see screenshot below​

See Screenshot Below

Answers

Answer 1

Answer:

A&D

Step-by-step explanation:

we want to solve the following equation for x:

[tex] \displaystyle ( {2}^{x} - 3) ({2}^{x} - 4) = 0[/tex]

to do so let [tex]2^x[/tex] be u and transform the equation:

[tex] \displaystyle (u - 3) (u - 4) = 0[/tex]

By Zero product property we obtain:

[tex] \displaystyle \begin{cases}u - 3 = 0\\ u - 4= 0 \end{cases}[/tex]

Solve the equation for u which yields:

[tex] \displaystyle \begin{cases}u = 3\\ u = 4 \end{cases}[/tex]

substitute back:

[tex] \displaystyle \begin{cases} {2}^{x} = 3\\ {2}^{x} = 4 \end{cases}[/tex]

take logarithm of Base 2 in both sides of the both equations:

[tex] \displaystyle \begin{cases} \log_{2} {2}^{x} = \log_{2} 3\\ \log_{2} {2}^{x} = \log_{2} 4 \end{cases}[/tex]

hence,

[tex] \displaystyle \begin{cases} x_{1} = \log_{2} 3\\ x_{2} = 2 \end{cases}[/tex]

Answer 2

Answer:

( A ) and ( D )

Step-by-step explanation:

( 2^x -3 ) ( [tex]2^x -4[/tex] ) = 0

When the the product of factors equals 0, atleast one factor is 0.

[tex]2^x [/tex]- 3 = 0

2^x - 4 = 0

Solve for x.

[tex]2^x [/tex]- 3 = 0 , [tex]2^x -4[/tex]

x = [tex]log_2[/tex] (3) , x = 2

The equation has two solutions;

[tex]x_1[/tex] = [tex]log_2[/tex] (3) , [tex]x_2[/tex] = 2.


Related Questions

There were 99 tulips in the field. Only 3/9 bloomed. How many tulips bloomed? How many did not bloom?

Answers

Answer: 33 tulips bloomed / 66 tulips did not bloom

Step-by-step explanation:

Given:

Total number of tulips = 99

Total number of tulips bloomed = 3/9 of total

Solve:

Step One: Find the number of tulips that bloomed

99 × (3/9) = 99 × (1/3) = 33 tulips

Step Two: Find the number of tulips that did not bloom

99 - 33 = 66 tulips

Hope this helps!! :)

Please let me know if you have any questions

Omggg guys please help me find those two boxes

Answers

Answer:

Both boxes are -20.25

Step-by-step explanation:

The y-value for the vertex is when you plug in the x-value of the vertex in. The vertex is at (2.5, -20.25). SInce the vertex is the lowest or highest point on a parabola, the range is y>=-20.25.

What is the inverse of the function f(x) = 2x + 1?|
Oh(x) =
Oh(x) -
12 12
2 1212
Oh(x) =
1
-X-2
2
Oh(x) =
(8) 글 +2

Answers

Answer:

1st option

Step-by-step explanation:

let y = f(x) and rearrange making x the subject

y = 2x + 1 ( subtract 1 from both sides )

y - 1 = 2x ( divide both sides by 2 )

[tex]\frac{y-1}{2}[/tex] = x

Change y back into terms of x with x being the inverse h(x)

h(x) = [tex]\frac{x-1}{2}[/tex] = [tex]\frac{1}{2}[/tex] x - [tex]\frac{1}{2}[/tex]

A car insurance company has determined that 9% of all drivers were involved in a car accident last year. Among the 10 drivers living on one particular street, 3 were involved in a car accident last year. If 10 drivers are randomly selected, what is the probability of getting 3 or more who were involved in a car accident last year?

Answers

Answer:

The correct answer: 0.05404

Step-by-step explanation:

Given:

Binomial distribution = x

n = 10

and p = 0.09

solution:

P(X=x) =1 0Cx*(0.09^x)*((1-0.09)^(10-x)) for x=0,1,2,...,10

So the probability is calculated by the Formula:

P(X>=3) = 1-P(X=0)-P(X=1)-P(X=2)

putting the given values in the formula

= 1-10C0*(0.09^0)*((1-0.09)^(10-0))-...-10C2*(0.09^2)*((1-0.09)^(10-2))

= 0.0540400

Thus, the correct answer: 0.05404

help me plsssssssssssss

Answers

Answer:

bro the co ordinates are in the picture itself

Answer:

A'(-3,0) ; B'(0,0); C'(3,6) ; D'(-3,6)

Step-by-step explanation:

O(-6,-6)

A( -5 , -4)  = A( -6+1 , -6 + 2)

A'(-6+3 ,-6+6) = A'(-3,0)

B(-4,-4) = B(-6+2 , -6+2)

B'(-6+6,-6+6)= B'(0,0)

C(-3,-2) = C(-6+3, -6+4)

C'(-6+9 , -6+12) = C'(3,6)

D(-5 , -2) = D(-6+1 , -6 +4)

D'(-6+3, -6+12)=D'(-3,6)

A startled antelope started running and covered 1,110 feet in 15 seconds. What was the antelope’s speed, in feet per second, during this short burst

Answers

Answer:

74 feet per second

Step-by-step explanation:

Divide 1,110 by 15 to get 74, which is how many feet the antelope ran per second in its short burst.

Hope this helps!

can i gets help with this 2x^2 – 9x + 2 = –1

Answers

answer should be x=4.137

The places X and Y are 76km apart on a highway one car starts from Y and other from X at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of two cars?​

Answers

Answer:

Fast car = 45.6

Slower car = 30.4

Step-by-step explanation:

Let the speed of the first car = x

Let the speed of the second car = y

Travelling towards each other.

x *1 + y*1  = 76 miles

x*5 - y*5 = 76 miles. This is kind of tricky. You have to understand that the first car that is 76 miles from the second car and makes up that 76 in 5 hours. The distance they both travel is subtracted out.

Divide by 5

x - y = 76/5

x - y = 15.2       The speeds differ by 15.2

x + y = 76

x - y  = 15.2

2x = 91.2

x = 45.6

y = 76 - 45.6 = 30.4

When the two vehicles speeds are multiplied by 5, the difference is 76 km

Please find attached herewith the solution of your question.

If you have any query, feel free to ask.

3. Given the graph below, determine whether each statement is true or false.

Answers

Answers:

TrueTrueTrueFalseFalse

======================================

Explanation:

In this context, a zero is another term for x intercept or root. This is where the graph either touches or crosses the x axis. This occurs in three locations: x = -3, x = 2, and x = 0. So those are the three roots. That makes the first three statements true, while the remaining two others are false.

Side note: x = 0 doesn't always have to be involved. Its quite possible to have x = 0 not be an x intercept. The term "zero" is a bit misleading in that regard. I prefer either "root" or "x intercept" instead.

PLEASE HELP!! i dont understand it

Answers

Answer:

 a.  y^ -1 = e^x    +2

Step-by-step explanation:

y = ln (x-2)

Exchange x and y

x = ln (y-2)

Solve for y

Raise each side with a base of e

e^ x = e^(ln(y-2)

e^x = y-2

Add 2 to each side

e^x  +2 =y

1. In the figure below, PU = 12, VT = 5, and VQ = 6. Which of the following is FALSE?

Answers

Answer:

for 1 its a and for 2 its c...

50 points. Please explain each step​

Answers

Sin[tex]\theta_{1}=\frac{3\sqrt{21}}{17}[/tex]

Solution given:

Cos[tex]\theta_{1}=\frac{10}{17}[/tex]

[tex]\frac{adjacent}{hypotenuse}=\frac{10}{17}[/tex]

equating corresponding value

we get

adjacent=10

hypotenuse=17

perpendicular=x

now

by using Pythagoras law

Hypotenuse ²=perpendicular²+adjacent ²

substituting value

17²=x²+10²

17²-10²=x²

x²=17²-10²

x²=189

doing square root

[tex]\sqrt{x²}=\sqrt{189}[/tex]

x=[tex]3\sqrt{21}[/tex]

now

In I Quadrant sin angle is positive

Sin[tex]\theta_{1}=\frac{perpendicular}{hypotenuse}[/tex]

Sin[tex]\theta_{1}=\frac{3\sqrt{21}}{17}[/tex]

Answer:

sin theta = 3 sqrt(21)/17

Step-by-step explanation:

cos theta = adj / hyp

We can find the opp by using the Pythagorean theorem

adj^2 + opp ^2 = hyp^2

10^2 +opp^2 = 17^2

100 + opp^2 = 289

opp^2 = 289-100

opp^2 = 189

Taking the square root

opp = sqrt(189)

opp = 3 sqrt(21)

Since we are in the first quad, opp is positive

sin theta = opp /hyp

sin theta = 3 sqrt(21)/17

Corine needs 4 pieces
each a foot long to make one
friendship bracelet. She has a total of 144 inches of string. How many friendship bracelets can Corina make?
[?]friendship bracelets

Answers

Answer:

Corina can make 3 friendship bracelets.

Step-by-step explanation:

Solve for how much string is needed for one friendship bracelet:

4 pieces × 1 foot

4 feet

Convert feet into inches (1 foot = 12 inches):

4 feet × 12 inches

48 inches

Divide the total string by each bracelet's string:

144 inches ÷ 48 inches

3 friendship bracelets

Answer:лаксдкннйд

Step-by-step explanation:

I need helppppppppppppppppppppppppppppppppppppppppppppp nowwwwwwwwwwwwwwww i am desperate

Answers

Answer:   14  2/3

This is the same as saying [tex]14\frac{2}{3}[/tex] which is the mixed number 14 and 2/3

whole part = 14

fractional part = 2/3

==================================================

Explanation:

To find the volume of a prism, we multiply the base area by the height.

The base area is shown in green as 7  1/3 square units.

This multiplies with the height 2 to get

2*(7  1/3) = 2*(7 + 1/3) = 2*(7) + 2*(1/3) = 14 + 2/3 = 14   2/3

As alternative notation, you can write  14  2/3  as 14 & 2/3.

Or you could write [tex]14 \frac{2}{3}[/tex]. Keep in mind that this does not mean 14 times 2/3.

Identify the dependent variable: the time it takes to make rag dolls for a mission in Africa and the number of people working on the dolls the distance travelled while walking and the time taken the cost of an end of year grade 9 party and the number of people attending

Answers

Answer:

The time it takes to make rag dolls for a mission in Africa.

The time taken.

The cost of an end year party.

Step-by-step explanation:

The dependent variable refers to the variable which is predicted or measured in an experiment , the value of the dependent variable relies on the variation in the independent or predictor variable.

The time it takes to make rag dolls for a mission in Africa and the number of people working on the dolls ;

DEPENDENT VARIABLE = The time it takes to make rag dolls for a mission in AFRICA. This is because time taken will depend on the number of people working.

The distance travelled while walking and the time taken ;

DEPENDENT VARIABLE = THE time taken

The time taken will depend on distance traveled.

The cost of an end of year grade 9 party and the number of people attending ;

DEPENDENT VARIABLE = The cost of an end year party.

Cost of partybwill depend on the number of people attending.

Which is enough information to prove that U|| V?

Answers

Answer:

∠4 = ∠8

Step-by-step explanation:

the lines are parallel if a pair of corresponding angles are congruent

HELPPPPP
A geometric series has three terms. The sum of the three terms is 42. The third term is 3.2 times the sum of the other two. What are the terms?

Answer is : 2,8, and 32
Please show steps because I'm very confused

Answers

Let x be the first term in the geometric sequence. Then the next two terms in the sequence are xr and xr ², where r is some constant. (This is the defining characteristic of geometric sequences.)

The sum of the first three terms is 42, so

x + xr + xr ² = 42

x (1 + r + r ²) = 42

The third term is 3.2 times the sum of the other two, so that

xr ² = 3.2 (x + xr )

Solve the second equation for r :

xr ² = 3.2 x (1 + r )

We can divide both sides by x since x ≠ 0. (This is obvious, since if x was zero, then all three terms in the sequence would be 0.)

r ² = 3.2 (1 + r )

r ² = 3.2 + 3.2r

r ² - 3.2r - 3.2 = 0

r ² - 16/5 r - 16/5 = 0

5r ² - 16r - 16 = 0

(5r + 4) (r - 4) = 0

==>   r = -4/5 or r = 4

Since there are two possible values of r that might work, there are two possible sequences that meet the criteria.

Plug either of these solutions into the first equation:

r = -4/5   ==>   x (1 + (-4/5) + (-4/5)²) = 42

… … … … … …   21/25 x = 42

… … … … … …   x = 50

r = 4   ==>   x (1 + 4 + 4²) = 42

… … … … …  21x = 42

… … … … …  x = 2

Then the two possible answers would be

• if r = -4/5, then the three terms are {50, -40, 32}

• if r = 4, then they are {2, 8, 32}

Answer:

Step-by-step explanation:

A geometric series means that we multiply one number by a common ratio to get the second number. Let's say our first number is x, and our common ratio is y. We can write the first term is x, and to get the second number, we multiply x by our common ratio, y. For example, if 5 was the first number and 2 was the common ratio, the second number would be 5*2 = 10, and the third would be 10 * 2 = 20.

For our question, the first number is x, the second is x*y, and the third is x*y*y = x*y²

The sum of these three terms is 42, so we can say

x + x*y + x*y² = 42

Next, the third term is equal to 3.2 times the sum of the other two. First, we have 3.2 times something. That something is the sum of the other two, so we must prioritize calculating the sum of the first two numbers, and then multiply that by 3.2 to get the third. We can write this as

(x + x*y) * 3.2 = x*y²

factor out x

x * 3.2(1 +y) = x*y²

divide both sides by x

3.2(1+y) = y²

expand

3.2 + 3.2y = y²

subtract (3.2 + 3.2y) from both sides to make this a quadratic equation

y²-3.2y-3.2 = 0

use the quadratic formula to solve for y  (note that +- here stands for "plus or minus")

[tex]y = \frac{-(-3.2) +- \sqrt{3.2^{2}-4(-3.2)(1)} }{2} \\= \frac{3.2+-\sqrt{10.24+12.8} }{2} \\= \frac{3.2+- 4.8}{2}[/tex]

=  -0.8 or 4

With these two possibilities, we can try each in our other equation to see what works.

x + x*y + x*y² = 42

for y = -0.8

x + -0.8x + 0.64x = 42

x - 0.16x = 42

0.84x = 42

multiply both sides by 1/0.84 to isolate the x

x=50

This works, with x (the first number) =50, the second number being 50 * -0.8 = -40, and the third being -40 * -0.8 = 32. 50+(-40) = 10, 10*3.2=32, and 50-40+32 = 42

Next, for y=4, we have

x+4x + 16x= 42

21x = 42

divide both sides by 21 to isolate the x

This works as well, with x=2, the second value being 2*4 = 8, and the third value being 8*4 =32. 2+8=10, 10*3.2 = 32, and 2+8+32 = 42

please help me out i need this answer very fast! 20points!!!!
Graph the system of equations on graph paper to answer the question.

{y=2/5x+4
y=2x+12



What is the solution for this system of equations?

Enter your answer in the boxes.

Answers

Answer: X=-19/5 Y=22/5

please help me with this problem !

Answers

Answer:

a you cant add if they are not the same denominator

Answer:

Finding the least common denominator

[tex]Answer: A[/tex]

------------------------

Hope it helps...

Have a great day!!

Consider functions p and q.

On which interval are both functions increasing?
(See Below)

Answers

Answer:

(-2, 3)

Step-by-step explanation:

Function given in the graph 'p' is increasing from x = -2 to x = ∞.

Another function 'q' represented by the equation is,

q(x) = -|x - 3| + 4

By using graphing utility, graph of the function will be as shown in the attachment.

Graph of the function 'q' will be increasing from x = -∞ to x = 3

Therefore, common domain in which both the function are increasing is (-2, 3)

Answer:

(-2, 3)

Step-by-step explanation:

PLATOO

Find the value of z such that 0.04 of the area lies to the left of z. Round your answer to two decimal places.

Answers

Answer: The value of z is -1.75.

Step-by-step explanation:

Given: P(Z<z)=0.04

To find the value of z such that 0.04 of the area lies to the left of z.

We will use z-score table to get the value of z here.

IN z-score table, we have

For P(Z<-1.7507)=0.04

Hence, the value of z is -1.7507.

Its approximate value is -1.75

So the final answer is z=-1.75.

Five years ago, Victor was twice as old as his daughter Anika. In 10 years, the sum of their ages will equal 90. Find their ages now.

Answers

Answer: 45 and 25

Step-by-step explanation:

Given

Five years ago victor was twice as old as his daughter

Suppose the current age of victor and his daughter are x and y

For five years ago

[tex]\Rightarrow (y-5)=2(x-5)\\\Rightarrow y-5=2x-10\\\Rightarrow y=2x-5\\\Rightarrow 2x-y=5\quad \ldots(i)[/tex]

In 10 years sum of their ages is 90

[tex]\Rightarrow (y+10)+(x+10)=90\\\Rightarrow x+y=70\quad \ldots(ii)[/tex]

On solving (i) and (ii) we get

[tex]\Rightarrow x=25,y=45[/tex]

So, the current age of victor is 45 and his daughter is 25

Answer:

45 , 25

Step-by-step explanation:

if x=(a+4 and y=(a-4),show that xy=a square -16 ​

Answers

(a+4) (a-4)

according to formula,

x square - y square : (x+y) (x-y)

(a+4) (a-4)

xy : a square - 4

Using a secant and a tangent, find angle WVT.

Answers

Answer:

[tex]m\angle WVT=40^{\circ}[/tex]

Step-by-step explanation:

When two secants or a secant and a tangent of a circle intersect outside the circle, the measure of the acute angle formed is equal to half of the positive difference of smaller and larger arc formed.

Therefore, we have the equation:

[tex]m\angle WVT=\frac{1}{2}(\widehat{TW}-\widehat{UW}),\\3x+4=\frac{1}{2}(14x+7-(7x+11))[/tex]

Distribute:

[tex]3x+4=\frac{1}{2}(14x+7-7x-11),\\\\3x+4=\frac{1}{2}(7x-4),\\\\3x+4=3.5x-2[/tex]

Add 2 to both sides and subtract [tex]3x[/tex] from both sides:

[tex]6=0.5x[/tex]

Divide both sides by 1/2:

[tex]x=\frac{6}{\frac{1}{2}}=6\cdot 2=12[/tex]

Now substitute [tex]x=12[/tex] into [tex]3x+4[/tex]:

[tex]m\angle WVT=3(12)+4,\\m\angle WVT=36+4,\\m\angle WVT=\boxed{40^{\circ}}[/tex]

2x times -y or (2x)(-y)

Answers

Answer:

(2x)(-y)

Step-by-step explanation:

Both are technically correct, but (2x)(-y) is more professional. You can also say 2x * -y.

Hope this helps!

ugh ,, im stuck again :( someone please explain this !!!

Answers

Answer:

63cm²

Step-by-step explanation:

Area of the shaded region = Area of the rectangle - Area of the two triangles

Area of the rectangle = 6(3+14)

Area of the rectangle = 6 * 17

Area of the rectangle = 102cm²

Area of the smaller triangle = 1/2 * 3 * 6

Area of the smaller triangle = 18/2 = 9cm²

Area of the larger triangle = 1/2 * 6 * (17-7)

Area of the larger triangle = 1/2 * 6 * 10

Area of the larger triangle = 60/2 = 30cm²

Area of the shaded part = 102 - (9+30)

Area of the shaded part = 102 - 39

Area of the shaded part = 63cm²

Find the domain of the relation R = {(4, 5), (6, 7), (8, 9)}

Answers

Hbhhhhhhhhfggbbbbnnjjjjjkjmkkkkkkkm

Solve the inequality -9y > 9

Answers

Hello!

-9y > 9 <=>

<=> -9y ÷ (-9) > 9 ÷ (-9) <=>

<=> y < -1 <=>

<=> y { -; -1 }

Good luck! :)

Solve for x.
4(x + 3) = x +42
x = [?]

Answers

Answer: x=10

Step-by-step explanation:

[tex]4(x+3)=x+42\\4x+12=x+42\\4x-x=42-12\\3x=30\\x=10[/tex]

Evaluate in 7
0.51
1.95
0.85
1.61

Answers

Answer:

We may log in directly in our scientific calculator the given value ln 7 and get an answer of 1.9459. On the other hand, we can rewrite the expression as,

                            log to the base e or 7 = x

which can be written as,

                              e^x = 7

The value of x from this is still equal to 1.9459.

Step-by-step explanation:

Other Questions
What is this including the integers please? Read the passage from "The Book of Martha."After a moment, Martha was able to take her hands fromher face and look again at the grayness around her andat God. "This can't be heaven," she said. "There'snothing here, no one here but you.""Is that all you see?" God asked.This confused her even more. "Don't you know what Isee?" she demanded and then quickly softened hervoice. "Don't you know everything?"God smiled. "No, I outgrew that trick long ago. You can'timagine how boring it was."Which statement best explains why Martha quicklysoftens her voice toward the end of this passage?O She is worried that God will be upset at her forsounding insistentO She does not want to talk loud enough for anyone butGod to hear.She feels confident that God can hear her no matterhow softly she speaks.She doesn't want God to hear her questions andprovide answers. PLEASE HELP AND BE RIGHT BEFORE ANSWERING if the pelican in item 3 was traveling at the same speed but was only 2.7m above the water, how far would the fish travel horizontally before hitting the water? A line passes through point (5, 3) and is perpendicular to the equation y = x. What's the equation of the line? Question 26 options: a) y = x b) y = x 7 c) y = x + 3 d)y = x + 2 donde se ubica el cuerpo de la carta easy biology question below first correct answer gets brainliest. When do solutions attempt to reach astate of equilibrium?A. Solutions never attempt to reach a state of equilibrium.B. Solutions rarely make attempts at equilibrium.C. Solutions always make attempts at equilibrium.D. While solutions make equilibrium, it happens randomly. The restrictions for f(x)=2x+3/x^24 are 2TrueFalse ESTRUCTURA 2 Describing people, things, and conditions: Ser vs.estar5-6 | Ser o estar Choose the appropriate vab to complete cach sentence.1. De dnde (os/est) Juan?2. (Son / Estn) las ocho en punto de la noche.3. (Es / Est ) importante estudiar espaol todos los dias4.-Cmo (cres/ests )?-Bien, gracias.5. Nosotros somos / estamos ) pacientes.6. Ellos ( son / estn ) cansados.7. Este (es/est) el libro de la profesora.8. Cmo (es/est) ella?- Inteligente y muy bonita.9. Yo soy / estoy ) en la biblioteca.10. El doctor (es/est) listo para comenzar a operar.5-7 La Clnica Campesina Choose the correct ending for cach sentence, according tothe verb used (ser or estar).1. La Clinica Campesina est(grande, en la calle Obradoiro)2. La clinica es(grande; abierta)3. El consultorio grande es(cerrado; del doctor Montero)4. El doctor Montero tipicamente es(activo; cansado)5. Pero hoy el doctor Montero estinteligente, cansado)6. El paciente es(un poco gordo; enfermo)7. La enfermera es(trabajando mucho hoy, trabajadora)8. El paciente tiene una cita a las dos. Ahora es(esperando; la una)9. La receta es(en el consultorio para la farmacia)10. El cuidado de la saludosen Paraguay, (bien; caro) Factor the trinomial x^2-8x-65 Antecedentes de la expansin de frica Bert has blonde hair (b). Molly has brown hair (B), but her genotype is Bb, meaning she carries a recessive blonde allele. What is the likelihood of Bert and Molly's second child having brown hair? The number of terms between 200 and 800 which are divisible by 7 isa) 80b) 86c) 85d) 87 Which of the following describes what happened on Black Tuesday?Option 1 - Billions of dollars of investors' money was lost in just a few hours. Option 2 - More than 640 commercial banks failed in one day. What is the value of x? PLEASE HELP What is this can someone help A physical count of merchandise inventory on July 30 reveals that there are 48 units on hand. Using the LIFO inventory method, the amount allocated to cost of goods sold for July is SELECT ALL THAT APPLY!!!!!!!!!The Cable Act of 1992 gave consumers the right to fair and effective cable. It also reflected the government's-keep cable operators from pushing broadcast networks out of the industry-allow the consumer to take the bulk of the responsibility for regulating cable television content-abolish all of the remaining portions of the Fairness Doctrine- protect the public from indecent content Q/29304199offer A stock will pay no dividends for the next 5 years. Then it will pay a dividend of $5 growing at 2%. The discount rate is 10%. What should be the current stock price?