[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:x = 5/2 [/tex]
[tex] \qquad \tt \rightarrow \: y = 3/2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2 \: \: \: \: \: \: \: \: - (1)[/tex]
[tex]\qquad \tt \rightarrow \: 7x -5 y = 10 \: \: - (2)[/tex]
[tex] \textsf{put value of x in equation 2} [/tex]
[tex]\qquad \tt \rightarrow \: 7 \bigg( \cfrac{y}{3} + 2 \bigg) - 5y = 10 [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} + 14 - 5y = 10 [/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y}{3} - 5y = 10 - 14[/tex]
[tex]\qquad \tt \rightarrow \: \cfrac{7y - 15y}{3} = - 4[/tex]
[tex]\qquad \tt \rightarrow \: - 8y = - 4(3)[/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{ - 12}{ - 8} [/tex]
[tex]\qquad \tt \rightarrow \: y = \cfrac{ 3}{ 2} [/tex]
[tex] \textsf{put value of y in equation 1 } [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{y}{3} + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \bigg (\cfrac{3}{2} \sdot\cfrac{1}{3} \bigg) + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{1}{2} + 2[/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{1 + 4}{2} [/tex]
[tex]\qquad \tt \rightarrow \: x = \cfrac{5}{2} [/tex]
Which of the following statements correctly describes this expression? 2x + 4
A. 4 less than 2 times a number
B. 2 times a number more than 4
C. The difference of 2x and 4
D. 4 times a number added to 2
Answer:
2 times a number more than 4
Answer:B
Step-by-step explanation:
What is the size of the angle, below?
Answer:
The size of the angle is between 180 and 360*. I cannot say the exact angle but my guess is correct and the correct answer is in between the 2 numbers.
Step-by-step explanation:
Solve the equation:
1-2 lnx = -4
~ [?]
X~
Round your answer to the nearest thousandth.
Answer:
x ≈ 12.182
Step-by-step explanation:
1 - 2lnx = - 4 ( subtract 1 from both sides )
- 2lnx = - 5 ( divide both sides by - 2 )
lnx = 2.5
x = [tex]e^{2.5}[/tex] ≈ 12.182 ( to the nearest thousandth )
Answer:
x = 12.182 (nearest thousandth)
Step-by-step explanation:
Given equation:
[tex]1-2 \ln x=-4[/tex]
Subtract 1 from both sides:
[tex]\implies 1-1 -2 \ln x =-4-1[/tex]
[tex]\implies -2 \ln x=-5[/tex]
Divide both sides by -2:
[tex]\implies \dfrac{-2 \ln x}{-2}=\dfrac{-5}{-2}[/tex]
[tex]\implies \ln x = \dfrac{5}{2}[/tex]
[tex]\textsf{As }\: \ln x=\log_ex \:\:\textsf{}[/tex], the natural logarithm can be canceled by giving both sides a base of e (Euler's number):
[tex]\implies e^{\ln x}= e^{\frac{5}{2}[/tex]
[tex]\implies x= e^{\frac{5}{2}[/tex]
[tex]\implies x=12.182\:\: \sf (nearest\:thousandth)[/tex]
Which triangles are similar to ABC
Answer:
DEF
Step-by-step explanation:
it is mathematically similar as the sides have a scale factor of 4
The first step in determining the solution to the system of equations, y = -x2 - 4x - 3 and y = 2x + 5, algebraically is to set the two equations equal as -x2 - 4x -3 = 2x + 5. What is the next step?
Answer:
See below
Step-by-step explanation:
Next step is to gather 'like' terms
-x2 - 4x -3 = 2x + 5.
x^2 + (4x + 2x) + (3+5) = 0 then simplify
x^2 + 6x + 8 = 0 then factor
(x+4)(x+2) = 0
so either of these terms = 0
x+4 = 0 means x = -4
x+ 2 = 0 means x = - 2
Answer:
d
Step-by-step explanation:
Combine like terms onto one side of the equation.
What is the area of Victor’s storage space?
The area of victor's storage space is 28 square inches
What is a polygon?A polygon is a plane shape with at least three sides.
Analysis:
Area of storage = area of triangle + area of rectangle
Height of triangle = 5 - 3 = 2 inches
Base of triangle = 12 - 4 = 8 inches
length of rectangle = 5 inches
width of rectangle = 4 inches
Area of storage = 5 x 4 + 1/2 x 8 x 2 = 28 square inches
In conclusion, the area of the storage space is 28 square inches.
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Mary and Julie both have a goal of raising $1000 for
charity. Mary raises $12 every 4 days. Julie raises $19
every 6 days.
Will Mary or Julie reach her goal first? Explain.
Answer:
julie
Step-by-step explanation:
12 x 4 +=48
19x 6 = 114
The sum of two numbers is 48. If one number is three more than twice the second number, which of the following is the
smaller number?
O 24
O 15
O 30
O 33
Answer:
15 (second option listed)
y = 15
x = 30
Step-by-step explanation:
setting up this statement algebraically:
[where x = one of our numbers, y = other number]
x + y = 48
x = (2y + 3)
x = 2y + 3
plug x [now in terms of y] into the original equation
(2y + 3) + y = 48
3y + 3 = 48
- 3 - 3
3 y = 45
÷3 ÷3
y = 15
from this value, we can plug it back into the y-value of the original equation to find our x-value
x + y = 48
x + 15 = 48
- 15 - 15
x = 33
{to check: 33 is 2y + 3}
we know that y = 15 (smaller number) and that x = 33 (larger number)
so, the solution to the question of which is the smaller number is 15
Are the equations -11(x-2)=8 and x-2=8+11 equivalent?
No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.
What is an equivalent expression?The equivalent is the expressions that are in different forms but are equal to the same value.
Then the equation is given below.
-11(x - 2) = 8
By simplifying, we have
x - 2 = - 8 / 11
No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.
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PLEASE HELP!! WILL GIVE BRAINLYEST AWARD TO 1st RIGHT!!
Answer:
-11 < x < 7
(first option listed)
Step-by-step explanation:
we know that x² + 4x < 77
first, we should rewrite our expression in standard
x² + 4x - 77 < 0
factor {find two numbers that multiply to c (77) and add to b (4) }
(x - 7) (x + 11) < 0
set both roots to 0:
x - 7 < 0
+ 7 + 7
x < 7
x + 11 < 0
x > -11
so, x will be < 7 and > -11
which can be expressed as
-11 < x < 7
So, -11 < x < 7
Answer:
-11 < x < 7
Step-by-step explanation:
1st option;
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
how to round to 4 decimal places using calculator with the given number of tan 30
Answer:
0.5774
Step-by-step explanation:
1) Input tan(30) into a calculator to get 0.5773502692...
2) To count 4 decimal places, we start after the decimal point. This means that we end it at the first 3. Additionally, we round 3 up to 4 because of the digit after it which is 5.
[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]
What is the tangent of 30, rounded to 4 decimal places?
.
[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]
First, let's focus on this phrase - "tan 30"
.
What in the world could that possibly mean?
"tan" is the tangent, which is one of the six trig ratios.
.
The simplest way to find the tangent of 30 degrees is ... with a calculator!
[tex]\bf tan\quad 30 \approx 0.5774[/tex]
The answer has been rounded to 4 decimal places, like you asked.
Since the fifth decimal place was more than 5, I added 1 to the fourth decimal place - 0.5774, and not 0.5773.
[tex]\rule{300}{1.7}[/tex]
[tex]\bf tan 30\approx 0.5574. \quad Hope\;you\;will\;have\;a\;fantabulous\;day![/tex]
~ [tex]\boxed{\bf aesthetic\;\not{101}}[/tex]~
Members of a soccer team raised $1818.50 to go to a tournament. They rented a bus for $960.50 and budgeted $35.75 per player for meals. Write and solve an equation which can be used to determine p, the number of players the team can bring to the tournament.
The equation formed by the given condition is 960.5 + 35.75p ≤ 1818.50 and the number of players they can bring is a maximum of 24.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given that,
The total amount that can be spent = $1818.50
Rent of bus = $960.50
Cost per player = $35.75/player
So,
Cost of bus + Cost per player × number of players ≤ The total amount that can be spent
960.50 + 35.75p ≤ 1818.50
35.75p ≤ 858
p ≤ 24
Hence "The equation formed by the given condition is 960.5 + 35.75p ≤ 1818.50 and the number of players they can bring is a maximum of 24".
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Equation:
Step-by-step explanation:
Solve for x in the diagram below.
Answer:
x = 34
Step-by-step explanation:
A straight line is 180 degrees
We can sum angles to form a straight line
x+12 + 100 +x = 180
Combine like terms
2x+112 = 180
2x+112-112 = 180-112
2x = 68
Divide each side by 2
2x/2 = 68/2
x = 34
answer:
=x+12+100+x =180
=x+x+12+100=180
=2x+112=180
=2x=180-112
=2x=68
=2/2x=68/2
=x=34
A dog sits at a corner of a square with side length 44 meters. the dog runs 10 meters along a diagonal toward the opposite corner. it stops, makes a 90 degrees right turn and runs 5 more meters. a scientist measures the shortest distance between the dog and each side of the square. what is the average of these four distances in meters?
Refer to the figure given below while reading the solution.
Suppose the dog reaches position A when traveled 10 m diagonally towards the opposite side.
And then position B when traveled 5 m towards the right turning 90°.
We can observe that APC is a right triangle with legs of equal length AC. And the coordinates of the point A is (AC, AC).
Also we can observe that APB is a right triangle with legs of equal length AD. Then the coordinates of the point D is (AC, AC-AD).
Hence, the coordinates of B will be (AC+AD, AC-AD).
Now, we since we have the coordinates we can calculate the shortest distances of B from each of the sides.
The shortest distance of B from PQ = AC-ADThe shortest distance of B from SR = 44-(AC-AD)The shortest distance of B from SP = AC+ADThe shortest distance of B from RQ = 44-(AC+AD)So, the average of the shortest distances of B from each side is [tex]\frac{(AC-AD)+44-(AC-AD)+(AC+AD)+44-(AC+AD)}{4}=\frac{44+44}{4}=22[/tex]
Hence, the average of the shortest distance of B from each side is 22 m
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Which sign should be used for the following equation? 0.452 _______ 0.712 < > ≤ ≥
Answer:
<
Step-by-step explanation:
0.4<0.7
4 is smaller than 7 so the sighn points to 0.7
3. A sequence of numbers is shown below. 1 5 9 13 17.
(a) Find an expression for the nth term of the sequence.
Answer:
Un= 1 + (n-1)4
Step-by-step explanation:
a=1
d=5-1=9-5=4
using the formula Un=a+(n-1)d
A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries. Choose a number between 80 and 96. This is the level of confidence you will use for this
The interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.
The complete question is
A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries.
Choose a number between 80 and 96. This is the level of confidence you will use for this section of problems. What is your number?
With the confidence level you chose, construct that % confidence interval for the population proportion of voters that answered correctly that 4th graders in the U.S. are above average in overall education compared to other countries. What is the margin of error for this confidence interval?What is Margin of Error ?It is defined as the margin by which the values calculated will differ from the real values .
Let the chosen number is 95 %
95% Confidence Interval ,
[tex]\rm p = p \pm \dfrac{Z_{0.05}}{2} \sqrt \dfrac{p(1-p)}{n}}\\\\= \dfrac{258}{700} \pm 1.96 \sqrt \dfrac{\dfrac{258}{700}(1-\dfrac{258}{700})}{700}}\\[/tex]
Therefore p at 95% Confidence Interval is given by 0.3329 , 0.4043
The margin of error is given by 0.4043-0.3329
= 0.0357
Therefore the interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.
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Write an equation for a polynomial with all the following features:
a. The degree is 5. b. The polynomial has 4 terms.
c. The graph of the polynomial crosses the vertical axis at y = 12.
2. Identify the approximate input values of any relative maximums and minimums of
this 5th degree polynomial.
Solve the Proportion.
10/a = 15/24
a=?
Answer:
a=16
Step-by-step explanation:
10/a=15/24, a≠0
10/a=5/8
80=5a
5a=80
a=16,a≠0
a=16
A trader mixes 2 kg
of butter which costs $8 per kg
with 3 kg of butter which costs $6 per kg. He sells the mixture at $2.55 per 250g. Express his profit as a percentage of his selling price.
Answer:
33.3333%
Step-by-step explanation:
Total number of kg- 2+3=5
Total money- (2×8)=16
(3×6)=18
16+18=34
$34=5000g
=250g
(250×$34)÷5000=$1.7
profit-2.55-1.7=0.85
(0.85/2.55)×100=33.333%
Which of the following will result in a rational number? Select all that apply.
An expression is defined as a set of numbers, variables, and mathematical operations
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given expression can be simplified as,
A.) 7 3/4 - (√11)/5 = (155-4√11)/20
B.) 7 3/4 ÷ (√11)/5 = 155/(4√11)
C) 7 3/4 + (√16)/5 = 166/20
D.) 7 3/4 + (√16)/5 = 31/5
The option that will result in a rational number is C and D.
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Help with Another Pre Calculus Question
The last equation h(x) = 2x+4/x+1.
What is a graph?The pictorial representation of quantities and how the increase or decrease in one affects the other.
Analysis:
The graph cuts the x-axis and y-axis at (-2, 0) and(0, -4) respectively.
gradient of the curve = y2 - y1/x2 - x1 = -4-0/0--2 = -4/2 = -2.
The equation with a gradient equal to -2 is, h(x) = 2x+4/x+1
differentiating the equation by quotient rule,
u = 2x+4, du/dx = 2, v = x+1 dv/dx = 1
dy/dx = [tex]\frac{(x+1)(2) - (2x+4)(1)}{(x+1)^{2} }[/tex] = [tex]\frac{-2}{(x+1)^{2} }[/tex]
When x = -2, dy/dx = -2
In conclusion, 2x+4/x+1 is the equation for the curve above.
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0 y-
Which of the following exponential equations
-2
|--1
2.0041
2.0123
3
2.0014
0 y=
x-3
Oy=3*-2-3
Oy-3-³+2
-3
3
3
-2
3
G
could be represented by the table below?
o
1
2.037
2.111
2.333
3
4
5
34:01
ما
11
Answer:
can you write these in proper way
A linear inequality that is represented by the graph include the following: C. y > 2/3(x) + 3.
What is the rules for writing an inequality?In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:
here, we have,
The line on a graph should be a solid line when the inequality symbol is (≥ or ≤).
The line on a graph should be a dashed (dotted) line when the inequality symbol is (> or <).
The line on a graph should be shaded above the line when the inequality symbol is (>).
Since the line on this graph was shaded above the line and it passes through the point (0, 3), it ultimately implies that 3 is part of its solution and as such, it is represented by this inequality equation:
y > 2x/3 + 3.
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Write the equation of the circle graphed below.
Step-by-step explanation:
eq of a circle is
(x-h)^2+(y-k)^2=r^2
h is 0
k=3
r is 1.5 this is radius of the circle
x^2+(y-3)^2=1.5^2
2. The wind blows the pinwheel below clockwise 180 degrees. What positions would the ribbon labeled A end up in after the wind blows it?
Answer: In between the red and yellow ribbons
Step-by-step explanation:
When something is rotated 180 degrees, you basically just mirror it. Since this pinwheel has an uneven amount of ribbons, there isn't a ribbon opposite of it, so it would be between red and yellow.
Se quieren llenar 100 botellas de agua con una capacidad de 1/4lt ¿cuantos litros de agua son necesarias?
Answer:
25
Step-by-step explanation:
Because 100 25+25+25+25 or 25/1/4
Where would 8.46 be located on a number line?
8.46 be located between 8.45 and 8.47 on a number line.
What is the number line?A number line is a horizontal line that has equally unfolded range increments. The numbers protected on the line will determine how the wide variety on the road may be responded to. The query that goes with the wide variety determines how it will likely be used, as an instance, in plotting a point.
What is a number line example?Numbers on various lines include all sets of numbers namely natural and complete numbers. An instance of a fixed of entire numbers is:(0, 1, 2, 3,5,6 …….) while the natural numbers consist of:1, 2, 3, four, five, 6…. a number of lines consists of 3 basic elements. within the center, the starting place is commonly plotted with 0.
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PLEASE HELP - mid term review question!
The isosceles triangle theorem states that if two sides of a triangle are _________, then the angles opposite those sides are congruent.
A. similar
B. adjacent
C. congruent
D. proportional
The isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent. The correct answer is option c.
What is the isosceles triangle?The triangle is having three sides in an isosceles triangle the two opposite sides are equal and the two adjacent angles with similar sides are equal.
The isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent.
Therefore the isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent. The correct answer is option c.
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Express in the form
1
:
n
.
Give
n
as a fully simplified fraction.
12
:
2
Answer:
1:(1/6) where n = 1/6