We are given a rectangle with the following dimensions;
[tex]\begin{gathered} l=(x+3) \\ w=(x+1) \end{gathered}[/tex]Also, placed inside the large rectangle, is a smaller shaded rectangle which has the dimensions;
[tex]\begin{gathered} l=(x+1) \\ w=x \end{gathered}[/tex]The ratio of both figures can be expressed as follows;
[tex]\text{Ratio}=a\colon b=\frac{a}{b}[/tex]Substituting for the values of both figures, we now have;
[tex]undefined[/tex]due in an hour pls help!!
Answer:
I think it's (4,5)
Step-by-step explanation:
29 + 17w = 624
w =
Help
Answer:
w = 35
Step-by-step explanation:
To solve this problem, you will need to undo it in reverse order. The first thing done to w is to multiply it by 17 and then add 29 to it. You need to undo the addition of 29 with subtraction first.
624-28=595
Next, you need to undo the multiplication by 17 with division.
[tex]\frac{595}{17} =35[/tex]
Therefore, your answer is 35
Which function is the inverse of f(x) = 8x + 4?A. 5-18) = —841 – 4)B. 7-14x) = 554OC. 5-11%) = 8.1 – 4)OD. 1x) = -1
ANSWER:
[tex]f^{-1}(x)=\frac{x-4}{8}[/tex]STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f(x)=8x+4[/tex]We calculate the inverse function as follows:
[tex]\begin{gathered} x=8\cdot f^{-1}(x)+4 \\ 8\cdot f^{-1}(x)=x-4 \\ f^{-1}(x)=\frac{x-4}{8} \end{gathered}[/tex]w + 3/5 = 1/2 solve for w and simplify your answer as much as possible
Answer: W=−1/10
Step-by-step explanation:
Move all terms not containing
W
to the right side of the equation.
Exact Form:
W=−1/10
Decimal Form:
W=−0.1
a pharmaceutical company knows that five percent of all users of a certain drug experience a serious side effect. a researcher examines a sample of 200 users of the drug. a. what is the probability of finding between 8 and 12 cases with side effects? (round final answer to 4 decimal places.) b. what is the probability of finding more than 16 cases with side effects? (round final answer to 4 decimal places.)
Using the normal distribution, the probabilities are given as follows:
a. Between 8 and 12 cases with side effects: 0.582 = 58.2%.
b. More than 16 cases with side effects: 0.0174 = 1.74%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the equation presented below:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure X is above or below the mean of the distribution, depending if the z-score is positive or negative.From the z-score table, the p-value associated with the z-score is found, and it represents the percentile of the measure X in the distribution.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution in this problem are given as follows:
p = 0.05, n = 200.
Hence the mean and the standard deviation of the approximation are given as follows:
E(X) = np = 200 x 0.05 = 10.[tex]\sqrt{V(X)} = \sqrt{np(1 - p)} = \sqrt{200(0.05)(0.95)} = 3.08[/tex]For item a, using continuity correction, the probability of between 8 and 12 cases with side effects is the p-value of Z when X = 12.5 subtracted by the p-value of Z when X = 7.5, hence:
X = 12.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (12.5 - 10)/3.08
Z = 0.81
Z = 0.81 has a p-value of 0.7910
X = 7.5:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (7.5 - 10)/3.08
Z = -0.81
Z = -0.81 has a p-value of 0.2090.
0.7910 - 0.2090 = 0.582 probability.
For item b, the probability of finding more than 16 cases with side effects is one subtracted by the p-value of Z when X = 16.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (16.5 - 10)/3.08
Z = 2.11
Z = 2.11 has a probability of 0.9826.
1 - 0.9826 = 0.0174 = 1.74% probability.
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24. The temperature in ° F on 20 days during the month of June
was as follows:
70° F, 76° F,
74° F, 74° F,
76° F,
78° F,
74° F,
76° F,
70° F, 70° F, 72° F,
78° F, 76° F,
74° F,
74° F, 78° F, 80° F,
80° F, 76° F
78° F
What is the mode of temperature for the month of June?
Karen made costumes for the annual school play. She used a total length of928.8 in of blue fabric. The fabric came in 2 rolls that each had the samelength. How much fabric was in each roll? Write your answer in yards.Use the table of conversion facts as necessary, and do not round your answer.=Conversion facts for length12 inches (in) = 1 foot (ft)3 feet (ft) = 1 yard (yd)36 inches (in) = 1 yard (yd)5280 feet (ft) = 1 mile (mi)1760 yards (yd) = 1 mile (mi)ydX 5 ?
Please only answer if you know the answer thank you.
Answer:
x = - 5;
y = 5;
Step-by-step explanation:
Identify the equation.
y = ( 2 / 3 )x + c;
Substitute a point.
5 = ( 2 / 3 )( - 2 ) + c;
5 = ( - 4 / 3 ) + c;
5 - ( - 4 / 3 ) = c;
5 + ( 4 / 3 ) = c;
19 / 3 = c;
y = ( 2 / 3 )x + ( 19 / 3 );
Substitute point A.
3 = ( 2 / 3 )x + ( 19 / 3 );
3 - ( 19 / 3 ) = ( 2 / 3 )x;
( 9 / 3 ) - ( 19 / 3 ) = ( 2 / 3 )x;
- ( 10 / 3 ) = ( 2 / 3 )x;
- ( 10 / 3 )( 3 / 2 ) = x;
( - 30 / 6 ) = x;
- 5 = x;
x = - 5;
Substitute point B. Use common sense and notice that point B is actually the same as the first point.
y = 5;
Answer:
x = -5
y = 5
Step-by-step explanation:
You could write the equation in the point slope form of a line
y - [tex]y_{1}[/tex] = m( x - [tex]x_{1}[/tex])
Use the slope they gave us 2/3. Use the point they gave us for [tex]x_{1}[/tex] ( -2 ) and [tex]y_{1}[/tex] ( 5)
y -5 = 2/3(x - -2)
y - 5 = 2/3(x + 2) Plug in 3 for y to solve for x
3-5 = 2/3(x + 2)
-2 = 2/3x + 4/3 subtract 4/3 from both sides of the equation
-2 - 4/3 = 2/3x
[tex]\frac{-6}{3}[/tex] - [tex]\frac{4}{3}[/tex] = 2/3x
[tex]\frac{-10}{3}[/tex] = 2/3 x Multiply both sides by [tex]\frac{3}{2}[/tex]
([tex]\frac{3}{2}[/tex])[tex]\frac{-10}{3}[/tex] = ([tex]\frac{3}{2}[/tex])([tex]\frac{2}{3}[/tex]) x
-5 = x
substitute in -2 for x to solve for y
y - 5 = 2/3(x + 2)
y - 5 = 2/3(-2+2)
y - 5 = 2/3(0)
y - 5 = 0 Add 5 to both sides
y = 5
Only 20 percent of the spectators left the contest discontented. If 6000 spectators left the contest contented,
how many left discontented?
There are 24000 spectators left the contest discontented.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
We have been given that Only 20 percent of the spectators left the contest discontented.
If 6000 spectators left the contest contented, then the contest left discontented are;
The spectators left the contest contented = 6000
20/ 100 x D = 6000
D = 6000 x 100/20
D = 30000
Now the contest left discontented are;
80 percent = 80/100 x 30000
= 24000
Hence, 24000 spectators left the contest discontented.
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Find the equation of a line perpendicular to 4x+4y=32 that passes through the point (7,1)
The equation of the line perpendicular to 4x + 4y =32 that passes through the point (7,1) is x - y = 6 .
In the question ,
it is given that
the required line is perpendicular to 4x + 4y =32
the slope of 4x + 4y =32
4y = -4x + 32
y = -x + 8
slope = -1
so the slope of the perpendicular line [tex]=[/tex] 1 .
the equation of the perpendicular line passing through (7,1) and slope as 1 is
(y - 1) [tex]=[/tex] 1 (x - 7)
y-1 = x-7
x - y = 7-1
x - y = 6
Therefore , The equation of the line perpendicular to 4x + 4y =32 that passes through the point (7,1) is x - y = 6 .
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If A and B are two disjoint sets with
n(A) = 4 and n(B) = 2, then
n(A −B) =
2
Step-by-step explanation:
n(A-B)
n(4-2)
n(2)
Therefore n(A-B)=2
a water tank is to contain 2,000 liters of water it is constructed to be 4 meters long and 1.5 meters wide. find the height of the tank.
Remember that
1 m3=1,000 lt
2 m3=2,000 lt
The volume of the tank is equal to
V=L*W*H
we have
V=2 m3
L=4 m
W=1.5 m
H=?
substitute given values
2=4*1.5*H
solve for H
2=6H
H=2/6
H=1/3 mWhat is the answer for this as the y- intercept of two points? (-6,-5) and (-4,-4)
The slope intercept form of the equation that passes through (-6, -5) and (-4, -4) is y = 1 / 2x - 2
How to represent equation in slope intercept form?The equation in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, let's find the slope of the lines using (-6, -5) and (-4, -4).
m = y₂ - y₁ / x₂ - x₁
m = -4 + 5 / -4 + 6
m = 1 / 2
Therefore, lets find the y-intercept using (-4, -4)
-4 = 1 / 2 (-4) + b
-4 = -2 + b
b = -4 + 2
b = -2
Therefore, y = 1 / 2x - 2
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The slope-intercept form of the equation that passes through (-6, -5) and (-4, -4) will be; y = 1 / 2x - 2
What is slope intercept form?The equation in slope intercept form can be represented as :
y = MX + b
where m is the slope, b is the y-intercept
Therefore, to determine the slope of the lines using (-6, -5) and (-4, -4).
m = y₂ - y₁ / x₂ - x₁
m = -4 + 5 / -4 + 6
m = 1 / 2
Therefore, the y-intercept using (-4, -4)
-4 = 1 / 2 (-4) + b
-4 = -2 + b
b = -4 + 2
b = -2
Thus, y = 1 / 2x - 2
The slope-intercept form of the equation that passes through (-6, -5) and (-4, -4) will be; y = 1 / 2x - 2
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Pick one of the remaining choices and explain on the lines below, why thatchoice contains two expressions that are not equivalent for any value of r.
If two expressions have the same coefficients of the variable, then the variable can be any number
For the first choice
3(3r + 3) = 9r + 9 === 1st expression
6r + 6 ===== 2nd expression
If we equate them
9r + 9 = 6r + 6
If we solve the equation we will find just one value of r
9r + 9 - 6r = 6r - 6r + 6
3r + 9 = 6
3r + 9 - 9 = 6 - 9
3r = -3
r = -1
But in the other choices, the two expressions have the same coefficients of r
Then when we equate them they will cancel each other
Then r can be any value
Because it does not affect the equation
Write the expression 16x + 28 as a product using the GCF as one of the factors.
Please help.
Answer:
4(4x + 7)
Step-by-step explanation:
To answer this question you need to understand what GCF is
GCF is Greatest Common Factor
GCF is the highest number that divides exactly into two or more numbers.
The expression is 16x + 28
The highest number that can divide 16 and 28 is 4
Dividing 16x + 28 gives => 16x/4 + 28/4 => 4x + 7
So the factored expression is
4(4x + 7)
Given a Figure whose points are A(9, 1), B(2, 3), C(-2, 4).
What would be the image of that figure if it goes under a translation (x, y) -> (x - 5, y + 8), what is the
coordinate of B'?
A. B'(-14, 11)
B. B'(3, 11)
C. B'(14, 11)
D. B'(-3, 11)
Answer:
B' (-3,11)
Step-by-step explanation:
B(2,3) The rule is saying subtract 5 from x and 8 add to y
(2 -5, 3 + 8)
(-3,11)
PLEASE HELP!!!! Solve using the quadratic formula
Answer:
Step-by-step explanation:
Given Equation
3x^2 + x = - 2x - 7
Solution
Add 2x + 7 to both sides
3x^2 +x + 2x + 7 = -2x - 7 + 2x + 7 Combine like terms
3x^2 + 3x + 7 = 0
Givens
a = 3b = 3 c = 7x = (-b +/(√b^2 - 4ac))/2
x = (-3 +/- (√3^2 - 4(3 *7)) / 2*3
x = (- 3 +/- (9 - 84)) / 2 *3
x = (- 3 +/- √ (-75))/6
x = (- 3 +/- 8.660i ) / 6
x = -.5 +/-1.443i
Answer
x = -.5 + 1.443.i
x = -.5 - 1.443i
What is the equation in slope-intercept form of the line that passes through the point(4,-11) and is perpendicular to the line represented by y=4x-1?
Answer:
y = (-1/4)x - 10
Step-by-step explanation:
y = 4x - 1
y = -1/4x - 1
(4, -11),
(x₁, y₁)
y - y₁ = m(x - x₁)
y - (-11) = (-1/4)(x - 4)
y + 11 = (-1/4)x + 1
-11 -11
-------------------------------
y = (-1/4)x - 10
I hope this helps!
Evelyn is thinking of constructing a swimming pool in the plot next to her house such that it is surrounded by grass as given in the figure below. The dimensions of the plot is 50 ft x 40 ft, and the area of the grass is 1184 ft^2. Find the dimensions of the pool.
The area of a pool from the given situation is 816 ft².
Given that, the dimensions of plot is 50 ft and 40 ft.
What is the area of a rectangle?The area occupied by a rectangle within its boundary is called the area of the rectangle. The formula to find the area of a rectangle is Area = Length × Breadth.
Here, area of a plot = Length × Width
= 50 × 40
= 2000 ft²
Area of a pool = Area of a plot - Area of a grass
= 2000 - 1184
= 816 ft²
Therefore, the area of a pool from the given situation is 816 ft².
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Question 7 013 points Redo Which theorem is depicted by the figure and information shown below? R S Theorem? ZRAZT 2Qazs A) Opposite sides of parallelograms are congruent (Tm 16-A) B) Opposte angles in a parallelogram are congruent. (Tm 16-B) C) The sum of any consecutive angles within a parallelogram equals 180 (Tm 16-C) D) The diagonals of a parallelogram bisect each other (Tm 16-D) E) The diagonal of a parallelogram separates it into two congruent triangles (Tm 16-E)
Answer:
B. Opposite angles in a parallelogram are congruent.
Explanation:
The figure shows a parallelogram. In this parallelogram, ∠R and ∠T are opposite angles and ∠Q and ∠S are opposite angles.
Since the information says that ∠R is congruent to ∠T and ∠Q is congruent to ∠S, the theorem is opposite angles in a parallelogram are congruent.
So, the answer is B. Opposite angles in a parallelogram are congruent.
What is the slope of the line? ASAP.
Answer:
The slope would be 25/1 or 25.
Step-by-step explanation:
Use the formula y2-y1 over x2-x1. Or use rise over run.
The graph of function f is shown. An exponential function on a coordinate plane passes through (minus 1, 7), (1, 2), (10, minus 1) and also intercepts the x-axis at 3 units and the y-axis at 4 units. Function g is represented by the table. x -1 0 1 2 3 g(x) 24 4 0 Which statement correctly compares the two functions? A. They have the same x- and y-intercepts. B. They have different x- and y-intercepts but the same end behavior as x approaches ∞. C. They have the same x-intercept and the same end behavior as x approaches ∞. D. They have the same y-intercept and the same end behavior as x approaches ∞.
Which number line represents the solutions to |x + 4| = 2?
Answer:
The first option is correct :)
Step-by-step explanation:
x=-6, x=-2
|x+4|=2
x+4=2, x=-2
x+4=-2, x=-6
:] (Tell me if this is incorrect!)
(brainliest would help a lot)
Answer: the first one (-2,-6)
Step-by-step explanation:
|x+4| = 2
subtract 4 from both sides and you get -2
|x+4| = -2
subtract 4 from both sides and you get -6
If you want to check your answers, plug it into the original equation
which equation represents a linear function
The linear function will be;
⇒ y = - 4x + 5
What is linear expression?
A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.
Given that;
The functions are,
1. y = - 3x² + 2
2. y = 2x²
3. y = - 4x + 5
4. y = x³
Now,
Since, The linear function has a variable raised to the first power.
Clearly, In first equation;
The highest power of the variable is 2.
So, It is not a linear function.
Clearly, In second equation;
The highest power of the variable is 2
So, It is not a linear function.
Clearly, In third equation;
The highest power of the variable is 1.
So, It is a linear function.
Clearly, In fourth equation;
The highest power of the variable has power 3.
So, It is not a linear function.
Therefore, The linear function will be;
⇒ y = - 4x + 5
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SAMANTHA HAS $27 TO RENT A BIKE FROM CYCLES RUS. SHE
HAS TO PAY A $IO FEE PLUS $2 FOR EVERY HOUR SHE HAS THE
BIKE. WRITE AND SOLVE AN INEQUALITY TO FIND THE
MAXIMUM NUMBER OF HOURS SAMANTHA CAN RENT THE BIKE.
Answer:
2 hours
Step-by-step explanation:
10+10= 20, so $20 fee
2+2= 4, so a fee for every hour she has the bike.
20+4= $24, so 2 hours maximum
If you tried adding another hour (which would be $12) that would equal $36 which is over her budget.
raph, a
scription
of values
context.
R24
mble.
written
of a
cion,
SHIPPING The OOCL Shenzhen, one of the world's largest
container ships, carries 8063 TEUS (1280-cubic-feet containers).
Workers can unload a ship at a rate of 1 TEU every minute. The
equation y = 8063 - 60x represents the number of TEUs on the
ship y after x hours of the workers unloading the containers from
the Shenzhen.
a. Find the x- and y-intercepts and interpret their meaning in the
context of the situation.
Graph the equation by using the intercepts
Answer:
23
Step-by-step explanation:
study questions from digital text book page 2.03 : Picture's down below
Question #1 : What is m∠SVT?
Question #2: What is the m∡BEC?
Disclaimer!! these are not from a Test, Quiz, or Assignment. these are from a practice page and i wanted to know how do these questions for a Future assignment with questions like these. I am just informing you guys because i didn't know the guidelines until now and i will no longer put test questions up because I am now aware its not ok to do so. So This Is not from a Test, Quiz, or Assignment. Thank you
The angle measures in this problem are given as follows:
1. Angle SVT: 79º.
2. Angle BEC: 65º.
Angle SVTAngles SVT and SVR are vertical, meaning that they have the same measure, hence we can find the value of y as follows:
8y - 33 = 5y + 9
3y = 42
y = 42/3
y = 14.
Hence the measure of the angle SVT is of:
m<SVT = 5y + 9 = 5(14) + 9 = 79º.
Angle BECThe two angles given in this problem are also vertical, meaning that we can solve for x as follows:
5x - 10 = 3x + 40
2x = 50
x = 50/2
x = 25º.
Then the bottom angle is:
3 x 25 + 40 = 115º.
The bottom angle is supplementary with angle BEC, hence we can find the measure of angle BEC as follows:
115 + m<BEC = 180
m<BEC = 180 - 115
m<BEC = 65º.
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REVIEW & REFRESH
42. Tell whether x and y are proportional.
43. What number is 60% of 35?
44. 27 is what percent of 75?
Just do 42 and 44
Using proportions, it is found that:
42. x and y are not proportional.
43. The number 21 is 60% of 35.
44. The number 27 is 36% of the number 75.
How to verify if two variables are proportional?Two variables, x and y, will represent a proportional relationship if the ratio between them is always the same.
From the table, the ratios are given as follows:
6/4 = 1.5.8/6 = 1.25.Different ratios, hence the variables x and y are not proportional.
Percentage of a numberTo find the percentage of a number, the decimal equivalent of the percentage is multiplied by the number.
The decimal equivalent of a percentage of 60% is:
60/100 = 0.6.
Hence the percentage of 35 is calculated as follows:
0.6 x 35 = 21.
The percentage that the number 27 represents of the number 75 is given by the division of 27 by 75 multiplied by 100%, hence:
27/75 x 100% = 36%.
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Which expression is equivalent to
09
O
15
8h6
O
2h²
15
2h6
g8
(295)³
(44²) ³²
8h
The equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].
What is inequality?
Expressions that are equivalent do the same thing even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Consider the given expression, [tex]\frac{(2g^5)^3}{(4h^2)^3}[/tex]
Using the rule, [tex](a^m)^n = a^m^n[/tex]
So, [tex]\frac{(2g^5)^3}{(4h^2)^3} = \frac{8g^1^5}{64h^6}[/tex]
After simplifying we get, [tex]\frac{g^1^5}{8h^6}[/tex]
Therefore, the equivalent expression of the given expression is [tex]\frac{g^1^5}{8h^6}[/tex].
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Which of the images above represents a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.
The image above represents a proof of the Pythagorean Theorem is image B.
What is Pythagorean Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a fundamental relationship in Euclidean geometry between the three sides of a right triangle.
It states that the sum of the squares of the leg lengths equals the square of the hypotenuse length.
This is illustrated as:
a² = b² + c²
The values in image 2 will be used to ascertain this. Therefore,
5² + 12² = 13²
25 + 144 = 169
169 = 169
Therefore, B is correct as the value is gotten.
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Answer:
u see the formula for the Pythagorean theorem is a^2 + b^2 = c^2 i hope this helps please mark as brainliest have a good day!!! :D Bye
Step-by-step explanation: