HELP PLEASE !!!
What is the measure of ‹1?

The vertex for the given equation [tex]y=x^2+5x-7 is (-2.5,-4.25)[/tex] and the solution  to the equation is x = -5,7/1. Similarly , the vertex for the given equation  [tex]y=-x^2+3x+8\ is\ (-3/2,1/4)[/tex] and the solution to the equation is [tex]x = -2,4[/tex].

The graph of a quadratic function is a symmetrical, U-shaped geometric form known as a parabola. It is the collection of all points that are equally spaced apart from a fixed point (referred to as the focus) and a fixed straight line (called the directrix).

A parabola's vertex is the location where its symmetry line and parabola intersect.

The vertex of a parabola is the highest or lowest point on the graph of the parabola. In the case of a parabola in the form of [tex]y = ax^2 + bx + c[/tex], the vertex is the point (h, k), where:

[tex]h = -b / 2a\\k = f(h) = a(h^2) + bh + c[/tex]

For the first equation: [tex]y = x^2 + 5x - 7[/tex]

The vertex would be:

[tex]h = -b/2a = -5/2 = -2.5\\k = f(h) = a(h^2) + bh + c = (1)((-2.5)^2) + (5)(-2.5) - 7 = 6.25 - 12.5 - 7 = -4.25[/tex]

So the vertex is [tex](-2.5,-4.25)[/tex]

For the second equation:[tex]y = -x^2 + 3x + 8[/tex]

The vertex would be:

[tex]h = -b/2a = -3/2(1) = -3/2\\k = f(h) = a(h^2) + bh + c = (-1)((-3/2)^2) + (3)(-3/2) + 8 = -9/4 + -9/2 + 8 = 1/4[/tex]

So the vertex is [tex](-3/2,1/4)[/tex]

To find the solutions or roots of the equation, you can set the equation equal to zero and solve for x.

[tex]y = x^2 + 5x - 7 = 0\\x^2 + 5x - 7 = 0\\x^2 + 5x - 7 + 7 = 0 + 7\\x^2 + 5x = 7\\x(x+5) = 7\\x = -5,7/1\\y = -x^2 + 3x + 8 = 0\\x^2 - 3x - 8 = 0\\(x-4)(x+2) = 0\\x = -2,4[/tex]

Solutions for first equation are x = -5 and x = 7/1 and for the second equation are x = -2 and x = 4

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Answer:

Step-by-step explanation:

1 quart =  2 pints  =  4 cups

1 pint = 2 cups

1/2 pint =  1  cup    .....so.....

First question

5 quarts  =  10 pints

10 * (3/4)  =  7.5 pint   contianers   will fill it  3/4  full  

7.5   pints   =    7  pints   +  1 cup

Answer:

Tori spends $342.00 on coffee over 9 months

Step-by-step explanation:

38 x 9 = 342

= $342.00

Answer:

Quadrant I

Step-by-step explanation:

b/c both are on the right side that means they are positive

9514 1404 393

Answer:

  -2

Step-by-step explanation:

Put 6 where x is and do the arithmetic.

  [tex]f(6)=\dfrac{5\cdot6-34}{2}=\dfrac{30-34}{2}=\dfrac{-4}{2}=\boxed{-2}[/tex]

The corresponding range value is -2.

__

The ordered pair is (6, -2).

Answer: 1/9 of the cake

Step-by-step explanation:

Charlie ate 2/3 of the cake which means that what is left to give the friends is:

= 1 - 2/3

= 1/3 of the cake

This was divided equally amongst three friends so the expression would be:

= 1/3 ÷ 3

This can also be written as:

= 1/3 * 1/3

= 1/9

Each friend got 1/9 of the cake.

Answer:

1/9 of the cake

Step-by-step explanation:

1  -  2/3    =   1/3   left

(1/3)  / 3   =    1/9   =  what each friend got

In  one fell  swoop  we  have  ( 1 - 2/3)  / 3     =   1/9

Answer:

y ≥ 1

Step-by-step explanation:

According to the graph, the y values start at 1 and go to ∞. Therefore, the range of the function is y ≥ 1.

[tex]\huge\text{Hey there!}\\\\\\\mathsf{\dfrac{3}{21}}\\\\\mathsf{= \dfrac{3\div3}{21\div3}}\\\\\mathsf{= \dfrac{1}{7}}\\\\\huge\text{Therefore, your\ answer\ should\ be: \huge\boxed{\mathsf{\dfrac{1}{7}}}}}\huge\checkmark\\\\\\\\\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

the picture is not available, pls try again

Therefore, if the cafeteria sells all of the pancakes made for 75 people, they will make $525.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary method can be used to complete it.

Two quantities are compared to form a ratio. An equality of two ratios is a percentage. How to format a ratio Analyze the ratio to see whether it is part to part or part to whole. Calculate the whole and the pieces as necessary.

If the cafeteria sells all of the pancakes made for 75 people, and the original recipe makes 14 pancakes, they would need to make 1475 = 1050 pancakes.

If they charge $0.50 per pancake and they sell all 1050 pancakes, they would make 1050$0.50 = $525.

Therefore, if the cafeteria sells all of the pancakes made for 75 people, they will make $525.

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Answer:

uhhugvtrctreex

Step-by-step explanation:

Answer:

9π units

Step-by-step explanation:

The arc length is calculated as

length = [tex]\frac{1}{2}[/tex] × 2πr ( r is the radius )

length = πr = π × 9 = 9π ← exact answer

Answer:

12 cups of water

Step-by-step explanation:

This question has to do with conversion

We are told that she buy 1 quart and 1/2 gallon of water.

Hence,

1 quart of water = 4 cups of water

1 gallon of water = 16 cups of water

1/2 gallon of water = x

Cross Multiple

x = 1/2 × 16 cups of water

x = 8 cups of water.

Therefore, the total cups of water that she bought = 4 cups of water + 8 cups of water = 12 cups of water

Answer: [tex]\$47,471[/tex]

Step-by-step explanation:

Given

Julien's parents want $64,000 at the end of 3 years

The rate of interest is 10% annually

Suppose they invested P amount initially

So, compound interest, compounded monthly is

[tex]\Rightarrow A=P\left( 1+\frac{r}{n}\right)^{nt}\quad [\text{n=Numner of compounding periods}]\\\\\text{Insert the values}\\\Rightarrow 64,000=P\left( 1+\frac{0.10}{12}\right)^{12\times 3}\\\\\Rightarrow 64,000=P\left( 1+\frac{10}{12}\right)^{36}\\\\\Rightarrow P=\dfrac{64000}{1.3481}\\\\\Rightarrow P=\$\ 47,471.37\approx \$ 47,471[/tex]

Step-by-step explanation:

credits are also on there

Answer:

28 classes

Step-by-step explanation:

84/3 = 28 classes

Answer:

28 classes didn't learn about the Holocaust

Step-by-step explanation:

If there are 84 classes and two-thirds learned about the Holocaust that means that you have to divide by three.

84 ÷ 3 = 28

Then, you can check your answer by multiplying 28 × 3 = 84

Answer:

Left triangle: 12.5 cm

Right triangle: 21 cm

Trapezoid: 50 cm

Total: 83.5

Step-by-step explanation:

Left triangle: The formula to find the area of a triangle is 1/2bh, in which b=base and h=height. The base of the left triangle is 5 cm and the height is 5 cm. 5*5=25. 25/2=12.5 cm.

Right triangle: Once again, use the area formula for a triangle. The base of the right triangle is 6 cm and the height is 5+2=7. 6*7=42. 42/2=21 cm.

Trapezoid: The formula to find the area of a trapezoid is a+b/2(h) in which a and b are the top and bottom of the trapezoid and h=height. In this case, a=9 cm and b=5+6=11 cm. The height is 5 cm. 9+11=20. 20/2=10. 10*5=50 cm.

Add all of the areas. 12.5+21+50=83.5. So, the total area is 83.5 cm.

The height of the tree to the nearest hundredth of a meter is 10.5 meters.

The length of Jai's shadow = length of tree's shadow - distance of standing of Jai

Length of Jai's shadow = 39.55 - 34.1

Performing subtraction on Right Hand Side of the equation

Length of Jai's shadow = 5.45 meters

Tan theta = height of tree/length of shadow = height of Jai/length of his shadow

height of tree/39.55 = 1.45/5.45

Keep the values in formula

Height of tree = 39.55×1.45/5.45

Performing multiplication

Height of tree = 57.35/5.45

Performing division

Height of tree = 10.5 meters

Thus, the height of tree is 10.5 meters.

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If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.

The following formula determines how many combinations of n objects can be taken r at a time: (n,r) = C(n,r)! .

She was a master of both wit and martial arts. The art and science of education blend beautifully. He saw slam poetry as the ideal synthesis of thought, writing, and theater. The desired mix is produced by the computer system (the perfect combination of arabica and robusta).

Five documentaries make up the total.

7 comedies total are available.

Four mysteries are present.

5 horror movies are there.

A total of 14 films, excluding comedies, are available.

If he wants to rent all 7 comedies, there are a total of 9 different combinations that he can do.

1 * (14*13)/2 = 91

If he wants to rent all 7 comedies, there are 91 different combinations of 9 movies that he could do so.

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Area of the region enclosed by one loop of the curve is pi/288.

To find the area of the region enclosed by one loop of the curve, we can use the formula for the area of a polar region:

A = 1/2 * ∫(r^2)dθ

We can use this formula with the equation for r given:

A = 1/2 * ∫(sin^2(6θ))dθ

This integral can be simplified by noting that sin^2(x) = (1/2)(1 - cos(2x))

Thus,

A = 1/2 * ∫(1/2)(1 - cos(12θ))dθ

This integral can be solved by noting that the antiderivative of (1/2)(1 - cos(12θ)) is (1/24)(sin(12θ) + θ).

Therefore, the area enclosed by one loop of the curve is

A = 1/2 * ((1/24)(sin(12θ) + θ)) evaluated from 0 to pi/6

A = (1/48)(sin(2pi) + pi/6)

   = (1/48)(0 + pi/6)

   = pi/288

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Answer:

y = 2x - 9

Step-by-step explanation:

y2 - y1 / x2 - x1

9 - (-1) / 9 - 4

10 / 5

= 2

y = 2x + b

-1 = 2(4) + b

-1 = 8 + b

-9 = b

Answer:

2x + 11 is your answer

Step-by-step explanation:

yeah just 2x + 11

Answer:

c) 2.2 feet

Step-by-step explanation:

1) Iris' puppy is 2 1/5 feet long. Which

decimal represents Iris' puppy's length?

c) 2.2 feet

Answer:

64

Step-by-step explanation:

Answer:

78

Step-by-step explanation:

13! / 11! · 2!

13 x 12 / 2

13 x 6 = 78

The value of GI, given that GH = 2x - 9 , HI = 14 , and GT = 3x - 8 will be 31.

An algebraic equation is formed by comparing two algebraic expressions to one another.

In G-H-I, GH = 2x - 9, HI = 14 , and GT = 3x - 8

If G-H-I is a line and GH, HI and GT lies between G to I

To find G to I ⇒ GI = GH + HI = GT

GI = 2x - 9 + 14 = 3x - 8

2x + 5 = 3x - 8

2x - 3x = -8 - 5

-x = -13

x = 13

Substituting x in GT = 3x - 8; GI = GT

GI = 3(13) - 8

GI = 39 - 8

GI = 31

Using algebraic expressions, if x is 13 then, 3x - 8 or 2x - 9 will be GI = 31

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The number of times the diameter of Uranus is larger than the diameter of Mars is 7.5 times

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

The diameters of Uranus and Mars

These diameters are given as

Diameter of Uranus: 5.11×10^4 kilometers

Diameter of Mars: 6.79×10^3 kilometers

Express the diameters properly

So, we have the following representation

Diameter of Uranus: 5.11 × 10⁴ kilometers

Diameter of Mars: 6.79 × 10³ kilometers

This means that

Number of times larger = Diameter of Uranus/Diameter of Mars

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

Number of times larger = 5.11 × 10⁴ kilometers/6.79 × 10³ kilometers

Evaluate the quotient

So, we have the following representation

Number of times larger = 7.5

Hence, the number of times is 7.5

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