The perimeter of a triangle is 59 cm. The first side is 7 cm shorter than the second side. The third side is 4 cm less than twice the length of the first side. Find length of each side
Given:
The perimeter of a triangle is 59 cm.
The first side is 7 cm shorter than the second side.
The third side is 4 cm less than twice the length of the first side.
To find:
The length of each side.
Solution:
Let x be the second side.
Then, according to the question,
First side = x-7
Third side = 2(x-7)-4
Perimeter of a triangle is the sum of all of its sides.
[tex](x-7)+x+(2(x-7)-4)=59[/tex]
[tex]x-7+x+2x-14-4=59[/tex]
[tex]4x-25=59[/tex]
Add 25 on both sides.
[tex]4x=59+25[/tex]
[tex]4x=84[/tex]
Divide both sides by 4.
[tex]x=21[/tex]
Now,
First sides =21 - 7=14 cm
Second side = 21 cm
Third side = 2(14)-4 = 24 cm
Therefore, the three sides of triangle are 14 cm, 21 cm and 24 cm respectively.
2 pts
Question 3
Select all parts from the expression above that represents a constant term.
-4.9
-4.9t?
1.8
22
22t
Which ones are constant terms pls help
40.5g of sugar is needed to make 5 cakes. How much sugar is needed for 8 cakes?
Answer:
64.8g
Step-by-step explanation:
First you would divide 40.5 by five which would equal 8.1 ; 8.1 resembles 8.1g of sugar per cake. So, 8.1 times 8 cakes would be 64.8g of sugar needed for 8 cakes.
simplify the square root of 4x^6
Answer:
2x^3
Solution
You simplify to the lowest value possible 4x^6
2x^3
6. Frank's Fish Washing Service charges a base fee to wash your fish plus a charge per
minute. The table shows the total cost, c, and the number minutes it took to wash
the fish, m. Which equation represents this situation?
o
y = 3x + 8
of Minutes, m
8
10
12
14
Total Cost (S),
30
36
42
48
y = -x + 8
3
O
y = 3x + 6
O
y =
1
-x+6
Answer:
C
Step-by-step explanation:
If you are doing a gift exchange, and everyone has to spend at least 10 dollars but less than 20 dollars, what inequality represents the situation
Answer:
10≥x<20
Step-by-step explanation:
Slope review
PROBLEM : What is the slope of the line whose equation has the following solutions? Give an exact number.
Solution: x = -2.5 y= 0.5
Solution: x=2 y = 2
The slope is:
To find slope, we must use the slope formula*.
[tex]m = \frac{2 - 0.5}{2 - (-2.5)} = \frac{1.5}{4.5}[/tex]
The slope is 1.5/4.5.
What is the quotient of -3/8 And -1/3?
Answer:
Actually, I didn't get your question, is it -3/8÷ -1/3 or -1/3÷ -3/8?
If it is -3/8÷ -1/3, the answer will be 9/8
But if is -1/3÷ -3/8, the answer will be 8/9
Step-by-step explanation:
-3/8÷ -1/3
= -3/8× 3/-1
= -9/-8
= 9/8
If your question is -1/3÷ -3/8, the answer is 8/9 in the same way.
how do I work this out, I've tried
[tex] \frac{6}{4} = \frac{k \times - 4}{ - 4} [/tex]
and that gave me
[tex] \frac{1}{ - 1.5} x[/tex]
Answer:
The required answer is [tex]y=-\mathbf{\frac{3}{2}}x\\[/tex]
Step-by-step explanation:
We are given that value of x and y vary directly so , if two values vary directly we can write
y∝x
y=kx
Now, we are given x=-4 and y=6 and we have to fill in the blank. We actually have to find value of k i.e y=____x . Yhe blanks must be filled by value of k because y=kx
Using values of x and y i.e x=-4 and y=6 to find value of k
[tex]y=kx\\6=k(-4)\\Divide \ both \ sides \ with \ -4\\\frac{6}{-4}= \frac{k(-4)}{-4} \\k=\frac{-3}{2}[/tex]
The value of k is [tex]\mathbf{\frac{-3}{2}}[/tex]
So, the required answer is [tex]y=-\mathbf{\frac{3}{2}}x\\[/tex]
Write the sentence as an inequality.
A number x is greater than 3
The inequality is
Answer:
X > 3
Step-by-step explanation:
The sentence as an inequality will be x > 3.
It is given that a number x is greater than 3.
We have to represent the sentence as an inequality.
What do you mean by inequalities ?
Inequalities are the expressions in which both sides are not equal and the equal sign in between is replaced by less than , greater than, etc.
As per the question ;
A number x is greater than 3.
So ,
Number is x.
and
It is greater than 3
i.e.,
we need to use a sign of greater than to represent the inequality i.e., > sign.
So ,
The sentence as an inequality can be written as ;
x > 3.
Thus , the sentence as an inequality will be x > 3.
To learn more about inequalities click here ;
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Solve 5.4p+13.1=−2.6p+3.5 . Check your solution.
p= __
5.4p +13.1 = −2.6p+3.5 .
5.4p + 2.6p = 3.5 -13.1
8.0p = -9.6
p = -9.6 / 8
p = -1.2
What is the value of x?
X=
Step-by-step explanation:
[tex]{:}\longrightarrow[/tex][tex]\sf 13x-12=7x-6 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 13x-7x=-6+12 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 6x=6 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x={\dfrac{6}{6}}[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf x=1 [/tex]
please answer this and don't do it for the points
Select the correct answer.
Which pair of statements correctly compares the two data sets?
А.The difference of the means is 1. This value is less than half of the mean absolute deviation of either data set.
B.The difference of the means is 1. This value is more than half of the mean absolute deviation of either data set.
C. The difference of the means is 1. This value is 1 times the mean absolute deviation of either data set.
D. The difference of the means is 1. This value is 2 times the mean absolute deviation of either data set.
Answer: B?
Step-by-step explanation:
Answer:
Go for B
Step-by-step explanation:
is 2.6666666667 a rational number
Answer:
No.
Step-by-step explanation:
I believe that the number above is irrational, because it repeats.
A store charges 5.5 % sales tax on all items. If an item costs d dollars before tax, which expression represents the total cost of the item, in dollars and cents, after tax?
Answer: d + 0.055d or 1.055d
Step-by-step explanation:
Cost of item = d
Sales tax percent = 5.5%
Total cost = Cost of item + Sales tax
= d + (5.5% × d)
= d + (5.5/100 × d)
= d + (0.055 × d)
= d + 0.055d
= 1.055d
Therefore, the expression that represents the total cost of the item, in dollars and cents, after tax will be:
d + 0.055d or 1.055d.
Andrea has $18 to spend. She spent $6.50, including tax, to buy a notebook. She needs to save $5.75, but she wants to buy a snack. If candy bars cost $1.15 per package including tax, what inequality would show the maximum number of packages that Andrea can buy? Solve your inequality by showing your work and steps. Please help
Answer: total cost of the stuff she buys ≤ 18 since she only has 18 dollars to buy stuff
Step-by-step explanation:
let's add up the cost of the stuff she buys:
- a flat cost of $6.50
- a savings of $5.75 (she's technically not spending money but we can count this as part of her expenses since it's taking away from the 18 dollars)
- some number (x) candy bars. if each candy bar costs $1.15 then the money she spends on candy bars is $1.15
with that being said:
6.50 + 5.75 + 1.15x ≤ 18
solve for x
since we are talking about whole # candy bars, if you get a decimal from this, round down to the nearest whole #
Answer:
Andrea can buy 5 candy bars.
Step-by-step explanation:
First to solve this we will subtract 6.50 from 18 because Andrea already spent that money. Then we must subtract 5.75 from 18 because Andrea can't spend that money. All the subtracting equals 5.75. After that we can divide the remaining money by 1.15 to see how many candy bars we can buy which equals 5. Finally the answer is that Andrea can buy 5 candy bars.
Using the periodic table, choose the more reactive nonmetal.
Si or S
Answer:
S
Step-by-step explanation:
S is closer to the top right of the table, which is a generally good rule for determining reactivity of NONMETALS. METAL reactivity increases to the bottom left.
Samir is getting balloons for his mother's birthday party. He wants each balloon string to be 9 feet long. At the party store, string is sold by the yard. If Samir wants to get 59 balloons, how many yards of string will he need?
Answer:
177 yards
Step-by-step explanation:
3 feet - 1 yard, so we have 3 yards for each balloon.
He wants 59 balloons, so 59 x 3 = 177
#8 linear inequality in two variables is shown below. -4y <-12. Which
graph would represent the solution set of linear inequality? (SOLVE FOR
Y!)
Can someone help explain it!!!
Answer:
J
Step-by-step explanation:
Step 1: solve for y
Step 2: graph y, use dashed line
Step 3: Shade in solutions, here y>3 so everything bigger then 3 is a solution.
Give 3 examples of integers which are greater than −2
Answer: -1 would be greater than negative two, along with 20, 1000.
-2 is a negative number, so any number that is -1 or higher is greater than -2
Answer:
1,2,3
Step-by-step explanation:
Aden spent $10 on a mug and then sold it, making 20% profit, how much did he sell the mug for
Answer: $2
Step-by-step explanation: 20 percent of 10 is 2
Hope I did this right
The selling cost of the mug is the amount of $12.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
For example, If Misha obtained a score of 57% on her exam, that corresponds to 67 out of 100.
We have been given that Aden spent $10 on a mug and then sold it, making a 20% profit.
The original cost of the mug is $10.
The selling cost of the mug = original cost + 20% of the original cost
The selling cost of the mug = $10 + 20% of $10
The selling cost of the mug = 10 + (20/100)10
The selling cost of the mug = 10 + 0.20 × 10
The selling cost of the mug = 10 + 2
The selling cost of the mug = $12
Therefore, the selling cost of the mug is the amount of $12.
Learn more about the percentages here:
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#2: Solve the linear system below using the elimination method. Type your
answer as an ordered pair in the form (#,#). *
5x + 7y = 33
11x + 7y = 39
+
The given linear system is:
[tex]\displaystyle \left \{ {{5x+7y=33} \atop {11x+7y=39}} \right.[/tex]
The question is asking to solve using elimination. When eliminating, you can either eliminate x or y. In this system, y is much easier to eliminate. The y variable in both equations are 7y. To eliminate, one of them has to be negative, so multiply one of the equations by -1.
I will be multiplying the second equation by -1.
[tex]\displaystyle (11x + 7y = 39) \times -1 = -11x-7y=-39[/tex]
Rewrite the system:
[tex]\displaystyle \left \{ {{5x+7y=33} \atop {-11x-7y=-39}} \right.[/tex]
Subtract:
[tex]5x+7y=33\\-11x-7y=-39[/tex]
[tex]5x-11x=33-39\\-6x=-6[/tex]
Lastly, you need to leave the variable x alone. The variable is currently -6x or -6 times x. To remove it, you need to do the opposite of it, which is dividing by -6.
[tex]\displaystyle \frac{-6x}{-6} =\frac{-6}{-6}[/tex]
[tex]\displaystyle x=1[/tex]
Now that you have the value of x, substitute it into one of the equations to find y. I will be substituting it into the first equation.
[tex]5x+7y=33 \rightarrow 5(1)+7y=33[/tex]
Open the parentheses and multiply:
[tex]5+7y=33[/tex]
Move 5 to the other side to leave the variable alone:
[tex]5+7y-5=33-5[/tex]
You will be subtracting since you're "removing" it by doing the opposite of it.
[tex]7y=28[/tex]
Lastly, divide both sides by 7 to leave y alone.
[tex]\displaystyle \frac{7y}{7} =\frac{28}{7}[/tex]
[tex]y=4[/tex]
[tex]\displaystyle (x,y) \rightarrow (1, 4)[/tex]
The answer is (1, 4).
Answer:
(1, 4)
Tbh this question was a bit of a challenge for me but hopefully it helps ya.
Step-by-step explanation:
First, let's solve for y. So we have to eliminate the x values.
(5x + 7y = 33 ) *11
(11x + 7y = 39) *-5
___________
55x + 77y = 363
-55x -35y = -195 This eliminates the x value.
42y = 168 Divide both sides by 42 to isolate y: 168/42= y = 4
Now let's solve for x.
(11x + 7y = 39) *7
(5x + 7y = 33 ) *-7
___________
77x + 49y = 273
-35x -49y = -231 This cancels out the y values, which leaves 42x = 42
x = 1 and y = 4, so the answer is (1, 4)
RootIndex 3 StartRoot StartFraction x cubed Over c y Superscript 4 Baseline EndFraction EndRoot = StartFraction x Over 4 y (RootIndex 3 StartRoot y EndRoot) EndFraction
Answer:
C. c = 64
Step-by-step explanation:
The question is incomplete. Here is the complete question.
What value of c makes the equation true? Assume x greater-than 0 and y greater-than 0
RootIndex 3 StartRoot StartFraction x cubed Over c y Superscript 4 Baseline EndFraction EndRoot = StartFraction x Over 4 y (RootIndex 3 StartRoot y EndRoot) EndFraction
c = 12
c = 16
c = 64
c = 81
Given the function;
[tex]\sqrt[3]{\dfrac{x^3}{cy^4} } = \dfrac{x}{4y\sqrt[3]{y} }[/tex]
We are to find the value of c from the expression.
Step 1: Take the cube of both sides;
[tex](\sqrt[3]{\dfrac{x^3}{cy^4} } )^3= (\dfrac{x}{4y\sqrt[3]{y} })^3\\\dfrac{x^3}{cy^4} = \dfrac{x^3}{(4y)^3(\sqrt[3]{y} )^3}\\\dfrac{x^3}{cy^4} = \dfrac{x^3}{(64y^3)(y)}\\\\\dfrac{x^3}{cy^4} = \dfrac{x^3}{64y^4}\\[/tex]
Step 2: compare the denominator of both sides of the equation;
[tex]\dfrac{x^3}{cy^4} = \dfrac{x^3}{64y^4}\\\\On \ comparing;\\\\cy^4 = 64y^4\\[/tex]
Step 3: Divide both sides by y₄
[tex]\dfrac{cy^4}{y^4} = \dfrac{64y^4}{y^4}\\c = 64\\[/tex]
Hence the value of c is 64. Option C is correct
Answer:
C is the anwser
Step-by-step explanation:
my bf told me to pick c, so therfore it is the right anwser. lol no but fr i did get it right on edge
If solving a system of linear equations by elimination or substitution I get that 2=3, it means (check all that apply)
If the system of equations is 2 linear equations in 2 variables, there is infinity number of solutions
If the system of equations is 3 linear equations in 3 variables, there is infinity number of solutions
If the system of equations is 2 linear equations in 2 variables, the system has no solutions
If the system of equations is 3 linear equations in 3 variables, the system has no solutions
Answer:
If I get 2=3 in solving the system, it means the following:
If the system of equations is 2 linear equations in 2 variables, the system has no solutions If the system of equations is 3 linear equations in 3 variables, the system has no solutionsStep-by-step explanation:
The solution of linear system of equations implies that a point has to be found that holds true on all equations involved.
The system may consist of two equations involving two unknowns or may consist of three equation with three unknowns.
When a system of equation has no solution, the variables are removed in solving the equations and we get an equation or values in the form.
constant = constant
So,
If I get 2=3 in solving the system, it means the following:
If the system of equations is 2 linear equations in 2 variables, the system has no solutions If the system of equations is 3 linear equations in 3 variables, the system has no solutionsSolve the system using the elimination method. - Which one should I do first
3x-4y+z=-5
6x-4y+z=1
x+y+z=6
Answer:
first equation and second equation
Step-by-step explanation:
it is more easier because both of them have the same y
Answer:
Use equation (1) and equation(2) and eliminate 4y+z
Step-by-step explanation:
3x-4y+z=-5 ...(1)
6x-4y+z=1 ...(2)
x+y+z=6 ...(3)
First, you find the equation that you can use the elimination method on;
there are multiples of them.
However, I would use equation (1) and equation(2) and eliminate 4y+z :
3x-4y+z=-5
- 6x-4y+z=1
-3x=-6
x=2
As you can see, both the terms with y and z are eliminated in one step, exposing the variable x.
From here is just my advice:
There are multiple ways for you to answer this question. In math, the process may sometimes not matter if the answer was correct. Nevertheless, you should try finding one way that fits you or makes it easier to solve. I personally think that how I have been trying this helped me later when math got more complicated. (Also, it was fun for me to find another way that I was not taught of)
GOOD LUCK!! and I HOPE THIS HELPS YOU!!!!
One root of f(x)=x^3-9x^2+26x-24 is x = 2. What are all the roots of the function? Use the Remainder Theorem.
Answer:
The roots of the of the function are 2,3 and 4.
Step-by-step explanation:
The given function is
f(x) = x³ - 9x² + 26x - 24
It is given that x=2 is a root of the function. So (x-2) is a factor of f(x).
According to the remainder theorem if a function is divided by (x-c), then the remainder is equal to f(c). If f(c) is equal to 0, therefore c is the root of the function.
Use synthetic method to divide f(x) by (x-2).
f(x) = (x - 2) (x² - 7x + 12)
f(x)= (x - 2) (x² - 4x - 3x + 12)
f(x)= (x - 2) (x(x - 4) - 3(x - 4))
f(x)= (x - 2) (x - 4) (x - 3)
To find the roots equation the function equate the function equal to 0.
0 = (x - 2) (x - 4) (x - 3)
Equate each factor equal to 0.
x = 2,3,4
Therefore the roots of the function are 2,3 and 4.
(btw this is someone else's answer i found since i got a little confused myself heh)
Answer:
The roots of the of the function are 2,3 and 4.
Step-by-step explanation:
\The roots of the of the function are 2,3 and 4.
32x + 342x thhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
374x
brrrrrrrrrrrrruhhhhhhhhhhhhhh
Answer:
374x
Step-by-step explanation:
Just add 32 and 342 together
32 + 342
374
Then add the x back on
374x
Hope this helped :)
সৌরজগতের গ্রহ গুলোর চিএসহ বননা দাও
Answer:
সৌরজগতে গ্রহগুলির ক্রম, সূর্যের নিকটতম সূচনা এবং বাইরের দিকে কাজ করা নিম্নরূপ: বুধ, শুক্র, পৃথিবী, মঙ্গল, বৃহস্পতি, শনি, ইউরেনস, নেপচুন এবং তারপরে সম্ভাব্য প্ল্যানেট নাইন। আপনি যদি প্লুটোকে অন্তর্ভুক্ত করার জন্য জেদ করেন তবে তা নেপচুনের পরে তালিকায় আসবে
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what is the GCF of 12 and 24