Triangles ABD, CBD and ADC are all isosceles. Find the angle x.
AC = AD

Answer:

The correct options are 1, 4 and 7.

Step-by-step explanation:

From the given figure it is clear that the vertices of preimage are A(-4,2), B(-4,-2) and C(-1,-2).

The vertices of image are A'(1,5), B'(1,1) and C'(4,1).

The relation between vertices of preimage and image is defined by the rule

[tex](x,y)\rightarrow (x+5,y+3)[/tex]

It means the figure ABC translated 5 units right and 3 units up.

Translations a rigid transformation. It means the size and shape of image and preimage are same.

We can say that,

(a) The sides of the image and preimage are congruent.

(b) The angles in the image and angles in the pre-image are same.

(c) The image is a slide of the preimage.

(d) The image and pre-image have same shape.

(e) Each point has moved in same direction.

(f) Each point has moved the same number of units.

Therefore the correct options are 1, 4 and 7.

Answer:

Problem 1: [tex]\frac{2x-3}{5}=x+6[/tex] gives x=-11

Problem 2: [tex]2x-\frac{3}{5}=x+6[/tex] gives x=33/5

Step-by-step explanation:

I will do it both ways:

Problem 1:

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

I don't like the fraction so I'm going to clear by multiplying both sides by 5:

[tex]2x-3=5(x+6)[/tex]

Distribute:

[tex]2x-3=5x+30[/tex]

Subtract 2x on both sides:

[tex]-3=3x+30[/tex]

Subtract 30 on both sides:

[tex]-33=3x[/tex]

Divide both sides by 3:

[tex]-11=x[/tex]

Problem 2:

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

Clear the fraction by multiplying both sides by 5:

[tex]5(2x-\frac{3}{5})=5(x+6)[/tex]

Distribute:

[tex]10x-3=5x+30[/tex]

Subtract 5x on both sides:

[tex]5x-3=30[/tex]

Add 3 on both sides:

[tex]5x=33[/tex]

Divide both sides by 5:

[tex]x=\frac{33}{5}[/tex]

For this case we must solve the following equation:

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

Multiplying by 5 on both sides we have:

[tex]2x-3 = 5 (x + 6)\\2x-3 = 5x + 30[/tex]

We add 3 to both sides of the equation:

[tex]2x = 5x + 30 + 3\\2x = 5x + 33[/tex]

Subtracting 5x on both sides:

[tex]2x-5x = 33\\-3x = 33[/tex]

Dividing between -3 on both sides:

[tex]x = \frac {33} {- 3}\\x = -11[/tex]

Answer:

-11

Answer:

The perimeter of the square in the projection is [tex]224\ cm[/tex]

Step-by-step explanation:

we know that

1 cm of the image on the monitor represents 8 cm on the screen

so

using proportion

Find out how much represent on the screen  7 cm on a computer monitor

Let

x ----> the length side of the square image on the screen

[tex]\frac{1}{8}\frac{monitor}{screen} =\frac{7}{x}\frac{monitor}{screen} \\ \\x=8*7\\ \\x=56\ cm[/tex]

Find the perimeter of the image on the screen

the perimeter of a square is equal to

[tex]P=4b[/tex]

[tex]b=56\ cm[/tex]

substitute

[tex]P=4(56)=224\ cm[/tex]

Answer:

224cm

Step-by-step explanation:

The scale factor of the dilation is 8, so a 1 cm by 1 cm square on the monitor represents a 8 cm by 8 cm

square on the screen.

The figure shows two squares. The larger square has a side of 56 centimeters. The smaller square has a side of 7 centimeters. The sides of the larger square are parallel to the sides of the smaller one.

The side length of the square in the projection is the product of the side length of the preimage and the scale factor.

h=7(8)

cm

Simplify.

h=56

cm

The perimeter of the square is

P=4(56)

cm

Simplify.

P=224

cm

Therefore, the perimeter of the square in the projection is 224

cm.

The fourth term of the arithmetic series is 38.

Given that, the first number in arithmetic series (a)=8 and common difference (d) =10.

The nth term of the arithmetic series is [tex]a_{n} =a+(n-1) \times d[/tex].

Now, the fourth term= [tex]a_{4} =8+(4-1) \times 10[/tex]

=8+30=38

Therefore, the fourth term of the arithmetic series is 38.

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Answer:

385/pi

Step-by-step explanation:

Circumference is given by

C= pi * d  where d is the diameter

385 = pi *d

Divide each side by pi

385/pi = pi * d/pi

385/pi = d

This is the final function f(x) = (-2(x-2))^5 after a horizontal shrink, reflection, and shift.

To determine which function results after applying a given sequence of transformations to the original function f(x) = x^5, we need to apply each transformation in the correct order. Transformations affect the graph and the function's formula. Here is how you would apply the transformations in the correct order:

f(2x): Multiply the independent variable by 2, which shrinks the graph horizontally by half. The function becomes f(x) = (2x)^5.

f(-2x): Negate the independent variable x, which flips the graph across the y-axis. The function becomes f(x) = (-2x)^5.

f(-2x-2): Subtract 2 from the result of -2x. This is incorrect as the sequence of operations should reflect transformations applied directly to the independent variable x. Instead, it should be f(x-2) after step (ii), which translates the graph to the right by 2 units.

If we were to correct the third operation and apply the transformations properly, the resulting function after applying a horizontal shrink, reflection across the y-axis, and horizontal shift would be f(x) = (-2(x-2))^5.

Answer:

[tex]x\:<\:50[/tex].

Step-by-step explanation:

The z-score for a normal distribution is calculated using the formula:

[tex]Z=\frac{x-\mu}{\sigma}[/tex].

From the question, the distribution has a mean of 50.

[tex]\implies \mu=50[/tex] and the standard deviation is [tex]\sigma=5[/tex].

For a z-score to be negative, then, [tex]\frac{x-\mu}{\sigma}\:<\:0[/tex].

[tex]\frac{x-50}{5}\:<\:0[/tex].

[tex]x-50\:<\:0\times 5[/tex].

[tex]x-50\:<\:0[/tex].

[tex]x\:<\:0+50[/tex].

[tex]\therefore x\:<\:50[/tex].

Any value less than 50 will produce a negative z-score

Answer:

see explanation

Step-by-step explanation:

If A +B = 45° then tan(A+B) = tan45° = 1

Expanding (1 + tanA)(1 + tanB)

= 1 + tanA + tanB + tanAtanB → (1)

Using the Addition formula for tan(A + B)

tan(A+B) = [tex]\frac{tanA+tanB}{1-tanAtanB}[/tex] = 1 ← from above

Hence

tanA + tanB = 1 - tanAtanB ( add tanAtanB to both sides )

tanA + tanB + tanAtanB = 1 ( add 1 to both sides )

1 + tanA + tanB + tanAtanB = 2

Then from (1)

(1 + tanA)(1 + tanB) = 2 ⇒ proven

Rectangular prism: 6 faces (4 lateral, 2 bases), 8 vertices, 12 edges, meeting all criteria specified.

let's break down the characteristics of each of the options provided:

1. **Square Pyramid**:

  - Faces: A square pyramid has five faces. It has a square base and four triangular faces.

  - Vertices: A square pyramid has five vertices.

  - Edges: A square pyramid has eight edges (the base square has four edges, and each triangular face has one edge).

2. **Triangular Prism**:

  - Faces: A triangular prism has five faces. It has two triangular bases and three rectangular lateral faces.

  - Vertices: A triangular prism has six vertices.

  - Edges: A triangular prism has nine edges (three on each base triangle and three connecting the lateral faces).

3. **Rectangular Prism**:

  - Faces: A rectangular prism has six faces. It has two rectangular bases and four rectangular lateral faces.

  - Vertices: A rectangular prism has eight vertices.

  - Edges: A rectangular prism has 12 edges (four on each base rectangle and four connecting the lateral faces).

4. **Triangular Pyramid**:

  - Faces: A triangular pyramid has four faces. It has a triangular base and three triangular lateral faces.

  - Vertices: A triangular pyramid has four vertices.

  - Edges: A triangular pyramid has six edges (three on the base triangle and three connecting the lateral faces).

Given the characteristics you provided: six faces, four lateral faces, two bases, eight vertices, and 12 edges, we can eliminate the options of square pyramid and triangular pyramid because they don't fit all the criteria.

Now let's look at the remaining options:

- **Triangular Prism** has five faces, six vertices, and nine edges. It doesn't match the given criteria.

- **Rectangular Prism** has six faces (two bases and four lateral faces), eight vertices, and 12 edges, which perfectly matches all the provided characteristics.

Therefore, the correct answer is the **Rectangular Prism**.

Answer:

b=4

Step-by-step explanation:

subtract the exponents

6-2=4

The value of b is 4.

Exponent is a mathematical method to express large numbers in power form. It will describe how many times a number multiplied by itself.

Example : 7⁵ , where the number 7 multiplied 5 times by itself.

Given, 5⁶/5² = 5ᵇ

We know that, in exponent, if [tex]a^{m}=a^{n}[/tex], then m=n

Here, 5⁶/5² = 5ᵇ

         ⇒ [tex]5^{6-2} =5^{b}[/tex]

         ⇒ [tex]5^{4} =5^{b}[/tex]

∴ By the above rule, b = 4

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Answer:

When you graph all the equations into a graphing calculator, you find the answer is:

C. x-2y=1 and 3x-y=-1

The system of equations has a solution of approximately (0.6, –0.8) are;

x + 2 y = - 1 and 3 x + y = 1

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

From this information, it is clear that the green line and the Purple line intersect each other at an approximate point (0.6, -0.8).

Since, the green line passes through the x-intercept (-1,0) and y-intercept (0,-0.5).

Therefore, the equation of the green line will be;

⇒ x + 2y = - 1

Again, the purple line passes through the point (0,1) and has a negative slope thus, the equation of purple line will be;

3x + y = 1 {Since it has negative slope}

Therefore, the first option will be the answer.

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Answer:

Option a) dodecahedron

Step-by-step explanation:

we know that

case a) Dodecahedron

it is a polyhedron that has 12 faces (from Greek dodeca- meaning 12). Each face has 5 edges (a pentagon)

case b) Octahedron

it is a polyhedron that has 8 faces (from Greek okto- meaning eight).

case c) Icosahedron

it is a polyhedron that has 20 faces (from Greek icos- meaning twenty).

case d) Terrahedron

it is a polyhedron composed of four triangular faces (from Greek tetra- meaning four).

therefore

The answer is dodecahedron

Answer:

(1, 0)

Step-by-step explanation:

Given the 2 equations

2x - 4y = 2 → (1)

- 4x + 6y = - 4 → (2)

Multiplying (1) by 2 and adding to (2) will eliminate the x- term

4x - 8y = 4 → (3)

Add (2) and (3) term by term

(- 4x + 4x) + (6y - 8y) = (- 4 + 4), simplifying gives

- 2y = 0 ⇒ y = 0

Substitute y = 0 in (1) or (2)

Substituting in (1) gives

2x - 0 = 2, that is

2x = 2 ( divide both sides by 2 )

x = 1

Solution is (1, 0 )

To find the surface area of a right triangular prism, we have to calculate the area of all its faces, which include the two triangular bases and the three rectangular faces.
1. **Triangular Bases:** If the right triangle base has sides of lengths `a`, `b`, where `b` is the base and `a` is the height of the triangle, then the area of one triangular base will be given by the formula:
  \[\text{Area of one triangular base} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times a \times b.\]
  Since there are two identical triangular bases, we multiply this area by 2:
  \[\text{Total area of triangular bases} = 2 \times \left( \frac{1}{2} \times a \times b \right) = a \times b.\]
2. **Rectangular Faces:** The three rectangular sides include two rectangles that are formed by the sides of the triangle (`a` and `b`) with the height (`h`) of the prism and one rectangle that is the width of the base `b` and the height of the prism. The areas of these rectangles will be:
  - Rectangle with side `a` and height `h`: \[a \times h.\]
  - Rectangle with base `b` and height `h`: \[b \times h.\]
  - Rectangle with the side corresponding to the hypotenuse `c` of the base triangle and height `h`: \[c \times h.\]
  Therefore, the total area of the three rectangles is the sum of the areas:
  \[\text{Total area of rectangular faces} = a \times h + b \times h + c \times h = h \times (a + b + c).\]
Putting it all together, the formula for the total surface area (SA) of the right triangular prism is:
\[ SA = a \times b + h \times (a + b + c).\]
So, the expression that will help you find the surface area of a right triangular prism is the sum of the areas of the two triangles and the three rectangles as given by this formula.

Answer:

A

Step-by-step explanation:

they're proportional

Answer: the answer is A

Step-by-step explanation:

have a good day

Answer:

x = 3, plus or minus, radical 5 all over 2

Step-by-step explanation:

Answer:

The length of the wire is 22.42 feet

The distance from the base of the pole to the spot where the wire touches the ground is 16.66 feet

Step-by-step explanation:

* Lets explain the situation in the problem

- The telephone pole , the wire and the ground formed a right triangle

- The wire is the hypotenuse of the triangle

- The height of the telephone pole and the distance from the base of

 the pole to the spot where the wire touches the ground are the legs

 of the triangle

- The angle between the wire and the ground is 42°

- The angle 42° is opposite to the height of the telephone pole

- The height of the telephone pole is 15 feet

* Lets use the trigonometry functions to find the length of the wire

 (hypotenuse) and the distance from the base of the pole to the spot

 where the wire touches the ground

∵ sin Ф = opposite/hypotenuse

∵ Ф = 42° and its opposite side = 15 feet

∴ sin 42 = 15/hypotenuse ⇒ by using cross multiplication

∴ sin 42° (hypotenuse) = 15 ⇒ divide both sides by sin 42

∴ hypotenuse = 15/sin 42° = 22.42 feet

∵ The length of the wire is the hypotenuse

∴ The length of the wire is 22.42 feet

∵ The distance from the base of the pole to the spot where the wire

   touches the ground is the adjacent side to the angle 42°

∵ tan Ф = opposite/adjacent

∴ tan 42° = 15/adjacent ⇒ by using cross multiplication

∴ tan 42° (adjacent) = 15 ⇒ divide both sides by sin 42

∴ adjacent = 15/tan 42° = 16.66 feet

∵ The adjacent side is the distance from the base of the pole to the

  spot where the wire touches the ground

∴ The distance from the base of the pole to the spot where the wire

   touches the ground is 16.66 feet

[tex]\bf \begin{array}{ccll} \stackrel{teaspoons}{pepper}&potatoes\\ \cline{1-2} \frac{1}{4}&3\\ x&9 \end{array}\implies \cfrac{~~\frac{1}{4}~~}{x}=\cfrac{3}{9}\implies \cfrac{~~\frac{1}{4}~~}{\frac{x}{1}}=\cfrac{1}{3}\implies \cfrac{1}{4}\cdot \cfrac{1}{x}=\cfrac{1}{3} \\\\\\ \cfrac{1}{4x}=\cfrac{1}{3}\implies 3=4x\implies \cfrac{3}{4}=x[/tex]

Answer:

Since 9 is 3 times the denominator of the first ratio, multiply the numerator of the first ratio by 3 to get the numerator of the second ratio. The amount of pepper is 3/4 teaspoon.

Step-by-step explanation:

Answer:

a.  A.  49m  B 30.5 m

Step-by-step explanation:

If I have understood the question correctly:

Ball A:

After each second the total distance travelled increases by 5 meters.

Ball A: after 10 seconds it has rolled 4 + (10-1) * 5 = 49m

Ball B:  after 10 seconds it has rolled 3.5 + (10-1)* 3 =  30.5 m.

Answer:

Option A. A: 49 m: B: 30.5 m

Step-by-step explanation:

Ball A rolls 4 meters in the 1st second, 9 meters in the 2nd second, 14 meters in the 3rd second, and so on.

We can see that after each second the total distance traveled by ball increases by 5 meters.

So, we can solve this as an arithmetic sequence that is [tex]a+(n-1)d[/tex]

For ball A, a = 4 n = 10 d = 5

Ball B rolls 3.5 meters in the 1st second, 6.5 meters in the 2nd second, 9.5 meters in the 3rd  second, and so on.

For ball B, a = 3.5 n = 10 d = 3

For ball A:

After 10 seconds, the distance will be [tex]4+(10-1)5[/tex]

= [tex]4+45[/tex] = 49 meters

For ball B:

After 10 seconds, distance covered will be [tex]3.5+(10-1)3[/tex]

= [tex]3.5+27[/tex] = 30.5 meters.

Hence, the answer is option A.

Answer:

x = 6 and x = -5

Step-by-step explanation:

The zeros are what 2 x-values makes this function equal to zero.

So we need to find  [tex]x^2-x-30=0[/tex]

Now we need 2 numbers multiplied that gives us -30 (constant) and added gives us -1 (coefficient in front of x).

The two numbers are : -6, and 5

Now we can write:

[tex]x^2-x-30=0\\(x-6)(x+5)=0\\x=6, -5[/tex]

Hence the zeroes are x = 6 and x = -5

Final answer:

The zeros of the function f(x) = x^2 - x - 30 are found by factoring the quadratic equation. They are x = 6 and x = -5.

Explanation:

To find the zeros of the function f(x) = x2 - x - 30, we need to solve the equation for when f(x) equals zero. This means we have to solve x2 - x - 30 = 0. This is a quadratic equation, and we can attempt to factor it to find the solutions.

The factors of -30 that add up to -1 (the coefficient of x) are -6 and +5. Thus, we can rewrite the quadratic as (x - 6)(x + 5) = 0. Now, we can set each factor equal to zero to find the zeros of the function:

x - 6 = 0, which gives x = 6

x + 5 = 0, which gives x = -5

Therefore, the zeros of the function are x = 6 and x = -5.

Answer:

Two Angles are Supplementary when they add up to 180 degrees.

Step-by-step explanation:

Notice that together they make a straight angle.

Answer:

+/- 1, [tex]\frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9}[/tex] ....

Step-by-step explanation:

The Rational root theorem states that If f(x) is a Polynomial with integer coefficients and if there exist a rational root of the form p/q then p is the factor of the constant term of the function and q is the factor of the  leading coefficient of the function

Given: f(x)= 9x^4-2x^2-3x+4

Factors of q (leading coefficient) are: +/-9, +/-3, +/-1

Factors of p (constant term) are: +/-4 , +/-2, +/- 1

According to the theorem we write the roots in p/q form:

Therefore,

p/q =+/- 1, [tex]\frac{+-1}{+-3},\frac{+-1}{+-9},+-2,\frac{+-2}{+-3},\frac{+-2}{+-9},+-4,\frac{+-4}{+-3}, \frac{+-4}{+-9}[/tex] ....

Answer:

see explanation

Step-by-step explanation:

1

6 = 3x - 9 ( add 9 to both sides )

15 = 3x ( divide both sides by 3 )

5 = x

2

x + 4 < 1 ( subtract 4 from both sides )

x < - 3

3

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

Multiply terms on both sides by 2

x + 6 = - 10 ( subtract 6 from both sides )

x = - 16

The graph of the inequality x > 34 is graphed

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Given the inequality:

3x > 102

Divide the inequality by 3:

x > 34

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Answer:

- 230°

Step-by-step explanation:

A coterminal angle is the given angle ± 360n ( where n is an integer )

Given 130°

Then a coterminal angle = 130° - 360° = - 230°

OR 130° + 360° = 490°

well, the difference is 21330 - 19700 = 1630.

now, if we take 21330 as the 100%, what is 1630 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 21330&100\\ 1630&x \end{array}\implies \cfrac{21330}{1630}=\cfrac{100}{x}\implies \cfrac{2133}{163}=\cfrac{100}{x} \\\\\\ 2133x = 16300\implies x=\cfrac{16300}{2133}\implies x \approx 7.64[/tex]

Answer:

Change in the price of the car was 7.64%

Step-by-step explanation:

Cindy bought a car for $21330.

After few years she sold the car for $19700.

Net loss she suffered = Selling price - Cost price

= 21330 - 19700

= $1630

Now the percent change in the value will be = [tex]\frac{\text{Difference in the price}}{\text{Cost price of the car}}\times 100[/tex]

= [tex]\frac{1630}{21330}\times 100[/tex]

= 7.64%

Therefore, change in the price of the car was 7.64%

Answer:

[tex]\large\boxed{b.\ 0,\ \pi,\ \dfrac{\pi}{3},\ \dfrac{5\pi}{3}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ \sin2x=2\sin x\cos x\\\\\sin2\O=\sin\O\\\\2\sin\O\cos\O=\sin\O\qquad\text{subtract}\ \sin\O\ \text{from both sides}\\\\2\sin\O\cos\O-\sin\O=0\qquad\text{distribute}\\\\\sin\O(2\cos\O-1)=0\iff\sin\O=0\ \vee\ 2\cos\O-1=0[/tex]

[tex]\sin\O=0\iff\O=0\ \vee\ \O=\pi\\\\2\cos\O-1=0\qquad\text{add 1 to both sides}\\\\2\cos\O=1\qquad\text{divide both sides by 2}\\\\\cos\O=\dfrac{1}{2}\iff\O=\dfrac{\pi}{3}\ \vee\ \O=\dfrac{5\pi}{3}[/tex]