h= -16t^2+24t+5
find the maximum height (represented by h)
and if the thrown object was caught 5 ft in the air, how long was it in the air? (seconds)

The distance between the two points (-5, 7) and (-1, 3) is 4√2 units.

Distance is the sum of an object's movements, regardless of direction.

The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.

Learn how to apply the Pythagorean theorem to find the distance between two points using the distance formula.

The Pythagorean theorem can be rewritten as d=(((x 2-x 1)2+(y 2-y 1)2) to calculate the separation between any two locations.

So, the distance formula:

d=(((x 2-x 1)2+(y 2-y 1)2)

The points we have are: (-5, 7) and (-1, 3)

d=(((x 2-x 1)2+(y 2-y 1)2)

d= (−5−(−1))2 +(7−3)2

d= 16+16

d= 32

d= 4√2

​

Therefore, the distance between the two points (-5, 7) and (-1, 3) is 4√2 units.

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Substitute the given number for the variable in the expression and then simplify the expression using the order of operations.

What is a mathematical expression?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. This mathematical operation may be addition, subtraction, multiplication, or division.

               Term is defined as a constant, a single variable, or a combination of a variable and a constant combined with multiplication or division. Algebra Expression Example: 3x + 9, 5x + 10

What are an equation and an expression?

In mathematics, an expression is a word or phrase that combines variables, operators, and numbers to represent the value of something. Two expressions are assigned equal to one another in a mathematical statement known as an equation.

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Total Twelve jars lorraine can fill with 4.5-gallon p tomatoes quantity and each jar will hold 1. 5 quarts of tomatoes.

We have, The quantity of tomatoes prepared by Lorraine = 4.5 gallon

The quantity of tomatoes which is hold by one jar = 1.5 quarts

As we know quarts and gallon are two basic units of measurement units. Also , we have

Total quantity to fill up in jars = 4.5 gallon

Conversion of measurement units : In terms of quarts units, one gallon quantity = 4 quarts

4.5 gallon quantity = 4 × 4.5 quarts

= 18.0 quarts.

Now, time's to determine how Maany jars Lorraine fill.

1.5 quarts tomatoes quantity filled up = one jar

1 quarts tomatoes quantity will fill = 1/1.5 jar

18 quarts tomatoes quantity will fill or number of jar that lorraine fill = 18× 1/1.5 = 18/1.5

= 180/15 = 12

So, the required number of jars is 12.

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Answer:

12

Step-by-step explanation:

i took the test :)

The length of each scarf is given by the equation A = 4.9 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the length of each scarf be represented as A

Now , the equation will be

The total length of all the scarves = 470.4 inches

The total number of scarves = 8 scarves

So , the length of each scarves = total length of all the scarves / total number of scarves

Substituting the values in the equation , we get

The length of each scarf A = 470.4 / 8

The length of each scarf A = 58.8 inches

Now , 12 inches = 1 foot

So , 1 inch = ( 1/12 ) foot

The length of each scarves A = 58.8 ( 1/12 ) feet

On simplifying the equation , we get

The length of each scarf A = 4.9 feet

Hence , the length of each scarf is 4.9 feet

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Non-linear relationships are those depicted by curved graphs. A curve denotes a variation in the rate (or speed) of a response over time.

Graphs representing reaction rates frequently have curves. A curve denotes a variation in the rate (or speed) of a response over time, while a straight line would represent a constant rate of reaction.

If a curve or straight line becomes horizontal, it means the reaction's rate has reached its maximum level and cannot vary any further.

Lines of best fit can also be used to spot outliers and anomalous data that won't fall along the line of greatest fit. Additionally, lines of best fit may be extrapolated (extended). This enables us to forecast values that are outside the range of the given data using a graph.

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The new [tex]$\Delta R^{\prime} S^{\prime} Q^{\prime}$[/tex] vertices exists [tex]$R^{\prime}(-1,-4) S^{\prime}(3,-5)$[/tex][tex]$Q^{\prime}(1,-3)$[/tex].

When two or more curves, lines, or edges come together, it forms a vertex in geometry. The intersection of two lines to form an angle, as well as the corners of polygons and polyhedra, are vertices according to this definition.

The intersection of two or more line segments or edges is known as a vertex in a shape (like a corner). Vertex is the singular form of the noun. A cube, for instance, has eight vertices, whereas a cone only has one. Although vertices are occasionally referred to as corners when discussing 2D and 3D shapes, vertices is the preferred term.

Given vertices R(4,-1), S(5,3) and Q(3,1) by 90° counterclockwise about the origin

Then we get point (x, y) rotate then R(4,-1) [tex]\rightarrow[/tex] R'(-1,-4)

we got point (y, -x)

[tex]$S(5,3) \rightarrow S^{\prime}(3,-5)$[/tex]

[tex]$Q(3,1) \rightarrow Q^{\prime}(1,-3)$[/tex]

Hence the new [tex]$\Delta R^{\prime} S^{\prime} Q^{\prime}$[/tex] vertices are [tex]$R^{\prime}(-1,-4) S^{\prime}(3,-5)$[/tex][tex]$Q^{\prime}(1,-3)$[/tex].

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The probability of getting either 1 or 6 more than two times is P(T)=121/1296

To find the probability we use the binomial distribution.

Here we have 4 independent experiments. Each time, the sample space is (1,2,3,4,5,6) so the prob of getting a 6 is 1/6.

so p=1/6

prob of coming 6 and q= 1-p = 1-(1/6)=5/6

prob of not coming 6 is 5/6

p= prob of success. here our success event is getting 6

q= prob of failure. here our failure event is not getting 6

no of trials n=4

now using the binomial distribution formula:

ncr(p)^n(1-p)^r

here we want at least two 6, desirable outcomes are two 6 or three 6, or four 6 because at least two 6 doesn't mean that we can't get more than two 6 .

so r in these cases take the value of 2,3,4 respectively.

so for r=2

c(4,2)*(1/6)^2*(5/6)^2

P(A)=  150/1296

for r=3

c(4,3)*(1/6)^3*(5/6)^1

P(B)= 20/1296

for r = 4

c(4,4)*(1/6)^4*(5/6)^0

P(C)= 1/1296

here we will add these prob ..Getting two 6 fulfills our condition so we will stop and calculate the prob and keep it aside

now adding these we get P(T)=P(A)+P(B)+P(C).

(150/216) +(20/216) + (1/216)

P(T)= 171/1296

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y=k/x is the equation represents relation between x and y and value of y is 16 when x is 21.

Two or more expressions with an Equal sign is called as Equation.

Given that y is inversely proportional to x.

When y is 7 and x is 9

y=k/x

k is the proportional constant and y=k/x is the equation connecting y and x.

We have to find the value of y when x is 21

9/7=21/y

Apply cross multiplication

9y=21×7

9y=147

Divide both sides by 9

y=147/9

y=16.3

Hence, y=k/x is the equation represents relation between x and y and value of y is 16 when x is 21.

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Answer: 2 [tex]\sqrt{170}[/tex]

Step-by-step explanation:

Using the Pythagorean theorem, 14^2 + 22^2 = x^2

196 + 484 = x^2

680 = x^2

x = [tex]\sqrt{680}[/tex]

   [tex]2\sqrt{170}[/tex]

Answer:

sqrt317

Step-by-step explanation:

Using the Pythagorean theorem, we know that a^2+b^2=c^2.

So, (14)^2+(11)^2=x^2

We multiply it out, giving us 196+121=x^2
This means that 317=x^2

We square root both sides, giving us x=sqrt317

Answer:

El CO, como el cianuro y el óxido nítrico (NO), inhibe la respiración mitocondrial al unirse al hemo ferroso a3 en el sitio activo de la COX, lo que detiene de manera efectiva la fosforilación oxidativa (16–21).

Step-by-step explanation:

No Solution.

Since, the x-axis (equation y=0) does not intersect y=-7 at any point. The given pair of equations has no solution

Consider the pair of linear equations in two variables x and y.

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Here a1, b1, c1, a2, b2, c2 are all real numbers.

Note that, a12 + b12 ≠ 0, a22 + b22 ≠ 0

1. If (a1/a2) ≠ (b1/b2), then there will be a unique solution. If we plot the graph, the lines will intersect. This type of equation is called a consistent pair of linear equations.

2. If (a1/a2) = (b1/b2) = (c1/c2), then there will be infinitely many solutions. The lines will coincide. This type of equation is called a dependent pair of linear equations in two variables

3. If (a1/a2) = (b1/b2) ≠ (c1/c2), then there will be no solution. If we plot the graph, the lines will be parallel. This type of equation is called an inconsistent pair of linear equations.

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According to data analyst to have contrast is that the color scheme uses a range of different colors.

The graphic depiction of data and information is the focus of the interdisciplinary topic of data and information visualization. When interacting with large amounts of data or information, such as a time series, it is especially effective.

Contrast is the difference in luminance or color that helps you differentiate one thing from another. Contrast in visual perception of the real world is determined by the contrast between an object and other things in the same field of vision in terms of color and brightness.

Color vision deficiency is a diminished capacity to tell some colors apart.

Frequently, the condition is hereditary. Medications and specific eye conditions are additional factors. Men are affected more than women.

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If Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. His monthly payment is $87.31.

Monthly payment can be defined as the money a person received on a monthly basis.

Now let find the monthly payment

Using this formula to find the monthly payment'

M = P(r/12) (1+ r/12)^12t / (1+r/12)^12t -1

Where:

M = Monthly payment = ?

P = Principal

r = Rate

t = Time

Monthly payment = 7900 (0.0429/12) ( 1+ 0.0429/12)^12×10 ÷  ( 1+ 0.0429/12)^12×10 -1

Monthly payment = 7900 (0.003575) ( 1+ 0.003575)^120÷  ( 1+ 0.003575)^120 -1

Monthly payment =7900 (0.003575) ( 1.003575)^120 ÷  ( 1.003575)^120 -1

Monthly payment = $87.31

Therefore the monthly payment is the amount of $87.31.

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The complete question is:

Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.  Suppose that Rich had decided to apply for a private loan rather than a federal loan. He is considering a 10-year lo"an with an interest rate of 5.9% .What will his monthly payments be?

2^x=32

Rewrite 32 as 2^5

2^x = 2^5

Since the bases are the same, the exponents have to be the same

x=5

2^x=32

Take log base 2 on each side

log2(2^x) = log2(32)

x = log2(32)

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The percentage of the adult population that reports having been "sick with a cold" on any given day throughout the year ranges from a little more than 2% to nearly 11%.

What is meant by Population ?

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Multi-step equations are those that must be solved over the course of two or more steps.

An equation that needs to be solved in two or more steps is known as a multi-step equation. There may be a combination of addition, subtraction, multiplication, and division in these questions. For proper equation solving, we could additionally need to combine like terms or apply the distributive property.

Similar to multi-step equations, multi-step inequalities might require combining like terms, the distributive property, and variables on both sides. Again, the only distinction when resolving inequalities is that when multiplying or dividing by a negative number, the sign must be reversed.

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Answer:

line segment

Step-by-step explanation:

the answer is above

A triangle contains three vertices, three sides, and three altitudes. The location where these three sides intersect is known as the orthocenter.

Every triangle has a different position for the orthocenter; for example, an equilateral triangle has the same orthocenter, circumcenter, incenter, and centroid, but other triangles will have a different position.

At Point M is at (1, 3) : The orthocenter is located inside an acute-angled triangle in this scenario.

At Point R is at (3, 9) : The orthocenter is located outside the triangle in the case of an obtuse-angled triangle.

At Point E is at (10, 2) : The orthocenter of a right-angled triangle is located at the right angle's apex.

A triangle is a basic three-sided polygon with three vertices. The "orthocenter of a triangle" is the intersection of a triangle's three altitudes, and it is typically depicted by the letter "H." A line segment drawn perpendicularly from each vertex to the opposite side of a triangle's opposing side is the triangle's height.

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Step-by-step explanation:

the 4th point (vertex) must have the same offset from (-7, -3) as (3, -4) has from (-4, 2).

so, from (-4, 2) to (3, -4)

x has to increase by +7 (from -4 to 3).

y has to decrease by -6 (from 2 to -4).

calculating the same offset from (-7, -3) :

(-7 + 7, -3 - 6) = (0, -9)

so, the 4th vertex is at (0, -9).

Answer: the 4th vortex is at (0, -9)

Step-by-step explanation:

The required value of k will the system of linear equations has infinite number of solutions is 8.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."

Given set of equations is

kx + 4y = k - 4 ...(i)

16x + ky = k ...(ii)

We apply Cramer's rule to find the value of k.

Here,

D = k² - (16 × 4)

= k² - 64

= (k + 8) (k - 8)

D1 = k (k - 4) - 4k

= k² - 4k - 4k

= k² - 8k

= k (k - 8)

D2 = k² - 16 (k - 4)

= k² - 16k + 64

= (k - 8)²

= (k - 8) (k - 8)

For infinite number of solutions, we must have

D = 0 = D1 = D2

⇒ k = 8,

since (k - 8) is the common factor in D, D1 and D2.

∴ the required value of k is 8.

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So, the midpoint of the line segment joining the points (1,2) and (3,4) lies in the Quadrant 2.

To find the midpoint of a line segment, we need to average the x-coordinates and the y-coordinates of the two given points.

The given points are (1, 2) and (3, 4)

The x-coordinate of the midpoint = (x1 + x2)/2 = (1 + 3)/2 = 2

The y-coordinate of the midpoint = (y1 + y2)/2 = (2 + 4)/2 = 3

So the midpoint of the line segment joining the points (1, 2) and (3, 4) is (2, 3)

The point (2,3) is in Quadrant 2 as x is positive and y is positive.

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The equation of the line which passes through (-4, -6) and is parallel to the line y = -3x + 3 is y = -3x -18

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line. Finding the slope between two separate locations and calculating the slope of a line are related tasks. In general, we require the values of any two separate coordinates of a line in order to determine its slope.

Any two different points on a line may be used to compute the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The slope of the given line

y = -3x + 3 is - 3 (from slope intercept form.

So the equation of the line is

y = -3x + c

where c is the y intercept.

The line passes through (-4, -6) so putting this values in the equation we get,

-6 = -3*(-4) + c

⇒ c = -6 - 12 = -18

The equation of the line which passes through (-4, -6) and is parallel to the line y = -3x + 3 is y = -3x -18

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The Round-off of 47 nearest to the 10th is 50. This process is called rounding off the numbers.

The process is used to simplify the numbers so that the number can easily be calculated, this is called round-off. The Round-off process can take place to the nearest 10, 100,1000, and so on. It can also be used for numbers as well as decimal numbers so that we can write the decimal number in simplified form. In round-off, the numbers 0,1,2,3,4 are considered as nearest to the "0" and the numbers 5,6,7,8,9,10 are considered as nearest to the "10" similarly in this question 47 is considered as nearest to the "50".

For example: suppose you have to go 99 km, what will be the round of the distance? = 100 km

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Any triangle's area or surface is equal to the result of multiplying the base by the height by two.

When referring to a math problem or an Expedient X, the letter "x" stands for what we do not understand.

An acutangular triangle might be scaleno, isosceles, or equilátero. A right triangle cannot ever be balanced. It may be an isosceles or an escaleno. Uneven triangulations cannot ever be balanced.

I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1.000 are the seven Latin alphabet letters that make up the roman numeral system.

The perimeter of this cube can be calculated by adding the lengths of each of its four sides.

3x + 4 / 21+35 = 5x-10/35

3x + 4/56 = 5x - 10/35

105x + 140 = 280x - 560

105x - 280x = -560 - 140\x = (-560 - 140)/(105 - 280)\x = 4

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Answer: -8

Step-by-step explanation: 1/4 + 1/4 = 1/2, -8 1/2 + 1/2 = -8

The formula for the distributive property is: a(b+c) = ab + ac.

When performing arithmetic operations, the numbers in mathematics should adhere to the characteristic quality. The many qualities include those that are associative, commutative, distributive, inverse, identity, and so on. The ability to multiply a number by a set of numbers that are added together is known as the distributive property.

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Thus, The formula for the distributive property is: a(b+c) = ab + ac.

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Natalie would have $136 more in her account than Tamika

The formula for compound interest is given by:

A = P (1 + r/n)^(nt)

Where:

A = the final amount (principal + interest)

P = the initial principal or starting amount

r = the annual interest rate (expressed as a decimal)

n = the number of times the interest is compounded per year

t = the number of years for which the interest is calculated.

For Natalie:

P =  $470, r = 8 7/8% = 0.08875, n = 365 and t = 14

A = P (1 + r/n)^(nt)

A = 470 (1 + 0.08875/365)^(365×14)

A = $1628

The formula for compound interest compounded continuously is:

A = P e^(rt)

For Tamika:

P =  $470, r = 8 1/4% = 0.0825, and t = 14

A = 470× e^(0.0825×14)

A = $1492

Difference = $1628 - $1492 = $136

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The axis of symmetry f(x) = x2 is 0 using standard form of axis of symmetry.

Given: y = x2

Using axis of symmetry formula,

x = -b/2a

x = -(0)/2(2)

x = 0

Therefore, axis of symmetry of parabola y = x2 is x = 0.

Formula for Axis of Symmetry

The axis of symmetry formula is used to quadratic equations when the line of symmetry and the equation's standard form are used. The axis of symmetry is a line that splits or bifurcates any object into two equal halves that are mirror images of one another. Any one of the three types of axis—horizontal (x-axis), vertical (y-axis), or inclined line—can be used to divide the objects.

The equation for the axis of symmetry can be shown when the parabola is in one of two forms:

1) standard form

2) Vertex form

1) standard form

Y = ax2 + b x + c is the quadratic equation in standard form.

with real numbers a, b, and c.

The axis of symmetry formula in this instance is x = - b/2a.

2) Vertex form

Y = a (x-h)2 + k is the quadratic equation in vertex form.

where the parabola's vertex is (h, k).

The axis of symmetry equation in this case is x = h.

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The base of the triangle x, with an area of 5 units square is equal to 2 units.

For any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;

Area of triangle = 1/2 × base × height

we have the area as 5 units square and the height as 5 units, so we solve for the base x as follows:

1/2 × x × 5 units = 5 units²

divide through by 5 units;

1/2 × x = 1 unit

multiply both sides by 2;

x = 2 units

Therefore, the base of the triangle x, with an area of 5 units square is equal to 2 units.

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Possible question:

The triangle with an area of 5 units square and height 5 units has the length of its base as x. Solve for x.