Expressions Task Card # 3
At the Pathway Shopping
store, you buy x bottles of
water for $2.50 each and a
magazine for $6. Write an
expression in simplest form
that represents the total
amount of money you spend.

Answer:

(1,-4)

Step-by-step explanation:

There are 3 different ways to solve systems of equations, but for this equation, since both are in standard form, we will use elimination.

First, to solve by elimination, both equations must have at least 1 coefficient in common to cancel each other out.

In this case, we will make 2x and 4x equal each other. To do so, we will multiply all the terms in the first equation by 4 and all the terms in the second equation by 2.

This gives us the following equations:

8x - 36y = 152

8x + 10y = -32

Subtract 8x + 10y = −32 from 8x − 36y = 152 by subtracting like terms on each side of the equal sign:

8x −8x − 36y − 10y = 152+32

8x cancels out, leaving us with:

−36y − 10y = 152 + 32

Combine like terms:

-46y = 184.

Divide 184 by -46, which leaves us with y = -4.

Substitute −4 for y in 4x + 5y= −16:

4x + 5 (−4) = −16

Multiply 5 times −4, then add 20 to both sides of the equation.

This leaves us with 4x = 4, which when simplified equals x = 1.

The triangles ABC and DBE are similar by the SAS similarity theorem

The measure of the side lengths AC is 16 units

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

The triangles ABC and DBE

These triangles have the following measures

This means that the triangles are similar by the SAS similarity theorem

Using the SAS similarity theorem, we have the following equation

(x + 1)/12 = (x + 5)/15

Cross multiply the equation

15x + 15 = 12x + 60

So, we have

3x = 45

Divide by 3

x = 15

This means that

x + 1 = 15 + 1 = 16

x + 5 = 15 + 5 = 20

Hence, the measure of the side lengths are 16 and 20 units

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Answer:

dilate by a scale of 2 and reflect over x-axis

Answer: THIS IS A GUESS lol number 2?

Step-by-step explanation:

Answer:

sorry but the picture if you put one on here isn't showing up maybe Repost and I could answer

Answer:

3 1/2

Step-by-step explanation:

Answer:

he would need 2 and 2/3 pounds of potatoes

Step-by-step explanation:

you would add 2/3 together 4 times.

2/3 + 2/3 + 2/3 + 2/3 = 2 and 2/3

so oscar would need 2 and 2/3 pounds of potatoes.

hope I could be of great assistance to you.

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

y = x + 1 [ alternate exterior angles ]

The Relative Maximum will be (7, 50) and minimum is (12, 0).

We have the graph showing average low temperatures in international falls minnesota.

From the graph the maximum y coordinate is 50.

So, the Relative Maximum will be (7, 50).

and, the minimum y coordinate is 0.

So, the Relative minimum is (12, 0)

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Answer:

87

Step-by-step explanation:

Smaller number = 43

Bigger number= 44

Sum = 43+44

Question Answer: 44+43 = 87

A graph which represent the solution set of y = x² − 4 and x + y + 2 = 0 is: D. graph D, Graph shows upward parabola and a line plotted on a coordinate plane. The parabola has vertex at (0, minus 4) with left slope at A (minus 2, 0) and right slope at B (2, 0). The line goes through (minus 2, 0) and (0, minus 2).

In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.

In order to determine the points to the left and right of the parabola, you should set the value of x to be greater than zero (0) i.e x > 0.

For the given quadratic function y = x² − 4, we can logically deduce that the graph (see attachment) represent an upward parabola because the coefficient of x² is positive and the value of "a" is greater than zero as shown in the image attached below.

In conclusion, graph D correctly represent the solution set for the system of equation.

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Answer:

The solution (3, -2).

Step-by-step explanation:

The easiest way to find this solution is inputting these two equations into Desmos Graphing Calculator!

Answer:

x = 3,y = -2

Step-by-step explanation:

Given data:

Y= -2

4x -3y=18

Solve:

Substitute the given y-value into 4x−3y=18 and solve for x

Since, y = -2,

\(4x-3(-2)=18\)

\(4x+6=18\)

\(4x+6-6=18-6\)

\(4x=12\)

\(\frac{4x}{4}=\frac{12}{4}\)

\(x = 3\)

The solution to the system of equations is x = 3, y = -2

~Learn with Lenvy~

Answer:

To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.

To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.

Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.

We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds

Step-by-step explanation:

Answer:

box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35

Step-by-step explanation:

The scores of the students represented on the dot plot are:

1 dot => 24

3 dots => 26, 26, 26

3 dots => 27, 27, 27

5 dots => 28, 28, 28, 28, 28

3 dots => 30, 30, 30

3 dots => 32, 32, 32

1 dot => 35

Quickly, we can ascertain 3 values from these data points of which we can use to find out which box plot represents the dot plot data.

The minimum score = 24

The maximum score = 35

The median score is the 10th value, which is the middle value of the data point = 28

Therefore, we can conclude that: "box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35".

There was 4 dollar of discount on the total amount.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars.

At the counter, he received a discount. If he only paid 22 dollars total, then

Total cost 11 + 15 = 26

But 26 - 22 = 4

Therefore, the discount was 4 dollar.

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Answer:

corresponding

Step-by-step explanation:

<1 and <5 are corresponding angles because they are on the same side of the transversal and on the same side of l and m

Answer:

5/4 > 5/6

Step-by-step explanation:

Answer:

A, C and G

Step-by-step explanation:

\(\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}\)

From inspection of the given right triangle:

Substitute the values into the trigonometric ratios:

\(\implies \sf \sin(25^{\circ})=\dfrac{a}{c}\)

\(\implies \sf \cos(25^{\circ})=\dfrac{b}{c}\)

\(\implies \sf \tan(25^{\circ})=\dfrac{a}{b}\)

\(\boxed{\begin{minipage}{4 cm}\underline{Trigonometric values} \\\\$\sin(90^{\circ}- \theta)=\cos \theta$\\$\cos(90^{\circ}- \theta)=\sin \theta$\\$\tan(90^{\circ}- \theta)=\cot \theta$\\\end{minipage}}\)

Using trigonometric values and the calculated trigonometric ratios:

\(\begin{aligned} \sf \sin(90^{\circ}- 25^{\circ})&=\sf \cos (25^{\circ})\\\implies \sf \sin(65^{\circ}) &=\sf \dfrac{b}{c}\end{aligned}\)

\(\begin{aligned} \sf \cos(90^{\circ}- 25^{\circ})&= \sf \sin(25^{\circ})\\\implies \sf \cos(65^{\circ}) &=\sf \dfrac{a}{c}\end{aligned}\)

\(\begin{aligned}\sf \tan(90^{\circ}- 25^{\circ})&= \sf \cot(25^{\circ})\\\implies \sf \tan(65^{\circ}) &= \sf \dfrac{1}{\tan(25^{\circ})}\\\implies \sf \tan(65^{\circ}) & = \sf \dfrac{b}{a}\end{aligned}\)

Therefore, the true equations are:

\(\sf A: \quad \cos(25^{\circ})=\dfrac{b}{c}\)

\(\sf C: \quad \sin(65^{\circ})=\dfrac{b}{c}\)

\(\sf G: \quad \sin(25^{\circ})=\cos(65^{\circ})\)

Answer:

35.44 and 35.391...

Step-by-step explanation:

Here are the number to the nearest tenth;

35.45≈35.5

34.42≈34.4

35.391≈35.4

35.44≈35.4

35.041≈35.1

Hope this helps, willing to help,

Hope you're having a splendiferous day!

Answer:

2991

Step-by-step explanation:

The correct statement is,

D) The median is less than the mean.

E) The mode and the mean are equal.

Given that;

Data set is,

⇒ {60, 5, 18, 20, 37, 37, 11, 90, 72}

Hence, We can formulate;

Mean = {60 + 5 + 18 + 20 + 37 + 37 + 11 + 90 + 72} / 9

Mean = 38.89

Arrange data set into ascending order,

⇒ 5, 11, 18, 20, 37, 37, 60, 72, 90

Hence,

Median = (9 + 1)/2

            = 5th term

            = 37

Mode = 37

Thus, The correct statement is,

D) The median is less than the mean.

E) The mode and the mean are equal.

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Answer:

15.5

Step-by-step explanation:

5+2x5-1+6/4=15.5

using a calculator this answer is correct.

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

Explanation:

This is the only point in the shaded region. The other points are either on the boundary line or outside the shaded region. Points on the boundary do not count because of the dashed line. The dashed line is due to no presence of an "or equal to" as part of the inequality sign.

See the diagram below.

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

A nonvisual approach will have you plug each of the coordinates into the given inequality.

For instance, choice A has x = 0 and y = 2 pair up which plug in to get

y < (-2/3)x + 2

2 < (-2/3)*0 + 2

2 < 2

which is false, so that's why choice A is not the answer. You should find that choices B and D are false too. Only choice C is true because

y < (-2/3)x + 2

0 < (-2/3)*0 + 2

0 < 2

which confirms the answer we got when we used the visual approach.

Answer: D) 7 3/4

Step-by-step explanation:

With averages, we add all the values and divide by the number of values. Here, we know three out of the four days, let's label the day we don't know x. There are four days, so we can divide by four. 7 1/4 is the average, so we can set the equation equal to 7 1/4.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x) / 4

Let's multiply both sides by 4 to get rid of the fraction. Let's also add what is in the parentheses

29 = 21 1/4 + x

Now we can isolate x by subtracting 29-21 1/4

so

x = 7 3/4 thus the answer is D

Answer:

D) 7 3/4

Step-by-step explanation:

Let x = amount of last feeding.

7 1/4 = (7 1/2 + 7 3/8 + 6 3/8 + x)/4

4 × 7 1/4 = 7 1/2 + 7 3/8 + 6 3/8 + x

28 + 1 = 7 4/8 + 7 3/8 + 6 3/8 + x

29 = 20 10/8 + x

(20 10/8 is the same as 20 + 10/8 = 20 + 8/8 + 2/8 = 20 + 1 + 1/4 = 21 + 1/4 = 21 1/4)

29 = 21 2/8 + x

29 = 21 1/4 + x

x = 29 - 21 1/4

x = 28 4/4 - 21 1/4

x = 7 3/4

Answer: 7 3/4

Answer:

-x-3y

Step-by-step explanation:

-5x+6y-9y+4x

-5x+4x+6y-9y

-x-3y

Weight of the two parcels 22lbs 5oz.

What is Weight?

The force exerted on an object by gravity is known as its weight. The gravitational force acting on the item is referred to as weight in several common textbooks. Some people refer to weight as a scalar quantity that measures the gravitational force's strength.

Given,

The weight of big parcel = 12lbs 11oz

The weight of small parcel = 12lbs 11oz - 3lbs 1oz

                                             = 9lbs 10oz

The weight of total parcel  = big parcel + small parcel

                                            = 12lbs 11oz + 9lbs 10oz

                                            = 21lbs 21oz = 22lbs 5oz

Hence, The weight of the 2 parcels is 22lbs 5oz.

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The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

Answer:

is 12 taro 7 fjuvdkb 7+€77*+"-{$=jjjjdjfjf

Answer:

Refer to the step-by-step explanation.

Step-by-step explanation:

Come up with a monomial expression and solve it.

A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.

Here are a few examples of an monomial expression:

\(\hrulefill\)

Let's work with the monomial expression, 3x²y³z.

To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.

Plug these values into the expression:

3x²y³z

=> 3(3)²(2)³(1)

=> 3(9)(8)(1)

=> 27(8)(1)

=> 216(1)

=> 216

Thus, the expression is solved.

Answer:

132 units

Step-by-step explanation:

the area of triangle = 1/2 × 6 × 8 = 24 units >>>1

the area of the rectangle = 3 × 8 = 24 units >>>2

the area of rectangle(2) = (21-(9+3)) × 8 = 9 × 8 =72 units >>>3

the area of triangle(2) = 1/2 × 3 × 8 = 12 units >>>4

then , from 1 , 2 , 3 and 4 the area of the figure = 24+24+72+12 = 132 units

Answer:

it's answer is 132

hope it helps you