Find the missing length indicated. i need help with steps

The original value for the first angle so that the angle measures form a triangle is 39.5°

For any triangle to be formed, its three interior angles must sum up to 180°. Thus the sum of the interior angles of a triangle is 180°

Considering, the angles: 115.1°, 47.5° and 93°, their sum which is 255.6° is not equal to 180° so they cannot form a triangle.

but a new value represented by x for the first angle 115.1° can be derived as follows;

x + 47.5° + 93° = 180°

x + 140.5 = 180° {subtract 140.5° from both sides}

x = 180° - 140.5°

x = 39.5°

Therefore, the new value for the first angle 115.1° that will make the angle measures form a triangle is 39.5°

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Answer:

125 days

Step-by-step explanation:

1.) First, you need to make the number equivalent!

1.5L=1500mL

2.) Then you need to divide 1500mL by how much she drinks every day!

1500mL divide by 12mL = 125 days

So the carton will last 125 days

:) Hope you have a good day!

Answer:

the carton will last for 125 days

Step-by-step explanation:

carton contain 1.5L

1.5L= 1.5×1000ml

= 1500ml

1day=12ml

1/12 ×1500 days = 1500ml

125 days = 1500ml

If Ellis drink 12ml of yoghurt everyday then the carton with 1.5L will last for 125 days.

∠1and∠2 form a linear pair, so by the Supplement Postulate, they are supplementary. That is, m∠1+m∠2=180°. m∠2+m∠3=180°.

We must determine the dimensions of angles 1 and 2. The geometric property can be used to: When two chords collide inside of a circle, the angle that is created is half the total of the intercepted arcs of the chords. In light of this, m1 = 50° and m2 = 130°.

According to the diagram, the angles 1 and 3 are vertical, and m1 = 90. Since their measurements are equivalent, m3 = 90 and 1 and 2 are additional. Angles 1 and 2 compliment one another. Two additional angles, the total of whose measurements equals 180 degrees.

The angles 1 and 2 complement one another. Because they have a similar side, angles 1 and 2 are neighbouring angles. Adjacent angles are two angles in a plane that do not share interior points but do share a vertex and a side.

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So on solving the provided question we can say that here, in triangle ABC and XYZ;  by SSS property they are similar.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

AB = XY

AC = XZ

BC = ZY

by SSS property, they are similar.

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1.)Monomial 2.) Constant term 3.) Formula 4.) Expression 5.)Variable.

A monomial is defined as an algebraic expression with one term, but it can have many variables and higher degrees. It can also be defined as the product of a number and variable(s).

Constant term is defined as the term that contains only a number with no variables.

A formula is defined as an equation that uses variables to state a rule term.

An expression is defined as one term or multiple terms connected by an addition or subtraction sign expression.

A variable a letter or symbol used to represent an unknown number formula.

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Answer:

[tex]\textsf{1.} \quad a_n=174-6n[/tex]

[tex]\textsf{2.\;a)} \quad A=5000\left(1.019\right)^{4t}[/tex]

   b)  9.25 years (to the nearest quarter)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given terms of an arithmetic sequence:

Substitute the given values into the arithmetic sequence formula to create two equations:

[tex]\implies a_{28}=a+27d=6[/tex]

[tex]\implies a_{22}=a+21d=42[/tex]

Subtract the second equation from the first equation to eliminate a and solve for d:

[tex]\implies 6d=-36[/tex]

[tex]\implies d=-6[/tex]

Substitute the found value of d into one of the equations and solve for a:

[tex]\implies a+27(-6)=6[/tex]

[tex]\implies a-162=6[/tex]

[tex]\implies a=168[/tex]

Substitute the found values of a and d into the formula to create an equation for the nth term of the sequence:

[tex]\implies a_n=168+(n-1)(-6)[/tex]

[tex]\implies a_n=168-6n+6[/tex]

[tex]\implies a_n=174-6n[/tex]

[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ A=P\left(1+\frac{r}{n}\right)^{nt}$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ final amount \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}[/tex]

Given values:

Substitute the given values into the compound interest formula to create an equation with respect to time, t:

[tex]\implies A=5000\left(1+\dfrac{0.076}{4}\right)^{4t}[/tex]

[tex]\implies A=5000\left(1.019\right)^{4t}[/tex]

To find when the value of the investment will be worth more than $10,000, substitute A = 10000 into the equation:

[tex]\implies 10000 < 5000\left(1.019\right)^{4t}[/tex]

[tex]\implies 2 < \left(1.019\right)^{4t}[/tex]

[tex]\implies \ln 2 < \ln\left(1.019\right)^{4t}[/tex]

[tex]\implies \ln 2 < 4t\ln\left(1.019\right)[/tex]

[tex]\implies \dfrac{\ln 2}{4 \ln\left(1.019\right)} < t[/tex]

[tex]\implies t > 9.20672924...[/tex]

Therefore, the investment will be worth more than $10,000 from 9.25 years (to the nearest quarter).

8 148

- 2 077

______

6 07 1

_______

you cannot minus 7 from 4 so you borrow from the next number which is 1 then it will be 14-7 and 0-0

Answer:

42, 50, 60

Step-by-step explanation:

42 is less than or equal to y.

That means y is greater than or equal to 42.

Answer: 42, 50, 60

The expression which represents the total cost of renting is C = nx.

What is an expression?

An expression is a mathematical phrase that can contain numbers, variables, and operators. It represents a value or a calculation, but it does not necessarily have an equal sign (=) to indicate that it is an equation.

Let us consider that, renting a Canoe for one hour is  $ x.

The total cost of renting is represented by C.

Since renting a Canoe for one hour is  $ x.

So that, for n hours, renting cost  = n*x

The total cost of renting, C= nx

Hence, the expression which represents the total cost of renting is C = nx.

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The sum of three consecutive numbers for 150 is 49,50,51.

Three consecutive numbers:  x+(x+1)+(x+2)

x+x+1+x+2= 150

3x+3 = 150

3x = 150-3

3x= 147

X = 147/3

49 =x

But we also need to find (x+1) and (x+2)

49+1= 50

49+2= 51

49+50+51 = 150

The three consecutive numbers are 49,50,51.

Meaning: Numbers that follow one another numbers sequentially are known as consecutive numbers. The difference between any two numbers is always 1. A series of numbers' mean and median are equal. If n is a number, then it follows that n, n+1, and n+2 are also numbers. Examples. 1, 2, 3, 4, 5.

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If A=(4,-5) and 8 (7,-9), 7 units is the length of AB

distance = √( (7−4)^2 + (−9−(−5))^2 )

Plugging in the numbers and solving, we get:

distance = √( (3)^2 + (−4)^2 )

distance = √( 9 + 16 )

distance = √49

distance = 7 units

Therefore, the length of AB is 7 units.

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Darren makes $210.83 monthly payments over a period of 5 years. Therefore, option D is the correct answer.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time.

Given that, principal =$11,000, rate of interest =3% and time period = 5 years.

Now, S.I. =(11,000×3×5)/100

= $1650

Now, 11,000+1650 =$12650

In 5 years there are 60 months

So, 12650/60

= $210.83

Therefore, option D is the correct answer.

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Answer:

How many couples bought tickets?

50

Step-by-step explanation:

s + 2c  = 196              Eq. 1

6s + 10c = 1076          Eq, 2

s = single tickets

c = couple tickets

From Eq. 1:

s = 196 - 2c                 Eq. 3

Replacing Eq. 3 in Eq. 2:

6(196-2c) + 10c = 1076

(6*196 + 6*-2c) + 10c = 1076

(1176 - 12c) + 10c = 1076

1176 - 2c = 1076

1176 - 1076 = 2c

100 = 2c

c = 100/2

c = 50

From Eq. 3:

s = 196 - 2c

s = 196 - 2*50

s = 196 - 100

s = 96

Check:

From Eq. 2:

6s + 10c = 1076

6*96 + 10*50 = 1076

576 + 500 = 1076

The other two sides of the triangle are 2.795 and 4.095 respectively.

Generally, The right triangle is a right-angled triangle where one angle is 90 degrees.

If the hypotenuse is 5 and one acute angle is 34°, we can use trigonometry to find the other two sides of the triangle.

Using sine function, the side opposite to 34° angle is

=(sin 34°) * hypotenuse

= 0.559 * 5

= 2.7959

Using cosine function, the side adjacent to 34° angle is (cos 34°) * hypotenuse = 0.819 * 5

= 4.095

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The inequalities that represent the situation can be presented as follows;

x + y ≤ 13

16·x + 6·y ≥ 120

Please find attached the graph of the inequality created with MS Excel

An inequality is a non equal comparison between expressions, quantities, or numbers.

The specified information are;

The amount Gabriella makes lifeguarding = $16 per hour

The amount she makes walking dogs = $6 per hour

The maximum number of hours Gabriella can work in a week = 13 hours

The minimum amount Gabriella must earn in a week = $120

Let x represent the number of hours Gabriella spends lifeguarding, and let y represent the number of hours Gabriella spends walking dogs.

The system of inequalities that can be obtained based on the above details are;

The graph of the above inequalities can be obtained by making y the subject of the inequalities as follows;

y ≤ 13 - x

y ≥ (120 - 16·x)/6 = 20 - (8/3)·x

y ≥ 20 - (8/3)·x

The feasible region is in the triangle with vertices (13, 0), (7.5, 0), (4.2, 8.8)

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Answer:

Step-by-step explanation:

9.5

Result is x = - 2 and y = 1.6 so the ordered pair ( -2, 1.6) is the solution of the system equations.

It is a mathematical expression that shows the equalities between two or more terms. There are different types of equation such as linear equation, quadratic equation, exponential equation and so on.

Given, the two systems of equation.

y = - 0.5x + 0.6

and y = x + 3³₅

rewrite the second equation and get y = x +18/5

                                                       5y = 5x + 18 ....  equation 2

                   the first equation is multiplied by 5 and we get.

                                               5y = - 2.5 x + 3

                                               5y = 5x +18

                                            -          -     -

                        we will now solve the above equations by addition method.

                                       0 = - 7.5 x - 15

                                    7.5 x = - 15

                                     x = -2

        putting the value of x in any equation, we get the value of y = 1.6

    x = - 2 and y =1.6

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division

john stops at toy store a to buy 16 toy cars. Toy store A sells 6 toy cars for $4.20. John stops at toy store b and sees that they sell 4 toy cars for $3.80. How much money did John save by buying toy cars at toy store A?

Dividing 3x³ - 4x² - 9x + 15 by 3x + 5. will yield a quotient of x² - 3x + 2 and a remainder of 5 that is (x² - 3x + 2) + 5/(3x + 5).

Applying the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder.

We shall divide the 3x³ - 4x² - 9x + 15 by 3x + 5 as follows;

3x³ divided by 3x equals x²

3x + 5 multiplied by x² equals 3x³ + 5x²

subtract 3x³ + 5x² from 3x³ - 4x² - 9x + 15 will result to -9x² - 9x + 15

-9x³ divided by 3x equals -3x

3x + 5 multiplied by -3x equals -9x² - 15x

subtract -9x² - 15x from -9x² - 9x + 15 will result to 6x + 15

6x divided by 3x equals 2

3x + 5 multiplied by 2 equals 6x + 10

subtract 6x + 10 from 6x + 15 will result to a remainder of 5

Therefore by the long division method, 3x³ - 4x² - 9x + 15 by 3x + 5 gives a quotient x² - 3x + 2 and a remainder of 5 and can be written as (x² - 3x + 2) + 5/(3x + 5).

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Because its a 1 in 6 chance to roll a five and a 1 in 4 chance to roll a yellow then you do 6 x 4 = 24.

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Answer:

Step-by-step explanation:

y=4x + (7/2)

when x=5

y=4(5)+ (7/2)

 =20+3.5             or         20+ (7/2)

 =23.5                 or          (40+7)/2 =47/2 =23.5

The onto functions (surjective functions) are:

c. f(m, n) = m + n + 1.

At first we have to identify onto (surjective) functions from Z x Z to Z, we need to check if each element in the codomain (Z) has at least one preimage in the domain (Z x Z).

a. f(m, n) = 2m - n

This function is not onto because for odd numbers in the codomain (Z), there is no pair of integers (m, n) in the domain that will map to them.

b. [tex]f(m, n) = m^2 - n^2[/tex]

This function is not onto because for negative numbers in the codomain (Z), there is no pair of integers (m, n) in the domain that will map to them.

c. f(m, n) = m + n + 1

This function is onto. For any integer 'z' in the codomain (Z), we can find a pair of integers (m, n) in the domain such that m + n + 1 = z.

For example, if z = 0, we can choose m = 0 and n = -1, and then m + n + 1 = 0.

d. f(m, n) = |m| - |n|

This function is not onto because negative numbers in the codomain (Z) cannot be obtained from the domain (Z x Z).

For example, there is no pair of integers (m, n) in the domain that maps to -1.

Hence, The onto functions (surjective functions) are:

c. f(m, n) = m + n + 1.

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So, here on solving the provided question, we can say that  [tex]5^{2/3}[/tex] to write it without exponent = [tex]25^{1/3} = 1.70997594668[/tex] and [tex]4^{-3/2} = 64^{1/2} = 8[/tex]

Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64.

here,

we have [tex]5^{2/3}[/tex] to write it without exponent = [tex]25^{1/3} = 1.70997594668[/tex]

and [tex]4^{-3/2} = 64^{1/2} = 8[/tex]

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The solution is

a) The ratio of x values to the y values from the table is 2 : 3

b) The ratio of x values to the y values from the graph is 2 : 3

c) The ratio of x values to the y values from the table and graph is equivalent

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Given data ,

Let the proportion be represented as A

Now , the equation will be

Let the x values from the table be x = { 8 , 10 , 12 }

Let the y values from the table be y = { 12 , 15 , 18 }

Now , y = kx , where k is the proportionality constant

Substituting the values in the equation , we get

12 = k ( 8 )

Divide by 8 on both sides of the equation , we get

k = 12/8

k = 3/2

So , the ratio of x values to the y values is 1/k = 2 : 3

Now ,

15 = k ( 10 )

Divide by 10 on both sides of the equation , we get

k = 15 / 10

k = 3/2

So , the ratio of x values to the y values is 1/k = 2 : 3

And ,

18 = k ( 12 )

Divide by 12 on both sides of the equation , we get

k = 18/12

k = 3/2

So , the ratio of x values to the y values is 1/k = 2 : 3

From the graph , the ratio is also 2 : 3

Hence , the ratio of x to y is given by 2 : 3

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The angles of the rhombus are

             m∠ADC = 58°

             m∠BCD = 122°

What is a rhombus?

An example of a quadrilateral is a rhombus. It is a unique instance of a parallelogram in which the diagonals bisect each other at a 90° angle and all sides are equal.

The properties of a rhombus are:

From the figure,

In ΔDOC.

∠ODC = 180° - ( 90+61) = 29°

The diagonal bisects ∠ADC

So ∠ADC = 2∠ODC = 2 × 29° = 58°

Since the diagonal bisects the angle, ∠BCD = 2∠ACD

                                                                           = 2×61° = 122°

Therefore the angles of the rhombus are

             m∠ADC = 58°

             m∠BCD = 122°

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Question 20

The quadrilateral is a rhombus because there are four congruent sides. The quadrilateral cannot be more specifically classified as a square because one of the interior angles is not a right angle.

Question 21

The quadrilateral is a parallelogram because the diagonals bisect each other.

Question 22

The quadrilateral is a square because it is a rhombus (four congruent sides) with a right angle.

The scale factor that would be applied to Figure A to produce Figure B is 10/3 = 3 (1/3).

By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are those that have been scaled.

Given two pentagons in Figure A and figure B.

We are asked the scale factor from figure A to figure B.

Hence the final figure is figure B and the initial figure is Figure A.

The scale factor of any figure is defined as formulated as:

Scale factor = Dimensions of final figure ÷ Dimensions of original figure

According to the given figures we can observe that:

Length of the base of the pentagon in figure A is 5 inches, and that of figure B is 1 (1/2) = 3/2 inches.

Substituting the dimensions in the formula of the scale factor we have:

Scale factor = 5 ÷ (3/2)

Scale factor = 10/3

Converting into mixed fraction:

10/3 = 3 (1/3)

Hence, the scale factor that would be applied to Figure A to produce Figure B is 10/3 = 3 (1/3).

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Answer:

First tank = 13 fish

Second tank = 13 fish + 8 more fish

13 + 8 = 21 fish in the second tank.

By comparing the population range to the mean of the sample ranges, the answer will be D) The population range equal the youngest official at the time of death and the mean of the sample ranges is equal to the oldest official at the time of death.

Creating a tonne of random numbers between 40 and 70 points so that we can see that the population range is equal to 70. That is presumably the oldest value that is still valid. The population range is the sum of the data generated at the highest level and the lowest level. The population range is now 30 points. by taking a handful of random samples.

We want a sample table containing random samples of the data so we don't have to worry about this. Going through the samples with the new table that will be generated here and want to find this range by taking the max of each sample. Subtracting the mean from each sample from the range samples from 1 to 10. The range for the initial data was 30 points because the entire range was 40 to 70 points; nevertheless, we can observe that this range varies from 64 to 70 points.

We made the table because we wanted the mean of the average of our separate ranges to be 21.7. The mean value of the ranges in 100 samples will be discovered if the sample size is increased. A sample's range is not representative of the population. We can infer that we do it since the samples' range and average range are greatly dissimilar.

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Answer:

y = (2/5)x - 3

Step-by-step explanation:

Brainliest pls

Answer: y = mx + b

y=-3  x=0 and m=2/5

-3 = (2/5)0 + b

Since 2/5(0) is 0, b must be -3

Step-by-step explanation: Since you know the slope and you know one point, all you have to do is plug the slope and the coordinates into the slope-intercept form and solve for b. You can check your answer by finding another point on the line and verifying that the equation works for that point, as well. Add the slope to the given point and you get ( 5 , -1 )

-1 = (2/5)5 - 3

-1 = 2 - 3 -1 = -1 So you know your answer is correct