w and x are whole numbers
w>60
x<50
Work out the smallest possible value of x-z

Answer:

y = 16.5 ft

Step-by-step explanation:

• in the right triangle BCD :

cos(∠BCD) = 8/14

________

• In the right triangle ABC :

cos(∠BCA) = 14/(8+y)

________

Since ∠BCD and ∠BCA are the same one

then

cos(∠BCD) = cos(∠BCA)

Therefore

[tex]\frac{8}{14} =\frac{14}{y+8}[/tex]

[tex]\Longleftrightarrow 8(y+8)=14^2[/tex]

[tex]\Longleftrightarrow 8y+64=196[/tex]

[tex]\Longleftrightarrow 8y=196-64[/tex]

[tex]\Longleftrightarrow 8y=132[/tex]

[tex]\Longleftrightarrow y=\frac{132}{8}[/tex]

[tex]\Longleftrightarrow y=16.5[/tex]

The single transformation that will cause the same effect as that of these two transformation is  the reflection of shape in the x-axis .

(x,y) -----------> (x,−y)

The change done to a shape on a coordinate plane by reflection ,translation and rotation is a called Transformation .

It is given that a shape is rotated to its origin

Then its image is reflected in the y axis.

The single transformation that would have the same result as the two transformations is (x,y) to (x,−y)

reflection of shape in x-axis .

The x stays the same, but the y changes sign.)

The change caused by Rotation by 180° about the origin,

(x,y) ------->  (−x,−y)

The change caused when reflected in the y-axis,

(x,y) --------> (−x,y)

Therefore the single transformation that will cause the same effect as that of these two transformation is  the reflection of shape in the x-axis .

(x,y) -----------> (x,−y)

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The new equation will become f(x) = 3([tex]2^{x}[/tex]).

The given information is the stretch factor which is 3 and the equation f(x)=[tex]2^{x}[/tex].

When there is a vertical strecth factor, you need to multiply the equation by the stretch factor.

By stretching the function, the value of y has to be multiplied by 3, will now be equal to 3f(x)

The new equation will become f(x) = 3([tex]2^{x}[/tex]).

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Answer:

No Solutions.

Step-by-step explanation:

original equation

3x+13 = 3(x+6)+1

distribute 3

3x+13 = 3x+18+1

simplify

3x+13 = 3x+19

since the slope is the same for both equations and the y-intercept is different the two equations are parallel meaning they will never intersect so there are no solutions.

Answer:

No solutions

Step-by-step explanation:

3x + 13 = 3 (x + 6) + 1

3x + 13 = 3x + 18 + 1

3x + 13 = 3x + 19

3x + 13 = 3x + 19 meaning no solution since they aren't equivalent to each other

It is impossible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.

A rule of inference in propositional logic and virtually every other deduction system is referred to as disjunction introduction.

It is right to state that it is not possible to use a disjunction introduction to derive any other type of formula besides disjunctive formulas.

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Answer:

7

Step-by-step explanation:

You were correct in setting the equation equal to 0 because the problem is asking for when the rock hits the ground and in this problem, you may  assume that the ground is y=0, unless the problem says otherwise.

Ok so where you went wrong is that when you factored out and got

(x-7)(x+2), which is correct, you forgot to set these equal to zero (because your actual equation is set to zero). So you should have

x-7 = 0

and

x+2 = 0

and this gives the actual answers +7 and -2. And since time cant be negative its 7 seconds.

This was a silly mistake and happens a lot more often than you think, so I wouldn't worry too much but make sure you practice more, better to lose points on harder questions than easy ones.

Good luck with your exam !

Answer:

7 seconds

Step-by-step explanation:

Given function:

[tex]y=-2x^2+10x+28[/tex]

where:

To find the time when the rock hits the ground, set the equation to zero and solve for x.

First, simplify by factoring out the common term  -2:

[tex]\implies -2(x^2-5x-14)=0[/tex]

Divide both sides by -2:

[tex]\implies x^2-5x-14=0[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b.

[tex]\implies ac=1 \cdot -14=-14[/tex]

[tex]\implies b=-5[/tex]

Therefore, the two numbers that multiply to -14 and sum to -5 are: -7 and 2

Rewrite b as the sum of these two numbers:

[tex]\implies x^2-7x+2x-14=0[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies x(x-7)+2(x-7)=0[/tex]

Factor out the common term (x - 7):

[tex]\implies (x+2)(x-7)=0[/tex]

Therefore:

[tex]\implies x+2=0 \implies x=-2[/tex]

[tex]\implies x-7=0 \implies x=7[/tex]

As time cannot be negative, the rock hits the ground in 7 seconds.

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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Answer:

5.1 yd

Step-by-step explanation:

tan(25°) = x/11

x = 11tan(25°)=5.1 yd

Answer:

Use Calculator:

Approximately. 1429.411

Step-by-step explanation:

Hope it Helps!!!

Answer:

5

Step-by-step explanation:

median basically means the number which is in the middle so 8,8,9, 5 ,10,4,9

the median is 5 because left and right middle is 5 that's why it is median

Answer:

B and D

Step-by-step explanation:

vertex(2,5) so D is correct

there are no real roots for the function B is correct

Answer:

Triangles:

- Equilateral: Has three equal sides

- Isosceles: Has two equal sides

- Right angled: One angle of a right angle triangle measures 90 degrees

- Scalene: All sides are different lengths

Quadrilaterals:

- Square: Has four right angles and four equal sides

- Rectangle: Has four right angles and opposite sides are equal

- Rhombus: A parallelogram with four equal sides

- Parallelogram: Opposite sides are equal and parallel

- Trapezium: At least one set of sides are parallel

- Kite: Two pairs of adjacent sides are the same length

Answer:

$30 is the original price.

Step-by-step explanation:

Let x be the original price of the gift.  The sisters got a 10% discount, so the price paid by them is 0.90x.

The five sisters each paid $5.40, so the total they paid was:

5*($5.40) = $27.

This is equal to the 0.90x:  

0.90x = $27

x = $27/0.90

x = $30

Chocolates

First we must solve the bottom situations.

___________________________________________ (2A and 2B)

First expression (2A): 2v+8.3+2v-6.1

⇒  Collect like terms

(2v + 2v)  + (8.3 - 6.1)

⇒ Simplify

4b + 2.2

Second expression (2B): 3v+14.4-v

⇒ Collect like terms

(3v - v) + 14.4

⇒ Simplify

2v + 14.4

They are not equivalent because when simplified they both have different coefficients and constants each of different values.

_____________________________________________ (4A and 4B)

First expression (4A): 10 + 3 (1/3x + 2)

⇒ Simplify 1/3x to x/3.

10 + 3(x/3 + 2)

⇒  Expand by distributing terms.

10 + x + 6

⇒ Collect like terms.

x + (10 + 6)

⇒ Simplify.

x + 16

Second expression: x + 16

This expression can not be simplified any further. This is because it is a simplified version of another expression.

These expressions are equivalent because expression 4B is the simplified version of expression 4A.

______________________________________

Level: 7th Grade

Unit: Distributing and Combing Like Terms

The ratio using fraction notation of $5 to $35 would be 7.

A fraction represents a part of a number or any number of equal parts.

To convert a ratio into a fraction,

We will simply use the first number as the numerator and the second number as the denominator.

So the fraction = 35/5.

= 7

Since there are no more common factors, the fraction is in its lowest form which is 7.

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Answer:

this one

Step-by-step explanation:

The length of KI is 10 cms.

The skill of measuring the lengths of objects and understanding the units of length is very crucial as it helps us to interact with our environment in a more organized manner.

Here, ΔRJS ≈ Δ IJK

then JR / JI = SR/KI

         1/2   =5 /ki

         kI = 5 X 2

        kI = 10 units.

Thus, The length of KI is 10 cms.

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Answer:

-20

2(xy-7)=-20 with x=-1 y=3

Step-by-step explanation:

2(xy-7)=?

When variables are connected such as xy, this means to multiply.

x=-1

y=3

Multiply the x and the y together.

-1*3=-3. Plug that into the equation.

2(-3-7)=?

Subtract the inside the parenthesis.

2(-10)=?

Multiply. Remember when multiplying a positive and a negative the answer will always be a negative.

2(-10)=-20

This means that 2(xy-7)=-20 with the x=-1 and y=3.

Hope this helps!

If not, I am sorry.

[tex]\huge\color{red} {\boxed{\tt{A}}} \color{blue} {\boxed{\tt{N}}} \color{hotpink}{\boxed{\tt{S}}} \color{blueviolet}{\boxed{\tt{W}}} \color{fuchsia}{\boxed{\tt{E}}}\color{lavender}{\boxed{\tt{R}}}[/tex]

[tex] \red{ \star} \pmb{Diameter \: of \: the \: sphere = 7 m}[/tex]

[tex] \red{ \star} \pmb{Radius =\frac{7}{2} = 3.5 m}[/tex]

[tex] \pink{\underline{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

[tex] \sf{Area \: available \: to \: motorcyclist \: for \: riding = Area \: of \: sphere}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 4πr^2}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 4*\frac{22}{7}*3.5*3.5}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf{= 154}[/tex]

The area available to the motorcyclist for riding is 154 m²

Diameter of the sphere = 7m

[tex]{Radius =\frac{7}{2} = 3.5 m}[/tex]

Area available to motorcyclist for riding = Area of sphere

[tex]{= 4πr^2} \\ \\ {= 4*\frac{22}{7}*3.5*3.5} \\ \\ {= 154}.[/tex]

The area available to the motorcyclist for riding is 154 m²

Based on the information provided, the equation of this new circle is equal to: B. (x - h)² + (y - k)² = r²

Mathematically, the equation of a circle can be derived by using Pythagorean theorem;

x² + y² = r²

Where:

After translating h units along the x-axis and k units along y-axis on a coordinate plane, the equation of this new circle is given by:

(x - h)² + (y - k)² = r²

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Answer: B) (x – h)2 + (y – k)2 = r2

Step-by-step explanation:

Answer:

8.49 × 10⁻³

Explanation:

Standard form of a number: A. × 10ᵇ

(where 'A' is the number, b is the exponent over 10)

For the number "0.00849​", move the decimal point 3 places right so the exponent of 10 is -3.

Standard form: 8.49 × 10⁻³

Other examples of standard/scientific forms are:   standard forms

i) 0.043, move the decimal point 2 places right = 4.3 × 10⁻²

ii) 4030, move the decimal point 3 places left = 4.03 × 10³

Answer:

when a number is given in that manner you have to take that decimal between two whole numbers.

and that is the main reason why I took that decimal from 0.0 to 8.49 and since it went towards the right my answer is going to be 8.49 *10 raised to negative 3.

The area of the kite ABCD will be 60 square millimeters.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

In the Kite ABCD, AB = 5√2mm = 7.07 mm, AP= 5mm, PD = 7mm

Then the area of the kite ABCD will be

Area = 2(area of triangle APB and area of triangle APD)

The side length of PB will be

AB² = AP² + PB²

PB² = AB² – AP²

PB² = 7.07² – 5²

PB² = 50 – 25

PB² = 25

 PB = 5 mm

Then the area will be

Area = 2[(1/2 × 7 × 5) + (1/2 × 5 × 5)]

Area = 60 square mm

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Answer: [tex]\frac{4}{3}[/tex] or about 1.333

Step-by-step explanation:

    We will use the "keep, change, flip" method to solve. Keep the first number the same, change the division to multiplication, and flip the second number so we have the reciprocal.

[tex]\displaystyle \frac{\frac{5}{8} }{\frac{15}{32} } \,\,\,\,\text{ becomes } \,\,\,\,\frac{5}{8} *\frac{32}{15} =\frac{5*32}{8*15} =\frac{160}{120} =\frac{4}{3}[/tex]

Answer: 4/3

Step-by-step explanation:

find the reciprocal of the divisor

15/32

32/15

Now multiply it with the dividend

5/8

15/32

=5/8

32/15

=5/32

8/15

=160/120

after reducing the fraction the answer is 4/3

in mix form 1 1/3

Answer:

1=76°

2=76°

3=36°

Step-by-step explanation:

To find 1, add the other angles in the triangle and subtract by 180.

85+19=104

180-104=76.

1 is equal to 2 so 2=76

To find 3, add 76 and 68, then subtract by 180.

76+68=144

180+144=36

3=36

Hope this helps!

If not, I am sorry.

Answer:

m∠1 = 76°

m∠2 = 76°

m∠3 = 36°

Step-by-step explanation:

The interior angles in a triangle sum to 180°

⇒ m∠1 + 85° + 19° = 180°

⇒ m∠1 + 104° = 180°

⇒ m∠1 + 104° - 104° = 180° - 104°

⇒ m∠1 = 76°

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

⇒ m∠2 = m∠1

⇒ m∠2 = 76°

The interior angles in a triangle sum to 180°

⇒ m∠2 + m∠3 + 68° = 180°

⇒ 76° + m∠3 + 68° = 180°

⇒ m∠3 + 144° = 180°

⇒ m∠3 + 144° - 144°= 180° - 144°

⇒ m∠3 = 36°

The correct answer is option B which is y > 3x + 2.

Inequality is the relationship between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” or < “less than.”.

The given statement says that On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2)

The plot of the inequality is given in the graph attached with the answer the inequality will be y > 3x +2 which passes through the points (-3,-7 ) and ( 0, 2 ).

Therefore the correct answer is option B which is y > 3x + 2.

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