A cup of tea costs $3 at a local cafe. Alan and his wife, Patty, have a coupon for $1 off their order. Alan says the expression 3t – 1 represents the cost for t cups of tea. Patty says the expression 3t + (–1) represents the cost. Are their expressions equivalent? Explain

Given :

[tex]\: {\qquad \sf \dfrac{4}{6} x + \dfrac{10}{4} = - \dfrac{6}{8}x - 10 }[/tex]

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To Find :

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Solution :

[tex] {\qquad \sf \dashrightarrow \: \dfrac{4}{6} x + \dfrac{10}{4} = - \dfrac{6}{8}x - 10 }[/tex]

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Subtracting [tex] \sf \: \dfrac{10}{4} [/tex] from both sides :

[tex] {\qquad \sf \dashrightarrow \: \dfrac{4}{6} x \: \: \cancel{+ \dfrac{10}{4}} \: \: \cancel{- \dfrac{10}{4}} = - \dfrac{6}{8}x - 10 - \dfrac{10}{4} }[/tex]

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Adding [tex] \sf \dfrac{6}{8} x[/tex] to both sides :

[tex]{\qquad \sf \dashrightarrow \: \dfrac{4}{6} x + \dfrac{6}{8}x = \cancel{- \dfrac{6}{8}x } \: \: \cancel {+ \: \dfrac{6}{8}x} - 10 - \dfrac{10}{4} }[/tex]

[tex]{\qquad \sf \dashrightarrow \dfrac{4}{6} x + \dfrac{6}{8}x = - 10 - \dfrac{10}{4}}[/tex]

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Adding the like terms :

[tex]{\qquad \sf \dashrightarrow \dfrac{32x + 36x}{24} = \dfrac{ - 40 - 10}{4} }[/tex]

[tex]{\qquad \sf \dashrightarrow \dfrac{68x}{24} = \dfrac{ - 50}{4} }[/tex]

[tex]{\qquad \sf \dashrightarrow \dfrac{34x}{12} = \dfrac{ - 25}{2} }[/tex]

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By doing cross multiplication we get :

[tex]{\qquad \sf \dashrightarrow {68x} = - 300 }[/tex]

[tex]{\qquad \sf \dashrightarrow {x} = \dfrac{ - 300}{68} }[/tex]

[tex]{\qquad \bf \dashrightarrow {x} = \dfrac{ - 75}{17} }[/tex]

Step-by-step explanation:

error

Polynomial error: You have used illegal character ( = )..

Step by Step Solution

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Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

49-((2+5)*2)=0

STEP

1

:

Equations which are never true:

1.1 Solve : 35 = 0

This equation has no solution.

A a non-zero constant never equals zero.

No solutions found

Step-by-step explanation:

AC+CB+BA=180

2x+23+3x-8+4x+1=180

9x+16=180

9x=180-16

9x=164

x=164/9

x=18.2

Answer:

yes

Step-by-step explanation:

as you can see if you count them they are

Answer:

The shape on the very left of the picture is not a quadrilateral. However, the three other shapes are quadrilaterals.

Step-by-step explanation:

A shape is a quadrilateral if it has four sides and four angles. The shape on the left has five sides and five angles, therefore, not a quadrilateral.

Answer:

1224

Step-by-step explanation:

group of 2 friends each receive 612

so you do 612 x 2 = 1224

Answer:

Hello

Step-by-step explanation:

The answer would be 165

Hope this helps

y=30 x=60 that should be the answer sorry if it isnt

Answer:

[tex]\frac{15}{16}[/tex] ton of pebbles will cover the whole garden.

Step-by-step explanation:

So [tex]\frac{3}{4}[/tex] ton covers [tex]\frac{4}{5}[/tex] of the garden.

Let x be pebbles required to cover the entire garden, we can set up a proportion:

[tex]\frac{\frac{3}{4} }{\frac{4}{5} } =\frac{x}{1}[/tex]

[tex]\frac{3}{4}[/tex] / [tex]\frac{4}{5}[/tex]  = x

[tex]\frac{3}{4}[/tex] * [tex]\frac{5}{4}[/tex] = x

[tex]\frac{15}{16}[/tex] = x

[tex]\frac{15}{16}[/tex] ton of pebbles will cover the whole garden.

Answer:

-5 > x

Explanation:

To do this, you have to use the inverse operations. Subtract 6 from each side. That equals -5. Bring everything down and that is your answer!

x+10 =5 that is the answer because look at the example

Answer:

x=11

Step-by-step explanation:

Subtract 3 from both sides

x+3=2x-8

x+3-3 =2x-8-3

Then simplify it

x=2x-11

Again, subtract 3 from both sides

x-2x=2x-11-2x

Simplify

-x=-11

Divide both sides and simplify and then you get x=11

Answer:

27 days

Step-by-step explanation:

15% of 180 = 27

DOLLARS             CENTS             DOLLARS                         CENTS

Answer:

329.9 ft^2

Step-by-step explanation:

area = π · r^2

diameter = 2r so radius = 10.25

area = 3.14 · 10.25^2

10.25^2 = 105.06

3.14 · 105.06 = 329.9 ft^2

Given :-

[tex] \\ \\ [/tex]

To find :-

[tex] \\ \\ [/tex]

Solution:

To find area first we should know value of radius.

Diameter is given , and from diameter we can find value of radius.

[tex] \\ [/tex]

We know :-

[tex] \bf \ddag\boxed{\rm Diameter =2 \: radius } \bf \ddag[/tex]

By using this formula we can find radius.

[tex] \\ \\ [/tex]

[tex] \hookrightarrow\sf Diameter =2 \: radius [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf 20.5 =2 \: radius [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf \dfrac{205}{10} =2 \: radius [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf \cancel\dfrac{205}{10} =2 \: radius [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf \dfrac{41}{2} =2 \: radius [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf2 \: radius = \dfrac{41}{2} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf \: radius = \dfrac{41}{2 \times 2} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\sf \: radius = \dfrac{41}{4} [/tex]

[tex] \\ [/tex]

[tex] \hookrightarrow\bf \: radius = 10.25[/tex]

[tex] \\ \\ [/tex]

Now let's find Area

we know :-

[tex] \bf \ddag\boxed{\rm Area = \pi radius {}^{2} } \bf \ddag[/tex]

[tex] \\ \\ [/tex]

So:-

[tex] \\ [/tex]

[tex] \dashrightarrow \sf Area = \pi radius {}^{2} [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf Area = \pi (10.5) {}^{2} [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf Area = \pi \times 10.5 \times 10.5 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf Area = \pi \times 110.25 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \sf Area = 3.14 \times 110.25 \\ [/tex]

[tex] \\ \\ [/tex]

[tex] \dashrightarrow \bf Area =346.19~ {ft}^{2} \{approx\}\\[/tex]

Answer: y-4=1.2(x-5)

Step-by-step explanation:

Answer: 245 degrees

Step-by-step explanation:

Answer:

(x-2)2=8

Step-by-step explanation:

Using Distance formula ,

[tex]\bold{d(AB) = \sqrt{ (x_{2} - x_{1}) {}^{2} + ( y_{2} - y_{1}) {}^{2} } }\\ \\\bold{5 = \sqrt{(5 - 1) {}^{2} + (2 - y) {}^{2} }} \\ \\\bold\blue{ squaring \: both \: sides\:,} \\ \\\bold{ 25 = (5 - 1) {}^{2} + (2 - y) {}^{2} }\\ \\\bold{ 25 = (4) {}^{2} + (4 + y {}^{2} - 4y)}\\ \\ \bold{25 = 16 + y {}^{2} - 4y + 4}\\ \\ \bold{25 = y {}^{2} - 4y + 20}\\ \\\bold{ y {}^{2} - 4y - 5 = 0}\\ \\\bold{ y {}^{2} - 5y + y - 5 = 0} \\\\\bold{ y(y - 5) + 1(y - 5) = 0}\\ \\\bold{ (y + 1)(y - 5) = 0 }\\\\\bold{ y = - 1 \: or \: y = + 5}[/tex]

therefore ,

possible coordinates of A are either ( 1 , -1 ) or ( 1 , 5 )

hope helpful~

Answer:

3)  48 units²

6)  46 units²

Step-by-step explanation:

Question 3

This shape is a parallelogram with base of 8 units and height of 6 units.

Area of a parallelogram = base × height

                                        = 8 × 6

                                        = 48 units²

Question 6

This shape is a quadrilateral.  It is made up of 3 triangles and a rectangle (see attached image for how to divide the quadrilateral)

Area of rectangle = width × length

                              = 4 × 6

                              = 24 units²

Area of a triangle = 1/2 × base × height

Triangle 1:   1/2 × 2 × 4 = 4 units²

Triangle 2:   1/2 × 6 × 2 = 6 units²

Triangle 3:   1/2 × 4 × 6 = 12 units²

Total area = 24 + 4 + 6 + 12 = 46 units²

Answer:

5 boxes

Step-by-step explanation:

Divide 15 by 3 and you'll get your answer

Hope that helps!

Step-by-step explanation:

1 = $3

x = $15

crossmultiply

3x = 15

x = 15/3

x = 5 boxes of cereal

if this helped pls give brainliest

The solution is, SA =36π unit² is the surface area of the sphere which is correct answer Option(A).

We know that, The formula for the surface area of a sphere of radius

R is 4πR².

here, we have,

According to question, we have the radius of sphere as 3 units.

So, surface area of a sphere

⇒4πR²

⇒4π(3)²

⇒36π

The surface area of a sphere is given by

SA = 4 pi r^2

SA = 4 * pi * 3^2

SA =36 pi

SA =113.10

Hence, the surface area of the sphere is 36π unit².

Learn more about  surface area of a sphere here:

brainly.com/question/14692728

#SPJ7

The value of alpha is 0.26, assuming a confidence level of 74%.

The significance level α is the probability of making the wrong decision when the null hypothesis is true.

Alpha levels which is also called as significance levels are used in hypothesis tests.

Given

When finding the margin of error for the mean of a normally distributed population from a sample.

The confidence interval = 74% = 0.74.

The value of the alpha is given by;

[tex]\rm \alpha =1- Confidence \ interval[/tex]

Substitute all the values in the formula

[tex]\rm \alpha =1- Confidence \ interval\\\\\alpha=1-0.74\\\\\alpha=0.26[/tex]

Hence, the value of alpha is 0.26, assuming a confidence level of 74%.

To know more about confidence interval click the link given below.

https://brainly.com/question/26725727

Answer:

-4

Step-by-step explanation:

Answer:

2y = 8

Step-by-step explanation:

an equation contains an = symbol.

the others are inequalities.

also, from looking at the question, you can assume that it is 2y = 8 because the other to are the same type of inequality

Answer:

x < 6

Step-by-step explanation:

Step 1: Subtract 12 from both sides.

Thus, the answer is x < 6.

Answer:

7. uses like or as to compare two things

8. personification - in this case, the tropical storm is being given the human quality of sleeping

Hope this helps!