The exponential function g, whose graph is given below, can be written as g(x)=a•b^x

Answer:

BC=[tex]\sqrt{95}[/tex]

Angle A (or BAC)=54.31466...

Angle C (or ACB)=35.68533...

Step-by-step explanation:

[tex]\frac{7}{\sin \left(\angle \:ACB\right)}=\frac{12}{\sin \left(90\right)}[/tex]

[tex]BC=\sqrt{12^2-7^2}[/tex]

[tex]\sqrt{12^2-7^2}=\sqrt{95}[/tex]

[tex]\frac{\sqrt{95}}{\sin \left(\angle \:BAC\right)}=\frac{12}{\sin \left(90\right)}\quad :\quad \angle \:BAC=54.31466[/tex]

[tex]\frac{7}{\sin \left(\angle \:ACB\right)}=\frac{12}{\sin \left(90\right)}\quad :\quad \angle \:ACB=35.68533[/tex]

Using the pythagorean theorem

[tex]AC^2=AB^2+BC^2\\BC=\sqrt{AC^2-AB^2}\\BC=\sqrt{12^2-7^2}\\BC=\sqrt{144-49}\\BC=\sqrt{95}[/tex]

[tex]sin A=\frac{BC}{AC}=\frac{\sqrt{95} }{12}\\A = sin^{-1}(\frac{\sqrt{95} }{12})\\A = 54.31[/tex]

[tex]A + C = 90\\C = 90-A\\C= 90- 54.31\\C = 35.69[/tex]

Answer:

Yes.

Step-by-step explanation:

Yes . This would be an isosceles triangle (2 angles being 9 units long.

Answer:

36

Step-by-step explanation:

ƒ(x) = 5x^2 − 9x + 18,

Let x=3

ƒ(3) = 5*3^2 − 9*3 + 18,

      =5*9 - 27+18

        45 - 27+18

         36

Answer: 1. infinitely many solutions

2. no solution

3. one solution

4. no solution

5. infinitely many solutions

Step-by-step explanation:

1. infinitely many solutions - when it is consistent and the number of variables is more than the number of nonzero rows

2. no solution - would mean that there is no answer to the equation. It is impossible for the equation to be true no matter what value we assign to the variable.

3. one solution - which is when one variable equals one number

4. no solution

5. infinitely many solutions

Answer:

work is pictured and shown

An expression to represent the given verbal expression is,

⇒ 100x + 8

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The verbal expression is,

''Eight more than the product of a number and 100.''

Let an number = x

So, We can formulate;

⇒ Eight more than the product of a number and 100.

⇒ 8 + x × 100

⇒ 8 + 100x

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The decimal value is 0.85 which can be used as the multiplier to find the new cost of the shoes if the pair of shoes is going to be discounted by 15%,

It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.

We have:

If a pair of shoes is going to be discounted by 15%

Let's suppose the original cost is 100%

It has a discount of 15%

So the new cost of the shoes = 100 - 15 = 85%

To convert it to decimal divide it by 100

= 85/100

= 0.85

Thus, the decimal value is 0.85 which can be used as the multiplier to find the new cost of the shoes if the pair of shoes is going to be discounted by 15%,

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Answer:

Step-by-step explanation:

Let the first three terms be a/r, a, ar... where a is the first term and r is the common ratio of the geometric sequence.

If the sum of the first two term is 24, then a/r + a = 24...(1)

and the sum of the first three terms is 26.. then a/r+a+ar = 26...(2)

Substtituting equation 1 into 2 we have;

24+ar = 26

ar = 2

a = 2/r ...(3)

Substituting a = 2/r into equation 1 will give;

(2/r))/r+2/r = 24

2/r²+2/r = 24

(2+2r)/r² = 24

2+2r = 24r²

1+r = 12r²

12r²-r-1 = 0

12r²-4r+3r -1 = 0

4r(3r-1)+1(3r-1) = 0

(4r+1)(3r-1) = 0

r = -1/4 0r 1/3

Since a= 2/r then a = 2/(-1/4)or  a = 2/(1/3)

a = -8 or 6

All the geometric sequence can be found by simply knowing the formula for heir nth term. nth term of  a geometric sequence is expressed as

if r = -1/4 and a = -8

Tn = -8(-1/4)^(n-1)

if r = 1/3 and a = 6

Tn = 6(1/3)^(n-1)

The nth term of the sequence above can be used to find all the geometric sequence where n is the number of terms

Answer:

There are none

Step-by-step explanation:

Because 1/8 = 0.125

Just divide 1 over 8

The number of 3's in  the given fraction number 1/8 is, Zero

Fraction is a mathematical term, which represents the portion or sub-parts of the whole thing. Basically, It has two parts: numerator and denominator.

Numerator is a number which lies on the top side, it indicates the number of equal parts taken and denominator is on the bottom side, it indicates the equal parts of the whole number.

Given that,

A fraction number, 1/8

The number of 3's = ?

⇒ 1/8 = 0.125

There is no number 3 present in the result of this division

Hence, the number of 3's  is Zero

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Answer:

2

Step-by-step explanation:

Add the students that take math and physics and subtract the ones that take both so that they are not double counted

65+43-10 =98

There are 100 students

100-98 =2

There are 2 that take neither math nor physics

Answer:

-3

Step-by-step explanation:

[tex]f(x)=-2x^3+x^2-2 \\\\f(1)=-2(1)^3+(1)^2-2= \\\\-2+1-2=\\\\-3[/tex]

Hope this helps!

Answer:

y = -8x - 5 ; function form is y = mx+b

Step-by-step explanation:

15 + 3y = -24x

3y + -24x - 15

y = -8x - 5

Answer:

so the answer is f, the last one

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

Explanation:

Think of x^4y as x^4y^1. When we raise this to the third power, we multiply the outer exponent 3 by each inner exponent

x^4 turns into x^12

y^1 turns into y^3

-----------

This is one way to show your work

(x^4y)^3

(x^4y^1)^3

x^(4*3)*y^(1*3) ... multiplying outer exponent by each inner exponent

x^12y^3

-----------

A more lengthy way to get the answer is to write x^4y out three times multiplying by itself that many times. The outer exponent 3 tells us we will have three copies of x^4y multiplied with itself.

(x^4y)^3 = (x^4y)*(x^4y)*(x^4y)

(x^4y)^3 = (x^4*x^4*x^4)*(y*y*y)

(x^4y)^3 = ( x^(4+4+4) ) * ( y^(1+1+1) )

(x^4y)^3 = x^12y^3

Answer:

(B) (22.5, -12.5)

Step-by-step explanation:

When the point [tex](9,-5)[/tex] is dilated by with a scale factor of 2.5

In a dilation, when its scale factor is less than 1, the pre-image will be lesser than the image.

However, when the scale factor is greater than 1, the pre-image will be greater than the image.

The Image of the dilation of [tex](9,-5)[/tex] with a scale factor of 2.5 is therefore:

[tex](9*2.5,-5*2,5)\\=(22.5, -12.5)[/tex]

The correct option is B.

Answer:

m<B = 44

Step-by-step explanation:

Since AB is a diameter, then angle C is a right angle.

That makes angles A and B complementary angles.

m<A + m<B = 90

46 + m<B = 90

m<B = 44

Answer:

B = 44

Step-by-step explanation:

The sum of the angles of a triangle is 180

A + B+ C = 180

<C = 90 since it is 1/2 of the intercepted arc which is 180

46+ B + 90 = 180

136 + B = 180

B = 180-136

B =44

Answer:

80.93

Step-by-step explanation:

15.40×7=107.80

188.73-107.80=80.93

Answer:

-1

Step-by-step explanation:

4u-5v=23

-2(2u+4v=16) We multiply by -2 here to destroy u's.

4u-5v=23

-4u-8v=16 we addition both processes

-13v=39 so, v=-3

4u-5(-3)=23, 4u=8 so, u=2

u+v= -3+2= -1

Answer:

3

Step-by-step explanation:

2x=2+4

2x=6

x=3

#RAVEN

Answer:

a) 17, 29, 41, 53, 65....

b) 12n + 5

Answer:

x=29

Step-by-step explanation:

isolate x, and multiply the 29 by -1

Answer:

Samuel : x

wife : y

sum of their age : 2+ x : 10

Answer:

8 nickels and 18 dimes

Step-by-step explanation:

Make a system of equations:

n + d = 26

5n +10d = 220

Solve by elimination by multiplying the top equation by -5. This gives you:

-5n -5d = -130

5n +10d = 220

Then solve to get 5d= 90, then d= 18.

Then plug 18 for d in the equation n + d= 26, so n + 18= 26

n= 8

Answer:

This shape is a rectangle so that means that the angles are 90°. From sum of angles of a triangle, x + 3x + 10 + 90 = 180 which means 4x + 100 = 180 → 4x = 80 → x = 20°.

Answer:

C

Step-by-step explanation:

Both A and B are true identities.

See attachment.

Answer: $J/3 + $5

Step-by-step explanation:

Here is the complete question:

Angela shared a cab with her friends. When they arrived at their destination, they evenly divided the $j fare among the 3 of them. Angela also paid a $5 tip. How much did Angela pay in total?

Write your answer as an expression.

Answer:

From the question, we are told that Angela shared a cab with her friends and when they arrived at their destination, they shared equally the $j fare among the 3 of them while Angela also paid a $5 tip.

The total number of friends are =3

The amount of fare = $ J

The fare is equally divided among the friends, therefore each friend will pay: $J/3

Angela paid $5 additional as a tip, therefore, her share will be: J/3 + 5

Therefore, Angela will pay $J/3 + $5

Answer:

4.06451 hours

note this answer is not rounded as you did not indicate round to what decimal values.

Step-by-step explanation:

Solving using equation

500 ≤ 248 + 62x

500-248 ≤  62x

252 ≤  62x

252/62 ≤  x

4.06451 ≤  x

Another way to solve

500-248= 252

she needs to travel 252 miles

speed = 62mph

note: speed =  distance/time

therefore time= distance/speed

time = 252/62 = 4.06451

Number of hours Sierra needs to travel to meet her goal is 4.065 hours.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Sierra wants to drive at least 500 miles today.

She has already driven 248 miles.

Remaining distance is driving at a constant speed of 62 miles per hour.

Let the time needed for the remaining distance to complete is x.

Speed = Distance / Time

Distance = Speed × Time

Distance = 62x

Total distance covered = 248 + 62x

This must be at least 500.

248 + 62x ≥ 500

62x ≥ 500 - 248

62x ≥ 252

x ≥ 252 / 62

x ≥ 4.065

Hence Sierra has to drive at least 4.065 hours to meet her goal.

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Answer:

9.46 ft

Step-by-step explanation:

Law of sines

10/sin(90)=x/sin(71)

x=(sin(71)*10)/sin(90)

x=9.46

Answer:

irrational

Step-by-step explanation:

Answer:

It is an irrational number.

Step-by-step explanation:

Whole numbers are numbers that include all natural numbers, (1 - infinity), and 0. Integers are numbers that can be written without fractional components. Rational numbers are numbers that can be written in the form P/Q, where p and q are integers. There only leaves irrational numbers.