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Answer: If u divide both sides by 3 you get the value o x 2 answer: Combine terms by transporting. The equation becomes 4x -7x = -21

Step-by-step explanation: 1. 4x=7(x-3) -----> Start with the given.

2. 4x=7x-21 -----> Distribute 7 by multiplying it to the individual terms inside the parenthesis. 7(x) - 7(3) = 7x -21

3. -3x=-21   ------> From step 2, combine like terms by transposing. The equation becomes 4x - 7x = -21. Simplifying, it becomes -3x = -21

4. x = 7 -----> Divide both sides by -3, you get the value o x.

Hope this helps :)

a) Option a) 9 - 1/2 is equal to 17/2.

b) Option b) 27 - 2/3 is equal to 79/3.

a) The expression 9 - 1/2 can be simplified by finding a common denominator for the terms. The common denominator for 9 and 1/2 is 2.

Multiplying 9 by 2/2, we get:

9 * (2/2) = 18/2

So, the expression 9 - 1/2 can be simplified to:

18/2 - 1/2 = 17/2

Therefore, option a) 9 - 1/2 is equal to 17/2.

b) The expression 27 - 2/3 can be simplified in a similar manner by finding a common denominator for the terms. The common denominator for 27 and 2/3 is 3.

Multiplying 27 by 3/3, we get:

27 * (3/3) = 81/3

So, the expression 27 - 2/3 can be simplified to:

81/3 - 2/3 = 79/3

Therefore, option b) 27 - 2/3 is equal to 79/3.

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Answer:

220

Step-by-step explanation:

GIven:

Joyce paid $143.00 for an item at the store that was 35 percent off the original price.

To Find:

What was the original price?

Solution:

Since that was 35 percent off the original price

Thus, 100 - 35 = 65

Equation:

143 = 0.65x

DIvide both sides by 0.65

143/0.65 = 0.65x/0.65

x = 220

Check Answer:

220 x 65% = 143

~Lenvy~

The factors of the given polynomial will be ( x + 2 ), ( x + 5 ) and ( x + 3 ).

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given expression will be solved as:-

f(x) = x³ + 10x² + 31x + 30

f(x) = ( x³ + 7x² + 10x + 3x² + 21x + 30

f(x) = ( x² + 7x + 10 ) ( (x + 3 )

f(x) = ( x²+ 5x + 2x + 10 ) ( x + 3 )

f(x) =[ x ( x+ 5 ) +2 ( x+ 5) ] ( x + 3 )

f(x) = ( x + 5 ) ( x + 2 ) ( x + 3 )

Therefore factors of the given polynomial will be ( x + 2 ), ( x + 5 ) and ( x + 3 ).

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Step-by-step explanation:

\( = \frac{75}{100} \\ \)

\( = \frac{75 \div 5}{100 \div 5} \\ \)

\( = \frac{15 \div 5}{20 \div 5} \\ \)

\( = \frac{3}{4} \\ \)

The total ounces of water Diane brought are 576 ounces and  the fraction of a gallon of water did she start the hike with is 3/16.

The cost price per ounce is the amount of money required to buy one ounce of a brand or goods.

To find the cost price per ounce, divide the total amount of cost of the goods to the total number of goods.

1. There are 8 ounces in 1 cup and 16 cups in 1 gallon. Diane brought 4.5 gallons of water to a campout.  Let x ounces of water, did she bring. Thus,

\(x=4.5\times16\times8\\x=576\rm\; ounces\)

Diane started a hike with 24 ounces of water in her backpack. The fraction of gallons in 24 ounces is,

\(n=\dfrac{24}{8\times16}\\n=\dfrac{3}{16}\)

Thus, the total ounces of water Diane brought are 576 ounces and  the fraction of a gallon of water did she start the hike with is 3/16.

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By using the fact that the sum of the interior angles is 900°, we will find that the value of x is 110.

We know that for a figure of N sides, the sum of the interior angles gives:

S = (N - 2)*180°

In this case, we have 7 sides, then the sum of the interior angles gives:

S = (7 - 2)*180° = 5*180° = 900°

Adding the 7 angles we get:

105° + 150° + 140° + x° + 135° + 125° +135° = 900°

790° + x° = 900°

x° = 900° - 790°

x = 110°

The value of x is 110.

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The present value (PV) of the investment today is approximately $2,965.05.

To find the present value (PV) of the investment today, we need to calculate the present value of each individual contribution and then sum them up. We can use the formula for the present value of an annuity to do this calculation.

The formula for the present value of an annuity is given by:

PV = C * [(1 - (1 + r)^(-n)) / r]

Where:

PV = Present Value

C = Cash flow per period

r = Interest rate per period

n = Number of periods

In this case, the cash flow per period (C) is $500, the interest rate per period (r) is 10.5% (or 0.105), and the number of periods (n) is 20 years.

Let's plug in these values into the formula and calculate the present value (PV):

PV = $500 * [(1 - (1 + 0.105)^(-20)) / 0.105]

Using a calculator, we can evaluate the expression inside the brackets:

PV = $500 * [(1 - 0.376889) / 0.105]

Simplifying further:

PV = $500 * [0.623111 / 0.105]

PV = $500 * 5.930105

PV = $2,965.05

Therefore, the present value (PV) of the investment today is approximately $2,965.05.

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Answer:

The sonar station will not detect the submarine.

Step-by-step explanation:

The area that the sonar station can detect can be modelled as a circle with center (0, 0) and radius 5 km.

The equation of a circle formula is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius.

Therefore, the equation of the circle modelling the perimeter of the sonar station detection area is:

\(\implies (x-0)^2+(y-0)^2=5^2\)

\(\implies x^2+y^2=25\)

To determine whether the sonar station will detect a swiss submarine traveling along a trajectory defined by y = -2/3x + 26/3, substitute the equation of the trajectory into the found equation of the circle.

\(\implies x^2+\left(-\dfrac{2}{3}x+\dfrac{26}{3}\right)^2=25\)

Simplify:

\(\implies x^2+\dfrac{4}{9}x^2-\dfrac{104}{9}x+\dfrac{676}{9}=25\)

\(\implies 9x^2+4x^2-104x+676=225\)

\(\implies 13x^2-104x+451=0\)

Solve the equation for x using the quadratic formula:

\(x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0\)

\(\implies x=\dfrac{-(-104) \pm \sqrt{(-104)^2-4(13)(451)}}{2(13)}\)

\(\implies x=\dfrac{104 \pm \sqrt{-12636}}{26}\)

\(\implies x=\dfrac{104 \pm 18\sqrt{39}\:i}{26}\)

\(\implies x=4 \pm \dfrac{9\sqrt{39}}{13}\:i\)

As the solutions are complex numbers, this means that the linear trajectory of the submarine will not intersect the detection area of the sonar station. Therefore, the sonar station will not detect the submarine.

Answer:

x≥2 and x<2 : ∅

x≥2 or x<2 : All real numbers

x≤2 and x≥2 : 2

Step-by-step explanation:

the first one must follow both conditions, so no number would work.

the second one works with any number, so all real numbers.

the third one has only one condition that works, 2

example:

The value of x is 22

Step-by-step explanation:

We are given that there are two numbers

First number is x

second number is 35

The sum of x and 35 is 57

so, we get equation as

now, we can solve solve x

So, subtract both sides by 35

Answer:

-20 + 14\(\sqrt{2}\)

Step-by-step explanation:

Answer:

20 students are randomly selected from the school.

Step-by-step explanation:

the slope perpendicular to y= ¾x is

-1 ÷ ¾ = -4/3

so the equation :

y-(-3)= -4/3(x-3)

y+3= -4/3x +4

y = -4/3x +4-3

y = -4/3x + 1

The transformation below that caused AB to transform into A'B' is a reflection across the y-axis

Given the following coordinates

A = (6, 2)

B = (2, 6)

A' = (-6, 2)

B' = (-2, 6)

According to the reflection rule, the reflection over y axis is given as:

\((x,y)\rightarrow (-x,y)\)

Note that the x-coordinate was negated as seen from the translation A to A' and B to '.

Hence the transformation below that caused AB to transform into A'B' is a reflection across the y-axis

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To know the area of a figure, you would like to know its shape and estimations. The steps to take on how to draw a figure with the use of a ruler and a pencil is given below.

Begin by selecting the kind of figure you need to draw. Make use of a ruler to draw the sides of the figure. Make sure that the lines are straight and have the right length.

E.g. If the figure may be a rectangle or a parallelogram, you wish to create beyond any doubt that inverse sides are parallel to each other. If the figure is triangle, you would like to draw three lines that shows at three distinctive points. At last, name the sides and vertices of the figure.

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The x-intercepts are:

t = (15 + √(385)) / 8 ≈ 1.94

t = (15 - √(385)) / 8 ≈ -0.819

To find the x-intercepts of the function, we set f(t) equal to zero and solve for t:

-16t² + 60t + 16 = 0

Dividing both sides by -4 (to simplify the equation) gives:

4t² - 15t - 4 = 0

Using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

with a = 4, b = -15, and c = -4, we have:

t = (-(-15) ± √((-15)² - 4(4)(-4))) / 2(4)

Simplifying:

t = (15 ± sqrt(385)) / 8

Therefore, the x-intercepts are:

t = (15 + √(385)) / 8 ≈ 1.94

t = (15 - √(385)) / 8 ≈ -0.819

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Answer:

0.5

Step-by-step explanation:

9 dollars divided by 18lbs.

9/18 = 0.5

$0.50/lbs

Answer:

Your answer will be "B" Trust me

Answer:

Number 2

Step-by-step explanation:

If you substitute -1 to the x in the second equation you'll get 3+15=18

18=18

The derivative of f(x) + g(x) is cosx+2cos2x

Derivative : In mathematical calculus, the derivative is the rate of change of a function at a instant point.

Derivative of a function is denoted by dy/dx, where derivative of y is happening with respect to x.

We have to add f(x) and g(x), then differentiate the whole addition with respect to x.

Given that, f(x) = sin(x) & g(x) = sin(2x)

So, f(x) + g(x) = sin(x) + sin(2x)

Now, differentiating with respect to x we get,

(f(x)+g(x))' = d/dx(sinx) + d/dx(sin 2x)

               = cosx+2cos2x

Derivative of  f(x) + g(x) = cosx+2cos2x

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Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

405 of the students

Step-by-step explanation:

Answer:

Four-thirds

Step-by-step explanation:

If you graph the first equation on desmos, then graph the equation x = -1, the intersection is at 1.333333, making the answer 4/3.

The Limit of f (x) as x approaches negative 1 is 4/3, the correct option is C.

A function is a law that relates a dependent and an independent variable.

f(x) = x² - (1/3)x    x ≠ -1

    = -1                  x = -1

\(\lim_{x \to \ -1} f(x)\) = (-1)² - (1/3)(-1)

                      f(x) = 1 + (1/3)

                      f(x) = 4/3

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Answer:

Step-by-step explanation:

In this scenario, the confidence interval represents the possible range of differences in the proportion of employees who skip breakfast when free breakfast is offered and when it's not. A confidence interval that does not include zero indicates that there is statistically significant evidence to suggest a difference in proportions between these two groups.

Therefore, for the first interval (-0.44,-0.16), since it does not include zero, we can be confident that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.

For the second interval (-0.25, 0.05), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

Similarly, for the third interval (-0.23, 0.15), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

So, the correct answer is:

For the interval (-0.44,-0.16), we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.

For the intervals (-0.25, 0.05) and (-0.23, 0.15), our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

y-(-9) = -6(x-(-4)), y = -6x-33