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Answer:

28cm²

Step-by-step explanation:

The area of a triangle is given as:

= 1/2 × b × h

= 1/2 × 7 × 8

= 28cm²

The value of the height of the prism is 8.68 inches

The surface area is the sum of the area of the faces.

The formula for calculating the surface area of the pyramid is;

TSA  = [tex]a^2+2a\sqrt{\frac{a^2}{4} + h^2}[/tex]

where

a is the side length. = 7in

h is the height

Substitute

[tex]189=7^2+2(7)\sqrt{\frac{7^2}{2} + h^2} \\189=49+14\sqrt{\frac{49}{2} + h^2}\\140=14\sqrt{\frac{49}{2} + h^2}\\10=\sqrt{\frac{49}{2} + h^2}\\[/tex]

Square both sides to have

100 = 49/2 + h²

h² = 100 - 49/2

h² = 151/2

h² = 75.5

h = 8.68in

Hence the value of the height of the prism is 8.68 inches

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Answer:

See below ~

Step-by-step explanation:

Sides of a rhombus are equal.

⇒ QT = TS

⇒ x² - 4x - 10 = 6x + 14

⇒ x² - 10x - 24 = 0

⇒ x² + 2x - 12x - 24 = 0

⇒ x (x + 2) - 12 (x + 2) = 0

⇒ (x + 2)(x - 12) = 0

⇒ x = -2 or x = 12

Substitute both values and see which gives a positive value for QT :

When x = -2 :

When x = 12 :

The 2 possible answers are :

An expression is defined as a set of numbers, variables, and mathematical operations. The solution of (4 x 3)² ÷ 6 is 24.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The solution of the expression (4 x 3)² ÷ 6 is,

(4 x 3)² ÷ 6

= (12)² ÷ 6

= 144 ÷ 6

= 24

Hence, the solution of (4 x 3)² ÷ 6 is 24.

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Answer:  [tex]\textsf{Option B, 81}\pi\textsf{ in}^2[/tex]

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Given: [tex]\textsf{Circumference = 18}\pi[/tex]

Find:  [tex]\textsf{The area of the circle}[/tex]

Solution:  We need to first determine the radius using the circumference formula and once we get the radius then we can plug in the value into the area formula and get our final answer.

Determine the radius

Determine the area

Therefore, the correct answer would be option B, 81π in2.

[tex](6^-^8)^4[/tex]

[tex]=6^-^2^4[/tex]

[tex]=\frac{1}{6^2^4}[/tex]

The function has a local minima at  ( 20 , -7 )

Function is a mathematical statement formed when two algebraic expression are equated by an equal sign.

The expression given is

y = -2 +5sin ( (π/12) (x-2))

the minima of the given expression will be when

the sine term = -1

as the lowest value sin can have is -1

y = -2 +5 * (-1)

y = -7

The sin ( (π/12) (x-2)) = -1

(π/12) (x-2) = 3π /2

On solving this

x = 20

Therefore the function has a local minima at  ( 20 , -7 )

It can also be confirmed form the graph attached with the answer.

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The f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2) , Option D is the right answer.

A function is a law that defines relation between two variables.

The function given in the question is

f(x) = 8x² +2

h(x) = -8x²-2

The graph is plotted and the similarities or differences are studied ,

It can be seen from the graph that

f(x) opens upward with a y-intercept at (0, 2); h(x) opens downward with a y-intercept at (0, -2).

Therefore Option D is the right answer.

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Answer:

(-2, -4)

Step-by-step explanation:

Use the (x,y) thing:

x = -2

y = -4

therefore, (-2, -4)

The process of Graphing a exponential decay function is shown in detail below.

There are two types of exponential equations: exponential decay and exponential growth. The fundamental shape of an exponential function and its corresponding graphs must be understood in order to fully comprehend the distinctions between exponential growth and decay. The fundamental distinction between the two is that in an exponential decay connection, the output values rise quickly as the input value rises, but in an exponential growth relationship, the output rises noticeably faster as the input value rises. Furthermore, neither of the two functions is linear, hence their rate of change is not constant. What distinguishes one equation from the other when they both have the same precise form, y = abx?

The value of the constant "b" is the fundamental factor in deciding whether the exponential function is one of growth or decay:

In this way we can graph a exponential decay function

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Probability helps us to know the chances of an event occurring. The probability of pulling a green or red card is 9 / 100.

Probability helps us to know the chances of an event occurring.

P =  [tex]\dfrac{Desired \ outcomes}{Posiible \ outcomes}[/tex]

The probabilities of different color cards being pulled are 1/25 for red, 1/20 for green, 1/15 for purple, and 1/10 for black Therefore, the probability of pulling  a green or red card is,

Probability = 1/20 + 1/25

                 = (5 + 4) /100

                 = 9 / 100

Hence, the probability of pulling a green or red card is  9 / 100.

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Answer:

z^0= 1

(2v+2)^0 = 1

3^0 = 1

0^0= 0

Step-by-step explanation:

When you raise (almost) anything to the power zero, you get 1 and when you raise 0 to any number except 0 is 0

The equation of the line that passes through the given points is            y= -4x+23.

A line can be represented by a linear function. The standard form for the linear equation is: ax+b , for example, y=2x+7. Where:

a= the slope

b=constant term that represents the y-intercept.

From the stardard form equation:

Solving the system for equations 1 and 2.

3=5a+b

-13=9a+b * (-1)

3=5a+b

13=-9a-b * (-1)

16= -4a

4= -a

a= -4

If a= -4 from equation 1, you have

3= 5 * (-4)+b

3= -20+b

b=23

Therefore, the line equation is y= -4x+23.

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Answer:

740

Step-by-step explanation:

$415-$230=$185

$185×0.25=740 max miles

Answer:

B: 2005

Step-by-step explanation:

Worked on edge 2022

My theorems include the Pythagoras theorem, midpoint theorem, and angle bisector theorem.

The Pythagoras theorem is used to find the length in a right angle.

The midpoint theorem states that the line segment in a triangle is parallel to the third side and is half the length.

The angle bisector theorem is concerned with the lengths of the two segments that the triangle side is divided into by a line which bisects the opposite angle.

I like them because they're important when solving triangle related problems.

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The product of variables in inverse proportion is constant, so the equation is [tex]\boxed{xy=-3}[/tex]

Answer:

∠A ≅ ∠D

Step-by-step explanation:

When writing a triangle congruency like ΔABC ≅ ΔDEF, the angles are congurent based on the orders listed. For example the first angle A is congruent with the first angle of the other triangle D.  

∠A ≅ ∠D

∠B ≅ ∠E

∠C ≅ ∠F

Thus, for drawing the graph for y = 3/4x + 7.

For drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.

All the points (and only those points) which lie on the graph of the function satisfy its equation.

Thus, if a point lies on the graph of a function, then it must also satisfy the function.

For this case, the equation given to us is:

y=3/4x+7

Any equation of the form y=mx+c where m and c are constants and x and y are variables is the equation of a straight line.

For a straight line to be characterized, only two points are sufficient.

For x = 0, the y-coordinate would be such that it would satisfy the equation

y=3/4x+7

Putting x = 0, we get:

y=3/4(0)+7

y=7

Thus, the y-coordinate of the point on this line whose x-coordinate is 0 is 7. Thus, (0,7) is one of the point coordinates on the considered line.

Putting x = 3, we get:

y=3/4(3)+7

y=9.25

Thus, the y-coordinate of the point on this line whose x-coordinate is 0 is 9.25. Thus, (0,9.25) is another of the point's coordinates on the considered line.

Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of __7_, a second point by going over 3 and up __8.25__, and then draw a line through the points.

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Answer:

It's +2

Step-by-step explanation:

As the positive occurs on the right side of the negatives in the number line so if we keep extending on the right side so we get +2

Answer:

yes

Step-by-step explanation:

the FIRST derivative of a function tells us the slope of a tangent line to the curve at any point. if is positive, then the curve must be increasing. If is negative, then the curve must be decreasing.

the SECOND derivative gives us the slope of the slope function (in other words how fast the slope of the original function changes, and if it is accelerating up - positive - or if it is avengers down - negative).

so, the first derivative would be fully sufficient to get the answer of if the slope of the function at that point is positive or negative.

but because it is only a "if" condition and not a "if and only if" condition, the statement is still true.

there are enough cases, where the slope is positive, but the second derivative is not > 0 (usually = 0).

but if even the second derivative is positive, then, yes, the slope of the original function must be positive too.

Using a trigonometric identity, it is found that the equivalent expression is given by 1.

Relating sine and cosine, we have that:

[tex]\sin^{2}{\beta} + \cos^{2}{\beta} = 1[/tex]

Then:

[tex]\cos^{2}{\beta} = 1 - \sin^{2}{\beta}[/tex]

For the tangent, we have that:

[tex]\tan{\beta} = \frac{\sin{\beta}}{\cos{\beta}}[/tex].

For the secant, we have that:

[tex]\sec{\beta} = \frac{1}{\cos{\beta}}[/tex].

In this problem, the expression is:

[tex]\frac{(1 - \sin{\beta})(1 + \sin{\beta})}{\cos^{2}{\beta}} = \frac{1 - \sin^2{\beta}}{\cos^2{\beta}} = \frac{\cos^2{\beta}}{\cos^2{\beta}} = 1[/tex]

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The confidence interval estimates that the confidence interval limits contain 0., suggesting that the garlic treatment did not affect the LDL cholesterol levels.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. The 95 percent confidence level is the most common, but other levels, like 90 percent or 99 percent, are occasionally used when computing a confidence interval.

Given in a test of effectiveness of garlic for lowering cholesterol, 50 subjects were treated with garlic in a processed tablet form.Both before and after the therapy, cholesterol levels were assessed.

LDL cholesterol variations had a mean of 4.4 and a standard deviation of 19.4 (in mg/dL). The best point estimate is 4.4.

We have to find 95% confidence interval estimate of the population mean

So,

x-bar = 4.4

ME = 1.96 = 5.27

H: no difference

Ha: is a difference

We fail to reject H since 0 is in the CI.

Hence the confidence interval estimates that the confidence interval limits contain 0., suggesting that the garlic treatment did not affect the LDL cholesterol levels.

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The graph is shown below:

A graph is a mathematical diagram which shows the relationship between two or more sets of numbers or measurements.

Given function: f(x) = x

We have to draw the graph for the function ,f(x) =x with two cases.

For x<2 and for x ≥ 2

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Answer:

1650 Cubic Centimeters

Step-by-step explanation:

To get the volume of the cereal boxes, you must multiply their 3 dimensions together.

Box A:

25×20=500

500×9=4500

Box B:

25×19=475

475×6=2850

Now, to find the difference of these volumes, you want to subtract the smaller volume from the larger volume.

4500-2850=1650

The answer is 1650 cubic centimeters.

Answer:

16.19

Step-by-step explanation:

Use the cosine rule:

[tex]\sqrt{a^{2} +b^{2} -2abcosy} \\\\\sqrt{16^{2} +20^{2} -(2)(16)(20)cos(52)} \\\\\\= 16.19cm[/tex]

The flux is 9.

Flux is the presence of a force field in a specified physical medium, or the flow of energy through a surface.

Given:

2x+2y+z= 1

F = 2i+2j + 2k

Now,

r = xi + yj + z( 1-2x-2y) K

dr/dx= i - 2k

dr/dy = j-2k

dr/dx* dr/dy

= ( i - 2k) * (j-2k)

= 2i + 2j + k

F(x)= 2i+2j + 2k

F(x). da = 4 +4 +2 = 10 dxdy

Hence, flux

= [tex]\int\limits^1_0 {\int\limits^{1-2y}_0 {10 } \, dx dy } \,[/tex]

=  [tex]\int\limits^1_0[/tex]  10(1-2y) dx

= [tex]\int\limits^1_0[/tex] 10-2y

= 10(1) - (1)²

=9

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The plane has intercepts (1/2, 0, 0), (0, 1/2, 0), and (0, 0, 1). Parameterize [tex]S[/tex] by the vector function

[tex]\vec s(u,v) = \dfrac{(1-u)(1-v)}2 \, \vec\imath + \dfrac{u(1-v)}2 \, \vec\jmath + v \,\vec k[/tex]

with [tex]0\le u\le1[/tex] and [tex]0\le v\le1[/tex]. (More explicitly, we have the parameterization

[tex]\vec s(u,v) = (1-v)((1-u) p_1 + u p_2) + v p_3[/tex]

where [tex]p_i[/tex] denote the given points.)

The normal vector to [tex]S[/tex] is

[tex]\vec n = \dfrac{\partial\vec s}{\partial u} \times \dfrac{\partial\vec s}{\partial v} = \dfrac{1-v}2\,\vec\imath + \dfrac{1-v}2\,\vec\jmath + \dfrac{1-v}4\,\vec k[/tex]

Then the flux of [tex]\vec F = 2\,\vec\imath+2\,\vec\jmath+2\,\vec k[/tex] across [tex]S[/tex] is given by the surface integral,

[tex]\displaystyle \iint_S \vec F \cdot d\vec\sigma = \iint_S \vec F \cdot \vec n \, dA[/tex]

[tex]\displaystyle = \int_0^1 \int_0^1 \left(2\,\vec\imath+2\,\vec\jmath+2\,\vec k) \cdot \left(\frac{1-v}2\,\vec\imath + \frac{1-v}2\,\vec\jmath + \frac{1-v}4\,\vec k\right) \, du \, dv[/tex]

[tex]\displaystyle = \frac52 \int_0^1 \int_0^1 (1-v) \, du \, dv[/tex]

[tex]\displaystyle  = \frac52 \int_0^1 (1-v) \, dv = \boxed{\frac54}[/tex]