If A=30°, a=12, b=28 how many triangles can be constructed?

Answer:

8

Step-by-step explanation:

Use the pythagorean theorem. The hypotenuse (c) is 10, and one of the sides, let's say (b), is 6. Therefore, we need to solve for a and plug and chug. Let's do that:

[tex]c^2 = a^2+b^2[/tex]

[tex]a = \sqrt{c^2-b^2}[/tex]

Now let's plug in what we know:

[tex]a = \sqrt{10^2-6^2} = \sqrt{64} = 8[/tex]

Therefore, a = x = 8

For this case we have the following quadratic equation:

[tex]2x ^ 2-4x + 9 = 0[/tex]

The solutions are given by:

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2a}[/tex]

We have to:

[tex]a = 2\\b = -4\\c = 9[/tex]

Substituting:

[tex]x = \frac {- (- 4) \pm \sqrt {(- 4) ^ 2-4 (2) (9)}} {2 (2)}\\x = \frac {4 \pm \sqrt {16-72}} {4}\\x = \frac {4 \pm \sqrt {-56}} {4}\\x = \frac {4 \pm \sqrt {-1 * 56}} {4}\\x = \frac {4 \pmi \sqrt {2 ^ 2 * 14}} {4}\\x = \frac {4 \pm2i \sqrt {14}} {4}\\x = \frac {2 \pm i\sqrt {14}} {2}[/tex]

Answer:

[tex]x_ {1} = \frac {2 + i \sqrt {14}} {2}\\x_ {2} = \frac {2-i \sqrt {14}} {2}[/tex]

Answer:

OPTION E: [tex]\frac{2+\sqrt{14}i}{2}[/tex]

Step-by-step explanation:

Given the Quadratic equation [tex]2x^2-4x+9=0[/tex], you can find the roots by applying the Quadratic formula. This is:

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

In this case you can identify that:

[tex]a=2\\b=-4\\c=9[/tex]

Then you can substitute values into the Quadratic formula:

[tex]x=\frac{-(-4)\±\sqrt{(-4)^2-4(2)(9)} }{2(2)}[/tex]

[tex]x=\frac{4\±\sqrt{(56} }{4}[/tex]

Remember that [tex]\sqrt{-1}=i[/tex], then:

[tex]x=\frac{4\±2\sqrt{14}i}{4}[/tex]

Simplifying, you get:

[tex]x=\frac{2(2\±i\sqrt{14}i)}{4}\\\\x=\frac{2\±\sqrt{14}i}{2}\\\\\\x_1=\frac{2+\sqrt{14}i}{2}\\\\x_2=\frac{2-\sqrt{14}i}{2}[/tex]

Answer:

Option B 3412

Step-by-step explanation:

we know that

step 1

75°+x=90° -----> by complementary angles

step 2

Solve for x

Subtract 75 both sides

75°-75°+x=90°-75°

step 3

x=15°

step 4

Verify

Substitute the value of x in the equation of the step 1

75°+15°=90°

90°=90° ----> is correct

therefore

The correct order is

3-4-1-2

Answer:

Step-by-step explanation:

a1 = 6

a2 = -1.2*a_(n-1)

a2 = -1.2*a_1

a2 = -1.2 * 6

a2 = -7.2

a3 = -1.2*a_(n-1)

a3 = -1.2*a_2

a3 = -1.2 * - 7.2

a3 = 8.64

a4 = -1.2 * a_3

a4 = -1.2 * 8.64

a4 = -10.368

Answer:  The correct option is (B) -10.368.

Step-by-step explanation:  Given that a sequence is defined b the following :

[tex]a_1=6,~~~a_n=-1.2a_{n-1}.[/tex]

We are to find the 4-th term.

To find the fourth term, we need to start from finding the first term.

If n = 2, then the second term is given by

[tex]a_2=-1.2\times a_1=-1.2\times 6=-7.2.[/tex]

If n = 3, then the third term is given by

[tex]a_3=-1.2\times a_2=-1.2\times (-7.2)=8.64.[/tex]

If n = 4, then the fourth term is given by

[tex]a_4=-1.2\times a_3=-1.2\times 8.64=-10.368.[/tex]

Thus, the fourth term of the given sequence is -10.368.

Option (B) is CORRECT.

Answer:

2/5x - 2y≥  2

Step-by-step explanation:

see attachment

Graph Function

  A         f(x) = x

  B        f(x) = x^2

  C         f(x) = x^3

  D         f(x) = √(x - 1)

  E          f(x) = 1/x

To match each graph with the function it represents, we need to consider the shape of the graph and the equation of the function.

Graph A: This graph is a straight line that passes through the origin and has a slope of 1.

This indicates that the function is linear and has the following equation:

f(x) = x

Graph B: This graph is a parabola that opens upwards and has its vertex at the origin.

This indicates that the function is quadratic and has the following equation:

f(x) = x^2

Graph C: This graph is a cubic function that opens upwards and has a point of inflection at the origin.

This indicates that the function has the following equation:

f(x) = x^3

Graph D: This graph is a square root function. It has a vertical asymptote at x = 1 and a horizontal asymptote at y = 1.

This indicates that the function has the following equation:

f(x) = √(x - 1)

Graph E: This graph is a reciprocal function. It has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.

This indicates that the function has the following equation:

f(x) = 1/x

Answer:

9.179999999999999e+103

Answer:

C) 7,900

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Answer: Option B) The y-intercept is 20. This is the cost of registration.

Given model is:  y = 15x + 20.

We compare this equation with y = mx + b.

So,

the slope = m = 15.

y-intercept = b = 20.

Given: The cost consist of a one-time registration fee. It means the fixed cost is the one-time registration fee. It will also be the y-intercept.

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Answer:

Step-by-step explanation:

we know that

The Domain of the function are all the values of x that can take the function

in this problem the domain is

The Range of the function are all the values of y that can take the function

in this problem the range is

therefore

{y | y = –7, –1, 0, 9}  baaaam

know my brain hurts i hope this helped because i really tried haha sorry if it doesnt

Answer: It is a whole number.

Step-by-step explanation: As the square root of 882252554089 is equal to 939283, which has no decimal or fraction included, it is a whole number.

Answer:

D

Step-by-step explanation:

Prism is the solid figure that has two parallel bases that are congruent polygons and rectangular faces joining the bases, i.e. option D.

A prism is a 3D figure with two parallel bases and two congruent bases. The bases, which also have two of the faces, can be any polygon and are congruent. The other faces are rectangles and joins bases. A prism is named according to the shape of its bases. i.e. Triangular prism, Rectangular prism, etc.

We have,

A solid figure with two parallel and congruent bases.

Now,

From the above mentioned definition,

i.e.

A prism is a 3D figure with two parallel bases and two congruent bases. The bases, which also have two of the faces, can be any polygon and are congruent. The other faces are rectangles and joins bases.

So,

It is clear that the given solid figure is of prism.

Hence, we can say that the Prism is the solid figure that has two parallel bases that are congruent polygons and rectangular faces joining the bases, i.e. option D.

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Answer:

O = 2 π n - π/2 for n element Z

Step-by-step explanation:

Solve for O:

sin(O) = -1

Hint: | Eliminate the sine from the left hand side.

Take the inverse sine of both sides:

Answer:  O = 2 π n - π/2 for n element Z

assuming you meant sin(θ) = -1, Check the picture below.

Answer:

can't understand the question.

What do you need? The mean? Mode? Median?

I'll use arithmetic series to find it.

First two-digit number divisible by 3 is 12, last such number is 99. Every 3rd number is divisible by 3.

So,

[tex]a_1=12\\a_n=99\\d=3\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=12+(n-1)\cdot 3\\3n-3=87\\3n=90\\n=30[/tex]

There are 30 such numbers.

Answer:

b) 2x + y = -4

Step-by-step explanation:

To go from the Point-Slope Formula [y - y₁ = m(x - x)₁] to the Slope-Intercept Formula [y = mx + b], move -1 to the RIGHT side of the equivalence symbol to get this: y = -2x - 4. Although this is a correct answer choice, this is NOT what the question is looking for because you have to go an extra step further, Standard Formula. To go from the Slope-Intercept Formula to the Standard Formula [Ax + By = C], move 2x to the LEFT side of the equivalence symbol, and you will end up with this: 2x + y = -4. So, your answer is b).

Answer:

b) [tex]2x+y=-4[/tex]

Step-by-step explanation:

We have been given an equation [tex]y+1=-2x-3[/tex]. We are asked to write our given equation in standard form.

We know that standard form of an equation is [tex]Ax+By=C[/tex].

Let us convert our given equation in standard form as:

[tex]y+1-1=-2x-3-1[/tex]

[tex]y=-2x-4[/tex]

[tex]y+2x=-2x+2x-4[/tex]

[tex]2x+y=-4[/tex]

Therefore, the standard form of our given equation would be [tex]2x+y=-4[/tex].

Answer:

We know

1 jar = 500 buttons

5 people bring 330 buttons EACH

We can find/solve by...

people x buttons = total buttons

total buttons / 500 = number of jars needed

So..

5 x 330 = 1650

1650 / 500 = 3.3

Your answer:

4 jars

Explanation

It's impossible to have 3.3 jars, so you must round up.

Step-by-step explanation:

The number of jar necessary to hold all buttons is 4 jars.

Unitary method is a process by which we find the value of a single unit from the value of multiple units and the value of multiple units from the value of a single unit.

Given that

1 jar holds = 500 buttons

5 people = 330 buttons each

So,

Total buttons 5 people bring

=330*5

=1650 buttons

Now,

number of jars needed= total buttons/500

number of jars needed= 1650/500

number of jars needed= 3.3 jar

Hence, the number of jars needed is 4 jars

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Answer:

(f+g)(x)

Step-by-step explanation:

(f+g)(x)=

[tex] {x}^{2} - 2x + 6x + 4 = {x}^{2} + 4x + 4[/tex]

[tex](x + 2)(x + 2) = 0[/tex]

[tex](x + 2) = 0 \\ x = - 2[/tex]

Answer:

In the middle of 2 and 3.

Step-by-step explanation:

2 < 2.49 < 3.

Therefore, 2.49 would be located in the middle of 2 and 3, assuming that the scale is 1.

Hope this helps!

It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.

In math, a number line can be described as a straight line with numbers positioned at equivalent intervals or parts along its length. A number line can be expanded infinitely in any direction and exists usually expressed horizontally.

It exists located to the right of the 0 on the line, and as you can see, the numbers stand increasing proceeding from left to right. 2.49 exists located 2.49 from 0.

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The answer to your question is b.

Answer:

m∠1 = 142

Step-by-step explanation:

38 + m∠1 = 180

m∠1 = 142

Answer:

B

Step-by-step explanation:

I'm pretty sure that the shaded space represents all possible solutions, meaning that the X has to be greater than or equal to 2.

Answer:

y = $6

Step-by-step explanation:

In the image below, the table of your question is attached

Based on the information presented in the table.

1 ounce of oregano costs $4

Because there are 4 ounces, this means that

x = 4*($4) = $16

1 ounce of garlic powder $3

Because there are 2 ounces, this means that

y = 2*($3) = $6

Total cost of the ingredients  =  x+y = 22 $

Answer:  [tex]y=\frac{1}{30}x+1[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

The slope of the line can be calculated with this formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Pick to  points of the given line. You can choose the point (60,3) and the point (30,2).

Then, substituting into the formula, you get:

 [tex]m=\frac{2-3}{30-60}=\frac{1}{30}[/tex]

You can observe in the graph that the line intercepts the y-axis at the point (0,1), therefore "b" is:

[tex]b=1[/tex]

Substituting the slope and the y-intercept found into  [tex]y=mx+b[/tex], you get the equation of this line:

 [tex]y=\frac{1}{30}x+1[/tex]

Where "y" represents the Height (1,000 ft) and "x" represents the Time in seconds.

Answer:

The equation of the given line is :y = 0.04x + 0.6.

Step-by-step explanation:

From the given data , we can select two coordinates to determine the equation of the given line:

Let the point be [tex](10,1),(60,3)[/tex]

The equation of the line will be determined by the help of point slope form:

Slope of the line = [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex](y-y_1)=m(x-x_1)[/tex]

The equation of the line is :

[tex]m=\frac{3-1}{60-10}=\frac{2}{50}=0.04[/tex]

[tex](y-1)=0.04(x-10)[/tex]

[tex]y-1=0.04x-0.4[/tex]

[tex]y=0.04x+0.6[/tex]

The equation of the given line is :y = 0.04x + 0.6.

Answer:

width = 14 , length = 42

Step-by-step explanation:

Here we have to find the width of the rectangle using the fact that length is 3 times the width and perimeter is given

Let the length of the rectangle = x

Hence the width of the rectangle = 3 x

The formula for the perimeter is

P=2(l+b)

Given P = 112

Hence

112=2(l+b)

l+b=56

substituting values of l and b in this

x+3x= 56

4x=56

x=14

Hence width = 14 cms

length = 3*14 = 42 cms

Answer:

None of these apply

Step-by-step explanation:

Step 1: Bring the equation into the form of y=mx+c

5x-2y = -6

-2y = -6-5x

y = 6+5x

       2

y = 5/2x + 3

Step 2: Identify the slope (m)

Slope is the number with x (5/2)

Step 3: Find slope of the perpendicular line.

Slope of line 2 (perpendicular line) = -1/slope of line 1

m2 = -1/m1

m2 = -1/5/2

m2 = -2/5

Step 4: Find the y-intercept of the perpendicular line,

slope = -2/5

x and y coordinates = (5, -4)

y = mx + c

-4 = -2/5 (5) +c

-4 + 2 = c

c = 2

Step 5: Form equation of perpendicular line

y = mx + c

y = -2/5x + 2

Step 6: Check all equations and match with y = -2/5x + 2

a) y = x - 2 (It does not apply because this equation does not have a slope and y-intercept is not the same).

b) 2x + 5y = -10

   5y = -10 -2x

   y = -2/5x - 2 (This does not apply because the y-intercept does not match-it should be +2))

c) 2x - 5y = -10

   -5y = -10 - 2x

     y = 2/5x + 2 (This does not apply because the slope does not match-it should be -2/5)

d) y + 4 = (x - 5)

  y = x-5-4

  y = x-9 (This does not apply as the slope and y - intercept do not match)

e) y - 4 = (x + 5)

  y = x + 9 (This does not apply as the slope and y - intercept do not match)

!!

Answer:

answer is 1/4 cup

Step-by-step explanation:

Answer:

Amount of cream in cups [tex]=\frac{1}{4}[/tex]

Step-by-step explanation:

Let x be the amount of cream in cups.

Amount of milk = 1 - x cups.

The milk contains 2% fat and cream contains 18% fat.

The mixture contains 6% fat, so we have

         [tex]1 \times \frac{6}{100}=x \times \frac{18}{100}+(1-x) \times \frac{2}{100}\\\\6=18x+2-2x\\\\16x=4\\\\x=\frac{1}{4}[/tex]

Amount of cream in cups [tex]=\frac{1}{4}[/tex]

Answer:

y = 14x -30

Step-by-step explanation:

The slope intercept form is:

y = mx + b,

Slope intercept form is useful for finding the slope and y intercept of a line, hence why it is called "slope intercept" because it is easy to see the slope and the y intercept of a line in this form. Since the slope denoted by m, and y intercept denoted by b are clearly given.

y + 2 = 7(2x - 4)

Distribute 7 across the parentheses by multiplying x and 2x and 4 by 7.

y+2 = 14x - 28

subtract 2 from both sides. This cancels the 2 on the left and moves it to the right, while keeping the equation balanced.

y+2 -2 = 14x - 28 -2

y  = 14x - 30

y = 14x -30

As you can see our y = 14x -30 now looks like the point slope equation we had above. m = 14, and  b = -30. This means the line goes up 14 for every single unit you move to the right, and intersects the y axis at  (0, -30).

Please mark me brainliest.

Answer:

5/96.

Step by Step explanation:

The volume = width * length * height

= 1/3 * 5/8 * 1/4

= 1*5*1 / 3*8*4

= 5 / 96.

=

paul and mary

peter and mary

peter and paul

Answer:

Peter and Neil

Step-by-step explanation:

Given rates of work:

Peter = 5 hours / room

Paul = 6 hours / room

Neil = 7.5 hours / room

Mary = 3.75 hours / room

Recall the formula for combined rate for two individuals A & B is given as

Combined rate = (A's rate x B's rate) / (A's rate + B's rate)

In our case , the combined rate is given to be 3 hours, so we must find a combination of rate A and rate B that will give us 3 hours.

If you try all the combinations in the above formula, we will find that if we substitute Peter's and Neil's rates into the formula, we will get exactly 3 hours.

Combined rate for Peter and Neil

= (Peter's rate x Neil's rate) / (Peter's rate + Neil's rate)

= (5 x 7.5) / (5+7.5) = 3 hours to complete 1 room

No other combination gives exactly 3 hours.