The ones digit is 2 less than the tens digit, and the sum of this number and its reversed number is 154.

Answer:

x<6

Step-by-step explanation:

2x/3<4

2x<12

x<6

Answer:

x < 6

Step-by-step explanation:

[tex]\frac{2x}{3}[/tex] < 4 ( multiply both sides by 3 to clear the fraction )

2x < 12 ( divide both sides by 2 )

x < 6

The probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.

Given: Randomly, a positive integer divisor of 12! is selected.

Prime factorization of 12! = 2¹⁰ × 3⁵ × 5² × 7¹ × 11

Total divisors of 12! = 11 × 6 × 3 × 2 × 2

The probability that the divisor chosen is a perfect square is given as:

(6 × 3 × 2)/(11 × 6 × 3 × 2 × 2)

= 1/22

=m/n

Therefore, the probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.

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Answer:I think $1064

Step-by-step explanation:

First you multiply 1/5 by 420 and then add, so 1/5 x 420 = 84 & 420 + 84 = 504. Then you multiply 1/3 by 420 and also add, so 1/3 x 420 = 140 & 420 + 140 = 560. After you add both totals to get your final answer, so 504 + 560 = 1064. Her income each month is $1064.

The measure of the angle ACB is 87°.

Angles produced by two beams are included in the plane that contains the rays. The intersection of two planes may also produce an angle. Dihedral angles are the name given to them. It is also possible to determine the angle between two crossing curves using the angle created by the rays that are perpendicular to each intersecting curve at that point.

An angle can also refer to a measurement of a rotation or an angle. This number represents the length-to-radius ratio of a circular arc.

When two crossing lines in a plane are not perpendicular to one another, Euclid defined a plane angle as the inclination between those intersecting lines.

In triangle ADE and triangle ACB, the triangles are similar.

So,

∠AED/ ∠ABC = ∠DAE/∠CAB

∠AED = ∠ABC

11x-2 = 6x + 13

11x - 6x = 13 + 2

5x = 15

x = 15/5

x = 3

So, the measure of angle ABC is

∠ ABC = 6(3)+13

∠ ABC = 18+13

∠ ABC  = 31°

Now, consider triangle ABC, the sum of all angles = 180°

So, 62° + 31° + ∠ACB = 180°

∠ACB + 93° = 180°

∠ACB =  180° - 93°

∠ACB = 87°

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The expression of the inequality is [tex]9 < 2x\le45[/tex]. It can be obtained using the operations of inequality.

What is inequality?

In matmathematics if two numbers are not equal even then there is a relationship. This relationship can be defined by inequality relationship.

According to the pharase, 9 is less than two times a number. Hence, consider the number is x and its two times means 2x. Now, 9 should be less than this number. Hence, 9<2x. Now, again the number 2x is not more than 45. Means, it can be equal to 45. Hence, it will give the expression [tex]2x\le45[/tex].

Now, combine the two expressions as follows:

9<2x

[tex]2x\le45[/tex]

[tex]9 < 2x\le45[/tex]

Hence, the expression of the inequality is [tex]9 < 2x\le45[/tex].

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Answer: (0,-2)

Step-by-step explanation: just multiply

Answer:

x=145 at 8 minutes

im not sure what tt means but please read my note at the end.

Step-by-step explanation:

if the initial temp is 65 and it increases at a rate of 10 per min the use

65+10(x)

let x be the number of minutes

65+10(8)

65 +80= 145

after 8 minutes the oven will be at 15 degrees. im not sure what tt is suppose to mean, but to find any other solution just plug it into x multiply x by 10 and add it to 65

The coordinate of image of P is (-6,-4)

What in math is a coordinate?

a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).

P (-2,2)
Translation (x,y)=(x-4,y-6)
x= -2
y= 2
x-4= -6
y-6= -4
Hence the coordinate of image of p is (-6,-4)

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Answer:

5/12

6/15

10/18

Step-by-step explanation:

Answer:

6x^2+17x+12

Step-by-step explanation:

(3x+4) * (2x+3)

3x * 2x = 6x^2

3x * 3 = 9x

+4 * 2x = +8x

+4 * +3 = +12

6x^2+ 9x+8x +12

Simplify:
6x^2+17x+12

Answer:

y = 2.60 (to 3sf)

Step-by-step explanation:

Since x is directly proportional to y², then x = ky², where k is a constant.

When x = 4, y = 3,

 4 = k(3)²

 4 = 9k

9k = 4

∴[tex]k =\frac{4}{9}[/tex]

∴ When x = 3,

[tex]\frac{4}{9}y^{2} = 3[/tex]

∴y = 2.60 (to 3sf)

Using the formula of simple interest, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.

In the given question,

The given principal amount = Rs 3000

The given time = 5 years

Interest amount = 525

Now finding the rate of interest.

As we know that the formula of simple interest.

I = P*R*T/100

525 = 3000*R*5/100

Multiply by 100 on both side we get

52500 = 15000*R

Divide by 15000 on both side

R = 52500/15000

R = 3.5

In the question we have to find the interest on Rs 2200 for 6 years at the same rate of interest.​

To find the interest put the value in I = P*R*T/100

As given P=2200, R=3.5%, T=6 years

I = P*R*T/100

I = 2200*3.5*6/100

I = 462

Hence, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.

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Using population growth modeling it is concluded that the population of insects after 1 hour will be about 1.05 times.

The method used to calculate the growth and decay of insects or bacteria are called growth and decay modeling.

Let us assume n₀ is the initial population, then the total population n(t) after t time is given by the formula:

n(t) = n₀ [tex]e^{rt}[/tex], where r = the relative rate of growth.

Suppose an initial number of insects is x and after 15 hours it becomes 2x.

2x = x[tex]e^{15r}[/tex]

[tex]e^{15r}[/tex] = 2

Take the log of both sides of the equation

ln [tex]e^{15r}[/tex]= ln 2

15r = ln 2

r = 0.693147/15

Now, population after 1-hour = x [tex]e^{r}[/tex]

= 1.047

≈ 1.05

Hence the population of insects after 1 hour will be about 1.05 times.

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The simplified answer is 8i-15.

What do you mean by iota?

Iota is a mathematical concept that is represented by the symbol i and has the value of [tex]i^{2}=-1[/tex] , or i =[tex]\sqrt{-1}[/tex] . It is an imaginary unit number that is denoted by i. You could have run into instances when the discriminant is negative while attempting to solve quadratic equations.

According to the given question,

We have: [tex](4i+1)^{2}[/tex]

Now, we will solving this by formula,

[tex](a+b)^{2}=a^{2} +b^{2}+2ab[/tex]

Putting the values in it,

[tex](4i+1)^{2}=(4i)^{2}+1^{2}+2(4i)(1)\\=16i^{2} +1+8i\\ =16(-1)+8i+1\\=8i-16+1\\=8i-15[/tex]

Therefore, the required answer is 8i-15.

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The amount that Omar will pay when he bought 3.5k of onions are 8.90 per kilo is $31.15.

From the information given, Omah wants to know the total amount that he will pay for the onions. It's important to know the cost for each kilogram of onion and then multiply it but the number of kilograms that are bought.

In this case, Omar bought 3.5k of onions are 8.90 per kilo.

The amount that Omar will pay for the onions will be:

= Number of kilograms × Cost per kg

= 3.5 × 8.90

= $31.15

In conclusion, the amount is $31.15.

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The skydiver falls a distance of 36 feet after 1.5 seconds.

Now, we have:

To calculate distance:

Therefore, the skydiver falls a distance of 36 feet after 1.5 seconds.

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Value of  [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.

What do you mean by algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.

There are 3 main types of algebraic expressions which include:

Monomial Expression

Binomial Expression

Polynomial Expression

An algebraic expression which is having only one term is known as a monomial.

Given expression:

a + 4/a = 4

We need to simplify the above expression and will find the value of a.

[tex]a+\frac{4}{a}=4[/tex]

⇒ [tex]\frac{a^2+4}{a}=4[/tex]

⇒ [tex]a^{2}+4=4a[/tex]

⇒ [tex]a^2-4a+4=0[/tex]

⇒ [tex]a^2-2a-2a+4=0[/tex]

⇒ a(a-2) -2(a-2) = 0

⇒ (a-2)(a-2) = 0

⇒ a = 2

Now, substitute this value of a in expression , [tex]a^5-\frac{1}{a^5}[/tex]

[tex]2^5-\frac{1}{2^5}[/tex]

= 32 - 1/32

= [tex]\frac{1024-1}{32} =1023/32 = 31.97[/tex]

Therefore, value of  [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.

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The loan amount at the end of 2 years is Rs. 12,127 .

In the given question we have, amount Rs. 11500 is borrowed by investor at the interest rate of 6% per annum.

compund interest is defined as the addition of interest to the principal of loan.

principal (P) = 11500

If interest is compunded quarterly then time(t) = 3 years = 12 , rate ( r%) = 6/4% = 2/3 %

Using the formula of Amount ,

Amount = P( 1 + r / 100) ᵗ

= 11500( 1 + 2/ 300)⁸

= 12127.83 ~ 12128

compound interest = Amount - principal =

12128- 11500 = Rs. 628

So, An investor has to pay total Rs. 12128 at the end of 2- year.

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Answer:

5 - [tex]\frac{40}{5}[/tex] = 5 - 8 = -3

Step-by-step explanation:

The first mistake made by the student is in Step A where the problem was not copied down correctly.

Answer:

20

Step-by-step explanation:

do parenthesis first

1/5(3+2+ 5)² =

1/5(10)² =

then exponent

1/5(10)² =

1/5(100) =

20

The vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the parabola is open downwards

From the given parabola

The vertex of the parabola is at (-2, 2)

The vertex of the parabola is defined as the the point at the intersection of the parabola and its line of symmetry.

The line of symmetry is at x = -2

The parabola is open downwards

Hence, the vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the given parabola is open downwards

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Answer: [tex]x=13, y=132[/tex]

Step-by-step explanation:

Using the same-side interior angles theorem, [tex]y=132[/tex].

Using the alternate interior angles theorem, [tex]5x-17=48 \implies x=13[/tex]

Answer:

48cm = 480mm

Step-by-step explanation:

1cm = 10mm

48cm = 48 X 10 mm

48cm = 480mm

Answer:

480mm

When converting from cm to mm, multiply by 10.

48 x 10 = 480

Step-by-step explanation:

the answer is Y=-1/2×+5

Explanation:

You put the gradient in M for Y=M×+C (substitute) then you substitute the coordinates it has given you into the X and Y part of linear equation. (x,y)

The following are the equations which matches the given word problems:

a. Skate rental charges an additional $3 :

y = x+3

b. Jeff is 3 years less than Tony's age:

y=x-3

c. Marie buys balloons for a party that are $3.00 each:

y = 3x

Given, we have the word problems:

a. Skate rental charges an additional $3 :

here, based on the fixed charge, additional charge is taken as $3.

let the total charge be represented as y and

x represent the fixed charge,

hence the equation we get is:

y = x+3

b. Jeff is 3 years less than Tony's age.

let y represent the age of Jeff

and x represent the age of Tony.

hence we frame the equation as:

y = x - 3

c. Marie buys balloons for a party that are $3.00 each:

let the cost of the balloon be represented as y

and x represent the number of balloons Marie wants to buy for $3 each.

hence the equation we frame is:

y = 3x

Hence we get the required equations.

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Miners excavated 1000 tons of dirt, and they found 8.892 ounces of gold.

Let X stand for the random variable determining how much gold is discovered for every 1,000 tonnes of dirt dug up. After that, we learn that:

X ~ N (12, 3²)

Let K be the required amount of discovered gold. 15% of the time, less than K worth of gold is discovered. Next, we have:

P (X ≤ K) = 0.15

When we transform this into a typical normal variable, we get:

P [Z ≤ (K - 12) / 3] = 0.15

From the common normal tables, we can deduce:

P (Z ≤ -1.036) = 0.15

Comparing the two equations above, we obtain:

(K - 12) / 3 = -1.036

K = 12 - (1.036 * 3) = 12 - 3.108 = 8.892

As a result, 8.892 ounces of gold are needed.

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The missing angle is as follows:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

In other words, two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal.

Therefore, the triangle ABC is congruent to EDF.

Hence,

∠A = ∠D

∠B = E

∠C = ∠F

Therefore,

m∠C = x

m∠F = 2x - 30

Hence,

m∠C = m∠F

x = 2x - 30

x - 2x = -30

-x = -30

x = 30

m∠C = 30 degrees

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Answer:

negative, as the points are slowly making their way "down" the graph :)