what’s the answer?? because I don’t understand this

The vertex form of parabola y = x² + 9 · x + 8 is the quadratic equation y + 49 / 4 = (x + 9 / 2)².

Herein we find the equation of a parabola in standard form, that is, a quadratic equation of the form:

y = a · x² + b · x + c

Where:

And we are asked to transform this expression into vertex form, that is, a quadratic equation of the form:

y - k = C · (x - h)²

Where:

This can be done by means of algebra properties. First, write the quadratic equation:

y = x² + 9 · x + 8

Second, use algebra properties until a perfect square trinomial is found:

y = x² + 9 · x + 8

y + 49 / 4 = x² + 9 · x + 81 / 4

Third, factor the perfect square trinomial:

y + 49 / 4 = (x + 9 / 2)²

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The first quadrant starts on (12,11)

If the quadrant moves 8 units left it will be located at (12-8, 11) = (4,11)

and if it moves 7 units down it will be located at (4,11-7) = (4,4)

So the new location of the quadrant is (4,4)

It's important to notice that the first quadrant starts on (12,11) and the coordinates are (x,y) where x is on the horizontal axis and y is on the vertical axis. So when it moves left it's decreasing the x value and when it moves down it's decreasing the y value

8. The ratio of the adjacent over the hypotenuse is 8:17

10. The ratio of the adjacent over the hypotenuse is 1:√2

From the question, we are to calculate the ratio of the adjacent over the hypotenuse in the given triangles

8.

Using angle A as the reference angle

Adjacent = 16

Hypotenuse = 34

Thus,

The ratio of the adjacent over the hypotenuse = 16/34

The ratio of the adjacent over the hypotenuse =  8/17

Hence, the ratio is 8:17

10.

First,

We will calculate the hypotenuse, H

From the Pythagorean theorem, we can write that

H² = 4² + 4²

H² = 16 + 16

H² = 32

H = √32

H = 4√2

Now,

Using angle A as the reference angle

Adjacent = 4

Hypotenuse = 4√2

Thus,

The ratio of the adjacent over the hypotenuse = 4/4√2

The ratio of the adjacent over the hypotenuse =  1/√2

Hence, the ratio is 1:√2

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The sum of all possible values of b is 124 in the given question.

If two or more objects have a common centre, they are said to be concentric in geometry.

Concentric shapes include spheres, circles, regular polyhedral, and regular polygons because they all share a central axis. In Euclidean geometry, concentric circles always have different radii but the same centre.

The difference between the areas is [tex]$ \frac{\pi(b^2 - a^2)}{4} = 48 \pi[/tex]

Therefore  b² = a² +1 92

We can write the equation as  (b−a)(b+a)=192

So b−a and b+a are factors of 192

Here are the possibilities:  

 b−a=1, b+a=192 ;

 b−a=2, b+a=96 ;

 b−a=3, b+a=64 ;

 b−a=4, b+a=48 ;

 b−a=6, b+a=32 ;

 b−a=8, b+a=24 ;

and

 b−a=12, b+a=16

Add the pairs of equations and divide by 2 (as long as the sum is even): b=49; b=26; b=19; b=16; and b=14.

49 + 26 + 19 + 16 + 14 = 124

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Answer:

The length would be 29.

Step-by-step explanation:

Follow the distance formula in the image.

-Hope this Helped

Answer:

2x4 is 8

Step-by-step explanation:

4 to times so 4+4 =8 thx

Answer:

  7.  VS = 17

  8.  QR = 6

  9.  UT = 17

Step-by-step explanation:

You have trapezoid QRTU with midsegment VS parallel to bases QR and TU. Given dimensions for two of these parallel lines, you want the measure of the third.

The markings on the parts of segments QU and RT indicate that points V and S are their midpoints, respectively. This makes segment VS a "midsegment", one that joins the midpoints of opposite sides. As such, its length is the average of the lengths of QR and TU:

  VS = (QR +TU)/2

This is the relation that is used for problem 7.

For problems 8 and 9, this is rearranged to give the values of QR and UT:

  QR = 2VS -UT

  UT = 2VS -QR

From above, ...

  VS = (QR +UT)/2 = (12 +22)/2

  VS = 17

From above, ...

  QR = 2VS -UT = 2(9) -12

  QR = 6

From above, ...

  UT = 2VS -QR = 2(11) -5

  UT = 17

__

Additional comment

You will note that the line segments form an arithmetic sequence: the difference in length between adjacent segments is the same.

  7: 12, 17, 22

  8: 6, 9, 12

  9: 5, 11, 17

Step-by-step explanation:

In order to share the money equally

We take the variables as 'x'

This is because the given values are in the form of a ratio

So to do this we plug these values into a equation which is,

[tex]x + 5x + 2x = 32[/tex]

Adding the values we get,

[tex]8x = 32[/tex]

Dividing both sides by 8 we get,

[tex]\frac{8x}{8}= \frac{32}{8}[/tex]

[tex]x = 4[/tex]

Now we multiply the given values by x which is 4 in order to find how much money each ratio get

[tex]x = 4[/tex]

[tex]5x = 5X4 = 20[/tex]

[tex]2x = 2X4 = 8[/tex]

4 + 20 + 8 = £ 32 (Proving)

There are times when I use or calculate percentages in my personal life or at work. This is true.

The benefits that result from using percentages in this application is that it gives one an idea of the value to be paid as tax. The drawback is that it can be complicated for large number.

A word problem that can Illustrate percentage is that "An income is $1000 and there's a tax of 10%, how much will be paid?"

A number or ratio expressed as a fraction of 100 is called a percentage. Divide the value by the total value to get the percentage, then multiply that number by 100.

For instance, many statistics in the media, bank interest rates, retail discounts, and inflation rates are all expressed as percentages. For understanding the financial aspects of daily life, percentages are crucial.

For example, an income is $1000 and there's a tax of 10%, the tax will be:

= 10% × $1000

= $100

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The correct linear equation which shows a proportional relationship is,

⇒ y equals two thirds times x.

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Now,

We know that;

The proportion relationship is,

⇒ y = kx

Where, k is constant of proportional.

By option 1;

The expression is,

⇒ y = 2/3 × x

⇒ y = 2/3x

Hence, It shows the linear equation.

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The statement that is true about the ratios comparing the width and length of each painting is:

The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

A ratio is a fraction which compares the values of two numbers. Such that they can be expressed as a ratio of one to the other. Example is the ratio of a to b which can be expressed as; a:b or a/ b.

From the first dimension of the canvas size, we have;

length = 6 feet

width = 4 feet

So that,

the ratio comparing the width and length = 4/ 6

                                                      = 0.6667

From the second dimensions of the canvas size, we have;

length = 3 feet

width = 2 feet

the ratio comparing the width and length = 2/ 3

                                                       = 0.6667

Therefore, the statement that is true about the ratios comparing the width and length of each panting is; The paintings' width to length ratios are equal because the ratio 4 to 6 is equal to the ratio 2 to 3.

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Answer:

Step-by-step explanation: i can't see the lab top

The equation for the temperature at midnight and the solution are Tm = 3T + 5 and -16 degrees Celsius respectively

An equation is a mathematical statement that is made up of two expressions joined by an equal sign.

Let T represent the temperature

The temperature tripled and then rose 5 degrees can be written as:

Tm = 3T + 5

where Tm is the temperature at midnight.

If the temperature at 8:00 AM was –7 degrees Celsius, we have:

Tm = 3(-7) + 5

Tm = -21 + 5

Tm = -16 degrees Celsius

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Answer:

----------------------------------

Since the triangle is isosceles, the two angles opposite to equal sides are congruent:

The sum of the three angles is 180°:

The angle measures are:

Answer:

Step-by-step explanation: Multiply 20 by 12 and divied 8 that should give u your answer

Answer:

[tex]\dfrac{917}{256}=3.58203125[/tex]

Step-by-step explanation:

The Riemann sum is a method by which we can approximate the area under a curve using a series of rectangles.

The Lower Riemann Sum uses the minimum height of the rectangle on each subinterval.  

As the Lower Riemann Sum is entirely below the curve, it is an underestimation of the area under the curve.

The number of partitions is the number of rectangles used.  

Partitions can be of equal length or not of equal length.

Given:

The given partition divides the interval [0, 1] into 3 subintervals:

To calculate the areas of the rectangles, multiply the width of each rectangle by its height.

The width is the difference between the x-values of each subinterval.

The height is the minimum value of the function across the subinterval. For the given function, this is the value of the function for the right side of the subinterval.

First rectangle [0, 1/2]:

[tex]\begin{aligned}\implies \left(\dfrac{1}{2}-0\right) \cdot f\left(\dfrac{1}{2}\right)&=\dfrac{1}{2} \cdot \left(4-\left(\dfrac{1}{2}\right)^3\right)\\\\&=\dfrac{1}{2} \cdot \dfrac{31}{8}\\\\&=\dfrac{31}{16}\end{aligned}[/tex]

Second rectangle [1/2, 3/4]:

[tex]\begin{aligned}\implies \left(\dfrac{3}{4}-\dfrac{1}{2}\right) \cdot f\left(\dfrac{3}{4}\right)&=\dfrac{1}{4} \cdot \left(4-\left(\dfrac{3}{4}\right)^3\right)\\\\&=\dfrac{1}{4} \cdot \dfrac{229}{64}\\\\&=\dfrac{229}{256}\end{aligned}[/tex]

Third rectangle [3/4, 1]:

[tex]\begin{aligned}\implies \left(1-\dfrac{3}{4}\right) \cdot f\left(1\right)&=\dfrac{1}{4} \cdot \left(4-\left(1\right)^3\right)\\\\&=\dfrac{1}{4} \cdot 3\\\\&=\dfrac{3}{4}\end{aligned}[/tex]

Therefore, the Lower Reimann Sum for the given function over the given interval and partitions is the sum of the area of the rectangles:

[tex]\implies \dfrac{31}{16}+\dfrac{229}{256}+\dfrac{3}{4}=\dfrac{917}{256}=3.58203125[/tex]

The team loses 20 people/audience with each loss.

The slope formula defines to the formula used to calculate the steepness of a line and determines how much it's inclined. To calculate the slope of the lines, the x and y coordinates of the points lying on the line can be used.

The formula to calculate slope is:

m = (y2 - y1)/(x2 - x1) = Δy/Δx

When the team lost eight games, 295 people attended the next game.

When the team lost 13 games, 199 people attended the next game.

Slope = 295-199/8-13

slope=100/-5

slope=-20

Therefore, the team loses 20 people/audience with each loss.

And the attendance loss is 20 times as great as the number of games lost/losses

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Solving given algebra problem, value of x is equal to -1. It is the area of mathematics that uses arithmetic to manipulate or operate abstract symbols rather than actual numbers.

Isolate the squared term and the constant term on the opposite sides of the equation to solve quadratic equations using the square root method. After that, take the square root of both sides, plus or minus the side with the constant term.

Given equation,

[tex]12+\sqrt{1-5x} =18\\\sqrt{1-5x}=18-12\\ \sqrt{1-5x}=6\\\\square\\ case1\\1-5x=64x=-1\\case2\\1-5x=-6\\x=7/5[/tex]

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Therefore , the solution of the given problem of speed comes out to be

the ball accelerates at 0.33 m/s2.

Speed is a pace that is measured in terms of how far an object travels in a given amount of time. Speed can be measured in a wide range of ways, including in miles an hour, laps every minute, and meters a second. There are connections between the units of time, distance, and speed. Three ways of expressing the relationship are

d = rt, r = dt, and t = dr.

Given -

The ball's initial speed is 0 meters per second.

v = 12 m/s is the ball's final speed.

36 seconds were used.

Determine the ball's acceleration.

Solution:

=> A = (v-u)/t

=>A = (12-0)/36

=> A = 12/36

=> A =1 /3

=> A = 0.33 m/s²

Consequently, the ball accelerates at 0.33 m/s2.

Therefore , the solution of the given problem of speed comes out to be

the ball accelerates at 0.33 m/s2.

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The product of -22/5 × - 1/3 is 12/15

A product in math is defined as the result of two or more numbers when multiplied together. For example if 5 is multiplied by 2 , the product is 10 i.e 5 × 2 = 10 , 10 is the product where 5 and 2 are the factors. Also 5×4 = 20, 20 is the product and the 5 and 4 are the products.

The division of this of the product with any of the factors will give the other factors.

To solve -2 2/5 × -1/3

we first change the mixed fraction to improper fraction.

We then multiply -12/5 with -1/3

-2 2/5 = -12/5

-12/5 × -1/3

= 12/15

therefore the value of -2 2/5 × -1/3 is 12/15

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The probability that a randomly chosen quadrilateral with four right angles will also have four equal side lengths is 25%.

Probability is a branch of mathematics that deals with the likelihood of an event occurring. It is the measure of how likely it is that something will happen or be the case. Probability is expressed as a number between 0 and 1, where 0 indicates impossibility and 1 indicates certainty. Probability can be used to calculate the chances of a certain outcome based on a set of conditions or data. Probability can also be used to make decisions and predictions about the future.

This is because of the Venn diagram that Bart created. If a quadrilateral has four right angles, then it can either have four equal side lengths (which makes it a square) or it can have four unequal side lengths. Since there are 8 quadrilaterals in the set with four equal side lengths (E) and 16 quadrilaterals in the set with four right angles (R), the probability that a randomly chosen quadrilateral with four right angles will also have four equal side lengths is 8/16, which is equivalent to 25%. Therefore, the probability that a randomly chosen quadrilateral with four right angles will also have four equal side lengths is 25%, rounded to the nearest whole percent.

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Answer: 5.75pi(yards)

Step-by-step explanation: We know the radius is 3 so the area is 9pi. The shaded area has an angle of 230 and the total angle of a circle is 360. We multiply the area by the fraction of the angle which is 230/360(9pi).

Answer:

D) 56

Step-by-step explanation:

[tex]\displaystyle \frac{8!}{(8-2)!}=\frac{8!}{6!}=\frac{8*7*6*5*4*3*2*1}{6*5*4*3*2*1}=8*7=56[/tex]

The given series consists of prime numbers starting from 2. So, the missing term is the prime number after 11, which is 13.

So, None of the above will be the correct answer.

A×(B∩C)=(A×B)∩(A×C)

We have B∩C={1,2,3,4}∩{5,6}=ϕ

∴ L.H.S = A×(B∩C)=A×ϕ=ϕ

A×B={(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4)}

A×C={(1,5),(1,6),(2,5),(2,6)}

∴R.H.S.=(A×B)∩(A×C)=ϕ

∴L.H.S=R.H.S

Hence A×(B∩C)=(A×B)∩(A×C)

To verify: A×C is a subset of B×D

A×C={(1,5),(1,6),(2,5),(2,6)}

B×D={(1,5),(1,6),(1,7),(1,8),(2,5),(2,6),(2,7),(2,8),(3,5),(3,6),(3,7),

(3,8),(4,5),(4,6),(4,7),(4,8)}

which is 13.

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By analytic geometry, the equations for lines represented by figure are:

In this problem we find the representation of five lines (red - yellow - green - blue - black). There is a horizontal line (green), a vertical line (blue) and three oblique lines (red - yellow - black). According to analytic geometry, we find the following definitions:

The slope for oblique lines is determined by secant line formula:

m = Δy / Δx

Where:

From picture we get the following hints:

Finally, we proceed to find the equations for each line:

Red line

Slope

m = 5 / 2.5

m = 2

Intercept

b = y - m · x

b = 5  - 2 · 0

b = 5

The equation for the red line is y = 2 · x + 5.

Yellow line

Slope

m = - 5 / 1.5

m = - 3.333

Intercept

b = y - m · x

b = 5 - (- 3.333) · 0

b = 5

The equation for the yellow line is y = - 3.333 · x + 5.

Black line

Slope

m = 6 / 3

m = 2

Intercept

b = y - m · x

b = - 6 - 2 · 0

b = - 6

The equation for the black line is y = 2 · x - 6.

Green line

The equation for the green line is y = - 2.

Blue line

The equation for blue line is x = 5.

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Answer:

-40 17/40

Step-by-step explanation:

Answer: -40 7/40

Step-by-step explanation:

Rewrite the decimal number as a fraction with 1 in the denominator
40.425=40.4251/1
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000
40.4251×1000/1000=40425/1000
Find the Greatest Common Factor (GCF) of 40425 and 1000 and reduce the fraction by dividing both numerator and denominator by GCF = 25
40425÷25
1000÷25
=1617/40

Simplify the improper fraction
in conclusion
-40 17/40
you must not forget the minus/negative sign :)

Given that for every hundred pages a thickness of 1/4 inch is added to the book, then the equation is:  y = 1/2 + 1/4*x

Considering that the book's front and back covers each have a thickness of 1/4 inch, adding them together results in a thickness of 1/2 inch for the book, regardless of how many pages it has.

Given that a book's thickness increases by a quarter of an inch for every hundred pages, the equation is:

y = 1/2 + 1/4*x

where y denotes the book's width and x is the number of bond paper pages printed every 100 pages. Y has a length of inches.

Equations that have the same roots or solutions are said to be equivalent.

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The pretax rate of return is the profit or loss on an investment before taxes are subtracted.

Pretax financial income, on the other hand, is the amount a firm earns before taxes are taken into account. Taxable income is the amount of income that a corporation must pay taxes on.

Generally speaking, investment income includes, but is not limited to: interest, dividends, capital gains, rental and royalty income, non-qualified annuities, income from firms engaged in trading financial instruments or commodities, and enterprises that are passive for the taxpayer.

The profit or loss on an investment prior to deducting taxes is known as the pretax rate of return. Taxes on investment income are levied by the government on any additional income derived from purchasing or disposing of investments. Securities that are profitably sold are subject to capital gains taxes.

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Answer: Considering both dividends paid and capital gains, Dylan’s pretax profit from his investment is $30. Dylan’s pretax return on investment (ROI) is 24%.

Step-by-step explanation: To determine Dylan’s profit from his investment, add his dividends of $5 and his capital gains of $25.total profit = $25 + $5= $30Before taxes are applied, Dylan can calculate his return on investment (ROI) by dividing his profit by the cost of his investment:30125 = 0.24, or 24%.

a) The 95​% confidence interval about μ with n = 26 is given as follows: (109, 117).

b) The 95​% confidence interval about μ with n = 15 is given as follows: (107.5, 118.5).

c) The 90​% confidence interval about μ with n = 26 is given as follows: (109.7, 116.3).

d) The intervals could not have been computed if the population was not normally distributed, as the sample size is less than 30.

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are presented as follows:

The sample mean and standard deviation for this problem are given as follows:

[tex]\overline{x} = 113, s = 10[/tex]

The critical values are given as follows:

The bounds of the interval for item a are given as follows:

The bounds of the interval for item b are given as follows:

The bounds of the interval for item c are given as follows:

The Central Limit Theorem states that the intervals can only be calculated for non-normal populations if the sample size is greater than 30.

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