Mathematics High School

In a 3-digit number, the hundreds digit is four more than the units digit, and the tens digit is three less than the sum of the other two digits. If the sum of all three digits in the number is 17, find the free digits. Then find the number

Answers

Answer 1

Step-by-step explanation:

the number is abc

c = units digit

b = tens digit

a = hundreds digit

a = c + 4

b = (a + c) - 3

a + b + c = 17

we use the first equation in the second and get

b = (c + 4 + c) - 3 = 2c + 4 - 3 = 2c + 1

abd we use the first and the second equation more in the third and get

c + 4 + 2c + 1 + c = 17

4c = 12

c = 3

b = 2c + 1 = 2×3 + 1 = 6 + 1 = 7

a = c + 4 = 3 + 4 = 7

so, the number is

773

Related Questions

Combining functions to write a new function that models a real-world situation

Answers

The new function of T that models the real-world situation in terms of N is T = 560N + 750

How to write a new function that models the real-world situation?

The equations of the functions are given as

A = 165N + 750

B = 395N

From the question, we understand that

T = A + B

Substitute the known values in the above equation

So, we have

T = 165N + 750 + 395N

Collect the like terms in the above equation

So, we have

T = 165N + 395N + 750

Evaluate the like terms in the above equation

So, we have

T = 560N + 750

Hence, the new function of T that models the real-world situation in terms of N is T = 560N + 750

Answers

After evaluating the expression for x=0, the equation 13-6.5x = 13

⇒ 13-6.5(0)

⇒ 13 - 0

⇒ 13

How to solve an equation?

To solve linear equations, utilize the steps that are provided below.

Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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Find the missing term of each geometric sequence. It could be the geometric mean or its opposite. 2/5,||| 8/45

Answers

The missing item in the given geometric sequence is: [tex]\frac{4}{15}[/tex].

What is a geometric progression?

A geometric progression, sometimes referred to as a geometric sequence in mathematics, is a series of non-zero numbers where each term following the first is obtained by multiplying the preceding one by a constant, non-zero value known as the common ratio.

Given: [tex]\frac{2}{5}[/tex], ___, [tex]\frac{8}{45}[/tex]

Here, Let b = missing term of the geometric sequence.

By using the concept of geometric mean, we can find the missing term; geometric mean is used to find the mean, i.e., the middle term between two terms.

GM = [tex]\sqrt{(term_1)(term_2)}[/tex]

Here, b = [tex]\sqrt{\frac{2}{5}\times\frac{8}{45}}[/tex]

=> b = [tex]\sqrt{\frac{16}{25\times9}}[/tex]

=> b = [tex]\frac{4}{5\times3}=\frac{4}{15}[/tex]

Hence, The missing item in the given geometric sequence is: [tex]\frac{4}{15}[/tex].

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Solve each equation. 7+b=11(b-3)

Answers

The solution of the above equation 7 + b = 11(b - 3) is b = 4.

According to the given question.

We have a linear equation in one variable

7 + b = 11(b - 3)

Since, we have to solve the above equation for b.

As we know tha, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofore, the solution of the above equation 7 + b = 11(b - 3) is given by

7 + b = 11(b - 3)

⇒7 + b = 11b - 33 ( distributive property)

⇒ 7 = 11b - b - 33 (subtract b from both the sides)

⇒ 7 = 10b -33

⇒ 7 + 33 = 10b ( adding 33 both the sides)

⇒ 40 = 10b

⇒ 40/10 = b ( dividing by 10 both the sides)

⇒ 4 = b or b = 4

Therefore, the solution of the above equation 7 + b = 11(b - 3) is b = 4.

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who is kay floxk i so confused so help me wit this

Answers

Do you mean Kay Flock? Because they are a rapper.

https://en.m.wikipedia.org/wiki/Kay_Flock

8x²2x (1+4x) +2. determined if the simplified expression is quadratic

Answers

The quadratic expression is 64[tex]x^{4}[/tex] + 16x³ + 2.

The quadratic expression:

Any expression with the variables of the highest exponent or the expression's degree as 2 is a quadratic expression.

The given expression is 8x²2x( 1 + 4x) + 2

An expression of the form ax² + bx + c, where a ≠ 0 is called a quadratic expression.

8x²2x( 1 + 4x) + 2

Now apply the distributive property we have

8x² × 2x + 8x² × 2x × 4x + 2

16x³ + 64 [tex]x^{4}[/tex] + 2

64[tex]x^{4}[/tex] + 16x³ + 2

Therefore the quadratic expression is 64[tex]x^{4}[/tex] + 16x³ + 2.

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You roll 3 dice. What is the probability that the outcome of at least two of the dice will be less than or equal to 4 ? Explain your reasoning.

Answers

6 out of 36 or I in 6 is the probability that the outcome of at least two of the dice will be less than or equal to 4 .

In statistics, what does a probability mean?

The probability serves as a gauge for how likely an event is to occur. It gauges how likely an event is. P(E) = Number of Favorable Outcomes/Number of Total Outcomes is the formula for probability.Probability is the branch of mathematics concerning the occurrence of a random event, and four main types of probability exist: classical, empirical, subjective and axiomatic.

There are 36 possible outcomes for rolling two dice.

There are six possible ways that the two dice will land on the same number, so the probability is 6 out of 36 or I in 6.

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A telephone tree is used to send messages. the person at the top calls 2 people. each person calls 2 more people. suppose it takes 1 min to call someone. a message is relayed until the bottom row of the tree has 256 people. how long did this take? how do you know? the tree has 8 rows because each time a person calls 2 people, they call two more people.

Answers

Time taken by people in 8rows of given tree with each time a person calls 2 people and it takes 1 min to call someone is 510 minutes.

As given,

Given tree: Person at the top calls 2 people. each person calls 2 more people

Time taken by each person to call someone=1minute

Row wise

First1 +1=2

Second2+2=4

Third4+4=8

Fourth8+8=16

Fifth16+16=32

Sixth32+32=64

Seventh64+64=128

Eighth128+128=256

Total time

2 +4+8+16+32+64 +128 +256=510 minutes

Therefore, time taken by people in 8rows of given tree with each time a person calls 2 people and it takes 1 min to call someone is 510 minutes.

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A particle P moves with constant velocity v. Initially P is at the point with position vector a. t seconds later P is at the point with position vector b. Find v when:

a= 2i + 3j, b= 6i + 13j , t = 2

Answers

Answer:

correct

Step-by-step explanation:

So the acute angle between the vectors is 7.122° (3sf). Explanation: The angle θ between two vectors →A and →B is related to the modulus.

: Write in standard form
(a) 567000
..... (1 mark)

Answers

The standard form of a given number is scientific notation which is given by the form of exponents of ten and written as 5.67 ×10⁵.

What is the number system?

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

What is the standard form?

Standard form is a way of writing down in the easy form very large or very small numbers.

Let E is the standard form of a given number

E = 567000

E = 500000 + 67000 + 7000

E = 0.567 × 10⁶ = 5.67 ×10⁵

E = 5.67 × 10⁵

Hence, the standard form of a given number is 5.67 ×10⁵.

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The figure above shows a graph of a line that goes through the origin. What is the value of (k)/(h) ? (A) 4 (B) 3 (C) (4)/(3) (D) -(4)/(3) (E) "-4"

Answers

The value of (k)/(h) from the graph of a line that goes through the origin is 4.

What is a graph of a line?

A line graph joins distinct data points that generally show quantitative values across an interval. Line graphs have two axes:

The x-axis (horizontal), andThe y-axis (vertical), which are visually expressed as (x,y).

From the image attached below, the value of (h,k) as translated on the graph in the negative x and y axis shows that:

(h,k) = (-1,-4) in terms of (x,y) respectively.

However, we are to determine the value of (k)/(h):

i.e.

(k)/(h) = -4/-1

(k)/(h) = 4

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pls help will mark brainlyiest

Answers

Answer:

Step-by-step explanation:

3/5 multiplied by itself 4 times is a fraction exponent so it’s either b or c.

But C is [tex]\frac{3^{4}}{5}[/tex]. 3/5 multiplied 4 times means the bottom has a exponent too so it’s not c.

How do u write and graph an inequality for
{x | x< 7}

Answers

The inequality expression x < 7 is equivalent to the given inequality expression {x | x < 7}

How to write and graph an inequality for the inequality expression?

The inequality expression is given as

{x | x < 7}

When the braces are removed, the inequality expression becomes

x < 7

This means that x < 7 is equivalent to the given inequality expression {x | x < 7}

Next, we represent the inequality expression on a plot

See attachment for the graph of the inequality expression

Answers

Step-by-step explanation:

Step 1: Draw any angle, say ∠ABC. Step 3: Now, taking D and E as centers and with the same radius as taken in the previous step, draw two arcs to intersect each other at F. Step 4: Join B to F and extend it as a ray. This ray BF is the required angle bisector of angle ABC.

Write the specified type of proof.
Flow proof of Corollary 4.1

Answers

The Corollary 4.1 states that , the acute angles of a right triangles are complementary.

What is Corollary ?

A corollary can be defined as a theorem that follows a direct result of an another theorem. With an original theorem, a corollary can be used as a reason to proof it. There are two main corollaries which follow directly from the Triangle Angle-Sum theorem. These are defined below :

Corollary 4.1

It states that the " acute angles of the right triangle are always complementary".

Abbreviation : Acute ∠s of rt. Δ are comp.

Corollary 4.2

It states that, "there is at most only one right angle or an obtuse angle in triangle".

Flow Proof of Corollary 4.1

Given : a triangle ABC, right angled at A

To Prove: ∠B and ∠C are complimentary

Proof :

step 1 : ∠A = 90°

step 2: According to angle-sum theorem

∠A + ∠B + ∠C = 180

step 3: 90 + ∠B + ∠C = 180

step 4: ∠B + ∠C = 180 - 90

step 5: ∠B + ∠C = 90

Thus, Corollary 4.1 is proved.

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Explain the difference between finding the vertex of a function written in vertex form and finding the vertex of a function written in standard form.

Answers

The equation in the vertex form will be y = (x + b/2a)² - b²/4a² + c/a and the equation in the standard form will be ax² + bx + c = 0.

What is a quadratic equation?

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.

Convert the standard equation into a vertex form, then we have

x² + (b/a)x + (c/a) = 0

x² + (b/a)x + b²/4a² - b²/4a² + c/a = 0

(x + b/2a)² - b²/4a² + c/a = 0

Put h = - b/2a and k = - b²/4a² + c/a, where (h, k) be the vertex of the parabola. Then the equation will be

(x - h)² + k = 0

The function written in vertex form will be y = (x - h)² + k and in the standard form will be ax² + bx + c = 0.

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While shopping for books, Dominique spent $38 less than 3 times what Roberto
spent. Write an equation to represent the scenario if Dominique spent $10.

Answers

The equation to represent the scenario is 3y - 38 = 10

How to write an equation to represent the scenario?

Represent the given parameters as

x = Dominique

y = Roberto

From the question, we have

Dominique spent $38 less than 3 times what Roberto spent

This means that

x = 3y - 38

Also, Dominique spent $10

So, we have

3y - 38 = 10

Hence, the equation to represent the scenario is 3y - 38 = 10

Answers

I think I answered this already £17.2

Gimme brainlliest

Factor completely. 2x³ - 4x² 30x
A (x+3)(x - 5)
B 2x(x² - 2x - 15)
2x(x+3)(x - 5)
- 5)
D 2x(x-3)(x
-

Answers

Hi! I'm just answering questions for points.

What is the correct form of the partial fraction decomposition for the expression StartFraction 7 x + 18 Over x squared + 9 x EndFraction?

Answers

The correct form of the partial fraction decomposition for the expression 7x+18/x^2+9x is 2/x + 5/(x + 9).

What is the Fraction?

The numerator and the denominator are the two components of a fraction. The number displayed above the fractional bar is known as the numerator. As an illustration, the numerator in 6/7 is 6. Denominator: The fractional bar's lowermost number is designated as the denominator.

Here,

x ² + 9x = x (x + 9), so the partial fraction decomposition would be

(7x + 18) / (x ² + 9x) = a/x + b/(x + 9)

where a, b are some constants. To find them, multiply both sides by x ² + 9x :

7x + 18 = a (x + 9) + bx

Solve for a and b :

7x + 18 = (a + b) x + 9a

[ a + b = 7

[ 9a = 18

→ a = 2, b = 5

(7x + 18) / (x ² + 9x) = 2/x + 5/(x + 9)

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i need help solving this angle problem

Answers

Answer:

corresponding angles are equal

Step-by-step explanation:

89*=(6x+5)*

89-5=6x

84=6x

x=14

I hope I could help.

Suppose a family drives at an average rate of 60 miles an hour on the way to visit relatives and then at rate of 40 miles an hour on the way back. The return trip takes 1 hour longer than the trip there. Let D be the distance in miles the family traveled. How many hours did it take to drive there?

Answers

Answer:

3 hours

Step-by-step explanation:

[tex]speed = \frac{distance}{time} \\ 60 = \frac{d}{t} \\ d = 60t \\ \\ speed = \frac{distance}{time} \\ 40 = \frac{d}{t + 1} \\ d = 40(t + 1)[/tex]

Since;

[tex]d = 60t \: \: \: and\\ d = 40(t + 1) \\ [/tex]

Therefore;

[tex]60t = 40(t + 1) \\ 60t = 40t + 40 \\ 60t - 40t = 40 \\ 20t = 40[/tex]

Divide both sides by 20

[tex] \frac{20t}{20} = \frac{40}{20} \\ t = 2 \: hours[/tex]

Since the return trip took an hour longer to get back home an hour will be added to the time

[tex]t + 1 = 2 + 1 \\ = 3 \: hours[/tex]

Ms Smith has 10 cubes in her hand. There are 10 students in her class. They each have 10 cubes in their hands. How many cubes do they all have?
answer choices
100
110
90
125

Answers

Answer:

110

Step-by-step explanation:

if each of the 10 students have 10 cubes, that's 100, plus the 10 cubes Ms Smith has is 110

I need help asap please!

Enter the numerator and denominator of the fraction in simplest form that is equal to the decimal number shown.
0.23=

Answers

Answer:

23/99

Step-by-step explanation:

I took the test and got it right.

Hope this helps!

Which is the most accurate way to estimate 15% of 43?

Answers

Answer:

Multiply 43 x 15%

Step-by-step explanation:

Answer will be 6.45. To doublecheck yourself multiply 43 x 85% which is 36.55. Add 36.55 to 6.45 = 43

Evaluate each function for the given value of x , and write the input x and output f(x) as an ordered pair.
f(x) = (7/3)x-9 for x=3

Answers

f (3) = -2 is the output for the given input .

How can you tell whether a function is linear or not?

Looking at a function's graph will reveal if it is linear or not with the greatest ease.When a linear function is plotted on a graph, a straight line is formed. A nonlinear function is curved in some way; it does not form a straight line.

f(x)= (7/3)x- 9

Put x = 3 ⇒ 7 * 3/3 - 9

⇒ 7 - 9

⇒ -2

Therefore f (3) = -2

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b. Without calculating, use the pattern to predict the sum of the squares of the first ten terms of the Fibonacci sequence.

Answers

Answer:23

Step-by-step explanation:

because you add the two

If 7/2 meler of wire ris cut from a 2 piece of 10 meter long wire, how much wire is left?

Answers

The wire left is 16 1/2 meters.

How to calculate the fraction?

From the information 7/2 wire is cut from piece of wire that is 2 piece of 10 meters.

Therefore, the wire that will be left will be:

= (2 × 10) - 7/2

= 20 - 7/2

= 20 - 3 1/2

= 16 1/2 meter

The wire left is 16 1/2 meters.

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Express 80 as the product of its prime factors
Write the prime factors in ascending order.

Answers

Answer:

Give brainliest - the crown thingy.

2*2*2*2*5

2^4 * 5

The * is the symbol on my keyboard for the multiplication symbol.

Step-by-step explanation:

The current value of a baseball card is 80 times its original value v (in dollars). The baseball card is worth $36. Write and solve an equation to find the original value of the baseball card.

Answers

The original value of the baseball in discuss according to the task content is; $0.45.

What is the original value of the baseball card?

It follows from the word phrase given that; the current value of a baseball card is 80 times its original value v (in dollars) where the current value is; $36.

Therefore, we have; 36 = 80 × v

Divide both sides by 80;

Hence; v = 36/80 = $0.45.