Answers
The simplified expression of the perimeter of the triangle is 3.75x - 7.
How to find the perimeter of a triangle?A triangle is a a polygon with three sides. The sum of angles in a triangle is 180 degrees.
The perimeter of a triangle is the sum of the whole three sides.
Therefore, the simplified expression that represents the perimeter of the triangle is as follows:
Hence, the three sides of the triangle are as follows;
1.5x - 31.5x - 30.75x - 1Hence,
perimeter of the triangle = 1.5x - 3 + 1.5x - 3 + 0.75x - 1
perimeter of the triangle = 1.5x + 1.5x + 0.75x - 3 - 3 - 1
perimeter of the triangle = 3.0x + 0.75x - 7
perimeter of the triangle = 3.75x - 7
Therefore, the simplified expression is 3.75x - 7
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Related Questions
5x+25=100
Please solve. I don't want any wrong answers!!
Answers
Answer:
x=15
Step-by-step explanation:
5x+25=100
Subtract 25 from both sides.
5x+25−25=100−25
5x=75
Divide both sides by 5.
5x÷5=75÷5
x=15
[tex]5x+25=100\\x=[/tex]
Subtract 25 from both sides:
[tex]5x+25-25=100-25\\5x=75[/tex]
Divide both sides by 5:
[tex]\frac{5x}{5} =\frac{75}{5}[/tex]
[tex]\fbox{x=15}[/tex]
A plumber charges a flat fee of 75 to visit a home and examine a clogged drain. The plumber charges an additional 22 per hour spent fixing the drain. The total cost, (in dollars), for fixing a drain that takes hours is given by the following.
Answers
The expression for the total cost is 75 + 22h
How to calculate the cost?From the information, the plumber charges a flat fee of 75 to visit a home and examine a clogged drain and also charges an additional 22 per hour spent fixing the drain.
Therefore, the amount that will be charged for each hour will be:
= 75 + (22 × h)
= 75 + 22h
where h = number of hours.
For example if the number of hours is 5 hours. This will be:
= 75 + 22h
= 75 + 22(5)
= 75 + 110
= 185
Your information was incomplete but an overview was given.
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Write the sentence as an equation.
271 decreased by k is 230
Answers
hope this helps!! <33
Solve the equation. -5x + 1 = 31 x=
Answers
we get that:
[tex]\begin{gathered} -5x+1=31\rightarrow-5x=31-1=30 \\ x=-\frac{30}{5}=-6 \end{gathered}[/tex]so the answer is x=-6
PLEASE HELP!!!
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at negative 3 comma 16, a point at negative 7 comma 0, a point at 1 comma 0, a point at negative 6 comma 7, and a point at 0 comma 7.
What is the standard form of the equation of f(x)?
f(x) = −x2 − 6x + 7
f(x) = −x2 + 6x + 7
f(x) = x2 − 6x + 7
f(x) = x2 + 6x + 7
Answers
The standard form of the equation of f(x) is option a -x² - 6x + 7
Given,
The graph shows a downward open parabola.
The vertex points are:
(-3, 16), (-7, 0), (1, 0), (-6, 7), (0, 7)
Now,
We have to find the standard form of the function f(x):
As from the graph:
Parabola opens downward, so the function will be negative.
We have the options with:
a = -1, b = -6 and c = 7
Now,
Use x = -b/2a
x = 6/2 × -1 = 6/-2 = -3
Now,
f(x) = -x² - 6x + 7
f(-3) = -(-3)² - 6(-3) + 7
f(-3) = -9 + 18 + 7
f(-3) = 9 + 7
f(-3) = 16
That is, the points for the vertex in this equation is (-3, 16)
Then, the standard form of the equation of f(x) is option a -x² - 6x + 7
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Find the indicated part round your answer to the nearest degree
Answers
Solution
For this case we can do the following:
tan x = 35/30
And we can solve for x and we got:
[tex]x=\tan ^{-1}(\frac{35}{30})=49.39[/tex]And rounded to the nearest degree is:
49º
Look at photo down below for question
Answers
The coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0)
What is translation of graph?Function translation takes a function (and its graph) and, by adding and subtraction, moves the graph around the plane without changing its shape.
Given is a triangle coordinate on x - y plane.
The rule (x, y) → (- x, - y) represents the rotation of a figure by 180 °.
Now, initially the coordinates of the triangle are -
(-2, 2) , (-3, 8) , (-7, 0)
After transforming the graph by the rotation of 180°, the new coordinates will be -
(2, - 2) , (3, -8) , (7, 0)
Plot the coordinates on the graph and you will get the rotated image.
Therefore, the coordinates of the rotated triangle will be (2, - 2) , (3, -8) , (7, 0).
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What is the slope that passes through these points?
(0, -4) and (-5, -5)
Answers
Answer: m=1/5
Step-by-step explanation:
Which shape has an area of b1 + b2 • h ÷2?
Answers
Answer:
Trapezoid
Step-by-step explanation:
The area of this parallelogram is its height (half-height of the trapezoid) times its base (sum of the bases of the trapezoid)
HELP IMMEDIATELY I WILL GIVE 75 BRAINLIST
Answers
Answer:
Step-by-step explanation:
(4x + 50)° = 150°
4x = 150° - 50°
4x = 100°
x = 100° / 4 = 25°
the average number of miles driven on a full tank of gas for a hyundai veracruz before its low fuel light comes on is 320. assume this mileage follows the normal distribution with a standard deviation of 30 miles. what is the probability that, before the low fuel light comes on, the car will travel
Answers
The probability that, before the low fuel light comes on the car will travel is 0.2576
Given,
The average number of miles driven on a full tank of gas before its low fuel light comes on is ( μ )= 320
It follows the standard deviation of ( δ ) = 30
For the normal distribution,
P(X < x) = P( Z < x - μ / δ)
a)
P( X < 330) = P( Z < 330 - 320 / 30)
= P( Z < 0.3333)
= 0.6306
b)
P( X > 308) = P( Z > 308 - 320 / 30)
= P( Z > -0.4)
= P( Z < 0.4)
= 0.6554
c)
P( 305 < X < 325) = P( X < 325) - P( X < 305)
= P( Z < 325 - 320 / 30) - P( Z < 305 - 320 / 30)
= P( Z < 0.1667) - P( Z < -0.5)
= 0.5662 - ( 1 - 0.6915)
= 0.2576
d) P(X = 340) = 0
Since X is a continuous random variable (For normal distribution).
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Rewrite the expression using only positive integer exponents. (m2/3n-1/3)^5
Answers
When the expression (m²/³ n⁻¹/³)⁵ is rewritten, the equivalent expression is ∛m¹⁰n⁻⁵
How to rewrite the expression?From the question, the expression is given as
(m2/3n-1/3)^5
Rewrite the expression properly
So, we have the following representation
(m²/³ n⁻¹/³)⁵
Express the radicals as roots
So, we have
(m²/³ n⁻¹/³)⁵ = (∛m² ∛n⁻¹)⁵
Remove the brackets in the expression
This is done by multiplying the exponents
So, we have
(m²/³ n⁻¹/³)⁵ = (∛m¹⁰ ∛n⁻⁵)
Combine the roots
(m²/³ n⁻¹/³)⁵ = ∛m¹⁰n⁻⁵
Hence, the equivalent expression is ∛m¹⁰n⁻⁵
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The required simplified expression is given as ∛[m¹⁰/n⁵].
Given that,
For an expression (m²/³n-¹/³)⁵ we have to deduce the function that the solution only consists of the positive integer exponents.
Here,
Rewriting the given expression,
= (m²/³n-¹/³)⁵
Simplifying the expression,
using the property, (xᵃ)ᵇ = xᵃᵇ
= m¹⁰/³n⁻⁵/³
= [m¹⁰n⁻⁵]¹/³
we imply cube root for the exponent 1/3.
= ∛[m¹⁰n⁻⁵]
= ∛[m¹⁰/n⁵] (using the property x⁻¹ = 1 / x )
Thus, the required simplified expression is given as ∛[m¹⁰/n⁵].
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24. Anna went bowling. She spent less than or equal to $30, but spent more
than $25. Create a number line that shows all the possible amounts that
Anna may have spent at the bowling alley.
Answers
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
What is a number line?In mathematics, a numbered line is a straight line with numbers organized at regular intervals or sections throughout its breadth. The beginning of period is frequently shown laterally and may be shifted in any position.
Anna visited a bowling alley. She did not spend less than or equal to $30, but she did spend more than $25.
The inequality is given as,
$25 < x ≤ $30
All the possible amounts that Anna may have spent at the bowling alley are presented on the number line.
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PLEASE HELP!!
Points A(-1, 2) and B(5,8) are the endpoints of AB. What are the coordinates of point C on AB such that AC is 2/3 the length of AB
Answers
The coordinates of the point C on the line AB such that AC is 2/3 the length of AB is (3,6) .
In the question ,
it is given that
the coordinates of the end points of A and B is A(-1,2) and B(5,8) .
also AC = 2/3(AB)
So , AC/AB = 2/3
and given that point C is on the line AB , hence AC+CB=AC
2+CB=3
So , CB=1
hence AC/CB = 2/1
so , the point C divides the line AB in the ration 2:1 .
and we have the coordinates of end points ,
that is x₁[tex]=[/tex] -1 , y₁=2 and x₂=5 , y₂ = 8 and the ratio m=2 and n=1 .
Substituting the above values in the section formula ,
which states that the coordinate of point C will be
((m*x₂+n*x₁)/(m+n) , (m*y₂+n*y₁)/(m+n))
= ((2*5+1*(-1))/(2+1) , (2*8+1*2)/(2+1))
= ((10-1)/3 , (16+2)/3)
= (9/3 , 18/3)
= (3,6)
Therefore , The coordinates of the point C on AB such that AC is 2/3 the length of AB is (3,6) .
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graph the linear equation 50 points will mark brainliest
Answers
You can see the three points where the result is equal to an integer in the photo below. Good luck!
Which expression is equivalent to sin (pi/12)cos(7pi/12) -cos(pi/12)sin(7pi/12)?
Answers
sin (pi/12)cos(7pi/12) -cos(pi/12)sin(7pi/12) is equivalent to sin(-pi/2)
Define Trigonometric functions
A right-angled triangle's angle can be related to side length ratios using real-world trigonometric functions.
We know the formula of sin(A - B) = sinAcosB - cosAsinB
And the given expression is
sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
Which is in the form of given formula of sin(A - B)
where, A = π/12 and B = 7π/12
put A and B values in sin(A - B),
sin(π/12 - 7π/12) = sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
sin(-6π/12) = sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
sin(-π/2) = sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12)
Hence, sin (π/12)cos(7π/12) -cos(π/12)sin(7π/12) is equivalent to sin(-π/2).
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Which of the following ordered pairs is either the x- or y-intercept of the function 3x + 2y = -6?
Answers
Answer:
x-intercept (-2,0)
y-intercept (0,-3)
Step-by-step explanation:
to find the x-intercept we set y=0
so 3x=-6
x=-2
to find the y-intercept we set x=0
so 2y=-6
y=-3
-
Bobby photographs a bird. If the bird, that measures 3.4 inches in the photo, is actually 3.75 feet tall, approximately how long is its boak if it measures 0.4 inches in the
photo?
Answers
We need to know about scaling of measurements to solve the problem. The length of the bird's beak is 5.29 inches.
In the given question we know that the height of the bird in the photo is 3.4 inches and the real height of the bird is 3.75 feet. We know that the length of the beak in the photo is 0.4 inches, we need to find out the real length of the beak. We need to find by how much the measurement of the bird is scaled down to fit in the photo. We need to convert feet to inches first to get the scaling factor, we can then divide the length of the beak given by the scaling factor.
3.75 feet= 3.75x12 =45 inches
scaling factor= 3.4/45=0.0756
real length of beak=0.4/0.0756=5.29 inches
Therefore the length of the beak of the bird is 5.29 inches.
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How much would $500 invested at 6% interest compounded monthly be worth after 5 years? Round your answer to the nearest cent. A.$669.11B.$674.43C.$886.41D.$512.63
Answers
Solution:
Given that;
[tex]\begin{gathered} Principal=P=\text{ \$500} \\ rate=r=\frac{6}{100}=0.06 \\ time=t=\text{ 5 years} \end{gathered}[/tex]To find the amount in 5 years, we will apply the compound interest formula below
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ Since,\text{ it is compounded montly, n = 12} \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]\begin{gathered} A=500(1+\frac{0.06}{12})^{(5\times12)}=500\left(1+\frac{0.06}{12}\right)^{60}=674.42507 \\ A=\text{ \$}674.43\text{ \lparen nearest cent\rparen} \end{gathered}[/tex]Hence, the answer is B
What is 3 / 5 x 8/9?
A. 8 /15
B. 11 /14
C. 27 / 40
D. 91 /40
Answers
Answer:
A) 8/15
Step-by-step explanation:
3 / 5 x 8/9
(3/5)(8/9)
(3*8)/(5*9)
(24/45)
8/15
Answer:
8/15
Step-by-step explanation:
3 / 5 x 8/9
Multiplying fractions
Rewriting
3/9 * 8/5
Simplify
1/3 * 8/5
Multiply the numerators
1*8 =8
Multiply the denominators
3*5 = 15
8/15
Ji-yoon has a savings account with $690 in it that earns 7% simple interest per year. How much money, to the nearest penny, will Ji-yoon have in 8 years? Give your answer in dollars.
Answers
Let's begin by identifying key information given to us:
Principal (p) = $690
Interest rate (r) = 7% = 0.07 per year
Time (t) = 8 years
The amount of money that Ji-yoon has in 8 years is calculated as shown below:
[tex]\begin{gathered} I=p\times r\times t \\ I=690\times0.07\times8=386.4 \\ I=\text{ \$}386.40 \\ \\ \text{The total amount Ji-yoon has after 8 years is:} \\ Total=\text{\$(}386.40+$690$) \\ Total=\text{\$}1,076.40 \end{gathered}[/tex]Suppose you are given the function t(x) = x^2 + 8x - 20 Explain how you would graph this function, making sure to include the following information: Coordinate(s) of the solutions/rootscoordinate of the y-intercept location of the line of symmetrycoordinate of the vertex whether the graph opens up or down and how you know
Answers
t(x) = x² + 8x - 20
Coordinate(s) of the solutions/roots
x² + 8x - 20 = 0 ==> (x -2)(x + 10) = 0
roots: x= 2 and x = -10
coordinate of the y-intercept
y-intercept is when x = 0 ==> t(x) = x² + 8x - 20 when x = 0: t(0) = -20
y-intercept: y = -20
location of the line of symmetry
x = -4
y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36) and line of symetry x = -4
coordinate of the vertex
(-4, -36)
y = (x + 4)² - 36, therefore coordinates of the vertex (-4, 36)
whether the graph opens up or down and how you know
Opens up
Because the coefficient of x² is positive
Can you please help me
Answers
EXPLANATION
The area of the figure can be obtained by applying the following relationship:
[tex]Area_{paralle\log ram}=base\cdot height[/tex]Where b=base and height=h
In order to find the height, we need to apply the trigonometric relationship:
[tex]\sin 45=\frac{opposite}{\text{hypotenuse}}=\frac{height}{\text{diagonal}}=\frac{h}{6.4}[/tex]Multiplying both sides by 6.4:
[tex]6.4\cdot\sin 45=h[/tex]Solving the argument:
[tex]6.4\cdot0.65=h[/tex]Switching sides:
[tex]h=4.16\text{ inches}[/tex]Now that we have the height, we can compute the area as follows:
[tex]\text{Area}_{\text{parallelogram}}=12.8in\cdot4.16in=53.24in^2[/tex]The answer is 53.24 squared inches.
Eli has 12 eggs. He uses his grandpa's recipe to bake 4 loaves of challah. Find how many eggs are left over if Eli uses 2 eggs for each loaf of challah?
Answers
Answer:
4 Eggs are left since he uses 2 eggs per 1 loaf so 2x4=8
Step-by-step explanation:
I really need help with this question
Answers
Write the linear equation in standard form.
y - 2 = 1/3(x + 6)
Answers
Answer: y=x/3 + 4
Step-by-step explanation:
distribute 1/3 to the (x+6): x/3 + 2add two to both sides: y=x/3 + 4
-5< x < 5Graph the solution set on a number line
Answers
- 5 < x < 5
Number line:
How many and of which kind of roots does the equation f(x) = x^4 - 2x³ - 11x² + 12x + 36 have?OA. 4 realB. 2 real; 2 complexOC. 4 real; 2 complexD. 3 realReset Selection
Answers
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=x^4\:-\:2x³\:-\:11x²\:+\:12x\:+\:36[/tex]We solve the polynomial as follows:
[tex]\begin{gathered} x^4-2x^3-11x^2+12x+36=0 \\ \\ \left(x+2\right)\frac{x^4-2x^3-11x^2+12x+36}{x+2} \\ \\ \begin{matrix}\texttt{\:\:\:-2¦\:\:\:\:1\:\:\:-2\:\:-11\:\:\:12\:\:\:36}\\ \texttt{\:\:\:\:\:¦\underline{\:\:\:\:\:\:\:\:-2\:\:\:\:8\:\:\:\:6\:\:-36}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:1\:\:\:-4\:\:\:-3\:\:\:18\:\:\:\:0}\end{matrix} \\ \\ \frac{x^4-2x^3-11x^2+12x+36}{x+2}=x^3-4x^2-3x+18 \\ \\ \left(x+2\right)\frac{x^3-4x^2-3x+18}{x+2} \\ \\ \begin{matrix}\texttt{\:\:-2¦\:\:\:1\:\:-4\:\:-3\:\:18}\\ \texttt{\:\:\:\:¦\underline{\:\:\:\:\:\:-2\:\:12\:-18}}\\ \texttt{\:\:\:\:\:\:\:\:1\:\:-6\:\:\:9\:\:\:0}\end{matrix} \\ \\ \frac{x^3-4x^2-3x+18}{x+2}=x^2-6x+9 \\ \\ (x+2)(x+2)(x^2-6x+9) \\ \\ (x^2-6x+9)=(x-3)^2 \\ \\ (x+2)^2(x-3)^2=0 \\ \\ x+2=0\rightarrow x=-2 \\ \\ x-3=0\operatorname{\rightarrow}x=3 \end{gathered}[/tex]Lisa has to stay under $200.00 while buying new clothes for spring. She has already spent $125.88 and wants to buy some shirts that each cost $20.80. Which of the following inequalities could be used to solve for x, the number of shirts Lisa can buy with the money she has left?
Answers
The correct inequality to solve for x will be;
⇒ $20.03x + $125.99 < $200.00
Where, 'x' is the number of shirts.
What is Inequality?
A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
Lisa buy new clothes for spring under $200.00
She spent $125.88 for buying some shirts that has each cost $20.80.
Let the number of shirts = x
Then, We can formulate for the given condition is;
The inequality for solution of the value of x is,
⇒ $20.03x + $125.99 < $200.00
Because we can solve for x, which is the number of shirts Lisa can buy with the money she has left.
Therefore,
The correct inequality to solve for x will be;
⇒ $20.03x + $125.99 < $200.00
Where, 'x' is the number of shirts.
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the 10th and 15 term of an AP are - 5 and - 7 1/2 respectively what is the sum of the first 20 terms ? I really need the answer pls A 60 B -105 C -52 1/2 D -20
Answers
Answer:
B
Step-by-step explanation:
before finding the sum we require to find first term and common difference.
the nth term of an AP is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
given a₁₀ = - 5 and a₁₅ = - 7 [tex]\frac{1}{2}[/tex] = - 7.5 then
a₁ + 9d = - 5 → (1)
a₁ + 14d = - 7.5 → (2)
subtract (1) from (2) term by term to eliminate a₁
0 + 5d = - 2.5
5d = - 2.5 ( divide both sides by 5 )
d = - 0.5
substitute d = - 0.5 into (1) and solve for a₁
a₁ + 9(- 0.5) = - 5
a₁ - 4.5 = - 5 ( add 4.5 to both sides )
a₁ = - 0.5
the sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
here a₁ = - 0.5 and d = - 0.5 , then
S₂₀ = [tex]\frac{20}{2}[/tex] [ (2 × - 0.5) + (19 × - 0.5) ]
= 10 (- 1 -9.5)
= 10 × - 10.5
= - 105