In △QRS , point A is between points Q and R, point B is between points R and S, and AB∥QS .

QA=23 cm , QR=41 cm , and RS=123 cm .

What is RB ?

Answer:

.63

Step-by-step explanation:

.37 = 0.37

probability = 1 – 0.37

= 0.63 or .63

Answer: We use the SSS

Step-by-step explanation:

SSS method or Side Side Side method is when we test to see if the triangles are the same or not. We know this by checking if the sides of the triangles change at the same rate or not!

Let test the YW is 4 and the WY is 8, we see the side multiply by 2

The VX is 5 and the XZ is 10, wee see the sided multiply by 2

So we use the SSS to show that both triangles are equal

Using the scale factor, the length of the new figures are as 21 inches, 21 inches and 36 inches.

Bill drew a scale drawing of the figure using a scale factor of 3.

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

The length of the drawing are 7 inches , 7 inches and 12 inches . The length of the new figure can be found as follows.

using the scale factor

length 1 = 7 × 3  = 21 inches

length 2 = 7 × 3  = 21 inches

length 3 =  12 × 3  = 36 inches

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Answer:

Step-by-step explanation:

it is an isosceles right triangle, we divide it in two parts and we have two  right triangles, with the Pythagorean theorem we find the hypotenuse and add it to the other side to get the perimeter (SEE FIGURE)

BC and AC = √(8²+6²)

BC and AC = √(64+36)

BC and AC = √100

BC and AC = 10 units

now we add the sides and find the perimeter

16 + 10 + 10 =

36 units

The measure of angle A and angle B is equal to 70° as per the given relation of both the angles.

As given in the question,

Given measure of angle A is equal to ( 8x + 6 )°

Given measure of angle B is equal to ( 4x + 38 )°

Given condition :

Measure of both the angles are equal to each other

Measure of ∠A = Measure of ∠B

⇒ ( 8x + 6 )° =  ( 4x + 38 )°

Now simplify the above equation to get the value of x

⇒(8x - 4x)° = (38 -6)°

⇒4x°= 32°

⇒x = 32°/4

⇒x = 8°

Measure of ∠A = 8(8) + 6

                         = 70°

Measure of ∠B = 4(8) +38°

                          = 70°

Therefore, the measure of both the angles A and B is equal to 70°.

The complete question is:

The measure of ∠A = (8x + 6)° , measure of ∠B = ( 4x+ 38)° and  both are equal to each other. Find the measure of each angle?

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By using the property of isosceles triangle, it can be proved that-

∆CDL is an isosceles triangle

What is isosceles triangle?

At first, it is important to know about triangle.

A triangle is a two dimensional three sided figure. A triangle has three sides and three interior angles.

A triangle whose any two sides are equal are called isosceles triangle.

JK || AB [Given]

[tex]\angle 1 \cong \angle 3[/tex] and [tex]\angle 2 \cong \angle 4[/tex] [Corrosponding angle]

[tex]\angle 1 \cong \angle 2[/tex] [Given]

[tex]\angle 3 \cong \angle 4[/tex] [Transitive property of congruence]

CL [tex]\cong[/tex] DL [Converse of isosceles triangle theorem]

∆CDL is an isosceles triangle [Def. of isosceles triangle]

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The correct option is a) online by $0.04.

The better deal is online, by $0.04 will save per diaper.

How do I solve for x in a equation?

Apply arithmetic operations to both sides of the equation to bring the variable to one side and all other values to the other side in order to find the value of x. To determine the outcome, simplify the values.

Cost of 56 diapers at Babies-R-Us = $28

Cost of 1 diaper at Babies-R-Us = [tex]\frac{28}{56}[/tex]

                                                    =  0.5

Cost of 112 diapers online = $52

Cost of 1 diaper online = [tex]\frac{52}{112}[/tex]

                                      = 0.46

So, the cost of diapers online is cheaper than that at Babies-R-Us.

Difference between 1 diaper in both case = $0.5- $0.46= $0.04

Online deal is better than and you will save by $0.04 per diaper.

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Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

The polynomial with the given roots 5, (3 + 2i), and (1 - 3i) is 45 - 35i = 0

Polynomial is an equation written as the sum of terms of the form kx^n.

where k and n are positive integers.

We have,

The roots of a given polynomial are:

5, 3 + 2i, and 1 - 3i

Now,

We can write it as,

5 (3 + 2i) (1 - 3i) = 0

(15 + 10i) (1 - 3i) = 0

15 - 45i + 10i - 30i² = 0

[ i = √-1, i² = -1 ]

15 - 45i + 10i + 30 = 0

Combining the like terms.

45 - 35i = 0

Thus,

The polynomial with the given roots 5, (3 + 2i), and (1 - 3i) is 45 - 35i = 0

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Answer:

the first company would be cheaper because it has a lower total cost.

Step-by-step explanation:

To determine which company is more cost-effective, you will need to compare the total costs for each company based on the amount of sugar being transported.

If the first company is used, the total cost for transporting x tons of sugar will be 3204 + 75.25x dollars.

If the second company is used, the total cost for transporting x tons of sugar will be 275.50x dollars.

To determine which company is cheaper for a given amount of sugar, you can compare these two equations by setting them equal to each other and solving for x.

For example, if you want to transport 100 tons of sugar, you can set the two equations equal to each other and solve for x:

3204 + 75.25x = 275.50x

Solving for x, we get: x = 3204 / (75.25 - 275.50) = 107.8 tons

This means that if you want to transport 100 tons of sugar, the first company would be cheaper, because it costs less than the second company for any amount of sugar greater than 107.8 tons.

If you want to transport a different amount of sugar, you can repeat this process to determine which company is cheaper.

Answer:

(1,3)

Step-by-step explanation:

Substitute in 3x for y in the equation x + y = 4

x + 3x = 4

4x = 4  Divide both sides by 4

x = 1

Substitute 1 for x in either of the 2 original equations

x + y = 4

1 + y = 4  Subtract 1 from both sides

y = 3

(1,3)

Answer:

y = -x - 4

Step-by-step explanation:

y = mx + b is slope intercept form,

where m is the slope, and b is the y-intercept.

As we can see from the picture, the line has a negative slope of 1 (we can also just say -1). We know this is the slope because it has a rise of -1 and a run of -1. (I hope that made sense lol :/)

[Side note, we use x instead of 1.]

The y-intercept is -4 since we can see the line passes through the y-axis at -4.

Therefore, the equation can be written as y = -x - 4

The value of the expression 24 + x ÷ 12 as required to be evaluated when the variable, x = -180 as required in the task content is; 9.

It follows from the task content that given expression is required to be evaluated for its value when the variable, x = -180.

Since the given expression is; 24 + x ÷ 12.

It follows that when the variable, x is given as; x = -180; we have that;

24 + ( -180 ) ÷ 12

Following from PEMDAS guidelines in which case;

Therefore, we have that;

24 + ( -180 / 12 )

= 24 + ( -15 )

= 24 - 15

= 9.

Upon evaluation, by means of the PEMDAS guidelines in which case; Parentheses, Exponents, Multiplication, Division , Addition and Subtraction are solved in order; the value of the expression is; 9.

Therefore, the required value of the expression; 24 + x ÷ 12; as required to be evaluated according to the given parameter; x = -180 is; 9.

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Yes subtracting a number is the same as adding its inverse. We have to find the additive inverse of a function.

The additive inverse of a number is the number which when we add to the number results zero.

Complex numbers are made up of both real and fictitious numbers. A + iB, where A is the real number and B is the imaginary number, is a complex number.

The additive inverse of A + iB should now be a value that, when added to a given complex number, produces the result zero. It will therefore be -(A + iB).

Suppose we have to find additive inverse of 5.

Let the additive inverse of 5 be x.

So,5+x=0

x=-5

So the additive inverse of 5 is -5.

Hence to find additive inverse of a positive number we have to just put a negative mark and for a negative number we have put positive mark in front of the number.

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The bound on the probability of such an event is 0.75 or 75 %.

Given :

In a study on eating habits, a particular participant averages 750 cm^3 of food per meal.

it is extraordinarily rare for this participant to eat more than 1000 cm^3 of food at once.

Number of favorable outcomes = 750

Number of possible outcomes = 1000

Probability :

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening.

P = Number of favorable outcomes / Number of possible outcomes

= 750 / 1000

= 75 / 100

= 3 / 4

= 0.75

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Full question:

In a study on eating habits, a particular participant averages 750 cm^3 of food per meal.

it is extraordinarily rare for this participant to eat more than 1000cm3 offood at once. find a bound on the probability of such an event.

Answer:

  A:) T(t) = 305(230/305)^(t/10) +70

  B:) T(20) ≈ 243.4 °F

Step-by-step explanation:

You have a pie removed from a 375° oven to a room temperature of 70° that has cooled to 300° after 10 minutes. You want to know its temperature after 20 minutes.

Newton's law of cooling tells you the rate of change of an object's temperature is proportional to the difference between the object's temperature and that of its surroundings. The differential equation describing this has an exponential function as its solution. That exponential function can be written as ...

  temperature = (initial temperature difference)·(cooling factor)^(time/(cooling time)) + (final temperature)

Here, the initial temperature difference between the pie and room temperature is ...

  initial temperature difference = 375° -70° = 305°

The final temperature is the room temperature:

  final temperature = 70°

The cooling factor is the multiplier applied to the temperature difference in the time period "cooling time". Here, the pie is at 300°, a temperature difference of 300° -70° = 230° after a cooling time of 10 minutes. The cooling factor is ...

  cooling factor = 230/305

These values let us write the equation as ...

  T(t) = 305(230/305)^(t/10) +70

The temperature after 20 minutes is found using this equation:

  T(20) = 305(230/305)^(20/10) +70 = 305(46/61)^2 +70 = 243 27/61

  T(20) ≈ 243.4 . . . . degrees F

__

Additional comment

The cooling factor can be expressed as a value that lets the exponent be t. Often, it is written as (e^k), where ...

  k = 1/10·ln(230/305) ≈ -0.0282232

Then the equation is ...

  T(t) = 305·e^(-0.0282232t) +70

It could also be written as ...

  T(t) = 305(0.972171^t) +70

where 0.972171 = (46/61)^(1/10).

The possible values of x in the figure are given as follows:

x > 3/2.

The possible values of x are obtained verifying if the given dimensions form a triangle, and the condition is that the sum of the lengths of the two smaller sides has to be greater than the length of the greatest side.

For the triangle given in the image, the dimensions are given as follows:

Hence, applying the condition, the inequality to obtain the values of x is given as follows:

2x + 4x - 3 > 4x.

Then, solving the inequality, the possible values of x in the triangle are given as follows:

2x + 4x - 3 > 4x

2x > 3

x > 3/2.

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Therefore , the height of the given square pyramid is 12 cm.

The area occupied within an object's three-dimensional bounds is referred to as its volume. The object's capacity is another name for it.

Here,

To calculate a square pyramid's volume in terms of h, use the formula h = [tex]\frac{3V}{s^{2} }[/tex]

With V = 400 and s = 10 cm, a square pyramid's height is 12 cm.

The equation for calculating the volume of a square pyramid is:

=> 1/3 [tex]s^{2}[/tex]h =V

=> h = [tex]\frac{3V}{s^{2} }[/tex]

Therefore we can rewrite the formula in terms of h you need to:

=> h = [tex]\frac{3V}{s^{2} }[/tex]

You must substitute these numbers into the following formula to determine the height of a square pyramid with volume V = 400 and side lengths s = 10 cm:

=> h = 3 * 400 / [tex]10^{2}[/tex]

=> 3* 400/100

=> 3*4

=> 12

Therefore , the height of the given square pyramid  is 12 cm.

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The required Polynomial equation is − 5x²+ 19x + 4.  

Factorization is the process of determining the factors of a given value or algebraic statement. The numbers or the algebraic expressions that are multiplied to create the original number or original expressions are known as factors.

If p(x) is polynomial, with factors (x + a) and (x - a) then p(x) will equal to product of (x + a) and (x - a) => p(x) = (x + a)(x - a)

Here we have

The factorization of a polynomial is −1(x − 4)(5x+1)

To find the Polynomial we need to multiply given factors as given below

=> −1(x − 4)(5x+1)

=> −1 [ (x − 4)(5x+1)]  

=> −1 [ 5x²−20x + x −4 ]     [ add like terms ]

=>  − 5x²+ 19x + 4       [ Multiply with  − 1 ]

Therefore,

The required Polynomial equation is − 5x²+ 19x + 4.    

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The value of [tex]\sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2[/tex] is [tex]\pi x^2 \sqrt{x}-17 x^3[/tex]

[tex]$$\begin{aligned}& \sqrt{x}(\pi-\sqrt{x} \cdot 17) x^2 \\& =x^2 \sqrt{x}(\pi-17 \sqrt{x})\end{aligned}$$[/tex]

Apply the distributive law: [tex]$\quad a(b-c)=a b-a c$[/tex]

[tex]$$\begin{aligned}& a=\sqrt{x} x^2, b=\pi, c=\sqrt{x} \cdot 17 \\& =\sqrt{x} x^2 \pi-\sqrt{x} x^2 \sqrt{x} \cdot 17 \\& =\pi x^2 \sqrt{x}-17 x^2 \sqrt{x} \sqrt{x} \\& 17 x^2 \sqrt{x} \sqrt{x}=17 x^3 \\& =\pi x^2 \sqrt{x}-17 x^3\end{aligned}$$[/tex]

What is distributive law?

The distributive property of binary operations in mathematics generalizes the distributive law, which states that in elementary algebra, equality is always true. For instance, in basic mathematics, one has to According to one, addition is distributed more evenly than multiplication.

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The probability that none are broken as calculated from the data given is 0.96.

No of eggs = 12

percentage of broken eggs = 4%

=4/100 * 12 = 0.48 eggs

therefore , probability of getting broken egg

= no of favorable outcome/ no of outcomes

=0.48/12

=0.04

hence probability of not getting any broken egg

= 1 - P(broken)

= 1- 0.04

= 0.96

There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us.

When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula.

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The number of cubic feet of concrete that would be needed is 586491840 cubic feet

From the question, we have the following parameters that can be used in our computation:

These parameters can be represented using the following notations

The number of cubic feet of concrete that would be needed is the volume of the dam

So, the number of cubic feet of concrete that would be needed can be calculated using the following volume equation

The number of cubic feet of concrete that would be needed = Length x Width x Height

Substitute the known values in the above equation, so, we have the following representation

The number of cubic feet of concrete that would be needed = 1224 * 660 * 726

Evaluate

The number of cubic feet of concrete that would be needed = 586491840

Hence, the cubic feet is 586491840

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Answer:

here

Step-by-step explanation:

1. How tall was the tree when Vlad moved into the house?

292-26*4.5=175 cm

2. How many years passed from the time Vlad moved in until the tree was 357 centimeters tall?

175+26*x=357

357-175=182=26*x

x=7  


hope this helped

AC:PC.= 3/5, as  Line l ∥ AB and passes through point M to intersect diagonal AC and leg BC at points P and N.

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides.

The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

A trapezoid is a closed, four-sided, two-dimensional figure that has both a perimeter and an area.

The bases of the trapezoid are the two sides of the shape that are parallel to one another. The legs or lateral sides of a trapezoid are the non-parallel sides. The altitude is the shortest distance between two parallel sides.

According to our question-

Consider about the triangles ACB and PCN.

These triangles contain

Since angle C is the common angle and the transversal BC cuts two parallel lines PN and AB, angles ABC and PCN are congruent as equivalent angles by virtue of the reflexive property.

In light of the AA Similarity Theorem, triangles ACB and PCN are comparable.

Similar triangles have matching sides that are proportionate, thus

3/8 / 5/8= 3/5

Hence, Due to the fact that Line l AB and goes via point M to intersect Leg BC and the diagonal AC at points P and N, AC:PC.= 3/5.

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To turn $900 into $900 over the course of two and a half years at the rate of 3.5%, we can use the following formula:

Copy code

investment = (900 * (1 + 0.035)) ^ (2.5 / 1)

In this formula, investment represents the amount of money you need to invest, 900 represents the final amount you want to end up with, 0.035 represents the interest rate of 3.5%, 2.5 represents the number of years you want to invest for, and 1 represents the number of times per year that the interest is compounded.

Plugging in the values from the problem into the formula, we get:

Copy code

investment = (900 * (1 + 0.035)) ^ (2.5 / 1)

investment = ($900 * 1.035) ^ (2.5 / 1)

investment = $931.75 ^ 2.5

investment = $1434.24

Therefore, to turn $900 into $900 over the course of two and a half years at the rate of 3.5%, you will need to invest $1434.24.

The weight of the baby at the end of the 8 months was 18.125lbs.

The weight of baby at birth = 7.25 lb

At the end of 8 months, the baby weighed 2.5 times its birth weight.

We need to find the weight of the baby at the end of 8 months.

[tex]\frac{2}{5}[/tex] = [tex]\frac{4+1}{2}[/tex] = [tex]\frac{5}{2}[/tex]

The weight of the baby at the end of 8 months is 5/2 times of its initial weight.

Total weight = 7.25 x [tex]\frac{5}{2}[/tex]

Total weight = 18.125

Therefore, the weight of baby at the end of 8 month is 18.125 lbs.

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

[tex]\textsf{A)} \quad -1\dfrac{3}{20}y+4[/tex]

Step-by-step explanation:

Given expression:

[tex]\left(11-9 \dfrac{3}{5}y\right)+\left(8 \dfrac{9}{20}y-7 \right)[/tex]

Remove the parentheses:

[tex]11-9 \dfrac{3}{5}y+8 \dfrac{9}{20}y-7[/tex]

Collect like terms:

[tex]8 \dfrac{9}{20}y-9 \dfrac{3}{5}y+11-7[/tex]

Subtract the numbers 11 - 7:

[tex]8 \dfrac{9}{20}y-9 \dfrac{3}{5}y+4[/tex]

Factor out y:

[tex]\left(8 \dfrac{9}{20}-9 \dfrac{3}{5}\right)y+4[/tex]

Partition the mixed numbers into fractions and whole numbers, and then subtract them separately.

Subtract the whole numbers:

[tex]\implies 8-9=-1[/tex]

Subtract the fractions by changing both fractions into equivalent fractions so both fractions have the same denominator:

[tex]\implies \dfrac{9}{20}-\dfrac{3}{5}[/tex]

[tex]\implies \dfrac{9}{20}-\dfrac{3 \cdot 4}{5 \cdot 4}[/tex]

[tex]\implies \dfrac{9}{20}-\dfrac{12}{20}[/tex]

[tex]\implies -\dfrac{3}{20}[/tex]

Put the two answers from the whole numbers and fractions back together:

[tex]\implies -1-\dfrac{3}{20}=- \left(1+\dfrac{3}{20}\right)=-1\dfrac{3}{20}[/tex]

Therefore:

[tex]\left(8 \dfrac{9}{20}-9 \dfrac{3}{5}\right)y+4=\left(-1\dfrac{3}{20}\right)y+4=-1\dfrac{3}{20}y+4[/tex]