Simplify the following expression:
–10x – 9x + 1

Answer:

i) x = 4°

ii) <ABC = 28°

Step-by-step explanation:

Given that BD bisects <ABC then it is true to say that;

Angle m < ABD=m < CBD

Hence;

4x-2 = 2x +6

4x-2x = 6 +2

2x = 8

x=8/2 = 4

x= 4°

Hence

Angle m< ABD = 4x-2 = 4*4 -2 = 16-2 =14°

Angle m < ABC = 2* 14° = 28°

Answer:

5

Step-by-step explanation:

Given

3n + 7 = 22

3n = 22 - 7

3n = 15

n = 15 / 3

n = 5

Hope it will help :)

Answer:

n = 5

Step-by-step explanation:

3n + 7 = 22

Solve for n.

----------------------

When we need to find a variable, we need to isolate the variable to the point that it is by itself.

3n + 7 = 22

Subtract 7 from both sides :

3n + 7 - 7 = 22 - 7

3n = 15

Divide both sides by 3 :

n = 5

Answer:

5

Step-by-step explanation:

5 is the correct answer

Answer:

6.12

Step-by-step explanation:

Have a nice day

The mean of the hemoglobin level is 117.2 g/dl and the standard deviation is 34.69 g/dl.

What is mean and standard deviation ?

The mean is a statistical measure used to determine the central tendency of a given data set, which reflects the average value. To calculate the mean, you add up all the values in the data set and divide the sum by the total number of values.

On the other hand, the standard deviation is a measure of the spread or variation in a set of data. It shows how much the values deviate from the mean value. To compute the standard deviation, you first subtract each data point from the mean, square the result, add up all the squared values, divide by the total number of data points, and then take the square root of the quotient.

Calculating the mean and standard deviation from the given data :

To calculate the mean of the hemoglobin level, we add all the values and divide by the number of values:

\((39 + 158 + 120 + 112 + 132 + 97 + 104 + 159 + 129) / 9 = 117.2\)g/dl

Therefore, the mean of the hemoglobin level is 117.2 g/dl.

To calculate the standard deviation of the hemoglobin level, we first need to calculate the variance:

Calculate the mean of the data set (117.2 g/dl)

For each data point, subtract the mean and square the result

\((39 - 117.2)^2 = 5969.44\)

\((158 - 117.2)^2 = 1668.64\)

\((120 - 117.2)^2 = 7.84\)

\((112 - 117.2)^2 = 26.44\)

\((132 - 117.2)^2 = 217.44\)

\((97 - 117.2)^2 = 408.04\)

\((104 - 117.2)^2 = 173.61\)

\((159 - 117.2)^2 = 1748.84\)

\((129 - 117.2)^2 = 140.4\)

Add up all the results

\(5969.44 + 1668.64 + 7.84 + 26.44 + 217.44 + 408.04 + 173.61 + 1748.84 + 140.4 = 10360.65\)

Divide the result from step 3 by the number of data points minus one (9-1=8)

\(10360.65 / 8 = 1295.08\)

Take the square root of the result

\(\sqrt{1295.08} = 34.69\) g/dl

Therefore, the standard deviation of the hemoglobin level is 34.69 g/dl.

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Answer: Lauren's unit rate is 2.95 Miles per hour (MPH)

Step-by-step explanation:

divide the distance Lauren traveled by the time it took to travel said distance

112/38 hours=2.95 mph

Answer:

2.95 miles/hour or 2.95mph

Step-by-step explanation:

112/38 = 2.94736842 ⇒ 2.95 miles/hour

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The value of AB is,

⇒ AB = 5.9

(rounded to nearest tenth)

We have to given that,

A right triangle ABC is shown.

Now, By trigonometry formula,

we get;

⇒ cos 33° = Base / Hypotenuse

Substitute all the values, we get;

⇒ cos 33° = AB / 7

⇒ 0.84 = AB / 7

⇒ AB = 0.84 × 7

⇒ AB = 5.88

⇒ AB = 5.9

(rounded to nearest tenth)

Thus, We get;

AB = 5.9

(rounded to nearest tenth)

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340

Hi there !

6(x – 2)(x – 3) + 4(x - 2)(x – 5) =

replace x

= 6(-3 - 2)(- 3 - 3) + 4(-3 - 2)(-3 - 5)

= 6(-5)(-6) + 4(-5)(-8)

= 6(30) + 4(40)

= 180 + 160

= 340

Good luck !

The value of the algebraic expression, 6 (x – 2)(x – 3) + 4(x - 2) (x – 5), when x = -3 is: 340.

Given the algebraic expression: 6(x – 2)(x – 3) + 4(x - 2) (x – 5)

To find the value of the expression when x = -3, plug in the value of x into the expression.

Thus:

\(6 (-3 - 2)(-3 - 3) + 4(-3 - 2) (-3 - 5) \\\\6(-5)(-6)+4(-5)(-8)\)

\(6(-5)(-6)+4(-5)(-8)\\\\6(30) + 4(40)\\\\180 + 160\)

= 340

Therefore, the value of the algebraic expression, 6 (x – 2)(x – 3) + 4(x - 2) (x – 5), when x = -3 is: 340.

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Answer:

Step-by-step explanation:

The reason behind the the functions f and g are differentiable for all real numbers for the limit 1 < c < 3 is the limitation of constant term.

Function in the math is known as  a kind of rule that, for one input, it gives you one output.

Here we the functions f and g are differentiable for all real numbers

And here we need to explain why there must be a value c for 1 < c < 3.

As we all know that in the differentiable function that is defined as a function that can be approximated locally by a linear function.

Where the general form of the function is written as,

=> [f(c + h) − f(c) h ] = f (c).

Here we have also know that the domain of f is the set of points c ∈ (a, b) for which this limit exists.

Here we know that the value of a = 1 and b = 3.

So due to the limitation the function will only work on the given range.

Complete Question:

The function f and g are differentiable for all real numbers and the value of  g'(3)=k, where k is a constant. The function h is given by h(x) = f(g(x))- g(f(x)). then explain the reason why there must be a value c for 1 < c < 3.

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\(w^2 - 6w + 4\) is a polynomial that represents how much more profit is earned by selling w apple trees than w pear trees.

The profit earned by selling w pear trees is 2w + 10

To find the difference in profit, we need to subtract the profit earned by selling w pear trees from the profit earned by selling w apple trees:

\((w^2 - 4w + 14) - (2w + 10)\)

Simplifying the expression:

\(w^2 - 6w + 4\)

Therefore, the polynomial that represents how much more profit is earned by selling w apple trees than w pear trees is \(w^2 - 6w + 4\).

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Answer: 10.7142857kg in each bag

Step-by-step explanation: If you divide 75 by 7 you would get 10.7142857. There fore there is about 10.7142857kg of chocolate in each bag.

Answer:

x = 40

Step-by-step explanation:

Given 2 secants to a circle from an external point, then

The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is

8(8 + x) = 12(12 + 20) ← distribute parenthesis on both sides

64 + 8x = 12 × 32 = 384 ( subtract 64 from both sides )

8x = 320 ( divide both sides by 8 )

x = 40

X = 30 degrees.

See the attached image

Answer:

solution

-V=17-2

-V=15

Answer:

B) 24

Step-by-step explanation:

Those are alternate interior angle which mean they are congruent or equal to each other

2x=48 divide

48÷2=24

Answer:

B) 24

step by step:

2x = 48 ( two straight lines are parallel forming and the internal stagger angle is equal)

√54²-43.8² +2(7)

54-1918.44+14

-1850.44

Answer:

See below

Step-by-step explanation:

Answer:

x = 18

Step-by-step explanation:

hope it helps:)

Answer:

C. The items have different y-intercepts and different rates of change

Step-by-step explanation:

Figure I shows a linear equation in the form y = mx + b, where "m" is the rate of change and "b" is the y-intercept. That means for y = 1/4 * x - 1/2, 1/4 is the slope and 1/2 is the y-intercept.

Figure II shows a table. The y-intercept is when x = 0, so look at where x = 0 is in the table and see the y-value which corresponds to it. The y-value in this case would be -0.25. To find the rate of change, assuming Table II is changing at a constant rate, subtract the subsequent y-value from a proceeding y-value and divide that by subtracting the corresponding x-values (any two sets of x and y-values should work): (3.75 - 7.75)/(-1 - -2) = -4/(-1 + 2) = -4/-1 = 4.

Thus, we know that the rates of change are different and the y-intercepts are different for both functions.

Answer:

The answer is seventeen (17)

The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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The calculated value of sec^-1(1.4) is 44.41 degrees

The inverse secant function, denoted as sec^-1(x), returns the angle whose secant is x.

In other words, if secθ = x, then sec^-1(x) = θ.

To find the value of sec^-1(1.4), we need to find the angle whose secant is 1.4.

However, we know that the range of the secant function is [-∞, -1] ∪ [1, ∞], which means that sec^-1(x) is only defined for values of x that fall within this range.

Uisng a graphint tool, we have

sec^-1(1.4) = 44.41

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The graph function that is representative of the function h(x) = -x² - 4 is the graph at option C. See further explanation below.

Option C is the correct graph because it satisfied the condition where:

h(x) = -4  given that x = 0

Step 1:

Take the above function and set x to zero to determine the relationship between h(x) and x

⇒ h(x) = -(0)² - 4

h(x) = -4

Lets try this with 1

⇒ h(x) = -(1)² - 4

h(x) = -1 -4

h(x) = -5

where x = 2,

⇒ h(x) = -(2)² - 4

h(x) = -8

The above plotted on the graph results in the curve shown in the attached graph. Hence the correct option is C.

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Answer:

(x,y)=(-2,3)

Step-by-step explanation:

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Answer:

Step-by-step explanation:

Given:

AB ≅ DC and AC ≅ DB

To Prove:

ΔABC ≅ ΔDCB

                  Statements                       Reasons

1). AB ≅ DC and AC ≅ DB         1). Given

2). BC ≅ CB                               2). Reflexive property

3). ΔABC ≅ ΔDCB                     3). SSS property of congruence