Solve 4(4f-9)=-(2-f)

Answer:

Let the quadratic equation be  [tex]2x^2 +12x+ 6[/tex]

Step 1: Take the coefficients of the [tex]x^2[/tex] term and divide the entire equation

Here the coefficient of [tex]x^2[/tex] is 2

So  dividing the entire equation by 2, we get

[tex]x^2 +6x+ 3[/tex]

Step 2:  Move the constant term to the right side of the equation

[tex]x^2 +6x = - 3[/tex]

Step 3: Complete the square on the left side of the equation and balance this by adding the same number to the right side of the equation

[tex](\frac{b}{2})^2[/tex] =  [tex](\frac{6}{2})^2[/tex] = [tex](3)^2[/tex]  =  9

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

[tex](x+3)^2 = 6[/tex]

Step 4: Take the square root on both sides of the equation

[tex](x+3) = \sqrt{6}[/tex]

[tex]x+3 = \pm 2.45[/tex]

Step 5 Subtract 3 from both sides:

[tex]x+3 - 3 = \pm 2.45 -3[/tex]

[tex]x = \pm 2.45 -3[/tex]

x =  2.45 - 3   or x = -2.45 - 3

x = - 0.55  or  x = -5.45

Answer:

5x+10

Step-by-step explanation:

you will add 7x_2x=5x

then 4+6=10

Answer:

y=-4/3x+2

Step-by-step explanation:

Answer:

C)Rhomus

Step-by-step explanation:

a rhombus is parallel

The correct answer is option C. The shape Amily's riddle best describes is Rhombus.

Let's analyze the riddle step by step to determine which shape Amily is describing.

1. Quadrilateral: The shape has four sides.

2. All sides are parallel: This indicates that opposite sides are parallel to each other, which means the shape is a type of parallelogram.

3. 4 angles, but they are not all equal: This means that although the shape has four angles, they are not all the same measure.

Given these clues, let's evaluate each option:

A) Pentagon: This is a five-sided shape, not a quadrilateral. So, this option is incorrect.

B) Rectangle: A rectangle has four sides and opposite sides are parallel. However, all the angles in a rectangle are equal (each angle is 90 degrees). So, this option is also incorrect.

C) Rhombus: A rhombus has four sides and opposite sides are parallel. Additionally, all sides are of equal length. However, a rhombus can have angles that are not all equal (typically, it has two pairs of equal angles). Given the description, this could be a potential answer, but let’s also consider the last option.

D) Trapezoid: A trapezoid has one pair of parallel sides. However, the riddle specifies that all sides are parallel, which does not match the definition of a trapezoid.

Given that the shape described has all sides parallel and the angles are not all equal, the best match is C) Rhombus.

Answer:

Length is w-5

Area  = length x width

84 = (w-5)w

84 = w^2 - 5w

0 = w^2 - 5w - 84

0 = (  w     -    12 )( w   +     7    )

w + 7 = 0 leads to negative measures.

w-12=0 ---> w = 12

width is 12, length is 5 less, or 7

The dimensions of the rectangle are 12 feet by 7 feet, determined by solving the quadratic equation derived from the relationship between the length and width and the given area of the rectangle.

To find the dimensions of a rectangle where the length is five feet less than its width and the area is 84 square feet, we can set up an equation. Let's define the width of the rectangle as w feet. Then, the length would be w - 5 feet. Since the area of a rectangle is defined as the product of its length and width, we get the following equation:

w times (w - 5) = 84

Expanding the left side gives us:

w^2 - 5w = 84

To solve this quadratic equation, move all terms to one side to set the equation to zero:

w^2 - 5w - 84 = 0

Factoring the quadratic equation, we look for two numbers that multiply to give -84 and add to give -5. These numbers are -12 and +7. So the equation factors as follows:

(w - 12)(w + 7) = 0

The solutions to the equation are w = 12 and w = -7. However, width cannot be negative in this context, so we discard w = -7. Thus, the width is 12 feet and the length is 12 - 5 = 7 feet.

Therefore, the dimensions of the rectangle are 12 feet by 7 feet.

Answer:

The height of the pyramid is 13.3 inches

Step-by-step explanation:

Let

h ----> the height of the pyramid

b ---> the base of the square pyramid

we know that

Applying the Pythagorean Theorem

[tex]15^2=h^2+(\frac{b}{2})^2[/tex]

see the attached figure to better understand the problem

we have

[tex]b=14\ in[/tex]

substitute

[tex]15^2=h^2+(\frac{14}{2})^2[/tex]

Solve for h

[tex]225=h^2+49\\h^2=225-49\\h^2=176\\h=\sqrt{176}\ in\\h=13.3\ in[/tex]

Answer:

x-2

Step-by-step explanation:

x-4+2 = x-2

Answer:

x^2 - 2x - 8

Step-by-step explanation:

Final answer:

To solve the equation 5(x+2)=24-2x, distribute, combine like terms, solve for x, and check the solution. The solution x = 2 satisfies the equation, so it is valid.

Explanation:

To solve the equation 5(x+2)=24-2x, we can justify each step as follows:

Distribute the 5 to the terms inside the parentheses: 5x + 10 = 24 - 2x

Combine like terms on both sides of the equation: 5x + 2x = 24 - 10

Combine the x terms: 7x = 14

Divide both sides of the equation by 7 to solve for x: x = 2

Check the solution by substituting it back into the original equation: 5(2+2) = 24 - 2(2)

Simplify the left side: 5(4) = 24 - 4

Multiply: 20 = 20

The solution x = 2 satisfies the equation, so it is valid.

Answer:

The term to add is

[tex]-\frac{1}{3} x[/tex]

Step-by-step explanation:

Let

b ----> the term to add

we have

[tex]\frac{5}{6}x-4+b=\frac{1}{2} x-4[/tex]

Solve for b

Adds 4 both sides

[tex]\frac{5}{6}x+b=\frac{1}{2} x[/tex]

subtract 5/6x both sides

[tex]b=\frac{1}{2} x-\frac{5}{6}x[/tex]

Remember that

[tex]\frac{1}{2}=\frac{3}{6}[/tex]

substitute

[tex]b=\frac{3}{6} x-\frac{5}{6}x[/tex]

[tex]b=-\frac{2}{6} x[/tex]

Simplify

[tex]b=-\frac{1}{3} x[/tex]

therefore

The term to add is

[tex]-\frac{1}{3} x[/tex]

Answer:

A

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

2 times 4 = 8

8 plus 6 = 14

14 divided by 2 = 7

7 squared = 49

49 minus 9 = 40

40 divided by 2 = 20

In this problem we convert the operations into an equation and solve it step by step until we get two possible answers. We pick the one that fits the conditions of the problem, which gives us 9 as the positive number the student had originally thought of.

Let's denote the number you are thinking of as x. Following your sequence of operations we can translate this into an equation:

(((4x + 6) / 2)² - 9) / x = 20

Solving this equation can be done step by step:

Since you mentioned that the number you thought of was positive, we disregard 0.25 (since the squared result after the first operations would be too small to subtract 9 and still divide by the original number to get 20). Therefore, the number you thought of was 9.

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Answer:

4

Step-by-step explanation:

The first digit after the decimal point is the tenths place. in this case, it would be 4

Answer:

4 Is in the tenths place

Step-by-step explanation:

7 in the hundreds

2 in the tens

9 in the ones

4 in the tenths

6 in the hundredths

Answer:

sum was 300000

Step-by-step explanation:

let sum of money is placed  is x rs

Term T = 3 years, rate R = 10%

Then simple interest for for 3 years is

[tex]SI= \frac{PTR}{100}\\ SI=\frac{x\times 3\times 10}{100} \\SI = 0.3x[/tex]

Sum of x will become x+0.3x = 1.3x after 3 years. now this 1.3x is kept for compound interest for two years. ie

[tex]A =P[1+R]^t\\471900=1.3x[1+\frac{10}{100} ]^2\\x=\frac{471900}{1.573} \\x=300000[/tex]

Sum was 300000

At the simple interest rate, the rate is applied only to the initial sum, while

at the compound interest, the rate is applied to the amount in the account.

Reasons:

Let P represent the sum of money invested, we have;

Where;

P = The initial sum invested

r = The simple and compound interest rate applied = 10% = 0.1

t₁ = The number of years the money is placed at simple interest = 3 years

t₂ = The number of years the money is placed at compound interest = 2 years

Therefore;

[tex]\mathbf{(P + P \times 0.1 \times 3) \times (1 + 0.01)^{2}} = 471900[/tex]

Which gives;

[tex]P \cdot (1 + 0.3 ) \times (1 .01)^{2} = 471900[/tex]

[tex]\displaystyle P =\mathbf{\frac{471900}{(1 + 0.3 ) \times (1 .01)^{2} }} \approx 355,847.466[/tex]

The sum of money invested, P ≈ Rs 355,847.466

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Answer:

Tony make 4 half-court shots and misses 16 half-court shots.

Step-by-step explanation:

Given:

Points earned for every successful, half-court shots = [tex]20[/tex]

Points deducted for missing the shots = [tex]5[/tex] or [tex]-5[/tex]

Total number of shots in the game = [tex]20[/tex]

Final points earned by Tony = [tex]0[/tex]

According to the question:

Let the number of successful half-court shot be [tex]x[/tex]

And the number of shots missed be [tex]20-x[/tex]

So,

In terms of points we can re-write it as:

⇒ [tex]20(x)-5(20-x) =0[/tex]

⇒ [tex]20x-100+5x=0[/tex]

⇒ [tex]25x-100=0[/tex]

⇒ [tex]25x-100+100=100[/tex]

⇒ [tex]25x=100[/tex]

⇒ [tex]\frac{25x}{25} =\frac{100}{25}[/tex]

⇒ [tex]x=\frac{100}{25}[/tex]

⇒ [tex]x=4[/tex]

Tony make 'x' shots that is 4 and the number of shot he missed is (20-x) =(20-4)=16

Final answer:

The expression given is factored to identify common factors of 30 and 44. By identifying factors like 3, 5 (for 30) and 2, 11 (for 44), it's shown that the expression is indeed divisible by both 30 and 44.

Explanation:

The student asked to prove that the value of the expression: (518−258)(164−213−45) is divisible by 30 and 44. To approach this proof, we will simplify and factor the expression where possible to find common factors of 30 (2*3*5) and 44 (4 × 11).

First, let's factor each part of the expression:

518 = (52)9 = 259

258 = (52)8 = 516

164 = (24)4 = 216

213 remains the same

45 = (22)5 = 210

Now, we rewrite the original expression with these factors:

(259 − 516)(216 − 213 − 210)

Looking at the first parenthesis, we see that 259 and 516 have a common factor of 516, so we can factor it out:

516(25−1)(216−213−210)

Recognizing that 25−1 = 24, and that 24 is divisible by both 3 and 8 (and thus 4), we have a clear division by 30.

For the second parenthesis, we can see that 210 is a common factor:

210(26−23−1)

Again, noticing that 26−23−1 leaves us with numbers of the form 2n − 2n-k − 1, we can confirm divisibility by 2 and potentially by 4 depending on the value of n. Checking the values, 26 − 23 − 1 equals 57, which is also divisible by 3.

So the original expression has factors that include 2, 3, 5, and 11, thereby confirming that the expression is divisible by both 30 and 44.

Answer:

426.9 Km²

Step-by-step explanation:

The shaded area is the area of the triangle subtract the area of the circle.

Area of triangle = 0.5 bh ( b is the base and h the perpendicular height )

Here b = 40 and h = 27, thus

Area = 0.5 × 40 × 27 = 20 × 27 = 540 Km²

Area of circle = πr² ← r is the radius

Here the diameter is 12, thus radius = 12 ÷ 2 = 6

Area = π × 6² = 36π ≈ 113.1 Km²

Shaded area = 540 - 113.1 = 426.9 Km²

Answer:

(0,9) for y-intercept

perp.: (-1/2)= m

y - 9 = (-1/2)x - 0

y = (-1/2)x + 9

Step-by-step explanation:

Answer: Decolonization as a result of World War II.

Step-by-step explanation:

Answer:

y=4x+40

Step-by-step explanation:

The equation  best shows the relationship between x and y is y = 4x + 40.

Given that,

John's total earnings, y, from selling x bars of ice cream

So based on this, the following equation should be considered

y = 4x + 40

Therefore, the last option is correct.

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Answer:

THE ANSWER IS 1.2068965517

Step-by-step explanation:

Answer:

The height of the rectangle is 4 cm.

Step-by-step explanation:

You find area by multiplying base and height.

The formula is  A=bh

so 100=25h

25 times 4 is 100

100=25*4

4cm is your answer

Answer:

c) 8.6

Step-by-step explanation:

Take the coordinates of the two points.

(0,8) and (7,3)

Formula:

√(x₁ - x₂)² + (y₁ - y₂)²

Substitute:

√(0 - 7)² + (8 - 3)²

√(-7)² + (5)²

√(49) + (25)

√(74) ≈ 8.6

The question appears to be incomplete as it doesn't provide the necessary coordinates for calculating the length of a line segment. The distance formula or Pythagorean theorem would generally be used to calculate this in Mathematics.

Given the format of the question, it seems that it's incomplete or missing the relevant coordinates we need to calculate the length of a line segment. Normally in mathematics, we would use the distance formula, or Pythagorean theorem, to compute the length of a line segment between two points in a plane. The formula is √[(x₂-x₁)² + (y₂-y₁)²], where (x₁,y₁) and (x₂, y₂) are the coordinates of the two points. In this scenario, without information about the coordinates, we can't compute the length of a line segment. However, if you provided me with the coordinates, I can guide you in computing the length of the line segment.

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Answer:

Angles: 42°, 114°, 24°, 30°, 150°.

Step-by-step explanation:

Pie Charts

They represent the comparative values of a given variable subject to study. The whole pie is cut in angular sections where all the angles must sum 360°. If the sum of all the values is S and one particular value is x, then the angle of its circular section is given by

[tex]\displaystyle angle=\frac{x}{S}\ 360^o[/tex]

We have the staff of an office is S=60. When asked about their favorite type of takeaway we get:

Pizza: 7. Its corresponding angle is

[tex]\displaystyle angle=\frac{7}{60}\ 360^o=42^o[/tex]

Curry 19.

[tex]\displaystyle angle=\frac{19}{60}\ 360^o=114^o[/tex]

Fish & chips 4

[tex]\displaystyle angle=\frac{4}{60}\ 360^o=24^o[/tex]

Kebab 5

[tex]\displaystyle angle=\frac{5}{60}\ 360^o=30^o[/tex]

Other 25

[tex]\displaystyle angle=\frac{25}{60}\ 360^o=150^o[/tex]

We can see the sum of all angles is 360°

The angles for the pie chart are as follows:

- Pizza: 42 degrees

- Curry: 114 degrees

- Fish & chips: 24 degrees

- Kebab: 30 degrees

- Other: 150 degrees

These angles can be used to create a pie chart that accurately represents the favorite take-away choices of the office staff.

To calculate the size of each angle for the pie chart representing the favorite take-away choices of the 60 office staff, we need to determine the percentage each category represents in the total.

First, add up the frequencies:

Pizza + Curry + Fish & chips + Kebab + Other = 7 + 19 + 4 + 5 + 25 = 60

Now, calculate the percentage for each category:

- Pizza: (7/60) * 100% = 11.67%

- Curry: (19/60) * 100% = 31.67%

- Fish & chips: (4/60) * 100% = 6.67%

- Kebab: (5/60) * 100% = 8.33%

- Other: (25/60) * 100% = 41.67%

Now that we have the percentages, we can calculate the corresponding angles for the pie chart.

Each percentage corresponds to a fraction of the total 360 degrees in a circle.

So, for example, Pizza would be (11.67/100) * 360 = 42 degrees, Curry would be (31.67/100) * 360 = 114 degrees, and so on.

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Angle 3 and angle 4 are supplementary angles and when added together need to equal 180 degrees.

To find angle 4 subtract angle 3 from 180.

Angle 4 = 180 - 101 = 79 degrees.

Answer:

your answer is correct

Step-by-step explanation: because each angle equals the same thing

5(x-2)-3x+7

5x-10-3x+7

2x-10+7

2x-3

Hope this step by step process helped

Answer: 251,203

Step-by-step explanation:

Martin pays 965 every month for seven years. Therefore,

965×12×7= 81,060

Then, he has a balloon payment of 170,143 to make. Therefore, totaal financed price he paid for his home is 81,060+170,143= 251,203.

Answer: 251,203

Step-by-step explanation:

Martin pays 965 every month for seven years. Therefore,

965×12×7= 81,060

Then, he has a balloon payment of 170,143 to make. Therefore, totaal financed price he paid for his home is 81,060+170,143= 251,203.

(–4, 3) (4, –3) (–3, –4) (3, 4)

this is a rather simple yet complex concept the easiest way to solve these is to do the exact opposite.

so in this instance it is refrcted across the y-axiss so we swap ONLY the x value NOT the Y ie (-4,3) would switch to (4,3)

same thing would apply if it reflected across x-axis ex (-4,-3)

If it reflect across orgin you change both signs. ex (4,-3)

ie.

(–4, 3) (4, –3) (–3, –4) (3, 4)

changes to

(4, 3) (-4, –3) (3, –4) (-3, 4)

hope it helps

The coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).

A reflection is an involution: when applied twice in succession, every point returns to its original location, and every geometrical object is restored to its original state.

Given is a point R = (-3, 4) we need to find the coordinates of the point R after it being reflected over y-axis,

So, we know that,

When dealing with reflection of a line or shape or a figure in the coordinate plane, especially if it is reflected across the y-axis, you just have to give the opposite of the given (original) x- coordinate in order to give a symmetric figure.

The rule of reflection over y-axis is =

(x, y) = (-x, y)

So,

R = (-3, 4), after it being reflected over y-axis =

R' = (3, 4)

Hence the coordinates of the image of vertex R after a reflection across the y-axis is (3, 4).

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Answer:

x = 3.6

Step-by-step explanation:

The 2 chords intersect inside the circle, thus

The product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord, that is

5x = 6 × 3 = 18 ( divide both sides by 5 )

x = 3.6

Answer:

[tex]Apple\ muffin\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ Bran\ muffin\\10\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 4\\15\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 6\\20\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8\\35\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 14[/tex]

Step-by-step explanation:

[tex]For\ 5\ apple\ muffins, bran\ muffin=2\\\\Ratio\ of\ bran\ muffin\ to\ apple\ muffin=\frac{number\ of\ bran\ muffin}{number\ of\ apple\ muffin}\\\\Ratio\ of\ bran\ muffin\ to\ apple\ muffin=\frac{2}{5}\\\\Bran\ muffin=\frac{2}{5}\times apple\ muffin\\\\When\ apple\ muffin=10\\\\Bran\ muffin=\frac{2}{5}\times 10=4\\\\When\ apple\ muffin=15\\\\Bran\ muffin=\frac{2}{5}\times 15=6\\\\When\ apple\ muffin=20\\\\Bran\ muffin=\frac{2}{5}\times 20=8[/tex]

[tex]When\ apple\ muffin=35\\\\Bran\ muffin=\frac{2}{5}\times 35=14[/tex]

Answer:

528

Step-by-step explanation:

because each class has 22 students and there are 24 classes you multiply them

Answer: 528 children

Step-by-step explanation: 22 children in each class. 24 total classes.

22•24=528