Identify the vertex of the graph. Tell whether it is a minimum or maximum.
(-2,-3); maximum
(-2,-3); minimum
(-3,-2); maximum
(-3,-2); minimum

If Sharon is 3 years younger, then it's s = 3-b. However, it's twice her brothers age, which makes the formula our final answer, A, or [tex]s = 3 - 2b[/tex]

The correct option is A

[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (\stackrel{x}{6},\stackrel{y}{10})\qquad \textit{we know that } \begin{cases} x=6\\ y=10 \end{cases}\implies 10=k6\implies \cfrac{10}{6}=k\implies \cfrac{5}{3}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{5}{3}x}[/tex]

to get another point, we simply can pick a random independent variable, namely "x", say hmmmm x = 9, thus

[tex]\bf y=\cfrac{5}{3}(\stackrel{\stackrel{x}{\downarrow }}{9})\implies y=5\cdot \cfrac{9}{3}\implies y=10~\hspace{7em}\boxed{(9, 10)}[/tex]

To find another point with integral coordinates on the graph of the equation representing a direct variation, we can use the given point (6, 10) and the fact that the equation represents a direct variation. By finding the value of the constant of variation, we can substitute an integral x-value to find the corresponding y-value for another point on the graph.

To find another point with integral coordinates on the graph of the equation representing a direct variation, we need to use the given point (6, 10) and the fact that the equation represents a direct variation. A direct variation equation has the form y = kx, where k is the constant of variation. In this case, we can use the given point to find the value of k. When x = 6 and y = 10 in the equation y = kx, we can substitute these values to solve for k: 10 = k * 6. Solving for k, we get k = 10/6 = 5/3.

Now that we know the value of k, we can find another point with integral coordinates. Let's try x = 3. Using the equation y = kx, we can substitute x = 3 and k = 5/3 to find y: y = (5/3) * 3 = 5.

So, another point with integral coordinates on the graph of the equation representing a direct variation is (3, 5).

Answer:

Simplify:

-3/5 ÷ 7/6

Step-by-step explanation:

1. To solve you have to switch the ÷ to x, but once you do that 7/6 would be switched too:

-3/5 x 6/7

2. Simplify,

-18/35

So, the answer to this is B.

Hope this Helped!!!!!

~Shane

➷ Use this formula:

density = mass / volume

Rearrange it for mass:

mass = density x volume

Substitute the values in:

mass = 100 x 19.3

Solve:

mass = 1930g

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Answer: [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The greatest GCF is 5 because 5 goes into 15, and 10. Therefor, the answer would be 2/3.

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Answer:

⅔

Step-by-step explanation:

Find all the factors of 10 and 15.

Factors of 10: 1, 2,     5, 10

Factors of 15: 1, 2, 3, 5,      15

The highest factor that is in both 10 and 15 is 5.

To reduce the fraction 10/15, divide both the numerator and denominator

by 5.

10/15 = (10 ÷ 5)/(15 ÷ 5) = ⅔

Answer: FIRST OPTION

Step-by-step explanation:

To solve this problem you must apply the Intersecting Secant-Tangent Theorem. By definition, when a secant line and a tangent lline and a secant segment are drawn to a circle from an exterior point:

[tex](Tangent\ line)^2=(Secant\ line)(External\ Secant\ line)[/tex]

The total measure of the secant shown is:

[tex]18+Diameter[/tex]

If the radius is 7, then the diameter is:

[tex]D=7*2=14[/tex]

Therefore:

[tex]Secant\ line=18+14=32[/tex]

You also know that:

[tex]External\ Secant\ line=18\\Tangent\ line=x[/tex]

Keeping the above on mind, you can substitute values and solve  for x:

[tex]x^{2}=32*18[/tex]

[tex]x=\sqrt{576}\\x=24[/tex]

The measure of the side length of the tangent line PQ to the circle O is 25 units

From the image, Line segment PQ is a tangent line because it touches the curve at point Q.

Therefore, triangle PQO forms a right triangle.

Leg 1 of the right triangle = OQ = 7

Leg 2 of the right triangle = PQ = x

Hypotenuse = PO = 18 + 7 = 25

Now, to solve for the measure of side length x, we use the Pythagoras theorem:

PQ = √( PO² - OQ² )

Plug in the values:

x = √( 25² - 7² )

x = √( 625 - 49 )

x = √576

x = 24

Therefore, the value of x is 24.

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Answer:

x = 1/2

Step-by-step explanation:

Subtract 2x from both sides

4x + 5x - 2x = 6

Combine 4x and -2x to get 2x.

2x + 5 = 6

Subtract 5 from both sides.

2x = 6 - 5

Subtract 5 from 6 to get 1.

2x=1

Divide both sides by 2.

x = 1/2

Answer:

14/14 = 1 and 56/14 = 4

Thus, 14:56 ratio simplified is 1:4

hope this helps:)sorry if it doesnt

brainliest plz

The answer is A because completing the square gives a minimum of 2,-9 and factorising gives roots of 5 and -1 :)

Answer:

Minimum at (2,-9)  and  intercepts are (-1,5)

Step-by-step explanation:

f(x) = [tex]x^2 -4x-5[/tex]

completing square method adding and subtracting the square of half of coefficient of 4 ,we get

f(x) = [tex]x^2 -4x+4 -4 -5[/tex]

f(x) =[tex](x-2)^2 -9[/tex]

on comparing it with standard vertex form [tex](x-h)^{2} +k[/tex]

                                 where k is suppose to be the minimum value

on comparing  it we get  k = -9

which is minimum value of f(x)

at x =2

and if we find the zeros of

[tex]x^2 -4x-5[/tex] ,we get

[tex]x^2 -5x+x -5[/tex]

[tex]x^2 -4x-5[/tex]

x(x-5)+1(x-5)

(x+1)(x-5)

on setting it equals zero ,we get

x+1 =0 and x=5

x =-1 and x=5

therefore option A is answer

Minimum at (2,-9)  and  intercepts are (-1,5)

Y=|x|. An absolute value has a V shape.

Final answer:

The equation that will make a V-shaped graph is y = |x|, as it plots the absolute value of x, creating a V shape by reflecting points on the positive side of the y-axis for both positive and negative values of x.

Explanation:

The student asked which of the following equations will make a V-shaped graph. The answer is y = |x|. This is because the absolute value function produces a graph that is V-shaped, reflecting the positive distance from zero for both positive and negative values of x. The other options presented, such as y = 2x, would produce a straight line; x² + 5 = y (correctly read as y = x² + 5) would produce a parabola; and y = 1/3x would also result in a straight line, just with a different slope. Only the graph of y = |x| has the distinct V shape as it plots the absolute value of x, meaning it reflects the points on the positive side of the y-axis for both positive and negative values of x.

Hello.

We are solving -9.4 > 1.7x + 4.2.

First we need to swap sides:

[tex]1.7x + 4.2 = -9.4[/tex]

Now we need to subtract 4.2 from both sides.

1.7x + 4.2 = -9.4

        -4.2 .  -4.2

Now let's combine -4.2 + 4.2 which is 0.

We get 1.7x < -9.4 - 4.2

Now let's divide both sides by 1.7

1.7x | -13.6

1.7     1.7

x < -13.6

      1.7

So we just divided to get x < -8.

Answer:

[tex]\boxed{\bold{x<-8}}[/tex]

Step By Step Explanation:

[tex]\bold{1.7x+4.2<-9.4}[/tex]

[tex]\bold{1.7x\cdot \:10+4.2\cdot \:10<-9.4\cdot \:10}[/tex]

[tex]\bold{17x+42<-94}[/tex]

[tex]\bold{17x+42-42<-94-42}[/tex]

[tex]\bold{17x<-136}[/tex]

[tex]\bold{\frac{17x}{17}<\frac{-136}{17}}[/tex]

[tex]\bold{x<-8}[/tex]

Answer:

40 un.

Step-by-step explanation:

The diagonals of the rhombus bisect each other at right angle. This gives us that

By the Pythagorean theorem,

[tex]VE^2=VS^2+ES^2,\\ \\VE^2=6^2+8^2,\\ \\ VE^2=36+64,\\ \\VE^2=100,\\ \\VE=10\ un.[/tex]

The sides of the rhombus are all of the same length, then the perimeter of the rhombus is

[tex]P_{VENU}=4\cdot 10=40\ un.[/tex]

Answer:

2(7.5x+3.5)

Step-by-step explanation:

I can't remember what these equations are actually called, however in order to solve this you simply multiply 7.5 by 2, and then 3.5 by 2.

The value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.

Exponential function is the function in which the function growth or decay with the power of the independent variable.

The curve of the exponential function depends on the value of its variable.

The exponential function with dependent variable y and independent variable x can be written as,

[tex]y=a^x[/tex]

Here, [tex]x[/tex] is the variable in the power of a number.

Given information-

The given exponential function in the problem is,

[tex]f(x)=8^x+1[/tex]

The value of function at the value of variable x as 1/3 has to be find to complete the table. Put 1/3 in the above equation on the place of x as,

[tex]f(x)=8^{\frac{1}{3}}+1[/tex]

The number 8 can be written as the [tex]2^3[/tex]. Thus,

[tex]f(x)=(2^3)^{\frac{1}{3}}+1\\f(x)=(2)^{\dfrac{3\times1}{3}}+1\\f(x)=(2)^1+1\\f(x)=2+1\\f(x)=3[/tex]

Thus the value of exponential function, which completes the table for variable x at 1/3 is 3. The option B is correct.

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To find the unit rate, divide total cost by number of cans bought.

$30 / 12 cans = $2.50 per can.

Now multiply the unit cost by the number of cans you want to buy:

2.50 x 100 = $250.00

2.50 x 250 = $625

Answer:

Step-by-step explanation:

Find out the price of one bagel by dividing the price by the number of bagels:

350 Bagels = $168

1 Bagel = $0.48

475 Bagels = $209

1 Bagel = $0.44

0.48 > 0.44

This means the second bakery has the lower price.

Louis wants 800 bagels, so multiply the price by 800.

0.44 * 800 = $352

You can check it's lower by comparing it with the first bakery.

0.48 * 800 = $384

384 > 352

Answer:

Step-by-step explanation:

The product of three and a number x: 3 · x = 3x

The sum of four and the product of three and a number x:

4 + 3x

Exponential decay because it is decreasing

The linear equation that models the cost of making a call lasting x minutes using a calling card is y = -0.1x + 1.45.

To write a linear equation that models the cost of making a call lasting x minutes using a calling card, we can use the given information about two calls. If a 5-minute call costs $0.95 and a 13-minute call costs $1.75, we can set up two equations:

0.95 = 5m + b

1.75 = 13m + b

Solving these equations, we find that m = -0.1 and b = 1.45. Therefore, the linear equation that models the cost of making a call lasting x minutes is y = -0.1x + 1.45.

Answer:

[tex]\large\boxed{8x^3+125=(2x+5)(4x^2-10x+25)}[/tex]

Step-by-step explanation:

[tex]8x^3+125=2^3x^3+5^3=(2x)^3+5^3\\\\\text{use}\ a^3+b^3=(a+b)(a^2-ab+b^2)\\\\=(2x+5)((2x)^2-(2x)(5)+5^2)\\\\=(2x+5)(4x^2-10x+25)[/tex]

Answer:

Step-by-step explanation:

Area = L * W

2/5 * 1/3 =

2 * 1 = 2

5 * 3 = 15

= 2/15 inches squared

What we do is find area

Area of rectangle=(l*w)

length=2/5

width=1/3

Area=2/5*1/3

Answer=2/15

Answer=2/15

➷ To figure this out, you need to understand that there are 60 minutes in an hour

Subtract 10 from this value:

60 - 50

As it isn't 60 minutes, it wouldn't be 9 anymore

9-1 = 8

The correct answer would be: 8:50

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Answer:

2A/h = b

Step-by-step explanation:

The formula for area of a triangle is

A = 1/2 bh

Multiply each side by 2

2A = 2*1/2 bh

2A = bh

Divide each side by h

2A/h = bh/h

2A/h = b

Answer:

b=2A/h

Step-by-step explanation:

The formula for area of a triangle is

A = 1/2 bh

Multiply each side by 2

 2*1/2 bh = 2A

bh = 2A

Divide each side by h

bh/h = 2A/h

b = 2A/h

The population of a town decreasing at a rate of 1.5% per year from an initial number of 4500 will drop below 4000 in approximately 9 years, around the year 2019.

The topic of this question concerns a decrease in population over time, which is generally described using exponential decay in mathematics. When we talk about a decrease of 1.5% per year, we're looking at an exponential decay factor of 1 - 0.015 = 0.985. We follow this process to determine the duration for the population to reduce below 4000:

Basically, it means:

4500 * (0.985^n) < 4000

. By solving this inequality, we find that

n ≈ 8.29

. Therefore, we can estimate the town's population will drop below 4000 in the 9th year (since we can't have a fraction of a year), which would be

2019

if we start counting from 2010.

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The population of the town would drop below 4000 in 2024.

To determine the year when the population of the town drops below 4000, we can use the formula for exponential decay:

Population = Initial population × (1 - Decay rate)^Time

where:

Population is the population at a given time

Initial population is the initial population (in 2010, which is 4500)

Decay rate is the decrease rate per year (1.5% or 0.015)

Time is the number of years since 2010

We want to find the Time when the Population is less than 4000. So, we can set up an inequality:

4000 > 4500 × (1 - 0.015)^Time

Dividing both sides by 4500, we get:

0.889 > (1 - 0.015)^Time

Taking the natural logarithm of both sides, we get:

ln(0.889) > Time × ln(1 - 0.015)

Dividing both sides by ln(1 - 0.015), we get:

Time ≈ 13.92

Since we're looking for the year when the population drops below 4000, we round up to the nearest whole year. Therefore, the population of the town would drop below 4000 in 2024.

Answer:6.928

Step-by-step explanation: formula A=√ 3*(side^2/4)

The area would be 7 cm

See the image

Answer:

168

14 times 12

Answer:

[tex]\dfrac{7.7.7.7.7}{7.7}[/tex]

Step-by-step explanation:

Finding the expression of the value [tex]\dfrac{7^{5} }{7^{2}}[/tex] is just like taking the spread out value of the two variables raised to their exponents.

[tex]\dfrac{7^{5}}{7^{}}=\dfrac{7.7.7.7.7}{7.7}[/tex]

So if we multiply all the values together we get:

=[tex]\dfrac{16807}{49}[/tex]

=343

This method is just one of the methods that can be used to finding the quotient of a variable raised to an exponent.