Answer:
Step-by-step explanation:
Perimeter 165 cm
1st. 65 cm < 2s
3rd. 10 cm < s
The 2nd side is twice than the first side but 10cm longer than the
3rd side, so it'll be
2nd. 2s + 10
a triangle has a perimeter of 165 cm. the first side is 65cm less than twice the second side. the third side is 10cm less than the second side. write and solve an equation to find the length of each side of the triangle
FIRST, we need variables. Once we define variables, it's much easier to turn this word problem into a math problem.
Let a = first side
Let b = second side
Let c = third side
NOW, we can turn the words into equations:
"a triangle has a perimeter of 165 cm."
a + b + c = 165
"the first side is 65cm less than twice the second side."
a = 2b - 65
"the third side is 10cm less than the second side."
c = b - 10
Before we finish, I have to ask: Who writes problems like this??? Pointless problems like these are why kids don't like math! Ugh. Drives me crazy. It's a shame, because solving math problems really does have a certain satisfaction, once you learn how. [Okay. I'm done. Back to the problem.]
If we could get this to have only one variable, we could solve it. Substitution to the rescue!
a + b + c = 165 (rewrote equation from above)
(2b - 65) + b + (b - 10) = 165 (substituted "a" and "c" from equations above)
See how that works? Let's solve it.
2b - 65 + b + b - 10 = 165 (dropped the parentheses, because there was nothing to distribute, not even a minus sign)
4b - 75 = 165 (combined like terms)
4b = 240 (added 75 to both sides)
b = 60 (divided both sides by 4)
We found the second side! We can find the first and third sides using those equations from above:
a = 2b - 65
a = 2*60 - 65
a = 120 - 65
a = 55
c = b - 10
c = 60 - 10
c = 50
All done.
brooke found the equation of the line passing through the points (-7,25) and (-4,13) in slope-intercept form as follows
Answer:
The equation of the line passing through the points (-7,25) and (-4,13) in slope-intercept form is [tex]\mathbf{y=-4x-3}[/tex]
Step-by-step explanation:
Equation of line passing through the points (-7,25) and (-4,13) in slope-intercept form.
The general equation of slope-intercept form is: [tex]y=mx+b[/tex]
First we need to find slope
The formula used for finding slope is: [tex]Slope=\frac{y_2-y_1}{x_2-x_1}[/tex]
We are given: [tex]x_1=-7, y_1=25, x_2=-4, y_2=13[/tex]
Putting values in formula and finding slope
[tex]Slope=\frac{y_2-y_1}{x_2-x_1}\\Slope=\frac{13-25}{-4-(-7)}\\Slope=\frac{13-25}{-4+7}\\Slope=\frac{-12}{3}\\Slope=-4[/tex]
So, slope m= -4
Now finding y-intercept
Using slope m=-4 and point (-7,25) we can find y-intercept
[tex]y=mx+b\\25=-4(-7)+b\\25=28+b\\b=25-28\\b=-3[/tex]
So, y-intercept b =-3
Now, the equation of required line having slope m=-4 and y-intercept b=-3 is:
[tex]y=mx+b\\y=-4x-3[/tex]
So, the equation of the line passing through the points (-7,25) and (-4,13) in slope-intercept form is [tex]\mathbf{y=-4x-3}[/tex]
need an answer please asap!
Answer:
Step-by-step explanation:
(A). The quadrilateral ABCD is a trapezoid.
(B). A = 36 units²
Please help with these questions!!:))
Answer:
The first one : decay
The second one : growth
When the argument of the exponential expression is bigger that 1 then it represents a growth
When it's less than 1 and above 0 then it's a decay
Emily purchased 5 packages of bottled water for $14.95. Each package of bottled water cost the same amount.What is the cost per package of bottled water?
Answer:
$2.9
Step-by-step explanation:
Given the following data;
Total cost of package = $14.50
Number of package = 5
To find the cost of each package;
[tex] Cost \; per \; package = \frac {Total \; cost \; of \; package}{Number \; of \; package} [/tex]
Substituting into the equation, we have;
[tex] Cost \; per \; package = \frac {14.5}{5} [/tex]
Cost per package = $2.9
Therefore, the cost per package of bottled water is $2.9.
In acute triangle $ABC$, points $D$, $E$, and $F$ are located on sides $\overline{BC}$, $\overline{AC}$, and $\overline{AB}$ so that $\overline{AD} \perp \overline{BC}$, $\overline{DE} \perp \overline{AC}$, and $\overline{DF} \perp \overline{AB}$. Let $R_1$ and $R_2$ be the radii of the circles around $\triangle ABC$ and $\triangle AEF$, respectively. Determine the number of degrees in the measure of $\angle A$ if the area of $\triangle ABC$ is equal to $R_1R_2$.
Answer:
////////A.
Step-by-step explanation://///////
I think
Jared has $500 in his checking account. He spent $180 on his light bill. What percent of his money is spent on his light bill?
Answer:
36%
Step-by-step explanation:
180/500=36
Hope this helped!
Given the graph of the function f(x) below, what happens to f(x) when x is a very small positive number?
F(x) is a negative number with a large absolute value
F(x) is a negatice number with a small absolute value
F(x) is a very small positive number
F(x) is a very large positive number
Using function concepts, it is found that what happens to f(x) when x is a very small positive number is that:
F(x) is a negative number with a large absolute value.
What is the limit of the function as x goes to 0 by the right?F(x) goes to negative infinity, that is, when x is a very small positive number, F(x) is a negative number with a large absolute value.
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Answer:
F(x) is a negative number with a large absolute value.
Step-by-step explanation:
what is the solution set to three parallel lines
Answer:
null
Step-by-step explanation:
they never intersect, cuz they are parallel
Answer:
lebron james to the 2nd power.
Step-by-step explanation:
When you flip a biased coin the probability of getting a tail is 0.35.
Find the probability of getting a head.
Answer:
0.65
Step-by-step explanation:
a coin has 2 sides so there is two outcomes
1-0.35=0.65
given f(x) = 4+1 , describe how the graph of g compares with compares with the graph of f?
I think you wrote an incomplete question. With a little research, I was able to find a question similar to you which is attached below. So, I would solve your question based on the question attached below, which anyways would clear your concept.
Answer:
[tex]g(x)[/tex] is the graph of [tex]f(x)[/tex] translated left [tex]3[/tex] units. Also, the comparison graph is attached below.
Step-by-step explanation:
Considering the complete question attached below
Given the function
[tex]f\left(x\right)\:=\:4x+1[/tex]
As for [tex]g(x)=f(x-h)[/tex], the graph of [tex]g(x)[/tex] is the graph of [tex]f(x)[/tex] translated right h units when '[tex]h[/tex]' is greater than zero, and left | [tex]h[/tex] | units when h is lesser than zero.
so it is clear if
[tex]g(x)=4(x+3)+1[/tex] and [tex]f\left(x\right)\:=\:4x+1[/tex], then [tex]g(x) = f(x+3)[/tex].
Hence, [tex]h = -4[/tex] ( lesser than zero i.e. h < 0).
Therefore, [tex]g(x)[/tex] is the graph of [tex]f(x)[/tex] translated left [tex]3[/tex] units. Also, the comparison graph is attached below.
Select the correct answer. How did the Battle of Saratoga affect the American Revolution? A. French troops joined the war on behalf of the colonists. B. The Hessian mercenaries were eliminated from the war. C. Continental soldiers were bribed to compromise the war. D. Washington withdrew from the war after another loss. E. About 10,000 Continental soldiers became prisoners of war.
Answer:
A. French troops joined the war on behalf of the colonists.
Step-by-step explanation:
The Battle of Saratoga is often seen as the turning point of the war. It renewed the morale of the American public and convinced potential foreign partners, such as France, that America could win the war and that it might be in their best interests to send aid.
Answer:
Its A
Step-by-step explanation:
Which pair of angles is supplementary?
A) ∠RXZ and ∠YXZ
B) ∠PXQ and ∠RXS
C) ∠YZX and ∠UZT
D) ∠WZX and ∠XYZ
Answer:
A) <RXZ and <YXZ
Step-by-step explanation:
I just took the test
Answer:
its a
Step-by-step explanation:
how do you this problem?
Answer:
8
Step-by-step explanation:
Answer:
x=11
Step-by-step explanation:
7x+13= 90 should be your equation.
when you solve you should have:
7x+13=90 but you want to start to solve so the first step would be to subract 13 from both sides because your adding 13 you wanna do the opposite of that and the opposite of addition is subtraction.
7x=77 now you wanna divide 7 from both sides
x=11
Thomas Jefferson borrowed an idea from John Locke that he used in the Declaration of Independence. What did Jefferson call this idea?
A. executive branch
B. peoples rights
C. natural rights
D. unalienable rights
Answer:
The answer to your question is D.unalienable rights.
Step-by-step explanation:
He borrowed this idea from John Locke, a political philosopher of the Enlightenment. Locke said people were given certain "natural rights" which were life, liberty, and property. So, to clarify, Jefferson called this idea "unalienable rights".
Answer:
I believe it is D) unalienable rights
Step-by-step explanation:
What is the answer??? Only if you know please i will report you no games
Answer:
the answer is a. it has to be more than 13 and less than 19
I give anwser keys to any kind of questions just comment below so I can help you
The graph of a function g is shown below.
Find its inverse.
A.)g-1( x) =2/5 x + 5
B.)g-1( x) =5/2 x + 2
C.)g-1( x) = - 2/5x + 2
D.)g-1( x) =5/2 x + 5
Answer:
D
Step-by-step explanation:
the slope =
[tex] \frac{0 - ( - 2)}{5 - 0} = \frac{2}{5} [/tex]
y =mx+b
m = slope
when x = 0 , y = -2
y =(2x/5)-2
x =(2y/5)-2
x+2 = (2y/5)
5x+10 = 2y
y =(5x/2)+5 = g-1(x)
Jack bought a new boat for $36,000. The value of the boat continuously
depreciates at a rate of 15%. Find the value of the boat after 5 years.
a. $17,005
b. $7,621
c. $7,240
d. $4,140
Answer:
$15973.4
Step-by-step explanation:
The formula for depreciation is:
a(1 - r)^t
a = Initial value =$36,000
r = depreciation rate = 15% = 0.15
t = time in years = 5 years
The depreciation value = $36000 × (1 - 0.15)⁵
= 36000(0.85)⁵
= $15973.39125
Approximately = $15973.4
The value of the boat is $15,973 after 5 years.
Given that,
New boat cost is (A) $36,000.Depreciation rate is (r) 15%.We need to find the value of boat after (t) 5 years.According to the scenario, computation of the given data are as follows,
Value of boat = [tex]A (1 - r )^{t}[/tex]
By putting the value, we get
Value = [tex]36,000(1 - 0.15)^{5}[/tex]
= [tex]36,000(0.85)^{5}[/tex]
= 36,000 [tex]\times[/tex] 0.4437053125
= $15,973.4 or $15,973
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Find the m *With work*
Answer:
MNI = 135º
Step-by-step explanation:
From the picture, we have the two internal angles as [tex]6x[/tex] and [tex]15x-12[/tex]. The third, the angle ∠MNL is 180 - 19x-2. Therefore,
[tex]15x-12+6x+(180-19x-2)=180[/tex]
So,
[tex]15x-12+6x+180-19x-2=180[/tex]
[tex]15x-14+6x-19x=0[/tex]
[tex]2x=14[/tex]
[tex]x=7[/tex]
Finally,
∠MNI = 19x+2 ⇒ ∠MNI = 19(7)+2 ⇒ ∠MNI = 135º
The value of the variable 'x' is 7. Then the measure of the angle ∠MNI will be 131°.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The exterior angle of a triangle is almost always equal to the addition of the interior and opposing interior angles. The term "external angle property" refers to this feature.
Then the equation is given as,
∠NLM + ∠LMN = ∠MNI
6x + 15x - 12 = 19x + 2
2x = 14
x = 7
Then the measure of the angle ∠MNI is calculated as,
∠MNI = 19 (7) - 2
∠MNI = 133 - 2
∠MNI = 131°
The value of the variable 'x' is 7. Then the measure of the angle ∠MNI will be 131°.
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which of the following expresses the possible number of positive real solutions for the polynomial equation shown below?
[tex]5x^{2} + x ^{2} - 7x + 28[/tex]
The equation that indicates the number of real solution in the polynomial is presented as follows;
[tex]\left(x^2-\dfrac{14426}{7535} \cdot x +\dfrac{42196}{15933} \right)\cdot \left(x+\dfrac{15933}{7535} \right)\cdot 5 = 0[/tex]
What is a polynomial?A polynomial is an expression that has two or more algebraic terms of the same variables that have different powers.
The specified expression is presented as follows;
5·x³ + x² - 7·x + 28
The polynomial equation can be factored using a graphing calculator to get;
5·x³ + x² - 7·x + 28 = [tex]\left(x^2-\dfrac{14426}{7535} \cdot x +\dfrac{42196}{15933} \right)\cdot \left(x+\dfrac{15933}{7535} \right)\cdot 5[/tex]
When the expression is equated to 0, we get;
[tex]\left(x^2-\dfrac{14426}{7535} \cdot x +\dfrac{42196}{15933} \right)\cdot \left(x+\dfrac{15933}{7535} \right)\cdot 5 = 0[/tex]...(1)
The discriminant of the expression [tex]\left(x^2-\dfrac{14426}{7535} \cdot x +\dfrac{42196}{15933} \right)[/tex] is less than 0, therefore, the expression [tex]\left(x^2-\dfrac{14426}{7535} \cdot x +\dfrac{42196}{15933} \right)[/tex] has no solution
The real solutions found from equation (1) is therefore;
[tex]x=-\dfrac{15933}{7535}[/tex]
There is therefore one solution to the expression
The equation that expresses the number of solutions is therefore;
[tex]\left(x^2-\dfrac{14426}{7535} \cdot x +\dfrac{42196}{15933} \right)\cdot \left(x+\dfrac{15933}{7535} \right)\cdot 5 = 0[/tex]
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QUICK SOLVE 2y=x+6 show work !!!
Answer:
y=0.5x+3
Step-by-step explanation:
Divide both sides by 2 which will give you y=0.5x+3.
5 over 6 divided by 3 over 7 is... bc it’s asking what’s the value?
Answer:
5/14Step-by-step explanation:
5/6×3/7 =5/2×1/7=5/14Four posts with 3-in. radii are bound together with a wire. Find the length of the shortest wire that will go around them.
A. 42.85 inches
B. 36.22 inches
C. 12.94 inches
D. 24.45 inches
A projectile is thrown upward off a 130ft cliff at a velocity of 15ft/second. How long before it reaches a height of 25ft?
Answer:
The time taken for the projectile to reach the given height is 1.2 s.
Step-by-step explanation:
Given;
height of travel, h = 25 ft
initial velocity of the projectile, u = 15 ft/s
The time taken for the projectile to travel a height of 25 ft is given by the following kinematic equation;
h = ut + ¹/₂gt²
25 = 15t + ¹/₂(9.8)t²
25 = 15t + 4.9t²
4.9t² + 15t - 25 = 0
solving the quadratic equation, we will have the following solution of t;
t = 1.2 s
Therefore, the time taken for the projectile to reach the given height is 1.2 s.
Suppose the sample space for a continuous random variable is 0 to 100. If the area under the density curve for the variable from 0 to 20 is 0.15, what is the area under the density curve from 20 to 100?
The solution is, 0.85 is the area under the density curve from 20 to 100.
What is area ?Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.
here, we have,
given that,
Suppose the sample space for a continuous random variable is 0 to 100. If the area under the density curve for the variable from 0 to 20 is 0.15
The area under the density curves for the continuous random variables always add up to unity.
Thus, the area under the density curve from 20 to 100 is ;
1 - 0.15
which is;
1 - 0.15
= 0.85
Hence, The solution is, 0.85 is the area under the density curve from 20 to 100.
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Kristin wants to make 12 ml of an 8% alcohol solution by mixing together a 32% alcohol solution and pure water. How much of each solution must she use?
Answer:
6% of each
Step-by-step explanation:
Using the picture what is the equation of the line in point slope form?*
Answer:
y=2/5(x+5)-3
Step-by-step explanation:
my work is attached
Help plz will get brainliest
Answer:
4 i think but im having mixed feelings
Step-by-step explanation:
6*60=360
360/9=4
Need help urgent!!!!
How many 1 cm^2 tiles are required to fill the boundary of a rectangle with area 32 cm^2?
Answer:
32
Step-by-step explanation:
Area of the rectangular tiles = 32cm²
Area of tiles inside the rectangle = 1m²
Number of tiles inside the triangle = area of rectangle/area if the tikes inside the rectangle= 32cm²/1cm² = 32
Hence 32 1cm² tiles can fill the boundary of the rectangle.