Answer:
3d+9
Step-by-step explanation:
7d + 12 − 4d − 3 = 7d + 12 + − 4d + − 3
Combine Like Terms:
= 7d + 12 + − 4d + − 3
= (7d + − 4d) + (12 + − 3)
= 3d + 9
Hope this helps :-)
The simplified value of the given expression is 3d+9
What is an expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given is an expression, 7d + 12 − 4d − 3, we need to simplify it,
7d + 12 − 4d − 3
Combine Like Terms:
= 7d + 12 + − 4d − 3
= (7d + − 4d) + (12 + − 3)
= 3d + 9
Hence, the simplified value of the given expression is 3d+9
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Judy planted vegetables on a piece of land. The land is in the right-angled triangular shape. Given the longest side of the land is y metre. The other two sides of the land are 2x metre and (2x+6) metre respectively. He fenced the land with 72 metres of barbed wire. Find the length, in metre , of each side of the land.
We know that the perimeter is 72 meters, so we have
[tex] y+2x+(2x+6)=72 \iff y+4x+6=72 \iff y=-4x+66 [/tex]
Now we can use the pythagorean theorem: the sum of the squares of the legs is the square of the hypotenuse:
[tex] (2x)^2+(2x+6)^2 = y^2 \iff (2x)^2+(2x+6)^2 = (-4x+66)^2 [/tex]
Expand the squares to get
[tex] 8 x^2 + 24 x + 36 = 16 x^2 - 528 x + 4356 [/tex]
Bring everything to the right hand side to get
[tex] 8 x^2 - 552 x + 4320 = 0 [/tex]
Divide both sides by 8:
[tex] x^2 - 69x + 540 = 0 [/tex]
This equation has solutions [tex] x=9,\ x=60 [/tex]
This solutions would yield the following side lengths:
[tex] x=9\implies\begin{cases} 2x = 18\\2x+6=24\\-4x+66=30\end{cases}[/tex]
[tex] x=60\implies\begin{cases} 2x = 120\\2x+6=126\\-4x+66=-174\end{cases}[/tex]
Since we can't have negative side lengths, we can only accept the solution x=9.
In fact, you can check that 18,24,30 is a pythagorean triplet, i.e.
[tex] 18^2+24^2=30^2 [/tex]
PLS HURRY!!
The graph represents Kara's trip. Which statement is true?
A) Between 10 and 20 minutes Kara's car was stopped.
B) Kara's highest speed was between 30 and 35 minutes.
C) Kara's highest speed was between 25 and 30 minutes.
D) Between 5 and 10 minutes Kara's speed was decreasing.
Answer:
B) Kara's highest speed was between 30 and 35 minutes.
Step-by-step explanation:
A zero slope (horizontal line) means a stopped car with zero speed.
The higher the slope, the steeper the line, the higher the speed.
Let's look at the options.
a) The car was stopped between 10 and 15 minutes, not 20. False.
b) Between 30 and 35 min, the graph shows the steepest slope, so this statement is True.
c) False, since here slope is not steepest.
d) Between 5 and 10 minutes, the graph is a straight line, so speed was constant. False.
the number of units in the perimeter of a square is less than or equal to the number of square units in the area of the square which side length of a square provides a counterexample?
Answer:
2
Step-by-step explanation:2+2
The side lengths of a square in which the perimeter of a square is greater than its area is 1 unit, 2 units, and 3 units.
What is a square?A square is a 2D figure of which all sides are equal.
We know that the perimeter of a square is the sum of the lengths of all the sides and the area of a square is (side)².
Assuming a square has a side length of 4 units.
Therefore the perimeter of the square is 4×side = 4×4 = 16 units.
Now the area of the square will be (4)² = 16 sq units.
Now assuming the side length of the square is 2 units.
The area of the square is (2)² = 4 units and the perimeter is (2×4) = 8 units.
∴ The side length which provides a counter-example is 2 units.
Basically, we have to determine the numbers that when multiplied by 4 are greater than it's square such numbers are 1, 2, 3.
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One number is 8 less than a second number. Twice the second number is 52 more than 5 times the first. Find the smaller of the two numbers.
Let x and y be the two numbers.
x = y - 4
2y = 5x - 10
solve the system of equations:
2y = 5(y - 4) - 10
2y = 5y - 20 - 10
-3y = -30
y = 10
x = 10 - 4 = 6
I will try my best...
Let x and y be the two numbers.
x = y - 4
2y = 5x - 10
Now, we solve the system of equations:
2y = 5(y - 4) - 10
2y = 5y - 20 - 10
-3y = -30
So...
y = 10
x = 10 - 4 = 6
Eighteen oranges are packaged in 3 containers. How many oranges are packaged in 7 containers?
Answer,
42
Explanation,
18/3 = 6
6 x 7 = 42
Hope this helps :-)
For his Science project, Timor has 1 pea plant and 3 bean plants. He measures the heights of the plants once a week. This week's data are shown in the table. Which expression will help him find the average height of the bean plants this week?
A) (10 + 12 + 11 + 20) ÷ 4
B) (12 + 11 + 20) × 3
C) (12 + 11 + 20) – 3
D) (12 + 11 + 20) ÷ 3
Answer:
D.) (12 + 11 + 20) ÷ 3
Step-by-step explanation:
One of Mr. Edward's students answered the following problem on her homework.
Her Answer-17.06 x 25.1 = 42.806
SHORT ANSWER
Explain to Mr. Edward whether or not the student got the question correct, and why.
Answer in at least 2 complete sentences.
Answer:
She did not get the correct answer because she did not put the decimal in the correct spot. The correct answer should be 428.206.
Step-by-step explanation:
17.06×25.1=428.206
what is the GCF of 45 and 70
GCF of 45 and 70 is 5
What is the measure of angle 1?
SOLUTION: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures. Question 345899: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures.
3x-1/2y +2 2/3y -5/6x
The question is about simplifying an algebraic expression, specifically 3x - 1/2y + 2 2/3y - 5/6x. This can be achieved by first consolidating like terms and performing multiplication and addition/subtraction to get the simplified expression 2 1/6x + 2 1/6y.
Explanation:This question appears to be about simplifying algebraic expressions. The expression at hand is 3x-1/2y +2 2/3y -5/6x. To simplify this, you should first consolidate your like terms. The 'like terms' in this case, are the X terms (3x and -5/6x) and the Y terms (-1/2y and +2 2/3y).
Secondly, perform the operations necessary for the terms – which involve multiplication and addition/subtraction. Thus, the sum of 3x and -5/6x is 2 1/6x (or 2.167x if we want it in decimal form). Similarly, the sum of -1/2y and +2 2/3y is 2 1/6y (or 2.167y in decimal form).
Finally, to complete the simplification, you should combine these totals. The simplified algebraic expression for 3x - 1/2y + 2 2/3y - 5/6x is therefore 2 1/6x + 2 1/6y.
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If h(x)=x-9, find h(13)
If you plug in h, the answer would be 13-9 which is 4.
h(13)=13-9=4,inlocuiesti x cu 13 si calculezi.
PQ=RQ?
Someone who is smart in math help me.
Answer:
a=43
Step-by-step explanation:
90+47=137 180-137=43
find the perimeter....
The perimeter is adding all the outside edges together:
4 + 1 +4 +1 + 3 + 1 = 14 cm.
Solve for x. x+23=−16 Enter your simplified answer in the box.
Answer:
x=-39
Step-by-step explanation:
subtract 23 from both sides
-16 - 23= -39
therefore x=-39
If y = 7x, what happens to x when y is increased by 5 times its original value?
A) x decreases 5 times its original value
B) x increases to 11/5 its original value
C) x also increases 5 times its original value
D) x decrease to 4/5 of its original value
Answer:
C) x also increases 5 times its original value
35/5=7
70/10=7
Step-by-step explanation:
When rounded to the nearest hundred I become 500. What numbers could I be
it could be 460-490 to round to 500
Answer:
450-549
Step-by-step explanation:
you can round up or down
Statistical questions will have A. only one correct answers., B.a variety of answers., C. fewer than three answers., D. no answer.
the answer is B. hope i helped!
What are the steps to solving systems of equations and inequalities
Step 1: Line up the equations so that the variables are lined up vertically.
Step 2: Choose the easiest variable to eliminate and multiply both equations by different numbers so that the coefficients of that variable are the same.
Step 3: Subtract the two equations.
Step 4: Solve the one variable system.
Step 5: Put that value back into either equation to find the other equation.
Step 6: Reread the question and plug your answers back in to check.
Final answer:
To solve systems of equations, one can use methods like graphing, substitution, or elimination, and check the solution by substituting it back into the original equations. For inequalities, graph the lines, decide where to shade by testing a point, and find the overlap of the shaded regions for the solution.
Explanation:
Steps to Solving Systems of Equations and Inequalities
The process of solving systems of equations and inequalities involves several steps. To solve a system of equations, you can use methods such as graphing, substitution, or elimination. When solving inequalities, additional considerations such as shading the solution region are necessary. Here's a step-by-step approach for both equations and inequalities:
For Equations:
Choose a suitable method (graphing, substitution, elimination).
Apply the selected method to find the point of intersection, which represents the solution to the system.
Check your solution by substituting it back into the original equations.
For Inequalities:
Graph the lines or curves that represent the inequalities, using dashed or solid lines.
Determine where to shade the region by testing a point not on the line.
Find the overlap of the shaded regions if there is more than one inequality.
It's important to practice these steps with different systems to become proficient in solving them. Remember to pay close attention to the signs of the inequalities when graphing and shading the solution regions.
The table shows the five most populated countries in the world. How many times as many people live in China then in the United States? Round to the nearest 10th if necessary.
The answer is about 4 times as many people live in China then in the United States
There are 4.4 times more people living in china than united states as the definition of ratio says "the quantitative relation between two amounts showing the number of times one value contains or is contained within the other".
What is ratio?The indicated quotient of two mathematical expressions is referred to as a ratio. A/B stands for an ordered pair of numbers where B does not equal 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Here,
To find that how many times as many people live in China then in the United States, we need to divide the population of china by the population of united states.
let x be the value of how many times as many people live in China then in the United States,
so, the population of china=1.325 billions
the population of united states=0.304 billions
x=1.325/0.304
x=4.356
x≈4.4 times
As stated in the definition of ratio, "the quantitative relation between two amounts showing the number of times one value contains or is contained within the other," there are 4.4 times as many people living in China as there are in the United States.
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how do I solve this?
Hey there!!
Multiply both the sides with 4/3.
Then we get
x = 5 ^ 4/3
x = 8.5 ( avg. )
Hope it helps!
Use properties to rewrite the given equation. Which equations have the same solution as 3/5x +2/3 + x = 1/2– 1/5x? Check all that apply.
a. 8/5x+2/3=1/2-1/5x
b. 18x + 20 + 30x = 15 – 6x
c. 18x + 20 + x = 15 – 6x
d. 24x + 30x = –5
e. 12x + 30x = –5
we have
[tex]\frac{3}{5}x+ \frac{2}{3}+x=\frac{1}{2}-\frac{1}{5}x[/tex]
Combine like terms in both sides
[tex](\frac{3}{5}x+ x)+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]
we know that
[tex](\frac{3}{5}x+ x)=(\frac{3}{5}x+ \frac{5}{5}x)=\frac{8}{5}x[/tex]
substitute in the expression above
[tex]\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]-----> equation A
Multiply equation A by [tex]5*3*2=30[/tex] both sides
[tex]30*(\frac{8}{5}x+\frac{2}{3})=30*(\frac{1}{2}-\frac{1}{5}x)[/tex]
[tex]48x+20=15-6x[/tex] ---------> equation B
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]48x+6x=15-20[/tex]
[tex]54x=-5[/tex] ---------> equation C
Solve for x
[tex]x=-\frac{5}{54} =-0.09[/tex]
We are going to proceed to verify each case to determine the solution.
Case a) [tex]\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]
the case a) is equal to the equation A
so
the case a) have the same solution that the given equation
Case b) [tex]18x+20+30x=15-6x[/tex]
Combine like terms in left side
[tex](18x+30x)+20=15-6x[/tex]
[tex](48x)+20=15-6x[/tex]
the case b) is equal to the equation B
so
the case b) have the same solution that the given equation
Case c) [tex]18x+20+x=15-6x[/tex]
Combine like terms in left side
[tex](18x+x)+20=15-6x[/tex]
[tex](19x)+20=15-6x[/tex]
[tex]19x+6x=15-20\\25x=-5\\x=-0.20[/tex]
[tex]-0.20\neq -0.09[/tex]
therefore
the case c) not have the same solution that the given equation
Case d) [tex]24x+30x=-5[/tex]
Combine like terms in left side
[tex]54x=-5[/tex]
the case d) is equal to the equation C
so
the case d) have the same solution that the given equation
Case e) [tex]12x+30x=-5[/tex]
Combine like terms in left side
[tex]42x=-5[/tex]
[tex]x=-5/42=-0.12[/tex]
[tex]-0.12\neq -0.09[/tex]
therefore
the case e) not have the same solution that the given equation
therefore
the answer is
case a) [tex]\frac{8}{5}x+\frac{2}{3}=\frac{1}{2}-\frac{1}{5}x[/tex]
case b) [tex]18x+20+30x=15-6x[/tex]
case d) [tex]24x+30x=-5[/tex]
Answer:
Option (a) , (b) and ( d) are equivalent to given expression [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]
Step-by-step explanation:
Given equation : [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]
We have to use properties to rewrite the given equation and check which are correct from thee given options,
Consider the given equation,
[tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]
Applying commutative property of addition , [tex]a+b=b+ a[/tex]
Equation becomes,
[tex]\frac{3}{5}x+x+\frac{2}{3}= \frac{1}{2}- \frac{1}{5}x[/tex]
Now adding x terms on right side , we get,
[tex]\frac{3+5}{5}x+\frac{2}{3}= \frac{1}{2}- \frac{1}{5}x[/tex]
[tex]\Rightarrow \frac{8}{5}x+\frac{2}{3}= \frac{1}{2}- \frac{1}{5}x[/tex]
Thus, obtained option (a).
Again consider given equation ,
[tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]
Taking LCM both sides, we get,
[tex]\frac{9x+10+15x}{15}= \frac{5-2x}{10}[/tex]
Solving , we get,
[tex]\frac{9x+10+15x}{3}= \frac{5-2x}{2}[/tex]
Cross multiply, we get,
[tex]2\times (9x+10+15x)=3\times(5-2x)[/tex]
[tex]18x+20+30x=15-6x[/tex]
Thus, obtained option (b).
Taking like terms together,
[tex]18x+6x+30x=15-20[/tex]
[tex]\Rightarrow 24x+30x=-5[/tex]
Thus, obtained option (d).
Thus, Option (a) , (b) and ( d) are equivalent to given expression [tex]\frac{3}{5}x+\frac{2}{3}+x= \frac{1}{2}- \frac{1}{5}x[/tex]
Algebra Word Problem, 9th Grade, Station 2, please help!
ANSWER
ANSWER TO QUESTION 1.
If you give [tex]x[/tex] surfing lessons, then you will earn $ [tex]25x[/tex]
If you are charged $200 for using the place, then your profit will reduce by $200.
The profit function is given by
[tex]P(x)=25x-200[/tex] dollars.
The y-intercept is [tex]-200[/tex]. It is negative because it is a cost which is a liability. So it does not add to your profit.
ANSWER TO QUESTION 2.
The slope is [tex]25[/tex]. It is positive because as the number of hours increases, the profit earned also increases. In other words there is a direct relation between the number of hours worked and the profit earned.
ANSWER TO QUESTION 3.
The slope intercept form is when an equation is written in the form;
[tex]y=mx+c[/tex],
where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept. The profit function in slope intercept form is
[tex]P(x)=25x-200[/tex]
ANSWER TO QUESTION 4.
If you break even, then the difference between the revenue and cost is zero. So we equate the profit function to zero.
[tex]25x-200=0[/tex]
[tex]25x=200[/tex]
[tex]x=8[/tex]
Therefore you need to give 8 different lessons to break even.
ANSWER TO QUESTION 5.
If you give 20 lessons, the [tex]x=20[/tex]. We need to substitute
[tex]x=20[/tex] in to the profit function to calculate the profit made after 20 lessons.
[tex]P(20)=25(20)-200[/tex]
[tex]P(20)=500-200[/tex]
[tex]P(20)=300[/tex].
ANSWER TO QUESTION 6.
If the new price is $75, then the new profit function becomes
[tex]P(x)=75x-200[/tex]
ANSWER TO QUESTION 7.
To find the number of lessons that lets you break even, we equate the new profit function to zero.
[tex]75x-200=0[/tex]
We solve for x by adding 200 to both sides of the equation.
[tex]\Rightarrow 75x=200[/tex]
We now divide through by 75
[tex]\Rightarrow x=\frac{200}{75}[/tex]
[tex]\Rightarrow x=2\frac{2}{3}[/tex]
Therefore you would have to 2\frac{2}{3} lessons to break even. That is approximately 3 lessons.
ANSWER TO QUESTION 8.
If you give 20 lessons and we want to find the profit you made with this new profit function, then we have to plug in [tex]x=20[/tex] in to [tex]P(x)=75x-200[/tex].
That is,
[tex]P(20)=75(20)-200[/tex]
[tex]P(20)=1500-200[/tex]
[tex]P(20)=1300[/tex] dollars
Refer to your math writing journal file named "Lines and Angles." What real-world examples did you describe for the three ways in which two lines may be related?
Answer:
Railway lines are example of parallel linesThe floor and the walls of a room are example of perpendicular linesTwo roads crossing at a signal can be termed as example of intersecting linesStep-by-step explanation:
The lines can be related in following three ways
Lines can be parallelLines can be perpendicularLines can be intersecting at an angle other than 90.Now three real life examples of above three scenarios are described below:
Railway lines are example of parallel linesThe floor and the walls of a room are example of perpendicular linesTwo roads crossing at a signal can be termed as example of intersecting linesAnswer:
1. KI
2. HI and DF
3. 8
4. 4 and 7
Step-by-step explanation:
For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. The proportion of wolves that are neither female nor hunt in medium-sized packs is
Thus, the proportion of female wolves that do not hunt in medium sized packs is 4/10 or 0.4. When expressed as percent, this is 40%.
in order to obtain energy animals must do what?
A. consume food
B. produce food
C. make new cells
D. get sunlight
Answer:
A. consume food
Step-by-step explanation:
The food they eat has energy. One eaten the energy the food had is passed along to the animal.
Which graph passes the vertical line test?
There are no graphs shown, but the vertical line test is something you can use to find out if a function works. If you make a vertical line anywhere on one of the graphs, it should only pass through one point. For example, a regular straight line almost always passes the vertical line test. If it's a sideways parabola, it will not.
Jasmine wants to make a double batch of muffins. The original recipe calls for 3/4 cup of sugar, how much sugar should she use?
URGENT! PLEASE HELP NOW!
Jasmine is 23 years old. Three years less, 20, half is 10. If I am correct, George is 10.
What is the probability of drawing 1 red marble out of a bag containing 4 red marbles 3 green marbles 2 blue marbles and 1 purple marbles?
4/10 Probability
-Hiadamcom
Answer:
2/5
Step-by-step explanation:
4 ÷ 10= 2/5
(4 ÷10 is for 4/10 which is red marbles to the total marbles)
The probability of the compliment is 3/5(for edge students)
Literal Equations Answer 5 and Ill mark brainliest!
3.- 5x-6=y
First you leave the variable alone along with 5 and you pass to the other side number 6 with the opposite sign
5x=y+6
then as 5 is multiplying you pass it dividing
y+6 x= 5
4.-2x-3y=8
First you leave the variable with 3 alone and you pass the 2x to the other side subtracting
-3y=8-2x
Then as -3 is multiplying you pass it dividing
y= 8-2x/-3
12.-7x-y=14
First you leave the variable with the 7 alone and you pass the -y to the other side adding
7x=14+y
then as 7 is multiplying you pass it dividing
x=14+y/7
18.-12x-4y=20
First you leave the variable y with the -4 alone and you pass the 12x to the other side subtracting
-4y=20-12x
Then as -4 is multiplying you pass it dividing
y= 20-12x/-4
20.- R-C/N=P
First you leave the R and the C alone and as N is dividing you pass it multiplying
R-C=PxN
Then as C is subtracting you pass it adding
R= (PxN)+C
I haven't done these types of problems in forever, so I did a few of the easier ones before I went onto a few of the harder ones. Sorry if 20 is incorrect, I wasn't too sure.