The sum of an integer and 2 times the next consecutive integer is -22. Find the value of the lesser integer

Answer: It would be D. 22.5°

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Given the attached graph, the statement that is NOT true about scarlet's dive is that "She hits the water at 3 seconds." (Option D) See the explanation below.

In mathematics, a graph is defined as a graphical representation or diagram that organizes facts or values. The graph's points frequently reflect the relationship between two or more objects.

In this scenario, the relationship represented is between Scarlet's descent from a 10-foot platform and the time it takes her to complete the trajectory from point of dive to point of reaching the water.

Hence, it is clear from the graph attached that Scarlet hits the water at 3.25 seconds.

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The circumference of the circle with a radius of 7 ft is 106.76 ft

The circumference of a circle is the perimeter of the circle

The given parameters are

Radius = 17 ft

As a general rule, radius are represented by the variable r

So, we have the following representation equation

r = 17

The circumference of the circle is then calculated as

C = 2πr

Next, we substitute the value of the variable r in the above equation

i.e. r = 17

So, we have the following equation

C = 2π * 17

From the question, we have

π = 3.14

So, we have the following equation

C = 2 * 3.14 * 17

Evaluate the products

So, we have the following equation

C = 6.28 * 17

Evaluate the products

So, we have the following equation

C = 106.76

Hence, the circumference is 106.76 ft

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Answer:

[tex]g(x)=-x^2+8x-11\\\\f(x)=x^2-8x+21[/tex]

Step-by-step explanation:

Generally when you're given the vertex of a quadratic, you can express it in vertex form: [tex]f(x)=a(x-h)^2+k[/tex], where (h, k) is the vertex, and "a" is some constant value that determines the stretch/compression and the direction (up or down)

So we know that: (h, k) = (4, 5), meaning we can plug those values into the equation: [tex]f(x)=a(x-4)^2+5[/tex]

we can change the function by changing the value of the constant "a".

we can use two arbitrary values, but in this example I'll use -1 and 1.

this gives us the following functions: [tex]f(x)=(x-4)^2+5\\g(x)=-(x-4)^2+5[/tex]

these two functions are actually very similar, the only different is they're reflected across the x-axis (and some vertical shift) since the y-value is being negated, or at least part of it.

In your question it states (of any form), so I'm assuming we can leave it in vertex form, but just in case I'll expand them further into standard form

[tex]f(x)=(x-4)^2+5\\\\f(x)=(x-4)(x-4)+5\\\\f(x)=x(x-4)-4(x-4)+5\\\\f(x)=x^2-4x-4x+16+5\\\\f(x)=x^2-8x+21[/tex]

We can also expand the other function similarly.

[tex]g(x)=-(x-4)^2+5\\\\g(x)=-[(x-4)(x-4)]+5\\\\g(x)=-[x(x-4)-4(x-4)]+5\\\\g(x)=-[x^2-4x-4x+16]+5\\\\g(x)=-[x^2-8x+16]+5\\\\g(x)=-x^2+8x-16+5\\\\g(x)=-x^2+8x-11[/tex]

The equation in slope intercept form of the line passes through the point (-3,0) and is parallel to the line represented by y = 3.2x+7.3 is y = 3.2x+9.6

The equation of the line that parallel to the line

y = 3.2x+7.3

Slope intercept form of the line

y = mx+b

y is the y coordinate

x is the x coordinate

m is the slope of the line

b is the y intercept

Compare it with the equation

The slope of the line m = 3.2

Point slope form of the line passing through the points (-3,0) with the slope of the line 3.2

[tex]y-y_{1}=m(x-x_{1} )[/tex]

Substitute the values in the equation

y-0 = 3.2(x-(-3)

y = 3.2(x+3)

y = 3.2x+9.6

Hence, the equation in slope intercept form of the line passes through the point (-3,0) and is parallel to the line represented by y = 3.2x+7.3 is y = 3.2x+9.6

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Answer:

Third option

Step-by-step explanation:

The intercept x-intercept of f¹(x) is 1 and y-intercept of f(x) is also 1.

Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right

The given equation is 3x-6y²+6y=0.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively.

Graph the parabola using the direction, vertex, focus, and axis of symmetry.

Direction: Opens Right

Vertex: (-1/2, 1/2)

Focus: (-3/8, 1/2)

Axis of symmetry: y=1/2

Directrix: x=-5/8

The coordinate points to plot (-1/2, 1/2), (0.5, 1.21), (0.5, -1.21), (1.5, 1.5) and (1.5, -0.5).

Therefore, Hamza should draw the vertex at (-0.5, 0.5), the directrix at -0.625, and the focus at (-0.375, 0.5). The parabola will open to the right.

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The sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse. The hypotenuse exists c = 50.

To determine the hypotenuse from the sides of a right triangle, use the Pythagorean theorem. Sum of squares is squared as c = √(a² + b²).

The longest side of a right-angled triangle, or the side opposite the right angle, exists comprehended as the hypotenuse in geometry. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

a² + b² = c²

⇒ c = √(a² + b²)

Where, a = 30 and b = 40, then

substitute the  values in the above equation, we get

30² + 40² = c²

900 + 1600 = c²

2500 = c²

50 = c

Therefore, the hypotenuse exists c = 50.

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Answer:

  10.97 seconds

Step-by-step explanation:

You want to know when a rocket will hit the ground if its height is given by y = -16x² +170x +61, where x is seconds after launch.

The formula for the solutions of a quadratic equation is ...

  [tex]\text{for }ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

When we apply this to the equation y=0, we have ...

  [tex]x=\dfrac{-170\pm\sqrt{170^2-4(-16)(61)}}{2(-16)}=\dfrac{170\pm\sqrt{32804}}{32}\\\\x\approx 10.97\quad\text{seconds}[/tex]

The rocket will hit the ground after about 10.97 seconds.

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Step-by-step explanation:

a) angles that share 1 side and are next to each other

<DBA, <ABE

<ABE, <EBC

b) two angles whose measures add to 180°

<ABE, <EBC

<ABD, <DBC

c) two adjacent angles whose noncommon sides lie on a line

<ABE, <EBC

<ABD, <DBC

a) The confidence interval is (0.13, 0.35) for the males who have this blood disorder.

b) The number of African males or the sample size is 88 for the value of P to be 0.20

It is mentioned that a geneticist is interested in the proportion of the African males who have a certain minor blood disorder. In a random sample of 100 males, 24 were found to be afflicted.

So we have,

n (total males) = 100

X (afflicted males)= 24

Let P be the sample porportion,

P = X/ n

∴ P = 24 / 100 = 0.24

a) Here it is given to find the confidence interval if the proportion of males is 99% who have this blood disorder so,

c = 99 % = 0.99

∴ α = [tex]1 -[/tex] c = 1 - 0.99 = 0.01

⇒ α/2 = 0.01/2 = 0.005

Using Z table,

Z of α/2 = [tex]Z_{0.005}[/tex] = 2.576

Margin of error E = [tex]Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }[/tex]

                            = 2.576 x [tex]\sqrt{\frac{0.24(1-0.24)}{100} }[/tex]

                            = 0.11

Now, 99 % confidence interval is P ± E

P-E < P < P +E

0.24 - 0.11 < P' < 0.24 + 0.11

P' = (0.13, 0.35) is the required confidence interval.

b) It is given to find the the number of African males when

P = 0.20

Z = 2.576

E = 0.11

Now E = [tex]Z_{0.005}\sqrt[2]{\frac{P(1-P)}{n} }[/tex]

⇒ 0.11 = 2.576 x [tex]\sqrt[2]{\frac{0.20(1-0.20)}{n} }[/tex]

⇒ 0.0427 = [tex]\frac{0.4}{\sqrt{n} }[/tex]

⇒ [tex]\sqrt{n}[/tex] = 9.37

⇒ n = [tex](9.37)^{2}[/tex]

⇒ n = 87.7969

Hence the approximate number of males is 88 for the proportion of males with this blood disorder to be 0.20

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Answer: (4, 2)

Step-by-step explanation:

1) Identify the values of a, b, and c.

a = -1

b = 8

c = -14

2) Use the vertex formula to find the x-value of the vertex.

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

[tex]{\displaystyle x={\frac {-8}{2(-1)}}}[/tex]

[tex]{\displaystyle x={\frac {-8}{-2}}}[/tex]

[tex]{\displaystyle x=4[/tex]

3) Plug the value into the original equation to get the y value.

f(x) = -x² + 8x - 14

f(x) = -(4)² + 8(4) - 14

f(x) = -(16) + 32 - 14

f(x) = 2

3) Put it in an ordered pair

(4, 2)

The answer is -1 and 5

The answer is given above

I hope this was helpful.

The original number is 0.8.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations. But the need to depict these shifting values is ongoing.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the number be x.

A certain number was multiplied by 5, then decreased by 3, then halved. The result was 0.3 less than the original number.

So, the mathematical expression is

1/2( 5x- 3) = x- 0.3

Now, solving for x

Multiply both side by 2

5x-3 = 2x- 0.6

5x- 2x= -0.6 + 3

3x= 2.4

Divide both side by 3

3x/3 = 2.4/3

x= 0.8

Hence, the original number is 0.8.

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Answer:  21 x=4 ​

Solve the system of equations

Steps:

​ Evaluate

{ 7x−7 x=4 ​

Calculate

{ x=4 21 ​

Solution

{ 21 x=4 ​

The answer to the given question is Oscar wrote the correct equation that would relate kilometers to miles.

1. Table

km         miles

152          95

2.  Set the proportion with / and solve for k

/ = 152 km / 95 miles

/ = 1.6 km / 1 miles

= 1.6 , where  1.6 / 1 represents kilometers per mile.

So, Oscar is right.

Maria is wrong because:

If we solve the proportionality:

/ = 152 km / 95 miles

/ = 95 miles / 152 km

= 0.625 , where 0.625 represents miles per kilometer

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The complete question is:

"Oscar and Maria each wrote an equation that they felt represented the proportional relationship between distance in kilometers and distance in miles. One entry in the table paired 152 km with 95 miles. If represents the number of kilometers and represents the number of miles, who wrote the correct equation that would relate kilometers to miles? Explain why.

Oscar wrote the equation = 1.6, and he said that the unit rate 1.6 / 1

represents kilometers per mile.

Maria wrote the equation = 0.625 as her equation, and she said that 0.625 represents kilometers per mile."

Answer:

t = 19.99h + 30

Step-by-step explanation:

t is the total cost and h is the hourly charge.  The 30 is a one time fee.

On the graph that is included with the solution, the temperature fluctuations are depicted.

A graph is a representation of the relationship between two variables, often measured along one of two right-angled axes each.

It is 56° at 6 a.m.

It rises to 61° for the next 5 hours because it is increasing by 1° per hour, and after another 4 hours it will rise to 69° because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it fell for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.

It is 56° at 6 a.m. The temperature rises to 61° for the next 5 hours because it is increasing by 1° per hour, and then after 4 hours it will rise to 69° again because it is increasing by 2° per hour. The temperature remained constant until 6 pm, after which it dropped for the following 3 hours, dropping to 66° before dropping steadily to 62° at midnight.

The final graph is shown in the below attached figure.

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In the quadratic function, the discriminants with no x-intercepts are (A) -4 and (C) -18.

So, there are no x-intercepts on the graph of a particular quadratic function.

Discriminant= D

For imaginary zeros, D must be negative.

The given option (A) and (C) which are -4 and -18 are negative and hence are the Discriminant with no x-intercepts.

Therefore, in the quadratic function, the discriminants with no x-intercepts are (A) -4 and (C) -18.

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First, we must find the total of females, it will be

Now we must look at the table how many females prefer suspense movies, it's

Now we do the quotient between the females that prefer suspense by the total of females:

Rounding it, we can say that approximately,

Or 20% of the females prefer suspense movies

In linear equation ,The mean  number that the test positive for the HIV virus is 2.1 .

What in mathematics is a linear equation?

Let x be the number of blood samples test positive for the HIV virus in a sample of 70 blood test.

Here X ~ Binom( n = 70, p = 0.03)

Using binomial distribution property , the mean of X is

μ = ηp

    = 70 * 0.03  = 2.1

The mean  number that the test positive for the HIV virus is 2.1 .

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The pay for the given weekly time is, $102.

What is the pay wage?

The key distinction between a salary and wages is that wage earners are compensated by the hour, whereas salaried employees receive set payments every pay period.

In the given example the total time for the morning and the afternoon is given.

The total time for the morning is 4 hours and the total time for the afternoon is 4.5 hours.

So, the total number of hours are 4 + 4.5 = 8.5 hours.

The wage of each hour is $12.

So, the wage of 8.5 hours is,

8.5 x $12 = $102.

Therefore, the pay for the given day of a weekly time card given a wage of $12/hr is $102.

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Answer: 1/2

Step-by-step explanation:

Answer:

The correct answer seems to be 1/2

The constant of proportionality of y = 9x is 9.

i.e  y ∝ x and y = 9x

Option B is the correct answer.

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

We have,

y = 9x

y = liters of water the baseball team drinks each practice

x = number of practice

We have an equation that after four practices, the team will have consumed 36 liters of water.

y = 36

9x = 38

x = 4

The equation can be written with a constant of proportionality as:

y ∝ x

y = 9x

So,

9 is the constant of proportionality.

Thus,

The constant of proportionality of y = 9x is 9.

i.e

y ∝ x

y = 9x

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Answer: The constant of proportionality of y = 9x is 9

To determine the value of v that makes the equation true, we have to solve the equation and obtain the value of v

The value of v that makes the equation true is v=8

Answer:

150

Explanation:

Alright so basically, 150 x 40 = 6000, right? So you want to find out how to find it using the division process. It is a whole number with no fractional part. As division with remainder the result of 6000 ÷ 40 = 150 R 0.

6000 divided by 40 ⇒ 150.

Here given that,

6000 is divisible by 40

since we know that,

Division is a process of repeated subtraction. It is the inverse action of multiplication. It is characterised as the formation of equal groupings. When we divide numbers, we split them down into smaller amounts so that the multiplication of those smaller numbers equals the larger number taken.

6000 is divisible by 40 we get,

⇒ 6000/40

⇒ 150

So, the quotient is 150

Hence,

After dividing 6000 by 40 we get 150.

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