Solve the system of equations without graphing

In order for the relationship zyx ~ wvu to be correct, the following conditions must be true:

Corresponding angles are congruent: The angles formed by matching vertices should have the same measures in both triangles. This ensures that the corresponding angles are equivalent.

Corresponding sides are proportional: The lengths of the sides that connect the corresponding vertices of the triangles should have a consistent ratio. This implies that the corresponding sides are proportional to each other.

These conditions are based on the definition of similarity between two triangles. If both the corresponding angles are congruent and the corresponding sides are proportional, then the triangles zyx and wvu are considered similar (denoted by ~).

Therefore, in order for zyx ~ wvu to be correct, the congruence of corresponding angles and the proportionality of corresponding sides must hold true.

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9514 1404 393

Answer:

  22.6

Step-by-step explanation:

The diagonal of the square is they hypotenuse of an isosceles right triangle with sides of 16 inches. The Pythagorean theorem tells you its length (d) is ...

  d^2 = 16^2 +16^2 = (16^2)(2)

Taking the square root, we have ...

  d = 16√2 ≈ 22.6 . . . . inches

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

1) The lower limit of the confidence Interval is: 1489.77.

The upper limit of the confidence Interval is: 1530.23

2) The lower limit of the confidence Interval is: 1478.32

The upper limit of the confidence Interval is: 15411.68

The formula to find the confidence interval is:

CI = x' ± z(σ/√n)

where:

CI is confidence interval

x' is sample mean

z is z-score at confidence level

σ is standard deviation

n is sample size

1) The parameters are:

σ = $234

x' = $1510

n = 362

z at 90% CL = 1.645

Thus:

CI = 1510 ± 1.645((234/√362)

CI = 1510 ± 20.23

CI = (1489.77, 1530.23)

2) The parameters are:

σ = $234

x' = $1510

n = 362

z at 99% CL = 2.576

Thus:

CI = 1510 ± 2.576((234/√362)

CI = 1510 ± 31.68

CI = (1478.32, 15411.68)

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Answer:

540

Step-by-step explanation:

you can draw  5 triangles from the center...

5*180-360 = 540

Answer:

A) З x,y : ( x/y < 1,  y/x < 1 )

B) ∀ Y : ( Y > 0 = 1/Y > 0 )

C) з x,y : ( x+y = xy )

D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))

E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )

F) n ( ( з x ∀ y ( x <y ) )

G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))

H) ∀x ( (x≠0) = ( з! y (xy = 1))

Step-by-step explanation:

since the domain of discourse is a set of all real numbers the logical expressions of the English statements are expressed with respect to real number:

A) З x,y : ( x/y < 1,  y/x < 1 )

B) ∀ Y : ( Y > 0 = 1/Y > 0 )

C) з x,y : ( x+y = xy )

D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))

E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )

F) n ( ( з x ∀ y ( x <y ) )

G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))

H) ∀x ( (x≠0) = ( з! y (xy = 1))

In translating English written expressions to logical expressions, we have to know the domain of the discourse. The domain of discourse can be said to be a set of all real numbers that the logical expressions of the English statements are expressed with respect to their real numbers. And as such, we arrive at each of this.

A) З x,y : ( x/y < 1,  y/x < 1 )

B) ∀ Y : ( Y > 0 = 1/Y > 0 )

C) з x,y : ( x+y = xy )

D) ∀ x,y : [ ( x>0 ) ∧( y > 0 ) = (( x/y > 0 ) ∧ ( y/x > 0 ))

E ) ∀ y : [ ( y > 0 ) ∧ ( y < 1) = ( 1 / y > 1 )

F) n ( ( з x ∀ y ( x <y ) )

G) ∀x (( x ≠ 0 ) = ( зy ( xy = 1 ) ))

H) ∀x ( (x≠0) = ( з! y (xy = 1))

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Answer:

Step-by-step explanation:480 x o.75=360

and now you add this amount on payed

360 + 480=840 was original price

The shape represents an isosceles trapezoid

The value of CP is 1.1 units

The given parameters are:

The diagonals of an isosceles trapezoid are congruent.

This means that:

\(CA = BD = 2.8\)

Also, we have:

\(CA = CP + AP\)

Substitute values for CA and AP

\(CP + 1.7 = 2.8\)

Subtract 1.7 from both sides

\(CP = 1.1\)

Hence, the value of CP is 1.1 units

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Answer:

35%

Step-by-step explanation:

The total number of cinema seats can seat 280 people. Since 98 people take up 98 seats of the cinema, they are taking up 98 cinema seats out of the 280 cinema seats originally available.

As a fraction this would be written as  \(\frac{98}{280}\) .

What you want to do is then divide 98 by 280 or 98/280, to get 0.35.

To get the percentage of seats filled, you must multiply the decimal you get by 100.

So it should look like this and your result should be 35%.

\(\frac{98}{280} = 0.35 *100=35\)%

Answer:

f^(-1)(x) = ±√(x - 5).

Step-by-step explanation:

Replace f(x) with y: y = x^2 + 5.

Swap the x and y variables: x = y^2 + 5.

Solve the equation for y. To do this, we'll rearrange the equation:

x - 5 = y^2.

Take the square root of both sides (considering both positive and negative square roots):

±√(x - 5) = y.

Swap y and x again to express the inverse function:

f^(-1)(x) = ±√(x - 5).

Answer:

There were 20 total questions.

Step-by-step explanation:

\(75\% = 0.75 = \frac{3}{4} \\ \frac{15}{ \frac{3}{4} } = \frac{15(4)}{3} = \frac{5 \times 3 \times 4}{3} = 5 \times 4 = 20\)

The minimum (smallest) data value is 9.8.

The maximum (largest) data value is 9.89.

The data value that shows up twice for the stem 9.5 is 9.55.

To analyze the stemplot provided, we can identify the minimum and maximum data values, as well as determine which data value shows up twice for the stem 9.5.

Looking at the stemplot:

Stem | Leaf

9.5 | 23556

9.6 | 689

9.7 | 246

9.8 | 001557

To find the minimum data value, we look for the smallest leaf value. In this case, the smallest leaf value is 0. The stem for this leaf value is 9.8. Therefore, the minimum data value is 9.8.

To find the maximum data value, we look for the largest leaf value. In this case, the largest leaf value is 9. The stem for this leaf value is 9.8. Therefore, the maximum data value is 9.89.

To determine which data value shows up twice for the stem 9.5, we examine the corresponding leaves for that stem. In this case, the leaves for the stem 9.5 are 2, 3, 5, 5, and 6. We can see that the leaf value 5 appears twice. Therefore, the data value that shows up twice for the stem 9.5 is 9.55.

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The value of x in the triangle is 10

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted by triangle ABC.

The sum of the three angles in a triangle is 180°.

Therefore

(5x - 5)° + 8x + (6x - 5) =180

5x-5+8x+6x-5 = 180

collect like terms

5x+8x+6x-5-5 = 180

19x = 180+10

19x = 190

divide both sides by 19

x = 190/19

x= 10

therefore the value of x is 10

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Answer:

reference attached

hope it helps you<3

Given:

The figure shown is a trapezium.

By the property of angles of trapezium,

The sum of angles in the quadrilateral is 360 degrees.

Therefore,

Hence, x= 40

We have the following equation given:

We can aggrupate similar terms in the left of the equation and we got:

And solving we got:

And if we divide both sides by 44 we got:

The value of function f (8) is, - 42 which is negative.

Since, A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

We have to given that;

The function is ,

⇒ f (x) = 6 (1 - x)

Now, WE can find the value of f (8) by substitute the value of x = 8 in above function,

⇒ f (x) = 6 (1 - x)

⇒ f (8) = 6 (1 - 8)

⇒ f (8) = 6 × - 7

⇒ f (8) = - 42

Thus, The value of function f (8) is, - 42 which is negative.

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Answer: If 34,500 copies sold in the first month of release represent 9.8% of the number of copies sold to date, we can use this information to find the total number of copies sold to date. We can set up the equation as:

(34,500 copies) / (9.8%) = (Total number of copies sold to date)

To solve for the total number of copies sold to date, we can cross-multiply and divide by 0.098:

(34,500 copies) * (100%) / (9.8%) = (Total number of copies sold to date)

(34,500 copies) * (100/9.8) = (Total number of copies sold to date)

This simplifies to:

(34,500 copies) * 10.20408163 = (Total number of copies sold to date)

Total number of copies sold to date = 353878.163.

Rounding the answer to the nearest whole number we get:

Total number of copies sold to date = 353878.

So the book has sold 353878 copies to date.

Step-by-step explanation:

352,041

Take 34,500 and divide it be 9.8.

Next, multiply it by 100.

not sure if this is the answer

Answer:

Hi

please mark brainliest ❣️

Thanks

Step-by-step explanation:

10 + x / 3 = 12

Cross multiply

10 + x = 12× 3

10 + x = 36

Collect like terms

x= 36 - 10

x = 26

Answer:

Future amount (A) = $1,258.77 (Approx)

Step-by-step explanation:

Given:

Amount deposit (p) = $693

Rate of interest monthly (r) = 4.9% / 12 = 0.003833

Number of month (n) = 13 × 12 = 156

Find:

Future amount (A)

Computation:

\(A = p [1+r]^n \\\\ A = 693 [1+0.003833]^{156}\\\\ A= 693[1.8163]\\\\ A = 1258.77\)

Future amount (A) = $1,258.77 (Approx)

The first expression

(-25) + 12

open the parentheses

-25 +12

= - 13

for the second expression

40 + (-63)

in mathematics

- x + = -

40 - 63

= -23

from the two results

-13 and -23

-13 is greater than -23, therefore -23 is less or 40 + (-63)

answer: 40 + (-63) is less

\(f(x)=x\) for \(x\leq0\), therfore \(f(0)=0\).

the first domain is true for f(0) so we substitute value of x in the first function

\(f(x) = x \\ f(0) = 0\)

Our polynomial is

This kind of polynomial is actually special, because create polynomials equivalent to it is very simple. For instance, the simplest equivalent polynomial we can create is generated by multiplying and dividing by "n". Doing that gives us

Answer:

y = 8 - 5x

Step-by-step explanation:

both equations shares the same gradient as they are parallel

from y= 9-5x, the gradient is -5

subst x = 0, y=8, and m= -5 into the y = mx + c to find the value of c

8 = (-5)(0) + c

c= 8

therefore the eqn is y = 8 - 5x

The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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Answer:

area of the parallelogram=6

area of the rectangle=20

total area=26 square units

Answer:

the anser is d

Step-by-step explanation:

Answer:

b) 7x² - 12x√14 + 72

Step-by-step explanation:

Let's solve the problem,

→ (x√7 - 3√8)(x√7 - 3√8)

→ (x√7 - 3√8)²

→ 7x² - 12x√14 + 72

Hence, option (b) is correct.

There are 540 men living in the mini city.

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

Therefore, there are 540 men living in the mini city.

To check our answer, we can substitute x = 540 into our original equation:

540 + (540 + 150) = 1230

690 = 1230

This is false, so there must be an error in our calculation. We can double-check our work by trying a different approach.

We know that the number of women exceeds the number of men by 150, so we can represent the number of women as (x + 150). We also know that the total number of people is 1230, so we can set up an equation:

x + (x + 150) = 1230

Simplifying this equation, we get:

2x + 150 = 1230

Subtracting 150 from both sides, we get:

2x = 1080

Dividing both sides by 2, we get:

x = 540

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