1. y = 4x + 3 for x = -1, 0,1

The height of tree is 475cm.

Step-by-step explanation:

Given,

Shadow of Samantha = 30cm

Actual height of Samantha = 150cm

Ratio of Shadow to actual height of Samantha = 30:150

Shadow of tree = 95cm

Actual height of tree = x

Ratio of shadow to actual height of tree = 95:x

Using proportion,

Ratio of Shadow to actual height of Samantha :: Ratio of shadow to actual height of tree

[tex]30:150::95:x\\[/tex]

Product of mean = Product of extreme

[tex]150*95=30*x\\14250=30x\\30x=14250\\[/tex]

Dividing both sides by 30;

[tex]\frac{30x}{30}={14250}{30}\\x=475\\[/tex]

The height of tree is 475cm.

Keywords: ratio, proportion

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To find the height of the tree, set up a proportion: 150 cm / 30 cm = x / 95 cm. Solving for x, the height of the tree is 475 cm.

To find the height of the tree, we can set up a proportion using the lengths of the shadows. Let x represent the height of the tree. The proportion would be:

150 cm / 30 cm = x / 95 cm

Cross-multiplying and solving for x, we get:

x = (150 cm times 95 cm) / 30 cm = 475 cm

Therefore, the height of the tree is 475 cm.

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The measure of the vertex angle of the isosceles Δ is 96°

Step-by-step explanation:

In the isosceles triangle

∵ The measure of one of the base angles of an isosceles Δ = 42°

- The base angles are equal in measure

∴ The measure of the other base angle = 42°

∵ The sum of the measures of the interior angles of any Δ = 180°

∴ 42 + 42 + measure of the vertex angle = 180

∴ 84 + measure of the vertex angle = 180

- Subtract 84 from both sides

∴ measure of the vertex angle = 96°

The measure of the vertex angle of the isosceles Δ is 96°

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Equation 5 + 5 = 10  and 5 + 5 + n = 10 + n are equivalent equation

Given that  

John wrote that 5 + 5 = 10   ------ (1)

Then wrote that 5 + 5 + n = 10 + n    ------ (2)

Need to determine are the equations written by John are equivalent.

First we need to keep in mind that whenever we apply same operation like addition, subtraction, multiplication and division on both the sides of equation that is left hand side and right hand side, we get the equivalent equation.

As in the second equation John added same value that is n on both sides of equation, we can say that equation with n is equivalent to the previous equation without n

Other way is let’s solve equation (2) and see if we can get equation (1)

5 + 5 + n = 10 + n  

On subtracting both the sides with n we get,

5 + 5 + n – n = 10 + n – n

=> 5 + 5 = 10 which is same as equation (1)

Hence we can conclude that equation 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent equation.

Final answer:

The equations 5 + 5 = 10 and 5 + 5 + n = 10 + n are equivalent because adding the same number 'n' to both sides of an equation does not change the original equality.

Explanation:

Yes, the equations that John wrote are equivalent. The first equation, 5 + 5 = 10, establishes that the sum of five plus five equals ten. The second equation, 5 + 5 + n = 10 + n, simply adds n to both sides of the first equation. This does not change the equality because, according to the properties of equality, if you add the same amount to both sides of an equal sign, the two sides remain equal. This can also be seen as an application of the commutative property of addition which states that numbers can be added in any order without changing the sum, as in A + B = B + A. Therefore, the original sum of 5 + 5 on the left side remains 10 when n is added to both sides, showing that 5 + 5 + n is indeed equal to 10 + n.

Answer:

The values of 'x' are -1.2, 0, 0, [tex]-4i[/tex] or [tex]4i[/tex].

Step-by-step explanation:

Given:

The equation to solve is given as:

[tex]5x^5+6x^4+80x^3+96x^2=0[/tex]

Factoring [tex]x^2[/tex] from all the terms, we get:

[tex]x^2(5x^3+6x^2+80x+96)=0[/tex]

Now, rearranging the terms, we get:

[tex]x^2(5x^3+80x+6x^2+96)=0[/tex]

Now, factoring [tex]5x[/tex] from the first two terms and 6 from the last two terms, we get:

[tex]x^2(5x(x^2+16)+6(x^2+16))=0\\x^2(x^2+16)(5x+6)=0[/tex]

Now, equating each factor to 0 and solving for 'x', we get:

[tex]x^2=0\\x=0\ and\ 0\\\\5x+6=0\\x=\frac{-6}{5}=1.2\\\\x^2+16=0\\x^2=-16\\x=\sqrt{-16}=\pm 4i[/tex]

There are 3 real values and 2 imaginary values. The value of 'x' as 0 is repeated twice.

Therefore, the values of 'x' are -1.2, 0, 0, [tex]-4i[/tex] or [tex]4i[/tex].

Answer:

The answer is definitely C. a naturally formed solid substance with a crystal structure

Answer:

98%

Step-by-step explanation:

There is 1 ace of diamonds.  So the probability of drawing any other card is 51/52 ≈ 98%.

Answer:

98 percent

Step-by-step explanation:

since drawing a ace of diamonds out of the deck is 1/52 not drawing it is a 51/52 which is about 98 percent

Answer:

[tex](31x)\times 16\%[/tex]

Step-by-step explanation:

Given: Discount offered is 16% on 20 or more job posting.

           x dollars is charged on every job posting on website.

Now, lets find the discount on 31 job posting.

∴ Total cost on 31 job posting = [tex]\textrm{charges for one job posting}\times \textrm{Total number of job posting}[/tex]

⇒ Total cost on 31 job posting= [tex]x\times 31= \$ 31x[/tex]

As we know 16% discount been offered for 20 or more job posting

∴ Discount offered on 31 job posting = [tex]31x\times 16\%[/tex]

Discount offered by JobFind to the employer is [tex](31x)\times 16\%[/tex]

Final answer:

The discount percentage for posting 31 jobs on JobFind is 16%, which remains constant as it meets the criteria of posting 20 or more jobs.

Explanation:

To express the discount as a percent for an employer posting 31 jobs on JobFind, we need to calculate the percentage reduction based on the original price. Since 31 jobs qualify for a 16% discount, the calculation is straightforward.

Given:
The original discount offered is 16% for 20 or more jobs.
The number of jobs being posted is 31, which exceeds the 20 job threshold.

Hence, the discount percentage for 31 jobs remains the same as the original discount percentage, which is: 16%.

No further calculations are necessary because the question simply asks to express the given discount, not to calculate the total discounted amount or savings.

Answer:

12 more feet

Step-by-step explanation:

Reason why is because if you add 14 and 4 you get 18 then you add 18 with 12 and you get 30. (hope this helps)

Answer:

[tex]T_n= 9+(n-1)[/tex]

Step-by-step explanation:

The Given sequence is 9, 10, 11, 12

We need to find the expression to describe the sequence.

Let [tex]T_n[/tex] be the [tex]n^{th}[/tex] term of the sequence.

Let n represent the position of the term.

Let a be the first term in the sequence.

and d be the common difference between the sequence

Hence the expression to find the above sequence is given below;

[tex]T_n= a+(n-1)d[/tex]

when n=1 d= 1 a = 9

[tex]T_1 = 9+(1-1)1 = 9 + 0 = 9[/tex]

when n=2 d= 1 a = 9

[tex]T_2 = 9+(2-1)1 = 9 + 1 = 10[/tex]

when n=3 d= 1 a = 9

[tex]T_3 = 9+(3-1)1 = 9 + 2 = 11[/tex]

when n=3 d= 1 a = 9

[tex]T_4 = 9+(4-1)1 = 9 + 3 = 12[/tex]

Hence the expression is [tex]T_n= 9+(n-1)[/tex]

The expression to describe the sequence 9, 10, 11, 12, ... is 8 + n, with n representing the position of the term in the sequence.

The sequence given is 9, 10, 11, 12, ..., which is an arithmetic sequence where each term increases by 1 from the previous term. To write an expression that represents the nth term of this sequence using n to represent the position of the term (with n = 1 for the first term), we need to find a formula that calculates the value of each term based on its position.

The first term of the sequence is 9 when n = 1. The second term is 9 + 1, and the third term is 9 + 2, and so on. Generalizing this, the nth term can be written as the first term value (9) plus the number of terms after the first one, which is (n - 1), since for the first term, n - 1 equals 0. Therefore, the final expression is:

9 + (n - 1)

We can simplify this expression as: 8 + n

This expression will give us the value of each term in the sequence based on its position n.

The two shorter sides in triangle A can be demonstrated to be the same length as the two shorter sides in triangle B by showing 'a' equals 'p' and 'b' equals 'q'. The two triangles would accordingly be congruent using the Side-Side-Side (SSS) Postulate.

Triangles A and B are right-angled triangles, which means each has one angle that measures 90 degrees. You're asking to show that the two shorter sides in triangle A have the same length as the two shorter sides in triangle B. This would mean that these sides are congruent.

Firstly, let the two shorter sides in triangle A are 'a' and 'b', and in triangle B are 'p' and 'q'. If triangle A and B are congruent, this means 'a' should equal 'p' and 'b' should equal 'q'.

Finally, the two triangles would be congruent based on the Side-Side-Side (SSS) Postulate, which states that if the three sides of one triangle are congruent to the three sides of a second triangle, then the two triangles are congruent.

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Final answer:

To show that two right angled triangles are congruent, you compare the two shorter sides. If they are equal in length, then the triangles are congruent by the Side-Angle-Side (SAS) postulate, as the right angle is also congruent.

Explanation:

To demonstrate that two right angled triangles, Triangle A and Triangle B, are congruent when the two shorter sides have the same length, first let's assume they are right angled at vertex C. If the sides AC and BC are congruent to the sides A'C' and B'C' respectively in triangles ABC and A'B'C', and since right angles are always congruent, then by the Side-Angle-Side (SAS) postulate of congruency, the two triangles are congruent.

According to the Pythagorean theorem, which states that in a right-angled triangle the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (this is expressed as c² = a² + b²), we know that if the two legs a and b are congruent in two right triangles, then the hypotenuses will also have to be congruent.

If Triangle A and Triangle B have sides of equal lengths and right angle at C, the triangles are congruent by the SAS postulate, proving that both triangles are identical in shape and size.

Final answer:

To find out how much of the circle is shaded by adding 1/3 and 2/7, we determine the least common denominator, convert each fraction, and then add the numerators. The shaded area of the circle is 13/21.

Explanation:

The student asked how much of the circle is shaded if you add the fractions 1/3 and 2/7. To find this, we need to calculate the sum of these two fractions. Since 1/3 is less than 1/2 and 2/7 is also less than 1/2, their combined value must be less than 1. To add fractions, you need a common denominator. The least common multiple of 3 and 7 is 21, so we will convert each fraction to have a denominator of 21:

Now, we add the numerators while keeping the denominator the same:

7/21 + 6/21 = 13/21.

This represents the shaded area of the circle in fraction form. Therefore, 13/21 of the circle is shaded.

The prepayment fee of $6182.58 would  be charged to Artemis for paying off her loan 16 years early.

Answer: Option C

Step-by-step explanation:

30 year loan at 9.6% interest yields.  

Number of month = 30 (12) = 360 months

Annual percent interest of [tex]\frac{9.6 \%}{12}[/tex] = monthly percent interest of .8%

The formula for the present value of an ordinary annuity, as opposed to an annuity due, is as follows

            [tex]P M T= \frac{P \times r}{1-(1+r)^{n}}[/tex]

With r and n adjusted for periodicity, where

P = the present value of an annuity stream

PMT = the dollar amount of each annuity payment

r = the interest rate (also known as the discount rate)

n = the number of periods in which payments will be made

              [tex]P M T= \frac{190000 \times 0.008}{1-(1+0.008)^{-360}} = \frac{1520}{1-(1.008)^{-360}} = \frac{1520}{1-0.0567}=\frac{1520}{0.9432}[/tex]

                   PMT = $1611.50 per month

Her loan 16 year early. It means

              [tex]\text { Worth of loan after } 14 \text { year } = 190000 \times(1.008)^{168} = 3.814 \times 190000=\$ 724641.16[/tex]

Worth of monthly payments for 14 year

           [tex] = \frac{1611.50 \times\left\{(1.008)^{168}-1\right)}{0.008} = \frac{1611.50 \times(3.81-1)}{0.008} = \frac{4.534 .6}{0.008} = \$ 566825.15[/tex]

Amount still owed after 14 year = difference of the above two

                                                    =$724641.16 - $566825.18

                                                    =$157816.01

Prepayment fee = [tex](0.8 \times 157816.02) \times\left((1.008)^{6}-1\right)[/tex]

                         = 126252.82 (1.049-1) = 126252.82 (1.0489-1) = $6182.63

Answer:

Ryan: 75

Shauna: 65

Step-by-step explanation:

x = ryan's height

x - 10 = shauna's height

x + (x - 10) = 140

2x - 10 = 140

2x = 150

x = 75

Shauna is 65 inches tall and Ryan is 75 inches tall.

Let the height of:

Shauna be represented with s

Ryan be represented with r.

Sum of their heights : s + r = 140

The equation that represents Shauna's height : r - 10

Substitute for Shauna's height in the first equation:

r - 10 + r = 140

Solve for r

2r = 150

r = 75 inches

Substitute for r in the first equation

75 + s = 140

s = 140 - 75

s = 65 inches

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Answer:

1. 81

2. 43

3. 14

4. 32

5. 216

6. 6,7760.25

Hope it's helpful ;)

Answer:

2:15 PM

Step-by-step explanation:

When the plane arrives in Seattle, the time in eastern time period would be 5:15 PM.  From eastern to pacific, the time goes back 3 hours. 5:15 - 3 hours is 2:15. Since the time is still in the afternoon, it is still PM.

Answer:

2:15pm

Step-by-step explanation:

1) Take 1:09pm and add 4 hours and 6 mins to the time

2) 1 hour and 9 minutes + 4 hours and 6 minutes = 5:15pm (in eastern time)

3) Subtract 3 hours from 5 hours and 15 minutes. This equals 2:15pm

This would be the answer because of the time zone change.

========================================

Work Shown:

9c + 90 < -27

9c + 90 - 90 < -27 - 90 .... see note 1

9c < -117

9c/9 < -117/9 ... see note 2

c < -13

-----------

note 1: I'm subtracting 90 from both sides to undo the "plus 90" that is happening on the left side

note 2: I divided both sides by 9 to undo the multiplication. The expression 9c is the same as 9*c or "9 times c". The inequality sign will not flip as we are dividing both sides by a positive number.

These two ratios are not equivalent, as 18 trucks and 4 cars simplifies to a ratio of 9:2, while 21 trucks and 6cars simplifoes down to a ratio of 7:2. Obviously, there is a difference between 9:2 and 7:2, so they are not equivalent.

Answer:

-32

Step-by-step explanation:

1/2x-9=-25

1/2x= -25+9

1/2x=-16 /multiply 2

x=-32

[tex]\text{Hello there!}\\\\\text{Solve:}\\\\\frac{1}{2}x-9=-25\\\\\text{Add 9 to both sides}\\\\\frac{1}{2}x=-16\\\\\text{Divide both sides by 1/2 or 0.5}\\\\\boxed{x=-32}[/tex]

Length and width of rectangle is 15 inches and 6 inches respectively

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.  

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

The formula for area of rectangle is given as:

[tex]\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}[/tex]

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

[tex]\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}[/tex]

On solving the above expression for x we get

[tex]\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}[/tex]

[tex]\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}[/tex]

Hence length and width of rectangle is 15 inches and 6 inches.

Answer:

He saved $25.

Step-by-step explanation:

To find the roots of the polynomial equation x^3 - 5x + 5 = 2x^2 - 5, rearrange the equation to equal zero and use methods such as synthetic division or factoring to solve the cubic equation.

To find the roots of the polynomial equation x3 - 5x + 5 = 2x2 - 5, we need to set the equation equal to zero and rearrange it:

x3 - 2x2 - 5x + 5 + 5 = 0

x3 - 2x2 - 5x + 10 = 0

Now, we can use various methods to solve this cubic equation, such as synthetic division, factoring, or using a graphing calculator. On finding the roots of the equation, we can determine the values of x.

Answer:

The Whole numbers that satisfies the condition A - B = 18 is

A = 25

B= 7

Step-by-step explanation:

Whole number:

Whole numbers are positive numbers, including zero, without any decimal or fractional parts.

They are numbers that represent whole things without pieces.

The set of whole numbers is represented mathematically by the set: {0, 1, 2, 3, 4, 5...}

so there are many answers to this question which satisfies A- B  = 18

Few are given below

A = 19 and B = 1     ∴   19 - 1  = 18

A = 20 and B = 2   ∴  20 - 2 = 18

A = 18 and B =0     ∴   18 - 0 = 18

A = 39 and B = 21   ∴  39 - 21 = 18

A = 25 and B= 7    ∴    25 - 7 = 18

i.e A should be always greater than B to satisfy  A- B = 18 condition.

Answer:

-11

Step-by-step explanation:

The answer to the  first one sould be  -11

2x^3 +5x^2−x−6

Write 5x^2  as  4x^2 + x^2......and we have.....

2x^3 + 4x^2 + x^2 - x - 6

2x^2 ( x + 2) + ( x + 2)(x - 3)

(x + 2) [ 2x^2 + x - 3]

(x + 2) (2x +3) (x - 1)

x^3−4x^2−3x+18 = 0

Using some synthetic division, we have

3  [   1   - 4      -3      18  ]

              3      -3     -18

      _______________

       1    -1      -6       0

The remaining polynomial  is   x^2  - x  - 6    which factors as  (x - 3) ( x + 2)

So ....   the factored form is  (x - 3) ( x - 3) ( x + 2)  = ( x + 2) ( x - 3)^2 = 0

Answer:

-11 is correct for all future users.

Step-by-step explanation:

Answer:

[tex]a_{7}[/tex] = - 160

Step-by-step explanation:

The n th term of a geometric sequence is calculated as

[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

Given

a₂ = - 5, then

a₁r = - 5, that is

2a₁ = - 5 ⇒ a₁ = - 2.5, thus

[tex]a_{7}[/tex] = - 2.5 × [tex](2)^{6}[/tex] = - 2.5 × 64 = - 160

Answer:

23/4 = 5.75

Step-by-step explanation:

Answer:

The correct answer is Helena

Answer:

A)  Out of 6,000 trials, one can expect 4800 successes.

Step-by-step explanation:

Here, the total number of trials  = 6,000

The probability of winning each trial = 0.8

Now, as we know in a BINOMIAL EVENT:

q = n x p

⇒ The number of success out of 6,000 trials

= 6,000 x (0.8)  = 4800

Hence, out of 6,000 trials, one can expect 4800 successes.

Answer:

CD = 5.196 cm

Area = 31.177 sq. cm.

Step-by-step explanation:

See the attached diagram.

Given that ∠ ACB = 90° in Δ ABC.

Now, CD ⊥ AB and ∠ CDB = ∠ CDA = 90°

Given that ∠ ACD = 60° and BC = 6 cm.

We have to find the length of CD and the area of Δ ABC.

Now, ∠ CAD = 90° - ∠ ACD = 90° - 60° = 30°  

Again, ∠ CBD = 90° - ∠ CAD = 90° - 30° = 60°.

Now, from Δ BCD, [tex]\sin 60 = \frac{CD}{BC} = \frac{CD}{6}[/tex]

{Since Δ BCD is a right triangle and ∠ CDB = 90°}  

⇒ [tex]CD = 6 \times \sin 60 = 5.196[/tex] cm. (Answer)

Now, from Δ ACD, [tex]\sin 30 = \frac{CD}{AC} = \frac{5.169}{AC}[/tex]

{Since Δ ACD is a right triangle and ∠ ADC = 90°}

⇒ [tex]AC = \frac{5.196}{\sin 30} = 10.392[/tex] cm

So, the area of Δ ABC = [tex]\frac{1}{2} \times BC \times AC = \frac{10.392 \times 6}{2} = 31.177[/tex] sq. cm. (Answer)

Answer:

CD=3√3

Step-by-step explanation:

Answer:

The number of new books sold  =  10

The number of used books sold (u)   = 15

The number of magazines  sold (m) =   20

Step-by-step explanation:

Let us assume the number of new books  = n

So, the number of used books sold  (u)  = New books sold + 5 =  n + 5

Also, the number of magazines sold (m)  = 2 x ( Number of new books sold)  

= 2 n

⇒  u = n + 5, m = 2 n

Here, the cost of each new book  n-  = $12

So, the cost of n new books = n  x ($12) = 12 n

the cost of each used book  u  = $8

So, the cost of u = (n+ 5)  used  books = n+5  x ($8) = 8 n + 40

the cost of each magazine  m  = $5

So, the cost of m = (2n )  magazines = 2n  x ($5) = 10 n

Also, total earnings = $340

⇒ 12 n + 8n +40 + 10 n = 340

or,  30 n =  300

or,n = 300/30 = 10

Hence the number of new books sold  = n = 10

The number of used books sold (u)  = n + 5  = 15

The number of magazines  sold  = m = 2 n = 20

Answer:

14

Step-by-step explanation:

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Answer:Here are some more problems to solve.

Calculate the volume of a paperback book with the following dimensions:

Length = 12 cm

Width = 3 cm

Height = 20 cm

Calculate the volume of a steel bar with the following dimensions:

Length = 5 cm

Width = 2 cm

Height = 30 cm

Now determine the density of the steel bar if its mass is 2.34 kg. (Hint: Convert to grams first.)

A cork has a volume of 5.0 cm3 and a mass of 1.2 grams. Calculate its density.

Water has a density of 1 g/cm3. If you placed a cork and a steel paper clip in a jar of water, what do you think would happen? Use your knowledge of density to explain the outcome.

Step-by-step explanation: