Find the measure of x.
X
56.76°
56.76
x = [?]
Round to the nearest hundredth.

Using the completing the square method, for the equation, we have the zeros as x = √26 + 4 and x = 4 - √26

The given equation is presented as follows

[tex]7 = \mathbf{ {x}^{2} - 8x - 3}[/tex]

Which, by completing the square, gives;

[tex] {x}^{2} - 8x - 3 - 7 = 0[/tex]

[tex] {x}^{2} - 8x - 10 = 0[/tex]

[tex] {x}^{2} - 8x + {\left(\frac{8}{2} \right) }^{2} - 10 - {\left(\frac{8}{2} \right) }^{2} = 0[/tex]

[tex] \mathbf{{(x - 4)}^{2} } =26[/tex]

The zeros of the equation;

[tex]7 = {x}^{2} - 8x - 3[/tex]

are;

[tex] \underline{x = \pm \sqrt{26} + 4}[/tex]

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Answer: 2.5

Step-by-step explanation:

[tex]1 \times 3=3\\\\3-\frac{1}{2}=2.5[/tex]

Hello,

Answer:

x = 20

Step-by-step explanation:

    3x + 10 = 4x - 10

⇔ 4x - 3x = 10 + 10

⇔ x = 20  

Answer:

20

Step-by-step explanation:

Since l ll m

( 3x + 10 ) and ( 4x - 10 ) are alternate exterior angles,

Property of parallel lines ( ll ) : -

Alternate exterior angles are equal.

4x - 10 = 3x + 10

4x - 3x = 10 + 10

x = 20

Zeros of this function

ZEros of reciprocal function

The equation

The interval where f is positive is [tex]0 \le x < 1.5[/tex]

The missing function is added as an attachment

From the attached graph, the function f(x) is positive from x = 0 to x = 1.5

As an interval notation, this can be represented as:

[tex]0 \le x < 1.5[/tex]

Hence, the interval where f is positive is [tex]0 \le x < 1.5[/tex]

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Answer:

The following lines is perpendicular, y=-x+6 and y=x+1

Step-by-step explanation:

(ex. slope of 2 stays 2 )

(ex. slope of 2 becomes -1/2)

y = -x + 6 and y = x + 1

the slope for y = -x + 6 is -1    (-1/1)

the slope for y = x + 1 is 1

the slope -1 is the negative reciprocal of 1

hence, the definition of perpendicular fits the given

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The rate at which the diameter decreases is 0.0159cm/min.

Given that a snowball melts and its surface area decreases at a rate of 1cm²/min.

The surface area of a solid object may be a measure of the entire area that the surface of the thing occupies.

The surface area of the snowball is A=4πr² because the snowball is spherical.

Here, r is the radius of the snowball.

Let D be the diameter of the snowball.

As the radius is half of the diameter

The surface area of a snowball can also be rewritten as

A=4π(D÷2)²

A=4π(D²÷4)

A=πD²

Given that the surface area decreases by 1cm²/min, so,

dA÷dt=-1cm²/min.

Differentiating both sides in A=πD² and get

dA÷dt=2πD(dD÷dt)

Given that the diameter is 12cm.

Substitute these values in the formula and find dD÷dt

-1=2π×12×(dD÷dt)

-1=24π×(dD÷dt)

-1÷24π=dD÷dt

-0.0159≈dD÷dt

Hence, the diameter decreases at the rate of 0.0159 cm/min when the diameter is 12 cm.

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Answer:

384 m²

Step-by-step explanation:

The formula to find the surface area of a cube is:

S.A. = 6a²

Here,

a ⇒ length of a side ⇒ 8m

Let us solve it now.

S.A. = 6a²

S.A. = 6 × 8 × 8

S.A. = 48 × 8

S.A. = 384 m²

Subtraction is a mathematical operation that reflects the removal of things from a collection. The difference between −9 4/5 and −3 2/3 is -6 2/15.

Subtraction is a mathematical operation that reflects the removal of things from a collection. The negative symbol represents subtraction.

The difference between −9 4/5 and −3 2/3 is,

−9 4/5 − (−3 2/3)

= −9 4/5 + 3 2/3

= (−9+3) + (−4/5 + 2/3)

= −6 + (-2/15)

= -6 2/15

Hence, The difference between −9 4/5 and −3 2/3 is -6 2/15.

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The unit rate per minute is 2/3.

In order to determine the unit rate, divide the temperature by the time. Division is the mathematical operation that is used to determine the quotient of a number.

Unit rate = temperature / time

10 / 15  = 2/3

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When the lightning occurs 4.5 km away then we will hear after 13.5 seconds and if we hear after 1.5 seconds then we are 0.5 km away from lightning.

Given With each km from the lightning 3 seconds passes.

a) The table of values for distances from 0 to 5 km.

      Distances                     Time

             0                              0

             1                               3

             2                              6

             3                               9

             4                               12

             5                                15

b) The graph of lightning is a linear relation because it is increasing constantly by 3 seconds. f(x)=3x

c) When distance =1  , the time be 3 seconds

when distance =4.5  , the time=3*4.5

=13.5 seconds.

d) When time is 3 seconds = 1km

when time =1.5 seconds , the distance be 1/2=0.5 km.

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Answer:

-x+3y=9

i think this is answer

The inequality is x + 5274 ≥ 10,000.

The total number of steps I have to take to reach my goal is 4726.

Here are inequality signs and what they mean:

Number of steps I have to take + number of steps I have taken ≥Total steps

X + 5274 + x ≥ 10,000

x ≥ 10,000 - 5274

x ≥ 4726

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Jordan can now hear the math teacher, whose classroom instruction was crucial in addition to what Jordan read in his textbook.

A hearing aid is a small electronic device that you wear in or behind your ear. It is used by people who cannot hear properly. Wearing this device makes sounds louder so that a person who cannot hear can listen, and talk to other people. A hearing aid can help people hear in every situation.

SCD is nothing but a specific learning disorder.

An SLD is specific to underachievement in academic skills that are not attributable to intellectual disability, developmental delay, or physical cause.

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Triangle JKL is transformed to create triangle J'K'L'. It can be a rigid or a non rigid transformation depending on whether the corresponding side lengths have the same measures.

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, rotation, reflection and dilation.

Dilation is the increase or decrease in the size of a figure.

A rigid transformation such as reflection, rotation and translation preserve the shape and size, hence the pre-image and image have the same corresponding angle and side measures.

A non rigid transformation such as dilation preserve the shape and not size, hence the pre-image and image have the same corresponding angle measures.

Triangle JKL is transformed to create triangle J'K'L'. It can be a rigid or a non rigid transformation depending on whether the corresponding side lengths have the same measures.

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Answer:

C

Step-by-step explanation:

2023

The angular speed of the wheel is calculated as 52.36 radians per second

The revolution of this wheel is said to be at 500 in a minute

This is also called the frequency of this wheel.

This can be written as

500rev in 60 seconds. 500/60 = 8.333 per second

Angular speed is given as

pi = 22/7

f = 8.333

Formular for angular speed = ω = 2*pi*f

w = 2 * 22/7 * 8.333

= 52.36 radians per second

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Answer:

12/25

Step-by-step explanation:

total number of possible outcomes =50

number of possible outcomes =24

probability of not selecting odd or prime numbers

=24/50

=12/25

The equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8

The equation of a line in point slope form is expressed as:

y - y1 = m(x-x1)

Given the equation y = -x + 2, the slope of the line parallel to the line is -1

Substitute the slope and point (-3, -5)

y -(-5) = -1(x - (-3))

y+5 = -(x + 3)

y+5 =-x - 3

y = -x - 3 - 5

y = -x - 8

Hence the equation for the line parallel to y = −x + 2 going through the point (−3, −5) is y = -x - 8

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Answer:

$420

Step-by-step explanation:

100.80/x = 24/100

with x being the regular price

x = (100.8*100)/24

x = 420

Answer:

[tex] \beta = 28.610[/tex]

Step-by-step explanation:

in this case we have a right angled triangle, whenever you see this triangle think of the TRIG RATIOS * sin, cos & tan* but if it was another triangle besides right angled triangle you use SINE RULE OR COSINE RULE

SOLUTION

[tex] \tan( \beta ) = \frac{opposite}{adjecent} \\ \tan( \beta ) = \frac{6}{11} \\ \beta = tan(inverse)( \frac{6}{11} ) \\ \beta = 28.61045[/tex]

The energy of the photon in each case is;

1. 2.97 * 10^-27 J

2. 3.2 * 10^-19 J

3. 6.6 * 10^-19 J

4. 2.64 * 10^-29 J

5. 8.6 * 10^-19 J

The energy of a photon is obtained form the Plank's equation; E = hf

1) E = hf

E =  6.6 × 10^-34 J s  *  4.5 × 10^6 Hz

E = 2.97 * 10^-27 J

2)E = hc/λ

E = 6.6 × 10^-34 J s  * 3 * 10^8/615  * 10^-9

E = 3.2 * 10^-19 J

3) E = hc/λ

E = 6.6 × 10^-34 J s  * 3 * 10^8/300 * 10^-9

E = 6.6 * 10^-19 J

4) E = hf

E = 6.6 × 10^-34 J s  * 4 × 10^4 Hz

E = 2.64 * 10^-29 J

5) E = hc/λ

E = 6.6 × 10^-34 J s  * 3 * 10^8/230  * 10^-9

E = 8.6 * 10^-19 J

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Answer:

m = 2/3

Step-by-step explanation:

Rewrite in slope-intercept form.

y = -3/2x + 7/2

Using the slope-intercept form, the slope is −3/2.

m = -3/2

The equation of a perpendicular line to y=−3/2x + 7/2 must have a slope that is the negative reciprocal of the original slope.

Answer:

[tex]\frac{2}{3}[/tex]

Step-by-step explanation:

• First rewrite the original equation in the form y = mx + c ,

where m = gradient:

[tex]3x + 2y = 7[/tex]

⇒ [tex]2y = -3x + 7[/tex]

⇒ [tex]y = \frac{-3}{2}x + \frac{7}{2}[/tex]

• From this equation, we can see that the gradient, m = [tex]\frac{-3}{2}[/tex] .

The gradient of a line perpendicular to another line with gradient m,  = [tex]\frac{-1}{m}[/tex].

∴ gradient of perpendicular = -1  ÷   [tex]\frac{-3}{2}[/tex]

                                              = [tex]\frac{2}{3}[/tex]    

The distance of the road junction form Timpson is given as 21.57 miles.

We have AT = [tex]\sqrt{TN^{2}+AN^{2} }[/tex]

√60² + 12² = 12√26

∠TMG = LN = 90 degrees

Therefore we have the system

[tex]\frac{TM}{60} = \frac{22}{12\sqrt{26} }[/tex]

When we cross multiply we would have to solve for TM

TM = 21.57 miles

Hence the distance of the road junction form Timpson is given as 21.57 miles.

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Answer:

I would assume you're referring to this test? if so the answer is

a, d and e

The expression that describes the slope properly are:

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

D. m = rise/run

E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

We have,

The slope of a line is a measure of its steepness or inclination.

It represents the rate of change between two points on the line, specifically the ratio of the vertical change (rise) to the horizontal change (run).

Mathematically, the slope (m) is calculated as:

m = change in vertical distance/change in horizontal distance

or

m = rise/run

or

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

Thus,

The expression that describes the slope properly are:

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

D. m = rise/run

E. Ratio of the change in y-values (rise) for a segment of the graph to the corresponding change in x-values (run).

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Answer:

Step-by-step explanation:

Answer: -1

Step-by-step explanation:

I assume the points are (-3, r) and (9,2).

Substituting into the slope formula,

[tex]\frac{r-2}{-3-9}=\frac{1}{4}\\\\\frac{r-2}{-12}=\frac{1}{4}\\\\r-2=-3\\\\r=-1[/tex]

Answer:

7/25

Step-by-step explanation:

there are 14 numbers greater than 30 and less than 45

   31   32  33  34 ......42  43   44         <=====14 numbers

14 choices out of 50  = 14/ 50 = 7/25

Answer:

Step-by-step explanation:

We can calculate a few points, such as when x = 0, y = 0 (which sometimes doesn't happen), and the lowest point (where y is the smallest)

When x = 0, y = 3, so (0,3) is one of the points, and is also the y intercept

When y = 0, x = -3, and it also happens that 0 is the lowest point that y can be, since no value of x would make y negative.

Now, we have two points, (0,3) and (-3,0)

Graph B is the one one which has both the points (0,3) and (-3,0) on it, and indeed, y never reaches below the x axis since y can't be negative