To prove ABC is isosceles, which of the following
statements can be used in the proof?

Answer:

[tex]0 = {x}^{2} + 14x + 46[/tex]

[tex] \boxed{ {x}^{2} - 14x - 46 = 0}[/tex]

[tex]x1.2 = \frac{ - b ±  \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]

[tex]x1.2 = \frac{ - 14  ± \sqrt{ { - 14}^{2} - 4(1 \times 46) } }{2 (1)} [/tex]

[tex]x1.2 = \frac{ - 14 ±  \sqrt{196 - 184} }{2} [/tex]

[tex]x1.2 = \frac{ - 14 ± \sqrt{12}  }{2} [/tex]

[tex]x1.2 = \frac{ \cancel{ - 14} ±  \sqrt{12} }{ \cancel{2} } [/tex]

[tex]x1.2 = - 7 ±  \sqrt{12} [/tex]

[tex]x1.2 = - 7 ±  \sqrt{4 \times 3} [/tex]

[tex] \boxed{ \bold{ - 7 ± 2 \sqrt{3}}} [/tex]

Answer:

its a I hope it's helps you

The values of a and b which make the equation true are; a = 3 and b = 4 respectively.

From the question; the expression given is;

[tex]\sqrt{648} = \sqrt{2^{a} * 3^{b} }[/tex]

In essence; we have;

648 = 2^a × 3^b

By expression of of 648 as the product of its lowest factors; we have;

648 = 2 × 2 × 2 × 3 × 3 × 3 × 3.

In which case; we have;

648 = 2³ × 3⁴

Ultimately, the values of a and b which make the equation true are 3 and 4 respectively.

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The complete question is -

What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b Baseline EndRoot a = 3, b = 2 a = 2, b = 3 a = 3, b = 4 a = 4, b = 3

Answer:

20

Step-by-step explanation:

a c will have the same angle as b d

Mr. Cahn’s total earnings in a year is $18,900.

The total earnings is a function of the annual salary, commission and Christmas bonus.

Total earnings = annual salary + commission + Christmas bonus

Commission = 6% x (160,000 - 20,000)

6% x $140,000

0.06 x 140,000 =  $8,400

Total earnings =  $8,400 + 10,000 + $500 = $18,900

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In the quadrilateral ABCD, in which angle A = 60° and angle B = 50°. The measure of angles C and D are,

∠C = 200° and ∠D = 50°

In the quadrilateral ABCD, it is given that,

A = 60° and angle B = 50°

Now, since AC is the angle bisector of angles A and C, we have,

∠DAC = ∠BAC ......... (1)

And ∠ACD = ∠ACB ............ (2)

Also, AC divides the quadrilateral ABCD into two triangles, ΔABC and ΔACD.

In ΔABC, ∠BAC = 30° [from (2)] and ∠ABC = 50°

Using angle sum property of a triangle, we have,

∠BAC + ∠ABC + ∠ACB = 180°

⇒ 30° + 50° + ∠ACB = 180°

80° + ∠ACB = 180°

∠ACB = 180° - 80°

∠ACB = 100°

From (1), ∠ACD = ∠ACB = 100°

∠C = ∠ACD + ∠ACB

⇒ ∠C = 100° + 100°

∠C = 200°

Now, according to the angle sum property of a quadrilateral,

∠A + ∠B + ∠C + ∠D = 360°

Substituting the values of ∠A, ∠B, and ∠C, we get,

60° + 50° + 200° + ∠D = 360°

310° + ∠D = 360°

∠D = 360° - 310°

∠D = 50°

Hence, in quadrilateral ABCD, ∠C = 200° and ∠D = 50°

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Assuming all the fishes caught by Bridget and her dad have the same total weight, then the first fish Bridget caught would weigh 5 ounces while the first fish caught by her dad weighed 17 ounces.

Weight can be defined as the force acting on an object or a physical body due to the effect of gravity. Also, the weight of a physical object (body) is typically measured in Newton or ounces.

First of all, we would determine the weight of all of the fishes caught by both Bridget and her father (dad) while translating the word problem into an algebraic equation as follows:

For Bridget, we have:

Bridget's fish = f + 2f + 3f + 2 + ½f + ⅗f

Bridget's fish = 7 f/10 + 2      ......equation 1.

For her dad, we have:

Dad's fish = 3f + 2 + ⅘f + 2f + 4 + ½f

Dad's fish = 6 3f/10 + 6            ......equation 2.

Equating eqn. 1 and eqn. 2, we have:

7 f/10 + 2 = 6 3f/10 + 6

7 f/10 - 6 3f/10 = 6 - 2

8f/10 = 4

8f = 40

f = 40/8

Bridget, f = 5 fishes.

Since her dad's fish weighed 2 more than 3 times, we have:

Dad = 3f + 2

Dad = 3(5) + 2

Dad = 15 +2

Dad = 17 ounces.

In conclusion, the first fish Bridget caught would weigh 5 ounces while the first fish caught by her dad weighed 17 ounces assuming all the fishes caught by Bridget and her dad have the same total weight.

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Complete Question:

Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was 2 times the weight of the first fish, another was 2 more than 3 times the weight of the first fish, the next was 1/2 the weight of the first fish, and the last was 3/5 the weight of the first fish. Bridget’s dad caught four fish. The first fish he caught weighed 2 more than 3 times the weight of the first fish caught that day. One fish weighed 4/5 the weight of the first fish caught that day, one weighed 4 more than 2 times the weight of the first fish caught that day, and the last weighed 1/2 the weight of the first fish caught that day.

If all the fish Bridget caught have the same total weight as all the fish her dad caught, then the first fish Bridget caught weighed___ ounces and the first fish her dad caught___ weighed ounces.

Please see the explanation of this question to see procedure for the dilation of the triangle ABC and the image attached below to know the result.

In this question we must apply a kind of rigid transformation known as dilation. A dilation of a point around a point of reference is defined by the following operation:

P'(x, y) = O(x, y) + k · [P(x, y) - O(x, y)]     (1)

Where:

Let assume that the point P is the origin of a rectangular system of coordinates. Then, the coordinates of the three vertices of the triangle ABC respect to the origin are: A(x, y) = (- 1, 2), B(x, y) = (- 1, - 1), C(x, y) = (2, 0).

Then, the vertices of the resulting triangle A'B'C' are, respectively:

A'(x, y) = (0, 0) + 3 · [(- 1, 2) - (0, 0)]

A'(x, y) = (- 3, 6)

B'(x, y) = (0, 0) + 3 · [(- 1, - 1) - (0, 0)]

B'(x, y) = (- 3, - 3)

C'(x, y) = (0, 0) + 3 · [(2, 0) - (0, 0)]

C'(x, y) = (6, 0)

Finally, we draw the resulting triangle with the help of a graphing tool.

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Service organizations are ideally suited for activity-based costing because virtually all of the costs for a service company are indirect and appear to be fixed.

Activity-based costing is a method of assigning overhead and indirect costs such as salaries and utilities to products and services.

The ABC system of cost accounting is based on activities that are considered any event, unit of work, or task with a specific goal.

Here, activity-based costing has been used in manufacturing products but can also be applied to service industries, or businesses that provide a service instead of a product.

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Chris and Jim must replace a total quantity of 17 tyres.

In this problem we must use an inequality of the form f(x) ≥ a, where f(x) is the difference between the number of tyres replaced by Jim and the number of tyres replaced by Chris:

(25/20) · x - x ≥ 3

(5/20) · x ≥ 3

x ≥ 12

Then, the minimum number of tyres to be replaced is n = 15 + 12 = 17 tyres.  

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The statement 6.05 can be read as "six and five-hundredths" is true and 11.8 can be read as "eleven and eight tens" is false

6.05

6 = ones

0 = tenths

5 = Hundredth

6.05 = six and five-hundredths

11.8

1 = Tens

1 = Ones

8 = tenths

11.8 = eleven and eight tenths

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Answer:

[tex]\huge\boxed{\sf 8:32\ AM}[/tex]

Step-by-step explanation:

Woke up = 7:30 AM

Time to:

Altogether:

= 14 + 9 + 39 min

(As we know that, 1 hour = 60 minutes)

So,

Time he reached the school:

7 hr 30 min + 1 hr 2 min

Combine like terms

7 hr + 1 hr + 30 min + 2 min

OR

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

Paul woke up for school at 7:30 AM. He took 14 minutes to get ready, 9 minutes to finish his breakfast and 39 minutes to commute to school. At what time did he reach the school?

In this question we are asked to calculate the time paul reach the school.

Altogether time paul took to get ready, to finish his breakfast and to commute to school.

(14 + 9 + 39) minutes

→ (23 + 39) minutes

→ 62 minutes

Now we will convert minutes into hour.

62 ÷ 60

→ 1 hr 2 min

Now we will calculate the time he reached his school.

7 hr + 30 + 1 hr 2 min

[tex]\begin{array}{cc}7 \sf{hrs} \: & \: 30 \sf{min} \\ \underline{1 \: \sf{hr}} & \underline{2 \sf{min} } \\ \pmb{8 \sf{hrs}}& \pmb{32 \sf{min}}\end{array}[/tex]

He will reach the school at 8:32 AM.

Step-by-step explanation:

Let the number of stamps of John be x.

Then number of Minghua's stamps:

John's: x

Minghua's: (3/2)x

Answer:

Step-by-step explanation:

This is what I am thinking.   - ,- ,- , -  I number goes in each space.  There are 10 numbers to choose from and I cannot use a digit more than once.  I only have 1 choice for last slot and that is the number 7.  I have 9 numbers left .  I could put any one of the 9 numbers in the first spot, then there are only 8 numbers to choose from, so I will put 8 in the second spot.  I now have only 7 numbers that are left for the third spot.

If I multiple this together 9x8x7x1 = 504

Answer:

sin-1 (24/25).

Step-by-step explanation:

We are given the opposite side  to the given angle (24 ft) and the hypotenuse (25 ft) .

sin = opposite / hypotenuse

- so it is  sin-1 (24/25).

The equation of the function is −3<x<1. See the explanation below.

Given the graph of function f is a parabola,

Thus, equation of parabola  is y=(x+3)(x+1)

⇒y=x² +4x+3

⇒y−3+2²

= x²+2× x ×2+2²

⇒y+1=(x+2)²

We can rewrite this as

 (x+2)² =4× (1/4) ×(y+1)

Comparing the above equation to the equation of a parabola, (x−h)² =4a(y−k), where (h,k) is the coordinates of vertex of parabola, we have,

(h,k)≡(−2,−1)

Hence, the x coordinate of the vertex is −2 which lies in the interval −3<x<1

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The solutions of the given quadratic equation is;  (1/4) + √7i/4 and  (1/4) - √7i/4

We are given the quadratic equation as;

2x² - x + 1 = 0

To solve this to find the root, we will use the quadratic formula which is given by;

x = [-b ± √(b² - 4ac)]/2a

Now, from the given quadratic equation, we can say that the values of a, b and c are;

a = 2; b = -1 and c = 1

Thus;

x = [-(-1) ± √((-1)² - 4(2 * 1))]/2(2)

x =  [1 ± √(1 - 8)]/4

x = [1 ± √(-7)]/4

x = (1/4) ± √7i/4

Thus;

x = (1/4) + √7i/4 and  (1/4) - √7i/4

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Answer: $37.50

Step-by-step explanation:

Answer: 18

Step-by-step explanation:

By the exterior angle theorem,

[tex]x+18+x+12=x+48\\\\2x+30=x+48\\\\x+30=48\\\\x=18[/tex]

Answer:

x = 18

Step-by-step explanation:

The sum of two interior angles im a triangle is equal to one exterior angle that is supplementary to the third interior angle:

x + 18 + x + 12 = x + 48 add like terms

2x + 30 = x + 48 transfer like terms to the same side of the equation

2x - x = 48 - 30

x = 18

The equations which gave the same solution as; 2.3p – 10.1 = 6.5p – 4 – 0.01p are;

It follows from the answer choices that the equation; 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation as the algebraic sum of p variables is evaluated on the right hand side.

The second equation; 230p – 1010 = 650p – 400 – p also is equivalent to the given equation, when multiplied through by 100.

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The distance between the bottom of the lighthouse and the boat is 77.6m.

The lighthouse and the boat would form a right triangle. The height would be the height of the lighthouse. The  distance between the top of the lighthouse and boat would be the hypotenuse. The  distance between the bottom of the lighthouse and the boat would be the base.

In order to determine the required distance, Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

125²  = 98²  + b²

b² = 125²  - 98²

b = √(25²  - 98² )

b = 77.6m

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The value of the piecewise function at the domain is f(-1) = 1

The complete question is added as an attachment

At x = -1, the function is

f(x) = x^2

So, we have:

f(-1) = (-1)^2

Evaluate

f(-1) = 1

Hence, the value of the piecewise function at the domain is f(-1) = 1

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Answer: Graph Y

Step-by-step explanation:

The ratio between the circle and triangle is described as 3:4.

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Transformation which can be used for mapping of one triangle to another are;

What does mapping mean in geometry?

We need to map one triangle to another ;

Hence, for mapping of one triangle to another,

The transformation which can be used from the given options are;

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Answer:

B. translation only

E. rotation then dilation

Step-by-step explanation:

B. translation only

E. rotation then dilation

The expression which expresses the number of square feet of wallpaper needed is 12[tex]x^{2}[/tex]-21.

Given that the length of family room is 3x, breadth be 3x , height be x and the length and breadth of door be 7 feet and 3 feet.

We are required to find the expression which shows the square feet of wallpaper needed for the walls of the family room.

Because the wallpaper is not usually used on the floor and the ceiling and on doors so we will deduct the area of ceiling , floor and door from the surface area of whole room or we will just find the area of four walls one by one and then deduct the area of door from it.

Area of four walls only=2(lh+bh)

=2(3x*x+3x*x)

=2(3[tex]x^{2}[/tex]+3[tex]x^{2}[/tex])

=2*6[tex]x^{2}[/tex]

=12[tex]x^{2}[/tex]

Area of door=length*breadth

=3*7

=21 [tex]feet^{2}[/tex]

Required area=12[tex]x^{2}[/tex]-21.

Hence the expression which expresses the number of square feet of wallpaper needed is 12[tex]x^{2}[/tex]-21.

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The value of x from the given triangle is 32√3/3

In order to determine the value of x, first we need to determine the hypotenuse side of the smaller triangle.

sin 60 = 8√2/H

H = 8√2/sin60

H = 8√2 * 2/√3

H = 16√2/√3
H = 16√6/3

For the value of x, we will use the expression

sin45 = (16√6/3)/x

1/√2 = 16√6/3x
3x = 16√12
3x = 32√3

x = 32√3/3

Hence the value of x from the given triangle is 32√3/3

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The equation of the circle with a center (-5, -6) and a radius of 5 is (x + 5)² + (y + 6)² = 25.

The standard equation for writing the equation of a circle is: (x - h)² + (y - k)² = r².

Given the following:

Center (-5, -6) = (h, k)

Radius = 5 = r

Plug in the values into the formula

(x + 5)² + (y + 6)² = 5²

(x + 5)² + (y + 6)² = 25

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Answer:

  (c)  5y -17x +99 = 0

Step-by-step explanation:

The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.

The midpoint of XZ is the average of the coordinates of X and Z.

  M = (X +Z)/2

  M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)

The slope of the median can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

The slope of line YM is ...

  m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

The line with slope 17/5 through point Y(7, 4) is ...

  y -4 = 17/5(x -7)

Subtracting the right side, and multiplying by 5 gives ...

  5(y -4) -17(x -7) = 0

  5y -17x +99 = 0 . . . . equation of the median through Y