Solve for X: 5x + 15 = 28

Check the picture below.

so the parabolic path of the object is more or less like the one shown below in the picture, now this object has an initial of 1240 ft, as it gets thrown from the ski lift, so from 0 seconds is already higher than 1000 feet.

\(h=-16t^2+32t+1240\hspace{5em}\stackrel{\textit{a height of 1000 ft}}{1000=-16t^2+32t+1240} \\\\\\ 0=-16t^2+32t+240\implies 16t^2-32t-240=0\implies 16(t^2-2t-15)=0 \\\\\\ t^2-2t-15=0\implies (t-5)(t+3)=0\implies t= \begin{cases} ~~ 5 ~~ \textit{\LARGE \checkmark}\\ -3 ~~ \bigotimes \end{cases}\)

now, since the seconds can't be negative, thus the negative valid answer in this case is not applicable, so we can't use it.

So the object on its way down at some point it hit 1000 ft of height and then kept on going down, and when it was above those 1000 ft mark  happened between 0 and 5 seconds.

7 raised to the power of 4 equals 2,401, and the exponent we were looking for is 4.

What is meant by power?

Power is a function that represents the number of times a base number is multiplied by itself. It is the rate at which work is done or energy is transferred, measured in watts.

What is meant by exponent?

An exponent is a mathematical notation used to indicate the number of times a quantity is multiplied by itself. It is written as a superscript and represents the power to which a number or expression is raised.

According to the given information

To find the value of the exponent that satisfies the equation 7ˣ = 2,401, we can take the logarithm of both sides of the equation with respect to base 7. This gives us:

log7(7ˣ) = log7(2,401)

x = log7(2,401)

Using a calculator, we can find that log7(2,401) is approximately 3. Therefore, the value of x that satisfies the equation 7ˣ = 2,401 is 3.

Alternatively, we could also use the fact that 2,401 is equal to 7⁴ - 2, which can be written as:

7⁴ - 2 = (7²)² - 2

= 49² - 2

= 2,401

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3900000×18% = 702000

702000÷2500 = 280.8 per share dividend

450×280.8 = 126360

According to the Dietary Guidelines for American 2015, you should limit your fat intake to 25% - 35% of your total calories. The correct option is B.

Food-based dietary guidelines also known as dietary guidelines are intended to serve as a foundation for public food and nutrition policies, health and agricultural policies, and nutrition education programs aimed at promoting healthy eating habits and lifestyles.

Calories are the units of energy released by your body when it digests and absorbs food. The higher the calorie content of a food, the more energy it can provide to your body. When you consume more calories than you require, your body stores the excess calories as fat. Even fat-free foods can be high in calories. In this case, the fay should not be more than 35%.

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Answer:

Rate of change = 3

Step-by-step explanation:

The rate of change is the slope.

Slope = 3

Answer:

7

Step-by-step explanation:

If m = -5 or m = 3, the system of linear equations has no solution.

To determine the values of m for which the system of linear equations has no solution, we need to check the determinant of the coefficient matrix, which is:

| 3 m |

| m+2 5 |

The determinant is

=  (3 x 5) - (m x (m+2))

= 15 - m^2 - 2m

= -(m^2 + 2m - 15)

= -(m+5)(m-3)

So, for the system to have no solution, the determinant must be zero, so we have:

-(m+5)(m-3) = 0

This gives us two values of m: m = -5 and m = 3.

Thus, if m = -5 or m = 3, the system of linear equations has no solution.

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Answer

2x-y <or =-6

2x<or=-6+y

divide both sides by 2

x<or=1/2y+3

5(1/2y+3)+4y>or=20

5/2y+15+4y>or=20

5/2y+4y>or=20-15

13/2y>or=5

divide both sides by 2/13

y>or=10/13

2x-10/13<or=-6

2x<or=-6+10/13

2x<or=-68/13

divide both sides by 2

x< or =-34/13

Answer:

The sum of the interior angle measures of a regular hexagon is 720°.

Step-by-step explanation:

To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

In the case of a hexagon, n = 6. So, we can plug this value into the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:

Sum of interior angles of hexagon = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

The approximately 99.7% of the students have commute distances between 13.9 miles and 24.1 miles, the area within two standard deviation is 95%

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

a) We have:

mean u = 19.0 miles,

\(\rm \sigma = 5.1 \ miles\)

According to the empirical rule, the area between \(\mu - \sigma\) and \(\mu + \sigma\) is 99.7%

\(\mu - \sigma = 19- 5.1 = 13.9\)

\(\mu + \sigma = 19+5.1 = 24.1\)

b) = P(8.8 < X < 29.2)

\(\rm P(\dfrac{8.8-\mu}{\sigma } < \dfrac{X-\mu}\sigma < \dfrac{29.2-\mu}{\sigma})\)

\(\rm P(\dfrac{8.8-19}{5.1} < Z < \dfrac{29.2-19}{5.1})\)

P(-2 < Z < 2)

Thus, the approximately 99.7% of the students have commute distances between 13.9 miles and 24.1 miles, the area within two standard deviation is 95%

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Answer:

1350 ounces

Step-by-step explanation:

If the bacteria doubles by every 3 hours since our initial amount is 135, it will be;

15hours/3hours = 5hrs

then multiply the bacteria by to find the single amount after the period of time

5hrs × 135 ounces = 675 ounces

then multiply this by two to find the doubled amount; 675 × 2= 1350 ounces

Answer:

4320 ounces.

Step-by-step explanation:

The bacteria doubles every 3 hours. Therefore in 15 hours it will double up 5 times.

at t=0 => \(2^{0}\)x135 = 135

at t=3 => \(2^{1}\)x135 = 270

at t=6 => \(2^{2}\)x135 = 540

at t=9 => \(2^{3}\)x135 = 1080

at t=12 => \(2^{4}\)x135 = 2160

at t=15 => \(2^{5}\)x135 = 4320

Answer:

After a translation, the measures of the sides and angles on any triangle would be the same since translation only involves changing the coordinates of the vertices of the triangle.

After a rotation, the measures of the sides and angles of a triangle would also be the same. Similar to translation, the proportion of the triangle is unchanged after a rotation.

After a reflection, the triangle's sides and angles would still be the same since reflection is a rigid transformation and the proportion of the sides and angles are not changed.

Step-by-step explanation:

Rigid transformations, i.e. translations, rotations, and reflections, preserve the side lengths and angles of any figure. Therefore, after undergoing a series of rigid transformations, the side lengths and angle measures of any triangle will be the same as the original triangle, generally speaking, in another position.

Answer:

They are all congruent or equal. The angles and side lengths are preserved through the rigid transformations.

Step-by-step explanation:

That’s what i put

Opposite angles in a cyclic quadrilateral always sum up to 180º.

Angle A is opposite to angle C.

Use the equation above to find the measure of angle C:

As arc DAB is twice as large as measure of angle C:

The length of side AB is about 5.87 units.

The triangle ABC is a right angle triangle. A right angle triangle is a triangle that has one of its angles as 90 degrees.

Therefore, let's find the length AB in the right triangle.

Using trigonometric ratios,

cos 33 = adjacent / hypotenuse

Therefore,

Adjacent side = AB

hypotenuse side = 7 units

cos 33° = AB / 7

cross multiply

AB = 7 cos 33

AB = 7 × 0.83867056794

AB = 5.87069397562

AB = 5.87 units

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Answer:

Step-by-step explanation:

For 2.

a and b both equal to 90

180 - 138 = 42

c = 42

42 + 90 = 132           180 - 132 = 48

d = 48

e = 132

ANSWER

EXPLANATION

Let the number be x

Twelve more than 5times the number means;

Difference between 47 and twice the number means;

Now, equating the two equations we have;

solving for x, we have;

dividing both side by 7, we have;

Therefore the number is

Answer:

0.3504 = 35.04% probability that a worthy proposal is disapproved by both panels

Step-by-step explanation:

We have that:

0.27 = 27% of the time, the proposal is judged worthy of funding by the first panel. So 100 - 27 = 73% probability of being disapproved.

52% of the time, the independent panel reverses the decision. So if the first panel disapproves the funding, 52% probability the second approves the funding and 100 - 52 = 48% probability it does not.

What is the probability that a worthy proposal is disapproved by both panels?

48% of 73%. So

0.48*0.73 = 0.3504

0.3504 = 35.04% probability that a worthy proposal is disapproved by both panels

Answer:

Step-by-step explanation:

You want the tangent and secant of the angle θ the line x-3y=0 makes with the negative x-axis.

The relations between the angle and its trig functions are ...

  Tan = Opposite/Adjacent

  Sec = Hypotenuse/Adjacent

We have shown the angle of interest in a unit circle with the "adjacent" side equal to the radius of the circle (1). Then the values of interest are ...

  tan(θ) = opposite side = 1/3 . . . . . . . equal to the slope of the line

  sec(θ) = hypotenuse = √(1 +(1/3)²) = √(10/9) = (√10)/3

The tangent is 1/3; the secant is (√10)/3.

__

Additional comment

A third-quadrant angle measured from the +x axis has a negative secant. The tangent is positive there.

Since this angle is measured from the -x axis, it isn't clear whether it is supposed to be considered a 3rd-quadrant angle or not. For the given acute angle θ shown, the trig functions are both positive. YMMV

If the length of the rectangle be (3x+2) units and width (4x+10)units then the area of the rectangle be \($x=-\frac{2}{3}, x=-\frac{5}{2}$$\).

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane.

A rectangle's sides determine its area. In essence, the length and breadth of the rectangle multiplied together gives the area of the rectangle.

Let the length of the rectangle be (3x + 2) units and width of the rectangle be (4x + 10)units.

Area of rectangle = length × breadth

= (3x +2) × (4x +10)

simplifying the above equation, we get

= (3x) × (4x +10) + 2(4x +10)

= 12x² + 30x +8x +20

12x² + 38x + 20 = 0

simplifying the above equation, we get

By using quadratic equation, then

\($x_{1,2}=\frac{-38 \pm \sqrt{38^2-4 \cdot 12 \cdot 20}}{2 \cdot 12}$$\)

simplifying the above equation, we get

\($$\begin{gathered}x_{1,2}=\frac{-38 \pm 22}{2 \cdot 12}\end{gathered}$$\)

Separate the solutions, we get

\($$\begin{aligned}& x_1=\frac{-38+22}{2 \cdot 12}, x_2=\frac{-38-22}{2 \cdot 12} \\& x=\frac{-38+22}{2 \cdot 12}:-\frac{2}{3} \\& x=\frac{-38-22}{2 \cdot 12}:-\frac{5}{2}\end{aligned}$$\)

The solutions to the quadratic equation are:

\($x=-\frac{2}{3}, x=-\frac{5}{2}$$\)

The complete question is:

Find the area of rectangle with length (3x+2) units and width (4x+10)units.

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Answer:

#1  (0,-4)

#2  (5,0)

#3  (3,1)

Step-by-step explanation:

#1.  (-3, 2) (0, y)  slope = -2

slope = rise/run    therefore slope = -2/1  or down 2 and over 1

so from -3 to 0 you are going over 3 units (or 3 times)  Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6      so 2-6 = -4

so y intercept (b)  = -4 0r (0,-4)

#2   (-7,-4)  (x,0)  slope (m) = 1/3   -7+12=5    x=5

#3   (4,-3)   (x, 1)   slope (m) = -4   (4/-1)   Moving one unit in slope  means

-3=4=1 for Y and 4-1=3 for X    therefore the point is (3, 1)

Step-by-step explanation:

sorry tried but dont know

The Original price of barbecue grill is 96.325.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

The final cost  barbecue grill is $79.95.

Discount = 25%

and Tax = 8%

let the original price be x

x- 0.25x + 0.08x = 79.95

0.83x = 79.95

x= 79.95/0.83

x = $96.325

Hence, the Original price of barbecue grill is 96.325.

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Answer:

Sample space = 216 elements

a) P = 25/72

b) P = 91/216

Step-by-step explanation:

If each die has six possible values, the number of possible outcomes for three dice is 6^3 = 216 possible outcomes

a)

If we want exactly one die to be red, we have that one die is red (probability of 1/6) and the other two are not red (probability of 5/6), and the red die can be any of the three dice (combination of 3 choose 1), so the probability is:

P = C(3,1) * (1/6) * (5/6) * (5/6) = 3 * 25/216 = 75/216 = 25/72

b)

To find the probability of at least one die is red, we can find the probability of all dice not being red, and then find the complement of this probability (1 - P).

The probability of one die not being red is 5/6, so we have:

probability of all dice not being red = (5/6)^3 = 125/216

probability of at least one die being red = 1 - 125/216 = 91/216

Option B is correct. Yes, (9, 22) is a solution to the inequalities and the measurements will fit in the space.

The formula for calculating the perimeter of the rectangular fence is expressed as:

A = 2(L + W) where:

L is the length

W is the width

If Jamie can afford at most 70feet to build a rectangular fence is expressed as:

2L + 2W ≤ 70

We are to check if the garden measure 9 feet by 22 feet. To do this we are to substitute L = 9 and W = 22 into the formula to check if the result will be less than 70

On substituting:

= 2(9) + 2(22)

= 18 + 44

= 62 feet

Since 63 feet is less than 70 feet, hence we can conclude that Yes, (9, 22) is a solution to the inequalities and the measurements will fit in the space.

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Answer:

The third side has a length of 4x² + x - 16

Step-by-step explanation:

We can solve this by taking the value given for the perimeter, and subtracting the values of the other two sides:

3x² + 8x - 9 - (x² + 11x + 5) - (-2x² - 4x + 2)

= 3x² + 8x - 9 - x² - 11x - 5 + 2x² + 4x - 2

= (3 - 1 + 2)x² + (8 - 11 + 4)x - (9 + 5 + 2)

= 4x² + x - 16

The test statistic (37.96) is greater than the critical value (11.345), we can reject the null hypothesis and conclude that there is a significant relationship between admission date and birthday.

The test statistic for this test is calculated by summing the squared differences between the observed and expected frequencies in each category, divided by the expected frequency in that category. This formula is:

X² = ∑(observed - expected)² / expected

The degrees of freedom for this test are equal to the number of categories minus one (4-1=3). Using a significance level of 0.01, the critical value for this test is 11.345.

To calculate the test statistic for this sample, we first need to calculate the expected frequencies. Each category should have an expected frequency of 196/4 = 49.

Category 1: expected frequency = 49, observed frequency = 12

Category 2: expected frequency = 49, observed frequency = 22

Category 3: expected frequency = 49, observed frequency = 65

Category 4: expected frequency = 49, observed frequency = 97

Using the formula above, we can calculate the test statistic:

X² = [(12-49)²/49] + [(22-49)²/49] + [(65-49)²/49] + [(97-49)²/49]

X² = 37.96

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Complete Question:

An article focuses on the existence of any relationship between the date of patient admission for treatment of alcoholism and the patient's birthday. Assuming a 365-day year (i.e., excluding leap year), in the absence of any relation, a patient's admission date is equally likely to be any one of the 365 possible days. The investigators established four different admission categories: (1) within 7 days of birthday, (2) between 8 and 30 days, inclusive, from the birthday, (3) between 31 and 90 days, inclusive, from the birthday, and (4) more than 90 days from the birthday. A sample of 196patients gave observed frequencies of 12, 22, 65, and 97 for categories 1, 2, 3, and 4, respectively. State and test the relevant hypotheses using a significance level of 0.01. Calculate the test statistic.

According to the concept of algebraic expression and arithmetic, the correct answers are A) Number of adults = N - 25. B) Number of adults when N = 124: 124 - 25 = 99

A) Let's denote the number of children as N. Since there are 25 fewer adults than children, the number of adults can be expressed as N - 25.

B) If there are 124 children, we substitute N with 124 in the expression from part A. Thus, the number of adults would be 124 - 25 = 99.

To arrive at these answers, we used the given information that there are "N" children and 25 fewer adults than children. By substituting the value of N, we determined the number of adults in terms of N and then calculated the specific number of adults when N is equal to 124.

Note: The given question is incomplete. The complete question is:

Some adults and children are watching a musical. there are 'N' number of children. There are 25 fewer adults than children.

A) find the number of adults in terms of 'N'.

B) if there are 124 children how many adults are there?​

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