Use a graphing calculator to approximate the vertex of the graph of the parabola defined by the following
equation.ñ
y = 2x^2 -x + 6

The triangles with the side lengths 10 ft, 24ft, 26 ft, is a right triangle while a triangle with side lengths of 7 yd, 5 yd, 9 yd is NOT based on the Pythagorean theorem.

A triangle is said to be a triangle based on the Pythagorean theorem, if the square of the longest side equals the sum of the squares of the other smaller sides of the triangle.

9² = 7² + 5²

81 = 74 (NOT TRUE), therefore, the triangle with the side lengths 7 yd, 5 yd, 9 yd, is not a right triangle.

26² = 10² + 24²

676 = 676 (TRUE), therefore, the triangle with the side lengths 10 ft, 24ft, 26 ft, is a right triangle.

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Answer:

2Tu = 90

Step-by-step explanation:

You can substitute the values T = 5 and u = 9 into the expression to get: 2 × 5 × 9 which is 90 (2 × 45 = 90)

Hope this helps!

The final result is 90 when T = 5 and u = 9.

Here, we have to evaluate 2Tu when T = 5 and u = 9, we substitute the values of T and u into the expression and perform the operations accordingly.

Given expression: 2Tu

T = 5

u = 9

Now, let's substitute the values:

2 * 5 * 9

Next, perform the multiplication:

2 * 5 = 10

10 * 9 = 90

So, when T = 5 and u = 9, the value of 2Tu is 90.

We get, to evaluate 2Tu, we first multiply T and u together, and then multiply the result by 2.

In this case, we have T = 5 and u = 9.

So, we perform the following steps:

Multiply T and u: 5 * 9 = 45

Multiply the result by 2: 2 * 45 = 90

Thus, the final result is 90 when T = 5 and u = 9.

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Answer:

  (b)  -7.275i -4.244j

Step-by-step explanation:

The projection of vector u onto vector v is the product of the unit vector v, the magnitude of vector u, and the cosine of the angle between them.

__

The dot product gives the product of the magnitudes of the two vectors and the cosine of the angle between them. To find the projection, we must divide the dot product by the magnitude of v and multiply by the unit vector in the direction of v.

  [tex]proj(u,v)=(\vec{u}\cdot\vec{v})\cdot\dfrac{\vec{v}}{|\vec{v}|^2}=\dfrac{((-8)(-12)+(-3)(-7))(-12\vec{i}-7\vec{j})}{(-12)^2+(-7)^2}\\\\=\dfrac{-(96+21)(12\vec{i}+7\vec{j})}{144+49}=-\dfrac{117}{193}(12\vec{i}+7\vec{j})\approx\boxed{-7.275\vec{i}-4.244\vec{j}}[/tex]

The number of each type of coin that Joan has are; 16 dimes and 3 quarters

We are told that Joan has a total of 19 coins.

Now, the worth of the coins is $2.35

Let dimes be d and let quarters be q. Thus;

10d + 25q = 235

d + q = 19

Substitute d = 19 - q in the 1st equation to get;

10(19 - q) + 25q = 235

190 - 10q + 25q = 235

15q = 45

q = 45/15

q = 3

Thus;

d = 19 - 3

d = 16

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Answer:

By proportional method

[tex] \frac{4}{6} = \frac{5}{x} [/tex]

4x= 30

x= 7.5

If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set

[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]

and as a type II region,

[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]

where we solve y = √(x + 1) for x to get x as a function of y.

A. The area of the type I region is

[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]

B. The area of the type II region is of course also

[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]

I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).

The shaded area expressed as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

From the question, we are to express the shaded area as a fraction, a decimal, and a percent of the whole.

In the diagram, there are 100 total squares and 23 of them are shaded

Expressing the shaded area as a fraction, we get

[tex]\frac{23}{100}[/tex]

Expressing the shaded area as a decimal, we get

[tex]\frac{23}{100}[/tex] = 0.23

Expressing the shaded area as a percent , we get

[tex]\frac{23}{100}\times 100\%[/tex] = 23%

Hence, the shaded area as a fraction, a decimal, and a percent of the whole is 23/100, 0.23 and 23% respectively

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Answer:

13,12,25

Step-by-step explanation:

Square root of 169 is 13.

Square root of 144 is 12

Square root of 625 is 25.

Answer:

[tex]\sqrt{169} = 13\\\\\sqrt{144} = 12\\\\\sqrt{625} = 25[/tex]

Step-by-step explanation:

[tex]\sqrt{169} = \left(13^2 \right)^{\tfrac 12} = 13^{\tfrac 22} = 13^1 = 13\\\\\sqrt{144} = \left( 12^2\right)^{\tfrac 12} = 12^{\tfrac 22} = 12^1 = 12\\\\\sqrt{625}= \left(25^2 \right)^{\tfrac 12} = 25^{\tfrac 22} = 25^1 = 25[/tex]

The shape of the resulting cross-section will be equal to the trapezoid.

A trapezoid is a quadrilateral having four sides whose two sides are parallel to each other and the other two sides are nonparallel to each other.

As it is given in the question the figure is sliced through points J. K. and When the shape is sliced from the given points it will create the trapezoidal shape that will have two parallel sides and the other two sides are Non-parallel

Therefore the shape of the resulting cross-section will be equal to the trapezoid.

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Answer:

Trapezoid

Step-by-step explanation:

I got it right on Edmentum

Hook me up with a 5 star and a thanks :)

Answer:

50

Step-by-step explanation:

The values of a, b and c from the given exponential function are 7, 9 and 4 respectively

According to the exponential law of indices

[tex]\sqrt[c]{a^b}[/tex]

This can be written as;

[tex]\sqrt[c]{a^b}=a^{\frac{b}{c} }[/tex]

Given the exponential expression

[tex]7^\frac{9}{4}[/tex]

Compare with the original expression

a = 7, b = 9 and c = 4

Hence the values of a, b and c from the given exponential function are 7, 9 and 4 respectively

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Answer: Yes it is possible

Example: Yeast is a single-celled fungus.

There are probably other types of fungus that are single-celled. However, some other fungi are multi-celled. You will likely need more information about the organism under the microscrope before you can classify it properly.

Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.

The two given numbers are -84 and 17.

We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).

If we multiply 21 and -4, we get the product as -84.

That is, 21×(-4)=-84

If we add 21 and -4, we get the sum as -17.

That is, 21+(-4)=21-4=17

Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

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Answer:

175 ft^2

Step-by-step explanation:

split the pentagon into 5 triangles with base length 10ft and height 7ft. each triangle then has an area of 10 * 7 * 1/2 = 35 ft^2

then the pentagon has an area 35*5 = 175 ft^2

Answer:

w = 5

Step-by-step explanation:

24w = (14)10

2w + 4 = 10 + 4

2w = 10

w = 5

Answer:

D) 9

Step-by-step explanation:

x = ½ × 13 = 6.5

y = ½ × 5 = 2.5

6.5 + 2.5 = 9

So the length of PC is 9

HOPE THIS HELPS AND HAVE A NICE DAY <3

Answer:

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Answer:

The IQR of the given distribution is

Step-by-step explanation:

The given distribution has the five-number

28, 34, 43, 59, 62

Divide these numbers in two equal parts.

(28, 34), 43,( 59, 62)

Now divide each parenthesis in two equal parts.

(28), (34), 43,( 59), (62)

It means first quartile is the average of 28 and 34. Third quartile is the average of 59 and 62.

The interquartile range (IQR) of this distribution is

Therefore the IQR of the given distribution is 29.5.

Answer:

area = 62ft

Step-by-step explanation

so you section the polygon into a big rectangle and 2 small rectangles

the area of the small rectangle will be 2ft x 3ft which will be 6 ft, and as there are 2 of them the area of it will be 12ft

the area of the big rectangle will be 10ft x 5ft, as 8ft - 3ft is 5ft so 5x10=50ft

now add the areas you got, 50+12 which is 62ft

hope this helps:)

The triangle △ABC and △DEC are similar to each other. Then the correct option is A, B, and D.

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Right triangle ABC is reflected over AC.

Then dilated by a scale factor of Two-thirds to form triangle DEC.

The triangle △ABC and △DEC are similar to each other.

△ABC ≅ △DEC

The dilation is 2/3. Then we have

DE / AB = 2 / 3

     3AB = 2DE

∠B ≅ ∠E = 90

There is no effect of dilation on angle.

Then the correct option is A, B, and D.

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Answer:

A. △ABC ~ △DEC

B. ∠B ≅ ∠E

D. 3DE = 2AB

Step-by-step explanation:

got it right on edge 23

Answer:

51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.

[tex]\begin{array}{ccll} feet&seconds\\ \cline{1-2} 19 & 1\\ 600& x \end{array} \implies \cfrac{19}{600}~~=~~\cfrac{1}{x} \\\\\\ 19x=600\implies x=\cfrac{600}{19}\implies \stackrel{\textit{about half a minute}}{x\approx 31.58~seconds}[/tex]

Answer:

  10/19 min ≈ 0.5263 min

Step-by-step explanation:

The woman's sprinting speed is given in feet per second, and we are asked for it in minutes per 600 feet. To find the time, we can use the relation ...

  time = distance / speed

Using the given numbers will give a time in seconds, so we need to do a units conversion to find the answer in minutes.

__

  time = distance/speed

  time = (600 ft) / (19 ft/s) = (600/19) s

Converting the units gives ...

  time = (600/19) s × (1 min)/(60 s) = (600·1)/(19·60) min

The time it takes the woman to sprint 600 feet will be ...

  time = 600/(19·60) min = 10/19 min ≈ 0.5263 min

(1) The missing term in the sequence, a₁₂  = 0.8.

(2) The missing term in the sequence, a₈ = 102.5.

(3) The missing term in the sequence, a₈ = 111.

(4) The missing term in the sequence, a₁₂ = -19.

(5) The missing term in the sequence, a₁₂ = 94.

(6)  The missing term in the sequence, a₆ = 40.

(7)  The missing term in the sequence, a₃₆ = -52.

(8)  The missing term in the sequence, a₂₁ = -58.

The missing term in the sequence is determined as follows;

Tₙ = a + (n - 1)d

T₄ = a + 3d

18.4 = a + 3d  ---(1)

T₅ = a + 4d

16.2 = a + 4d  ---(2)

subtract (1) from (2)

-2.2 = d

18.4 = a + 3(-2.2)

a = 25

a₁₂  = a + 11d

a₁₂  = 25 + 11(-2.2)

a₁₂  = 0.8

a₂ = a + d

57.5 = a + d -- (1)

a₅ = a + 4d

80 = a + 4d  --- (2)

solve (1) and (2)

d = 7.5

a = 50

a₈ =  a + 7d

a₈ = 50 + 7(7.5)

a₈ = 102.5

a₁₀ = a + 9d

141 = a + 9d --- (1)

a₁₃ = a + 12d

186 = a + 12d --- (2)

Subtract (1) from (2)

d = 15

a = 6

a₈ = a + 7d

a₈ = 6 + 7(15)

a₈ = 111

a₂₂ = a + 21d

-49 = a + 21d ---- (1)

a₂₅ = a + 24d

-58 = a + 24d --- (2)

subtract (1) from (2)

d = -3

a = 14

a₁₂ = a + 11d

a₁₂ = 14 + 11(-3)

a₁₂ = -19

a₄ = a + 3d

-2 = a + 3d --- (1)

a₈ = a + 7d

46 = a + 7d ---- (2)

Subtract (1) from (2)

d = 12

a = -38

a₁₂ = a + 11d

a₁₂ = -38 + 11(12)

a₁₂ = 94

a₉ = a + 8d

64 = a + 8d --- (1)

a₁₂ = a + 11d

88 = a + 11d --- (2)

Subtract (1) from (2)

d = 8

a = 0

a₆ = a + 5d

a₆ = 0 + 5(8)

a₆ = 40

a₂₀ = a + 19d

-4 = a + 19d ---- (1)

a₂₃ = a + 22d

-13 = a + 22d --- (2)

Subtract (1) from (2)

d = -3

a = 53

a₃₆ = a + 35d

a₃₆ = 53 + 35(-3)

a₃₆ = -52

a₂₈ = a + 27d

5 = a + 27d ---- (1)

a₃₃ = a + 32d

50 = a + 32d --- (2)

Subtract (1) from (2)

d = 9

a = -238

a₂₁ = a + 20d

a₂₁ = -238 + 20(9)

a₂₁ = -58

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Answer:

D

Step-by-step explanation:

are the same length and intersect at different angles

The exact height of the triangle is 20.8ft

The area of the right tringle in radical form is 72√3 ft²

The area of the triangle in decimal form is 124.7 ft²

The side XY or height of the triangle can be found as follows:

Using trigonometric ratios,

tan 60° = XY / 12

XY = 12 tan 60°

XY = 12 × 1.73205080757

XY = 20.7846096908

height = 20.8ft

The area of XYZ = 1 / 2 bh

where

Therefore,

The area of XYZ = 1 / 2 × 12 × 20.8 = 124.707658145  = 124.7 ft²

The area in radical form = 1 / 2 × 12 × 12 tan 60°

The area in radical form =  1 / 2 × 12 × 12 × √3 = 144√3 / 2 = 72√3 ft²

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Considering the definition of exponential function, the value of the car is 11,287.25 dollars.

An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

f(x)= aˣ

Being a a positive real, a > 0, and different from 1, a ≠ 1.

When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.

In this case, the value of that car depreciates based on the function f(t)=12,000×[tex]0.96^{t}[/tex] where t is measured in years after purchase.

After 3/2 years, the value of the car is calculated as:

f(3/2)=12,000×[tex]0.96^{3/2}[/tex]

Solving:

f(3/2)= 11,287.25

Finally, the value of the car is 11,287.25 dollars.

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Answer:

  4 square units

Step-by-step explanation:

The vertices of the figure are on grid points, so it is appropriate to use Pick's theorem to find the area.

__

Pick's theorem tells you the area is ...

  A = i +b/2 -1

where i is the number of grid points interior to the figure (0), and b is the number of grid points on the boundary (10).

Using the counted values in the formula, we find the area to be ...

  A = 0 +10/2 -1 = 4

The area of the polygon is 4 square units.

_____

Additional comment

There are several other ways to find the area. Here are a couple:

decompose the figure

A horizontal line 1 unit up from the bottom will divide the figure into a trapezoid and a triangle. The trapezoid has bases 4 and 1, and height 1, so its area is ...

  A = 1/2(b1 +b2)h = 1/2(4 +1)(1) = 5/2

The triangle has base 1 and height 3, so its area is ...

  A = 1/2bh = 1/2(1)(3) = 3/2

Then the total area is 5/2 +3/2 = 8/2 = 4 square units.

subtract empty space

The figure occupies a 4×4 square with triangles removed from the left side and the top. Each of those triangles has a base of 4 and a height of 3. The remaining (shaded) area is ...

  A = s² -1/2bh -1/2bh

  A = 4² -1/2(4)(3) -1/2(4)(3) = 16 -12 = 4 square units

By solving a linear equation, we will see that the total cost for renting the bus is $90.

Let's say that the total cost is C.

When there are 20 students, each student should pay:

p = C/20

When the other 10 students are added (for a total of 30) each student pays:

p' = C/30.

We know that the cost for each of the original 20 students decreased by $1.50, so:

p' = p - $1.50

Then we have 3 equations to work with:

p = C/20

p' = C/30.

p' = p - $1.50

Now we can replace the first and second equations into the third one:

C/30 = C/20 - $1.50

Now we can solve this linear equation for C:

C/20 - C/30 = $1.50

C*( 1/20 - 1/30) = $1.50

C*(30/600 - 20/600) = $1.50

C*(10/600) = $1.50

C*(1/60) = $1.50

C = 60*$1.50 = $90

So the total cost for renting the bus is $90.

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{\underline{y} varies inversely with \underline{x}}}{y=\cfrac{k}{x}}\qquad \textit{we also know that} \begin{cases} y=49\\ x=17 \end{cases} \\\\\\ 49=\cfrac{k}{17}\implies 833=k~\hfill \boxed{y=\cfrac{833}{x}} \\\\\\ \textit{when y = 7, what is "x"?}\qquad 7=\cfrac{833}{x}\implies x=\cfrac{833}{7}\implies x=119[/tex]