Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a.

10x2 + 80x + 220 = 0

Select the best answer from the choices provided

Answer:

48xy+4

Step-by-step explanation:

Because we know that a square has 4 sides, we can multiply this expression by 4, thus ending in 48xy+4. Hope this helps :)

For this case we have by definition, that the perimeter of a square is given by the sum of its sides. As the sides measure the same, then the perimeter is:

[tex]p = 4l[/tex]

Where "l" represents the side of the square:

Then, they tell us that:

[tex]l = 12xy + 1[/tex]

So:

[tex]p = 4 (12xy + 1)\\p = 48xy + 4[/tex]

ANswer:

[tex]p = 48xy + 4[/tex]

Answer:-2.125

Step-by-step explanation:

1. simplify the function

-2(x+3)2-5

(-2x-6)2-5

(-4x-12)-5

-4x-17

2. formula for axis of symmetry: -b/2a

a=-4 b=-17

-(-17)/2(-4)=17/-8=-2.125

Answer:

The axis of symmetry for the function f(x) is x=-3.

Step-by-step explanation:

The vertex form of a quadratic function is

[tex]y=a(x-h)^2+k[/tex]                 .... (1)

Where, (h,k) is vertex and x=h is the axis of symmetry.

The given function is

[tex]f(x)=-2(x+3)^2-5[/tex]           .... (2)

From (1) and (2), we get

[tex]a=-2,h=-3,k=-5[/tex]

The axis of symmetry is

[tex]x=h[/tex]

Substitute h=-3 in the above equation.

[tex]x=-3[/tex]

Therefore the axis of symmetry for the function f(x) is x=-3.

Answer:

880

Step-by-step explanation:

First we have to convert 1 mile into inches.

1 mi * 5280 ft/mi * 12 in/ft = 63,360 inches

Each rotation covers 72 inches, so the number of rotations is:

63,360 in / (72 in / rotation) = 880 rotations

Answer:

880

Step-by-step explanation:

I got it right on my test.

Answer:

you need to give more info please

Step-by-step explanation:

To measure length to the nearest fourth inch, use a ruler or measuring tape that shows inches and fractions of an inch. Align the beginning of the ruler or tape measure with one end of the object and identify the nearest one-fourth inch mark.

When measuring length to the nearest fourth inch, you can use a ruler or a measuring tape that shows inches and fractions of an inch. Start by aligning the beginning of the ruler or tape measure with one end of the object you want to measure. Then, identify the nearest one-fourth inch mark on the ruler or tape measure and record the measurement. For example, if the object aligns with the 3 1/4 inch mark, the length can be recorded as 3 1/4 inches.

Answer:4/3

Step-by-step explanation:BY PHYTHAGORAS THEOREM

OPP=X,ADJ=3,HYP=5

5^2=3^2+X^2

25=9=X^2

25-9=X^2

16=X^2

4=X

BY TRIGONOMERTRY

SOHCAHTOA

TAN=OPP/ADJ

=4/3

The answer is:

[tex]Tan(\beta)=Tan(53.13)=1.33\°[/tex]

or

[tex]Tan(\beta)=\frac{4}{3}[/tex]

To find the answer, we first need to find the value of the given angle, we can calculate it since we already know the cosine of that angle.

So, solving we have:

[tex]Cosine(\beta)=\frac{3}{5} \\\\Cosine((\beta)^{-1}=Arccos(\frac{3}{5})\\\\\beta =53.13\°[/tex]

Now, that we know that the angle is equal to 53.13°, we can calculate the value of the tangent, so:

[tex]Tan(\beta)=Tan(53.13)=1.33\°[/tex]

Also, we can find it using the Pythagorean Theorem and the trigonometric identities:

We have that:

[tex]Cosine=\frac{Adjacent}{Hypothenuse}[/tex]

So, using the given information we have:

[tex]Cosine=\frac{3}{5}[/tex]

Where,

Hypothenuse, is equal to 5.

Adjacent, side is equal to 3.

So, we are looking for the opposite side.

Then, substituting it into the Pythagorean Theorem formula, we have:

[tex]Hypothenuse^{2}=Adjacent^{2}+Opposite^{2}\\\\5^{2}=3^{2}+Opposite^{2}\\\\Opposite^{2}=25-9=16\\\\Opposite=\sqrt{16}=4[/tex]

Now that we already know the opposite side, we can find the value of the tangent that will be:

[tex]Tan(\beta)=\frac{Opposite}{Adjacent}=\frac{4}{3}[/tex]

Have a nice day!

Your answer should be x < 0 or x > 4.

I'm 3 Brainliests away from ranking up, so one would be much appreciated. Thank you, and good luck!

since this a 45 45 90 right triangle to get the side lengths you divide 2 times the square root of 2 and you get 2, since this has two congruent angles which makes it an Isosceles triangle. your a and b value are 2.

Answer:

y-axis The vertical number line in a coordinate graph. The line in the coordinate plane, usually vertical, or in space, containing those points whose first coordinates (and third, in space) are 0. y-coordinate The second coordinate of an ordered pair or ordered triple.

Step-by-step explanation:

[tex](4t-\dfrac{8}{5})-(3-\dfrac{4}{3}t)---------------\dfrac{16t}{3}-\dfrac{23}{5}[/tex]

[tex]5(2t+1)+(-7t+28)--------------3t+33[/tex]

[tex](\dfrac{-9}{2}t+3)+(\dfrac{7}{4}t+33)-----------------\dfrac{-11t}{4}+36[/tex]

[tex]3(3t-4)-(2t+10)-------------7t-22[/tex]

a)

[tex](4t-\dfrac{8}{5})-(3-\dfrac{4}{3}t)[/tex]

Firstly we will open the parentheses term and then on combining the like terms and then solving them.

[tex]=4t-\dfrac{8}{5}-3+\dfrac{4}{3}t\\\\i.e.\\\\=4t+\dfrac{4}{3}t-\dfrac{8}{5}-3\\\\=\dfrac{4t\times 3+4t}{3}+\dfrac{-8-3\times 5}{5}\\\\=\dfrac{16t}{3}-\dfrac{23}{5}[/tex]

b)

[tex]5(2t+1)+(-7t+28)\\\\=5\times 2t+5\times 1-7t+28\\\\=10t+5-7t+28\\\\=10t-7t+5+28\\\\=3t+33[/tex]

( Here we used distributive property for first bracket and open the parentheses term and them we combined the like terms and finally simplified our terms )

c)

[tex](\dfrac{-9}{2}t+3)+(\dfrac{7}{4}t+33)[/tex]

We firstly open our parentheses term but there will be no change in the terms since the sign before parentheses is positive.

and then we will combine the like terms and simplify them.

[tex]=\dfrac{-9}{2}t+3+\dfrac{7}{4}t+33\\\\\\=\dfrac{-9}{2}t+\dfrac{7}{4}t+3+33\\\\\\=\dfrac{-9t\times 2+7t}{4}+36\\\\\\=\dfrac{-11t}{4}+36[/tex]

d)

[tex]3(3t-4)-(2t+10)[/tex]

i.e. we use the distributive property for first bracket and open second parentheses term. since the sign before the second parentheses is negative hence the sign of the terms will get interchanged.

i.e.

[tex]=3\times 3t+3\times (-4)-2t-10\\\\i.e.\\\\=9t-12-2t-10\\\\=9t-2t-12-10\\\\=7t-22[/tex]

Answer:

x = -4.5

Step-by-step explanation:

We shall be using the following property of logarithms;

[tex]lna+lnb=ln(a*b)[/tex]

Therefore, In -x + In 8 can be re-written as;

[tex]ln-x+ln8=ln(-8x)\\\\ln(-8x)=ln36\\\\-8x=36\\\\x=-4.5[/tex]

Answer:

about 54% of the people surveyed were females

Step-by-step explanation:

to calculate the % of females out of everyone, you need to add everyone up, and then add up only the females.

119+150+447+735+1174+103+171+512+710+756=4877

4877 is the Total number of people surveyed

119+150+447+735+1174=2625

2625 is the total number of females surveyed

so

to convert 2625/4877 to a %, first turn it into a decimal

2625/4877=0.538

now multiply 0.538 by 100

0.538*100=53.8%

so about 54% of the people surveyed were females

D) about 54% of the people were women

Answer:

Step-by-step explanation:

It seems that the question was cut off before it was completed. To provide an answer related to the domain in mathematical terms, the domain is an essential component of a function. Let me explain it in detail:
In mathematics, when we talk about a function, f(x), the domain of the function represents the set of all possible input values (x-values) for which the function is defined. It's essentially the set of "allowable" values that we can plug into our function to get an output.
To determine the domain of a given function, we have to consider the nature of the function itself and any mathematical rules or constraints that apply. Here are several examples that can come up:
1. **For a polynomial function**, such as f(x) = x^2 - 3x + 2, there's no restriction on the x-values. So the domain is all real numbers, often written as (-∞, ∞).
2. **For a rational function** (a ratio of two polynomials), like f(x) = (2x + 1) / (x - 3), we must exclude x-values that would make the denominator equal to zero, since division by zero is undefined. In this case, the domain is all real numbers except x = 3, or in interval notation: (-∞, 3) U (3, ∞).
3. **For a square root function**, such as f(x) = √(x - 4), the expression inside the square root must be non-negative, since we're typically considering real-valued functions. So the domain of this function is x ≥ 4, or in interval notation, [4, ∞).
4. **For a logarithmic function**, like f(x) = log(x), the argument of the logarithm must be positive. Therefore, the domain is x > 0, or in interval notation, (0, ∞).
5. **For trigonometric functions**, such as f(x) = sin(x), since there are no restrictions on the input of sine function in terms of real numbers, the domain is all real numbers.
In conclusion, to define the domain of a particular function, we need to consider the mathematical constraints such as not dividing by zero, keeping the radicand of square roots non-negative, and ensuring the arguments of logarithms positive, among others. Once these conditions are taken into account, we can specify the domain of the function, which is often expressed as an interval or a set of intervals on the real number line.

Answer:

B. 8.37 ft

Step-by-step explanation:

⇒This question is on circumference

⇒The water sprinkler covers a circular pattern as it moves to cover 300° and remain with 60° to cover so as to complete a single circular pattern.

⇒The remaining distance asked is the one represented by 60°

⇒Apply the formula for circumference of a circle with angle theta

[tex]c=2\pi r\alpha/360[/tex]   where alpha is the angle in degrees

Given that r=8ft and ∝=60°

c=3.14×2×8×60°/360°

c=8.37 ft

We have the function [tex]y = \frac{2}{3} x -3[/tex] and we want to find a function that has the same y-intercept than the previous function.

First, let's find the y-intercept by subtituting 0 for 'x'.

[tex]y = \frac{2}{3} (0) -3 = -3[/tex]

Now that we found that y-intercept =-3, any lineal function of the type: [tex]y = ax - 3[/tex] will have the same y-intercept. Where 'a' can take all the real values.

Also, any quadratic function of the type: [tex]y=ax^{2} + bx - 3[/tex] will have the same y-intercept. Where 'a' and 'b' can take all the real values.

Answer:

r=64°

Step-by-step explanation:

angles in a triangle = 180°

180 -37 -27 = 116

angles in a straight line = 180°

180 -116 = 64

r= 64

Answer:

d. 64

Step-by-step explanation: i had it on usa testprep

Answer:

[tex]32x^3+4x^2+41x-35[/tex]

Step-by-step explanation:

We have these two polynomials

[tex](8x-5)(4x^2+3x+7)[/tex]

Now we need to distribute one polynomial to all of the terms to the other.

[tex]32x^3+24x^2+56x-20x^2-15x-35[/tex]

Next we can combine all of the like terms

[tex]32x^3+24x^2+56x-20x^2-15x-35\\\\32x^3+4x^2+41x-35[/tex]

Answer: 32x^3 + 4x^2 + 41x - 35

Step-by-step explanation:

Answer:

2.  18 cubic cm.

3. 27 cubic cm

5. 90 cubic m

Step-by-step explanation:

2. Triangular prism

So, we have a triangular prism with a width of 3 cm, a height of 1.5 cm and a length of 4.  We'll take the triangle shape as the base.

Like for any prism, the volume is the base multiplied by the height.

So, the area of the base is found with the regular formula: base x height:

so, 3 x 1.5 = 4.5 sq cm for the base.

Then we multiply the base by the length to get the volume: 4.5 x 4 = 18 cubic cm.

3. Trapezoidal prism

Again, first step is to calculate the area of the trapezoid shape, then multiply by its depth.

The area of a trapezoid is calculated with the formula:

A = h/2 * (a + b) where a and b represent the short and long sides respectively.

So, for our given trapezoid:

A = 1.5/2 * (2+4) = 0.75 * 6 = 4.5 sq cm.

Then we multiply the base area by the height to get the volume:

V = 4.5 * 6 = 27 cubic cm

5. Triangular prism 2

The best way to approach this one is to consider it's a triangle prism with a height of 3 cm, and use the triangle shape (with sides of 13 and 5) as the base.

But to calculate the area of that triangle we need to find out the missing length. Using Pythagore's theorem, we can easily find the length of the other side with the hypotenuse formula:

hypotenuse² = sideA² + sideB²

In our case, we have:

13² = x² + 5²

169 = x² + 25

x² = 144

x = 12

Now we can calculate the area of the triangle easily:

A = (b x h)/2 = (5 x 12)/2 = 30 sq m

Then multiply by the thickness of the prism....

V = 30 x 3 = 90 cubic m

Answer:

The given quadrilateral is a rectangle.

Step-by-step explanation:

We are given the vertices of a quadrilateral,

We can use the slopes and modulus of all sides to determine whether it is a rectangle or not. The four sides of the quadrilateral are Ab, BC, CD and AD. So finding slopes of all sides using the formula

[tex]Slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where x_1 and y_1 are the coordinates of firsst vertex and x_2 and y_2 are coordinates of second vertex.

So.

Slopes are:

Slope of AB = 2 and Length=2.23

Slope of BC = -1/2 and length = 4.47

Slope of CD = 2 and length = 2.23

Slope of AD = -1/2 and length = 4.47

As we can see that the slope of AB and CD is equal which means that they are parallel and their lengths are also same.

Similarly BC and AD have same slope which means that they are also parallel and their lengths are also equal.

More over the product of slopes of AB and CD, BC and CD, CD and AD and AD and AB is equal to -1 which indicated that these sides are parallel to each other so it can be concluded that as the opposite sides of the quadrilateral are equal and the interior angles are 90 degrees so the quadrilateral is a rectangle ..

Answer:

I am given that the vertices of quadrilateral ABCD are A(-1, 6), B(-2, 4), C(2, 2), and D(3, 4). The slope formula applied to each pair of adjacent vertices gives the slopes (m) of the sides:

slope of AB (m AB) = 4 - 6 / -2 - -1)  = -2 / -1 =2

slope of BC (m BC) = 2 - 4 / 2 - (-2)  = -2 / 4 = - 1 / 2

slope of CD (m CD) = 4 - 2 / 3 -2  = 2 / 1 =  2

slope of DA (m DA) = 6 - 4 / - 1 -3  = 2 / - 4 =  - 1 / 2

Because line segments with equal slopes are parallel, segment AB is parallel to segment CD and segment BC is parallel to segment DA.

Multiplying the slopes of one pair of adjacent sides, I find that.

mAB * mBC = 2 * - 1/2 = - 1

If the product of the slopes of two segments is -1, then they are perpendicular. Since both pairs of opposite sides have been proven parallel, proving one pair of adjacent sides perpendicular implies that the other pair of adjacent sides are also perpendicular. Therefore, by definition, quadrilateral ABCD is a rectangle.

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

The common difference d of an arithmetic sequence is

d = [tex]a_{2}[/tex] - [tex]a_{1}[/tex] = [tex]a_{3}[/tex] - [tex]a_{2}[/tex]

Substitute in values and solve for k, that is

5k - 1 - 2k = 6k + 2 - (5k - 1)

3k - 1 = 6k + 2 - 5k + 1

3k - 1 = k + 3 ( subtract k from both sides )

2k - 1 = 3 ( add 1 to both sides )

2k = 4 ⇒ k = 2

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

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] + (n - 1)d

[tex]a_{1}[/tex] = 2k = 2 × 2 = 4 and

d = 5k - 1 - 2k = 3k - 1 = (3 × 2) - 1 = 5

Hence

[tex]a_{8}[/tex] = 4 + (7 × 5) = 4 + 35 = 39

6 ft person casts 18 ft shadow

x ft tree casts 20 ft shadow

6*20 = 18x

120 =18x

x=120/18

×≈6.67

The height of the tree is 6.67 feet.

The term proportionality describes any relationship that is always in the same ratio.

Given that, a tree casts a 20-foot shadow at the same time the person who is 6 feet tall casts a shadow 18 ft, we need to find the height of the tree.

Here, using the concept of proportionality, since, the phenomena is happening at the same time, therefore, the ratio of the height and length if the shadow will be equal for all.

Let the height of the tree be x,

20 / x = 18 / 6

120 = 18x

x = 6.67

Hence, the height of the tree is 6.67 feet.

Learn more about proportionality, click;

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Answer:  B) y = -4 sin(x - π/2)

Step-by-step explanation:

The graph of a sine function is the cosine function shifted π/2 units to the right.

Similarly, the graph of a cosine function is the sine function shifted π/2 units to the left.

[tex]b=a+5[/tex]

Hope this helps.

Answer:

b=a+5

Step-by-step explanation:

6-1=5

7-2=5

8-3=5

9-4=5

Please rate brainliest! :D

Answer: what are the options?

Step-by-step explanation:

answer: f(x)<4

I really hope that heped

Answer:

D The bottom choice.

Step-by-step explanation:

The range is the y value of (in this case) an absolute value. The maximum value of this is 4. Everything else is less than 4. The answer would be written as

4≥f(x) which is the same thing as D

Answer:

A

Step-by-step explanation:

AE=EC

5x-10=2x+5

5x-2x=5+10

3x=15

x=5

Answer:

The correct answer is option A.  5

Step-by-step explanation:

It is given a rectangle ABCD

To find the value of x

It is given that,

AE = 5x - 10 and EC = 2x + 5

Since ABCD is a rectangle, All diagonals are equal.

AC = BD and AE = EC

AE = EC

5x - 10 = 2x + 5

5x - 2x = 5 + 10

3x = 15

x = 15/3 = 5

Therefore the correct answer is option A.  5

Answer:

see explanation

Step-by-step explanation:

Given

2x - [tex]\frac{3}{x}[/tex] = 1

Multiply through by x

2x² - 3 = x ( subtract x from both sides )

2x² - x - 3 = 0 ← in standard form

To factorise the quadratic

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x- term.

The factors are + 2 and - 3

product = 2 × - 3 = - 6 and sum = 2 - 3 = - 1

Use these factors to split the x- term

2x² + 2x - 3x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x + 1) - 3(x + 1) = 0 ← factor out (x + 1) from each term

(x + 1)(2x - 3) = 0

Equate each factor to zero and solve for x

x + 1 = 0 ⇒ x = - 1

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = [tex]\frac{3}{2}[/tex]

The blue dot on the number line has a value of 6.

To determine the value of the blue dot on the number line, we need to understand the spacing between consecutive dots. Given that the fifth dot is marked as 2 and the seventh dot is marked 10, we can calculate the spacing between each consecutive dot.

The spacing between each pair of dots is given by:

[tex]\[ \text{Spacing} = \frac{\text{Value of Seventh Dot} - \text{Value of Fifth Dot}}{\text{Number of Dots between}} \][/tex]

Substitute the given values:

[tex]\[ \text{Spacing} = \frac{10 - 2}{7 - 5} = \frac{8}{2} = 4 \][/tex]

Now, calculate the value of the blue dot:

[tex]\[ \text{Value of Blue Dot} = \text{Value of Fifth Dot} + (\text{Spacing} \times \text{Number of Dots to the Blue Dot}) \][/tex]

[tex]\[ \text{Value of Blue Dot} = 2 + (4 \times 1) = 6 \][/tex]

Therefore, the blue dot on the number line has a value of 6.

Answer:

Step-by-step explanation:

Let me give you an example of a exponential equation and if you need more help let me know.

Ex: 3^2x-1=27

3^2x-1=3^3 (3x3x3=27)

2x-1=3

2x+4

x= 2.

Hope my answer has helped you!

Solving exponential equations involves understanding exponential notation, the concept of logarithms, the rules of division in exponentials, and the relationship between the exponent and the decimal shifts.

To solve exponential equations, understanding exponential notation is crucial. This notation is used to express very large and very small numbers as a product of two numbers. The first number of the product referred to as the digit term, is usually not less than 1 and not equal to or greater than 10. The second component of the product considered the exponential term, is written as 10 with an exponent. Definitely, knowing about the squaring of exponentials is helpful, where you square the digit term in the typical way and multiply the exponent of the exponential term by 2.

What also comes in handy in this process is the concept of logarithms. For instance, the logarithm of a product of two numbers is the sum of the logarithms of the two numbers. To put it in a mathematical expression, log xy = log x + log y.

Moreover, when dealing with division in exponential equations, you typically divide the numbers out front and subtract the exponents. For example, if you have 10⁶ divided by 10³, you will get 10^(6-3) = 10³.

Lastly, the power or exponent of 10 is equal to the number of places the decimal is shifted. For example, 1,230,000,000 can be written as 1.23 × 10⁹, and 0.00000000036 can be written as 3.6 × 10⁻¹⁰.

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Answer:

d

Step-by-step explanation:

Hey there! :)

Equation 1 : -5x + 3y = 2

Equation 2 : -5x - 5y = -30

Because both equations contain a like term (which in this case is 5x), we can easily subtract these equations from one another.

Subtract equation 1 from equation 2 :

-5x - (-5x) = 0

3y - (-5y) = 3y + 5y --> 8y

2 - (-30) = 2 + 30 --> 32

This leaves us with 8y = 32. Simplify this to get y by dividing both sides by 8.

8y ÷ 8 = 32 ÷ 8

Simplify.

y = 4

Now, plug in 4 for y in our first equation.

-5x + 3(4) = 2

Simplify.

-5x + 12 = 2

Subtract 12 from both sides.

-5x = 2 - 12

Simplify.

-5x = -10

Divide both sides by -5.

-5x ÷ -5 = -10 ÷ -5

Simplify.

x = 2

Therefore, our answer is :

(2, 4) where x = 2, y = 4

~Hope I helped!~