Question 1 of 10
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The corresponding sides of the triangles are congruent.
B. The triangles have the same shape.
C. The corresponding angles of the triangles are congruent.
D. The triangles have the same size.

SAS triangle congruence theorem can be used to prove the triangle are congruent.

A triangle is a simple polygon with three sides and three interior angles. It is one of the basic forms of geometry in which three vertices are connected, and is represented by the symbol △. There are different types of triangles, classified based on their sides and angles. Two triangles are congruent if all three corresponding sides are equal and all three corresponding angles are equal. These triangles can be moved, rotated, flipped, and flipped to look identical. When rearranged they match each other. The congruence symbol is "≅".

Angle is the space between two intersecting lines or surface at or close to the point where they meet.

The SAS Postulate says that is the  triangles are congruent if any pair of the  corresponding sides and I their included angles are be congruent.

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s+f=24 and s=3f are system of equations to represent the situation and there are 18 spoons and 6 folks in the drawer.

Two or more expressions with an Equal sign is called as Equation.

Let s=number of spoon

Let f=number of forks

Since there are 3 times as many spoons as forks, s=3f

s+f=24

3f+f=24

4f=24

Divide both sides by 4

f=6

Now put f value in s=3f

s=3(6)

s=18

Hence, s+f=24 and s=3f are system of equations to represent the situation and there are 18 spoons and 6 folks in the drawer.

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The value of 'b' obtained for the given exponential function is 0.055.

The stated exponential function is-

y = 5832(b)ˣ

This, function contains the point (3, 1).

Put the value in the r function;

1 = 5832(b)³

(b)³ = 1/5832

b = ∛1/5832

b = 0.055

Thus, the value of 'b' obtained for the given exponential function is 0.055.

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The measure of side BC is 12 units in a right  ∆ABC if the altitude CH to the hypotenuse AB intersects angle bisector AL in point D.

A right angle is defined as an angle that is exactly 90 degrees in geometry and trigonometry. If a ray is positioned so that its terminal is on a line and the angles are also equal, the angles are said to be at right angles. The phrase derives from the Latin angulus rectus, where rectus denotes the upright vertical line that is perpendicular to a horizontal base line.

Perpendicular lines—defined as lines that meet at right angles—and orthogonality—defined as the ability to intersect at right angles—are closely connected and crucial geometrical notions.

Given,

m∠CAL = m∠BAL

m∠C = 90°

AD = 8 cm

DH = 4 cm

We have to apply sine rule for ΔADH,

sinθ=opposite side/hypotenuse

sin(∠DAH)=DH/AD

=4/8

=1/2

∠DAH=sin⁻¹(1/2)

∠DAH=30°

Therefore, ∠CAB=2(∠DAH)

=2(30°)

=60°

Now, we have to apply tangent rule in  ∆AHD

tan( ∠DAH)=DH/AH

tan(30°)=4/AH

1/√3=4/AH

AH=4√3

Now, we have to apply cosine rule in ∆AHC

cos(60°)=AH/AC

1/2=4√3/AC

AC=8√3

Now, we have to apply tangent rule in ∆ACB

tan(∠CAB)=opposite side/adjacent side

tan(60°)=BC/AC

√3=BC/8√3

BC=8√3(√3)

BC=24units.

Therefore, the measure of side BC is 12 units in a right  ∆ABC if the altitude CH to the hypotenuse AB intersects angle bisector AL in point D.

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Therefore,  the speed is  792/5 ft/sec  and distance covered during 15 second free fall is 1,584 ft.

The rate at which something or someone is moving is known as their speed. If you are aware of the distance traveled and the time required to get there, you can calculate the average speed of an object. The equation speed = distance * time is used to calculate speed.

Here,

Given:

The maximum free fall speed for a parachutist is 108 miles per hour.

5280 feet make up a mile.

Thus,

The speed is given by

=> 108 x 5280 x 1/3600 sec

=> 792/5 = 792/5 ft/sec  

and the distance of the parachutist fall during 15 seconds of free fall is given  by

=> 792/5 ft/sec x 10 sec = 1,584 ft

Therefore,  the speed is  792/5 ft/sec  and distance covered during 15 second free fall is 1,584 ft.

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After solving, the surface integral S is [tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14.

In the given question, we have to evaluate the surface integral.

(x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6.

Now the surface integral is:

[tex]\int\int_{S}(x + y + z) dS[/tex]

x = u+v, y = u−v, z = 1+2u+v, 0 ≤ u ≤ 8, 0 ≤ v ≤ 6

The parametric curve is

r(u,v) = <u+v, u−v, 1+2u+v>

Then surface integral is calculated as

[tex]\int\int_{S}(x + y + z) dS=\int\int_{A}f(x(u,v), y(u,v), z(u,v))|r_{u}\times r_{v}| dudv[/tex]

Now find partial derivatives of parametric curve with respect to u and v

[tex]r_{u}[/tex](u,v) = <1, 1, 2>

[tex]r_{v}[/tex](u,v) = <1, -1, 1>

Now find cross product

[tex]r_{u}\times r_{u}[/tex] = <1, 1, 2> × <1, -1, 1>

[tex]r_{u}\times r_{u}[/tex] = <1+2, 2-1, -1-1>

[tex]r_{u}\times r_{u}[/tex] = <3, 1, -2>

Now parametric function is

x+y+z = u+v+u-v+1+2u+v

x+y+z = 4u+v+1

Then the surface integral is:

[tex]\int\int_{S}(x + y + z) dS=\int^{6}_{0}\int^{8}_{0}(4u+v+1)\sqrt{14}dudv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(4\frac{u^2}{2}+uv+u)^{8}_{0}dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}[(4\frac{(8)^2}{2}+8v+8)-(4\frac{(0)^2}{2}+0\cdotv+0)]dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(128+8v+8)dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}\int^{6}_{0}(136+8v)dv[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}(136v+8\frac{v^2}{2})^{6}_{0}[/tex]

[tex]\int\int_{S}(x + y + z) dS=\sqrt{14}[(136\times6+8\frac{6^2}{2})-(136\times0+8\frac{0^2}{2})][/tex]

[tex]\int\int_{S}(x + y + z) dS[/tex] = √14×(816+144)

[tex]\int\int_{S}(x + y + z) dS[/tex] = 960√14

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The formula for estimating the population variance from the sample requires calculating the sum of squared deviations and dividing it by the number of observations. This is true for both the t-test for dependent means and the t-test for independent means.

This formula is referred to as the "variance sum of squares"or the t-test for dependent means, the formula is:

Where:

x1 = observation 1

x2 = observation 2

N = number of observations

For the t-test for independent means, the formula is:

Sample Variance = [(Σx12)/N + (Σx22)/N]/2

Where:

x1 = observation 1

x2 = observation 2

N = number of observation

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Answer:

1,229

Step-by-step explanation:

100 + 100 = 200

1,000 + 200 = 1,200

9 + 9 = 18

1,200 + 18 = 1,218

1,218 + 11 = 1,229

[tex]\sqrt[3]{63}[/tex]  , [tex]\sqrt[3]{60} , \sqrt[3]{-100}[/tex] three radical expressions are already simplyfird form .

Any expression with the radical () symbol is referred to as a radical expression. This symbol, which is frequently used to calculate the square root of a number, is frequently called the "square root" symbol by mistake. But it can also refer to a cube root, a fourth root, or something higher.

60 = 2 × 2 × 3 × 5. As a result, √60 = √2 + 2 + 3 + 5 = 2 + 15. Therefore, 2 15 is the square root of 60 in its lowest radical form.

3√600 =73.34

3√729 =9

A radical expression is any expression that uses the radical () symbol.

[tex]\sqrt[3]{63}[/tex]  , [tex]\sqrt[3]{60} , \sqrt[3]{-100}[/tex] three radical expressions are already simplyfird form .

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Answer:

15√3

Step-by-step explanation:

√ 15 ⋅ √ 45

Because both of them have the same base is the square root of two, we can combine them

√15 ⋅ 45

√675

Next, we factor √675 out and get

√15^2 ⋅ 3

= 15√3

So, the answer is  15√3

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Answer:

(x - 3)² + (y + 3)² = 9

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

the radius r is the distance from the centre to a point on the circle.

given (3, - 3 ) is the centre and (3, 0 ) is a point on the circle

since the x- coordinates of both points are 3 then r is the absolute value of the difference of the y- coordinates, that is

r = | - 3 - 0 | = | - 3 | = 3

then equation of circle is

(x - 3)² + (y - (- 3) )² = 3² , that is

(x - 3)² + (y + 3)² = 9

Using substitution method, the system of linear equations showed that there 27 and 35 quarters and nickel respectively

System of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables.

To solve this problem, we have to write a system of linear equations which consist of two linear equations.

Let;

x + y = 62...eq(i)

0.25x + 0.05y = 8.50 ...eq(ii)

Using substitution method

From equation (i)

x + y = 62

x = 62 - y ...eq(iii)

Put equ(iii) into eq(ii)

0.25( 62 - y) + 0.05y = 8.50

y = 35

Put y = 35 in equation (i)

x + 35 = 62

x = 27

The number of quarters and nickels are 27 and 35 respectively

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The system of equations is  0.05n+0.10d=1.90  and n=d+2

What is an equation?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.

The calculation is as follows:

We know that

One nickel = $0.05,

So n nickels are worth 0.05n.

One dime = $0.10,

so dd dimes are worth 0.10d.

Now

The total 0.05n+0.10d =  $1.90

i.e.  

0.05n+0.10d=1.90

And,  

n=d+2

Therefore we can conclude that The system of equations is  0.05n+0.10d=1.90  and n=d+2

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The value of the equation 4 is multiplied by the difference of 5 and a number is A = 20 - 4n

where n is the number

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be represented as n

Let the equation be A

Now , the value of A is

4 is multiplied by the difference of 5 and a number is

Substituting the values in the equation , we get

A = 4 ( 5 - n )

where n is the number

On simplifying the equation , we get

The value of A = 4 ( 5 ) - 4 ( n )

The value of A = 20 - 4n

Therefore , the value of equation A is A = 20 - 4n

Hence , The value of the equation 4 is multiplied by the difference of 5 and a number is A = 20 - 4n , where n is the number

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Answer: 325

Step-by-step explanation:

723 -73 =650 divided by 2

Hope this helps

The multiplication of polynomial in descending powers is,

32x^2 + 68x + 21.

What is polynomial?

A polynomial is a mathematical expression made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x^2 + 4x + 7 is an illustration of a polynomial with a single indeterminate x.

Consider, the given polynomials

(8x + 3)(4x + 7)

Taking multiplication,

8x(4x + 7) + 3(4x + 7)

Simplifying,

32x^2 + 56x + 12x + 21

32x^2 + 68x + 21

Hence, the multiplication of polynomial in descending powers is,

32x^2 + 68x + 21.

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Answer:

[tex]\sqrt[4]{256}[/tex]

Step-by-step explanation:

1. simplify the expression

4^4 = 256

2.  calculate the fourth root of 256 because we used the power of 4

[tex]\sqrt[4]{256}[/tex] = 4

So option b. x² + x is the correct option of the given statement Because option b satisfy the requirement of polynomial.

A polynomial is a mathematical equation made up of variables (sometimes called indeterminates) and coefficients, and can be expressed using just the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

By noticing which formulas only contain the operations of addition, subtraction, multiplication, and non-negative integer exponents, the polynomials can be located. Expressions with additional operations are considered non-polynomial expressions. Describe the reasons why the expressions are not polynomials.

A polynomial function is a function in an equation that exclusively employs positive integer exponents or non-negative integer powers of a variable. Examples of such equations include the cubic equation, the quadratic equation, and others. For example, 2x+5 is a polynomial with an exponent of 1.

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Both abbreviations are correct:

PEMDAS stands for:

BODMAS stands for:

PEMDAS and BODMAS are both mathematical acronyms that are used to help people remember the order of operations when solving a math problem.

The order of operations should be followed when solving an equation because it ensures that the problem is solved correctly and accurately. It is important to remember that both acronyms represent the same order of operations, and that each step should be followed in the order given.

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PEMDAS stands for

Parenthesis

Exponents

Multiplication and Division

Addition and Subtraction

BODMAS stands for

Bracket

Orders

Division and Multiplication

Addition and Subtraction

Both of these are the same, just a different acronym and way of representing them.

The characteristic polynomial  x³ - 7x² + 16x - 12  The characteristic polynomial of a square matrix in linear algebra is a polynomial that is invariant under matrix similarity and has the eigenvalues as roots.

Its coefficients include the determinant and the trace of the matrix.

Characteristic polynomial of a 3×3 matrix A is given by ; x³ - trace(A)x² + (A​​​​​​11 + A​​​​​​22 + A​​​​​​33 )x - determinant(A)

Where A​​​​​​ii is the determinant of the matrix obtained by deleting i​​​​​​ th row and i th column.

Here trace(A) = sum of the diagonals = 12 - 7 + 2 = 7

A​​​​​​11 = -7 × 2 = -14

A​​​​​​22 = 2 × 12 = 24

A​​​​​​33 = ( 12×-7) - (-10×9) = 6

Determinant(A) = 12(-7×2 - 0) + 10(2×9 - 0) = 12

Substituting these values in above equation , we obtain;

x³ - 7x² + (-14 + 24 + 6)x - 12 = x³ - 7x² + 16x - 12.

Hence x³ - 7x² + 16x - 12 is the characteristic polynomial of A.

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Tiles are needed = 90

The number of tiles measuring 40cm by 40cm  that are needed to completely cover a wall 4m by 3.6m is 90.

Squares

Square,  a plane figure with four equal sides and four right (90°) angles. A square is a special kind of rectangle (an equilateral one) and a special kind of parallelogram (an equilateral and equiangular one).

Number of tiles needed

Convert the Meters to Centimeters

4m = 400cm

3.6m = 360 cm

Then

4m by 3.6m = 400 cm × 360 cm

4m by 3.6m = 144000 cm²

Tiles are needed

Number of needed tiles =  144000 cm² / ( 40 cm × 40 cm)

Number of needed tiles =  144,000 cm² /1600 cm²

Number of needed tiles =  90

Tiles are needed = 90

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People withe the appropriate clearance and a signed non-disclosure agreement may access classifies information within a company or organization.

People must have a favorable determination of eligibility at the proper level, have a "need-to-know", and have signed an appropriate non-disclosure agreement before accessing classified information. Any individual who falls to meet these requirements is not authorized to access classified information.

Classified information may be made available to a person only when the possessor of the information establishes that the person has a valid "need-to-know" and the access is essential to the accomplishment of official government duties.

Data classification is the process of organizing data into categories that make it easy to retrieve,sort and store for future use. A well-planned data classification system makes essential data easy to find and retrieve.

Given question is incomplete.

Who can access classified data?

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The way to organize 100 toothpicks in a way that fits with the structure of the base ten system as well as how your organization reflects the structure of the base ten system and  others is given below.

According to the base-10 system, each digit of a number can, depending on its position, have an integer value ranging from 0 to 9 (10 possibilities). Powers of 10 are used to determine the locations or positions of the numbers. The term "base-10" refers to a system of numbers where each place is 10 times the value to its right.

Since we have 10 fingers, we employ the base 10 system. Since base 10 only uses the numerals 0 through 9 for its ten digits, students start to realize that there are only 0-9 digits in each place value.

Therefore,  This becomes very vital while adding and subtracting since, depending on the operation, if we have a digit larger than 9, we must either regroup or ungroup to make it less than 10.

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The functions that model a mountain with steeper sides are (c) g(x) = -|3x - 1| +2 and (d) g(x) = -|4x-2| +1​

From the question, we have the following parameters that can be used in our computation:

f(x) = -|x - 2| + 1

The above function is an absolute value function

An absolute value function is represented as

f(x) = a|x - h| + k

Where

Slope = a

So, the slope of f(x) = -|x - 2| + 1 is

Slope = -1

Take the absolute value of this slope

Steep = 1

This means that the slopes of the functions in the options are

Slope (a) = -1/4

Slope (b) = -1/3

Slope (c) = -3

Slope (d) = -4

Take the absolute values of the above slope

Steep (a) = 1/4

Steep (b) = 1/3

Steep (c) = 3

Steep (d) = 4

A slope with a greater absolute value means a steeper line

3 and 4 are greater than 1

This means that the equations (c) and (d) are steeper than the given equation

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The given two triangles are congruent by  Side Side Side congruency.

As from the question we get to know that ΔRST and Δ UTS  

and

RS = UT

RT = US

The proof for the above claim

RS = UT    {given}

RT = US    {given}

ST = TS     {Common}

Therefore, we can say that by SSS theorem ΔRST and Δ UTS  is congruent to each other.

ΔRST  ≅ Δ UTS    by SSS Theorem

If two geometric figures are identical in every way, they are said to be congruent.

For example, two squares having the same side-length are congruent.

Similarly, two circles with the same radius are congruent.

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. If moved, they coincide with one other. ’ ≅’ is the congruence symbol.

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Using the given ratio we can see that there are 27 units of potassium on the sample.

We know that the ratio of nitrogen to potassium in a sample of soil is 12:9.

So for each 12 units of nitrogen, we have 9 units of potassium.

So if we have N units of nitrogen, the units of potassium are given by:

P = N*(9/12)

In that sample, we have 36 units of nitrogen, using the formula written above we will get:

P = 36*(9/12) = 27

There are 27 units of potassium on the sample.

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Answer: 1

Step-by-step explanation:

Answer:

a) 191.3 students

b) 433.8 students

Step-by-step explanation:

a) Since x represents years since 1998, on the graph, the number of student in 2005 is represented at x = 7.

So, to solve for the number of students studying abroad in 2005, find the approximate y-coordinate of the point on the graph at x = 2005 - 1998 = 7:

(7, 191.296)

         ↓

   191.296

Finally, round this to the nearest tenth.

192.296 ≈ 191.3 students

See the attached images for a graph and an algebraic solution for the coordinate.

b) Since x represents years since 1998, on the graph, the number of student in 2018 is represented at x = 2018 - 1998 = 20.

So, to solve for the number of students studying abroad in 2018, find the approximate y-coordinate of the point on the graph at x = 20:

(20, 433.761)

         ↓

   433.761

Finally, round this to the nearest tenth.

433.761 ≈ 433.8 students

Answer: m= 6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

because slope is the amount of times your changing the line