In an arithmetic sequence, T1=4 and T7=22.
Using Simultaneous equations find the values of a and d.

Answer:

2/9

Step-by-step explanation:

The sum of two numbers is 5/9 can be expressed as:

[tex]\displaystyle \large{x+y=\dfrac{5}{9}}[/tex]

One of the numbers is 1/3. Find the other - this means that either x or y is 1/3 but that doesn’t matter as we can either let x = 1/3 or y = 1/3 via property:

[tex]\displaystyle \large{x+y = y+x}[/tex]

Hence, let x = 1/3:

[tex]\displaystyle \large{\dfrac{1}{3}+y=\dfrac{5}{9}}[/tex]

Solve for y - subtract both sides by 1/3:

[tex]\displaystyle \large{\dfrac{1}{3}-\dfrac{1}{3}+y=\dfrac{5}{9}-\dfrac{1}{3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1}{3}}[/tex]

We know that we can only evaluate the fractions if both have same denominator so what we have to do is to multiply 1/3 by 3 for both top and bottom:

[tex]\displaystyle \large{y=\dfrac{5}{9}-\dfrac{1\cdot 3}{3\cdot 3}}\\\displaystyle \large{y=\dfrac{5}{9}-\dfrac{3}{9}}\\\displaystyle \large{y=\dfrac{2}{9}}[/tex]

Therefore, the other number is 2/9

Answer:

The other number is 2/9

Step-by-step explanation:

"a" is the other number

The equation:

[tex]a+\frac{1}{3} =\frac{5}{9}[/tex]

Then

[tex]a=\frac{5}{9} -\frac{1}{3} =\frac{15-9}{27} =\frac{6}{27}[/tex]

simplifying the fraction:

[tex]a = \frac{2}{9}[/tex]

Hope this helps

Answer:

lol same but that's okay we can all for sure get better at it :)

Step-by-step explanation:

Answer:

Horizontal: y = 9

Vertical: x = 3

Step-by-step explanation:

Any point is given in the form (x,y). The first number is the x and the second number is the y.

Horizontal lines (a left-right line like the horizon) have an equation in the form "y = anumber" This works because a horizontal line has ZERO slope. So there is no x in the equation because--

y = 0x + b

y = b (a number, use the y-number from the point)

A vertical line has undefined slope so you can't even pretend to use a slope equation. A vertical line (up and down) has an equation in the form

"x = anumber" Use the x from the point.

Horizontal line through (3,9) is y=9.

Vertical line through (3,9) is x=3

Answer:

y = 12/5 = x + 7

hope this helped

lol

There are 160 students in seventh grade.  Divide the partial amount by the percentage of the partial amount to get the total amount.

A percentage is a number or ratio that is expressed as a fraction of one hundred. The percent sign, "%," is commonly used, but the abbreviations "pct.", "pct," and sometimes "pc" are also used. A percentage is a number with no dimensions; it has no unit of measurement.

A total is the result of adding several numbers together or counting how many items there are in a group. The total number or cost of something is the total number or cost obtained by adding or counting all of its parts.

Percentages can also be expressed as decimals or fractions, such as 0.6%, 0.25%, and so on. Academic marks are calculated in terms of percentages for any subject.

To Find the Total Amount :

No. of student in seventh grade = 8/5 * 100 = 160

So, there are 160 students in seventh grade.

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Answer to first four-

first one- 2f+2f=60

4f=60

f=15

second one-18+2d=38

2d=20

d=10

(short side is 9)

third one-2a+a+5+a+5=26

4a+10=26

a=4

long side is 9

short side is 8

fourth one-3xy+3xy+xy=63

7xy=63

xy=9

long side is 27

Answer:

Circumference = 50.24 units

Area = 200.96 units²

Determining the area of the circle:

The formula of finding the area of the circle is π(r)² or π(d/2)².

(Where "r" represents the radius and "d" represents the diameter)

In this case, we are given the diameter. Thus, we will use the formula π(d/2)². Simply substitute the diameter in the formula to determine the area of the circle.

⇒ π(D/2)² = Area of circle

⇒ π(16/2)² = Area of circle

⇒ π(8)² = Area of circle

⇒ π × 64 = Area of circle

[Exact form of pie: 22/7; Approx form of pie: 3.14]

⇒ Area of circle ≈ 3.14 × 64

⇒ Area of circle ≈ 200.96 units²

Determining the circumference of the circle:

The formula of finding the circumference of a circle is 2πr or πd.

(Where "r" is radius and "d" is diameter)

In this case, we are given the diameter. Thus, we will use the formula πd. Simply substitute the diameter in the formula to determine the circumference of the circle.

⇒ πd = Circumference of circle

⇒ π(16) = Circumference of circle

[Exact form of pie: 22/7; Approx form of pie: 3.14]

⇒ (3.14)(16) ≈ Circumference of circle

⇒ 50.24 units ≈ Circumference of circle

Answer:

140

Step-by-step explanation:

We already have our first value 35 and the second value 25. Let's assume the unknown value is Y which answer we will find out.

As we have all the required values we need, Now we can put them in a simple mathematical formula as below:

35 = 25% × Y

35 = 25/100 × Y

Multiplying both sides by 100 and dividing both sides of the equation by 25 we will arrive at:

Y = 35 × 100/25

Y = (35 × 100)/25

Y = 140

Finally, we have found the value of Y which is 140 and that is our answer.

Hope this is a better break down than before!

Answer:

140

Step-by-step explanation:

You can think of this as 35 = 25% of x.

25% = 0.25, so 35 = 0.25x.

You can multiply by 4 on each side to get

140 = 4(0.25)x which simplifies to

140 = x

[tex]\text{Given that,}\\\\(x_1,y_1) = (4,-2)~~ \text{and slope,}~ m =\dfrac 12\\\\\text{Point - slope form,}\\\\y-y_1 = m(x-x_1)\\\\\implies y -(-2) = \dfrac 12(x-4)\\\\\implies y+2=\dfrac 12(x-4)[/tex]

(4,-2) are points [tex](x_1, y_1)[/tex] respectively and [tex]\frac{1}{2}[/tex] is the slope

Point-slope:

[tex]y-y_1 = m(x-x_1)[/tex]      

Now you have to replace the variables with numbers

[tex]y+2 = \frac{1}{2}(x-4)[/tex]

Thus your equation would be:

[tex]y+2 = \frac{1}{2}(x-4)[/tex]

Hope this helped!

Answer:

[tex]328units^2[/tex]

Step-by-step explanation:

First off,  I do want to say that you could word this more easily.

98 is the perimeter. length is 41. width is 8.

the area is length*width for rectangles.

98-41=57

57-41=16

16/2=8

8*41=328 units^2

Answer:

3 eggs constitutes 1/4 of the original 12 eggs

Step-by-step explanation:

Divide "12 eggs" by "4 people," obtaining 3 eggs/person.

3 eggs constitutes 1/4 of the original 12 eggs.

Answer:

f(x) = -x^2 + x + 12.

Step-by-step explanation:

f(x) = a(x - 4)(x + 3)    as the x-intercepts are  -3 and 4.

a is some costant.

At the y intercept x = 0 so we have:

y = 12 = a(0-4)(0+3)

12 = -12a

a = -1

So our eaution is f(x) = -(x - 4)(x + 3)

= -(X^2 - x - 12)

=  -x^2 + x + 12

Answer:

r={21}

Step by Step Explanation:

PREMISES

Two times three plus a number, say, r=27

ASSUMPTIONS

Let r=the number

CALCULATIONS

The numerical expression “two times three plus a number r=27” can be denoted as:

(2×3)+r=27

6+r=27

6–6+r=27–6

0+r=27–6

r=21

PROOF

If r=21, then the equations

(2×3)+r=27

6+21=27 and

27=27 prove the root (zero) r=21 of the statement (2×3)+r=27

PREMISES

Two times three plus a number, say, r=27

ASSUMPTIONS

Let r=the number

CALCULATIONS

The numerical expression “two times three plus a number r=27” can be denoted as:

(2×3)+r=27

6+r=27

6–6+r=27–6

0+r=27–6

r=21

PROOF

If r=21, then the equations

(2×3)+r=27

6+21=27 and

27=27 prove the root (zero) r=21 of the statement (2×3)+r=27

Answer:

5 and 6

Step-by-step explanation:

let the 2 numbers be x and y , then

3x + 2y = 28 → (1)

2x + 3y = 27 → (2)

multiplying (1) by 2 and (2) by - 3 and adding will eliminate x

6x + 4y = 56 → (3)

- 6x - 9y = - 81 → (4)

add (3) and (4) term by term to eliminate x

0 - 5y = - 25

- 5y = - 25 ( divide both sides by - 5 )

y = 5

substitute y = 5 into either of the 2 equations and solve for x

substituting into (1)

3x + 2(5) = 28

3x + 10 = 28 ( subtract 10 from both sides )

3x = 18 ( divide both sides by 3 )

x = 6

The 2 numbers are 6 and 5

The total interest paid for the period of three months will be $5225 on the loan amount of $450000.

The interest is the charges levied on the amount which we borrow from any bank for a particular period of time.

Here in the question given data is

P= $450000

R=2.2%+2.8%=5%

T=1/4 years or three months

So from the simple interest formula

[tex]\rm SI=\dfrac{P\times R\times T}{100}[/tex]

[tex]\rm SI=\dfrac{450000\times 5\times 1}{100\times 4}[/tex]

[tex]\rm SI= \$5625[/tex]

Hence the total interest paid for the period of three months will be $5225 on the loan amount of $450000.

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Answer:

<GBF

Step-by-step explanation:

Supplementary angles add up to = 180 degrees. Usually, they are side by side in transversals such as this one. The angle supplementary to <GBH is <GBF or <FBG.

Hope this helps!

Answer:

I think he made a mistake in the first one

Step-by-step explanation:

Marcel made an error which is both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses" option (A) is correct.

The distributive property is the property that expresses the distributive law of algebraic multiplication. Similarly, in polynomial expression we can use the distributive property, for example, we can write a(c+b)  in the form of (ac+bc).

The expression is:

= 32x - 16

= 8x(4) - 2(8)

= 8(4x - 2)

The error is "both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses"

Thus, Marcel made an error which is both terms aren’t multiplied by 8x, so 8x can’t go in front of the parentheses" option (A) is correct.

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Answer:

b and d and e

Step-by-step explanation:

7/doubles(2)/4weeks so you have to multiply the • means multiplication a another way to show multiplication.b-7×8(2×4)=56.d-7×2×2×2×2(2×4)=56.e-7×2×4(2×4=8)=56.

hmmm taking a peek at the triangles inside the park, hmmm let's notice both triangles have all interior angles of 60°, meaning the triangles are equilateral both, so all sides are equal, since we know one side is 50 yards, well, all sides are 50 yards, so the top and bottom straight-lines are both 50 each.

looking at the left and right sides, hmmm those are just sectors of a circle, both have a radius of 50 yards and a central angle of 120°.

[tex]\textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=50\\ \theta =120 \end{cases}\qquad \implies s=\cfrac{(120)\pi (50)}{180}\implies s=\cfrac{100\pi }{3} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{straight~lines}{2(50)}~~ + ~~\stackrel{circular~lines}{2\left( \cfrac{100\pi }{3} \right)}\implies 100+2\left( \cfrac{100(3.14) }{3} \right)~~\approx~~309~yards[/tex]

Answer:

Pretty sure its 60

Step-by-step explanation:

Basic geometry

Answer:

B

Step-by-step explanation:

12:

BY, BP, BG, VY, VP, VG, WY, WP, WG, RY, RP, RG

The milk can is in the shape of a cylinder.

The surface area of cylinder is defined as the sum of curved surface and the two circular bases of the cylinder;

‎ㅤ‎ㅤ‎ㅤ➙ (curved surface ) + 2(base area )

‎ㅤ‎ㅤ‎ㅤ➙ 2πrh + 2πr²

‎ㅤ‎ㅤ‎ㅤ➙ 2πr( h + r )

Here, in this question we have;

Therefore, Surface Area ( S.A ) :

➝ S.A = 2πr( r + h )

➝ S.A = 2 × π × 1 ( 1 + 6 )

➝ S.A = 2π ( 7 )

➝ S.A = 2 × 3.14 × 7

➝ S.A = 14 × 3.14

➝ S.A = 43.96cm²

Answer:

Surface area of cylindrical milk can is 43.96cm²

Step-by-step explanation:

Given :-

To find:-

Solution:-

formula for surface area cylindrical milk can :-

2πr(h+r)

putting the known values ,

2 × 3.14 × 1 (6+1) cm²

Surface area :- 43.96 cm²

The fraction computed shows that the number of peanut butter sandwiches that can be made will be 14.

From the information given, it was stated that there are 2 1/3 cup of peanut butter and that they put 1/16 cup of peanut butter on each sandwich.

Therefore, the number of peanut butter sandwiches that can be made will be:

= 2 1/3 ÷ 1/6

= 7/3 × 6/1

= 14

In conclusion, the correct option is 14.

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The new monthly salary will be $1,457.50.

You received a monthly salary of $1,375.00

Now by economy expansion, causing wages to increase by = 6%

Increment of the salary = 6% of 1,375.00

[tex]= \frac{6}{100} \times 1,375[/tex]

[tex]= 0.06 \times 1,375 =\$82.50[/tex]

Monthly Salary means Employee's monthly salary, before deductions.

Therefore our new monthly salary would be

[tex]= $1,375.00 + $82.50\\ = $1,457.50[/tex]

Therefore our new monthly salary will be $1457.50.

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Answer:

14 : 24

Step-by-step explanation:

If 10 of the 24 pupils are female, then that means the other 14 is male. Therefore, the ratio of males : total would be 14 : 24.

I hope this helps! Have a lovely day!! :)

(brainliest is much appreciated!!)

Answer:

14:24

Step-by-step explanation:

24 pupils = total

24 total - 10 females = 14 males

The ratio is

males : total

14 males : 24 people total

the simplified ratio is

7 males : 12 people

Answer:

When we think of the number line -5 is the coldest temperature on the number line. -5 -4 -3 -2 -1 0 1 2 3 -5 °C is the coldest temperature and 2 °C is the hottest temperature.

Answer:

150.79645

Step-by-step explanation:

Fist of all half of your diameter is your raduis which is how you get three

V=πr2h3=π·32·163≈150.79645

Answer:

150.8

Step-by-step explanation:

v= (πr^2h)/3

r=6/2=3

3^2xπx16=ans

ans/3=150.8

Answer:

(4, -18)

Step-by-step explanation:

First  Use this formula for the x -axis  -b/2a  

-8/2(1) is -4

Then plug in -4 to the equation

(-4)^2+8(-4)-2 = -18

You should keep 0.97 seconds of distance between you and the vehicle ahead.

The formula for calculating distance is expressed as:

distance  = speed * time

Time = Distance/Speed

Given the following parameters

Distance = 50 feet

Speed = 35mph = 51.3ft/s

Time taken = 50/51.3
Time taken = 0.97

Hence you should keep 0.97 seconds of distance between you and the vehicle ahead.

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Answer:

c. b. a.

Step-by-step explanation:

yan po sagot sana po makatulong ito lang po alam ko ehh