The longer leg of a 30°-60°-90° triangle measures [tex]9\sqrt{3}[/tex] inches. What is the length of the shorter leg?

A. 18 inches

B. [tex]18\sqrt{3}[/tex] inches

C. [tex]9\sqrt{3}[/tex] inches

D. 9 inches

bearing in mind that the variable with the positive sign is the "y", meaning the hyperbola  is opening vertically, and thus its vertices/foci will be along the center's y-coordinate.

[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf 4y^2-25x^2=100\implies \cfrac{4y^2-25x^2}{100}=1\implies \cfrac{4y^2}{100}-\cfrac{25x^2}{100}=1 \\\\\\ \cfrac{y^2}{25}-\cfrac{x^2}{4}=1\implies \cfrac{(y-0)^2}{5^2}-\cfrac{(x-0)^2}{2^2}=1\qquad \begin{cases} h=0\\ k=0\\ a=5\\ b=2 \end{cases} \\\\\\ \stackrel{\textit{vertices}}{(0, 0\pm 5)}\implies \begin{cases} (0,5)\\ (0,-5) \end{cases}[/tex]

Answer:

1) given

3)being alternate angleS

5)ASA condition

6)corresponding sides of congruent triangle are equal

7)Pt=Rt and ST =QT

Answer:

-7x(x + 4)

Step-by-step explanation:

Not sure exactly what you're doing with this, but I know you're not solving it for x because there's no " = " there so I am assuming you're simplifying it as much as possible.  I'm going with that.

First thing is to distribute through the parenthesis by multiplying 4x by 3x and then 4x by -7 to get:

[tex]12x^2-28x-19x^2[/tex]

Now combine like terms to get

[tex]-7x^2-28x[/tex]

The last thing you could do now is pull out what's common between each of those terms which is -7x.  When you do that, you're left with

-7x(x + 4)

Answer:

  6.  quadratic

  7.  linear

Step-by-step explanation:

6. First differences are ...

Second differences are ...

These are constant at -2, so the data are quadratic. The data can be described by y = 6-(x-3)^2.

__

7. The x-values are evenly spaced (though decreasing). For our purpose, we can still look at the first differences of the table values in the order given. First differences are ...

These are constant at +4, so the data are linear. The data can be described by y = -4x +12.

Answer:

0 is the answer

Step-by-step explanation:

Answer:

B. 75 Degrees

Step-by-step explanation:

A triangle is up to 180 degrees. Since you're given two angles already, you can add both of those together and subtract it from 180.

75 + 35 = 105

180 - 105 = 75

75 + 75 + 35 = 180

Answer:

  see below

Step-by-step explanation:

Eric will drive between 70 -4 = 66 mph and 70+4 = 74 mph. He will not drive less than 66 or more than 74 mph.

Answer:

Step-by-step explanation:

In general, solutions to absolute value inequalities, as in this case, take two forms:

If | x | <a, then x<a or x> -a.

If | x |> a, then x> a or x <-a.

In this case, you have |x − 70| ≤ 4. So, you have two cases:

x − 70 ≤ 4 and x − 70 ≥ -4

Solving both equations:

x − 70 ≤ 4      

x ≤ 4 + 70

x≤ 74

and

x - 70 ≥ -4

x ≥ -4+70

x ≥ 66

It is convenient to graph both solutions, as shown in the attached image .

The intersection between both conditions is the solution to the inequality (that is, in the image it is shown as the interval painted by both colors). In this case, the solution is 66≤x≤74

This indicates that Eric can drive within this speed range.

The range of speeds Eric would not drive at under the given conditions is x≤66 and x≥74,  as shown in the other image.

Answer:

Step-by-step explanation:

By definition, Volume of Sphere = [tex]\frac{4}{3}[/tex]πr³

If r = 4 in,

then Volume = [tex]\frac{4}{3}[/tex]π(4)³ = 268.08 in³

Answer:

267.95

Step-by-step explanation:

4/3 * pi * 4^3

4/3 * pi *64

256/3* pi = 267.95

Answer: The temperature is -1 degrees

Step-by-step explanation: Trust me!

Answer:

PD = 10.6

Step-by-step explanation:

Point P has coordinates (3,-1) and point Q has coordinates (-5,6)

(3 - (-5) ) = 8

-1 - 6 = -7

PD = √8^2 + (-7)^2

PD = √(64 + 49)

PD = √113

PD = 10.6

Answer:

A) It takes Brian longer to bike home because his work is farther away.

Step-by-step explanation:

Out of the four statements, A makes the most sense. B and C are implausible based on the given information. D makes no sense seeing that it isn't given that they work in/at the same place, making it something that can't be proven.

Answer:

[tex]\large\boxed{a.\ 23}[/tex]

Step-by-step explanation:

[tex]\dfrac{y-8}{5}=3\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup^1\cdot\dfrac{y-8}{5\!\!\!\!\diagup_1}=5\cdot3\\\\y-8=15\qquad\text{add 8 to both sides}\\\\y-8+8=15+8\\\\y=23[/tex]

Law of cosines.

Cos(angle) = Adjacent Leg / Hypotenuse

Cos(60) = 20 / x

X = 20/cos(60)

x = 40 ft.

Answer:

40

Step-by-step explanation:

You have a 30-60-90 right triangle. The hypotenuse is twice the length of the short leg.

BC = 2 * 20 = 40

Answer:

  see below

Step-by-step explanation:

A regular tessellation involves repeated use of a single regular polygon to cover the plane.

A semiregular tessellation involves repeated use of two or more regular polygons (in the same order around each polygon vertex) to cover the plane.

The first and third diagrams do not involve regular polygons. The fourth involves only a single regular polygon. Hence the second diagram is the one of interest.

The required second diagram is a semiregular tessellation.

Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex.

Regular tessellation uses one regular polygon repeatedly to cover the plane, while semiregular tessellation involves two or more regular polygons used in the same order around each polygon vertex to cover the plane. The second diagram, which involves semiregular tessellation, is of interest. The first and third diagrams do not use regular polygons, and the fourth diagram only uses a single regular polygon.

Thus, the required second diagram is a semiregular tessellation.

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Answer:

[tex]x=140\degree[/tex]

Step-by-step explanation:

The tangents meet the circle at right angles.

The sum of angles in a quadrilateral is 360 degrees

The two given angles will therefore add up to 180 degrees.

This implies that;

[tex]x+40\degree=180\degree[/tex]

We solve for x to obtain:

[tex]x=180\degree-40\degree[/tex]

This simplifies to

[tex]x=140\degree[/tex]

[tex]\therefore x=140\degree[/tex]

Answer:

Step-by-step explanation:

1. There are several ways the area can be divided up so that formulas for common figures can be used to find the areas of the pieces. In the attached figure, we have identified an overall rectangle ABXE and a trapezoid BXDC that is subtracted from it.

The area of the rectangle is the product of length and width:

  area ABXE = (180 cm)(140 cm) = 25,200 cm²

The area of a trapezoid is the product of its height (DX = 70 cm) and the average of its base lengths ((BX +DC)/2 = 95 cm).

  area BXDC = (70 cm)(95 cm) = 6650 cm²

Then the area of figure ABCDE is the difference of these areas:

  area ABCDE = area ABXE - area BXDC = (25,200 - 6,650) cm²

  area ABCDE = 18,550 cm²

__

2. In order to find the area of the figure, we need to know the length DE. That length is one leg of right triangle DEA, so we can use the Pythagorean theorem. That theorem tells us ...

  DE² + EA² = AD²

  DE² + (8 ft)² = (10 ft)² . . . . . substitute the given values

  DE² = 36 ft² . . . . . . . . . . . . .subtract 64 ft²

  DE = 6 ft . . . . . . . . . . . . . . . take the square root

Now, we can choose to add the area of triangle DEA to that of square ABCE, or we can treat the whole figure as a trapezoid with bases AB=8 ft and DC=14 ft. In the latter case, the average base length is ...

  (8 ft + 14 ft)/2 = 11 ft

and the area is the product of this and the 8 ft height:

  area ABCD = (11 ft)(8 ft) = 88 ft²

Answer:

Step-by-step explanation:

Real solutions equal

x=6,3,1

Hope that helps!

ANSWER

[tex]x=1,x=3,x=6[/tex]

EXPLANATION

To solve an equation using the x-intercept method, we must graph the corresponding function and locate x-values of the x-intercepts.

The given polynomial equation is

[tex] {x}^{3} - 10 {x}^{2} + 27x - 18 = 0[/tex]

The graph of the corresponding function

[tex]y = {x}^{3} - 10 {x}^{2} + 27x - 18 [/tex]

Is shown in the attachment.

The x-intercepts are:(1,0), (3,0), (6,0)

Therefore the solutions are,

[tex]x=1,x=3,x=6 [/tex]

Answer:

2) 64°

Step-by-step explanation:

If A and B are complementary, that means that they add up to 90.  Therefore, A + 26 = 90 and A = 64.

Answer:

2.) 64 degrees

Step-by-step explanation: 90-26 = 64

Reminder: Complementary are 90 degrees angle

Supplementary are 180 degrees angle

See the attached picture.

The negative sign in front of the 2 makes the graph an upside down U shape.

We know that the general equation of a parabola in vertex form is given by:

[tex]y=a(x-h)^2+k[/tex]

where the vertex of the parabola is at (h,k)

and if a>0 then the parabola is open upward and if a<0 then the parabola is open downward.

a)

[tex]f(x)=-2(x+3)^2-1[/tex]

Since, the leading coefficient is negative.

Hence, the graph of the function is a parabola which is downward open.

The vertex of the function is at (-3,-1)

b)

[tex]f(x)=-2(x+3)^2+1[/tex]

Again the leading coefficient is negative.

Hence, graph is open downward.

The vertex of the function is at (-3,1)

c)

[tex]f(x)=2(x+3)^2+1[/tex]

The leading coefficient is positive.

Hence, graph is open upward.

The vertex of the function is at (-3,1)

d)

[tex]f(x)=2(x-3)^2+1[/tex]

The leading coefficient is positive.

Hence, graph is open upward.

The vertex of the function is at (3,1)

Answer:

A

Step-by-step explanation:

using formula

area of triangle=1/2 × AB×AC×sinA

WHERE AB=10 andAC=15 and sinA=37○

Answer: the answer is A

Step-by-step explanation:

ANSWER

The vertex of this parabola is (-7,4)

EXPLANATION

The given parabola has equation:

[tex] {y}^{2} - 4x - 8y - 12 = 0[/tex]

[tex] {y}^{2} - 8y = 4x +12[/tex]

Complete the square for the quadratic equation in y.

[tex]{y}^{2} - 8y + {( - 4)}^{2} = 4x + 12 + {( - 4)}^{2} [/tex]

[tex]{y}^{2} - 8y + {( - 4)}^{2} = 4x + 12 + 16[/tex]

[tex]{( y- 4)}^{2} = 4x + 28[/tex]

[tex]{( y- 4)}^{2} = 4(x +7)[/tex]

The vertex of this parabola is (-7,4)

Answer:

(-7, 4)

Step-by-step explanation:

We are given the following equation for which we have to complete the square in order to find the vertex of this parabola:

[tex] y ^ 2 - 4 x - 8 y - 1 2 = 0 [/tex]

[tex]y^2-(\frac{8}{2} )^2-4x-12=(\frac{8}{2} )^2\\[/tex]

[tex] y ^ 2 - 1 6 - 4 x - 1 2 = 1 6 [/tex]

[tex] ( y - 4 ) ^ 2 - 4 x - 1 2-16=0[/tex]

[tex](y-4)^2=4x+28[/tex]

[tex](y-4)^2=4(x+7)[/tex]

[tex]x+7=0, y-4=0[/tex]

x = -7, y = 4

Therefore, the vertex of this parabola is (-7, 4).

Answer:

Step-by-step explanation:

98*x = 101.92

x = 101.92/98 = 1.04

The % increase is 1.04%

Final answer:

The percent increase of the company's rates from $98 to $101.92 is 4%. It is calculated by dividing the increase in rates by the original rate and then multiplying by 100.

Explanation:

To calculate the percent increase for a company's rate change from $98 a month to $101.92 a month, we first find the difference in rates. The increase is $101.92 - $98 = $3.92. To find the percentage, we divide the increase by the original amount and multiply by 100. Therefore, the percent increase is ($3.92/$98)  imes 100.

Calculating this gives us a percent increase of approximately 4%. So, the company's rates have increased by 4 percent. The percentage change, or growth rate, indicates how significantly the rates have increased in comparison to the starting rate.

Answer:

x = 25/4

Step-by-step explanation:

Because of the known similarity of the triangles, we know that

10       x

----- = ----

16      10

Cross-multiplying, we get 16x = 100, and thus x = 100/16 = 50/8 = 25/4

x = 25/4

For the given triangle the value of x is 25/4.

Hence the correct option is E.

The Pythagorean theorem states that,

For a right-angle triangle,

(Hypotenuse)²= (Perpendicular)² + (Base)²

Given that,

In ΔBAC

CB = 16

DB = x

AB = 10

Then CD = 16-x

Apply the Pythagorean theorem in ΔBAC,

Hypotenuse = CB

Perpendicular = AC

Base = AB

(Hypotenuse)²= (Perpendicular)² + (Base)²

(CB)²= (AC)² + (AB)²

(16)²= (AC)² + (10)²

(AC)² = 256 - 100

(AC)² = 156 ......(i)

Apply the Pythagorean theorem in ΔADB,

Hypotenuse = AB

Perpendicular = AD

Base = DB

Therefore,

(AB)²= (AD)² + (DB)²

(10)²= (AD)² + x²

(AD)²= 100 - x²   ......(ii)

Again apply the Pythagorean theorem in ΔADC,

Hypotenuse = AC

Perpendicular = AD

Base = CD

Therefore,

(AC)²= (AD)² + (CD)²

(AC)²= (100 - x²) + (16-x)²                          [ from (ii) ]

(AC)²= 100 - x² + 256 + x² - 32x              [Since (a-b)² = a² + b² -2ab ]

(AC)²= 356 - 32x  ....(iii)

Equating the equation (i) and (iii)

356 - 32x = 156

32x = 200

x = 200/32

x = 25/4

Hence, the value of x is 25/4.

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Answer:

0.18 seconds

Step-by-step explanation:

Using the given function, it is found that the object will be 3 inches above the rest position after 0.18 seconds.

The function for an object's height after t seconds is given by:

[tex]h(t) = 8\sin{\left(\frac{2\pi}{3}t\right)}[/tex]

The height is of 3 inches when h(t) = 3, hence:

[tex]h(t) = 8\sin{\left(\frac{2\pi}{3}t\right)}[/tex]

[tex]3 = 8\sin{\left(\frac{2\pi}{3}t\right)}[/tex]

[tex]\sin{\left(\frac{2\pi}{3}t\right)} = \frac{3}{8}[/tex]

[tex]\sin^{-1}{\sin{\left(\frac{2\pi}{3}t\right)}} = \sin^{-1}{\left(\frac{3}{8}\right)}[/tex]

[tex]\frac{2\pi}{3}t = 0.3844[/tex]

[tex]t = \frac{3 \times 0.3844}{2\pi}[/tex]

[tex]t = 0.18[/tex]

The object will be 3 inches above the rest position after 0.18 seconds.

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The value of x is 11/10.

To solve for x in the equation 5(2x - 1) = 6, we need to follow these steps:

Distribute the 5 into the parenthesis:

5 × 2x - 5 × 1

= 10x - 5

Set up the equation:

10x - 5 = 6

Add 5 to both sides of the equation to get

10x = 11

To solve for x, which gives us

x = 11/10

This question is not complete because his height and age was not indicated in the above question.

Complete Question:

Rick is a healthy 19-year-old college student who is 70 inches tall and weighs 205 pounds. He has decided to "get a six-pack" over the summer with a diet and exercise program. As part of his new plan, he has stopped drinking soda and is eating more salads in addition to his usual diet. Besides of these changes, he is unclear on how to proceed to reach his fitness goal. Rick's mother wants to make sure his approach will not interfere with his normal growth and development, and has asked him to seek reliable information to help him make a reasonable plan.

If Rick wishes to reduce his BMI to 27, he needs to eat fewer kcalories than he expends. For an adolescent who carries excess fat, the recommended maximal weight loss is one pound per week. Since there are 3500 kcalories in a pound of body fat, a deficit of 3500 kcalories for the week or 500 kcalories per day would be required. Calculate the maximum number of kcalories Rick can consume per day to achieve a weight loss of one pound per week. Assume that his weight is 205 pounds and that his physical activity factor is "low active."

Answer:

2696 kilocalories

Step-by-step explanation:

STEP 1

First we need to calculate Rick's Basal Metabolic Rate( BMR)

Weight in pounds = 205 pounds

Age = 19 years

Height in inches = 70 inches

The formula for calculating Basal Metabolic Rate for men =

BMR = 66.47 + ( 6.24 × weight in pounds ) + ( 12.7 × height in inches ) − ( 6.755 × age in years )

BMR = 66.47 + ( 6.24 × 205 ) + ( 12.7 × 70 ) − ( 6.755 × 19)

= 2247

STEP 2:

The next step is to calculate the maximum amount kilocalories per day Rick should consume

Formula is given as :

For a person with physical activity factor of a ' low Active'

Maximum amount of kilocalories to consume per day = Basal Metabolic rate × 1.2

= 2247 × 1.2

= 2696 Kilocalories (kcalories) per day

Answer:

I guess c I just plain out guessed

Answer:

[tex]g(x)= \frac{1}{9} \times x^2[/tex]

Step-by-step explanation:

Here we can see that the parent function is [tex]f(x)=x^2[/tex] and the translated function is g(x). f(x) is a parabola.

Rule says that any factor if multiplied by f(x) is going to contract the graph towards the y axis and vice versa.

Similarly any factor if  f(x) is divided by some factor it is going to be stretch the graph away from the y axis and vice versa.

Here we can see that the translated graph g(x) is stretched away from the y axis with reference to the parent function f(x). Hence as per he rule discussed above, we get a preliminary information that the parent function f(x) is being divided by some factor.

now we are given that

[tex]f(x) = x^2[/tex]

[tex]f(3) = 3^2 = 9[/tex]

Where as

[tex]g(3) = 1[/tex]  {as given in the graph}

Hence

at x=3 , f(x) = 9 and g(x) = 1 , and also we have discussed above that f(x) is divided by some factor. Hence [tex]g(x)= \frac{1}{9}f(x)[/tex]

[tex]g(x)= \frac{1}{9} \times x^2[/tex]

Answer:

x = 13

Step-by-step explanation:

There are two ways to do this. You could use the Pythagorean Theorem because you are given that the triangles are right angled triangles.

Method One

a^2 + b^2 = c^2

a = 5

b = 12

c = ?

c^2 = 5^2 + 12^2

c^2 = 25 + 144

c^2 = 169

sqrt(c^2) = sqrt(169)

c = 13

x = 13

Method Two

You can do this problem with similar triangles.

48/12 = 52/x                    Cross multiply

48x = 12 * 52                   Combine the right  

48x = 624                        Divide by 48

48x/48 = 624/48              Do the division

x = 13  

Answer:

53 miles per hour

Step-by-step explanation:

This is the correct answer

I hope this helps you!