Please solve the equation
[tex]5 {}^{2x + 1} - 26(5 {}^{x} ) \: + 5 = 0[/tex]
​

This week 41 students showed up to the archery class that cannot be broken into multiple groups of equal sizes.

Prime numbers are numbers that cannot be divisible by any other numbers besides 1 and itself. Between 30 and 50, there are 4 prime numbers, which are 31, 37, 41, and 43. So, these prime numbers cannot be divided into equal sizes of multiple groups. But by adding 2 (If Betty and Wilma join the students) in 31, 37, and 43 we get composite numbers that can be divided into multiple groups of equal sizes.

So, 41 students showed up to the archery class this week and as 41 is a prime number, Betty and Wilma could not break the archers up into groups of equal size, and even if Betty and Wilma joined the students there will be 43 archers which even is a prime number and thus cannot be divided.

41 is the only possible number of students between 30 and 50 which cannot be broken into groups of equal sizes even if Betty and Wilma join the archers.

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Step-by-step explanation:

The formula D = 401t + 5940 can be used to approximate the total average credit card debt in a U.S. household (in dollars) t years after 1995. Use this formula to predict what the total average credit card debt will be in the year 2028.

2028 - 1995 = 33 years, so t = 33

D = 401t + 5940

D = 401(33) + 5940

D = 13,233 + 5940  

D = 19,173

Answer: In the year 2028, the total average credit card debt for a U.S. household will be $19,173

154.5

Step-by-step explanation:

left triangle and right triangle has the same degree.

M to Q 107/2 = P to R 53.5

O to N 110/2 = R to Q 55

Find X

M to N 92/2 = P to Q 46

Perimeter- 53.5+ 55+ 46= 154.5

Answer:

Step-by-step explanation:

5 + 4 × 3 - 2

9 × 3– 2 =

27–2 = 25

Step-by-step explanation:

the picture is very blurry.

I understand we need the y-intercept in every case and then move the pictures into the empty frames based on sorting these numbers from lowest to highest.

the y-intercept is the point, where a function/curve intersects the y-axis.

in other words, it is the y-value of the point, where x = 0.

so,

1. 0

2. -6

3. looks like -2 (again, very blurry)

4. looks like +2

5. +6

6. +4

sorting these gives us

2. -6 3. -2 1. 0 4. +2 6. +4 5. +6

therefore the 6 frames need to receive the original pictures in that sequence.

Answer:

These fractions are equivalent, with 4/7 being the simplest form of both.

Step-by-step explanation:

8/14 can be simplified to 4/7 also by dividing both sides by two :)

Answer:

vyfyxfrr6c*"8&"; hxh6 byhd,tf7zg5gzyfe55eE4E45w522

Step-by-step explanation:

6dyxg9yyfz6t bztrfr 4.Sabina the tortoise is an 56,123 way of Policy for recharge of the angles and tricks of Policy in order for me and I have a wonderful experience and a

Answer:

2x^2

__________

x+3 | 3

2x + 2

3

- 2 x - 3

_________

R = - 1

Answer:

5/8 - 1/4 = 3/8

Step-by-step explanation:

1 x 2 = 2, 4 x 2 = 8, so we're left with 2/8

Answer:

3/8

Step-by-step explanation:

5/8 - 1/4

to be able to compare fractions or add/subtract them directly, we need to bring them all to the same denominator (the bottom part of the fractions).

it is usually easier to bring the smaller to a larger number than the other way around, because of the existing numerators (the top part of a fraction).

since we are dealing with fractions (divisions !), the best way to manipulate them is by multiplying or dividing them by a factor.

so, what do we need to multiply with 4 to get 8 (the other denominator) ?

2, as 4×2 = 8.

aha.

but now careful, we cannot just multiply the denominator by 2. that would change the value of the whole original fraction.

we have to multiply denominator AND numerator by the same factor. that way the original value of the fraction remains the same, because we are essentially multiplying the whole fraction just by 1.

so,

1/4 × 2/2 = 2/8

and now we can easily use it in a calculation with other 8ths :

5/8 - 2/8 = 3/8

A rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

In the given question we have to find the maximum area of the rectangular area.

Liana has 3200 yards of fencing to enclose a rectangle.

So we know that the perimeter of rectangle is

P= 2(l+b)

Let length of the rectangle is x yards and width is y yards.

So the equation should be

2(x+y) = 3200

Divide by 2 on both side we get

x+y = 1600................(1)

As we know the area of rectangle is

A = xy

From the equation the value of y is 1600-x.

Now putting the value of y

A = x(1600-x)

A = 1600x-x^2

On differentiating

dA/dx = 1600-2x

Putting dA/dx=0

1600-2x=0

Subtract 1600 on both side we get

-2x= -1600

Divide by -2 on both side we get

x = 800 yards

Now putting the value of x in the y=1600-x

y=1600-800

y=800 yards

So the maximum area is

A= 800*800

A= 640,000 square yards

Hence, a rectangle that maximize the enclosed area has a length 800 yards and width is 800 yards. The maximum area is 640,000 square yards.

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The number of buttons A will be 11. And the number of buttons B will be 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

A container of buttons contains a similar number of each kind of button it contains 220g of buttons. The weight of the button is given as,

Let x be the number of each button. Then the equation is given as,

8x + 12x = 220

20x = 220

x = 11

The number of buttons A will be 11. And the number of buttons B will be 11.

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The range of scores that Marjorie's can receive in the final exam to earn a C in the course is 67 to 82  .

in the question ,

it is given that

the Marjorie's score in the tests are 67 , 78 , 75 , 78 .

let the score in the final exam be "x"

it is given that the final exam score is worth 6 test scores , which means

the score in final exam is = 6x

and the total number of tests = 6+4 = 10

given that to get the grade C minimum average is = 70

that is  (67 + 78 + 75 + 78 + 6x)/10 = 70

67 + 78 + 75 + 78 + 6x = 700

298 + 6x = 700

6x = 700 - 298

6x = 402

x = 402/6

x = 67

given that to get the grade C maximum average is = 79

that is  (67 + 78 + 75 + 78 + 6x)/10 = 79

67 + 78 + 75 + 78 + 6x = 790

298 + 6x = 790

6x = 790 - 298

6x = 492

x = 492/6

x = 82

the range of scores is 67 to 82 .

Therefore , The range of scores that Marjorie's receive in the final exam to earn a C in the course is 67 to 82  .

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The missing angle is as follows:

When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.

In other words, two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal.

Therefore, the triangle ABC is congruent to EDF.

Hence,

∠A = ∠D

∠B = E

∠C = ∠F

Therefore,

m∠C = x

m∠F = 2x - 30

Hence,

m∠C = m∠F

x = 2x - 30

x - 2x = -30

-x = -30

x = 30

m∠C = 30 degrees

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Answer:

182 minutes

Step-by-step explanation:

0.09x+5=21.38

         -5.   -5

0.09x=16.38

/0.09.   /0.09

  X=182

182 minutes

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Answer:

a = 1

Step-by-step explanation:

Given equation,

→ 7(5a - 4) - 1 = 14 - 8

Now the value of a will be,

→ 7(5a - 4) - 1 = 14 - 8

→ 35a - 28 - 1 = 6

→ 35a - 29 = 6

→ 35a = 6 + 29

→ a = 35/35

→ [ a = 1 ]

Hence, the value of a is 1.

For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years.

As given in the question,

The formula given to us is A = P[tex]e^{rt}[/tex] where

A = accumulation value

P = principal money

t = time period

r = interest rate compounded

P = 9500

A = 2*9500

r = 0.12

By applying it in the given formula we get

19000 = 9500 * [tex]e^{0.12t}[/tex]

2 =    [tex]e^{0.12t}[/tex]

Take natural log on both sides

㏑(2) = 0.12t

0.6931 = 0.12t

t = 5.775

Therefore , For the given accumulated value, principal money and interest rate compounded continuously the time t is equal to 5.8 years after rounding it off to one place after decimal.

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The length of the base edge of the given square pyramid is 3.67 feet.

What is the Surface Area?

The sum of all an item's faces makes up the surface area of a three-dimensional object. When wrapping, painting, and finally creating things to get the finest possible design, we apply the idea of surface areas of various items in real life.

What is a Square Pyramid?

Steps to Calculate the Base Edge Length of Square Pyramid

The formula for surface area of square pyramid is given by, [tex]SA=a^{2} +2a\sqrt{\frac{a^{2} }{4}+h^{2} }[/tex],    -----(1)

where [tex]a[/tex] is the length of the base edge and [tex]h[/tex] is the square pyramid height.

In the question, it is given that the surface area of the square pyramid is 96 square feet.

The height of the square pyramid is two-thirds of the base edge length.

[tex]\implies h=\frac{2a}{3}[/tex]  ------(2)

Now substituting the given values in (1), we get

[tex]96=a^{2} +2a\sqrt{\frac{a^{2} }{4}+(\frac{2a}{3} )^{2} }\\\implies 96=a^{2} +2a\sqrt{\frac{a^{2} }{4}+\frac{4a^{2} }{9} }[/tex]

Simplifying, we get

[tex]96=a^{2} +2a\times 0.834a^{2} \\\implies 96=a^{2} +1.668a^{3} \\\implies 1.668a^{3}+a^{2} -96=0[/tex]

Finally, we get the value of [tex]a=3.67[/tex] feet.

Therefore, the base edge length of the given square pyramid is 3.67 feet.

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Answer:

Step-by-step explanation:

weight of 1 sheet= (28/7)g

                            =4g

1.5kg=1.5 X 1000g

         =1500g

no. of papers that will weigh 1.5 kg= 1500/4

                                                          =375

Answer:  375 sheets of paper

Step-by-step explanation: First, to find the weight of one sheet of paper, we can do 28 divided by 7 to get 4 grams. Then, since 1.5 kg is 1500 grams, we can do 1500 divided by 4, which equals 375. So, 375 sheets of paper will weigh 1.5 kg.

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In a one-period binomial model of an option value, the probabilities of an up-move and a down-move are "calculated from the model inputs."

The number of survivors, x, in n independent tests is described by a binomial model. The number of tests must be predetermined, the results—success or failure—must be statistically independent for each test, and the survival probability—p—must be constant throughout the tests. When a process is repeated a certain number of times (for example, in a set of patients), the result for each patient can either be a success or a failure, the binomial distribution model enables us to calculate the probability of observing a specified number of "successes."

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Answer:

answer: -35

Step-by-step explanation:

if it's not sorry

Answer:

-12

Step-by-step explanation:

5x+(-y)+8-6x+9y

Answer:

C

Step-by-step explanation:

C has a directly proportional relationship. 27 glasses are in 9 cases, and 81 glasses are in 27 cases. Directly proportional since 9×3=27 (cases) and 27×3=81 (glasses)

The solution of the system of equation by substitution is x = 3 and y = -1.

System of equation can be solved using different techniques such as substitution method, elimination method and graphical method.

Let's solve the system of equation by substitution method

Therefore,

3x + 2y = 7

x = 3y + 6

Substitute equation(ii) in equation(i)

3(3y + 6) + 2y = 7

9y + 18 + 2y = 7

9y + 2y + 18 = 7

11y = 7 - 18

11y = -11

y = -11 / 11

y = -1

Hence, let's find x

x = 3(-1) + 6

x = -3 + 6

x = 3

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Answer: 13,8 litres

Step-by-step explanation:

£1.45 ------------ 1 L

 £20 ------------- ?

?= [tex]\frac{20 *1}{1.45} = 13,79310345 L[/tex] = 13,8 L

Answer:

x = -6

Step-by-step explanation:

x - 2 = x (4) + 16

x - 2 = 4x + 16

4x - x = -2 - 16

3x = -18

3/3 x = -18/3

x = -6

Answer:

719.412

Step-by-step explanation:

S(x)=-.228x^2+8.154x-8.3 x=7 feet

Plug in 7 for x, you'll convert to inches at the end

S(x)=.228(7^2) +8.154(7)-8.3

S=49(.228)+8.154(7)-8.3

S=11.173+57.078-8.3

S=59.951

Multiply by 12 to get inches

719.412

(If this answer doesn't work then you probably need to convert to inches before plugging in for x. 7 x 12=84 so plug that in.)

Answer:

4.5

Step-by-step explanation:

45/10=4.5

Answer:

1,070 g

Step-by-step explanation:

Half-life is the length of time it takes for half of the radioactive atoms of a radionuclide to decay. In this scenario, the amount of radioactive atoms is halved after 15 minutes. After 45 minutes, then, the amount of radioactive atoms is halved three times. Therefore:

1st half-life: 8,560 ÷ 2 = 4,280 g

2nd half-life: 4,280 ÷ 2 = 2,140 g

3rd half-life: 2,140 ÷ 2 = 1,070 g

The equation of the graph given in the diagram which represents an absolute value function is: y = |x - 3| + 5.

The equation, in vertex form, of a absolute value function is expressed as y = a|x – h| + k, where:

From the graph, we know that:

Vertex (h, k) = (3, 5)

Substitute h = 3 and k = 5 into the equation, y = a|x – h| + k:

y = a|x - 3| + 5

A point on the graph is (5, 7). To find the value of a, substitute x = 5 and y = 7 into the equation y = a|x - 3| + 5:

7 = a|5 - 3| + 5

7 = 2a + 5

7 - 5 = 2a + 5 - 5 [subtraction property of equality]

2 = 2a

Divide both sides by 2

2/2 = 2a/2 [division property of equality]

Substitute a = 1 into y = a|x - 3| + 5:

y = |x - 3| + 5 [equation of the absolute value function]

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The simplified expressions for the questions will be, 1) 3w, 2) 8x, 3) 10p, 4) 8b.

The simplification of an algebraic expression generally means breaking the equation into a smaller form for easier calculation with the help of formulas or using the rule of BODMAS.

Here, all the questions can be solved by using the BODMAS rule.

1) 7w + 2w - 6w

= (7w + 2w) - 6w

= 9w - 6w

= 3w.

2) 9x - 3x + 2x

= (9x + 2x) -3x

= 11x - 3x

= 8x.

3) 8p + 3p - p

= (8p + 3p) - p

= 11p - p

= 10p.

4) 6b - 3b + 5b

= (6b +5b) - 3b

= 11b -3b

= 8b.

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Step-by-step explanation:

[tex]7w + 2w - 6w \\ 9w - 6w \\ = 3w[/tex]

[tex]9x - 3x + 2x \\ 6x + 2x \\ = 8x[/tex]

[tex]8p + 3p - p \\ 11p - p \\ = 10p[/tex]

[tex]6b - 3b + 5b \\ 3b + 5b \\ = 8b[/tex]

The equation of a line in point- slope form, that passes through (1, -7) and has a slope of -2/3 is (y + 7) = -2/3 (x - 1)

Information gotten from the question include

a slope of -2/3

points (1, -7)

A linear function consists of functions where the variables has exponents of 1.

The equation of a line in point- slope form is expressed in the form.

(y - y₁) = m (x - x₁)

Definition of variables

(y and y₁) = refers to variables in the y direction

m = slope

x and  x₁ = refers to variables in the x direction

substituting into the slope and point (1, -7) equation gives

()y + 7) = -2/3 (x - 1)

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