Simplify each expression using the order of operations. Then, match the expression (term) on the left with its solution (definition) on the right.

Match Term Definition

42 + 3 − 2(3) A) 18

22 ⋅ 8 ÷ 2 + 2 B) 44

(42 + 16) + 12 C) 75

8 ⋅ 32 + 3 D) 13

Answer: Solve by combining like terms.

Solve for x by simplifying both sides of the equation, then isolating the variable.

x > [tex]-\frac{99}{4}[/tex]

As a decimal is: x > −24.75

On simplify both sides of the inequality the solution for the inequality -2/5x - 9 < 9/10 is x > -247.5.

To simplify both sides of the inequality, we'll perform the necessary mathematical operations step by step:

-2/5x - 9 < 9/10

Step 1: Add 9 to both sides of the inequality to isolate the term with "x":

-2/5x - 9 + 9 < 9/10 + 9

Simplify:

-2/5x < 9/10 + 90/10

Step 2: Combine the fractions on the right side:

-2/5x < (9 + 90)/10

-2/5x < 99/10

Step 3: To eliminate the fraction, multiply both sides by the reciprocal of (-2/5), which is (-5/2). When you multiply an inequality by a negative number, remember to flip the inequality sign:

(-5/2) * (-2/5x) > (-5/2) * (99/10)

Simplify:

x > -5/2 * (99/10)

x > -495/20

Step 4: Reduce the fraction on the right side:

x > -247.5

Now, the simplified inequality is:

x > -247.5

So, the solution for the inequality is "x > -247.5."

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The weight of the body when the distance is 750 miles if it is inversely proportional is 3,920 pounds.

w = k/d²

Where,

k = constant of proportionality

w = 180 pound

d = 3,500 miles

w = k/d²

180 = k/3500²

180 = k/12,250,000

cross product

k = 180 × 12,250,000

k = 2,205,000,000

Therefore, when d = 750 miles

w = k/d²

w = 2,205,000,000 / 750²

= 2,205,000,000 / 562,500

= 3,920 pounds

Hence, the weight of the body is 3,920 pounds.

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Using the base and the acute angle on the base, to find the height of the dam, you would need to multiply the base by the tangent of the angle.

Height = 100 * tan(40)

Final answer:

When considering that yards vary directly as feet and 2 feet represent 30 yards, we determine that 3 feet represent 45 yards by setting up a direct variation proportion.

Explanation:

In the problem where yards vary directly as feet, we are given that 2 feet represent 30 yards. To find out how many yards represent 3 feet, we need to set up a proportion based on the given information that 1 yard equals 3 feet. Using the direct variation, we can create the equation: 2 feet / 30 yards = 3 feet / x yards, where x represents the unknown number of yards.

If we simplify the first ratio, 2 feet is to 30 yards as 1 foot is to 15 yards, since dividing both sides by 2 gives us: 1 foot / 15 yards. Therefore, we can continue the proportion as: 1 foot / 15 yards = 3 feet / x yards.

Now, let's solve for x by multiplying both sides of the equation by the denominator on the right side (x yards) to eliminate the fraction: 1 foot / 15 yards = 3/x, which simplifies to x = 3 * 15. After performing the multiplication, we get x = 45 yards. Therefore, 3 feet represent 45 yards on the drawing scale.

Oh this is easy.I completed the table. C) 40%

THE ANSWER IS C (◡ ‿ ◡ ✿)

Polygon A: 20 ft x 60 ft

           P = 2(20) + 2(60)

              =   40    +  120

              =         160

Polygon B: 3 ft x 9 ft

          P = 2(3) + 2(9)

             =   6   +   18

             =       24

Ratio of Perimeters: [tex]\frac{160}{24} = \frac{20}{3}[/tex]  = 20:3      

Answer:

Rate of Pratap in still water is 4.5 miles/hour and rate of current is 0.5 miles/hour.

Step-by-step explanation:

Pratap Puri rowed 10 miles down a river in 2 ​hours, but the return trip took him 2.5 hours.

We know that, [tex]Speed = \frac{Distance}{Time}[/tex]

So, the speed of Pratap with the current will be:  [tex](\frac{10}{2})miles/hour = 5[/tex] miles/hour

and the speed of Pratap against the current will be:  [tex](\frac{10}{2.5})miles/hour = 4[/tex] miles/hour.

Suppose, the rate of Pratap in still water is [tex]x[/tex] and the rate of current is [tex]y[/tex].

So, the equations will be........

[tex]x+y= 5 .............................. (1)\\ \\ x-y=4 .............................. (2)[/tex]

Adding equation (1) and (2) , we will get......

[tex]2x=9\\ \\ x=\frac{9}{2}= 4.5[/tex]

Now, plugging this [tex]x=4.5[/tex] into equation (1), we will get.....

[tex]4.5+y=5\\ \\ y=5-4.5 =0.5[/tex]

Thus, Pratap can row at 4.5 miles per hour in still water and the rate of the current is 0.5 miles/hour.

Pratap's rowing speed in still water is 4.5 miles per hour, and the speed of the current is 0.5 miles per hour.

First, we need to understand that Pratap's velocity, or speed, is the sum of his own rowing speed and the speed of the current when he rows downstream, and the difference of his speed and the current when he rows upstream. To find these speeds, we can use the formula for speed, which is distance/time.

When Pratap is rowing downstream (with the current), he covers 10 miles in 2 hours, giving a speed of 10/2 = 5 miles per hour. When rowing upstream (against the current), he covers the same distance in 2.5 hours, giving a speed of 10/2.5 = 4 miles per hour.

Now, if we add these two speeds together and divide by 2, we get the rowing speed of Pratap in still water (since half the time he gets an assist from the current, and half the time he is fighting against it). This is (5+4)/2 = 4.5 miles per hour.

The speed of the current would be the difference between Pratap's rowing speed and the overall speed when he is rowing downstream, which is 5 - 4.5 = "0.5 miles per hour".

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Answer:

Only one solution

Step-by-step explanation:

Given that there is a coordinate plane (say xy)

Two lines are given.

One line crosses the y axis at 3 and has a slope of negative 1.

hence equation of I line is y = -x+3

The other line crosses the y axis at 3 and has a slope of two thirds.

So equation is y = 2x/3 +3

Since the two lines lie in the same plane and are having different slopes, they intersect at one point.

Eliminate y to get

-x+3=2x/3+3

Or x=0

y=3

Hence solutionis (0,3) for the system.

Answer:

One solution

Step-by-step explanation:

we know that

The solution of the system of equations  is equal to the intersection point both graphs

we have

[tex]y=-x+3[/tex] ------> equation A

[tex]y=-(2/3)x+3[/tex] ------> equation B

Using a graphing tool

see the attached figure to better understand the problem

In this problem the intersection point is only one

therefore

The system of equations has one solution

The solution is the point [tex](0,3)[/tex]

Number of Horses in Avery's farm, after t years from now is given by function H(t); where  [tex]H(t) = 25(2)^{t}[/tex]

The amount of hay, in tons, that is produced on her farm t years from now is given by function A(t); where  [tex]A(t) = 150(1.5)^{t}[/tex]

The predicted yearly supply of hay, in tons, available to each horse in Avery's farm t years from now is given by function F(t); where F(t) = A(t)/H(t)

So, F(t) = [tex]\frac{150(1.5)^{t}}{25(2)^{t}}[/tex] = [tex]6 (\frac{1.5}{2}) ^{t}[/tex] = [tex]6 (0.75)^{t}[/tex] tons/horse

The formula for F(t) in terms of H(t) and A(t) is F(t) = (150(1.5)^t) / (25(2)^t).

To find the formula for F(t), we need to divide the amount of hay produced, A(t), by the number of horses, H(t). So, the formula for F(t) is F(t) = A(t) / H(t). Substituting the given functions, we have F(t) = (150(1.5)^t) / (25(2)^t).

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Answer: Single deposit by Edward=$3594 to make it  amount for college=$50,000 in 10 years.

Step-by-step explanation:

Here Compound amount =$50,000

Time=10 years

Rate of interest=4.3%

By the Daily compound  interest formula ,we have

[tex]Amount=Principal(1+rate/365)^{365\times\ time}\\\Rightarrow\ Amount=Principal(1+4.3/365)^{365\times\ 10}\\\Rightarrow\ 50000=P(1+.011)^{3650}\\\Rightarrow\ 50000=P(1.011)^{3650}\\\Rightarrow\ 50000=P(13.911)...........(approx)\\\Rightarrow\ P=\frac{50000}{13.911}=3594......(approx)[/tex]

Therefore Principal amount deposited by Edward is $3594.

Answer:

$32,526.67

Step-by-step explanation:

Let the Principle be P

amount here A= $50,000

time n= 10 years n= 10*365=3650 days

rate of interest= 4.3% compounded daily= 4.3/365

let us use compound interest formula to calculate the principle

[tex]A= P(1+\frac{r}{100})^n[/tex]

putting all the values we get

[tex]50000=P(1+\frac{4.3}{100\times365})^10times365[/tex]

on solving we get P= $32,526.67

therefore he need to deposit $32,526.67

Distance covered in 12 gallons tank of gas = 420 miles

So, distance covered in 1 gallon tank of gas = [tex]\frac{420}{12}[/tex] miles

Now, distance covered in 8 gallons will be =

[tex]8*\frac{420}{12}[/tex] =280 miles

Hence, distance covered by Mr.Fink's economy car in 8 gallons tank of gas is 280 miles.

The measure of the indicated angle [tex]\angle A$ is 46 degrees[/tex]

We can use the fact that the sum of the angles in a triangle is 180 degrees to solve for the missing angle.

Since we are given that [tex]\angle C = 46^\circ$,[/tex]  we can write the following equation:

[tex]m\angle A + m\angle B + 46^\circ = 180^\circ[/tex]

Solving for [tex]$m\angle A[/tex] we get:

[tex]m\angle A = 180^\circ - m\angle B - 46^\circ[/tex]

Since [tex]$\angle B$[/tex]  is the missing angle, we can substitute the given information into the equation to solve for its measure:

[tex]m\angle A = 180^\circ - 46^\circ - 46^\circ = 98^\circ - 92^\circ = 46^\circ[/tex]

Therefore, the measure of the indicated angle $\angle A$ is 46 degrees.

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Final answer:

The solution to the inequality [tex]x^2 - 3x - 28[/tex]≥ 0 is found by factoring the quadratic equation to find its roots, which are x = 7 and x = -4. The solution to the inequality is x ≤ -4 or x ≥ 7.

Explanation:

To determine the solution to the quadratic inequality  [tex]x^2 - 3x - 28[/tex] ≥ 0, we first need to find the roots of the equation  [tex]x^2 - 3x - 28 = 0.[/tex]We can do this by factoring the quadratic expression.

We look for two numbers that multiply to give -28 and add to give -3. These numbers are -7 and +4. So we can rewrite the equation as (x-7)(x+4) = 0. Setting each factor equal to zero gives us the roots x = 7 and x = -4.

Now, we test intervals that are determined by these roots to see where the inequality holds true. The intervals are (-infinity, -4), (-4, 7), and (7, infinity). If we test a number from each interval in the inequality [tex]x^2 - 3x - 28[/tex] ≥ 0, we find that the inequality is true for x ≤ -4 and x ≥ 7. Therefore, the solution to the inequality is x ≤ -4 or x ≥ 7.

Answer:

it is PRIME

Step-by-step explanation:

It has 2 factors: 1 and 5

Area of Bull's Eye:

A = π r²

   = π (1)²

   = π

Area of Inner Ring:

A = π r²

   = π (3-1)²

   = 4π

Ratio between Inner Ring and Bull's Eye:

[tex]\frac{InnerRing}{Bull's Eye} = \frac{4\pi }{\pi} = 4[/tex]

Answer: It is 4 times harder to hit the Bull's Eye than it is to hit the Inner Ring

Final answer:

The Inner Ring is 8 times larger than the Bull's Eye.

Explanation:

To determine how much harder it is to hit the Bull's Eye compared to the Inner Ring, we can compare their areas.

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius of the circle.

The area of the Bull's Eye can be calculated as A = π(1)^2 = π square inches.

The area of the Inner Ring can be calculated as A = π(3)^2 - π(1)^2 = 9π - π = 8π square inches.

Therefore, the Inner Ring is 8 times larger than the Bull's Eye.

B) 5 mph

hope this helped

Answer:

Its 16

100% Correct

Step-by-step explanation:

USA TEST PREP

The sum of the measures of the angles of a hexagon is equal 720°.

Therefore we have the equation:

[tex]160^o+75^o+132^o+113^o+108^o+x^o=720^o\\\\588^o+x^o=720^o\ \ \ \ |-588^o\\\\x^o=132^o[/tex]

Answer: x = 132

Answer:

Sali's speed was 18.75 km/h.

Step-by-step explanation:

Jane took 3.5 hours to cycle the 63 km.

As,  [tex]Speed= \frac{Distance}{Time}[/tex] , so the speed of Jane will be:  [tex]\frac{63}{3.5} km/h = 18 km/h[/tex]

Suppose, the speed of Sali is  [tex]x[/tex] km/h

Sali caught up with Jane when they had both cycled 30 km.

So, the time required for Jane to cycle 30 km [tex]= \frac{30}{18}=\frac{5}{3} hours[/tex] and the time required for Sali to cycle 30 km  [tex]=\frac{30}{x} hours[/tex]

Given that, Sali started to cycle 4 minutes or [tex](\frac{4}{60}) or (\frac{1}{15}) hours[/tex] after Jane started to cycle. So, the equation will be.......

[tex]\frac{5}{3}-\frac{30}{x}= \frac{1}{15}\\ \\ \frac{30}{x}= \frac{5}{3}-\frac{1}{15}\\ \\ \frac{30}{x}= \frac{24}{15}\\ \\ 24x=450\\ \\ x= \frac{450}{24}= 18.75[/tex]

Thus, the speed of Sali was 18.75 km/h.

Answer:Thus, the speed of Sali was 18.75 km/h.

Step-by-step explanation:

Sali's speed was 18.75 km/h.

[tex]1.\\\dfrac{9}{2}(8-x)+36=102-\dfrac{5}{2}(3x+24)\ \ \ \ |\text{multiply both sides by 2}\\\\\not2^1\cdot\dfrac{9}{\not2_1}(8-x)+2\cdot36=2\cdot102-\not2^2\cdot\dfrac{5}{\not2_1}(3x+24)\\\\9(8-x)+72=204-5(3x+24)\ \ \ \ |\text{use distributive property}\\\\(9)(8)+(9)(-x)+72=204+(-5)(3x)+(-5)(24)\\\\72-9x+72=204-15x-120\ \ \ \ |\text{use commutative and associative property}\\\\-9x+(72+72)=-15x+(204-120)\\\\-9x+144=-15x+84\ \ \ \ |\text{subtract 144 from both sides}[/tex]

[tex]-9x=-15x-60\ \ \ \ |\text{add 15x to both sides}\\\\6x=-60\ \ \ \ |\text{divide both sides by 6}\\\\\boxed{x=-10}[/tex]

[tex]2.\\-12x-0.4 > 0.2(36.5x+80)-55\ \ \ \ |\text{use distributive property}\\\\-12x-0.4 > (0.2)(36.5x)+(0.2)(80)-55\\\\-12x-0.4 > 7.3x+16-55\ \ \ \ |\text{use associative property}\\\\-12x-0.4 > 7.3x+(16-55)\\\\-12x-0.4 > 7.3x-39\ \ \ \ |\text{add 0.4 to both sides}\\\\-12x > 7.3x-38.6\ \ \ \ |\text{subtract 7.3x from both sides}\\\\-19.3x > -38.6\ \ \ \ \ |\text{change the signs}\\\\19.3x < 38.6\ \ \ \ |\text{divide both sides by 19.3}\\\\\boxed{x < 2}[/tex]

2)

-12x - 0.4 > 0.2(36.5x + 80) - 55

Distributive property

-12x - 0.4 > 7.3x + 16 - 55

Combine like terms

-12x - 0.4 > 7.3x -39

Subtract both sides by 7.3x

-19.3x - 0.4 > - 39

Add 0.4 to both sides

-19.3x > -38.6

Divide both sides by -19.3 (remember when dividing a negative number, the sign will be flipped)

x < 2

1)

9/2(8 -x) + 36 = 102 - 5/2(3x+24)

Multiply both sides by 2

9(8 -x) + 72 = 204 - 5(3x+24)

Distributive propery

72 - 9x + 72 = 204 - 15x - 120

Combine like terms

- 9x + 144 = -15x + 84

Add 15x to both sides

6x + 144 = 84

Subtract 144 from both sides

6x = -60

 x = -10

Hope they help.

answer:  [tex]-15 - x[/tex]

work:

[tex]5-(x+4)[/tex]  | distribute the negative into the parentheses, which means multiply   into the parentheses.

[tex]5 - x - 20[/tex]  | combine like terms

[tex]-15 - x[/tex]  | final answer

correct me if anything is wrong, otherwise hope this helps! ❤ from peachimin

Hello there!

Distributive property you had to used their formula like:

↓

a(b+c)=ab+ac

5-(x+4)

First you had to distribute by the negative signs.

5+-1(x+4)

5+-1x+(-1)(4)

5+-x+-4

Then you combine like terms of

↓

5+-x+-4

(-x)+(5+-4)

Simplify

=-x+1

Answer⇒⇒⇒⇒-x+1

Hope this helps!

Thank you for posting your question at here on Brainly.

-Charlie

answer is equal to2:1/2=4:1

4 cups are required

Final answer:

For every cup of butter in the recipe, 4 cups of flour are needed. This is found by analyzing the ratio of flour to butter given in the recipe, which is 2 cups flour to 0.5 cup butter.

Explanation:

The question asks how many cups of flour are needed to mix with each cup of butter according to a given recipe. To determine this, we look at the provided ratios and find that the recipe calls for 2 cups of flour and 0.5 cup of butter. This results in the ratio of 4 cups of flour for every 1 cup of butter.

To calculate the amount of flour required for each cup of butter, we use a simple proportion:

0.5 cup butter : 2 cups flour
1 cup butter : x cups flour

To solve for x (the amount of flour needed for 1 cup of butter), we cross-multiply and get:

0.5x = 2
x = 2 / 0.5
x = 4

So, for every cup of butter, 4 cups of flour are needed.

For a line you would draw a straight line with arrows on each end and for a ray you would draw a straight line with an arrow on only one end (depends on which way ray is pointing)

:)

6. vertical

7. LSM and MSN are vertical angles

8. MSN

Answer:

6. Which type of angle pair are LSM and OSN?

Answer - D. Vertical angles

Vertical angles are pairs of opposite angles made by two intersecting lines.

7. Which of the following statements are false?

Answer - C. LSM and MSN are vertical angles.

Vertical angles are pairs of opposite angles made by two intersecting lines.

8. Which angle is supplementary to LSM?

Answer - D. MSN

Two angles are supplementary when they add up to become 180 degrees.

Here adding both we will get angle S as 180 degrees.

ANSWER

[tex]7.26451[/tex] correct  to 3 decimal places is [tex]7.265[/tex]

EXPLANATION

We start counting from the first number after the decimal point.

So starting from 2, we count 3 decimal places to the right and land on 4.

Next, we check to see if the number after 4, is greater or equal 5, then we round up, else we round down.

Since that number is 5, it is greater than or equal to 5.

Therefore we round up to obtain [tex]7.265[/tex]

7.264 51 correct to 3 decimal places is 7.265.

What is means to write a number to three decimal places is that after the decimal point, there should be three numbers. It means that the number should be rounded off to the nearest thousandth.

In order to round off to 3 decimal places take the following steps:

Examine the number in the ten thousandth place:

The number in the ten thousandth place is 5, so the number in the thousandth place increases by 1. The number becomes 7.265.

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I just took the test. For PLATO the first blank is 30 and the second blank is 2.

Answer:

Part 1) The inequality that describes the relationship between the number of cookies each one of them has is [tex]x^{2} -30x+224\geq 0[/tex]

Part 2) Jessica has at least 2 cookies more than Martha.

Explanation:

Let Jessica has x cookies.

Let Martha has y cookies.

Total cookies they have = 30

Equation forms:

[tex]x+y=30[/tex] or [tex]y = 30-x[/tex]      .....(1)

Each of them ate 6 cookies from their bag.

Cookies left with Jessica = [tex]x-6[/tex]

Cookies left with Martha = [tex]y-6[/tex]

The product of the number of cookies left in each bag is not more than 80.

[tex](x-6)(y-6) \leq 80[/tex]    ....(2)

Substituting [tex]y = 30-x[/tex] in equation (2)

[tex](x-6)(30-x-6) \leq 80[/tex]

=> [tex](x-6)(24-x) \leq 80[/tex]

=> [tex]24x-x^{2}-144+6x \leq 80[/tex]

=> [tex]-x^{2}+30x-144 \leq 80[/tex]

=> [tex]-x^{2}+30x-224 \leq 0[/tex]

Multiplying both sides by -1.

[tex]x^{2} -30x+224 \geq 0[/tex]

Solving this quadratic equation, we get

[tex]x\leq 14[/tex] or [tex]x\geq 16[/tex]

We will take x = 16 (bigger value as Jessica has more cookies)

And y = [tex]30-16=14[/tex]

y = 14

So, Jessica has 16 cookies.

Martha has 14 cookies.

Cookies left in the bag :

Jessica : [tex]16-6=10[/tex] cookies

Martha  : [tex]14-6=8[/tex] cookies

Therefore, Jessica has at least 2 cookies more than Martha.