1. What is the algebraic expression for the following word phrase:
a. the sum of 4x and 3
b. the quotient of 5 and the sum of 9 and y
C.
the quotient of 7 and y

The quadratic function f(x) = 2x² – 44x + 185 is written in vertex form is f(x) = 2(x –  11)² – 57.

It is a polynomial that is equal to zero. Polynomial of variable power 2, 1, and 0 terms are there. Any equation having one term in which the power of the variable is a maximum of 2 then it is called a quadratic equation.

The quadrattic equation is f(x) = 2x² – 44x + 185.

Take common 2 from the equation, we have

[tex]f(x) = 2(x^2 - 22x )+ 185[/tex]

Add and subtract 121, we have

[tex]f(x) = 2(x^2 - 22x +121 - 121 )+ 185\\\\f(x) = 2[(x^2 - 11)^2-121]+ 185\\\\f(x) = 2(x-11)^2 - 242 + 185\\\\f (x ) = 2(x-11)^2 -57[/tex]

And we know that the standard equation

f(x) = a(x - h)² + k

On comparing, we have

The vertex (h, k) is (11, -57).

More about the quadratic equation link is given below.

https://brainly.com/question/2263981

Answer:

1. 2

2. 2

3. 11

4. -57

Step-by-step explanation: actual answers

Volume Formula: length x width x height

---Let's first write down what we're given.

Volume = 80

Length = 4

Width = 4

Height = ?

---Now, plug what we know into the formula for volume and solve for the missing variable.

80 = 4 x 4 x h

80 = 16 x h

h = 5

g = 5 centimeters

Hope this helps!

Answer:

1,900 miles in 3 days is going fast than 2,700 miles in 3 days

Step-by-step explanation:

1,900 divided by 2 is = 950

2,700 miles divided in 3 days is = 900

Answer:

your family traveled faster

Step-by-step explanation:

your family traveled 1,9000 miles in 2 days and to find speed you need to divide 1,900 by 2 (answer is 950)

do the same for 2,700 and 3 (900 is answer)

compare the two and you have your answer!

Hope this helps and that you have a wonderful evening/day!

Answer:

8

Step-by-step explanation:

The required, following the given condition of the equation model,  8 times 8 equals 64.

We start with the equation 8x = 64, where x represents the unknown value we're trying to find. The equation states that when we multiply 8 by x, the result is 64.

To solve for x, we want to isolate it on one side of the equation. In this case, we can achieve this by dividing both sides of the equation by 8. Dividing both sides by 8 gives us:

8x = 64

(8x) / 8 = 64 / 8

Simplifying, we have:

x = 8

Therefore, 8 times 8 equals 64.

Learn more about the equation here:

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Answer:

$1.30

Step-by-step explanation:

We need to figure out how much each friend gets out of the 5.20 so we will have to divide :)

5.20/4 = $1.30

Have an amazing day!!

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Answer:

Step-by-step explanation:

Given function:

The function is linear and it represents:

According the above explanation the correct answer choice is C

Slope intercept form of a line is given by y=mx+b

Compare to our given function

Here

As it's about height

The rate of change in height is denoted here

Option C is correct

Answer:

this is easy the a sewer is 12

Answer:

254.47sqft (square feet) of paint

Step-by-step explanation:

The surface area of the cylinder (282.74) minus the area of the one circle that doesn't need to be painted (28.27) is 254.47sqft which is the amount of paint he will need Mr. Jones.

Answer:

 [tex]\frac{c-3p}{7}[/tex]

Step-by-step explanation:

1) 4(2a+p)=c+p+a

2) Expand: 8a+4p=c+p+a

3) subract a and 4p: 7a=c-3p

4) Divide: a=[tex]\frac{c-3p}{7}[/tex]

Answer provided by Education Point

S1: ∠YLF ≅ ∠FRY (Given)

S2: ∠RFY ≅ ∠LFY (Given)

S3: FY ≅ FY (Transitive property)

S4: ΔFRY ≅ ΔFLY (AAS theorem)

The AAS congruence theorem states that if two triangles have two pairs of corresponding congruent angles, and a pair of corresponding non-included side that are congruent, then both triangles area congruent.

To prove that ΔFRY ≅ ΔFLY, the proof that shows they are congruent by the AAS congruence theorem is:

S1: ∠YLF ≅ ∠FRY (Given)

S2: ∠RFY ≅ ∠LFY (Given)

S3: FY ≅ FY (Transitive property)

S4: ΔFRY ≅ ΔFLY (AAS theorem)

Learn more about the AAS Theorem on:

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Answer:

The price for each pound of tuna is not always the same.

Step-by-step explanation:

What we do is divide the price by the amount of tuna to find the price for each amount of tuna

For the 1st one, we have $8 for 2 tuna so we do 8/2

8/2 = 4

For the 2nd we have $16 for 4 so we do 16/4

16/4 = 4

For the 3rd, we have $27 for 9 so we do 27/9

27/9 = 3

Step-by-step explanation:

Given: A parallelogram ABCD with AC as its diagonal

To prove: <A=C & <B=<D

Proof:

Opposite sides of parallelogram is parallel

So, AB || DC and AD || BC.

Since AB || DC

& AC is the transversal

< BAC = < DCA (Alternate angles...(1) )

Since AD || BC & AC is the transversal

<DAC = < BCA (Alternate angles)...(2)

when adding equation 1 and 2

<A=<C

In similar case,

<B=<D

Answer:

First, we bring the equation to the form ax²+bx+c=0, where a, b, and c are coefficients. Then, we plug these coefficients in the formula: (-b±√(b²-4ac))/(2a) . See examples of using the formula to solve a variety of equations.

That 6 should be -6

Let me solve it for you

[tex]\\ \rm\rightarrowtail 2x-x-6=0[/tex]

So

[tex]\\ \rm\rightarrowtail x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(2)(-6)}}{2(2)}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{1\pm \sqrt{1+48}}{4}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{1\pm 7}{4}[/tex]

[tex]\\ \rm\rightarrowtail x=\dfrac{8}{4}\:or\:\dfrac{-6}{4}[/tex]

[tex]\\ \rm\rightarrowtail x=2\:or\:\dfrac{-3}{2}[/tex]

Answer:

[tex]\left( x-3\right)^{2} +\left( y-\frac{3}{2} \right)^{2} =\frac{13}{4}[/tex]

Step-by-step explanation:

Let  A(2,3) and B(4,0) be the end points of the diameter

then the segment AB is the diameter of the circle

Then the center of the circle (point M) is the midpoint of segment AB

Then M( (2+4)/2 , (3+0)/2 ) then M( 3 , 3/2 )

Now let’s find the radius r of our circle :

r = AB/2

Then

[tex]r=\frac{AB}{2} =\frac{\sqrt{(0-3)^{2}+(4-2)^2} }{2} =\frac{\sqrt{13} }{2}[/tex]

Then Equation of the circle is:

[tex]\left( x-3\right)^{2} +\left( y-\frac{3}{2} \right)^{2} = \left( \frac{\sqrt{13} }{2} \right)^{2} \\\Longrightarrow \left( x-3\right)^{2} +\left( y-\frac{3}{2} \right)^{2} =\frac{13}{4}[/tex]

Total outcomes:

So the final answer is "60"

scenario - as it describes the story and the character's action.

Ella wrote 8 more stories than Anna in the fifth grade.

let s, be the number of pages Anna wrote.

Expression:

s + 8

keeping in mind that a line with a slope of "0" is a horizontal line, Check the picture below.

Answers:

AREA OF A CIRCLE = pi x r^2

5m circle:

when it says 5 i think it means diameter so divide by 2 for radius

5/2 = 2.5

3.14 x 2.5^2=

3.14 x 6.25=

19.625m^2

50mm circle:

50/2= 25

3.14 x 25^2=

3.14 x 625=

1962.5mm^2

40in circle:

40/2= 20

3.14 x 20^2 =

3.14 x 400=

1256in^2

7ft circle:

7/2= 3.5

3.14 x 3.5^2=

3.14 x 12.25=

38.465ft^2

21mm circle:

21/2= 10.5

3.14 x 10.5^2=

3.14 x 110.25=

346.185mm^2

70cm circle:

70/2=35

3.14 x 35^2=

314 x 1225=

3846.5cm^2

Hope that helps :)

Step-by-step explanation:

a scale factor normally applies to lengths (one-dimensional sizes).

the perimeter of a triangle is calculated only by using lengths, so we can apply the scaling factor directly to the perimeter.

perimeter of the new triangle = 2 × perimeter of the old triangle = 2×8 = 16

Answer:

The answer is 68°

Step-by-step explanation:

Recall that tan ∅° = [tex]\frac{Opposite}{Adjacent}[/tex] for a right triangle.

The value opposite to your angle is 5, and the value that is adjacent to it is 2.

In order to solve for the degree, you use tan^-1([tex]\frac{5}{2}[/tex]) on your calculator.

This gives a value of 68.19459, rounded to just 68.

Answer:

3 times bigger

Step-by-step explanation:

[tex]circumference \: of \: a \: circle \: has \: the \: formular \\ c = 2\pi \: r \\for \: the \: original \: circle \: c = 2 \times 3.14 \times 10 = 6.28 \\ = 63 \: approxiately \\ for \: the \: new \: circle \: c = 2 \times 3.14 \times 30 = 188.8 \\ = 188 \: approximately \\ them \: \frac{188}{63} =2.984 \\ = 3 \: approximately \\ therefore \: the \: bigger \: circumferene \: is \: 3 \: times \: the \: smaller \: circumference[/tex]

Answer:

a) 1

Step-by-step explanation:

Tan 5pi/4: 1

Tan (-5pi/4): -1

Tan 5pi/4 in degrees: tan (225°)

Based on the definition of the diagonals of a rhombus, m∠AED = 90°.

A rhombus has two diagonals that bisect each other at right angles, that is they are perpendicular to each other.

Angle 90 is formed at the intersection of the two diagonals of a rhombus.

In rhombus ABCD, ∠AED is formed at the intersection of the diagonals of the rhombus.

Therefore, based on the definition of the diagonals of a rhombus, m∠AED = 90°.

Learn more about diagonals of a rhombus on:

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Answer:

Average velocity

Step-by-step explanation:

The average speed is only different from average velocity because it has direction.

The average speed will be calculated with the hypotenuse A_C, but average velocity will be calculated with the two directions AB_BC.

Answer:

C

Step-by-step explanation:

0.081+6.18 =6.261

0.21+4.93 =5.14  

6.261 - 5.14 = 0.13

so Mai had booming sales of $2500, now her commission used to be 5%, but since she rules it went up to 6%, how much is her commission on that?

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6\% of 2500}}{\left( \cfrac{6}{100} \right)2500}\implies 150[/tex]

since her salary which used to be $200 but is now 200 + 25 = $225, so for that week she earned 225 + commission or 225 + 150 = 375.

Answer:

3 7/8 would be your answer

Answer:

13 [tex]\frac{1}{3}[/tex]% are green

Step-by-step explanation:

totalling the marbles

red = 6

blue = 7

green = 4

orange = 13

total marbles = 6 + 7 + 4 + 13 = 30

fraction of green marbles = [tex]\frac{4}{30}[/tex] = [tex]\frac{2}{15}[/tex]

To change a fraction to a percentage multiply the fraction by 100%

[tex]\frac{2}{15}[/tex] × 100% = 0.1333.. × 100% = 13.33 % = 13 [tex]\frac{1}{3}[/tex]%

Answer:

63

Step-by-step explanation:

30 percent * 210 =

(30:100)* 210 =

(30* 210):100 =

6300:100 = 63