Solve the word problems using systems.

The sum of two numbers is 842. The difference is 314. Find the numbers.

Answer:

y = -5x + 21

Step-by-step explanation:

The perpendicular slope is opposite of the inverse.  The inverse of 1/5 is 5/1, and the opposite of that is -5/1.

So m = -5.

Then use point-slope form:

y + 4 = -5 (x - 5)

If you wish, convert to slope-intercept form:

y + 4 = -5x + 25

y = -5x + 21

Answer:  

-2x^3 + 2x^(1/2)

Step-by-step explanation:

step one- plug in the values of each in f(x) - g(x)

x^(1/2)-x - (2x^3-×^(1/2)-x) ; g(x) is in parentheses bc we need to distribute the negative

x^(1/2)-x-2x^3 + x^(1/2) + x ; combine like terms (letters with the same exponents) ; the x's cancel, and the x^(1/2) + x^(1/2) combine to form 2x^(1/2); the -2x^3 remains

you should get

-2x^3 + 2x^(1/2)

Answer:

[tex]f(x) - g(x) = 2(\sqrt{x}-x^3)[/tex]

Step-by-step explanation:

We have the functions

[tex]f(x)= x^{\frac{1}{2}}-x[/tex]  and   [tex]g(x) = 2x^3-x^\frac{1}{2}-x[/tex]

The operation [tex]f (x) -g (x)[/tex] is the subtraction of the function f(x) minus the function g(x). Thus

[tex]f(x) - g(x) = x^{\frac{1}{2}}-x -(2x^3-x^\frac{1}{2}-x)[/tex]

Simplifying the expression we have left that:

[tex]f(x) - g(x) = x^{\frac{1}{2}}-x -2x^3+x^\frac{1}{2}+x[/tex]

[tex]f(x) - g(x) = 2x^{\frac{1}{2}}-2x^3[/tex]

[tex]f(x) - g(x) = 2(\sqrt{x}-x^3)[/tex]  Because [tex]x^{\frac{a}{n}} = \sqrt[n]{x^a}[/tex]

To determine the amount of milk needed for 36 servings of pancakes, multiply one and two-thirds cups of milk by the number of servings. This results in a total of 60 cups of milk required.

To find out how many cups of milk are needed for 36 servings of pancakes, when one serving requires one and two-thirds cups of milk, we use multiplication. We can make a conversion factor using our original recipe, likening it to a mathematical relationship or a stoichiometric relationship in chemistry. Here is the step-by-step calculation:

So, for 36 servings of pancakes, you would need 60 cups of milk.

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I got B for the answers

Answer:

( 3 × 2 ) × 7

Step-by-step explanation:

To find the volume of a rectangular prism you have to do

Length × Width × Height

3 × 2 × 7 = 42 yd³

Answer:

$150

Step-by-step explanation:

Given

The graph with speed over speed limit on x-axis and amount of ticket on y-axis. In order to find the answer a person must know how to translate or read graphs.

As it is given in the question that the person is charged based on the extra miles over the speed limit. If the speed limit was 50 mph and the driver was driving at 61 mph, then the number of miles over the speed limit

=> 61-50

=> 11 miles

So, we have to look for 11 on x-axis and then we look for the y-axis's intercept that intersects with 11.

So, in the given graph, the value 11 of x-axis intercepts with the $150 on y-axis.

So the fine will be $150 ..

considering the diagram,the top part is a triangle with the base of 3.2m and height of 2.2m. since the triangle 8s is a right angle triangle. we use Pythagoras theorem to solve for the hypotenus

Final answer:

The length of the wire connecting the tops of two poles of heights 3.8m and 6m, and spaced 3.2m apart is approximately 3.9 meters when calculated using the Pythagorean theorem.

Explanation:

To calculate the length of the wire connecting the tops of two poles of different heights, we can use the Pythagorean theorem.

This theorem states that in a right angle triangle, the square of the length of the hypotenuse (the wire) is equal to the sum of the squares of the lengths of the other two sides (the distances between the tops of the poles and the ground).

Let's denote:

Pole A as the shorter pole with a height of 3.8m

Pole B as the taller pole with a height of 6m

The distance between the two poles as 3.2m

The difference in height between the two poles is 6m - 3.8m, which is 2.2m. Thus, we have a right triangle where one leg is 3.2m (distance between poles) and the other leg is 2.2m (height difference between poles).

Applying Pythagorean theorem:

c² = a² + b²

c² = 3.2² + 2.2²

c² = 10.24 + 4.84

c² = 15.08

c = √15.08

c ≈ 3.9m

Therefore, the length of the wire is approximately 3.9 meters.

Answer:

Step-by-step explanation:

[tex](6)=6\\\\(-6)=-6\neq6\\\\-(6)=-6\neq6\\\\-(-6)=6\\\\(0-6)=(-6)=-6\neq6\\\\(-2)\cdot(3)=-6\neq6[/tex]

The expressions that are equal to 6 are:

                       (6) , -(-6)

We are asked to find the expressions which are equal to 6.

a)

          (6)

We know that on opening the parentheses term if the sign before the parentheses is positive then the number remains the same.

but if the sign before the parentheses is negative then the number gets reversed.

Hence, the number is equal to 6.

b)

         (-6)

The number is equal to -6.

c)

          -(6)

The number is equal to -6.

d)

           -(-6)

The number is equal to 6.

e)

          (0-6)

The number is equal to -6.

f)

    (-2) · (3)

The number is equal to -6.

( We know that the multiplication of a negative and a positive number is always a negative number ).

Answer:

90-73=17

the correct answer is 17

For this case we must find the angle "x" of the figure shown.

If we look at the figure, we have to:

AC equals 90 degrees.

So we have to:

[tex]73 + x = 90[/tex]

We clear the value of "x":

[tex]x = 90-73\\x = 17[/tex]

Thus, the value of "x" is 17 degrees.

Answer:

17 degrees

Option A

ANSWER

The amplitude is 1.6

EXPLANATION

The amplitude is half of the highest value minus the least values.

The highest value on the graph also occurs at 0, which is 5.20

The least value is 2

The amplitude is

[tex] = \frac{5.20-2}{2} = 1.6[/tex]

Therefore the amplitude is 1.6

Answer:

41

Step-by-step explanation:

First, set up the equation (2x+5) + (3x-2)+(3x)+(x)= 57. Add all of the sides together and solve for x. Next, plug in x to 2x+5, and you have your answer. I hope this helps

Answer:

Step-by-step explanation:

[tex]f(x)=3\sqrt{x+3}-6\\\\\text{Domain:}\ x+3\geq0\to x\geq-3\\\\\text{The zero}\to f(x)=0\\\\3\sqrt{x+3}-6=0\qquad\text{add 6 to both sides}\\\\3\sqrt{x+3}=6\qquad\text{divide both sides by 3}\\\\\sqrt{x+3}=2\iff x+3=2^2\\\\x+3=4\qquad\text{subtract 3 from both sides}\\\\x=1[/tex]

Answer:

x=1

Step-by-step explanation:

Given function,

[tex]f(x)=3\sqrt{x+3}-6[/tex]

Since, the zeroes of a function are those input values for which the function gives the output zero,

So, for the zeroes of f(x),

f(x) = 0

[tex]\implies 3\sqrt{x+3}-6=0[/tex]

[tex]3\sqrt{x+3}=6[/tex]      ( Adding 6 on both sides )

[tex]\sqrt{x+3}=2[/tex]        ( Dividing both sides by 3 )

[tex]x+3=4[/tex]                ( Taking square of both sides )

[tex]x = 1[/tex]                   ( Subtracting 3 from both sides )

Hence, the zero of the given function is, x = 1.

First option is correct.

Answer:

Where are the followings

Step-by-step explanation:

A valid FICO credit score ranges from 300 to 850. A score outside this range is not valid. Key components of a FICO score include credit mix and the impact of new credit, both accounting for 10% of the score respectively.

When it comes to determining what is not a valid FICO credit score, it's important to understand that FICO scores range from 300 to 850. Any score that is not within this range would be considered invalid. Components that make up a FICO score include payment history, amounts owed, length of credit history, new credit, and credit mix. Credit mix refers to the variety of credit types you have, such as credit cards, retail accounts, installment loans, finance company accounts, and mortgage loans, and makes up 10% of your FICO score. Regarding new credit, opening a new account can temporarily lower your score because it reduces the average age of your accounts, which also accounts for 10% of your FICO score.

Two common myths are that opening a new retail credit card is always good for your credit score and that it hurts your score to comparison shop for loans. In reality, opening a retail credit card can lower your score initially, though responsibly managing your new credit can eventually have a positive effect. When it comes to loan comparison shopping, FICO provides a grace period for hard inquiries that are related, bundling them into a single inquiry if they occur within a 14 to 45-day span, depending on the type of credit. This is designed to not penalize consumers who are responsibly shopping for the best rates.

Answer:

see explanation

Step-by-step explanation:

1

Given

y - 4 = 5(x + 2) ← distribute parenthesis

y - 4 = 5x + 10 ( add 4 to both sides )

y = 5x + 14 → B

Subtract y from both sides

0 = 5x - y + 14 ( subtract 14 from both sides )

- 14 = 5x - y → C

--------------------------------------------------

2

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 5 and c = 1, thus

y = 5x + 1 → A

Answer:

Slope: 5/3

Y - intercept: -2/3

Step-by-step explanation:

The slope is the coefficient of the x term, so that is 5/3. The y - intercept is the number being added to the x term, which is -2/3.

For this case we have by definition, that the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It is the slope of the line

b: It is the cut point with the "y" axis

We have the following equation:

[tex]y = - \frac {5} {3} x- \frac {2} {3}[/tex]

So we have to:

[tex]m = - \frac {5} {3}\\b = - \frac {2} {3}[/tex]

Answer:

The slope is[tex]- \frac {5} {3}[/tex]and the intersection with "y" is [tex]- \frac {2} {3}[/tex]

Answer:

y = mx+b

Step-by-step explanation:

Answer:

y = mx +b

Step-by-step explanation:

m=slope

b=y-intercept

The simplification of the expression 10.26 - 1.9 x 3.7 + 0.1, using proper order of operations, gives the result of 3.33.

The student's question asks to simplify a mathematical expression. To accomplish this, we use the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

The given equation to simplify is 10.26 - 1.9 x 3.7 + 0.1. First, perform the multiplication: 1.9 x 3.7 = 7.03. Substitute this value into the expression to get 10.26 - 7.03 + 0.1. Then, perform subtraction and addition from left to right. This will result in 3.23 + 0.1 = 3.33. Therefore, the simplified result of the expression 10.26 - 1.9 x 3.7 + 0.1 is 3.33.

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Answer:

1

Step-by-step explanation:

These numbers have no common factors. The only comon factor they have is one. Therefore, the GCF of 117, 19, and 110 is one.

i would think teachers

Answer:

C

Step-by-step explanation:

Given that the 2 triangles are similar then the ratios of corresponding sides are equal.

This enables RT to be found, that is

[tex]\frac{4}6}[/tex] = [tex]\frac{10}{RT}[/tex] ( cross- multiply )

4RT = 60 ( divide both sides by 4 )

RT = 15

Hence

perimeter of ΔRST = 6 + 12 + 15 = 33 units

The perimeter of triangle RST which is similar to triangle MNO is: C. 33 units.

The perimeter of a triangle = sum of all its 3 sides.

Since triangles MNO and RST are similar triangles, then their corresponding side lengths are proportional to each other.

This means that:

MN/RS = MO/RT = NO/ST

Find RT using MN/RS = MO/RT:

4/6 = 10/RT

RT = (10×6)/4

RT = 15 units.

Perimeter of triangle RST = RS + ST + RT = 6 + 12 + 15 = 33 units.

Learn more about the perimeter of a triangle on:

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Answer: x=-16/11

6+11x+10=0

We add all the numbers together, and all the variables

11x+16=0

We move all terms containing x to the left, all other terms to the right

11x=-16

x=-16/11

Answer:

Vertex:

Roots: [tex]x=\frac{5}{3}[/tex] or [tex]x=2[/tex]

Step-by-step explanation:

The given quadratic equation is:

Let [tex]f(x)=3x^2-11x+10[/tex]

We obtain the vertex form by completing the square;

[tex]f(x)=3(x^2-\frac{11}{3}x)+10[/tex]

Add and subtract the square of half the coefficient of x.

[tex]f(x)=3(x^2-\frac{11}{3}x+(-\frac{11}{6})^2+10-3(-\frac{11}{6})^2)[/tex]

This simplifies to

[tex]f(x)=3(x-\frac{11}{6})^2-\frac{1}{12}[/tex]

Hence the vertex is [tex](\frac{11}{6},-\frac{1}{12})[/tex]

We now solve to obtain:

[tex]3(x-\frac{11}{6})^2-\frac{1}{12}=0[/tex]

[tex]3(x-\frac{11}{6})^2=\frac{1}{12})[/tex]

[tex](x-\frac{11}{6})^2=\frac{1}{36})[/tex]

[tex](x-\frac{11}{6})=\pm \sqrt{\frac{1}{36}}[/tex]

[tex]x=\frac{11}{6}\pm \frac{1}{6}[/tex]

[tex]x=\frac{5}{3}[/tex] or [tex]x=2[/tex]

Answer:

22

Step-by-step explanation:

8 - (-14)

keep, change, change

8 + 14 = 22

Answer:

6

Step-by-step explanation:

-14 is smaller than -8.  We subtract -14 from -8, obtaining +14 - 8, or +6.

The positive difference between -8 and -14 is 6.

Answer:

The system of inequalities is

[tex]y\leq x+3[/tex] and [tex]y\leq -2x+3[/tex]

The solution is the shaded green area

Step-by-step explanation:

step 1

Find the equation of the inequality A

The line is solid and goes through the points negative 3, 0, negative 4, negative 1 and is shaded in below the line

Find the slope

(-3,0),(-4,-1)

m=(-1-0)/(-4+3)=1

The equation of the line is y=mx+b

we have

m=1

b=3 ----> the y-intercept (see the graph)

substitute

y=x+3 -----> equation of the solid line A

The equation of the inequality is

[tex]y\leq x+3[/tex] -----> inequality A

step 2

Find the equation of the inequality B

The line is solid and goes through the points 1, 1, 2, negative 1 and is shaded in below the line

Find the slope

(1,1),(2,-1)

m=(-1-1)/(2-1)=-2

The equation of the line is y=mx+b

we have

m=-2

b=3 ----> the y-intercept (see the graph)

substitute

y=-2x+3 -----> equation of the solid line B

The equation of the inequality is

[tex]y\leq -2x+3[/tex] -----> inequality B

therefore

The system of inequalities is

[tex]y\leq x+3[/tex] -----> inequality A

[tex]y\leq -2x+3[/tex] -----> inequality B

The solution is the shaded green area

The graph represents the system of inequalities y >= -x - 3 and y >= -3x + 4. This is concluded by observing the slopes, intercept points, and shading regions.

The system of inequalities represented by the graph you provided can be deduced by the slopes, intercept points, and the regions of shading. Given the information, the solid line that goes through the points (-3, 0) and (-4, -1) can be represented by the equation y >= -x -3. Since the line is solid and the area below the line is shaded, the inequality symbol includes an equal sign which means the line itself is part of the solution.

For the second solid line that goes through the points (1, 1) and (2, -1), it can be represented by the equation y >= -3x + 4. Similarly, because the line is solid and the region below this line is shaded, the inequality symbol includes an equal sign.

Therefore, the system of inequalities that the graph represents is y >= -x - 3 and y >= -3x + 4.

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Answer:

[tex]\large\boxed{\left\{\begin{array}{ccc}y-17z=-15&(a)\\-2y+17z=13&(b)\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x-3y+5z=5&(1)\\4x-5y-7z=-5&(2)\\-6x+7y+2z=-2&(3)\end{array}\right\\\\\\\text{From (1) and (2)}\\\left\{\begin{array}{ccc}2x-3y+5z=5&(1)&\text{multiply both sides by (-2)}\\4x-5y-7z=-5&(2)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-4x+6y-10z=-10\\4x-5y-7z=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad y-17z=-15\qquad(a)[/tex]

[tex]\text{From (1) and (3)}\\\left\{\begin{array}{ccc}2x-3y+5z=5&(1)&\text{multiply both sides by 3}\\-6x+7y+2z=-2&(3)\end{array}\right\\\underline{+\left\{\begin{array}{ccc}6x-9y+15z=15\\-6x+7y+2z=-2\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad-2y+17z=13\qquad(b)[/tex]

Answer:

A, E

Step-by-step explanation:

Remember SOH-CAH-TOA:

Sine = Opposite / Hypotenuse

Cosine = Adjacent / Hypotenuse

Tangent = Opposite / Adjacent

Therefore, we can say:

sin 20° = LN / 8

cos 70° = LN / 8

tan 70° = MN / LN

Only the first and last options are correct.

Answer: Lucie is 8 and her brother is 13

Step-by-step explanation: the only possible way for Lucie to be half her brother's age while being 5 years younger at the same time, is if she's 5 and he's 10. that's how old they were 3 years ago. now you just add 3 to 5 and 10 to find their current ages; 5+3=8 so Lucie is 8, and 10+3=13 so her brother is 13.

                                                             :)

Answer:

 Lucie is 8 and her brother is 13

Step-by-step explanation:

Lucie is 5 years younger than her brother. Three years ago, Lucie was twice younger than her brother.

Let L be the Lucie age

and B be the brothers age

Lucie is 5 years younger than her brother

L= B-5

Three years ago, Lucie age is L-3

brother is B-3

Lucie was twice younger than her brother.

2(L-3)= B-3

Plug in B-5 for L

2(B-5-3)= B-3

2B - 16= B-3

Subtract B from both sides

B - 16 = -3

Add 16 on both sides

B= 13

Age of brother = 13

Age of Lucie = brother -5 = 13-5 = 8

56 students represents 100 % and

X boys represent 34%,

so x= 56•34/100= 19.04 so approximately 19 boys

56-19= 37 girls signed up.

Now 37 girls represent 100% and 31 girls represent x % ,

So x= 31•100/37= 83.78% about 84% of the girls attended

To find the percentage of girls who attended the auditions, calculate the number of boys and girls who signed up, and then determine the percentage of girls who attended. About 83.78% of the girls who signed up for the school play attended the auditions.

The question: 56 students signed up for the school play. About 34% were boys. At the auditions, only 31 girls attended.

Calculate the number of boys who signed up: 56 x 0.34 = 19 boys.

Find the number of girls who signed up: 56 - 19 = 37 girls.

Calculate the percentage of girls who attended auditions: (31 girls / 37 girls) x 100% = 83.78%.

4x - x

If there is a single variable with no number in front you can assume that there is a 1. How I think of it is that all singular variables have an invisible one in front

so...

4x - 1x

Since these are like terms you may subtract them like normal numbers. The only difference is that you'll have to add an x at the end of your answer

4 - 1

3

(REMEMBER to add the x back to the three)

so...

4x - x = 3x

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

[tex]r= 2(cos(\theta) + 3sin(\theta))[/tex]

Step-by-step explanation:

To convert an equation of rectangular shape to polar form use the following equivalences

[tex]x=rcos(\theta)[/tex]

[tex]y=rsin(\theta)[/tex]

[tex]x^2 + y^2=r^2[/tex]

In this case we have the following equation.

[tex](x-1)^2 + (y-3)^2=10[/tex]

First we expanded the expression

[tex](x-1)^2 + (y-3)^2=10\\\\(x^2 -2x +1) +(y^2 -6y + 9) = 10\\\\\\x^2 +y^2 -2x -6y = 10-9-1\\\\x^2 +y^2 -2x -6y = 0[/tex]

Now we know that [tex]x^2 + y^2=r^2[/tex], [tex]x=rcos(\theta)[/tex] and [tex]y=rsin(\theta)[/tex]

So

[tex]r^2 -2rcos(\theta) -6rsin(\theta) = 0\\\\r^2 - 2r(cos(\theta) + 3sin(\theta))=0\\\\r^2 = 2r(cos(\theta) + 3sin(\theta))\\\\r= 2(cos(\theta) + 3sin(\theta))[/tex]

Answer:

3 gallons = 12 quarts

$98.52/12 quarts = $8.21/quart

To find the price per quart of a 3-gallon bucket of paint costing $98.52, divide the total cost by the number of quarts in 3 gallons, which is 12. The price per quart comes out to be approximately $8.21.

To find the price per quart for a bucket of paint that costs $98.52 per 3 gallons, we first need to know the number of quarts in 3 gallons. Since 1 gallon equals 4 quarts, 3 gallons will be equal to 3 × 4 quarts, which is 12 quarts.

Therefore, if a 3-gallon bucket costs $98.52, to find the cost per quart, we need to divide the total cost by the total number of quarts.

So, the equation to find the price per quart would be:

Price per quart = Total cost / Number of quarts

Substituting the given values:

Price per quart = $98.52 / 12

Calculating the above, we find:

Price per quart = $8.21 (rounded to two decimal places)

Thus, the price per quart of the paint is approximately $8.21.