The graph of a quadratic function with vertex (-1,-4) is shown in the figure below.
Find the domain and the range.

The shape of the ABCD is a rhombus. The diagonals are not equal to each other.

What is the 2-dimensional shape?

A two-dimensional shape with horizontal and vertical axes is known as a 2d shape (x-axis and y-axis). Two-dimensional shapes have only length and width. There is no thickness or height to these shapes.

Given the vertices of ABCD are  A(-3,0), B (1,5), C(-3,10) and D(-7,5).

The formula distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

The distance between A and B is √[(1 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between B and C is √[(-3 - 1)²+(10 - 5)²] = √(4²+5²) = 6.4

The distance between C and D is √[(-7 - (-3))²+(5 - 10)²] = √(4²+5²) = 6.4

The distance between A and D is √[(-7 - (-3))²+(5 - 0)²] = √(4²+5²) = 6.4

The distance between A and C is √[(-3 - (-3))²+(10 - 0)²] = √(10²) = 10

The distance between B and D is √[(-7 - 1)²+(5 - 5)²] = √(8²) = 8

The slope of a line passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of AB is (5-0)/(1-(-3))=5/4

The slope of BC is (10-5)/(-3-1)=-5/4

The slope of CD is (5-10)/(-7-(-3))=5/4

The slope of AD is (5-0)/(-7-(-3))=-5/4

The number of vertices of the quadrilateral is 4.

Thus it is either a square or rectangle or rhombus or parallelogram.

Since the length of all sides is equal thus it is either a square or rhombus.

Since the diagonals are not equal it is a rhombus.

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Answer:

Graph is attached below

Step-by-step explanation:

To start off, let's find the y-intercept, which is when x=0

So, when x=0,

[tex]y=\frac{3}{4}(0)+5[/tex], which is y=5.

So we can put a point on (0, 5)

From there, since the slope is 3/4. We can go up 3 and right 4 to plot a point there, you can also do down 3 and down 4 from the y-intercept point, then keep going either, up 3 and right 4 or down 3 and left 4, which should give you a diagonal line that looks something like;

Considering the context of the question and the mathematical expression, the height of the frame. after the width is reduced to 3 inches will be 1.8 inches.

Dimension is a term that is used to describe the measurement of the size or distance of an object or region or space in one direction.

Generally, the term dimension is the measurement of the length, width, and height of anything.

In this case, as given in the question

A frame is 10in wide and 6 in tall.

reduces to a width of 3 in

let us assume that the height of the frame after reducing the width to 3in be = x

then the equation becomes original width/ original length = reduced width/reduced length

put all the value, we get

[tex] = 10 \div 6 = 3 \div x[/tex]

solve the above

[tex]x = (6 \times 3) \div 10 \\ x \: = 1.8in[/tex]

Therefore, in this case, it is concluded that the correct answer is 1.8in, which will be the tall or height of the frame.

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The group of 20 students will save $144 by using the promotional deal. Half of the group, or 10 students, will get the free cotton candy, so that's $30 saved. 14 of the students will get the free soda, so that's another $28 saved. Added together the group of 20 students will save $58 on the cotton candy and $28 on the soda for a total savings of $144.

Answer:

Not sure what you meant and could of used some specifics but I got this with my experience in algebra and geometry.

9906513923.77

98765 times triangle A 32598765÷325

Answer

[tex] - 5 \sin(5x) [/tex]

Using the concept of proportions and ratio, the building of 6ft casts a shadow of 3.33ft

Proportions are a way of comparing two or more quantities by expressing them as fractions or ratios. They are used to describe the relationship between parts of a whole.

A proportion can be written in different ways. For example, the proportion of red apples to total apples can be written as "3 out of 5", "3:5", or "3/5". In this case, 3 is the number of red apples, 5 is the total number of apples and 3/5 is the proportion of red apples.

Data;

Setting up a proportions or two ratios for this.

36 / 20 = 6 / x

cross multiply both sides and solve for x

36 * x = 20 * 6

36x = 120

x = 3.33

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The time needed to travel the entire distance is given as follows:

1.27 minutes.

Before obtaining the time, we need to obtain the entire distance.

The distance is the perimeter of the rectangle, which is the sum of all the outer side lengths of the right triangle.

The sides of the right triangle are given as follows:

40 yards and 70 yards.

Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:

h² = 40² + 70²

[tex]\sqrt{40^2 + 70^2}[/tex]

h = 80.6 yards.

Then the total distance is given as follows:

40 + 70 + 80.6 = 190.6 yards.

The time is given by the division of the distance by the velocity of 150 yards per minute, hence:

t = 190.6/150

t = 1.27 minutes.

The problem is given by the image presented at the end of the answer.

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Answer:

To calculate the tip, we first need to find 24% of the total bill. To do this, we can multiply the bill amount by 24% (expressed as a decimal).

Tip = 0.24 * 73.25

= 17.58

Therefore, the tip should be $17.58 in dollars.

Answer:

85 inches

Step-by-step explanation:

7*12+1=84+1=85

Answer:

A

Step-by-step explanation:

-3 x 4 = -12

[tex]10^{3}[/tex] x [tex]10^{6}[/tex] = [tex]10^{9}[/tex]  You add the exponents when you are multiplying powers with the same bases.

Answer:

Step-by-step explanation:

24²=24×24

Which is 576

Answer:

Pythagorean theorem:

[tex]a ^{2} + b ^{2} = c^{2} [/tex]

[tex]2 ^{2} + 11 ^{2} = c^{2} [/tex]

2×2=4 11×11=121

4+121=125

[tex]c = \sqrt{125} [/tex]

The total surface area of the rectangular prism is 160 inches².

Since the base of the rectangular prism is a square, we know that the edge length of the base is the square root of the area of the base. The area of the base is 16 square inches (since it can be completely covered by 16 squares with edge length of 1 inch), so the edge length of the base is 4 inches.

Since the height of the prism is twice the edge length of the base, the height of the prism is 8 inches.

The total surface area of a rectangular prism is given by the formula:

2lw + 2lh + 2wh

Where l is the length, w is the width and h is the height

So, the total surface area of the rectangular prism is:

2(4 inches * 4 inches) + 2(4 inches * 8 inches) + 2(4 inches * 8 inches)

= 160 square inches

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The x-intercept of the equation y=-13x+234 is (18,0).

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

The equation of the point slope form is: (y - y₁) = m(x - x₁)

where, (x, y) is a random point on the line and m is the slope of the line.

1) From the give table, we have (18, 0) and (15, 39).

Here, slope(m) = (39-0)/(15-18)

m= -13

2) Substitute m= -13 and (x₁, y₁)=(18, 0) in point slope form, we get

(y-0)= -13(x-18)

y=-13x+234

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (18,0)

y-intercept(s): (0,234)

Therefore, the x-intercept of the equation y=-13x+234 is (18,0).

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The simplified form of the given expression is 3(i-2)

A term can be a number, a variable, product of two or more variables or product of a number and a variable. An algebraic expression is formed by a single term or by a group of terms. For example, in the expression 4x + y, the two terms are 4x and y.

Given is an expression, (−8+i)+(2+2i)

Simplifying the expression,

(−8+i)+(2+2i)

= -8 + i + 2 + 2i

= -8+2+2i+i

= -6+31i

= 3(i-2)

Hence, the simplified expression is 3(i-2)

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Using circle theorems, the value of x in the cyclic quadrilateral is 6 units

A cyclic quadrilateral is a four-sided shape whose vertices all lie on the same circle. This means that all four angles of the quadrilateral are equal to one another.

This is further explained by circle theorem which is a branch of mathematics that deals with the properties of circles and their relationships with other shapes. It is based on the fact that all points on a circle are equidistant from the center of the circle. Circle theorem has many applications, such as finding the area of a circle, calculating the circumference of a circle, and even determining the angles of a triangle formed by three points on a circle.

In this given problem, to find the value of x, we have to use proportions or ratios of the sides given.

This becomes;

(x + 6) / x = 12 / x

when the denominators cancel out;

x + 6 = 12

Collect like terms

x = 12 - 6

x = 6

The value of x is 6

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Answer:

12 students

Step-by-step explanation:

The number of students surveyed: 53 + 46 = 99 students
The number of student having both: 99 - 87 = 12 students

A worker's starting wage at this job is $13.5.

$31.70 per hour can be expected after 7 years of experience.

What is the system of equations?

System of equations, also known as simultaneous equations, Two or more equations to be solved together in algebra (i.e., the solution must satisfy all the equations in the system). The number of equations must equal the number of unknowns for a system to have a unique solution.

Given that a worker earns $16.10 per hour with 1 year of experience.

The other worker earns $21.30 per hour with 3 years of experience.

The model that represents the wages of a worker is

y = ax + b

Where x is the number of years of experience, and y is total wages.

Now putting x =1 and y = 16.10 in y = ax + b:

16.10 = a + b .....(i)

Now putting x =3 and y = 21.30 in y = ax + b:

21.30 = 3a + b .....(ii)

Subtract equation (ii) from equation (i)

3a + b =21.30

a + b = 16.10

(-)  (-)    (-)

__________

2a = 5.2

a = 2.6

Putting a = 2.6 in equation (i)

16.10 = 2.6 + b

b = 16.10 - 2.60

b = 13.5

The model is y = 2.6x + 13.5

A worker's starting wage is $13.5 at this job.

Putting x = 7  in y = 2.6x + 13.5:

y = 2.6×7 + 13.5

y = $31.70

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Answer:

[tex]5y^3-2x^2+2[/tex]

Step-by-step explanation:

I like to start off by rearranging the like terms next to each other, going from the greatest power to the least, so that they are more clear.

So in this case it would be: [tex]2y^3+3y^3+x^2-3x^2+1+5-4[/tex]

Now you can add them together. Remember you can only add/subtract coefficient or variable with the same base and power.

And with that in mind, the final result should be,
[tex]5y^3-2x^2+2[/tex]

Hope this helps!

When the number of blue frogs increased by 60% and the number of green frogs decreased by 60%, the percentage of the overall increase is solved to be 60%

Assuming the number of blue frogs and the number of green frogs are equal and = y

Then the total number of frogs = y + y = 2y

Increasing the percentage of each by 60%, the factor for percentage increase by 60% is 1.6

hence 1.6y + 1.6y = 3.2y

percentage change

= change in price / original price * 100

= (3.2y - 2y) / 2y * 100

= 1.2y / 2y * 100

= 0.6 * 100

= 60

hence the percentage change is 60%

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Answer:

z = -8/3 - 5i

Step-by-step explanation:

Sorry, I don't know what a ti-84 calculator is.

But, I can solve this question normally.

Let the real part of z be x and the imaginary part be y.

z = x + iy

|z| = √(x²+y²)

z + |z| = x + iy + √(x²+y²) = 3 - 5i

Now, y has to be -5 as |z| is a real number so the only component affecting i is y. Therefore, y = -5.

Now, lets figure out the real part.

Cancel out imaginary part.

x + √(x² + 25) = 3

3 - x = √(x² + 25)

squaring on both sides,

9 + x² - 6x = x² + 25

6x = -16

x = -8/3

Hence the required complex number is -8/3 - 5i

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The geometric shape formed is a rhombus.

A quadrilateral is a four-sided shape enclosed shape, where the sum of the internal angle is 180°.

Here,
It is mentioned in the question, we have to construct a quadrilateral with two pairs of parallel sides and two angles measuring 125°.
So, the construction of a quadrilateral is shown.
As seen in the figure, the figure is of a rhombus.

Thus, the geometric shape formed is a rhombus.

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Beginning at the y-intercept (0,35),Line is solid, slopes down one and over one, and is shaded beneath.

Choose your variables first.

If x is the amount of hours spent mowing lawns,

Let y equal the number of hours worked at the clothes business.

A minimum of $400 must be earned from both employment (400 or more)

15x + 10y ≥ 400

In order to graph y = -15/10x +35, get y.

10 hours minimum every day in the store.

35 hours maximum per week

x + y ≤ 35

To graph y = -x + 35, find y.

Making the graph: 0 to 35 for the x and y axes.

First equation: y = -15/10x + 35 y-intercept = 35 slope: solid line on the y-axis starting at 35, going down 12, over 10 Shade above solid line

Second formula: y 10

At y=10, draw a solid horizontal line; more than should be shaded above the line.

Third formula: y = -x + 35

beginning at the y-intercept (0,35)

Line is solid, slopes down one and over one, and is shaded beneath.

The overlapping region on the graph will appear as a little triangle with its points under the line from the third equation, above the horizontal line, and above the line from the first equation.

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What else is part of the problem?

Answer:

39

Step-by-step explanation:

x+x+1+x+2=120

3 consecutive numbers leading to x=39 !

Answer:

Let's call the total amount of the lottery winnings x.

If Kelly took one half of the earnings, then she took 1/2x and Toey took 1/2x as well.

Toey spent 1/4 of his earnings, so he spent 1/4*(1/2x) = 1/8x

So Joey spent 1/8 of the total lottery winnings.