**Area** of a **triangle** ABC with the given vertices is 3 square units.

Given that, the vertices of a triangle ABC, A(3,-6), B(5,-6), and C(7,–9).

What is the area of triangle formula in coordinate geometry?In Geometry, a **triangle** is a three-sided polygon that has three edges and three vertices. The **area** of the **triangle** is the **space** covered by the triangle in a two-dimensional **plane**.

Area of a triangle = [tex]\frac{1}{2} ( |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|)[/tex]

Here, (x1, y1) = A(3,-6), (x2, y2) = B(5,-6), and (x3, y3) = C(7,–9)

Now, the **area** of a **triangle** = 1/2 (|3(-6+9)+5(-9+6)+7(-6+6)|)

= 1/2 (|3(3)+5(-3)+7(0)|)

= 1/2 (|(9-15)|)

= 1/2 × 6

= 3 square units

Therefore, **area** of a **triangle** ABC with the given vertices is 3 square units.

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Write the equation for the graph below.Tomato Prices108Price (In dollars)01 2 3 4 5 6 7 8 9 10Weight(in pounds)

The form of the linear equation is

y = m x + b

m is the slope of the line

b is the y-intercept

The rule of the slope is

[tex]m=\frac{y2-y1}{x2-x1}[/tex](x1, y1) and (x2, y2) are two points on the line

Since (0,0) and (10, 12) are two points on the line

x1 = 0 and y1 = 0

x2 = 10 and y2 = 12

Now substitute them in the rule to find m

[tex]m=\frac{12-0}{10-0}=\frac{12}{10}=1.2[/tex]The slope of the line is 1.2

Substitute it in the form of the equation

y = 1.2 x + b

b is the y-intercept which means value y at x = 0

Since at x = 0, y = 0

Then b = 0

The equation of the line is

**y = 1.2 x**

a cylinder had a radius of 3 and height of 2 need answer quick

To find the volume of a cylinder with radius 3 and height 3

we will use the formular below:

[tex]V=\pi r^2h[/tex]where r is the radius and h is the height

From the question, r=3 and h = 2

substitute the value into the formula

[tex]V=\pi(3)^2\times2[/tex][tex]V=18\pi[/tex]If we substitute the value of pie = 22/7

Then,

[tex]V=18\times\frac{22}{7}[/tex][tex]V\approx56.57\text{ cubic unit}[/tex]A shopper pushes a grocery cart with a force F of 50 N downward and to the right, as shown in the figure below. The anglethe handle makes with the horizontal is 37°, and the cart is moved 14 m. Find the work W done, in joules (1).Ed

**Solution**

For this case we can create the following plot:

We want to find the work so we can use this formula:

[tex]W=Fd\cos \theta[/tex]Replacing we got:

[tex]W=50\cdot14m\cdot\cos 37=559.04J[/tex]Trevor's bonus last year with $6720 and this was 12% of his base salary. what is his base salary?

**Answer:**

$56,000.

**Explanation:**

Let his base salary = s

12% of his base salary = $6720

Thus, we have:

[tex]12\%\text{ of s=6720}[/tex]Next, solve for s:

[tex]\begin{gathered} \frac{12}{100}\times s=6720 \\ 12s=6720\times100 \\ s=\frac{6720\times100}{12} \\ s=56,000 \end{gathered}[/tex]**His base salary is $56,000.**

X Consider lines L and M on the graph below. Which of the following BEST describes the slope of these two lines? y L М. 10 9 8 7 6 5 3 2 1 X 0 1 2 3 4 5 6 7 8 9 10 L has a greater slope than M. Land M have the same slope. M has a greater slope than L.

since they are parellel lines, we conclude that **they have the same slope**, the second option is the correct one.

Write the following sentence using mathematical symbols:

n is greater than or equal to 0.

The sentence using **mathematical symbols **would form an **inequality **as; n ≥ 0.

**Inequality **is defined as the relation which makes a non-equal comparison between two given **functions**. If the equation or inequality contains **variable **terms, then there might be some values of those variables for which that equation or inequality might be **true**. Such values are called **solutions **to that equation or inequality. The Set of such values is; called the solution set to the **considered equation **or inequality.

We need to write a **sentence **using mathematical **symbols**:

Given that "n is **greater **than or **equal **to 0"

The **inequality **form as;

n ≥ 0

Therefore, the sentence using **mathematical symbols **would form an **inequality **as; n ≥ 0.

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Use the sketch tool to mark the picture with the given information. Then choose what postulate proves the triangles congruent.

We choose **ASA Postulate** to prove this triangle **congruent**.

In the given question given that

[tex]\overline{AC}[/tex] **bisects** [tex]\angle BAD[/tex].

[tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].

Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BAD[/tex].

So [tex]m\angle BAC\cong m\angle DAC[/tex]

Since, [tex]\overline{AC}[/tex] bisects [tex]\angle BCD[/tex].

So [tex]m\angle BCA\cong m\angle DCA[/tex]

Then [tex]AC\cong AC[/tex]

Then [tex]\triangle BAC\cong \triangle DAC[/tex]

There given **postulate** are AAS, ASA, SSS, SAS.

We have proved using the ASA postulate.

Now describing the ASA postulate.

**ASA** means **Angle-Side-Angle Postulate**.

According to ASA Postulate, two triangles are congruent if two angles and the included side of one triangle are congruent with two angles and the included side of another triangle.

Hence, we choose **ASA** Postulate to **prove** this **triangle congruent**.

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The difference of seven times a number and five is one hundred find the number

Let the number be x

seven times the number = 7x

The difference of seven times a number and five is one hundred. It means that

7x - 5 = 100

7x = 100 + 5

7x = 105

x = 105/7

x = 15

**The number is 15**

(04.01 LC)The graph shows a system of equations:y = x + 433y = -2x + 2-3-4-5What is the solution to the system of equations?0 1-2, 2)(2, 2)(2,-2)O(-2,-2)

Explanation:

We have two equation of line. Both lines intersect at a point.

The point of intersection of two graphs, is the solution of the graph.

At this point, both will have same x and y values

Tracing the graph:

The point of intersection occurs at x = -2, y = 2

Hence, the solution is at (-2, 2)

HELP PLSSSSSSSSSSSSSS

**Answer: 64**

**Step-by-step explanation:**

Length x width x higth= volume

4 x 8 x 2 = 64

**Answer:**

4 cm

**Step-by-step explanation:**

First, find the volume of the rectangular prism.

4*8*2=32*2=64 cm^-3

Now, the formula for the volume of the cube is:

Volume = side ^ 3

We know the volume is 64 cm^3, so plug it in to the equation:

64 = side ^ 3

take the cube root of both sides

4 = side

write down in terms of n, an expression for the nth term of the following sequences

-7,-12,-17,-22,-27

The expression for the **nth term of the sequence** -7, -12, -17, -22, -27... is -5n-2

The sequence is -7, -12, -17, -22, -27...

The first term = -7

The **common difference** = The second term - The first term

= -12 - (-7)

= -12+7

= -5

The nth term of the sequence = a+(n-1)d

Where a is the** first term**

d is the common difference

n is the n terms

Substitute the values in the equation

The nth term of the sequence = -7+(n-1)-5

= -7-5n+5

= -5n-2

Hence, the expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2

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How do you do this step by step?

-7 + 9 + (-8)

**Step-by-step explanation:**

-7 + 9 + (-8)

2 + (-8)

-6

Hope this helps! :)

**Step-by-step explanation: Remove parenthesis. If there is a "+" in front of an expression in parenthesis, the expression remains the same.**

**-7+9-8. Calculate the sum or difference. You should get ****-6.**

HELP ASAP

Solve z3 = 27.

z = 9

z = −9

z = 3

z = ±3

If z3=27

Z*3=27

Z=27/3

Z=+9

Z*3=27

Z=27/3

Z=+9

**Answer:**

the answer is 3

**Step-by-step explanation:**

a1 = 1; d = 3a1 = 1; d = −3a1 = 17; d = 3a1 = 17; d = −3

**Given:**

A graph is given and the points on the graph are as:

(1, 17), (2, 14), (3, 11), (4, 8), (5, 5), (6, 2)

**Required:**

To determine the value of

[tex]a_1[/tex]and d for the given sequence.

**Explanation:**

We can observe from the graph that the given sequence is an arithmetic sequence.

Here

[tex]a_1[/tex]represent the first value and d represent the common ratio.

So the values are as:

[tex]\begin{gathered} a_1=1 \\ d=14-17=\text{ -3} \end{gathered}[/tex]**Final Answer:**

The second option is the correct answer.

Jose invests $8,216 in a savings account with a fixed annual interest rate of 7% compounded 12 times per year. What will the account balance be after 11 years?

After 11 years, the **account balance **is **$17,704.987. **(approx.)

The **principle **of the first loan is multiplied by the annual interest rate multiplied by the number of compound periods minus one to calculate **compound interest.**

The **principal **of the loan plus **compound interest **will then be what is left.

Given,

**P = $8,216 **for the principal value.

Interest rate**, r = 7% or 0.07.**

Period, with** t = 11.**

Interest applied** n times** every time period, or** 12 times.**

As far as we are aware, **A = P(1 + r/n) n*t**

where** A** is the whole **sum**.

Fill out the **formula **with the values,

=> **A = 8216(1 + 0.07/12) ^ 11*12**

= 8216((12 + 0.07)/12) ^ 132

Upon calculation, we obtain,

≅ $17,704.987

As a result, after 11 years, the account will have a balance of** $17,704.987 **(about).

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The data represents the number of cars that the sales staff at Templeton Motors sold this week.

4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3

Which line plot correctly displays the data?

OA.

Formula Sheet

3.

Number of Cars Sold

X X

X X X

X X X X X X

+++

AHH

+

0 1 2 3 4 5 6 7 8 9 10

X

Number of Cars Sold

X X X X X X X

H

0 1 2 3 4 5 6 7 8 9 10

OC.

OD.

←

Number of Cars Sold

X X

X X X

X X X X X X X

++

0 1 2 3 4 5 6 7 8 9 10

X X

Number of Cars Sold

X X

X X X

H11

0 1 2 3 4 5 6 7 8 9 10

The **line plot** that correctly displays the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, is: A.

A **line plot** is a graphical representation of a data whereby the frequency of each data point is represented by a dot on the **line plot**.

The dots on each data point on the **line plot** corresponds to the frequency of a data point in a data distribution.

Given the data set, 4, 7, 6, 8, 3, 5, 4, 3, 4, 5, 2, 3, the frequency for each data point is:

2 - 1 dot

3 - 3 dots

4 - 3 dots

5 - 2 dots

6 - 1 dot

7 - 1 dot

8 - 1 dots

Thus, the **line plot** that correctly represents these data points alongside their frequencies is: A.

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The country of Latveria has a population of 11.2 million at the start of 1988, which grows at 4.4% per year.A) Write a recursive equation for the population of Latveria.B) Write an explicit equation for the population of Latveria.C) To the nearest tenth of a million, what is the population of Latveria at the start of 1994.

A) The recursive formula takes into account the previous term. For each term, the next term is expressed in respect to it

Looking at the given scenario, the popularion is increasing by 4.4%. This means that the common ratio is

1 + 4.4/100 = 1.044

Given that the initial population is 11200000, the recaursive formula or equation would be

[tex]\begin{gathered} f_n=\text{ 1.044}f_{n\text{ - 1}} \\ \text{where f}_1=\text{ 11200000} \end{gathered}[/tex]B) For the explicit formula, the general formula for a geometric sequence is

an = a1 * r^(n - 1)

a1 = first term = 11200000

r = common ratio = 1.044

The explicit equation would be

an = 11200000 * 1.044^(n - 1)

C) At the start of 1994, the number of terms, n = 7

We would find a7 by substituting n = 7 into the explicit equation. We have

a7 = 11200000 * 1.044^(7 - 1)

a7 = 11200000 * 1.044^6 = 14501770

Ms.Macncheese has 7 plates of fish sticks if she ate 4 how many dose she have left?

A. 3

B. 2

C.1

D.11

3 plates .. 4+3=7 plates ..

Answer:

3

Step-by-step explanation:

7 - 4 is 3

Your friend has a coln that is not fair. It comes up heads 70% of the time and talls 30% of the time. You flip it twice. Let Xbe the number of heads that come up. Find the probability distribution for X

Let X be the number of heads that come up

[tex]\begin{gathered} \text{Probability of head = 70\% = }\frac{70}{100} \\ \text{Probability of tail = 30\% = }\frac{30}{100} \end{gathered}[/tex]Step 1: Write out the formula for the binomial probability distribution

[tex]P_x=^nC_xp^xq^{n-x}[/tex][tex]undefined[/tex]Please solve for x using steps 1/3x= 1/3+6/x

You have the following algebraic equation:

**1/3x = 1/3 + 6/x**

In order to solve the previous equation you first multiply both sides of the equation by **x, **thus, you can quit x denominators in the equation. Proceed as follow:

**1/3x = 1/3 + 6/x **multiply by x both sides

**1/3 = x/3 + 6 ** multiply by 3 both sides

**1 = x + 18** subtract 18 both sides

**1 - 18 = x + 18 - 18**

**-17 = x**

-17 = x is the same as x = -17.** The solution to the given equation is x = -17.**

HELP ASAP WILL GIVE BRAINLEST

How many times larger is (1.064 x 10^1) than (7 x 10^−1)?

0.152

15.2

6.58

7.448

1.064 x 10¹ is 15.2 **times **larger than the 7 x 10⁻¹. It is obtaining the taking **ratio** of the given number. Option B is correct.

It is defined as the **operation **in which we do the **addition **of **numbers**, subtraction, **multiplication**, and **division**. It has basic four operators that are +, -, ×, and ÷.

We'll apply division by splitting into equal **halves **or groups, the **division **may be used to decide how to **distribute** a dish of cookies evenly among a **group**.

Let 7 x 10⁻¹ be x times the number 1.064 x 10¹.

The value of x is obtained by taking the **ratio **of 1.064 x 10¹ and 7 x 10⁻¹.

x = 1.064 x 10¹ / 7 x 10⁻¹

x = 15.2

Thus,1.064 x 10¹ is 15.2 **times **larger than the 7 x 10⁻¹. It is obtaining the taking **ratio **of the given number. Option B is correct.

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If Y (-7, -4) and Z (5, 2), find the slope of a line perpendicular to YZ

**Answer:**

slope of perpendicular line = - 2

**Step-by-step explanation:**

calculate the slope of YZ using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = Y (- 7, - 4 ) and (x₂, y₂ ) = Z (5, 2 )

[tex]m_{YZ}[/tex] = [tex]\frac{2-(-4)}{5-(-7)}[/tex] = [tex]\frac{2+4}{5+7}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2

Don buys a shirt for $24.85. His friend Daryl spends $3.15 more for his shirt. Sean paid the same price as Daryl for his shirt but bought 2. How much did Sean spend for his 2 shirts?

**Solution**

- Don buys a shirt for $24.85.

- Daryl spends $3.15 more for his shirt. This means that Daryl spends

[tex]\$24.85+\$3.15=\$28[/tex]- Thus, Daryl spends $28 on his shirt.

- Sean paid the same price as Daryl, that is, he paid $28 for each shirt.

- Sean bought two shirts, thus, Sean spends:

[tex]\$28+\$28=\$56[/tex]**Final Answer**

**Sean spends $56 on his 2 shirts**

How much hectares is 61,230 km²￼

**Answer:**

6 hecters in the khlathmandu

Which graph represents the solution set of the system of inequalities-2x+y<_4 y>x+2

The **graph **of the **solution set **of the system of **inequalities **y > x + 2 and

- 2x + y ≤ 4 is shown in **figure**.

**What is mean by Inequality?**

A **relation **by which we can compare two or more mathematical expression is called an **inequality**.

Given that;

The **inequalities **is,

⇒ y > x + 2

And, - 2x + y ≤ 4

Now,

The **inequality **is,

⇒ - 2x + y ≤ 4

**Add **2x both side, we get;

⇒ - 2x + y + 2x ≤ 4 + 2x

⇒ y ≤ 2x + 4

And, The second **inequality **is;

⇒ y > x + 2

So, Plot the **graph **of the **inequalities **y ≤ 2x + 4 and y > x + 2.

We get the **solution set **of the system of inequalities.

Which is shown in figure.

Thus, The **graph **of the **solution set **of the system of **inequalities **y > x + 2 and - 2x + y ≤ 4 is shown in **figure**.

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How much grain can a farmer hold in this silo? Use π = 3.14.A. 2,093.3 ft³B. 11,513.3 ft³C. 9,420 ft³D. 12,560.2 ft³

To find out how much grain the farmer can hold we need to find the volume of the silo. The silo is made from a circular cylinder and half a sphere.

The volume of the cylinder is given by:

[tex]V=\pi r^2h[/tex]In this case r=10 and h=30, plugging this values in the equation above we have that the volume of the cylinder is:

[tex]\begin{gathered} V=(3.14)(10)^2(30) \\ V=9420 \end{gathered}[/tex]Hence the volume of the cylinder is 9420 cubic feet.

Now we need to find the volume ot half the sphere, the volume og an sphere is given by:

[tex]V=\frac{4}{3}\pi r^3[/tex]Plugging the radius we have that:

[tex]\begin{gathered} V=\frac{4}{3}(3.14)(10)^3 \\ V=4186.6 \end{gathered}[/tex]Now, we only need half this volume then the volume of the top of the silo is:

[tex]V=2093.3[/tex]Finally we add the volume of the cylinder and half the sphere, **therefore the volume of the sylo is:**

**and the answer is B.**

The variables x and y vary directly. Write an equation that relates the variable. Then find x when y=16.

7) We know that x = 5 and y = 2

We can write an equation that relates this values as a proportion.

Let's say there is a number r such as:

x*r=y

That's a equation that relates x and y. Let's solve for the values given.

[tex]5\cdot r=2[/tex]Now solve for r:

[tex]r=\frac{2}{5}[/tex]The relation we found is:

[tex]x\cdot\frac{2}{5}=y[/tex]Now to find the value of x when y = -6, we replace it in the equation:

[tex]\begin{gathered} x\cdot\frac{2}{5}=-6 \\ x=-6\cdot\frac{5}{2}=-15 \end{gathered}[/tex]Then with this relation, x = -15 when y = -6

A= hlba)10. The volume of a large can of tuna fish can be calculated using the formula V = ar?h.Write an equation to find the radius, r, in terms of V and h. Determine the diameter, tothe nearest inch, of a large can of tuna fish that has a volume of 66 cubic inches and aheight of 3.3 inches.

Given the formula for volume:

[tex]V\text{ = }\pi r^2h[/tex]Let's rewrite the formula in terms r, V and h.

i) Rewriting for r in terms of V and h :

[tex]\begin{gathered} V\text{ = }\pi r^2h \\ \frac{V}{h}=\pi r^2 \\ \\ \sqrt[]{\frac{V}{\pi h}}=r \\ \\ r\text{ = }\sqrt[]{\frac{V}{\pi h}} \end{gathered}[/tex]2) Given:

Volume, V = 66 cubic inches

height, h = 3.3 inches

We know that diameter is radius multiplied by 2.

To find the diameter, first find the radius.

Therefore, we have:

[tex]\begin{gathered} r\text{ = }\sqrt[]{\frac{V}{\pi h}} \\ \\ r\text{ = }\sqrt[]{\frac{66}{3.3\pi}} \\ \\ r\text{ = }2.52\text{ inches} \end{gathered}[/tex]Since the radius is 2.52 inches, the dia,eter will be:

D = r x 2 = 2.52 x 2 = 5.04 inches

To the nearest inch = 5 inches

**ANSWER:**

**diameter = 5 inches**

razy GolfmathsdivThe current value of a baseball card is 60 times its original value v (in dollars). The baseball card is worth$15. Write and solve an equation to find the original value of the baseball card.Equation:= 15Original value: $

**Answer:**

Equation: 60v = 15

Original value: $0.25.

**Step-by-step explanation:**

Current value: $15

Original value: v

The current value is 60 times the original value.

So, the equation is:

Equation: 60v = 15

Now we solve the equation to find the original value.

60v = 15

v = 15/60

v = 0.25

Original value: $0.25.

solve the equations and verify the answer

**Answer:**

See below

**Step-by-step explanation:**

I THINK what you wrote is:

2(x-2) - 3(x-3) = (5x-5) - 4(x-8)

2x -4 -3x+9 = 5x-5 -4x+ 32

2x-3x-5x+4x = 4 -9 -5 +32

-2x = 22 ** *** EDITED *****

**x = - 11 **

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