pls solve me this functions question ​

A solid right prism ABCDEF  has a height of 16.  A part of the prism is sliced off with a straight cut through points  X, Y, and Z. CXYZ is a  triangular pyramid and its surface area is 48 + 9√3 + 3√91  or 92.2

The situation can be depicted in the attached picture. CXYZ is a triangular pyramid.

The surface area of CXYZ is equal to:

area CXYZ = area ΔCXY +  area ΔCYZ +  area ΔCXZ + area ΔXYZ

ΔABC and ΔCXY are congruent, hence ΔCXY is a equilateral triangles with its sides are 1/2 those of ΔABC.

CX = CY = XY = 1/2 x 12 = 6

To find the area of ΔCXY, find its height first.

√3/2 = h/6

h = 3√3

Area ΔCXY = 1/2 x 3√3 x 6 = 9√3

ΔCXZ is a right triangle at C. Hence,

Area ΔCXZ =  1/2 x CX x CZ

                   = 1/2 x 6 x 8 = 24

ΔCYZ = ΔCXZ

Hence,

Area ΔCYZ =  24

To find the area of ΔXYZ, find XZ first using the Pythagorean Theorem.

XZ² = CX² + XZ²   (XZ = 8, since Z is midpoint of CD)

XZ² =  6² + 8²

XZ² = 10²

XZ = 10

Find the height of ΔXYZ

h = √(10² - 3² )

h = √91

Therefore,

Area ΔXYZ = 1/2 x XY x h

                   = 1/2 x 6 x √91 =3√91

Finally,

area CXYZ = area ΔCXY +  area ΔCYZ +  area ΔCXZ + area ΔXYZ

                  = 9√3 + 24 + 24 + 3√91

                  = 48 + 9√3 + 3√91

                  = 92.2

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The exact value is required. In this case, they don't have enough for 1 3/4 cups of flour.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split.

From the information, the person had 2/3 cup of flour in a bin and 7/8 flour was still in the bag. In this case, it should be noted that they also wanted to know of they had enough for 1 3/4 cups of flour.

This will be calculated thus:

= 2/3 + 7 / 8

= 16/24 + 21/24

= 37 / 24.

= 1 13 / 24

This is not enough for 1 3/4 cups of flour.

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Answer:

35 [tex]\frac{0}{1}[/tex]

Step-by-step explanation:

If each score is doubled, and then 5 is subtracted from that result, then the mean and standard deviation will be 115 and 36 respectively.

A huge group of test results has a mean of 60 and a standard deviation of 18. If each score is doubled and then 5 is deducted from the result, the mean and standard deviation are “ mean = 115; standard deviation = 36”. Mean = 2 x 60 -5 = 120 -5 = 115

2 x 18 = 36 standard deviation

The mean is the average and is calculated as the sum of all the results from the example divided by the total number of events.

The standard deviation (SD) is a statistic used to assess the degree of variation or dispersion in a set of data values.

A low standard deviation indicates that the information points slant toward being near the mean of the set, whereas an exclusive expectation deviation or a high standard deviation indicates that the information points tilt toward being near the mean of the set.

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Answer:

x= 35⁰ - obtuse triangle

Step-by-step explanation:

since the sum of angles of the triangle = 180⁰

(3x-5) + (x+10) + (x) =180⁰

5x+5= 180

(subtracting 5 from both sides)

5x=180-5

5x= 175

(dividing by 5)

x= 35⁰

so the angles of the triangle are

(3x-5) = 105-5= 100⁰

(x+10) = 45⁰

(x) = 35⁰

then this triangle is an obtuse triangle

Yes, infinity times 0 is still 0 because if we multiply 0 to any number is 0.

Yes, infinity times 0 is still 0 because if we multiply 0 to any number is 0.

0 * 0 * 0 * 0= 0

Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present. It is the only integer (and, in fact, the only real number) that is neither negative nor positive. A number which is not zero is said to be nonzero. A root of a function f is also sometimes known as "a zero of f."

The Schoolhouse Rock segment "My Hero, Zero" (Multiplication Rock, Season 1, Episode 2, 1973) extols the virtues of zero with such praises as, "My hero, zero Such a funny little hero But till you came along We counted on our fingers and toes Now you're here to stay And nobody really knows How wonderful you are Why we could never reach a star Without you, zero, my hero How wonderful you are."

Zero is commonly taken to have the factorization 0=0·1 (e.g., in the Wolfram Language's FactorInteger[n] command). On the other hand, the divisors and divisor function sigma_k(0) are generally taken to be undefined, since by convention, n|0 (i.e., n divides 0) for every n except zero.

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Equations with three variables that are linear. Ax + by + cz = r is referred to as a linear equation in three variables.

A linear equation is one that has the form y=mx+b in algebra. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

given

equations with three variables that are linear. Ax + by + cz = r is referred to as a linear equation in three variables if all four variables—a, b, c, and r—are real values and not equal to 0.

(The x, y, and z are the "three variables"). The coefficients of the equation are designated by the numerals a, b, and c.

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Answer:

10^11

Step-by-step explanation:

This question helps you practice some exponent rules. To "fix" a negative exponent you push it across the fraction bar. The 10^-3 on the bottom becomes a 10^3 on the top. See image.

Then, when you have 10^8 • 10^3, that is when you are multiplying, you add the exponents.

10 ^ (8+3)

= 10^11

see image

The midpoint of 1 and 2 and 3 and 4 is (2,3).

The formula for midpoint = (x1 + x2)/2, (y1 + y2)/2.

The end of a line at a point that is equally distant from both ends, a time interval between an event's beginning and end.

The point on a graph or figure where the figure stops might be referred to as the endpoint. It can be the point joining the sides of a polygon (the vertex), the common endpoint of two rays making an angle, the two extreme points of a line segment, the one end of a ray.

Use numbers, fractions, mixed numbers, or decimals to enter two points. The midpoint calculator displays the required research:

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It will cost $10.00 to waterproof a canvas truck cover that is 15' x 24'.

To find this, we need to first convert the dimensions of the canvas truck cover from feet to yards, since the cost is given per square yard. 15' x 24' = 180 sq ft. 1 sq yard is equal to 9 sq ft, so 180 sq ft/9 sq ft/yard = 20 sq yard. Then we multiply the square yards by the cost per square yard to find the total cost:

It's important to note that the measurements of the canvas truck cover are given in feet and the cost is given per square yard. It's important to convert it to square yards to match the unit of measurement and calculate the cost.

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a. The current sale price for the computer system is given as follows: $618.4.

b. The amount paid by the club members, with the discount, is given as follows: $587.48.

The prices are found applying the proportions, which are the decimal equivalent of the percentages relative to each discount.

The selling price is of:

$773.

The markdown is of 20%, hence the current sale price is 100 - 20 = 80% of the selling price, hence:

0.8 x 773 = $618.4.

Club members get an additional discount, of 5%, meaning that they pay 95% of $618.4, and the amount is obtained as follows:

0.95 x 618.4 = $587.48.

The problem is given by the image presented at the end of the answer.

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Answer:

4.472135955

Step-by-step explanation:

Meaning of the △ is: the given symbol is the representation of the geometrical figure triangle.

Therefore, the meaning of the given symbol △ is the representation of the triangle.

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Draw a line and locate the origin '0', mark the positive numbers on the right and the negative number on the left of '0' at an equal distance.

A number line is a horizontal straight line in which the integers are placed in equal intervals. All the numbers can be represented in a number line. This line can be extended indefinitely at both ends. 

A number line is a graphical representation of numbers on a straight line. It is used for comparing and ordering numbers. It can be used for representing any real number that includes every whole number and natural number.

Draw a line and locate the point ‘0’. This point is known as the origin. If the given number is positive, draw it on the right side of the origin. If it is a negative number, draw it on the left side of zero. Divide each unit into the values equal to the denominator of the given fraction.

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Area of the pond is 86.625 m²

Given data :

Diameter of the pond = 14m

Radius of the inner circle (pond), r = 7 m

Width of the concrete path = 1.75m

Radius of outer circle (Including pond + Path), R = 7 + 1.75 = 8.75 m

Area of the path = Area of the outer circle − Area of the inner circle.

= πR² - πr²

= 22 / 7 x ( 8.75 + 7) ( 8.75 − 7 )

= 86.625 m²

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Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.

A mathematical equation is a formula that connects two statements using the equal sign (=) to denote equivalence. An algebraic equation is a mathematical statement that establishes the equality of two mathematical expressions. For example, the variables 3x + 5 and 14 are separated by an equal sign in the equation 3x + 5 = 14. Mathematical equations are used to express the connection between two phrases on either side of a letter. There is frequently just one variable, which is also the symbol. example: 2x - 4 = 2.

given

DE = DC + CE

44 = 5n – 30 +  6n – 25

44 = 11n - 55

44 + 55 = 11n

n = 9

Segment Addition Postulate states that n has a value of 9 when DC = 5n - 30 and CE = 6n - 25 and DE = 44.

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[tex]sin(A)+cos(A)=\sqrt{2}\hspace{10em}tan(A)+cot(A)=2 \\\\[-0.35em] ~\dotfill\\\\ tan(A)+cot(A)=2\implies \cfrac{sin(A)}{cos(A)}+\cfrac{cos(A)}{sin(A)}=2 \\\\\\ \cfrac{sin^2(A)+cos^2(A)}{cos(A)sin(A)}=2\implies \boxed{\cfrac{1}{cos(A)sin(A)}=2} \\\\[-0.35em] ~\dotfill[/tex]

[tex]sin(A)+cos(A)=\sqrt{2}\implies (~~sin(A)+cos(A)~~)^2=(\sqrt{2})^2 \\\\\\ sin^2(A)+2sin(A)cos(A)+cos^2(A)=2 \\\\\\ 2sin(A)cos(A)+sin^2(A)+cos^2(A)=2\implies 2sin(A)+1=2 \\\\\\ 2sin(A)cos(A)=1\implies \boxed{2=\cfrac{1}{cos(A)sin(A)}}[/tex]

now, another way to look at this identity will  be as a unified system of equations

[tex]\begin{cases} (~~sin(A)+cos(A)~~)^2=2\\\\ ~~ ~tan(A)+cot(A)=2 \end{cases}\implies (~~sin(A)+cos(A)~~)^2=tan(A)+cot(A)[/tex]

and we'd end up with the same rigamarole.

The measure of length of FG is 105 units.

What is bisection?

To determine the roots of a polynomial problem, utilise the bisection method. It splits and separates the interval in which the equation's root is located. The continuous functions intermediate theorem serves as the method's guiding premise.

From the given diagram, since Line DF bisects angle EDG, then -

EF = FG

Given the following parameters -

EF = 9n - 3

FG = 8n + 9

Equating both expressions -

9n - 3 = 8n + 9

9n - 8n = 9 + 3

n = 12

Get the measure of FG -

FG = 8n + 9

FG = 8(12) + 9

FG = 96 + 9

FG = 105

Hence, the line FG measures as 105 units.

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Answer:

Step-by-step explanation:

The four options just swap the order, and you should choose them all

62.5 of the yellow balloons lack strings. The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the probability.

The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood. The formula is: Probability of an Event P(E) = (Number of Favorable Outcomes) (Sample space).

The ratio of positive outcomes to all outcomes in that sample space is generally referred to as the likelihood.

A sample is created in this way, and using the data collected, the calculation can be done. The formula for calculating probabilities is probability = Favorable instances / Possible cases x 100, given as a percent.

25/40 * 100 = 0.625*100 = 62.5.

62.5 of the yellow balloons lack strings.

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Rounded to the nearest tenth, the measure of side ST is 8.0.

In order to find the measure of side ST, you will need to use the concept of similarity. If two triangles are similar, then their corresponding sides are in proportion. If we let x be the measure of side ST, then we can set up a proportion using the given information:

[tex]OP/PQ = ST/RQ[/tex]

We also know that

[tex]OP/PQ = 2/3[/tex]

and

[tex]RQ = 12[/tex]

So we can substitute these values into the proportion and solve for x:

[tex](2/3) = ST/12[/tex]

[tex]ST = (2/3) * 12[/tex]

[tex]ST = 8[/tex]

Rounded to the nearest tenth, the measure of side ST is 8.0.

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Total 56 bags of hardwood and 140 bags of pine bark bags are sold.

In the given question, a local boys club sold 196 bags of mulch and made a total of $357.

It sold two types of mulch: hardwood for $2.00 a bag and pine bark for $1.75 a bag.

We have to find how many bags of each kind of mulch did it sell.

Let total number of x bags of hardwood sell.

Let total number of y bags of pine bark sell.

Now the equation should be

2x + 1.75y = 357............................(1)

Total number of bags sold 196.

So x + y = 196............................(2)

From the equation 2 the value of x = 196-y. Now putting the value of x in equation 1.

2(196 - y) + 1.75y = 357

392 - 2y + 1.75y = 357

392 - 0.25y = 357

Subtract 392 on both side, we get

-0.25y = -35

Divide by -0.25 on both side, we get

y = 140

Now putting the value of y in x = 196-y

x = 196 - 140

x = 56

Hence, 56 bags of hardwood and 140 bags of pine bark bags are sold.

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Dimensions of the parallelogram are:

Its perimeter is:

Its area is:

Perimeter is 2 times greater:

Area is 2*2 = 4 times greater:

Perimeter is 3 times greater:

Area is 3*3 = 9 times greater:

Perimeter is 2 times smaller:

Area is 2*2 = 4 times smaller:

The area of one base of the triangular prism is given as 16√3 square cm, and since the base is equilateral, the sides of the triangle are of equal length.

The formula to calculate the area of an equilateral triangle is (sqrt(3)/4) * s^2 where s is the length of a side of the triangle.

So, plugging in the given area of base, 16√3, we can find the length of a side of the equilateral triangle, s.

16√3 = (sqrt(3)/4) * s^2

s = (4*16√3)/sqrt(3) = 16√3 cm

Now we can use the height of the prism, which is given as 30 cm, to find the area of the rectangular surface.

Area of the rectangular surface = 2 * base area * height = 2 * 16√3 * 30 cm²

This simplifies to:

960√3 cm²

So the total area of the rectangular surface of the prism is 960√3 square cm.

The time taken for his return flight, in hours could be  4 hours.

What is time ?

Time is defined as the sequence of events that occurs which can be from past through present or to future.

Given,

Benji's flight from Chicago to San Jose took 0.5 hour longer than his return flight from San Jose to Chicago.

If Benji's flight from Chicago to San Jose was 4.5 hours long

let,

chicago to san jose = san jose  to chicago+0.5

4.5 - 0.5  = san jose to chicago

san jose to chicago  = 4 hours

Hence,  How  long was his return flight, in hours is 4 hours.

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Step-by-step explanation:

the range is (-32, 28)

note that when the bubble is not filled in it should be an open bracket

The equation of a parabola that intersects the x-axis at points (-1, 0) and

(3, 0) is y = x² - 2x - 3.

What is a parabola?

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola.

Since the parabola intersects x-axis at points (-1,0) and (3,0), the parabola has its axis parallel to y-axis.

The general equation for such parabola is,

y = ax² + bx + c

The roots of the quadratic equation is found when y = 0

We know that when y = 0, x = -1 , 3

So (x+1) (x - 3) = 0

Solving the above equation we can find the equation of parabola

x² - 3x + x -3 = y

Therefore y = x² - 2x- 3 is the equation of a parabola that intersects the x-axis at points (-1, 0) and (3, 0).

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