[tex]\sf\purple{No, \:Sara\: is \:wrong.}[/tex]
[tex]2x + 3≠ \frac{x}{2} + \frac{3}{4} [/tex]
[tex]\sf\red{Here's\:why:}[/tex]
[tex]L. H. S. = 2x + 3[/tex]
[tex]R. H. S = \frac{x}{2} + \frac{3}{4} \\ = \frac{x \times 2}{2 \times 2} + \frac{ 3}{4} \\ = \frac{2x + 3}{4} [/tex]
Clearly,
[tex]2x + 3≠ \frac{2x + 3}{4} \\✒ \: L.H.S.\:≠\:R. H. S. [/tex]
[tex]\boxed{Therefore,\:the\:two\:expressions \:are\:not\:equivalent.}[/tex]
To make them equivalent, Sara can simply divide L. H. S. by 4.
By doing so, she'll have
[tex] \frac{2x + 3}{4} = \frac{2x + 3}{4} \\ ๛L.H.S.=R. H. S[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]
20.48=8v
Solve for v
Answer:
2.56
Step-by-step explanation:
Divide 20.48/8
I hope this helped!
Which best describes the orthocenter of a triangle?
• A. The point where the three altitudes of the triangle intersect
• B. The point where the three angle bisectors of the triangle intersect
O C. The point where the three medians of the triangle intersect
O D. The point where the perpendicular bisectors of the three sides of
the triangle intersect
Will give brainlest!!! Please view picture for question.
Step-by-step explanation: 6 4 12 00
V = a²(h/3) where a is the length of a side s and since h = (2/3)s
V = s²(2s/3)/3
V = s³(2/9) I'll go the D
Find three consecutive integers such that the sum of the first two is three times the third.
Answer:
-3, -4, -5
Step-by-step explanation:
x = 1st integer
x+1 = 2nd integer
x+2 = 3rd integer
x+x+1 = 3(x+2)
2x + 1 = 3x + 6
1 = x + 6
-5 = x
-4 = x+1
-3 = x+2
Using the following image, solve for FE
Answer:
FE = 3
Step-by-step explanation:
FE + ED = 11.
(2x - 17) + (x-2) = 11
Combine like terms, and you'll get:
3x -19 = 11
3x = 11+19 = 30
x = 10
FE = 2x - 17
= 2(10) - 17
= 20 - 17
= 3
Find the value of x in these Complementary Angles
Answer:
Aids
Step-by-step explanation:
AIDS is what ur mom has
Answer:
[tex]x=53\\[/tex]
Step-by-step explanation:
Together they make 90 degrees,
Now, form an equation to solve:
[tex]x+37=90[/tex]
[tex]x=90-37[/tex]
[tex]x=53[/tex]
{CHECK: [tex]53+37=90[/tex]}
hope this helps.....
Identifying the Graph of a Solution
Which graph is the solution to the inequality?
✓x
+
+
+
96
1
99
97
98
100
y - 13 > -85M
Graph A
+
95
Graph B
4
-74
Graph
4
-100
Graph D
+
-73
1
-71
1
-70
-72
-69
13 < -85+y
1
-99
+
-98
+
-97
+
-96
y + 13 <-85
1
-73
+
-72
+
-71
+
-70
-74
-69
Answer:
C
Step-by-step explanation:
C
Given AD|GJ. Refer to the figure and provide an appropriate name for
Check the picture below.
I REALLY NEED HELP WITH THIS!!!! I WILL GIVE BRAINLIEST!!!!!!!!!
Consider the equation:
3+x=x^2+3x
1) Rewrite the equation by completing the square.
Your equation should look like (x+c)^2=d or (x-c)^2=d
2) What are the solutions to the equation?
Answer:
1
[tex]3 + x = {x}^{2} + 3x \\ {x}^{2} + 2x - 3 = 0 \\ ( {x}^{2} + 2x + 1) - 3 - 1 = 0 \\ {(x + 1)}^{2} - 4 = 0 \\ {(x + 1)}^{2} = 4[/tex]
2
[tex] {(x + 1)}^{2} = 4 \\ x + 1 = ±2 \\ x = 1 \: or \: - 3[/tex]
Answer:
first answer is (x+1)^2=4 and the second one is x=-1 plus or minus 2
When the admission price for a baseball games was $4 per ticket, 40,000 tickets were sold. When the price was raised to $5, only 35,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $95,000 respectively.
A) Find the profit P as a function of x, the number of tickets sold P(x)=
B) Select the graph of P
C) find the marginal profits when 20,000 tickets were sold and when 40,000 tickets were sold. P'(20,000)= $ Per ticket P'(40,000)= $ Per ticket
Answer and explanation:
A. profit P as a function of x, the number of tickets sold
P(x)= total revenue - total cost
For 40000 tickets at $4
=40000×4-0.10×40000+$95000
=$160000-$99000
=$61000
For 35000 tickets at $5
= 35000×$5-0.10×35000+$95000
= $175000-$98500
= $76500
B. P has a downward slope like a demand curve. Increase in price equal to decrease in profit.
C. P(40000)= $4-$0.10+$95000/40000
= $4-$2.475
= $1.525
Price for 20000 tickets was not stated in question but feel free to use an arbitrary price(price should be higher than that for 35000 tickets and 40000 tickets)
If f(x) = 4 – x^2 and g(x) = 6x, which expression is equivalent to (g- 1)(3)?
Answer:
the value of g
Step-by-step explanation:
Brianna went to a carnival. She played five games and rode six rides. Justin went to the same carnival and played seven games and rode eight rides. If Brianna paid $11.75 and Justin paid $16.15, how much did one game cost to play?
Explain pls
Find the area of circle H
Answer: AREA OF H IS S= R4
Step-by-step explanation:
If the side lengths of a cube are 14 feet, what is the correct way to write the expression to represent the volume of the cube in exponential form?
143
314
14 ⋅ 3
14 ⋅ 14 ⋅ 14
PLEASE ANWSER !!!!!
(100 points given)
Answer: Choice A) [tex]14^3[/tex]
This is the same as writing 14^3
===================================================
Explanation:
Since all the sides are 14 feet long, we can basically say length = width = height = 14.
Or put another way:
length = 14width = 14height = 14The volume of the cube is length*width*height = 14*14*14 = 14^3 = 2744 cubic feet.
-----------
The term 14^3 has a base of 14 and exponent of 3.
The base is what we multiply out while the exponent tells us how many copies of the base to multiply. In this problem, we have 3 copies of 14 being multiplied. So that's why 14^3 = 14*14*14
If you were to say something like 3^14, then you would have 14 copies of 3 multiplied out, which is a much larger value. So we'll cross choice B off the list.
Choice C isn't correct either since again we're using exponents and not multiplication to tie together the 14 and 3.
Choice D would be correct if your teacher wanted it in expanded form, instead of exponent form.
Answer:A is the answer
Step-by-step explanation:
Can someone help me with this please!
Answer:
Maybe 24 ft.......................????
Answer:
24 feet.
Step-by-step explanation:
We can solve this with a proportion.
[tex]\frac{Height}{Shadow}=\frac{Height}{Shadow}\\\frac{Height}{12}=\frac{2}{1}\\Height=\frac{2}{1}(12)\\Height = 24[/tex]
Therefore, the height of the sailboat is 24 feet.
Can someone help me please
Answer: A
Step-by-step explanation:
Please show work thank you
Answer: 70 mph
Step-by-step explanation:
Given the vector u with magnitude 8 and direction 150° and the vector v with magnitude 3 and direction 115º, find the components of the vector u + v. Round to
four decimal places
======================================================
Explanation:
Vector u has magnitude 8 and direction 150 degrees.
So r = 8 and theta = 150
The polar form
r*(cos(theta)+i*sin(theta))
updates to
8*(cos(150)+i*sin(150))
---------------------
Use your calculator to evaluate that last expression to get it into a+bi form
8*(cos(150)+i*sin(150))
8*(-0.866025 + i*0.5)
-6.9282 + 4i
So this is the a+bi form of vector u. It's a rough approximation of it.
-----------------------
Repeat those steps for vector v
v = r*(cos(theta)+i*sin(theta))
v = 3*(cos(115)+i*sin(115))
v = 3*(-0.422618 + i*0.906308)
v = -1.267854 + 2.718924i
----------------------
We're converting each vector to a+bi form so that we can add the vectors.
The general idea is that if you want to add v = a+bi and w = c+di, then
v+w = (a+c)+(b+d)i
we simply add the corresponding real components together, and the imaginary components are added together as well.
-----------------------
Add up u and v
u+v = (-6.9282 + 4i) + (-1.267854 + 2.718924i)
u+v = (-6.9282 + -1.267854) + (4i + 2.718924i)
u+v = -8.196054 + 6.718924i
When rounding to four decimal places, the real and imaginary components are -8.1961 and 6.7189 respectively. These represent the x and y components of the vector.
So we can say vector u+v is approximately < -8.1961, 6.7189 >
Suppose that nine Massachusetts athletes are scheduled to appear at a charity benefit. The nine are randomly chosen from eight volunteers from the Boston Celtics and four volunteers from the New England Patriots. We are interested in the number of Patriots picked.
a. In words, define the random variable X.
b. List the values that X may take on.
c. Give the distribution of X. X ~ _____(_____,_____)
d. Are you choosing the nine athletes with or without replacement?
Answer:
a) Random Variable - The value of this variable occur according to the frequency distribution
b) X may be volunteers from the Boston Celtics or the volunteer from New England Patriots
c) Distribution 1 to 13
d) Without replacement
Step-by-step explanation:
a) Random Variable - The value of this variable occur according to the frequency distribution
b) X may be volunteers from the Boston Celtics or the volunteer from New England Patriots
c) Distribution 1 to 13
d) Without replacement
What are the year-2 CPI and the rate of inflation from year 1 to year 2 for a basket of goods that costs $25.00 in year 1 and $25.50 in year 2? NEED FAST REALLY IMPORTANT IF CORRECT WILL MARK AS BRAINLIEST
Answer:
The answer is A, the CPI is 25.50, and the rate of inflation is 2%.
Step-by-step explanation:
I took the test and I know the correct answer. :)
Answer:
E) 102 and 2%
Step-by-step explanation:
If the graphs of the linear equations shown below are perpendicular, what is the value
of a?
y = 3x +8
2y = ax - 5
Answer:
[tex]a=-\frac{2}{3}[/tex]
Step-by-step explanation:
We are given the lines, [tex]y=3x+8[/tex] and [tex]2y=ax-5[/tex]. For the latter equation, we can isolate the variable y to have the same format as the first. We want to create a y=mx+b equation where m represents the slope of the line. We now have the equations:
[tex]y=3x+8[/tex] and
[tex]y=\frac{a}{2}x-2.5[/tex]
The definition of perpendicular lines is that their slopes must be the negative reciprocal of each other. Thus:
[tex]-\frac{1}{3}=\frac{a}{2} \\\\a=-\frac{2}{3}[/tex]
I hope this helps! Let me know if you have any questions :)
If x = 3, what is the value of x(14 - x)?
Answer:
33
Step-by-step explanation:
x(14 - x)
Step One: Substitute
3(14 - 3)
Step Two: Brackets/Parenthesis
3(11)
Step Three: Multiply
33
Answer:
33
Step-by-step explanation:
1. Subtract the numbers
(14-3)
2. Multiply the numbers
3*11= 33
Find the missing terms of the arithmetic sequence below.
..., 36, , ,21, ...
Answer:
Rule:-15
Step-by-step explanation:
36,21,6,-9,-24,-39,-54,-69...
Find the product of (x − 7)2
Answer:
the answer is 2x-14.
Step-by-step explanation:
because 2 multiply both the number 2 and x
I’ll give brainliest if you answer this correctly
Answer:
B y = (-7/4)x - 7
Step-by-step explanation:
Slope intercept form is
y = mx + b
Where m is the slope and b is the y-intercept
m = rise/run
m = ∆y/∆x
m = (y₂ - y₁) / (x₂ - x₁)
m = (-7 - 0) / (0 - -4)
m = -7/4
From the graph the y-intercept
b = -7
-------------------------
y = (-7/4)x - 7
78, 68, 75, 65, find the next term
Answer:
73,63
Step-by-step explanation:
it just goes down by 2 everytime
A laundry basket contains 15 socks, of which 5 are yellow.
What is the probability that a randomly selected sock will be yellow?
Write your answer as a fraction or whole number.
Answer:
5/15
Step-by-step explanation:
Out of 15, 5 are yellow. Converted to a fraction this will be 5/15. Hope this helps!! :)
Answer:
1/3
Step-by-step explanation:
Take the total number of socks and compare it to the number of yellow socks. 15 and 5. Now divide the total by the specified group (yellow socks), by doing so, you get 3.
Every 1 in 3 socks is yellow, meaning the chance of picking a yellow sock at random is 1/3.
Calculate the sum of the first 20 terms of an arithmetic sequence with the 3rd term 8 and the 8th term 143.
Answer:
4670
Step-by-step explanation:
that is the workings above
If the third term is 8 and eighth term is 143 then the sum of first 20 terms is 4210.
What is arithmetic progression?Arithmetic progression is a sequence in which all the terms have equal differences. Nth term will be a+(n-1)d in which a is first term, d is difference and n is number of term.
How to calculate sum?We have been given that third term is 8 and eight term is 143 and we have to calculate the sum of first 20 terms.
[tex]A_{3}[/tex]=a+(3-1)d
8=a+2d-----1
[tex]A_{8}[/tex]=a+(8-1)d
143=a+7d---2
Subtract equation 1 from equation 2.
a+7d-a-2d=143-8
5d=135
d=27
Put the value of d in equation 1.
a+2d=8
a+2*27=8
a+54=8
a=-46
We know that,
[tex]S_{n}[/tex]=n/2[2a+(n-1)d]
=20/2[2*(-46)+(20-1)*27]
=10(-92+19*27)
=10(-92+513)
=10*421
=4210
Hence if the third term is 8 and eighth term is 143 then the sum of first 20 terms is 4210.
Learn more about arithmetic progression at https://brainly.com/question/6561461
#SPJ2
Which are solution of
[tex] \frac{x}{5} = \frac{1}{x + 4} [/tex]
Answer:
x = 1, x = -5
[tex]x/5 = 1/x+4\\Apply Fraction and Multiply : \\\\x(x+4)=5 x 1\\Simplify :\\x(x+4) = 5\\Solve.[/tex]
I hope this is what you were looking for !
Mariko needs about 18 wheelbarrows full of stone for her Japanese garden. Her wheelbarrow has vertical sides with the given shape and is 2 1/2 feet wide. How many cubic yards of stone should she order?
Answer:
I don't know yet haheuehehheejejejej
