a x = ±5
b. x = ±5i
C. x = ±3√√5
d. x = ±3√3
e. x = ±3i√√3
f. x= ±3i√√5

1. x^2+45=0
2. x^2=-25
3. x^2-25=0
4. x^2-45=0
5. x^2=27
6. x^2+27=0

Match the items

Answer:

7 : 20

Step-by-step explanation:

2km = 2000m

Then the ratio of 700m to 2 km​ is :

700 / 2000

Then the ratio in simplest form is :

7 / 20

Answer:

Step-by-step explanation:

eq. of any line perpendicular to 5x+6y=-6 is

5y-6x=c

where c is a constant.

it passes through (-2,-1) so

5(-1)-6(-2)=c

c=-5+12=7

so reqd. eq. is 5y-6x=7

or 6x-5y=-7

or

slope of given line =-5/6

slope of reqd. line=6/5

eq. of line through (-2,-1) with slope 6/5 is

y+1=6/5(x+2)

5y+5=6x+12

5y=6x+12-5

or 5y=6x+7

or

6x-5y=-7

Answer: I am pretty sure you are correct from my standpoint

Step-by-step explanation:

If you look closely he is pretty close to the answer or it is the answer or this is just answer on my point or if its wrong try b

The linear functions are: y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

As a general rule, linear functions take any of the following forms:

y = mx + b

Ax + By = C

y - y1 = m(x - x1)

Any equation that take a different form is not a linear function

Using the above as a guide, the linear functions are:

y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

Other functions are nonlinear

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The number of solutions there are for the functions, -f(x) and f(-x) are; 2 and 2 respectively.

According to the task content, the function given initially is; f(x).

Hence, the function -f(x) represents a reflection of the function f(x) over the x axis. And in this case scenario, the reflection also has 2 solutions as it only cuts the x-axis at two points.

Also, the function f(-x) represents a reflection of the function f(x) over the y-axis. And in this case scenario, the reflection also has 2 solutions as it only cuts the x-axis at two points.

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Answer:

100

Step-by-step explanation:

Forming algebraic equations and solving:

Let the number of boys originally  at the stop = 'x'

Let the number of girls originally at the stop = 'y'

25  girls get on the first bus.

⇒ The number of girls now at the stop = y -25

Ratio of boys to girls:

        [tex]\sf \dfrac{x}{y -25}= \dfrac{3}{2}\\\\Cross \ multiply,\\\\2x = 3*(y- 25)\\\\2x = 3y - 3*25\\\\2x = 3y - 75 ------[/tex](I)

15 boys get on the second bus.

Now, the number of boys at the stop = x - 15

Number of girls at the stop = y - 25

Ratio of boys to girls,

     [tex]\sf \dfrac{x - 15}{y -25} = \dfrac{1}{1}\\\\Cross \ multiply, \\\\x - 15 = y -25\\\\[/tex]

             x = y -25 + 15

             x = y - 10

Plugin x = y - 10 in equation (I)

          2*(y-10) = 3y -75

          2y - 20  = 3y -75

                -20 = 3y - 75 - 2y

                -20 = y -75

         -20 +75 = y

                 [tex]\sf \boxed{\bf y = 55}[/tex]

Plugin y = 55 in equation (I)

       x = 55 -10

        [tex]\sf \boxed{\bf x = 45}[/tex]

Number of students originally at the stop = x + y

                                                                     = 55 + 45

                                                                     = 100

Answer:

1. Shorter Side: 4

2. Longer Side: 7

3. Hypotenuse: [tex]\sqrt{65}[/tex]

Step-by-step explanation:

[tex]4^{2} +7^{2} =65[/tex]

The inverse proportional relationship that models this variation is given as follows:

[tex]y = \frac{10,000}{x}[/tex]

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

An inverse proportional relationship is given as follows:

[tex]y = \frac{k}{x}[/tex]

In this problem, we have an inverse relation in which y(2) = 5000, hence the constant k is found as follows:

[tex]y = \frac{k}{x}[/tex]

[tex]5000 = \frac{k}{2}[/tex]

k = 10,000

Hence the relation is:

[tex]y = \frac{10,000}{x}[/tex]

As stated in the problem, when x = 5, y = 2,000, which we can verify replacing in the relation.

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Answer:

Option (4)

Step-by-step explanation:

Each value of x maps onto only one value of y, so it is a function.

Using the z-distribution, we have that:

a) The confidence interval is: (24.33%, 30.37%).

b) The correct option is: No, the confidence interval includes 0.25, so the true percentage could easily equal 25%.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

The other parameters are given as follows:

[tex]n = 427 + 161 = 588, \pi = \frac{161}{588} = 0.2735[/tex]

Then the bounds of the interval are:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2735 - 1.645\sqrt{\frac{0.2735(0.7265)}{588}} = 0.2433[/tex]

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.2735 + 1.645\sqrt{\frac{0.2735(0.7265)}{588}} = 0.3037[/tex]

As a percentage, the interval is: (24.33%, 30.37%).

25% is part of the interval, hence the correct statement is:

No, the confidence interval includes 0.25, so the true percentage could easily equal 25%.

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Answer:

[tex]\huge\boxed{\sf f^{-1}(x)=5x+10}[/tex]

Step-by-step explanation:

[tex]\displaystyle f(x)=\frac{x}{5} -2[/tex]

Put f(x) = y

[tex]\displaystyle y=\frac{x}{5} -2[/tex]

Swap x and y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Now, solve for y

[tex]\displaystyle x = \frac{y}{5} -2[/tex]

Add 2 to both sides

[tex]\displaystyle x + 2 =\frac{y}{5}[/tex]

Multiply 5 to both sides

[tex]5(x+2)=y[/tex]

Distribute

[tex]5x + 10 =y[/tex]

Put y = f⁻¹(x)

[tex]\boxed{f^{-1}(x)=5x+10}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

ascxne rdsjazs bcbnnnncccd

The attached figure represents the image of A"B"C" after the transformation

The transformation rule is given as:

A"B"C" = Ro90° (T(-4,3)(ABC))

This means that we rotate the triangle 90 degrees clockwise, and then translate the triangle

From the figure, the coordinates of ABC are

A = (-1, 2)

B = (1, 4)

C = (3, -1)

The rule of 90 degrees clockwise rotation is

(x,y) ⇒ (y,-x)

So, we have

A' = (2, 1)

B' = (4, -1)

C' = (-1, -3)

The translation of the triangle by T(-4,3) is

(x,y) ⇒ (x - 4, y + 3)

So, we have

A'' = (-2, 4)

B'' = (0, 2)

C'' = (-5, 0)

See attachment for the image of the transformation

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Answer:

-24

Step-by-step explanation:

-6 × f(3) - 6 × g(-1) = ?

to answer this we need to find the functional values of the functions at the specified points.

f(3) = -2

we find this easily : we go to x = 3 on the x-axis, and then see there at what y value a vertical line is intersecting the functional graph. the intersection is below the x-axis, so the y value is negative.

g(-1) = 6

we go to x=-1, and we find that a vertical line there will intersect the g curve at y = 6.

and that's really it.

now we need to calculate it all in the main expression :

-6 × -2 - 6 × 6 = 12 - 36 = -24

you remember, that multiplications and divisions have to happen before any addition of subtraction ?

Answer:

Step-by-step explanation:

According to the picture, the angles with measure of 65° and x are included between two parallel pairs of lines.

It makes them equal:

y is the exterior angle of the triangle with two remote interior angles with measure of 40° and 65°.

As per definition of the exterior angle its measure is same as the sum of remote interior angles:

Using equivalent angles, the solutions to the equation are given as follows:

[tex]\theta = 255^\circ, \theta = 285^\circ[/tex]

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

In this problem, the equation is:

[tex]\sin{\theta} = -0.966[/tex]

Applying the inverse relation:

[tex]\theta = \arcsin{-0.966} = 255^\circ[/tex]

Which is on the third quadrant. The equivalent angle on the fourth quadrant is given as follows:

[tex]270^\circ + (270^\circ - 255^\circ) = 285^\circ[/tex]

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The solution to the system of equations is (3, 2)

Give the system of equation below

y = -x + 5

y=x-1

Equate both expression

-x+5 =x - 1

Equate

-x - x = -1 - 5

-2x = -6

x = 3

Since y = x - 1

y = 3 - 1

y = 2

Hence the solution to the system of equations is (3, 2)

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Answer: 80 1/4 is 5% of 1605

Step-by-step explanation:

5 percent of some number = 80.25

let x = some number

[tex]\frac{5}{100} *x = 80.25[/tex]

[tex]=\frac{100}{5} *\frac{5}{100} *x=80.25*\frac{100}{5}[/tex]

[tex]=x=80.25*20[/tex]

[tex]=x=1605[/tex]

Answer:

Step-by-step explanation:

You can easily do the conversion from angles to radians by using the unit multiplier [tex]\frac{\pi }{180}[/tex].

210°×[tex]\frac{\pi }{180}[/tex]

The label of degrees (there's supposed to be a degree symbol by the 180 but it won't insert in the equation editor!) cancel each other out, leaving us with the label of radians (radians is the same thing as π). Then reduce between the 210 and the 180. Both are divisible by 30, so the simplification of

[tex]\frac{210\pi }{180}=\frac{7\pi }{6}[/tex]

Do the same with the 315 angle:

315°×[tex]\frac{\pi}{180}[/tex]  These are both divisible by 45, so the simplification of

[tex]\frac{315\pi}{180}=\frac{7\pi}{4}[/tex]

The two radian measures exists [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].

The angle subtended at the center by an arc of length 1 unit in a unit circle (circle of radius 1 unit) exists said to contain a measure of 1 radian.

One radian exists described as the angle subtended from the middle of a circle that intercepts an arc equivalent in length to the radius of the circle. When no symbol exists utilized, radians exist supposed. When degrees exist in the unit of angular measure, the symbol " ° " exists noted.

Degree to radian [tex]$=D \times \frac{\pi}{180}$[/tex]

Substitute the values and simplifying the above equation, we get

For [tex]$210^{\circ}=210 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{6}$[/tex]

For, [tex]$315^{\circ}=315 \times \frac{\pi}{180}[/tex] [tex]$=\frac{7 \pi}{4}$[/tex]

So the missing measures are [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex]

Therefore, the correct answer is [tex]$\frac{7 \pi}{6}$[/tex] and [tex]$\frac{7 \pi}{4}$[/tex].

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The numerical values of the mean and standard deviation are 4 and 1.55, respectively

The given parameters are:

n = 10

π = 0.4

The probability is then calculated as:

[tex]P(x) = ^nC_x * \pi^x *(1-\pi)^{n-x}[/tex]

So, we have:

[tex]P(6) = ^{10}C_6 * 0.4^6 *(1-0.4)^4[/tex]

Apply the combination formula

[tex]P(6) = \frac{10!}{6!4!} * 0.4^6 *0.6^4[/tex]

So, we have:

[tex]P(6) = 210 * 0.4^6 *0.6^4[/tex]

Evaluate

P(6) = 0.1115

Hence, the numerical value of the probability that x = 6 is 0.1115

The mean value is:

[tex]\bar x = n\pi[/tex]

This gives

[tex]\bar x = 10 * 0.4[/tex]

[tex]\bar x = 4[/tex]

The standard deviation value is:

[tex]\sigma = \sqrt{\bar x(1-\pi)[/tex]

This gives

[tex]\sigma = \sqrt{4(1-0.4)[/tex]

[tex]\sigma = 1.55[/tex]

Hence, the numerical values of the mean and standard deviation are 4 and 1.55, respectively

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Answer: [tex](-2, 5)[/tex]

Step-by-step explanation:

The graphs are shown in the attached image.

The solution is where they intersect.

The solution to the system of equations is x = -2 and y = 5.

i.e

The solution is = (-2, 5)

We have,

To find the solutions, you need to set the two equations equal to each other because they both represent the same variable "y."

So, you'll have:

(-7/2)x - 2 = -2x + 1

Now, let's solve for x:

Step 1:

Get rid of the fractions by multiplying both sides by 2:

2 * ((-7/2)x - 2) = 2 * (-2x + 1)

This simplifies to:

-7x - 4 = -4x + 2

Step 2:

Isolate the x terms on one side of the equation.

Let's move the -4x to the left side by adding 4x to both sides:

-7x - 4 + 4x = -4x + 4x + 2

This simplifies to:

-3x - 4 = 2

Step 3:

Now, isolate the constant term by moving the -4 to the right side by adding 4 to both sides:

-3x - 4 + 4 = 2 + 4

This simplifies to:

-3x = 6

Step 4:

Finally, solve for x by dividing both sides by -3:

x = 6 / -3

x = -2

Now that you've found the value of x, plug it back into either of the original equations to find the corresponding y value.

Let's use the first equation y = (-7/2)x - 2:

y = (-7/2) * (-2) - 2

y = 7 - 2

y = 5

Thus,

The solution to the system of equations is x = -2 and y = 5.

i.e

(-2, 5)

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The product of the ages 2 years from today is 924

Let the ages of the three cousins be x, y and z. If the product of their ages is 1716, hence;

xyz = 1716

If the product of their ages last year is 1320, then;

(x-1)(y-1)(z-1) = 1320

Two years ago, the product of their ages will be;

(x-2)(y-2)(z-2) = 1320- (1716-1320)

(x-2)(y-2)(z-2) = 1320-396

(x-2)(y-2)(z-2) =924

Hence the product of the ages 2 years from today is 924

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The brief report about what the attached data in the box plot shows that: "Women appear to marry around three years younger than males, although the shape and dispersion of the two distributions are extremely comparable."

A boxplot is a type of graph that shows how the values in the data are distributed.

A boxplot is a standardized technique of representing data distribution based on a five-number summary ("minimum", first quartile (Q1), median, third quartile (Q3), and "maximum").

It can provide information about your outliers and their values.

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Full Question:

In​ 1975, did men and women marry at the same​ age? Here are boxplots of the age at first marriage for a sample of U.S. citizens then. Write a brief report discussing what these data show.

Answer:

7/16

Step-by-step explanation:

(2+5)/(2+3+5+6) = 7/16

The probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.

The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favourable Outcomes/Number of total outcomes.

According to the given question.

Numnber of yellow balls = 2

Number of green balls = 3

Number of red balls = 5

Number of black balls = 6

So,

The total number of balls in a bag = 2+ 3+ 5 + 6 = 16

And,

The sum of yellow and red ball = 2 + 5 = 7

Therefore,

The probability of either a yellow or a red ball being drawn if only one ball is drawn

= [tex]\frac{total\ number\ of \ red \ and \ yellow\ balls }{Total\ number\ of \ balls}[/tex]

[tex]= \frac{7}{16}[/tex]

Hence, the probability of either a yellow or a red ball being drawn if only one is drawn is 7/16.

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From the given system of linear equations, we have;

a. The system of linear equations can be expressed as follows;

y = 22•x - 9.5

y = 2.5•x + 4.1

Rewriting the equations to have the constants on the right, we have;

y - 22•x = - 9.5

y - 2.5•x = 4.1

Solving the above equations using matrices method on a calculator gives;

By direct solving, we have;

22•x - 9.5 = 2.5•x + 4.1

22•x - 2.5•x = 4.1 + 9.5

19.5•x = 13.6

x = 13.6 ÷ 19.5 ≈ 0.697

y = 22•x - 9.5

y = 22×(13.6/19.5) - 9.5 ≈ 5.84

b. 8•x + y - 18 = 0

5•x + 9•y + 4 = 0

Rewriting gives;

8•x + y = 18

5•x + 9•y = -4

Solving with technology gives,;

Solving directly gives;

Which gives;

18 - 8•x = -(5•x + 4)/9

9×(18 - 8•x) = -(5•x + 4)

162 - 72•x = -(5•x + 4)

5•x - 72•x = -162 - 4 = -166

67•x = 166

x = 166 ÷ 67 ≈ 2.478

y = 18 - 8•x

Therefore;

y = 18 - 8 × (166 ÷ 67) ≈ -1.82

c. 6•x + y = 12

5•x + 8•y = -100

Solving the above linear system using technology, we have;

Solving directly, we have;

y = 12 - 6•x

5•x + 8•y = -100

y = (-100 - 5•x)/8

12 - 6•x = (-100 - 5•x)/8

8 × (12 - 6•x) = (-100 - 5•x)

96 - 48•x = (-100 - 5•x)

48•x - 5•x = 96 + 100

43•x = 196

x = 196/43 ≈ 4.56

y = 12 - 6•x

Therefore;

y = 12 - 6×(196/43) ≈ -15.35

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The function g(x) is g(x)= (3x)^2

The complete question is in the image

From the graph in the image, we have:

f(x) = x^2

The function f(x) is stretched by a factor of 3 to form g(x).

This means that:

g(x) = f(3x)

So, we have:

g(x)= (3x)^2

Hence, the function g(x) is g(x)= (3x)^2

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The boat in discuss is 9.03 miles from lighthouse B.

The distance of the boat from lighthouse B as required can be determined by means of the cosine law in which case we have;

c² = 10² + 6² - (2×6×10Cos 63)

c = 81.52

c = 9.03miles.

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The exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

An exponential function is represented as:

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

The base is 3.

So, we have:

[tex]y = 3^x[/tex]

It is stretched vertically by 2/3.

So, we have:

[tex]y = \frac23(3)^x[/tex]

When reflected over the y-axis, we have:

[tex]y = \frac23(3)^{-x}[/tex]

An asymptote of y = 2, makes the function becomes

[tex]y = \frac23(3)^{-x} + 2[/tex]

Lastly, it passes through the point (0, 3.5).

So, we have:

[tex]y = \frac23(3)^{-x+h} + 2[/tex]

This gives

[tex]3.5 = \frac23(3)^{-0+h} + 2[/tex]

[tex]3.5 = \frac23(3)^{h} + 2[/tex]

Subtract 2 from both sides

[tex]1.5 = \frac23(3)^{h}[/tex]

Multiply by 3/2

[tex]2.25 = (3)^{h}[/tex]

Take the logarithm of both sides

log(2.25) = h * log(3)

Solve for h

h = 0.74

Substitute h = 0.74 in [tex]y = \frac23(3)^{-x+h} + 2[/tex]

[tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

Hence, the exponential equation is [tex]y = \frac23(3)^{-x+0.74} + 2[/tex]

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