If f(x) = x + 1 and g(x) = 2x - 7, which expression is equivalent to [fog|(3)?

9514 1404 393

Answer:

  (a)  c = 4

  (b)  c < 4

  (c)  c > 4

Step-by-step explanation:

(a) The solutions to the system of equations can be found by substituting one expression for y into the other equation:

  3x^2 -5x = 2x^2 -x -c

  x^2 -4x +c = 0 . . . . . . . subtract the right side expression

The discriminant is

  d = b^2-4ac = (4)^2 -4(1)(c) = 16-4c.

The system will have exactly one solution when d = 0.

  16 -4c = 0

  4 -c = 0

__

(b) There will be more than one real solution when d > 0

  4 -c > 0

  c < 4 . . . . two real solutions

__

(c) There will be no real solutions when d < 0.

  4 -c < 0

  c > 4 . . . . no real solutions

_____

Additional comment

The question posed here simply asks for a value of c. It does not ask for the solutions (x, y). We can count them without knowing exactly what they are.

Answer: 12.9

Step-by-step explanation:

A line of infinite extent whose points correspond to the real numbers according to their distance in a positive or negative direction from a point arbitrarily taken as zero. I hope this explain the answer better!

Answer:

19/24 option d is correct

Answer:684

Step-by-step explanation:

A= 1/2 h (b1+b2)

A= 1/2 19 (46+26)

A= 9.5 (72)

A=684

Answer:

Step-by-step explanation:

1. Write a equation

[tex]10,000(1+\frac{0.08}{4})^4^x[/tex]

2. plug in 20,000 to y

[tex]20,000=10,000(1+\frac{0.08}{4})^4^x[/tex]

3. Solve

Answer:

Yield on this bond = 4.5%

Step-by-step explanation:

Given:

Face value of bond = $10,000

Annual interest receives from bond = $450

Find:

Yield on this bond

Computation:

Yield on bond = [Annual interest / Face value]100

Yield on this bond = [Annual interest receives from bond / Face value of bond]100

Yield on this bond = [450 / 10,000]100

Yield on this bond = [0.045]100

Yield on this bond = 4.5%

Answer:

5/108

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

5/108

Step-by-step explanation:

2/3 * 1/8 is 2/24

^2/24 can be simplified to 1/12

^ 5/9 * 1/12 is 5/108.

Therefore,

Your answer is 5/108 , if I understood the question correctly.

Answer:

[tex]x = 4[/tex]

[tex]y =1[/tex]

Step-by-step explanation:

Given

The attached figure

Required

x and y

If the attached is a parallelogram, then:

Either segment of a diagonal are equal; So, we have:

[tex]3x = 12[/tex]

[tex]x + y = 5y[/tex]

In [tex]3x = 12[/tex]

Divide both sides by 3

[tex]x = \frac{12}{3}[/tex]

[tex]x = 4[/tex]

Substitute [tex]x = 4[/tex] in [tex]x + y = 5y[/tex]

[tex]4 + y = 5y[/tex]

Collect like terms

[tex]5y - y =4[/tex]

[tex]4y = 4[/tex]

Divide both sides by 4

[tex]y = \frac{4}{4}[/tex]

[tex]y =1[/tex]

Step-by-step explanation:

For 18:

[tex] {10}^{2} + {y}^{2} = {26}^{2} \\ 100 + {y}^{2} = 676 \\ {y}^{2} = 676 - 100 \\ {y}^{2} = 576 \\ y = \sqrt{576} \\ y = 24 \: in[/tex]

For 19

[tex] {10}^{2} + {( \frac{15}{2}) }^{2} = {c}^{2} \\ 100 + \frac{225}{4} = {c}^{2} \\ \frac{625}{4} = {c}^{2} \\ c = \sqrt{ \frac{625}{4} } \\ c = \frac{25}{2} \\ c = 12.5 \: m[/tex]

Answer:

5 faces

8 edges

5 vertices

Answer:

C:  3

Step-by-step explanation:

The graph touches or crosses the x-axis in 3 places; thus, there are 3 real zeros.

Answer:

x = 13/8

Step-by-step explanation:

(4x−1)(2)=11

Simplify both sides of the equation.

(4x−1)(2)=11

(4x)(2)+(−1)(2)=11 (Distribute)

8x+−2=118x+−2=11

8x−2=11

Add 2 to both sides.

8x−2+2=11+2

8x=13

Divide both sides by 8.

8x/8 = 13/8

which brings you to the answer of

x = 13/8

(Note:If this was a little confusing,feel free to ask me any questions revolving around this topic)

Answer:

B 84 is our answer

Step-by-step explanation:

triangle formula for surface area is base x height divided by 2 so 7 x 6 = 42 42 ÷ 2 = 21 All the other triangles are going to be the same so 21 x 4 = 84 so 84 is our surface area

Answer:

[tex]y\leq 3x-2[/tex]

Step-by-step explanation:

Answer:

i hate these questions lol her name do be karen sorry um you do multiplicaton for this question i hate aleks expesially thqat question i feel you bro

Step-by-step explanation:

Answer: it’s all in the explanation!

Step-by-step explanation:

So, in the question, it states that she’s gunna have two tables for every six guests. You’re gonna need to find out how much people are going to be at ONE table, so two divided by six! And as you know, that equals three. For the first space, since it’s a odd number, you need to use the three instead of six since there’s gunna be one table by itself. So three times 5. The first space is gunna be 15 :). The second space is somewhat the same process. What times three equals 21? Seven! So for the second space, you’re gunna pit seven. For the third one, you do 8 times three, which equals 24. And for the last space, it’s 10, for three times ten :), hoped this helped!

Answer:

For a gestation period of 6 months, the life span is 15.

Step-by-step explanation:

Gestation(months)   x        8     2.1    1.3     1    11.5    5.3   3.8    24.3

Life span (years)       y       30    12      6      3   25      12    10     40

y =?   x= 6 months

Assuming the variables x and y have a significant correlation

Graphing the data on a spreadsheet

Using the linear equation obtained

y =  1.5229*x + 6.3425

x=6

y = 1.5229*6 + 6.3425

y = 15. 5

Answer:

m(minor arc KL) = 153°

Step-by-step explanation:

"Measure of intercepted arcs between two diameters are equal in measure"

By this property,

m(JK) = m(HL)

(7x - 1)° = (5x + 7)°

7x - 5x = 7 + 1

2x = 8

x = 4

Therefore, m(arc HL) = (5x + 7)

                                  = 5(4) + 7

                                  = 27°

Now measure of minor arc KL = m(arc KH) - m(arc HL)

                                                  = 180° - 27°

                                                  = 153°

Therefore, measure of minor arc KL is 153°

Answer:

The standard error of the difference in the mean number of fish caught before and after the fire is 0.2153.

or

sqrt [ (1.6^2)/195 + (2.1^2)/143 ]

Answer:

4.67 feet

Step-by-step explanation:

The computation of missing dimension of the triangle is given below:

As we know that

Area of the triangle = 1 ÷ 2 × base × height

14 = 1 ÷ 2 × base × 6

14 = 3 × base

So, the base is

= 14 ÷ 3

= 4.67 feet

Here we assume the area to be 14 square feet

Answer:

4⅔ or 4.67 feet

Step-by-step explanation:

Area of a triangle is ½bh

½×b×6=14

3b=14

14÷3=4⅔

Answer:

1/6 x 1/6 = 1/36

1/36 is our probability of getting two heads and four tails.

Answer:

Not a linear relationship

Step-by-step explanation:

Given

The attached table

Required

Linear or not

To do this, we simply calculate the slope of the table at different intervals.

Slope (m) is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Let:

[tex](x_1,y_1) = (0,0)[/tex]

[tex](x_2,y_2) = (0.5,7.2)[/tex]

So, the slope is:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{7.2 - 0}{0.5-0}[/tex]

[tex]m = \frac{7.2}{0.5}[/tex]

[tex]m = 14.4[/tex]

Let:

Let:

[tex](x_1,y_1) = (1,10.7)[/tex]

[tex](x_2,y_2) = (2,12.2)[/tex]

So, the slope is:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

[tex]m = \frac{12.2 - 10.7}{2 - 1}[/tex]

[tex]m = \frac{1.5}{1}[/tex]

[tex]m = 1.5\\[/tex]

See that the calculated slopes are not equal.

Hence, it is not linear

Hope this helps you solve your math problem.

Answer:

Step-by-step explanation:

Since J is the midpoint of HK,  then HJ=JK   and 3x+5=9x-3  solve for x

6x=8   x=8/6=4/3     so HJ=3x+5=3(4/3)+5=9 = JK   HK=2(9)=18

the full segment HK is 18,  each half of it is 9 =HJ=JK

Answer:

40 cubic units

Step-by-step explanation:

16x 3 = 48

48- 8 is 40

Answer:

15 cubic units

Step-by-step explanation:

Use multiplication (V = l x w x h) to find the volume of a solid figure.

3*5=15