What is :

(49^x)(7^x^2)=2401^2

Answers

Answer 1

Answer: $(49^x)(7 ^(x^2))=2401^2 \n \n( (7^2)^x)(7 ^(x^2))= (7^4) ^2 \n \n 7 ^(2x)\cdot 7^(x^2)=7^(8) \n \n 7 ^(2x+x^2) =7^(8) \n \n2x+x^2 =8$

$x^2-2x-8 = 0\n \n a=1, \ b=-2, \ c=-8 \n \n\Delta =b^2-4ac = (-2)^2 -4\cdot1\cdot (-8) = 4 +32 =36 \n \nx_(1)=(-b-√(\Delta) )/(2a)=(2-√(36))/(2 )=( 2-6)/(2)=(-4)/(2)=-2 \n \nx_(2)=(-b+√(\Delta) )/(2a)=(2+√(36))/(2 )=( 2+6)/(2)=(8)/(2)= 4 \n \nAnswer: \ x=-2 \ \ or \ \ x=4$

Answer 2

Answer: $(49^x)(7^(x^2))=2401^2\n \n7^(2x) \cdot7^(x^2)=(7^4)^2\n \n7^(2x+x^2)=7^8\ \ \ \Leftrightarrow\ \ \ 2x+x^2=8\ \ \ \Leftrightarrow\ \ \ x^2+2x-8=0\n \nx^2-2x+4x-8=0\ \ \ \Leftrightarrow\ \ \ x(x-2)+4(x-2)=0\n \n(x-2)(x+4)=0\ \ \ \Leftrightarrow\ \ \ ( x-2=0\ \ \ \vee\ \ \ x+4=0)\n.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=2\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-4$

Related Questions

How to solve for 4d-7=25/4
some one plz help What is the difference? 1/6 - 5/8 a. -19/24 b - 11/24 c. 11/24 d. 2
The area of triangle AED is 20 square meters. Find the area of parallelogram ABCD.20 square meters52 square meters15 square meters104 square metersdiagram below.
20 pointsA large amount of peanuts was divided equally into 6 small bags. The total number of peanuts, p, was 342. Whichstatements can be used to write an expression and then find the number of peanuts that ended up in each bag?Check all that apply.The operation is division.The operation is multiplication.The variable is the number of bags.342 divided by 6 equals 57.Write the division expression as a fraction,To evaluate, substitute 342 for the variable.Each bag will have 57 peanuts.The constant is 342.
Please answer as soon as possible

On a vacation to Puerto Rico Rose jumped off a cliff into a river in Elion forest preserve her height as a function of time to be modeled by the function HFT equal 16 T squared +16 T +480 where T is the time after jumping in seconds and H is the height in feet how many seconds it take Rose to hit the water round your answer to the nearest hundredth

Answers

To solve for t, you will use the equation given: -16t^2 + 16t + 480 = 0. First, simplify the equation by dividing everything by 16: -t^2 + t + 30 = 0. Then complete reverse FOIL: (-t + 6)(t + 5) = 0. Next, set each of these equations to 0 separately, and solve for t. You will get t = 6, and t = -5. Since time can't be negative (Rose can't have hit the water after a negative number of seconds), the answer is 6.

Translate the verbal phrase into an inequality. All real numbers that are greater than or equal to -1.5 and less than 9.2

Answers

Answer: -1.5 ≤ x < 9.2

Step-by-step explanation:

Hi, to answer this question we have to analyze the information given:

"All real numbers": we will use the variable x to represent all the real numbers.

"All real numbers that are greater than or equal to -1.5". This means that x is greater or equal (≤) to the number 1.5.

"And less than 9.2": less is represented with the symbol <

Mathematically speaking:

-1.5 ≤ x < 9.2

Feel free to ask for more if needed or if you did not understand something.

4 is because it is greater and less than

Find the measure of each exterior angle for a regular hexagon. Round to the nearest tenth if necessary.

Answers

The measure of each exterior angle for a regular hexagon is 60⁰.

What is Hexagon?

A hexagon is a six-sided polygon or 6-gon. The total of the internal angles of any simple hexagon is 720°.

In a regular Hexagon, all sides are same size and measure of all interior angles are same.

The sum of interior angles of hexagon is (n−2)×180⁰

where n is number of sides of polygon. (6−2)×180⁰ = 720⁰.

here n=6 because hexa means 6

Each interior angle =720⁰/6=120⁰

As we know that the sum of interior and exterior angles is 180⁰

Exterior angle + interior angle =180⁰

Exterior angle +120⁰ = 180⁰

Exterior angle =180⁰−120⁰ = 60⁰

Thus, the measure of each exterior angle for a regular hexagon is 60⁰.

Learn more about Hexagon from:

brainly.com/question/14338151

#SPJ2

Sum of exterior angles: 360 degreesNumber of sides: 6Formula to find the measure of each exterior angle for a regular hexagon:360/n (n=number of sides)So: 360/660So yeah, you are right. The measure of each ext. angle for a regular hexagon is 60 degrees.

The diagram shows 2 wheels of radii 15 cm and 24 cm. Their centres, H and K, are 41 cm apart. ( Refer to the attatchment given )Help me find the lengthof the belt by providing workings. Thanks!

Answers

Hello,

$1) \ncos(\widehat{HKR})= (9)/(41) ==\ \textgreater \ \widehat{HKR}=1.34948188...rad\n\nsin(\widehat{KHR})= (9)/(41) ==\ \textgreater \ \widehat{KHR}=0,22131444...rad\n\n$

$\widehat{QKA}=\pi-1,34948188...=1,792110769...rad\n\n$\overset{\frown}{QA}$=24*1,792110769...=43,010658459...\n\n\widehat{KHB}= (\pi)/(2)-0,22131444...=1,3494888...\n\n$\overset{\frown}{PB}$=15*1,3494888...=20,2422282\n\n$

2)
$|HR|=√(9^2+41^2) =41,976183723\n\n$

length=2*(43,010658459+20,2422282+41,976183723)=210,458140764

A pencil box and a notebook together cost $6.28 the notebook cost $0.70 more than the pencil box . How much does the notebook cost?

Answers

The cost of notebook is $3.49.

What is a word problem?

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Let the cost of pencil box be x

Let the cost of notebook be y

Total cost = $6.28

⇒ $x+y = 6.28 ----- (1)$