For what value of the constant c is the function f continuous on
(−∞,∞) where

f(b) = { cb + 9 if b ≤ 3
c(b)² − 9 if b > 3

Answer:

[tex]a=\dfrac{1}{5}[/tex] and b = 1

Step-by-step explanation:

Given that,

[tex]\dfrac{1}{5}+\sqrt7=a+b\sqrt7[/tex]

We need to find the value of a and b.

We should compare both sides of the above equation i.e.

[tex]a=\dfrac{1}{5}[/tex]

and

b = 1

Hence, the values of a and b are 1/5 and 1 respectively.

Answer:

f(x)=-7x-5

f(6)=-7(6)-5

f(6)=-42-5

f(6)=-47

Answer:

(2,32)

(3,48)

Step-by-step explanation:

2×16=32

3×16=48

Answer: D, C, A

Step-by-step explanation:

An exterior angle is an angle that is supplementary to an interior angle.

The angle between the extended side and its adjacent side is called the exterior angle so the option (D), (C), and (A) will be the correct answers.

Exterior angles become by a side of that figure and its extended adjacent side.

The exterior angle has been attached.

Since in the graph angle, ∠3 become by two extended lines but for exterior angle, there should be only one extended line which is ∠6, ∠5, and ∠2.

Hence angles ∠6, ∠5, and ∠2 will be the exterior angles.

For more information about Exterior angle

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Answer:

(1,-2)

Step-by-step explanation:

WE can see that the X value below is 1 and the Y value is -2

Answer:

10

Step-by-step explanation:

1. Find 5% of 200.

2. 5100×200.

3. =10.

4. so 5% of 200 will be 10.

Answer:

You just said the answers. 54

Step-by-step explanation:

5

Answer:

3/2

Step-by-step explanation:

find 2 points and go up til you are even with it(3 in this case) this is your rise, then go over to the other point(2 in this case) this is your run, so the slope (rise/run) is 3/2

-Todo <3

Answer:

x = 2 and x = -1/5

Step-by-step explanation:

Factors into (x-2)(5x+1) = 0 and you have your two values for x.

Or solve by quadratic formula [tex]x = \frac{-(-9) \pm \sqrt{9^{2} - 4(5)(-2)} }{2\cdot5} \\x = \frac{9 \pm 11}{10}.\\[/tex]

Two values, [tex]x = \frac{20}{10} = 2\\x = \frac{-2}{10} = -1/5[/tex]

Answer:

sum of all angle= 180 given angle = 3 X, 10 X AND 7 X

3X + 10X + 7X = 180

20X = 180

X= 180/20

X = 9

X= 9 IS apply to given angle 3X, 10 X  , 7X

3X = 3 ×9=27

10X = 10 ×9 = 90

7X = 7 ×9 =63

ANS IS 27,90,63

Step-by-step explanation:

Answer:

If they won 90 out of 162, they won 55.(5)% of their games.

Step-by-step explanation:

I assume they WON 90 of the 162 games.

90/162 = 45/81 = 15/27 = 5/9

5/9 = 55.(5)%; (because 1/9 = 11.(1)%)

Answer:

55.56%

Step-by-step explanation:

1. Put into a fraction = 90/162

2. Simplify = 5/9

3. Calculate the fractions value by dividing the numerator by the denominator.

4. Multiply the answer by 100

5. Simplify

Hopefully this helps!

Answer:

it's really hard to see the numbers.. but I can explain how to do it. the 5 is on the x axis and the 0 is on the y axis. if you from 0 to 5 on the x axis and the line crosses through that point then it is true.

Answer:

A=πr2=π·52≈78.53982m²

Step-by-step explanation:

Answer:

78.57 m^2

Step-by-step explanation:

answer is 78.57

Answer:

C≈9.42cm

Step-by-step explanation:

This is the correct answer for your question

Answer:

3.71

Step-by-step explanation:

Answer:

Step-by-step explanation:

Remark

The diagonal is found by using the Pythagorean Theorem: a^2 + b^2 = c^2. This only works for certain figures. The rectangle is one of them.

Givens

a = 10

b = 8

c = ?   This is the length of the diagonal.

Solution

a^2 + b^2 = c^2

10^2 + 8^  = c^2

100 + 64 = c^2

c^2 = 164

√c^2 = √164

c = 12.806

Given:

The given equation is

[tex]x^2-8x+16=0[/tex]

To find:

The correct statement for the given equation.

Solution:

We have,

[tex]x^2-8x+16=0[/tex]

It can be written as

[tex]x^2-2(x)(4)+(4)^2=0[/tex]

Using the identity of perfect square trinomial, we get

[tex](x-4)^2=0[/tex]            [tex][\because (a-b)^2=a^2-2ab+b^2][/tex]

[tex](x-4)=0[/tex]

[tex]x=4[/tex]

Here, x=4 has multiplicity two because the power of factor (x-4) is 2.

x=4 is a double root and the equation is a perfect trinomial.

Therefore, the correct options are C and E.

Answer:

B) Factor to solve.

C) x = 4 is a double root.

E) The equation is a perfect square trinomial.

Step-by-step explanation:

Factor to solve.<

By inspection, the equation is a perfect square trinomial.

x = 4 is a double root

By inspection, the middle term's coefficient 8 is twice the square root of 16, the constant; therefore, it is a perfect square trinomial.

x2 − 8x + 16 = 0 → (x − 4)(x − 4) = 0 → x = 4 is a double root.

Hope This Help??

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Answer:

1296 sorry if im wrong

Step-by-step explanation:

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Answer:

area of the square = (SIDE)2

=( 4)^2

= 16 answer

Answer:

Step-by-step explanation:

Answer:

The number of people who like winter season is 1000.

Step-by-step explanation:

Event event correspond to a set in the Venn diagram, and we use it to find the percentages.

I am going to say that:

Event A: Like summer season

Event B: Like winter season.

55% like summer season

This means that [tex]P(A) = 0.55[/tex]

20% like winter season

This means that [tex]P(B) = 0.2[/tex]

40% don't like both seasons

This means that 100% - 40% = 60% like at least one, which means that [tex]P(A \cup B) = 0.6[/tex]

Proportion who like both:

This is [tex]P(A \cap B)[/tex]. The measures are related by the following equation:

[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]

[tex]P(A \cap B) = P(A) + P(B) - P(A \cup B)[/tex]

Using what we have

[tex]P(A \cap B) = 0.55 + 0.2 - 0.6 = 0.15[/tex]

750 like both seasons.

This is 15% of the sample. So the total number of people is t, for which:

[tex]0.15t = 750[/tex]

[tex]t = \frac{750}{0.15}[/tex]

[tex]t = 5000[/tex]

20% like winter season

Out of 5000. So

0.2*5000 = 1000

The number of people who like winter season is 1000.

Answer:

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Answer:

sry i dont know

Step-by-step explanation:

lolz

Step-by-step explanation:

A quadrilateral is made up of four sides. This means the sum of all the side equals 43. This is given as;

(x + 7)  + (x² - 2x ) + (x +3)  + (2x - 2) = 43

x² - 2x + 4x + 8 = 43

x²  - 2x - 35 = 0

Upon solving for x by factorization;

( x - 5) ( x + 7) = 0

The values of x are; 5 and - 7

Since the side of shape cannot have a negative value, -7 is ignored.

x = 5

The length of the sides are;

- X+7 = 5 + 7 = 12

- x² - 2x = 5² - 2(5) = 25 - 10 = 15

- X+3  = 5 + 3 = 8

2x-2 = 2(5) - 2 = 10 -2 = 8

Check:

8 + 8 + 15 + 12 = 43

Answer:

15 points

Step-by-step explanation:

The start and end point of the caterpillar path are;

Start point = (-3, -4)

End point = (25, 38)

The slope of the caterpillar's path, 'm', given the 'x', and y-coordinates of two points is given by the following formula;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Therefore, m = (38 - (-4))/(25 - (-3)) = 1.5

The equation of the caterpillar's path in point and slope form is given as follows;

y - (-4) = 1.5 × (x - (-3))

y + 4 = 1.5 × (x + 3)

y + 4 = 1.5·x + 4.5

y = 1.5·x + 4.5 - 4 = 1.5·x + 0.5

y = 1.5·x + 0.5

Given that the 0.5 is added to the product of 'x' and 1.5, the points that have both integer points for 'x', and 'y' are the points that have odd number values of 'x', as follows;

(-3, -4), (-1, -1), (1, 2), (3, 5), (5, 8), (7, 11), (9, 14), (11, 17), (13, 20), (15, 23), (17, 26), (19, 29), (21, 32), (23, 35), (25, 38)

Therefore, we have 15 points counting the start and end points with integer coordinates

Answer:

64.6x

Step-by-step explanation:

if 2 quarts=1/2 galleon on the graph.

Then half of 2 quarts will be half of 1/2 galleons.

Therefore 1 quart=1/4 galleons.

Hope it helps!

Step-by-step explanation:

According to the pythagrean equation, it should be

[tex]AC^2 = AB^2 + BC^2\\[/tex]

8² = 6² + BC²

64 = 36 + BC²

BC² = 28

BC = ✓28 = 5.29