The base of a triangle is 1 cm more than the height. If the area is 10 cm², find the base and the height.
Part 1 of 2
What is the base of the triangle?

What is the height of the triangle?

Filled box will be:

Box 1: Sum of angles on starlight line is 180°.

Box 2: m ∠LQR + m ∠MQR = 180°

Box 3: m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR

Box 4: m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR

Box 5: If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel.

From the given figure we have to prove that LM ∥ NP.

m ∠LQR + m ∠QRN = 180° [Given]

m ∠LQR + m ∠MQR = 180° [Sum of angles on starlight line is 180°]

m ∠LQR + m ∠QRN = m ∠LQR + m ∠MQR [Transitive property of Equality]

m ∠LQR + m ∠QRN - m ∠LQR = m ∠LQR + m ∠MQR - m ∠LQR [Subtraction property of Equality]

m ∠QRN = m ∠MQR [Definition of Congruence]

LM ∥ NP [If two lines and a transversal form alternative angles and Alternative angles are equal then the lines must be parallel]

Hence it is proved that, LM ∥ NP.

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The number of years that it would take for the investment to double, given a continuous compounding rate, is 17. 33 years.

The formula for continuous compound interest is given by:

[tex]A = Pe ^{rt}[/tex]

We are given $ 8, 000  and want to know how long it would take for this amount to double and become $ 16, 000.

The formula would be:

[tex]16,000 = 8, 000 e ^{0.04 t}2 = e ^{0.04t}[/tex]

ln ( 2 ) = 0 .04t

t = ln ( 2 ) / 0. 04

= 17. 33 years

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Entonces, la probabilidad de que el CD elegido al azar sea defectuoso es del 1.3%.

Para calcular la probabilidad de que el CD elegido al azar sea defectuoso, debemos considerar la proporcion de CD's defectuosos para cada marca y su cantidad en el lote total.

En primer lugar, podemos calcular el número total de CD's en el lote:

500 (marca A) + 400 (marca B) + 100 (marca C) = 1000 CD's

Luego, podemos calcular el número de CD's defectuosos para cada marca:

Marca A: 1% de 500 CD's = 5 CD's defectuosos

Marca B: 1.5% de 400 CD's = 6 CD's defectuosos

Marca C: 2% de 100 CD's = 2 CD's defectuosos

Por lo tanto, el numero total de CD's defectuosos en el lote es:

5 (marca A) + 6 (marca B) + 2 (marca C) = 13 CD's defectuosos

Finalmente, la probabilidad de que el CD elegido al azar sea defectuoso es simplemente la proporción de CD's defectuosos en el lote total:

P(CD defectuoso) = 13/1000 = 0.013 o 1.3%

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Answer:

A

Step-by-step explanation:

0.15 × 12 = 1.8

ps : i'm not sure if it's true or not, but i think this is the answer. i'm sorry if i get you wrong

The trigonometric value relations are solved and

a) cos 45° = √2/2

b) tan 30° = √3/3

c) sin 60° = √3/2

Given data ,

Let the trigonometric relations be represented as A

Now , the value of A is

a)

cos x = √2/2

On simplifying , we get

cos x = 1/√2

Taking inverse on both sides , we get

x = cos⁻¹ ( 1/√2 )

x = 45°

b)

tan x = √3/3

On simplifying , we get

tan x = 1/√3

Taking inverse on both sides , we get

x = tan⁻¹ ( 1/√3 )

x = 30°

c)

sin x = √3/2

Taking inverse , we get

x = 60°

Hence , the trigonometric relations are solved

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The expression is equivalent to 10w - 25 = 0

It is important to note that algebraic expressions are described as expressions that are made up of terms, variables, coefficients, factors and constants.

These expressions are also made up of arithmetic operations. These operations are;

From the information given, we have that;

D =  2w - w - 7

C = 3w - 6

To determine the value of the expression  D + 3C

substitute the expression

2w - w - 7 + 3(3w -6)

expand the bracket

2w - w - 7 + 9w - 18

collect the like terms and add

10w - 25 = 0

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Step-by-step explanation:

70 ÷ 3 = 23  1/3

The value of TU is 31.7 cm and the area of the triangle is 69.08 cm².

Give is triangle UVW, we need to find the value of TU and the area of the triangle UVW,

So, using the trigonometric ratios,

Sin 49° = TU/WU

TU = Sin 49° × WU

TU = Sin 49° × 42

TU = 31.7 cm

So, TU is the height of the triangle UVW, we know that the area of a triangle = 1/2 × height × base

= 1/2 × 31.7 × 44

= 31.7 × 22

= 69.08 cm²

Hence the value of TU is 31.7 cm and the area of the triangle is 69.08 cm².

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The number of square meters that the space that Araceli rents is, is 30. 66 square meters.

The space that Araceli rents has a rectangular space so to find the area of the rectangular space that Araceli rents, we need to multiply the length by the width.

The given width is 4. 2 meters and the length is 7. 3 meters.

The area of the space in square meters is therefore :

Area = Length × Width

Area = 7. 3 meters × 4. 2 meters

Area = 30. 66 square meters

In conclusion, the space that Araceli rents has an area of 30. 66 square meters.

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The solution of the fraction is n = 2 (option c).

Now, let's consider the equation n/32 = 1/16, where n is a variable that we want to solve for. This equation tells us that the ratio of n to 32 is equal to the ratio of 1 to 16. In other words, if we divide n by 32, we get the same result as if we divide 1 by 16.

To solve for n, we can use algebraic techniques to isolate the variable on one side of the equation. One way to do this is to multiply both sides of the equation by 32, which gives us:

n = (1/16) * 32

We can simplify the right-hand side of this expression by multiplying 1/16 by 32, which gives us:

n = 2

Therefore, the answer to this problem is n = 2. (option c).

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Complete Question:

n/32 = 1/16. Fine the value of n.

a. n = one-half

b. n = 4

c. n = 2

d. n = 512

The requried it will take 98.8 years for the account balance to reach 1 million dollars.

(a) The formula for compound interest is:

[tex]A = P(1 + r/n)^{(nt)}[/tex]

In this case, P = $500, r = 0.0425, n = 1 (compounded annually), and we want to find the function for A as a function of t. Therefore, the equation is:

[tex]A = 500(1 + 0.0425/1)^{(1t)}\\A = 500(1.0425)^t[/tex]

(b) To find the amount of time it takes for the account balance to reach 1 million, we need to solve for t in the equation:

[tex]1,000,000 = 500(1.0425)^t[/tex]

t ≈ 98.8 years

Therefore, it will take approximately 98.8 years for the account balance to reach 1 million dollars.

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The correct congruency for prove that ΔPQR ≅  ΔRSP is,

⇒ SAS

We have to given that;

In the figure below,

∠PQR ≅ ∠ RSP

And, both equal 90 degrees.

Now, In ΔPQR and ΔRSP;

∠PQR ≅ ∠ RSP

PR = RP

PS = QR

Thus, By SAS congruency theorem,

ΔPQR ≅  ΔRSP

So, The correct congruency for prove that ΔPQR ≅  ΔRSP is,

⇒ SAS

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Answer:

y = (-2/3)x + 5

Step-by-step explanation:

To write the equation of a line, we need to find its slope and y-intercept using the given points.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:slope = (y2 - y1) / (x2 - x1)

Using the points (-3,7) and (9,-1), we can find the slope as:slope = (-1 - 7) / (9 - (-3))

     = -8 / 12

     = -2/3

Now that we have the slope, we can use the point-slope form of the equation of a line to find the y-intercept. The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is:y - y1 = m(x - x1)

Using the point (-3,7) and the slope we just found (-2/3), we get:y - 7 = (-2/3)(x - (-3))

Simplifying this equation, we get:y - 7 = (-2/3)x - 2

y = (-2/3)x + 5

Answer:40.6779661017

Step-by-step explanation:

Answer: F(x) = (-5/6) x + 13/42

Step-by-step explanation: The provided points are (x1, y1) = (2/7, 3/7) and (x2, y2) = (-1/7, 11/14) respectively.

The following formula can be used to determine the slope of the line connecting the two points:

m = (y2 - y1)/(x2 - x1)

m = (11/14 - 3/7)/(-1/7 - 2/7)

m = (5/14)/(-3/7)

m = -5/6

In order to construct the equation of the line, we can now utilize the point-slope form:

y - y1 = m(x - x1)

The result of substituting the values of m, x1, and y1 is:

y - 3/7 = (-5/6)(x - 2/7).

The number of hours that Konner is left with till they can reach their destination is 1 ¹ / ₃ hours

We can start by using a proportion to set up an equation to solve for the time needed to arrive:

Distance traveled / total distance = time traveled / total time

Using a ratio, we infer that 5 / 6 of an hour is equivalent to 1 / 3 of the way.

This means that if there are 2 / 3 of the way left, the hours left till Konner reaches is:

= 5 / 6 x 2

= 10 / 6

= 5 / 3

= 1 ¹ / ₃ hours

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Question is:

How much longer till he arrives ?

The complement of a set C, denoted by C', contains all the elements of the universal set that are not in C. In this case, the universal set is A, which contains all the flavors and toppings available.

Given data ,

a) {vanilla, strawberries, sprinkles}

This set contains vanilla, strawberries, and sprinkles but does not contain any elements from C. Therefore, C' = A - {vanilla, strawberries, sprinkles} = {chocolate, hot fudge, peanuts, whipped cream}.

b) {chocolate, hot fudge, peanuts, whipped cream}

This set contains all the elements of C but does not contain any elements from A that are not in C. Therefore, C' = A - C = {vanilla, strawberries, sprinkles}.

c) {vanilla, hot fudge, sprinkles, whipped cream}

This set contains hot fudge, sprinkles, and whipped cream but does not contain any elements from C. Therefore, C' = A - {hot fudge, sprinkles, whipped cream} = {vanilla, chocolate, strawberries, peanuts}.

d) {chocolate, strawberries, sprinkles}

This set contains strawberries and sprinkles but does not contain any elements from C. Therefore, C' = A - {strawberries, sprinkles} = {vanilla, chocolate, hot fudge, peanuts, whipped cream}.

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The length of the tree line, t, to the nearest foot, is 20 ft.

We have,

From the figure,

t can be considered as the hypotenuse.

And,

The other two sides are::

15 - (7 + 5) = 15 - 12 = 3

30 - 10 = 20

Now,

Applying the Pythagorean theorem,

t² = 3² + 20²

t² = 9 + 400

t² = 409

t = 20

Thus,

The length of the tree line, t, to the nearest foot, is 20 ft.

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Answer:

  B.  quadratic

Step-by-step explanation:

You want to know the kind of function that would best fit the points shown on the graph.

The points on the graph demonstrate a slope that starts out positive and decreases through 0 to a slope with a negative value.

A linear function has a constant slope.

An exponential function has a continuously increasing or continuously decreasing slope.

A quadratic function has a slope that changes sign, matching the slope of the curve joining the given points.

The equation that best fits the given data will be quadratic.

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The solution is, Option B.) one culture will have always 50 more bacteria than the other.

We have,

Calculating the exponential growth or decay of a given collection of data is done using an exponential function, which is a mathematical function. Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread.

Given:

We have,

The population, P, of bacteria in a culture can be calculated at any time, t, using the equation P= a(2).

In the equation, the initial number of bacteria is a.

The initial number of bacteria in two different cultures were 100 and 125.

so, in one cultures population, P, of bacteria is = 100(2)

                                                                             = 200

in the other cultures population, P, of bacteria is = 125(2)

                                                                             = 250

so, we get,

the two populations compare over time = 250 - 200

                                                                   = 50

Hence, The solution is, Option B.) one culture will have always 50 more bacteria than the other.

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The average score of the spelling test is 90.6%

To find the average score of the test, we need to add up all the scores and divide by the total number of students. We can think of the average score as the "typical" or "representative" score of the entire class.

First, let's add up all the scores:

2(100) + 9(95) + 10(90) + 3(80) + 1(70) = 200 + 855 + 900 + 240 + 70 = 2265

Next, we divide by the total number of students:

Average score = (2 + 9 + 10 + 3 + 1) / 25 * 100% = 25 / 25 * 100% = 90.6%

Therefore, the average score of the spelling test is 90.6% when rounded to one decimal place.

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Answer:

Question 5 : 10% decay

Question 6 : Amar is right

Step-by-step explanation:

If the radius of a cylindrical construction pipe is 1.5ft, the volume of the construction pipe is approximately 452 cubic feet.

To find the volume of a cylinder, we use the formula V = πr²h, where r is the radius of the base, h is the height, and π is a constant approximately equal to 3.14.

In this problem, the radius is given as 1.5ft and the height is given as 16ft. Therefore, we can plug in these values to get:

V = π(1.5ft)²(16ft)

Simplifying this expression, we get:

V = 9π(16ft)

Using the value 3.14 for π, we can approximate the volume as:

V ≈ 9(3.14)(16ft) ≈ 452ft³

It's important to include the correct unit in the answer, which in this case is cubic feet.

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Answer:

Hi

You can identify which is the shortest and longest by converting the fractions to decimal or by finding the L.C.M

The longest time is 1

and the shortest is 1/4

The difference would be 1-1/4= 3/4

Answer:

The answer is approximately 24

Step-by-step explanation:

tan0 =x/adj

tan15=x/90

x=90×tan15

x≈24

Answer:

A is the correct answer.

Angle 2 is an exterior angle of the triangle because Angles 2 and 3 are supplementary angles.

The rate of change of the circumference is 8π feet per second

Given data ,

The circumference of a circle is given by C = 2πr, where r is the radius. We need to find how fast the circumference is changing when the radius is 19 feet and the rate of increase of the radius is 4 feet per second.

We can start by taking the derivative of both sides of the equation C = 2πr with respect to time t:

dC/dt = 2π(dr/dt)

Here, dC/dt represents the rate of change of the circumference with respect to time, and dr/dt represents the rate of change of the radius with respect to time.

We are given that dr/dt = 4 feet per second, so we can substitute this value into the equation above:

dC/dt = 2π(4) = 8π

So when the radius is 19 feet, the circumference is C = 2π(19) = 38π feet. At this point, the rate of change of the circumference is dC/dt = 8π feet per second.

Hence , when the radius is 19 feet, the circumference is increasing at a rate of 8π feet per second

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Answer:

5 pints

Step-by-step explanation:

every 2 cups is 1 pint

10 Divide by 2 is 5

4 cups = 2 pints

6 cups = 3 pints

8 cups = 4 pints

10 cups = 5 pints