Write 17/4 as a mixed number. explain your work.

x = hot dogs

y = snacks

x +y = 175

x = 175-y

2.50x + 0.75y = 262.50

2.50(175-y) +0.75y = 262.50

437.50-2.50y + 0.75y = 262.50

-1.75y = -175

y = -175 / -1.75 = 100

100 snacks & 75 hot dogs

The number of hot dogs sold is 75 while the number of snacks sold is 100.

Based on the information, the equation to solve the question will be:

x + y = 175 ....... i

2.50x + 0.75y = 262.50 ....... ii

From equation i, x = 175 - y.

We'll put the value of x into 2.50x + 0.75y = 262.50 and this will be:

2.50x + 0.75y = 262.50

2.50(175 - y) + 0.75y = 262.50

437.50 - 2.50y + 0.75y = 262.50

Collect like terms

-2.50y + 0.75y = 262.50 - 437.50

-1.75y = -175

y = 175/1.75

y = 100

The number of snacks sold is 100.

Since x + y = 175

x = 175 - 100

x = 75

The number of hot dogs sold is 75

Therefore, 75 hot dogs and 100 snacks were sold.

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Answer:

Step-by-step explanation:

repeating or circulating decimal is decimal representation of a number whose digits are periodic or infinitely repeated.

To convert a fraction into decimal form we have to divide numerator by denominator.

a.  2/3 = 0.666666

b.  9/11 = 0.8181818

c.  2/9 = 0.222222

d.  11/3 = 3.666666

e.  5/6 = 0.833333

f.  14/3 = 4.666666

Answer:

192 feet fence would be used for 6 cows.

Step-by-step explanation:

Given,

64 feet of fence is used for 2 cows,

Ratio in fence and cows = [tex]\frac{64}{2}[/tex] = 32,

96 feet of fence is used for 3 cows,

Ratio in fence and cows = [tex]\frac{96}{3}[/tex] = 32,

128 feet of fence is used for 4 cows,

Ratio in fence and cows = [tex]\frac{128}{4}[/tex] = 32,

Thus, by the above explanation it is clear that in every case the ratio of the length of fence and number of cows is 32,

Let x be the length of cows that is used for x cows,

[tex]\implies \frac{x}{6}=32[/tex]

[tex]\implies x = 192[/tex]

Hence, 192 feet fence would be used for 6 cows.

The correct answers are:

Answer:

ABC would be right angle triangle if C(1,-1) or C(-3,2)

Step-by-step explanation:

In △ABC , the coordinates of vertices A and B are A(1,2), and B(−3,−1)

We need to find the third vertex of triangle ABC.

ABC is a right angle triangle.

A(1,2) and B(-3,-1)

Using A and B, Two possible right angle triangle.

Case 1: If we draw a vertical line at A and horizontal line at B then intersection point of vertical and horizontal would be third vertex of triangle ABC.

Vertical line at A, x=1

Horizontal line at B, y=-1

Vertex C: (1,-1)

Case 2: If we draw a horizontal line at A and vertical line at B then intersection point of vertical and horizontal would be third vertex of triangle ABC.

Vertical line at B, x=-3

Horizontal line at C, y=2

Vertex C: (-3,2)

Thus, ABC would be right angle triangle if C(1,-1) or C(-3,2)

Please see the attachment to see the process graphically.

The interior angles on the same side of a transversal cutting parallel lines are always congruent.

The interior angles on the same side of a transversal cutting parallel lines are always congruent.

When a transversal intersects two parallel lines, it creates several pairs of corresponding angles. The corresponding angles that are on the same side of the transversal are congruent or equal in measure. This is known as the Alternate Interior Angles Theorem.

For example, if line m is parallel to line n and a transversal line t cuts both lines at points A and B, then the angle formed by the intersection of line t and line m, and the angle formed by the intersection of line t and line n on the same side of the transversal are congruent.

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1 is the answer bruvy

Answer: 1

Step-by-step explanation:

From the given picture, it can be seen that there is a plane H on which two pints J and K are located.

One of the Axiom in Euclid's geometry says that "Through any given two points X and Y, only one and only one  line can be drawn "

Therefore by Axiom in Euclid's geometry , for the given points J and K in plane H , only one line can be drawn  through points J and K.

A fraction is a way to describe a part of a whole. The number of students who voted is 401. The correct option is B.

A fraction is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25.

Given that the total number of students in the senior class is 535. Now, if  3/4 of the class voted. Then we can write,

The number of seniors who voted = 3/4 of 535

                                                         = (3/4) ×  535

                                                         = 401.25 ≈ 401

Hence, the number of students who voted is 401.

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Answer:

His acceleration was -1/5 m/s²

Step-by-step explanation:

We can find the acceleration by using the formula to find the final velocity in terms of initial velocity and acceleration and then solving for a. The formula is   V2 = V1 + (a)(t) where V2 is final velocity, V1 is initial velocity and t is time in seconds.

We are going to substitute the values given in the problem:

V2 = 0 m/s

V1 = 6 m/s

t = 4 seconds

[tex]V2=V1+at\\0=6+a4\\0=6+4a\\-6=4a\\-6/4=a\\-1.5=a[/tex]

Therefore, his acceleration was -1.5 m/s²

Answer:

i need helppp

Step-by-step explanation:

this same problems but where is everyone getting the 6.25 from.

The focus point of the satellite is (-5.5,0).

This is a parabola by the looks of the equation and the fact that it's a satellite dish. The vertex of the equation is (-6,0) and the focus is 2/4, 1/2. 1/2 plus -6 is -5.5. the focus is (-5.5,0).

This refers to the plane curve that is U-shaped and is formed by the intersection of a cone.

Hence, we can see that based on the equation, y^2=2(x+6), we can see that the adjustments made by Samara where the x and y are in inches, the focal point based on the vertex of the equation which is (-6,0) and the focus is 2/4, 1/2.

Therefore, the focal point is 1/2 + -6 which is -5.5.

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Final answer:

The equations y = 5x + 9 and y - 5x = 3 have the same slope of 5, indicating that their graphs are parallel lines. The difference lies in their y-intercepts; the first line crosses the y-axis at 9 and the second at 3, meaning they are parallel but at different vertical positions.

Explanation:

To compare and contrast the graphs of y = 5x + 9 and y - 5x = 3, we first need to rewrite the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The first equation is already in this form, with a slope of 5 and a y-intercept of 9. We can rearrange the second equation by adding 5x to both sides to get y = 5x + 3, which has a slope of 5 and a y-intercept of 3.

Both lines have the same slope of 5, which means they are parallel and will never intersect. The difference between them is their y-intercepts; the first line intersects the y-axis at 9, whereas the second line intersects the y-axis at 3. This difference in y-intercepts means that while they have the same steepness and direction, they are located at different vertical positions on the coordinate plane.

Final answer:

The base and height of the triangle are found using the area formula for triangles, with the base being 7 feet more than the height. Using this relationship and the fact that the area is 114 square feet, we solve a quadratic equation to find the height to be 12 feet and the base to be 19 feet.

Explanation:

The student is given that the base of a triangle exceeds the height by 7 feet and that the area of the triangle is 114 square feet. To find the base and height of the triangle, we can use the area of a triangle formula A = (1/2) × base × height. Let's denote the base as b and the height as h. From the given information, b = h + 7.

Substituting the values into the area formula, we get:
114 = (1/2) × (h + 7) × h. Simplifying this, we get 114 = (1/2) × h² + 7/2 × h. Multiplying both sides by 2 to clear the fraction, we obtain 228 = h² + 7h. This is a quadratic equation in the form of h² + 7h - 228 = 0, which we can solve by factoring or using the quadratic formula. Factoring gives us (h + 19)(h - 12) = 0, leading to two potential solutions for h: -19 or 12. Since a height cannot be negative, we discard -19, leaving us with h = 12 feet. Therefore, the base b = h + 7 = 19 feet

The base of the triangle is 19 feet, and the height is 12 feet.

The area of the blue glass that will be needed to fill each butterfly dot would be 144π.

The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.

The circumference of the circle = 2πr

We have given the distance around each dot is 24pi inches.

So, The circumference of the circle = 2πr

                                                 24π = 2πr

                                                 r = 12

The artist plans to fill the inside of each dot with blue-colored glass.

Now, we know that

The area of the circle = [tex]\pi r^{2}[/tex]

                                    = π x 12 x 12

                                    = 144π

Thus, the area of the blue glass that will be needed to fill each butterfly dot would be 144π.

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The equation to model the total income, y, for selling x calendars will be y=5x.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, each calendar will sell for $5.00. the total income is y and the calendars to be sold be x.

Since each calendar costs $5, the total revenue (y) is equal to the number of calendars sold (x).

y=5x

The above equation is in the one variable known as the linear equation in one variable. It had the form y = mx. x and y are the variables in the equation.

Thus, the equation to model the total income, y, for selling x calendars will be y=5x.

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The expression for the sum of these integers is 3n

Let the first number be n-2

Let the middle number be n

Let the third number be n+2

The expression for the sum of these integers will be:

=(n - 2) + n + (n + 2)

= n - 2 + n + n + 2

Collect like terms

= 3n

The expression for the sum of these integers is 3n

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We cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm solely based on its area being 12 cm², as the side lengths are not confirmed by the second statement, thus not properly applying the Law of Detachment.

The question involves the use of the Law of Detachment in deductive reasoning within mathematics. The Law of Detachment, also known as modus ponens, is a logical form that states if the following two statements are true: 'If p, then q' and 'p is true', then we can conclude 'q is true'. In the given scenario, the first statement is 'If a rectangle has side lengths 3 cm and 4 cm, then it has an area of 12 cm2'. The second statement is 'Rectangle LMNO has area 12 cm2'.

To use the Law of Detachment, we need the second statement to confirm that rectangle LMNO has side lengths of 3 cm and 4 cm. However, we are only told the area of rectangle LMNO, not its side lengths. Therefore, based on the information given, we cannot properly apply the Law of Detachment because there is no direct statement verifying the specific side lengths of rectangle LMNO. For the Law of Detachment to be used correctly, the second statement must directly assert that LMNO has the side lengths in question.

Given the information provided, we cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm just because its area is 12 cm2.

To solve for 'a' in the equation 5a^2 = 320, first divide both sides of the equation by 5 to get a^2 = 64. Then, take the square root of both sides which provides two possible solutions, a = 8, and a = -8.

The student is asking to solve for 'a' in the algebraic equation 5a2 = 320. To find the solution, we first need to isolate 'a' on one side of the equation. Begin by dividing both sides of the equation by 5:

a2 = 320 / 5

This simplifies to:

a2 = 64

To solve for 'a', we take the square root of both sides:

a = √64

Therefore, the solutions are:

a = 8, a = -8

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