Johnny spends half of his weekly paycheck on
groceries. He then earns $55 doing yard work for
his grandma. He ends the week with $216. How
much is his paycheck?

m x H = [tex]\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right][/tex]

Step-by-step explanation:

Step 1; Multiply 5 with this matrix  [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get a matrix [tex]\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right][/tex]

Multiply the fraction  [tex]\frac{2}{5}[/tex] with the matrix  [tex]\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right][/tex] and we get [tex]\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right][/tex]

Step2; Now equate corresponding values of the matrices with each other.

-5 = [tex]\frac{-2m}{5}[/tex] and so on. By equating we get the value of m as [tex]\frac{25}{2}[/tex]

Step 3; Add the matrices to get the value of matrix m.

Adding the three matrices on the RHS we get  [tex]\left[\begin{array}{ccc}2&9&-9\\\end{array}\right][/tex].

Step 4; Adding the matrices on the LHS we get the resulting matrix as H +

[tex]\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right][/tex]. Equating the matrices from step 3 and 4 we get the value of H as [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]

Step 5; Now to find the value of m x H we need to multiply the value of [tex]\frac{25}{2}[/tex] with the matrix [tex]\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right][/tex]

Step 6; Multiplying we get the matrix m x H = [ -25  [tex]\frac{75}{2}[/tex]  [tex]\frac{-25}{2}[/tex] ]

[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{-1}{6}[/tex]

Solution:

Given expression is [tex]-2\frac{1}{2} +1\frac{1}{3}[/tex].

Let us first convert mixed fraction into improper fraction.

[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{(-2\times 2) +1}{2} +\frac{(1\times 3) + 1}{3}[/tex]

              [tex]=\frac{-4 +1}{2} +\frac{3 + 1}{3}[/tex]

              [tex]=\frac{-3}{2} +\frac{4}{3}[/tex]

Take LCM for the denominators (LCM of 2, 3 = 6) and make the same.

              [tex]=\frac{-3\times3}{2\times3} +\frac{4\times2}{3\times2}[/tex]

              [tex]=\frac{-9}{6} +\frac{8}{6}[/tex]

              [tex]=\frac{-1}{6}[/tex]

[tex]-2\frac{1}{2} +1\frac{1}{3}=\frac{-1}{6}[/tex]

Hence the fraction form of [tex]-2\frac{1}{2} +1\frac{1}{3}[/tex] is [tex]\frac{-1}{6}[/tex].

Answer: A. -14

Step-by-step explanation:

Answer: A. -14

Step-by-step explanation: Use PEMDAS

(5+4-2) x (-2)

= (9-2) x (-2)

= 7 x (-2)

= -14

Answer:

54

Step-by-step explanation:

4.5x=3(x+27)

4.5x=3x+81

1.5x=81

x=54

Answer:

your answer is 70

Step-by-step explanation:

Answer:

6. ○ [tex]\displaystyle 33,1°; 123,1°[/tex]

5. [tex]\displaystyle See\:above\:image[/tex]

4. [tex]\displaystyle See\:above\:image[/tex]

Explanation:

6. Supplementary Angles sum up to 180°, whereas complementary angles sum up 90°. So, use subtraction for both types of angles:

[tex]\displaystyle 123,1° = -56,9° + 180° \\ 33,1° = -56,9° + 90°[/tex]

* Make sure that they are in the exact same order that exercise gives you.

5. Acute Angles measure greater than 0° and less than 90°.

4. Every segment must have C in it, and you must be EXTREMELY CAREFUL of their markings [ray, segment, and line].

I am joyous to assist you anytime.

Answer:

14/25

Step-by-step explanation:

p(red or blue)=6/(6+8+11) +8/(6+8+11)=6/25+8/25=14/25

Answer:

56% yall

Step-by-step explanation:

Answer:

6(26-4)= 132

Step-by-step explanation:

There isn't any variable in the equation

Answer:

1/3

Step-by-step explanation:

David cooks 6 cups of rice and his family eats 4 cups. To find the fraction, we must first do 6-4 to get 2. We place 2 in the numerator and 6 in the denominator. We have 2/6. We can simplify 2/6 by dividing both the numerator and the denominator by 2 to get 1/3.

Answer:

by definition

The coordinates of point A are:

(cosθ , sinθ)

Answer:

Therefore the scale used is 1 inch : 6.667 inches

Step-by-step explanation:

i) Scale used is 9 inches = 5 feet

ii) Scale used 9 inches = 5 [tex]\times[/tex] 12 inches = 60 inches

iii) Scale used is 1 inch  [tex]= \dfrac{60}{9}\hspace{0.2cm} = \hspace{0.2cm}\dfrac{20}{3} \hspace{0.2cm} = 6.667\hspace{0.2cm} inches[/tex]

iv) Therefore the scale used is 1 inch : 6.667 inches

Answer:
it is proportional

Step-by-step explanation:

Proportional functions will be in the form y = kx and non-proportional functions will be in the form y = mx + b

Answer:

∠ U = 117°

Step-by-step explanation:

Since the triangles are congruent then corresponding angles are congruent.

∠ T = ∠ Q = 27°

The sum of the 3 angles in a triangle = 180°, thus

∠ U = 180° - (∠ s + ∠ T) = 180° - (36 + 27)° = 180° - 63° = 117°

Answer:

5) The correct answer is D.

6) The correct answer is A.

7) m = (10 - 6)/(1 - 0) = 4/1 = 4

The correct answer is C.

8) The correct answer is B.

Answer:

[tex]PN=64\ units[/tex]

Step-by-step explanation:

The complete question is

Given the quadrilateral is a rectangle, if LO = 15x+19 and QN = 10x+2 find PN

see the attached figure to better understand the problem

we know that

The diagonals of a rectangle are congruent and bisect each other

so

[tex]QN=\frac{1}{2}LO[/tex]

substitute the given values

[tex]10x+2=\frac{1}{2}(15x+19)[/tex]

solve for x

[tex]20x+4=15x+19\\20x-15x=19-4\\5x=15\\x=3[/tex]

Find the length of PN

Remember that

[tex]PN=LO[/tex] ----> diagonals of rectangle are congruent

[tex]LO=15x+19[/tex]

substitute the value of x

[tex]LO=15(3)+19=64\ units[/tex]

therefore

[tex]PN=64\ units[/tex]

Answer:

Step-by-step explanation:

The only possible simplification of the slope -5/1 is -5.

Answer:

No

Step-by-step explanation:

You only distribute the 3 to the x but not to 1 1/2. In order for the two equations to be the same, you have to distribute 3 to both the x and 1 1/2. Then the answer will look like this : 3x + 4 1/2 or 3x + 9/2

The original expression 3(x + 1 1/2) is not equivalent to 3x + 1 1/2; rather,it simplifies to 3x + 4.5 after distribution and simplification.

Step 1: Distribute the Number Outside the Parentheses:

To determine equivalence, distribute the 3 to both terms inside the parentheses: 3(x) + 3(1 1/2).

Step 2: Simplify Inside the Parentheses:

Multiply 3 by x: 3x.

Multiply 3 by 1 1/2: 3 × 1 + 3 × 1/2

= 3 + 1.5

= 4.5.

Step 3: Combine the Terms:

The distributed expression simplifies to 3x + 4.5.

Step 4: Evaluate the Expression in Question:

The expression provided is 3(x + 1 1/2).

The equivalent expression, as derived, is 3x + 4.5.

Step 5: Compare the Expressions:

The expression 3(x + 1 1/2) simplifies to 3x + 4.5, not 3x + 1 1/2.

Therefore, the original expression 3(x + 1 1/2) is not equivalent to 3x + 1 1/2; rather,it simplifies to 3x + 4.5 after distribution and simplification.

Answer:

-$336.00

Step-by-step explanation:

-$248.00+-$73.00+-$15.00=-$336.00

The midpoint is [tex](\frac{1}{2}, \frac{13}{2})[/tex]

The distance between points S and T is 7.1 units

Solution:

Given points are S(−2, 4) and T(3, 9)

Find the coordinates of the midpoint of ST

The midpoint is given as:

[tex]m(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)[/tex]

Here in this sum,

[tex](x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)[/tex]

Substituting the values, we get

[tex]m(x, y)=\left(\frac{-2+3}{2}, \frac{4+9}{2}\right)\\\\m(x, y)=\left(\frac{1}{2}, \frac{13}{2})[/tex]

Thus the midpoint is [tex](\frac{1}{2}, \frac{13}{2})[/tex]

Find the distance between points

The distance is given by formula:

[tex]d=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}[/tex]

Here in this sum,

[tex](x_1, y_1) = (-2, 4)\\\\(x_2, y_2) = (3, 9)[/tex]

Substituting the values, we get

[tex]\begin{aligned}&d=\sqrt{(3-(-2))^{2}+(9-4)^{2}}\\\\&d=\sqrt{5^{2}+5^{2}}\\\\&d=\sqrt{25+25}\\\\&d=\sqrt{50}=7.071 \approx 7.1\end{aligned}[/tex]

Thus the distance between points S and T is 7.1 units

The coordinates of the midpoint [tex]\( M \) are \( (0.5, 6.5) \),[/tex] and the distance between points S and T approximately 7.0 units.

To find the coordinates of the midpoint M of the line segment ST, we use the midpoint formula:

[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

 Given the coordinates of [tex]\( S \) and \( T \) are \( S(-2, 4) \) and \( T(3, 9) \)[/tex] respectively, we substitute these values into the formula:

[tex]\[ M = \left( \frac{-2 + 3}{2}, \frac{4 + 9}{2} \right) \][/tex]

[tex]\[ M = \left( \frac{1}{2}, \frac{13}{2} \right) \][/tex]

[tex]\[ M = (0.5, 6.5) \][/tex]

Now, to find the distance between points S and T,  we use the distance formula:

[tex]\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \][/tex]

Substituting the coordinates of S and T into the formula:

[tex]\[ d = \sqrt{(3 - (-2))^2 + (9 - 4)^2} \][/tex]

[tex]\[ d \approx 5 \times 1.4 \][/tex]

[tex]\[ d \approx 7 \][/tex]

The coordinates of the midpoint  [tex]\( M \) are \( (0.5, 6.5) \),[/tex] and the distance between points S and T  is approximately 7.0 units.

Answer:

-x^2

Step-by-step explanation:

Answer:

-x^2

Step-by-step explanation:

Answer:

Your answer is C Straight angle

Step-by-step explanation:

Answer:

The Proof is below.

Therefore the Perimeter of Christmas paper is 32 feet  ..Proved

Step-by-step explanation:

Let the Christmas Paper have Dimensions as

Length = 8 feet

Width = 8 feet

To Show:

Perimeter of Christmas Paper = 32

Solution:

Christmas Paper is in Rectangle  Shape,

Therefore Perimeter of a Rectangle is given as

[tex]Perimeter\ of\ Rectangle=2(Length+Width)[/tex]

Substituting the values we get

[tex]Perimeter=2(8+8)=2\times 16=32\ feet[/tex]

Therefore the Perimeter of Christmas paper is 32 feet  ..Proved

The perimeter of a square is calculated by adding the lengths of all four sides. An 8 ft by 8 ft square has a perimeter of 32 ft, because 8 ft multiplied by 4 (the number of sides in a square) equals 32 ft.

This question involves understanding the concept of perimeter in the context of a square. If you have a piece of Christmas paper that is 8 feet long and 8 feet wide, you actually have a square because all sides are of equal length. To calculate the perimeter of a square, you simply add up the lengths of all four sides.

Since each side is 8 feet, the perimeter P is given by:

P = side + side + side + side
P = 8 ft + 8 ft + 8 ft + 8 ft
P = 32 ft

So, the perimeter of the Christmas paper, if shaped like a square, is 32 feet, which is simply four times the length of one side.

Answer:

x ≤ -7

Step-by-step explanation:

Symbolically, we have 11 - 3x ≥ 32

and we can solve this for x as follows:

Add 3x to both sides.  We get:

11 - 3x + 3x ≥ 32 + 3x

Then 11 ≥ 32 + 3x

Reversing the order, we get  3x + 32 ≤ 11

Subtracting 32 from both sides, we get:

3x ≤ -21

Finally, dividing both sides by 3 yields:

x ≤ -7

Answer:

x = 36.87 degrees.

Step-by-step explanation:

4 cos x + 3 sin x = 5    

Use the Auxiliary angle method:

R sin (α  + x) = R sin α cos x + R cos α  sin x

Comparing coefficients:

R sin α  = 4 and R cos α  = 3

R sin α / R cos α  = 4/3

So tan α  = 4/3

α  = 53,13 degrees.

Now R^2(sin^2 α + cos^2 α ) = 3^2 + 4^2 = 25

R^2 = 25

R = 5.

R sin (x + 53.13) = 5

5 sin ( x + 53.13) = 5

sin (x + 53.13) = 1

x  + 53.13 = 90

x = 36.87 degrees.

Final answer:

The greatest common factor of 75 and 20 is 5, and by applying the distributive property, the expression 75+20 can be factored as 5(19).

Explanation:

The greatest common factor (GCD) of 75 and 20 is 5. Applying the distributive property to factor out 5, we get:

75 + 20 = 5 × (15 + 4)

Here's the breakdown:

Find the GCD: The largest factor that divides both 75 and 20 is 5.

Divide each term by the GCD: Divide 75 by 5 to get 15 and divide 20 by 5 to get 4.

Rewrite with the GCD factored out: Combine the results from step 2 and multiply by the GCD: 5 × (15 + 4).

Therefore, the factored expression using the distributive property is 5 × (15 + 4).

Thus, the factored form of the expression 75+20 is 5(19).

Answer:

The hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

Step-by-step explanation:

Given:

A theater group made appearances into cities the hotel charge before tax and the second city was 1500 higher than the first.

The tax of the first city was 6% and the tax of the second city was 10%.

Total hotel tax paid for two cities with $670.

Now, to find the hotel charge in each city before tax.

Let the hotel charge in first city before tax be [tex]x.[/tex]

And the hotel charge in second city before tax be [tex]y.[/tex]

So, as the hotel charge of the second city was 1500 higher than the first.

Thus,

[tex]y=x-1500[/tex]   ........(1)

And as given, the tax of the first city was 6% and the tax of the second city was 10%, total hotel tax paid for two cities with $670.

6% of [tex]x[/tex] + 10% of [tex]y[/tex] = $670.

[tex]\frac{6x}{100} +\frac{10y}{100} =670[/tex]

[tex]0.06x+0.10y=670[/tex]

Substituting the value of [tex]y[/tex] from equation (1) we get:

[tex]0.06x+0.10(x-1500)=670[/tex]

[tex]0.06x+0.10x-150=670[/tex]

[tex]0.16x-150=670[/tex]

Adding both sides by 150 we get:

[tex]0.16x=820[/tex]

Dividing both sides by 0.16 we get:

[tex]x=5125.[/tex]

The hotel charge in first city before tax = $5125.

Now, substituting the value of [tex]x[/tex] in equation (1) we get:

[tex]y=x-1500[/tex]

[tex]y=5125-1500[/tex]

[tex]y=3625.[/tex]

The hotel charge in second city before tax = $3625.

Therefore, the hotel charge in each city before tax was $5125 of the first city and $3625 of the second city.

Answer:

Investor invested $7,800 at 8% and $6,200 at 6.5%

Step-by-step explanation:

Use formula

[tex]I=P\cdot r\cdot t,[/tex]

where

I = interest

P = principal

r = rate (as decimal)

t = time

First investment:

[tex]P_1=x\\ \\r_1=0.08\\ \\t_1=1[/tex]

then

[tex]I_1=x\cdot 0.08\cdot 1\\ \\I_1=0.08x[/tex]

Second investment:

[tex]P_2=14,000-x\\ \\r_2=0.065\\ \\t_2=1[/tex]

then

[tex]I_2=(14,000-x)\cdot 0.065\cdot 1\\ \\I_2=0.065(14,000-x)[/tex]

The amount of interest earned for 1 year was $1,027, then

[tex]I_1+I_2=1,027\\ \\0.08x+0.065(14,000-x)=1,027\\ \\0.08x+910-0.065x=1,027\\ \\0.08x-0.065x=1,027-910\\ \\0.015x=117\\ \\x=7,800\\ \\14,000-x=6,200[/tex]

Investor invested $7,800 at 8% and $6,200 at 6.5%