Q # 4 if anybody can help me

This is asking you to solve the equation ...

... 27 = 3^x

You can use logarithms to find

... log(27) = x·log(3)

... log(27)/log(3) = x = 1.43136376.../0.47712125...

... x = 3

Or, you can use your knowledge of small cubes and match exponents.

... 3^3 = 3^x

... 3 = x

Answer:

C. consecutive interior angles

Step-by-step explanation:

The subject angles are between lines a and b, so are interior (not exterior). They are on different corners of the intersection, so are not corresponding. They are on the same side of line c, so are not alternate. The share a side, but not a vertex, so they are consecutive. The appropriate choice is ...

... C. consecutive interior angles

Answer: C. consecutive interior angles

k = - 2 is excluded from the domain

the denominator of f(x) cannot be zero as this would make f(x) undefined. Equating the denominator to zero and solving gives the value that k cannot be

solve k + 2 = 0 ⇒ k = - 2 ← excluded value

Answer:

parallel

Step-by-step explanation:

Translation moves each point the same amount in the same direction. Essentially, the original segment becomes the side of a parallelogram, whose other side is the image, and whose ends are the vectors specifying the translation.

In the attachment, we have designated (a, b) as point A, and (c, d) as point B. We had to choose specific values for these in order to plot them, but the description of the effect of translation applies no matter what the point coordinates are chosen to be.

(a) 6% of the value of the investment is added each year. This means the value of the investment is multiplied by 1.06 each year. After 15 multiplications, the value is ...

... $3000×1.06¹⁵ ≈ $7189.67

(b) The interpretation of this result is ...

... After 15 years, the investment is worth $7189.67.

The future value of a $3000 investment at an annual interest rate of 6%, compounded annually for 15 years, is approximately $8093.97. This means that the original sum will grow to this amount after the set period.

To find the future value of an investment, we use the formula for compound interest which is A = P(1 + r/n)^(nt). Where:

Given are P = $3000, r = 6%/100 = 0.06 (annually), n = 1 (since it's compounded annually), and t = 15 years. Plugging these into the formula, we get A = $3000(1 + 0.06/1)^(1*15) = $3000(1.06)^15 = $8093.97.

Interpreting this, it means that investing $3000 at 6% compounded annually would grow to approximately $8093.97 after 15 years.

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Read the problem and answer choices. You want to get from ABCD to EFGH, so you need to figure out how to do that with reflection, translation, and dilation—in that order.

The reflection part is fairly easy. ABC is a bottom-to-top order, and EFG is a top-to-bottom order, so the reflection is one that changes top to bottom. It must be reflection across a horizontal line. The only horizontal line offered in the answer choices is the x-axis. Selection B is indicated right away.

The dimensions of EFGH are 3 times those of ABCD, so the dilation scale factor is 3. This means that prior to dilation, the point H (for example), now at (-12, -3) would have been at (-4, -1), a factor of 3 closer to the origin. H corresponds to D in the original figure, which would be located at (0, -2) after reflection across the x-axis.

So, the translation from (0, -2) to (-4, -1) is 4 units left (0 to -4) and 1 unit up (-2 to -1).

The appropriate choice and fill-in would be ...

... B. Reflection across the x-axis, translation 4 units left and 1 unit up, dilation with center (0, 0) and scale factor 3.

_____

You can check to see that these transformations also map the other points appropriately. They do.

Its A i did the test

Answer:

(a) 0

(b) 2

(c) 0

(d) 1

Step-by-step explanation:

All of these can be solved easily by a graphing calculator. The attached graphs show the real solutions of those equations that have them. Here, you can also answer the question from the sign of the discriminant.

For y = ax² +bx +c

the value of the discriminant is

... b² -4ac

When the discriminant is negative, both solutions are complex. When 0, there is one solution. When positive, there are two real solutions.

(a) The discriminant is ...

... (-9)² -4(12)(4), a negative number. There are no real solutions.

(b) This needs to be rearranged to ...

... y = -x² -10x +2

Then the discriminant is ...

... (-10)² -4(-1)(2), a positive number. There are 2 real solutions.

(c) This needs to be rearranged to ...

... y = 5x² -x +9 . . . . add 7-3y

Then the discriminant is ...

... (-1)² -4(5)(9), a negative number. There are no real solutions.

(d) This equation is in vertex form, and the vertex is (4, 0). Since the vertex is the only x-intercept, there is one real solution.

A. -2/3 because you would go down two and then to the right three. I hope that helps.

Solution :

Given ,line that passes through the  pair of points (1,7) and (10,1)

The slope of the line passing through the points [tex](x_{1},y_{1} ) \:and \:(x_{2},y_{2})[/tex] is given by,

                         [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Here,  [tex](x_{1},y_{1} ) =(1,7)\:and \:(x_{2},y_{2})=(10,1).[/tex]

[tex]\Rightarrow m=\frac{1-7}{10-1} \\\Rightarrow m=\frac{-6}{9}=\frac{-2}{3}[/tex]

Hence , slope of the line passing through the pir of points (1,7) and (10,1) is [tex] \frac{-2}{3}[/tex] ( first option)

The straight line joining the points A(3,-5) and B(6,k) has a gradient of 4.

Gradient is the slope

So the slope of the line joining the points A(3,-5) and B(6,k) is 4

Slope of line joining two points = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

A(3,-5) and B(6,k) are (x1,y1)  and (x2,y2)

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

slope = [tex]\frac{k-(-5)}{6-3}=\frac{k+5)}{3}[/tex]

We know slope =4

 [tex]\frac{k+5)}{3}=4[/tex]

Cross multiply  and solve for k

k + 5 = 12

k = 7

The value of k = 7

complex roots occur in conjugate pairs

given 2 - 3√5 is a root then 2 + 3√5 is also a root

one of the other roots is 2 + 3√5

there are 2 roots of - 4

one of the other roots could be another - 4

Final answer:

The princess can conclude that one of the other roots is 2+ 3√5, one of the other roots could be another −4, and one of the other roots could be another 2− 3√5.

Explanation:

The princess can draw the following conclusions about the other two roots:

These conclusions are based on the fact that the princess has already traced one root to be 2−3√5 and at least two roots are labeled −4.

x = 3

2x + y - z = 3 → (1)

- x + y + 2z = 0 → (2)

3x + 2y + z = 9 → (3)

we require to eliminate the y and z terms from the equations

(1) + (3) : 5x + 3y = 12 → (4)

multiply (1) by 2

4x +2y - 2z = 6 → (5)

(2) + (5) : 3x + 3y = 6 → (6)

(4) - (6) : 2x = 6 ⇒ x = 3

Answer:

2.

1.

Step-by-step explanation:

Angles 135° and (2x+15)° together make up a line (the transversal crossing m and n). Such angles are called a "linear pair" and their sum is always 180°. That means we can write the equation ...

... 135° + (2x+15)° = 180°

... 150 +2x = 180 . . . . . . . remove the degree symbol, combine terms

... 2x = 30 . . . . . . . . . . . . subtract 150

... x = 15 . . . . . . . . . . . . . . divide by 2

Angle 1 and angle (2x+15)° are on opposite sides of the transversal line, and are both between the parallel lines m and n. This makes them alternate interior angles. Such angles are congruent—they have the same measure. We know the measure of angle (2x+15)° is (2·15+15)° = 45°, so we know the measure of ∠1 is also 45°.

a) The sum of angles in a triangle is always 180°. This means ...

... (15x +10)° + (15x -10)° + (3x +15)° = 180°

... 33x +15 = 180 . . . . . . . drop the ° symbol, combine terms

... 33x = 165 . . . . . . . . . . subtract 15

... x = 5 . . . . . . . . . . . . . . . divide by 33

b) ∠A = (15x+10)° = (15·5 +10)°

... ∠A = 85°

(1)

(a)

the sum of the angles in a triangle = 180°, hence

3x + 15 + 15x - 10 + 15x + 10 = 180

33x + 15 = 180 ( subtract 15 from both sides )

33x = 165 ( divide both sides by 33 )

x = 5

(b) ∠A = 15x + 10 = (15 × 5 ) + 10 = 75 + 10 = 85°

(2)

2x + 15 + 135 = 180 ( straight angle )

2x + 150 = 180 ( subtract 150 from both sides )

2x = 30 ( divide both sides by 2 )

x = 15 ⇒ 2x + 15 = 45

∠1 = 45° ( alternate angles are congruent )

[tex]\frac{6}{8}[/tex]

let x be the unknown value in the ratio, hence

[tex]\frac{6}{x}[/tex] = [tex]\frac{9}{12}[/tex] ( cross- multiply )

9x = 72 ( divide both sides by 9 )

x = 8

thus [tex]\frac{6}{8}[/tex] = [tex]\frac{9}{12}[/tex]

2/6 is remaining from Jillian's whole.

[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

Since the denominators of both fractions are common , that is 6

To subtract, subtract the numerators leaving the denominator

[tex]\frac{5}{6}[/tex] - [tex]\frac{3}{6}[/tex] = [tex]\frac{5-3}{6}[/tex] = [tex]\frac{2}{6}[/tex]

This fraction may be simplified by dividing the numerator/ denominator by 2

[tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex] ← in simplest form

The area of the sector of a circle with diameter 34 feet and an angle of π/5 radians is approximately 9.0095 square feet.

To find the area of the sector of a circle, we need to use the formula A = πr2θ/360, where A is the area, r is the radius, and θ is the angle in radians. The given diameter is 34 feet, so the radius is 17 feet. The angle is π/5 radians. Plugging these values into the formula, we get A = π(17)2(π/5)/360. Simplifying, we find A = 9.0095 square feet. Rounded to four decimal places, the area of the sector is 9.0095 square feet.

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To find the area of the sector of a circle, you use the formula A = 0.5 * r² * θ where r is the radius (half of the diameter) and θ is the angle in radians. After plugging in the provided values, you calculate the area to four decimal points.

The subject is related to finding the area of the sector of a circle. The formula to calculate the area of the sector is A = 0.5 * r² * θ, where r is the radius and θ is the angle in radians. In the given problem, the diameter of the circle is given as 34 feet, so the radius will be 17 feet, and the angle is given as π/5 radians.

Step 1: First, note down the radius from the given diameter, which would be 17 feet, as radius = diameter/2.

Step 2: Plug the value of the radius and the angle into the formula for the area of a sector. The calculation will look like this: A = 0.5 * (17)² * (π/5).

Step 3: Calculate the area by multiplying the values. The final answer will be rounded to four decimal places.

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75% of X  = $51, thus x or the original price is $68 . Thus the sales price is  $17 less.

First we need to know how much the discount was so 5% is actually 0.05 then we need to multiply it by 53.75 which would equal 2.6875 then subtract it by 53.75 which would equal -51.0625.

B) .95(53.75)

This is a trick question because D) could also be correct if they said you could subtract it but it's not saying use the distributive property.

The answer would be B) .95(53.75)

352 divided by 53 is 6.64150943

Hi TaeArmy23,

352 / 53

= 6.6415

= 6.6

Hope This Helps!

You are told to ignore the amount of principal paid, so you are apparently to assume the loan amount was for $50 thousand.

a) The old monthly payment was $10.67×50 = $533.50

b) The new monthly payment is $11.72×50 = $586.00

c) The increase in monthly payment is figured in the usual way:

... (new/old -1)×100% = (1.0984-1)×100% = 9.84%

_____

In reality, about 3% of the loan will have been paid at the end of 2 years. Thus, the original loan amount may have been near $51,500. This problem is telling you to ignore the difference.

Remark

The first fact you need to know is that the bank has taken money from you and nothing has been reduced from the principle. Crafty people those bankers; you are going to pay off the interest before touching the principle. They're like you to refinance for the rest of your life at the rates you currently have.

Point. You started out with a 50k debt. You still have that same debt.

Solution

Givens

number of thousands (n) = 50000/1000 = 50

Amount paid per thousand (A) = 10.67

Total monthly payments (T) = ?

Part A

T = n * A

T = 50 * 10.67

T = 533.50 is the old monthly payment

Part B

T = n * A

T = 50 * 11.72

T = 586.00  new monthly payment.

Part C

This is a notes question. What have you been told in your notes on this question. You can find the raw amount just by subtracting 586 - 533.50 = 52.50

But how do you find the % increase. Which one of the payments do you use as your base?

In point of fact, you should be using the first number 533.5

What % will you get when you multiply that by 533.5 and get 52.50?

You are not trying to find 586. You are trying to find the number that you add to 533.5 to get to 586

The answer is (52.50 / 533.5)*100% = 9.84% is the % increase.

Answer: x = -2 and y = 4

Step-by-step explanation:

We have given a system of equations

2x + 4y =12   ...........(1)

and

x + y = 2         .............(2)

Now to plot them in graph we need to find the points of the above linear equations .

From equation 1  ,we get

[tex]4y=12-2x\\\Rightarrow\ y=\frac{12-2x}{4}\\ \Rightarrow\ y=3-\frac{x}{2}\\\text{Put x=0, then} \\y=3-\frac{0}{2}=3\\\Rightarrow\ \text{Put x=6}\\y=3-\frac{6}{2} =3-3=0[/tex]

So get the points (0,3) and (6,0).

From equation 2 ,we get

[tex]y=2-x\\\text{Put x=0}\\y=2-0=2\\\text{Put x=2}\\y=2-2=0[/tex]

So we get the points (0,2) and (2,0).

So after plotting these points we get two lines intersecting at (-2,4).

Therefore our solution is x=-2 and y= 4.

Answer:

(-2, 4)

Step-by-step explanation:

y = -2x - 3

To make a table, we assume any number for x  and find out y

Lets assume x= -1

y = -2x - 3 = -2(-1) -3 = 2-3 = -1

Lets assume x= 0

y = -2x - 3 = -2(0) -3 = 0-3 = -3

Lets assume x= 1

y = -2x - 3 = -2(1) -3 = -2-3 = -5

Lets assume x= 2

y = -2x - 3 = -2(2) -3 = -4-3 = -7

Table is

x      y = -2x-3

-1       -1

0        -3

1        -5

2       -7

Your question answers itself.

You have shown the correct answer for the first drop-down: -161/289

You have shown the 3 incorrect answers out of the 4 choices for the second drop-down. The correct choice is the remaining one: -240/161.

_____

Even if all you know is that tan = sin/cos, you would suspect that answer choice based on the numerator of the cosine: 161. That value is likely the one in the denominator of the tangent value.

_____

cos(2θ) = 2cos(θ)² . . . . trig identity

... = 2(-8/17)² -1 = 128/289 -1 = -161/289

sin(2θ) = √(1-cos(2θ)²) . . . . trig identity

... = √(289² -161²)/289 = √57600/289 = 240/289

tan(2θ) = sin(2θ)/cos(2θ) . . . . trig identity

... = (240/289)/(-161/289) = -240/161

look at the shaded right-angled triangle on the left

8 is the hypotenuse n a is opposite to the 40-degree angle

by definition, sin = opposite side / hypotenuse

so sin40=a/8

rearranging a=8sin40

Two right-angled triangles share a common side with length a.

For the inverted triangle on the left, a is the opposite side to the 40-deg angle.

Its longest side, hypotenuse, is 8cm.

Use the sine function, sin40 = opposite/hypotenuse = a/8

Multiply 8 on both sides, a = 8sin40

300

divide 9 × [tex]10^{6}[/tex] by 3 × [tex]10^{4}[/tex]

= [tex]\frac{9}{3}[/tex] × [tex]10^{6}[/tex] / [tex]10^{4}[/tex]

= 3 × [tex]10^{6-4}[/tex] = 3 × [tex]10^{2}[/tex] = 300

Hey!

We have:

... 3x + 5y = 2

... 2x - 6y = 20

In order to get 5x - y , we will need to add both the equations.

3x+5y=2

2x-6y=20

____________________________________________________

...5x - y = 22

Hence, the required answer is 22.

Hope it helps!

Linear equations in two variables are solved to obtain the values of variables. Thus, the value of the equation [tex]5x - y[/tex] is [tex]\bold{22}[/tex].

Given equations are mentioned below:

[tex]3x + 5y = 2\\2x - 6y = 20[/tex]

We need to determine the values of the expression [tex]5x - y[/tex].

For calculating the value of the above expression, first we need the value of the variables x and y.

[tex]\begin {aligned}3x + 5y &= 2\\3x&=2-5y\\x&=\dfrac{2-5y}{3} \end{aligned}[/tex]

Now, substitute the value of the x in another expression and solve it further.

[tex]\begin{aligned}2 \times \dfrac{2-5y}{3} -6y&=20\\ \dfrac{4-10y}{3}-6y&=20\\4-10y-18y&=60\\28y&=-56\\y&=-2 \end{aligned}[/tex]

Now, calculate the value of x.

[tex]\begin{aligned}x&=\dfrac{2-5 \times -2}{3}\\&=\dfrac{12}{3}\\&=4 \end{aligned}[/tex]

Now, calculating the value of  [tex]5x - y[/tex].

[tex]5\times4 - (-2)=22[/tex]

Hence, the value of the expression [tex]5x - y[/tex] is 22.

Learn more about the linear equations in two variables here:

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B

to calculate percent increase use

[tex]\frac{increase}{original}[/tex] × 100%

increase = $650 - $525 = $125

percent increase = [tex]\frac{125}{525}[/tex] × 100% = 24% → B

Answer:

The answer is B) 24%

Step-by-step explanation:

The formula for percentage increase is given as:-

Percentage Increase = ( New Price - Old Price ) /old price * 100

old price = $525

New Price = $650

Percentage Increase = 24%

Hence the price increases by 24%

"Opposite sides of the transversal..." Alternate

"Between the other two lines." Interior

Alternate Interior angles.

If they were outside the two lines they would be alternate exterior angles and if they were on the same side of the transversal then they would be corresponding angles.

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

the equation of a line in slope-intercept form is

y = mx + c (m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 4, 0 ) ← points from graph

m = [tex]\frac{0-2}{-4-0}[/tex] = [tex]\frac{-2}{-4}[/tex] = [tex]\frac{1}{2}[/tex]

from the graph the y-intercept = (0, 2 ) → c = 2

y = [tex]\frac{1}{2}[/tex] x + 2 ← is the equation

The equation of the line is [tex]y = \frac{1}{2}x + 2[/tex]

The equation of a line in slope-intercept form is

y = mx + c

Here m is the slope and c is the y-intercept  

Now  

[tex]m = ( y_2 - y_1 ) \div (x_2 - x_1 )[/tex]

Here

[tex](x_1, y_1 )[/tex]= (0, 2 ) and [tex](x_2, y_2 )[/tex] = (- 4, 0 )  

Now  

[tex]m = (0-2) \div (-4-0)\\\\= -2\div -4\\\\= \frac{1}{2}[/tex]

From the graph the y-intercept = (0, 2 ) i.e. c = 2

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