how many 4 letter code words can be made using the letters in the word pencil

The value of the variable x is 72 degrees

A supplementary angle is simply defined as a  pair of angles that sum up to 180 degrees.

The properties of supplementary angles includes;

From the information given, we have that;

108 degress + x = straight line

But we know that angles on a straight line is 180

Then,

108 + x = 180

collect like terms

x = 180 - 108

subtract the values

x = 72 degrees

Hence, the value is  72 degrees

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Answer:

huh what do you mean

Step-by-step explanation:

im really sorry

The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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As h decreases, the value of (the change in x^2)/h increases, since 16h gets divided by a smaller value of h. For example, when h=0.1, (the change in x^2)/h = 16/0.1 = 160.

a. If h=1, then (the change in x^2)/h = 16/1 = 16

b. If h=0.1, then (the change in x^2)/h= 16/0.1 = 160

c. If h=0.01, then (the change in x^2)/h= 16/0.01 = 1600

d. If h=0.001, then (the change in x^2)/h= 16/0.001 = 16000

The change in x^2 refers to the difference in the value of x^2 when x is increased from 4 to 4+h. In other words, it is the difference between (4+h)^2 and 4^2. The change in x^2 is 16h, since (4+h)^2 = 16h + 4^2. To find (the change in x^2)/h, we simply divide 16h by h, which gives us 16. So, for each of the values of h given, when x is increased from 4 to 4+h, (the change in x^2)/h is 16. As h decreases, the value of (the change in x^2)/h increases, since 16h gets divided by a smaller value of h. For example, when h=0.1, (the change in x^2)/h = 16/0.1 = 160.

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Answer:

\(-\frac{9}{1}\)

Step-by-step explanation:

Its just the same way as making positive 9
a fraction, but just add the negative sign.

Hope this helps :))

The solution is, (4,1)

Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.

here, we have,

The question is

Find the image of the given point

we know that

The rule of the translation is

(x,y)  → (x-3,y+2)

That means ---> The translation is 3 units at left and 2 units up

we have the point (7,-1)

Apply the rule of the translation to the point (7,-1) (pre-image) to obtain the image

(7,-1)  → (7-3,-1+2)

(7,-1)  → (4,1)

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Answer:

The novelist can write 4/15ths of a page in an hour.

Step-by-step explanation:

Just multiply 3/5 by the reciprocal of 9/4, which is 4/9. Multiply 3/5 and 4/9 to get 12/45 or 4/15. In conclusion, the writer can write 4/15th of a page in an hour.

Answer:

All squares are rectangles. Rectangles have 4 right angles. Therefore, all squares have 4 right angles.

All recatangles have 4 angles which are 90°. Though all squares are rectangles, remember, not all rectangle are squares

Hope this helps, Bye!

The true statement is "All squares are rectangles. Rectangles have 4 right angles. Therefore, all squares have 4 right angles".

That rectangle whose all sides are equal is called a square.

A square has its diagonals perpendicular bisector to each other and is of the same length. (this is actually a characteristic property, which means that if a quadrilateral has its diagonals equal and perpendicular,

then it is a square for sure).

A square is always a rectangle, parallelogram, a rhombus, and a quadrilateral but its reverse statement may or may not be true.

also, it is not always necessary that a rectangle is a square or a parallelogram is a square or a rhombus is a square.

All squares are rectangles. Rectangles have 4 right angles.

Therefore, all squares have 4 right angles.

All rectangles have 4 angles which are 90°. Though all squares are rectangles, remember, not all rectangles are squares

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Answer:

Step-by-step explanation:

Do tell, if that's what you mean. If you're asking me, I'm not sure I know!

Answer:

-5+√2 and -5-√2

Step-by-step explanation:

With the quadratic formula:

\(\displaystyle x^2 + 10x + 25 = 2\\\\x^2+10x+23=0\\\\x=\frac{-10\pm\sqrt{10^2-4(1)(23)}}{2(1)}=\frac{-10\pm\sqrt{100-92}}{2}=\frac{-10\pm\sqrt{8}}{2}=\frac{-10\pm2\sqrt{2}}{2}=-5\pm\sqrt{2}\)

We can also complete the square (which is faster):

\(x^2+10x+25=2\\(x+5)^2=2\\x+5=\pm\sqrt{2}\\x=-5\pm\sqrt{2}\)

2/5

Step-by-step explanation:

0.4

= 4/10 → divided by 2

= 2/5

Answer:

False

Step-by-step explanation:

Answer:

A quadrilateral can't have 2 reflex angles

Step-by-step explanation:

A quadrilateral can't have 2 reflex angles because reflex angles > 180° so if you add two together, it is > 360°

An expression for the area of △KNM is = 1/2 x 2b x a

Given,

In the question:

In triangle KNM ;

The length of the base (MK) = 2b

and, height of the triangle is= a

To write an expression  for the area of △KNM .

Now, According to the question:

We know that :

Area of triangle is = 1/2 x base x height

The length of the base (MK) = 2b

and, height of the triangle is= a

Plug all the values in the area of triangle :

Here, Area of triangle is = 1/2 x 2b x a

Hence, An expression for the area of △KNM is = 1/2 x 2b x a.

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Answer:

87 000 000

Step-by-step explanation:

Answer:

48%

Step-by-step explanation:

I like to look at percentages as test grades. If you got a 130/250 on a test, you would simply need to view the dash line as a 'divided by'. So you would figure 130 divided by 250 is .52, or 52%... Then, you would need to subtract 52 from 100 to get 48% to get the percentage of people who do not walk to school.

48%

48% of 250 is 120

120+130=250

Answer: 2

Step-by-step explanation:

Answer:

I think it's 2kg

Step-by-step explanation:

13/5 ÷ 13/10

Reciprocate

13/5 × 10/13

= 26/13

=2kg

Step-by-step explanation:

=4(2)×9÷(4-2)

=8×9÷2

=72÷2

=36

Answer:

x = 58

Step-by-step explanation:

Hope this helps

enjoy

Answer:

the answer is d because that is how much degrees it is

Step-by-step explanation:

Answer:

a. 2/3

b. \(\sqrt{2}\)

c. 3

d. 5

e. 2

f. Undefined

Step-by-step explanation:

a. \(f(x)=\frac{|x-3|}{x+2}\)

To find f(1), plug in 1 where every x is in the equation

\(f(1)=\frac{|1-3|}{1+2}=\frac{|-2|}{3}=\frac{2}{3}\)

b. \(f(x) = \sqrt{x+1}\)

\(f(1) = \sqrt{1+1}=\sqrt{2}\)

c. \(f(x) = x^2+5x-3\)

\(f(1) = (1)^2+5(1)-3=1+5-3=6-3=3\)

d. \(f(x)=\frac{2x+3}{x}\)

\(f(1)=\frac{2(1)+3}{1}=\frac{5}{1}=5\)

e. \(f(x) = |2x-4|\)

\(f(1) = |2(1)-4|=|2-4|=|-2|=2\)

f. \(f(x)=\frac{7-2x}{x-1}\)

\(f(1)=\frac{7-2(1)}{1-1}=\frac{5}{0}\)

This equation is undefined when x=1 because 0 is the denominator of the fraction.

The arctan function has the following property: if x is positive, then

arctan(1/x) + arctan(x) = π/2

This means

\(\displaystyle \int_{1/\sqrt3}^1 \arctan\left(\frac1x\right) \, dx = \int_{1/\sqrt3}^1 \left(\frac\pi2 - \arctan(x)\right) \, dx \\\\\\ = \frac{(3-\sqrt3)\pi}6 - \int_{1/\sqrt3}^1 \arctan(x) \, dx\)

For the remaining integral, integrate by parts with

\(u = \arctan(x) \implies du = \dfrac{dx}{x^2+1}\)

\(dv = dx \implies v = x\)

\(\displaystyle \int_a^b \arctan(x) \, dx = uv\bigg|_a^b - \int_a^b v \, du\)

\(\implies \displaystyle \int_{1/\sqrt3}^1 \arctan(x) \, dx = x\arctan(x) \bigg|_{1/\sqrt3}^1 - \int_{1/\sqrt3}^1 \frac{x}{x^2+1} \, dx\)

We have arctan(1) = π/4 and arctan(1/√3) = π/6, and

\(\displaystyle \int \frac{x}{x^2+1} \, dx = \frac12 \int \frac{d(x^2+1)}{x^2+1} = \frac12\ln(x^2+1) + C\)

which gives

\(\displaystyle \int_{1/\sqrt3}^1 \arctan(x) \, dx = \frac\pi4 - \frac\pi{6\sqrt3} - \frac{\ln(2) - \ln\left(\frac43\right)}2 \\\\\\ = \frac{(9-2\sqrt3)\pi}{36} + \frac12\ln\left(\frac23\right)\)

so that

\(\displaystyle \int_{1/\sqrt3}^1 \arctan\left(\frac1x\right) \, dx = \frac{(3-\sqrt3)\pi}6 - \frac{(9-2\sqrt3)\pi}{36} - \frac12\ln\left(\frac23\right) \\\\\\ = \boxed{\frac{(9-4\sqrt3)\pi}{36} - \frac12\ln\left(\frac23\right)}\)

Alternatively, you can integrate by parts immediately:

\(u = \arctan\left(\dfrac1x\right) \implies du = \dfrac{-\frac1{x^2}}{1+\frac1{x^2}} \, dx = -\dfrac{dx}{x^2+1}\)

\(dv = dx \implies v = x\)

so that

\(\displaystyle \int_{1/\sqrt3}^1 \arctan\left(\frac1x\right) \, dx = x\arctan\left(\frac1x\right) \bigg|_{1/\sqrt3}^1 + \int_{1/\sqrt3}^1 \frac{x}{x^2+1} \, dx\)

You'll end up with the same result either way.

Answer:

9

Step-by-step explanation:

8 5/6

5/6 is close to 1 so it will round up

8+1 = 9

8 5/6 rounds to 9

Answer:

\(9\)

Step-by-step explanation:

Step 1:  Round \(8\frac{5}{6}\) to the nearest whole number

In order to round up, the fraction needs to be either 1/2 or greater than 1/2.  In our case, it is greater than half therefore we will round up to 9.

Answer:  \(9\)

The amount of Bruno's yearly pay deducted for FICA is approximately

A. $4,524.15. The closest option provided is A. $4521.15.

To calculate the amount of FICA deducted from Bruno's yearly pay, we need to consider the specific FICA tax rates for Social Security and Medicare.

As of 2021, the Social Security tax rate is 6.2% on income up to a certain threshold, and the Medicare tax rate is 1.45% on all income.

Given that Bruno's gross income per pay period is $4925 and he is paid monthly, we can calculate the yearly gross income as follows:

Yearly gross income = $4925 * 12 = $59,100

To calculate the FICA deduction, we need to find the sum of the Social Security and Medicare taxes. Using the respective tax rates mentioned earlier:

Social Security deduction = $59,100 * 6.2% = $3,667.20

Medicare deduction = $59,100 * 1.45% = $856.95

Adding these two deductions together:

FICA deduction = $3,667.20 + $856.95 = $4,524.15

Therefore, the amount of Bruno's yearly pay deducted for FICA is approximately $4,524.15.

The closest option provided is A. $4521.15.

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Answer:

a. Unikely

b. Likely

c. Equally likely

d. Unlikely

e. Equally likely

f. Equally likely

g. Unlikely

h. Likely

i. No SPINNER SHOWN?

j. NO SPINNER SHOWN?

Step-by-step explanation:

Answer:

See below for explanation

Step-by-step explanation:

The area of an isosceles triangle is \(A=\frac{1}{2}bh\), so let's write the base as an equation of y:

\(\displaystyle 9x^2+4y^2=36\\\\4y^2=36-9x^2\\\\y^2=9-\frac{9}{4}x^2\\\\y=\pm\sqrt{9-\frac{9}{4}x^2\)

As you can see, our ellipse consists of two parts, so the hypotenuse of each cross-section will be \(\displaystyle 2\sqrt{9-\frac{9}{4}x^2\), and each height will be \(\displaystyle \sqrt{9-\frac{9}{4}x^2}\).

Hence, the area function for our cross-sections are:

\(\displaystyle A(x)=\frac{1}{2}bh=\frac{1}{2}\cdot2\sqrt{9-\frac{9}{4}x^2}\cdot\sqrt{9-\frac{9}{4}x^2}=9-\frac{9}{4}x^2\)

Since we'll be integrating with respect to x because the cross-sections are perpendicular to the x-axis, then our bounds will be from -2 to 2 to find the volume:

\(\displaystyle V=\int^2_{-2}\biggr(9-\frac{9}{4}x^2\biggr)\,dx\\\\V=9x-\frac{3}{4}x^3\biggr|^2_{-2}\\\\V=\biggr(9(2)-\frac{3}{4}(2)^3\biggr)-\biggr(9(-2)-\frac{3}{4}(-2)^3\biggr)\\\\V=\biggr(18-\frac{3}{4}(8)\biggr)-\biggr(-18-\frac{3}{4}(-8)\biggr)\\\\V=(18-6)-(-18+6)\\\\V=12-(-12)\\\\V=12+12\\\\V=24\)

Therefore, this explanation confirms that the correct volume is 24!

The difference of the algebraic expressions is 3x² - 11x + 4

An algebraic expression is an expression that is made up of variables and constants, along with algebraic operations like addition, subtraction, square root, etc.

The difference of two algebraic expressions means the subtraction of the expressions. That is:

(-4x+3) - (7x - 3x² - 1) = -4x+3 -7x+3x²+1

                                 =  3x² - 11x + 4

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Answer:

12/5 gallons/minute, or 2 2/5 gallons/minute

Step-by-step explanation:

Find the unit rate with time as the independent variable:

2 gallons

---------------- = 12 gallons / 5 minutes = 12/5 gallons/minute

5/6 minute

Answer:

.41666 or 5/12 Gallons per minute

Step-by-step explanation:

5/6 divided by 2

The function f(x) = -2(4)ˣ⁺¹ +140 represents the number of tokens a child has x hours after arriving at an arcade. The practical domain and range of the function are x ≥ 0 and The practical range of the situation is [140, ∞).

The given function is f(x) = -2(4)ˣ⁺¹+ 140, which represents the number of tokens a child has x hours after arriving at an arcade.

To determine the practical domain and range of the function, we need to consider the constraints and limitations of the situation.

For the practical domain, we need to identify the valid values for x, which in this case represents the number of hours the child has been at the arcade. Since time cannot be negative in this context, the practical domain is x ≥ 0, meaning x is a non-negative number or zero.

Therefore, the practical domain of the situation is x ≥ 0.

For the practical range, we need to determine the possible values for the number of tokens the child can have. Looking at the given function, we can see that the term -2(4)ˣ⁺¹represents a decreasing exponential function as x increases. The constant term +140 is added to shift the graph upward.

Since the exponential term decreases as x increases, the function will have a maximum value at x = 0 and approach negative infinity as x approaches infinity. However, due to the presence of the +140 term, the actual range will be shifted upward by 140 units.

Therefore, the practical range of the situation will be all real numbers greater than or equal to 140. In interval notation, we can express it as [140, ∞).

To summarize:

- The practical domain of the situation is x ≥ 0.

- The practical range of the situation is [140, ∞).

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Answer:

-81,-1.3,-1/3,0.1,12

Step-by-step explanation:

ur welcome :)