Solve for x : 7x + 8 < 1/6 (42x+48)
X = all real number
X has no solution
X = 0

To prove that △DFE ~ △GFH by the SSS similarity theorem, the correct answer is; Option C: HF is 4 units and GH is 2 units

The SSS Similarity theorem states that two triangles are similar If all the three sides of one of the triangles are in same proportion to the three sides of the other triangle.

Since triangle DFE is similar to triangle GHF as seen in the attached diagram, then we can say that;

DF/GF = DE/GH

20/5 = 8/GH

GH = 2 units

Also:

EF/HF = DF/GF

(12 + HF)/HF = 20/5

HF = 4 units

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Answer:

3/2

Step-by-step explanation:

comparing the straight line with ax + bx + c = 0,

we get a = 3 and b = -2

we know,

slope of line = -a/b

= -3/-2

= 3/2

Hope it helped

Answer: 1.3062

Step-by-step explanation:

0.311 * 4.2 = 1.3062

Answer:          D. 8x² + x + 3

Sum means the answer to an addition problem. To find the sum of polynomials, we will add like terms.

Like terms can be combined using addition or subtraction and have the same variables. Constants are also like terms with each other because they have no variables.

(4x² + 1) + (4x² + x + 2)      Starting equation from the question

= 4x² + 1 + 4x² + x + 2       Remove brackets

= 4x² + 4x² + x + 1 + 2       Rearrange to group like terms together

= 8x² + x + 1 + 2                Add like terms with the same 'x²' variables

= 8x² + x + 3                     Add like terms that are constants

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Answer:

[tex]\circledast \ \ f\circ f\left( x\right) = x[/tex]

[tex]\circledast \ \ g\circ g\left( x\right) =4x - 21[/tex]

Step-by-step explanation:

[tex]f(x)=\frac{5}{2x}[/tex]

g(x) = 2x - 7

==============

[tex]f\circ f\left( x\right) =\frac{5}{2\left( f\left( x\right) \right) }[/tex]

             [tex]=\frac{5}{2\left( \frac{5}{2x} \right) }[/tex]

             [tex]=\frac{5}{\left( \frac{5}{x} \right) }[/tex]

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

             [tex]=x[/tex]

_____________

[tex]g\circ g\left( x\right) =2(g(x)) - 7[/tex]

            = 2(2x - 7) - 7

           = 4x - 14 - 7

           = 4x - 23

Answer:

simple interest is $281(nearest whole number)

Step-by-step explanation:

S. I=PXTXR

100

P=$6609

T=5

R=8.5 or 85/10

S. I=6609X5X85

100X10

=280.8825

=281

I assume you meant [tex]f(x)=100(0.7)^{x}[/tex]. The graph is shown in the image below.

Answer:

Graph A. On a coordinate plane, a curve approaches y = 0 in quadrant 1 and curves up into quadrant 2. It goes through (2, 49) and (0, 100).

Step-by-step explanation:

Edge

Answer:

The number of computers that must be surveyed is 1681.

Step-by-step explanation:

The formula to find the sample size is given by:-

[tex]n=p(1-p)(\frac{\frac{z_{\alpha } }{2} }{E} )^{2}[/tex]

where p = prior population proportion,

[tex]\frac{z_{\alpha }}{2}[/tex]= Two-tailed z-value for ∝

E= Margin of error.

As per the given, we have

Confidence level :

1 - ∝ = 0.90

⇒∝= 1 - 0.90= 0.10

Two -tailed z-value for ∝= 0.10 : [tex]\frac{z_{\alpha }}{2}[/tex] = 1.64

E= 2%=0.02

We assume that nothing is known about the percentage of computers with new operating systems.

Let us take p=0.5  [we take p= 0.5 if the prior estimate of proportion is unknown.]

The required sample size will be:-

[tex]n= 0.5(1-0.5)(\frac{1.64}{0.02} )^{2}[/tex]

=> [tex]0.25(82)^{2}[/tex]

=> 1681

Hence, the number of the computer must be surveyed = 1681

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umm....... I think it was exactly 2 head

Answer:

please provide the diagram

Step-by-step explanation:

for the solution figure is necessary so provides us to solve this problem

The sounds of music are related to trigonometric functions because trigonometry is used in measuring the level of the pitch of a sound wave or musical note.

It should be noted trigonometry is important for measuring pitch level. The notes are measured in Hertz.

A sound wave's amplitude relates to the change in the pressure that's caused by the wave measured at a specific location.

The sound is perceived as louder when the amplitude increases.

Pieces of music often have repetitive choruses or bars, similar to patterns. In mathematics, we look for patterns to interpret and predict the unknown. Music uses the same techniques. If you look at a piece of music, artists look at the notes they see to find the rare (high or low) and uncommon notes.

In this way, the notes are related. Relationships are important in mathematics and create an interesting link between music and mathematics.

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Answer:

$127

Step-by-step explanation:

[tex](.10 \times 1000) + (.20 \times 100) + (.70 \times 10) = 100 + 20 + 7 = 127[/tex]

Answer:

1. 30 ft

2. sqrt(2164) yd

3: 12 cm

Step-by-step explanation:

For all three questions I'll be using the Pythagorean Theorem which states that a^2 + b^2 = c^2 where c is the hypotenuse and a and b are the base and height

Question 1:

40^2 + d^2 = 50^2

1600 + d^2 = 2500

d^2 = 900

d = 30

Question 2:

42^2 + 20^2 = c^2

2,164 = c^2

c = sqrt(2164)

Question 3:

5^2 + a^2 = 13^2

25 + a^2 = 169

a^2 = 144

a = 12

sinusoidal curve equation 29 sin ([tex]\pi[/tex]/9 x)-49

Given the graph of a sinusoidal function, we can write its equation in the form y = A·sin(B(x - C)) + D using the following steps. D: To find D, take the average of a local maximum and minimum of the sinusoid. y=D is the "midline," or the line around which the sinusoid is centered.

In the state of Michigan, the lowest average temperature of the year is in January and is about 20 °F.

The highest monthly average temperature occurs in July at 78 °F

Assume the period is 12 months and January is at the origin of the graph of this function.

sinusoidal curve equation that models the data y

Then, Graph the curve using x = 0 for January, and x = 11 for December, so that x = 12 will be the start of the next year, or end of the period.

So, using the property of sinusoidal curve equation we have

=29 sin ([tex]\pi[/tex]/9 x)-49

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Answer:

To solve this quadratic equation, take the square root of both sides.

Since the left side is a perfect square, it will just be reduced to:

4y - 3

For the constant on the right side, the positive and negative roots must be considered.

√72 = ±6√2

Equating the two:

4y - 3 = ±6√2

4y = 3 ± 6√2

y = (3 ± 6√2)/4

y = (3 + 6√2) / 4 = 2.87

and

y = (3 - 6√2) / 4 = -1.37

There are [tex]\binom62=15[/tex] ways of selecting any two fruit from the basket, where

[tex]\dbinom nk = \dfrac{n!}{k!(n-k)!}[/tex]

is the so-called binomial coefficient.

If the baby picks out [tex]k[/tex] oranges, where [tex]k\in\{0,1,2\}[/tex], it can do so in

[tex]\dbinom 3k \dbinom3{2-k} = \dfrac{3!}{k!} \dfrac{3!}{(2-k)! (1 + k)!}[/tex]

ways.

Then the PMF (probability mass function) of [tex]X[/tex] is

[tex]P(X=x) = \begin{cases} \dfrac{\binom30 \binom32}{\binom62} = \dfrac3{15} & \text{if }x=0 \\\\ \dfrac{\binom31 \binom31}{\binom62} = \dfrac9{15} & \text{if }x = 1 \\\\ \dfrac{\binom32 \binom30}{\binom62} = \dfrac3{15} & \text{if }x=2 \\\\ 0 &\text{otherwise}\end{cases}[/tex]

The amount of interest after 3 years will be $15.

The complete question is given below.

You loaned a friend $100 and will charge him 5% annual simple interest when he pay it back. What is the amount of interest after 3 years?

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

The interest is given as

I = (P × R × T) / 100

Where, P is the initial amount, R is simple interest rate, and T is the time.

We have

P = $100

R = 5%

T = 3 years

Then the interest will be

I = (100 × 5 × 3) / 100

I = $15

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Answer:

x = -2

Step-by-step explanation:

1. Square both sides
x^2 +3x + 6 = x^2
2. Subtract x^2 from both sides
3x + 6 = 0
3. Subtract 6 from both sides and divide by 3
x = -2

The Venn diagram to illustrate this information is given in the image attached.

The number of children who took plantain and beans only are:

Let  beans = a

Rice = b

Plantain = P

So:  a + b = 24 - 9 - 5 = 10

Note that 24 children took plantain.

9 children took only Plantain.

5 took the 3 food items.

So:

b + c = 18 -2 - 5 = 11

a + c = 21 - 3 - 5 = 13

P∩B = a + 5

= 6 + 5 = 11

R ∩ B = C + 5

=7 + 5 = 12

None of the three items of food =  

50 - (3 + 2 + 9 + 6 + 4 + 7 + 5)

= 50 - 36

=14

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Polynomial is an expression that consists of indeterminates(variable) and coefficients. The possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

Given the roots of the polynomial, therefore, the following details can be written as,

Therefore, the polynomial will become,

P(x) = (x-2)²(x-0)²(x+2)¹

      = (x²+4-4x) (x)² (x+2)

       = (x²+4-4x) (x³+2x²)

       = x⁵ + 2x⁴ + 4x³ + 8x² - 4x⁴ -8x³

       = x⁵ - 2x⁴ - 4x³ + 8x²

Hence, the possible formula for P(x) is x⁵ - 2x⁴ - 4x³ + 8x².

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Answer:

22

Step-by-step explanation:

Is easy just multiple

Answer:

To find the slope:

[tex]\frac{(y_{1} - y_{2})}{(x_{1} - x_{2})} =\frac{(-3-(-4))}{(-5-0)} =\frac{1}{-5}[/tex]

Hope it helps!

The equation for the red graph will be g(x) = x² + 3.

A statement, principle, or policy that creates the link between two variables is known as a function.

The function f(x) is given below.

f(x) = x²

Then the function g(x) will be given as

g(x) = x² + 3

Then the equation for the red graph will be g(x) = x² + 3.

The missing graph is given below.

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Answer:

usually at the login screen it gives you an option to reset your password if you forgot, it will appear in blue as "forgot password?" or "trouble logging in?"

The value of the variable x is 30° and the value of the variable y is 10°.

The missing diagram is attached below.

The angle is the distance between the intersecting lines or surfaces.

Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.

Vertically opposite angle – When two lines intersect, then their opposite angles are equal.

Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.

If angle ∠1 = 105°, angle ∠12 = (3x + 15)°, and angle ∠7 = (8y-5)°.

∠1 = ∠5 = ∠9 = 105° (corresponding angles)

∠1 = ∠4 = 105° (Vertical opposite angles)

∠1 + ∠2 = 180° (linear angle)

       ∠2 = 75°

∠2 = ∠3 = 75° (Vertical opposite angles)

∠3 = ∠8 = ∠12 = 75° (corresponding angles)

Then the value of x and y will be

   ∠9 = ∠12

   ∠1 = ∠12

105° = (3x + 15)°

  3x = 90°

    x = 30°

∠6 = ∠7

75° = (8y – 5)°

8y = 80°

  y = 10°

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The company needs 41 labels on average, each minute.

The perimeter of a circle (circumference): 2 π radius

Replacing with the values given:

C = 2 (3.14) 2 = 12.56 cm

So, the area of one label is:

Area of a rectangle: length x width = 12.56 x 7 = 87.92 cm sq.

Now, the number of label be n

87.92 x n = 3612.64 cm2

n = 3612.64 / 87.92

n = 41.09

Hence, The company needs 41 labels on average, each minute.

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