Assume that T is a linear transformation. Find the standard matrix of T:R2→R2T:R 2→R 2 first rotates points through −3π/4−3π/4 radian (clockwise) and then reflects points through the horizontal x1x 1-axis.

Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The complete question is:

Maya is solving the quadratic equation by completing the What should Maya do first? square.

4x² + 16x + 3 = 0

We have a quadratic equation:

4x² + 16x + 3 = 0

To make the perfect square

Maya should do first:

Isolate the variable x²

To make the coefficient of x² is 1.

4(x² + 4x + 3/4) = 0

x² + 4x + 3/4 = 0

x² + 4x + 2² - 2² +  3/4 = 0

(x + 2)² - 4 + 3/4 = 0

(x + 2)² = 13/4

x + 2 = ±√(13/4)

First, take the positive and then the negative sign.

x = √(13/4) - 2

x = -√(13/4) - 2

Thus, Maya should Isolate the variable x² option (A) Isolate the variable x² is correct.

Learn more about quadratic equations here:

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Two ratios that are equal to 7:6 are 14:12 and 21:18, as they are the same, but 7 and 6 are multiplied by the same number (2 in the first, and 3 in the second.)

Answer:

B

Step-by-step explanation:

Given

x² + 14x = 51

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(7)x + 49 = 51 + 49 , that is

(x + 7)² = 100 ( take the square root of both sides )

x + 7 = ± [tex]\sqrt{100}[/tex] = ± 10 ( subtract 7 from both sides )

x = - 7 ± 10

Thus

x = - 7 - 10 = - 17

x = - 7 + 10 = 3

Answer:

neither

Step-by-step explanation:

First we must determine if both x and -x are in the domain of the function

since it is a polynomial function our first condition is satisfied

Then we should calculate the image of -x :

2x(-x)^3 + 3*(-x)² = -2x^3+3x²

it is not equal to f(x) nor -f(x)

Answer:

3

Step-by-step explanation:

Triangle ABC is an isosceles triangle, so

[tex]x^2+x^2=(6\sqrt{2} )^2\\2x^2=6^2*2\\x^2=6^2\\x=6.[/tex]

Triangle BCD is a notable triangle and the sides are

BD=x, CD=[tex]x\sqrt{3}[/tex],BC=2x=6

2x=6

x=3

the value of x is 115°.

hope its helpful to uh..

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 7.2

For the alternative hypothesis,

H1: µ ≠ 7.2

This is a two tailed test.

Since the population standard deviation is given, the test statistic would be the z score determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 7.2

x = 7.3

σ = 0.8

n = 250

z = (7.3 - 7.2)/(0.8/√250) = 1.976

Test statistic is 1.976

Answer:

Hello!

________________________

5c + 16.5 = 13.5 + 10c

Exact Form:  c = 3/5

Decimal Form: c = 0.6

Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.

Hope this helped you!

Answer:

3000+3d=noods

Step-by-step explanation:

Answer: 6x^2

Step-by-step explanation:

The area of a triangle is 1/2bh

Thus, simply multiply 2x*3x = 6x^2

Hope it helps <3

Answer:

Solution,

Base(b)= 3x

Height(h) = 2x

Now,

Finding the area of triangle:

[tex] \frac{1}{2} \times b \times h[/tex]

[tex] \frac{1}{2} \times 3x \times 2x[/tex]

[tex] \frac{1}{2} \times 6 {x}^{2} [/tex]

[tex]3 {x}^{2} [/tex]

Hope this helps....

Good luck on your assignment....

Answer:

C

Step-by-step explanation:

undefined slope means tat the denominator=0 in the equation

m=y2-y1/x2-x1

A: m=-1-1/1+1=-2

B;2-2/2+2=0

C: 3+3/-3+3 = 6/0 undefined

D: 4+4/4+4=1

Answer:

[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]    

[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]    

And the best option for this case would be:

a. (17.5, 21.7)

Step-by-step explanation:

Information given

[tex]\bar X= 19.6[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma= 5.8[/tex] represent the population deviation

n=42 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

The degrees of freedom, given by:

[tex]df=n-1=42-1=41[/tex]

Since the Confidence is 0.98 or 98%, the significance would be [tex]\alpha=0.02[/tex] and [tex]\alpha/2 =0.1[/tex], and the critical value would be [tex]t_{\alpha/2}=2.42[/tex]

Replacing we got:

[tex]19.6-2.42\frac{5.8}{\sqrt{42}}=17.43[/tex]    

[tex]19.6+2.42\frac{5.8}{\sqrt{42}}=21.77[/tex]    

And the best option for this case would be:

a. (17.5, 21.7)

Answer:

The 98% confidence interval for the population mean is between 17.5 hours and 21.7 hours.

Answer:

26 rows

Step-by-step explanation:

[tex]number \: of \: rows \\ = \frac{40}{ \frac{20}{13} } \\ \\ = \frac{40 \times 13}{20} \\ \\ = 2 \times 13 \\ \\ = 26 \: [/tex]

Answer:Yes indeed!

Step-by-step explanation:

Your right!

Answer:

D

Step-by-step explanation:

We calculate the z-score for each

Mathematically;

z-score = (x-mean)/SD

z1 = (1.9-2.1)/0.2 = -1

z2 = (2.3-2.1)/0.2 = 1

So the proportion we want to calculate is;

P(-1<x<1)

We use the standard score table for this ;

P(-1<x<1) = P(x<1) -P(x<-1) = 0.68269 which is approximately 68%

Answer:

68

Step-by-step explanation:

Answer:

15√20/6√125

=√20/√5

=2

Step-by-step explanation:

Answer:

The upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.

Step-by-step explanation:

Compute the mean difference and standard deviation of the difference as follows:

[tex]\bar d=\frac{1}{n}\sum d_{i}=\frac{1}{15}\times [1380+3370+2580+...+3520]=2642.67\\\\S_{d}=\sqrt{\frac{1}{n-1}\sum (d_{i}-\bar d)^{2}}\\=\sqrt{\frac{1}{15-1}[(1380-2642.67)^{2}+(3370-2642.67)^{2}+...}=525.69[/tex]

The degrees of freedom is:

df = n - 1

   = 15 - 1

   = 14

Th critical value of t is:

[tex]t_{\alpha/2, (n-1)}=t_{0.05/2, 14}=2.145[/tex]

*Use a t-table.

Compute the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus as follows:

[tex]\text{Upper Confidence Bound}=\bar d+t_{\alpha/2, (n-1)}\cdot \frac{S_{d}}{\sqrt{n}}[/tex]

                                        [tex]=2642.67+2.145\cdot \frac{525.69}{\sqrt{15}}\\\\=2642.67+291.15\\\\=2933.82[/tex]

Thus, the upper confidence bound for the true average difference between 1-minute modulus and 4-week modulus is 2933.82.

Answer:

96.08% probability that their mean rebuild time is less than 8.9 hours.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 8.4, \sigma = 1.8, n = 40, s = \frac{1.8}{\sqrt{40}} = 0.2846[/tex]

Find the probability that their mean rebuild time is less than 8.9 hours.

This is the pvalue of Z when X = 2.9.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{2.9 - 2.4}{0.2846}[/tex]

[tex]Z = 1.76[/tex]

[tex]Z = 1.76[/tex] has a pvalue of 0.9608

96.08% probability that their mean rebuild time is less than 8.9 hours.

Answer:

a) 12

b) 129

Step-by-step explanation:

a)

[tex]w, x \in \mathbb{Z}_{\ge 0}[/tex]

[tex]w>50\\x<40[/tex]

For the smallest value of [tex]w-x[/tex], we gotta figure out the smallest value for w and the highest value for x.

[tex]w>50 \Rightarrow \text{ smallest value is } 51[/tex]

For [tex]x[/tex], once [tex]-(-x)=x[/tex], we conclude that [tex]x[/tex] cannot be negative and therefore, [tex]x=39[/tex].

[tex]51-39=12[/tex]

b)

[tex]y, z \in \mathbb{Z}_{\ge 0}[/tex]

[tex]y<70\\z\leq 60[/tex]

For the largest value of [tex]y+z[/tex], we gotta figure out the highest value for y and z.

[tex]y<70 \Rightarrow \text{ highest value is } 69[/tex]

[tex]z\leq 60 \Rightarrow \text{ highest value is } 60[/tex]

[tex]y+z=69+60=129[/tex]

Answer:

4.428 hours

Step-by-step explanation:

If the learning rate is 0.81, the slope of the learning curve is:

[tex]b=\frac{ln(0.81)}{ln(2)} \\b=-0.304[/tex]

The time it takes to produce the n-th unit is:

[tex]T_n=T_1*n^b[/tex]

If T1 = 8 hours, the time required to produce the seventh unit will be:

[tex]T_n=8*7^{-0.304}\\T_n=4.428\ hours[/tex]

It will take roughly 4.428 hours.

Answer:

You will have $29,000 in 30 years, and you need to start with about $2,772.28 to make $14,000 in 9 years

Step-by-step explanation:

To find the total investment use the equation [tex]A = P(1 + rt)[/tex]

Where A equals total investment, P is your start investment, r is your rate, and t is time.

[tex]A=2,000(1+(0.45 * 30))[/tex]

[tex]A=2,000(1+13.5)[/tex]

[tex]A=2,000*14.5[/tex]

[tex]A=29,000[/tex]

To find the start investment use the equation [tex]P = A / (1 + rt)[/tex]

[tex]P=14,000/(1+(0.45*9))[/tex]

[tex]P=14,000/(1+4.05)[/tex]

[tex]P=14,000/5.05[/tex]

[tex]P=2,772.28[/tex]

Answer:

It's written as

[tex]2.6 \times {10}^{ - 3} [/tex]

Hope this helps you

Answer:

2.6 × 10⁻³

Step-by-step explanation:

To write a number in scientific notation, move the decimal to the right or left until you reach a number that is 1 or higher.

In the decimal 0.0026, the first number that is 1 or higher is 2.

0.0026 ⇒ 2.6

When trying to figure out the exponent, here are some things to keep in mind:

- when you move the decimal to the right, the exponent is negative

- when you move the decimal to the left, the exponent is positive

You moved the decimal to the right three places. So the exponent will be -3.

The result is 2.6 × 10⁻³.

Hope this helps. :)

Answer:

x=9

Step-by-step explanation:

3x subtracted by 2y

is 1 then 1 multiplied by 2 is 2 then 7 + 2 is 9

PEMDAS

Answer:

The answer is 60cm^2.

hope it helps..

Answer: The equations are

w + s = 4500

2.25s = 4500

Step-by-step explanation:

Let w represent the number of bottles of water that the football manager bought.

Let s represent the number of bottles of soda that the football manager bought.

The manager needs to buy a total of 4,500 drinks. This means that

w + s = 4500

He also needs to have 25% more water than soda.

25% of soda = 25/100 × s = 0.25s

25% more of water than soda = s + 0.25s = 1.25s

The equation would be

1.25s + s = 4500

2.25s = 4500

Answer:

Step-by-step explanation:

Given the equation, 2x- y = 5, if x = 3, to get y we will simply substitute the value of x into the expression given as shown;

[tex]2x - y = 5\\\\Substituting \ x = 3\ into \ the \ equation\\\\2(3) - y = 5\\\\6 - y = 5\\\\subtracting\ 6\ from\ both\ sides\\\\6-6-y = 5- 6\\\\-y = -1\\\\multiplying\ both\ sides\ by \ -1\\-(-y) = -(-1)\\\\y = 1[/tex]

Hence, the value of y is 1

Answer:

GCF - 4

Step-by-step explanation:

36 - 1, 2, 3, 4, 6, 9, 12, 18, 36

44 - 1, 2, 4, 11, 44

Hope this helps! :)

Answer:

C

Step-by-step explanation:

If two lines are parallel, their slopes are the same.

Since the slope of line l is 4/9, this means that the slope of line m must also be 4/9.

Answer:

C. 4/9

Step-by-step explanation:

Parallel lines have equal slopes.

Since line l and line m are parallel, then their slopes must be the same.

[tex]m_{l} =m_{m}[/tex]

We know that the slope of line l is 4/9

[tex]\frac{4}{9} = m_{m}[/tex]

Line l has a slope of 4/9, therefore line m must also have a slope of 4/9.

The correct answer is C. 4/9

Answer:

The correct option is (A)

A. Replace row 4 by its sum with - 4 times row 3.

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]

w = 8

x = 17/2

y = 6

z = -5

Step-by-step explanation:

The given matrix is

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&4&5&-1\end{array}\right][/tex]

To solve this matrix we need to create a zero at the 4th row and 3rd column which is 4 at the moment.

Multiply 3rd row by -4 and add it to the 4th row.

Mathematically,

[tex]R_4 = R_4 - 4R_3[/tex]

So the correct option is (A)

A. Replace row 4 by its sum with - 4 times row 3.

So the matrix becomes,

[tex]\left[\begin{array}{ccccc}1&-4&4&0&-2\\0&2&-6&0&5\\0&0&1&2&-4\\0&0&0&-3&15\end{array}\right][/tex]

Now the matrix may be solved by back substitution method.

Bonus:

The solution is given by

Eq. 1

-3z = 15

z = -15/3

z = -5

Eq. 2

y + 2z = -4

y + 2(-5) = -4

y - 10 = -4

y = -4 + 10

y = 6

Eq. 3

2x - 6y + 0z = 5

2x - 6(6) = 5

2x - 12 = 5

2x = 12 + 5

2x = 17

x = 17/2

Eq. 4

w - 4x + 4y + 0z = -2

w - 4(17/2) + 4(6) = -2

w - 34 + 24 = -2

w - 10 = -2

w = -2 + 10

w = 8

Answer:

Step-by-step explanation:

Answer/Step-by-step explanation:

Let x = 4 (you and 3 friends)

Ticket cost per head = $5.50

Drink cost per head = $2.50

Popcorn cost per head = $4.00

Expression representing total amount of money spent = $5.50(x) + $2.50(x) + $4.00(x)

Evaluate the expression by plugging in the value of x = 4

Total amount of money spent = $5.50(4) + $2.50(4) + $4.00(4)

= $22 + $10 + $16 = $48

Total amount of money spent = $48