Question 9 (4 points)
Chee is saving up to buy a new phone. The situation is represented by the equation y = 5.45x +
70 where x is the number of weeks and y is the total saved. How much total money would
Chee have after 6 weeks of saving?
A) $81.45
OB) $32.70
OC) $75.45
D) $102.70

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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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

Answer:

  the Pythagorean theorem was used

Step-by-step explanation:

You want to know the missing side in a right triangle with hypotenuse 15 cm and one side 9 cm.

The Pythagorean theorem tells you the relationship between sides 'a' and 'b' and hypotenuse 'c' in a right triangle is ...

  a² +b² = c²

  9² +?² = 15² . . . . use the given values

  ?² = 225 -81 = 144 . . . . subtract 9²

  ? = √144 = 12 . . . . . . . take the square root

The length of the missing side is 12 cm.

__

Additional comment

The little green square in the upper corner tells you that is a right angle, and the triangle is a right triangle.

All units of length are in cm.

Answer: 325

Step-by-step explanation:

723 -73 =650 divided by 2

Hope this helps

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

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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Clarice did not verified the answer to verify the check should be 5×[tex]1\frac{1}{2}[/tex] = [tex]7\frac{1}{2}[/tex]

A division is a process of splitting a specific amount into equal parts.

Given,

[tex]7\frac{1}{2}[/tex]÷[tex]1\frac{1}{2}[/tex]

15/2÷3/2

When fraction is divided by fraction the denominator turns to reciprocal and multiplied with numerator

15/2×2/3=5

Clarice did not verified the answer

5×[tex]1\frac{1}{2}[/tex] should be equal to [tex]7\frac{1}{2}[/tex]

Hence, Clarice did not verified the answer to verify the check should be 5×[tex]1\frac{1}{2}[/tex] = [tex]7\frac{1}{2}[/tex]

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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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Answer: m= 6

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

because slope is the amount of times your changing the line

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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Answer:

Step-by-step explanation:

You want the length of the minimum perimeter fence to enclose 3 sides of a rectangular area of 128 m² with one side of the enclosure provided by a river. You also want the enclosure dimensions.

If x represents the dimension of the enclosure parallel to the river, then the other dimension of the enclosure is found from ...

  A = LW

  128 = x·W

  W = 128/x

There will be two sides of this length, so the perimeter is ...

  P = L +2W = x +2(128/x)

  P = x + 256/x

This has an extreme value (minimum) where its derivative is zero:

  dP/dx = 0 = 1 -256/x²

Solving for x gives ...

  x² = 256

  x = √256 = 16

and the perimeter is ...

  P = 16 +256/16 = 32

The other dimension is 128/16 = 8.

The minimum perimeter is 32 meters; the enclosure is 16 by 8 meters.

__

Additional comment

This can be solved without using derivatives by working the reverse problem: the largest area for a given perimeter.

Using the same definition of x, the area in terms of perimeter is ...

  A = x · (P -x)/2

This is a quadratic equation with a maximum halfway between its zeros at x=0 and x=P. So, the value of x for maximum area is x = P/2. That area is ...

  A = (P/2)(P -P/2)/2 = (P/2)(P/4) = P²/8

Or, the minimum perimeter for a given area is ...

  P = √(8A)

In this problem, that is ...

  P = √(8·128) = √1024 = 32

The dimensions of the enclosure are (P/2)×(P/4) = 16×8.

Explanation:

You want to show cos(4t) +4cos(2t) = 8cos⁴(t).

Use the cosine double-angle identity:

  cos(2t) = cos²(t) -sin²(t) = cos²(t) -(1 -cos²(t)) = 2cos²(t) -1

Then

  cos(4t) = 2cos²(2t) -1 = 2(2cos²(t) -1)² -1 = 2(4cos⁴(t) -4cos²(t) +1) -1

  = 8cos⁴(t) -8cos²(t) +1

Substituting these expressions into the left side of the identity of interest, we have ...

  cos(4t) +4cos(2t) = 8cos⁴(t) -3 . . . . . . . . . . . . . . . . . . identity to prove

  (8cos⁴(t) -8cos²(t) +1) +4(2cos²(t) -1) = 8cos⁴(t) -3 . . . substitute

  8cos⁴(t) -8cos²(t) +1 +8cos²(t) -4 = 8cos⁴(t) -3 . . . . . eliminate parentheses

  8cos⁴(t) -3 = 8cos⁴(t) -3 . . . . . . combine like terms; Q.E.D.

Option B.

Don't be the only person without a great gift at the next baby shower.

What is the bandwagon technique?

It is a psychological phenomenon whereby the rate of uptake of beliefs, ideas, fads and trends increases with respect to the proportion of others who have already done so. As more people come to believe in something, others also "hop on the bandwagon" regardless of the underlying evidence.

Below are some examples of the Bandwagon Effect: Diets: When it seems like everyone is adopting a certain fad diet, people become more likely to try the diet themselves. Elections: People are more likely to vote for the candidate that they think is winning.

Hence ,  Don't be the only person without a great gift at the next baby shower is the correct answer .

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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

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 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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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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[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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The original amount of the loan is $23,000.

What is the simple interest?

Simple interest is, by definition, the amount of interest paid on a specific principal sum of money when an interest rate is applied. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

The formula of simple interest is I = PRT.

I =  interest

P = Principal

R = rate of interest

T = time

Given that the rate of interest is 6.5%. Thus R = 6.5% = 0.065

The interest that she paid after 1 year is $149.50.

Thus I = $149.50 and T = 1

Putting R = 0.065, I = $149.50, and T = 1 in I = PRT

149.50 = P × 0.065 × 1

Divide both sides by 0.065

P = 23000

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The words that can be used to fill in the blanks are;

3) Work

4) fulcrum

5) simple machine

6) compound machine

7) All of these

8) pulley

9) wheel and axle

10) screw

11) wedge

12) inclined plane

We know that the term force has to do with a push or a pull force has to do with that which could cause an object to move some distance in the direction of the force that has been applied.

There are several kinds of simple machine. Let us recall that a machine has to do with any material that eases our work. It is the material that helps us to exert a lesser effort in order to move a heavier load.

The various kinds of simple machines that we have are;

The Lever is a simple machine that is composed of the load, the fulcrum and the effort.

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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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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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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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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 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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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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Answer:

First blank: 90°  Second blank: 12

Step-by-step explanation:

The two shapes have a ratio of 4:1, and have the same angles.

This means that if m∠B = 90°, then m∠D = 90°.

Because the shape ratio is 4:1 (16:4 simplified) we can use this to find out 48:?    48/4 = 12

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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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.