Which of the following equations have exactly one solution?
Choose all answers that apply:
Choose all answers that apply:

(Choice A)
A
6
x
−
6
=
15
x
+
15
6x−6=15x+156, x, minus, 6, equals, 15, x, plus, 15

(Choice B)
B
6
x
+
15
=
6
x
+
15
6x+15=6x+156, x, plus, 15, equals, 6, x, plus, 15

(Choice C)
C
6
x
−
15
=
6
x
+
15
6x−15=6x+156, x, minus, 15, equals, 6, x, plus, 15

(Choice D)
D
6
x
−
6
=
6
x
+
15
6x−6=6x+156

1a) The additional information required using SAS Congruency postulate is; ∠AOB ≅ ∠BOD

1b) The additional information required using ASA Congruency postulate  is BC ≅ QR

2a) The symbolic form of the congruent triangles is written as;

ΔABC ≅ ΔADC

2b) The congruence rule used is SAS Congruency postulate.

1a) We want to prove that the triangles are congruent by SAS Congruency postulate. SAS congruency postulate means Side - Angle - Side. Thus, the additional information is;

∠AOB ≅ ∠BOD

1b) We want to prove that triangle ABC is congruent to triangle PQR by ASA Congruency. We have that;

∠Q = ∠B and ∠R = ∠C. Thus;

The additional information is BC ≅ QR

2a) The symbolic form of the congruent triangles is written as;

ΔABC ≅ ΔADC

2b) The congruence rule used here is SAS Congruency postulate.

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The equation of line passes through the point (1, -5) will be;

⇒ y = - 3x - 14

What is Equation of line?

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The point on the line are (1, -5).

And, The slope of the line is,

⇒ m = - 3

Now,

Since, The equation of line passes through the point (1, -5).

And, Slope of the line is,

⇒ m = - 3

Thus, The equation of line with slope - 3 is,

⇒ y - 1 = - 3 (x - (-5))

⇒ y - 1 = - 3 (x + 5)

⇒ y - 1 = - 3x - 15

⇒ y = - 3x + 1 - 15

⇒ y = - 3x - 14

Therefore, The equation of line passes through the point (1, - 5) will be;

⇒ y = - 3x - 14

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Answer

Step-by-step explaination:

This is an algebraic equation. We have to solve it like this......

16-2t=5t+9

-5-2t=-16+9

-7t=-7

Ans: -7t=-7

The correct option regarding the correlation coefficient is that A. I can’t be confident at all; this is about as close to a random guess as you can get.

The correlation coefficient is a statistical measure of the strength of a two-variable linear relationship. Its values can range between -1 and 1. A correlation coefficient of -1 denotes a perfect negative, or inverse, correlation, in which values in one series rise while those in the other fall, and vice versa.

A coefficient of one indicates that there is a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 indicates that no linear relationship exists. In science and finance, correlation coefficients are used to assess the degree of association between two variables, factors, or data sets.

In this case, the fat that the person gets 0 implies that it's probably a random guess. In conclusion, the correct option is A.

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In the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.

As given in the question,

In the given triangle KLM,

Coordinates of the triangle KLM are given by :

K(0,2) ,L(2 ,9) ,M(4,2)

Dilation from the origin is represented by:

a. K'(0,2) , L'(8,9) , M'(16, 2)

Dilation scale factor does not effect on all the coordinates .

Not a correct option.

b. K'(0,2) , L'(2,36) , M'(16, 2)

Dilation scale factor does not effect on all the coordinates .

Not a correct option.

c. K'(0,8) , L'(8,36) , M'(16, 8)

Multiply by scale factor 4.

Dilation exist.

d. K'(4,6) , L'(6,13) , M'(8, 6)

Scale factor of addition of 4.

Dilation does not exist.

Therefore, in the given triangle KLM with coordinates K(0,2) ,L(2 ,9) ,M(4,2), the sets of points which represent the dilation from the origin is K'(0,8), L'(8, 36) , M'(16, 8) multiply by scale factor 4.

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Answer:

6 hours.

Step-by-step explanation:

Subtract initial fee from total. (67 - 19 = 48).

Divide by the hourly rate. (48 / 8 = 6).

The bike was rented for 6 hours.

Answer:

Yes they are equivalent.

Step-by-step explanation:

$12 divided by 3 is $4
$36 divided by 9 is also $4
Therefore they are equivalent.

Your welcome

Answer:

Yes!

Step-by-step explanation:

You divide 3 by 12 because that's how much they work for an hour. That means they make $36 for 9 hours.
12 ÷ 3 = 4

36 ÷ 9 = 4

They have the same answer which makes them equivalent.

Answer:

14

Step-by-step explanation:

[tex](33 - (15) + 10) \div 2 \\ 33 - 15 + 10 \div 2 \\ 18 + 10 \div 2 \\ 28 \div 2 \\ = 14[/tex]

Answer:14

Step-by-step explanation:1/2 (24+9- 5 x 3 + 10

Answer:

The number of books bought in each store would be 4 The amount spent will be the same in either store.

Step-by-step explanation:

Comment

The question has to make the assumption that no matter how many books are bought from store 1, the shipping charge is 8 dollars. Otherwise there is no solution.

Givens

Book1: 10 and  8 dollars total for shipping

Book2: 12 dollars, no shipping costs.

Equation

12x = 10x + 8         Subtract 10x from both sides

Solution

12x - 10x = 10x - 10x + 8      Combine

2x = 8                                   Divide both sides by 2

2x/2 = 8/2

x = 4

Answer:

n = 7

Step-by-step explanation:

The equation is,

→ n - 3n = 14 - 4n

Now the value of n will be,

→ n - 3n = 14 - 4n

→ -2n = 14 - 4n

→ -2n + 4n = 14

→ 2n = 14

→ n = 14/2

→ [ n = 7 ]

Hence, the value of n is 7.

1. The pairs of polygons are similar.

2. The pairs of polygons are not similar.

3. The missing measure is of x = 5.2.

4. The missing measure is of x = 16.

5. The value is AB = 6.

6. The perimeter of the yellow tile is of 240 cm.

7. The value is DF = 0.75.

Similar polygons are polygons that share these two following features:

Hence, for itens 1 and 2, we have that:

For item 3, the side lengths are proportional, hence:

x/2.6 = 8/4

x/2.6 = 2

x = 2 x 2.6

x = 5.2.

Same as item 4, hence:

x/10 = 9.6/6

x/10 = 1.6

x = 16.

For item 5, considering the equivalent side lengths, we have that:

AB/8 = 12/16

AB/8 = 3/4

AB = 24/4

AB = 6.

The perimeter of the yellow tile is of 240 cm in item 6, as the ratio between the side lengths is of 3, hence the ratio of the perimeters will also be of 3, then:

3 x 80 cm = 240 cm.

For item 7, we have that:

DF/3.4 = 2.25/9

DF = 3 x 2.25/9

DF = 0.75.

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That aint no question

Answer: $4

Step-by-step explanation: we know he spent 28 dollars in total and 16 of those was on a pair of pants so we can subtract 16 from 28 to get 12

we also know he bought 3 shirts in total and because 12/3=4 each shirt must have cost 4 dollars.

We can check the answer by combining the price of the shirts (12)

with the price of the pants (16) because 12+16=28 we know the cost of each shirt has to be $4.

Answer:

Each shirt was 4 dollars.

Step-by-step explanation:

28 - 16 = 12. 12 divided by 3 = 4.

The maximum and minimum measurements are 5 and -3 respectively.

f ( x ) = -x^3 +3x^2+ 45 x + 10

f' l x ) = 0

0 = - 3x^2 +6x +45

x = 5,- 3.

f ( 4 ) = - ( 4 )^3+ 3( 4 )^ 2 + 45 ( 4 ) + 10 = 174

f ( - 4 ) = - ( - 4 )^3 + 3( - 4 )^2 + 45(- 4) + 10 = - 58

f ( - 3 ) = -(- 3 )^3 + 3 ( - 3)^2 + 45 (- 3) + 10 = - 7 1

+ ( 5 ) = -(5)^3 + 3(5 )^2 +45(5)+ 10 = 185

Absolute maximum = maxis{ f(4 ),f(5),f(-4),f( - 3 )}

                        = 185 at x=5

Absolute mininum=minis{f(4 ),f(5),f(-4),f( - 3 )}

                      = - 71 at x= -3

In light of this, the maximum and minimum values are 5 and -3, respectively.

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The cost of feed for a cow in a month is $15.08

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls)

Similarly the ratio of the cost of cow's food to pig is 2:1

represent the cost of feed of a cow by x and the cost of feed for a pig to be y

therefore x= 2y

there are 46 cows, therefore the cost of feed for 46 cows is 46x

there are 22 pigs, therefore the cost of pig is 22y

46x+22y= 860

representing 2y for x

46(2y)+22y= 860

114y= 860

y= 860/114

y=$ 7.54

recall x=2y

x= 7.54×2= $15.08

therefore $15.08 is spent on a cow in a month

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The 95% confidence interval for the average number of units that students in their college are enrolled in is (11.46,12.53)

We are given the number of students, n =  46, and  the mean of the sample which is x= 12.5, and the standard deviation of the sample which is s= 1.8 , the formula  we are referring to for calculating the confidence interval which is :

x ± t (s/√(n))

since for  this case, the degree of freedom is one less than the mean, which is 45, the critical value for the confidence of 95% with  the degree of freedom of 45 is 2.015

x + t(s/√(n)) = 12.5 +2.015*(1.8/6.78)=  12.53

x - t(s/√(n))= 12.5 -2.015*(1.8/6.78)= 11.46

The interval is (11.46,12.53)

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Proportionality denotes a linear relationship between two quantities or variables.

A.  Table is mentioned below.

B. Yes, it is a proportional relation.

C. y = 1/24 x

Therefore,

Part C : We know that,

1 day = 24 hours,

⇒ 1 hour = 1/24 day

As a result, the number of days in x hours (say y) = hours number of days in each hour

⇒ y = 1/24 x

Which is an equation of line.

Part A :

Hours       1              2           3           4          5      

Days       1/24       1/12        1/8         1/6       5/24

Part B :

∵ a line passes through the origin always shows a proportional relation,

Since, for (0, 0),

0 = 1/24 (0) ( True )

i.e. there is a proportional relation between number of days and number of hours.

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Answer:

  600

Step-by-step explanation:

You want to use distributive property to answer (15x6) + (85x6).

The distributive property shows you what you can do with a common factor:

  (15×6) + (85×6) = (15 +85)×6 . . . . . . apply the distributive property

  = 100 × 6 . . . . . . evaluate the sum in parentheses

  = 600 . . . . . . perform the multiplication

The standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1

Define Parabola

The equation of parabola in standard form is y = ax² + bx + c

We have given the points,

(1, 0), (2, -3), and (3,-10)

Let's put each point in parabola equation and form three equation as,

Equation for point (1, 0)

0 = a * (1)² + b * 1 + c

a + b + c = 0                --------------------eq(i)

Now, equation for point(2, -3)

-3 = a * (2)² + b * 2 + c

4a + 2b + c = -3           --------------------eq(ii)

And, equation for point (3, -10)

-10 = a * (3)² + b * 3 + c

9a + 3b + c = -10         ---------------------eq(iii)

Now, we have three equation let's put them together

a + b + c = 0                --------------------eq(i)

4a + 2b + c = -3           --------------------eq(ii)

9a + 3b + c = -10         ---------------------eq(iii)

Now, form equation which is of two variable.

For that, we take first two equation and subtract eq(ii) from eq(i)

4a+2b+c = -3

a + b + c = 0

-    -     -      -

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

3a + b = -3                      ---------------eq(a)

Now, subtract eq(iii) from eq(ii)

9a + 3b + c = -10

4a + 2b + c = -3  

-     -        -      -

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

5a + b  = -7                   ------------------eq(b)

Now, we get eq(a) and eq(b) consist of two variable.

3a + b = -3                       ---------------eq(a)

5a + b  = -7                      ----------------eq(b)

Now, solve this equation simultaneously and find the value of a and b.

3a + b = -3

5a + b  = -7  

-     -        -

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

-2a = 4

a = -2

put a = -2 in eq(a) to find b

3a + b = -3

⇒3 * -2 + b = -3

⇒-6 + b = -3

⇒b = 3

We get the values of a and b. And, left with value of c for that just put the a and b value in eq(i) and find c

a + b + c = 0

-2 + 3 + c = 0

c = -1

Now, we get all the necessary values for equation.

Next, just put a, b and c values in parabola equation.

y = ax² + bx + c

y = -2x² + 3x - 1

Hence, the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1

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The relationship between the number of weeks and cars are proportional since they are dependent on each other.

Ratio and Proportion are explained majorly based on fractions. When a fraction is represented in the form of a:b, then it is a ratio whereas a proportion states that two ratios are equal. Here, a and b are any two integers. Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

In this question, Alfred, buy three car each week. As the number of weeks increase, so is the number of his car increasing at definite proportions.

This implies that we can set an equation to represent the number of cars Alfred will have after certain number of weeks.

Let;

y = 3x

At week 10, Alfred will have

y = 3(10) = 30 cars

After 10 weeks, Alfred will have 30 cars

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Answer:

x = 1/6.

Step-by-step explanation:

3x+4=9x+3

STEP 1: Subtract 4 from both sides...

3x+4 -4 = 9x+3 -4

3x = 9x-1

STEP 2: Subtract 9x from both sides...

3x - 9x = 9x-1 -9x

-6x = -1

STEP 3: Divide both sides by -6x...

-6x / -6x = -1/ -6x

x = 1/6x.

REMEMBER: 2 negatives are equal to positive.

Answer:

a = 6.63 cm

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (12)² = a² + (10)²

→ 144 = a² + 100

→ a² = 144 - 100

→ a = √44

→ [ a = 6.63 cm ]

Hence, value of a is 6.63 cm.

Determine which steps are used to find the product shown. Put the steps in the order in which they would be performed.

See photo below. Comment for more clarification.

Answer:

11 - 2i

Step-by-step explanation:

Given expression:

[tex](4-3i)(2+i)[/tex]

Expand:

[tex]\implies 4(2+i)-3i(2+i)[/tex]

[tex]\implies 8+4i-6i-3i^2[/tex]

[tex]\implies 8-2i-3i^2[/tex]

Apply the imaginary number rule  i² = -1 :

[tex]\implies 8-2i-3(-1)[/tex]

Simplify:

[tex]\implies 8-2i+3[/tex]

[tex]\implies 11-2i[/tex]

Step-by-step explanation:

well, when 2 summed teens are multiplied, every part of one term is multiplied with every part of the other term :

(4 - 3i)(2 + i) = 8 + 4i - 6i - 3i² = 8 - 2i + 3 = 11 - 2i

The value of y when x = -2, 0,2 is 1/49, 7, 49.

Simplification is an algebraic expression is when we utilize a range of approaches to make algebraic expressions more efficient and compact - in their simplest form - without changing the value of the original expression.

Given function y =[tex]7^{x}[/tex]

We have to determine the y values when x = -2, 0, 2

Now substitute the x values in the given function

If x = -2 then

Y = 7(-2)

Y = 1/49

If x = 0 then

Y = 7(0)

Y = 1

If x = 2 then

Y = 7(2)

Y = 49

Therefore the value of y when x = -2, 0 ,2 is 1/49, 7 , 49

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4(a + 8)

multiply out:

= 4a + 32