1 Let a = 5.2 and b = 4.7.
a Find the exact value of 3a + b3.
Xena estimates that the answer to part a is 140.
b Find the percentage error made by Xena in her estimation.

Answer

See below :)

Step-by-step explanation:

Experimental Verification

Step 1 : Three triangles with different shapes and sizes are drawn. Suppose the name of each triangle is ABC.

( Draw the triangles in such a way that you can each angle by using a protractor )

( See attached picture )

Step 2 : Measure each angle of these three triangles with the help of protractor and fill up the following table.

_________________________________

Figure < A < B < C < A + <B + <C Result

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

( i ) 180°

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

( ii ) 180°

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

(iii) 180°

________________________________

Conclusion : The sum of the angles of any triangle is equal to 180°

Theoretical proof

( See attached picture )

Given : <ABC , <BCA and <BAC are the angles of ∆ABC.

To prove : <ABC + <BCA + <BAC = 180°

Construction : Through the vertex A , a straight line XY parallel to BC is drawn.

Proof :

_________________________________

Statements Reasons

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

1. < XAB = <ABC 1. XY // BC and alternate

angles

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

2. <YAC = <BCA 2. XY//BC and alternate

angles

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

3. <XAB + <BAC + 3. whole part axiom

<YAC = <XAY

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

4. <XAB + <BAC + 4. < XAY is a straight angle.

<YAC = 180°

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

5. <ABC + <BAC + 5. from statements ( 1 ),

<BCA = 180° ( 2 ) and (4)

_______________________________

Proved

Hope I helped!

Best regards!!

Answer:

no because it has 2 of the same x-intercepts.

Step-by-step explanation:

Answer:

[tex]K(6,8)[/tex]

Step-by-step explanation:

Given

Midpoint, M = (8,9)

J = (10,10)

Required

Find K

The midpoint of segments is calculated using;

[tex]M(x,y) = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})[/tex]

Where [tex]x = 8[/tex] and  [tex]y = 9[/tex]

Take J as J(x1,y1);

So:

[tex]x_1 = 10[/tex]     [tex]y_1 = 10[/tex]

Substitute values for x and y in the given formula

[tex](8,9) = (\frac{10 + x_2}{2}, \frac{10 + y_2}{2})[/tex]

Solving for x2, we have

[tex]8 = \frac{10 + x_2}{2}[/tex]

Multiply both sides by 2

[tex]2 * 8 = \frac{10 + x_2}{2} * 2[/tex]

[tex]2 * 8 = 10 + x_2[/tex]

[tex]16 = 10 + x_2[/tex]

Make x2 the subject of formula

[tex]x_2 = 16 - 10[/tex]

[tex]x_2 = 6[/tex]

Solving for y2

[tex]9 = \frac{10 + y_2}{2}[/tex]

Multiply both sides by 2

[tex]2 * 9 = \frac{10 + y_2}{2} * 2[/tex]

[tex]2 * 9 = 10 + y_2[/tex]

[tex]18 = 10 + y_2[/tex]

Make y2 the subject of formula

[tex]y_2 = 18 - 10[/tex]

[tex]y_2 = 8[/tex]

So,

[tex](x_2,y_2) = (6,8)[/tex]

So, the coordinates of K is

[tex]K(6,8)[/tex]

Answer:

Null hypothesis : top speed = height

Alternative hypothesis : top speed ≠ height

Dependent variable : speed

Independent variable : Height

Step-by-step explanation: The experiment aims to determine the relationship between the height of ramp and the top speed reached by her skateboard.

The Null hypothesis: top speed = height

while the alternative hypothesis will negate the Null.

Alternative hypothesis : top speed ≠ height

The dependent variable in the experiment will be her top speed, because it is the variable we want to evaluate. We want to determine if thwre will be a change in the top speed of the skateboard if there is change in another variable 'height' of ramp. The variable which might cause a change in value of our dependent variable is called the independent or predictor variable, which in this case is the height variable.

Answer:

-216

Step-by-step explanation:

-6 x -6 =36

36 x -6 = -216

Answer:

-216

Step-by-step explanation:

Answer:

4 eggs

Step-by-step explanation:

40 divided by 10 = 4

Answer:

4

Step-by-step explanation:

40/10=4

Answer:

0.34 ends in the hundredths place. so the fraction will be over one hundred

34/100 -- simplify this by dividing each side by 2: 17/50

0.252525... is a repeating decimal

set up an equation so the numbers to the right of the decimal place are the same

100x = 25.2525...

x = 0.2525...

subtract

99x = 25

divide

x = 25/99

5.7777... is also a repeating decimal

set up an equation so the numbers to the right of the decimal place are the same

10x = 57.777...

x = 5.777...

subtract

9x = 52

x = 52/9

Answer:

a) (-3, 4) and radius = 2.

b) 7 cms.

Step-by-step explanation:

x^2+ y^2 + 6x - 8y + 21 = 0

x^2 + 6x + y^2 - 8y = -21

Completing the square on the x and y terms:

(x + 3)^2 - 9 + (y - 4)^2 - 16 = -21

(x + 3)^2 + (y - 4)^2  = -21 + 9 + 16 = 4

a) So the center is (-3, 4) and the radius = sqrt4 = 2.

Ill come back to you later with the second part.

(b) For the point P to be a maximum distance from the origin the line must pass through the center of the circle:

Distance of the center from origin:

= √(-3 - 0)^2 + (4 -0)^2)

= 5.

So the dsitance of P from  the origin is  5 + radius

= 7 cm.

Answer:

x=9

Step-by-step explanation:

combine like terms

[tex]4+6x+5=7x[/tex]

4+5=9

9+6x=7x

to get 6x with 7x subtract 6x from both sides as its positive

6x-6x=0

7x-6x=x

9=x

x=9

Answer:

[tex]r=8[/tex]

Step-by-step explanation:

[tex]r-7=1[/tex] add seven to both sides

[tex]r=1+7\\r=8[/tex]

Hope this helps

Answer:

The correct answer to this problem is r = 8.

Step-by-step explanation:

To solve this problem, we have to remember that our goal is to get the variable (in this case, r) by itself on one side of the equation.  To do this, we have to get rid of the -7 on the left side of the equation.  Therefore, our first step is to add 7 to both sides of the equation.  This gives us:

r - 7 = 1

r - 7 + 7 = 1 + 7

r = 8

Thus, your answer is r = 8.

Hope this helps!

Answer:

Second choice

Step-by-step explanation:

f(x) = (1/4)(x + 4)^2 - 9

f(x) = (1/4)(x^2 + 8x + 16) - 9

f(x) = (1/4)x^2 + 2x + 4 - 9

f(x) = (1/4)x^2 + 2x - 5

(1/4)x^2 + 2x - 5 =

= (1/2 x + 5)(1/2 x - 1)

Answer: Second choice

Answer:

La altura del globo con respecto al suelo es 449,6 metros.

Step-by-step explanation:

La afirmación está incompleta. El enunciado completo es: "Un globo vuela entre dos ciudades A y B, que distan entre sí 1.500 m. Los tripulantes del globo ven la ciudad A con un ángulo de depresión de 27°, mientras que para ver la ciudad B es de 36°. ¿Cuál es la altura aproximada del globo con respecto al suelo?

El diagrama geométrico de la situación se encuentra descrita en el archivo adjunto. La altura aproximada del globo puede obtenerse con ayuda de las funciones trigonométricas, en este caso, se recomienda utilizar la función tangente de los ángulos de depresión:

Ciudad A

[tex]\tan 27^{\circ} = \frac{h}{1500\,m-x}[/tex]

[tex]0,510 = \frac{h}{1500\,m-x}[/tex]

Ciudad B

[tex]\tan 36^{\circ} = \frac{h}{x}[/tex]

[tex]0,727 = \frac{h}{x}[/tex]

Donde [tex]h[/tex] y [tex]x[/tex] son la altura con respecto al suelo y la distancia horizontal con respecto a la ciudad A.

A continuación, se elimina la altura de ambas ecuaciones por igualación y se determina la distancia horizontal del globo con respecto a la ciudad A:

[tex]0,727\cdot x = 0,510\cdot (1500\,m-x)[/tex]

[tex]1,237\cdot x = 765\,m[/tex]

[tex]x = 618,432\,m[/tex]

Finalmente, la altura del globo con respecto al suelo es:

[tex]h = 0,727\cdot x[/tex]

[tex]h = 0,727\cdot (618,432\,m)[/tex]

[tex]h = 449,600\,m[/tex]

La altura del globo con respecto al suelo es 449,6 metros.

Answer:

Still (0,6)

Step-by-step explanation:

The point is actually on the y-axis.  It can't change in a y-axis reflection, only in an x-axis reflection.

Answer:

1) [tex]\huge\boxed{ 250\°}[/tex]

2) [tex]\huge\boxed{75\° + 25\°t }[/tex]

Step-by-step explanation:

Initial Temperature = 75°

Per minute Increase = 25°

After 7 minutes:

=> 75 + 25 ( 7 )

=> 75 + 175

=> 250°

After t minutes:

=> 75 + 25 (t)

=> 75° + 25°t

Answer:

[tex]\Large \boxed{\mathrm{a) \ 250\° \ \ \ b) \ 75\° +25\°t}}[/tex]

Step-by-step explanation:

Before baking, Joshua preheats the oven at an initial temperature of 75°. The temperature increases at a rate of 25° per minute.

Temperatute after 7 minutes,

[tex]75 \° + 25 \°(7)=75\° +175 \° =250 \°[/tex]

Tempertaure after t minutes,

[tex]75 \° +25 \° t[/tex]

Answer:

[tex]R = \frac{1}{6}[/tex]

Step-by-step explanation:

Given that she sold half the paintings and gives out one-third

Required

Determine the fraction left with her

The relationship between the paintings is as follows;

Sold Paintings + Giveaway Paintings + Remaining Paintings = 1

From the question;

Sold Paintings = 1/2

Giveaway = 1/3

Represent Remaining Paintings with R

Substitute these values in the above formula

[tex]\frac{1}{3} + \frac{1}{2} + R = 1[/tex]

Take LCM

[tex]\frac{2+3}{6} + R = 1[/tex]

[tex]\frac{5}{6} + R = 1[/tex]

Make R the subject of formula

[tex]R = 1 - \frac{5}{6}[/tex]

Take LCM

[tex]R = \frac{6-5}{6}[/tex]

[tex]R = \frac{1}{6}[/tex]

Hence, the fraction of the paintings left with her is [tex]\frac{1}{6}[/tex]

no❤️   ,,,,,,,,,,,,,,,,,,,      

8 dimes 4 nickels

ur crazy bb why’d you even ask this question

Answer:

-11xy\26x\2y\6

Step-by-step explanation:

Answer:

x = 6, PLEASE MARK AS BRAINLIEST

Step-by-step explanation:

Let this number be x:

1) Increase x by 30 = x + 30

2) Divide the result by 2 = [tex]\frac{x+30}{2}[/tex]

3) The number obtained is 3 times the original number =

[tex]\frac{x + 30}{2} = 3x[/tex]

[tex]{x + 30} = 6x[/tex]

[tex]30 = 5x[/tex]

[tex]x = \frac{30}{5}[/tex]

[tex]x = 6[/tex]

Answer:

Yes

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

log ₐ (aˣ) = x

3 log ₂ (4)

3 log ₂ (2²)

3 * 2

6

If two angles are complementary, then the

sum of their measures is 90 degrees.

We can find the m<B by taking 90 minus the measure of <A.

So here, we have 90 - 15 which is 75.

So m<A is 75 degrees.

Answer:

  5 years

Step-by-step explanation:

Simple interest on a loan of P for t years at rate r per year is ...

  I = Prt

  4800 = 12,000(0.08)(t)

  4800/960 = t = 5

It will take Joel 5 years to pay off the loan.

Step-by-step explanation:

g(x) = y = 8 - 2x

(A) First transform the function in terms of x :

x = y - 8 / 2

(B) Replace x with y :

[tex] {g}^{ - 1} (x) = y = \frac{x}{2} - 4[/tex]

Answer:

Below.

Step-by-step explanation:

Left side = 2 cos^2 ( π/4 - A/2) - 1

= 2 ( cos π/4  cos A/2 + sin π/4  sin A/2)^2 - 1

Now sin π/4 and cos π/4 = 1 /√2 so:

= 2 ( 1/√2 cos A/2 + 1/√2 sin A/2)^2 - 1

= 2  * 1/2( cos^2 A/2 + sin^2 A/2 + 2 sin A/2 cos A/2) - 1

But cos^2 a/2 + sin^2 A/2 = 1 so we have:

2 * 1/2( 1 +  2sin A/2 cos A/2) - 1

= 1  + 2 sin A/2 cos A/2 - 1

=  2 sin A/2 cos A/2

Using the identity 2 sin A cos A = sin 2A

2 sin A/2 cos A/2 = sin A  = right side.

So left side = right side and the identity is proved.

Answer:  see proof below

Step-by-step explanation:

Use the Double Angle Identity:  cos 2A = 2cos²A - 1

Use the Difference Identity:  cos (A - B) = cosA · cosB + sinA · sinB

Use the Unit Circle to evaluate:  cos (π/2) = 0   &     sin (π/2) = 1

Proof  LHS → RHS

[tex]\text{Given:}\qquad \qquad \qquad \qquad 2\cos^2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)-1\\\\\\\text{Double Angle Identity:}\quad \cos2\bigg(\dfrac{\pi}{4}-\dfrac{A}{2}\bigg)\\\\\\\text{Simplify:}\qquad \qquad \qquad \quad \cos\bigg(\dfrac{\pi}{2}-A\bigg)\\\\\\\text{Difference Identity:}\qquad \cos\dfrac{\pi}{2}\cdot \cos A+\sin \dfrac{\pi}{2}\cdot \sin A\\\\\\\text{Unit Circle:}\qquad \qquad \qquad 0\cdot \cos A+1\cdot \sin A\\\\\\\text{Simplify:}\qquad \qquad \qquad \qquad \sin A[/tex]

LHS = RHS:   sin A = sin A   [tex]\checkmark[/tex]

Answer:

1X+2Y

Step-by-step explanation:

3x - 2x = 1x

3y - 1y = 2Y

Answer:

3x+2y

Step-by-step explanation:

Let's simplify step-by-step.

3x+3y−y

=3x+3y+(−y)

Combine Like Terms:

=3x+3y+(−y)

=(3x)+(3y+(−y))

=3x+2y

Answer:

=3x+2y

HOPE THIS HELPS!!!!!! :)

<333333

Answer:

No a greater slope is not always steeper

Step-by-step explanation:

If line A has a slope of 10 and line B has a slope of 6. The slope of line A will definetely be steeper than line B. In a negative slope, if line A's slope is -20 and line b's slope is 5 the line A will be steeper even though it is actually less than 5.

Answer:

Marcus is picking songs to play during a slideshow. The songs are each 3\dfrac123  

2

1

​  

3, start fraction, 1, divided by, 2, end fraction minutes long. The slideshow is 31\dfrac1231  

2

1

​  

31, start fraction, 1, divided by, 2, end fraction minutes long.

Step-by-step explanation: