If x − √a is a factor of 2x4 − 2a 2x 2 − 3x + 2a3 − 2a2 + 3 , find the value of a.

Answer:

[tex]2a=6b\\a=3b[/tex]

Step-by-step explanation:

Let [tex]a[/tex] equal the amount of apples and [tex]b[/tex] equal the amount of bananas.

[tex]2a=6b\\a=3b[/tex]

Answer:

every 2 apples there

are 6 bananas​

Step-by-step explanation:

2a=6b

Answer:

1.     [tex]16 = 4^2[/tex]

2.    [tex]2 = {16}^{\frac{1}{4}}[/tex]

3.    [tex]log_2 y=z[/tex]

Step-by-step explanation:

[tex]1.\ log_2 16=4[/tex]

Write in exponential form

Using the law of logarithm which says if

[tex]log_b A=x[/tex]

then

[tex]A = b^x[/tex]

By comparison;

A = 16; b = 2 and x = 4

The expression [tex]log_2 16=4[/tex] becomes

[tex]16 = 4^2[/tex]

[tex]2.\ log_{16} 2=\frac{1}{4}[/tex]

Write in exponential form

Applying the same law as used in (1) above;

A = 2; b = 16 and [tex]x = \frac{1}{4}[/tex]

The expression [tex]log_{16} 2=\frac{1}{4}[/tex] becomes

[tex]2 = {16}^{\frac{1}{4}}[/tex]

[tex]3.\ 2^z=y[/tex]

Write in logarithm form

Using the law of logarithm which says if

[tex]b^x =A[/tex]

then

[tex]log_b A=x[/tex]

By comparison;

b = 2; x = z and A = y

The expression [tex]2^z=y[/tex] becomes

[tex]log_2 y=z[/tex]

The given equations written in exponential or logarithmic form as the case is is;

1) 2⁴ = 16

2)16^(¼) = 2

3) Log_2_y = z

Usually in logarithmic exponential functions expressions;

When we have;

Log_n_Y = 2

It means that; n² = Y

Applying that same principle to our question means that;

1) log_2_16 = 4

This will now be;

2⁴ = 16

2) log_16_2 = ¼

This will now be;

16^(¼) = 2

3) For 2^(z) = y

We have;

Log_2_y = z

Read more about properties of logarithmic exponents at; https://brainly.com/question/10005276

Answer:

Area of Rectangle A

[tex]Area = 4x^2[/tex]

Area of Rectangle B

[tex]Area = 2x^2[/tex]

Fraction

[tex]Fraction =\frac{2}{3}[/tex]

Step-by-step explanation:

From the attached, we understand that:

The dimension of rectangle A is 2x by 2x

The dimension of rectangle B is x by 2x

Area of rectangle is calculated as thus;

[tex]Area = Length * Breadth[/tex]

Area of Rectangle A

[tex]Area = 2x * 2x[/tex]

[tex]Area = 4x^2[/tex]

Area of Rectangle B

[tex]Area = x * 2x[/tex]

[tex]Area = 2x^2[/tex]

Area of Big Rectangle

The largest rectangle is formed by merging the two rectangles together;

The dimension are 3x by 2x

The Area is as follows

[tex]Area = 2x * 3x[/tex]

[tex]Area = 6x^2[/tex]

The fraction of rectangle A in relation to the largest rectangle is calculated by dividing area of rectangle A by area of the largest rectangle;

[tex]Fraction = \frac{Rectangle\ A}{Biggest}[/tex]

[tex]Fraction =\frac{4x^2}{6x^2}[/tex]

Simplify

[tex]Fraction =\frac{2x^2 * 2}{2x^2 * 3}[/tex]

[tex]Fraction =\frac{2}{3}[/tex]

Answer:

The last graph.

Step-by-step explanation:

The last graph is the only one that has a constant pattern that can have a rule, which is every number is multiplied by two.

Hope this helped ! good luck :)

Answer:

  PR, PW, RW

Step-by-step explanation:

The sides of a triangle are named by naming the vertices at either end.

Triangle PWR has vertices P, W, R. The sides connecting these are named ...

   PW, WR, RP

Any name can have the letters reversed. That is, PR names the same segment that RP does.

Answer:

100%

Step-by-step explanation:

The numbers odd or greater than 1 are 1, 2, 3, 4, 5, and 6.

6 numbers out of 6.

6/6 = 1.

P(odd or greater than 1) = 100%

Answer:

100%

Step-by-step explanation:

So the original fraction is 6/6 because is is odd and 3 and 5 also 2,4,6 are all more than 1.

Answer: 108 inches

Step-by-step explanation: The answer would be 108 inches because if you multiply the number that coverts a inch into a foot it would be 12 because 12 inches is equivalent to 1 foot. So you know that 1 foot is equal to 12 inches so you multiply the number of feet by 12. You expression is 9 times 12 and after you multiply the two numbers you get 108 inches.

Answer: 108 inches

Step-by-step explanation: To convert 9 feet into inches, we use the conversion factor for feet and inches which is 12 inches = 1 foot.

Next, notice that we're going from a

larger unit, feet, to a smaller unit, inches.

When we go from a larger unit to a smaller unit, we

multiply 9 by the conversion factor, 12 to get 108.

So 9 feet = 108 inches.

Answer:

3/4

Step-by-step explanation:

r= a3/a2=3/4

or

r= a2/a1= 4÷16/3= 4×3/16= 3/4

Answer:

33 lbs  10 ounces

Step-by-step explanation:

   13 lb 14oz

+ 30 lb 12 oz

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

32 lbs  26 oz

But we know that 16 ounces 1 1 lb

Subtract 16 ounces and add 1 lb

32 lbs  26 oz

+1 lb   - 16 ounces

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

33 lbs  10 ounces

Answer:

let the number of calories from lunch be called L. As such, breakfast is then L + 128, and dinner is 2L - 400. We can then sum the three meals and equate it to the total caloric intake, the known value of 1932.

  So: 1932 = L + L + 128 + 2L - 400 = 4L - 272.

  Lunch = 551

Breakfast = 551 + 128 = 679

Dinner = 2*551 - 400 = 702

Third option is the correct answer.

Answer:

[tex] y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg][/tex]

Step-by-step explanation:

[tex]y - y_1 = m(x - x_1) \\ \\ y - 0 = \bigg[ \frac{2b}{(2a - c)} \bigg] (x - c) \\ \\ y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2b}{(2a - c)} \bigg]c \\ \\ \purple { \boxed{ \bold{y = \bigg[ \frac{2b}{(2a - c)} \bigg]x - \bigg[ \frac{2bc}{(2a - c)} \bigg]}}} \\ [/tex]

Answer:

If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution

Step-by-step explanation:

For this problem we are assumeing that the random variable X is :

[tex] X \sim Bin(n,p)[/tex]

If the value of n gests smaller then the distribution of X would be more skewed, that's a property of the binomial distribution and if we don't satisfy this two conditions:

[tex] n p>10[/tex]

[tex]n(1-p) >10[/tex]

Then we can't use the normal approximation

Answer:

Complementary angles are angles that add up to 90°

To find the complementary angle for an angle of 70° subtract it from 90°

That's

90° - 70° = 20

Hope this helps

Answer:

20

Step-by-step explanation:

Complementary angles add to 90 degrees

70 +x = 90

Subtract 70 from each side

70+x-70 = 90-70

x = 20

The complement is 20

Answer:

A) S,T,R

Step-by-step explanation:

Answer:

67 inches

Step-by-step explanation:

Let's call the height of Louise 'L', the height of Miriam 'M' and the height of Jeffery 'J'.

Then, we can write the following equations and inequations:

[tex]L \leq M - 1[/tex]

[tex]L \geq J + 2[/tex]

[tex]J = 64[/tex]

[tex]M \leq J + 5[/tex]

Substituting J in the second and four inequations, we have:

[tex]L \geq 66[/tex]

[tex]M \leq 69[/tex]

If we assume the maximum value for M, in the first inequation we have that:

[tex]L \leq 68[/tex]

So the height of Uncle Louise is greater than or equal 66, and lesser than or equal 68, so his height could be 67 inches for example.

Answer:

lateral area =150 square feet

Step-by-step explanation:

lateral area =(perimieter of prism base) times the height of the prism

so, the perimeter of the base is 9 ft*2 + 6 ft*2 which equals 30 ft

then you multiply the perimeter of the base by the height of the prism

so, height of prism =5 ft, so 5 ft times 30 ft =150 feet

therefor, the lateral area of the prism = 150 feet squared

Recall that for |x| < 1, we have

[tex]\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n[/tex]

Replace x with 2x, multiply 4, and call this function f :

[tex]f(x)=\dfrac4{1-2x}=\displaystyle4\sum_{n=0}^\infty(2x)^n[/tex]

Take the derivative:

[tex]f'(x)=\dfrac8{(1-2x)^2}=\displaystyle8\sum_{n=0}^\infty n(2x)^{n-1}=\boxed{8\sum_{n=0}^\infty (n+1)(2x)^n}[/tex]

By the ratio test, the series converges for

[tex]\displaystyle\lim_{n\to\infty}\left|\frac{(n+2)(2x)^{n+1}}{(n+1)(2x)^n}\right|=|2x|\lim_{n\to\infty}\frac{n+2}{n+1}=|2x|<1[/tex]

or |x| < 1/2, so the radius of convergence is 1/2.

Answer:

19,000

Step-by-step explanation:

Here, we are to estimate the population in the year 2010

From the question, we can see that within a period of a decade which is 10 years, 1000 was lost

So within the period of another decade, it is possible that another 1000 be lost

The estimated population in the year 2010 is thus 20,000 - 1,000 =

19,000

Answer:

C

Step-by-step explanation:

A reflection is when the original diagram or picture is fliped exactly over the x axis.

HEYA!!

Answer:

Your Answer of the Question is C

if you want to prove it you can do the same thing in real life by drawing a 'W' on a paper and see its reflection on the mirror

HOPE IT MATCHES!!

Answer:

you can either factorise or use tge formula method

Step-by-step explanation:

3x2−7x−20=03x2-7x-20=0

Use the quadratic formula to find the solutions.

−b±√b2−4(ac)2a-b±b2-4(ac)2a

Substitute the values a=3a=3, b=−7b=-7, and c=−20c=-20 into the quadratic formula and solve for xx.

7±√(−7)2−4⋅(3⋅−20)2⋅37±(-7)2-4⋅(3⋅-20)2⋅3

Simplify.

Tap for more steps...

x=7±176x=7±176

The final answer is the combination of both solutions.

x=4,−53

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▹ Answer

y-intercept = -6

▹ Step-by-Step Explanation

The format of slope is:

y = mx + b

The b represents the y-intercept which is, -6.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer: -6

Step-by-step explanation: This equation is written in slope-intercept form which is more commonly known as y = mx + b form where the multiplier or the coefficient of the x term represents the slope of the line and the b or the constant term represents the y-intercept.

So this line has a y-intercept of -6.

This means it crosses the y-axis 6 units up from origin.

Answer:

-10, 3

Step-by-step explanation:

-10, 3 work since

-10 + 3 = -7

Answer:

x = 25; both labeled angles are 65º

Step-by-step explanation:

To find the value of x, recall that the angles formed by two parallel lines on the same line are equal if they correspond to each other.

In the figure given above, we have two parallel line given. The angle formed by each parallel line is corresponding to the other. Therefore, both angles formed are equal.

Thus,

(3x - 10)° = (x + 40)°

Solve for x

3x - 10 = x + 40

Subtract x from both sides

3x - 10 - x = x + 40 - x

3x - x - 10 = x - x + 40

2x - 10 = 40

Add 10 to both sides

2x - 10 + 10 = 40 + 10

2x = 50

Divide both sides by 2

2x/2 = 50/2

x = 25

*Plug in the value of x to find the measure of each labelled angles:

(3x - 10)° = 3(25) - 10 = 75 - 10 = 65°

(x + 40)° = 25 + 40 = 65°

Answer:

-1(3 - y)

Step-by-step explanation:

If you factor out a negative 1, you will get the opposite signs you already have, so -1(3 - y). To check, we can simply distribute again:

-3 + y

So our answer is 2nd Choice.

Answer:

C. 35

55 degrees + 35 degrees= 90 degrees

Answer:

[tex]y =log_e(x+3)[/tex]

Step-by-step explanation:

It is given that the graph corresponds to a natural logarithmic function.

That means, the function [tex]y[/tex] has a natural log (Log with base [tex]e[/tex]) of some terms of x.

It is given that asymptote of given curve is at [tex]x= -3[/tex]. i.e. when we put value

[tex]x= -3[/tex], the function will have a value [tex]y \rightarrow \infty[/tex].

We know that natural log of 0 is not defined.

So, we can say the following:

[tex]log_e(x+a)[/tex] is not defined at [tex]x= -3[/tex]

[tex]\Rightarrow x+a =0\\\Rightarrow x = -a[/tex]

i.e. [tex]x =-a[/tex] is the point where [tex]y \rightarrow \infty[/tex]

a = 3

Hence, the function becomes:

[tex]y =log_e(x+3)[/tex]

Also, given that the graph crosses x axis at x = -2

When we put x = -2 in the function:

[tex]y =log_e(-2+3) = log_e(1) = 0[/tex]

And y axis at 1.

Put x = 0, we should get y = 1

[tex]y =log_e(0+3) = log_e(3) \approx 1[/tex]

So, the function is: [tex]y =log_e(x+3)[/tex]

Answer:

1. The margin of error is of 66.96 square feet.

2. The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 22 - 1 = 21

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 21 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.08

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.08*\frac{151}{\sqrt{22}} = 66.96[/tex]

In which s is the standard deviation of the sample.

The margin of error is of 66.96 square feet.

The lower end of the interval is the sample mean subtracted by M. So it is 1500 - 66.96 = 1433.04 square feet

The upper end of the interval is the sample mean added to M. So it is 1500 + 314 = 1566.96 square feet

The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet

Answer:

Probability is 1

Step-by-step explanation:

We are given;

mean;μ = $2,075

Standard deviation;σ = $300

n = 55

x' = $1,985

Now, we want to find x' to be at least $1,985 which is P(x' > $1,985).

The z-value is calculated from;

z = (x' - μ)/(√σ/n)

Plugging in the relevant values;

z = (1985 - 2075)/(√300/55)

z = -38.536

So, P(x' > $1,985) = P(z > -38.536)

This transforms to;

P(z < 38.536)

Probability from z distribution table is 1

Answer:

Option (D)

Step-by-step explanation:

Subtraction property of equality tells that whatever subtracted from one side of the equation must be subtracted from the other side.

If x + 2 = 2,

By the property of subtraction of equality,

x + 2 - 2 = 2 - 2

x = 0

But in the given question,

[tex]\frac{x}{2}-7=-7[/tex]

[tex]\frac{x}{2}-7+7=-7+7[/tex]

shows the addition property of equality in step (2)

Therefore, subtraction property of equality was not applied.

Option (D) will be the answer.