A triangle has a base that measures 12.5 centimeters and a height that measures 20.4 centimeters. What is the area of the triangle? A 120 cm2 B) 255 cm? c) 127.5 cm? 240.2 cm?.

Answer:

The simplified form of the expression 7y - 4(3y - 8) is - 5y + 32

Step-by-step explanation:

Answer:

D. -5y+32 is Correct.

Answer:

B.

Step-by-step explanation: it is A. not B.

The length of each edge of the cube : C : 2∛12

Three-dimensional space is quantified by volume.

V= a³ => 96 = a³ => a= ∛96 =2∛12

The length of each edge of the cube : C : 2∛12

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Answer:

45+30r

Step-by-step explanation:

Answer:45+30r

Step-by-step explanation:

Because first you multiply 5x9 that gets you 45 then you multiply 5 again with 6 that gets you 30 but don’t forget the r hope this helped!

Answer:

he buys 40 juice boxes

Step-by-step explanation:

Answer: good boy good boy

The graph of the function \(f(x) = (9/4)x^2\) is a symmetric upward-opening parabola.

Overall, the graph represents a quadratic function with a positive leading coefficient, resulting in an upward-opening parabolic curve. The graph has been attached.

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Answer:

0.18 meters

Step-by-step explanation:

Answer:

10,13,14,20,30.............

The scale factor and the value of x for each figure is given as follows:

A) Scale factor of 1/3, x = 7 m.

B) Scale factor 0.4747, x = 4.5 in.

For Figure A, we have that the ratio between the areas is given as follows:

510/4590 = 1/9.

As the area is measured in square units, while the side lengths are measured in units, the scale factor is the square root of 1/9, hence it is given as follows:

1/3.

Then the value of x is obtained as follows:

x = 21 x 1/3

x = 7 m.

For Figure B, we have that the ratio between the areas is given as follows:

16/71 = 0.22535.

The scale factor is then the square root of 0.22535, which is given as follows:

0.4747.

Then the value of x is given as follows:

x = 9.5 x 0.4747

x = 4.5 in.

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Answer:

About 3.5 hours

Step-by-step explanation:

divide

Answer:

y = x + 60

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (20, 80) and (x₂, y₂ ) = (40, 100) ← 2 points on the line

m = \(\frac{100-80}{40-20}\) = \(\frac{20}{20}\) = 1

the line crosses the y- axis at (0, 60 ) ⇒ c = 60

y = x + 60 ← equation of line

Answer:

Corresponding angles are equal so,

m<6= 110° (being the corresponding angle)

.°. m<6= 110°

Hope this helps you!

Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

The dimensions of the rectangle with the given area are; 23 ft by 15 ft

We are given;

Perimeter of rectangle = 10x + 16

The width is five more than three times a unit of measure. Thus;

Width = 3x + 5

Formula for perimeter of a rectangle is;

Perimeter = 2(Width + Length)

10x + 16 = 2(3x + 5 + Length)

Divide both sides by 2 to get;

5x + 8 = 3x + 5 + Length

Length = 2x + 3

Formula for area of rectangle is;

Area = Length * Width

Area = (2x + 3) * (3x + 5)

Area = 6x² + 19x + 15

We are given the area as 345 ft². Thus;

6x² + 19x + 15 = 345

6x² + 19x - 330 = 0

Using online quadratic equation calculator, we have;

x = 6

Thus;

Width = 3(6) + 5

Width = 23 ft

Length = 2(6) + 3

Length = 15 ft

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The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

0.2835 = 28.35% probability that an average person makes at least one MONTHLY visit to doctors' office and hospitals

Step-by-step explanation:

Mean during a time period means that we use the Poisson distribution.

Poisson distribution:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

In which

x is the number of sucesses

e = 2.71828 is the Euler number

\(\mu\) is the mean in the given interval.

It is estimated that an average person makes four visits a year to doctors' offices and hospitals.

A year has 12 months, which means that the monthly mean is \(\mu = \frac{4}{12} = \frac{1}{3}\)

What is the probability that an average person makes at least one MONTHLY visit to doctors' office and hospitals?

This is:

\(P(X \geq 1) = 1 - P(X = 0)\)

In which

\(P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}\)

\(P(X = 0) = \frac{e^{-(\frac{1}{3})}*(\frac{1}{3})^{0}}{(0)!} = 0.7165\)

\(P(X \geq 1) = 1 - P(X = 0) = 1 - 0.7165 = 0.2835\)

0.2835 = 28.35% probability that an average person makes at least one MONTHLY visit to doctors' office and hospitals

Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Answer:

Step-by-step explanation:

y = a * log_b (x - h) + k

(h,k) = (x,y)

h = shift right/left

k = shift up/down

Original Points of y = log_3

y = log_3 (x + 2)

h = -2 thus shift left.

Asymptote: x = -2
Domain: [-2 , +inf)

Range: (-inf , +inf)

Answer:

C is the answer (98%)

Step-by-step explanation:

pls mark brainliest

We proved that if the number of non-zero singular values of a square matrix A equals the number of its columns, then A is invertible.

Let A be invertible and all the singular values of A are non-zero.

Then there exists two orthogonal matrices

U ∈ R(n×n)

V ∈ R(m×m)

Σ ∈ R(n×m)

It states that:

Σ(1,1) ≥ Σ(2,2) ≥ ... ≥ 0 such that A=UΣV^{⊤}, and U and V are invertible.

Since the diagonal of Σ is non-zero, Σ is invertible.

So A=UΣV^{⊤} is invertible.

Also if now we assume A is invertible.

Then we can show that:

σ1(A)σ1(A^{−1}) ≥ 1

where σ1(A) and σ1(A^{−1}) represents the largest singular value of A and A^{−1}.

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Answer:

Step-by-step explanation:

B. The number is represented by a non terminating, non-repeating decimal.

(Strictly speaking it is irrational because it cannot be expressed as a ratio of two integers. All rational numbers can be expressed as a ratio of two integers.)

Answer:

Step-by-step explanation:

i am working on the assumption that nobody does all three of them

i got 4 because including the people that do swimming and park, the total number of people that do swimming is 22.

the same logic goes for cycling: including the people that do swimming and visit the national park, the total is 23.

so that means that find how many people do swimming and cycling, we have to add the people doing only swimming, with the people doing both swimming and park and then subtract that answer from 22 which gives you 4

add the number of students first for the buses. 24+26=50 then 50/2=25 25 kids for each bus. Then each bus group needs to be divided by five so 25/5=5

Answer:

\(\displaystyle\)\(\displaystyle f'(1)=-\frac{9}{e^3}\)

Step-by-step explanation:

Use Quotient Rule to find f'(x)

\(\displaystyle f(x)=\frac{3x^2+2}{e^{3x}}\\\\f'(x)=\frac{e^{3x}(6x)-(3x^2+2)(3e^{3x})}{(e^{3x})^2}\\\\f'(x)=\frac{6xe^{3x}-(9x^2+6)(e^{3x})}{e^{6x}}\\\\f'(x)=\frac{6x-(9x^2+6)}{e^{3x}}\\\\f'(x)=\frac{-9x^2+6x-6}{e^{3x}}\)

Find f'(1) using f'(x)

\(\displaystyle f'(1)=\frac{-9(1)^2+6(1)-6}{e^{3(1)}}\\\\f'(1)=\frac{-9+6-6}{e^3}\\\\f'(1)=\frac{-9}{e^3}\)

Answer:

\(f'(1)=-\dfrac{9}{e^{3}}\)

Step-by-step explanation:

Given rational function:

\(f(x)=\dfrac{3x^2+2}{e^{3x}}\)

To find the value of f'(1), we first need to differentiate the rational function to find f'(x). To do this, we can use the quotient rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Quotient Rule for Differentiation}\\\\If $f(x)=\dfrac{g(x)}{h(x)}$ then:\\\\\\$f'(x)=\dfrac{h(x) g'(x)-g(x)h'(x)}{(h(x))^2}$\\\end{minipage}}\)

\(\textsf{Let}\;g(x)=3x^2+2 \implies g'(x)=6x\)

\(\textsf{Let}\;h(x)=e^{3x} \implies h'(x)=3e^{3x}\)

Therefore:

\(f'(x)=\dfrac{e^{3x} \cdot 6x -(3x^2+2) \cdot 3e^{3x}}{\left(e^{3x}\right)^2}\)

\(f'(x)=\dfrac{6x -(3x^2+2) \cdot 3}{e^{3x}}\)

\(f'(x)=\dfrac{6x -9x^2-6}{e^{3x}}\)

To find f'(1), substitute x = 1 into f'(x):

\(f'(1)=\dfrac{6(1) -9(1)^2-6}{e^{3(1)}}\)

\(f'(1)=\dfrac{6 -9-6}{e^{3}}\)

\(f'(1)=-\dfrac{9}{e^{3}}\)

Answer:

Step-by-step explanation:

Hello!

We want to know the area of the original circle - the now circle.

The original circle's diameter is 110 meters.

To figure out the area you use this formula: \(r^2*pi\)

The diameter is 107 meters, so the equation is \(55^2\)\(*\pi\).

The area is about 9503.3 meters.

The next area is the "now circle".

The now circle's diameter is 107 meters.

When you use this formula, you end up with  \(53.5^2*\pi\).

The area is about 8892 meters.

So it's just basic subtraction!

I'll let you figure out the rest.

:)

A graph that represents the solution set of the compound inequality is: graph D.

In Mathematics, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

Next, we would solve the given compound inequality by making x the subject of formula as follows;

x + 3 < 1/2(4x - 12) < 20

Multiplying all through by 2, we have the following:

2x + 6 < 4x - 12 < 40

Next, we would solve the compound inequality in parts:

2x + 6 < 4x - 12

4x - 2x < 12 + 6

2x < 18

x < 18/2

x < 9.

4x - 12 < 40

4x < 40 + 12

4x < 52

x < 52/4

x < 13.

In conclusion, the line on a number line (graph) should be open when the inequality symbol is greater than (>) or less than (<).

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Answer:

-2, 5/3

Step-by-step explanation:

y=2/3(-2)+3

2/3(-2)=-4/3

y=-4/3+3