Solve the equation.

–3x + 1 + 10x = x + 4

x = 1/2
x = 5/6
x = 12
x = 18

Answer:

The equation can be used to determine the total number of guests is 13.50g + 540 = 1512  and the total number of guest are 72 .

Step-by-step explanation:

As given

Mrs. Howard is hosting a catered dinner party to celebrate her daughter's graduation.

The catering company she plans to use charges $13.50 per plate of food and an additional fee of $540 to cover linens and tableware.

The total bill for the catering services is $1,512.

Total number of guests, g .

Than the equation becomes

1512 = 540 + 13.50 g

1512 - 540 = 13.50 g

972 = 13.50 g

[tex]g = \frac{972}{13.50}[/tex]

g = 72

Therefore the equation can be used to determine the total number of guests is 13.50g + 540 = 1512  and the total number of guest are 72 .

Answer:  About 2 times.

Step-by-step explanation:

Given : In 2010, the national debt of the United States was about 14 trillion dollars.

We know that 1 trillion [tex]=1,000,000,000,000= 10^{12}[/tex]

then, In 2010, the national debt of the United States was about [tex]14\times10^{12}[/tex]

dollars.

In 2003 it was about [tex]7\times10^{12}[/tex] dollars.

Now, the number of times the national debt was larger in 2010 than 2003 :-

[tex]\dfrac{ 14\times10^{12}}{7\times10^{12}}\\\\=\dfrac{14}{7}\times10^{12-12}\\\\=2\times10^0=2[/tex]

Hence, national debt was about 2 times larger in 2010 than 2003 .

Answer:

$7,632 would have been contributed to the 401(k) plan after 2 years.

Step-by-step explanation:

A technical writer makes salary per year = $45,000

She contributing 8% of her salary to her 401(k) plan = 8% of 45,000

0.08 × 45,000 = $3,600

Her employer matches 6% of her contributions = 6% of 3,600

= 0.06 × 3,600 = $216.00

Total contribution for one year = 3,600 + 216.00 = $3,816

After 2 years = 3,816 × 2 = $7,632.00

$7,632 would have been contributed to the 401(k) plan after 2 years.

Answer: The steps for using a compass and straightedge to construct a square are as follows :-

1. Use a straightedge to draw line a and label a point on the line as point P.

2. Construct a line perpendicular to line a through point P.

3. Label a point on this line as point R.

4. With the compass open to the desired side length of the square, place the compass point on point P and draw an arc on line a and an arc on PR←→.

5. Label the points of intersection as points S and T.

6. Keeping the same compass width, place the compass on point T and draw an arc in the interior of∠SPT to intersect the previously drawn arc.

7. Label the point of intersection as point Q.

8. Without changing the compass width, place the compass point on point S and draw an arc in the interior of∠SPT .

9. Use the straightedge to draw QS ,QT,SR and RT.

Here we have finished with the square RTQS.

Answer: 15x3y

Step-by-step explanation:

We rewrite the expressions by using factorisation method of their primes. This will give:

60x4y7= 2×2×3×5×x×x3×y×y6

45x5y5= 3×3×5×x×x4×y×y4

75x3y= 3×5×5×x×x2×y

Common factors= 3 × 5 × x3 × y

= 15x3y

Answer:

its B

Step-by-step explanation:

The expression so it forms a perfect square trinomial is 14x.

We have given that,

The expression so it forms a perfect-square trinomial.

We have to determine the  x² +___ x + 49.

A divisor of an integer n also called a factor of n, is an integer m that may be multiplied by some integer to produce n.

In this case, one also says that n is a multiple of m.

(x + 7)(x + 7)

x^2 + 14x + 49

The expression so it forms a perfect square trinomial is 14x.

To learn more about the perfect square visit:

https://brainly.com/question/1538726

#SPJ2

I think it's B but I'm not 100% sure

Answer:

B

Step-by-step explanation:

To solve this, you need to know first how many weeks will take Richard replacing the money.

We will call X the number of weeks so we say

$85 * X =$950

X= 11.17

This means it will take at least ≈12 weeks to pay his debt.

To know which scenario it's not possible, use the equation to choose the right option.

A: $85*5= $425

After 5 weeks, he paid $425, this mean he's $525 in debt.

B: $85*6= $510

After 6 weeks, he paid $510, this means he's $440 in debt.

C. $85*7= $595

After 7 week,s he paid $595, this means he's $355 in debt.

D. $85*8= $680

After 7 weeks, he paid $680, this means he's $270 in debt.

The not possible scenario is B because he will be paying at least $85 or more so he will debt $440 or less al week 6.

The solution to the system of equations  are (1, 3) and (-5, -3)

Given the following functions

Y=x^2+5x-3

Y-x=2; y = x + 2

Equating both outputs will give

x^2+5x-3 = x + 2

x^2+5x-3 - x - 2 = 0

x^2 + 4x - 5 = 0

Factorize the equation

x^2 + 5x - x - 5=0

x(x+5) - 1(x+5) = 0

(x-1)(x+5) = 0

x = 1 and -5

Recall that y = x + 2

y = 3 and -3

Hence the solution to the system of equations  are (1, 3) and (-5, -3)

Learn more here: https://brainly.com/question/20360246

The solution to a linear quadratic system of equations can be found by substitifying one equation into the other and solving. In this case, the solutions are (1,3) and (-5,-3).

To find the solution of a linear quadratic system of equations, you need to substitute one equation into the other. In this case, for the equations [tex]Y = x^2 + 5x - 3[/tex] and [tex]Y - x = 2[/tex], you would first isolate Y in the linear equation, resulting in [tex]Y = x+2.[/tex]

Then, you substitute (x + 2) for Y in the quadratic equation, leading to [tex]x + 2 = x^2 + 5x - 3.[/tex]

Next, rearrange the equation to get it in the standard quadratic form: 0 = [tex]x^2 + 5x - x - 3 - 2.[/tex] Simplifying this results in the equation [tex]0 = x^2 + 4x - 5.[/tex]

Finally, solve this equation by factoring or using quadratic formula, which gives the solutions as x = 1, -5. Substituting both 1 and -5 into the equation Y = x + 2 gives the corresponding y-values, Y = 3 and -3. Therefore, the solutions to the system of equations are (1,3) and (-5,-3).

https://brainly.com/question/12039832

#SPJ11

x = total number of students

equation is:

 (3/4)x = 1464

 to solve for x divide both sides by 3/4

x = 1464 / 3/4 = 1952

 x = 1952

 there are 1952 total students

To find the missing digit to make 2,72_ divisible by 6, add the digit 4.

To find the digit that makes 2,72_ divisible by 6, we need to focus on the divisibility rules for 6. In this case, a number is divisible by 6 if it is divisible by both 2 and 3. For 2, the last digit must be even, and for 3, the sum of the digits must be a multiple of 3.

Given the number 2,72_, the blank digit needs to be 4 to make the number divisible by 6. This is because when the digit 4 is added, the number becomes 2,724, which is divisible by both 2 and 3.

Answer:

THE ANSWER COULD BE 14

Final answer:

Using the law of detachment, if it is sunny on Tuesday and there is a habit of going outside in nice weather, one can conclude that they will go outside on Tuesday.

Explanation:

The law of detachment is a concept in logic used to form conclusions given a conditional statement and its hypothesis being true. For instance, in the scenario provided:

If it is sunny on Tuesday (hypothesis).

I will always go outside if the weather is nice (conditional statement).

By applying the law of detachment, we can conclude that:

I will go outside on Tuesday (conclusion).

This logical reasoning assumes that a 'nice' weather includes a sunny day. Hence, if it is indeed sunny on Tuesday, the condition for going outside is met.

To solve the inequality -3 < 2x + 1 < 7 for the number x, subtract 1 from all parts and then divide by 2. The solution is the range of numbers greater than -2 and less than 3.

The problem statement here results in an inequality that can be expressed algebraically. If 'x' represents the unknown number, we can write the inequality as -3 < 2x + 1 < 7.

To solve for 'x', we will isolate the variable on one side by following the rules of inequalities similar to solving equations.

First, subtract 1 from all parts of the inequality to get the pure inequality without a constant.

-4 < 2x < 6

Now, divide all parts of the inequality by 2, which yields:

-2 < x < 3

All numbers greater than -2 and less than 3 satisfy the original problem statement. Therefore, the range of numbers that solve the inequality is from -2 to just below 3.

the answer to this question is 19!

Answer:

answer is b

Step-by-step explanation: