Dawson simplifies the equation 4y-3=4(y + 1) and says it has no solution. Is dawson correct?

Answer:

Step-by-step explanation:

where is the triangle

The surface area of the rectangular prism is 130ft^2.

The surface area of a rectangular prism can be calculated by finding the area of each of the six faces and then adding them together.

The formula for the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

In this case, the length is 10ft, the width is 1ft, and the height is 5ft. Plugging these values into the formula, we get:

Surface area = 2(10ft)(1ft) + 2(10ft)(5ft) + 2(1ft)(5ft)

Surface area = 20ft^2 + 100ft^2 + 10ft^2

Surface area = 130ft^2

Therefore, the surface area of the rectangular prism is 130ft^2.

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The given problems are solved:

An equation is a statement that asserts the equality of two expressions, the expressions are written one on each side of an '=' equal to sign.

Question 4:

To calculate angle A,

Consider tan function.

[tex]tan A=\frac{opposite side }{adjacent side}[/tex]

[tex]tan A=\frac{9.6}{7.2}[/tex]⇒ 1.34

A= 53.26°

Question 7:

In triangle PQR, ∠Q=80°, PQ=8 and QR= 6,

PR=?

Area of triangle = 1/2 *a*b*sinC

                          = 1/2*8*6*sin°80

                          =24*0.984

Area of triangle = 23.616 square units.

Question 8:

Consider the triangle JKL, here two sides and one angle is given,

we can use cosine law,

The equation set us is given by,

           [tex]a^{2} = b^{2}+ c^{2} -2bcCos\alpha\\b ^{2} = a^{2}+c^{2} -2acCos\beta\\ c^{2} = b^{2} +a^{2} -2baCos\gamma[/tex]

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Answer:

Step-by-step explanation:

x/y=(5/6)/(3/4) = 5/6*4/3 = 10/9

x/y=10/9

y/x=9/10

y=9/10 * x

Second option

Answer:

y=5/8x

Step-by-step explanation:

The required distance across the lake (LM) is 205 m.

Similar triangles are those triangles that have similar properties,i.e. angles and proportionality of sides.

Here,

As from the figure,

Triangle KLM is similar to triangle KNO so,
KL/KN = LM/NO
180+70/180 = LM/147.6
LM = 205 m

Thus, the required distance across the lake (LM) is 205 m.

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The amount in the account after 15 years after round of to the nearest hundredth is $6,671.67, the correct option is B.

If n is the number of times the interested is compounded each year, and 'r' is the rate of compound interest annually, then the final amount after 't' years would be:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

We are given that;

The amount earned is A equal to P quantity 1 plus 0.054 over 2 end quantity all raised to the power of 2 times t

Rate of compound interest= 5.4%

Investment= $3000

Time= 15years

Now,

A = 3000(1+0.054/2)^2*15

A = 3000(1+0.054/2)^30

A = $6,671.67

So, amount = principal + interest

Principal = $3,000.00

Interest = $3,671.67

=$6,671.67

Therefore, the compound interest will be $6,671.67

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Penelope has, 52quarters, 104 dimes, 416 nickels, and 162 pennies.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

From the given information let, 'x' be the number of quarters,

Therefore, Dimes is 2x, Nickels is 8x and Pennies is 3x.

So, x + 2x + 8x + 4x = 780.

15x = 780.

x = 52, The number of quarters.

2×52 = 104, The number of Dimes.

8×52 = 416 Nickels.

3×52 = 162 Pennies.

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The function notation that moves a pre-image 4 units right and 7 units down is f(x) ⇒ (x + 4, y - 7)

Translation is the movement of a point on the coordinate plane either left, right, up or down. Translation is a rigid transformation because it preserves the shape and size. Reflection and rotation are also rigid transformations.

If a point A(x, y) is translated a units right and b units down, then the new point is A'(x + a, y + b)

The function notation that moves a pre-image 4 units right and 7 units down is (x, y) ⇒ (x + 4, y - 7)

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Answer:

v = 9

Step-by-step explanation:

4v - 18 = 6(v - 6)

1.) Distribute 6 into the parenthesis

4v-18 = 6v - 36

2.) Move 6v to the other side by subtracting from both sides

4v - 6v -18 = -36

3.) Move 18 to the other side by adding 18 on both sides

4v - 6v = 18 + -36

4.) Combine like terms

-2v = -18

5.) Divide -2 on both sides to get v by itself

v = 9

Answer:

the answer is 9

Step-by-step explanation:

4v-18=6(v-6)

4v-18=6v-36

4v-6v= -36+18

-2v= -18

divide both sides by -2

v=9

Answer:

To solve this problem, we need to calculate the cost of each travel and instruction option and then determine which options Treena can afford with her $1000 scholarship.

Option 1: Air travel and individual instruction

Travel cost: $335

Instruction cost: 7 x $60 = $420

Total cost: $335 + $420 = $755

Option 2: Air travel and group instruction

Travel cost: $335

Instruction cost: 7 x $40 = $280

Total cost: $335 + $280 = $615

Option 3: Train travel and individual instruction

Travel cost: $125

Instruction cost: 7 x $60 = $420

Total cost: $125 + $420 = $545

Option 4: Train travel and group instruction

Travel cost: $125

Instruction cost: 7 x $40 = $280

Total cost: $125 + $280 = $405

Now we need to determine which options Treena can afford with her $1000 scholarship. We'll start with the most expensive option and work our way down.

Option 1: $755

This option is too expensive for Treena's $1000 scholarship.

Option 2: $615

This option is also too expensive for Treena's $1000 scholarship.

Option 3: $545

This option is within Treena's budget, but she won't have any money left for food.

Option 4: $405

This option is also within Treena's budget, and she'll have $595 left for food.

Therefore, Treena's choices of travel and instruction plans that she could afford to make are:

- Train travel and group instruction with $595 left for food

- Train travel and individual instruction with no money left for food

The value of the variable r  when t = 5h and d = 240m is 48m/h

Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.

They are also made up of mathematical operations like subtraction. division, addition, multiplication, floor division, etc

From the information given, we have the equation;

d = rt

Make 'r' the subject of formula

r = d/t

Now, substitute the values into the equation, we get

r = 240/5

Divide the values

r = 48m/h

Hence, the value is 48m/h

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Answer: (6y + 1) (y + 4)

Step-by-step explanation: (6y + 1) (y + 4)   (6y)(y) + (6y)(4) + (1)(y) + (1)(4) 6y^2 + 24y + 1y + 4 6y^2 + 25y + 4

Answer:

multiply 6×2 an you get 12

step:1 =4×12y⁴ ¹+25y¹ ¹

step:2=48y⁴ ¹ +25y¹ ¹

step:3=48y³+25y⁰

step:4=48y³+25×1

step:5=48y³+25

answer=48y³+25

The amount of each deposit that Abbie made was $8

The amount of each deposit that Abbie made can be found by dividing the total amount she put into her savings account by the number of deposits she made.

In this case, we can use the formula: Amount of each deposit =

Total amount / Number of deposits

Substituting the given values into the formula, we get:

Amount of each deposit = $40 / 5

Amount of each deposit = $8

Therefore, the amount of each deposit that Abbie made was $8. In conclusion, if Abbie has put $40 into her savings account and has made 5 deposits of the same amount, then the amount of each deposit is $8.

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Answer:

Q1. The larger number is 54 and the smaller number is 37.

Q2. The number is 4.

Q3. The three numbers are 7, 8 and 9.

Step-by-step explanation:

Q1.

Let the larger number be x and the smaller number be y.

x+y= 91   (1)

x-y= 17   (2)

From (2) :

x= y+17   (3)

sub (3) into (1) :

y+17+y= 91

2y= 74

y= 37   (4)

sub (4) into (3) :

x= 37+17

 = 54

Q2.

Let the unknown number be x.

2x+16= 24

2x= 8

x= 4

Q3.

Let the smallest number be x.

2nd no. : x+1

3rd no. : x+2

x+(x+2)= (x+1)+8

2x+2= x+9

x= 7

x+1= 8

x+2= 9

The probability of getting: A. a five-card hand that has three Jacks and two Queens is 0.000009, or 0.000923% and B. a "four of a kind" is 0.00024, or 0.02401%.

A. The probability of getting a five-card hand that has three Jacks and two Queens can be calculated by using the formula:
P(3 Jacks and 2 Queens) = C(4,3) x C(4,2) / C(52,5)
Where C(n,k) is the combination of n items taken k at a time.

= (4 x 6) / 2598960
= 24 / 2598960
= 0.00000923

Therefore, the probability of getting a five-card hand that has three Jacks and two Queens is 0.000009, or 0.000923% when rounded to six decimal places.

B. The probability of getting a "four of a kind" can be calculated by using the formula:
P(four of a kind) = (C(13,1) x C(4,4) x C(12,1) x C(4,1)) / C(52,5)

= (13 x 1 x 12 x 4) / 2598960

= 624 / 2598960
= 0.00024010

Therefore, the probability of getting a "four of a kind" is 0.00024, or 0.02401% when rounded to five decimal places.

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To find the missing dimension of a cone when the height is 4.2 and the volume is 3.6 cubed is to equate the general formula with the given information.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

To obtain the missing dimension of a cone we must equate the general formula for the volume of a cone to the given information.

Therefore, (1/3)πr²×4.2 = 3.6

(1/3)πr² = 0.86.

r² = 0.86/1.05.

r² = 0.82.

r = 0.9

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The product of the rational expression shown above include the following: B. x² - 36/(x² - 9).

In Mathematics, a rational expression simply refers to a type of expression  which is expressed as a fraction. This ultimately implies that, a rational expression is composed of two (2) main parts and these include the following:

In this exercise, we would determine the product of the numerator for this rational expression and the product of the denominator for this rational expression as follows;

Product of numerator = (x + 6)(x - 6)

Product of numerator = x² + 6x - 6x - 36

Product of numerator = x² - 36

For the denominator, we have the following:

Product of denominator = (x + 3) × (x - 3)

Product of denominator = x² - 3x + 3x - 9

Product of denominator = x² - 9

Therefor, the product of the rational expression is given by x² - 36/(x² - 9).

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Answer: To multiply the expression, we first distribute the constant factors:

2p^3q^4r^2 * 2p^4q^2t^3 * 3r = 6p^3q^4r^3 * 2p^4q^2t^3

Next, we multiply the variables by combining like terms:

6p^3q^4r^3 * 2p^4q^2t^3 = 6p^7q^6r^3t^3

This is the final simplified expression, and we can circle or highlight it as the answer.

Step-by-step explanation:

The side lengths form a proportional relationship, and the ratios are as follows:

17.955/11.97 = 14.565/9.71 = 5.415/3.61.

Similar triangles are triangles that share these two features presented as follows:

They must have Congruent angle measures.

They have Proportional side lengths.

Here, the triangles are similar, as they have the same angle measures.

17.955/11.97 = 14.565/9.71 = 5.415/3.61.

Thus, the side lengths form a proportional relationship, as the equivalent side have a ratio of 1.5.

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The value of n is 443 inches when using the triangle rule and law of sine.

The formula is given as

a / sin A = b / sin B = c / sin C

In this triangle NOP, we can find the value of angle P

∠N + ∠O + ∠P = 180

57 + 55 + ∠P = 180  : Sum of angles in a triangle is equal 180 degrees

∠P = 180 - 112

∠P = 68

Using law of sine

p/sin P = n/sin N

490/sin68 = n / sin57

n = [(490 × sin 57) / sin 68]

n = 443 inches

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Answer:

Step-by-step explanation:

The middle one

There are 15 total blocks that is your denominator.

There are 5 shaded that is your numerator.

5/15

The graph is a linear function with a growth factor of 4

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The graph has the shape of a straight line, so it is linear.

The graph starts at point (0, 0). It passes through point (1, 4).

slope = 4/1 = 4

The slope is 4. Growth factor is the same as slope for a linear function.

Hence, the graph is a linear function with a growth factor of 4

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the mean and the median of the given data set are 16.75 and 9.5 respectively.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

Given,  A data set 8, 9, 10, 40

From the general formula of mean:

mean =  (sum of observations) ÷ (total number of observations).

mean = (8 + 9 + 10+ 40)/4

mean = 67/4

mean = 16.75

Since the median is:

The median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values.

Thus,

the median of the given data set = (9 +10)/2

the median of the given data set =  9.5

Therefore, the mean and the median of the given data set are 16.75 and 9.5 respectively.

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Answer:

y=2/3x+-1

Step-by-step explanation: