Hector left his house at (-7,11) on a map of coleville and walked to the zoo at (-7,3) from there he walked east to his friends house. He walked a total distance of 25... if each unit on the map represents one block, what are the coordinates of Hectors friends house?​

The error is that vertical angles are congruent, and don't necessarily add to 180°. Vertical angles only add to 180° if they are right angles.

[tex]13x+45+19x+3=180 \\ \\ 32x+48=180 \\ \\ 32x=132 \\ \\ x=33/8[/tex]

Answer:

x = 7

Step-by-step explanation:

Vertical Angle Theorem

When two straight lines intersect, they form two pairs of angles.  The vertically opposite (non-adjacent) angles are congruent.

Angles on a Straight Line Theorem

The sum of angles formed on a straight line is equal to 180°.

The error made is confusing the Vertical Angle Theorem with the Angles on a Straight Line Theorem.  To find x, we should either:

Applying the Vertical Angle Theorem:

[tex]\boxed{\begin{aligned} (13x+45)^{\circ} &=(19x+3)^{\circ} \\13x+45&=19x+3\\13x+42&=19x\\42&=6x\\x&=7\end{aligned}}[/tex]

Applying the Angles on a Straight Line Theorem:

[tex]\boxed{\begin{aligned}(6x+2)^{\circ}+(19x+3)^{\circ}&=180^{\circ}\\6x+2+19x+3&=180\\25x+5&=180\\25x&=175\\x&=7\end{aligned}}[/tex]

Therefore, the value of x is [tex]\boxed{x=7}[/tex] .

An expression which is equivalent to the given expression 18x² +14x + 7 is given by 14x + 18x² + 7.

As given in the question,

Given expression is :

18x² +14x + 7

Simplify all the optional expression to check which one is equivalent to given expression:

a. 7(18x² + 14x)

   = 126x² + 98x

Not equivalent.

b. 14x + 18x²+ 7

Rearrange it

18x²+14x + 7 .

Equivalent.

c. 32x³ + 7

Degree is 3.

Not equivalent.

d. 18x²(14x + 7)

= 252x³ +126x²

Not equivalent.

Therefore, an equivalent expression of 18x²+14x + 7 is 14x + 18x²+ 7.

The complete question is:

Which of the following is an equivalent expression of 18x²+14x + 7?

7(18x² + 14x)

14x + 18x²+ 7

32x³ + 7

18x²(14x + 7)

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Answer: -5j+15

step by step equation

The time taken by the rock to hit the ground is  3 seconds.

It is given in the question that:-

[tex]t=\frac{\sqrt{h} }{4}[/tex]

Where,

t represents the time (in seconds) taken by the object to reach the ground, and

h represents the height from which the object is falling

We have to find the time taken by a rock to hit the ground after falling from a height of 125 feet.

Using the formula given in the question, we can write,

[tex]t=\frac{\sqrt{125} }{4}=\frac{5\sqrt{5} }{4}[/tex]

We know that,

[tex]\sqrt{5}[/tex] ≈ 2.23

Hence, we can write,

t ≈ (5*2.23)/4 ≈ 2.7875 ≈ 3 seconds (estimated to nearest integer)

Hence, it takes around 3 seconds for the rock to hit the ground after falling from a height of 125 feet.

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Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB. We have angles ∠B=35°,∠U=62°,∠P=21°. The angles are ∠1=56° and ∠2=62°.

Given that,

In picture there is a triangle with the intersection line in between the triangles.

Triangle PUB is divided into 2 triangles that is ΔPUM and ΔPMB.

We have angles

∠B=35°,∠U=62°,∠P=21°

We have to find the angle of angle 1 and 2.

We know,

In triangle sum of the 3 angles is 180°.

Now, we take ΔPMB

We find the other angle of M.

21°+35°+M=180°

M=180°-21°-35°

M=180°-56°

M=124°

So, now we can find the angle 1.

the straight line has a angles of 180°.

124°+∠1=180°

∠1=180°-124°

∠1=56°

Now, we find angle 2.

Take ΔPUM

62°+∠1+∠2=180°

62°+56°+∠2=180°

∠2=180°-62°-56°

∠2=180°-118°

∠2=62°

Therefore, the angles are ∠1=56° and ∠2=62°.

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The maximum that the company can expect for returned items is C. $5972.65

From the information, the average daily profit of an electronics store is $31,435 and the company estimates that 15% is lost each day to returns, with a margin of error of ±4%.

In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and research results using the margin of error.

The maximum the company can expect for returned items will be:

= (15% + 4%) × Profit

= 19% × $31,435

= 0.19 × $31,435

= $5972.65

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Answer:

370000

Step-by-step explanation:

So it would go from 962-1000. So 370000

Answer:

1. (3 + 7) ÷ 2 = 5

2. (4 + 9) x 3 = 39

3. 10 ÷ (4 x 5) = 1/2

4.(1 + 2) ÷ 20 = 3/20

The value of x and y for given equation are (2,15) and (12,24).

Using hit and trial method, we can calculate that the values of given equation are (2,15) and (12,24)

The hit and trial approach is used to balance chemical equations by selecting the least whole number coefficient. tally the instances of each ingredient on either side of a reaction. The element with the lowest frequency of recurrence is considered to be balanced.

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Answer:

y = 3x + 19

Step-by-step explanation:

Here m is the slope and b is the y-intercept.

     y = 3x + 4

m = 3

Parallel lines have same slope.

   m = 3

y = 3x + b

Substitute (-5,4) in the above equation.

        4 = 3*(-5) + b

        4 = -15 + b

  4 + 15 = b

           b = 19

Equation of the line: y = 3x + 19

Answer: y = 3x +19

Step-by-step explanation:

-Parallel lines have the same gradient

y = 3x + c

rearrange to give c= y - 3x

substitute x = -5 and y = 4

c = 3 - (3x-5)

c= 19

so the equation is y = 3x + 19

Combine X. which is 2x, -5x, x.

we combine -2x and -5x and gives me -3x.

2x -10 -5x -1 +x

now i combine the last x, which is -3x and x and gives us -2x.

-3x -10 -1 +x

now we just combine the rest of the numbers. -10 and -1 and gives me -11.

-2x -10 -1

we have now combine all the numbers and there's nothing else to combine. we're done combining.  :))

ANSWER:

-2x-11

Answer: The correct answer is B.

Step-by-step explanation:

To evaluate this expression you must divide x-1 though the expression or factor out the upper half of the equation and cancel out what is necessary.

The division method: attached below :)

Answer:

107.5 and 72.5

Step-by-step explanation:

actually the number is "x", which oddly enough is the 100%, so we know that 45% of "x" is 99, what is "x" anyway?

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 99& 45 \end{array} \implies \cfrac{x}{99}~~=~~\cfrac{100}{45} \\\\\\ \cfrac{x}{99}=\cfrac{20}{9}\implies 9x=1980\implies x=\cfrac{1980}{9}\implies x=220[/tex]

Anna uses 120 g of chocolate and 360 grams of margarine to needed to bake biscuits.

We have data as follows; To make 24 biscuits Anna uses following proportion of Ingredients;

80 g sugar

120 ml syrup

200 g oats

120 g margarine

40 g chocolate

Now We can analysis that anna uses 40 g chocolate to make 24 biscuits

So for 120 g of chocolate Anna can bake [tex] \frac{24(120)}{40}  [/tex]

=  24 (3)

= 72 biscuits

∴ Anna can bake 72 biscuits if she uses 120 g of chocolate.

We want to find how many grams of margarine will she need to make 72 biscuits and this can be done as follows;

Ingredients for 24 biscuits require 120 g margarine

∴ For 72 biscuits anna require [tex] \frac{72(120)}{24}  [/tex] g of margarine

= 3 (120)

= 360 g of margarine.

Hence 360 grams of margarine anna needed.

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Answer: The factors of 12 are 1, 2, 3, 4, 6, and 12

Hope this helps!

Answer:

The factors of 12 are 1, 2, 3, 4, 6 and 12.

The translation of y = |x| left 9 units and up 11 units is y = |x+9|+11 .

The process of translating an existing graph or equation into a new graph is known as graph translation.

We know that for translation we have to change the x-coordinate and the y-coordinate by the amount that is stated in the translation.

Therefore from the graph we can see that the graph of y =|x| is represented by the blue line and the graph of  translation y = |x+9|+11 is represented by the red line.

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m=x1+x2/2 or m=y1+y2/2

hope you understand

Given the algebraic expression 3x⁴ - 5x + 2, each of following represents:

An algebraic expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables, numerical quantities (constants), accompanied with the use of different mathematical operations.

In Mathematics, a coefficient simply refers to a constant quantity or numerical value (number or numeral) that is typically placed before the variable in an algebraic expression.

In conclusion, an exponent is an operation that raises a numerical value or quantity to the power of another and it is generally written as bⁿ.

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The expression that shows the price x of a new car minus à 25% down payment is x - 0.25 = 0.75x

Based on the information given, it should be noted that the information is to simply illustrate find the expression that shows the price x of a new car minus a 25% down payment.

This will be illustrated as:

= x - (25% × x)

= x - 0.25x

= 0.75x

Therefore, the expression is 0.75x.

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Ian is 144 centimeters tall now by solving the equation.

A mathematical statement called an equation includes the sign "equal to" between two expressions with equal values.

Let Lisa, Ian, and Jim's real heights are L, I, and J, respectively.

Lisa's friend Ian is 4 centimeters taller than her, therefore L=4+I

In the sentence "Ian is 8 cm taller than Jim.": I=8+J, 

Hence, J=I-8 

Thus, Lisa, Ian, and Jim are 4+I, I, and I-8 correspondingly in height.

Since their heights increase by 2 cm every 4 months, this results in an 8-centimeter height increase.

Thus, after four months, Lisa, Ian, and Jim reach the following heights:

4+I+I+8, I+8, and I-8+8 that equal to I+12, I+8, and I respectively

"The total of Ian's and Jim's heights will be 140 centimeters more than Lisa's height in four months" means:

(I + 8) + I = 140 + (I + 12)

⇒2I + 8 = 152+I

⇒I = 144

⇒I=152-8

=144

Therefore, Ian is 144 centimeters tall now.

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Answer:

[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]

Step-by-step explanation:

The bars either side of an expression or a value are the absolute value symbol.  "Absolute value" means how far a number is from zero.   Therefore, the absolute value of a number is its positive numerical value.  

The values of a, b and c are negative. All expressions except "a" are absolute values, and are therefore positive numerical values. Therefore, "a" is the least expression.

The simplest way to calculate each expression's numerical value is by assigning approximate numbers to each value, then carrying out each calculation.

From inspection of the graph:

[tex]\begin{aligned} \implies |a - b| & \approx |-3.8 - (-1.3)|\\ & = |-2.5| \\ &= 2.5\end{aligned}[/tex]

[tex]\begin{aligned} \implies |b - c| &\approx |-1.3 - (-0.7)| \\ &= |-0.6| \\ &= 0.6\end{aligned}[/tex]

[tex]\implies a \approx -3.8[/tex]

[tex]\begin{aligned} \implies |a - c| &\approx |-3.8 - (-0.7)| \\ &= |-3.1| \\ &= 3.1\end{aligned}[/tex]

Therefore:  -3.8 < 0.6 < 2.5 < 3.1

Hence, the expressions from least to greatest are:

[tex]\boxed{a} \quad \boxed{|b - c|} \quad \boxed{|a - b|} \quad \boxed{|a - c|}[/tex]

Using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.

As given in the question,

Given: ∠1 ≅ ∠4. Prove ∠2 ≅ ∠3.

(Using angle addition postulate)

    Statements                                              Reasons

1. ∠1 ≅ ∠4           Given

2. ∠1 = 180 - ∠2  Being supplementary angles (angle addition postulate)

3. ∠4 = 180 - ∠3  Being supplementary angles (angle addition postulate)

4. 180 - ∠2 = 180 - ∠3      Substituting Statements 2 & 3 into Statement 1.

5. ∠2 = ∠3                        Simplifying Statement 4 algebraically.

In statement 4, the constants 180 cancel out from either of left hand side (LHS) and right hand side (RHS). Thus the equation gets simplified to Statement 5. It is worthwhile to mention that Supplementary angles or linear pair always sum up to 180° in measure. Additionally linear pair form a straight line together.

Therefore, using angle addition postulate when ∠1 ≅ ∠4 it is proved that ∠2 ≅ ∠3.

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The Compound Interest of Principle 2000 will become 2420 within 2 years when the rate of interest is 21%

Compound interest = P(1 + R ÷ 100) to the power of n,

where P = Principle

           R = Rate of Interest

           n = no. of years

According to the given question,

Principle(P) =Rs2000

Rate of interest (R) =?

no. of years(n) = 2 years

given CI (Compound Interest) = Rs2420

CI = 2000(1 + R ÷ 100)² = 2420

    = 20(100 +R) = 2420

    = 100 + R = 2420 ÷ 20

    = 100 + R = 121

    = R = 121 - 100

    = R = 21%

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0.6004 is standard deviation of equation .

Why is there a standard deviation?

=0.6004$P(120≤X≤153)=0.6004​

The mean is μ=147, and the standard deviation is σ=16.

0.6462−0.0458=0.6004.

Thus, P(120≤X≤153)=0.6004.

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