2

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

V = 3.14 * 5^2 * .25

V =19.625 cm^2

Answer:

option c is the correct ans .

because we can easily substitute the value of y in equn 2 to get value of x..

Answer:

To me, the third one is the best.

Note:  y has  been made subject of formula which makes it easy to substitute it into equation 2 and find x .

Step-by-step explanation:

Answer:

(a) y = -3/5 x + 13/5

(b) y = 5/3 x + 1/3

Step-by-step explanation:

(a) The slope of the tangent line is dy/dx.  Use implicit differentiation:

x² + y² + 4x + 6y − 21 = 0

2x + 2y dy/dx + 4 + 6 dy/x = 0

2x + 4 + (2y + 6) dy/dx = 0

x + 2 + (y + 3) dy/dx = 0

(y + 3) dy/dx = -(x + 2)

dy/dx = -(x + 2) / (y + 3)

At the point (1, 2), the slope is:

dy/dx = -(1 + 2) / (2 + 3)

dy/dx = -3/5

Using point-slope form of a line:

y − 2 = -3/5 (x − 1)

Simplifying to slope-intercept form:

y − 2 = -3/5 x + 3/5

y = -3/5 x + 13/5

(b) The normal line is perpendicular to the tangent line, so its slope is 5/3.  It also passes through the point (1, 2), so point-slope form of the line is:

y − 2 = 5/3 (x − 1)

Simplifying to slope-intercept form:

y − 2 = 5/3 x − 5/3

y = 5/3 x + 1/3

Answer:

Answer A is the first step

Step-by-step explanation:

Normally, to prove an identity, you start by writing all trig expressions in their most simple forms using the two basic trig functions sin and cos. That is done in option A, with writes tan and cot in terms of sin and cos.

Answer:

A. Garden plants grow better in wet soil than in dry soil.

Step-by-step explanation:

A testable hypothesis is theory that can actually be proven by facts rather than opinions

Answer:

0.16 P(Yellow or Brown)=0.16

Answer: 0.44

Step-by-step explanation:

0.4 + 0.28 = 0.68

1.00 - 0.68 = 0.32

0.32 divided by 2.0 = 0.16

Total answer is 0.44

GLAD TO HELP:)

HAVE A NICE DAY!

BTW: I WAS DOING A TEST, BUT TOOK MY TIME TO HELP YOU! :)

PLEASE BRAINLEST ME!

Step-by-step explanation:

i think the answer is -3 only

Answer: B

Step-by-step explanation:

Makes the most sense out of all the options because it’s the most random or unpredictable

Answer:

95 degrees

Step-by-step explanation:

Since the sum of the angles in a quadrilateral must add up to 360 degrees:

95+85+Z+85=360

Z+265=360

Z=95 degrees

Hope this helps!

Answer:

Z = 95°

Step-by-step explanation:

if W = Y => X = Z => Z = 95°

Answer: 260

Step-by-step explanation: When we 200 times 130% we will get 260.

Answer:

45% of students are female or 15/32

Step-by-step explanation:

We find out their is 72 Boys and 60 Girls

We add both together to get 132 Students

Then we divide to get our number/fraction

60/132 = 15/32 or 45%

MARK AS BRAINLIEST

Answer:

There are 9 llamas.

Step-by-step explanation:

For Billy, we have to find a number that is divisible by four, because he has one group of lambs, and 3 times as many llamas, which gives us 4 groups altogether. The number must be below 10 in order to not go above 17 when Milly's number of animals are included, but above 4 itself in order to reach the target of 17 in the first place.

As you can guess, the only number that fits all the criteria is 8. It's divisible by 4 and below 10, but above 4 itself.

If Billy has three times as many llamas as lambs, then he must have 2 lambs, and 6 llamas, as 2 × 3 = 6.

If we know that Billy has 8 animals, then we also know that Milly must have 9 animals, as 17 - 8 = 9.

We also know that Milly has 3 groups of animals; one group of llamas, and two groups of lambs, meaning we divide the number of animals she has by 3.

9 ÷ 3 = 3.

This tells us Milly has just 3 llamas, because 3 is one group of 9, and 3 × 2 = 6,  because she has twice the amount of lambs.

Billy has 2 lambs and 6 llamas.

Milly has 6 lambs and 3 llamas.

The amount of lambs is irrelevant to our final answer, so we can disregard them and do a final sum of 6 + 3 = 9, which gives us our answer.

Answer:

Billy: Has 4 lots of animals

Milly: Has 3 lots of animals

17 animals in total means that Billy must have 4 lots of 2 (8 animals) and Milly must have 3 lots of 3 (9 animals) So Billy has 6 llamas and Milly has 3, giving 9 llamas in total

Answer: 5x + 1

Step-by-step explanation:

f(x) - g(x)

(3x + 2) - (-2x + 1)       Here you distribute the negative sign to (-2x + 1)

3x + 2 + 2x - 1            Here you combine like terms

5x + 1                         This is the answer.

Answer: A

Slope = -6

Step-by-step explanation:

Given that the column of the table are:

Column X (-2,-1,0,1,2) and

Column Y (8,2,-4,-10,-16) 

Since the table represent a linear function, the equation of the function will obey the general linear equation

Y = MX + C

Where M = slope

M = ( Y2 - Y1 ) / ( X2 - X1 )

Let Y1 = 8, Y2 = 2 and X1 = -2 and X2 = -1

Substitutes all the parameters into the formula

M = ( 2 - 8 )/( -1 - - 2 )

M = ( 2 - 8 ) / ( -1 + 2 )

M = -6/1

M = -6

Therefore, the slope of the function is -6

Answer:

Pretty easy (if you know geometry)!

Step-by-step explanation:

First, we know that A and B have angle bisectors. This means the angles that are divided by that angle bisector are equal (or their measures).

Thus, m<DBA= 1/2 Beta; m<DAB=1/2 Alpha.

Time to find m<ADB. Using the sum of all angles in a triangle = 180* theorem, we can come up with this equation:

[tex]180= m<ADB+\frac{1}{2} \alpha +\frac{1}{2} \beta[/tex]

So, solving:

[tex]180-\frac{1}{2} \alpha -\frac{1}{2} \beta =m<ADB[/tex]

So there you go! Hope this helps!