Please help me with this question

Answer:

For x² + kx + 16/9 to be a perfect square, k should be equal to 8/3

Step-by-step explanation:

If x² + kx + 16/9 is a perfect square then it must satisfy the formula of (a + b)² i.e. equal to a² + 2ab + b².

So, first we will form a equal that looks similar to the formula:

[tex] \rm \implies {x}^{2} + kx + \dfrac{4 \times 4}{3 \times 3} \\ \\ \rm \implies {x}^{2} + kx + { \bigg( \dfrac{4}{3} } \bigg)^{2} [/tex]

Now by comparing we get,

[tex] \rm \implies k \cancel{x} = 2 \times \cancel{x}\times \frac{4}{3} \\ \\ \rm \implies k = \dfrac{8}{3} [/tex]

Without decimal, 4 canisters need to buy for making 5 meatloafs for party or if answer in decimal values needed then it is 3.333 canisters.

From the provided data, we have

number of meatloafs = 5

Here we have need the cup measurements the number of meatloafs made per recipe and the net weight of canister.

net weight of the contents of 1 canister = 15 ounces

1 cup = 8 ounces

1.25 cups = 10 ounces

10 ounces of breadcrumbs makes 1 meatoafs.

but we made 5 meatloafs so, for 5 meatloaf needed breadcrumbs = 5×10

= 50

If we consider 4 canisters then

15ounces × 4 canisters = 60 ounces which are 10 more than the needed ( > 50 ounces.

and if we are consider 3 canisters then

15 ounces × 3 canisters = 45 ounces which is not enough.

So, we need 4 canisters of breadcrumbs and we will have 2/3 of a canister left over.

approximately 3.333 is a value of needed canisters in decimals values. If decimal values are not need ,i.e, whole are canisters are not partial then 4 canisters is right .

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Complete question:

you're planning on making 5 meatloafs for a party. you go to the store to buy breadcrumbs, and see they are sold by the canister. how many canisters do you need to buy?

First, determine what information you need to answer this question, then click here to display that info (along with other info).

How much breadcrumbs does the recipe call for? It calls for 1 1/4 cups of breadcrumbs. How many meatloafs does the recipe make? It makes 1 meatloaf.

How many servings does that recipe make? It says it serves 10.

How big is the canister? It is cylindrical, 3.5 inches across and 7 inches tall.

What is the net weight of the contents of 1 canister? 15 ounces.

How much does a canister cost? $2.39

How much does a cup of breadcrumbs weigh? I'm not sure, but maybe something from the nutritional label will help.

The expressions 25x−(6x+12) and (25x−6x)+12 are equivalent expressions.

In this question we have been given two expressions 25x−(6x+12) and (25x−6x)+12

We know that the associative property of addition.

For any real numbers a, b, c

a + (b + c) = (a + b) + c

Consider an expression,

25x − (6x + 12)

= (25x - 6x) + 12                   ..........(Associative property)

Therefore, the expressions 25x−(6x+12) and (25x−6x)+12 are equivalent expressions.

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The volume of prism with 1 layer=16 inch³; The volume of prism with 3 layer=48 inch³;The volume of prism with 5 layer=80 inch³;The volume of prism with 7 layer=112 inch³.

The total amount of space an object occupies in three dimensions is indicated by its volume. The term "capacity" describes something's ability to hold, absorb, or receive by an object .

Here,

Since each layer is of 1 inch.

So the volume of first prism,

=4*4*1

=16 inch³

When there is 3 layer, so the height is 3 inch,

=4*4*3

=48 inch³

When there is 5 layer, so the height is 5 inch,

=4*4*5

=80 inch³

When there is 7 layer, so the height is 7 inch,

=4*4*7

=112 inch³

The volume of a prism with one layer is equal to 16 inch³; with three layers, it is 48 inch³; with five layers, it is 80 inch³; and with seven layers, it is 112 inch³.

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Sherry needs to invest 2000$ in mutual fund and 13200$ in bond to earn 548$ at the end of the year.

A percentage is just one of the many ways that a number, ratio, or fraction can be expressed. It is a number or ratio expressed as a fraction of 100.

Given:

Sherry has 15200$ to invest in mutual funds and in bonds.

Sherry has selected a mutual fund that earns 1% a year and a bond that earns 4% a year.

Here we need to find how much does she need to invest in each type of account if she wants to earn 548 at the end of the first year.

Here we have total amount = 15200$

So, let us consider x be the amount invested in mutual funds, then the amount invested in bonds will be 15200 - x.

It can be written in the following matrix

[x     15200-x ]

We know that the total amount earned at the end of the year is 548.

So, it can be written as

amount invested x percentage = final amount

[tex]\left[\begin{array}{cc}x&15200-x\\\\\end{array}\right][/tex]*[tex]\left[\begin{array}{ccc}1/100\\4/100\\\end{array}\right][/tex] = 548

We can simply it as

[x*1/100 + (15200 - x)*4/100] = 548

⇒ x/100 + 60800/100 - 4x/100 = 548

⇒ x + 60800 - 4x = 54800

⇒ -3x = 54800 - 60800

⇒ -3x = -6000

⇒ x = 2000

⇒ 15200 - 2000 = 13200

Therefore, Sherry invests 2000$ in mutual funds and 13200$ in bond to earn 548 at the end of the year.

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The show is 1 hour 4 minutes long.

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:

Ben watched 3/8 of his television show.

There are still 40 minutes left.

let the show be x long.

So, 3/8x + 40 = x

x- 3/8x= 40

5x/8 = 40

x= 320/5

x= 64 minutes

x= 1 hour 4 minutes

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Answer:

1-10.

Step-by-step explanation:

The fraction of the entire square that is shaded is 2/5.

A square is a two dimensional object that four sides that are of equal length. This means that the dimensions of the length and the width have the same value. A square has two diagonals that bisect each other at 90°.

A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above and the denominator is the number below. An example of a fraction is 1/2.

Fraction = number of shaded squares / total number of squares

16 / 40

When expressed in its simplest form, the fraction becomes 2/5.

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Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.

A mathematical assertion in which you use mathematical symbols to demonstrate that two sums are equal.

As per specified data-

Let 'x' be the number of weeks required to complete the amount.

The equation becomes.

378 = 15.75x

For the number of week required.

x = 378/15.75

x = 24

Thus, Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.

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The total cost of the shirts that have same cost when x=5 is,

c=70

A mathematical equation is a formula that joins two expressions and expresses their equivalence using the equals symbol (=). The definitions of the word equation and its cognates in different languages may differ slightly.

The entire cost is c

c = 40 + 6x

c = 20 + 10x

The quantity of shirts is x.

Via utilizing one of the equations to solve for one of the variables and then substituting that variable's value into the other equation, you can solve by substitution.

40+6x=20+10x

4x=20

x=5

You would solve for c in the first equation in this problem.

40+6x where x=5 then,

c=70

Since it has already been solved for c, all that is left to do is swap out c with its equivalent in the second equation.

20+10x where x=5 then,

c=70

Therefore, the total cost of the shirts that have same cost is c=70 when x=5.

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Answer:

A)- 65

B)- 25

c)- 25

To find A- pay attention to the bottom..add 60+55 then subtract that from 180

yu get 65..now we know that 65+90= 155 subtract that from 180 you get 25. so now we have B..B and C are congruent meaning they are equals

hope this helps

Answer:A - 200

B - 1 Class Ring and 796 yearbooks

C - No, they would come up short 2800 dollars

Step-by-step explanation:

Answer: [tex]g(2n)=4n^2 -8n[/tex]

Step-by-step explanation:

Substituting [tex]2n[/tex] for [tex]x[/tex],

[tex]g(2n)=(2n)^2 -4(2n)\\\\g(2n)=4n^2 -8n[/tex]

The number of large boxes of porridge that William bought, using a system of equations, was of:

8.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of the problem.

For this problem, the variables are defined as follows:

William buys 5 small boxes of oat porridge, hence:

x = 5.

The total weight of his purchase is of 6825 grams, hence, considering the weight of each box, the following equation is built:

325x + 650y = 6825.

It is already stated on the problem that x = 5, hence the value of y can be obtained as follows:

325(5) + 650y = 6825.

y = (6825 - 325(5))/650

y = 8 large boxes.

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The rate of change of volume is 418.6  inch³/s .

Rate of increase of radius with time is ( dr/dt ) = 5

rate of decrease of height with time is (dh/dt ) = -3

volume of a cone is given by (V) =  [tex]\frac{1}{3} \pi r^{2}h[/tex]

Now the rate of change of volume  with respect to time is given by dV/dt

∴ dV/dt = d( [tex]\frac{1}{3} \pi r^{2}h[/tex]) / dt

dV/dt =  [tex]\frac{1}{3} \pi (2rh\frac{dr}{dt} + r^{2}\frac{dh}{dt} )[/tex]

value of radius and height when volume is changing are :

r = 20 inches

h = 40 inches

dV/dt = [tex]\frac{1}{3} \pi ([/tex] 2×20×40 ×5 - [tex]20^{2}[/tex]×3 )

dV/dt = [tex]\frac{1}{3} \pi[/tex](1600 - 1200)

dV/dt = (400/3) 3.14

dV/dt = 418.66 inch³/s

So the rate of change of the volume is 418.66 inch³/s.

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The speed of 213.25 mph  is the red car actually traveling along the road.

What is speed?

The definition of speed is the pace of movement of an object (covering a particular distance). It defines only the magnitude and not the direction, making it a scalar quantity.

The meter per second (m/s) unit of speed is taken from the SI.

let distance between the police and red cars = h

distance from the red car to a point horizontal to the police car = a

distance from from the road to the police car = b

=>[tex]h^2=a^2+b^2[/tex]

take the derivative with respect to time

=>hh' = aa' + bb' b'=0

=>174.64(75) = 90a'

=>a' = 174.64(75)/90 = 145.4ft/sec

=>145.4ft/sec = 145.4(5280)/60^2 = about 213.25 mph

Here ,1 mile = 5280 feet

=>1 hour = 60 minutes x 60 seconds = 3600 seconds

=>1 mile per hour = 5280 feet per 3600 seconds

=>1 foot per second = 5280/3600 mph = 1.4666...mph

=>145.4x 1.4666... = 213.25 mph

Hence 213.25 mph speed  is the red car actually traveling along the road.

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The equation of line t in slope intercept form is 5y - 3x = -1

The equation of line s is y=3/5x + 2/5

This is in the slope intercept form

y = mx + c

where m represents the slope of the line

The slope of the line  y=3/5x + 2/5 is 3/5

The slope of two parallel line is same

The slope of line t is 3/5, it passes through the points (2, 1)

The equation of the line is

y - y₁ = m(x - x₁)

y - 1 = 3/5 (x - 2)

5y - 5 = 3x - 6

5y - 3x = -6 + 5

5y = 3x  -1

y = 3/5 x - 1/5

Therefore, the equation of line t in slope intercept form is 5y - 3x = -1

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Answer:

The red symbol drawn over ∠2 and ∠3 indicates that the two angles total 90°. Therefore:

[tex]m\angle{2}+m\angle{3}=90^{\circ}[/tex]

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

Mixture word problems require you to combine two or more separate items, and then calculate some quantity of the resulting mixture (such as a percentage, price, or number of liters, for example). There will always be some type of "rate," like miles per hour or price per pound. Mixtures are substances that contain two or more distinct substance categories. To separate them, utilize physical tools. Examples include air, different gases, a mixture of sugar and water, a solution of salt and water, and so on.

Given,

A pharmacist wants to mixture of 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution.

Equation:

X + y = 119

y = 119 - x

0.40x + 0.12y = 119 of 0.32

0.40x + 0.12y = 38.08

Using y = 119 -x

0.40x + 0.12(119 - x) = 38.08

0.40x + 14.28 - 0.12x = 3808  Eq(2)

0.28x = 23.8

x = 85

y = 119 - 85

y = 119 - 85

y = 34

Equating values in equation (2),

0.40(85) + 0.12(34)

34 + 4.08

38.08

A pharmacist wants to mix a 40 % saline solution with a 12% saline solution to get 119 ml. of a 32% saline solution. He used 85 ml of 40% saline solution and 34 ml of 12% saline solution.

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Answer:26.5

Step-by-step explanation:

The equation of the line that passes through the points (6,2) and (7,1) is y = -x+8

The points are

(6,2) and (7,1)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the function.

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the value in the equation

The slope of the line = (1-2) / (7-6)

= -1/1

=-1

The point slope form is

[tex](y-y_1)=m(x-x_1)[/tex]

Choose one point and substitute the values in the equation

y-2 = -1(x-6)

y-2 = -x+6

Move the 2 to right hand side of the equation

y = -x+6+2

y = -x+8

Hence, the equation of the line that passes through the points (6,2) and (7,1) is y = -x+8

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A person must have a score of 126.26 to qualify Mensa.

it is given that,

Mean [tex](\mu) = 100,[/tex]

Standard deviation [tex](\sigma) = 15[/tex].

A person must score in the upper 4% of the population,

100% - 4% = 96% = 0.96

P(X < Xo) = 96% = 0.96

P(X < 1.7507) = 0.96          ....................................using the Normal distribution table,

Or, when the Invnorm function is used, Invnorm(0.96) = 1.7507

Therefore, The required value of X is,

[tex]Z = \frac{(X - \mu )}{ \sigma }[/tex]

1.7507 = (X - 100) / 15

X - 100 = 26.26

X = 100 + 26.26

X = 126.26

thus, the score a person must have to qualify Mensa is 126.26.

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[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{8}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~3 - 8~~)^2 + (~~8 - 2~~)^2} \implies PQ=\sqrt{( -5 )^2 + ( 6 )^2} \\\\\\ PQ=\sqrt{ 25 + 36 } \implies PQ=\sqrt{ 61 }\implies PQ\approx 7.8[/tex]

This graph represents a continuous function. Also, the domain of this function is 0 ≤ x ≤ 6 and the range of this function is 20 ≤ y ≤ 200.

Mathematically, a range can be defined as the set of all real numbers that is associated with the elements of a domain. This ultimately implies that, a range simply refers to the set of all possible output numerical values which are shown on the y-coordinate (y-axis) of the graph of a function.

In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined and it connects with the range.

This ultimately implies that, a domain is the set of all possible input numerical values to a function. Additionally, the domain of the graph of a function comprises all the input numerical values which are shown on the x-coordinate (x-axis).

From the information provided, the total weight of the barbell and plates in pounds is represented by this function:

f(x) = 30x + 20.

When x = 6, we have:

f(6) = 30(6) + 20.

f(6) = 180 + 20

f(6) = 200 lb.

Therefore, the domain is equal to 0 ≤ x ≤ 6 while the range of this function is 20 ≤ y ≤ 200.

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Answer: 16

Step-by-step explanation:

The first triangle has an area of [tex]\frac{1}{2}(7)(2)=7[/tex].

The second triangle has an area of [tex]\frac{1}{2}(6)(3)=9[/tex].

Adding these areas together yields an area of 16.

Answer:

5/9

Step-by-step explanation:

The result of a spin is either an odd number or an even number.  The two outcomes are complements.

If the probability of getting an odd number is 4/9, the probability of getting an even number is  1 - 4/9 = 5/9.

The events “blonde hair” and “brown eyes” are not independent.

What are independent events?

The term "independent events" refers to those whose occurrence is not reliant on another event.

When two events A and B are independent then the intersection of the two events is equal to zero. i.e. They do not have any element in common.

But from the given table we can see that the intersection of the events of  "blonde hair" and "brown eyes" exists.

Therefore, the events "blonde hair" and "brown eyes" are not independent.

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Pineapple originally gather is 27

Quadratic equations are what?

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

Step-by-step explanation:

Working Backward strategy

Remaining Pineapple = 3
[tex]\frac{2}{3}x+3=x[/tex]
x=9
Remaining Pineapple now = 9

ATQ  [tex]\frac{1}{4}x+9=x[/tex]

x = 12
Remaining Pineapple now = 12
ATQ  [tex]\frac{x}{3}+12=x\\[/tex]
x=18
Remaining Pineapple now =18
ATQ    [tex]\frac{x}{3}+18=x[/tex]
x=27
hence The ans is 27

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Answer:

Step-by-step explanation:

Ok:

1. Caculate all of the two triangles' angles

First triangle on the left!

50+90= 140+40= 180degrees

So: Angles for first one are 50,90,40

Second Triangle on right

51+90= 141+39= 180degrees

So: Angles for second one are 51,90, 39

2. Subtract the corners added together from 180 degrees

40+39= 79 degrees

180-79=101 degrees

3. Answer: Choice B or 101 degrees!