What is the solution to the system below? x + 5y = 4
x - 5y = -16

(6,-2)
(2,-6)
(-6,2)
(-2,6)​

Answer:

Step-by-step explanation:

h

The result of each trigonometric functions are:

a) sin X = 7√149 / 149

b) sin Z = 10√149 / 149

c) cos X = 10√149 / 149

d) cos Z = 7√149 / 149

In a right triangle, the sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse, and the cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. Using this trigonometric functions, we can calculate sin X, sin Z, cos X, and cos Z as follows

sin X = YZ / XZ = 7 / √149

cos X = XY / XZ = 10 / √149

sin Z = XY / XZ = 10 / √149

cos Z = YZ / XZ = 7 / √149

To simplify these fractions, we can rationalize the denominator by multiplying the numerator and denominator by √149:

sin X = 7√149 / 149

cos X = 10√149 / 149

sin Z = 10√149 / 149

cos Z = 7√149 / 149

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The given question is incomplete, the complete question is:

Find sin X, sin Z, cos X, and cos Z. Write each answer as a simplified fraction.

Answer:

x/7<-3

x<-21

Step-by-step explanation:

x/7<-3

multiply the seven to get rid of x denominator

x<-21

Answer:

x/7<-3x<-21

Step-by-step explanation:

HOPE IT HELPS :)

Answer:

Isosceles triangle

Step-by-step explanation:

Given

Triangle ABC

Required

Reflect across BC and name the triangle according to length of its side

When the triangle is reflected across line BC, the new triangle is ACA (see new attachment)

And the sides of this ACA are:

AC, CA and AA

Such that

AC = CA

and

\(AA = 2 * AB\)

\(AA = 2AB\)

From the description above, we have two sides (AC and CA) of the triangle to be equal.

By classification of sides, when two sides of a triangle are equal; such triangle is an isosceles triangle

Triangle ACA' has two equal sides, based on the side lengths, triangle ACA' can be classified as: an isosceles triangle.

Recall:

Given that triangle ABC is a right triangle, if we reflect it across line BC, we will have  mirror figure of right triangle ABC, forming triangle ACA'.

That is, two right triangles of ABC, which are reflections of each other, will form triangle ACA'. (See image attached).

Thus, this means that:

Therefore,

Also, CA = C'A (congruent sides)

This means that, triangle ACA' has two equal sides that are opposite to each other.

Therefore, based on the side lengths, triangle ACA' can be classified as: an isosceles triangle.

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We can write the product in polar form as 226.27(cos 74.73° + i sin 74.73°).

To multiply two complex numbers, we use the distributive property and combine like terms. In this case, we can use the FOIL method:

(12 + 9i) (12 + 9i) = 12 × 12 + 12 × 9i + 9i × 12 + 9i × 9i

= 144 + 108i + 108i + 81i²

Recall that i represents the imaginary unit, which is defined as √(-1). Thus, i² is equal to -1. We can substitute this value into our expression:

144 + 216i - 81 = 63 + 216i

Therefore, (12 + 9i) (12 + 9i) simplifies to the complex number 63 + 216i. This means that the product of (12 + 9i) and (12 + 9i) is a complex number with a real part of 63 and an imaginary part of 216.

We can also represent the product in polar form by converting the rectangular form into polar form. To do this, we first need to find the magnitude and argument of the complex number. The magnitude is given by the formula |z| = sqrt(a^2 + b^2), where a and b are the real and imaginary parts of the complex number, respectively:

|63 + 216i| = sqrt(63^2 + 216^2) ≈ 226.27

The argument is given by the formula arg(z) = arctan(b/a):

arg(63 + 216i) = arctan(216/63) ≈ 74.73°

Therefore, we can write the product in polar form as 226.27(cos 74.73° + i sin 74.73°).

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Answer:

The answer is B. I believe :)

Step-by-step explanation:

Hope this helped!

Answer:

d.) \((-2,1,2,5)\)

Step-by-step explanation:

For (x,y), x is the independent variable, and the value of y depends on x. This also means that x would be the input, and y would be the output. Record all of the points on the graph, and then note all the y values:

\(points:(-2,5)(-1,1)(2,-2)(5,2)\\\\y-values:-2,1,2,5\)

The correct answer is d.

:Done

Answer: 18.6

Step-by-step explanation: 15^2= 225

11^2=121, so then we added 225+121= 346, then square root it, and the answer is 18.60, so we need to do it to the nearest tenth is 18.6

Answer:

44

Step-by-step explanation:

Gina is four years younger so

18+4=22

since its twice davids age

22×2=44

For a rectangle where length of its is five less than the width length, the expression for the area of rectangle is equals to the w(w - 5). So, the option(b) or second is right answer.

Area is defined as the surface covered by the specific shape. The area of a rectangle is calculated by multiplication of length of the rectangle by the width of the rectangle. We have some information regarding the rectangle. Let the Area, length and width of a rectangle shape be 'A', 'l' and 'w'. Now, length of rectangle is 5 less than the width w. So, the expression is written as, l = w - 5 --(1)

Using the formula of area of rectangle, A = length × width

=> A = l× w

Substitute the value of 'l' from equation (1), A = ( w - 5) × w

= w² - 5w

= w( w - 5)

Hence, required expression is w(w -5).

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Complete question:

The attached figure complete the question.

Answer:

Step-by-step explanation:

example

we are given: slope = 5, y-intercept = 9

y=mx+b

we just plug it in

y=5x+9

Elise's number is 29.

If you think of multiplying a value by -3 to get -33, it would obviously be 11.

So in this case, you would want to add 18 to 11 to get Elise's number, which is 29. Subtracting 18 from 29 would get you back to the value of 11, which you can then multiply it by  -3 again to get -33.

Answer:

C. 3(6+1) =21

Step-by-step explanation:

33/3 is done first and that is 11+10= 21

6+1=7(3)= 21

Let us make the line from the picture, pointing the given equations:

From the draw and the given equations, we note that:

Therefore, we can solve the equation for y as follows

Where in the last line, we add the similar terms, for example 3y+4y=7y. Let us continue the calculations

where in the second line of the equation above, we pass the 12 from the right to the left with opposite sign. We discover y as follows

That is, we have y=6.

Let us now calculate the value of RD an RT. We know from the question that

as we discover that y=6, substituting this value in the equations above we find:

We conclude that RS=27 and ST =27 .

Answer:

32.59 (nearest hundredth)

Step-by-step explanation:

Geometric sequence

General form of a geometric sequence: \(a_n=ar^{n-1}\)

(where a is the first term and r is the common ratio)

Given:

\(\displaystyle \sum^{20}_{n=1} 4 \left(\dfrac{8}{9}\right)^{n-1}\)

Therefore:

Sum of the first n terms of a geometric series:

\(S_n=\dfrac{a(1-r^n)}{1-r}\)

To find the sum of the first 20 terms, substitute the found values of a and r, together with n = 20, into the formula:

\(\implies S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}\)

\(\implies S_{20}=32.58609013...\)

\(\implies S_{20}=32.59\:\: \sf (nearest\:hundredth)\)                    

General form of geometric progression

On comparing to the summation

Apply Sum formula

\(\boxed{\sf S_n=\dfrac{a(1-r^n)}{1-r}}\)

\(\\ \implies \sf S_{20}=\dfrac{4\left(1-\left(\frac{8}{9}\right)^{20}\right)}{1-\left(\frac{8}{9}\right)}\)

\(\\ \implies\sf S_{20}=32.586\)

\(\\ \sf\mplies S_{20}=32.59\)

Answer:

1]first one

Step-by-step explanation:

because it is in the x line and its - so its the first one

Answer:

\(x^2 + 3x +2 = 0\\x^2 +2x +x +2 = 0\\x(x + 2) +1(x+2)=0\\(x+1)(x+2)=0\)

Answer:

B - I HOPE THIS IS RIGHT. ...

As a result, the two phrases are logically equal. The two formulations are not logically identical, as we can see. The two formulations are not logically identical, as we can see.

An expression or mathematical expression is a finite collection of symbols that is well-formed according to context-dependent norms.

Here,

(a) The first statement can be expressed as:

(~j -> (l v ~r))

The second statement can be expressed as:

((r ^ ~l) -> j)

To determine whether the two expressions are logically equivalent, we can use truth tables. A truth table is a method for checking the validity of logical equivalences by comparing the truth values of the two expressions for all possible combinations of inputs.

Truth table for (~j -> (l v ~r)) and ((r ^ ~l) -> j):

j l r (~j -> (l v ~r)) ((r ^ ~l) -> j)

T T T T T

T T F T T

T F T F F

T F F T T

F T T T T

F T F T T

F F T T T

F F F T T

Since both expressions have the same truth values for all possible combinations of inputs, we can conclude that the two expressions are logically equivalent.

(b) The first statement can be expressed as:

(j -> ~l)

The second statement can be expressed as:

(~j -> l)

Truth table for (j -> ~l) and (~j -> l):

j l (j -> ~l) (~j -> l)

T T T F

T F T T

F T T T

F F T T

Since the expressions have different truth values for some combinations of inputs, we can conclude that the two expressions are not logically equivalent.

(c) The first statement can be expressed as:

((r v ~l) -> j)

The second statement can be expressed as:

(j -> (r ^ ~l))

Truth table for ((r v ~l) -> j) and (j -> (r ^ ~l)):

j l r ((r v ~l) -> j) (j -> (r ^ ~l))

T T T T T

T T F T T

T F T T T

T F F T T

F T T T F

F T F T F

F F T T F

F F F T T

Since the expressions have different truth values for some combinations of inputs, we can conclude that the two expressions are not logically equivalent.

We can conclude that the two expressions are logically equivalent. We can conclude that the two expressions are not logically equivalent. We can conclude that the two expressions are not logically equivalent.

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On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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The value of the triple integral \(\int\int\int_EvdV\)where E is enclosed by the paraboloid z = x² + y² and plane z = 16 is 8192.

We have,

To evaluate the triple integral \(\int\int\int_EzdV\), where E is enclosed by the paraboloid z = x² + y² and the plane z = 16, we need to determine the limits of integration for each variable (x, y, and z).

The region E is the volume between the paraboloid z = x² + y² and the plane z = 16.

To find the limits of integration, we need to determine the bounds for each variable over the region E.

The paraboloid z = x² + y² intersects the plane z = 16 when x² + y² = 16. This represents a circle with a radius of 4 centered at the origin in the xy-plane.

Let's set up the limits of integration:

For z:

Since the paraboloid z = x² + y² and the plane z = 16 intersect at z = 16, the limits for z will be from 0 to 16.

For y:

The region E lies within the circle with radius 4 in the xy-plane.

So, the limits for y will be from -4 to 4.

For x:

Given y and x are symmetric, and the paraboloid is circularly symmetric, the limits for x will also be from -4 to 4.

Now, the triple integral becomes:

\(\int\int\int_E zdV = \int\int\int_E z dV\)

= ∫(from x=-4 to 4) ∫(from y=-4 to 4) ∫(from z=0 to 16) z dz dy dx

Now, integrate with respect to z:

∫(from z=0 to 16) z dz

= [z²/2] (from z=0 to 16)

= (16²/2) - (0²/2)

= 128

Now, integrate with respect to y:

∫(from y=-4 to 4) 128 dy

= 128 * [y] (from y=-4 to 4)

= 128 * (4 - (-4))

= 128 * 8

= 1024

Now, integrate with respect to x:

∫(from x = -4 to 4) 1024 dx

= 1024 [x] (from x = -4 to 4)

= 1024 * (4 - (-4))

= 1024 * 8

= 8192

Therefore,

The value of the triple integral \(\int\int\int_EvdV\)where E is enclosed by the paraboloid z = x² + y² and plane z = 16 is 8192.

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The complete question:

Evaluate \(\int\int\int_E vdV\)where E is enclosed by the paraboloid z = x² + y² and the plane z = 16

Resuepstaa

179/4=

44,75

Answer:

-82

Step-by-step explanation:

84/21=4

-25x4=-100

-3x-6=18

-100+18=-82

Answer:

drake saved up $150

Step-by-step explanation:

Answer:

125- 50=75, 75+75=150 so he saved $150

Answer:

yes you can

Step-by-step explanation:

if you rounded 18.3 to the tenth it would be 183 and if you rounded it to the hundreds it would be 1,830

Answer:

A

Step-by-step explanation:

Continuous data is a continuous scale that covers a range of values without gaps, interruptions, or jumps.

The actual dimensions of Abigail's house are 18 ft by 20 ft.

Abigail's house is represented by a scale drawing with dimensions of 9 cm by 10 cm. We are told that 6 cm on the scale drawing equals 12 ft. To find the actual dimensions of Abigail's house, we need to determine the scale factor.

First, we calculate the scale factor by dividing the actual length (12 ft) by the corresponding length on the scale drawing (6 cm). The scale factor is 12 ft / 6 cm = 2 ft/cm.

Next, we can use the scale factor to find the actual dimensions of Abigail's house. We multiply each dimension on the scale drawing by the scale factor.

The actual length of Abigail's house is 9 cm * 2 ft/cm = 18 ft.
The actual width of Abigail's house is 10 cm * 2 ft/cm = 20 ft.

Therefore, the actual dimensions of Abigail's house are 18 ft by 20 ft.

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Answer:

x=3

y=5

Step-by-step explanation:

x+y=8

x=8-y

2.5(8-y)+0.5y=10.00

20-2.5y+0.5y=10.00

20-2y=10

-2y=-10

-y=5

y=5

Replace y with 5:

x+y=8

x+5=8

x=3

The value of y after solving the triangle using sine rule is 46.15.

Sine rule is a rule that relates the sides of a triangle with the sine of their opposite angles.

To calculate the value of y, we use the sine rule formula

Formula:

Where:

From the question,

Given:

Susbtitute these values into equation 1 and solve for y

Hence, the value of y is 46.15.

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Answer:

Let x be the daily fee

0.5(48) +x = 64  is the equation,

Multiply:

24 + x = 64

Subtract:

x=40

The daily fee is $40

Answer:

C ; 20 weeks

Step-by-step explanation:

\(y=0.25x+18\\23=0.25x+18\\23-18=0.25x+18-18\\5=0.25x\\\frac{5}{0.25}=\frac{0.25x}{0.25} \\20=x\)