Solve for 3a: 4a − 2 = a + 4 3a =

What is the value of x in the equation 1.5(x + 4) - 3 = 4.5(x - 2)?

Mila [183]

The answer is b on edge

5 0

2 years ago

Solve the following using Substitution method 2x – 5y = -13 3x + 4y = 15

Digiron [165]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Solve the following using Substitution method

2x – 5y = -13

3x + 4y = 15

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$\left. \begin{array} { l } { 2 x - 5 y = - 13 } \\ { 3 x + 4 y = 15 } \end{array} \right.$

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

$2x-5y=-13, \: 3x+4y=15$

Choose one of the equations and solve it for x by isolating x on the left-hand side of the equal sign. I'm choosing the 1st equation for now.

$2x-5y=-13$

Add 5y to both sides of the equation.

$2x=5y-13$

Divide both sides by 2.

$x=\frac{1}{2}\left(5y-13\right) \\$

Multiply $\frac{1}{2}\\$ times 5y - 13.

$x=\frac{5}{2}y-\frac{13}{2} \\$

Substitute $\frac{5y-13}{2}\\$ for x in the other equation, 3x + 4y = 15.

$3\left(\frac{5}{2}y-\frac{13}{2}\right)+4y=15 \\$

Multiply 3 times $\frac{5y-13}{2}\\$ .

$\frac{15}{2}y-\frac{39}{2}+4y=15 \\$

Add $\frac{15y}{2} \\$ to 4y.

$\frac{23}{2}y-\frac{39}{2}=15 \\$

Add $\frac{39}{2}\\$ to both sides of the equation.

$\frac{23}{2}y=\frac{69}{2} \\$

Divide both sides of the equation by 23/2, which is the same as multiplying both sides by the reciprocal of the fraction.

$\large \underline{ \underline{ \sf \: y=3 }}$

Substitute 3 for y in $x=\frac{5}{2}y-\frac{13}{2}\\$ . Because the resulting equation contains only one variable, you can solve for x directly.

$x=\frac{5}{2}\times 3-\frac{13}{2} \\$

Multiply 5/2 times 3.

$x=\frac{15-13}{2} \\$

Add $-\frac{13}{2}\\$ to $\frac{15}{2}\\$ by finding a common denominator and adding the numerators. Then reduce the fraction to its lowest terms if possible.

$\large\underline{ \underline{ \sf \: x=1 }}$

The system is now solved. The value of x & y will be 1 & 3 respectively.

$\huge\boxed{ \boxed{\bf \: x=1, \: y=3 }}$

8 0

2 years ago

Use the difference of two squares to find the product of 22 and 18.

vladimir2022 [97]

Answer:

396

Step-by-step explanation:

Difference of two squares is breaking down numbers into pieces and using the distributive property to solve. The pieces should be in the form (a-b)(c+d).

Write 22 as (20 + 2) and 18 as (20-2).

(20+2)(20-2) = 400 + 40 - 40 - 4 = 400 - 4 = 396

4 0

2 years ago

Joe is making a recipe that calls for 3/4 tsp of cinnamon. His only measuring spoon holds 1/8 teaspoon. How many times will he n

SashulF [63]

6 times because you find the common denominator which is 8 so 3/4 is 6/8. He needs to fill his cup 6 times.

5 0

3 years ago

Which angle in triangle DEF has the largest measure?

nordsb [41]

Answer:

D is the largest angle

Step-by-step explanation:

The angle opposite the largest side is the largest and the angle opposite the smallest side is the smallest.

Since 12 is the largest side, angle D is the largest

8 is the smallest side, F is the smallest angle

7 0

3 years ago