What is the area of triangle ABC? Round your final answer to the nearest cm.

The area of the cross section that is parallel to side PQRS in this rectangular box is: A. 12 square units.

In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:

A = LW

Where:

A represent the area of a rectangle.

W represent the width of a rectangle.

L represent the length of a rectangle.

By substituting the given side lengths into the formula for the area of a rectangle (PQRS), we have the following;

Area of rectangle = PQ × QR

Area of rectangle = 4 × 3

Area of rectangle = 12 square units.

Complete Question:

What is the area of the cross section that is parallel to side PQRS in this rectangular box?

A. 12 square units

B. 16 square units C. 30 square units D. 40 square units

The volume of the rectangular box is 60 cubic units.

Given that the area of one side of the box is 12 and the area of another side is 15, and both dimensions are integers greater than 1, we can find the dimensions and the volume of the box as follows:

Possible dimensions:

For the side with area 12, the possible integer dimensions are (3, 4) and (4, 3) since 3 x 4 = 4 x 3 = 12.

For the side with area 15, the possible integer dimensions are (3, 5) and (5, 3) since 3 x 5 = 5 x 3 = 15.

Valid dimensions combination:

We need to find a combination of dimensions where the two sides mentioned above are not the same.

The only valid combination is (3, 4) for the side with area 12 and (5, 3) for the side with area 15.

Volume of the box:

The volume of the box is calculated by multiplying the length, width, and height.

In this case, the volume is 3 (length) x 4 (width) x 5 (height) = 60 cubic units.

Therefore, the volume of the rectangular box is 60 cubic units.

Question

The dimensions of a rectangular box are integers greater than 1. If the area of one side of this box is 12 and the area of another side 15, what is the volume of the box?

Answer:

[tex]P(A^c)=\frac{3}{7}[/tex]

Step-by-step explanation:

We have been given a table containing a list of few places that are either city or in North America.

Total number of places in that list = 7

That means sample space has 7 possible events.

Given that a place from this table is chosen at random. Let event A = The place is a city.

Now we need to find about what is [tex]P(A^c)[/tex].

That means find find the probability that chosen place is not a city.

there are 3 places in the list which are not city.

Hence favorable number of events = 3

Then required probability is given by favorable/total events.

[tex]P(A^c)=\frac{3}{7}[/tex]

Answer:

the answer is 3/7

Step-by-step explanation:

Answer: 35,190

Step-by-step explanation: If you multiply these together your product will be 35,190

Answer:

See below.

Step-by-step explanation:

Neither are correct:  a parallelogram with 3 congruent sides could be a square. Also a parallelogram will  have 2 pairs of congruent sides  but it does not have to be a rhombus.

Answer with explanation:

A rhombus has all sides equal that is four congruent sides.

Statement of Claire

 If she draws a parallelogram with 2 congruent sides, it must be a rhombus.

As Rhombus has four Congruent sides.2 Congruent sides does not Guarantee that the Parallelogram will be Rhombus.If Adjacent sides are congruent than Claire statement will be right otherwise not.

Statement of Jacob

If Jacob draws a parallelogram with at least 3 congruent sides ,it must be a rhombus.

Yes ,three congruent sides Guarantees that Parallelogram will be a rhombus because in a Parallelogram opposite sides are equal to each other.So congruency of three sides in a Parallelogram guarantees that this Parallelogram will be a rhombus.

So, we can Conclude that Jacob is correct.

Answer:

E. Investigating how the amount of annual precipitation affects the distribution of a tree species.

Step-by-step explanation:

Abiotic factors are factors in an ecosystem that are non-living. Abiotic factors include water, soil, temperature, light, and air. Among all the choices, only choice E considers an abiotic factor, which is precipitation.

Precipitation is water, and as mentioned earlier, water is an abiotic factor. The case here is the study of the annual precipitation and effects on distribution of species. The study is specific to the precipitation.

The other choices involve biotic factors, like food source, the organisms and the like.

A.Conjunction

Step-by-step explanation:

Answer:

37%

Step-by-step explanation:

35% of 55% is equal to the percent of boys on honor roll in the student body.

100 - 55 = 45%, which is the percent of girls in the student body.

40% of 45% is equal to the percent of girls on honor roll in the student body.

35% * 55% = 19.25%

40% * 45% = 18%

Adding them up, we get:

19.25 + 18 = 37.25%

Round it to the nearest percent.

37.25 --> 37%

Rounded to the nearest percent, 37% of the student body is on honor roll.

first use the formula it is 1/3 × base area × height =volume of pyramid

so we just need to replace some of the information given in the statement to our formula

so it's going to be,i'll let the height as unknown X

128=1/3 × (8 × 8) × X

so it's going to be

128=64/3X

so X is 128 ÷ 64/3=6cm

Answer:

I'm Sure the answer is 6 cm.

ANSWER

A. 168 units^3

EXPLANATION

The volume of a pyramid is given by the formula:

[tex]Volume= base \: area \: \times \: vertical \: height[/tex]

Area of triangular base

[tex] = \frac{1}{2} bh[/tex]

[tex] = \frac{1}{2} \times 8 \times 6[/tex]

[tex] = 24 \: {units}^{2} [/tex]

The height of the prism is 7 units.

The volume

[tex] = 24 \times 7[/tex]

[tex] = 168 {units}^{3} [/tex]

Answer:

168

Step-by-step explanation:

Answer:

15-6+7=16. The expression should be written as 15-(6+7).

Step-by-step explanation:

The sum of 6 and 7 is (6+7). 15 minus the sum of 6 and 7 would then be written as 15-(6+7), because this way you subtract the entire sum from 15. The expression 15-6+7 just subtracts 6 from 15, then adds 7 onto this number, which is not the same thing as subtracting 6+7 from 15.

The expression 15 - 6 + 7 does not represent '15 minus the sum of 6 and 7'. The correct expression should be 15 - (6 + 7). Evaluating Harper's expression gives 16, while the correct expression gives 2.

The expression 15 - 6 + 7 does not properly relay the concept of '15 minus the sum of 6 and 7'. To correctly express this idea, parentheses should be used: 15 - (6 + 7).

To evaluate Harper's expression, one would operate in the order of their entry: 15 - 6 is 9, then, add 7 to 9 and the result is 16.

However, in the correct expression 15 - (6 + 7), the sum of 6 and 7 equals 13 is computed first, according to the order of operations (PEMDAS/BODMAS). Then, subtract this sum from 15 to get 2.

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[tex]\bf \cfrac{1}{2}\div 3\implies \cfrac{1}{2}\div \cfrac{3}{1}\implies \cfrac{1}{2}\cdot \cfrac{1}{3}\implies \cfrac{1}{6}[/tex]

3 friends equally shared 1/2 pound of trail mix, during the hike.

Total quantity of trail mix = 1/2 pound

Quantity shared by each friend is 1/3 rd of the trial mix

= 1/3 * 1/2 pound

= 1/6 pound

Therefore, during the hike, each friend shared 1/6 pound of the trail mix.

Hope this helps ..!!

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Answer:

0.66

Step-by-step explanation:

24.95 x 25%=6.23

24.94 - 6.23 = 18.72

25.80 x 30% = 7.74

25.80 - 7.74 = 18.06

18.72 -18 .06 = 0.66

For this case we have:

Store 1:

We propose the following rule of three:

24.95 -----------> 100%

x -------------------> 25%

Where the variable x represents the discount amount:

[tex]x = \frac {25 * 24.95} {100}\\x = 6.2375[/tex]

Thus, the price of the ball is:

[tex]24.95-6.2375 = 18.7125[/tex]

Store 2:

We propose the following rule of three:

25.80 -----------> 100%

x -------------------> 30%

Where the variable x represents the discount amount:

[tex]x = \frac {30 * 25.80} {100}\\x = 7.74[/tex]

Thus, the price of the ball is:

25.80-7.74 = 18.06

Thus, the price difference is:

[tex]18.7125-18.06 = 0.6525[/tex]

ANswer:

0.6525

Answer: 82

Simply pug in 6 for [tex]x[/tex]

[tex]2(6)^2+5\sqrt{(6-2)} \\72+5\sqrt{4} \\72+5(2)\\72+10=\\82[/tex]

Hope this helps and have a great day!!!

[tex]Sofia[/tex]

For this case we have a function of the form [tex]y = f (x).[/tex]

Where:[tex]f (x) = 2x ^ 2 + 5 \sqrt {x-2}[/tex]

We must find the value of the function when x = 6, that is, f (6):

Then, replacing the value of "x"[tex]f (6) = 2 (6) ^ 2 + 5 \sqrt {6-2}\\f (6) = 2 * 36 + 5 \sqrt {4}\\f (6) = 72 + 5 (2)\\f (6) = 72 + 10\\f (6) = 82[/tex]

So, [tex]f (6) = 82[/tex]

ANswer:

[tex]f (6) = 82[/tex]

Answer:

47184

Step-by-step explanation:

1+0=1

7*1=7

7+1=8

4*2=8

Answer:

c because is right

Step-by-step explanation:

Answer:

-3.8, 3

Step-by-step explanation:

The solution to a system is where the graph cross each other.  If you look to where they intersect to the left of the origin, where x is negative, it appears that they intersect ALMOST at -4, but not quite.  So -3.8 is going to have to do since we don't have the equations of either graph to find the exact values of x.  To the right of the origin, where x is positive, the graphs cross where x = 3..

Answer:

  x = −3.8, 3

Step-by-step explanation:

The solutions to f(x) = g(x) are the x-coordinates of the points of intersection of their graphs. Those x-values appear to be about -3.8 and +3.

Answer:

14.2

Step-by-step explanation:

For this case, we have to define trigonometric relations in a rectangle triangle that, the tangent of an angle is given by the leg opposite the angle on the leg adayed to it. According to the figure we have:[tex]tg (35) = \frac {c} {5}\\c = tg (35) * 5\\c = 0.70020754 * 5[/tex]

[tex]c = 3.5010377[/tex]

Answer:

Option D

1.50c +4A =2200$ would be the correct awnser

Answer:

2x + 11 = 20

Step-by-step explanation:

let's start by assigning the variable x to certain number , if we two times a certain number we got 2x, and if we added to 11 the result is 20. So, ordering the equation we will obtain:

2x + 11 = 20

ANSWER

2x+11=20

EXPLANATION

Let the number be x.

Two times this number is 2x

If 11 is added to two times the number, the expression becomes;

2x+11

If the result is 20, then we equate the expression to 20 to get:

2x+11=20

The correct choice is the last option;

I'll assume you're supposed to compute the line integral of [tex]\nabla f[/tex] over the given path [tex]C[/tex]. By the fundamental theorem of calculus,

[tex]\displaystyle\int_C\nabla f(x,y)\cdot\mathrm d\vec r=f(4,48)-f(1,3)[/tex]

so evaluating the integral is as simple as evaluting [tex]f[/tex] at the endpoints of [tex]C[/tex]. But first we need to determine [tex]f[/tex] given its gradient.

We have

[tex]\dfrac{\partial f}{\partial x}=3y\sin(xy)\implies f(x,y)=-3\cos(xy)+g(y)[/tex]

Differentiating with respect to [tex]y[/tex] gives

[tex]\dfrac{\partial f}{\partial y}=3x\sin(xy)=3x\sin(xy)+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=0\implies g(y)=C[/tex]

and we end up with

[tex]f(x,y)=-3\cos(xy)+C[/tex]

for some constant [tex]C[/tex]. Then the value of the line integral is [tex]-3\cos192+3\cos3[/tex].

This question involves vector calculus and requires finding the line integral along a segment of a parabola.

The given question is related to the subject of Mathematics. It involves the application of vector calculus and requires analyzing a segment of the parabola using vector analysis and gradient fields.

To find the ∫f vector, we need to evaluate the partial derivatives of f(x, y) and multiply them with the corresponding unit vectors. Plugging in the given values, we find that ∫f = 3y·sin(xy)·ᵢ + 3x·sin(xy)·ᵢ.

Learn more about Vector calculus here:

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Answer:

$135

Step-by-step explanation:

step 1

Let

x----> amount of money shared by Danny

y----> amount of money shared by Amira

z----> amount of money shared by Tyler

we know that

x/y=6/4 ----> x=1.5y ----> equation A

x/z=6/3 ---> z=x/2 ---> equation B

Amira used 1/2 of her money to buy a watch that costs $30

so

(1/2)y=$30

y=$60

Substitute the value of y in the equation A and solve for x

x=1.5y ----> x=1.5(60)=$90

Substitute the value of x in the equation B and solve for z

z=x/2 -----> z=90/2=$45

so

The amount of money shared by Danny was $90

The amount of money shared by Amira was $60

The amount of money shared by Tyler was $45

step 2

Find out how much money they have left in total.

Danny gave 1/3 of his money to his sister ----> left --> (2/3)($90)=$60

Amira used 1/2 of her money -----> left --> $60/2=$30

Tyler --------> left ----> $45

Total=$60+$30+$45=$135

Total left = Danny + Amira + Tyler = $60 + $30 + $45 = $135.

The question deals with dividing a sum of money among Danny, Amira, and Tyler by the ratio 6 : 4 : 3, calculating how much Amira spent, and how much Danny gave away.

Let's assume the total sum of money is M, shared according to the ratio 6x : 4x : 3x, which means:

Since Amira spent 1/2 of her money on a watch costing $30, we can deduce:

Therefore, the total sum of money M is 6x + 4x + 3x = 13x, which gives us:

Danny gave away 1/3 of his share to his sister, which is:

After spending and giving money away, they have left:

Total left = Danny + Amira + Tyler = $60 + $30 + $45 = $135.

Answer:

A. 110

Step-by-step explanation:

Angles 4 and 6 are supplementary so if we add them together they will equal 180.

(5a + 10)° + (3a + 10)° = 180°

Simplify a bit to get 8a + 20 = 180

and 8a = 160.

a = 20.  Now sub that value of a into the expression for angle 4:

5a + 10 --> 5(20) + 10 = 110°

Answer:

Option A.

Step-by-step explanation:

Given information: m║n, [tex]m\angle 4=(5a+10)^{\circ}[/tex] and  [tex]m\angle 6=(3a+10)^{\circ}[/tex].

If a transversal line intersect two parallel lines, then the interior angles on the same sides are supplementary angles. It means their sum is 180.

From the given figure it is clear that angle 4 angle 6 are interior angles on the same side. So, angle 4 and 6 are supplementary angles.

[tex]m\angle 4+m\angle 6=180^{\circ}[/tex]

[tex](5a+10)+(3a+10)=180[/tex]

On combining like terms we get

[tex](5a+3a)+(10+10)=180[/tex]

[tex]8a+20=180[/tex]

Subtract 20 from both sides.

[tex]8a+20-20=180-20[/tex]

[tex]8a=160[/tex]

Divide both sides by 8.

[tex]a=20[/tex]

The value of a is 20.

[tex]m\angle 4=(5a+10)^{\circ}\Rightarrow 5(20)+10)^{\circ}=110^{\circ}[/tex]

Therefore, the correct option is A.

Answer:

The correct answer option is true.

Step-by-step explanation:

We are given the following statement and we are to tell if its true or not:

'The scale of quantities should always start at zero'.

To get the correct and accurate measure of any quantity, the scale of that very quantity should always start from zero.

If it does not start from zero, there can be errors in the measure. Therefore, the given statement is true.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}6x+3y=-21&\text{divide both sides by (-3)}\\2x+5y=5\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-2x-y=7\\2x+5y=5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad4y=12\qquad\text{divide both sides by 4}\\.\qquad\qquad y=3\\\\\text{Put it to the second equation:}\\2x+5(3)=5\\2x+15=5\qquad\text{subtract 15 from both sides}\\2x=-10\qquad\text{divide both sides by 2}\\x=-5[/tex]

a. Parameterize [tex]C[/tex] by

[tex]\vec r(t)=(1-t)(5\,\vec\imath)+t(2\,\vec\jmath)=(5-5t)\,\vec\imath+2t\,\vec\jmath[/tex]

with [tex]0\le t\le1[/tex].

b/c. The line integral of [tex]\vec F(x,y)=-y\,\vec\imath+x\,\vec\jmath[/tex] over [tex]C[/tex] is

[tex]\displaystyle\int_C\vec F(x,y)\cdot\mathrm d\vec r=\int_0^1\vec F(x(t),y(t))\cdot\frac{\mathrm d\vec r(t)}{\mathrm dt}\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^1(-2t\,\vec\imath+(5-5t)\,\vec\jmath)\cdot(-5\,\vec\imath+2\,\vec\jmath)\,\mathrm dt[/tex]

[tex]=\displaystyle\int_0^1(10t+(10-10t))\,\mathrm dt[/tex]

[tex]=\displaystyle10\int_0^1\mathrm dt=\boxed{10}[/tex]

d. Notice that we can write the line integral as

[tex]\displaystyle\int_C\vecF\cdot\mathrm d\vec r=\int_C(-y\,\mathrm dx+x\,\mathrm dy)[/tex]

By Green's theorem, the line integral is equivalent to

[tex]\displaystyle\iint_D\left(\frac{\partial x}{\partial x}-\frac{\partial(-y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy=2\iint_D\mathrm dx\,\mathrm dy[/tex]

where [tex]D[/tex] is the triangle bounded by [tex]C[/tex], and this integral is simply twice the area of [tex]D[/tex]. [tex]D[/tex] is a right triangle with legs 2 and 5, so its area is 5 and the integral's value is 10.

A vector parametric equation was computed for the line segment between the points P and Q. This was used to compute the line integral of the vector field along the segment, which was found by substituting the parametrization into the field, deriving it and computing the dot product and integral. The clockwise integral around the triangle was then computed as the negative of the one we obtained earlier.

To solve this, consider the given points as vectors, i.e., ℒ = <5,0> and № = <0,2>. First, let's find a vector parametric equation ℝ(τ) for the line segment cc. To do this, we're going to create a vector equation that shows the progression from point ℒ to № with 0 ≤ τ ≤ 1.

Since t changes from 0 to 1, an equation for that movement is ℝ(τ) = (1-τ) * ℒ + τ * №. With insertions, the equation converts to ℝ(τ) = (1-τ) * <5,0> + τ<0,2> = <5-5t,2t>.

For the line integral Along C, our F(x, y) = -yi + xj, when we substitute our ℝ(τ) into this equation, our F becomes F(ℝ) = -2ti + (5-5t)j.

Derivation of ℝ(τ) will give us the rate of change of our function and help in the computation of the line integral. So, ℝ'(τ) = -5i + 2j. The integrand function for line integral then becomes F(ℝ) . ℝ'(τ) = -10t + 10t - 10t2. So our line integral ∫F .  dℝ from 0 to 1 will be ∫ (-10t + 10t - 10t2) dt.

For the clockwise integral around the triangle, since our original line integral was done in a counterclockwise direction, it will simply be the negative of the one we just computed.

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if you don't have a Unit Circle, this is a good time to get one, you can find many online.

Check the picture below.

Answer:

B . √3/3.

Step-by-step explanation:

Tan theta = opposite side/ adjacent

= 1/2 / √3/2

= 1/2  * 2/√3

= 1 /√3

= √3/3.

Answer:

x      f(x)=1.5^x     Function(x,f(x))     Inverse(f(x), x)    

0      (1.5)^0=1            (0, 1)                      (1, 0)

1             b                     a                           c

-1            l                      e                           g

2            f                      h                            i

4            o                     k                           d

.

Answer:

Functions and x abcd

Step-by-step explanation:

It looks like you're given

[tex]g(x)=\displaystyle\int_{6x}^{7x}\frac{u^2-1}{u^2+1}\,\mathrm du[/tex]

Then by the additivity of definite integrals this is the same as

[tex]g(x)=\displaystyle\int_0^{7x}\frac{u^2-1}{u^2+1}\,\mathrm du-\int_0^{6x}\frac{u^2-1}{u^2+1}\,\mathrm du[/tex]

(presumably this is what the hint suggests to use)

Then by the fundamental theorem of calculus, we have

[tex]\dfrac{\mathrm dg}{\mathrm dx}=7\dfrac{(7x)^2-1}{(7x)^2+1}-6\dfrac{(6x)^2-1}{(6x)^2+1}=\dfrac{1764x^4+169x^2-1}{1764x^4+85x^2+1}[/tex]

The Fundamental Theorem of Calculus Part 1 states the relationship between differentiation and integration. For a given function, transform the integral as hinted in the question, then use the theorem to differentiate the function by simply replacing the variable of integration with the upper limit of the integral.

The Fundamental Theorem of Calculus Part 1 is primarily used to identify the relationship between differentiation and integration, which are two basic operations in calculus. For a given function g(x) = ∫7x u² − 1 u² + 1 du from a to x, we first identify the function inside the integral, let's say f(u) = 7x u² − 1 u² + 1. Now, the mentioned integral transformation hints us that: 7x ∫f(u) du from 6x to 0 equals ∫f(u) du from 6x to 0 + ∫7x f(u) du from 0 to 6x.

Next, we simply differentiate g(x) using Part 1 of the Fundamental Theorem of Calculus, which states that if g(x) is the integral from a to x of f(t) dt, then the derivative of g(x) is f(x). So, by applying this, the derivative function g'(x) of given g(x) will be f(x), i.e., 7x x² − 1 x² + 1.

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Answer:

C.5

Step-by-step explanation:

y = (x - 3)^2

This is in the form y= a(x-h)^2 +k  where (h,k) is the vertex

The vertex is at (3,0)

y = x^2 - 4

This is in the form y= a(x-h)^2 +k  where (h,k) is the vertex

The vertex is at (0,-4)

The distance between the points is found by

d = sqrt( (x2-x1)^2 + (y2-y2)^2)

  = sqrt(( 0-3)^2 + (-4-0)^2)

  = sqrt( 9 + 16)

  = sqrt(25)

   = 5

Answer:

B. 1/2 tespoon of salt per 1 teaspoon of baking soda.

Step-by-step explanation:

If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.

Answer:

B. 1/2 tespoon of salt per 1 teaspoon of baking soda.

Step-by-step explanation:

If you're starting with 1/2 tsp of baking soda and 1/4 tsp of salt, you can multiply that by two and still have the same ratio of salt to baking soda.