The figure below shows a square ABCD and an equilateral triangle DPC:

ABCD is a square. P is a point inside the square. Straight lines join points A and P, B and P, D and P, and C and P. Triangle D

Ted makes the chart shown below to prove that triangle APD is congruent to triangle BPC:

Statements Justifications
In triangles APD and BPC; DP = PC Sides of equilateral triangle DPC are equal
In triangles APD and BPC; AD = BC Sides of square ABCD are equal
In triangles APD and BPC; angle ADP = angle BCP Angle ADC = angle BCD = 90° so angle ADP = angle BCP = 60°
Triangles APD and BPC are congruent SAS postulate
What is the error in Ted's proof? (1 point)

He writes the measure of angles ADP and BCP as 60° instead of 45°.
He uses the SAS postulate instead of AAS postulate to prove the triangles congruent.
He writes the measure of angles ADP and BCP as 60° instead of 30°.
He uses the SAS postulate instead of SSS postulate to prove the triangles congruent.

a) The person will save $15,120 by the day before his 60th birthday. b) David would have had £2000 when he is 37 years old.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

a) Let x be a number of months.

Now, we will find a number of years between 60 and 18 years.

There will be 42 years from 18th birthday to 60th birthday.

Now, we will convert 42 years into months.

42 × 12 = 504

In order to find the total amount saved in 504 months, we will substitute  in expression:

30x = 30(504) = 15120

Hence, the person will save $15,120 by the day before his 60th birthday.

b) David starts saving £100 annually from his 18th birthday

We would save £2000 after

(2000/100) years = 20 years

Since his 18th birthday is the first of the 20 years and so he will save £950 for the next 19 years, which is

18 + 19 = 37 years old

Hence, David would have had £2000 when he is 37 years old.

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Answer:

B. False

Step-by-step explanation:

Just like last time, solve it first to check.

128(4+2)=(128/4)+2

Remember PEMDAS, parenthesis first.

128(6)=(32)+2

Now multiply the left side and add the right side.

128*6=768. The star sign is just another way to write a multiplication sign.

32+2=34

768≠34

This is a false statement. 768 does not equal 34.

Hope this helps!

If not, I am sorry.

The solution of the equation is x=3 or x=-5.

Given that the equation is (x+2)²-2(x-+2)-15=0 and use u substitution method to solve.

Let's assume that the (x+2)=u.

The given equation is rewritten as u²-2u-15=0.

Factorize the quadratic equation by adding or subtracting two number that gives the sum of -2u and product 15u² as

u²-5u+3u-15=0

u(u-5)+3(u-5)=0

Taking out (u-5) as common and get

(u-5)(u+3)=0

Compare each equation with 0 and get

u-5=0 or u+3=0

u=5 or u=-3

Performing back substitution by substituting the values of u in x+2

when u=5 then x is

x+2=5

x=3

And when u=-3 then x is

x+2=-3

x=-5

Hence, the solutions of the (x+2)²-2(x-+2)-15=0 is x=3 and x=-5.

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Answer:X=-5 and X=3

Step-by-step explanation:

Anne will walk a distance of 7 km, and she takes 2 hours to walk that distance.

The total distance is 18.5 km.

She travels 10km by train and 1.5km by bus, for a total of 11.5km.

The distance that she walks is given by:

18.5km - 11.5km = 7km

So she walks for a distance of 7 km, at a speed of 3.5km per hour.

Remember the relation:

distance = time*speed

That can be rewritten to:

time = distance/speed.

Then the time that she walks is given by:

T = (7 km)/(3.5 km/hour) = 2 hours

She walks for 2 hours.

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Answer:

EF = 2.9

Step-by-step explanation:

The geometric figures are similar so we can use the similarity ratio to calculate the length of EF:

GF/ CB = EF/AB

5/29 = EF/17 cross multiply expressions

29EF = 85 divide both sides by 29

EF = 2.9 approximately

Answer:

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. Each of these equations on their own could have infinite possible solutions.

Answer:

a = 2.36

Step-by-step explanation:

a-(-3.75)=6.11

The negative 3.75 is being subtracted from the 'a'. A negative number being subtracted from another number makes it positive. So, 3.75 is actually being added to 'a' which is equal to 6.11

I re-wrote the question as:

a + 3.75 = 6.11

Subtract 3.75 from both sides to leave 'a' by itself

a + 3.75 = 6.11

   -3.75    -3.75

a = 2.36

Answer:

initial hieght = 72.4 cm

final hieght = 86.2 cm

change in hieght = 9.8 cm

percentage increase = (9.8 ÷ 72.4 ) * 100 = 13.59 %

Answer:

Given:  L is the midpoint of [tex]\overline{JM}[/tex]  (given)

[tex]\overline{JL} =\overline{LM}[/tex]  (definition of a midpoint)

Given:  [tex]\overline{JK} \parallel \overline{NM}[/tex]  (given)

[tex]\angle KJL \cong \angle NML[/tex] (alternate interior angles theorem)

[tex]\angle JKL \cong \angle MNL[/tex] (alternate interior angles theorem)

[tex]\triangle JKL \cong \triangle MNL[/tex]  (SAA postulate)

(I have also created it in table form and attached a screenshot)

Answer:

6x-4

Step-by-step explanation:

3x•2= 6x

-2•2=-4

-------------------------------------------------------------------------------------------------------------

Answer:  [tex]\textsf{9x}^2\textsf{ - 12x + 4}[/tex]

-------------------------------------------------------------------------------------------------------------

Given:  [tex]\textsf{(3x - 2)}^2[/tex]

Find: [tex]\textsf{Simplify the expression}[/tex]

Solution:  It looks like 2 is at the end of the parenthesis where the power would be instead of distributing the number.  If so the following steps would be followed.

Expand

Simplify

Therefore, after following the provided information we are able to determine that the expanded form would be 9x^2 - 12x + 4.

Answer:

[tex] log_{b}(x) - log_{b}(y) [/tex]

Answer:

the answer is L

Step-by-step explanation:

that's just how u round

Answer:

3497.47 feet

I think it's the answer because when you look where I've drawn...that's where the angle of depression is and 6600 is the hypotenuse, so you use the sine method where you have opposite over hypotenuse

[tex] \sin(32 = opposite \6600) [/tex]

and you'll get your answer as 3497.47

Answer:

(x+6)(y+3)

Step-by-step explanation:

Function: y = 3x - 2

To find x-intercept, set [y = 0]:

[tex]\rightarrow \sf 3x - 2 = 0[/tex]

[tex]\rightarrow \sf 3x = 2[/tex]

[tex]\rightarrow \sf x = \dfrac{2}{3}[/tex]

The x-intercept: (2/3, 0)

To find y-intercept, set [x = 0]

[tex]\rightarrow \sf y = 3(0) - 2[/tex]

[tex]\rightarrow \sf y = - 2[/tex]

The y-intercept: (0, -2)

When [y = 5], x is:

[tex]\rightarrow \sf 3x - 2 = 5[/tex]

[tex]\rightarrow \sf 3x = 5 + 2[/tex]

[tex]\rightarrow \sf 3x = 7[/tex]

[tex]\rightarrow \sf x = \dfrac{7}{3}[/tex]

[tex]\rightarrow \sf x = 2 \dfrac{1}{3}[/tex]

Value of x is 2.33...

When [x = 0.5], y is

[tex]\rightarrow \sf y =3(0.5) - 2[/tex]

[tex]\rightarrow \sf y =-0.5[/tex]

Value of y is -0.5

Graph shown:

The tension in both cables are calculated as; T₁ = 127.63 N and T₂ = 185.48 N

Resolving forces in the y direction gives us;

T₁ sin 29° + T₂ sin 53° = 210  ------(eq 1)

Resolving forces in the horizontal direction gives;

T₁ cos 29° = T₂ cos 53°   ----(eq 2)

T₁ = T₂ cos 53°/cos 29°

Thus;

(T₂ cos 53°/cos 29°)sin 29° + T₂ sin 53° = 210  

0.3336T₂ + 0.7986T₂ = 210

T₂ = 210/1.1322

T₂ = 185.48 N

Thus;

T₁ = 185.48 cos 53°/cos 29°

T₁ = 127.63 N

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Inequalities help us to compare two unequal expressions. The correct option is B.

Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed.

It is mostly denoted by the symbol <, >, ≤, and ≥.

The solution to two systems of inequalities in the region where the area of the two inequalities overlaps. As it can be observed in this case that the overlap area is B.

Hence, the correct option is B.

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The surface area of a hexagonal prism willl be 251.13844 cm².

The total land area of all the faces of a three-dimensional object is its surface area. When we wish to wrap something in real life, we employ the notion of surface areas of distinct things.

A=6ah+3√3a²

A=6×4×7+3√3×4²

A≈251.13844

Hence the surface area of a hexagonal prism willl be 251.13844 cm².

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The Chee has to pay $35 to the pizza shop if she bought 12 slices of pizza this month and for x slices, the cost would be ($1.25x + 20)

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have:

The membership costs $20 per month and members get a discounted price of $1.25 per slice of pizza.

Cost for 12 slices = 12×1.25 = $15

Total cost = 20 + 15 = $35 (for this month if  she bought 12 slices of pizza)

The monthly cost for x slices of pizza:

= 1.25x + 20

x is the number of slices

Thus, the Chee has to pay $35 to the pizza shop if she bought 12 slices of pizza this month and for x slices, the cost would be ($1.25x + 20)

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Usando la fórmula de combinación, se encuentra que hay 35 manerias distintas de ocupar esos asientos.

El orden en que se sientan las personas no es importante, por lo que se utiliza la fórmula de combinación para resolver este problema.

[tex]C_{n,x}[/tex] es el número de combinaciones diferentes de x objetos de un conjunto de n elementos, dado por:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

3 personas son selecionadas de un conjunto de 7, por eso, el número de maneras es dado por:

[tex]C_{7,3} = \frac{7!}{3!4!} = 35[/tex]

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Peter should buy 0.4 pound weight package

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct," "pct," and occasionally "pc" are also used, the percent sign, " percent ", is frequently used to signify it. A % is a number without dimensions and without a measurement system.

Given Peter's father told Peter to buy four-tenths of a pound of chili powder and Each package is marked with its weight.

We have to find which weight package should Peter buy

The four-tenths of a pound will be 40 % of one pound which is 0.4 pound. So peter should buy 0.4 pound weight package.

Hence Peter should buy 0.4 pound weight package

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An equation is formed when two equal expressions. There are 21 $20 bills and 24 $5 bills.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the number of $5 bills be x, while the number of $20 bills be y.

Given there were 3 more $5 bills than $20 bills. Therefore, this can be represented as

x = y + 3

Also, The total worth of the dominations is $540. Therefore, we can write,

5x + 20y = 540

Substitute the value of x form the first equation,

5x + 20y = 540

5(y+3) + 20y = 540

5y + 15 + 20y = 540

25y = 525

y = 21

Substitute the value of y in the first equation,

x = 21 + 3

x = 24

Hence, there are 21 $20 bills, and 24 $5 bills.

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Answer:

[tex]6x^3+3x^2y+2xy+y^2[/tex]

Step-by-step explanations:

[tex](2x+y)(3x^2+y)\\2x*3x^2+2xy+3x^2y+y*y - Distribute\\6x^3+3x^2y+2xy+y^2 - Simplify[/tex]

Answer:

6x^3 + 2xy + 3x^ 2y + y^2

Step-by-step explanation:

Apply the distributive property of multiplication.  First multiply (3x^2 + y) by 2, obtaining 6x^3 + 2xy, and then multiply (3x^2 + y) by y, obtaining

3x^2y + y^2.  Finally, combine like terms (if any) in these two results:

6x^3 + 2xy + 3x^ 2y + y^2

Answer:

D

Step-by-step explanation:

I looked at the vertical asymptotes. -1 and 2. from the knowledge I have the answer with x=-1, 2 is D.

Answer:

d. 15

Step-by-step explanation:

Let A and C be the initial number of marbles Ali and Cho have, respectively.

We are told that:

A = 3C  [Ali had 3 times as many marbles as cho does]

We then discover that  

C-4 = A-18   [After cho gives 4 marbles to Ali, Ali has 18 more marbles than cho does]

How many more marbles does cho have in the beginning?

We have 2 equations and 2 unknowns (A and C).  That means we can likely rearrange one of the equations and isolate one unknown on the left, and then use that in the second equation.

The first equation already has one of the unknowns isolated (A) so I'll use that in equation 2.

Eq. 1:   A = 3C

Eq. 2:  C-4 = A-18

Use the definition of A from Eq. 1 (=3C) to replace A in Eq. 2:

Eq. 2:  C-4 = A-18

          C-4 = (3C)-18    [Replace A with 3C, as promised in E1q. 1]

        -2C = -14

            C=7

If C = 7, then from Eq. 1,  A = 21

In the beginning, Ali has 21 marbles and Cho has 7.

Cho has 15 more marbles than Ali in the beginning.

a. 5

b. 9

c. 10

d. 15

The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is [tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]

The expression given is [tex]9^{1/3}=\sqrt[3]{9}[/tex].

The equation that justifies [tex]9^{1/3}=\sqrt[3]{9}[/tex] is as follows:

Therefore, using indices law,

[tex]a^{x/y} =\sqrt[y]{a^{x} }[/tex]

Hence,

[tex]9^{1/3}=\sqrt[3]{9}[/tex]

Therefore, the equation that shows it is correct is as follows;

[tex](9^{1/3}) ^{3} = 9^{3/3} = 9[/tex]

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