Q5.
The diagram shows a rectangle.
B=(x + 4) cm
H=(x-5) cm
The area of the rectangle is 90 cm².
Set up and solve a quadratic equation to work out the value of x.

The 45° and 55° base angles of the triangle that share a vertex with the inverted triangle that have the vertex angle (at the shared vertex) marked x, indicates that x is 80°

A shared vertex is a common point to two or more figures that is also a vertex to the figures that share the point.

The measure of the vertex angle of the triangle at the top which is inverted = x

The measure of the base angles of the triangle at the bottom are;

45° and 55°

The measure of the vertex angle of the triangle at the base = y

From the diagram of a similar question, angle x and angle y are vertical angles (angle x and angle y are formed by the intersection of two lines)

45° + 55° + y = 180° (angle sum property of a triangle)

y = 180° - (45° + 55°) = 80° (subtraction property of equality)

y = 80°

x ≅ y (vertical angles theorem)

x = y (definition of congruent angles)

x = 80° (substitution property of equality)

The measure of angle x is 80°

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If the dimensions of a right rectangular prism are (8)/(5)cm,(10)/(3)cm, and (7)/(4)cm. Then volume of the prism is 401/60 cm³

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A rectangular prism is a three-dimensional solid shape with six faces that including rectangular bases

The dimensions of a right rectangular prism are width is 8/5 cm, Length is 10/3cm and Height is 7/4cm

Volume=Width×Height×Length

=8/5×10/3×7/4

=96+200+105/60

=401/60 cm³

Hence volume of the right rectangular prism is 401/60 cm³

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Using the GCF to factor and the distributive property 28 + 24 = 4(7 + 6)

28 + 24 as a product of the two factors using greatest common factor and the distributive property can be represented as follows:

The greatest common factor is defined as the largest number that is a factor of two or more numbers.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

Therefore, lets solve 28 + 24 using GCF and the distributive property.

The GCF of 28 and 24 is 4. Hence,

28 + 24 = 4(7 + 6)

Therefore,

28 + 24 = 4(7 + 6)

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We must combine 3 servings of Ta-sty Pocket, 2 serving of P-ita Roll, and 1 serving of In-sta Pancake to get 754 calories, 19.2 g of f-at, and 78.9 g of carbohydrates.

According to the question,

Three brands of breakfast food represents the calories , f-at, and carbohydrates.

To get 754 calories, we should combine

= 450 + 238 + 66

= 3 (150) + 2 ( 119) + 1 (66)

= 3 serving of Ta-sty Pocket + 2 serving of P-ita Roll + 1 serving of In-sta Pancake

To get 19.2g of f-at, we should combine

= 14.4 + 4.6 + 0.2

= 3(4.8) + 2( 2.3) + 1(0.2)

= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake

To get 78.9 g of carbohydrates, we should combine

= 29.4 + 28 + 21.5

= 3(9.8) + 2( 14) + 1 (21.5)

= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake

Hence, we should combine 3 serving of Tasty Pocket, 2 serving of P-ita Roll, 1 serving of In-sta Pancake

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The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

In the question ,

it is given that ,

the equation is given as |y [tex]+[/tex] 6| [tex]=[/tex] 2 ,

after removing the modulus  , we get the two equations , that are

y + 6 = 2 and y + 6 = -2

Solving y + 6 = 2 , we get

y + 6 = 2

Subtracting 6 from both LHS and RHS ,

we get

y = 2 - 6

y = -4

On Solving y + 6 = -2 ,

we get

y + 6 = -2,

Subtracting 6 from both LHS and RHS ,

we get

y = - 2 - 6

y = -8 .

the two solutions are y = -8 and y = -4 .

Therefore , The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

The given question is incomplete , the complete question is

Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply.

(a) There will be one solution

(b) There will be two solutions.

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Answer:

8

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so:

[tex]\frac{A'B'}{12}=\frac{4}{6} \implies A'B'=8[/tex]

Using the given inequality we can calculate that this is equivalent to

(B) x ≤-1 or x ≥1

The given inequality is |8x| ≥ 2 .

Now we have to solve this inequality to find the range of the value of x.

|8x| ≥ 2

now we will try to remove the modulus function.

either 8x ≥ 2 ⇒ x ≥ 1/4

or, -8x ≥ 2 ⇒ x ≤ -1/4

Therefore the solution of the inequality is x ≤ -1/4 or x ≥ 1/4

Now of the given options the most plausible option or inequality that also satisfies this inequality is given by B)  x ≤-1 or x ≥1

In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On the number line, size comparisons between two numbers are typically conducted.

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The price of one sweater - x

The price of one shirt - y

From what the problem states, we can assume:

x + 4y = 55

4x + 5y = 110

Multiply both sides of x +4y = 55 by four. This results in 4x + 16y = 220. We then subtract 16y on both sides, resulting in 4x = 220 - 16y. We then insert this into the other equation, which, as a reminder, is 4x + 5y = 110. We replace 4x with 220 - 16y, which results in 220 - 16y + 5y = 110. Now, we can solve it.

Now that we have found out the value of y, we can replace all instances of y in the first equation.

According to the Pythagoras theorem, the value of the slope of the ramp is 10.44

Pythagoras theorem

Pythagoras theorem states that the sum of squares of the sides equal to the square of the hypotenuse.

The general form of the Pythagoras theorem is,

c² =  a² + b²

where

c refers the hypotenuse

a and b refers the sides of the triangle.

Given,

Here we have the ramp with the side values 3 and 10.

Now, we have to find the value of the slope.

Let us consider x be the hypotenuse or slope of the ramp.

We know that the Pythagoras theorem states that the square of the hypotenuse is equal to the sum of square of the sides.

So, it can be written based on these,

x² = 3² + 10²

x² = 9 + 100

x² = 109

x = √109

When we simplify this one then we get the value of slope as 10.44.

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The polar form of the complex number z = - 2√3 - i 6 is z = (4√3) · (cos 4π / 3 + i sin 4π / 3). (Correct choice: D)

Complex numbers are numbers of the form z = a + i b, where a and b are real numbers. This form is known as rectangular form. The polar form equivalent to that number is:

z = r · (cos θ + i sin θ)

Where:

The norm and the direction of the complex number are, respectively:

r = √(a² + b²)

θ = tan⁻¹ (b / a)

If we know that a = - 2√3 and b = - 6, then the polar form of the complex number is:

r = √[(- 2√3)² + (- 6)²]

r = 4√3

θ = tan⁻¹ [(- 6) / (- 2√3)]

θ = 4π / 3

z = (4√3) · (cos 4π / 3 + i sin 4π / 3)

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Answer:Yes, the obtuse angles for both triangles are equailateral

Step-by-step explanation:

Using Euler'formula, the difference between maximum and minimum possible numbers of faces is 96.

A polyhedron is a 3D shape with flat faces, straight edges, and sharp vertices (corners). "polyhedron" meaning "many" and "polyhedron" meaning "area". Therefore, when many planes are joined, they form a polyhedron.

Because all faces are triangles. So on a triangular base with triangular faces on both sides that meet at the vertex.

Therefore, the minimum number of triangular faces of a regular polyhedron is = 4

Next, the double pyramid has "2n" triangular faces. where n is a natural number greater than 2 and 'n' represents the number of sides of the base of the pyramid.

A polyhedron having equal quadrilateral faces is known as regular hexahedron.

quadrilateral faced polyhedron with total sides 100 and vertices 6 , then using Euler's formula

F + V-E = 2

=> F + 6- 100= 2 => F = 96 maximum faces possible = 96

Now the difference between maximum and minimum number of faces = 100 - 4 = 96

So the difference between maximum and minimum faces is 96.

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Answer:

9:5

5:14

Step-by-step explanation:

We know that:

                      x = 10 + y

In the next equation {-3x + y = -28}  x is the same as the first, so:

-3(10 + y) + y = -28

-30 - 3y + y = -28

-30 - 2y = -28            

We add 30 to both sides:

-2y = 2

and divide both sides by (-2):

y = -1

Now we can put y = -1 to the first equation:

  x = 10 + y

  x = 10 - 1

   x = 9

So,

Solving for f(-2) in the function f(x) = 3x^2 + 2x + 4 gave the solution

From the given function f(x) = 3x^2 + 2x + 4 we substitute for x = -2  which is same as function of -2

f(x) = 3x^2 + 2x + 4

pugging in x = -2

f(-2) = 3(-2)^2 + 2(-2) + 4

solving the squared and opening the parentheses

f(-2) = 3 * 4 + -4 + 4

f(-2) = 12 - 4 + 4

f(-2) = 12

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Answer:

540= 2x2x3x3x3x5

       or

540= [tex]2^{2}[/tex]x[tex]3^{3}[/tex]x5

Step-by-step explanation:

The AER on the savings account, based on the interest rate and the period it is paid is 8.16%

The AER stands for Annual Equivalent Rate which shows the periodic rate of an interest rate, based on the number of compounding periods of the savings account or investment.

The formula for Annual Equivalent Rate (AER) is:

= ( 1 + interest rate / number of payment or compounding periods) ^ number of payment or compounding periods - 1

The AER on the savings account is therefore:

= ( 1 + 8% / 2 semi annual periods) ² - 1

= 0.0816

= 8.16%

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Answer:

5u - 4u = 1u

1u = 15

9u = 135

∴ Both girls have 135 yo-yos together.

Answer:

Step-by-step explanation

TS=13 as opp sides in an isosceles triangle are equal

AngleT=60

as 60+60+T=180

Answer:

======================

Sum of interior angles of 6-sides polygon is:

Set equation for the sum of interior angles and solve for x:

Find the measure of angle L:

Correct choice is C.

[tex]\underset{in~degrees}{\textit{sum of all interior angles}}\\\\ S = 180(n-2) ~~ \begin{cases} n=\stackrel{number~of}{sides}\\[-0.5em] \hrulefill\\ n=6 \end{cases}\implies S=180(6-2)\implies S=720 \\\\[-0.35em] ~\dotfill\\\\ (120)+(8x)+(6x-7)+\stackrel{\measuredangle L}{(7x-3)}+(5x)+\stackrel{\measuredangle O}{(90)}=720\implies 26x+200=720 \\\\\\ 26x=520\implies x=\cfrac{520}{26}\implies x=20~\hfill \underset{\measuredangle L}{\stackrel{7(20)~~ - ~~3}{\text{\LARGE 137}}}[/tex]

The complex number in rectangular form is 17√2 / 2 - i 17√2 / 2. (Correct choice: A)

In this problem we have a complex number in polar form, whose formula is described below:

z = r · (cos θ + i sin θ)

Where:

And the rectangular form of the complex number is represented by:

z = a + i b, where a = r · cos θ and b = r · sin θ.

If we know that r = 17 and θ = 315°, then the rectangular form of the complex number is:

a = 17 · cos 315°

a = 17√2 / 2

b = 17 · sin 315°

b = - 17√2 / 2

The rectangular form of the complex number is 17√2 / 2 - i 17√2 / 2.

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The values of x and y will be 10 and 4 respectively, using congruent of the triangle.

What is congruent of the triangle?

The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.

Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."

Here, ΔRWS ≅ ΔTUV

Here 2y + 10 = 30

2y = 30-10

y=20/2

y=10.

Agian ∠R = ∠T

Here ∠T = 90 -32 =58°

So 8x+26 = 58°

8x = 58-26

x = 32/8

x = 4.

Hence the values of x and y will be 10 and 4 respectively.

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The total number of votes which is reduced by the ratios of yes and no votes will be: 4580; + 6412 = 10992;

What are Ratios?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the part to the whole is 5: 10, meaning that 5 out of every 10 people enjoy reading.

In the given question, we have:

The ratio of yes votes to no votes was 7 to 5.

Total Number of Yes votes = 6412;

So, Let us assume the total number of no votes be x;

So, according to the question,

[tex]\frac{7}{5} = \frac{6412}{x}[/tex]

Cross Multiplying the terms:

⇒7 × x = 6412 ×5

⇒x = 4580;

So, The total number of no votes is 4580;

So, The total number of votes will be: 4580; + 6412 = 10992;

Hence,

The total number of votes will be: 4580; + 6412 = 10992;

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Answer: 16\/729

Step-by-step explanation:

Answer:

six raised to the fourth power divided by three raised to the tenth power

Step-by-step explanation:

(6^−2 • 3^5)^−2 = 6^(-2*-2) * 3^(5*-2) = 6^4 * 3^(-10) = 6^4 / 3^10

Answer:

4 or -8

Step-by-step explanation:

180-148=x(x+4)

32=x^2 + 4x

x^2 +4x - 32

x = 4 or -8

Answer:

∠DEA
I think, adjacent means "next to, or adjoining something else."
Since ∠BEC, and ∠DEA are sharing point E, I think they are adjacent.

(I haven't done this kind of math in forever..)

12x³ - 39x² -   111x + 30 is polynomial in standard form .

What in mathematics is a polynomial?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents.

standard form g(x) = 3(x + 2)(4x - 1)(x - 5)

                      g(X) = 3[ 4x² - x + 8x - 2 )( x - 5 ) ]

                             = 3[ ( 4x² + 7x - 2 ) ( x - 5 )]

                             = 3 [ 4x³ + 7x² - 2x - 20x² - 35x + 10 )]

                             = 3[ 4x³ - 13x² - 37x + 10 ]

                             = 12x³ - 39x² -   111x + 30

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The GCF: x

answer: x(x+2)

Answer:

[tex]\frac{13}{4}[/tex]

(Decimal: 3.25)

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)

Answer:

5.25

Step-by-step explanation:

1/4+1/3(10-1)

*do what's in parenthesis first!*

10 - 1 = 9

1/4 + 1/3 = 7/12

then you multiply 7/12 x 9 = 5.25

DONT FORGET!

Please Excuse My Dear Aunt Sally

P  E M D A S

Answer:

$250

Step-by-step explanation:

He expected to collect 37.5% less than $400.

First, we find 37.5% of $400.

Then we subtract that amount from $400.

37.5% of $400 is:

37.5% of $400 = 0.375 × $400 = $150

Now, subtract $150 from $400:

$400 - $150 = $250

Answer: $250