Without plotting the function
y = f(x) on a graph paper, find the coordinates of the common points of the axes when
a) f(x) = 4x² - 25
b) f(x) = 3x² - 5x

Answer:

  -448

Step-by-step explanation:

The sum of 28 terms of the arithmetic sequence with first term 92 and common difference -8 can be found using the formula for the sum of an arithmetic series.

  Sn = (2a1 +d(n -1))(n/2) . . . . sum of n terms with first term a1, difference d

__

Using the above formula with a1=92, d=-8, and n=28, the sum is ...

  S28 = (2·92 -8(28 -1))/(28/2) = (184 -216)(14) = -448

The sum of the first 28 terms of the sequence is -448.

Answer:

[tex]4\frac{7}{8}[/tex]

Step-by-step explanation:

The three heaviest eggs are between [tex]1\frac{1}{2}[/tex] and [tex]1 \frac{3}{4}[/tex]

Hope this helps and please feel free to comment, ask questions, give feedback, and correct me if I am wrong!

Have a great day!

:)

Answer:

The Area is 25

Step-by-step explanation:

You will need distance formula for this questions

for AD, (0,4) and (4,7)

The formula is here

[tex]\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]

which gives you

[tex]\sqrt{\left(4-0\right)^2+\left(7-4\right)^2} = 5[/tex]

for AB

(0,4),(3,0)

[tex]\sqrt{\left(3-0\right)^2+\left(0-4\right)^2}=5[/tex]

The answer will be 5*5, which is 25

Answer:

The area is: 28.26 units^2

The diameter is: 18.84 units

Step-by-step explanation:

Area A=pie(3.14)R^2

Diameter D=pie(3.14)R2

Answer:

x=101

Step-by-step explanation:

Fun angles......................

Answer:

x = 79°

Step-by-step explanation:

The arrows on the line segments indicate that the lines are parallel.

As the parallel line segments are the same length, the other pair of opposite line segments are also parallel and the same length.  Therefore, we can apply the Alternate Interior Angles Theorem.

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Therefore, the missing angle in the triangle including angle x is 28°.

Interior angles of a triangle sum to 180°

⇒ 73° + 28° + x = 180°

⇒ x = 180° - 73° - 28°

⇒ x = 79°

a) [tex](a+b)(x)=a(x)+b(x)=7x+10+12x-18=\boxed{19x-8}\\[/tex]

b) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]

c) [tex](a-b)(x)=a(x)-b(x)=(7x+10)-(12x-18)=7x+10-12x+18=\boxed{-5x+28}[/tex]

d) [tex]a(b(x))=a(12x-18)=7(12x-18)+10=84x-126+10=\boxed{84x-116}[/tex]

Answer:

The answer would be D.

Step-by-step explanation:

If there is a 1/7 chance that the archer will hit it, there is a 6/7 chance he/she wont. 6/7 times 6/7 is equal to 36/49, getting you your answer of D. I hope this helps! :)

Answer:

  0.98 seconds

Step-by-step explanation:

We assume the height of the volleyball is described by the equation for ballistic motion. We want to find the time it takes for the height to become zero.

__

The general form of the equation of height for ballistic motion is ...

  [tex]h(t)=-16t^2+v_0t+h_0\qquad\text{$v_0$ and $h_0$ are the initial velocity and height}[/tex]

The coefficient 16 in the equation is an approximation of 1/2g, where g is the acceleration due to gravity in ft/s². This means the units of time and distance are expected to be seconds and feet.

For the problem at hand, the initial velocity and height are 10.5 ft/s and 5 ft. Then the height equation is ...

  h(t) = -16t² +10.5t +5

__

Marsha has until the ball hits the ground to react to the serve. To find out how long that is, we need to solve the height equation for t when h=0. This is most easily done using the quadratic formula with ...

The solution is ...

  [tex]t=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}= \dfrac{-10.5\pm\sqrt{10.5^2-4(-16)(5)}}{2(-16)}\\\\=\dfrac{10.5\pm\sqrt{430.25}}{32}=\dfrac{21\pm\sqrt{1721}}{64}[/tex]

The positive solution is ...

  t ≈ 0.976327 ≈ 0.98

Marsha has about 0.98 seconds to react before the volleyball hits the ground.

_____

Additional comment

After about 0.33 seconds, Marsha knows she doesn't need to react at all. The serve will not clear the net. Its maximum height is about 6' 8 5/8". A women's volleyball net is 7' 4 1/8" high. Jennifer's serve velocity must be at least 12.3 ft/s for the ball to go over the net. With that upward velocity, Marsha has about 1.06 seconds to react.

The solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

The figure is not given;

However, the question can still be solved without it

The given parameters are:

a = 31, b = 23, and c = 20

Calculate angle A using the following law of cosine

a² = b² + c² - 2bc * cos(A)

So, we have:

31² = 23² + 20² - 2 * 23 * 20 * cos(A)

Evaluate

961 = 929 - 920 * cos(A)

Subtract 929 from both sides

32 =- 920 * cos(A)

Divide both sides by -920

cos(A) = -0.0348

Take the arc cos of both sides

A = 92.0

Calculate angle B using the following law of sine

a/sin(A) = b/sin(B)

So, we have:

31/sin(92) = 23/sin(B)

This gives

31.0189 = 23/sin(B)

Rewrite as:

sin(B) =23/31.0189

Evaluate

sin(B) =0.7415

Take arc sin of both sides

B = 47.9

Calculate angle C using:

C = 180 - 92.0 - 47.9

Evaluate

C = 40.1

Hence, the solution to the triangle is A = 92.0, B = 47.9 and C = 40.1

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Answer:

The lines would be equal, meaning the slope of the red line is also -3.

Step-by-step explanation:

SIMPLE:
Parallel lines have the same slope.

Answer:

18 inches = 1.5 feet

8 inches = 2/3 foot

y = 1.5 + (2/3)x

Answer:

20.14

Step-by-step explanation:

so to find it i added 75% to 11.85 so 11.85 + 75% = 20.14

Hope This Helped

Answer:

15.8

Step-by-step explanation:

11.85/75 = x/100

x = 15.8

11.85 is 75% of 15.8

Brainliest please!

hope this helps :)

Answer:

6

Step-by-step explanation:

hope it helps

Step-by-step explanation:

The function translation / transformation rules: f (x) + b shifts the function b units upward. f (x) − b shifts the function b units downward. f (x + b) shifts the function b units to the left

Answer:

Step-by-step explanation:

The plane that would produce a triangle is A, a cut parallel to the vertical axis, directly through the vertical axis.

A square pyramid is a geometric shape having four triangles, five faces and a square.  

Since the sides are equal, cutting parallel to the vertical axis forms a triangle.

Therefore, a cut parallel to the vertical axis, directly through the vertical axis would produce a triangle.

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Answer:

25 Questions.

Explanation:

Original or full is always 100%

Mentioned:

76% ⇒ 19

=========

1% ⇒ (19 ÷ 76) = 0.25

Solve for Total:

100% ⇒ 0.25 × 100 = 25

Answer:

2Tu = 90

Step-by-step explanation:

You can substitute the values T = 5 and u = 9 into the expression to get: 2 × 5 × 9 which is 90 (2 × 45 = 90)

Hope this helps!

The final result is 90 when T = 5 and u = 9.

Here, we have to evaluate 2Tu when T = 5 and u = 9, we substitute the values of T and u into the expression and perform the operations accordingly.

Given expression: 2Tu

T = 5

u = 9

Now, let's substitute the values:

2 * 5 * 9

Next, perform the multiplication:

2 * 5 = 10

10 * 9 = 90

So, when T = 5 and u = 9, the value of 2Tu is 90.

We get, to evaluate 2Tu, we first multiply T and u together, and then multiply the result by 2.

In this case, we have T = 5 and u = 9.

So, we perform the following steps:

Multiply T and u: 5 * 9 = 45

Multiply the result by 2: 2 * 45 = 90

Thus, the final result is 90 when T = 5 and u = 9.

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Answer:

x>3

Step-by-step explanation:

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

The size of the unknown angle "x".

We'll have to check which one is appropriate from SOHCAHTOA.

In this question we'll have to use cos because hypotenuse and adjacent is given.

[tex]\large\boxed{cos(A)=\frac{adj}{hyp}}[/tex]

Substitute according to the formula.

[tex]cos \: x= \frac{7}{11}[/tex]

We'll have to use cos inverse.

[tex]x={cos}^{-1}(\frac{7}{11})[/tex]

[tex]x=50.47880364[/tex]

[tex]\large\boxed{x=50.5°}[/tex]

Therefore, the size of the unknown angle "x" is 50.5°

The required measure of the angle x is given as 50°.

Given that,
The diagram shows a right-angled triangle. 7cm and 11cm and x degrees.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Apply cosine equation,
cosx =  7 / 11
cosx = cos50
x = 50°

Thus, the required measure of the angle x is given as 50°.

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Answer:

8= 24b

8/8=24b/8

b=3

Step-by-step explanation:

Based on my own learning

Answer:

width=5yd and length=10yd

Step-by-step explanation:

To solve this problem, you need to start by asking what you do and don't know (always where to start with word problems)

We know that Area (A) = Length (L) * Width (W)

You know Area (A) = 50 sq. yds.

You don't know anything about the width, so let's just say Width (W) = x

And you know that the length is 5 yds longer than the width, so L = W + 5yd and, since W = x, we can say L = x + 5yd

Now, we recall that A = L * W, and, since A = 50, we can say 50 sq yd = L * W.

Well, now just plug in. What does W equal and L equal?

From above we plug in and can say that 50 sq yd = x * (x + 5 yd).

Multiply it out and you get 50 = x^2 + 5x (removing units for a moment so they don't clutter the lines).

Now there are a number of ways to solve this. You can tell (because of the "x^2") that it is quadratic. So let's get it equal to zero:

0 = x^2 + 5x - 50

Now you can factor it, use your quadratic formula, or (if you hated yourself) do it as a completing the square problem. I'm going to factor.

I can see from going through a list in my head that the factors 10 and -5 multiply to -50 and add to 5, so I know that

0 = x^2 + 5x - 50 = (x + 10)(x - 5)

And so you know that x = -10 or 5.

Well, you know the parking lot cannot be -10 yd long. So we must say that W = x = 5, and, since L = W + 5, then L = 5+5 = 10. So your width is 5 yd and length is 10 yd.

Answer:

Step-by-step explanation:

3a 2b ×2a 6b = (3 × 2)×(a × b) × (2 × 6)×(a × b)   [commutative property]

                      = (6×ab) × (12×ab)  [associative property]

                      = (6×12) × (ab×ab)  [commutative + associative]

                      = (72) × (ab)²

                      = 72× (ab)²

                      = 72a²b²  [exponent property]

for an angle of 780°, we can say that is really a 360° + 360° + 60°, so two full revolutions plus an extra 60°. Check the picture below, with the coterminal in green.

Answer:

120 ft²

Step-by-step explanation:

The formula to find the area of a triangle is :

Area = [tex]\frac{1}{2}[/tex] × base × height

Given that,

base ⇒ 30 ft

height ⇒ 8 ft

Let us solve it now.

Area =  [tex]\frac{1}{2}[/tex] × base × height

Area =  [tex]\frac{1}{2}[/tex] × 30 ft × 8 ft

Area =  [tex]\frac{1}{2}[/tex] × 240 ft²

Area =  120 ft²

In this question we are provided with the base and height of a triangle. We are asked to calculate the area of the triangle.

Base = 30 feet

Height = 8 feet

We know,

[tex] \large \star \: \small\boxed{ \rm{ Area_{(triangle)} = \dfrac{1}{2} × b × h}}[/tex]

Where,

Substituting the values we get

[tex] \small\sf{ Area_{(triangle)} = \dfrac{1}{ \cancel{2}} × 30 × \cancel{8} \: \: 4}[/tex]

[tex] \longmapsto \small\rm Area_{(triangle)} = 30 × 4[/tex]

[tex] \small \underline{ \boxed{\sf {Area_{(triangle)} =120 \: {feet}^{2} }}}[/tex]

Hence,the area of the triangle is 120 feet².

[tex]\underline{\rule{71mm}{3pt}}[/tex]

If 5x - 17 ≥ 0, then |5x - 17| = 5x - 17 and the equation reduces to

-8 - 2 (5x - 17) = -14

-8 - 10x + 34 = -14

-10x = -40

x = 4

If 5x - 17 < 0, then |5x - 17| = -(5x - 17) = -5x + 17 and we have

-8 - 2 (-5x + 17) = -14

-8 + 10x - 34 = -14

10x = 28

x = 2.8

Domain of f(x) is {x | x ≠ 6} and Domain of g(x) is {x | x ≠ +7 and x ≠ +7}.

The domain of a function is the set of all input values that make the function possible.

Now, for f(x) = (x + 6)/(x² - 12x + 36)

To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;

x² - 12x + 36 = 0

Solving this using quadratic formula gives; x = 6. Thus, domain of f(x) is;

Domain = {x | x ≠ 6}

Now, for g(x) = (x + 7)/(x² - 49)

To find the domain, we equate the denominator to zero to find the numbers that can't be a domain. Thus;

x² - 49 = 0

Solving this using quadratic formula gives; x = +7 or -7. Thus, domain of g(x) is; Domain = {x | x ≠ +7 and x ≠ +7}

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