solve for the valuable d 12d - 37 = 119 explain the steps to solve the equation

Answer:

All real numbers

Step-by-step explanation:

Answer:4

Step-by-step explanation:

because when looking at the whole blue circle we see 4 boxes 1 kid that likes only milk and 3 kids that like mild and another drink

Answer:

Step-by-step explanation:

a) Angle of line of sightFrom a point O in the school compound, Adeolu is 100 m away on a bearing N 35° E and Ibrahim is 80 m away on a bearing S 55° E. (a) How far apart are both boys? (b) (c) What is the bearing of Adeolu from point O, in three-figure bearings? What is the bearing of Ibrahim from point O, in three-figure bearings?The angle of the line of sight of Adeolu from the point O is given by:α = 90 - 35α = 55°.The angle of the line of sight of Ibrahim from the point O is given by:β = 90 - 55β = 35°.a) By using the Sine Rule, we can determine the distance between Adeolu and Ibrahim as follows:$

\frac{100}{sin55^{\circ}} = \frac{80}{sin35^{\circ}

100 sin 35° = 80 sin 55°=57.73 mT

herefore, both boys are 57.73 m apart. b) The bearing of Adeolu from the point O can be determined as follows:OAN is a right-angled triangle with α = 55° and OA = 100. Therefore, the sine function is used to determine the side opposite the angle in order to determine AN.

Thus:$$sin55^{\circ} = \frac{AN}{100}$$AN = 80.71 m.

To find the bearing, OAD is used as a reference angle. Since α = 55°, the bearing is 055°.

Therefore, the bearing of Adeolu from the point O is N55°E. c) Similarly, the bearing of Ibrahim from the point O can be determined as follows:OBS is a right-angled triangle with β = 35° and OB = 80. Therefore, the sine function is used to determine the side opposite the angle in order to determine BS.

Thus:$$sin35^{\circ} = \frac{BS}{80}$$BS = 46.40 m.

To find the bearing, OCD is used as a reference angle. Since β = 35°, the bearing is 035°.Therefore, the bearing of Ibrahim from the point O is S35°E. A boy walks 5 km due North and then 4 km due East. (a) Find the bearing of his current posi- tion from the starting point.

(b) How far is the boy now from the start- ing point?The boy's position is 5 km North and 4 km East from his starting position. The Pythagorean Theorem is used to determine the distance between the two points, which are joined to form a right-angled triangle. Thus

:$$c^2 = a^2 + b^2$$

where c is the hypotenuse, and a and b are the other two sides of the triangle. Therefore, the distance between the starting position and the boy's current position is:$$

c^2 = 5^2 + 4^2$$$$c^2 = 25 + 16$$$$c^2 = 41$$$$c = \sqrt{41} = 6.4 km$$

Therefore, the boy is 6.4 km from his starting point. (a) The bearing of the boy's current position from the starting point is given by the tangent function.

Thus:$$\tan{\theta} = \frac{opposite}{adjacent}$$$$\tan{\theta} = \frac{5}{4}$$$$\theta = \tan^{-1}{\left(\frac{5}{4}\right)}$$$$\theta = 51.34^{\circ}$$

Therefore, the bearing of the boy's current position from the starting point is N51°E.

For such more question on triangle

https://brainly.com/question/1058720

#SPJ8

About 71 members of the group are expected to be between 51 years old and 59 years old.

The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:

Considering the mean of 55 years and the standard deviation of 4 years, ages between 51 and 59 years are within one standard deviation of the mean, hence the percentage is of:

68%.

Out of 104 people, the number of people with ages in the range is given as follows:

0.68 x 104 = 71 people. (rounded to the nearest integer).

More can be learned about the Empirical Rule at https://brainly.com/question/10093236

#SPJ1

Answer: y=2.5x-8, the two points necessary to graph would be (2,-3) and (0,-8)

Step-by-step explanation: If the line passes thru (2,-3), let us plug in and find c. -3-2.5(2)=c

-3-5=c

c=-8 so y=2.5x-8

The line will represent the graph of the equation y=2.5x-8.

The two points necessary to graph would be (2,-3) and (0,-8).

The slope-intercept form is y=mx+c

If the line passes through (2,-3),

let us plugin and find c.

So we get,

\(-3-2.5(2)=c\)

\(-3-5=c\)

\(c=-8\)

So, The equation of the line is y=2.5x-8.

To learn more about the equation visit:

https://brainly.com/question/2972832

Answer:

h and k are simply variables that stand in for the x and y of a point. Math books could have easily have used x1, x2 y1 y2, etc, but h and k is the convention.

anyway, this is a guess n check question. Substitute the x value of the point for h, and y value for k, and whichever one gives you a true equation is the right one.

Answer:

Step-by-step explanation:

y = a(x-h)²+k is the “vertex-form equation” for a vertical parabola with vertex (h,k).

Since a>0, the parabola opens upwards. (If a<0, it opens downwards. If a=0, it is not a parabola at all.)

The parabola y = a(x-h)²+2k is the same shape as the first equation, but it is shifted vertically by k units.

Since (2,4) is a point on the first parabola, (2,4+k) is a point on the second parabola.

Answer:

43,200

Step-by-step explanation:

25,000x .20=5,000

30,000 x .20=6,000

36,000x.20=7,200

43,200x.20=8,640

51,840x.20=10,368

The value of is -26

First, to determine the value of x, we need to know that index forms are described as mathematical forms that are used to represent numbers of values that are too small or large in more convenient forms

From the information given, we have that;

5⁷ˣ⁺⁵ = 125²ˣ⁻⁷

Now,  make that the bases are like terms, we have that;

125 = 5³

Substitute the value and we have;

5⁷ˣ⁺⁵ = 5³⁽²ˣ⁻⁷⁾

Take the exponents, we get;

7x + 5 = 6x - 21

collect the like terms, we have;

7x - 6x = -21 - 5

x = - 26

Learn more about index forms at: https://brainly.com/question/15361818

#SPJ1

Answer:

-13

Step-by-step explanation:

Substitute:  -5 + 4 × (-2)

Remove the parentheses: -5 -4 ×2

Calculate the product or quotient: -5 -8

Calculate the sum or difference: -13

Answer:

The answer is 77.7777 or 77.8 if to round to tenth.

Step-by-step explanation:

Answer:

This identity holds as long as \(\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}\) for all integer \(k\).

For the proof, make use of the fact that:

\(\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\) (definition of tangents,) and

\(\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}\) (Pythagorean identity,) which is equivalent to \(1 - \cos^{2}(\theta) = \sin^{2}(\theta)\).

Step-by-step explanation:

Assume that \(\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}\) for all integer \(k\). This requirement ensures that the \(\tan(\theta)\) on the left-hand side takes a finite value. Doing so also ensures that the denominator \(\sqrt{1 - \sin^2(\theta)}\) on the right-hand side is non-zero.

Make use of the fact that \(\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}\) to rewrite the left-hand side:

\(\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}\).

Apply the Pythagorean identity \(\sin^{2}(\theta) = 1 - \cos^{2}(\theta)\) and \(\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}\) to rewrite this fraction:

\(\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}\).

Hence, \(\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\).

Answer:

c=9.1 miles

Step-by-step explanation:

a^2+b^2=c^2

6.2^2+6.7^2=c^2

38.44+44.89=c^2

83.33=c^2

√83.33=c

c=9.12852671574

Round to nearest 10th

c=9.1

If this helps please mark as brainliest

Answer:

9.1 miles

Step-by-step explanation:

6.7²+6.2²=h² 44.89+38.44=h² 83.33=h² find the square root of 83.33

Answer:

The slope is 1/2

Step-by-step explanation:

To find the slope of the line, put the equation in slope intercept form.

y= mx+b where m is the slope and b is the y intercept

4y -2x = -30

Add 2x to each side

4y -2x+2x = 2x-30

4y = 2x-30

Divide by 4

4y/4 = 2x/4 -30/4

y = 1/2x -15/2

The slope is 1/2

Answer:

0.5

Step-by-step explanation:

To find the slope of the line you have write this in slope intercept form.

That is,

Here,

m - Slope

c - y intercept

Now, to write this expression in slope intercept form, you have to make y the subject of this expression.

\( 4y - 2x = - 30\)

Add 2x to both sides.

4y = 2x - 30

Now divide both sides by 4.

y = 2/4x - 30/4

Accordingly,

\(y = 0.5x - 7.5\)

Slope of the line (m) = 0.5

The first and last expressions are identified as a limit that exists.

'In Mathematics, a limit is defined as a value that a function approaches the output for the given input values.'

According to the given problem,

For expression 1,

     \(\lim_{n \to4}\frac{x^{2}-x-12 }{2-x}\)

⇒ \(\lim_{n \to4} \frac{x^{2}-4x+3x-12 }{4-x}\)

⇒ \(\lim_{n \to4}\frac{-x(4-x)-3(4-x)}{4-x}\)

⇒ \(\lim_{n \to4}\frac{(4-x)(-x-3)}{4-x}\)

⇒ \(\lim_{n \to4 }(-x-3)\)

Now, we put the value of x as 4

⇒ - 4 - 3

= -7

Therefore, the limit exists.

For the last expression,

    \(\lim_{x \to 2} \frac{x^{2}+3x-10 }{x^{2} -4}\)

⇒ \(\lim_{x \to 2} \frac{x^{2}+5x - 2x-10 }{(x+4)(x-4)}\)

⇒ \(\lim_{x \to2} \frac{x(x+5) -2(x+5)}{(x+4)(x-4)}\)

⇒ \(\lim_{n \to 2} \frac{(x+5)(x-2)}{(x+4)(x-4)}\)

Now, putting the value of x = 2 in the expression,

⇒ (2+5)(2-2) / (2+4)(2-4)

⇒ 7*0 / 6*(-2)

= 0

Therefore, the limit exists.

For the other expressions, we cannot factorize the numerator or the denominator to cancel out the denominator because of which if we put the values of x directly into the denominator without cancelling it out, the denominator would be zero, which means infinity because zero in the denominator of a fraction means infinity or undefined or does not exist.

Hence, we can conclude that expressions 1 and 6 are limits that exist.

Learn more about limits here: https://brainly.com/question/13100668

#SPJ2

Answer:

He would make $234.00.

Step-by-step explanation:

Divide $169 by 13 hours, this will tell you how much money he earns every hour. $169 divided by 13 = $13. Now, you know that Adbul makes $13 per hour. Then, multiply $13 by 18 hours of work. $13 x 18 = $234.00.

That is your answer!

Given

Find

Length of AC

Explanation

as we have given right angle triangle

by pythagoras theorem ,

as

AB = 6 + 6 = 12

so ,

Final Answer

Hence , the length of AC is 13.6 . So , the correct option is 4

Answer:

  5

Step-by-step explanation:

Substitute the given values and do the arithmetic.

  \(0.3y+\dfrac{y}{z}=0.3\cdot 10+\dfrac{10}{5}=3+2=\boxed{5}\)

Step to step explanation:

Confidence interval for mean, when population standard deviation is unknown:

\(\overline{x}\pm t_{\alpha/2}\dfrac{s}{\sqrt{n}}\)

, where \(\overline{x}\) = sample mean

n= sample size

s= sample standard deviation

\(t_{\alpha/2}\) = Critical t-value for n-1 degrees of freedom

We assume the family size is normal distributed.

Given, n= 31 , \(\overline{x}=3.1\), s= 1.42 ,

\(\alpha=1-0.9=0.10\)

Critical t value for \(\alpha/2=0.05\) and degree of 30 freedom

\(t_{\alpha/2}\) = 1.697  [By t-table]

The required confidence interval:

\(3.1\pm ( 1.697)\dfrac{1.42}{\sqrt{31}}\\\\=3.1\pm0.4328\\\\=(3.1-0.4328,\ 3.1+0.4328)=(2.6672,\ 3.5328)\approx(2.67,\ 3.53)\)

Hence,  the 90% confidence interval for the estimate = (2.67, 3.53)

Answer:

x = 2 √ 2 , − 2 √ 2

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

\(\displaystyle x=\±2\sqrt{2}\)

Step-by-step explanation:

\(3x^2-24=0\)

\(3x^2-24+24=0+24\)

\(3x^2=24\)

\(\displaystyle \frac{3x^2}{3}=\frac{24}{3}\)

\(x^2=8\)

\(x=\±\sqrt{8}\)

\(x=\±2\sqrt{2}\)

Answer:

They are collinear if they are on the same line

The options that correctly show the points of the given graph are;

Option 4: A is on the y-axis

Option 5; D is on the x-axis

Usually in mathematical equation graphs, the y-axis represents the range of the function which is a set of all possible output values for given input values . Whereas, the domain is usually represented on the x-axis and it shows the set of all possible input values of the function.

Now, from the given graph, we see the following;

A is on the y-axis

B is at the origin

C is at the point (1, 2)

D is on the x-axis

Looking at the options, we can tell that options 4 and 5 are correct representations of the given graph because they correctly denote the points on the x-axis and y-axis.

Read more about Graph Axis at; https://brainly.com/question/15709421

#SPJ1

Answer:

45 degree

Step-by-step explanation:

3x - 9 + 24 + 30 = 180 degree (being sum of interior angles of a triangle)

3x + 45 = 180

3x = 180 - 45

x = 135/3

x = 45 degree

Answer:45 độ

Step-by-step explanation:

3x - 9 + 24 + 30 = 180 độ (là tổng 3 góc của tam giác)

3x + 45 = 180

3x = 180 - 45

x = 135/3

x = 45 độ

Answer:

28

-4 × 4 = 16

3 × 4= 12

12 + 16 =28

(i) The domain of f(x) is all real numbers, since there are no restrictions on the input variable x.

(ii) We have:

f(x) = x^4 - 2x^3

f'(x) = 4x^3 - 6x^2

f''(x) = 12x^2 - 12x

(iii) To find the critical points, we need to solve the equation f'(x) = 0:

4x^3 - 6x^2 = 0

2x^2(2x - 3) = 0

x = 0 or x = 3/2

So the critical points are (0,0) and (3/2, -27/16).

(iv) To determine where f(x) is increasing or decreasing, we need to examine the sign of f'(x) on different intervals. We can make a sign chart for f'(x):

| x | -∞ | 0 | 3/2 | +∞ |

|---------|--------|-------|-------|--------|

| f'(x) | - | 0 | + | + |

From the sign chart, we see that f(x) is decreasing on the interval (-∞, 0) and increasing on the interval (0, 3/2) and (3/2, +∞).

(v) To find the relative extrema, we need to examine the sign of f'(x) around the critical points. We can make a table:

| x | 0- | 0+ | 3/2- | 3/2+ |

|---------|-------|-------|-------|-------|

| f'(x) | - | + | - | + |

| f(x) | 0 | 0 | -27/16| -27/16|

From this table, we see that f(x) has a relative minimum of -27/16 at x = 3/2, and no relative maximum or minimum at x = 0.

(vi) To find the intervals where f(x) is concave up or concave down, we need to examine the sign of f''(x) on different intervals.

We can make a sign chart for f''(x):

| x | -∞ | 0 | 1 | +∞ |

|---------|--------|-------|------|--------|

| f''(x) | + | - | + | + |

From the sign chart, we see that f(x) is concave down on the interval (-∞, 0) and concave up on the intervals (0, 3/2) and (3/2, +∞).

(vii) To find the points of inflection, we need to solve the equation f''(x) = 0:

12x^2 - 12x = 0

12x(x - 1) = 0

x = 0 or x = 1

So the points of inflection are (0,0) and (1, -1).

(viii) To sketch the graph of f(x), we can use the information we have gathered so far.

At x = 0, f(x) has a relative minimum of 0 and is concave down. At x = 3/2, f(x) has a relative minimum of -27/16 and is concave up. The point (1, -1) is a point of inflection.

Based on this information, we can sketch a graph of f(x) that looks like this:

```

|

|

|

|

|

|

|

--------o------------o-------

0 3/2 x-axis

```

The graph is a "U" shape that opens upward, with a relative minimum at (3/2, -27/16) and a point of inflection at (1, -1).

The number of bases Elena stole is 9 if Natasha stole three fewer bases than twice the number Elena stole.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Natasha stole three fewer bases than twice the number Elena stole. If Natasha stole 15 bases,

Let n be the number of bases stolen by Natasha

Let e be the number of bases stolen by Elena.

From the data given in the question:

The linear equation in two variables can be framed:

n = 2e -3

Plug n = 15

15 = 2e - 3

After solving:

e = 9

e = 9 bases stolen by Elena

Thus, the number of bases Elena stole is 9 if Natasha stole three fewer bases than twice the number Elena stole.

Learn more about the linear equation here:

brainly.com/question/11897796

#SPJ5

Graphing a Quadratic Equation

Let's take as an example the function:

The vertex form of a quadratic function is:

Where a is the leading coefficient and (h,k) is the vertex.

If a is positive, the function is concave up, if negative the function is concave down.

The first step is to obtain the parameters by comparing the given equation with the general equation.

Thus, we have: a = -2. Vertex = (3,5)

Now we locate the vertex in the coordinate plane and draw the parabola opening down.

For more precision, we can substitute some points around the vertex, like for example:

x={1,2,4,5}

We get the y-coordinates:

y={-3,3,3,-3}

Then we plot the graph as follows:

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

For more questions on bags

https://brainly.com/question/31835238

#SPJ8