= How many gallons of a 60% antifreeze solution must be mixed with 60 gallons of 30% antifreeze to get a mixture that is 50% antifreeze?​

Using the Pythagorean Theorem, it is found that the length of AB is of 8.54 units, considering that BC = 3 and that AC = 8.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

For this triangle, we have that:

Hence the length of AB is given as follows:

h² = 3² + 8²

h² = 73

h = sqrt(73)

h = 8.54 units.

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The property of addition that represents this is the zero property of addition

The equation is given as:

a + bi + 0 + 0i = a + bi

In the above equation, the number is added by 0 and the result is the initial number

The property of addition that represents this is the zero property of addition

Because it states that

a + 0 = 0

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Answer:

A)50°F = 10°C

B)75°C = 167°F

C)-40°C = -40°F

Step-by-step explanation:

A) 50°F = 10°C

Formula

(50°F − 32) × 5/9 = 10°C

B) 75°C = 167°F

Formula

(75°C × 9/5) + 32 = 167°F

C) -40°C = -40°F

Formula

(-40°C × 9/5) + 32 = -40°F

Answer's:

27. vertex: (-4, -5) and x-intercept: (√5 - 4, 0) and (-√5 - 4, 0)

28. vertex: (-5, -11) and x-intercept: (√11 - 5, 0) and (-√11 - 5, 0)

29. vertex: (1, 16) and x-intercept: (-3, 0) and (5, 0)

To find vertex, the quadratic function should be in f(x) = a(x - h)² + k form.

where:

27.

g(x) = x² + 8x + 11

completing square:

g(x) = (x² + 8x) + 11

g(x) = (x + 4)² + 11 - (4)²

g(x) = (x + 4)² - 5

g(x) = (x - (-4))² - 5

To find x-intercept: set y = 0

[tex]\sf (x + 4)^2 - 5 = 0[/tex]

[tex]\sf (x + 4)^2 = 5[/tex]

[tex]\sf x + 4 = \pm \sqrt{5}[/tex]

[tex]\sf x= \sqrt{5}-4, \ - \sqrt{5}-4[/tex]

Hence, the vertex is (-4, -5) and x intercepts (√5 - 4, 0) and (-√5 - 4, 0).

28.

f(x) = x² + 10x + 14

completing square:

f(x) = (x² + 10x) + 14

f(x) = (x + 5)² + 14 - (5)²

f(x) = (x + 5)² - 11

Find x intercept, so y = 0:

[tex]\sf (x + 5)^2 - 11 = 0[/tex]

[tex]\sf (x + 5)^2 = 11[/tex]

[tex]\sf x + 5 = \pm\sqrt{11}[/tex]

[tex]\sf x = \sqrt{11} -5, \ -\sqrt{11} -5[/tex]

Hence, the vertex is (-5, -11) and x intercepts (√11 - 5, 0) and (-√11 - 5, 0).

29.

f(x) = -(x² - 2x - 15)

f(x) = -((x² - 2x)) + 15

f(x) = -(x - 1)² + 15 + (-1)²

f(x) = -(x - 1)² + 16

Find the x-intercept's:

[tex]\sf -(x - 1)^2 + 16 = 0[/tex]

[tex]\sf -(x - 1)^2 = -16[/tex]

[tex]\sf (x - 1)^2 = 16[/tex]

[tex]\sf x - 1 = \pm\sqrt{16}[/tex]

[tex]\sf x - 1 = \pm4[/tex]

[tex]\sf x = -3, \ 5[/tex]

Hence, the vertex is (1, 16) and x intercepts (-3, 0) and (5, 0).

Answer:

[tex]\textsf{27.} \quad \textsf{Vertex}:(-4,-5) \quad \textsf{$x$-intercepts}: x=-4+\sqrt{5}, \:\:x=-4-\sqrt{5}[/tex]

[tex]\textsf{28.} \quad \textsf{Vertex}:(-5,-11) \quad \textsf{$x$-intercepts}: x = -5+\sqrt{11}, \:\:x=-5-\sqrt{11}[/tex]

[tex]\textsf{29.} \quad \textsf{Vertex}:(1,16) \quad \textsf{$x$-intercepts}: x = 5, \:\:x=-3[/tex]

Step-by-step explanation:

Vertex form of a quadratic function:

[tex]\boxed{y=a(x-h)^2+k}[/tex]

where:

Given function:

[tex]g(x)=x^2+8x+11[/tex]

Change to vertex form by completing the square.

Add and subtract the square of half the coefficient of x:

[tex]\implies g(x)=x^2+8x+11 +\left(\dfrac{8}{2}\right)^2-\left(\dfrac{8}{2}\right)^2[/tex]

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

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

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

Factor the perfect trinomial:

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

Therefore, the vertex is (-4, -5).

To find the x-intercepts, set the function to zero and solve for x:

[tex]\begin{aligned}g(x) & = 0\\\implies (x+4)^2 -5 & = 0\\(x+4)^2 & = 5\\\sqrt{(x+4)^2} & = \sqrt{5}\\x+4&=\pm\sqrt{5}\\x+4-4&=-4\pm\sqrt{5}\\x&=-4\pm\sqrt{5}\end{aligned}[/tex]

Therefore, the x-intercepts are:

[tex]x = -4+\sqrt{5}, \quad x = -4-\sqrt{5}[/tex]

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

Given function:

[tex]f(x)=x^2+10x+14[/tex]

Change to vertex form by completing the square.

Add and subtract the square of half the coefficient of x:

[tex]\implies f(x)=x^2+10x+14+\left(\dfrac{10}{2}\right)^2-\left(\dfrac{10}{2}\right)^2[/tex]

[tex]\implies f(x)=x^2+10x+14+25-25[/tex]

[tex]\implies f(x)=x^2+10x+25+14-25[/tex]

[tex]\implies f(x)=x^2+10x+25-11[/tex]

Factor the perfect trinomial:

[tex]\implies f(x)=(x+5)^2-11[/tex]

Therefore, the vertex is (-5, -11).

To find the x-intercepts, set the function to zero and solve for x:

[tex]\begin{aligned}f(x) & = 0\\\implies (x+5)^2 -11 & = 0\\(x+5)^2 & = 11\\\sqrt{(x+5)^2} & = \sqrt{11}\\x+5&=\pm\sqrt{11}\\x+5-5&=-5\pm\sqrt{11}\\x&=-5\pm\sqrt{11}\end{aligned}[/tex]

Therefore, the x-intercepts are:

[tex]x = -5+\sqrt{11}, \quad x = -5-\sqrt{11}[/tex]

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

Given function:

[tex]f(x)=-(x^2-2x-15)[/tex]

Change to vertex form by completing the square.

Add and subtract the square of half the coefficient of x:

[tex]f(x)=-\left(x^2-2x-15+\left(\dfrac{-2}{2}\right)^2-\left(\dfrac{-2}{2}\right)^2\right)[/tex]

[tex]f(x)=-\left(x^2-2x-15+1-1\right)[/tex]

[tex]f(x)=-\left(x^2-2x+1-15-1\right)[/tex]

[tex]f(x)=-\left(x^2-2x+1-16\right)[/tex]

Factor the perfect trinomial:

[tex]f(x)=-\left((x-1)^2-16\right)[/tex]

Simplify:

[tex]f(x)=-(x-1)^2+16[/tex]

Therefore, the vertex is (1, 16).

To find the x-intercepts, set the function to zero and solve for x:

[tex]\begin{aligned}f(x) & = 0\\\implies -(x-1)^2 +16 & = 0\\(x-1)^2 -16 & = 0\\(x-1)^2 & = 16\\\sqrt{(x-1)^2} & = \sqrt{16}\\x-1&=\pm4\\x-1+1&=1\pm4\\x&=5,-3\end{aligned}[/tex]

Therefore, the x-intercepts are:

[tex]x = 5, \quad x=-3[/tex]

Answer:

A, B, C yes

D no

Step-by-step explanation:

A. is a no-brainer. yes, that is indirectly implied.

B. this is compared to D a hidden assumption, that the money you give is guaranteed to be spent on worthwhile causes (not to mention what THAT actually means).

C. this goes combined with B. it is suggested that charity A is not engaging in unworthy causes (again, whatever that means).

D. is not hidden. that is openly said.

Answer:

Step-by-step explanation:

You want the exact values of sine and cosine of the angle whose terminal point is at x=2/5 on the unit circle in the first quadrant.

The coordinates of a point on the unit circle are (cos(θ), sin(θ)). You already know that the x-coordinate is 2/5, so ...

  cos(θ) = 2/5

The Pythagorean identity in trigonometric terms is ...

  sin²(θ) +cos²(θ) = 1

Then the sine of the angle is ...

  sin(θ) = √(1 -cos²(θ))

  sin(θ) = √(1 -(2/5)²) = √((25 -4)/25)

  sin(θ) = (√21)/5

The exact values of sine and cosine are ...

Answer: C=550+121m

Step-by-step explanation:

Answer:

1/8

3/4 - 5/8

*2/2

6/8 - 5/8 = 1/8

Step-by-step explanation:

[tex](\frac{-4}{5} )[/tex] in the form of Equivalent Fraction can be written as [tex]\frac{-4x}{15x}[/tex], where "x" is any integer.

As per the question statement, we are provided with a fraction, [tex](\frac{-4}{5} )[/tex].

We are required to rewrite the above mentioned fraction in the form of a general Equivalent Fraction.

To solve this question, we need to know what an equivalent fraction is.

Equivalent fractions are those fractions that have different numerators and denominators but are equal to the same value, when simplified.

For example, [tex](\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8})[/tex] all equate to [tex]\frac{1}{2}[/tex] when simplified.

Now, for this case, equivalent fractions of [tex](\frac{-4}{5} )[/tex] are [tex](\frac{-8}{30}, \frac{-12}{45}, \frac{-16}{60},...)[/tex], where

[tex]\frac{-8}{30}=\frac{(-4)*2}{15*2}\\\frac{-12}{45}=\frac{(-4)*3}{15*3}\\ \frac{-16}{60}=\frac{(-4)*4}{15*4}[/tex]

i.e., the equivalent fractions of [tex](\frac{-4}{5} )[/tex] are in the form of  [tex]\frac{-4x}{15x}[/tex], where "x" can be any integer, (...-6, -5, -4, -3, -2, -1, 2, 3, 4, 5, 6...)

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Answer:

8

Step-by-step explanation:

(4/5)/(1/10)

oreja

take the top most number and bottom most number, multiply the two. Then multiply the two middle numbers.

(4*10)/(5*1)

Simplify and you get:

40/5

=8

The proportional relationship of the given statement is a between x and y and the constant of proportionality is 0.5.

According to the statement

We have to find that the constant of proportionality.

So, For this purpose, we know that the

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

From the given information:

each equation represents a proportional relationship.

Then

We know that the A proportional relationship is one in which two quantities vary directly with each other

That's why

An equation has a proportional relationship if it can be written in the form y=kx where k is the constant of proportionality.

A linear function of x is given as y = 0.5x - 2.

Yes, this function of x represents a proportional relationship between x and y.

The constant of proportionality is given to be 0.5 provided that the dependent variable y has an initial value of - 2 at x = 0.

The graph of this equation will be a straight line and that means that the equation consists of a proportional relationship.

So, The proportional relationship of the given statement is a between x and y and the constant of proportionality is 0.5.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Determine whether each equation represents a proportional relationship. if it does identify the constant of proportionality. y = 0.5 x -2

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Answer: 433.52

Step-by-step explanation: it depends if you have the pass or not

Consequently, the carpet's price is diversely correlated with its size. Then the cost of the carpet will be $647.82.

160 square feet of a certain carpet were purchased for $878.40 last week at Abe's carpet shop. The identical carpet, measuring 85 square feet, cost $466.65 at Bob's Carpet.

The cost of carpet per square foot in both cases will be

In the First case, we have

⇒ 878.40 / 160

⇒ $5.49 per square foot

In the second case, we have

⇒ 466.65 / 85

⇒ $5.49 per square foot

Consequently, the carpet's price is directly correlated with its size. Then the equation will be

Cost = 5.49 x Area

Then the cost of the carpet when the area is 118 square feet will be

Cost = 5.49 x 118

Cost = $647.82

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Answer:

f(X) = ( - X) ½

is the answer

pls brainliest

The values of the piecewise function is g(1) = 3, g(2) = 1 / 2, g(3) = 1 / 4.

Piecewise functions are functions consisting in two or more expression constrained by intervals. In this case, we find a piecewise function formed by three equations. In this exercise we need to evaluate the function, whose expression depends on the x-value to be used. There are three values to be evaluated:

x = 1

g(1) = (1 + 1)² - 1

g(1) = 2² - 1

g(1) = 4 - 1

g(1) = 3

x = 2

g(2) = - (1 / 4) · 2 + 1

g(2) = - (1 / 2) + 1

g(2) = 1 / 2

x = 3

g(3) = - (1 / 4) · (3) + 1

g(3) = - (3 / 4) + 1

g(3) = 1 / 4

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Answer: -8w+2v+2

Step-by-step explanation:

Answer:

radius

Step-by-step explanation:

Answer: 1/10

Step-by-step explanation:2 * 1/5 is 2/5 and 1*3/10 is 3/10 and when you subtract them you get 1/10

Answer:9/10

Step-by-step explanation:get 2 1/5 into a improper fraction thats 11/5 then multiply by to for the common demontor thats 22/10

get 1 3/10 into a improper fraction 13/10

then minus 22-13 thats 9

then bring in the bottom 9/10 hope that helps

Answer:

49

Step-by-step explanation:

Because 49/7 is 7 which makes it a perfect square.And it saids the square root of x is 49

Hope that helped!

Have any questions? Feel free to ask questions

[tex]{\sf{12 \times ( - 4) = -48}}[/tex]

Answer:

Q3

Slope = 5

Standard= y=5X+15

Q5

Slop =-4

Standard= y=-4x+4

Step-by-step explanation:

m=-5-5/-4+2=-10/-2= 5

y-5=5(x+2)

y-5=5x+10

y=5x+15

The statement that best interprets the quotient is "there are 6( 1/4 ) two  - third in 4( 1/6 )".

In mathematics, the sum obtained by diluting two numbers is known as a quotient. The term "quotient" is used frequently in mathematics and is sometimes known as the integer portion of a division, a fraction, or a ratio.

Any integer may be used as the larger number in a fraction, which is a number that represents a percentage of the larger number. It is shaped like a denominator and a numerator.

For step 1:

The shaded part is:

4 + 1/6 = 4(1/6) = 25/6

Now, dividing the shaded part by the unshaded part,

( 25/6 ) / ( 2/3 ) = ( 25/6 ) × ( 3/2 )

( 25/6 ) / ( 2/3 ) = 25/4

( 25/6 ) / ( 2/3 ) = 6( 1/4 )

Hence, there are 6( 1/4 ) two  - third in 4( 1/6 ).

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The measure of the each angle is a 45° and 135°.

According to the statement

We have to find that the measure of the each angle.

So, For this purpose, we know that the

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

From the given information:

Two angles a form a linear pair. The measure of one angle is 1/3 the measure of the other angle.

Then

Since the two angles form a linear pair, the sum of their angles is equal to 180°. The condition given in the problem is that one angle is one-third of the other angle, or simply speaking, one angle is three times more than the other angle. We find the values of the angles by dividing the sum of the angles by 4 and assigning 3 and 1 times the dividend.

180°/4 = 45°

By obtaining the dividend, we obtain the values of the angles to be 45°

Then

the other angle is

Other angle = 180 -45

Other angle = 135.

So, The measure of the each angle is a 45° and 135°.

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Answer:

25 and 32

Step-by-step explanation:

32 - 25 = 7

32 x 25 = 800

The average number of miles she would have to ride each day to meet her goal is 4.7.

It is required to find the average number of miles she would have to ride each day to meet her goal.

A part of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

Given:

Bilquis wants to ride her bicycle 47.6 miles this week. She has already ridden 8 miles. she rides for 6 more days.

According to given question we have,

8+4x=26

Rearrange unknown terms to the left side of the equation:

4x=26-8

4x=18

Divide 4 on both sides of the equation we get,

4x/4=18/4

x=18/4

x=4.7

Therefore, the average number of miles she would have to ride each day to meet her goal is 4.7.

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A valid claim based on the graph is that: D. Evan studied twice as long as Ted.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

By critically observing the graph (see attachment), we can logically deduce the following data points:

From the information provided, we have the following true statements:

S = T

E = 2T

In conclusion, we can reasonably infer and logically deduce that a valid claim based on the graph is that Evan studied twice as long as Ted.

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Answer:

Henderson family spent 40 hrs, while Ramirez spent 15 hrs.

Step-by-step explanation:

Let t = time in hrs the Henderson family used their sprinkler

Let 55 - t = time in hrs the Ramirez family used their sprinkler.

40t+35*(55-t)=2125

40t+1925-35t=2125

calculcate this and you will get t=40.

then 55-40=15.

So, Henderson family spent 40 hrs, while Ramirez spent 15 hrs.

Answer: x=28

Step-by-step explanation:

4x-7=3x+21

4x-3x-7=3x-3x+21

x-7=21

x=28