Could someone help me with the first two parts of this geometry question? I can do the third and fourth myself.

Could Someone Help Me With The First Two Parts Of This Geometry Question? I Can Do The Third And Fourth

Answers

Answer 1

Answer:

see image

Step-by-step explanation:

see image. We can use the given info and definition of isosceles (congruent sides) and reflexive property (something is congruent to itself) to prove (i) by SSS.

The using "Corresponding Parts of Congruent Triangles are Conguent" (CPCTC) to get more info to prove (ii) by SAS

Could Someone Help Me With The First Two Parts Of This Geometry Question? I Can Do The Third And Fourth

Related Questions

x is directly proportional to w²
When w = 4, x = 48

y is inversely proportional to x³
When x = 2, y = 14

Find a formula for y in terms of w.
Give your answer in its simplest form.

Answers

The formula for x in terms of w is x = 3w² and the formula for y in terms of x is y = (1/112)x³

Variation

x = k × w²

w = 4, x = 48

48 = k × 4²

48 = k × 16

48 = 16k

k = 48/16

k = 3

So,

x = k × w²

x = 3 × w²

x = 3w²

y = k/x³

x = 2, y = 14

14 = k / 2³

14 × 2³ = k

14 × 8 = k

112 = k

So,

y = k/x³

y = 112/x³

y = (1/112)x³

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You are tasked with constructing a rectangular box with a square base, an open top, and a volume of 184 in3. Determine what the dimensions of the box should be to minimize the surface area of the box. What is the minimum surface area

Answers

The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.

Dimensions to Minimize the Surface Area of the Box

It is given that the box is square based with an open top.

⇒ The box has one square and 4 rectangles

Thus, the total surface area of the box is given as,

S= a²+ab+ab+ab+ab  

S= a²+4ab ______________ (1)

Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.

This equation is later used for minimization of the surface area.

Also, the volume, V = a²b

It is also given that volume of the box is 184 in³.

⇒ 184 = a²b _____________ (2)

Forming a One-Variable Equation

From equation (2), b=184/a²

Now, substitute this value of b in equation (1) to get,

S = a² + 4a(184/a²)

S = a² + 4(184/a)

S = a² + 736/a

Minimization of Surface Area to find the Dimension

We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0

dS/da = 2a -736/a²

0 = 2a -736/a²

⇒ 0 = 2a³- 736

2a³ = 736

a³ = 736/2

a³ = 368

a = ∛368

a= 7.17 in

∵V = a²b

184 = (7.17)²b

b = 184/7.17²

b = 184/51.4089

b = 3.58 in

Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..

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Type the correct answer in the box. Use numerals instead of words.
What is the length of the diagonal shown in the rectangular prism? Round your answer to the nearest tenth.
7 ft
ft
4 ft
5 ft

Answers

The length of diagonal is 9.5 ft

What is Pythagoras theorem?

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

We will find the length of diagonal as shown below:

l= 7 ft

h= 5 ft

w= 4 ft

Let diagonal be d.

Let v be the diagonal of the base.

Using Pythagoras theorem

[tex]v=\sqrt{7^2+4^2}[/tex]

[tex]=\sqrt{49+16}[/tex]

[tex]v=\sqrt{65}[/tex]

For finding the value of d again using Pythagoras theorem

[tex]d=\sqrt{v^2+h^2}[/tex]

[tex]=\sqrt{(\sqrt{65})^2+5^2 }[/tex]

[tex]=\sqrt{65+25}[/tex]

[tex]=\sqrt{90}[/tex]

=9.4868

Rounding to nearest tenth

=9.5

Hence, the length of diagonal is 9.5 ft

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The diagram below shows a logo formed by removing a semicircle with diameter AB and a
rhombus DEFG from an isosceles trapezium ABCE where AE = BC.
Find the area of the logo.

Answers

The area of the logo is 136. 14 cm²

Determining the area

First, let's find the area of the semicircle

Area of semicircle = 1/2(πr²)

radius = 8/2 = 4cm

Substitute into the formula

Area of semicircle = [tex]\frac{1}{2} * 3. 142 * 4 * 4[/tex] = 25. 135 cm²

Now, let's find area of trapezium

Area of trapezium = [tex]\frac{a + b}{2} * h[/tex]

Area =  [tex]\frac{12 + 10. 2}{2} * 10[/tex]

Area = [tex]11. 1 * 10[/tex]

Area = 111 cm²

Area of logo = Area of trapezium + area of semicircle

Area of logo = 111 +  25. 135

Area of logo = 136. 14 cm²

Thus, the area of the logo is 136. 14 cm²

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What is the area of triangle lmn? 3 square units 4 square units 6 square units 8 square units

Answers

The area of the triangle LMN is 4 units squared.

How to find area of a triangle?

The area of a triangle can be described as follows:

The area of the triangle by using the base and height of the triangle.

area of a triangle = 1 / 2 bh

where

base of the triangleheight of the triangle

Therefore,

base = NL = 4 units

height = PM = 2 units

Therefore,

area of the triangle = 1 / 2 × 4 × 2

area of the triangle = 8 / 2

area of the triangle = 4 units²

Therefore, the area of the triangle LMN is 4 unit squared.

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Answer: B. 4 Square Units

Step-by-step explanation:

A spiral tile has a width of 1/4 foot how many tiles will fit end to end on a 4 foot wall

Answers

16 tiles will fit end to end on a 4 foot wall.

In unitary method we will learn how to find the value of a unit from the value of a multiple and the value of a multiple from the value of a unit.

When we go to the market to buy any article, we ask the shopkeeper to tell the price of the article. This is called unit price. We calculate the price of number of articles, we want to buy, with the help of this unit price. Sometimes, we calculate unit price when the price of a multiple is given.

1 tile in 1/4 foot

So in 4 foot wall the number of tiles = 4/(1/4) = 16 tiles.

Thus 16 tiles will fit end to end on a 4 foot wall.

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Find the term that must be added to the equation x2−6x=7 to make it into a perfect square.

Answers

answer:

+16

steps:

number without the x should be 9

number without the x should be 9c to be 9 needs +16

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divide the number next to the x by 2

-6 divided by 2 is -3

find the square

-3 squared is 9

number without the x should be 9

x²-6x=7

make the equation = 0

x²-6x-7=0

a is the number next x²

b is the number next to x

c is the number without the x

c has to be 9

c is -7

c to be 9 needs +16

x²-6x+9 =0

x²-6x+(-3)² =0

(x-3)²

Answer:

9

Step-by-step explanation:

Completing the square  is a method used to solve the quadratic equation.

 Divide the co efficient of  'x' by 2.

        Coefficient of x is '6'. 6 ÷ 2 = 3

 Square the quotient of  (x ÷ 2)  and add to the both side of the equation.

       3² = 9

            x² - 6x + 9 = 7 + 9

Answer: To make into a perfect square, 9 must be added.

please help me i need to turn this in soon and i don't understand

Answers

Answer:

(a) C=88pi

    A=1936pi

(b) Area

(c) Circumference

Step-by-step explanation:

Circumference formula = 2r(pi)

Area formula = pi(r^2)

Circumference = 2(44)(pi) = 88pi

Area = pi(44^2) = 1936pi

When something is paved it is the whole area not just the border so AREA

The chain will surround the place not fill it up so CIRCUMFERENCE

PLEASE HELP BEST ANSWER GETS BRIANLIST

Answers

Answer:

-3

Step-by-step explanation:

So just like the picture provides, the slope can be defined as: [tex]\frac{\text{change in y}}{\text{change in x}}[/tex]. So this means we can take any two points and find the change in x and y to define the slope, since the slope is constant throughout the entire line, since it's a linear line, meaning it's straight.

So you can use the points (0, 15) and (2, 9). So let's look at the x-values, and you want to make sure, you maintain the order at which you look at the  "change in x", for example I can define the change in x through the two points as 0 to 2, or 2 to 0, one case is 2, and the other is -2, but if I look at the change from 0 to 2, then I looked at the first point first then the second, this means when looking at the y-values I have to find the change from 15 to 9, and not 9 to 15, since I did 0 to 2 in the first case. I could look at the change from 9 to 15, but only if I looked at the changed from 2 to 0.

Anyways let's find the change from 0 to 2, it's 2. Now let's look at the change from 15 to 9, it's -6 (since the value went down). So this gives us equation: -6 / 2 = -3

The slope is -3

write 1/c + 1/d - c-d/cd as a single fraction in its simplest form

Answers

imagine the cd/cd as 1 which is a whole number. then, add the denominators (d+c-cd)/cd

A survey of several 10 to 11 year olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46 Construct the 98% confidence interval for the average amount spent by 10 to 11 year olds on a trip to the mall. Assume the population is approximately normal. Step 3 of 4 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

The 98% confidence interval for the average amount spent by 10 to 11-year-olds on a trip to the mall is 23.36 ± 2.933.

How to calculate the confidence interval and its critical value?

The confidence interval for a given level of percentage is given by

C. I = μ ± Z(σ/√n)

Where,

μ - mean, σ - standard deviation, n - sample size, and z - critical value.

The critical value is calculated by

step 1: 100% - (the confidence level)

step 2: Converting the step 1 result into decimal value

step 3: dividing the step 2 result by 2

This is indicated by α/2. So, from the normal distribution table, the z-value at α/2 is said to be the required critical value and denoted by Z_(α/2) or Z.

Calculation:

It is given that,

A survey of several 10 to 11-year-olds recorded the following amounts spent on a trip to the mall: $18.31,$25.09,$26.96,$26.54,$21.84,$21.46

Sample size n = 6

Step 1: Finding the mean for the given amounts of the survey:

Mean μ = (18.31 + 25.09 + 26.96 + 26.54 + 21.84 + 21.46)/6

             = 23.36

Step 2: Finding the standard deviation:

Standard deviation σ = √summation(x - mean)²/n

On calculating, we get σ = 3.09

Step 3: Finding the critical value:

It is given that the confidence level is 98%

So, (100% - 98%) = 2%

Converting into decimal gives 0.02

So, α/2 = 0.02/2 = 0.01

Thus, at 0.01, the critical value Z = 2.326

Step 4: Constructing the confidence interval:

C.I = 23.36 ± (2.326) × (3.09/√6)

    = 23.36 ± (2.326 × 1.261)

    = 23.36 ± 2.933

So, the lower bound = 23.36 - 2.933 = 20.427

the upper bound = 23.36 + 2.933 =26.293

Therefore, the 98% confidence interval lies from 20.427 to 26.293.

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12 yds
9 yds
3 yds
These triangles are similar. What value is x?
I
yds

Answers

Answer:

x=4

Step-by-step explanation:

the proportion between 9 and 3 is 1/3

so u just apply the fraction to the corresponding side

so 1/3 of 12 is 4

so x is 4

trying to see what my answer would be

Answers

Answer:

B. [tex]2^{-14}*5^{10}[/tex].

Step-by-step explanation:

Use the power of a power property.

[tex](2^{-7}*5^{5} )^{2}[/tex]

Multiply all the exponents in the parenthesis by 2.

[tex](2^{-7}*5^{5} )^{2}=(2^{-14}*5^{10} )[/tex]

The answer is B. [tex]2^{-14}*5^{10}[/tex].

Hope this helps!

A right cylinder and an oblique cylinder have the same radius and the same height. How do the volumes of the two
cylinders compare?
A. The volumes are the same, based on Cavalieri's principle.
B. The volumes are not the same, because Cavalieri's principle does not apply to oblique solids.
C. The volumes are not the same, because the two solids do not have the same cross-sectional
area at every level parallel to the bases.
D. The volumes are not the same, because an oblique solid has less volume thanits corresponding
right solid with the same height.

Answers

Answer:

  A.  The volumes are the same, based on Cavalieri's principle.

Step-by-step explanation:

Cavalieri's principle tells us the volumes of solids will be identical if their cross sectional areas are identical at every height.

Application

A right cylinder and an oblique cylinder of the same height and radius will both have circular cross sections of the given radius at any height. Since the radius is the same, the area of the circle is the same. Hence the requirements of Cavalieri's principle are met, and the cylinders have the same volume.


Use the function f(x) = 5x² + 2x-3 to answer the questions.
Part A: Completely factor f(x). (2 points)
Part B: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part C: Describe the end behavior of the graph of f(x). Explain. (2 points)
Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. (4 points)

Answers

A)f(x)=3/5 and -1.

B)f(x)=(3/5, 0) and (-1, 0).

C)f(x)=(-0.2, -3.2)

D)f(x)= = -0.2.

What is factorization and example?Factorization in mathematics is dividing a large number into smaller ones that, when multiplied together, give you the original number. Factorization is the division of a number into its factors or divisors.For instance, the factorization of the integer 12 might appear as 3 times 4.

Function: f(x) = 5x² + 2x-3.

a) Completely factor f(x)

  f(x) = 5x² + 2x-3.

        = 5x² + 5x-3x − 3

         = 5x(x+1)-3(x+1)

         =(5x-3)(x+1)

f(x)=3/5 and -1.

b)The x-intercepts of the graph of f(x):

    f(x) = 5x² + 2x-3.

At f(x) = 0, the x-intercepts are present.

Therefore, x-intercepts are (3/5, 0) and (-1, 0).

c) The end behavior of the graph of f(x):

      f(x) = 5x² + 2x-3.

The middle of the zeros is the vertex's x-coordinate.

           =-0.2

Find the y-coordinate of the vertex, and substitute the found value of x into the given equation:

   f(-0.2)= 5(-0.2)² + 2(-0.2) − 3

           =-3.2

d)The steps you would use to graph f(x):

The axis of symmetry is the x value of the vertex.

Therefore, the graph is symmetrical at about x = -0.2.

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1) (x-y)(y-2)(x+2) / 2x^2+4yz+6 =
2) 4(x+y)(x-y)(y-x) / t+d+m =
3) ( √25+√9 / 2 ) + √21675 =
4) (9x^2+3x+27)(3+6y)(4+6y) / 1+2a+38+4c+2000z =
5) (x^2+6x+5) / (x+2)(x+6) =
^^^Simplify
6) (xy/m) + (xm/y) - (m/x) = 63 x=
Isolate

Could anyone help me with these?

Answers

See below for the solution to each expression

How to solve the expressions?

Expression 1

The expression is given as:

(x-y)(y-z)(x+z)/(2x^2+4yz+6)

Expand the numerator

(x^2 - y^2 -xz + yz)(x + z)/(2x^2+4yz+6)

Further, expand the numerator

(x^3 - xy^2 - x^2z + xyz + x^2z - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Evaluate the like terms

(x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Hence, the equivalent expression of (x-y)(y-z)(x+z)/(2x^2+4yz+6) is (x^3 - xy^2  + xyz - y^2z - xz^2 + yz^2)/(2x^2+4yz+6)

Expression 2

The expression is given as:

4(x+y)(x-y)(y-x)

Apply the difference of two squares

4(x^2 - y^2)(y - x)

Expand the expressions in the brackets

4(x^2y - x^3 - y^3 + xy^2)

Open the bracket

4x^2y - 4x^3 - 4y^3 + 4xy^2

Hence, the equivalent expression of 4(x+y)(x-y)(y-x) is 4x^2y - 4x^3 - 4y^3 + 4xy^2

Expression 3

The expression is given as:

(√25+√9/2) + √21675

Take the square roots of 25, 9 and 21675

(5 +3/2) + 5√867

Evaluate the sum

13/2 + 5√867

Hence, the equivalent expression of (√25+√9/2) + √21675 is 13/2 + 5√867

Expression 4

The expression is given as:

(9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z

Factor out 3 and 2 from the numerator

3(3x^2 +x + 9) * 3(1 + 2y) * 2(2 + 3y)/1+2a+38+4c+2000z

This gives

18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

The expression cannot be further simplified.

Hence, the equivalent expression of (9x^2+3x+27)(3+6y)(4+6y) /1+2a+38+4c+2000z is 18(3x^2 +x + 9)(1 + 2y)(2 + 3y)/1+2a+38+4c+2000z

Expression 5

The expression is given as:

(x^2+6x+5)/(x+2)(x+6)

Factorize the numerator

(x + 1)(x + 5)/(x + 2)(x + 6)

Hence, the equivalent expression of (x^2+6x+5)/(x+2)(x+6) is (x + 1)(x + 5)/(x + 2)(x + 6)

Expression 6

6) (xy/m) + (xm/y) - (m/x) = 63

Factor out x

x(y/m + m/y) - m/x = 63

Evaluate the sum

x(y^2 + m^2)/y - m/x = 63

Multiply through by xy

x^2(y^2 + m^2) - my = 63xy

Add my to both sides

x^2(y^2 + m^2)  = 63xy + my

The above implies that the variable x cannot be isolated from the equation

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In an algebra class, there are 10 less than twice as many boys as girls. If the total number of students is 38, how many boys and girls are there in class?

Answers

Answer: 16 girls and 22 boys

Step-by-step explanation:

This can be solved with simple algebra.

Let's say that the number of girls is x.

Since there are 10 less than twice as many boys as girls, the number of boys would be 2x-10. (2x for twice as many, and -10 for ten less.)

The total number of students is 38. Adding the girls, the equation is now 3x-10=38.

3x=48

x=16.

2x-10=the number of boys, as said earlier. SO, 32-10=22=the number of boys.

To check our work, add 16+22. This equals 38.

Which of the measurements of triangleBAC are correct

Answers

Answer:

yes

no

yes

Step-by-step explanation:

sin C = opp/hyp = 9/15 yes

tan B = opp/adj = 12/9 no

tan B = 12/9; B = tan^-1 12/9 = 53.13°

Anya was rowing up the river and noticed it takes longer to row upstream than downstream. She knows that in still water she can row 9 mph. She timed herself rowing approximately 4 miles upstream and then back in 1.5 hours. She then calculated the current of the river.

Answers

If the speed of boat in still water iss 9 mph and takes 1.5 miles to go and come 4 miles uptream and downward then the current of the river is 9.24 mph.

Given that the speed in still water be 9 mph, time to travel 4 miles upstream and downward is 1.5 hours.

We are required to find the speed of current of the river.

let the speed of current be c mph.

Effective speed in downstream=9+c

Effective speed in upstream=9-c

Total time=1.5 hours.

Total distance=4 miles.

Time for upstream stream+ time for downward stream=1.5 hours

2/(9+c)+2/(9-c)=1.5

18-2c+18+2c=1.5(9+c)(9-c)

36=1.5(81-[tex]c^{2}[/tex])

36=121.5-1.5[tex]c^{2}[/tex]

1.5[tex]c^{2}[/tex]=121.5-36

[tex]c^{2}[/tex]=85.5

c=9.24 mph.

Hence the speed of the current of the river is 9.24 mph.

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What is the volume of this rectangular prism?
3/2cm
1/2
4 cm

Answers

Answer:

7.62

Step-by-step explanation:

length* width* height = 3/2*1/2*4=7.62 cm


Select the correct answer.
Which expression and quotient does the diagram model?

Answers

The expression (quotient) which is modelled by the given diagram as in the task content is; (x²+x-2)/(x-1) = x +2.

Which expression and quotient is depicted by the diagram model as in the task content?

It follows from the task content that the diagram model in discuss by observation involves a quotient in which case, the division is; (x-1).

Additionally, the dividend in the quotient by observation is the sum of terms as follows;

x² + x +x -x -1 -1 = x²+x -2.

Ultimately, the result of the division according to the model is; (x +2).

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verify commutative property of multiplication and addition 5 4
- -
2 5
then what will the answer of this with prof and detaling

Answers

The commutative property of multiplication addition is illustrated below.

How to illustrate the information?

The commutative property implies that the changing of orders of the numbers doesn't have a effect on the value.

In this case, 5 × 4 = 20. Also, changing them to 4 × 5 is still 20.

Likewise 2 + 5 as 5 + 2 gives 7.

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Identify the segments that are parallel, if any, if ∠EDA≅∠HCB.

Answers

In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

What is the line segment about?

Note that by examining the the image if ∠EDA≅∠HCB, the two lines can never intersect even if they go a longer distance.

The reason why is that there are no parallel lines on it and as such, they cannot intercept.

Hence, In the above question, (image attached) The option that shows the segments that are parallel, if any, if ∠EDA≅∠HCB is option A: None of these.

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a brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. the brick has a density of 2.7 grams per cubic centimeter. find the mass of the brick to the nearest gram a brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches. the brick has a density of 2.7 grams per cubic centimeter. find the mass of the brick to the nearest gram

Answers

The mass of brick is 2478 gram.

What is a rectangular prism?

A rectangular prism has a total of 6 faces, 12 sides, and eight vertices. Like a cuboid, it has three dimensions- the base width, the height, and the length. The top and base of the rectangular prism are rectangular in shape. The pairs of opposite faces of a rectangular prism are identical or congruent.

A brick is in the shape of a rectangular prism with a length of 8 inches, a width of 3.5 inches, and a height of 2 inches.

The volume of rectangular prism = length×width×height

                                                        = 8×3.5×2

                                                        = 56

Thus volume of brick is 56 cubic inches.

Convert inches to centimeter

1 inch = 2.54 centimeter

Therefore,

56 cubic inches = 56 x 2.54 x 2.54 x 2.54 cubic centimeter

56 cubic inches = 917.676 cubic centimeter

Thus, we get,

volume of a rectangular prism = 917.676 cubic centimeter

The brick has a density of 2.7 grams per cubic centimeter

Density = 2.7 grams

The mass of brick is given by formula = density × volume

[tex]\Rightarrow[/tex]                                                            = 2.7 × 917.676

[tex]\Rightarrow[/tex]                                                            = 2477.72

[tex]\Rightarrow[/tex]                                                            ≅ 2478  

Thus mass of brick is 2478 gram.

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Which table represents a quadratic function?

Answers

Answer:

  A  (see attached)

Step-by-step explanation:

There are a couple of things you can look for to see if a table represents a quadratic function:

do the values increase, then decrease, or vice versado the differences have a constant difference.

Observation

In the first of the given tables, the f(x) values start out decreasing, and end up increasing. This is a good indication the table represents a quadratic function.

In the remaining tables, the f(x) values are always increasing.

table 2: differences are always +2 (linear function)table 3: differences are always +4.5 (linear function)table 4: table values have a common ratio of 2 (exponential function)

Analysis

The f(x) values in table 1 have differences of ...

  -3, -1, 1, 3

These values have differences of ...

  2, 2, 2

The constant "second differences" mean that the function can be represented by a 2nd-degree polynomial, a quadratic. In fact, the equation for this table is ...

  f(x) = x² +2

help please its khan academy

Answers

6t = 9
i’m not sure if this is correct but it seems like it

Based on the graphs of the equations y = x + 7 and y = x2 – 3x + 7, the solutions are located at points:

Answers

The correct option is A. (4, 11) and (0, 7).

The solution of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points: (4, 11) and (0, 7).

What is the system of linear equation?

Estimate the y-intercept, slope, and express the equation in the form of the y-intercept (y = mx + b) to find the graphed equation. The slope is the difference between the y- and x-axis values.

A graph equation is an equation in graph theory where the unknown is a graph. Isomorphic ideas are one of the key issues in graph theory.

The equations are; y = x + 7 and y = x² - 3x + 7

At the solution, the u-values are equal, which gives;

y = y

x + 7 = x² - 3·x + 7

x² - 3·x + 7 - (x + 7) = 0

x² - 4·x = 0

x·(x - 4) = 0

x = 4, or x = 0

When x = 4, y = 4 + 7 = 11

When x = 0,

         y = 0 + 7 = 7

Therefore, the solution for the equations  y = x + 7 and y = x² - 3x + 7 are are located at points: (4, 11) and (0, 7).

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The complete question is-

Based on the graphs of the equations y = x + 7 and y = x² – 3x + 7, the solutions are located at points:

A. (4, 11) and (0, 7)

B. (4, 11) and (–7, 0)

C. (–7, 0) and (1.5, 4.75)

D. (1.5, 4.75) and (0, 7)

Complete the following conversions. i) 1 m2 = a cm2 ii) 1 cm2 = b mm2 iii) 1 km2 = c m2

Answers

The values that complete the conversions are

a = 10000

b = 100

c = 1000000

Conversion of units

From the question, we are to complete the given conversions

i)

1 m² = a cm²

NOTE: 1 m² =  10000 cm²

∴ a = 10000

ii)

1 cm² = b mm²

NOTE: 1 cm² = 100 mm²

∴ b = 100

iii)

1 km² = c m²

NOTE: 1 km² = 1000000 m²

∴ c = 1000000

Hence, the values that complete the conversions are

a = 10000

b = 100

c = 1000000

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Emma has money in two savings accounts. One rate is 6% and the other is 14%. If she has $950 more in the 14% account and the total interest is $342, how much is invested in each savings account?

Answers

The amount invested in the account that has a rate of 14% is $1767

The amount invested in the account that has a rate of 6% is $1425.

What are the linear equations that represent the question

0.06a + 0.14b = 342 equation 1

b - a = $950 equation 2

Where:

a = amount invested in the account that has a rate of 6%

b =  = amount invested in the account that has a rate of 14%

How much was invested in each account?

Multiply equation 2 by 0.06

0.06b - 0.06a = 57 equation 3

Subtract equation 3 from equation 2

285 = 0.2a

a = 285 / 0.2

a = 1425

Substitute for a in equation 2

b - 1425 = 342

b = 1425 + 342

b = $1767

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The sine, cosine, cosecant, and secant functions have period _______; the tangent and cotangent functions have period _______.

Answers

The sine, cosine, cosecant, and secant functions have period 2π; the tangent and cotangent functions have period π.

Definition for Period of a Trigonometric Function :

The pause between any function's repetitions is known as the function's period. The duration of one complete cycle is the period of a trigonometric function. Trigonometric functions include three basic types: sin, cos, and tan, which have periods of -2π, 2π, and π respectively.

If a function repeats itself repeatedly at a predetermined frequency, it is said to be periodic. The formula for t is f(x) = f(x + p), where p is a real number that denotes the period of the function. Period is the interval between two occurrences of the wave.

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