the length of a rectangle is 10 cm and its width is 2 cm less than 1/2 of its length. find the area of the rectangle​

The correct answer is, by choosing a = -2 and b = 1, we satisfy both inequalities .a < b:

To make both inequalities true, we need to select values for a and b that satisfy the given conditions:

a < b: This inequality means that the value of a should be less than the value of b.

|b| < |a|: This inequality means that the absolute value of b should be less than the absolute value of a.

One possible solution that satisfies both conditions is:

a = -2

b = 1

With these values, we have:

-2 < 1 (a < b)

|-1| < |2| (|b| < |a|)

Therefore, by choosing a = -2 and b = 1, we satisfy both inequalities.a < b:

This inequality states that the value of a should be less than the value of b. In other words, a needs to be positioned to the left of b on the number line. To satisfy this condition, we can choose a to be any number that is less than b. In the example I provided, a = -2 and b = 1, we can see that -2 is indeed less than 1, fulfilling the requirement.

|b| < |a|:

This inequality involves the absolute values of a and b. The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. The inequality states that the absolute value of b should be less than the absolute value of a. To satisfy this condition, we can choose b to be any number with a smaller absolute value than a. In the example I provided, |1| is less than |(-2)|, as 1 is closer to zero than -2, fulfilling the requirement.

By selecting a = -2 and b = 1, we satisfy both inequalities: a < b and |b| < |a|. The specific values of -2 and 1 were chosen as an example, but there are multiple other values that would also satisfy the given conditions. The important aspect is that a is indeed less than b, and the absolute value of b is smaller than the absolute value of a.

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Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

y - 1 = 3/2 (x + 3)

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

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

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

y - 1 = (3/2)(x + 3)

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

y - 1 = 3/2 (x + 3)

The area covered by the signal is 181.37 m²

Here we can see that the area covered by the signal is the fourth of a circle of radius R = 15.2m

The area of a circle of radius R is given by:

A = 3.14*R²

Then the area of a fourth of a circle is:

A = (3.14/4)*R²

Replacing the value of the radius in the formula we will get:

A =  (3.14/4)*(15.2m)² = 181.37 m²

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Answer:

11 + c

Explanation:

In the parenthesis, 7 + c cannot be simplified, so there is no need for them. Now we have 7 + c + 4. Only 7 and 4 can be added. 7 + 4 = 11. The answer is 11 + c.

Answer:

c+11

Step-by-step explanation:

Answer:

19/50   40%     0.37

Step-by-step explanation:

19/50 = 0.38

0.37 = 0.37

40% = 0.40

40%, 19/50, 0.37

Answer:

First, we rearrange the equation to isolate the y-term on one side:

dy/dx + ytanx = secx

Then, we multiply both sides by the integrating factor, which is e^(∫tanx dx) = e^(ln|secx|) = |secx|: | secx| dy/dx + ysecx tanx = 1

Next, we can write this as the derivative of a product using the product rule: d/dx (y |secx|) = 1

Integrating both sides with respect to x, we get:  y |secx| = x + C

where C is the constant of integration. Solving for y, we have:

y = (x + C)/|secx|

Note that there is a singularity at x = (2n + 1)π/2, where the denominator |secx| is zero. At these points, the solution is not defined

For the function f( x) = 3x- 2 and g( x) = x2, the workout fg( x) is 3x2- 2.

What is function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are inclusively appertained to as the function's sphere and codomain, independently. originally, functions represented the idealized relationship between two changing amounts.

A formula, rule, or legislation that specifies how one variable( the independent variable) and another variable are related( the dependent variable).

Four orders of functions live functions with return values and arguments.

This function accepts arguments and gives back a result.

functions that take arguments but have no return values.

functions with return values and no arguments.

functions that have no arguments or return values.

we are given two function f( x) and g( x);

f( x) = 3x- 2 and

g( x) = x2

So, for fg( x), we've to put value of g( x) into f( x);

Hence, the equation will be;

fg( x) = 3x2- 2.

thus, for the function f( x) = 3x- 2 and g( x) = x2, the fg( x) is 3x2- 2.

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Answer:

There are 60,634 coins in all.

Answer:

HG = 3

Step-by-step explanation:

HF = HG + GF

11 = HG + 8

11 - 8 = HG

3 = HG

Answer:

HG = 3

Step-by-step explanation:

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Answer:

2

Step-by-step explanation:

2*3+3*4 x 1/3 power 2

6+12 x 1/9

18 x 1/9

2 x 1 (because 9 and 18 are cutted by each other)

2

2

To evaluate the expression (2b+3a)×(c^2) when a=4, b=3, and c=1/3, we substitute the given values into the expression and perform the indicated arithmetic operations:

(2b + 3a) × (c^2)

= (2(3) + 3(4)) × ((1/3)^2) (substitute a=4, b=3, c=1/3)

= (6 + 12) × (1/9) (evaluate 2(3) + 3(4) and (1/3)^2)

= 18/9

= 2

Therefore, when a=4, b=3, and c=1/3, the expression (2b+3a)×(c^2) equals 2.

All 3 angles add up to 180 degrees.

so 40 + 2x + 3x = 180

40 + 5x = 180

5x = 140

x = 28

So angle A = 2x = 2(28) = 56 degrees.

Answer: 56°

Step-by-step explanation:

We know that a triangle's angles add up to 180 degrees. We will create an equation to help us solve for x using this information.

     Given:

           2x + 3x + 40 = 180

     Combine like terms:

           5x + 40 = 180

     Subtract 40 from both sides of the equation:

           5x = 140

     Divide both sides of the equation by 5:

           x = 28

Next, we will substitute this value of x into the expression for ∠A.

     ∠A = 2x = 2(28) = 56°

Answer:

which class you are plz say dude

Answer:

750160 ez

Step-by-step explanation:

Formula for circumference that involves the radius ⇒ C = 2πr

Since we are given that the circumference is 86 cm, substitute it in.

86 = 2πr

Now, π is equal to approximately 3.14 so we can

plug 3.14 in for π and we have 86 cm = 2(3.14)r.

Now solve the equation.

2(3.14) is 6.28 and we have 86 cm = 6.28r.

Now divide both sides by 6.28 and we have 13.6942 = r.

So the radius of the hula hoop is 13.6942 cm.

Answer:

43

Step-by-step explanation:

Answer:

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides. Observe the following triangle ABC, in which we have BC2 = AB2 + AC2. Here, AB is the base, AC is the altitude (height), and BC is the hypotenuse. It is to be noted that the hypotenuse is the longest side of a right-angled triangle.

Pythagoras Theorem Equation

The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

Answer:

Answer:

4.8 cups

Step-by-step explanation:

you set up a proportion of 3/5 and x/8 and then cross multiply to get your answer

The expression for the number of sundaes shop owner needs to sell in September is 3x.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, the ice cream shop owner wants to triple her sale of sundaes from August to September.

If the ice cream shop owner sold x sundaes in August, then she will sell

3×x=3x sundaes in September.

Therefore, number of sundaes shop owner sold in September is 3x.

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Answer:

The simultaneous inequation representing the recomended storage temperature is:

\(50\,^{\circ}F \leq T \leq 55.4\,^{\circ}F\)

Step-by-step explanation:

In this case, the statement must be represented mathematically by a simultaneous inequation, in which temperature must be equal to or greater than 10 ºC, expressed in Fahreheit degrees, and equal or less than 13 ºC, expressed in Fahrenheit degrees.

Bounds can be converted into Fahrenheit degrees from Celsius degrees:

\(T_{F} = \frac{9}{5} \cdot T_{C}+32\,^{\circ}F\) (Eq. 1)

Where:

\(T_{C}\) - Temperature, measured in Celsius degrees.

\(T_{F}\) - Temperature, measured in Fahrenheit degrees.

Lower bound (\(T_{C} = 10\,^{\circ}C\))

\(T_{F} = \frac{9}{5}\cdot (10\,^{\circ}C) + 32\,^{\circ}F\)

\(T_{F} = 50\,^{\circ}F\)

Upper bound (\(T_{C} = 13\,^{\circ}C\))

\(T_{F} = \frac{9}{5}\cdot (13\,^{\circ}C) + 32\,^{\circ}F\)

\(T_{F} = 55.4\,^{\circ}F\)

The simultaneous inequation representing the recomended storage temperature is:

\(50\,^{\circ}F \leq T \leq 55.4\,^{\circ}F\)

Answer:

The answer is D

Hello! :)

Equation: 1/4 + 1/3 + 3/4

    2. make the denominators the same as the LCD: \(\frac{1*3}{4*3} + \frac{1*4}{3*4} + \frac{3*3}{4*3}\)

    3. simplify: 3/12 + 4/12 = 9/12

    4.  join the denominators: \(\frac{3+4+9}{12}\)

    5.  simplify: 16/12

    6.  simplify:  4/3

    7.  convert to mixed fraction: 1 1/3

Hope this helps! Have a wonderful day! :D

Answer:

-2.72

Step-by-step explanation:

Answer:

\(3t = - 8.16 \\ t = - \frac{8.16}{3} \\ t = - 2.72 \)

\(( 7{c}^{3} {d}^{2} + 2b {c}^{2} d + ab) - ( - 4 {c}^{3} {d}^{2} + ab - 7b {c}^{2} d) \\ 7{c}^{3} {d}^{2} + 2b {c}^{2} d + ab+ 4 {c}^{3} {d}^{2} - ab + 7b {c}^{2} d) \\7{c}^{3} {d}^{2} + 4 {c}^{3} {d}^{2} + 2b {c}^{2}d + 7b {c}^{2} d + ab - ab \\ 11 {c}^{3} {d}^{2} + 9b {c}^{2} d\)

PLEASE GIVE BRAINLIEST

Answer:

Step-by-step explanation:

i don't know sorry

Answer: 112 people.

Step-by-step explanation:

Answer:

You would need 112.5 people to eat all the stacks of pancakes.

Step-by-step explanation:

45 times 5 = 225

and then 225 divided by 2 is 112.5

Hope this helps!

Good question lol

Answer:

12x + 32

Step-by-step explanation:

Multiply 8 and 4 to get 32.

Answer:

Yep looks good to me! :)

Step-by-step explanation:

Answer:

I am mostly sure it is correct please let me know if I am wrong

Step-by-step explanation:

Answer:

gh1

Step-by-step explanation:

19 is prime and 29 is not divisible by 19 therefore 1g is the highest. 5 and 3 are both prime so again, 1h and finally, 5 is a prime number so gh1 is the greatest factor

Answer:

The answer is "Option a"

Step-by-step explanation:

The Rejecting or the null hypothesis is refused by the refuting were used when the significance for our data analysis is less than the cut-off points, for example, either 0.05 or 0.01, therefore reject the null accept the alternative hypothesis, that's why in this question, the first choice is correct.

Answer:

\(54\)

Step-by-step explanation:

Formula for average A of two numbers m and n is:

\(A=\frac{m+n}{2}\)

Substitute the value m=36 and n=72

\(A=\frac{36+72}{2}\)

This is equivalent to:

\(A=\frac{108}{2}\)

The average is:

\(A=54\)

Answer:

\( E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22\)

And we can find the second moment with this formula:

\( E(X^2) = \sum_{i=1}^n X^2_i P(X_i)\)

And replacing we got:

\( E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72\)

And we can find the variance like this:

\( Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516\)

And the deviation would be:

\( Sd(X)= \sqrt{14.9516}= 3.867\)

Step-by-step explanation:

For this case we have the following dataset given:

Payment     $7     $9     $11    $13    $15  $17

Probability 0.18  0.08  0.09  0.16  0.08   0.41

For this case we can calculate the mean with this formula:

\( E(X) = \sum_{i=1}^n X_i P(X_i)\)

And replacing we got:

\( E(X) = 7*0.18 +9*0.08 +11*0.09 +15*0.08 +17*0.41 =13.22\)

And we can find the second moment with this formula:

\( E(X^2) = \sum_{i=1}^n X^2_i P(X_i)\)

And replacing we got:

\( E(X^2) = 7^2*0.18 +9^2*0.08 +11^2*0.09 +15^2*0.08 +17^2*0.41 =189.72\)

And we can find the variance like this:

\( Var(X) = E(X^2) -[E(X)]^2= 189.72- (13.22)^2 =14.9516\)

And the deviation would be:

\( Sd(X)= \sqrt{14.9516}= 3.867\)