Which expression is equivalent 3m+1-m?
2+ m-1+m
1+m
3m-1
3m

Answer:

Step-by-step explanation:

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initial number of sweets               |   18                   |      18

                                                       |                          |

Sue gives Tony x sweets              |   18 - x              |      18 + x

                                                       |                          |

Sue ,eats 5 of her sweets. and   |  18 - x - 5 =       |      (18 + x)/2 =

Tony ,eats half of his sweets        | 13 - x                |     9 + x/2

To write the given equation in logarithmic form, we can use the definition of logarithms. The equation 10^m = w can be rewritten as a logarithm with base 10: log10(w) = m

The general relationship between exponents and logarithms is as follows:

base^(exponent) = result

In logarithmic form, it's written as:

log_base(result) = exponent

For our given equation, 10^m = w, we have:

base = 10

exponent = m

result = w

Applying the general logarithmic relationship, we write:

log10(w) = m

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The value of t₄ in the arithmetic sequence is 103/8.To determine the value of t₄ in an arithmetic sequence, we need to use the given information that t₁ = 11 (the first term of the sequence) and S₉ = 243 (the sum of the first 9 terms of the sequence).

We know that the formula for the sum of an arithmetic sequence is Sₙ = (n/2)(2a + (n-1)d), where Sₙ is the sum, a is the first term, n is the number of terms, and d is the common difference.

From the given information, we have S₉ = 243, a = 11, and n = 9. Plugging these values into the sum formula, we can solve for d:

243 = (9/2)(2(11) + (9-1)d)

243 = 9(22 + 8d)

243 = 198 + 72d

45 = 72d

d = 45/72 = 5/8

Now that we have the common difference, we can find t₄ using the formula for the nth term of an arithmetic sequence:

tₙ = a + (n-1)d

t₄ = 11 + (4-1)(5/8)

t₄ = 11 + 3(5/8)

t₄ = 11 + 15/8

t₄ = 88/8 + 15/8

t₄ = 103/8

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On solving the equations y = (-1/2)x + \(4\frac{1}{2}\) and 3x - 4y = 12 graphically , the solution is (6 , 3/2) .

In the question ,

it is given that

the equations are y = (-1/2)x + \(4\frac{1}{2}\)  and 3x - 4y = 12

which can be written as y = (-1/2)x + 9/2  and 3x - 4y = 12

to plot the graph of the given equations , we need intercept .

For the equation y = (-1/2)x + 9/2

when x= 0  , y = (-1/2)(0) + 9/2 = 9/2

when y = 0 ,

0 = (-1/2)x + 9/2

(1/2)x = 9/2

x = 9

the points are (0 , 9/2) and (9 , 0)

For the equation 3x - 4y = 12

when x = 0 , 3(0) - 4y = 12

-4y = 12

y = -3

when y = 0 , 3x -4(0) = 12

3x = 12

x = 4

the points are (0,-3) and (4,0) .

after plotting the lines on the graph , we can see that the both the lines intersect at the point (6 , 3/2) ,

Therefore , On solving the equations y = (-1/2)x + \(4\frac{1}{2}\) and 3x - 4y = 12 graphically , the solution is (6 , 3/2) .

The given question is incomplete , the complete question is

Consider this equation y = (-1/2)x +  \(4\frac{1}{2}\)  and 3x - 4y = 12 .

Solve the system by graphing. label each graph.

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Answer:

64°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the third angle be x , then

x + 90° + 26° = 180°

x + 116° = 180° ( subtract 116° from both sides )

x = 64°

the other angle is 64°

to do this

Step 1

Let y=f(x)

swap positions x and y

step 2

solve for y,

Answer:

−15x2+23x−6

Step-by-step explanation:

(3x−1)(−5x+6)

=(3x+−1)(−5x+6)

=(3x)(−5x)+(3x)(6)+(−1)(−5x)+(−1)(6)

=−15x2+18x+5x−6

=−15x2+23x−6

The value of the variable x is 53.

The measures of the angles include the following:

m∠P = 96°.

m∠Q = 95°.

m∠R = 53°.

In Mathematics, a triangle can be defined as a two-dimensional (2D) geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.

Furthermore, the sum of the angles in a triangle is equal to 180. This ultimately implies that, we would sum up all of the angles as follows;

m∠P + m∠Q + m∠R = 180

Substituting the given parameters into the mathematical expression, we have the following;

(2x - 10)° + (x + 42)° + x° = 180°

4x - 32° = 180°

4x = 180° + 32°

x = 53.

For the measure of the angles, we have:

m∠P = (2(53) - 10)° = 96°.

m∠Q = (53 + 42)° = 95°.

m∠R = 53°.

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Table one and table four represent a linear function.

A linear function is simply a function that represents a straight line on the coordinate plane.

For a function to be linear, the differences of the y-values must be constant.

For table 1.

Let get the differences of the y-values

-1 - (-2) = 1

0 - (-1) = 1

1 - 0 = 1

2 - 1 = 1

Since the differences of the y-values are all 1 ( constant ), table one is a linear function.

For table 2.

2 - (-3) = 5

0 - 2 = -2

-2 - 0 = -2

3 - (-2) = 5

Since the differences of the y-values are not the same ( constant ), table two is not a linear function.

For table 3.

0 - 2 = -2

-1 - 0 = -1

0 - (-1) = 1

2 - 0 = 2

Since the differences of the y-values are not the same ( constant ), table three is not a linear function.

For table 4.

1 - 3 = -2

-1 - 1 = -2

-3 - (-1) = -2

-5 - (-3) = -2

Since the differences of the y-values are all -2 ( constant ), table four is a linear function.

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Answer:

The amount in table as positive negative numbers: -5, 4, -1, 3, -2.

The spinner lands on red the change to Lisa's amount of money is -$5.

Step-by-step explanation:

Consider the provided table.

Part(A)

The table list how much a player receives or pays for various.

Paying some money is represented by a negative sign while receiving money is represented by a positive sign.

For red they needs to pay $5 which can be written as -5.

For blue they received $4 which can be written as 4.

For yellow they needs to pay $1 which can be written as -1.

For green they received $3 which can be written as 3.

For orange they needs to pay $2 which can be written as -2.

So, the amount in table as positive negative numbers: -5, 4, -1, 3, -2.

Part(B)

Now, we need to describe the change to Lisa’s amount of money when the spinner  lands on red.

If spinner lands on red then she needs to pay $5.

Thus, if the spinner lands on red the change to Lisa's amount of money is -$5.

Answer:

4 marble lost

Step-by-step explanation:

1/6×24=4

so 4 marble lost

Answer:

C

\(slope = \frac{(y _{2} - y _{1})}{(x _{2} - x _{1}) } \\ = \frac{( - 3 - 6)}{(2 - ( - 1))} \\ = \frac{ - 9}{3} \\ slope = - 3\)

let's firstly convert the mixed fraction to improper fraction and proceed from there.

\(\stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{4}\div \left(\cfrac{3}{8}\div \cfrac{1}{2} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{8}\cdot \cfrac{2}{1} \right)\implies \cfrac{9}{4}\div \left(\cfrac{3}{4} \right) \\\\\\ \cfrac{9}{4}\cdot \left(\cfrac{4}{3} \right)\implies \cfrac{9}{3}\cdot \cfrac{4}{4}\implies 3\cdot 1\implies \text{\LARGE 3}\)

Answer:

13.1 cm² (nearest tenth)

Step-by-step explanation:

Use the sine rule for area of a triangle with 2 sides and an included angle (SAS).

Sine rule for area

\(\textsf{Area ABC}=\dfrac12ab \sin C\)

(where \(a\) and \(b\) are the side lengths and \(C\) is the included angle)

Given:

\(\implies \textsf{Area}=\dfrac12\cdot 8 \cdot 7 \cdot\sin (28\textdegree)\)

               \(=13.14520376...\)

               \(= 13.1 \textsf{ cm}^2 \textsf{ (nearest tenth)}\)

Use sine rule

Area:-

\(\\ \sf\longmapsto \dfrac{1}{2}Base\times Height sin\theta\)

\(\\ \sf\longmapsto \dfrac{1}{2}(8)(7)sin28\)

\(\\ \sf\longmapsto 28sin28\)

\(\\ \sf\longmapsto 13.1cm^2(Approx)\)

Answer:

1) 30 pounds is the weight of the bag all together

2) science book is the heaviest book

Step-by-step explanation:

bag=4 pounds

library book=2 pounds

maths book=2×4=8 pounds

science book=8×2=16 pounds

4+2+8+16=30 pounds all together

heaviest book= science book (16 pounds)

Since √3 is not equal to 1.70 but a little more than that (approximately 1.7302) then √3 would be better located between 1.7 and 1.8

1) Considering the number line and the irrational number √3

2) Since √3 is an irrational number, let's find an approximation to that:

So Let's place it considering that √3 is not exactly 1.7, but someplace between 1.7 and 1.8

3) Since √3 is not equal to 1.70 but a little more than that (approximately 1.732) then √3 would be better located between 1.7 and 1.8

Answer:

$28.32

Step-by-step explanation:

Answer:

4500

Step-by-step explanation:

250 x 18 = 4500

Answer:

m = 2  b = 10

y = 2x + 10

Positive Slope

Step-by-step explanation:

Answer:

y = 36

Step-by-step explanation:

given y varies directly  with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition when x = 5 , y = 15

15 = 5k ( divide both sides by 5 )

3 = k

y = 3x ← equation of variation

when x = 12 , then

y = 3 × 12 = 36

Answer:

$352

Step-by-step explanation:

x = total money she had

spent 25% of x = 88

solve for x

x = 88/0.25

x = $352

The composite function f·g(x) is 4x⁴+24x³.

The given functions are f(x)=x²+6x and g(x)=4x².

We need to find f·g(x).

We know that, f·g(x)=f(x)×g(x)

Here, f·g(x)=(x²+6x)×4x²

= x²×4x²+6x×4x²

= 4x⁴+24x³

Therefore, the composite function f·g(x) is 4x⁴+24x³.

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Answer:

 1  5/24 cups

Step-by-step explanation:

The lengths of the other two sides of the right triangle are 24m and 25m, respectively.

Let's assume the consecutive integers representing the lengths of the other two sides of the right triangle are x and x + 1, where x is the smaller integer. We are given that the shortest side measures 7m. Now, we can use the Pythagorean theorem to solve for the lengths of the other two sides.

According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Using this theorem, we have the equation:

\(7^2 + x^2 = (x + 1)^2\)

Expanding and simplifying this equation, we get:

\(49 + x^2 = x^2 + 2x + 1\)

Now, we can cancel out \(x^2\) from both sides of the equation:

49 = 2x + 1

Next, we can isolate 2x:

2x = 49 - 1

2x = 48

Dividing both sides by 2, we find:

x = 24

Therefore, the smaller integer representing the length of one side is 24, and the consecutive integer representing the length of the other side is 24 + 1 = 25.

Hence, the lengths of the other two sides of the right triangle are 24m and 25m, respectively.

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First, we have to analyze how each number grows (the number of thumbs and the number of sticks for each diagram)

So we can build two equations that give us the number of thumbs and the number of sticks for each diagram, let be n for the number of the diagram, so :

Now we can know the number of thumbs and sticks for any diagram, and we can solve the questions provided, first, let's draw the 4th diagram:

Now

How do I know how many sticks are in the sixth diagram?

sticks= 4(6) = 24

There are 24 sticks in the sixth diagram.

How many thumb tacks are in the seventh diagram? ​

thumbs= 3(7)+1 = 22

There are 22 thumbs in the seventh diagram.

Answer:

Step-by-step explanation:

25%

80%

60%

100%

25%

Answer:

O

Step-by-step explanation:

THIS IS ASSUMING THAT THE RADIUS OF THE CIRCLE IS 4 1/4 UNITS!

Answer:

Standard Equation: (x + 5)^2 + (y+5)^2 = 18.06

General Form: x^2 + 10x + y^2 + 10y + 31.94 = 0