Use the distributive property to solve.
0.5(x+9)=32
Solve by dividing first
0.5(x+9)=32
Use the distributive property to solve.
2(x+12)=50
Solve by dividing first
2(x+12)=50

Answer:3ta+5a

Step-by-step explanation:

just times it, its that easy

The answer for  8.9395 +1.2973 is 10.2368 for .2.8862 +8.2758=11.162, and for 5.9529 +2.0043 = 7.9572.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

1. 8.9395 +1.2973=10.2368

2.2.8862 +8.2758=11.162

3. 5.9529 +2.0043 = 7.9572

4. 1.223+0.4643=1.6873

5. 3.2292 +9.45 =12.6792

6. 2.421 +6.0473=8.4683

7. 5.2697 + 4.4603=9.73

8. 0.0003 +2.6035 =2.6038

9. 3.7092 +9.2965=13.0057

10. 7.0551 +0.8388=7.8939

Thus, the answer for  8.9395 +1.2973 is 10.2368 for .2.8862 +8.2758=11.162, and for 5.9529 +2.0043 = 7.9572.

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From the given parameters of linear equation, we can say that;

The number of $10 bills is; 24

The number of $20 bills is; 13

Let x be the number of the $20 dollars bills.

Then the number of the $10 dollars bills is (x + 11), according to the condition.

The money equation is expressed as;

20x + 10*(x + 11) = 500

Simplify and solve for x.  

20x + 10x + 110 = 500

30x = 500 - 110

30x = 390

x = 390/30

x = 13

Then number of $10 bills is 13 + 11 = 24

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Answer: 500

Step-by-step explanation:

$2000

$45,000 divided by 90 = 500

It will take her 500 weeks to pay $45,000'

Hope this helps

The expression which is equivalent to rm ÷ rn exists rm − n.

A mathematical expression is a finite combination of symbols that is well-formed in accordance with context-specific rules.

A mathematical expression is a phrase that includes at least two numbers or variables, at least one math operation, and the expression itself. Any one of the following mathematical operations can be used. A sentence has the following structure: Number/variable, Math Operator, Number/Variable is an expression.

Combining operators, constants, and variables creates an expression. One or more operands, 0 or more operators, and a value can all be part of an expression.

Let the expression be rm ÷ rn

[tex]$=\frac{r m}{r n}=\frac{m}{n}$[/tex]

simplifying the above equation, we get

[tex]$r^m \div r^n$[/tex]

[tex]$=\frac{r^m}{r^n}=r^{m-n}$[/tex]

Therefore, the correct answer is option A. rm − n.

The complete question is:

Which expression is equivalent to rm ÷ rn? (4 points)

A. rm − n

B.rm + n

C. rm ⋅ n

D.rm ÷ n

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-0.25 is the z-score of a person who scored 80 on the exam.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data

Given,

On a standardized exam, the scores are normally distributed

mean is 85 and a standard deviation is 20.

We need to find z-score of a person who scored 80 on the exam.

Z=x-μ/σ

x=80, μ=85 and σ=20

Z=80-85/20

Z=-5/20

Z=-1/4

Z=-0.25

Hence, -0.25 is the z-score of a person who scored 80 on the exam.

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The correct dividend of 76 is required to yeild a quotient of 25 and a remainder of 1 when divided by 3.

We can know the dividend, the quotient and the remainder of the division using the division formula: (Divisor x Quotient) + Remainder = Dividend

Divisor = 3

Quotient = 25

Remainder = 1

(3 × 25) + 1 = 75 + 1

(3 × 25) + 1 = 76

Thus, the dividend 76 divided by the divisor 3 have the quotient 25 and a remainder when of 1.

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Answer:

[tex]\huge\boxed{\sf x = 3}[/tex]

Step-by-step explanation:

f(x) = 3x - 5

Given that, f(x) = 4

Put it in the above equation.

4 = 3x - 5

Add 5 to both sides

4 + 5 = 3x

9 = 3x

Divide 3 to both sides

3 = x

x = 3

[tex]\rule[225]{225}{2}[/tex]

The statement that least-squares solution of a x = b is the vector in the column space of a closest to b  is; true

One  method for computing a least-squares solution of Ax = b is;

Now, If b is in the column space of A then it tells us that there is at least one exact solution to the system Ax = b. In this case, it means that every solution to the system minimizes |Ax − b| (makes it zero) and as such  is a least squares solution.

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The equation is y = 300x + 1,750. And the total cost after 1 hour and 20 hours of work will be $2,050 and $7,750, respectively.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A lawyer charges a proper expense for an underlying gathering and an hourly charge for the entire hours worked after this gathering. She charges $1750 for an underlying gathering and $300 consistently worked.

Let 'x' be the number of hours and 'y' be the total cost. Then the equation is given as,

y = 300x + 1750

The total cost after 1 hour of work will be

y = 300 (1) + 1,750

y = 2,050

The total cost after 20 hours of work will be

y = 300 (20) + 1,750

y = 7,750

The equation is y = 300x + 1,750. And the total cost after 1 hour and 20 hours of work will be $2,050 and $7,750, respectively.

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Answer:

5 4/9

Step-by-step explanation:

our equation is 4 2/3+7/9

2/3=6/9.

So we have 4 6/9+7/9

Simplify:

4 13/9

5 4/9

The number of periods of the function y = sinx are there between -10π < 0 ≤ 6π is 8.

The given trigonometric function is y=sinx.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Here, the interval is -10π < 0 ≤ 6π

Graph the trigonometric function using the amplitude, period, phase shift, and vertical shift.

Amplitude: 1

Period: 2π

Phase Shift: None

Vertical Shift: None

Plot (0, 0), (π/2, 1), (π, 0), (3π/2, -1) and (2π, 0)

Therefore, the number of periods of the function y = sinx are there between -10π < 0 ≤ 6π is 8.

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First picture answer:

⇒Sum of interior angles of a triangle is equal to 180°

⇒This means that ∠D+∠E+∠F=180°

⇒∠D is (5x-2)°,∠E is (9x+3)°,∠F is (11x-21)°

⇒Plug in the values of the angles in the general equation above.

[tex](5x-2)+(9x+3)+(11x-21)=180\\[/tex]

⇒Group the like terms together and simplify.

[tex]5x+9x+11x-2+3-21=180\\25x-20=180\\25x=180+20\\25x=200\\\frac{25x}{25} =\frac{200}{25} \\x=8[/tex]

⇒x=8°

________________________________________________________

Second picture answer:

⇒If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.

⇒ ∠C is the exterior angle.

⇒ ∠A and ∠B are the interior angles.

The above statement simply means

∠C=∠A+∠B

⇒ Given that ∠A is (13x-11)°

∠B is(4x+1)°

∠C is (18x-15)°

⇒Plug in the values of the angles and solve for x.

[tex](18x-15)=(13x-11)+(4x+1)\\[/tex]

⇒Group the like terms and solve.

[tex]18x-13x-4x=-11+1+15\\x=5[/tex]

⇒ x=5°

Number of sides = 13, sum of Interior angles = 1980°, the measure of one Interior angle = 152.30°, sum of exterior angles = 360°, and the measure of one exterior angle = 27.69°.

A polygon is given in the figure

According to the given question, the required solution would be as:

Number of sides = 13

Interior angles of a polygon = (sides - 2) × 180°

In this case, the number of sides is 13

Sum of Interior angles = (13 - 2) × 180

Sum of Interior angles = (11) × 180

Sum of Interior angles = 1980°

the measure of one Interior angle = 1980°/13

the measure of one Interior angle = 152.30°

The sum of exterior angles is always 360° in the regular polygon.

Sum of exterior angles = 360°

the measure of one exterior angle = 360°/13

the measure of one exterior angle = 27.69°

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well, we can simply divide 210 by (3 + 4) and then distribute accordingly

[tex]\stackrel{James}{3}~~ : ~~\stackrel{John}{4} ~~ \implies ~~ \stackrel{James}{3 ~~ \cdot \frac{210}{3+4}}~~ : ~~\stackrel{John}{4~~ \cdot \frac{210}{3+4}} ~~ \implies ~~ \stackrel{James}{3 \cdot \frac{210}{7}}~~ : ~~\stackrel{John}{4 \cdot \frac{210}{7}} \\\\\\ \stackrel{James}{3(30)}~~ : ~~\stackrel{John}{4(30)} ~~ \implies ~~ \stackrel{James}{90}~~ : ~~\stackrel{John}{120}[/tex]

Answer:

James- 90 and John- 120

Step-by-step explanation:

Since you want to divide 210 with a ratio of 3:4. It's easiest to first add your 3 and 4. This =7. Now you know you have to divide 210 by 7 before you give them to James and John. 210 divided by 7 = 30. Now do 30 times each ratio.

James has 30 x 3 and John has 30 x 4

this leaves you with 90 and 120

Answer:

first graph

Step-by-step explanation:

x > n

the graph will have an open circle at the value n , indicating that x cannot equal n ( note solid circle if x ≥ n )

the arrow from n will point in the right direction, indicating values of x greater than n.

the graph representing x > n is the first graph

The values of the exponential function are f(1) = 1/12, f(-1) = 12 and f(1/2) = √1/12

From the question, we have the following functions that can be used in our computation:

f(x) = (1/12)^x

Also from the question, we have the following x values

f(1), f(-1) and f(1/2)

This means that x = 1, -1 and 1/2

Substitute x = 1, -1 and 1/2 in the equation f(x) = (1/12)^x

So, we have the following representations

f(1) = (1/12)¹ = 1/12

f(-1) = (1/12)⁻¹ = 12

f(1/2) = (1/12)¹/² = √1/12

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The group that contains numbers that all round most closely to 1 is group 2 (10/11, 5/6, 7/9,)

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, it should be noted the group 2 that has 10/11, 5/6, and 7/9 are close to 1.

Therefore, the correct option is B.

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Answer:

1. mileage of the bike = 40Km

2. petrol needed to cover 320Km = 8L

The required percentage change in the number of teen births between 2000 and 2015 is 52.5%.

Given that,
In 2000, there were 47,000 teen births in the United States. In 2015, there were 22,300 teenage births. The percent change in the number of teen births between 2000 and 2015 is to be determined.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
Number of teens in the year 2000 = 47,000
Number of teens in the year 2015 = 22300
Percentage change = 47000-22300/47000 × 100 = 52.5%

Thus, the required percentage change in the number of teen births between 2000 and 2015 is 52.5%.

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Converting 195 ml to liters using unit fractions is 39/200.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

It should be noted that 1000 millimeters = 1 liters

Therefore, 195 ml to l will be:

= 195 / 1000

= 39/200

Therefore, it is 39/200.

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Of the four relationships the ones that have the constant of proportionality of 2 are

The constant of proportionality is the constant that relates the input with output terms

Relationship A

the output, y dies it equal 2 * input

an instance = 2 * 3 = 6 not 2 2/3

Relationship B

y = 2x has the constant written out already

Relationship C

Represents a linear function

Relationship D

y = 6, x = 3

y = 2x

when x = 3 y = 6

when x = 6 y = 12

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Answer:

Step-by-step explanation:

The answer is C.

1 minute = 11/2 pounds

a day= 1440 minutes = 11/2 × 1440 = 7920 pounds

The ratio of the area of the two squares is 9:16.

A square has four corners and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.

A square is a closed object with four sides that are all the same length, and its interior angles are all 90 degrees. A square can have many different characteristics. The following list includes some of a square's key characteristics.

If it is square:

The ratios of the sides of two squares = 3:4

Let the common multiple of the above ratio be x.

So, side of one square = 3x

and side of the other square = 4x

Area of square = (side)²

Area of square with side 3x = (3x)² = 9x²

Area of square with side 4x = (4x)²= 16x²

Ratio of the areas of the two squares = Area of square with side 3x/Area of square with side 4x = 9x²/16x² = 9/16 = 9:16

Therefore, the ratio of the area of the two squares is 9:16.

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The equation of parabola for the given statement is: [tex]x^{2} = -60y[/tex]

The locus of points where point moves under a restriction that its distance from a fixed point Focus(F) and fixed line Directrix always remain constant

Solution: here focus of parabola is on -ve y axis so we will take general equation of parabola whose focus is on -ve y axis and directrix will be above x axisi.e[tex]x^{2} =-4ay[/tex]

here a is the distance between vertex and focus and here vertex is origin so by distance formula it comes out to be a = 15

put back in above equation we get its equation[tex]x^{2} = -60y[/tex]which is our required equation of parabola.

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Applying Side-side-side (SSS), the two-column proof that explains why ∠T ≅ ∠S is shown below.

The side-side-side (SSS) postulate states that two triangles that have all their three corresponding sides equal are definitely congruent triangles.

The two-column proof that shows that ∠T ≅ ∠S is explained below:

Statement                                  Reason                                                  

1. U is the midpoint of ST          1. Given

2. RT ≅ RS                                 2. Given

3. TU ≅ SU                                3. Definition of a midpoint

4. UR ≅ UR                                4. Reflexive property

5. ΔTUR ≅ ΔSUR                      5. Side-side-side (SSS)

6. ∠T ≅ ∠S                                6. CPCTC

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Answer:

[tex]\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$U$ is the midpoint of $ST$}&1.\;\sf Given\\\cline{1-2}2.\;RT \cong RS&2.\; \sf Given\\\cline{1-2}3.\;TU \cong SU & 3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;UR=UR&4.\;\sf Reflexive\;property\\\cline{1-2}5.\; \triangle TUR \cong \triangle SUR&5.\;\sf Side-Side-Side\;(SSS)\\\cline{1-2}6.\;\angle T \cong \angle S&6.\;\sf CPCTC\\\cline{1-2}\end{array}[/tex]

Step-by-step explanation:

Midpoint

The point that is halfway between the endpoints of the line segment.

Reflexive Property

For every number a:

Side-Side-Side (SSS) Congruence Theorem

If all three sides of one triangle are equal to all three corresponding sides of another triangle, then the two triangles are congruent.

Corresponding parts of congruent triangles are congruent (CPCTC)

If two or more triangles are congruent, their corresponding angles and sides are congruent.

[tex]\large\begin{array}{|l|l|}\cline{1-2}\sf Statement&\sf Reason\\\cline{1-2}1.\;\textsf{$U$ is the midpoint of $ST$}&1.\;\sf Given\\\cline{1-2}2.\;RT \cong RS&2.\; \sf Given\\\cline{1-2}3.\;TU \cong SU & 3.\; \sf De\:\!finition\;of\;a\;midpoint\\\cline{1-2}4.\;UR=UR&4.\;\sf Reflexive\;property\\\cline{1-2}5.\; \triangle TUR \cong \triangle SUR&5.\;\sf Side-Side-Side\;(SSS)\\\cline{1-2}6.\;\angle T \cong \angle S&6.\;\sf CPCTC\\\cline{1-2}\end{array}[/tex]

Awnser : 240km

Step-by-step explanation:

Step-by-step explanation:

Answer is D.

Breaking it down;

1/3 + 2/6 = 4/6.

4/6 - 5/6 = -1/6

-1/6 × 3/11 = -3/66