Solve the application problem.

Find the area of a rectangular garden that measures 4 feet by 6/7 feet.

A. 3 3/7 ft
B. 9 5/7 ft^2
C. 9 5/7 ft
D. 3 3/7ft^2​

Answer:

See below

Step-by-step explanation:

The area (triangle) marked 'x' in the diagram below

The third term will be 5 in the explicit arithmetic sequence.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

The formula to find the general term of an arithmetic sequence is,

aₙ = a₁ + (n-1)d

The explicit formula of an arithmetic sequence is given in the question as:

F(n) = 3n -4   ....(i)

To determine the term 3.

Substitute the value of n = 3 in equation (i),

T₃ = 3(3) - 4

T₃ = 9 - 4

Apply the subtraction operation,

T₃ = 5

Therefore, the third term will be 5 in the explicit arithmetic sequence.

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New equation will be 4x + 6y = 24, if we multiply the equation 2x + 3y = 12 by -2.

We can rapidly determine the total number of things by multiplying. When multiplying, we'll consider the number of groups with similar sizes and the number of items in each group. A fact involving multiplication is the result of two distinct integers. Additionally, the product is unaffected by the arrangement of the numbers. For instance, 32=6 and 23=6. The distributive, commutative, associative, removes a common factor, and neutral element characteristics of multiplication.

Given,

Equations:

2x + 3y = 12

4x - 7y = -54

Multiplying the top equation by -2:

-2(2x + 3y) = -2(12)

-2(2x) -2(3y) = -24

Product:

-4x - 6y = -24

Taking - common,

-(4x + 6y) = -24

4x + 6y = 24

New equation will be 4x + 6y = 24, if we multiply the equation 2x + 3y = 12 by -2.

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Answer: D because 8 1/5 is smaller than 8 1/3

Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

According to the question,

We have the following information:

In 8 years, Estelle's bank account earned $1,270 simple interest at 2.5%.

Now, let's take the principal amount to be $x.

We know that the following formula is used to find simple interest:

Simple interest = (principal*rate*time)/100

(x*2.5*8)/100 = 1270

Using the cross multiplication method:

20x = 127000

x = 127000/20

x = $6350

Hence, Estelle has deposited $6350 in her bank account when the simple interest was 2.5% per year.

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10.5 miles far upstream can Tom's boat go on the Little River in 1.5 hours.

The relative velocity formula is written as follows. V is equal to  

V → = V A B → + V B C →

Where. VAB is the velocity in relation to A and B, VBC is the velocity in relation to B and C, and VAC is the velocity in relation to A and C.

The current on the Little River is 8 mph.

Tom's boat goes 15 mph in still water.

For Upstream

the Velocity of the boat  = 15 mph - 8mph

                    = 7mph

How far upstream

can Tom's boat go on the Little River in 1.5 hours = 7* 1.5 = 10.5 miles

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According to the questions that are asked in the various Government exams that are held across the nation, the boat and stream concept is one of the most frequently covered subjects.

Boat speed in still water = 1/2 (downstream speed + upstream speed).

Boat's speed in still water equals 1/2 (13+7) = 1/2 × 20 = 10 km/hr.

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Answer:

7/12

Step-by-step explanation:

12/12 - 5/12 = 7/12

Answer: See coordinate graph below.

Step-by-step explanation: The black point is the original point and the red point is the reflected point.

Ordered pair of the reflected point:

A': (1, -4)

Let me know if this is right! :)

Answer:

A denominator of 10: 5/10

A denominator of 100: 50/100

The theorem that will prove similarity of triangle ΔGHS and ΔFES is AAA ( angle angle angle) theorem. The value of FE is 45m.

AAA theorem states that if two triangles have all three corresponding angles equal then they are similar triangles.

In the given figure FE║GE means FE is parallel to GE.

so ∠EFS = ∠HGS

and ∠FES = ∠GHS

also ∠S is common for both.

If two triangles are similar then ratio of corresponding sides are also same.

So, by applying this

[tex]\frac{FS}{GS}[/tex] = [tex]\frac{FE}{GH}[/tex]

54/24 = FE/20

( 54*20 ) / 24 = FE

FE = 45m.

Therefore the triangles will be similar by theorem AAA and the value of FE will be 45m.

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Answer: The answer to this question is $90.

Step-by-step explanation:

The Simple interest is $90.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.

For example, if you borrowed $100 from a friend and agree to repay it with 5% interest, then the amount of interest you would pay would just be 5% of 100: $100(0.05) = $5.

Given:

P= 1500

R = 12%

T= 6 month = 1/2 year

Using, formula of Simple Interest

I = P x R x T /100

I = 1500 x 12 x 1/ 2x100

I = 18000/200

I = 90

Hence, the interest is $90.

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48.4 % percent of all rodents on the ship preferred peanut butter.

acc to our question-

hence,48.4 % percent of all rodents on the ship preferred peanut butter.

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Answer:

4x(2x−1)

Step-by-step explanation:

[tex] {8x}^{2} - 4x[/tex]

Factor out 4.

[tex]4( {2x}^{2} - x)[/tex]

Consider

[tex] {2x}^{2} - x[/tex]

Factor out x.

x(2x−1)

Rewrite the complete factored expression.

=4x(2x−1)

The minimum age of Johnny is 21 as calculated by linear inequality.

Let Johnny 's age be x.

hence bobby's age = (x+5)/2

Now the sum of their ages is over 66 years.

So we will set an inequality to find the minimum age of Johnny.

x + (x+5)/2 > 66

or, 2x + x + 5 > 66

or, 3x > 61

or, x > 20 1/3

Therefore age cannot be fraction hence the minimum age of Johnny is 21 years.

In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On that number line, size comparisons between two numbers are typically done. Different notations can be used to represent various kinds of inequalities, including:

A is smaller than b, as shown by the symbol a < b.

When the expression a > b is employed, it means that a is greater than b.

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Answer:

  see attached (red)

Step-by-step explanation:

You want the graph of the transformed triangle defined by the lines y=x, x=6, y=-1/3x+4 after rotation 270° and reflection across the y-axis.

A graph of the lines shows the vertices of the triangle are ...

  A(3, 3), B(6, 6), C(6,2)

Rotation 270° is described by the transformation ...

  (x, y) ⇒ (y, -x)

Reflection across the y-axis is described by ...

  (x, y) ⇒ (-x, y)

Then the composition of these transformations is ...

  (x, y) ⇒ (-y, -x) . . . . . . . . equivalent to reflection over y=-x

Applying this composition to the triangle vertices, we find its final location to be ...

  A(3, 3) ⇒ A''(-3, -3)

  B(6, 6) ⇒ B''(-6, -6)

  C(6,2) ⇒ C''(-2, -6)

The triangle with these vertices is shown in red in the attachment.

The constant of proportionality of the equation y =−7.48​x is - 7.48.

Proportional relationships are relationships between two variables where their ratios are equivalent

In other words, two variables have a proportional relationship if the ratios of the variables are equivalent.

Therefore, a proportional relationship is one in which two quantities vary directly with each other.

Hence, in mathematical form,

y ∝ x

y = kx

where

y varies directly as the variable x.

In the equation,

k = - 7.48

Therefore, the constant of proportionality  is - 7.48.

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If their combined weight is 175 pounds, The amount of Luna weight is D. 82 pounds.

Let x represent the weight of Cooper

Let x +25 represent the weight of Daisy

Let 3x -20 represent the weight of Luna

Hence,

x + (x +25) + (3x -20) = 175

5x +5 =175

Combine like terms

5x = 175 -5

5x =170

Divide both side by 5x

x = 170/5

x =34

Weight of Luna

3x -20  where x= 34

3(32) -20

= 102 -20

= 82 pounds

Therefore the correct option is D.

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Answer:

Pedro can buy 4 pounds of pears and 3 pounds of apples.

Step-by-step explanation:

Pedro has a total of $18, Apples cost $2 a pound, and Pears cost $3 a pound.

$2×3lb + $3×4lb=$18

Given that Max wanted to test a new dishwasher detergent to see if it was less likely to leave residue on his dishes, the suitable null hypothesis in Max’s experiment will be "the new detergent will leave more residue than the old one".

In statistics, a null hypothesis means a typical theory which suggests that no statistical relationship and significance exists in a set of given single observed variable between the two sets of observed data and measured phenomena.

Therefore, the Option B is correct.

Missing options' The new detergent will leave less residue than the old one. The new detergent will leave more residue than the old one. O The new detergent is equally likely to leave residue compared to the old detergent. The old detergent will leave more residue than the new detergent."

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Graph 2 represents that the function is positive for the entire interval [-3,-2].

Every possible input value results in exactly one output value in a function. "The output is a function of the input," we state. The domain is made up of the input values, while the range is made up of the output values.

Four different graphs for various functions are provided. We must identify the graph that is positive throughout the range [-3,-2].

We make the following observation from the given graphs.

1. The function in graph 1 has a value of 0 at -3 and decreases in value from -3 to -2. As a result, in the provided interval, the function is negative.

2. Graph 2 makes it abundantly evident that the function has a positive value for the entire specified interval.

3. In graph 3, the function shows a negative value entirely in the given interval.

4. In graph 4, the function exhibits both positive and negative values in the given interval and is not positive in the entire interval.

Thus, the function in graph 2 is positive for the entire interval [-3,-2].

The missing image is attached with the answer below,

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Answer:

yes

Step-by-step explanation:

The speed of the current is equal to 8 miles per hour.

Mathematically, speed of any physical object can be calculated by using this formula;

Speed = distance/time

Let the variable c represent the speed of the current in miles per hour. Therefore, the downstream and upstream speed relative to the water would be given by this mathematical expression:

Speed downstream = 14 + c.

Speed upstream = 14 - c.

Additionally, the total time would be given by:

Total time = total distance/speed

Time upstream + time downstream = 6.5 hours

33/(14 - c) + 33/(14 + c) = 7.0

Multiplying both sides of the equation by (14 - c)(14 + c), we have:

33(14 + c) + 33(14 - c) = 7.0(14 - c)(14 + c)

462 + 33c + 462 - 33c = 7.0(196 - c²)

924 = 7.0(196 - c²)

Dividing both sides of the equation by 7.0, we have:

132 = 196 - c²

Speed of the current, c² = 196 - 132

Speed of the current, c² = 64

Speed of the current, c = √64

Speed of the current, c = 8 miles per hour.

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Answer:

300/100%=3%

Step-by-step explanation:

sorry, can't explain.Ihave class tomorrow

It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX

Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:

Diagonal WY bisects angles ZWX and ZYX because:

all corresponding parts of both triangles are congruent. (Option A).

If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.

Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.

If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).

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The expression as power is written as 2¹⁰ and 2^9

The values are

power or exponents as used in mathematics are number written on top of a base number. The power says how many times the base nmber multiplies itself.

8• 2^7

= 2 * 2 * 2 * 2^7

= 2^10

= 1024

16•32

2^5 = 2 * 2 * 2 * 2 * 2

2^4 = 2 * 2 * 2 * 2

16•32 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

= 2^9

= 512

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Answer:

  DNE

Step-by-step explanation:

You want to know the y-intercept of x = -4.

The y-intercept is the point where a graph crosses the y-axis.

The line x=-4 is a vertical line parallel to the y-axis, so does not cross the y-axis.

There is no y-intercept. It does not exist (DNE).

By the sequence of term to term rule the value of : a)  [tex]U_{1}[/tex]= [tex](U_{0})^{2}[/tex] + 3 =[tex]1^{2}[/tex] + 3 = 4    b). [tex]U_{2}[/tex] = [tex](U_{1})^{2}[/tex] + 3 = [tex]4^{2}[/tex] + 3 =19     c). [tex]U_{3}[/tex] = [tex](U_{2})^{2}[/tex] + 3 = [tex]19^{2}[/tex] + 3 = 364 .

Give the first number in the sequence and then describe the pattern of the numbers to get the term-to-term rule. Three is the first number. The rule for terms to terms is "add 4." All of the terms in the series can be located once the initial term and term to

[tex]$$\mathrm{u}_0=1$$[/tex]

The difference is given by[tex]$u_{n+1}=\left(u_n\right)^2[/tex]+ 3

We have to simply put the value in their places to get the proper answer -

a). Put the [tex]$u_{n+1}=u_1$[/tex]

n+1 = 1  ⇒ n = 0

put n = 0in the formula[tex]$\mathrm{u}_{n+1}=\left(\mathrm{u}_n\right)^2[/tex] +3

we wil get

[tex]$$u_1=\left(u_0\right)^2[/tex] + 3 = [tex]1^{2}[/tex] =3 = 4

b). Put the [tex]$u_{n+1}=u_2$[/tex]

n + 1 = 2 => n = 1

put  n=1 in the formula [tex]$u_{n+1}=\left(u_n\right)^2[/tex]+3

we wil get:

[tex]$$u_2=\left(u_1\right)^2[/tex]+3= [tex]4^2[/tex]+3=19

c). Put the  [tex]$u_{n+1}=u_3$[/tex]

n + 1 = 3 => n = 2

Put n=2 in the formula+3

we wil get :

[tex]$$u_3=\left(u_2\right)^2[/tex] +3= [tex](19)^2[/tex] +3 =364

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