Given: △ABC, m∠A=60°
m∠C=45°, AB = 9
Find: Perimeter of △ABC
Area of △ABC
Please don't use trig

Answer:

175 ft^3

Step-by-step explanation:

The easiest way of thinking about this problem is to divide the shape into two rectangular prisms. Prism 1 has height of 7 ft, width of 3 ft, and depth of 7 ft. Prism 2 has height of 2 ft, width of 2 ft, and depth of 7 ft.

After dividing up the shape, find the volume of each prism:

Prism 1: V = l*w*h = 7*3*7 = 147 ft^3

Prism 2: V = l*w*h = 2*2*7 = 28 ft^3

The total volume is found by adding the volume of the two prisms together:

147+28 = 175 ft^3

The triangle of given dimensions is isosceles and acute triangle.

Triangle is a shape with three sides and hence three angles. We know that triangles are classified according to the sides and angles. Based on angles, the classification of triangle is acute, obtuse and right triangle.

Based on sides, the classification of triangle is equilateral, isosceles and scalene triangle. Now, if the dimensions will form a triangle or not can be estimated through the formula -

side 1 + side 2> side 3

We see that 17 + 17 > 12

34 > 12

Thus, the triangle will form.

Moreover the two sides are equal hence it will be isosceles triangle. Since two sides are equal thus two angles will also be equal.

Now, if we square the sides and find their sum, it will be greater than square of third side. Hence, it is acute triangle.

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Answer:

-8,-7

Step-by-step explanation:

I think

Answer:

try pressing the help button, it looks like it mightve glitched

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

-5/6x = -10/3

x = -10/3 / -5/6

x = 4

Topic: algebraic equations

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Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:

a) t = 4

b) v = pi j + 5 k

c) rt = 1i + (pi t) j + (20 +5t )k

Step-by-step explanation:

You have the following vector equation for the position of a particle:

\(r(t)=cos(\pi t)\hat{i}+sin(\pi t)\hat{j}+5t\hat{k}\)    (1)

(a) The height of the helix is given by the value of the third component of the position vector r, that is, the z-component.

For a height of 20 you have:

\(5t=20\\\\t=\frac{20}{5}=4\)

(b) The velocity of the particle is the derivative, in time, of the vector position:

\(v(t)=\frac{dr(t)}{dt}=-\pi sin(\pi t)\hat{i}+\pi cos(\pi t)\hat{j}+5\hat{k}\)    (2)

and for t=4 (height = 20):

\(v(t=4)=-\pi sin(\pi (4))\hat{i}+\pi cos(\pi (4))\hat{j}+5\hat{k}\\\\v(t=4)=-0\hat{i}+\pi\hat{j}+5\hat{k}\)

(c) The vector parametric equation of the tangent line is given by:

\(r_t(t)=r_o+vt\)      (3)

ro: position of the particle for t=4

\(r_o=cos(\pi (4))\hat{i}+sin(\pi (4))\hat{j}+20\hat{k}\\\\r_o=\hat{i}+0\hat{j}+20\hat{k}\)

Then you replace ro and v in the equation (3):

\(r_t=(1\hat{i}+20\hat{k})+(\pi \hat{j}+5\hat{k})t\\\\r_t=1\hat{i}+\pi t \hat{j}+(20+5t)\hat{k}\)

Part(a): The value of \(t=4\)

Part(b): Required vector \(L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})\)

Given vector equation is,

\(r(t)=cos(\pi t)\widehat{i}+sin(\pi t)\widehat{j}+5t\widehat{j}\)

Vector equation:

A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector, and with an arrow indicating the direction.

Part(a):

When the particle has a height of 20

\(5t=20\\t=4\)

Part(b):

The point on the curve is \((cos(4\pi),sin(4\pi),20) =(1,0,20)\)

Differentiating the given equation with respect to \(t\).

\(r'(t)=- \pi sin(\pi t)\widehat{i}+\pi cos(\pi t)\widehat{j}+5\widehat{k}\\r'(t)=- \pi sin(4\pi t)\widehat{i}+\pi cos(4\pi t)\widehat{j}+5\widehat{k}\\r'(4)=0\widehat{i}+\pi \widehat{j}+5\widehat{k}\\L(t)=r(4)+(t-4)r'(4)\\L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})\)

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Answer:

- 27.88

Step-by-step explanation:

Probability of earthquake = 0.0012

P(earthquake). = 0.0012

P(no earthquake) = 1 - p(earthquake) = 1 - 0.0012 = 0.9988

X ____ 60,000 ______ - 100

P(X) ___ 0.0012 _____ 0.9988

The expected value of the policy :

E(X) = Σx*p(x)

E(X) = (0.0012 * 60000) + (0.9988 * - 100)

E(X) = 72 - 99.88

E(X) = - 27.88

Answer:

4.2 gigabytes

Step-by-step explanation:

$60.60 - $48.00 = $12.60

$12.60 / $3 = 4.2 GBs

Step-by-step explanation:

Dilation :

the scale factor is 3 and the center of dilation is the origin.

A(1,1) => A'(3, 3)

B(3,1) => B'(9, 3)

C(2,3) => C'(6,9)

The transformations A(1,1) → A'(3, 3), B(3,1)→ B'(9, 3), and C(2,3) → C'(6,9) represents a dilation centered at the origin.

On the coordinate plane, you may dilate figures. The origin is frequently utilized as the center of dilatation. If you are distorting a figure centered at the origin, you may find the points in the image by multiplying the coordinates of the points in the preimage by the scale factor.

As per the given question,

We have the scale factor i.e. 3 multiplying the coordinates of the points (x, y) for the center of dilation is the origin.

A(1,1) → A'(3, 3)

B(3,1)→ B'(9, 3)

C(2,3) → C'(6,9)

Thus, the transformations A(1,1) → A'(3, 3), B(3,1)→ B'(9, 3), and C(2,3) → C'(6,9) represents a dilation centered at the origin.

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Answer:

$110.46

Step-by-step explanation:

1 bath towel is $15.78 we need 7. So the equation is 15.78 x 7 = 110.76.

Answer:

5 dollars

Step-by-step explanation:

Let's call the price of a package of pens n, and the cost of a box of paper r.

3n+r=26

2n+7r=49

Multiply the first equation by 7:

21n+7r=182

Subtract the second equation from the first:

19n=133

Divide both sides by 19 to isolate n:

n=7

Plug this back in to find the value of a box of paper:

3(7)+r=26

21+r=26

r=5

Hope this helps!

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{-11})\hspace{10em} \stackrel{slope}{m} ~=~ 4 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-11)}=\stackrel{m}{ 4}(x-\stackrel{x_1}{(-3)}) \implies y +11 = 4 ( x +3) \\\\\\ y+11=4x+12\implies {\Large \begin{array}{llll} y=4x+1 \end{array}}\)

The equation is:

Work/explanation:

Recall that the point slope formula is \(\rm{y-y_1=m(x-x_1)}\),

where m is the slope and (x₁, y₁) is a point on the line.

Plug in the data:

\(\rm{y-(-11)=4(x-(-3)}\)

Simplify.

\(\rm{y+11=4(x+3)}\)

Simplified to slope intercept:

\(\rm{y+11=4x+12}\)

\(\rm{y=4x+1}\) <- this is the simplified slope intercept equation

The incorrect statement is

In mathematics, dilation can be defined as a transformation which alters the size of an object, though its shape remains unchanged. It is described as a specific similarity transformation where all dimensions associated with the given object (i.e. height, width and length) are increased or decreased uniformly by a particular scale factor.

A dilation thus produces an alteration in size, with the figure being either magnified or diminished while keeping its unique shape intact.

The scale factor used in the dilation is 9/7 instead of 7/3.

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Using a system of equations, the rental cost for a movie and a video game is as follows:

A system of equations is two or more equations solved concurrently or at the same time.

A system of equations is also described as simultaneous equations.

                                  Movies   Video     Total

                                                Games    Cost

First month rental           3          5          $32

Second month rental    12          2          $29

Let the rental cost per movie = x

Let the rental cost per video game = y

3x + 5y = 32 ... Equation 1

12x + 2y = 29 ... Equation 2

Multiply Equation 1 by 4:

12x + 20y = 128 ... Equation 3

Subtract Equation 2 from Equation 3:

12x + 20y = 128

-

12x + 2y = 29

18y = 99

y = 5.5

Substitute y = 5.5 in Equation 1 or 2:

12x + 2y = 29

12x + 2(5.5) = 29

12x + 11 = 29

12x = 18

x = 1.5

Thus, based on simultaneous equations, the rental cost for a movie is $1.50 while a video game's is $5.50.

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a) The value of number is, 9.

b) The value of number is, 6.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

a) When you double my number and subtract 9, you get my original number.

b) When you double my number and add 5, you get 17.

For a;

Let a number = x

So, We can formulate;

When you double my number and subtract 9, you get my original number.

⇒ 2x - 9 = x

Solve for x;

⇒ 2x - 9 = x

⇒ 2x - x = 9

⇒ x = 9

For b;

When you double my number and add 5, you get 17.

⇒ 2x + 5 = 17

Solve for x;

⇒ 2x + 5 = 17

⇒ 2x = 17 - 5

⇒ 2x = 12

⇒ x = 6

Thus, We get;

a) The value of number is, 9.

b) The value of number is, 6.

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After answering the presented question, we can conclude that inequality therefore, the solution for z is z < -7.

In mathematics, an inequality is a non-equal connection between two expressions or values. As a result, imbalance leads to inequity. In mathematics, an inequality connects two values that are not equal. Inequality is not the same as equality. When two values are not equal, the not equal symbol is typically used (). Various disparities, no matter how little or huge, are utilised to contrast values. Many simple inequalities can be solved by altering the two sides until just the variables remain. Yet, a lot of factors contribute to inequality: Negative values are divided or added on both sides. Exchange left and right.

\(15 - 3(2 - z) < -12\\15 - 6 + 3z < -12 \\9 + 3z < -12 \\3z < -21 \\z < -7 \\\)

Therefore, the solution for z is z < -7.

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Answer:

yes

Step-by-step explanation:

yes yes you need to do the thing yeah

Answer:

yes

Step-by-step explanation:

a) Imagine you and your friend get a new card with an 18% APR and a $10 minimum payment and use this card to purchase the same mobile phone. If the first friend pays the minimum each month, while the second friend pays $20, what will their balances be after one month?

Answer:

f-'(x) = \(\sqrt[3]{x+2}\)

Step-by-step explanation:

Answer:

jaylon makes 2x an hour.

Step-by-step explanation:

Answer:

1. 5/42

2. 9/20

Step-by-step explanation:

(hope this helps!)

Answer:

the answer is 2

Step-by-step explanation:

2

When r is less than 5 and we substitute r = 4 into the expression [3r-15], the result is -3.

The expression [3r-15] represents an algebraic expression that depends on the value of r. The condition given is that r is less than 5. To evaluate this expression, we substitute the value of r into the expression and simplify it.

Given that r is less than 5, let's substitute r = 4 into the expression:

[3(4) - 15]

= [12 - 15]

= -3

Therefore, when r is less than 5 and we substitute r = 4 into the expression [3r-15], the result is -3.

It's important to note that this answer is specific to the given condition that r is less than 5. If the condition changes or if r is greater than or equal to 5, the result of the expression may be different.

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The value of a quantity after reducing it to some percentage can be found by taking the difference of the old value and the percent of the old value. The original price is $226.27.

A percentage is a value that indicates 100th part of any quantity.

To convert percentage into a fraction it is divided by 100.

Given that,

The percentage of decrease in price = 81%

The new price is $24.89.

Since the new price is obtained by substracting the decrease percentage from the original price. The expression for the original price is given as,

Suppose the original price be P.

P - 81% of P = 24.89

=> P - (89 / 100) × P = 24.89

=> (11 / 100) × P  = 24.89

=> P = 226.27

Hence, the original price is given as $ 226.27.

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Answer:

The midpoint between the joining points C and D is (2, -3)

Step-by-step explanation:

How to find a midpoint

Suppose we have a line segment and want to cut that section into two equal parts. To do so, we need to know the center. We can achieve this by finding the midpoint. You could measure with a ruler or just use a formula involving the coordinates of each endpoint of the segment. The midpoint is simply the average of each coordinate of the section, forming a new coordinate point. We shall illustrate this below.

Midpoint formula

If we have coordinates (x₁,y₁) and (x₂,y₂), then the midpoint of these coordinates is determined by (x₁ + x₂)/2, (y₁ + y₂)/2. This forms a new coordinate you can call (x₃,y₃).  It is possible to divide a line segment into any given ratio, not just 1:1.

Answer:

outside the circle

sorry if I'm wrong

The number of years it would it take for there to be one person for every square yard is 108,325.68 years.

When there is one person for every square yard, it means that the population and land area are equal in value.

Number of years = (In FV / PV) / r

(In 19 billion / 4,079,000) / 0.043 = 108,325.68 years

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Answer:

a) Median amount of time that is spent is around 2.3, rounded to 2.

b) 4 unit time

c) Mean amount of time is bigger than the median.

Step-by-step explanation:

Find the given attachment.

Note: Complete Question, along with the diagram is added

The axis of symmetry is x = -1 and the vertex is (-1, -2).

A parabola is a U-shaped curve that can be formed by graphing a quadratic function. It is a type of conic section, which is a curve formed by intersecting a plane with a cone at a certain angle.

To graph the function F(x) = x² + 2x - 1, we can first find the vertex and axis of symmetry using the formula:

x = -b/2a

where a and b are the coefficients of the x² and x terms, respectively. In this case, a = 1 and b = 2, so:

x = -2/(2*1) = -1

So the axis of symmetry is x = -1. To find the vertex, we can substitute this value of x into the function to get:

F(-1) = (-1)² + 2(-1) - 1 = -2

So the vertex is (-1, -2).

To graph the function, we can plot the vertex and then use symmetry to plot points on either side of the axis. We can also note that since a = 1 is positive, the parabola opens upward.

A rough sketch of the graph is shown.

The x-axis represents the axis of symmetry, and the y-axis represents the values of the function F(x). The vertex (-1, -2) is marked with an "x", and other points on the graph are marked with "x" to show the general shape of the parabola.

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