Simplify using basic trigonometric identities

Only for c = 49 the given expression is the square of a binomial.

We want to find the values of c such that:

[tex]4x^2 + 14x + c[/tex]

Is the square of a binomial.

Remember that:

[tex](a + b)^2 = a^2 + 2ab + b^2[/tex]

Now we can rewrite our expression as:

[tex](2x)^2 + 2*7*x + c[/tex]

If you compare that with the general binomial expansion, we can see:

[tex]a = 2x[/tex]

[tex]b = 7[/tex]

Then c must be equal to 7 squared:

[tex]7^2 = 49 = c[/tex]

Only for c = 49 the given expression is the square of a binomial.

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there are "x" amount of cars in the lot, and oddly enough that's 100%, if we know that 60 is 40% of that, what is "x"?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 60& 40 \end{array} \implies \cfrac{x}{60}=\cfrac{100}{40}\implies \cfrac{x}{60}=\cfrac{5}{2} \\\\\\ 2x=300\implies x=\cfrac{300}{2}\implies x=150[/tex]

Answer:

betewwn them?

Step-by-step explanation:

[tex]\left(\sqrt[3]{- \dfrac 18} \right)^3+3\dfrac3 4\\\\\\=\left[\left(-\dfrac 18 \right)^{\tfrac 13}\right]^3+ \dfrac{12+3}4\\\\\\=\left(-\dfrac 18 \right)^{\tfrac 33\right)+ \dfrac{15}4\\\\\\=\dfrac{15}{4}- \dfrac 18\\\\\\\\=\dfrac{30-1}{8}\\\\\\=\dfrac{29}8\\\\\\=3\dfrac 58 \\\\\\= 3.625[/tex]

Answer:

29/8

Step-by-step explanation:

The events A and B are independent events, and the values of P(A) and P(B) are 7/12 and 1/2, respectively

The event A is given as:

A : Sum greater than 6

In the sample space of a roll of two dice, there are 21 outcomes that are greater than 6, out of a total of 36 outcomes

This means that:

P(A) = 21/36

Simplify

P(A) = 7/12

The event B is given as:

B : Sum is divisible by 2

In the sample space of a roll of two dice, there are 18 outcomes that are divisible by 2, out of a total of 36 outcomes

This means that:

P(B) = 18/36

Simplify

P(B) = 1/2

Hence, the probability values of P(A) and P(B) are 7/12 and 1/2, respectively

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Answer:

output = - 68

Step-by-step explanation:

given

output = input × 17

when input = - 4 , then

output = - 4 × 17 = - 68

If no train has more than 25 seats. Then the number of cars in the first, second, and third train will be 17, 18, and 20 respectively.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Three trains are made of identical train cars, so each car has the same number of seats.

The first train has 418 seats, the second train has 456 seats, and the third train has 494 seats.

If no train has more than 25 seats.

Then the number of the cars on each train will be

Let x, y, and z be the number of the cars in the first, second, and third train.

Then we have

x = 418 / 25

x = 16.75

x ≅ 17

y = 456 / 25

y = 18.24

y ≅ 18

z = 294 / 25

z = 19.76

z ≅ 20

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Answer:

11 cars in the 1st train, 12 cars in the 2nd train and 13 cars in the 3rd train

Step-by-step explanation:

There is a difference of 38 between the numbers 418, 456 and 494.

[tex]418/38=11\\456/38=12\\494/38=13[/tex]

Trust me, this is 100% the correct answer!

hope this helps!

Answer:

the answer is 14 hopes this helps

Step-by-step explanation:

Ac/b=?

-2(-12)=24/3

24/3=8

8-(a+d)=?

8-(-2(+-)4)=?

8-(-2-4)=?

8+2+4=?

10+4=?

14

Answer:

25 customers

Explanation:

To find the number of people preferred cake, multiply the percentage by total customers.

People who preferred cake:

⇒ 35% × 71

⇒ 24.85

⇒ 25 (rounded to nearest whole number)

Answer:

25(1+2)

Step-by-step explanation:

25 goes into 25 once and 50 twice.

Answer:In the diagram, there are 28 tiles. You can do that with easy multiplication or just counting. Each square length is 1.5 feet, or 18 inches. You get that by multiplying 12 by 1.5. The area of a square is 324 inches, found by multiplying 18 by 18. Divide 324 by the area of a tile, 36 (6*6), to get 9. There are 9 tiles in each square. Multiply 9 by 28 to get... 252

Step-by-step explanation:

Answer:

1232 square meters

Step-by-step explanation:

The lateral surface area are all the rectangles.

1st rectangle:

A = lw

A = 25(22)

A = 550

2nd rectangle:

A= lw

A = 7(22)

A = 154

3rd rectangle:

A = lw

A = 24(22)

A = 528

Add the areas together.

550 + 154 + 528 = 1232

Answer:

x = 2, - 4

Step-by-step explanation:

The factors of 8 are:

1, 8

2, 4

You can combine 2 and 4 to create 2.

( x - 2 ) ( x + 4 ) = 0

0 can either be x - 2 or x + 4

Therefore, x = 2 or - 4

Hey there!

Use the quadratic formula to find the solution(s). x² + 2x - 8 = 0

x = -4 or x = 2 ✅

Quadratic formula : ax² + bx + c = 0 where a ≠ 0

The number of real-number solutions (roots) is determined by the discriminant (b² - 4ac) :

The roots of the equation are determined by the following calculation:

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

Here, we have :

1) Calculate the discriminant :

b² - 4ac ⇔ 2² - 4(1)(-8) ⇔ 4 - (-32) ⇔ 36

b² - 4ac = 36 > 0 ; The equation admits two real-number solutions

2) Calculate the roots of the equation:

▪️ (1)

[tex]x_1 = \frac{ - b - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x_1 = \frac{ - 2 - \sqrt{36} }{2(1) } \\ \\ x_1 = \frac{ - 2 - 6}{2} \\ \\ x_1 = \frac{ - 8}{2} \\ \\ \blue{\boxed{\red{x_1 = -4}}}[/tex]

▪️ (2)

[tex]x_2 = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x_2 = \frac{ - 2 + \sqrt{36} }{2(1)} \\ \\ x_2 = \frac{ - 2 + 6}{2} \\ \\ x_2 = \frac{4}{2} \\ \\ \red{\boxed{\blue{x_2 = 2}}}[/tex]

>> Therefore, your answers are x = -4 or x = 2.

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The height of the triangular pyramid will be equal to H=12 feet.

A triangular pyramid is a pyramid having triangular faces the other sides of the pyramid are simliar triangles.

It is given that:-

The Volume of the pyramid=80 cubic meters

The Base area of the pyramid=20 square meters

The height of the pyramid=?

We know that the volume of a pyramid is given as:-

V=(1÷3)x Base area x height

V=(1÷3)x20 x H

H=(80x30)÷20

H=12 feet

Hence the height of the triangular pyramid will be equal to H=12 feet.

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The graph of the parent function y = x² transformed to produce the graph of y = 3(x+1)². It is translated 1 unit left and stretched vertically by a factor of 3.

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

The graph of the parent function y = x² transformed to produce the graph of y = 3(x+1)²

We need to find how the parent function transformed to produce the graph of y = 3(x+1)².

The parent graph is shifted 1 unit towards the left by the rule of transformation.

[tex]f(x) = f(x+1)[/tex]

By applying this rule then,

[tex]y(x) = f(x+1)^2[/tex]

Now, the parent function stretched vertically 3 times the previous graph  by the rule

[tex]f(x) = 3f(x)[/tex]

Apply this rule then, we get

[tex]y(x) = 3(x+1)^2[/tex]

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Answer:

6

Step-by-step explanation:

g(f(0)) means that the input of f(x) is 0 and this value of f(x) found is the input of g(x). This is known as composite functions.

Let's find the value of f(0).

f(x)= x²

f(0)= 0²

f(0)= 0

Now, we can find the value of g(f(0)).

g(x)= x +6

g(f(0))

= g(0)

= 0 +6

= 6

[tex]~~~~~~6=2x^2 -11x\\\\\implies 2x^2 -11x -6 = 0\\\\\implies 2x^2 -12x +x-6=0\\\\\implies 2x(x-6) +(x-6) = 0\\\\\implies (2x+1)(x-6) = 0\\\\\implies x = -\dfrac 12,~~ x= 6\\\\\text{Since }~p > q,}~~ p =6~ \text{and}~ q = -\dfrac 12\\ \\\text{So,}~ p-q = 6 -\left(- \dfrac 12 \right)\\\\~~~~~~~~~~~~~=6+\dfrac 12 \\\\~~~~~~~~~~~~~=\dfrac{13}2\\\\~~~~~~~~~~~~~=6.5[/tex]

The value of p -q is 6.5.

Suppose that the given quadratic equation is

ax^2 + bx + c = 0

Then its roots are given as:

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

The equation 6 = 2x^2 - 11x has two solutions, p and q, with p being greater than q.

[tex]6 = 2x^2 - 11x \\\\ 2x^2 - 11x - 6 = 0\\\\ 2x^2 - 12x + x- 6 = 0\\[/tex]

(2x + 1) (x-6) = 0

Thus, x = -1/2 , 6

Since p>q

p = 6 , q = -1/2

So, p -q = 6 - (-1/2)

= 6 + 1/2

= 13/2

= 6.5

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Answer:

B

Step-by-step explanation:

Answer:

B) 1 1/3

Step-by-step explanation:

4 x 1/3 = 4/3

4/3 = 1 1/3

Answer:

441 square feet.

Step-by-step explanation:

Area = length times width. Both length and width are 21 feet (3×7).

Answer:

152

Step-by-step explanation:

950 x 16% simple as that

Answer:

hope this will help you

Step-by-step explanation:

[tex]b { }^{2} - 81 = 0 \\ b {}^{2} = 81 \\ b = \sqrt{81} \\ b = 9[/tex]

Answer: Heyaa! :D

Your Answer Is... 9

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula,

a²−b²=(a + b)(a − b) where a = B and

b = 9.

(B + 9)(B − 9)

The maximum amount of water the birdbath can hold is 288 cubic in which is the volume of the cuboid.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

We have a rectangular birdbath in his garden. The dimensions are 24, 8, and [tex]1\dfrac{1}{2}[/tex] inches

The maximum amount of water in the birdbath = volume of the birdbath

[tex]\rm = 24 \times 8 \times 1\dfrac{1}{2}[/tex]

[tex]\rm = 24 \times 8 \times \dfrac{3}{2}[/tex]

= 288 cubic in

Thus, the maximum amount of water the birdbath can hold is 288 cubic in which is the volume of the cuboid.

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Answer:

Mean-average

Median-middle

Mode-Most Often Digit Entered (Most Common Digit)

Range-Least To Greatest

Step-by-step explanation:

By applying the law of cosine, the smallest angle which the swimmers must turn between the buoys is 41.4°.

In order to determine the smallest angle which the swimmers must turn between the buoys, we would apply the law of cosine.

Given the following data:

Form the law of cosine, we have:

[tex]CosC =\frac{a^2 + b^2 - c^2}{2ab} \\\\CosC =\frac{500^2 + 600^2 - 400^2}{2 \times 500 \times 600}\\\\CosC =\frac{450000}{600000}\\\\C = cos^{-1} 0.75\\\\[/tex]

C = 41.4°.

For angle B, we have:

[tex]CosB =\frac{a^2 + c^2 - b^2}{2ac} \\\\CosB =\frac{500^2 + 400^2 - 600^2}{2 \times 500 \times 400}\\\\CosB =\frac{1}{8}\\\\B = cos^{-1} 0.125\\\\[/tex]

B = 82.8°.

For angle A, we have:

[tex]CosA =\frac{b^2 + c^2 - a^2}{2bc} \\\\CosA =\frac{600^2 + 400^2 - 500^2}{2 \times 600 \times 400}\\\\CosA =\frac{9}{16}\\\\A = cos^{-1} 0.5625\\\\[/tex]

A = 55.8°.

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Answer:

in particular, the relationship between height of stack and number of cups yields a non-whole number of cups, corresponding to a height of 95 cm. In this context, that is not possible because we do not allow for parts of cups.

Step-by-step explanation:

It is possible for a stack of cups to be 95 cm tall depends on the size and shape of the cups and how they are stacked.

The area of Rectangle is length times of width.

Assuming the cups are all the same size and shape, the height of the stack would depend on the number of cups in the stack.

if each cup is 5 cm tall, a stack of 19 cups would be 95 cm tall (19 x 5 = 95).

If the cups are irregularly shaped or have varying sizes, it may be more difficult to stack them in a way that reaches 95 cm in height.

It is possible for a stack of cups to be 95 cm tall depends on the size and shape of the cups and how they are stacked.

It is possible for some stacks of cups to reach this height, but not necessarily all stacks of cups.

Hence, it is possible for a stack of cups to be 95 cm tall depends on the size and shape of the cups and how they are stacked.

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Answer:

D

Step-by-step explanation :

Answer:

Step-by-step explanation:

Question 1:

Franco made 36 invitations and gave out 14. How many invitations does he have left?

Simple. Solve for the bottom:

That is the answer D.

Question 2:

Ebba gave out 36 invitations and still has 14 left. How many invitations does she have in all?

Complicated (a bit). Solve:

That is the answer C.

Answer:

If the circle touches all 4 sides, the diameter is 2 so the area us 3.14(4) = 12.56.

16 - 12.56 = your answer

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