What other information do you need to show that the triangles are congruent? Vocabulary and Core Concept Check. In Exercises 3–6, decide whether enough ...

Answer:

64a^6b^9c^15

hope that helps

\( \dashrightarrow \tt8(2.5 – 0.5)\)

\( \\ \\ \)

\( \dashrightarrow \tt8(3)\)

\( \\ \\ \)

\( \dashrightarrow \tt8 \times 3\)

\( \\ \\ \)

\( \dashrightarrow \tt24\)

Answer:

16

Step-by-step explanation:

I think the question is either incorrect or a number is being omitted in the options.

But, lets make do with what we have here so you have an idea of how its been solved.

USING THE ORDER OF OPERATIONS IS BEING FOLLOWED SO THAT EVERYONE CAN ARRIVE AT THE SAME ANSWER.

8(2.5 - 0.5)  = 8 (2)    = 16

Answer:

15/1

Step-by-step explanation:

Yeah... that's the answer. Believe me I don't know how to explain this but I know that is the answer.

The value of x in the equilateral triangle in radical form is  \(\frac{10\sqrt{3} }{3}\).

The figure in the image is a right an equilateral triangle, meaning all its three sides are equal.

Since all its three sides are equal, each sides is x.

Meaning half of each side is x/2.

Dividing the equilateral triangle into two wqual halves forms a right triangle:

Hypotenuse = x

Leg 1 = 5

Leg 2 = x/2

Using pythagorean theorem, we can solve for x:

( hypotenuse )² = ( leg 1 )² + (leg 2 )²

x² = 5² + ( x/2 )²

x² = 5² + ( x/2 )²

x² = 5² + x²/2²

x² = 25 + x²/4

x² - x²/4 = 25

3x²/4 = 25

3x² = 25 × 4

3x² = 100

x² = 100/3

x = √(100/3)

\(x = \frac{10\sqrt{3} }{3}\)

Therefore, the value of x is  \(\frac{10\sqrt{3} }{3}\)

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Answer:

30 (random guess)

Step-by-step explanation:

Answer:

equilateral:  E

scalene:  F

isosceles:  G

Step-by-step explanation:

equilateral = all sides are equal

scalene = no sides are equal

isosceles = two sides are equal

The tangent to a circle equation \(x^2+ y^2=a^2\) at (a cos θ, a sin θ ) is x cos θ+y sin θ= a. The tangent to a circle equation \(x^2+ y^2=a^2\) for a line

y = mx +c is y = mx ± a √[1+ m2].

In Geometry, the tangent is defined as a line touching circles or an ellipse at only one point. Suppose a line touches the curve at P, then the point “P” is called the point of tangency. In other words, it is defined as the line which represents the slope of a curve at that point.

If a tangent line to the curve y = f (x) makes an angle θ with x-axis in the positive direction, then dy/dx = slope of the tangent = tan = θ.

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Problem 1

PMT = 505.76 = monthly payment

k = monthly interest rate in decimal form

k = 0.043/12 = 0.003583333 (approximate)

n = 5*12 = 60 months

PVOA = present value of ordinary annuity

PVOA = PMT * ( 1 - (1+k)^(-n) )/k

PVOA = 505.76 * ( 1 - (1+0.003583333)^(-60) )/0.003583333

PVOA = 27,261.436358296

When rounding to the nearest dollar, we get $27,261

Your teacher made a mistake in choosing the formula. S/he mixed up present value ordinary annuity with annuity due. The (1+k) portion at the end is ignored. I rewrote the 1/( (1+k)^n ) sub-portion as (1+k)^(-n) to avoid a bit of clutter.

--------

To type this into excel we will write

=PV(0.043/12,5*12,505.76,0,0)

That will produce the result of -27,261.44. The negative is to indicate a cash outflow.

Don't forget about the equal sign up front when writing excel formulas.

=====================================================

Problem 2

L = loan amount = 23099

k = interest rate per month = 0.051/12 = 0.00425 exactly

n = number of months = 5*12 = 60 months

PMT = monthly payment

PMT = (Lk)/(1 - (1 + k)^(-n) )

This formula is the result of solving PVOA = PMT * ( 1 - (1+k)^(-n) )/k for "PMT". The PVOA value is the loan amount in this case.

Let's plug in the values mentioned

PMT = (Lk)/(1 - (1 + k)^(-n) )

PMT = (23099*0.00425)/(1 - (1 + 0.00425)^(-60) )

PMT = 436.965684557303

PMT = 437 when rounding to the nearest whole number

--------

To do this in excel, we type in

=PMT(0.051/12,5*12,23099,0,0)

The output should be -436.97 which rounds to -437.

The value is negative to represent a cash outflow, but your teacher mentions to post the answer as a positive value.

Answer:

7/6

Step-by-step explanation:

Answer:

k = 7/6

Step-by-step explanation:

Answer:

Points B and C are opposite

Step-by-step explanation:

0 on the number line marks the center of the number line. To the right on the number line are positive integers and to the left from zero are negative integers.

Points B and C are opposite because they are each half way between 0 and 1 on the right and 0 and -1 on the left

Answer:

b and c are opposites

Step-by-step explanation:

other guy was right

The scatter plot shows any linear association. Option (B)

A scatter plot (aka scatter chart, scatter graph) uses dots to represent values for two different numeric variables. The position of each dot on the horizontal and vertical axis indicates values for an individual data point. Scatter plots are used to observe relationships between variables.

A table is an arrangement of information or data, typically in rows and columns, or possibly in a more complex structure.

Advantages of scatter plot

From the above advantages, we can conclude on the answer which is Option (B)

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Answer:

x = -7

Step-by-step explanation:

2x+3 = x-4

2x-x = -4-3

x = -7

hope it helps ☺️

The graph relationship is betsween distance travelled and price of the airfare. The rate of change gives information on how one quantity changes in relation to another. The equation is given as

y = 0.7x + 200

The price of airfare increases by $0.70 for each miles travelled.

We can see that as the distance increases the price of airfare also increases.

Answer:

22.47

Step-by-step explanation:

7/100 = 0.07 (the tax rate) 21 * 0.07 = 22.47, the tax adds on 1.47

Answer: For which item was he charged twice? 42.25 – 29.50 = 12.75, so he was charged twice for the hat.

It may be incorrect! This is in my math book and it was this answer. Please forgive me if it’s incorrect!

The exponential function that represents the given scenario is
y = (30.5)(0.7)ˣ.  

The exponential function is a type of mathematical equation that can be used to determine if anything is increasing or decreasing exponentially, such as population, money, or price.

The general form of an exponential function is given by

           f(x) = abˣ   or y = abˣ

Where 'x' is a variable and a and b are constants

Here we have

The graph shows the number of games system sold since 2005.

As we know an exponential function is represented as:  

=> y = abˣ

From the given graph x = 0 and y = 30.5

=> 30.5 = ab⁰  

=> 30.5 = a(1)

=> a = 30.5  

When x = 1, y = 21.35

=> 21.35 = (30.5)(b¹)  

=> b = 0.7

So the required exponential function can be written as

=> y = (30.5)(0.7)ˣ    

Therefore,

The exponential function that represents the given scenario is
y = (30.5)(0.7)ˣ.    

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The smallest number of digits that should be used to label the population is 4, since there are 1,020 students in the school.

To determine the smallest number of digits needed to label the population, we will follow these steps:

1. Determine the total number of students in the population.
2. Identify the number of digits needed to represent the largest student number.
3. Apply this number of digits to all student labels.

Let's apply these steps to your question:

1. The total number of students is 1,020.
2. The largest student number is 1,020, which requires 4 digits (since it has four numbers: 1, 0, 2, and 0).
3. To label the entire student population consistently, use 4 digits for all student labels.

So, the smallest number of digits that should be used to label the population is 4.

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Answer:

1. 7 Nickels, 13 Dimes

2. 30 Nickels, 15 Quarters

3. 74 Girls, 106 Boys

4. 180 tickets bought before and 113 bought at the gate

Step-by-step explanation:

Answer:

Step-by-step explanation:

1)

Nickel: n = 5c, Dime: d = 10c

Equations as per given:

Substitute d:

2)

Nickels: n = 5c, Quarters: q = 25c

Equations as per given:

Substitute n:

3)

Boys = b

Girls = g

Equations as per given:

Substitute b:

4)

Tickets purchased at the gate: g = $15

Tickets purchased before the concert: b = $10

Equations as per given:

Substitute b:

The other three angles are 72° , 108° and 108°.

Two strait lengths of wire are placed on the ground forming vertical angles. The measure of one of the angles formed is 72° . We know that sum of all four angles will be 360°. We also know that the vertical angles are congruent. If the measure of one angle out of four angles is 72° and straight lines equal 180°.  So, we need to subtract 72° from 180°.

180° - 72° = 108°

The other angle will be 108°. As the vertical angles are equal, so the four angles will be 72° , 72° , 108° and 108°.

The other three angles are 72° , 108° and 108°.

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The length of tree is 78.47 m which is obtained using sine rule on the trainlge.

so in this question as shown in figure below we have all 3 angles in the question and have 1 side length so we can find other side length using sine rule as in sine rule we need 2 angles and 1 side length then we can find other side.

The sine rule states that:

\(\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}\)

where A,B,C are angles of the traingle and a,b,c are side lengths of traingle.

as shown in the figure disatnce of hisham from tree is 100m.

in the figure we had shown all the 3 angles of the traingle

since all the 3 angles of traingle is less than 90 degree so the traingle is a acute angle traingle.

let length of tree be x m

so applying the sine rule to the traingle shown in the fugure

\(\frac{x}{sin(40^0)} = \frac{100}{sin(55)}\)

x = sin(40 degree) / sin( 55 degree) * 100 = 0.7847 * 100

after calculation x = 78. 47 m

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Answer:

When we look at relative frequency, we are looking at the number of times a specific event occurs compared to the total number of events.

Step-by-step explanation:

Hey now you can give me a brainliest for actually giving an answer haha :)

The volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base.

To find a formula for the volume of the box with surface area A and square base with side x, we first need to find the height of the box. Since the box has a square base, the area of the base is x^2. The remaining surface area is the sum of the areas of the four sides, each of which is a rectangle with base x and height h. Therefore, the surface area A is given by:

A = x^2 + 4xh

Solving for h, we get:

h = (A - x^2) / 4x

The volume V of the box is given by:

V = x^2 * h

Substituting the expression for h, we get:

V = x^2 * (A - x^2) / 4x

Simplifying, we get:

V = (Ax^2 - x^4) / 4

The domain of V is all non-negative real numbers, since both x^2 and A are non-negative.

To graph V as a function of x, we can use a graphing calculator or plot points using a table of values. The graph will be a parabola opening downwards, with x-intercepts at 0 and sqrt(A) and a maximum at x = sqrt(A) / sqrt(2).

To find the maximum value of V, we can take the derivative of V with respect to x and set it equal to 0:

dV/dx = (2Ax - 4x^3) / 4

Setting this equal to 0 and solving for x, we get:

x = sqrt(A) / sqrt(2)

Plugging this value of x into the formula for V, we get:

V = A^1.5 / (4sqrt(2))

Therefore, the maximum value of V is A^1.5 / (4sqrt(2)).

To find the formula for the volume of a box having surface area 10, we simply replace A with 10 in the formula we derived earlier:

V = (10x^2 - x^4) / 4

Simplifying, we get:

V = 2.5x^2 - 0.25x^4

Therefore, the volume of the box with surface area 10 is given by the formula V = 2.5x^2 - 0.25x^4, where x is the length of a side of the square base. The domain of V is all non-negative real numbers.

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When comparing R-squared values between different regressions, it is essential to use the same set of observations. If the regressions use different sets of observations, it is not valid to directly compare the R-squared values. The R-squared value is specific to the data used in the regression analysis and cannot be generalized across different sets of observations.

R-squared (coefficient of determination) is a statistical measure that indicates the proportion of the variance in the dependent variable that can be explained by the independent variables in a regression model. It ranges from 0 to 1, where a value of 1 indicates a perfect fit of the model to the data.

The R-squared value is specific to the particular set of observations used in the regression analysis. Changing the set of observations will likely result in different R-squared values, even if the same independent variables are used.

When comparing R-squared values between different regressions, it is important to ensure that the regressions use the same set of observations. If the regressions use different sets of observations, the R-squared values cannot be directly compared because they are calculated based on different data

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Answer:

C (-13,-2)

Step-by-step explanation:

The boiling point of a solution containing 310.3 grams of NiCl3 in 55 mL of water is higher than the boiling point of pure water.

To calculate the boiling point of the solution, we need to consider the effect of the solute (NiCl3) on the boiling point of water. The boiling point elevation (∆Tb) can be calculated using the formula:

∆Tb = Kb * m

Where Kb is the molal boiling point elevation constant and m is the molality of the solution. To find the molality, we need to calculate the moles of solute (NiCl3) and the mass of the solvent (water).

Moles of NiCl3 = Mass / Molar mass

Molar mass of NiCl3 = 58.69 g/mol + (35.45 g/mol * 3) = 164.29 g/mol

Moles of NiCl3 = 310.3 g / 164.29 g/mol = 1.886 mol

Mass of water = Volume * Density

Mass of water = 55 mL * 0.997 g/mL = 54.835 g

Molality (m) = Moles of solute / Mass of solvent

Molality (m) = 1.886 mol / 0.054835 kg = 34.380 mol/kg

Now, we can use the molality to calculate the boiling point elevation (∆Tb). The molal boiling point elevation constant (Kb) for water is approximately 0.512 °C/m.

∆Tb = 0.512 °C/m * 34.380 mol/kg = 17.610 °C

Finally, we add the boiling point elevation (∆Tb) to the boiling point of pure water, which is 100 °C.

Boiling point of the solution = 100 °C + 17.610 °C = 117.610 °C

Therefore, the boiling point of the solution containing 310.3 grams of NiCl3 in 55 mL of water is higher than the boiling point of pure water.

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Answer:

third box

first box

second box

Step-by-step explanation:

1/3x + 1/4 -2/3x; combine like terms

-1/3x + 1/4 (third box)

1/3x + 1/4 + 2/3x; combine like terms

(3/3)x +1/4 (first box)

3/3 is 1, so we don't have to write it

2/3 + 3/4x -1/3; combine like terms

1/3 + 3/4x (swap, and is second box)

Answer:

The function of g(x) = 5x + 2

Step-by-step explanation:

Let us use the composite function to solve the question

∵ f(x) = 2x - 1

∵ f(g(x)) = 10x + 3

→ f(g(x)) means substitute x in f(x) by g(x)

∴ f(g(x)) = 2[g(x)] - 1

→ Equate the two right sides of f(g(x))

∴ 2[g(x)] - 1 = 10x + 3

→ Add 1 to both sides

∴ 2[g(x)] - 1 + 1 = 10x + 3 + 1

∴ 2[g(x)] = 10x + 4

→ Divide each term into both sides by 2

∵ \(\frac{2[g(x)]}{2}\) = \(\frac{10x}{2}\) + \(\frac{4}{2}\)

∴ g(x) = 5x + 2

∴ The function of g(x) = 5x + 2

Answer:

First one

Step-by-step explanation:

5sin(3pix)+8=4

5sin(3pix) = -4

sin(3pi x) = -0.8

Basic angle: sin^-1(0.8) = 0.927295218

3pi x = pi+0.927295218, 2pi-0.927295218

3pi x = 4.068887872, 5.355890089, 4.068887872 + 2pi, 5.355890089 + 2pi, 4.068887872 + 4pi, 5.355890089 + 4pi,

x = above values/3pi

x = 0.43217, 0.568, 1.0984, 1.235, 1.765, 1.9016

If the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.

Given that, a full pond containing 625 gallons of water begins losing its water at a rate of 20% per week.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Here, number of gallons water being used for x weeks is

625-320=305 gallons

Now, number of gallons of water used in a week= 20% of 305

= 20/100 ×305

= 0.2 ×305

= 61 gallons

So, number of weeks = x=305/61

= 5

Therefore, if the pond now contains 320 gallons of water, number of weeks it has been since the pond was at full capacity is 5 week.

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Answer:

5

Step-by-step explanation:

Look that guys answer is better