What are the solutions to the quadratic equation below x^2+20x+100=7​

ANSWER

The solution is

(x,y)=(1,-5)

EXPLANATION

The equations are:

1st equation: 6x +5y=-19

2nd equation: 12x-8y=52

Multiply the first equation by 2:

3rd equation: 12x +10y=-38

Subtracy the 2nd equation from the 3rd equations.

12x-12x+10y--8y=-38-52

18y=-90

Divide both sides by 18.

y=-5

Put y=-5 into any of the equations and solve for x.

Preferably, the first equation will do.

6x +5(-5)=-19

6x -25=-19

6x=25-19

6x=6

x=1

The solution is

(x,y)=(1,-5)

Answer:

160

Step-by-step explanation:

The top right quadrant is 90 and the given is 70, adding them equal 160. It is the only option that is greater than 90 degrees anyway.

Answer:

x = - 9, x = - 3

Step-by-step explanation:

Given

x² + 12x + 27 = 0

To factorise the quadratic

Consider the factors of the constant term (+ 27) which sum to give the coefficient of the x- term (+ 12)

The factors are + 9 and + 3, since

9 × 3 = 27 and 9 + 3 = 12, hence

(x + 9)(x + 3) = 0

Equate each factor to zero and solve for x

x + 9 = 0 ⇒ x = - 9

x + 3 = 0 ⇒ x = - 3

Answer:  3

Step-by-step explanation:

Median is the middle number if it is an odd number or if it is even you add the two middle numbers and divide by 2

The median cleanliness rating for Restaurant A is 3.

The median of Restaurant A's cleanliness ratings can be found by arranging the ratings in order from lowest to highest and determining the middle value. In this case, the ratings are 1, 2, 3, 4, and 5. Since there is an odd number of ratings, the median is the middle value, which is 3. Therefore, the median cleanliness rating for Restaurant A is 3.

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Answer:

[tex]96\ basketballs[/tex]

Step-by-step explanation:

step 1

Find the volume of the cylinder (hollow drum)

The volume is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]h=48\ in[/tex]

[tex]r=24\ in[/tex]

substitute

[tex]V=\pi (24)^{2} (48)[/tex]

[tex]V=27,648\pi\ in^{3}[/tex]

step 2

Find the volume of one basketball

The volume of the sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=6\ in[/tex]

substitute

[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]

[tex]V=288\pi\ in^{3}[/tex]

step 3

Find the maximum number of basketballs that the cylindrical drum contains

so

Divide the volume of the cylinder by the volume of one basketball

[tex]27,648\pi/288\pi=96\ basketballs[/tex]

Answer:

abc is the one that must be a simicircle

Answer:

A. ABC.

Step-by-step explanation:

We have been given an image of a circle. We are asked to choose the arc, which must be a semicircle of our given circle.

Upon looking at our given diagram, we can see that AC divides our given circle into two semicircles ABC and ATC.

From our given choices, we can see that option A is the correct choice.

Answer:

Option C

Step-by-step explanation:

we know that

Two angles are complements if their sum is equal to 90 degrees

we have that

∠SWT=50°

so

Its complement must be equal to 40 degrees

we know that

∠USP=40°

∠TSV=40°

therefore

∠USP and ∠TSV are complements to ∠ SWT

Answer:

You could divide $12 with either method

If you divided 12 by 1/4 you would get $48.

Divided by 1/3, $36.

Answer:

9

i did this question before

Answer:

The value of x is 9.

Step-by-step explanation:

Given equation,

[tex](x+2)^2=a[/tex]

If x = 1 is the solution of this equation,

Then it will satisfy the equation,

[tex]\implies (1+2)^2=a[/tex]

[tex]\implies (3)^2=a[/tex]

[tex]\implies a = 9[/tex]

Hence, the value of x is 9 if x = 1 is the solution of the given equation.

Answer:

Part 1) The new distance from the water to the top of the tank is [tex]1.979\ in[/tex]

Part 2) The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Step-by-step explanation:

step 1

Find the total volume of the tank

[tex]V=20*10*15=3,000\ in^{3}[/tex]

step 2

Find the volume of the tank if the water level is two inches below the top of the tank

[tex]V=20*10*(15-2)=2,600\ in^{3}[/tex]

step 3

Find the volume of the glass sphere

The volume of the glass sphere is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=1\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{4}{3}(3.14)(1)^{3}[/tex]

[tex]V=4.2\ in^{3}[/tex]

step 4

What is the new distance from the water to the top of the tank?

we know that

[tex]2 in -----> represent (3,000-2,600)=400\ in^{3}[/tex]

so

using proportion

Find how many inches correspond a volume of [tex]4.2\ in^{3}[/tex]

[tex]\frac{2}{400}\frac{in}{in^{3}}=\frac{x}{4.2}\frac{in}{in^{3}}\\ \\x=4.2*2/400\\ \\x=0.021\ in[/tex]

The new distance from the water to the top of the tank is

[tex]2-0.021=1.979\ in[/tex]

step 5

Find how many of these balls can be put into the tank with the tank not overflowing

we know that

The volume of one ball is equal to  [tex]4.2\ in^{3}[/tex]

using proportion

[tex]\frac{1}{4.2}=\frac{x}{400}\\ \\x=400/4.2\\ \\x=95.23\ balls[/tex]

therefore

The maximum number of balls that can be put into the tank with the tank not overflowing is 95

Answer:

16

Step-by-step explanation:

Exterior angle theorem - the sum of two interior angles (which in this case would be angle R and N) is equal to the measure of the exterior angle.

A line parallel to 2x - 3y = 9 would have the same slope, 2/3, and a different y-intercept, represented as y = (2/3)x + b, where 'b' is any real number.

The equation 2x - 3y = 9 represents a line in a standard form. To find a line that is parallel to it, we need another line with the same slope. The slope-intercept form of the given equation, by isolating y, is y = (2/3)x - 3. A parallel line must have the same slope, which is 2/3 in this case. Therefore, a line parallel to 2x - 3y = 9 could be represented as y = (2/3)x + b, where 'b' is any y-intercept. For example, if b = 5, a parallel line would be given by y = (2/3)x + 5.

Answer: 10.5 gallons

Step-by-step explanation:

One imperial gallon is approximately 1.2 US gallons. The US gallon is used in the United States and is equal to exactly 231 cubic inches or 3.785411784 liters. The Imperial gallon or UK gallon is used in the United Kingdom and is equal to approximately 277.42 cubic inches. Its exact value is defined as 4.54609 liters.

Answer:

[tex]\large\boxed{(8\times6)-(4\times2)=48-8=40}[/tex]

The expression (8*2)*2 + 6 + 2 uses the numbers 8, 6, 4, and 2 to equal 40. The question tests knowledge of basic arithmetic operations.

The question involves using the numbers 8, 6, 4, and 2 to create an expression that equals 40. This is a problem dealing with basic arithmetic operations like addition, subtraction, multiplication, and division. The expression can be formed as follows:

So, the expression is: (8*2)*2 + 6 + 2 = 40

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Answer:

Step-by-step explanation:

Use the given information to determine what the angles can be.

  g = 2x -90 . . . . given

  g > 0 . . . . . . . . . given

  2x -90 > 0

  2x > 90 . . . . . add 90

  x > 45 . . . . . . divide by 2

__

  h = 180 -2x

  h > 0

  180 -2x > 0

  180 > 2x

  90 > x

__

The requirement that both angles be greater than zero puts limits on x:

  45 < x < 90

We can put this back into the given relations for g and h:

  g = 2x -90

  x = (g +90)/2

  45 < (g +90)/2 < 90 . . . . substitute for x

  0 < g/2 < 45 . . . . . . . . . . subtract 45

  0 < g < 90 . . . . . . . . . . . . g is an acute angle

Similarly, ...

  h = 180 -2x

  x = (180 -h)/2 = 90 -h/2

  45 < (90 -h/2) < 90 . . . . substitute for x

  -45 < -h/2 < 0 . . . . . . . . . subtract 90

  90 > h > 0 . . . . . . . . . . . multiply by -2; h is an acute angle

__

We can add the angle measures to see if they are supplementary or complementary:

  g + h = (2x -90) +(180 -2x)

  g + h = 90 . . . . . simplify; the angles are complementary

__

The relevant observations are ...

Answer: 3 yd

Step-by-step explanation: The radius is 3 yards because the diameter is 6 and the radius is d/2. 6/2 is equal to 3.

Hope this helps!

Answer:

240 units^3

Step-by-step explanation:

To find the volume of a rectangular prism you just multiply length times width times height. So, 8*6*5 which equals 240 units^3.

The dimensions of the prism is given as Length = 8 units, width = 6, Height = 5. Therefore, the volume of the prism is 240 units^3.

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units,

then its volume is given as:

[tex]V = a\times b \times c \: \: unit^3[/tex]

The dimensions of the prism is given as

Length = 8 units

width = 6

Height = 5

To find the volume of a rectangular prism

[tex]V = a\times b \times c \: \: unit^3[/tex]

V = 8 x 6 x 5

V = 240 units^3.

Therefore, the volume of the prism is 240 units^3.

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Answer:

Step-by-step explanation:

The total number of marbles is 24 + 36 + 60 = 120

Red: 24/120 = 1/5

Blue: 36/120 = 6/20 = 3/10

Yellow: 60 / 120 = 1/2

ANSWER

An ordered pair that is the solution to the system of equations lies on the y-axis.

The y-coordinate of a solution to the system of equations is 4.

EXPLANATION

The given system has equations:

[tex]y = {x}^{2} + 2x + 4[/tex]

[tex]y = - x + 4[/tex]

We equate both equations to get:

[tex] {x}^{2} + 2x + 4 = - x + 4[/tex]

This implies that,

[tex] {x}^{2} + 2x + x + 4 - 4 = 0[/tex]

[tex] {x}^{2} + 3x = 0[/tex]

[tex]x(x + 3) = 0[/tex]

[tex]x = 0 \: or \: x = - 3[/tex]

When x=0, y=-(0)+4=4

When x=-3, y=-(-3)+4=7

The solutions are: (0,4) and (-3,7)

The true statements about the system of equations are:

The system of equations is given as:

f(x)=−x^2+2x+4

g(x)=−x+4

From the graph of the system of equations (see attachment), we have the following point of intersections

(x,y) = (0,4) and (3,1)

So, the true statements about the system of equations are:

(a), (c), (d) and (e)

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Answer:

120 square units

Step-by-step explanation:

In triangle PSQ, PS=SQ. Let PS=SQ=x units.

Since SQ-PQ=1, PQ=SQ-1=x-1 units.

The perimeter of the triangle PSQ is 50 units, so

PS+SQ+PQ=50 units.

Substitute PS=SQ=x un. and PQ=x-1 un.

x+x+x-1=50

3x=51

x=17

Hence

PS=SQ=17 units,

PQ=16 units.

Use Heron's formula to find the area:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]

where p is semi-perimeter and a,b,c are lengths of sides.

[tex]p=\dfrac{17+17+16}{2}=25,\\ \\\\A=\sqrt{25(25-17)(25-17)(25-16)}=\sqrt{25\cdot 8\cdot 8\cdot 9}=5\cdot 8\cdot 3=120\ un^2.[/tex]

Answer:

$ 5674.076

Step-by-step explanation:

The question is on compound interest

The formulae = A= P(1+ r/n) ^nt .......where P is the principal amount, r is the rate of interest in decimal, n is number of compoundings per year and t is the total number of years.

Given; P= $4,000.00 , r=12/100=0.12, n=2 and t=3

Substituting values in the equation  A= P(1+ r/n) ^nt

A= 4000 ( 1+0.12/2)^2×3

A=4000(1.06)^6

A=$ 5674.08

Answer:

The answer is the second option

Minimum = 203, Q1 =217, median = 230, Q3 = 245, maximum = 290

Step-by-step explanation:

First order the data from lowest to highest

203, 216, 217, 224, 224, 236, 245, 245 ,262 ,290

Minimun = 203

Maximum =290

Now divide the data in half

203, 216, 217, 224, 224,            236, 245, 245 ,262 ,290

Divide half of the first half of the data. The data of the medium is the first quartile

1) 203, 216, [217], 224, 224

                      Q1

Divide half of the second half of the data. The data of the medium is the third quartile

2)  236, 245, [245] ,262 ,290

                         Q3

The average between the two values that are in the center of the 10 ordered data is the median

203, 216, 217, 224,  [224, 236], 245, 245 ,262 ,290

[tex]Median =\frac{224+236}{2}=230[/tex]

Median=230

The answer is the second option

Minimum = 203, Q1 =217, median = 230, Q3 = 245, maximum = 290

Answer:

the answer is B :D

Step-by-step explanation:

Answer:

Josh's salary is 20% less than Jeff's.

Step-by-step explanation:

Let

x----> Jeff's salary

y----> Josh's salary

we know that

x=1.25y

Solve for y

y=(1/1.25)x

y=0.8x

therefore

Josh's salary is 80% of Jeff's salary

or

Josh's salary is 20% less than Jeff's.

The area is 64. Area, as you probably know, is the length times the width of the figure. The length from A to C is approximately radical 128, and the length from C to D is approximately radical 32 (btw, the radical is the check mark with line that goes above and next to the radicand (the number on the inside of the radical)). Multiply these two to get the area, and you should end up with 64.

If the quadrilateral has vertices at (-8, 0), (-4,-4), (0,8), and (4,4). Then the area of the quadrilateral will be 64 square units.

It is a polygon with four sides. The total interior angle is 360 degrees.

The quadrilateral shown below has vertices at (-8, 0), (-4,-4), (0,8), and (4,4).

Then the area of the quadrilateral will be

Assume the points

(x₁, y₁) = (-8, 0)

(x₂, y₂) = (-4, -4)

(x₃, y₃) = (4, 4)

(x₄, y₄) = (0, 8)

Then the area of the quadrilateral is given as

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₄ + x₄y₁) - (y₁x₂ + y₂x₃ + y₃x₄ + y₄x₁)]|

Area = 1/2|[(-8 × -4 + -4×4 + 4×8 + 0×0) - (0 × -4 + -4 × 4 + 4 × 0 + 8 × -8)]|

Area = 1/2|[(32 - 16 + 32) - ( -16 - 64)]|

Area = 1/2|[48 + 80]|

Area = 1/2|128|

Area = 64

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Answer:

[tex]-11b^2+8b-4[/tex]

Step-by-step explanation:

We can substitute in our expressions for P and Q to get

[tex]P=-4b^2+6b-9\\Q=7b^2-2b-5\\\\(-4b^2+6b-9)-(7b^2-2b-5)[/tex]

Next, we need to distribute the negative to the values within the parenthesis. Then we can combine like terms in order to get our answer

[tex](-4b^2+6b-9)-(7b^2-2b-5)\\\\-4b^2+6b-9-7b^2+2b+5\\\\-11b^2+8b-4[/tex]

Answer:

-11b^2 + 8b - 4

Step-by-step explanation:

(-4b^2 + 6b - 9) - (7b^2 - 2b - 5) =

Drop the first set of parentheses because it is unnecessary. To drop the second set of parentheses, you must distribute the negative sign. That means you must change every sign inside the second set of parentheses.

= -4b^2 + 6b - 9 - 7b^2 + 2b + 5

Now, group like terms.

= -4b^2 - 7b^2 + 6b + 2b - 9 + 5

Finally, combine like terms.

= -11b^2 + 8b - 4

Answer:

I think it is A.

Step-by-step explanation:

Hope my answer has helped you!

The true statement is:

Hence, such points could never form a triangle.

Because a triangle is formed with the help of three non-collinear points.

Hence, the points will be coplanar (i.e. they lie in the same plane)

Answer:

x = 8.9 (nearest tenth)

Step-by-step explanation:

6^2 - 4^2 = 36 - 16 = 20

So

x = 2 * (√20)

x = 2 * 4.47

x = 8.94

Answer:

The value of x = 4√5

Step-by-step explanation:

Points to remember

For a right angled triangle

Hypotenuse² = Base² + Height²

To find the value of x

From the figure we can see a right angled triangle with,

hypotenuse = 6 and height = 4

Value of x = 2 * base

we have, Hypotenuse² =  + Height²

Base² = Hypotenuse² - Height²

 = 6² - 4²

 = 36 - 16  = 20

Base = √20 = 2√5

x = 2 * 2√5 = 4√5

The value of x = 4√5

Answer:

22

Step-by-step explanation:

The perimeter of the isosceles triangle with a point of tangency that divides one leg into 3 cm and 4 cm segments is 22 cm, having both legs 7 cm each and the base 8 cm.

Given an isosceles triangle with a point of tangency that divides one of the equal legs into segments of 3 cm and 4 cm, we can determine the perimeter of the triangle by first understanding the properties of such a triangle. The two legs are congruent, and by the Theorem 6, the radius from the center to the point of tangency is perpendicular to the tangent and bisects it. Knowing that the point of tangency divides a leg into two parts, we can denote the entire length of one leg as 3 cm + 4 cm, which equals 7 cm.

Since the triangle is isosceles, both legs are equal in length. This means the other leg is also 7 cm. To find the base, we recall the perpendicular from the center bisects it (Theorem 6). Hence, the base is twice one of the segments, either 3 cm or 4 cm. We will choose the longer segment to ensure that the vertex angles remain acute, and hence the base would be 2 * 4 cm = 8 cm.

Now the perimeter (P) of the triangle can be found by adding the lengths of the two legs and the base: P = 7 cm + 7 cm + 8 cm = 22 cm. Therefore, the perimeter of the isosceles triangle is 22 cm.

Answer:

The 51 and 62 triangle is 67°

The 43 triangle is 47°

Step-by-step explanation:

Angles in a triangle add to 180°

180 - ( 51 + 62 ) = 180 - ( 113 ) = 67°

180 - ( 43 + 90 ) = 180 - 133 = 47°

Answer: 36ft

Step-by-step explanation: 180*.2=36

Answer:

36 ft

Step-by-step explanation:

to find 20% of 180 ft, multiply 180 ft by 0.20:  0.20(180 ft) = 36 ft