Help with Algebra! (Photo attached)

Answer:

Option C.

Step-by-step explanation:

From the graph we can find the points (2,3) for first straight line (blue) and (2,2) for second straight line (red). These points Andre satisfied by option C.

x+2y=8

2+2×3=8

8=8.

Again, 2x+4y=12

2×2+4×2=12

12=12

The correct answer is Option C.

x + 2y = 8

2x + 4y = 12

In its simplest format in algebra, the definition of an equation exists as a mathematical statement that indicates that two mathematical expressions exist equal. For instance, 3x + 5 = 14 exists an equation, in which 3x + 5 and 14 exist two expressions separated by an 'equal' sign.

Equation of line in Two point form

When we know any two points on a line lets say [tex](a_1,b_1)[/tex] and [tex](a_2,b_2)[/tex], we can write its equation as:

[tex]y-b_1=m(x-a_1)[/tex]

where

[tex]m=\dfrac{b_2-a_2}{b_1-a_1}[/tex]

Here we have points of red line:( from graph) (0,3) and (6,0)

Equation of line: y-3=m(x-0)

m=0-3/6-0=-1/2

Equation:2y-6=-1(x)

               2y+x=6

Now from graph, we can see that the blue line is parallel to red line, therefore their slopes are same

The equation of blue line is as follows

y=mx+c

Point on blue line :(0,4)

4=(-1/2)*(0)+c

c=4

The equation is x+2y=8.

Therefore, it matches with option C.

x + 2y = 8

2x + 4y = 12

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Answer:

  see attachment

Step-by-step explanation:

The directions tell you what you need to know. It is a matter of adding up the values shown and finding the missing number to make the total be -20. Of course, it works best to start with a row, column, or diagonal that has 4 numbers already.Then, you're only finding the 5th number.

You can start with either diagonal, column 1 or 4, and row 4 or 5. Filling the missing numbers in those spots (red) will let you find the remaining missing numbers (green, then blue).

The square at row 2, column 2 can be filled on the first round using the down-right diagonal. I have shown it as filled on the second round after row 5 column 2 is filled.

Using a spreadsheet can make this easier, because you can write formulas for the sums in each row, column, and diagonal. Then you're just making those sums be -20.

___

For example, consider the up-right diagonal. The sum of the given values, -6, 0, -4, -2, is -12. Then the spot at row 1, column 5 must be filled with -8 to make the sum be -20.

Answer:

x° = 54°

Step-by-step explanation:

The angle where the diameter meets the tangent line is a 90° angle, so the angle x° is complementary to the angle 36°. (Thus the sum of angles in the triangle is 180°.)

x = 90 -36 = 54

it would be 7.2cm

because

45÷12=3.75

so thats the scale you use

and 27÷3.75 equals 7.2

Answer:

D. 1024 π units²

Step-by-step explanation:

We have sphere, with a radius of 16 units.

The surface area of a sphere is given by the following formula:

Surface Area of a sphere = 4 π r²

We already know r, which is 16.  So,

SA = 4 * π * 16² = 256 * 4 * π  = 1024 π  units²

That's enough for our answer, which matches answer D from the list.

If we want to have an actual number.... we would have to multiply 1024 by π.

SA = 1024 * π = 3217 units²

Answer:

option D

1024π units²

Step-by-step explanation:

Given in the question that radius of a sphere = 16 unit

Formula to use to calculate the surface area of the sphere

here r is the radius of the sphere

4 π (16)²

4 π (256)

1024π units²

Surface area of a sphere with radius 16 units = 1024π units²

Answer:

Day 5

Step-by-step explanation:

There are 2 ways to solve this, one using exponents and the other using logs. The equation regardless of how you solve it looks like this:

[tex]y=3^x[/tex]

where y is the number of customers on day x.  Filling in the number of customers we were given:

[tex]243=3^x[/tex]

There's a rule in exponents that says if the bases on both sides of the equals sign are like, then their exponents are equal to each other.  So if we can rewrite 243 in terms of a base of 3, then we're good.  I went to my calculator and started raising 3 to increasing powers of x:  3 to the first is 3; 3 squared is 9; 3 cubed is 27; 3 to the fourth is 81; 3 to the fifth is 243!  That means that

[tex]3^5=3^x[/tex]

Since the bases are like, then x = 5.

Using logs to solve it:

Take the log of both sides:

[tex]log(243)=log(3)^x[/tex]

There's a law of logs that says when you take the log of a number with an exponent, you can bring down the exponent in front like this:

[tex]log(243)=xlog(3)[/tex]

Now to solve for x, divide both sides by log(3):

[tex]\frac{log(243)}{log(3)}=x[/tex]

You can do that on your calculator and get that x = 5.

Whichever way is easier for you to understand OR whichever way your teacher is teaching according to where you are in your log unit, do it that way!  You can see that both give the same answer, the methods to get there vary.

Answer:

700 im not sure

Step-by-step explanation:

Answer:

68%

Step-by-step explanation:

The mean is 25 and the standard deviation is 5.  So 20 is one standard deviation below the mean and 30 is one standard deviation above the mean.

According to the Empirical Rule, 68% of the normal curve is between ±1 standard deviations.  So the answer is 68%.

Answer:

The correct option is 2.

Step-by-step explanation:

Given information: The population mean is μ=25 and standard deviation is σ=5.

[tex]Z=\frac{X-\mu}{\sigma}=\frac{X-25}{5}[/tex]

We need to find the percent of the trees that are between 20 and 30 years old.

[tex]P(20<X<30)[/tex]

Subtract 25 from each side.

[tex]P(20-25<X-25<30-25)[/tex]

[tex]P(-5<X-25<5)[/tex]

Divide each side by 5.

[tex]P(-1<\frac{X-25}{5}<1)[/tex]

[tex]P(-1<Z<1)=P(Z<1)-P(Z<-1)[/tex]

Using standard normal table we get

[tex]P(-1<Z<1)=0.84134-0.15866=0.68268\approx 0.68=68\%[/tex]

68% of the trees are between 20 and 30 years old.

Therefore the correct option is 2.

Three forths (75%, 0.75, 3/4)

24

Explanation:

8×3=24

To solve the equation 3/(y - 5) = 15/(y + 4) for the value of y, cross multiply to eliminate the fractions. Then collect the y terms on one side and the constant terms on the other side. Finally, divide both sides by the coefficient of y to find the value of y.

To solve the equation 3/(y - 5) = 15/(y + 4) for the value of y, we first cross multiply to eliminate the fractions.

This gives us 3(y + 4) = 15(y - 5). Expanding this equation, we have 3y + 12 = 15y - 75.

Next, we collect the y terms on one side and the constant terms on the other side. Simplifying the equation, we get 12 + 75 = 15y - 3y.

Combining like terms, we have 87 = 12y. Finally, we divide both sides of the equation by 12 to solve for y.

Therefore, the value of y is 7.25.

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Answer:

Step-by-step explanation:

lets do 3/7.

3.0/7 is .4 and .2

.20/7 is .14 and 6/7

.4+.14 is .54

but with 6/7 hundredth you add 1 more

so .55

To find the volume of a hemisphere-shaped water storage tank with a radius of 20 ft, use the formula V = (2/3)πr³, resulting in approximately 16746.66 cubic feet.

A water storage tank is in the shape of a hemisphere (half a sphere). To find the volume of the tank, we can use the formula for the volume of a hemisphere, which is V = (2/3)πr³, where r is the radius. Given that the radius is 20 ft, we can substitute to find the volume.

Answer:

B

Step-by-step explanation:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex]

where h and k are the coordinates of the center of the circle and the radius is squared.  The radius is easy...take the square root of 25 to get that the radius is 5.  Since the pattern for the standard form is "x-" and "y-", if (x+2)^2 is the horizontal placement of the center, it actually was originally written as (x-(-2))^2, so the h coordinate is -2.  Same goes for the vertical movement of the center.  (y-(5))^2 means that the k coordinate is a positive 5.

Answer:

Third choice is the one you want

Step-by-step explanation:

First off, we need to remember that for a line to be perpendicular to another line, its slope is the opposite reciprocal to the other line. The slope of our line is -1/4, so the opposite reciprocal slope is +4/1 or just 4. Now we know that m = 4.

The point-slope form of a line is

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

where m is the slope, y1 is the y coordinate of the point, and x1 is the x coordinate of the point. Filling in:

[tex]y-5=4(x-(-3))[/tex] which simplifies to

[tex]y-5=4(x+3)[/tex] which simplifies further to

[tex]y-5=4x+12[/tex]

Add 5 to both sides to get the equation into slope-intercept form:

y = 4x + 17

choice 3

Answer:

95%

Step-by-step explanation:

Assuming each person can only vote once, just divide the amount of people that voted divided by the number of members. 38/40 gives a decimal of 0.95, and to find the percentage, just simply times it by 100.

Answer:

no

Step-by-step explanation:

Answer:

Final answer is [tex]\frac{49}{4}[/tex].

Step-by-step explanation:

Given expression is [tex]x^2-7x+c[/tex].

Now we need to find about what value for c will make the given expression [tex]x^2-7x+c[/tex], a perfect square trinominal.

Coefficient of middle term that contains x, in [tex]x^2-7x+c[/tex] -7.

Take half of that so we get [tex]-\frac{7}{2}[/tex].

Then take square of the half value.

We get [tex]\left(-\frac{7}{2}\right)^2=\frac{49}{4}[/tex].

We add the square value to make perfect square trinomial.

Hence final answer is [tex]\frac{49}{4}[/tex].

Answer:

D. [tex]\frac{49}{4}[/tex].

Step-by-step explanation:

We have been given a trinomial [tex]x^2-7x+c[/tex]. We are asked to find the value of c, which will make the expression a perfect square trinomial.

We know that a perfect trinomial is in form [tex]a^2\pm2ab+b^2[/tex].

We will use complete the square process to solve for c.

To complete a square, we need to add square of half the coefficient of x term. We can see that coefficient of x is -7, so the value of c would be:

[tex](\frac{b}{2})^2=(\frac{-7}{2})^2=\frac{(-7)^2}{2^2}=\frac{49}{4}[/tex].

Therefore, the value of c required to make the given expression a perfect trinomial is [tex]\frac{49}{4}[/tex] and option D is the correct choice.

Answer:

C

Step-by-step explanation:

The volume of a cone is given by  [tex]V=\frac{1}{3}\pi r^2h[/tex]

The volume of a cylinder is given by  [tex]V=\pi r^2 h[/tex]

Where h is the height and r is the radius

The first figure is a cone with height 6 and radius 5, we can put it into the formula and find the volume:

[tex]\frac{1}{3}\pi r^2 h\\\frac{1}{3}\pi (5)^2 (6)\\=157.08[/tex]

The second figure is a cylinder with height 50 and radius 1, we can put it into the formula and find the volume:

[tex]\pi r^2 h\\\pi (1)^2 (50)\\=157.08[/tex]

We can see that they are equal. So answer choice C is right.

Answer:

10

Step-by-step explanation:

The vertical scale gives us the frequency or the number of pets under each category . From the diagram;

The number of Dogs is 11 while there is only 1 horse

The difference between this numbers will be the solution to the question posed;

11 - 1 = 10

Therefore, 10 more dogs are pets than horses

Answer: 10

Step-by-step explanation:

11 - 1

Answer: the answer to your question is D i graphed them all that one is correct D

The equation of the line will be y = 2/3 x + 4.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

[tex]\rm (y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

George is drafting his dissertation paper for his doctoral program.

The graph below shows the line of best fit for the data recorded on the number of pages of the dissertation writing as a function of the number of hours George spends on the draft each week.

(x₁, y₁) → (0, 4)

(x₂, y₂) → (6, 2)

Then the equation of the line will be

y - 4 = [(6 - 4) / (3 - 0)] (x - 0)

y - 4 = 2/3 x

    y = 2/3 x + 4

Then the correct option is D.

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The remaining 4600 numbers are neither multiples of 2 nor 5.

There are 10,000 total four-digit numbers (1000 through 9999).

Multiples of 2 end in 0, 2, 4, 6, and 8.

4-digit numbers are those numbers that consist of only 4 digits in which the first digit should be 1 or greater than 1 and the rest of the digits can be any number between 0 and 9.

There are 9*10*10*5 = 4500 four-digit multiples of 2.

Multiples of 5 end in 0 or 5.

There are 9*10*10*2 = 1800 four-digit multiples of 5.

There is redundancy between the two sets of numbers, namely those that end in 0, which are both multiples of 2 and 5.

There are 9*10*10*1 = 900 four-digit multiples of both 2 and 5.

Then there are 4500 + 1800 - 900 = 5400

total four-digit numbers that are either multiple of 2 or 5,

which means the remaining 4600 numbers are neither multiples of 2 nor 5.

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Answer:

3600

Step-by-step explanation:

9000 total 4 digit numbers minus 5400 multiples of both 2 and 5=3600 numbers

The probabilities of drawing all hearts, face cards, or even cards are calculated with the formula: [tex](n/52) * ((n-1)/51) * ((n-2)/50)[/tex] where n is the total number of cards that match the desired outcome.

The subject here is probability, specifically, how to determine the likelihood of a particular outcome when drawing cards from a standard deck. Let's deal with each probability one at a time.

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Answer:

The area of pentagon B is [tex]83\frac{1}{3}\ in^{2}[/tex]

Step-by-step explanation:

step 1

Find the scale factor

we know that

If two figures are similar, then the ratio of its perimeters is equal to the scale factor

Let

z-----> the scale factor

x----> perimeter pentagon B

y----> perimeter pentagon A

[tex]z=\frac{x}{y}[/tex]

substitute the values

[tex]z=\frac{25}{15}[/tex]

Simplify

[tex]z=\frac{5}{3}[/tex] ----> scale factor

step 2

Find the area of pentagon B

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

z-----> the scale factor

x----> area pentagon B

y----> area pentagon A

[tex]z^{2}=\frac{x}{y}[/tex]

we have

[tex]z=\frac{5}{3}[/tex]

[tex]y=30\ in^{2}[/tex]

substitute and solve for x

[tex](\frac{5}{3})^{2}=\frac{x}{30}[/tex]

[tex](\frac{25}{9})=\frac{x}{30}[/tex]

[tex]x=30*(\frac{25}{9})=83.33\ in^{2}[/tex]

convert to mixed number

[tex]83.33=83\frac{1}{3}\ in^{2}[/tex]

To find the area of pentagon B, we can use the fact that similar polygons have their corresponding sides proportional.

To find the area of pentagon B, we can use the fact that similar polygons have their corresponding sides proportional. If the perimeter of pentagon A is 15 in and the perimeter of pentagon B is 25 in, we can set up the proportion:

perimeter of pentagon B / perimeter of pentagon A = corresponding side lengths of pentagon B / corresponding side lengths of pentagon A

To find the corresponding side lengths of pentagon B, we can multiply the corresponding side lengths of pentagon A by the ratio of the perimeters:

corresponding side lengths of pentagon B = corresponding side lengths of pentagon A * (perimeter of pentagon B / perimeter of pentagon A)

Once we have the corresponding side lengths of pentagon B, we can use the formula for the area of a regular pentagon: Area = (1/4) * sqrt(5 * (5 + 2 * sqrt(5))) * s^2, where s is the length of a side. Calculate the area of pentagon B using the corresponding side lengths.

Answer:

10d² + 8

Step-by-step explanation:

Given

(11 + 4d²) - (3 - 6d²) ← distribute parenthesis, second by - 1

= 11 + 4d² - 3 + 6d² ← collect like terms

= (4d² + 6d²) + (11 - 3)

= 10d² + 8

Answer:

(500π)÷3

Step-by-step explanation:

area=4πr^2 , volume=4(πr^3)÷3

area=100π ,so r=5

Answer:

[tex]\frac{500\pi }{3}[/tex] ft³

Step-by-step explanation:

The surface area of a sphere = 4πr², hence

4πr² = 100π ( divide both sides by 4π )

r² = 25 ( take the square root of both sides )

r = [tex]\sqrt{25}[/tex] = 5, hence

V = [tex]\frac{4}{3}[/tex]πr³

   = [tex]\frac{4}{3}[/tex]π × 5³

   = [tex]\frac{4}{3}[/tex]π × 125 =   [tex]\frac{500\pi }{3}[/tex] ft³

Answer:

325 cents per pound

Step-by-step explanation:

Answer:

325 cents per pound

Step-by-step explanation:

Answer:

The given statement is true.

Step-by-step explanation:

In order to inscribe a circle in a triangle, the circle's center must be placed at the incenter of the triangle.

This statement is true.

The INCENTER is the center of the circle that is inscribed in the triangle. Like the centroid, the incenter is always inside the triangle.

Answer:

true

Step-by-step explanation:

Split up the interval [0, 2] into 4 subintervals, so that

[tex][0,2]=\left[0,\dfrac12\right]\cup\left[\dfrac12,1\right]\cup\left[1,\dfrac32\right]\cup\left[\dfrac32,2\right][/tex]

Each subinterval has width [tex]\dfrac{2-0}4=\dfrac12[/tex]. The area of the trapezoid constructed on each subinterval is [tex]\dfrac{f(x_i)+f(x_{i+1})}4[/tex], i.e. the average of the values of [tex]x^2[/tex] at both endpoints of the subinterval times 1/2 over each subinterval [tex][x_i,x_{i+1}][/tex].

So,

[tex]\displaystyle\int_0^2x^2\,\mathrm dx\approx\dfrac{0^2+\left(\frac12\right)^2}4+\dfrac{\left(\frac12\right)^2+1^2}4+\dfrac{1^2+\left(\frac32\right)^2}4+\dfrac{\left(\frac32\right)^2+2^2}4[/tex]

[tex]=\displaystyle\sum_{i=1}^4\frac{\left(\frac{i-1}2\right)^2+\left(\frac i2\right)^2}4=\frac{11}4[/tex]

Answer:

20

Step-by-step explanation: