Write the equation of the line that passes through (4, -8) and is parallel to the line y = -2x - 13.

​

Answer:

The area of all faces of the cuboid is 94 square units

Step-by-step explanation:

Given:

Length = 5

Breadth = 4

Height = 3

To Find :

The area of all faces = ?

Solution:

The area of all the faces  =  surface area of the cuboid

The surface area of the cuboid  =  2(LB + BH + HL)

where

L is the length

B is the breadth

H is the height

Now substituting the values,

The surface area of the cuboid

=> [tex]2(5 \times 4 + 4\times 3 + 3\times 5)[/tex]

=> [tex]2(20 + 12+ 15)[/tex]

=> [tex]2(47)[/tex]

=>94 square units

Answer:

i think IV.

Step-by-step explanation:

Answer:

Step-by-step explanation:

y = -4/3x + 1

in y = mx + b form, the number in the b is the y intercept...so ur y intercept is

(0,1).....this is where ur line crosses the y axis

to find ur x axis, sub in 0 for y and solve for x

y = -4/3x + 1

0 = -4/3x + 1

4/3x = 1

x = 1 / (4/3)

x = 1 * 3/4

x = 3/4........and ur x intercept is (3/4,0)...this is where ur line crosses the x axis.

in y = mx + b form, the letter m represents ur slope....so ur slope is

-4/3.....that negative means ur line is descending.....so when we graph, we will start at the y int.

go ahead and plot ur intercepts.......(0,1) and (3/4,0)....now look at ur slope -4/3.....the numerator (either go up or down)....the denominator (go right)

if the numerator is negative....go down....if it was positive u would go up.

so start at (0,1).....slope is -4/3.....so go down 4 and to the right 3...plot that point......then go down 4 and to the right 3...plot that...ur gonna keep on going down 4 and to the right 3 as far as u need to...connect ur points and u have ur line

if it helps, ur line will be going through points (3,-3), (6,-7),(-3,5), (-6,9).....those are some whole number points.....its kinda hard to graph when ur intercepts dont fall on whole numbers

The graph of the function y = -4/3x + 1 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = -4/3x + 1

The above function is a linear function that has been transformed as follows

Next, we plot the graph using a graphing tool by taking note of the above transformations

The graph of the function is added as an attachment

Read more about functions at

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Answer:

12% discount

Step-by-step explanation:

Answer:

x=4, y=-1. (4, -1).

Step-by-step explanation:

x-3y=7

3x+3y=9

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

x=3y+7

3(3y+7)+3y=9

9y+21+3y=9

12y+21=9

12y=9-21

12y=-12

y=-12/12

y=-1

x-3(-1)=7

x+3=7

x=7-3

x=4

Answer:

the smaller angle = 40

Step-by-step explanation:

Let x be the smaller angle.

Other angle = x + 10

x + x+ 10 = 90

2x  = 90 - 10

2x= 80

x = 80/2

x = 40

Answer:

40 degrees. A set of complementary angles make up 90 degrees. 90 - 40 is 50, which is 10 more than forty.

Answer:

Exact Form:

y  =  − 25 /8

Decimal Form:

y  = − 3.125

Answer:

Step-by-step explanation:

[tex]f(x)=2x^2+5x-3\\\\x-\text{intercept for}\ f(x)=0\\\\2x^2+5x-3=0\\\\2x^2+6x-x-3=0\\\\2x(x+3)-1(x+3)=0\\\\(x+3)(2x-1)=0\iff x+3=0\ \vee\ 2x-1=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\\boxed{x=-3}\\\\2x-1=0\qquad\text{add 1 to both sides}\\2x=1\qquad\text{divide both sides by 2}\\\boxed{x=0.5}\\\\-3<0.5[/tex]

hope this helps you mate

Final Answer:

The area of the screen cleared  IS 9900/7 cm² or about 1414.29 cm².

Explanation:

The question asks about finding the area cleared by a windscreen wiper that sweeps out an angle of 180 degrees (or a semi-circle) with a length (or radius) of 30 cm. We can calculate the area cleared using the formula for the area of a circle, A = πr², but since the wiper covers only half the circle, we'll divide the result by 2.

Given the radius (r) is 30 cm, and using π as 22/7, we calculate the area as follows:

First, calculate the area of the full circle: A = πr² = (22/7) * (30)²

Then, since the wiper clears half the circle, we divide this result by 2.

Substituting the values:

A = (22/7) * 900 = 19800/7 cm²

Half of that area is 19800/7 / 2 = 9900/7 cm²

Therefore, the area of the screen cleared by the windscreen wiper is 9900/7 cm² which is approximately 1414.29 cm².

The area cleared by the windscreen wiper is approximately 86 square centimeters.

To find the area cleared by the windscreen wiper, we first need to determine the area of the sector formed by the angle cleared (108°) and then subtract the area of the triangle formed by the radius of the wiper (30 cm) and the two radii that define the angle cleared.

Given:

- Radius of the wiper,  r = 30  cm

- Angle cleared by the wiper, [tex]\( \theta = 108° \)[/tex]

- Value of π, [tex]\( \pi = \frac{22}{7} \)[/tex]

Let's break down the solution step by step:

1. Calculate the area of the sector:

  The formula to calculate the area of a sector of a circle is:

  [tex]\[ \text{Area of sector} = \frac{\theta}{360°} \times \pi r^2 \]\\[/tex]

  where [tex]\( \theta \)[/tex] is the angle in degrees,[tex]\( \pi \)[/tex] is the constant pi, and  r  is the radius of the circle.

  Substituting the given values:

 [tex]\[ \text{Area of sector} = \frac{108°}{360°} \times \frac{22}{7} \times (30)^2 \][/tex]

2. Calculate the area of the triangle:

  The area of a triangle can be calculated using Heron's formula, which states:

  [tex]\[ \text{Area of triangle} = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]

  where  s  is the semi-perimeter of the triangle, and  a ,  b , and  c  are the lengths of its sides.

  In this case, the sides of the triangle are all equal to the radius of the wiper,  r = 30  cm, so  a = b = c = 30  cm.

  The semi-perimeter  s  can be calculated as [tex]\( s = \frac{3r}{2} \).[/tex]

3. Subtract the area of the triangle from the area of the sector:

  [tex]\[ \text{Area cleared} = \text{Area of sector} - \text{Area of triangle} \][/tex]

Let's perform the calculations:

1. Calculate the area of the sector:

  [tex]\[ \text{Area of sector} = \frac{108}{360} \times \frac{22}{7} \times (30)^2 \][/tex]

  [tex]\[ = \frac{108}{360} \times \frac{22}{7} \times 900 \][/tex]

  [tex]\[ = \frac{108}{360} \times 286 \][/tex]

  [tex]\[ = 102 \text{ cm}^2 \][/tex]

2. Calculate the area of the triangle:

  [tex]\[ s = \frac{3r}{2} = \frac{3 \times 30}{2} = 45 \text{ cm} \][/tex]

  [tex]\[ \text{Area of triangle} = \sqrt{45(45 - 30)(45 - 30)(45 - 30)} \][/tex]

  [tex]\[ = \sqrt{45 \times 15 \times 15 \times 15} \][/tex]

  [tex]\[ = \sqrt{506250} \][/tex]

 [tex]\[ = 225 \text{ cm}^2 \][/tex]

3. Subtract the area of the triangle from the area of the sector:

  [tex]\[ \text{Area cleared} = 102 \text{ cm}^2 - 225 \text{ cm}^2 \][/tex]

  [tex]\[ = -123 \text{ cm}^2 \][/tex]

The negative value indicates that the area of the triangle is greater than the area of the sector. This suggests an error in calculation or reasoning. Let's recheck the calculations.

Upon reviewing, it seems there was a mistake in the calculation of the area of the triangle. We should not have taken the square root of the semi-perimeter. Instead, we should have used the correct Heron's formula without the square root. Let's correct this:

[tex]\[ \text{Area of triangle} = \sqrt{s(s - a)(s - b)(s - c)} \][/tex]

[tex]\[ = \sqrt{45(45 - 30)(45 - 30)(45 - 30)} \][/tex]

[tex]\[ = \sqrt{45 \times 15 \times 15 \times 15} \][/tex]

[tex]\[ = 337.5 \text{ cm}^2 \][/tex]

Now, let's subtract the corrected area of the triangle from the area of the sector:

[tex]\[ \text{Area cleared} = 102 \text{ cm}^2 - 337.5 \text{ cm}^2 \][/tex]

[tex]\[ = -235.5 \text{ cm}^2 \][/tex]

It seems that there is an error in the calculation, as the area cannot be negative. Let's reassess the approach and correct any errors.

Upon reevaluation, it appears that we should not subtract the area of the triangle from the area of the sector, as the triangle represents the area covered by the wiper itself, not the area cleared on the windscreen. Instead, we should calculate the area of the sector and use it as the area cleared by the windscreen wiper.

Let's correct the approach and recalculate the area of the sector:

1. Calculate the area of the sector:

  [tex]\[ \text{Area of sector} = \frac{\theta}{360°} \times \pi r^2 \][/tex]

  [tex]\[ = \frac{108°}{360°} \times \frac{22}{7} \times (30)^2 \][/tex]

  [tex]\[ = \frac{108}{360} \times \frac{22}{7} \times 900 \][/tex]

  [tex]\[ = \frac{108}{360} \times 286 \][/tex]

  [tex]\[ = 86 \text{ cm}^2 \][/tex]

So, the corrected area cleared by the windscreen wiper is[tex]\( 86 \, \text{cm}^2 \).[/tex]

In summary, the area cleared by the windscreen wiper is [tex]\( 86 \, \text{cm}^2 \).[/tex]

The Correct Question is:

A windscreen wiper of a vehicle of length 30 cm clears out an angle of 108° as shown in the diagram below. What is the area of 6 the screen cleared? (Take π =22/7)?

In the problem, one paper clip equals three matches, one pencil is greater than one paper clip, and twenty-two paper clips are greater than sixty-seven matches.

In this scenario, one paper clip is equivalent, or equal to, three matches. This is ascertained from the first sentence which states that each paper clip can be traded for three matches. Similarly, one pencil is greater than a single paper clip as it can be traded for six paper clips. This conclusion is drawn from the second sentence. Lastly, the value of twenty-two paper clips is greater than sixty-seven matches since one paper clip is equal to three matches, hence twenty-two paper clips would be worth sixty-six matches, but since we have sixty-seven matches, twenty-two paper clips are worth more.

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Final answer:

To simplify the expression 7(2 + 4) - 3(6) + 2(3 + 5), calculate within the parentheses, do the multiplications, and then the additions and subtractions to get the result, which is 40.

Explanation:

To simplify the numerical expression 7(2 + 4) - 3(6) + 2(3 + 5), you need to follow the order of operations, which is often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Here's how you simplify the expression step by step:

First, calculate the expressions within the parentheses: (2 + 4) and (3 + 5).

Then, multiply each result by the number outside the parentheses.

Afterward, complete any multiplication or division from left to right.

Finally, perform the addition and subtraction from left to right.

Now let's apply these steps to the expression:

Calculate the expressions inside the parentheses: 2 + 4 = 6 and 3 + 5 = 8.

Multiply each result by the respective number outside the parentheses: 7 * 6 = 42 and -3 * 6 = -18 and 2 * 8 = 16.

Now rewrite the expression with these calculated values: 42 - 18 + 16.

Now it's just addition and subtraction: 42 - 18 = 24, and 24 + 16 = 40.

Therefore, the simplified expression is 40.

Answer:

0.3125

Step-by-step explanation:

Use definition of geometric probability:

[tex]P=\dfrac{\text{Desired Length}}{\text{Total Length}}[/tex]

In your case,

Total Length = 8 miles

Desired Length = 7 - 4.5 = 2.5 miles,

so the probability is

[tex]P=\dfrac{2.5}{8}=\dfrac{25}{80}=\dfrac{5}{16}=0.3125[/tex]

Final answer:

The probability of finding the lost cell phone by searching from mile 4.5 to mile 7 along an 8-mile path is 0.3125 or 31.25%.

Explanation:

The student's question deals with the probability of finding a lost cell phone on an 8-mile path by searching between the 4.5 and 7 mile markers.

To calculate this probability, we consider the length of the path where the phone could potentially be found (the search area) and the total length of the path.

The search area is from mile 4.5 to mile 7, which is 2.5 miles long. Since the phone could be anywhere along the 8-mile path, the probability of finding the phone is the length of the search area divided by the total path length:

Probability = Length of Search Area / Total Path Length = 2.5 miles / 8 miles = 0.3125 or 31.25%.

[tex]\frac{105}{8}[/tex] inches of snowfall measured for entire month

Solution:

Given that first week she measured [tex]3\frac{3}{4}[/tex] inches of snow

Second week she measured twice as much snow, and the third week she measured half as much snow as the first week

It did not snow at all in the fourth week

To find: Amount of snowfall measured for entire month

First week:

[tex]\text{ first week } = 3\frac{3}{4} = \frca{4 \times 3 + 3}{4} = \frac{15}{4} inches[/tex]

Second week:

She measured twice as much snow as the first week

[tex]\text{ second week } = 2 \times \frac{15}{4} = \frac{15}{2} inches[/tex]

Third week:

The third week She measured half as much snow as the first week

[tex]\text{ third week } = \frac{1}{2} \times \frac{15}{4} = \frac{15}{8} inches[/tex]

Fourth week:

It did not snow at all in the fourth week

fourth week = 0

Total snowfall for entire month:

Total snowfall = first week + second week + third week + fourth week

[tex]\rightarrow \frac{15}{4} + \frac{15}{2} + \frac{15}{8} + 0\\\\\rightarrow 15(\frac{1}{4} + \frac{1}{2} + \frac{1}{8} )\\\\\rightarrow 15(\frac{2+4+1}{8})\\\\\rightarrow 15 \times \frac{7}{8} = \frac{105}{8}[/tex]

Therefore [tex]\frac{105}{8}[/tex] inches of snowfall measured for entire month

Answer:25%

It's spit into fourths so yeah

Step-by-step explanation:

Answer:  88 degrees

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

Explanation:

Sides AC and AB are tangents to the circle, so 90 degree angles form at points C and B.

Angle O = 92

Angle B = 90

Angle C = 90

Angle A = unknown

----------

The four interior angles of any convex quadrilateral always add to 360 degrees

(angle O) + (angle A) + (angle B) + (angle C) = 360

92 + A + 90 + 90 = 360

A + 272 = 360

A+272-272 = 360-272

A = 88

-----------

A shortcut is to subtract angle O from 180

angle A = 180 - (angle O)  = 180 - 92 = 88

we get the same answer

4x + 2 = -14

4x = -16

x = -4

4(-4) + 2 = -14

-16 + 2 = -14

-14 = -14

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Answer:

The cost of 5 gallons of fuel would be 5x assuming the cost of 1 gallon to be x.

Step-by-step explanation:

An old truck has a fuel efficiency rating of 12 mpg.

We have to find the cost of gasoline that will be used up after we drive 60 miles.

To drive 60 miles , it uses 5 gallons.

let the cost of 1 gallon of fuel be x.

We have to find the cost of 5 gallons of fuel.

So the cost of 5 gallons of fuel = 5[tex]\times coat of 1 gallon of fuel[/tex]

                                                      = 5x

Answer:

Time taken by train in onward journey = 12 hours.

Step-by-step explanation:

Given:

Speed of train making a trip to a repair = 25 mph

Speed of train on return trip = 20 mph

Time taken for return trip = 15 hours

To find the time taken on the on wards trip.

Solution:

The distance traveled by the train on the trip and return trip is the same as the y are of same trips in opposite directions.

Distance can be calculated by using the data for the return trip.

Distance= [tex]Speed\times Time[/tex]

Distance= [tex]20\ mph\times 15\ h=300\ miles[/tex]

Speed of train for on ward trip = 25 mph

Time taken = [tex]\frac{Distance}{Speed}[/tex]

Time taken = [tex]\frac{300\ miles}{25\ mph}= 12\ h[/tex]

Thus, time taken by train in onward journey = 12 hours.

Answer:

The simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex].

Step-by-step explanation:

Given rational expression is  

[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]

Now to simplify the given rational expression:

[tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}[/tex]

[In the above expression 6 and 3 cancelled and the result is 2, (x-2) and (x-2) getting cancelled each other]

[tex]=\frac{2x(x+3)}{x+9}[/tex]

Now applying distributive property to the above expression

[tex]=\frac{2x^2+6x}{x+9}[/tex]

Therefore [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]

Therefore the  simplified given rational expression is [tex]\frac{6x(x+3)(x-2)}{3(x-2)(x+9)}=\frac{2x^2+6x}{x+9}[/tex]

Answer:

-14

Step-by-step explanation:

6(-7/3)=-42/3=-14

Answer: 25 purple beads

Step-by-step explanation: Hope this helps :)

Answer:

25 beads

Explanation For 4 to get to 20 you need to multiply it by 5. You then do the same thing with 5 to get 25 beads.

well,I am not sure about the answer.

Answer:

32 meters

Step-by-step explanation:

we know that

The scale is [tex]\frac{2}{16} \ \frac{cm}{m}[/tex]

That means ----> 2 cm on a map represent 16 m in the actual

so

using proportion

Find out the distance between union and sun valley if they are 4 cm apart on a map

[tex]\frac{2}{16} \ \frac{cm}{m}=\frac{4}{x} \ \frac{cm}{m}\\\\x=16(4)/2\\\\x=32\ m[/tex]

Answer:

A) quantitative data.

Step-by-step explanation:

'quantitative' derives from 'quantity', almost synonymous with a measure or measurement.

Answer:

11:55

Step-by-step explanation:

Answer:

Therefore,

[tex]y=\dfrac{5}{6}[/tex]

Step-by-step explanation:

Given:

[tex]2+\dfrac{5}{6}\sqrt{6}=2+\sqrt{6}y[/tex]

To Find:

x = ?

Solution:

[tex]2+\dfrac{5}{6}\sqrt{6}=2+\sqrt{6}y[/tex]

Subtract 2 from both the side.

[tex]2-2+\dfrac{5}{6}\sqrt{6}=2-2+\sqrt{6}y[/tex]

Then we have

[tex]\dfrac{5}{6}\sqrt{6}=\sqrt{6}y[/tex]

Divide [tex]\sqrt{6} [/tex]on both the side

[tex]\dfrac{5}{6}\dfrac{\sqrt{6}}{\sqrt{6}}=\dfrac{\sqrt{6}}{\sqrt{6}}=y[/tex]

Then we have

[tex]\dfrac{5}{6}=y[/tex]

Therefore,

[tex]y=\dfrac{5}{6}[/tex]

Answer:

Δ PQT ~ Δ QRS  .....{S-S-S test for similarity}...Proof is below.

Step-by-step explanation:

Given:

In Δ PQT

PQ = 30 ft

QT = 28 ft

TP = 20 ft

In Δ QRS

QR = 15 ft

RS = 14 ft

SQ = 10 ft

To Prove:

Δ PQT ~ Δ QRS

Proof:

First we consider  the ratio of the sides

[tex]\frac{PQ}{QR}=\frac{30}{15} = \frac{2}{1}[/tex]            ..............( 1 )

[tex]\frac{QT}{RS}=\frac{28}{14} = \frac{2}{1}[/tex]            ..............( 2 )

[tex]\frac{TP}{SQ}=\frac{20}{10} = \frac{2}{1}[/tex]            ..............( 3 )

So By equation ( 1 ), ( 2 ) and  ( 3 ) we get

[tex]\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}[/tex]

Now in Δ PQT  and Δ QRS we have

[tex]\frac{PQ}{QR}=\frac{QT}{RS} = \frac{TP}{SQ}[/tex]

Which are corresponding sides of a similar triangle in proportion.

∴ Δ PQT ~ Δ QRS  .....{S-S-S test for similarity}...Proved

Answer:

sss similarity

Step-by-step explanation:

i took the test

Answer:

y=1

x=1

Step-by-step explanation:

Answer:

Option D 2.6% is right.

Step-by-step explanation:

Given that at a certain grocery store 65% of the customers regularly use coupons.

Proportion of  the customers regularly use coupons.=0.65

Proportion of customers who do not  regularly use coupons.

=1-0.65 = 0.35

Sample size = 340

In usual notation we write this as

[tex]p=0.65\\q=0.35\\n = 340[/tex]

Std deviation = [tex]\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.65*0.35}{340} } \\=0.025867[/tex]

In percentage this can be written as 2.5867% ~2.6%

Option D 2.6% is right.

Answer:

D

Step-by-step explanation:

BECAUSE                                          

WHEN

YOU

LOOK

AT

A

B

OR

C

OH

NO

THERE

IS

NO

MORE

SPACE

!!!!!!!!!!!!!!

Answer:

x = 16/5

Step-by-step explanation: