The expression 2x + 3.4 is equal to ? for x =1.6.

Answer:

Step-by-step explanation:

Each intercept is found by setting the other variable to zero and solving for the variable value of interest.

  2x +3y = 54

x-intercept:

  2x = 54

  x = 27

y-intercept:

  3y = 54

  y = 18

__

By definition, the intercept values are the values that satisfy the equation when the other variable is zero.

x-intercept: To score 54 points, the team would have to make 27 2-point baskets if no 3-point baskets were made.

y-intercept: To score 54 points, the team would have to make 18 3-point baskets if no 2-point baskets were made.

Area of the rectangle is 60

Area of the semi circle 14.13 ir 14.1

60 plus 14.1 is 74.1

I hope its right

The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 \(\geq\) 9p+8 true are : -3, -4, -5

Let's solve the inequality first

4p -7 \(\geq\)  9p  +8

Taking p's on the same side we will get :

-7 - 8 \(\geq\) 9p - 4p

-15 \(\geq\) 5p

Divide by 5 into both sides

-3 \(\geq\) p

i.e. p \(\leq\) -3

Therefore p must be less than or equal to -3

From the set, we have the numbers -3,-4,-5 which are less than or equal to -3

Hence the integers -3,-4,-5 will make the  inequality 4p-7 \(\geq\) 9p+8 true

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An example of a function that models a linear relationship between two quantities, x and y is y = mx + b

We need to use the equation of a straight line, which is commonly expressed in slope-intercept form as:

y = mx + b

In this function, x represents the independent variable, m is the slope of the line, and b is the y-intercept. To use this function, we simply plug in the values of x, m, and b that correspond to the specific relationship we are modeling.

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Answer:

\(\text{Standard Form: }x^2 - (2\sqrt{2})x - 48\\\text{Factored Form: }(x+4\sqrt{2})(x-6\sqrt{2})\)

Step-by-step explanation:

We're given the equation: \(x^2 - (\sqrt{2})x - 12\)

We can find the zeroes of this function by using the quadratic formula defined as: \(x=\frac{-b\pm \sqrt{b^2 - 4ac}}{2a}\)

In this case: \(a=1,b=-\sqrt{2}, c=-12\). So if we substitute these values in we get the following:

\(x=\frac{-(-\sqrt{2})\pm \sqrt{(-\sqrt{2})^2 - 4(1)(-12)}}{2(1)}\\\\x=\frac{\sqrt{2} \pm \sqrt{2 + 48}}{2}\\\\x=\frac{\sqrt{2} + \sqrt{50}}{2}\\\\x = \frac{\sqrt{2} \pm \sqrt{25} * \sqrt{2}}{2}\\\\x = \frac{\sqrt{2} \pm 5\sqrt{2}}{2}\)

So from here we'll get our two zeroes, but you may notice, regardless of whether we pick the positive or negative square root, the denominator is two. So if we're looking for an equation with \(2\alpha \text{ and }2\beta\) we just multiply this by two to get:

\(x = \sqrt{2} \pm 5\sqrt{2}\)

Now from here let's find both solutions. First let's take the positive square root to get: \(x = \sqrt{2} + 5\sqrt{2} \implies 6\sqrt{2}\)

If we take the negative square root we get: \(x = \sqrt{2} - 5\sqrt{2}\implies -4\sqrt{2}\)

So now that we have the two zeroes, let's start forming our quadratic equation. In this case it's really useful to start with factored form. In this form we express a quadratic or generally any polynomials in terms of its factors.

The factored form of quadratic looks something like this: \(f(x)=a(x-b)(x-c)\)

where b and c are zeroes and a is some value that determines the stretch/compression of the quadratic.

The "a" value doesn't change the zeroes, so for simplicity let's just say, that a=1 in this case. This gives us the quadratic: \((x-(-4\sqrt{2}))(x-6\sqrt{2})\implies (x+4\sqrt{2})(x-6\sqrt{2})\)

We can leave it in this factored form, but we can also expand this using FOIL to express it in standard form.

\((x + 4\sqrt{2})(x-6\sqrt{2})\implies x^2 - (6\sqrt{2})x + (4\sqrt{2})x - 48\implies x^2 - (2\sqrt{2})x - 48\)

The launching of the hot air balloon is from the ocean beach is an illustration of a projectile motion

The function is given as:

\(p(x) =-\frac{2}{2500}x^2 + 0.7x\)

Differentiate

\(p'(x) =-\frac{4}{2500}x + 0.7\)

Set to 0

\(-\frac{4}{2500}x + 0.7 = 0\)

Subtract 0.7 from both sides

\(-\frac{4}{2500}x =- 0.7\)

Multiply through by -2500/4

\(x =437.5\)

Hence, the horizontal distance which a maximum height is attained is 437.5 meters

In (a), we have:

\(x =437.5\)

Substitute \(x =437.5\) in p(x)

\(p(437.5) =-\frac{2}{2500} * 437.5^2 + 0.7 * 437.5\)

Evaluate

\(p(437.5) =153.125\)

Hence, the maximum height above the sea level is 153.125 metres

In (b), the maximum height above the sea level is 153.125 metres

The ratio of the height on land and sea is given as:

Land : Sea = 2 m : 20 m

For the maximum height, we have:

Land : 153.125 m= 2 m : 20 m

Express as fraction

Land / 153.125 m = 2 /20

Multiply both sides by 153.125

Land = 15.3125

Approximate

Land = 15.3

Hence, the maximum height above the ground level is 15.3 meters

We have:

\(p(x) =-\frac{2}{2500}x^2 + 0.7x\)

Substitute 50 for P(x)

\(-\frac{2}{2500}x^2 + 0.7x = 50\)

Using a graphing calculator, we have:

x = 78.465 and 796.535

Hence, the horizontal distances where the balloon 50 m above the ground are 78.465 and 796.535 meters

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The domain value that corresponds to a range value of 4 is,

⇒ x = 1/2

Given that;

Function is,

y = 4x + 2

Since, the equation equal to the range value:

4 = 4x + 2

Then, we can solve for "x":

4 - 2 = 4x

2 = 4x

x = 1/2

Now that we have the value of "x", we can find the corresponding value of "y" by substituting it into the given equation:

y = 4x + 2

y = 4(1/2) + 2

y = 4 + 2

y = 6

Therefore, the domain value that corresponds to a range value of 4 is,

⇒  x = 1/2

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Julio accidentally put in an extra 1/10 cup of sugar.

To calculate the number of extra cups of sugar that Julio put in, we need to find the difference between what the recipe called for (3/10 cups) and what he actually added (4/10 cups).

The difference can be calculated as follows:

Actual amount - Required amount = Extra amount

= 4/10 - 3/10

= 1/10

Therefore, Julio accidentally put in an extra 1/10 cup of sugar.

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Answer:

A

Step-by-step explanation:

To solve the equation 7x-3(x-6)=30, we need to use the distributive property to simplify the left-hand side of the equation:

7x - 3(x-6) = 30

7x - 3x + 18 = 30

4x + 18 = 30

Next, we need to isolate the variable term on one side of the equation. To do this, we can subtract 18 from both sides:

4x + 18 - 18 = 30 - 18

4x = 12

Finally, we can solve for x by dividing both sides by 4:

4x/4 = 12/4

x = 3

Therefore, the solution to the equation 7x-3(x-6)=30 is x = 3. Answer A is correct.

According to the information given in the exercise:

• The cost of admission for couples is $12 and $7 for singles.

• On Friday the total amount of money for admissions was $2706.

• On Friday a total number of 268 people attended.

Knowing this, you can set up the following System of Equations, where "c" is the number of couples at the dance club on Friday night and "s" is the number of singles at the dance club on Friday night.

You can use the Elimination Method in order to find the value of "s":

1. Multiply the second equation by -12:

2. Add the equations:

3. Solve for "s":

Therefore, the answer is: There were 102 singles.

Answer:

€327.6

Step-by-step explanation:

==>Given:

Post office exchange rate=> £1 = €1.17

==>Required:

Amount of Euros that will get me £280

==>Solution:

Using the exchange rate at the list office as stated in the question, convert £280 to euros:

Let x be the amount in euros

£1 = €1.17

£280 = x

Cross multiply to equate

x*£1 = €1.17*£280

Divide both sides by £1 to make x the subject of formula

x = (€1.17*£280)/£1

x = €327.6

You will get €327.6 for £280

Answer:

6/49  

Step-by-step explanation:

-2/7  *   -3/7   = (-2 * -3) / (7*7) =  6/49

The statement that is equivalent to |6x-3|=3 is: 6x-3=3 or 6x-3=-3

For the equation to be true, two scenarios need to be considered:

When the expression 6x-3 is positive and equals 3:

6x-3 = 3

When the expression 6x-3 is negative and equals -3:

6x-3 = -3

By solving these two equations, we can find the equivalent statement:

Solving 6x-3 = 3:

Adding 3 to both sides gives us:

6x = 6

Dividing both sides by 6:

x = 1

Solving 6x-3 = -3:

Adding 3 to both sides gives us:

6x = 0

Dividing both sides by 6:

x = 0

Therefore, the equivalent statement to |6x-3|=3 is:

6x-3=3 or 6x-3=-3, which can be further simplified to:

6x-3=3 or 6x-3=-3

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Answer:

$2,403.02

Step-by-step explanation:

To calculate the amount of interest earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded monthly, we can use the compound interest formula:

\(\boxed{\begin{minipage}{8.5 cm}\underline{Compound Interest Formula}\\\\$ I=P\left(1+\frac{r}{n}\right)^{nt}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $A =$ interest earned. \\ \phantom{ww}$\bullet$ $P =$ principal amount. \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form). \\ \phantom{ww}$\bullet$ $n =$ number of times interest is applied per year. \\ \phantom{ww}$\bullet$ $t =$ time (in years). \\ \end{minipage}}\)

Given values:

Substitute the values into the formula and solve for I:

\(I=12585\left(1+\dfrac{0.035}{12}\right)^{12 \cdot 5}-12585\)

\(I=12585\left(1.00291666...\right)^{60}-12585\)

\(I=12585(1.19094282...)-12585\)

\(I=14988.015...-12585\)

\(I=2403.01550...\)

\(I=\$2403.02\)

Therefore, the interest earned on an investment of $12,585 at 3.5% interest over 5 years if the interest is compounded monthly is $2,403.02 (to the nearest cent).

Tiled floor with 225 square tiles means the area of the square room is 225.

Formula needed: A = (side)^2 or in short

A = s^2.

We need to find s.

225 = r^2

sqrt{225} = sqrt{r^2}

15 = r

There are 15 tiles are along an edge of the room.

If hole for a bird feeder post is 3 feet deep, the top of the post needs to be at least 5 feet above the ground. Then  x-3≥5  is the inequality that represents the required length of the post.

a relationship between two expressions or values that are not equal to each other is called 'inequality.

Given,

The hole for a bird feeder post is 3 feet deep,

the top of the post needs to be at least 5 feet above the ground

We need to find the inequality that represents the required length of the post.

Let x be the length of the post.

As, it is deeper then it has negative three.

There is given atleast, so it should be greater than or equal to.

x-3≥5

Hence, x-3≥5  is the  inequality that represents the required length of the post.

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Answer:The inequality represented by the equation y = -11/7x - 4 can be written as:

y ≤ -11/7x - 4

This represents a less than or equal to inequality, indicating that the values of y are less than or equal to the expression -11/7x - 4.

Step-by-step explanation: .

Answer:*

Step-by-step explanation:

Answer:

15.42 inches

Step-by-step explanation:

-formula : perimeter of semi circle= πr+2r

r=3 inch

π.3+2.3

=3π+6

Answer:

15.425 or 6+3π

Step-by-step explanation:

If the radius of the circle is 3 inches and the diameter is double the radius, we know the diameter is 6 inches. Then we find half of the perimeter of a circle with radius 3. The perimeter formula of a cirle is 2πr. Plugging in the radius we get: 2(3)π or 6π. Then we divide by 2 as it is a semicircle and get 3π or ≈9.425. We add 6 to this and we get the answer of 15.425 or 6+3π.

Answer:

All of them.

Step-by-step explanation:

Khan Academy 7th grade math, quiz 3.

All the values of j, 3,4, and 5 satisfy the inequality 10≥ j + 5. The correct options are A, B, and C.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given that the inequality is 10≥ j + 5. The inequality can be solved at different points as below,

At the value j = 3,

10 ≥ j + 5

10 ≥ 3 + 8

10 ≥ 8

10 is greater than 8.

At the value j = 4,

10 ≥ j + 5

10 ≥  4 + 5

10 ≥  9

10 is greater than 9.

At the value j = 5,

10 ≥ j + 5

10 ≥ 5 + 5

10 ≥  10

10 is equal to 10.

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Answer:

1. 1

2. 28

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :D

Answer:

68 people

Step-by-step explanation:

Find how many finished in under 3 hours by multiplying 80 by 0.85

80(0.85)

= 68

So, 68 people finished in under 3 hours

The equation to represent the growth of the trees is given by

AA=32+6t and BB=20+9t and both the trees will be of equal height after 3 years.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

Equation is defined as the quality of being equal and is frequently represented by a mathematical statement with equal values on either side or by a problem requiring consideration of a number of factors.

Given that tree A is 32 inches tall and tree B is 20 inches tall.

Tree A grows 6 inches per year.

Length of the tree A after t years = 32 + 6t

Tree B grows 9 inches per year

Length of the tree B after t years = 20 + 9t

Now let us consider that both trees grows equal after a certain period of time.

If we equate both the expressions then we can form an equation to calculate the value of t.

∴ 32+6t = 20+9t

or, 6t - 9t = 20 - 32

or, -3t = -12

or,  t = 4 years

The trees will be of equal length after 4 years.

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Answer:

18 hdhb

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

21/1 x 6/7

21 x 6 = 126

1 x 7 = 7

126 / 7 = 18

Answer:

third option

Step-by-step explanation:

under a counterclockwise rotation of 90° about the origin

a point (x, y ) → (y, - x )

Then

A (- 1, - 2 ) → (- 2, - (- 1) ) → (- 2, 1 )

B (2, - 2 ) → (- 2, - 2 )

C (1, - 4 ) → (- 4, - 1 )

The new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

From the question, we have the following parameters that can be used in our computation:

The figure,

Where, we have

A = (-1, -2)

B = (2, -2)

C = (1, -4)

The rule of 90 degrees counterclockwise is

(x, y) = (-y, x)

Using the above as a guide, we have the following:

A = (2, -1)

B = (2, 2)

C = (4, 1)

Hence, the new coordinates are (d) A = (2, -1) B = (2, 2) and C = (4, 1)

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Answer will be 27.

Given,

3√81

Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.

For example, squares of

1² = 1

2² = 4

3² = 9

4² = 16

5² = 25

6² = 36

7² = 49

8² = 64

9² = 81
10² = 100

Square roots,

√100 = 10

√81 = 9

√64 = 8

√49 = 7

√36 = 6

√25 = 5

√16 = 4

√9 = 3

√4 = 2

√1 = 1

Now ,

3√81 = 3× 9

= 27.

Thus the value is 27.

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By knowing the blood pressure and applying the quadratic formula, the age of a man whose normal blood pressure is 129 mm Hg is 40 years old.

In this problem we have a quadratic function that models the blood pressure as a function of age. As the latter is known, we must use the quadratic formula to determine the former:

129 = 0.006 · A² - 0.02 ·A + 120

0.006 · A² - 0.02 · A - 9 = 0

\(A = \frac{0.02 \pm \sqrt{0.006^{2}-4\cdot (0.006)\cdot (- 9)}}{2\cdot (0.006)}\)

A = 1.667 + 38.733

A = 40

By knowing the blood pressure and applying the quadratic formula, the age of a man whose normal blood pressure is 129 mm Hg is 40 years old.

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For given measurements, the perimeter of the quadrilateral is 30cm.

The length of a quadrilateral's border, or what remains after joining all four of its sides to form a single line segment, is referred to as the quadrilateral's perimeter. As a result, a quadrilateral's perimeter is measured in the same linear units as its sides, such as meters, inches, centimeters, etc.

This may be stated using a straightforward formula. For instance, the formula for a quadrilateral ABCD's perimeter may be written as,

AB + BC + CD + DA = The perimeter

perimeter of the quadrilateral = sum of all sides.

perimeter of the quadrilateral = 1 + 9 + 12 + 8

= 30 cm.  

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The solution to the nonlinear system of equations is (x, y) = (-3, -2) and (x, y) = (1, 6). These points represent the coordinates where the two equations intersect and satisfy both equations simultaneously.

To solve the nonlinear system of equations:

Equation 1: \(y = -x^2 + 7\)

Equation 2: y = 2x + 4

We can equate the right sides of both equations since they both represent y.

\(-x^2 + 7 = 2x + 4\)

To simplify the equation, we can rearrange it to be in the standard quadratic form:

\(x^2 + 2x - 3 = 0\)

Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. In this case, let's use factoring:

(x + 3)(x - 1) = 0

From this equation, we get two possible solutions:

x + 3 = 0 => x = -3

x - 1 = 0 => x = 1

Now, we substitute these x-values back into either equation to find the corresponding y-values.

For x = -3:

y = 2(-3) + 4

y = -6 + 4

y = -2

For x = 1:

y = 2(1) + 4

y = 2 + 4

y = 6

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