What Is the lateral area of the triangular pyramid?

Answer:

75

Step-by-step explanation:

9x5=45

15x5=75

Answer:

75

Step-by-step explanation:

9:15=45: _

very similar to cross multiplying

9/15  =  (45/ something)

something =  45 / (9/15)  =   45 * (15/9) = 5*15 = 75

Answer:

Base of quilt is 8 inch.

Step-by-step explanation:

Refer to the attachment.

Given that pattern on the quilt is right angle triangle. Consider ΔABC as right angle triangle where ∠ABC=90°.

Given that area of triangle is 24 in² and height is 6 inch that is, AB = 6 inch.

To find the base use formula for area of right angle triangle.

[tex]Area\:of\:triangle=\dfrac{1}{2}\times base\times height[/tex]

Substituting the values,

[tex]24=\dfrac{1}{2}\times base\times 6[/tex]

Simplifying,

[tex]24=\dfrac{6}{2}\times base[/tex]

Multiplying both sides by [tex]\dfrac{2}{6}[/tex],

[tex]24\times \dfrac{2}{6}=\dfrac{6}{2}\times base\times \dfrac{2}{6}[/tex]

Simplifying,

[tex]24\times \dfrac{2}{6}=base[/tex]

Dividing the numbers,

[tex]8=base[/tex]

Therefore, length of base of each quilt piece is 8 inch.

Answer:

4

Step-by-step explanation:

10 times 4 equals 40

4 will be the value of n for the given expression.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, an expression 10n = 40

Simplifying the equation for n

=> 10n = 40

divide by 10 into both sides

=> 10n/10 = 40/10

=> n = 4

Therefore, the value of n for the given expression will be 4.

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Answer:

in scientific notation​ the answer is 5.75x10^8

Answer: [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex]

Step-by-step explanation: To write a number in scientific notation, first write a decimal point in the number so that there is only one digit to the left of the decimal point.

So here, we have 5.75000000 and notice that there

is only one digit to the left of the decimal point.

Next, we count the number of places the decimal point would

need to move to get back to the original number, 575,000,000.

Since we would need to move the decimal point 8 places to the right,

we have an exponent of positive 8.

Now, scientific notation is always expressed as a number between 1 and 10 including 1 but not 10 and it is multiplied by 10 to a certain power that must be an integer.

So we have [tex]5.75000000[/tex] [tex]x[/tex] [tex]10^{8}[/tex].

Notice that the exponent is positive.

This is because we would need to move the decimal point to the right in order to get back to the original number.

So 575,000,000 can be written in scientific notation

as [tex]5.75000000[/tex] [tex]x[/tex] [tex]10^{8}[/tex] or just [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex].

Remember that we can drop zeroes at the end of a decimal.

So we have [tex]5.75[/tex] [tex]x[/tex] [tex]10^{8}[/tex].

Jerry will spend $355.7988 on molding.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

we have,

Scale: 1 foot = 14 inches

As, the measurement of walls is 2372 inches.

The, using Scale the wall measured

= 2372/14

= 169.428 foot

Now, the molding costs $2.10 per foot then the cost of 169.428 foot is

= 169.428 x 2.10

= $355.7988

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The most vital factor for classifying two species into the same group is if they evolved from a shared ancestor, reflecting their place in the same clade and genetic similarities.

The most important factor for classifying two species into the same group is their evolutionary history, specifically whether they evolved from a shared ancestor. When scientists classify species, they adhere to the fundamental principle that all members of a group, or "clade," must have a recent common ancestor that is not shared with species from other groups. This is based on the idea that species within the same group will share more genetic similarities and phylogenetic traits than with those from different groups due to their more recent common ancestry.

Option A might seem plausible, as species in a group often share similar traits, but shared traits alone are not enough for classification without evolutionary context. Option C is incorrect because common names do not reflect scientific classification. Option D is also incorrect as geographic location is not a determinant for taxonomic classification. Thus, the correct answer to the original question is B, "The species have different common ancestors," as having a recent common ancestor is the most critical criterion for grouping species together.

Step-by-step explanation:

The combination of Wendell and Maggie’s ages is 33. Let Maggie's age is x. It is mentioned that Wendell’s age is 3 less than 3 times the age of Maggie. It means, Wendell’s age is (3x-3).

ATQ,

[tex]x+(3x-3)=33\\\\4x-3=33\\\\4x=36\\\\x=9[/tex]

The age of Maggie is x. So, Wendell's age is :

[tex]y=(3x-3)\\\\y=(3(9)-3)\\\\y=24[/tex]

So, Wendell age is 24 years.

Answer:

-5

Step-by-step explanation:

plug -3 into the equation (x)-2

-3-2=-5 if you subtract a number from a negative you will get a negative.

-5

Answer:

-5

Step-by-step explanation:

You plug in the value of -3 in the place of x, which gives you the equation of -3-2. You would then solve by subtracting 2 from -3, which gives you -5

Rectangle

Area = w × h

w = width

h = height

25ft × x=1125 ft²

=> x=1125 ft²/25 ft

x=45 ft

Answer:

x=1125÷25=45ft

Area=length × width therefore

length= area÷width

Answer:

G. sqrt (74)

Step-by-step explanation:

Use the Pythagorean theorem to find AB, which is represented by c in the theorem.

a^2 + b^2 = c^2

7^2 + 5^2 = c^2

49 + 25 = c^2

74 = c^2    (Take the square root of each side)

c = sqrt (74)

So, AB = sqrt (74)

Length AB is an illustration of Pythagoras theorem.

The length of AB is (G) [tex]\mathbf{\sqrt{74}}[/tex]

The given figure is a right-angled triangle.

Such that:

AC = 7

BC = 5

AB = ?? The hypotenuse

Using Pythagoras theorem, we have:

[tex]\mathbf{AB^2 = AC^2 + BC^2}[/tex]

Substitute values for AC and BC

[tex]\mathbf{AB^2 = 7^2 + 5^2}[/tex]

Evaluate squares

[tex]\mathbf{AB^2 = 49 + 25}[/tex]

Add

[tex]\mathbf{AB^2 = 74}[/tex]

Take square roots

[tex]\mathbf{AB = \sqrt{74}}[/tex]

Hence, the value of AB is (G) [tex]\mathbf{\sqrt{74}}[/tex]

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Answer:

12y=$3

114 cans

Step-by-step explanation:

Let the cost of every can be represented by y. Therefore, for 12 cans, the cost will be the product of y cans and 12 hence cost is 12y

Since the cost incurred is $3 then we can represent these as

12y=$3

To solve for y, we divide both sides by 12 hence

Y=$3/12=$0.25

To find the number of cans that one will get with a buget of $28.5, we divide the budget by the cost of a can. This will be $28.5/$0.25=114 cans

List the numbers from least to greatest:

1, 3, 3, 4, 5, 6, 8, 9, 10

Mode: ( most number repeated in the list)

Mode: 3

The mode of the numbers 6, 4, 1, 9, 3, 8, 3, 5, 10 is 3, as it is the number that appears most frequently in the set.

The question asks to find the mode of the following numbers: 6, 4, 1, 9, 3, 8, 3, 5, 10. The mode is a measure of central tendency that represents the most frequently occurring number in a set of values. To find the mode, we need to count how many times each number occurs in our set.

Since the number 3 appears more frequently than any other number in the set, occurring twice, the mode of this set of numbers is 3.

Answer: I'm probably wrong, but I think it's 2

Step-by-step explanation:  Estimate.

Answer:

Blank 1: 40

Blank 2: 10

Step-by-step explanation:

You can start by representing the speed of the water as x and the speed of the dolphin as y, and writing an equation.

y+x=50

y-x=30

Adding these two equations together, you get:

2y=80

y=40 for the speed of the dolphin in still water. Now, you an use one of the previous equations to find the speed of the current.

40-x=30

x=10

Hope this helps!

Answer:

The sum of 7 and 2 in simplest form is 9

Step-by-step explanation:

7+2=9

Answer:

Area of sector = 84.861

Step-by-step explanation:

Given

The radius of the circle = 9

central angle of sector = [tex]120^{o}[/tex]

value of pi π = 3.143

To find : the area of sector = ?

We know that the formula to calculate area of sector is given as:

area of sector = (π [tex]r^{2}[/tex]Θ)/ [tex]360^{o}[/tex]

where, r  is radius and Θ is the central angle of the sector

Substituting the known values in above formula, we get

area of sector = (3.143 x [tex]9^{2}[/tex] x [tex]120^{o}[/tex]) / [tex]360^{o}[/tex]

                        = 84.861

Hence area of sector is 84.861

Answer:

27 pi

Step-by-step explanation:

just did this one

Answer:

0

Step-by-step explanation:

2 plus 2 is 4 then you add 2 which makes 6 then subtract 6 to get the answer of 0.

Answer:

l=8

Step-by-step explanation:

w=l-7

Area=l*(l-7)=8 u

l^2-7l-8=0

l^2- 8l+l-8=0

l(l-8)+l-8=0

(l-8)*(l+1)=0

l-8=0  ,   l=8  or

l+1=0,   l=-1 impossible

so l=8

To find the length of a rectangle when its width is the length minus 7 units and its area is 8 units, you can set up an equation and solve it. In this case, the length of the rectangle is 8 units.

To solve this problem, you need to set up an equation based on the given information. Let's assume the length of the rectangle is 'L'. According to the problem, the width of the rectangle is the length minus 7 units. So, the width can be represented as 'L-7'.

The area of a rectangle is given by the formula 'length x width'. In this case, the area of the rectangle is 8 units. So, the equation would be: L x (L-7) = 8.

To find the length of the rectangle, you need to solve the equation. Expand the equation: L^2 - 7L = 8. Rearrange it to form a quadratic equation: L^2 - 7L - 8 = 0. Factorize or use the quadratic formula to find the values of 'L'. It turns out that the length of the rectangle is 8 units.

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Answer:(t-4)(4mn-1)

Step-by-step explanation:

Answer:

y = - [tex]\frac{3}{2}[/tex] x

Step-by-step explanation:

Given that x and y vary directly then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = - 4, y = 6, thus

6 = - 4k ( divide both sides by - 4)

[tex]\frac{6}{-4}[/tex] = k, or k = - [tex]\frac{3}{2}[/tex]

y = - [tex]\frac{3}{2}[/tex] x ← equation of variation

Answer:

the coordinates of B is (-5,7)

The coordinates of the other end of the line segment, point B, are calculated by rearranging the midpoint formula and substituting the given values, resulting in B = (-5,7).

In mathematics, the midpoint of two points, A and B, can be calculated using the midpoint formula: ((x1 + x2) / 2, (y1 + y2) / 2). In this case, you are given the midpoint, M, and one of the points, A, and asked to find the other point, B. Given that M is (-3,2) and A is (-1,-3), you can rearrange the midpoint formula to solve for B: ((2 * xm - xA), (2 * ym - yA)).

Substitute the given values into this equation and you get B = ((2 * -3 - -1), (2 * 2 - -3)). Then perform the operations to find that B = (-6+1, 4+3) which simplifies to B = (-5,7).

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Answer:

Step-by-step explanation:

Answer:

Proved down

Step-by-step explanation:

To prove that a triangle is isosceles use the distance formula to find the length of its side and check if there are two sides equal.

To prove that a triangle is right find the square of the longest side and then find the sum of the squares of the other two sides, if the two answers are equal, then the triangle is right (converse of Pythagoras Theorem).

The formula of the distance between two points is:

[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

∵ x = (-1 , 5) and y = (4 , 4)

∴ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = 4

∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 4

- Substitute them in the formula of the distance to find xy

∵ [tex]xy=\sqrt{(4--1)^{2}+(4-5)^{2}}=\sqrt{25+1}[/tex]

∴ [tex]xy=\sqrt{26}[/tex]



∵ x = (-1 , 5) and z = (-2 , 0)

∴ [tex]x_{1}[/tex] = -1 and [tex]x_{2}[/tex] = -2

∴ [tex]y_{1}[/tex] = 5 and [tex]y_{2}[/tex] = 0

- Substitute them in the formula of the distance to find xz

∵ [tex]xz=\sqrt{(-2--1)^{2}+(0-5)^{2}}=\sqrt{1+25}[/tex]

∴ [tex]xz=\sqrt{26}[/tex]

∵ xy = xz

- The isosceles triangle has two equal sides

∴ Δ xyz is an isosceles triangle

∵ y = (4 , 4) and z = (-2 , 0)

∴ [tex]x_{1}[/tex] = 4 and [tex]x_{2}[/tex] = -2

∴ [tex]y_{1}[/tex] = 4 and [tex]y_{2}[/tex] = 0

- Substitute them in the formula of the distance to find yz

∵ [tex]yz=\sqrt{(-2-4)^{2}+(0-4)^{2}}=\sqrt{36+16}[/tex]

∴ [tex]yz=\sqrt{52}[/tex]

yz is the longest side lets find its square

∵ (yz)² = ([tex]\sqrt{52}[/tex] )²

∴ (yz)² = 52

- Lets find the sum of the squares of the other two sides

∵ (xy)² + (xz)² =  ([tex]\sqrt{26}[/tex] )² +  ([tex]\sqrt{26}[/tex] )²

∴ (xy)² + (xz)² = 26 + 26 = 52

∴ (yz)² = (xy)² + (xz)²

- That means the angle opposite to yz is a right angle

∴ Δ xyz is a right isosceles triangle

Answer:

the answer is c

Step-by-step explanation:

Answer:

C. y + 8 = –5(x – 3)

second part is also C. y = –5x + 7

Step-by-step explanation:

Answer:

[tex]i_m=8.322\%\\\\624 \ compoundings\\\\A_{12}=\$1,304.88[/tex]

Step-by-step explanation:

#The equivalent interest rate per annum is equal to the effective interest rate.

-Given 8% compounded weekly( Take 1 yr=52 weeks) the effective interest rate is calculated as:

[tex]i_m=(1+i/m)^m-1\\\\\#where\\i=stated \ interest\ rate\\m=number \ of \ compoundings \ per \ year\\\\\therefore i_m=(1+0.08/52)^{52}-1\\\\=0.08322\approx 8.322\%[/tex]

Hence, the equivalent interest rate is 8.322%

-Assuming one year has 52 weeks,   the number of compoundings will be :

[tex]=compoundings \ per \ year \times \ no \ of \ years\\\\=52\times 12\\\\=624\ compoundings[/tex]

-The investment amount after 12 years is calculated as:

[tex]A=P(1+i_m)^n, n=number \ of \ years\\\\=500(1.08322)^{12}\\\\=1304.88[/tex]

Hence, the amount after 12 years is $1304.88

Answer:

8% annual interest rate when compounded weekly =

(1 + .08/ 52)^52 = 1.00153846153846154^52 = 1.08322047419671 =

8.322047419671% equivalent interest rate

In 12 years this will be compounded 624 times

12 year Total = 500 * (1.08322047419671)^12 =

1,304.8852611583 =

1,304.89 (rounded)

Answer:

I would say c

Step-by-step explanation:

Given:

Given that AGN is a triangle with circle inscribed in it.

The circle touch the triangle at the point R, T and E.

The length of AR is 35 units.

The length of RG is 21 units.

The length of NE is 19 units.

We need to determine the perimeter of the triangle AGN.

Length of GE:

Since, we know the property that, "if two segments from a exterior point are tangent to the circle, then they are congruent".

Since, RG and EG from an exterior point G are tangents to the circle, then RG and EG are congruent.

Thus, we have;

[tex]RG=EG[/tex]

 [tex]21=EG[/tex]

Thus, the length of GE is 21 units.

Length of TN:

Since, we know the property that, "if two segments from a exterior point are tangent to the circle, then they are congruent".

Since, TN and NE from an exterior point N are tangents to the circle, then TN and NE are congruent.

Thus, we have;

[tex]TN=NE[/tex]

[tex]TN=19[/tex]

Thus, the length of TN is 19 units.

Length of AT:

Since, we know the property that, "if two segments from a exterior point are tangent to the circle, then they are congruent".

Since, AT and AR from an exterior point A are tangents to the circle, then AT and AR are congruent.

Thus, we have;

[tex]AT=AR[/tex]

[tex]AT=35[/tex]

Thus, the length of AT is 35 units.

Perimeter of AGN:

The perimeter of AGN is given by

[tex]\triangle AGN=AR+RG+GE+EN+TN+AT[/tex]

Substituting the values, we get;

[tex]\triangle AGN=35+21+21+19+19+35[/tex]

[tex]\triangle AGN=150[/tex]

Thus, the perimeter of the triangle AGN is 150 units.

Answer:

150

Step-by-step explanation:

Segment AE divides the triangle into two congruent right angle triangles

AG = AN = 35 + 21 = 56

NG = 2(19) = 38

Perimeter = 56 + 56 + 38

150

Answer:

For the first cone: r = 7 cm, h = 21 cm

For the second cone: r = 8 cm, h = 24 cm

Step-by-step explanation:

The volume of the first cone is [tex]343\pi cm^3[/tex]

The volume of the second cone is [tex]512\pi cm^3[/tex]

We are told that the height of each cone is 3 times its radius, hence:

h = 3r

The volume of a cone is given as:

[tex]V = \frac{1}{3} \pi r^2h[/tex]

Substituting h = 3r:

[tex]V = \frac{1}{3} \pi r^2(3r)\\\\\\V = \frac{1}{3} \pi (3r^3)\\\\\\V = \pi r^3[/tex]

For the first cone, V = [tex]343\pi cm^3[/tex], radius, r, will be:

[tex]343\pi = \pi r^3\\\\\\=> r^3 = 343\\\\\\r = \sqrt[3]{343} \\\\\\r = 7 cm[/tex]

∴ Its height will be:

h = 3r = 3 * 7 = 21 cm

For the second cone, V = [tex]512\pi cm^3[/tex], radius, r, will be:

[tex]512\pi = \pi r^3\\\\\\=> r^3 = 512\\\\\\r = \sqrt[3]{512} \\\\\\r = 8 cm[/tex]

∴ Its height will be:

h = 3r = 3 * 8 = 24 cm

The radius and height of the first cone are 7 cm and 21 cm respectively while the radius and height of the second cone are 8 cm and 24 cm respectively.

Answer:

24

Step-by-step explanation:

This is a simple sequence, and they are asking only for the third number in the sequence, so repeated subtraction using is the optimal method for solving for the final answer.

First start with the first term in the sequence, which is 38. The next term is found by subtracting 7.

2nd term = 1st term - 7 (original equation)

2nd term = 38 - 7 (substitute values)

2nd term = 31 (combine like terms by subtracting)

Then repeat this process to find the third term.

3rd term = 2nd term - 7 (original equation)

3rd term = 31 - 7 (substitute values)

3rd term = 24 (combine like terms by subtracting)

Therefore the third term is 24.