1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
PSYCHO15rus [73]
3 years ago
11

4. solve e) 4^x-10.2^x+16=0 I think the dot means multiply?

Mathematics
2 answers:
suter [353]3 years ago
6 0
4^x-10\cdot2^x+16=0\Rightarrow(2^2)^x-10\cdot2^x+16=0\Rightarrow(2^x)^2-10\cdot2^x+16=0

subtitute\ 2^x=t > 0\\\\t^2-10t+16=0\\t^2-2t-8t+16=0\\t(t-2)-8(t-2)=0\\(t-2)(t-8)=0\iff t-2=0\ or\ t-8=0\\\\t=2\ or\ t=8\\\\t=2^1\ or\ t=2^3\\\\therefore\ 2^x=2^1\ or\ 2^x=2^3\\\\Answer:\boxed{x=1\ or\ x=3}
zubka84 [21]3 years ago
3 0
2^x=a
4^x=(2^2)^x=(2^x)^2=a^2

a^2-10a+16=0
Δ=10^2-4*1*16=100-64=36
√Δ=6
a1=(10+6)/2=16/2=8
a2=(10-6)/2=4/2=2
2^x=8=2^3⇒ x=3 or
2^x=2=2^1⇒ x=1


There are 2 solutions : x=1 or x=3
You might be interested in
What is the solution to the system of equations?
Brrunno [24]

Answer:

(8 - 12 )

Step-by-step explanation:

Given

\frac{1}{4} x - \frac{1}{2} y = 8

\frac{1}{2} x + \frac{3}{4} y = - 5

Multiply both equations through by 4 to clear the fractions

x - 2y = 32 → (1)

2x + 3y = - 20 → (2)

Multiplying (1) by - 2 and adding to (2) will eliminate the x- term

- 2x + 4y = - 64 → (3)

Add (2) and (3) term by term to eliminate x

0 + 7y = - 84

7y = - 84 ( divide both sides by 7 )

y = - 12

Substitute y = - 12 into either of the 2 equations and solve for x

Substituting into (1)

x - 2(- 12) = 32

x + 24 = 32 ( subtract 24 from both sides )

x = 8

solution is (8, - 12 )

5 0
2 years ago
Identify the type of data (qualitative/quantitative) and the level of measurement for the following variable. Explain your choic
AleksAgata [21]

Answer:

Option  C. Quantitative, because numerical values, found by either measuring or counting, are used to describe the data.              

Step-by-step explanation:

We are given the following in the question:

Variable: Final exam scores (from 0 to 100) for graduating high school seniors.

The following variable is a quantitative variable.

Quantitative variable:

  • Their values are expressed in numerical.
  • They are either measured or counted.
  • Descriptive terms are not used to describe them.
  • They can either be continuous or discrete.

Since final scores have numerical values and are counted, they are quantitative variables.

Option  C. Quantitative, because numerical values, found by either measuring or counting, are used to describe the data.

Level of measurement:

A score of zero means no true existence for score. That is true zero exist.

Thus, it is ratio because difference between the values in data can be compared meaningful and they have a true zero.

7 0
3 years ago
What is the length of the diagonal d, of the rectangular prism shown below? Round to nearest tenth
babymother [125]

Answer:

5

Step-by-step explanation:

The diagonal is the length which is 5

solution

5 to the nearest tenth is 6

3 0
2 years ago
The ratio of Monarch butterflies to Queen butterflies at a butterfly farm was 5:2. If there are no additional butterflies at the
andrew-mc [135]
So we know if there are 5 groups/dozens of Monarch butterflies, there are 2 groups/dozens of Queen butterflies. In other words, there are 5 Monarch butterflies for every 2 Queen butterflies.

Then we can turn that into an equation.

5x = m \\ \\ 2x =q \\ \\ 5x + 2x = m + q
From the last equation we wrote we can see that the total number of butterflies in the farm is 7x.

When we compare the Queen butterflies to total butterflies, we get \frac{q}{m + q} = \frac{2x}{5x + 2x} = \frac{2x}{7x} = \frac{2}{7}

The ratio of Queen butterflies to total butterflies is 2:7.
7 0
2 years ago
2w+w^3-1/2w^2 for w=2
mars1129 [50]

The required value is 8

How can we find value?

We will find the value by putting the value of w in the given function to get the required value.

We can find the value of given function foe w=2 as shown below:

Given, function is 2w+w^3-1/2w^2

Let A=2w+w^3-1/2w^2

for w=2

A=2(2)+(2)^3-1/2(2)^2

= 2+8-1/2(4)

=2+8-2

=8

Hence, the required value is 8.

Learn more about function here:

brainly.com/question/875118

#SPJ1

8 0
1 year ago
Other questions:
  • Plesae help ASAP this question give you 80 points!!!!
    6·2 answers
  • -5 is greater than or equal to -2; add 7 to both sides
    13·1 answer
  • I NEED HELP ASAP!!!!
    11·2 answers
  • In the right triangle shown, AC = BC = 7? What is AB?
    15·2 answers
  • Find the least common multiple of 5 10 and 15
    8·1 answer
  • Fabiano wants to score at least 6 . 5 6.5 points in a major chess tournament. He scores 1 1 point for each game that he wins, an
    8·1 answer
  • How many inches are in 4 feet 3 inches?
    6·2 answers
  • A hiking trail down the side of Mt. Tom drops a vertical distance of 60 meters over a horizontal distance of 300 meters. What is
    10·1 answer
  • Math question angles
    5·1 answer
  • can someone please help me with this, I did it and I got 54 the answer, but 54 isn't an answer choice​
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!