1. Jackie's balance at the beginning of October was $432.23. During that month she made
deposits totaling $752.34, wrote checks totaling $532.13, paid a maintenance fee of $11, and
earned $3.42 in interest on the account. What was the balance at the end of the month?

Answer:

Proved below.

Step-by-step explanation:

Parallel lines and angles:

     Given: p // q and ∠1≅ ∠2

Proof:

        p //q, l is transversal,

            ∠3 ≅ ∠1   -----(I)    {Corresponding angles are congruent}

          ∠1 ≅ ∠2   ---------(II)    {Given}

From (II) & (I),

        ∠3 ≅ ∠2

∠3 and ∠2 are alternate interior angles. Alternate interior angles are congruent only if the lines are parallel.

⇒ l // m

Answer:

Cost per egg = 8.4/12 = 0.7

Cost per hundred egg =Rs70

Let selecting price per hundred be Rs.y

⇒ 70/y-70 ×100 = 15

⇒ 10y−700 = 105

Answer:

Step-by-step explanation:

C

That indicates that in order to make a solution that is 60% acid, you will need to add a total of 300 milliliters of pure acid into the mixture.

This is further explained below.

In general, pure acid refers to an acid concentration of 100%. It is feasible to formulate the following equation if you assume that X represents the volume addition of the pure acid:

[tex]Va=100 \%X + 600 * 40 \%[/tex]

[tex]Va= (600+X)60 \% (M_1V_1=M_1 V_2)[/tex]

100X + 24000 = 36000 + 60x

X = 300.

In conclusion, That implies in order to generate a solution that is 60% acid, you will need to add 300 milliliters of pure acid.

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The tree is 79 feet tall if the ground is 79 feet from the tree and the angle of elevation is 45°.

Angle of elevation:

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

Therefore, the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

Given,

The angle of elevation to a nearby tree from a point on the ground is measured to be 45 degrees.

Here we need to find how tall is the tree if the point on the ground is 79 feet from the tree and we have also need to round the  answer to the nearest hundredth of a foot.

Here we know that

The angle of elevation = 45°

Distance of the point from the tree = 79 feet

Suppose h is the height of the tree.

Then the value of h is calculated as,

=> h / 79 = tan 45°

We know that, the value of tan 45° = 1,

So,

=> h/79 = 1

Then  the value of h is,

=> h = 79

Thus, the height of the tree is 79 feet.

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Answer:

4:8:12

Step-by-step explanation:

To find the ratio of 24 in 1:2:3,

first add the ratios = 6 then divide each ratio as a fraction of the total

Therefore, 24 in ratio 1:2:3 is 4:8:12

The domain and range of the function f(x) = 4x - 6 in order from least to greatest include the following:

A range can be defined as the set of all real numbers that connects with the elements of a domain. This ultimately implies that, a range refers to the set of all possible output numerical values, which are shown on the y-axis of a graph.

A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.

In order from least to greatest, the range and domain of the given function f(x) = 4x - 6 are as follows:

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Answer: You would pay $7.97 for the bagels.

Step-by-step explanation:

(Price per Dozen * Amount) - Coupon = Price of Bagels

(5.98 * 1.5) - 1 = Price of Bagels

8.97 - 1 = Price of Bagels

Price of Bagels = $7.97

a) By definition of standard form, a light-year is equal to 5.880 × 10¹² miles.

b) By simple rule of three, a magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.

In this problem we need to convert a magnitude in miles to an equivalent magnitude in light-years and another magnitud in light-years to an equivalent magnitude in miles. Standard form is a notation used to represent both large and small number with no significant loss of precision. This form is described by the following form:

a.b × 10ⁿ

Where:

a) A light-year is equal to 5.880 × 10¹² miles.

b) The equivalent magnitude in miles is found by the following simple rule of three:

x = 4.25 ly × (5.880 × 10¹² mi / ly)

x = 2.499 × 10¹³ mi

A magnitude of 4.25 light-year is equivalent to a magnitude of 2.499 × 10¹³ miles.

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Answer:

(5,7)

Step-by-step explanation:

Answer:

(5,7)

Step-by-step explanation:

Abscissa of D will be the abscissa of A. A(5,9)

Abscissa of D = 5

Ordinate of D will the ordinate of C. C(8,7).

Ordinate of D = 7

So, D(5,7)

Answer: true

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

To find the number of extra flowers ordered, we can start by forming an equation based on the total amount paid by the customer.

Let the number of extra flowers be n.

Total paid

= cost of standard arrangement +(number of extra flowers)(cost per additional flower)

= $25 +n($1.25)

Given that the customer paid $45,

25 +1.25n= 45

Now that we have formed the equation, let's solve for n.

Subtract both sides by 25:

1.25n= 45 -25

1.25n= 20

Divide both sides by 1.25:

n= 20 ÷1.25

n= 16

The first graph from the right as shown in the reference image attached hereby alongside the question statement, represents a function.

As per the question statement, we are provided with 4 distinct graphs attached hereby alongside.

We are required to determine, which of the above-mentioned graphs represent a function.

To solve this question, we need to know about the characteristics of a function, which we can match against our provided graphs and identify our required function.

A function is an operator, and hence, there will be a fixed pattern or sequence among it's outputs, which we can only find in the first graph from the right as shown in the reference image, since it is a straight line parallel to the Y-axis at (x = 1).

Therefore, the first graph from the right as shown in the reference image attached hereby alongside the question statement, represents a function.

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Answer: This is the graph

The  statements that would prove the lines are parallel are;

∠GHI ≅ ∠KJH

∠MJH + ∠NHJ = 180°

∠KJH + ∠IHJ = 180°

In congruency of angles formed in this type of scenario, we will make use of the following rules;

Using the above congruency rules and applying them to our question, we can say that for lines HN and KM to be parallel to each other, then;

∠GHI ≅ ∠KJH because they are corresponding angles

∠MJH + ∠NHJ = 180° because they are supplementary angles

∠KJH + ∠IHJ = 180° because they are supplementary angles

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Answer: 0.93

There are 9 tenths

Step-by-step explanation:

Missing side length of the given measures of the triangle is equal to           x = 1/2 units (approximately).

As given,

Given measures of the triangle ABC are

Angle A=(18 +18)°

             =36°

Consider side opposite to ∠A=a ,∠B=b ,∠C=c

Given side length

AC=b

     =20

AB=c

    =12

BC=c

    =x+12

Using cosine law

cos A= (b²+c²-a²)/2bc

⇒cos36°= [20²+12²-(x+12)²]/2(20)(12)

⇒(1+√5)/4=(544-x²-24x-144)/480

⇒x²+24x-280+120√5=0

⇒x²+24x-11.7=0

Now, x = [-24±√24²-4(1)(-11.7)]/2(1)

           = (-24±24.955)/2

           ≈ (-24 ±25)/2

Hence, x = (-24+25) /2

               = 1/2

or x = -24.5 side length cannot be negative.

Therefore, Missing side length of the given measures of the triangle is equal to x = 1/2 units (approximately).

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The required absolute value linear inequality is 15 ≤ t ≤ 20.

What is absolute value linear inequality?

A variable enclosed by the absolute value sign of an inequality is known as an absolute value inequality.

Given highest temperature as 20°C and lowest temperature as 15°C

Given variable is t.

From the first condition we get t ≤ 20  ...........(1)

From  the second condition we get 15 ≤ t  .....(2)

From the inequalities (1) and (2), we get

15 ≤ t ≤ 20

Therefore, the required absolute value linear inequality is 15 ≤ t ≤ 20.

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By taking some products between fractions and mixed numbers, we will see that your trip along the bank has a length of (2 and 9/24) miles.

Here we know that the total distance of the travel is (14 + 1/4) miles.

In this case, we know that 1/3 of that distance is traveled in the woods, so the total distance traveled in the woods is given by the product:

D = (1/3)* (14 + 1/4) mi = (14/3 + 1/12) mi

Now we know that 1/2 of the distance traveled in the woods is traveled along the bank of a strem, then the distance that we are looking for is given by the product:

D' = (1/2)*(14/3 + 1/12) mi = (7/3 + 1/24)mi

Now we can simplify that mixed number as:

(7/3 + 1/24)mi = (6/3 + 1/3 + 1/24) mi = (2 + 8/24 + 1/24)mi = (2 + 9/24) mi

Your trip along the bank of the stream has a length of (2 + 9/24) miles.

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The simplified expression for the given algebraic expression -2(3x – 2) -5(7 – x) will be ( -x - 31)

As per the question statement, we are supposed to find the simplified expression for the given algebraic expression -2(3x – 2) -5(7 – x).

For solving the above expression, we should be having good knowledge of all mathematical operators and BODMAS.

Let y =  -2(3x – 2) -5(7 – x)

y = -6x + 2*2 - 5*7 + 5x

y = -6x + 4 - 35 +5x

y = -x - 31

Therefore, the simplified expression for the given algebraic expression -2(3x – 2) -5(7 – x) will be y = ( -x - 31)

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The zeroes of the equation f(x) is 3x² + 18x + 32 is x =  -18 -7.75/ 6 and x = -18 + 7.75/ 6

Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.

Given f(x) = 3x² + 18x + 32

3x^2 + 18x + 32 = 0

Here, a = 3

b = 18

c = 32

-b ±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]

-18 ± [tex]\frac{\sqrt{18^2-4(3)(32)} }{2(3)}[/tex]

-18 ± [tex]\frac{\sqrt{324-84} }{6}[/tex]

-18 ± [tex]\frac{\sqrt{-60} }{6}[/tex]

-18 ± [tex]\frac{-7.75}{6}[/tex]

X = -18 (-7.75)/ 6 and x = -18 – (-7.75)/ 6

X = -18 -7.75/ 6 and x = -18 + 7.75/ 6

Therefore, the zeroes of the polynomial are X = -18 -7.75/ 6 and x = -18 + 7.75/ 6

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Check the picture below.

[tex]\stackrel{\measuredangle U}{(3x-4)}~~ + ~~\stackrel{\measuredangle V}{(x+20)}~~ + ~~\stackrel{\measuredangle W}{(6x+6)}~~ = ~~180 \\\\\\ 10x+22=180\implies 10x=158\implies x=\cfrac{158}{10}\implies {\Large \begin{array}{llll} x=\cfrac{79}{5} \end{array}}[/tex]

Answer:

1500

Step-by-step explanation:

600 divided by 4 to see how much hotdogs are sold EACH home football game. This gives you 150 each game so you multiple it by ten in order to get the total for ten home games

Answer:

Step-by-step explanation:

Area = L times w ( length times width.)

Your lengthyot Length is 4 units and width is 4. so what is 4 times 4?

your right, its 16. Answer A is correct.

Answer:

[tex]7 * x^2[/tex]

Answer:

2/3

Step-by-step explanation:

The amount of honey each jar holds is 2/3 cups.

Fraction

The fraction is termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 5/8 is a fraction where the upper part denotes the numerator and the lower part is the denominator.

Given that:-

Number of equal sized jars filled by Isabelle = 24 jars

Total amount of honey brought by Isabelle to the sell at the farmer's market = 16 cups

We have to find the amount of honey each jar holds.

From the data given in the question, we can write,

24 jars = 16 cups

Hence, using the equation, we can write the fraction,

1 jar = (16/24) cups

1 jar = 2/3 cups

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Answer: A

Step-by-step explanation:

A. True by the definition of a bisector.

B. False, this is an assumption based on appearances.

C. False, this is an assumption based on B.

D. False, this is an assumption that LN and JK are perpendicular.

E. False, assumption based on appeareances

F. False, assumption based on D.

1 small pizza and 4 large pizza feeds people according to the system of equations.

Let the number of small pizza be x and the number of large pizza be y.

So, we get the two equations as:

3 x + 4 y = 19 ...(1)

5 x + 5 y = 25 ...(2)

Taking 5 common from equation 2, we get that:

x + y = 5

x = 5 - y

Put it in equation 1, we get that:

15 - 3 y + 4 y = 19

15 + y = 19

y = 4

x = 5 - 4 = 1

Therefore, we get that, 1 small pizza and 4 large pizza feeds people according to the system of equations.

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