Find the measure of A

Answer:

see explanation

Step-by-step explanation:

the domain ( values of x ) that a quadratic can have is all real numbers

domain : - ∞ < x < ∞

the range ( values of y ) are from the vertex upwards , that is

range : y ≥ - 2

Answer:

68

Explanation:

Sets of equations:

1) a + b = 10

2) a - b = 6

Make 'a' the subject:

1) a = 10 - b --- equation 1

2) a = 6 + b --- equation 2

Solve them by substituting:

⇒ 10 - b = 6 + b

⇒ -b - b = 6 - 10

⇒ -2b = -4

⇒ b = 2

Find value of 'a', a = 10 - b, a = 10 - 2 = 8

Then find (a²+b²), by inserting a = 8, b = 2,

⇒ ((8)²+(2)²) = 64 + 4 = 68

Step-by-step explanation:

given,

a+b=10.............( eqn 1)

a-b=6................(eqn 2)

adding eqn1 and eqn2

a+b=10

a-b=6

______

2a=16

a=16/2

a=8

putting the value of a in eqn 1

a+b=10

8+b=10

b=10-8

b=2

now,

(a²+b²)= 64+4=68

Answer:

2 1/3 longer

Step-by-step explanation:

yw ;)

Answer:

⅓

Step-by-step explanation:

Expression : 3 ⅚ - 3 ½

3 ½ would become 3 3/6.

3 ⅚ - 3 3/6 = 2/6 = 1/3

Answer:

The answer is The function g because the graphs of ƒ and g are symmetrical about the line y = x

Step-by-step explanation:

A function and its inverse function become symmetrical across the line y = x.  

Answer:

A) $4,905 B) $5,310

Step-by-step explanation:

To get the answer, just simply add the amount by the percentage.

4,500 + 9% = A

For 2 years, just do 9 x 2 = 18 because it's 2 years

4,500 + 18% = B

Answer:

2.8

Step-by-step explanation:

To find the mean aboslute deviation, you first need to find the mean:

(4 + 6 + 7 + 10 + 13)/5 = 8

Then, subtract the mean from each value, and take the abosulte value. Absolute value is essentially the same number, but if it is negative, make it positive.

4 - 8 = -4 = 4

6 - 8 = -2 = 2

7 - 8 = -1 = 1

10 - 8 = 2 = 2

13 - 8 = 5 = 5

Then, take the mean of all of these values:

(4 + 2 + 1 + 2 + 5)/5 = 2.8

The table that represents the survey conducted by Isabel is:

                               Like Dolls        Don't like Dolls    Total

Like Trains                40                             15                  55

Don't like Trains         17                               8                 25

Total                           57                             23                80

The total number of kids that like dolls = total number kids - total number of kids that don't like dolls

80 - 23 = 57

Number of kids that don't like Trains but like dolls = total number kids that like dolls - Number of kids that  like Trains and dolls

57 - 40 = 17

Number of kids that don't like dolls and but like trains :

30% x 23 = 7

(23 - 7) /2 + 7 = 15

Number of kids that don't like dolls and trains = (23 - 7) / 2 = 8

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Answer:

transition 1 would be 5 to the right

transition 2 would be 1 down

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Answer:

There is only 1 variable and it is v.

There is no coefficient.

That means the coefficient is 1.  

The coefficient of the variable in the expression ½ + v - 3 is [tex]\frac{1}{2}[/tex]

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b, and c). When the coefficients are themselves variables, they may also be called parameters.

Given that,

[tex]\frac{1}{2}[/tex] is the coefficient

[tex]v[/tex] is the variable

[tex]3[/tex] is the constant

Therefore, The coefficient of the variable in the expression ½ + v - 3 is [tex]\frac{1}{2}[/tex]

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Answer:

The solutions to this equation are x = -8/9 and x = -16/3.

Step-by-step explanation:

We have this equation here:

First, let's simplify the right sight of the equation by simplifying 6/3 to 2.

Multiply both sides of the equation by 3 in order to get rid of the fractions.

Move the terms on either side of the equation to set them equal to 0.

Now, we can split this equation up into 4 possible cases. In each case, we make the absolute values negative or positive.

Simplify this equation by distributing -6 inside the parentheses.

Combine like terms.

Add 16 to both sides of the equation and divide by -7.

Distribute the negative sign and -6 inside of their respective parentheses.

Combine like terms.

Add 8 to both sides of the equation and divide by -9.

Distribute the negative sign inside the parentheses first.

Now, distribute -6 inside the parentheses.

Combine like terms.

Subtract 8 from both sides of the equation and divide by 5.

Distribute the negative signs inside the parentheses first.

Distribute -6 inside the parentheses.

Combine like terms.

Subtract 16 from both sides of the equation and divide by 3.

Whenever we solve problems with absolute values, we will always need to check for extraneous solutions.

Definition: These are solutions that may come up while solving but do not actually fit in the domain of the original problem.

Checking for these is tedious, but it will help eliminate wrong answers, so let's plug every "solution" for x that we found back into the original equation.

Substitute this value back into the original equation.

If we do all the calculations correctly, we will get:

Since this equation is NOT true, this means that x = -16/7 is NOT A SOLUTION.

Substitute this value back into the original equation.

If we do all the calculations correctly, we will get:

Since this equation IS true, this means that x = -8/9 IS A SOLUTION.

Substitute this value back into the original equation.

If we do all the calculations correctly, we will get:

Since this equation is NOT true, this means that x = -8/5 is NOT A SOLUTION.

Substitute this value back into the original equation.

If we do all the calculations correctly, we will get:

Since this equation IS true, this means that x = -16/3 IS A SOLUTION.

The two true solutions of the double absolute value equation, shown above, are:

Answer:

  x = -16/3 or -8/9

Step-by-step explanation:

The equation can be rewritten as a piecewise linear function with two breakpoints, or three domain regions. Each breakpoint is at the value of x where the argument of the absolute value function is zero: at x=4 and x=-2.

For each absolute value, we have ...

  |q| = -q   for q < 0

  |q| = q   for q ≥ 0

Then the three parts of the domain are ...

__

Subtracting the right side, the equation becomes ...

  1/3|x -4| -2/3x -2|x +2| = 0

Then the three piecewise functions are ...

Both absolute value arguments are negated.

  1/3(-(x -4)) -2/3x -2(-(x +2)) = 0

  x(-1/3 -2/3 +2) +4/3 +4 = 0 . . . . . collect terms

  x +5 1/3 = 0 . . . . . . . simplify

  x = -5 1/3 . . . . . . . . . subtract 5 1/3. This result is in the domain

__

Only the argument of |x -4| is negated.

  1/3(-(x -4)) -2/3x -2(x +2) = 0

  x(-1/3 -2/3 -2) +4/3 -4 = 0 . . . . collect terms

  -3x -8/3 = 0 . . . . . . . simplify

  -3x = 8/3 . . . . . . . add 8/3

  x = -8/9 . . . . . divide by -3. This result is in the domain

__

Neither absolute value function argument is negated.

  1/3(x -4) -2/3x -2(x +2) = 0

  x(1/3 -2/3 -2) -4/3 -4 = 0 . . . . . collect terms

  -7/3x -8/3 = 0 . . . . . . . . . simplify

  -7/3x = 8/3 . . . . . . . . add 8/3

  x = -8/7 . . . . . . . . . divide by -7/3. This result is not in the domain.

There is no solution in this region.

__

The solutions are ...

[tex]\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}[/tex]

Since the equation provided isn't in it's general form , let's first convert it ~

General form of a Linear equation -

[tex]\bold{ax + b = 0}[/tex]

The equation after getting converted will be as follows ~

[tex] - 7 + ( \frac{4x + 2}{2} ) = 8 \\ \\ \implies \: \frac{ - 14 + 4x + 2}{2} = 8 \\ \\ \implies \: - 14 + 4x + 2 = 16 \\ \\ \implies \: 4x = 16 + 14 - 2 \\ \\ \implies \: 4x = 28 \\ \\\bold{ General \: form \: \dashrightarrow \: 4x - 28 = 0}[/tex]

hope helpful ~

Answer:

30 miles²

Step-by-step explanation:

To solve the area of the prism we have to multiply the area of the base * the height of the prism. The base of the prism is a right triangle.

(b*h)÷2 = Area of a triangle

Base = 4

Height = 3

Now:

(4*3)/2 = 6 miles²

Now we have to multiply 6 miles² by 5 as our height.

We get 30 miles² as the volume of the figure.

Answer:

Answer "A" is correct

Step-by-step explanation:

I got it right on edge test

Answer:

Rates of change:

school library: $0.25 per day;

city library: $0.35 per day

| Snapsolve. ... where \(c\) is the total cost and \(d\) is the number of days a book is late. The fees charged by a city library are shown in the table

Step-by-step explanation:

Hey ! there

Answer:

Step-by-step explanation:

In this question we are provided with right angle triangle having hypotenuse ( longest side ) = c , perpendicular = 5 and base = 12 . And we are asked to find the length of missing side i.e. hypotenuse and if necessary we have to round it off to 2 decimal places.

We can find the missing side by using Pythagorean Theorem . It states that sum of squares of perpendicular and base is equal to square in a right angle triangle that is ,

[tex] \: \qquad \: \qquad \: \underline{\boxed{ \frak{H {}^{2} = P {}^{2} + B {}^{2} }}}[/tex]

Where ,

SOLUTION : -

Substituting value of hypotenuse as c , perpendicular as 5 and base as 12 in formula :

[tex] \quad \longmapsto \qquad \: (c) {}^{2} = (5) {}^{2} + (12) {}^{2} [/tex]

Squaring 5 and 12 :

[tex] \quad \longmapsto \qquad \:(c) {}^{2} = 25 + 144[/tex]

Adding 25 and 144 :

[tex] \quad \longmapsto \qquad \:(c) {}^{2} = 169[/tex]

Applying square root to both sides :

[tex] \quad \longmapsto \qquad \: \sqrt{(c) {}^{2} } = \sqrt{169} [/tex]

On simplifying , We get :

[tex] \quad \longmapsto \qquad \orange{\underline{\boxed{\frak{c = 13}}}} \quad \bigstar[/tex]

Verifying : -

Now we are checking our answer by putting all values in formula . So ,

Therefore , our answer is correct .

Answer :

[tex] \: [/tex]

Step-by-step explanation :

Here, A right angled triangle is given with the measure of two sides and we are to find the measure of the third side.

We'll find the measure of third side with the help of the Pythagorean theorem,

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}} \\ \\[/tex]

Here,

[tex] \: [/tex]

So, substituting the values in the formula we get :

[tex]\\ {\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= (12) {}^{2} + (5 {)}^{2} }}} \\ [/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= 144 + 25 }}} \\ [/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad (c {)}^{2}= 169 }}} \\ [/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad c = \sqrt{169} }}} \\[/tex]

[tex]{\longrightarrow \pmb{\sf {\qquad c= 13 }}}\\ \\[/tex]

Therefore,

Answer:

I think that the answer is -81

Step-by-step explanation:

We have 3x+4x-81-14 x is given as 2.So we'll have 3*2+4*2-81-14= -81 per my calculations. TRY THIS

Answer:

100

Step-by-step explanation:

75 + 80 + 100 divided by 3 = 85

Step-by-step explanation:

[tex]y - y_1 = m.(x - x_1)[/tex]

[tex]y - ( - 9) = 8.(x - ( - 2))[/tex]

[tex]y = 8x + 16 - 9[/tex]

[tex]y = 8x + 7[/tex]

Answer:

y = 8x + 7

Step-by-step explanation:

We are given that a line contains the point (-2, -9), and a slope of 8

We want to write the equation of this line

There are multiple ways to write the equation of the line:

The most common of these 3 methods is slope-intercept form, so let's write our equation this way

As we are already given the slope, we can immediately plug that into our formula for m

Replace m with 8:

y=8x+b

Now we need to find b

As the equation passes through (-2, -9), we can use its values to help solve for b

Substitute -2 as x and -9 as y:

-9 = 8(-2) + b

Multiply

-9 = -16 + b

Add 16 to both sides

7 = b

Substitute 7 as b.

y = 8x + 7

Topic: finding the equation of the line

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Answer:

See below ~

Step-by-step explanation:

The statements which are true :

Using it's concept, it is found that the probability that a person consumes 1,500 to 2,000 calories in a day is given by:

D. 0.50

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching the problem on the internet, it is found that out of 500 people, 250 consume 1,500 to 2,000 calories in a day, hence the probability is given by:

p = 250/500 = 0.5.

Which means that option D is correct.

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Answer:

(573+9/2 cubic inches

Step-by-step explanation:

the answer is A

Figure a: The area of the triangle is 13.3 sq. km.

Figure b: The area of the rectangle is 57.4 sq. cm.

Figure c: The area of the parallelogram is 45.5 sq. km.

Figure d: The area of the trapezoid is 24.36 sq. m.

The area of a two-dimensional closed figure is the total space within its boundary.

In the question, we are asked to find the area of the given shapes.

Figure a:-

It is showing a triangle.

The area of a triangle is calculated using the formula:

Area = (1/2)*Base*Height.

Thus, the area of the triangle

= (1/2)*7*3.8 sq. km

= 13.3 sq. km.

Figure b:-

It is showing a rectangle.

The area of a rectangle is calculated using the formula:

Area = Length*Width.

Thus, the area of the rectangle

= 8.2*7 sq. cm

= 57.4 sq. cm.

Figure c:-

It is showing a parallelogram.

The area of a parallelogram is calculated using the formula:

Area = Base*Height.

Thus, the area of the parallelogram

= 9.1 * 5 sq. km

= 45.5 sq. km.

Figure d:-

It is showing a trapezoid.

The area of a trapezoid is calculated using the formula:

Area = (1/2)*(Sum of parallel sides)*(height).

Thus, the area of the trapezoid

= (1/2)*(2.7 + 8.9)*4.2 sq. m.

= 11.6 * 2.1 sq. m.

= 24.36 sq. m.

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Step-by-step explanation:

a) 1*7=7 (Litres);

b) 1*2*5=10 (Litres);

c) 10*0.5*1/0.5=10 (bottles)

Answer:

On a coordinate plane, a line goes through (0, 3) and (3, negative 1).

Answer: the bottom left

Step-by-step explanation:

you will find it or just look it up if im wrong

Answer:

9) Vincent will not get the correct answer because the + 484 is unneccesary, as he already subtracted it.

10a) 310,000 + x = 465,000; so x = 155,000

10b) 930,000/310,000 = 3 times more

Step-by-step explanation:

Answer:

x = 7

The length of the side is 18

Step-by-step explanation:

40 / 16 = 2.5

meaning the shape is dilated by 2.5

45 / (2x + 4) = 2.5

→ multiply both side by the denominator

45 / (2x + 4) * (2x + 4) = 2.5 * (2x + 4)  

→ simplify

45 = 2.5 * (2x + 4)  

→ divided both side by 2.5

45 / 2.5 = 2.5 * (2x + 4)  / 2.5

18 = 2x + 4

→ subtract 4 from both sides (want x alone)

18 - 4 = 2x + 4 - 4

14 = 2x

→ divid both side by 2

14 / 2 = 2x / 2

7 = x

Plug in x:

2x + 4 = 2(7) + 4

14 + 4 = 18

Answer:

61 hot dogs

122 sodas

Step-by-step explanation:

x+x2=183

3x=183

183÷3=

61