I got no clue how to do this.

Answer:

Step-by-step explanation:

A = x² - 5x - 14

Factor using AC method.  Here, a = 1, b = -5, and c = -14.

ac = 1×-14 = -14

Factors of -14 that add up to -5 are -7 and 2.

A = (x - 7)(x + 2)

So the dimensions are x-7 and x+2.

The dimensions of the rectangle represented by the quadratic equation x² - 5x - 14 could be 7 and -2, but in a physical context we only consider the positive value 7.

The area of a rectangle is given by multiplying its length and width. In this case, the area is expressed as a quadratic equation, x² - 5x - 14 = 0. Quadratic equations typically represent parabolas when graphed on a two-dimensional plot, but in this case, we're looking for linear dimensions of a rectangle. To find the dimensions of the rectangle, we need to factor this equation.

The factors of this quadratic equation are (x - 7) and (x + 2). Therefore, the two dimensions of the rectangle could be 7 and -2. However, in real-world scenarios, dimensions are often positive values due to physical constraints (you can't have a rectangle with negative length or width). So, normally, we would only consider the dimension of 7 (from the factor x - 7) as the real solution to this problem.

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Answer:

Final answer is that function g(x) has the largest maximum value, which is 6.

Step-by-step explanation:

Given function is [tex]F(x)=-4(x-6)^2+3[/tex].

Now we need to find about what is the maximum value of the given function [tex]F(x)=-4(x-6)^2+3[/tex] and explain the method about how did you find the maximum value.

Given function [tex]F(x)=-4(x-6)^2+3[/tex] looks similar to the quadratic function of the form [tex]f(x)=a(x-h)^2+k[/tex].

Comparing both we get: h=6, k=3

We know that maximum value occurs at the vertex where maximum value is given by "k"

Hence maximum value of the given function [tex]F(x)=-4(x-6)^2+3[/tex] is = 3

From graph we can clearly see that function g(x) has maximum height at 6.

So the final answer is that function g(x) has the largest maximum value, which is 6.

Answer:

I'm not sure if this is the answer answer but this what the graph is a parabola

The function represented by the graph is y = 1/4(x - 2)^2 + 1

What function does this graph represent?

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

The graph

The graph is the graph of a quadratic function

By definition:

A quadratic function is represented as

y = a(x - h)^2 + k

Where

Vertex = (h, k)

From the graph, we have

Vertex = (2, 1)

So, we have

y = a(x - 2)^2 + 1

Using the point (0, 2) on the graph, we have

a(0 - 2)^2 + 1 = 2

4a + 1 = 2

4a = 1

a = 1/4

So, we have

y = 1/4(x - 2)^2 + 1

Hence, the function this graph represent is y = 1/4(x - 2)^2 + 1

Answer:

3x-8y=-16

The y intercept is;

(0, 2)

-5x-10y=7

The y intercept is;

(0, -0.7)

Step-by-step explanation:

The y-intercept refers to the point where the graph of an equation intersects or crosses the y-axis. At this point, the corresponding value of x is 0.

From the first equation given;

3x-8y=-16

Substitute x with 0 in the equation and solve for y;

3(0) -8y = -16

-8y = -16

y = 2

The y intercept is thus;

(0, 2)

From the second equation;

-5x-10y=7

Substitute x with 0 in the equation and solve for y;

-5(0) - 10y = 7

-10y = 7

y = -0.7

The y intercept is thus;

(0, -0.7)

Answer:

So, Width  = 7/2 or 3.5

Length =  4

Step-by-step explanation:

Area of rectangle = 14 ft^2

Let width of rectangle 2 = x

and Length of rectangle = 2x-3

Formula used for area of rectangle

Area = Length * Width

14 = (2x - 3) x

14 = 2x^2 - 3x

=> 2x^2 -3x -14 = 0

Solving the quadratic equation using factorization

-28 x^2 = -7x * -4x

2x^2 -7x + 4x -14 = 0

x (2x -7) +2(2x-7) = 0

(x+2) (2x-7) =0

=> x + 2 =0 and 2x -7 = 0

x = -2 and x = 7/2

Since width cannot be negative so, x= 7/2

Width= x = 7/2

Length = 2x -3 => 2(7/2) - 3

=> 7 -3

=> 4

So, Width =  7/2 or 3.5

Length =  4.

Length= 2width-3

Width=x

Length=2x+3

X(2x-3)=14

x must equal 3.5

Length=4

Width=3.5

Answer:

-12

Step-by-step explanation:

According to the graph, [tex]f(-3)=-3[/tex] and [tex]g(-7)=6[/tex]

When given the equation [tex]-6*f(-3)-5*g(-7)[/tex] we can substitute in the values on the graph that we have found.

[tex]-6*f(3)-5*g(-7)\\\\-6*(-3)-5*(6)\\\\18-30=-12[/tex]

Answer:

90 units²

Step-by-step explanation:

The area (A) of a kite is calculated as

A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ ← diagonals

d₁ = 3 + 3 = 6 and d₂ = 20 + 10 = 30, hence

A = 0.5 × 6 × 30 = 90 units²

8 Females have to leave the room which then it would be 22 males and 22 females which is a 1-1 ratio

A ratio shows us the number of times a number contains another number. The number of females who should leave the conference room is 8.

A ratio shows us the number of times a number contains another number.

The ratio of females to males in the room is 15 to 11, therefore, the numbers of female to male ratio can be represented by 15x to 11x.

The sum of the total number of people in the room is 52, and can be represented as,

15x + 11x = 52

26x = 52

x = 2

Thus, the number of females in the conference room is 30(15x=15×2), while the number of males in the conference room is 22(11x=11×2).

Now, for the ratio to be 1:1, the number of males should be the same and the number of females should be equal to the number of males. Therefore, the number of females who should leave the conference room is,

Number of females who should leave conference room = Number of females before - Number of females after

Number of females who should leave conference room = 30 - 22 = 8

Hence, the number of females who should leave the conference room is 8.

Learn more about Ratios:

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Answer:

2.4

Step-by-step explanation:

We have to find the mean first

[tex]Mean = \frac{Sum}{No.\ of\ values}\\ = \frac{2+4+7+2+3+7+9+3+1+7}{10}\\ = \frac{45}{10}\\ = 4.5[/tex]

Now we have to find deviations.

Note that the deviations are calculated by subtracting the mean from the value. The distance is always positive so the deviations will be positive

Value         Deviation

2                 2-4.5 = |-2.5| = 2.5

4                  4-4.5 = |-0.5| = 0.5

7                  7-4.5 = 2.5

2                 2-4.5 = |-2.5| = 2.5

3                 3-4.5 = |-1.5| = 1.5

7                  7-4.5 = 2.5

9                  9-4.5 = 4.5

3                 3-4.5 = |-1.5| = 1.5

1                 1-4.5 = |-3.5| = 3.5

7                  7-4.5 = 2.5

The last step is to find the mean of deviations.

[tex]Mean\ of\ deviations = \frac{(2.5+0.5+2.5+2.5+1.5+2.5+4.5+1.5+3.5+2.5}{10}\\ = \frac{24}{10} \\=2.4[/tex]

The mean absolute deviation of given data set is 2.4 ..

Answer:

The radius of circle L is [tex]7.8\ in[/tex]

Step-by-step explanation:

Remember that a line that passes through the center divide the circle into two equal parts

YV=VM=6 in

VL is perpendicular to YM

so

The triangle VLM is a right triangle

The radius is equal to LM ----> hypotenuse of the triangle VLM

Applying the Pythagoras Theorem

[tex]LM^{2}=VM^{2}+VL^{2}[/tex]

substitute the given values

[tex]LM^{2}=6^{2}+5^{2}[/tex]

[tex]LM^{2}=61[/tex]

[tex]LM=7.8\ in[/tex]

The answer is 8 times bigger.

Hope this helps!

Answer:

2times bigger.

Step-by-step explanation:

Original volume of a rectangular prism = length × width × height

V = lwh... (1)

If the original dimension is doubled

New volume V2 = 2l × 2w × 2h

V2 = 2(lwh)...(2)

Taking the ratio of both volumes

V2/V = 2(lwh)/lwh

V2/V = 2

V2 = 2V

This shows that the new volume was two times bigger than the original volume

Answer:

x=0 and x=1

Step-by-step explanation:

4(1)-4=0

2(3)^(1)-6=0

4(0)-4=-4

2(3)^(0)-6=-4

Answer:

see the attached figure

Step-by-step explanation:

The best unit of measurement that represent each description in the attached figure

Answer:

Step-by-step explanation:

Miles

1. Distance traveled on a bike ride

2. Length of the border between Texas and Oklahoma

3. Distance around a lake.

Feet

1. Distance traveled by a base ball.

2. Height of a mature tree

Inches

1. Diagonal of a computer screen

2. Diameter of a basket ball

3. Width of a sheet of a paper.

It's a much more interesting problem when we have to estimate the shadow length from a photo.

The crater is a curvy bumpy surface, but let's approximate it as part of a sphere and just conflate the arc and chord length, so the 400 m shadow corresponds to a 400 m chord from the edge at the surface to the bottom.

The shadow as a chord forms a hypotenuse right triangle with the depth d being the leg opposite the 48 degree angle of the sun.

[tex] d = 400 \sin 48 \approx 297 \textrm{  m}[/tex]

Answer: 297 m

The depth is 297.26 m.

It is the application of trigonometry.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

The shadow is estimated to be 400 m long.

And the angle of elevation of the sun is 48°.

The depth of a crater.

Hypotenuse = 400m

Angle = 48°

The by the sine rule

[tex]\begin{aligned} \rm sin \theta &= \rm \dfrac{Depth}{Hypotenuse}\\\\\rm sin 48^o &= \rm \dfrac{depth}{400}\\\\\rm depth &= \rm sin 48^o * 400\\\\\rm depth &= 297.2579 \approx 297.26 \end{aligned}[/tex]

Thus, the depth is 297.26 m.

More about the height and distance link is given below.

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Answer:

13 < n < 51

Explanation:

Basically to find the lowest possible length, all you need to do is subtract the lower number from the higher number (32 - 19), and to find the greatest possible length, add the lower number and the higher number (32 + 19). Then you'd plug it in to this inequality: a < n < b, a being the difference, and b being the sum. But, if the triangle were a right triangle that would be a whole different story.

Answer:

C The shaded circle

Step-by-step explanation:

numbers greater than -2

-1,0,1,2,3....

please mark as brainlyest

False.

For a point to lie on the X-axis, the second number needs to be 0, not the first one.

When the first number is 0, the point is on the Y-Axis.

[tex]\bf \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{75\% of 62500}}{\left( \cfrac{75}{100} \right)62500}\implies 46875[/tex]

1st Answer: B.) (-1,170, -23,400) and (170, 3,400)

2nd Answer: 170

Answer:

that answer is verified 100% correct

Step-by-step explanation:

So we are given the following function: [tex]y=-(x + 2)^{2}[/tex].

Before we can solve this problem, we need to know the following:

Know we can solve the problem!

1. [tex]y=-(x + 4)^{2}[/tex]. Translated left by 2 units.

2. [tex]y=-(x + 2)^{2} - 2 [/tex] Translated down by 2 units

3. [tex]y=(x - 2)^{2}[/tex] Reflected across the x-axis and the y-axis

4. [tex]y= 2-(x + 2)^{2}[/tex] Translated up by 2 units

5. [tex]y=-(x)^{2}[/tex] Translated right by 2 units

6. [tex]y=(x + 2)^{2}[/tex] y = (x + 2)2 Reflected across the x-axis

Volume = 54π units³

Work is attached in the image provided.

Answer:

15

Step-by-step explanation:

5 ! = 120

Since 5 ! = 5 × 4 × 3 × 2 × 1, then

5 × 3 = 15 is the greatest odd factor of 5 !

The greatest odd integer that is a factor of 5 factorial (5!) is 5. This is because the definition of factorial involves multiplying a number by every number below it until reaching 1 and 5 is the largest odd number within this range.

The greatest odd integer that is a factor of 5! (or 5 factorial) is 5. The factorial, represented by the symbol '!', is a function that multiplies a number by every number below it until it reaches 1. For example, 5! means 5 * 4 * 3 * 2 * 1. To find the greatest odd integer that is a factor of 5!, you simply need to identify the largest odd number that is a part of this multiplication, which is 5.

Let's clarify this with some simple math. Start from the number 5 itself, then move down: 5 (it's an odd number), 4 (it's even, exclude), 3 (it's odd, but less than 5), 2 (it's even, exclude), 1 (it's odd, but less than 5). Hence, the largest odd integer that is a divisor of 5! is 5.

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Answer: (1) 120° (2) 6.5

Step-by-step explanation:

(1)

[tex]\dfrac{major\ arc-minor\ arc}{2}=intercepted\ angle\\\\\\\dfrac{(360-x)-x}{2}=60[/tex]

360 - 2x =  120

       - 2x = -240

            x = 120

(2)  

2.5²  +  6² = x²

6.25 + 36 = x²

     42.25 = x²

         6.5 = x

Answer:

(36.692,-6.538) or simplified (36.7,-6.5)

Step-by-step explanation:

2x-3y=93

x+5y=4

You would multiply both sides of the bottom equation by -2

-2(x+5y)=4(-2) > -2x-10y=-8

   2x-3y=93

+  -2x-10y=-8

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

-13y=85

divide both sides by -13

y=-6.538

plug in y for any of the two original equations, I chose the first one

2x-3(-6.5)=93

2x+19.5=93

  -19.5     -19.5

2x=73.5

divide both sides by 2

x=36.692

Answer:

3 and -1

Step-by-step explanation:

Took the test.

Answer:

Each friend will get more than 4 whole bagels.

Step-by-step explanation:

First off, although the question asks for 13 bagels divided between 3 friends, let's use a number that results in a whole number when divided by 3, but is close to 13.

This number can be 12.

12 divided by 3 is 4, so each friend gets 4 bagels if there are a total of 12 bagels.

However, there are more than 12 bagels so we know that each of the the 3 friends will get more than 4 bagels each.

Each friend will get 4 whole bagels, with 1 bagel left over.

In a baker's dozen, there are 13 bagels. Hillary, Mark, and Tam share the bagels equally. To determine if each friend will get more than or fewer than 4 whole bagels, we divide the total number of bagels by the number of friends.

13 bagels / 3 friends = 4 remainder 1

Each friend will get 4 whole bagels, with 1 bagel left over.

Division is one of the four basic operations of arithmetic. The other operations are addition, subtraction, and multiplication. What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient.

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Answer:

19

Step-by-step explanation:

We can solve this problem using a system of equation in two unknowns.

Let b = number of birds.

Let c = number of cats.

The care of a bird costs $5.50, so for b number of birds, the cost of care is 5.5b.

The care of a cat costs $8.50, so for c number of cats, the cost of care is 8.5c.

The total cost of care for the birds and cats is 5.5b + 8.5c.

The total cost of care is $291.50. This must equal the expression we have above, so we get our first equation.

5.5b + 8.5c = 291.5

The total number of birds and cats is b + c, but we are told it is 41, so our second equation is:

b + c = 41

We now have the following system of two equations in two unknowns.

5.5b + 8.5c = 291.5

b + c = 41

Rewrite the first equation.

Multiply both sides of the second equation by -8.5, and write it under the first equation. Then add the equations.

      5.5b + 8.5c = 291.5

+    -8.5b - 8.5c = -348.50

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

        -3b            = -57

Divide both sides of the equation by -3.

b = 19

Answer: there were 19 birds

By defining the number of birds and cats as variables and setting up a system of equations, we solved for the number of birds to be 19.

Let's define the number of birds as b and the number of cats as c. From the problem, we have the following equations:

b + c = 41 (total number of birds and cats)

5.50b + 8.50c = 291.50 (total cost of caring for birds and cats)

To solve for the number of birds, we follow these steps:

Step 1: Express the number of cats in terms of birds.

From the first equation, we get:

c = 41 - b

Step 2: Substitute this expression into the second equation.

5.50b + 8.50(41 - b) = 291.50

Expand and simplify the equation:

5.50b + 348.50 - 8.50b = 291.50

Combine like terms:

-3b + 348.50 = 291.50

Step 3: Solve for b.

Subtract 348.50 from both sides:

-3b = 291.50 - 348.50

-3b = -57

Divide both sides by -3:

b = 19

Therefore, there were 19 birds at the shelter on Thursday.

Answer:

2

Step-by-step explanation:

Step 1: Take the cube root of 8.

[tex] \sqrt[3]{8} = 2[/tex]

Answer:

The answer is 2.

Step-by-step explanation:

We need to find the value of

[tex]\sqrt[3]{8}[/tex]

We know ∛ = 1/3

and 8 = 2*2*2

2*2*2 can be written as 2^3 solving:

[tex]=\sqrt[3]{8} \\\\=\sqrt[3]{2*2*2}\\ =\sqrt[3]{2^3}\\= (2^3)^{1/3}\\= 2[/tex]

So, The answer is 2.

Answer:

an acute triangle

Step-by-step explanation:

Given:

vertex 1 = (7,3)

vertex 2 = (9,0)

vertex 3 = (5,-1)

Now finding the length of each side of the triangle

Using distance formula, to find the length of side between vertex 1 and 2

d=[tex]\sqrt{(x2-x1)^{2}+ (y2-y1)^{2} }[/tex]

Putting values of x1=7 , x2=9, y1=3 and y2=0

d=[tex]\sqrt{(9-7)^{2}+ (0-3)^{2} }\\ =\sqrt{2^{2}+ 3^{2} }\\ =\sqrt{4+9} \\=\sqrt{13}[/tex]

Using distance formula, to find the length of side between vertex 1 and 3

Putting values of x1=7 , x2=5, y1=3 and y2=-1

d=[tex]\sqrt{(5-7)^{2}+ (-1-3)^{2} }\\ =\sqrt{2^{2}+ 4^{2} }\\ =\sqrt{4+16} \\=\sqrt{20[/tex]

Using distance formula, to find the length of side between vertex 2 and 3

Putting values of x1=9 , x2=5, y1=0 and y2=-1

d=[tex]\sqrt{(5-9)^{2}+ (-1-0)^{2} }\\ =\sqrt{4^{2}+ 1^{2} }\\ =\sqrt{16+1} \\=\sqrt{17[/tex]

Hence the three sides of triangle are:

√13, √20, √17

by Pythagoras theorem

if c^2= a^2 + b^2 then triangle is right triangle

if c^2> a^2 + b^2 then triangle is obtuse triangle

if c^2<a^2 + b^2 then triangle is acute triangle

Now let a=√13 b=√17 and c=√20 then:

a^2 + b^2 = 13+17

                 = 30

c^2=20

and 20 < 30 which means c^2<a^2 + b^2 then triangle is acute triangle !

To determine the type of triangle formed by the points G(7,3), H(9, 0), and (5, -1), one needs to calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem to determine if it is a right, acute, or obtuse triangle.

The coordinates G(7,3), H(9, 0), and (5, -1) can form a triangle on a Cartesian plane, and we need to determine the type of triangle they form. To solve this problem, we need to calculate the lengths of the sides of this triangle using the distance formula, which is √((x2-x1)² + (y2-y1)²) for two points (x1, y1) and (x2, y2). Once we have all three sides, we can determine the type of triangle by applying the Pythagorean theorem, where the square of the length of the longest side (the hypotenuse 'c') is equal to the sum of the squares of the other two sides (a and b).

By applying the Pythagorean theorem, if the sum of the squares of the two shorter sides equals the square of the longest side, the triangle is a right triangle. If the square of the longest side is greater than the sum of the squares of the other two sides, it is an obtuse triangle. And if it’s less, the triangle is an acute triangle.

Given the way the coordinates are arranged in the fragmented information, it appears the triangle they form is relevant to understanding relationships between sides and angles. The mnemonic SOHCAHTOA is often used to remember the ratios of sides in a right triangle. Since the information for determining the lengths of the sides directly is not fully provided, we can't explicitly state the type of triangle formed by the points G(7,3), H(9, 0), and (5, -1) without further calculation.

Answer:

The triangle is rotated 360° ⇒ answer D

Step-by-step explanation:

* Lets revise some transformation

- If point (x , y) rotated about the origin by angle 90° anti-clock wise

∴ Its image is (-y , x)

- If point (x , y) rotated about the origin by angle 90° clock wise

∴ Its image is (y , -x)

- If point (x , y) rotated about the origin by angle 180°

∴ Its image is (-x , -y)

* There is no difference between rotating 180° clockwise or  

anti-clockwise around the origin

- If point (x , y) rotated about the origin by angle 360°

∴ Its image is (x , y)  the point itself

* There is no difference between rotating 360° clockwise or  

anti-clockwise around the origin

* Now lets solve the problem

∵ The vertices of the triangle ABC are:

  A is (-6 , 3) , B is (-5 , 7) , C is (-4 , 3)

∵ The triangle map onto itself

∴ A = A'

∴ B = B'

∴ C = C'

∴ The triangle is rotated 360° about the origin

D= 360

When you’re talking about rotation you go counterclockwise and each quadrant is another 90 degrees.

Answer:

Indirect measurement is a method of using proportions to find an unknown length or distance in similar figures.

Answer/ Explanation:

Indirect Measurement is a method of measuring liquids, gas or solids within a system indirectly. This method is utilized when there are no means of direct methods of measurement available.

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