What is the solution to the equation 3^x = 10?

The value of x that makes △PQR ∼ △TUV is 27.

What is the similarity of triangles?

The similarity of triangles refers to the relationship between two or more triangles in which the corresponding angles are congruent (equal in measure) and the corresponding side lengths are in proportion.

Two triangles are similar if and only if the corresponding angles are congruent and the corresponding side lengths are in proportion.

If △PQR ∼ △TUV, then we can write:

PQ/UV = QR/UT = RP/VT = k (the proportionality constant)

If we know the value of two of the sides in one triangle and the corresponding two sides in the other, we can find the value of k.

we know that,

PQ = 27, TU = 18, QR = 36, and UV = x.

We can find the value of k by using the proportionality constant:

k = PQ/UV = 27/x

Then we can use k to find the value of RP:

RP/VT  = k, so RP = k * VT

We can find the value of VT by using the similar triangles:

QR/UV = RP/VT,

QR/UV = k,       ............(RP/VT  = k)

so,

(36/18) = (27/x) * VT

VT = (2/1) * (x/27)

Finally, we can find the value of x by solving this equation:

1/x = (2/1) * (1/(27*VT))

1/x = 2/(27*VT)

1/x = (2/1) * (1/(27*((2/1) * (x/27))))

1/x = (2/1) * (1/(27*(2/1) * (x/27)

1/x = (2) * (1/(27*2) * (x/27)

1/x² = 1/729

x = 27

Hence, the value of x that makes △PQR ∼ △TUV is 27.

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The the probability of picking a 2 and then picking a factor of 12 is 1/6.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means.

Given:

Sample space = {1, 2, 3, 4}

The probability of just picking up a 1 is 1/4.

Now, the remaining cards = 3

So, the probability of getting a factor of 12 (i.e., 3 and 4} is

= 2/3

Thus, the combined probability is

= 1/4 x 2/3

= 2/12

= 1/6

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The x - intercept and y - intercept of the linear function are 10 and 4

A graph of a linear function is a straight line. The line will always pass through the origin (0,0) and have a constant slope. The equation for a linear function is y = mx + c, where m is the slope of the line and c is the y-intercept.

In this problem, we can model the linear function into the slope-intercept form and the plot using a graphing calculator.

-2x - 5y = -20

-5y = -20 + 2x

5y = 20 - 2x

y = (20 - 2x) / 5

y = 4 - 2/5x

Plotting this on a graph using a graphing calculator

The y - intercept is at 4, and the x - intercept is at 10

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The additive inverse of 7 11 is -7 11, which is the same number but with the opposite (or negative) sign. This means that when added together the two numbers will total zero.

Additive inverse of 7 11 = -7 + 11 = -7 11

The additive inverse of a number is the same number with the opposite sign, which can be helpful when solving equations. For example, if we have the number 7 11, the additive inverse would be -7 11. To find the inverse, we simply switch the sign from positive to negative (or vice versa). This means that when the two numbers are added together, the total sum will be zero. For example, 7 11 + (-7 11) = 0. The inverse of a number can also be helpful when we are looking for an unknown variable in an equation. For example, if we have the equation 3x + 7 11 = 4, we can find the value of x by subtracting 7 11 from both sides:

3x + 7 11 = 4 --> 3x

= -7 11 + 4 --> 3x

= -3 11 --> x = -1 11.

This means that x = -1 11.

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The center camera and the two angled cameras cover a total of 60° + 60° + 60° = 180°.

The total angle covered by the three cameras is 180°. The center camera has a field of 60° and the other two cameras, which are angled 45° away from the center camera, each has a field of 60°.

Therefore, together, the center camera and the two angled cameras cover a total of 60° + 60° + 60° = 180°.

When two rays are united at a common point, an angle is created. The two rays are referred to as the arms of the angle, while the common point is referred to as the node or vertex. The symbol "°" stands for the angle. The Latin word "Angulus" is where the word "angle" originated.

Typically, an angle is measured with a protractor and expressed in degrees. Angles of 30°, 45°, 60°, 90°, and 180° are shown here. The many types of angles are determined by the angles' degrees values.

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Answer:

d. parallel

I wish you luck in your assignments.

The amount of the apple pie that was left will be 3/4.

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

From the information, Bert found 2 1/2 of an apple pie in the refrigerator. He shared 1 3/4 of the pie with his friends.

The amount of the apple pie that was left will be:

= 2 1/2 - 1 3/4

= 3/4

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Complete question

Bert found 2 1/2 of an apple pie in the refrigerator. He shared 1 3/4 of the pie with his friends. How much of the apple pie was left?

No, segment PQ is not a perpendicular bisector of segment RS. A perpendicular bisector is a line that passes through the midpoint of a segment and is perpendicular to it.

To determine if a line is a perpendicular bisector, we can use the equation (x1 + x2)/2 = xmid and (y1 + y2)/2 = ymid to find the midpoint of the segment and then use the equation y = mx + b to find the equation of the line. If the slope of the line is the negative reciprocal of the slope of the segment, then the line is a perpendicular bisector. In this example, if the coordinates of the endpoints of segment RS are (x1,y1) and (x2,y2), then the midpoint of the segment is (xmid, ymid) where xmid = (x1 + x2)/2 and ymid = (y1 + y2)/2. The equation of the line PQ can be written as y = mx + b. To determine if PQ is a perpendicular bisector, we must calculate the slope of the segment RS and the slope of the line PQ and then compare the two slopes. If the slope of the line PQ is the negative reciprocal of the slope of the segment RS, then PQ is a perpendicular bisector. Otherwise, PQ is not a perpendicular bisector.

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The area of triangle with the base 24 centimetres and height 15 centimetres is 180 cm².

The area of triangle is calculated by the formula -

Area of triangle = 1/2 × b × h, where b represents base of the triangle and h represents height of the triangle.

Keep the values in formula to find the area of triangle.

Area of triangle = 1/2 × 24 × 15

Performing division on Right Hand Side of the equation

Area of triangle = 12 × 15

Performing multiplication on Right Hand Side of the equation

Area of triangle = 180 cm²

Thus, the area of triangle is 180 cm².

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The resulting 3D shape would be a cylinder.

A cylinder is a geometrical shape which is three dimensional figure. It has two circular bases which are parallel and they are connected with a curves surface.

We have to find the resulting 3D shape when you repeated  the paper scaling with a piece of paper that was circular.

Suppose that we are scaling with a circular object like coin.

We place coins repeatedly on a surface where one coin is placed on the top of the last placed coin and then continue the process.

If you place coins on top of each other, it will result in a cylinder.

Hence the scaling of circular piece of paper repeatedly results in a cylinder.

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The cost of one bag of pretzel is $ 1.80

The cost of one bag of granola bars is $ 3.15

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

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

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the cost of one pretzel be represented as x

Let the cost of one granola bar be represented as y

Now , the equation will be

4 bags of pretzels and 2 boxes of granola bars for $13.50

Substituting the values in the equation , we get

4x + 2y = 13.50   be equation (1)

And , 1 bag of pretzels and 5 boxes of granola bars for $17.55

Substituting the values in the equation , we get

x + 5y = 17.55   be equation (2)

Multiply equation (2) by 4 , we get

4x + 20y = 70.2   be equation (3)

Subtracting equation (1) from equation (2) , we get

18y = 56.70

Divide by 18 on both sides of the equation , we get

y = $ 3.15

So , the cost of one granola bar is $ 3.15

Substituting the value of y in equation (1) , we get

4x + 2 ( 3.15 ) = 13.50

4x + 6.30 = 13.50

Subtracting 6.30 on both sides of the equation , we get

4x = 7.20

Divide by 4 on both sides of the equation , we get

x = $ 1.80

So , the cost of one pretzel is $ 1.80

Hence , the equations are solved

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Answer: 4. No, not Similar

Step-by-step explanation:

<QSR = 62

because of vertical angles

we have 3 different angles and no sides

Answer:

6g+6h

Step-by-step explanation:

This is one way to re-write using the distributive property

Answer:

6g+6h

Step-by-step explanation:

The distributive property tells us how to solve expressions in the form of a(b + c). So, one simple way of rewriting the equation would just be 6g + 6h.

For the mathematical series, the total of the first 25 terms is 1850.

Arithmetic progression or arithmetic sequence is a numerical series in which the difference between subsequent terms is constant. For example, the sequence 5, 7, 9, 11, 13, 15.. An arithmetic sequence is a series of integers that are ordered and share a common difference between each succeeding term. In the arithmetic sequence 3, 9, 15, 21, 27, for example, the common difference is 6. An arithmetic progression is another name for an arithmetic sequence.

Here,

This is an arithmetic sequence as each term has a common difference to the previous term.  Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number.

We know that a=2 and d=(20-14)=(14-8)=(8-2)=6 so

a(25)=2+6(25-1)

a(25)=146  

The sum of an arithmetic sequence is the average of the first and last terms times the number of terms, in this case:

s(25)=25(2+146)/2

s(25)=1850

The sum of the first 25 terms is 1850 for the arithmetic sequence.

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Using similar triangle theorem, the similarity statement will be "ΔGJL ≈ Δ HLK".

Similar triangles are two or more triangles that have the same shape but may be different sizes. They have the same angles and sides that are proportional to each other.

If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. This proves that the ratio of the area of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.

In this problem, we can see that both triangles are similar and have the same angle.

The correct similarity statement will be "ΔGJL ≈ Δ HLK"

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Answer:

4

Step-by-step explanation:

(8x-2)+15x+90=180

Combine like terms

23x+88=180

-88 -88

23x=92

÷23 ÷23

X=4

To solve the 3 step equation, we have to solve the one equation in two variable. Then substituting the value in other equation and further solving according to the given rule.

In the substitution approach, we will examine the two equations and choose which variable is the most straightforward to solve for in order to transform one of the equations into x =, y =, or z =. The other equation's x, y, or z will then be appropriately replaced. The outcome will be an equation we can solve that has just one unknown. A variable whose coefficient is 1 or -1 should be isolated.

Use the steps below to solve systems using substitution:

(1) Choose an equation and determine the value of one of its variables.

(2) Substitute the variable you just solved in the other equation.

(3) Address the fresh equation.

(4) Enter the discovered value into any equation that calls for both variables, then get the value for the other one.

(5) Verify the answers to the two initial equations.

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a) Yes, the given triangle is Angle - Angle similarity posulate.

b) Yes , 2 triangles are similar using AA similarity posulate.

c) If the triangles are follow the AA similarity posulate then they are congruent to each other also.

What is triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.

What is AA similarity posulate?

According to the AA Similarity Postulate and Theorem, each triangle must have two matching angles that are congruent in order to demonstrate that two triangles are similar.

Think about the triangles which are given in the question;

ΔABC with scale factor of [tex]\frac{AB}{DE}[/tex]  to create ΔA'B'C'.

ΔABC is dilated about point P with a scale factor of [tex]\frac{AB}{DE}[/tex]  to create ΔA'B'C'.

After a dilation, corresponding angles are congruent, thus

∠B ≅ ∠B'

Therefore,  ∠B' ≅ ∠E.

Similarly, ∠A ≅ ∠A'

therefore, ∠A' ≅ ∠F . Due to the scaling factor being [tex]\frac{AB}{DE}[/tex]

A'B' = [tex]\frac{AB}{DE}[/tex] · AB = DE

So, [tex]\overline{A'B'}[/tex] ≅ [tex]\overline{F'E'}[/tex].

Now, we have to prove ΔABC [tex]\sim[/tex] ΔDEF.

We know that,

∠B' ≅ ∠E , ∠A' ≅ ∠F and [tex]\overline{A'B'}[/tex] ≅ [tex]\overline{F'E'}[/tex].

This means that,

ΔA'B'C' ≅ ΔDEF by ASA rule.

Consequently, a series of stiff transformations must occur that will convey;

ΔDEF to ΔA'B'C' then there will be a dilatation.

ΔA'B'C' to ΔABC.

About the initial two triangles, it was all that was known was two sets of parallel angles. You have therefore demonstrated that AA is a need for triangle similarity.

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Yes, the sides 7 cm 24 cm 25 cm form a right angled triangle.

The right angled triangle contains hypotenuse, which is opposite the 90° angle. Other two sides are base and perpendicular. The side of right angled triangle follows Pythagoras theorem.

It says, hypotenuse² = perpendicular² + base²

We know 25 cm will be hypotenuse as it is the longest side. Keeping the values now -

25² = 24² + 7²

Taking square of all the values

625 = 576 + 49

Performing addition on Right Hand Side of the equation

625 = 625

As the square of hypotenuse is equal to sum of square of other two sides, it is right angled triangle.

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Best Market sells strawberries at a cheaper unit price.

The definition of a unit of measurement is a particular magnitude of a quantity that has been established and accepted by law or convention and is used as a standard for measuring other quantities of the same kind. Any other quantity of that type can be expressed as a multiple of the unit of measurement.

For instance, a length is a physical quantity. The metre is a unit of length that corresponds to a particular, predetermined length (symbol m). For instance, "10 metres" (or 10 m) is 10 times the fixed, predetermined length known as "metre."

In best Market, the price y for x pounds of strawberries is given by

y = 2.90x

Lets find the slope of Fine Foods strawberries

y - y₁ = m(x - x₁)

From the graph take two points, lets say (3, 6) and  (5, 10)

Put the points in the formula

10 - 6 = m(5 - 3)

4 = 2m

m = 4/2 = 2

The slope is 2

Now, lets convert it to slope intercept form

y - 10 = 2(x - 5)

y = 2x - 10 + 10

y = 2x - 10 + 10

y = 2x

For a certain same price Fine Foods provides 2x pounds of strawberries while Best Market provides 2.90x pounds of strawberries.

Thus, Best Market sells strawberries at a cheaper unit price.

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Answer: 14

Step-by-step explanation: Because if altogether they have 22 and Kevin already has 8 then you just add 14 more

Therefore , the solution of the given problem of test statistics comes out to be in light of this, Z = 1.19 is the answer to the test statistic puzzle.

A test statistic in a research study is the figure that is applied to decide whether to confirm or refute hypothesis. This statistic compares the results of a study or sample to what the null hypothesis would predict.

A conjecture is a proposal that makes sense in light of the available information but has neither been confirmed nor refuted. A assertion on which hypotheses will be based is referred to as a hypothesis in statistics (also known as a statistical hypothesis).

Here,

given:

=> 60= μ

=> 15.9 = σ

=> n=40

=>x' = 63

utilized formula is

=> Z = (x' - μ) / σ/(√n)

=> Z = (63 -60) / 15.9 / √40

=> Z = 3 / 15.9/√40

=> Z = 3 / 2.5140

=> Z = 1.19

Therefore , the solution of the given problem of test statistics comes out to be in light of this, Z = 1.19 is the answer to the test statistic puzzle.

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Answer:

P(not red) = 90%

Step-by-step explanation:

There are 3 red, 3 green, 15 yellow, and 9 purple marbles in all:

3 + 3 + 15 + 9 = 30

You are trying to find the probability of not obtaining a red marble. There are 3 red marbles, and 30 marbles in all. This means that there are 27 marbles that are not red. Divide 27 with 30:

27/30 = 0.9

0.9 = 90/100 = 90%

90% is your answer.

P(not red) = 90%.

~

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Answer: 90%

Step-by-step explanation:

therefore Makayla runs = 3/5+3/5+3/5+3/5+3/5+3/5=18/5  = 3.6 miles in one hour

Makayla run 3/5 of a mile in 1/6 of an hour.

How far, in mile per hour, doe he run

in one hour = 1/6+1/6+1/6+1/6+1/6+1/6=1

therefore he runs = 3/5+3/5+3/5+3/5+3/5+3/5=18/5

 = 3.6

What is linear equation?

An algebraic equation of the form y=mx+b is referred to as a linear equation involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. Occasionally, the above is called a "linear equation of two variables," where y and x are the variables.

Driving separate vehicles on the same highway are Makayla and Addison,

another eample Makayla is 290 miles away from stadium,

Makayla driving speed is  40 miles per miles.

345 miles separate Addison from the stadium.

Addison driving speed is 51 miles per hour.

Let tt represent hours.

Therefore the equation is

Mm=290-40tt

Aa =345-51tt.

question

One​ month, two search engines were used to conduct a total of 3.52 billion online searches. Search engine A was used to conduct 0.66 billion more searches than search engine B. How many searches were conducted on each search​ engine?

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u have to use the inequity expresstion to anwser the perentieses first it would come out to be a persent then turn that to a fration by devieding by the first numer in the perenthies by sencond number the answer would be 3 over six but negitive

This prompt is about being able to represent time and distance on a graph called Distance-Time Graph. See the graph attached.

A Distance-Time Graph is a sort of graph that depicts the relationship between distance and time for a moving object.

It is a handy tool for studying an object's motion since it allows one to simply ascertain the object's speed and acceleration. It is also significant because it gives a visual depiction of an object or subject's motion, making the underlying physical ideas easier to grasp.

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Full Question:

Tanisha left her house at time zero and drove to the store, which is 8 blocks away, at a speed of 4 blocks per minute. Then she stopped and went into the store for 3 minutes. From there, she drove in the same direction at a speed of 3 blocks per minute until she got to the bank, which is 12 blocks away from the store. She stopped at the bank for 7 minutes. Then she drove home at a speed of 5 blocks every 2 minutes. Make a graph of showing the number of blocks away from home that Tanisha is xx minutes after she leaves her house, until she gets back home.

Make a graph of showing the number of blocks away from home that Tanisha is x minutes after she leaves her house, until she gets back home.