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3 years ago

Consider the function , f(x)=4x-5 what is the domain value that correspond to an output of f(x) = 11

Mathematics

1 answer:

kati45 [8]3 years ago

6 0

Answer:

x = 4

Step-by-step explanation:

given f(x) = 11 then equate f(x) = 11 and solve for x

4x - 5 = 11 ( add 5 to both sides )

4x = 16 ( divide both sides by 4 )

x = 4 ← value of x in the domain

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a sequence of numbers begins at 400. If the pattern increases by consecutive multiples of 5 starting with 5, then find the next

bazaltina [42]

Given :

A sequence of numbers begins at 400.

To Find :

If the pattern increases by consecutive multiples of 5 starting with 5, then find the next 3 numbers in the sequence 400, ___, ___, ___ .

Solution :

This is the a question of arithmetic progression .

The first term is , a = 400 .

Now , it is given that the next numbers increase by the multiples of 5 starting with 5 .

So , common difference is , d = 5 .

Now , we know , $n^{th}$ number in A.P is given by :

$a_n=a+(n-1)d$

Putting value of n = 2 , 3 , 4 .

We get :

$a_2=a+(2-1)d=400+5=405\\\\a_3=a+(3-1)d = 400 + (5\times 2) = 410\\\\a_4=a+(4-1)d = 400 +(5\times 3)=415$

Therefore , the next 3 numbers in the sequence is 400 , 405 , 410 , 415 .

Hence , this is the required solution .

8 0

3 years ago

If 9x is an odd integer, represent the next odd integer as the algebraic expression in x.

Luba_88 [7]

Any odd integer can be expressed as 2n+1, for some integer n.

The next odd integer, after 2n+1, is 2n+1+2=2n+3

thus 9x=2n+1, means that 9x-1=2n, so n=(9x-1)/2

the next odd number after 2n+1 is 2n+3= 2* (9x-1)/2+3=9x-1+3=9x+2

Remark : this result could also have been found directly.

Answer: 9x+2

8 0

3 years ago

20 POINTS! Please help

Marysya12 [62]

The complete square will be $(x-3)^{2}$ = 3

Step-by-step explanation:

Given,

$2x^{2} -12x+12=0$

or, $x^{2} -6x+6=0$ [ by eliminating 2 from both the sides]

To make it square

$x^{2} -6x+6=0$

or, $x^{2} -2xX3+9-9+6=0$ [ $(a+b)^{2}=a^{2} +2ab+b^{2}$

or, $(x-3)^{2}$ = 9-6

or, $(x-3)^{2}$ = 3

Hence the correct option is B

3 0

3 years ago

What theorem states that if two sides and the included angle of one triangle are congruent to the corresponding parts of another

lianna [129]

The given statement is proved by side-angle-side (SAS) theorem.

Yes, if two sides and the included angle of one triangle are congruent to the corresponding parts of another triangle the triangles are congruent.

The statement is proved by SAS theorem

<u>Side-Angle-Side (SAS) theorem: </u>

The triangles are congruent if two sides and the included angle of one triangle are equivalent to two sides and the included angle of another triangle.

Hence, The given statement is proved by side-angle-side (SAS) theorem.

To read more about Angles

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7 0

1 year ago

Please help thank you

Gemiola [76]

Question 1:

This is a 45-45-90 right triangle. If the leg length is $x$ , then the hypotenuse length will be $x \sqrt{2}$ .

The leg length of this 45-45-90 right triangle is 8. Multiply that with the square root of 2. You get $8 \sqrt{2}$ . Thus, the last choice is your answer.

Question 2:

This triangle can be identified as a 30-60-90 right triangle.
Let's say the smallest leg as a length of $x$ .
Then, the longer leg will have a length of $x \sqrt{3}$ .
Also, the hypotenuse will have a length of $2x$

This triangle follows this format, making it a 30-60-90 right triangle. Thus, the angles are 30, 60, and 90.

Hope this helps! :)

5 0

3 years ago