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The answer is y = 5x.

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Answer:

y=5x

Step-by-step explanation:

I did the test

the value of blank is 23.

Given series is,

8,15,27,_,20

We have to find the blank number.

Let the no. be x.

Since on observing the above series we find that the ratio of 15 to 8 is equal to the ratio of 27 to 15.

Hence, [tex]\frac{15}{8} =\frac{27}{15}=1.8[/tex]

This follows for the remaining terms also,

So, [tex]\frac{x}{27} =\frac{20}{x}[/tex]

[tex]x^{2} =20\times27\\x=\sqrt{540} \\x=23.23[/tex]

since, 23.23 is not a whole number so we take here 23.

Hence the value of blank is 23.

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Answer:

x ≥ 25

Step-by-step explanation:

In the seventh grade, fifty students are trying for sports supplies to raise at least $2000. They already have $750.

Let us assume that each student has to raise $x more to meet the goal.

Then, a total of 50 students will raise $50x more.

Therefore, the inequality to solve for x will be  

750 + 50x ≥ 2000

⇒ 50x ≥ 1250

⇒ x ≥ 25 (Answer)

Final answer:

Each seventh grade student should raise at least $25 in order to collectively meet the goal of raising $2000 for their sports supplies after having already raised $750.

Explanation:

The goal amount for the seventh grade sports supplies fundraiser is $2000. They have already raised $750, leaving them with $1250 still needed to reach their goal. If there are 50 students working on the fundraiser, we can set up an inequality to determine how much money each student should raise minimally to meet the goal of $2000. Here's the inequality:

Let x be the amount each student needs to raise.

50x + $750 ≥ $2000

To solve for x, we subtract $750 from both sides of the inequality:

50x ≥ $2000 - $750

50x ≥ $1250

Now divide both sides by 50 to find the amount each student should raise:

x ≥ $1250 / 50

x ≥ $25

Therefore, each seventh grade student should raise at least $25 to meet the $2000 goal.

Answer:

[tex]12\sqrt{2}\ cm[/tex]

Step-by-step explanation:

step 1

Find the length side of the square

we know that

The area of a square is equal to

[tex]A=b^{2}[/tex]

where

b is the length side

we have

[tex]A=144\ cm^2[/tex]

substitute in the formula of area

[tex]144=b^{2}[/tex]

solve for b

square root both sides

[tex]b=12\ cm[/tex]

step 2

Find the length of the diagonal

Applying the Pythagorean Theorem

[tex]d^2=b^2+b^2[/tex]

see the attached figure to better understand the problem

substitute the given values

[tex]d^2=12^2+12^2[/tex]

[tex]d^2=288[/tex]

square root both sides

[tex]d=\sqrt{288}\ cm[/tex]

simplify

[tex]d=12\sqrt{2}\ cm[/tex]

Answer:

10 cups

Step-by-step explanation:

First, we need to find the unit rate. 24/8 equals to 3. 3 is the amount of flour per cupcake. 24 + 3= 27 + 3= 30. You added twice to get to 30. 8+2=10

Answer:

[tex]\frac{7}{3}[/tex]

Step-by-step explanation:

Im going to assume a faction greater than one means an improper fraction.

Converting [tex]2 \frac{2}{6}[/tex] gets [tex]\frac{14}{6}[/tex] which simplified is [tex]\frac{7}{3}[/tex]

Answer:

[tex]f(5)=10[/tex]

Step-by-step explanation:

A sequence is defined by the recursive formula [tex]f(n+1)=f(n)-2[/tex]

If [tex]f(1)=18,[/tex] then

for [tex]n=1: f(2)=f(1+1)=f(1)-2=18-2=16[/tex]

for [tex]n=2: f(3)=f(2+1)=f(2)-2=16-2=14[/tex]

for [tex]n=3: f(4)=f(3+1)=f(3)-2=14-2=12[/tex]

for [tex]n=4: f(5)=f(4+1)=f(4)-2=12-2=10[/tex]

Answer:

10!

Step-by-step explanation:

Answer:

A would be best

Step-by-step explanation:

200 km is roughly 124.2 miles

200 m is about 0.12 miles

200 cm and 200 mm is way too small to be distances between cities because 200 cm is like 78.7 inches

200 mm is like 7.8 inches

124.2 miles or 200 km would be a reasonable distances between two cities.

Answer:

A. 200km is your answer

Step-by-step explanation:

Answer:

y = 12 ; x = 14

Step-by-step explanation:

2x + 7 =3x - 7                   { corresponding angles}

7 + 7 = 3x - 2x

14 = x

x = 14

12y + 1 + 3x - 7 = 180     {co interior angles}

12y + 1 + 3 * 14 - 7 = 180

12y + 1 + 42 - 7 = 180

12y + 36 = 180

12y = 180 - 36

12y = 144

y = 12

Step-by-step explanation:

2x+y = 5 (divided by 2)

If x= 0, y=5

If x= 1, y=3

If x=-1, y=7

So, coordinate points are (0,5),(1,3),(1,7) and so on.

Continue above explanation.

After , draw a graph on x,y axis .

Answer: I used a graphing calculator.

Step-by-step explanation:

Answer:

y = - 7x + 73

Step-by-step explanation:

y = mx + b   m: slope       b: y intercept

m = (y-y') / (x-x') = (31-3) / (6-10) = 28 / - 4 = -7

b = y - mx = 3 - (-7) x 10 = 73

equation: y = -7x + 73

check: 31 = -7 x 6 +73 = -42 + 73 = 31      (6,31)

Answer:

The cost of one lime is $0.65

Step-by-step explanation:

Let

x ---> the cost of one lemon

y ---> the cost of one lime

we know that

Mickey

[tex]5x+3y=3.70[/tex] ----> equation A

Minnie

[tex]15x+4y=7.85[/tex] ---> equation B

Solve the system by elimination

Multiply by -3 both sides equation A

[tex]-3(5x+3y)=-3(3.70)[/tex]

[tex]-15x-9y=-11.10[/tex] ----> equation C

Adds equation C and equation B

[tex]-15x-9y=-11.10\\15x+4y=7.85\\--------\\-9y+4y=-11.10+7.85\\-5y=-3.25\\y=0.65[/tex]

therefore

The cost of one lime is $0.65

Answer:705 cm

Step-by-step explanation:

3525 divided by 5

=705

Ron’s feather flew 705 cm

Ron’s feather flew 705 cm with his magic.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Hermione can lift a feather 3,525 centimeters (cm) into the air. 5 times as high as Ron can lift a feather.

So

We have to 3525 divided by 5;

3525 / 5

=705

Hence, Ron’s feather flew 705 cm with his magic.

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Answer:

y-8=5/6(x-12)

Step-by-step explanation:

y-y1=m(x-x1)

y-8=5/6(x-12)

The required equation of the line is [tex]\rm y = \dfrac{5}{6}x-2[/tex].

Given that,

The equation of the line is,

[tex]\rm y = \dfrac{5}{6}(x-10)[/tex]

It passes through the point (12, 8).

We have to determine

The equation of the line is parallel to the given line.

According to the question,

The equation of the line is,

[tex]\rm y = \dfrac{5}{6}(x-10)[/tex]

The slope of the line [tex]\rm m_1[/tex] is 5/6.

If the two lines are parallel to each other then the slope of these lines is the same.

[tex]\rm m_1 = m_2\\\\\dfrac{5}{6} = \dfrac{5}{6}[/tex]

Therefore,

The equation of line passes through the point (12, 8) is,

[tex]\rm( y -y_1) = m (x-x_1)\\\\(y-8) = \dfrac{5}{6} (x-12)\\\\6 (y-8) = 5(x-12)\\\\6y-48=5x-60\\\\6y = 5x-60+48\\\\6y = 5x-12\\\\y = \dfrac{5}{6}x- \dfrac{12}{6}\\\\y = \dfrac{5}{6}x-2[/tex]

Hence, The required equation of the line is [tex]\rm y = \dfrac{5}{6}x-2[/tex].

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Answer:

The periodic interest rate is 1.62 %

Step-by-step explanation:

Given:

Annual percentage rate  = 19.66%

Time period  = 30 days

To Find:

Periodic interest rate  =?

Solution:

The periodic interest rate r is calculated using the following formula:

r = (1 + \frac{i}{m})^{\frac{m}{n}} - 1

Where,

i = nominal annual rate

n = number of payments per year i.e., 12 for monthly payment, 1 for yearly payment and so on.

m = number of compounding periods per year

The period interest rate per payment is integral to the calculation of annuity instruments including loans and investments.

Now substituting the values we get

[tex]r = (1 + \frac{19.66}{12})^{\frac{12}{12}} - 1[/tex]

[tex]r = (1 + \frac{19.66}{12})^1 - 1[/tex]

r = (1 +1.638 ) - 1

r = (2.638 ) - 1

r = 1.638 %

Answer:

125, 119, 113, 107, 101

Step-by-step explanation:

All you have to do is keep subtracting 6 from the numbers.

125 - 6 = 119

119 - 6 = 113

113 - 6 = 107

107 - 6 = 101

Answer:

119,210,337,506,723

Step-by-step explanation:

x³-6 where x=5,6,7,8,9

5³-6=15-6=119

6³-6= 216-6=210

7³-6=343-6= 337

8³-6=512-6=506

9³-6= 729-6=723

Answer:

60.59

Step-by-step explanation:

73%=0.73

0.73*83=60.59

60.59 is the number you're looking for.

Hope this helps, if not, comment below please!!!!

Answer:

y = -5x -8

Explanation:

Find b in equation y = mx + b

Insert numbers to find b

-3 = -5· -1 + b

Step 1: Simplify both sides of the equation.

−3=(−5)(−1)+b

−3=5+b

−3=b+5

Step 2: Flip the equation.

b+5=−3

Step 3: Subtract 5 from both sides.

b+5−5=−3−5

b=−8

Insert into equation

y = -5x - 8

[tex]

x^2-1 < 18 \\

x^2 < 19 \\

x < \sqrt{19}

[/tex]

Hope this helps.

Answer:

  M(t) = 741·(1/2)^(t/5730)

Step-by-step explanation:

One way to write an exponential function is this:

  value at time t = (initial value) · (multiplier over period)^(t/period)

Here, the initial value is given as 741 grams, and the time period is 5730 years. The multiplier over that period is 1/2, since half of the quantity remains after that time. The problem statement tells us that "value at time t" is M(t), so we have ...

  M(t) = 741·(1/2)^(t/5730) . . . . . t in years; M(t) in grams

Answer:

5

Step-by-step explanation:

The day of the month Christmas falls on is 25th because Christmas falls on 25th December. The square root of 25 is 5 because 5 squared is 25

The expression to calculate the total cost of a jacket with an original price of x is 0.7x + 5 % of 0.7x

Solution:

Given that at a clothing store, jackets are on sale for 30% off

Sales is 5 %

To find: Expression to calculate the total cost of jacket

Let "x" be the original price of Jacket

Price of jacket after offer = original price of Jacket - 30 % of original price

Price of jacket after offer = x - 30 % of x

Price of jacket after offer = [tex]x - \frac{30}{100}x = 0.7x[/tex]

The total cost of jacket is sum of price of jacket after offer and sales tax

total cost of jacket = price of jacket after offer + sales tax

total cost of jacket = 0.7x + 5 % of 0.7x

Thus the expression to calculate the total cost of a jacket with an original price of x is 0.7x + 5 % of 0.7x

Answer:

x^2(5x-4)

Step-by-step explanation:

5x^3-4x^2=x^2(5x-4)

Answer:

2x-y=8

Step-by-step explanation:

(6,4)-(5,2)=(1,2)

L: 2x-y=k

(5,2) -> L, k=8

2x-y=8

Answer:

That would be about 11.667

The number that is 2/3 of the way from 7 to 13 on a number line is 11. This is found by calculating 2/3 of the distance between the two numbers and adding it to the starting number.

To find the number that is 2/3 of the way from 7 to 13 on a number line, you first calculate the distance between the two numbers, which is 13 - 7 = 6. Then you take 2/3 of that distance, which is 2/3 * 6 = 4. Lastly, you add this result to the starting number, in this case, 7, giving you 7 + 4 = 11. Therefore, the number that is 2/3 of the way from 7 to 13 is 11.

Natalie ordered a total of 117 muffins.

A bakers dozen is equal to 13 items. If Natalie orders 9 bakers dozen of muffins, we can calculate the total number of muffins by multiplying 13 by 9.

Number of muffins = 13 * 9 = 117

Therefore, Natalie ordered 117 muffins.

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Answer:C: x = the quantity of 1 plus or minus the square root of 17 all over 2

Step-by-step explanation:

Answer:

The answer is option C: x = the quantity of 1 plus or minus the square root of 17 all over 2

Step-by-step explanation:

The general form of the quadratic equation is ax² + bx + c = 0

The general solution of the quadratic equation is:

[tex]x=\frac{-b \pm \sqrt{b^2-4ac} }{2a}[/tex]

The given equation is x² − x − 4 = 0

So, a = 1 , b = -1 and b = -4

Substitute with a , b and c at the formula of the general solution.

The solution of the given equation = [tex]\frac{-(-1) \pm \sqrt{(-1)^2 - 4 * 1 * (-4)} }{2*1}= \frac{1\pm \sqrt{1 +16} }{2}=\frac{1\pm \sqrt{17} }{2}[/tex]

Comparing the solution with the given options

So, the answer is option C: x = the quantity of 1 plus or minus the square root of 17 all over 2

The half-life h is calculated to be approximately 2.41.

To determine the half-life h from the given half-life function:

[tex]\[ Q(t) = 28550 \cdot \left( \frac{3}{4} \right)^{\frac{t}{h}} \][/tex]

we need to solve for h in the equation:

[tex]\[ \left( \frac{3}{4} \right)^h = \frac{1}{2} \][/tex]

To solve for  h , we take the natural logarithm (ln) of both sides of the equation:

[tex]\[ \ln \left( \left( \frac{3}{4} \right)^h \right) = \ln \left( \frac{1}{2} \right) \][/tex]

Using the logarithmic property [tex]\(\ln(a^b) = b \ln(a)\)[/tex], we get:

[tex]\[ h \ln \left( \frac{3}{4} \right) = \ln \left( \frac{1}{2} \right) \][/tex]

Now, solve for h :

[tex]\[ h = \frac{\ln \left( \frac{1}{2} \right)}{\ln \left( \frac{3}{4} \right)} \][/tex]

Calculate the natural logarithms:

[tex]\[ \ln \left( \frac{1}{2} \right) = \ln(0.5) \approx -0.6931 \\\[ \ln \left( \frac{3}{4} \right) = \ln(0.75) \approx -0.2877 \][/tex]

Now, divide these values to find  h :

[tex]\[ h = \frac{-0.6931}{-0.2877} \approx 2.41 \][/tex]

So, the half-life  h  is approximately:

[tex]\[ h \approx 2.41 \][/tex]

Therefore, the half-life  h  rounded to the nearest hundredth is:

h = 2.41

b and d can be eliminated because there are multiple solutions.

answer: A, because it shows all solutions to the equation

Answer: A line that shows the set of all solutions to the equation

Step-by-step explanation:

Given :

y = -4x + 7

The graph is a linear graph with negative slope.

the variable x could be any number , this means there could be as many solutions as possible.

this means that option B is out already.

Also , the equation is  a graph and not a point , so option C and D  are also out.

Option A will definitely fit in.