You divide two numbers and the quotient is 2.5. What might the two numbers be? Show at least 5 solutions.

Answer:

Therefore the value of x is 4.

Step-by-step explanation:

Given:

AO = 5x - 8

BO = 3x

AM ≅ BM

To Find :

x = ?

Solution:

In  Δ AMO and Δ BMO

AM ≅ BM     ……….{Given}

∠ AMO ≅ ∠ BMO    …………..{measure of each angle is 90° given}

MO ≅ MO      ……….{Reflexive property}

ΔAMO  ≅ Δ BMO ….{ By Side-Angle-Side test}

∴ AO ≅ BO ...{corresponding sides of Congruent triangles or CPCT}

on substituting the values we get

[tex]5x-8=3x\\\\5x-3x=8\\\\2x=8\\\\x=\frac{8}{2}=4[/tex]

Therefore the value of x is 4.

Answer:

[tex]\large\boxed{y=\dfrac{1}{2}x^2-2x+1}[/tex]

Step-by-step explanation:

The vertex form of an equation of a parabola:

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

(h, k) - vertex

a - leading coefficient in equation y = ax² + bx + c

From the grap we can read coordinates of the vertex (2, -1) and y-intercept (0, 1).

Therefore h = 2, k = -1

Put the values of h, k and coordinates of the y-intercept to the equation of parabola:

[tex]1=a(0-2)^2-1[/tex]     add 1 to both sides

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

[tex]2=4a[/tex]              divide both sides by 4

[tex]\dfrac{2}{4}=\dfrac{4a}{4}\\\\\dfrac{1}{2}=a\to a=\dfrac{1}{2}[/tex]

Therefore we have the equation:

[tex]y=\dfrac{1}{2}(x-2)^2-1[/tex]

Convert to the standard form:

[tex]y=\dfrac{1}{2}(x-2)^2-1[/tex]       use (a - b)² = a² - 2ab + b²

[tex]y=\dfrac{1}{2}(x^2-2(x)(2)+2^2)-1[/tex]

[tex]y=\dfrac{1}{2}(x^2-4x+4)-1[/tex]           use the distributive property

[tex]y=\dfrac{1}{2}x^2-\dfrac{1}{2}\cdot4x+\dfrac{1}{2}\cdot4-1[/tex]

[tex]y=\dfrac{1}{2}x^2-2x+2-1[/tex]          combine like terms

[tex]y=\dfrac{1}{2}x^2-2x+1[/tex]

Answer: The second table

Step-by-step explanation:

For the table to show  proportional relationship between x and y , then they must have a common ratio. that is x/y must be the same throughout

Table 1

[tex]x_{1}[/tex] = 1                [tex]y_{1}[/tex] = 2

[tex]x_{2}[/tex] = 3               [tex]y_{2}[/tex] = 5

[tex]x_{3}[/tex] = 4               [tex]y_{3}[/tex] = 8

[tex]x_{4}[/tex] = 7               [tex]y_{4}[/tex] = 14

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

[tex]\frac{x_{2}}{y_{2}}[/tex] = 3/5

[tex]\frac{x_{3}}{y_{3}}[/tex] = 4/8 = 1/2

[tex]\frac{x_{4}}{y_{4}}[/tex]= 7/14 = 1/2

Since the ratio is not the same throughout , then x and y are not proportional

Table 2

[tex]x_{1}[/tex] = 7               [tex]y_{1}[/tex] = 1

[tex]x_{2}[/tex] = 14               [tex]y_{2}[/tex] = 2

[tex]x_{3}[/tex] = 28               [tex]y_{3}[/tex] = 4

[tex]x_{4}[/tex] = 35              [tex]y_{4}[/tex] = 5

[tex]\frac{x_{1}}{y_{1}}[/tex] = 7/1 = 7

[tex]\frac{x_{2}}{y_{2}}[/tex] = 14/2 = 7

[tex]\frac{x_{3}}{y_{3}}[/tex] = 28/4 = 7

[tex]\frac{x_{4}}{y_{4}}[/tex]= 35/5 = 7

Since the ratio is the same throughout , it means that x and y are proportional.

Doing the same for table 3 and 4 , x and y are not proportional

Answer:

SAS , ASA, SSS

Step-by-step explanation:

SAS , side A= side A . Angle B= Angle C, side R= side R

ASA, Angle A= Angle A . Side B= side C, Angle R= Angle R

SSS

side A= side A . Side B= side c, side R= side R

Note: Since you missed to add the figure. So, after a little research I am kind of able to find the figure and hence, assuming it as a reference. Hence, I am attaching the figure and solution of that figure is also visible in the same figure. Please check the attached figure (a)

Answer:

Segment B'D' will be parallel to segment BD and will be shorter than segment BD. Please see the attached figure (a) for better understanding.

Step-by-step explanation:

As we know that there are certain rules when a quadrilateral is dilated by a certain scale centered around a certain point.

So,

Let suppose P(a, b) is the point.

The dilation rule by a scale factor of 1 over 3 or (1/3) centered around (1, 2) is

P(a, b) → [tex]P(\frac{x+2}{3}, \frac{y+4}{3})[/tex]

Hence,

            A(1, 2) → A'(1, 2)

            B(2, 3) → B'(4/3, 7/3)

            C(4, 2) → C'(2, 2)

             D(2, 1) → D'(4/3, 5/3)

The attached figure show that if we draw the all these points in the coordinate plan i.e. A(1, 2), B(2, 3), C(4, 2), D(2, 1) and A'(1, 2), B'(4/3, 7/3), C'(2, 2), D'(4/3, 5/3), we can determine that Segment B'D' will be parallel to segment BD and will be shorter than segment BD.

Keywords: dilation, quadrilateral, segment

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Answer: C) segment B prime D prime will be parallel to segment BD and will be shorter than segment BD.

The total profit is :$37.46. Number of boxes for pop B to purchase more is 56 boxes.

Step-by-step explanation:

1.

Pop B number =36

Remaining Pop B after meeting = 36-17 =19

Amount obtained after selling remaining Pop B = 19* 0.75 = $14.25

Pop A number =75

Remaining Pop A after meeting = 75-8 =67

Amount obtained after selling pop A = 67*0.5 =$33.5

Profit in Pop B = $14.25-$3.79 =$10.46

Profit in Pop A =$33.5 -$6.50 = $27

Total profit after sell of Pop A and B = $10.46+$27 = $37.46

2.

The target profit is $250

Subtracting profit meet = $250 - $ 37.46 =$212.54

Profit to be attained by the sell of pop B only should be =$212.54

Selling price of pop B per box is $3.79

Number of boxes for pop B to purchase more will be;

$212.54/ $3.79 = 56.08 ⇒ 56  more boxes

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Answer:

The area of each triangle face is 27 square feet .

Step-by-step explanation:

Given as :

The base area of square pyramid = A = 36 square feet

The total surface area of square pyramid = TSA = 144 square feet

Let The area of each triangle face = x square feet

Now, According to question

Total surface Area of square pyramid = Base area of square pyramid + Area of four triangle faces

Or, TSA = A + 4 × x

Or, 144 ft² = 36 ft² + 4 × x  ft²

Or, 4 × x = 144 ft² - 36 ft²

Or  4 ×  x = 108 ft²

∴     x = [tex]\dfrac{108}{4}[/tex]

i.e  x = 27   ft²

So, The area of each triangle face = x = 27 square feet

Hence, The area of each triangle face is 27 square feet . Answer

Answer:

Step-by-step explanation:

Convert to the slope-intercept form (y = mx + b):

[tex]2y=5x+11[/tex]             divide both sides by 2

[tex]\dfrac{2y}{2}=\dfrac{5x}{2}+\dfrac{11}{2}\\\\y=\dfrac{5}{2}x+\dfrac{11}{2}[/tex]

We choose any three x values ​​and calculate the y value:

for x = -1

[tex]y=\dfrac{5}{2}(-1)+\dfrac{11}{2}=-\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{6}{2}=3\to A(-1,\ 3)[/tex]

for x = 1

[tex]y=\dfrac{5}{2}(1)+\dfrac{11}{2}=\dfrac{5}{2}+\dfrac{11}{2}=\dfrac{16}{2}=8\to B(1,\ 8)[/tex]

for x = -3

[tex]y=\dfrac{5}{2}(-3)+\dfrac{11}{2}=-\dfrac{15}{2}+\dfrac{11}{2}=-\dfrac{4}{2}=-2\to C(-3,\ -2)[/tex]

Mark the points on the coordinate plane and draw a line through the given points.

Answer:

18000×75÷100 =13500 ×3 =40500 .

Answer:

b=-108

Step-by-step explanation:

To solve this equation for b, you simply multiply each side by 18. The reason you do this is to isolate the b.

[tex]-6=\frac{b}{18}[/tex]

[tex]18(-6)=(\frac{b}{18} )(18)[/tex]

[tex]-108=b[/tex]

Answer:

4 foot

Step-by-step explanation:

√50.25 / 3.1416 = 4

The diameter of the circular sprinkler is 16 feet.

To find the diameter of the circular sprinkler, we can use the formula for the circumference of a circle: C = πd, where C is the circumference and d is the diameter. In this case, we are given the length of the copper tubing used, which is equal to the circumference. So we can rearrange the formula to solve for the diameter: d = C/π. Plugging in the given values, we have d = 50.25/π. Using the value of π as approximately 3.14, we can calculate the diameter to the nearest whole foot.

d ≈ 50.25/3.14 ≈ 16.01 feet

Therefore, the diameter of the circular sprinkler to the nearest whole foot is 16 feet.

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Answer:

A lipid

Step-by-step explanation:

When 1 "Glycerol "and 3"Fatty Acids" form a bond the new molecule is called "Triglyceride" which is a type of "Lipid"

Answer:

The standard form is [tex]7x^7 +6x^5-3x^3 + 8x[/tex]

Step-by-step explanation:

Given:

[tex]6x^5 + 8x-3x^3+7x^7[/tex]

To Find :

standard form of [tex]6x^5 + 8x-3x^3+7x^7[/tex]

Solution:

A polynomial is in standard form when its term of highest degree is first, its term of 2nd highest is 2nd etc.

In order to write any polynomial in standard form, you look at the degree of each term. You then write each term in order of degree, from highest to lowest, left to write.

Now lets check the degree of each term in the polynomial

The degree of 6x is 5

The degree of 8x is 1

The degree of 3x is 3

 The degree of 7x is 7

Now rewrite  the polynomial in the order of the degree, from highest to lowest

[tex]7x^7 +6x^5-3x^3 + 8x[/tex]

Answer:

x=-3, y=-1. (-3, -1).

Step-by-step explanation:

y=x+2

y=-3+2=-1

Answer:

70 degrees

Step-by-step explanation:

Complementary angles sum up to 90.

To find the larger angle, you find the total of the values in the ratio, divide the larger value of the ratio by the total and multiply it by 90.

(7/7+2)×90=7/9×90

=7×10

=70

OR

Write an equation:

7x+2x=90

9x=90

x=10

Then multiply x by the larger value.

7x=7 (10)=70

Answer:

$952

Step-by-step explanation:

I don't know why sheet is after 56, but I think they just want you to multiply 57 and 17.

Answer:

-The ordered pair (-1, 5) is a solution to the first equation because it makes the first equation true.

-The ordered pair (-1, 5) is a solution to the second equation because it makes the  second equation true.

-The ordered pair (-1, 5) is a solution to the system because it makes both equations true

Step-by-step explanation:

The correct question is

Which statements are true about the ordered pair (−1, 5) and the system of equations?

x+y=4

x−y=−6

we know that

If a ordered pair is a solution of  a equation, then the ordered pair, must satisfy the equation (makes the equation true)

If a ordered pair is a solution of the system of equations, then the ordered pair, must satisfy the equations of the system (makes both equations true)

we have

[tex]x+y=4[/tex] ----> first equation

[tex]x-y=-6[/tex] ----> second equation

step 1

Verify if the ordered pair satisfy  the first equation

Substitute the values of x and y of the ordered pair in the first equation  

For x=-1, y=5    

[tex]-1+5=4[/tex]

[tex]4=4[/tex] ---> is true

The ordered pair satisfy the first equation

so

The ordered pair is a solution to the first equation because it makes the first  equation true

step 2

Verify if the ordered pair satisfy  the second equation

Substitute the values of x and y of the ordered pair in the second equation  

For x=-1, y=5    

[tex]-1-5=-6[/tex]

[tex]-6=-6[/tex] ---> is true

The ordered pair satisfy the second equation

so

The ordered pair is a solution to the second equation because it makes the second  equation true

therefore

The ordered pair (-1, 5) is a solution to the system because it makes both equations true

Answer:

Bryson’s age is 14 years

Step-by-step explanation:

Let

x ----> Bryson’s age

we know that

Bryson’s age multiplied by 3 minus 4 must be equal to 38

so

The linear equation that represent this situation is

[tex]3x-4=38[/tex]

solve for x

Adds 4 both sides

[tex]3x=38+4[/tex]

[tex]3x=42[/tex]

Divide by 3 both sides

[tex]x=14[/tex]

therefore

Bryson’s age is 14 years

Answer:

[tex]\frac{49\sqrt3}{2}[/tex]

Step-by-step explanation:

30 60 90 Right Trianlge.

Final answer:

To find out how many medals Germany secured in the 2006 Winter Olympics, we denote the number of medals Sweden won as S and create an equation based on the problem's description. Solving for S, we find that Sweden won 14 medals, so Germany, with one more than twice the number of Sweden's medals, secured 29 medals in total.

Explanation:

The question requires us to solve a problem that involves understanding and creating equations based on the given information.

Let's denote the number of medals Sweden won as S. According to the problem, China won S - 3 medals, and Germany won 2S + 1 medals. The total number of medals won by all three countries is 54, so the equation to represent this information is:

S + (S - 3) + (2S + 1) = 54

By combining like terms, we get:

4S - 2 = 54

Now, we will solve for S:

4S = 56 ⇒ S = 14

Now that we know Sweden won 14 medals, we can determine the number of medals Germany secured, which is 2S + 1:

2(14) + 1 = 29

Therefore, Germany secured 29 medals in the 2006 Winter Olympics.

Answer:

2 years

4% of 2500 is 100

So 100x2 years would be 200

Answer:

Step-by-step explanation:

SI = PRT/100

$200 = 2500 * 4*T/100

200 *100 / 2500 *4 = T

T = 200 * 100 /2500*4 = 2

T = 2 years

subtract 7 from both sides

4x = -2x + 12

add 2x to both sides

6x = 12

divide both sides by 6

x = 2

Answer:

Oh it is C

Step-by-step explanation:

Answer:

40 miles per hour

Step-by-step explanation:

1 hour=3600 seconds

(1/4)/22.5=x/3600

cross product

22.5*x=(1/4)(3600)

22.5x=3600/4

22.5x=900

x=900/22.5

x=40

Answer:

D. Patel found the incorrect quotient and checked his work using multiplication incorrectly.

Step-by-step explanation:

The dividend is [tex]8,[/tex] the divisor is [tex]\dfrac{1}{6}.[/tex] Divide the dividend by the divisor (division by fraction means multiplication by its reciprocal):

[tex]8\div \dfrac{1}{6}=8\times \dfrac{6}{1}=8\times 6=48,[/tex]

so the quotient is 48, not [tex]\dfrac{1}{48}.[/tex]

To check the answer, Patel has to multiply the quotient by the divisor to get the dividend. Check answer:

[tex]48\times \dfrac{1}{6}=\dfrac{48}{6}=8[/tex]

Hence, Patel found the incorrect quotient and checked his work using multiplication incorrectly.

The most accurate description of Patel's work is option D. Patel found an incorrect quotient and checked his work using multiplication incorrectly. therefore, option D. Patel found an incorrect quotient and checked his work using multiplication incorrectly.

Patel initially calculated 8 divided by 1/6 as 1/48, which is incorrect.

The correct quotient is 48.

When Patel multiplied 1/48 by 6, he got 1/8, which is also incorrect.

The correct result should be 48, not 1/8.

So, Patel's division was incorrect, and his check using multiplication was also incorrect.

In summary, Patel made an error in the initial division and didn't accurately check his work using multiplication, leading to an incorrect final result in both cases.

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Answer: A) 1.44 B) 13 C) 3

Step-by-step explanation:

A) 1.2 * 1.2 =1.44

B) (8) +17 - (12)= (8+17) -12= (25)- (12)= 13

C) (9*9) / (3*3*3)= (81) / (27)= 3

Answer:

Step-by-step explanation:

2.75g + 4.75r = 20.50

g = 2r

2.75(2r) + 4.75r = 20.50

5.50r + 4.75r = 20.50

10.25r = 20.50

r = 20.50 / 10.25

r = 2 <==== Aaron went on 2 rides

g = 2r

g = 2(2)

g = 4 <==== Aaron played 4 games

check...

2.75g + 4.75r = 20.50

2.75(4) + 4.75(2) = 20.50

11 + 9.5 = 20.50

20.50 = 20.50 (correct)

Answer:

The Range is {3, 6}.

Step-by-step explanation:

The correct question is

Find the range of the function below if the domain is {-1,0,2} f(x)=x^2 -2x+3

we know that

The domain represents all possible values of x.

The range represents all possible values of f(x)

Substitute all of the possible x-values (domain) into the formula to find all possible f(x) values (the range).

For x=-1

[tex]f(-1)= (-1)^{2} - 2(-1) + 3[/tex]

[tex]f(-1)=1+2+ 3[/tex]

[tex]f(-1)=6[/tex]

For x=0

[tex]f(0)= (0)^{2} - 2(0) + 3[/tex]

[tex]f(0)=0-0+ 3[/tex]

[tex]f(0)=3[/tex]

For x=2

[tex]f(2)= (2)^{2} - 2(2) + 3[/tex]

[tex]f(2)=4-4+ 3[/tex]

[tex]f(2)=3[/tex]

therefore

The Range is {3, 6}.

Answer:

[tex]x^{4} -18x^{3}+104x^{2} -172x-100[/tex]

Step-by-step explanation:

The 3 roots are given out of which 2 are real and 1 is imaginary. For a polynomial of least degree having real coefficients, it must have a complex conjugate root as the 4th root. Therefore, based on 4 roots, the least degree of polynomial will be 4. Finding the polynomial having leading coefficient=1 and solving it based on multiplication of 2 quadratic polynomials, we get:  

[tex]\\\\x_{1} = 2-\sqrt{6} \\x_{2} = 2+\sqrt{6} \\x_{3}=7-i \\x_{4}=7+i \\\\P(x)=1(x-x_{1})(x-x_{2} )(x-x_{3} )(x-x_{4} ) \\\\=(x-(2-\sqrt{6}))(  x-(2+\sqrt{6} )) (x-(7-i))( x-(7+i))\\=((x-2)+\sqrt{6})( ( x-2)-\sqrt{6} ) ((x-7)+i)( (x-7)-i)\\=((x-2)^{2} -(\sqrt{6} )^{2} )((x-7)^{2}-(i)^{2})\\=(x^{2} -4x-2)(x^{2} -14x+50)\\=x^{4} -18x^{3}+104x^{2} -172x-100\\[/tex]

Answer:

X^4-16x^3+73x^2-30x-250

Step-by-step explanation:

Answer:

Step-by-step explanation:

the first day he used 30 cups

the second day he used 15% of the remaining cups...a total of 90 cups were used on second day.

so 15%of the remaining cups = 90.....so if u let x be the total cups, then the remaining cups would be x - 30

15% of (x - 30) = 90.....turn ur percent to a decimal..." of " means multiply

0.15(x - 30) = 90

0.15x - 4.5 = 90

0.15x = 90 + 4.5

0.15x = 94.5

x = 94.5 / 0.15

x = 630 total cups <==

lets check..

start with 630 cups....used 30 the first day....leaving u with 600 cups....15% of the remaining cups = 90.....so 15% of 600 = 90....lets check it

15%of 600 = 0.15(600) = 90...yep, thats correct....there were 630 cups in the new un-opened box

Answer:

630

Explanation:

15% * number of remaining cups = 90

15% * (x-30) = 90

0.15(x-30) = 90

0.15x - 4.5 = 90

0.15x = 94.5

x = 630