Can you characterize all N such that the sum of the first N positive integers is a perfect square?
No answer needed!

Answer:

Given

a=-5

b=2

c=1

i) b - a + c

= 2 -(-5) + 1

=2 + 5 + 1

=8.

ii)2b + 6c

= 2(2) + 6(1)

=4 + 6

=10.

iii) abc = (-5)(2)(1)

= -10.

iv) -2ab/c

= -2(-5)(2)/1

= 20.

The vertex of point A' in the dilated triangle A'B'C' is (6, 4.5).

1. Start by calculating the distance between the vertices of the original triangle ABC:

  - Distance between A(4, 3) and B(3, -2):

    Δx = 3 - 4 = -1

    Δy = -2 - 3 = -5

    Distance = √((-\(1)^2\) + (-\(5)^2\)) = √26

  - Distance between B(3, -2) and C(-3, 1):

    Δx = -3 - 3 = -6

    Δy = 1 - (-2) = 3

    Distance = √((-6)² + 3²) = √45 = 3√5

  - Distance between C(-3, 1) and A(4, 3):

    Δx = 4 - (-3) = 7

    Δy = 3 - 1 = 2

    Distance = √(7² + 2²) = √53

2. Apply the scale factor of 1.5 to the distances calculated above:

  - Distance between A' and B' = 1.5 * √26

  - Distance between B' and C' = 1.5 * 3√5

  - Distance between C' and A' = 1.5 * √53

3. Determine the coordinates of A' by using the distance formula and the given coordinates of A(4, 3):

  - A' is located Δx units horizontally and Δy units vertically from A.

  - Δx = 1.5 * (-1) = -1.5

  - Δy = 1.5 * (-5) = -7.5

  - Coordinates of A':

    x-coordinate: 4 + (-1.5) = 2.5

    y-coordinate: 3 + (-7.5) = -4.5

4. Thus, the vertex of point A' in the dilated triangle A'B'C' is (2.5, -4.5).

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Answer:

\(x=-\frac{4}{5}\)

Step-by-step explanation:

\(6=\frac{3}{4}(10x+16)\\\mathrm{or,\ }6\times 4=3(10x+16)\\\\\mathrm{or,\ }24=30x+48\\\\\mathrm{or,\ }-24=30x\\\\\mathrm{\therefore}\ x=-\frac{4}{5}\)

Answer:

(50+10n)+(90+7n)

The survey method which will produce the best representative sample is option B.  survey 3 randomly selected students from every homeroom.

Sampling methods are methods used to select a sample using specific methods. This includes various types of probability sampling and non probability sampling methods.

Here given that,

a middle school principal wants to change the lunch menu at the school.

It is impossible to survey the whole students in school.

In order for the survey results to be the best representative of the whole school, it is important to survey students representing each class and group.

So when we survey every fifth student who rides in a car to school, survey will be biases to only the students who travels in car.

When the survey only done to seventh grade students, it is also biased.

When the survey is done in art and music classes, again the survey will be biased since only the music students takes place.

If students from every homeroom is selected, it will represent the whole school.

Hence the best method is option B.

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A middle school principal wants to change the lunch menu at the school. The principal surveys the students to determine how the students would feel about the changes. Which survey method will produce the best representative sample? A: survey every fifth student who rides in a car to school B: survey 3 randomly selected students from every homeroom C: survey every tenth seventh grade student during lunch D: survey 5 randomly selected students from every art, drama, and music class

Answer:

Well, if it is 20 min usual, then 22 minutes if they left 2 minutes late

Step-by-step explanation:

did you miss part of the question while typing?

let's firstly convert the mixed fraction to improper fraction and proceed from there.

\(\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{4}\div \left(\cfrac{3}{8}\div \cfrac{1}{2} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{8}\cdot \cfrac{2}{1} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{4} \right) \\\\\\ \cfrac{9}{4}\cdot \left(\cfrac{4}{3} \right)\implies \cfrac{9}{3}\cdot \cfrac{4}{4}\implies 3\cdot 1\implies \text{\LARGE 3}\)

Therefore, it would take approximately 19.02 years for an investment to at least double its original amount at a semi-annual compound interest rate of 3.62%.

When an investment is made with a certain amount, the compound interest rate is used to calculate the return on investment. In addition, the number of times interest is compounded each year can have an impact on the investment's outcome.

This question asks about how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%.

To solve for how long it would take for an investment to double at a semi-annual compound interest rate of 3.62%, we need to use the formula for the future value of an annuity:

Future value of an annuity = Payment (1 + r/n)^(nt)where:r is the annual interest raten is the number of times interest is compounded per year Payment is the original amount is the number of years

To solve for t, we can rearrange the formula as follows:t = log(Payment/Future value of an annuity) / log(1 + r/n)where log is the natural logarithm.

The future value of the investment is double the original amount, so we can plug in 2 for Future value of an annuity and simplify the formula to get:t = log(2) / log(1 + 0.0362/2)t = 19.02 years

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Answer:

\(6x^4y^8\sqrt{5x}\)

Step-by-step explanation:

\(\textsf{When $x > 0$ and $y > 0$, we want to find the expression that is equivalent to}\) \(\sqrt{180x^9y^{16}}.\)

\(\textsf{First, apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{180}\sqrt{x^9}\sqrt{y^{16}}\)

\(\textsf{Rewrite $x^9$ as $x^{8+1}$:}\)

\(\sqrt{180}\sqrt{x^{(8+1)}}\sqrt{y^{16}}\)

\(\textsf{Apply the exponent rule:} \quad a^{b+c}=a^b \cdot a^c\)

\(\sqrt{180}\sqrt{x^{8}\cdot x^1}\sqrt{y^{16}}\)

\(\sqrt{180}\sqrt{x^{8}}\sqrt{x}\sqrt{y^{16}}\)

\(\textsf{Apply\:the\:radical\:rule:\:}\sqrt[n]{a^m}=a^{\frac{m}{n}},\:\quad a\geq 0\)

\(\sqrt{180}\;x^{\frac{8}{2}}\sqrt{x}\;y^{\frac{16}{2}}\)

\(\sqrt{180}\;x^4\sqrt{x}\;y^8\)

\(\sqrt{180}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Rewrite $180$ as $(6^2 \cdot 5)$:}\)

\(\sqrt{6^2 \cdot 5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}\)

\(\sqrt{6^2} \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0\)

\(6 \sqrt{5}\sqrt{x}\;x^4\;y^8\)

\(\textsf{Apply the radical rule:} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}\)

\(6 \sqrt{5x}\;x^4\;y^8\)

\(\textsf{Rearrange:}\)

\(6x^4y^8\sqrt{5x}\)

\(\textsf{Therefore, when $x > 0$ and $y > 0$, the expression that is equivalent to}\)

\(\sqrt{180x^9y^{16}}\;\textsf{is}\;\;\boxed{6x^4y^8\sqrt{5x}}\:.\)

In the given similar triangles below, we have to find the measure of Dwrite. Triangle 1, ABC, is similar to Triangle 2, DEF. The two triangles are similar because their corresponding angles are congruent and their sides are proportional.

In order to find the measure of Dwrite, we can use the concept of proportionality. The sides of similar triangles are proportional to each other.

This means that if we know the ratio of the sides of one triangle, we can use that ratio to find the corresponding sides of the other triangle. We can use this property to find the value of Dwrite.

To start, let's write down the ratio of the sides of Triangle 1 and Triangle 2. We can choose any two corresponding sides to do this, but we'll choose AB and DE because they are easiest to measure: AB/DE = 6/8.5We know that the measure of AB is 6, so we can solve for the measure of DE: DE = AB x (DE/AB)DE = 6 x (8.5/6)DE = 8.5Now we know that the measure of DE is 8.5.

We can use this to find the measure of Dwrite. We know that DE and Dwrite are corresponding sides of Triangle 2 and Triangle 1, respectively.

So we can write a proportion using the ratio of DE to Dwrite: DE/Dwrite = 8.5/xWe know that DE is 8.5, so we can substitute that in:8.5/Dwrite = 8.5/Now we can solve for x by cross-multiplying:8.5x = 8.5Dwrite = 1Therefore, the measure of Dwrite is 1.

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Answer:

A: The area of it would be the equation (10x8)x(26)= 2,080 Inches

The perimeter would be (10+32+10+20)= 72

B: Perimeter on the top part of the frame

C: The area of it would be the equation (10x8)x(26)= 2,080 Inches

D: (10+32+10+20)= 72

Plz mark me brainsliestttt!!

Answer:

Tina will pay $12.95 for shipping and handling.

Step-by-step explanation:

Because you literally just have to multiply $62.95 by .2 and you have your answer.

Answer:

Angle 2

Step-by-step explanation:

Find S and find X.

Then find U.

The angle at X connected to S and U is the angle number.

The cross-section of the cylinders and cones is always round.

The cross-sectional area is the region of a two-dimensional shape produced when a three-dimensional object, such as a cylinder, is cut perpendicular to a preset axis at a point.

A cylinder is one of the most basic curvilinear geometric shapes and has traditionally been solid in three dimensions. In elementary geometry, it is regarded as a prism with a circle as its basis.

A three-dimensional geometric shape known as a cone has a flat base and a smooth, tapering vertex. A cone is made up of several line segments, half-lines, or lines that connect to a single point.

As a result, the cross sections of the cones and cylinders are always round.

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Step-by-step explanation:

So this will be an upside down parabola....the leading coefficient (for x^2 ) will be negative ...

Vertex at   60,90   <=====given

 Vertex form   y = a (x-h) ^2 + k

                        y = a ( x -60)^2 + 90    to find 'a' substitute in a point on the parabola...I'll use   0,0

                       0 = a ( 0-60)^2 + 90    shows a = - 1/40

so the equation is   y =  -1/40 ( x -60)^2 + 90  

           (  or expanded to y=   -1/40 x^2 + 3x )

Solve for 'x' when y = 6 ft  ( to keep from hitting your head)

      6 = -1/40x^2 +3x

      0 = -1/40 x^2 + 3x - 6      Use Quadratic Formula to find x = ~ 2 feet

Answer:

B. (-12)(-12)=144 Hope that helps

Step-by-step explanation:

Answer:

your answer should be 6! :)

Answer:

b

Step-by-step explanation:

one trip = 2724 miles

one round trip = 2 trips = 2724 * 2 = 5448 miles

We want to see how many round trips go into the miles needed for a free flight. We want to see how many times 5448 goes into 25000. To do this, we can use division.

25000/5448 ≈ 4.6

If we only have 4 round trips, it will not be enough for 4.6, so we will not be able to obtain a free flight. If we have 5, we will be able to, as 5 > 4.6

Answer: To find the angle θ in a right triangle given the cosine value, we can use the inverse cosine function, also known as arccos.

cos θ = A/H = 22/38

θ = arccos (22/38)

Using a table of trigonometric values or a calculator, we can find the value of arccos (22/38) to be approximately 56.3 degrees.

So, θ = 56.3° (rounded to the nearest degree).

Step-by-step explanation:

By algebra properties and trigonometric formulas, the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b².

In this problem we must prove that the trigonometric expression (a · cos A + b · sin A)² + (a · sin A - b · cos A)² is equivalent to the algebraic expression a² + b², this can be done both by algebra properties and trigonometric formulas. First, write the given expression:

(a · cos A + b · sin A)² + (a · sin A - b · cos A)²

Second, expand the expression by algebra properties:

a² · cos² A + 2 · a · b · cos A · sin A + b² · sin² A + a² · sin² A - 2 · a · b · cos A · sin A + b² · cos² A

(a² + b²) · cos² A + (2 · a · b - 2 · a · b) · cos A · sin A + (a² + b²) · sin² A

(a² + b²) · (cos² A + sin² A)

Third, use the fundamental trigonometric formula:

a² + b²

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x = 1 level

x + 4 (since it starts with 5 treasures and one level = 1) = 5

so if you want to see level 5 for instance it would be:

x+4 = y which would be 5+4 = y = 9

hope this helps

Answer:

The ratios are not equal, so this is not a dilation.

Step-by-step explanation:

4/3 is the first ratio

3/4 is the second ratio

Since these ratios are not equal there is not a dilation.

Simplify the equation to obtain the complete square.

So answer is,

\(44+\cfrac{7}{8}r\implies 44+\cfrac{7}{8}\left( -\cfrac{1}{2} \right)\implies 44-\cfrac{7}{16}\implies \cfrac{(16)44~~ - ~~(1)7}{\underset{\textit{we'll use this LCD}}{16}} \\\\\\ \cfrac{704~~ - ~~7}{16}\implies \cfrac{697}{16}\implies 43\frac{9}{16}\)

Answer:7  jogadore participaram do jogo

Answer:

12

Step-by-step explanation:

Answer:

The Third Table

Step-by-step explanation:

The solution in interval notation is; (-∞,  49/2).

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

To solve the equation 5/16x - 7/4 < 3/4x + 21/2, we can simplify both sides:

5/16x - 7/4 < 3/4x + 21/2

Combining like terms:

5/16x  -3/4x  < 21/2 + 7/4

8/16x < 49/4

1/2x < 49/4

Simplifying the fraction;

x < 49/2

Therefore, the solution in interval notation is (-∞,  49/2).

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