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Aceelerated 7th grade math!
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Answer:

2.1 cm (nearest tenth)

Step-by-step explanation:

The radius (r) of a circle is the distance between its center and its circumference.  Therefore, from inspection of the given circle:

⇒ r = OX = OY = OA

Given:

⇒ AB = OA + OB

⇒ 3.5 = r + OB

⇒ OB = 3.5 - r

As OX = OY and AB is perpendicular to XY then XB = BY.

As XY = 3 cm:

⇒ XB = BY = 1.5 cm

Therefore, for ΔOBX:

Pythagoras Theorem

[tex]a^2+b^2=c^2[/tex]

where:

Use Pythagoras Theorem and the defined sides of ΔOBX to find r:

[tex]\implies OB^2+XB^2=OX^2[/tex]

[tex]\implies (3.5-r)^2+1.5^2=r^2[/tex]

[tex]\implies 12.25-7r+r^2+2.25=r^2[/tex]

[tex]\implies 14.5-7r+r^2=r^2[/tex]

[tex]\implies 14.5-7r+r^2-r^2=r^2-r^2[/tex]

[tex]\implies 14.5-7r=0[/tex]

[tex]\implies 14.5=7r[/tex]

[tex]\implies 7r=14.5[/tex]

[tex]\implies \dfrac{7r}{7}=\dfrac{14.5}{7}[/tex]

[tex]\implies r=2.07142857...\: \sf cm[/tex]

Therefore, the radius of the circle is 2.1 cm (nearest tenth).

Answer:

116 g

Step-by-step explanation:

Zn:Cu = 4:19

so 551 x (4/19) = 116

Answer:

y = x + 9

Step-by-step explanation:

y = mx + b  Use the x and y from the point (-5,4) and the slope to find b.  They you can write the equation.  An ordered pair is in the form of (x,y)

y = mx + b

4 = (1)(-5) + b

4 = -5 + b   Add 5 to both sides of the equation

9 = b

Now write the equation

y = x + 9

5. The relationship is Linear and the equation is 500 × 1.1 + 500 = 1050.

6. The relation ship is Linear and the equation is 6 × 2/3 = 4

Given,

5. The population of a town = 500

    The growth of population expected by the city planner = 1.1

    That is, 500 × 1.1 + 500 = 1050

This is a Linear equation.

6. The distance from where the basketball fall down = 6 feet

    Basket ball bounce back its previous height = 2/3

That is,  6 × 2/3 = 4

This is a Linear equation.

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Answer:

72

Step-by-step explanation:

Step-by-step explanation:

QC = Qu + UC

Qu= 22

Uc= 70

QC= 22 + 70

QC = 92

The solution of the equations −6x − 6y = −42 and −x + 2y = 8 will be (2, 5).

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The equations are given below.

−6x − 6y = −42      ...1

−x + 2y = 8            ...2

From equation 2, we have

x = 2y − 8

Put the value of x in equation 1, then we have

−6(2y − 8) − 6y = −42

−12y + 48 − 6y = − 42

18y = 90

y = 5

Then the value of x will be

x = 2(5) − 8

x = 10 − 8

x = 2

The solution of the equations −6x − 6y = −42 and −x + 2y = 8 will be (2, 5).

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The number 78.263 using ones, tenths, and thousandths means

This is the value of each digits based on its position in a number.

It is divided into whole number part and fractional part.

Whole number part:

Fractional part:

78.263

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Pat and John will meet in 3 hours.

It should be noted that speed = Distance / Time

The appropriate equation will be:

80t + 24t = 312

104t = 312

t = 312/104

t = 3. hours

Therefore, it will take them 3 hours to meet.

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To spray on 2 lawns is required [tex]3\frac{1}{9}[/tex]  gallons.

Mixed fraction A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Given ;

  A container with [tex]3\frac{1}{2}[/tex] gallons of weed killer can spray =  [tex]2\frac{1}{4}[/tex] lawans

∵ in [tex]\frac{9}{4}[/tex] lawn the week killer can spray =  [tex]\frac{7}{2}[/tex]gallons

∴ in 1 lawn the weed killer is  used = [tex]\frac{7}{2}[/tex] × [tex]\frac{4}{9}[/tex] gallon

∴ in 2 lawns the weed killer can spray =[tex]\frac{7}{2}[/tex]  ×  [tex]\frac{4}{9}[/tex]× 2 =[tex]\frac{28}{9}[/tex]  gallon =[tex]3\frac{1}{9}[/tex]gallons

  [tex]3\frac{1}{9}[/tex] gallons require to spray 2 lawns.

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The equation which describe the relationship between the profit, y, and the number of candles sold, x is x - y = 3.

Given that:-

When 10 candles are sold, the store makes a profit of $7.

When 15 candles are sold, the store makes a profit of $12.

When 20 candles are sold, the store makes a profit of $17.

We have to write an equation which describe the relationship between the profit, y, and the number of candles sold, x.

As we can observe from the given data,

number of candles sold - 3 = profit (in $)

Hence, we can write,

x - 3 = y

x - y = 3.

Where,

x represents the number of candles sold and,

y represents the profit

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1. The value of x is 14°

2. The value of x is 23°

3. The value of x is 22.5°

From the question, we are to determine the value of x in the given diagrams.

1.

∠ CBA = 180° - 6x (Linear pair theorem)

and

m ∠BAC + m ∠CBA = m ∠FCB (Exterior angle theorem)

Thus,

2x + 180° - 6x = 124°

180° - 4x = 124°

180° - 124° = 4x

56° = 4x

x = 56/4

x = 14°

Hence, the value of x is 14°

2.

m ∠ABE = 4x (Alternate angles theorem)

m ∠ABD + m ∠ABE + m ∠EBF = 180° (Sum of angles on a straight line)

x + 4x + 65° = 180°

x + 4x = 180° - 65°

5x = 115°

x = 115°/5

x = 23°

Hence, the value of x is 23°

3.

m ∠EAB = 2x (Vertical angles theorem)

m ∠AEB = 180° - 4x (Linear pair theorem)

m ∠ABE = 180° - 6x (Linear pair theorem)

m ∠EAB + m ∠AEB + m ∠ABE = 180° (Sum of angles in a triangle)

Thus,

2x + 180° - 4x + 180° - 6x = 180°

180° + 180° - 180° = 6x + 4x -2x

180° = 8x

x = 180°/8

x = 22.5°

Hence, the value of x is 22.5°

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The total volume of the solid = 1,035,000 cm³

Volume of a Pyramid = 1/3(length)(width)(height).

Volume of a cuboid = (length)(width)(height).

Volume of the Pyramid = 1/3(length)(width)(height)

Volume of the Pyramid = 1/3(90)(50)(240 - 225)

Volume of the Pyramid = 1/3(90)(50)(15)

Volume of the Pyramid = 22,500 cm³

Volume of the cuboid = (length)(width)(height)

Volume of the cuboid = (90)(50)(225)

Volume of the cuboid = 1,012,500 cm³

The total volume of the solid = 22,500 + 1,012,500

The total volume of the solid = 1,035,000 cm³

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Answer:

0.4

Step-b0.y-step explanation:

Answer:

51/8

Step-by-step explanation:

each bracelet length as a fraction will be 51/8 inches if the artist uses the 51 inches of the string to make 8 bracelets

The statement that is true about the segment connecting points B and C is D. The segment has a finite length that can be measured.

It should be noted that ieometry, a line segment is the part of a straight line bounded by two distinct end points, and contains every point on the line that is between its endpoints.

It should be noted that the length of a line segment is given by the Euclidean distance between its endpoints.

Therefore, in this case, the statement that is true about the segment connecting points B and C is that the segment has a finite length that can be measured.

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Answer:

28°

Step-by-step explanation:

63 -35 = 28

Probability is nothing but the ratio of favorable cases to all possible cases or in simple terms it is the ratio of sample set to all set

We are required to find all the cases in which sum of any two bills is 20$ or more

The total number of bills are two $ 1 bills, two $ 5 bills, two $ 10 bills, and two $ 20 bills.

The total case of drawing any two bills will be =

2 for $ 1 bill x two for 5$ bill x two for 10$ bill x two 20$ bills

=2 x 2x2x2 =16

Hence 16 ways in which two bills can be drawn at random

Cases in which bill can be greater than 20$= (1,20)(20,1)(5,20)(20,5)(10,10)(20,10)(10,20) (20,20)= 8 cases

Hence, total number of possible outcomes = 8

Hence the probability of bill to be 20$ or more= favorable outcome/total outcome

=8/16 =1/2

Hence the probability is 1/2

Disclaimer: the fraction sign is missing in question options

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answer:

1.

[tex]9y - 1[/tex]

2.

[tex] { \times }^{3} - { \times }^{2} + \times [/tex]

3.

[tex] - 3 {a}^{2} + a + 2[/tex]

4.

[tex] - { \times }^{2} [/tex]

5.

[tex] - 4 { \times }^{5} + 16 { \times }^{3} - 20 { \times }^{2} [/tex]

6.

[tex]8 { \times }^{3} + 6 { \times }^{2} - 32x + 15[/tex]

7.

[tex] { \times }^{2} - \times - 20[/tex]

8.

[tex]24 { \times }^{2} - 6 \times + 1[/tex]

9.

[tex] { \times }^{2} - 6 \times + 5[/tex]

10.

[tex]10 { \times }^{5} + 3 { \times }^{3} - 2 \times [/tex]

Answer:

Median

Step-by-step explanation:

Median: (16+17)/2= 16.5

Mean: 11+13+15+15+16+17+18+19+19+20= 163

163/10= 16.3

Median is greater.

Rick will have to wash the plates for three minutes.

By first figuring out the value of a single unit and then multiplying the number by that value, the unitary approach in mathematics can be used to determine the required value.

• The unitary technique can be used to determine how many kilometres can be covered with 2 litres of gasoline, for instance, if a car goes 80 km on 6 l of fuel.

He washed 4 dishes in 2 minutes, thus we need to calculate how long it would take Rick to wash 6 plates. 4 plates, according to the rule, equals 2 minutes. Applying the unitary approach 1 plate in 2/4 of a minute 1 plate Equals 12 minute. 3 minutes equals 6 plates (12 times 6.6 plates).

Therefore, Six dishes will need to be washed in 3 minutes.

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Answer: 6 hours

Step-by-step explanation: 6 apartments divided by 2 is 3 apartments and 4 hours divided by 2 is 2 hours. 3 apartments per 2 hours. So, 3/2 x 3/3 is 9/6 which is 9 apartments for 6 hours.

The correct answer for  0.504 ÷ 8 is option B which is 0.063

0.504 / 8 is solved by removing the decimals first and then the division as required.

0.504 / 8

= 504/1000 / 8

= 504 / 8000

= ( 504 / 8 ) * ( 1 / 1000 )

= 63 *  ( 1 / 1000 )

= 0.063

These are class of numbers that can be represented as fractions inform of two integers. Such numbers while in fractions, the denominator should not be zero and while decimal do not need to approximations to terminate them.

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The area of the base is 216 cm².

The volume of a cuboid is 1296 cm³.

The breadth of the cuboid is double the height of the cuboid and the length of the cuboid is triple the height of the cuboid.

Let the length, breadth, and height of the cuboid be l, b, and h respectively.

Then,

l = 3(h)

b = 2(h)

The volume of a cuboid is given as:

V = l × b × h

1296 = 3(h) × 2(h) × h

1296 = 6 × h³

h³ = 1296 / 6

h³ = 216

h = ∛216

h = ∛(6)³

h = 6 cm

Therefore, the length of the b is l = 3(h) = 3 × 6 = 18 cm

The breadth of the cuboid will be:

b = 2(h)

b = 2 × 6

b = 18 cm

Now the volume of the cuboid is also given as:

Volume = base area of  cuboid × height

1296 = base area × 6

base area = 216 cm²

The base area is 216 cm².

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An equation to find the number of treats t that was in the original package is t=10+4(15).

First, you set aside the 10 and that is the start of your equation.

We need to find an equation to find the number of treats t that was in the original package.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, t=10+4(15)

⇒t=10+60

⇒t=70

Therefore,  an equation to find the number of treats t that was in the original package is t=10+4(15).

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The factors of the equation is  (x - 5)  (x + 2).

Given the equation is x²-3x-10

we are asked to factorize the equation.

Factorization is the process of identifying two or more expressions whose product is an algebraic expression. It is often referred to as finding the factors of an expression. Finding two or more expressions whose product is the given expression—known as factorization—is the process of breaking down algebraic expressions. A factor is any number that divides the given number by itself without leaving any remainder. It simply implies representing a number as the product of two other integers.

x²-3x-10

x² - 5x + 2x - 10

x(x - 5) + 2(x - 5)

(x - 5)  (x + 2)

Thus, the factorization of the given expression  x²-3x-10

= (x - 5)  (x + 2)

Hence we get the factors as (x - 5)  (x + 2)

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Answer:

To factor the quadratic expression a2 - 3x - 10, we need to find two numbers that multiply to give -10 and add to give -3. These numbers are -5 and 2. Therefore, we can write:

a2 - 3x - 10 = (a - 5)(a + 2)

So the factors of the quadratic expression a2 - 3x - 10 are (a - 5) and (a + 2).

Solutions of given exponents are :

1.  [tex]9^{18}[/tex]   2. [tex]16x^4[/tex]   3.  [tex]\frac{6561}{y^2}[/tex]

In, mathematics a exponent or exponential equation or exponential function is inverse of a logarithmic function. That means, we can easily convert the logarithmic function into exponential function and vice versa. The shows the behavior of something to the power of something. The basic form of the exponential can be written as [tex]a^x[/tex]

where, a = the base of function

            x = exponential

Important properties of exponential :

According to the question,

1. given, [tex](9^{3})^6[/tex]

  use the property, [tex](a^n)^m = a^{nm}[/tex]

   [tex](9^{3})^6[/tex] = [tex]9^{3.6} = 9^{18}[/tex]

2. Given, [tex](2x)^4[/tex]

   use the property, [tex](ab)^n = a^n.b^n[/tex]

    [tex](2x)^4[/tex] = [tex]2^4.x^4 = 16x^4[/tex]

3. Given , [tex](\frac{3^4}{y}) ^{2}[/tex]

    use the property, [tex](\frac{a}{b})^n = \frac{a^n}{b^n}[/tex]

     [tex](\frac{3^4}{y}) ^{2}[/tex] = [tex]\frac{(3^4)^2}{y^2}[/tex]

    now use ,  [tex](a^n)^m = a^{nm}[/tex]

     = [tex]\frac{3^8}{y^2} = \frac{6561}{y^2}[/tex]

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Answer:

1. A, 450 = 2(p+w); 450 = 3(p-w)

2. A, 2 units

3. D, Between step 6 and step 7

Step-by-step explanation:

1. This one is confusing on first glance.

[tex]450 = 2(p+w); 450 = 3(p-w)[/tex] Lets break down this equation.

[tex]2(p+w)[/tex] means, the plane speed, plus the windspeed, will take 2 hours to travel 450 KM. The reason we add the plane speed and the windspeed is because we have a tailwind instead of a headwind, the wind is pushing us forward, adding to the planes speed.

[tex]3(p-w)[/tex] means, the plane speed, minus the windspeed, will take 3 hours to travel 450 KM. We subtract the wind speed from the plan speed because the wind is a headwind, it's pushing us backwards, taking away from the planes speed.

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2. Let set these up as two-sided equations.

[tex](6x+3) + (4x) + (2x + 1) = (5x) + (5x) + (3x+2)[/tex]

Combine like terms

[tex]12x + 4 = 13x + 2[/tex]

Subtract 12x from both sides

[tex]4 = 1x + 2[/tex]

Subtract 2 from both sides

2 = 1x, or x = 2.

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3. Take a look at step 6. You want to get x by itself, to do that, and get rid of the 8, you'd divide both sides by 8 to get [tex]x = -\frac{15}{4}[/tex]

Answer: 20 cm

Step-by-step explanation: if the length of R-N= 5cm therefore you multiply 5 by each dot so H-O is 5 cm, H-R is 10 cm, H-N is 15 cm, and H-S is 20 cm.