An exponential function f(x)= ab^x passes through the points (0,10) and (3,1250). What are the values of a and b?

a = I know it’s 10
b = ?

Answer:

[tex]\boxed{x=24}[/tex]

Step-by-step explanation:

[tex]\displaystyle \frac{x}{32} =\frac{15}{20}[/tex]

[tex]\sf Cross \ multiply.[/tex]

[tex]20 \times x=32 \times 15[/tex]

[tex]20x=480[/tex]

[tex]\sf Divide \ both \ sides \ by \ 20.[/tex]

[tex]\displaystyle \frac{20x}{20} =\frac{480}{20}[/tex]

[tex]x=24[/tex]

Answer: x = 24

Step-by-step explanation: To solve for x in the given proportion, we use the means-extremes property.

The product of the extremes, (x)(20),

equals the product of the means, (32)(15).

So we have (x)(20) or 20x equals (32)(15) or 480.

So we have 20x = 480.

Dividing both sides by 20, x = 24.

Answer:

  15 liters

Step-by-step explanation:

Let v represent the number of liters of 10% solution to be mixed with 5 liters of a 50% solution to obtain a 20% solution. The amount of salt in the final solution is ...

  0.10x +0.50(5) = 0.20(x+5)

  1.5 = 0.10x . . . . . simplify, subtract 1+0.10x

  15 = x . . . . . . . . . multiply by 10

15 liters of 10% solution must be added.

Answer:

[tex]\huge\boxed{r = 4.8\ cm}[/tex]

Step-by-step explanation:

Since it's a hemisphere, the volume will be:

Volume of Hemisphere = [tex]\frac{2}{3} \pi r^3[/tex]

Given that Volume of hemisphere = 230 cm³

230 = [tex]\frac{2}{3} \pi r^3[/tex]

Multiplying both sides by 3

230 * 3 = 2πr³

690 = 2πr³

Dividing both sides by 2π

690 / 2π = r³

r³ = 109.8

Taking cube root on both sides

r = 4.8 cm

Answer:

[tex]\large \boxed{\mathrm{4.79 \ cm}}[/tex]

Step-by-step explanation:

The volume of a hemisphere is half the volume of a sphere.

The formula for the volume of hemisphere is V = 2/3πr³.

The volume is given.

230 = 2/3πr³

Solve for r or radius.

Multiply both sides by 3/2.

230 × 3/2 = 2/3πr³ × 3/2

345 = πr³

Divide both sides by π.

(345)/π = (πr³)/π

109.816910733 = r³

Take the cube root of both sides.

∛(109.816910733) = ∛(r³)

4.78876002459 = r

Answer:

-40

Step-by-step explanation:

8i* 5i

40 i^2

We know that i^2 = -1

40 *-1

-40

Answer:

-40

I hope this helps. i had the same question and it was right

====================================================

Explanation:

With any parallelogram, the adjacent angles always add to 180 degrees.

(angle ADC) + (angle DCB) = 180

(angle ADC) + 120 = 180

angle ADC = 180 - 120

angle ADC = 60 degrees

--------

Angles 1 and 2 combine to form angle ADC by the angle addition postulate. This is just the idea of gluing smaller angles to form larger ones.

(angle 1) + (angle 2) = angle ADC

45 + (angle 2) = 60

angle 2 = 60-45

angle 2 = 15 degrees

The Range of f(x) → Range ∈ [- 4, ∞).

We have a graph of a function f(x) given.

We have to determine the range of f(x).

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes.

According to the question -

We can see that the function is defined for all values of x (assuming that the graph will continue after the arrows at the top). Hence, the domain of f(x) will be set of all real numbers.

Now, the graph curves back after reaching a minimum value of  -4. Therefore, the set of all possible values f(x) takes belongs to the set

[-4, ∞).

Hence, the Range of f(x) → Range ∈ [- 4, ∞)

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Option 4 is correct, Teresita worked 15 hours during the second week.

Given that Teresita worked [tex]1\frac{1}{2}[/tex]  times the number of hours during the second week.

Therefore, she worked 1.5x hours during the second week.

The total number of hours she worked during the two weeks is given as 25.

So we can set up the equation:

x + 1.5x = 25

Combining like terms, we have:

2.5x = 25

Dividing both sides of the equation by 2.5, we get:

x = 25/2.5

x = 10

Therefore, Teresita worked 10 hours during the first week.

To find the number of hours she worked during the second week, we can substitute this value back into the equation:

1.5x = 1.5 × 10

= 15

Therefore, Teresita worked 15 hours during the second week.

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Answer:

T≥2

Step-by-step explanation:

3t+9≥15

3T≥15-9

3T≥6

T≥2

Answer:

t ≥ 2

t ∈ [2 ; +oo)

Step-by-step explanation:

3t + 9 ≥ 15

3t ≥ 15 - 9

3t ≥ 6

t ≥ 6 : 3

t ≥ 2

t ∈ [2 ; +oo)

Answer:

256 in²

Step-by-step explanation:

Answer:

256 inches squared

Step-by-step explanation:

You find the area of all of the area on the sides and then add them

Answer:

x=4      or    x= - 16

Step-by-step explanation:

|x+6|

Now subtract 7 which equals to 3.

|x+6|-7=3

|x+6|=10

Now remove the mode by adding plus minus sign in the front of 10.

x+6=±10

x+6=10 or x+6=-10

x=4      or x=-16

Answer:

The equivalent expression to this equation is -30x⁸4y⁶

Step-by-step explanation:

For this expression, we have to multiply the terms. We can do this by following the order of operations.

(-3x³y²)(5x⁵y⁴)2

First, we have to multiply -3x³y² and 5x⁵y⁴ together.

(-15x⁸2y⁶)2

Now, we  multiply these terms together.

-30x⁸4y⁶

So, the expression that is equivalent to this equation is -30x⁸4y⁶

Answer:

Step-by-step explanation:

Step-by-step explanation:

The shoes are bought for $60 and were 40% off which means $60 is 60% of the original price

if 60% = $60 the 100% = $100 (the price of the shoe before discount).

Answer:

❁ 25% ❁

Explanation:

❁ The answer would be 25% ❁

Answer:

x^ -10

Step-by-step explanation:

x^2 * x ^ -12

We know that a^b * a^c = a^ (b+c)

x^2 * x^-12

x^(2+-12)

x^ -10

Answer:

[tex]\frac{1}{x^{10}}[/tex]

Step-by-step explanation:

The two "x" terms are being multiplied, so combine the terms

Subtract the power signs:

[tex]x^2 * x^-12[/tex] = [tex]x^2/x^{12}[/tex]

[tex]x^(2 - 12)[/tex] = [tex]x^-10[/tex]

[tex]x^-10[/tex] = [tex]\frac{1}{x^{10}}[/tex]

[tex]\frac{1}{x^{10}}[/tex] is your answer.

~

Answer:

-9x + y = 43

Step-by-step explanation:

We can put the equation into y = mx + b form first, then change it to Ax + By = C

First, we can find the slope by doing rise/run (y2 - y1) / (x2 - x1)

(-2 - 7) / (-5 + 4)

-9/-1 = 9

We can put this into the equation y = mx + b, along with another point, to find b:

y = mx + b

7 = 9(-4) + b

7 = -36 + b

43 = b

Now, we know the equation will be y = 9x + 43, and we can rearrange this:

Subtract 9x from both sides:

-9x + y = 43 will be the equation of the line

Answer:

A is A=25

B=10

B is 40

C is A=10

B=6.428

hope i helped you

sorry if it is incorrect

Answer:

-2+12=10

-10+20=10

1+9=10

9+1=10

8-(-2)=10

2-(-8)=10

-30+40=10

Step-by-step explanation:

Answer:

The radius is 1/6 m

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

1/162 * pi = 4/3 pi r^3

Divide each side by pi

1/162  = 4/3 r^3

Multiply each side by 3/4

3/4 *1/162  =3/4* 4/3 r^3

1/216 = r^3

Take the cube root of each side

(1/216)^ 1/3 = (r^3)^1/3

1/6 = r

The radius is 1/6 m

Answer:

Perimeter of the shaded region= 22/7cm

Area = 36.48 cm²

Step-by-step explanation:

First of all for the perimeter.

The radius of the arc is 8cm

At an angle of 90°

Perimeter of of the shape is perimeter of the the 2 arc

The both arc are equal so let's determine the perimeter of one first.

Perimeter of the arc= 2πr*(90/360)

Perimeter of the arc= 2*22/7*1/4

Perimeter of the arc= 11/7 cm

Perimeter of the shades region= 2*11/7

Perimeter of the shaded region= 22/7cm

Area of the sector = πr²*(90/360)

Area of the sector= 50.24cm²

Area of non sector= 64-50.24

= 13.76

But non sector is two

Area of non sector= 2*13.76

= 27.52

Area of the shaded region = area of the square -(area of non sector)

= 64-27.52

= 36.48 cm²

Answer:

x = 18

Step-by-step explanation:

Because the 2 lines are parallel we can use same side interior theorem to find  x

This would mean the equation is 6x + 30 + 2x + 6 = 180

When you solve that this would be 18

Answer:

x = 18

Step-by-step explanation:

→ Utilise the fact that interior angles add up to 180

6x + 30 + 2x + 6 = 180

→ Simplify

8x + 36 = 180

→ Minus 36 from both sides to isolate 8x

8x = 144

→ Divide both sides by 8 to isolate x

x = 18

Answer:

Hope it helps this is an isosceles triangle

Answer: 8 hours

Step-by-step explanation:

Let x be the time before they meet ( in hours)

Speed of Sam = 12 mph

Sped of Fred = 9 mph

Distance = Speed × time

Distance covered by Sam in x hours = 12x

Distance covered by Fred in x hours = 9x

                                               (Distance)     (rate1) (time1)          (rate2) (time2)  

Total distance between them: 168             =     12      x        +      9    x

[tex]\Rightarrow\ 168= 21x\\\\\Rightarrow\ x=\dfrac{168}{21}=8[/tex]

Hence,  the number of hours before they meet if Sam runs 12 mph and Fred runs 9 mph. = 8

So "MATHCOUNTS" has 10 letters.

And "MATH" has 4 letters.

So the probability of you getting the letters "M" "A" "T" "H" is 4/10 or 2/5.

But it has to be in order...

There are 32 ways you can arrange the 4 letters. There is only 1 way you can write "MATH"

So 1/32 probability of 2/5 is 2/160 or 1/80

The probability of getting the word MATH is 1/80

The study of likeliness of an event to happen is probability .

It is given that

Total letters in MATHCOUNTS : 10 letters.

Total chances of getting letter M , A , T , H  is  4

Probability of getting the letters M , A , T , H is 4/10

= 2 /5

The probability of getting the word MATH is 1

And the total number of ways the letters can be arranged is 2⁴

= 32

The probability of getting the word MATH is

= 1 /32 * 2 /5

=1/80

Therefore , The probability of getting the word MATH is 1/80

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Answer:

-399/17

Step-by-step explanation:

D+26/-17=-25

D=-25-(-26/17)

D=-25+26/17

D=-425/17+26/17

D=-399/17

Answer:

Step-by-step explanation:

Area of a rectangle = l × w

where

l is the length

w is the width

From the question

Area = 6052 m²

width = 68 m

To find the length substitute the values into the above formula

6052 = 68l

Divide both sides by 68

We have the final answer as

Hope this helps you

Answer:

6

Step-by-step explanation:

We first want to rewrite it and make the square roots into power of 1/2 as its is easier in most cases to work with.

We will first solve for a^2 because it appears twice

3+2×2^1/2

3+2.828=5.828427

Now we will solve 1/a^2

1/5.828427=.171572

.171572+5.828427

now you add them and it equals 6.

Answer:

1) 4^3

2) x^6 + 2

Step-by-step explanation:

1) 4 is the main number.

Then, however many fours there are is the exponent

( there are 3 fours )

2) x is the main variable

Then however many x's there are, that number will be your exponent

( there are 6 x's )

Answer:

Step-by-step explanation:

1) 4 ∙ 4 ∙ 4 is equivalent to 4^3:  4 is the base and 3 is the final exponent of this base.

2)  x ∙ x ∙ x ∙ x ∙ x ∙ x + 2 * needs clarification.  What do you mean by "  2 * ?"

x ∙ x ∙ x ∙ x ∙ x ∙ x + 2 *  could be rewritten as x ∙ x ∙ x ∙ x ∙ x ∙ x      +      2, which is equivalent to x^6 + 2.  If you're still interested in solving this problem, please double check to ensure that you have copied it down correctly.  Thank you.

The answer is D because then triangles DEF and ABC would map onto one another

Triangle is a plane figure with three straight sides and three angles.

The answer is D because then triangles DEF and ABC would map onto one another.

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Answer:

a) ◇G = ◇H - T◇S wiĺl be negative.

b) It will be a spontaneous reaction.  

Explanation:

As ◇H is less than 0 and T◇S is greater than 0 so if we put it in the equation we would get the negative maximum result. And when the energies are with negative sign they are said to be spontaneous.

Answer:

3 quarts.

Step-by-step explanation:

The wall is 20 feet by 15 feet. That means the area of the wall is 20 * 15 = 300 feet squared. Since one quart of paint covers 100 square feet, they will need to purchase 300 / 100 = 3 quarts of paint.

Hope this helps!