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The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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Answer:

5/9

Step-by-step explanation:

Multiply the numerators 2 and 5 to get 10|
Multiply the denominators 3 and 6 to get 18

10/18 simplifies to 5/9

The ratio of the areas of two similar polygons can be found by using the ratio of their perimeters or the ratio of similarity and squaring it which is true.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

Similar polygons are those whose perimeter ratios are identical to their respective scale factors. The common fraction of the sizes of two matching sides of two identical polygons is known as a scale factor.

The given statement is true.

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On solving the provided question, we can say that the equation,  x² - 16x + 4 = 0 => ( x - 12)(x + 2) = 0 => x = 12, -2

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation,

x² - 16x + 4 = 0

( x - 12)(x + 2) = 0

x = 12, -2

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Answer:

D. \( 4\frac{2}{5} \)

Step-by-step explanation:

Area of fabrics = 2¾ square yards

Width of fabrics = ⅝ yard

Length of fabrics = x

Area = length * width

Therefore:

2¾ = ⅝*x

Change the mixed fraction to improper fraction

\( \frac{11}{4} = \frac{5x}{8} \)

Cross multiply

\( 4*5x = 11*8 \)

\( 20x = 88 \)

Divide both sides by 20

\( \frac{20x}{20} = \frac{88}{20} \)

\( x = \frac{22}{5} \)

\( x = 4\frac{2}{5} \)

\( length = 4\frac{2}{5} \)

The value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.

The value of angle x and angle y is calculated by applying principle of angles formed by parallel lines as follows;

The value of angle adjacent x = 102⁰

The value of angle x   is calculated as;

x = 180 - 102 ( sum of angles on a straight line)

x = 78⁰

The value of angle y is calculated as follows;

y = 115⁰ (corresponding angles are equal)

Thus, the value of angle x and angle y is determined as 78⁰ and 115⁰ respectively.

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Answer:

0.325

Step-by-step explanation:

Let A represent the event: winning a prestigious scholarship
Let B represent the event: plays a varsity sport

Given

Therefore the probability that someone wins the scholarship given that they play a varsity sport is 0.325

The measure of angle x on the straight line is 130 degrees.

The sum of interior angles in a triangle equals 180 degrees.

To determine the value of x, we first determine its suplemetary angle x .

Hence:

40 + 90 + ( suplemetary angle of x ) = 180

Solve for the suplementary angle:

130 + ( suplemetary angle of x ) = 180

Suplementary angle of x = 180 - 130

Suplemetary angle of x = 50 degree

Now, we can find the measure of  angle x.

Note that, sum of angles on a straight line equals 180 degree.

Hence:

x + ( suplemetary angle of x )  = 180

x + 50 = 180

Solve for x

x = 180 - 50

x = 130 degrees.

Therefore, the value of x is 130 degrees.

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The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

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Answer:

54 hours

Step-by-step explanation:

So, first of all subtract the money she has from the total amount.

540-60=480 She still needs $480. So divide this number by the amount she gets in an hour. (9)

480/9 =53.33333 since she can't work half hours, i rounded up.

Answer:

2 forms

Step-by-step explanation:

hope this helps <3

\( \sf \longrightarrow \: \frac{8}{5} \div 6 \\ \)

\( \sf \longrightarrow \: \frac{5}{8} \times 6 \\ \)

\( \sf \longrightarrow \: \frac{5 \times 6}{8} \\ \)

\( \sf \longrightarrow \: \frac{30}{8} \\ \)

\( \sf \longrightarrow \: \frac{8}{30} \\ \)

\( \sf \longrightarrow \: 0.26 \\ \)

_____________________________

Answer:

x² - 6x + 8 = 0

or, x² - (4+2)x + 8 = 0

or, x² - 4x - 2x + 8 = 0

or, x(x-4) -2(x -4)= 0

or , (x-4) (x-2) = 0

either,

x - 2 = 0

x = 2

OR,

x - 4 = 0

x = 4

next ,

x-p = 9

or, 2-p = 9

p= -7

either,

x-p = 9

or, 4 - p = 9

or, p= -5

hope this will help you

Answer:

C is correct. If the scale factor is greater than 1, the image is an enlargement. The segment UT could be an enlargement of the segment ST.

Step-by-step explanation:

A. If > 1, then the image of could be .  

B. If 0 < < 1, then the image of could be . ( If the scale factor is between 0 and 1, the image is a reduction )

C. If > 1, then the image of could be .

D.If = 2, then the image of is itself.

A is not correct.  If the scale factor is between 0 and 1, the image is a reduction.

B is not correct.  If the scale factor is between 0 and 1, the image is a reduction.

C is correct.  If the scale factor is greater than 1, the image is an enlargement.

D is not correct.  If the scale factor is 1, the figure and the image are congruent.

The dilation factor for triangle PST (K₁) is less than that of triangle PUV (K₂).

Given is a diagram that represents a dilation with a center at {P}. The scale factor of the dilation is {K}.

The dilation factor for triangle PST (K₁) is less than that of triangle PUV (K₂).

Therefore, the dilation factor for triangle PST (K₁) is less than that of triangle PUV (K₂).

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x² + 3x - 2

(5)² + 3 × 5- 2

25 + 15 - 2

40 - 2

38...

Answer:

It is 6mn² if you want to know the greatest common factor.

Step-by-step explanation:

Let me start with the coefficients. Since 6 can divide all coefficients, we should pick 6.

For the variables, the least power of m found in the expression is m¹ or simply m.

The least power of n found in the expression is n². Wrapping this up, you get 6mn².

But the expression has many common factors.

e.g. 2, 3, 6, m, n, n², . . .

You can also say -2, -3, -6, -m, -n, -n².

Generally, you may have many common factors, but you will have only one greatest common factor.

Answer:

  18 cubic inches

Step-by-step explanation:

The formulas for the volumes of a cone and a cylinder can be used to answer this question.

The volume of a cone is given by ...

  V = 1/3πr²h . . . . . volume of cone with radius r and height h

The volume of a cylinder is given by ...

  V = πr²h . . . . . volume of a cylinder with radius r and height h

Comparing the formulas, we see that the volume of a cone is 1/3 the volume of a cylinder with the same radius and height.

  (cone volume) = 1/3(cylinder volume)

Multiplying this equation by 3 gives ...

  3×(cone volume) = (cylinder volume)

Using the given value for cone volume, we have ...

  cylinder volume = 3×(6 in³) = 18 in³

The volume of the cylinder is 18 cubic inches.

Answer:

x=5

Step-by-step explanation:

x to the 3rd power = 5 to the 3rd power

x=5

Answer:

9576

Step-by-step explanation:

Area of the triangle × height

(1/2×28×19)×36

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

Answer:

31.4

Step-by-step explanation: multiply 10 and 3.14 as the measurements

Answer:

Her unit rate remained the same

Step-by-step explanation:

80 is twice as much as 40. 5 minutes is twice as long as 2 1/2 minutes. Her unit rate never changed.

Answer:

her unit rate remained the same

Step-by-step explanation:

Answer:

C. DIvide both sides by -6 to get 1/9.

Step-by-step explanation:

a) Both events occur: A ∩ B

b) At least one event occurs: A ∪ B

c) Neither event occurs: A' ∩ B'

d) Exactly one event occurs: (A ∩ B') ∪ (A' ∩ B)

In Event A and B, the intersection A ∩ B tells us the outcome where both events occur. The Union of A and B tells us the outcome where at least one event occurs. The intersection of the complements of A and B (A' ∩ B') tells us the outcome where neither event occurs.

Finally, the union of the intersection of A and the complement of B and the intersection of the complement of A and B ( (A ∩ B') ∪ (A' ∩ B) ) tells us the outcome where exactly one event occurs.

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(-3, 3) and (4, -1) are the points that can be used to form a right triangle to derive the distance formula to find the length of the line segment

Given the line on the xy-plane, we are to determine the points on the line that can be used to determine the distance between the two points.

The required points on the line will be the two endpoints on the line. The end points are (-3, 3) and (4, -1). The distance between this points is expressed as:

D = √(-1-3)²+(4+3)²
D = √14 + 49
D = √63

Hence the points that can be used to form a right triangle to derive the distance formula are (-3, 3) and (4, -1)

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Answer: It’s -1,-3

Step-by-step explanation:

got 100 on the test

Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

Approximately 34.87% of the readers surveyed don't use e-readers.

To find the approximate sample proportion of readers who use e-readers, we divide the number of readers who said they read books on e-readers (1954) by the total number of readers surveyed (3000):

Approximate sample proportion = Number of readers who use e-readers / Total number of readers surveyed

Approximate sample proportion = 1954 / 3000 ≈ 0.6513

To express this as a percentage, we multiply the sample proportion by 100:

Approximate sample proportion as a percentage = 0.6513 × 100

= 65.13%

Therefore, the approximate sample proportion of readers who use e-readers is approximately 65.13%.

This means that approximately 65.13% of the readers surveyed use e-readers.

To determine the percentage of readers who don't use e-readers, we subtract the sample proportion from 100%:

Percentage of readers who don't use e-readers = 100% - 65.13%

= 34.87%

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The total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

Given:

Court lines are 50 mm wide.

Court paint covers 7 m² per litre of paint.

The centre circle is a complete circle, so the circumference is given by the formula: Circumference = 2πr

Radius of the entire circle = 9 m / 2 = 4.5 m

Radius of the centre circle = 4.5 m - 0.05 m (converted 50 mm to meters) = 4.45 m

Circumference of the centre circle = 2π(4.45 m) = 27.94 m

Next, let's calculate the circumference of the semicircles:

The semicircles are half circles, so the circumference is given by the formula: Circumference = πr

The radius (r) of the semicircles is the same as the radius of the entire circle, which is 4.5 m.

Circumference of a semicircle = π(4.5 m) = 14.14 m

Total length = Circumference of the centre circle + 2 x Circumference of a semicircle

Total length = 27.94 m + 2(14.14 m)

Total length = 56.22 m

Therefore, the total length of the centre circle and the two goal semi circles to be repainted is 56.22 meters.

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The greatest common factor, GCF, of 8y, -12x, and 4xy is 4

From the question, we are to determine the greatest common factor of the given expressions.

The given expressions are 8y, -12x, and 4xy

To determine the greatest common factor, we will express each of the expressions as a product of their factors.

8y = 2 × 2 × 2 × y

-12x = 2 × 2 × 3 × -x

4xy = 2 × 2 × x × y

From above, we can observe that the greatest common factor is

2 × 2

= 4

Hence, the greatest common factor is 4

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