Juan and Franco collect baseball cards. Juan has baseball cards. Franco has 18 fewer baseball cards than Juan. Together they have 150 baseball cards. How many baseball cards does Franco have?

The value of length BC is 18.9

Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

Therefore,

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

Therefore, the length of BC is 18.9

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In the triangle, the value of the side BC is 18.9cm to 1 decimal place

The side BC can be found using the cosine formula, Remember that Cosine Rule states that the square of the length of any side of a given triangle is equal to the sum of the squares of the length of the other sides minus twice the product of the other two sides multiplied by the cosine of angle included between them.

The cosine formula states that

c² = a² + b² - 2abcosC

To find the length BC we use cosine rule.

c² = 13² + 7² - 2(13)(7)cos140

c² = 218 - 182cos140

c² = 218-(-139.42)

c² = 218+139.2

c² = 357.2

c = √357.2

c = 18.9

In conclusion, the value of  the length of BC is 18.9cm

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Using equation of proportionality, the unit rate of canine cakes is 1.5, for bark bits is 1.64 and for woofy waffles is 1.2

A unit rate is a rate in which the second quantity in a comparison is one unit. In other words, it is the rate per unit of the first quantity.

Unit rates are useful for making comparisons and for solving problems. For example, if you are comparing the prices of two similar products that come in different sizes, you can use the unit price to determine which product is a better value. The unit price is the price per unit of measurement, such as price per ounce, price per pound, or price per item.

To find the unit rate of the item, we can apply the concept of proportion here;

y = kx

k = constant of proportionality

For canine cakes

24 = 16k

k = 24/16 = 1.5

We can solve for bark bits

82 = 50k

k = 82/50

k = 1.64

And for woofy waffles

48 = 40k

k = 48/40 = 1.2

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9514 1404 393

Answer:

Step-by-step explanation:

The equations can be written in factored form and vertex form to see the x-intercepts, axis of symmetry, and extreme value.

The y-intercept is the constant in the equation in standard form.

The axis of symmetry is the vertical line through the vertex.

__

f(x) = x² -2x -8 = (x -4)(x +2) = (x -1)² -9

  x-intercept (-2, 0), y-intercept (0, -8), axis of symmetry x = 1

__

g(x) = x² +6x +8 = (x +2)(x +4) = (x +3)² -1

  x-intercept (-2, 0), y-intercept (0, 8), minimum value -1

__

h(x) = -x² +2x = -(x)(x -2) = -(x -1)² +1

  axis of symmetry x = 1

_____

Additional comment

We have only listed the intercepts, axis, and extreme where the values match a label.

Answer:

D. No x-intercept, y-intercept 9

Step-by-step explanation:

The line intercepts at (0, 9)

Answer:

10.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions to calculate the hypotenuse.

We know the opposite side from the angle labeled 59 degrees.

sin 59 = opp side / hypotenuse

sin 59 = 9.2/x

x = 9.2/ sin 59

x = 10.733

The area of the shaded region is 3915 units².

We have,

Area of the sector.

= 13.08 units²

Now,

To find the area of an isosceles triangle with side lengths 5, 5, and 4 units, we can use Heron's formula.

Area = √[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, calculated as:

s = (a + b + c) / 2

In this case,

The side lengths are a = 5, b = 5, and c = 4. Let's calculate the area step by step:

Calculate the semi-perimeter:

s = (5 + 5 + 4) / 2 = 14 / 2 = 7 units

Use Heron's formula to find the area:

Area = √[7(7 - 5)(7 - 5)(7 - 4)]

= √[7(2)(2)(3)]

= √[84]

≈ 9.165 units (rounded to three decimal places)

Now,

Area of the shaded region.

= Area of the sector - Area of the isosceles triangle

= 13.08 - 9.165

= 3.915 units²

Thus,

The area of the shaded region is 3915 units².

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Answer: You want to ship 80 items, and each case holds 7 items. To find the number of cases needed to ship the 80 items, you can use the formula:

Number of cases = (Number of items) / (Items per case)

So in this case, the number of cases needed to ship 80 items is:

Number of cases = 80 / 7

Which simplifies to 11.428571428571429, so you will need 12 cases to ship 80 items.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given equation:

The left side is absolute value, we know it is zero or positive value but never negative.

The right side is negative so the equation can't have solutions as we have contradiction above.

\( \rm |x + 7| = - 4\)

The statement is false for any value of x because the absolute value function is always positive or 0.

The pair of numbers that yields the maximum product when their sum is 24 is (12, 12), and the maximum product is 144. The corresponding quadratic function is P(x) = -x^2 + 24x, and the parabola opens downwards.

To find a pair of numbers whose sum is 24 and whose product is as large as possible, we can use the concept of maximizing a quadratic function.

Let's denote the two numbers as x and y. We know that x + y = 24. We want to maximize the product xy.

To solve this problem, we can rewrite the equation x + y = 24 as y = 24 - x. Now we can express the product xy in terms of a single variable, x:

P(x) = x(24 - x)

This equation represents a quadratic function. To find the maximum value of the product, we need to determine the vertex of the parabola.

The quadratic function can be rewritten as P(x) = -x^2 + 24x. We recognize that the coefficient of x^2 is negative, which means the parabola opens downwards.

To find the vertex of the parabola, we can use the formula x = -b / (2a), where a = -1 and b = 24. Plugging in these values, we get x = -24 / (2 * -1) = 12.

Substituting the value of x into the equation y = 24 - x, we find y = 24 - 12 = 12.

So the pair of numbers that yields the maximum product is (12, 12). The maximum product is obtained by evaluating the quadratic function at the vertex: P(12) = 12(24 - 12) = 12(12) = 144.

Therefore, the maximum product is 144. This quadratic function has a maximum value because the parabola opens downwards.

To graph the function, you can plot several points and connect them to form a parabolic shape. Here is an uploaded image of the graph of the quadratic function: [Image: Parabola Graph]

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hi the answer is ( - ∞, -25/152) U (0, +∞)

Answer:

$212.55

Step-by-step explanation:

hope it helps and give brainliest

Answer:

(5, 1 ) and (3, 1 )

Step-by-step explanation:

2x - 3y = 7 → (1)

- 3x + 7y = - 8 → (2)

multiplying (1) by 3 and (2) by 2 and adding will eliminate x

6x - 9y = 21 → (3)

- 6x + 14y = - 16 → (4)

add (3) and (4) term by term to eliminate x

0 + 5y = 5

5y = 5 ( divide both sides by 5 )

y = 1

substitute y = 1 into either of the 2 equations and solve for x

substituting into (1)

2x - 3(1) = 7

2x - 3 = 7 ( add 3 to both sides )

2x = 10 ( divide both sides by 2 )

x = 5

solution is (5, 1 )

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

4x - 3y = 9 → (1)

2x + 3y = 9 → (2)

adding the 2 equations term by term will eliminate y

6x + 0 = 18

6x = 18 ( divide both sides by 6 )

x = 3

substitute x = 3 into either of the 2 equations and solve for y

substituting into (2)

2(3) + 3y = 9

6 + 3y = 9 ( subtract 6 from both sides )

3y = 3 ( divide both sides by 3 )

y = 1

solution is (3, 1 )

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard as a function of x is (150/x - 10)(x - 4).

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides.

x = width of the billboard designer

Total Area including margin = 150 ft^2

Height of the billboard = Area/width

Height of the billboard = 150/x

Before the height of the billboard = (150/x - 5 × 2)

Before the height of the billboard = (150/x - 10) ft

The width of the printed region billboard = (x - 2 × 2)

The width of the printed region billboard = (x - 4) ft

The area of the printed region of the billboard = The width of the printed region billboard × The height of the printed region billboard

The area of the printed region of the billboard = (150/x - 10)(x - 4)

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The complete question is:

A billboard designer has decided that a sign should have 5-ft margins at the top and bottom and 2-ft margins on the left and right sides. Furthermore, the billboard should have a total area of 150 ft^2 (including the margins).

If x denotes the width (in feet) of the billboard, find a function in the variable x giving the area of the printed region of the billboard.

Area as a function of x =

Answer:

\(f(-3)=3\)

Step-by-step explanation:

\(f(x)=x^2+2x\\\\f(-3)=(-3)^2+2(-3)\\\\f(-3)=9-6\\\\f(-3)=3\)

Answer:

f(-3) = 3

Step-by-step explanation:

plug in -3 for x in the equation.

(-3)^2 + 2(-3)

9 + (-6)

9 - 6

3

The value of x is 58.51 degree.

We have,

Perpendicular= 8

Base = 4.9

Using trigonometry

tan x = Perpendicular/ Base

tan x = 8/4.9

tan x= 1.63265306122449

x = 58.51253064

Thus, the value of x is 58.51 degree.

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Answer:

1. Group B

2. Group A

3. The median.

Answer:

1. Group B has the lowest age range out of both groups. Group B has at least 18 students under 16 and Group A has ages from 5 through 30.

2. Group A has more of a variability of ages because it is more scrambled than Group B. Group B had more students that had ages that were all close to each other.

3. I think it's best to use the median because it measures the age above which is found. If we use the mean, it will only be calculated by adding all numbers together and then dividing the sum of the numbers by the number of numbers.

Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

3.1 Activity: Procedural and Conceptual Understanding in Action

Content Area: Fractions

Problem: Comparing Fractions

Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.

Activity Steps:

Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).

Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.

After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:

What does it mean for one fraction to be greater than or less than another?

Can you explain why we need a common denominator when comparing fractions?

How can you visually represent and compare fractions to better understand their relative sizes?

Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.

Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.

Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.

Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.

By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.

3.2 Example: Conceptual Knowledge vs. Procedural Knowledge

Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.

Example: Division of Fractions

Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.

Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.

In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.

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Answer:

0, 1, 2

Step-by-step explanation:

There is a way for them to intersect at 0 points, for example y=x^2 and y = -1

The way to intersect at 1 point is for the linear function to be tangent to the parabola, like y = x^2 and y = 0

The way to intersect 2 points is just for the linear function to be a secant to the parabola, like y = x^2 and y = 1

9, your graph is going up by 2 per box. so half a box is just 1.

Answer:

2 1/2

Step-by-step explanation:

(two and one half)

Answer:

\(2\frac{1}{2}\)

Step-by-step explanation:

\(\frac{5}{8} /\frac{1}{4}\)

When dividing fractions, the best idea is to multiply by the reciprocal of the divisor

The expression can be rewritten as \(\frac{5}{8}* \frac{4}{1}\) , the answer would be \(\frac{5}{2}\) or \(2\frac{1}{2}\)

Hope this helps :)

Have a great day!

Answer:

b. your welcome

Answer:

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

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

Answer:

48

Step-by-step explanation:

Cat = x

Dog = 8x

x + 8x = 54

9x = 54

x = 6, Dog = 8 * 6 = 48

SOLUTION

Given the question in the question tab, the following are solution steps to get the elements of B that belong to the given set.

Step 1: Define rational numbers

A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. Non-terminating decimals that do not have repeated numbers after the decimal point are not rational numbers.

Step 2: Write out the given sets

Step 3: Write out the rational numbers from set B

Hence, it can be seen from the explanations in Step 3 that the following are rational numbers:

Option B:

Answer:20

Step-by-step explanation:this is wrong

Answer:

40

Step-by-step explanation:

subtract median of dogs and median of cats

The equation of the line perpendicular to y=4x+5 and passes through (-3,4) is y=-1/4 (x-13).

Given that the line whose equation is to be found is perpendicular on y=4x+5 and passes through (-3,4).

We are required to find the equation of the line that is perpendicular to y=4x+5 and passes through (-3,4).

When the lines are perpendicular the product of slopes is -1.

Slope intercept form of the equation is y=mx+c in which m is slope of the line.

From the above equation and comparison with y=4x+5 the slope of the line is 4.

Suppose the slope of the line be m.

According to given rule the following will come:

m*4=-1

m=-1/4

Required equation will be as under:

y-4=-1/4 (x+3)

y=-x/4 -3/4+4

y=-x/4+13/4

y=-1/4 (x-13)

Hence the equation of the line perpendicular to y=4x+5 and passes through (-3,4) is y=-1/4 (x-13).

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Answer:

The two true statements concerning this situation and equation are:

The car was bought for $15,000. (This is true because the initial value or starting value, represented by "a" in the equation, is $15,000.)

The value of the car is decreasing. (This is true because the common ratio, represented by "b" in the equation, is 0.85 which is less than 1. Therefore, the value of the car decreases with each passing year or period.)

Step-by-step explanation:

The given equation y = 15000 (0.85) x represents the value of a recently bought used car where y is the value of the car after x years, 15000 is the initial value or starting value of the car, and 0.85 is the common ratio.

The initial value of the car is $15,000, which means that at x=0, the value of the car is $15,000. This is because the initial value is represented by the constant value of "a" in the equation.

The common ratio of 0.85 means that the value of the car decreases by 15% each year or period. This is because the common ratio is less than 1, which indicates that the value of the car is decreasing over time. This decrease in value is represented by the exponent "x" in the equation, which represents the number of years that have passed since the car was bought.

Therefore, the value of the car is decreasing with each passing year or period. For example, after one year (x=1), the value of the car will be 0.85 times its previous value, which is $12,750. After two years (x=2), the value of the car will be 0.85 times its previous value of $12,750, which is $10,838.75, and so on.

To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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The median is 81.5.

The median of the lower half of the data is 67.

The median of the upper half of the data is 92.

Given a data set,

82, 62, 95, 81, 89, 51, 72, 56, 97, 98, 79, 85

Median of a data set is the middle element when the data are arranged in a order.

Arranging in ascending order,

51, 56, 62, 72, 79, 81, 82, 85, 89, 95, 97, 98

There are even number of data sets.

So, Median = Average of the middle two elements.

Median = (81 + 82) / 2 = 81.5

Lower half of the data set is,

51, 56, 62, 72, 79, 81

Median = (62 + 72) / 2 = 67

Upper half of the data set is,

82, 85, 89, 95, 97, 98

Median = (89 + 95) / 2 = 92

Hence the median is 81.5, lower half median is 67 and upper half median is 92.

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