Big Ideas:
Explain your reasoning.

The equation of line passes through the points (0, 0) and (3a, 5g) will be;

⇒ y = (5g/3a) x

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (0, 0) and (3a, 5g).

Now,

Since, The equation of line passes through the points (0, 0) and (3a, 5g).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (5g - 0) / (3a - 0)

m = 5g / 3a

Thus, The equation of line with slope 5g/3a is,

⇒ y - 0 = 5g/3a (x - 0)

⇒ y = (5g/3a) x

Therefore, The equation of line passes through the points (0, 0) and

(3a, 5g) will be;

⇒ y = (5g/3a) x

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Straight line has the equation is, y = 5x - 4.

An endless number of points that are connected on both sides of the point make up a straight line.

The slope of a straight line, "m," is determined by:

m = y2 - y1 / x2 - x1

A linear equation has the expression y = mx + b in slope-intercept form. X and Y are the variables in the equation. The numbers m and b stand for the line's slope (m) and the value of y at x = 0.

The graph's acquired points are (0,-4) and (1,1)

The slope is ,

m = 1-(-4) / 1-0

  = 5/1

  = 5

The line's equation will be as follows since it crosses the y-axis at its intersection point, where C = -4.

⇒ y = mx + c

⇒ y = 5x + (-4)

⇒ y = 5x - 4

As a result, y = 5x - 4 is the equation for the straight line depicted below.

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The area of the triangular plot of land from the vertices is 20 square units

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

A(1,5), B(7,5), and C(8,0)

Represent the vertices properly

So, we have the following representation

A = (1,5)

B = (7,5)

C = (8,0)

The area of the triangle is calculated from the vertices using the following equation

Area = 0.5 * |Ax(By - Cy) + Bx(Ay - Cy) + Cx(Ay - By)|

Substitute the known values in the above equation, so, we have the following representation

Area = 0.5 * |1 * (5 - 0) + 7 * (5 + 0) + 8 * (5 - 5)|

Evaluate the sum of products

Area = 0.5 * |40|

Remove the absolute bracket

Area = 0.5 * 40

Evaluate

Area = 20

Hence, the area of ABC with vertices is 20 square units

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Complete question

The vertices of a trangular plot of land are A(1,5), B(7,5), and C(8,0)

Calculate the area.

EXPLANATION

2025 is a perfect square number hence we can determine its square root. 45 is the square root of 2025 as 45 multiplied by 45 gives the number 2025. Interestingly, – 45 × – 45 is also 2025. Hence It is represented as √2025 = 土45.

Based on the provided information, the APR is 71.4%.

Annual Percentage Rate (APR) is defined as the interest rate which is charged by a lender on an annual basis, expressed in the form of a percentage. The formula for APR is given by

APR = (((Interest Charge+Fees)/(Loan Principal))/(Number of days in loan term)) * 365 * 100

The finance terms in the given case is $29.99 per week for 73week. Hence,

Total amount paid = 29.99*73 = $2,189.27

Loan principal = $1,095

Interest charged = Total amount paid – Loan principal amount = 2,189.27 – 1,095 = $1,094.27

Fees = 0 (as it not mentioned in the question)

Number of days in loan terms = 73*7 = 511 days

Substituting the values in the formula,

APR = ((1094.27/1095)/511) * 365 * 100

APR = 71.4%

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So, on solving the provided question, we can say that the outlier from the following data set will be 8.

Outliers are data points that deviate from the distribution's typical pattern. a value that is "outside" of the record's typical range (either significantly lower or substantially greater). For instance, both 3 and 85 are "outliers" when the scores are 25, 29, 3, 32, 85, 33, 27, 28, etc. Move away. Look for values that are significantly larger or significantly smaller than all other values to identify outliers. Because it is significantly smaller than all other values, Value 4 is an outlier. An observation that differs unusually from other values in a population sample taken at random is referred to as an outlier.

outlier = 4, 5, 1, 7, 4, 5, 8, 9, 6, 5, 4, 9, 7

outlier = 8

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Answer:

M(4,0)

K(0,5)

L(6,5)

go down one

A person can rent any of the vehicles shown in the table for a minimum of two to three days before it becomes more expensive for a week.

Algebra state that it is the study of the laws and symbols of mathematics as well as the manipulation of these symbols.

The rent of the small car for a week is $250 and for a day is $100. Then,

The maximum number of days that a car could be rented is,

= 250÷100

= 2.5 days

≅ 3 days

Then, for the medium car is,

= 290÷110

= 2.7 days

≅ 3 days

For the luxury car is,

= 325÷120

= 2.7 days

≅ 3 days

For Small van is,

= 350÷150

= 2.3 days

≅ 2 days

For Large van is,

= 390÷170

= 2.2 days

≅ 2 days

We can conclude from the above calculations that a person can rent a car for 2-3 days before it becomes more expensive for a week.

The complete question is -

For any of the vehicles listed in the table, how many days can you rent the vehicle before it would be less expensive to rent for the week?

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Using the provided expression and the law of indices, The power get subtracted in division, The answer is [tex]6^{22}[/tex] .

A mathematical expression is a combination of numbers, variables, and mathematical operations that defines a specific value or a set of values. Examples of mathematical expressions include 2+3, x^2+y^2, and sin(x) + cos(y). These expressions can be evaluated to find a specific numerical value or they can be simplified, rearranged or manipulated using algebraic rules.

The laws of indices, also known as the laws of exponents, are a set of rules that govern how exponents (or indices) are used in mathematical operations. These laws include:

These laws allow us to simplify expressions with exponents and make it easier to perform calculations involving them.

[tex]= \frac {6^{15}}{6^{-7}}\\= 6^{15-(-7)}\\= 6^{15+7}\\=6^{22}[/tex]

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The correct statement based on the data is,

⇒ The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

Option 2 is true.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

The given table shows the number of mangos that were used for each of the different sizes of smoothies that the friends ordered.

       Mangos Used    Smoothie Size

Kim         1                         8 oz

Bri           3                        24 oz

Angela    4                        32 oz

Now, By definition of ratio, we get;

The ratio of smoothie size to mangos used for Bri is,

⇒ 24 : 3

⇒ 8 : 1

And, The ratio of smoothie size to mangos used for Angela is,

⇒ 32 : 4

⇒ 8 : 1

Thus, The ratio of smoothie size to mangos used for Bri is the same as the ratio of smoothie size to mangos used for Angela.

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Answer:

  y = -5x +4

Step-by-step explanation:

You want the point-slope equation of the line with y-intercept +4 and through the point (1, -1).

The graph shows you the line decreases 5 units from +4 to -1 as x increases 1 unit from 0 to 1. This tells you the slope is ...

  m = rise/run = -5/1 = -5

The y-intercept is the value of y where the line crosses the y-axis:

  b = 4

These values go into the point-slope equation:

  y = mx +b . . . . . . line with slope m and y-intercept b

  y = -5x +4 . . . . . . line with slope -5 and y-intercept 4

The scale factor of dilation explains how the size of the figure has changed. An expansion has a scale factor of x > 1 (greater than 1).

A reduction is a scale factor that is 0 <1 (higher than 0 but less than 1).

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

A dilatation that results in a reduction (imagine shrinking) or an expansion (think stretching) produces a smaller or bigger picture, respectively.

The picture is reduced if the scale factor is between 0 and 1.

The picture is an enlargement if the scale factor is larger than 1.

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The solution of this system of linear equations is x=3, y=-5.

To solve this system of linear equations, you can use various methods such as substitution, elimination, or matrices. Here is one way to solve using the substitution method:

4((11+y)/2) + 8y = 24

3((11+y)/2) + 2y = 15

y = -5

x = (11 + (-5))/2

x = 3

4(3) + 8(-5) = 24

3(3) + 2(-5) = 15

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The question is -

Solving a system of linear equations in two variables,

Answer:

it is a function because it passes a vertical line test.

Step-by-step explanation:

Answer:

true :)

Step-by-step explanation:

The cone should have its maximum volume. V=1/*3r2h is the formula for calculating the volume V of a cone with height h and radius r.

The cone has a volume of

V=πr2h/3

Therefore, we must calculate the values of r and h in terms of R. R is the diameter of the cone's top-circular circle, and h is the cone's height.

R is the cone's slant height, and it serves as the hypotenuse of a right triangle.

R2 = h2 + r2, or r2 = R2-h2.

So V = (1/3)π

[R2-h2]

h = (π/3)[R2h-h3]

You must take the derivative of the cone's volume, set it to zero, then solve for h to determine the cone's maximum volume.

dV/dh=(π/3)[R2-3h2]

R2-3h2=0 --> h2=R2/3 -> h = R/√3

Now we can determine r:

r2=R2-R2/3 = (2/3)R2

The volume formula with r and h substituted:

V = (π/3)

r2h = (π/3)(2R2/3)

(R/√3)

V(R)=2πR3/(9√3)

The complete question is:

A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup (Your answer may depend on R).

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Answer:

[tex] \sf \: \frac{14}{3} [/tex]

Step-by-step explanation:

Given problem,

[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]

Let's solve the problem,

[tex] \sf \rightarrow \: \frac{7}{9} \times 6[/tex]

[tex] \sf \rightarrow \: \frac{(7 \times 6)}{9} [/tex]

[tex] \sf \rightarrow \: \frac{42}{9} [/tex]

[tex] \sf \rightarrow \: \frac{14}{3} [/tex]

Hence, the product is 14/3.

The ball will reach a height of 3 feet at t = 5/4 seconds.

To find the time (t) when the ball reaches a height of 3 feet, we need to use the equation for the height of the ball: h = -16 [tex]t^2[/tex] + 40t + 5

We are given that the height of the ball is 3 feet, so we can set up the equation:

3 = -16[tex]t^2[/tex] + 40t + 5

Then we can solve for t by isolating t on one side of the equation and then solving for t:

3 = -16[tex]t^2[/tex] + 40t + 5

-5 = -16[tex]t^2[/tex] + 40t

16[tex]t^2[/tex] - 40t - 5 = 0

We can factor the left side of the equation:

(4t - 5)(4t + 1) = 0

So we have two possible solutions:

t = 5/4 or t = -1/4

However, the time cannot be negative, so the only valid solution is t = 5/4.

So the ball will reach a height of 3 feet at t = 5/4 seconds.

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The percent discount on the new phone is 15%.

Discount refers to a reduction in the original price of a product or service. It is a way for businesses to incentivize customers to purchase their products by offering a lower price than the original price.

To find the percent discount, we need to divide the amount of the discount by the original price, and then multiply by 100 to express the answer as a percentage.

Discount = Original Price - Sale Price

Discount = $46 - $39.10

Discount = $6.90

Percent Discount = (Discount / Original Price) x 100

Percent Discount = ($6.90 / $46) x 100

Percent Discount = 15%

Therefore, the percent discount is 15%.

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Answer:

False

Step-by-step explanation:

y < -2x -2 Substitute in -1 for x and 0 for y and see if the statement is true.

0 < -2(-1) - 2

0 < 2-2

0 < 0  

This is a false statement.                                                                                                                                                                                                                                                                  

Answer: A / No.

Step-by-step explanation:

     We will substitute the point given, (-1, 0) and see if the inequality is true after simplifying.

     Given:

y < -2x - 2

     Substitue:

0 < -2(-1) - 2

     Multiply:

0 < 2 - 2

     Subtract:

0 < 0 ✗

     0 is not less than 0, so this point is not a solution.

This given figure carries onto themself at 360, 180, and 60 degrees respectively.

If a rotation between 0° and 360° around the center of a figure in the plane may map the figure onto itself, the figure possesses rotational symmetry. From its starting point, the figure can be rotated and mapped onto itself. The symmetry is of order 4. As a result, the figure displays both rotational and line symmetry.

Given three figures those figures have rotational symmetry from their center point.  The fixed point that the rotation revolves around in a figure or object with rotational symmetry is referred to as the center of rotation.

for figure 1

figure 1 does not have rotational symmetry on any given angles thus, its rotational symmetry would be 1 since it carries onto itself at 360°.

for figure 2

figure 2 has rotational symmetry at 180°. thus, its rotational symmetry would be 2 since it carries onto itself at 180° and 360°.

for figure 3

figure 3 has rotational symmetry at 60, 120, 180, and 240. thus, its rotational symmetry would be 6 since it carries onto itself at 60, 120, 180, 240, and 360°.

therefore, the given figures have 1, 2, and 6 rotational symmetry.

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The solution in interval notation b ∈ (-∞ , -7)

-5 times b is no less than 35.

5b  ≥ 35

n order to isolate the variable in this linear inequality, we need to get rid of the coefficient that multiplies it.

-[tex]\frac{5b}{5} = \frac{-35}{5}[/tex]

This can be accomplished if both sides are divided by .

Notice that the inequality sign has changed.

b ≤ -7

We need to reduce this fraction to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

In our example, this is the common factor:5

b ∈ (-∞ , -7)

We have already found the solution to the inequality, but since we want to represent the solution in interval notation, we have changed it.

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Answer:

1. 6:2

2.for every 1 yellow paint, she needs 3 red paints

3.an orange

Step-by-step explanation:

1. It would be 6:2 because for every 2 parts yellow she needs 6 parts red

2. Since the ratio is first 6:2, just divide it by 2 since there is 2 yellow and it's asking how much red you need for 1 yellow

The direction of A with respect to B. N B 73° N A is 287

A direction is the way that something is moving, directing, or moving toward something or someone. The directions could be Up, Down, Left, and Right, or North, South, East, and West.

The ability to specify where one thing is in relation to another is known as position in mathematics. Defining direction entails explaining the direction in which something moves, such as forward, backward, or in a full or half turn.

It is possible to define direction using relative terms like up, down, in, out, left, right, forward, backward, or sideways. A direction can also be denoted by one of the four cardinal directions: north, south, east, or west.

Angles at a point add up to 360 degrees.

⇒ Bearing from A to B is = 360° - 73° = 287°.

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After solving, the smallest number of yellow marbles are 4.

In the given question, all of Marcy's marbles are blue, red, green, or yellow.

One third of her marbles are blue, one fourth of them are red, and six of them are green.

We have to find the smallest number of yellow marble.

The 6 green marbles and yellow marbles of the total marbles = 1 - (1/3) - (1/4)

The 6 green marbles and yellow marbles of the total marbles = 5/12

Now, suppose the total number of marbles is x

We know the number of yellow marbles is 5/12 x-6 and a positive integer.

Therefore, 12 must divide x

Trying the smallest multiples of 12 for x.

We see that when x = 12

We get there -1 yellow marbles, which is impossible.

However, when x = 24 here are

= 5/12 x - 6

= 5/12*24 - 6

= 4

So, the yellow marbles are 4 which must be the smallest possible.

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Answer:

  see attached

Step-by-step explanation:

Given the pictorial equations, you want to know the single-digit values of each of the images.

There are 6 equations in 5 unknowns, but no numerical values are assigned. Solving the equations will only give ratios of values. From those, we need to determine the numerical values that will keep all numbers in the range 1–9.

Let the icons be represented by letter variables as follows:

Rewriting the equations to standard form, we have ...

  h +b -m -s = 0 . . . . . [eq1]

  h -b +t = 0 . . . . . . . . [eq2]

  b -3s = 0 . . . . . . . . . [eq3]

  h -s -t +m = 0 . . . . .  [eq4]

  h +2s -m = 0 . . . . . . [eq5]

  h +b +s -2t = 0 . . . . . [eq6]

We can add [eq4] to [eq1] and [eq5] to eliminate the m variable.

  (h +b -m -s) +(h -s -t +m) = 0   ⇒   2h +b -2s -t = 0 . . . . [eq7]

  (h +2s -m) +(h -s -t +m) = 0   ⇒   2h +s -t = 0 . . . . . . . . . [eq8]

Adding [eq2] to [eq6], and [eq7] will eliminate the b variable.

  (h +b +s -2t) +(h -b +t) = 0   ⇒   2h +s -t = 0 . . . . same as [eq8]; no help

  (2h +b -2s -t) +(h -b +t) = 0   ⇒   3h -2s = 0 . . . . . [eq9]

Now, we have 3 equations in 4 unknowns:

  b -3s = 0 . . . . . . . [eq3]

  3h -2s = 0 . . . . . . [eq9]

  2h +s -t = 0 . . . . . [eq8]

The smallest positive integer values that will satisfy [eq9] are ...

  h = 2, s = 3

Using these in the remaining equations gives ...

  b -3·3 = 0   ⇒   b = 9

  2·2 +3 -t = 0   ⇒   t = 7

And we can find m using [eq5]:

  m = h +2s = 2 +2·3 = 8

Then the solution is ...

Using the concept of conditional probability and the conditions provided, The answer is [tex]\frac {p^2}{2pq}[/tex] .

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. Probabilities can be calculated using the ratio of the number of favorable outcomes to the total number of possible outcomes. It helps us to understand the uncertainty of events.

A false positive result is when a test indicates that a particular condition or attribute is present, when in reality it is not. For example, in medical testing, a false positive result would occur when a test for a disease returns a positive result but the person being tested does not actually have the disease. False positives can have serious consequences, as they can lead to unnecessary treatments, further testing, and anxiety for the person being tested.

p=probability of occurrence

q=1-p

P(false positive for both subjects | false positive for one subject) = P(false positive for both subjects and false positive for one subject) / P(false positive for one subject)

P(false positive for both subjects | false positive for one subject) = p^2 / (2pq)

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Answer:

Step-by-step explanation:

a) x and 53 are adjacent angles of a parellelogram:

therefore, their sum will be 180 degrees

x + 53 = 180 --> x = 180 - 53 = 127 degrees

b) We know that opposite angles in a parallelogram are equal:

therefore, x = 113 degrees

c) Similarly, x = 80 degrees

d) x + 62 = 180

x = 180 - 62 =  118 degrees