What is the solution to this equation log(2x-100)=3

Answer:

y + 13 = 5(x + 2)

Step-by-step explanation:

        [tex]\sf \boxed{\bf y - y_1=m(x-x_1)}[/tex]

Slope intercept of the line : y =5x - 3

Comparing with y = mx +b , m =slope = 5

m = 5 and Point (-2 ,-13)

     y - [-13] = 5(x - [-2])

     y + 13 = 5(x + 2)

Answer:

155°

Step-by-step explanation:

z = 65° + y

y is a right angle

=> y = 90°

=> z = 65° + 90° = 155°

Answer:

2, 7.5

Step-by-step explanation:

2(2x - 1) + 7 < 13

4x - 2 + 7 < 1

4x + 5 < 13

4x < 8

x < 2

-2x + 5 ≤ -10

-2x ≤ -10 - 5

-2x ≤ -15

x ≤ -15 / -2

x ≤ 7.5

If a radioactive substance remains 80% of the initial amount then the half life of the radioactive substance is 2.5 years.

Given 80% of the initial amount of a radioactive substance remains.

If after 1 year the value or weight of the radioactive substance remains 80% means the rate of disappearing is 20% per annum.

If we clearly observe then it is forming a geometric progression and the rate is 80%.

Geometric progression will be if we assume the initial quantity be 100

is:

100,80,64,.........

we have to calculate the value of years in the value of term is 0.

the value of nth term of a geometric progression is [tex]ar^{n-1}[/tex]

so,

r is 0.8

100*[tex]0.8^{n-1}[/tex]=0

[tex]0.8^{n-1}[/tex]=0

if we calculate this we will find n-1=11

n=12

So the full life of radioactive substance is 12 and the half life will be 6 years.

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Answer:

60 points

100 - 5x

Step-by-step explanation:

If she got 8 questions wrong she missed (8 * 5) points or 40 points. This means she only got 60 points

This can be further generalized by simply subtracting the amount of questions someone got wrong by 5 from the total available points of 100

100 - 5x

The right step followed in the system to get he equations is (D). To get the system B. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution of system A.

A simultaneous equation can be defined as an equation that possesses two unknowns and one constant.

The solution to the problem can only be gotten by solving it side by side with another equation of the same format.

In conclusion, The right step followed in the system to get he equations is (D). To get the system B. The second equation in system A was replaced by the sum of that equation and the first equation multiplied by 6. The solution to system B will be the same as the solution of system A.

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Answer: 484/5

Step-by-step explanation:

For this word problem, it seems confusing with the wording but the equation would just be:

968÷10=x

solving for x, we get 484/5.

[tex]2 {x}^{5} {y}^{8} [/tex]

Step-by-step explanation:

yes

The area of a 2D form is the amount of space within its perimeter. The area of the rectangle is 12 units². Thus, the correct option is A.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

As per the given information, the graph of the rectangle can be made as shown below. It can be observed from the graph that the length of the rectangle and width of the rectangle are 4 units and 3 units, respectively. Therefore, the area of the rectangle is,

Area = 4 units × 3 units = 12 units²

Hence, the area of the rectangle is 12 units². Thus, the correct option is A.

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Answer:Shake hands when you meet someone.Make direct eye contact with the person you are speaking with.Unless the movie theater is crowded, do not sit right next to someone.Do not stand close enough to a stranger to touch arms or hips.Cover your coughs.

Step-by-step explanation:trust me

The correct answer for the given expression is 99.22.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division

The expression will be solved as:-

E = [tex]({5 -\dfrac{10}{27}})^3[/tex]

E = [tex](\dfrac{135-10}{27})^3[/tex]

E =[tex]\dfrac{125}{27}^3[/tex]

E = 99.22

Therefore the correct answer for the given expression is 99.22.

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Answer:

Step-by-step explanation:

According to the first statement, "Three years ago, Dedrick's age was a third of Francisca's age":

D - 3 = (1/3) * (F - 3)

According to the second statement, "In 13 years, Francisca's age will be twice Dedrick's age":

F + 13 = 2 * (D + 13)

Now, we have a system of two equations. We can solve these equations to find their current ages.

Step 1: Solve the first equation for D in terms of F:

D - 3 = (1/3) * (F - 3)

3D - 9 = F - 3

3D = F + 6

D = (F + 6) / 3

Step 2: Substitute the expression for D into the second equation:

F + 13 = 2 * ((F + 6) / 3 + 13)

Step 3: Solve for F:

F + 13 = 2 * ((F + 6) / 3 + 13)

F + 13 = 2 * (F + 6 + 39)

F + 13 = 2 * (F + 45)

F + 13 = 2F + 90

F - 2F = 90 - 13

-F = 77

F = -77

Step 4: Find D using the expression we found earlier:

D = (F + 6) / 3

D = (-77 + 6) / 3

D = -71 / 3

Now, we have found their ages, but we encounter a problem. Both Francisca and Dedrick's ages are coming out as negative, which is not meaningful in this context. It suggests that there might be an error in the initial information provided or in the equations derived from it.

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The volume of the air space surrounding the cone inside the cylinder is 1055.04 cm³

The volume of the air space surrounding the cone inside the cylinder is as follows:

volume of the air space = volume of cylinder - volume of a cone

volume of cylinder = πr²h

volume of cylinder = π16 × 5²

volume of cylinder = 400π

volume of the cone = 1 / 3 πr²h

volume of the cone = 1 / 3 × π × 12 × 4²

volume of the cone = 64π

Therefore,

volume of the air space = 400π - 64π

volume of the air space = 336π

volume of the air space = 1055.04 cm³

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9) Diagonals of a parallelogram bisect each other, so KN=NM. Thus, KM=13.5+13.5=27 cm

10) Opposite sides of a parallelogram are congruent, so LM=KJ=17 cm

11) Based on Question 9, MN=13.5 cm

The probability of getting at most one heads is 1/2

Let H represents Head and T represents Tail.

The sample space of two coin is:

S=(H,T),(T,T),(T,H),(H,H).

In the above sample, we have:

At most one head = 2

Total = 2

The required probability is then calculated as:

P = 2/4

Simplify

P = 1/2

Hence, the probability of getting at most one heads is 1/2

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The probability of wearing blue shirts on both days is 3/28.

Probability is the measure of the likelihood of an occurrence.

Given:

8 shirts are available out of which 3 are blue, 1 is green and 2 are white.

P(blue on Monday) = 3/8

Now, 7 shirts are left to wear on Tuesday

P(blue on Tuesday) =2/7

So,

the probability of wearing blue shirts on both days = 3/8 * 2/7 = 3/28

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Answer:

The answer will be equation

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known. The value of x is 117.8°. thus, the correct option is A.

The law of cosine helps us to know the third side of a triangle when two sides of the triangle are already known the angle opposite to the third side is given. It is given by the formula,

[tex]Cos(\theta) = \dfrac{a^2+b^2-c^2}{2ab}[/tex]

where

c is the third side of the triangle

a and b are the other two sides of the triangle,

and θ is the angle opposite to the third side, therefore, opposite to side c.

As per the law of cosine, the measure of angle x can be written as,

[tex]Cos(x) = \dfrac{12^2+5^2-15^2}{2(5)(12)}\\\\Cos(x) = \dfrac{-56}{120}\\\\x = 117.8^o[/tex]

Hence, the value of x is 117.8°. thus, the correct option is A.

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Answer:

x=67.4

Step-by-step explanation:

well sin30:1/2

So y is not 30 since 5/13 doesn’t equal 1/2

So it’s either the the third or fourth option

And x>y

So option 4 is correct

Answer:

[tex]\fbox {Perimeter = 37.92}[/tex]

Step-by-step explanation:

Finding the missing side :

⇒ Take the tan value of the listed angle

⇒ tan 60° = √3 = 6/x

⇒ x = 6/√3 × √3/√3 = 2√3 = 2(1.73) = 3.46

Solving :

⇒ Perimeter = 10 + 2(6 + 3.46)

⇒ Perimeter = 10 + 2(9.46)

⇒ Perimeter = 19 + 18.92

⇒ Perimeter = 37.92

Answer:

yes

Step-by-step explanation:

it's hard but you'll figure it out so don't worry

The amount of the investment at the end of the 10 years period if compounded quarterly is $2,649.6.

A = P(1 + r/n)^nt

= 1200(1 + 0.08/4)^(4×10)

= 1200(1 + 0.02)^40

= 1200(1.02)^40

= 1200(2.208)

= $2,649.6

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The points would you find on the graph for |x| +1 < 3 are -1, 0 and 1

The inequality is given as:

|x| + 1 < 3

Subtract 1 from both sides

|x| < 2

This means that the absolute value of x is less than 2

From the list of options, the true values are -1, 0 and 1.

Because their absolute values are less than 2

Hence, the points would you find on the graph for |x| +1 < 3 are -1, 0 and 1

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Answer:

Kathy

Step-by-step explanation:

Answers:

(a) The ledge can support the plant box. It is safe to put it there.

(b) No the density would not change.

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

Explanation for part (a)

We'll need the volume of the cube.

volume = side*side*side

volume = 13*13*13

volume = 2,197

Or you could do

volume = (side)^3

volume = (13)^3

volume = 2,197

The volume of the cube is 2,197 cubic cm. Multiply this with the density to determine its weight.

1.33*2197 = 2,922.01

The soil weighs 2,922.01 grams which is below the 2400 gram weight limit. Therefore, the ledge can support the planter.

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

Explanation for part (b)

The weight would go down if you only put in half the soil, but the density would not change regardless of how much soil is in there. Why doesn't the density change? Because the density is the amount of stuff per unit volume. The density tells us how packed in a material is. We can scale the amount of material up or down, and retain the same density.

This is based off physics concepts which are bit beyond the scope of this math course, but different materials have different densities. It's common to use a reference table to look up densities of various materials. For instance, ice is less dense than water. This is why ice floats rather than sinks. As another example, gold is more dense than iron. So 1 cubic unit of gold will weigh more compared to 1 cubic unit of iron.

Answer:

c2

Step-by-step explanation:

Answer:

a=75

b=70

c=110

d=105

e=110

f=105

Step-by-step explanation:

Answer:

1. 570 mL = 0.57 L

2. 623 cm3 = 0.000623 m3

3. 38 gal. = 608 cups

4. 585mL = 39.5624 tbsp

5. 20 fl. oz. = 120 tsp

6. 12 hrs = 720 min

Step-by-step explanation:

1. 570 mL to L

divide the volume value by 1000, 570 / 1000 = 0.57

2. 623 cm3 to m3

divide the volume value by 623/10^6 = 0.000623

3. 38 gal. to c

1 gallon is 16 cups,  

multiply the volume value by 16, 38 x 16 = 608c

4. 585mL to tbsp

for an approximate result, divide the volume value by 14.787

14.787 x 585 = 39.5624

5. 20 fl. oz. to tsp

multiply the volume value by 6, 20 x 6 = 120

6. 12 hrs to min

1 hour is 60 minutes

multiply the time value by 60

12 x 60 = 720