Acellus
Type SSS, SAS, ASA, SAA, or HL to
justify why the two larger triangles are
congruent?

Answer:

y = (1/3)*x + 5

Step-by-step explanation:

Step 1: determine slope or m

m = change in y-coordinates ÷ change in x-coordinates

m = (4-7)/(-3-6) = -3/-9 = 1/3

Step 2: determine y-intercept or b

y = m*x + b

y = (1/3)*x + b

4 = (1/3)*(-3) + b

4 = -1 + b

b = 5

Step 3: substitute values for m and b into the slope intercept equation

y = (1/3)*x + 5

Answer:

range is subtracting the highest number from the lowest number. so we want to find the difference

Step-by-step explanation:

all you do is 105-85 which is 15.

The bearing of R from P is 019 and the distance |PR| is 8.75

A cyclist set out from a town P on a bearing of 060 to a town Q, 5 km away. He then moves on a bearing of 345 to a town R, 6km from Q.

See attachment

Start by calculating the distance PR using the following cosine ratio

PR² = PQ² + QR² - 2 * PQ * PR cos(Q)

Substitute known values

PR² = 5² + 6² - 2 * 5 * 6 cos(105)

Evaluate

PR² = 76.53

Take the square root of both sides

PR = 8.75

Next, calculate angle R using the following sine ratio

PQ/sin(R) = PR/sin(Q)

Substitute known values

5/sin(R) = 8.75/sin(105)

Evaluate the quotient

5/sin(R) = 9.06

Multiply both sides by sin(R)

9.06 * sin(R) = 5

Divide both sides by 9.06

sin(R) = 0.5519

Take the arc sin of both sides

R = sin⁻¹(0.5519)

Evaluate

R = 34

Calculate angle P using:

P = 180 - 34 - 105

P = 41

The bearing of R from P is then calculated as:

Bearing = 060 - 41

Evaluate

Bearing =  019

Hence, the bearing of R from P is 019

In (b), we have:

PR = 8.75

Hence, the distance |PR| is 8.75

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3 hearts

4 triangle

H:T

3:4

So, ratio of hearts to triangles in simplest form is 3:4

(we can't simplify any further - HCF of 3 & 4 is 1)

Hope this helps!

Answer:

Polynomial

Step-by-step explanation:

⇒ It cannot be option 1 as y does not vary with an exponent

⇒ It cannot be option 2 as y does not relate to any logarithmic values of x

⇒ It cannot be a option 4 as there no irrational numbers under a root

⇒ Therefore it is a polynomial, as it is written in the form : y = ax³ + bx² + cx + d (cubic polynomial)

Answer: See the screenshots below

I'm answering in this format because the questions aren't numbered, so its hard to reference them consistently (so we're both on the same page).

All decimal values are approximate. I decided to round to 4 decimal places, but feel free to use another level of precision.

Answer:

7

Step-by-step explanation:

[tex]\dfrac 13(15+6)\\\\\\=\dfrac{21}3\\\\\\=7[/tex]

Answer:

x= 0.21428571428 or x=0.2

Step-by-step explanation:

-7x+7x^2=9  1. simplify 7x^2

-7x+ 7x(7x)=9   2. combine like terms

-7x+49x=9    3. combine like terms

42x=9           4. /42 on both sides

x= 0.21428571428 or x=0.2

Answer:

16 square units

Step-by-step explanation:

16 square units

Using the given information, the diver's score is 6.2

From the question, we are to calculate the diver's score

From the given information,

The five judges score a dive as 6.0, 6.3, 6.2, 6.8, and 6.1.

Since the highest and lowest scores are discarded

Then, we will discard 6.8 and 6.0

The remaining scores are 6.1, 6.2, and 6.3

Now, the diver's score will be the average of the remaining scores

∴ The diver's score = (6.1 + 6.2 + 6.3) /3

The  diver's score = 18.6 / 3

The diver's score = 6.2

Hence, the diver's score is 6.2

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The material wasted is 7915.375 sq cm.

The product of its length and breadth.

Area = length* breadth

Given:

length= 150 ac, breadth = 100 cm

d= 0.9m 5cm

r= 47.5 cm

Area of rectangle,

= l * b

= 150*100

= 15000 sq. cm

Area of Circular cloth,

= πr²

=3.14*47.5*47.5

=7084.625 sq cm.

Hence, the wasted material is = 15000-7084.625

                                                  = 7915.375 sq cm

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Answer:

See below

Step-by-step explanation:

Each 32 feet of depth is 1 more atmosphere of pressure on the diver  

Answer:

(a)  128 ft

(b)  4 s

(c)  Vertex:  (1, 144)

Step-by-step explanation:

Given information:

The height of the projectile at launch is the value of h(t) when t = 0 (the y-intercept).

Therefore, from inspection of the graph, the y-intercept is (0, 128).

So the height of the projectile at launch is 128 ft.

The length of time it took for the projectile to land is the time from the beginning (when t = 0) to when the height is 0 (the x-intercept).  

From inspection of the graph, the x-intercept is (4, 0)

So the length of time it took for the projectile to land is 4 s.

The vertex is the turning point (minimum/maximum point).

Therefore, from inspection of the graph, the vertex is (1, 144).

The vertex represents the time and height at which the projectile was at its maximum.  So at the time of 1 second, the projectile was at its maximum height of 144 ft.

The number of days it will take to consume the given power = 4.5 days

The amount of power consumed per day = 1440watt-hours

Therefore X days = 6480 watt-hours?

Make X the subject formula;

X = 1 × 6480/1440

X = 4.5 days

Therefore, The number of days it will take to consume the given power = 4.5 days.

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Answer:

Step-by-step explanation:

Comment

There was a flat fee of 10 dollars

Each 1/4 hour brought in 3,75

The total charge was 55 dollars.

Equation

Charge = 10 + 4*3.75*x                     as an hourly rate,

Solution

55 = 10 + 4*3.75x                                Combine

55 = 10 + 15x                                       Subtract 10 from both sides

55-10= 10-10 + 15x

45 = 15x                                               Divide by 15

45/15 = 15x/15

x = 3 hours

Answer 3 hours  

The rocket's height when the distance between you and the rocket is 100 feet is 98.9 feet

The function is given as:

d = √216 +h²

At a distance of 100 feet, it means that:

d = 100

So, we have:

√216 +h² = 100

Take the square of both sides

216 +h² = 10000

Subtract 216 from both sides

h²= 9784

Take the square root of both sides

h = 98.9

Hence, the rocket's height when the distance between you and the rocket is 100 feet is 98.9 feet

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Answer:

y= -1/2x+5

Step-by-step explanation:

Answer:

a)  1 cupcake = $5.50

b)  1 Popsicle = $3.50

Step-by-step explanation:

Let s = cost of one soda

Let c = cost of one cupcake

Let p = cost of one Popsicle

From the given information we can create 3 equations:

Subtract Equation 1 from Equation 2 to eliminate the variable s:

    s + 3c + 3p = 40

-        s + c + p = 22

          2c + 2p = 18

Substitute Equation 3 into this new equation and solve for p:

⇒ 2c + 2p = 18

⇒ 2(p + 2) + 2p = 18

⇒ 2p + 4 + 2p = 18

⇒ 4p = 14

⇒ p = 3.5

Substitute the found value of p into Equation 3 and solve for c:

⇒ c = p + 2

⇒ c = 3.5 + 2

⇒ c = 5.5

To find the cost of a soda (s), substitute the found values of p and c into Equation 1:

⇒ s + c + p = 22

⇒ s + 5.5 + 3.5 = 22

⇒ s = 13

Therefore,

Answer:

What is the value of x in the equation?

Step-by-step explanation:

Answer:

Slope is undefined.

Step-by-step explanation:

Answer:

4×(x+1)(3x-8)(x+4)= (4x²+4)(3x-8)(x+4)= (12x³-32x²+12x²-32)(x+4)= (12x³-20x²-32)(x+4)= 12x⁴+48x³-20x³-80x²-32x²-128x= 12x⁴+28x³-112x²-128x

Answer:

2(7x-4) = 7x(2)-4(2) = 14x-8

but

(7x-4)^2 = (7x-4) (7x-4)

Answer:

[tex]\frac{\left(3x^2-6x+3\right)}{\left(x-1\right)3x-93x^2-3x^3x-33x^2-6}: -\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]
[tex]\frac{3x^2-6x+3}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{\left(x-1\right)\cdot \:3x-126x^2-3x^3x-6}[/tex]
[tex]\frac{3\left(x-1\right)^2}{-3\left(x^4+41x^2+x+2\right)}[/tex]
[tex]\frac{\left(x-1\right)^2}{-\left(x^4+41x^2+x+2\right)}[/tex]
[tex]-\frac{\left(x-1\right)^2}{x^4+41x^2+x+2}[/tex]

Answer:

3x-3

Step-by-step explanation:

use synthetic division

Answer:

[tex]\textsf{A)} \quad 5u^3-2u^2+5u+8[/tex]

Step-by-step explanation:

Given expression:

[tex](-2u^3+5u-1)+(7u^3-2u^2+9)[/tex]

Remove parentheses:

[tex]\implies -2u^3+5u-1+7u^3-2u^2+9[/tex]

Collect like terms:

[tex]\implies -2u^3+7u^3-2u^2+5u-1+9[/tex]

Combine like terms:

[tex]\implies 5u^3-2u^2+5u+8[/tex]

Option A

The approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour

The missing part of the question is represented by the following function:

[tex]T(h) = \frac{386 + 110h}{h}[/tex]

10:00 a.m is 3 hours after 7:00 am and 1:00 p.m is 6 hours after 7:00 am.

This means that:

h = 3 at 10:00 am

h = 6 at 1:00 pm

Next, we calculate T(3) and T(6)

[tex]T(3) = \frac{386 + 110*3}{3} =238.7[/tex]

[tex]T(6) = \frac{386 + 110*6}{6} =174.3[/tex]

The average rate of change is then calculated as:

[tex]T'(h) = \frac{T(3) - T(6)}{3 - 6}[/tex]

This gives

[tex]T'(h) = \frac{238.7 - 174.3}{-3}\\[/tex]

Evaluate

T'(h) = -21

This means that the approximate rate of change in the number of tickets sold between 10:00 a.m. and 1:00 p.m. -21 tickets per hour

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Answer:

213.75

Step-by-step explanation:

95×9=855

855÷4=213.75

The coordinates of the point that divides the segment into a 3:2 ratio is (-2.2, -1.2)

The points are given as:

G = (-4,3)

H = (-1,-4)

Ratio, m : n = 3 : 2

The coordinate of the point is calculated using:

[tex](x,y) = \frac{1}{m + n} * (mx_2 + nx_1, my_2 + ny_1)[/tex]

This gives

[tex](x,y) = \frac{1}{3 + 2} * (3 * -1 + 2 * -4, 3 * -4 + 2 * 3)[/tex]

Evaluate

[tex](x,y) = \frac{1}{5} * (-11, -6)[/tex]

Evaluate the product

(x,y) = (-2.2, -1.2)

Hence, the coordinate of the point is (-2.2, -1.2)

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Answer: The awnser is linear.

I hope this helped.

Step-by-step explanation: