The required values of x and y are x = 2 and y = 11.
We have been given that parallelogram PQRS which has:
PT = y, TR = 5x+1, QT = 2y, TS = 6x+10
We know that the diagonals of a parallelogram bisect each other.
So, PT = TR and QT = TS
Substitute the values and we have a system of equations:
y = 5x + 1 ....(i)
2y = 6x + 10 ....(ii)
Substitute the value of the equation y = 5x + 1 in equation (ii), and solve for x
2(5x + 1) = 6x + 10
10x + 2 = 6x + 10
10x - 6x = 10 - 2
4x = 8
x = 8/4
x = 2
Substitute the value of x = 2 in equation (i), and solve for y
y = 5(2) + 1
y = 10 + 1
y = 11
Therefore, the required values of x and y are x = 2 and y = 11.
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What constant must be added to both sides of the equation x^2-6x=-5 in order to complete the square?
Answer: 9
Step-by-step explanation:
Clark deposited $5,000 at 3.8% interest, compounded continuously, when he was
18 years old. How much will be in the account after 22 years, if he made no other
deposits or withdrawals?
O $8,800.00
O $19,000.19
O $11,535.60
O $10,691.38
Clark will have $5820.80 in his account when he turns 22.
With an example, what is compound interest?
The interest you earn on interest is known as compound interest. Simple math may be used to demonstrate this: if you have $100 and it generates 5% interest annually, you will have $105 at the end of the first year. You will wind up with $110.25 at the conclusion of the second year.
Clark reportedly placed $5000 at a constant 3.8% interest rate when he was 18 years old.
Using the compound interest calculation, we can calculate how much Clark will make when he turns 22.
[tex]A=P . e^{rT}[/tex]
A= Amount after T years.
P= Principal amount.
e= Mathematical constant e.
r= Interest rate (in decimal form).
T= Time in years.
Let's decimalize the interest rate we've been given.
3.8 percent = 3.8/100 = 0.038
When we enter our provided values into the formula above, we will obtain,
[tex]A=5000 * e^{0.038(22-18)} \\A=5000*e^{0.038(4)}\\A=5000*e^{0.152}\\A=5000*1.1641\\A=5820.80[/tex]
Clark will therefore have $5820.80 in his account when he turns 22.
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Marvin is factoring the expression 54a^4+16ab^3 completely. What is the result
The factors of the given expression 54a⁴ +16ab³ are (C) 2a(27a³+8b³).
What are the factors?Writing a number or other quantitative item as the result of numerous factors—typically smaller or easier objects of the same kind—is known as factorization or factoring in math.
For instance, the equation x2 - 4 and the integer 15 can both be multiplied by the number 3 5.
So, we got the expression:
54a⁴ +16ab³
Now, factorize as follows:
54a⁴ +16ab³
Both 54 and 16 are multiples of 2 and have variables as common:
2a(27a³ + 8b³)
Therefore, the factors of the given expression 54a⁴ +16ab³ are (C) 2a(27a³+8b³).
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The temperature outside changed from 76°F to 41°F over a period of five days. If the temperature changed by the same amount each day, what was the daily temperature change?
A.
35°F
B.
-35°F
C.
7°F
D.
-7°F
Answer:
C. 7°F
Step-by-step explanation:
Question 5 of 23
LIGHTHOUSE Maya wants to know how far she is standing from a lighthouse. The end of Maya's shadow coincides with the end of the
lighthouse's shadow.
ft
48 ft
a. What is the distance from the lighthouse to the end of the lighthouse's shadow, x?
b. What is the distance from Maya to the lighthouse, y?
ft
6 ft
8 ft
The distance from the lighthouse is 64 ft and the distance from Maya to the lighthouse is 56 ft
The distance from the lighthouse to the end of the lighthouse's shadowFrom the question, we have the following parameters that can be used in our computation:
Height of lighthouse = 48 ft
Height of Maya = 6 ft
Using the above parameters and the attached figure, we have the following equivalent ratio
48 : x = 6 : 8
Multiply the second ratio by 8
So, we have
48 : x = 48 : 64
This means that
x = 64
What is the distance from Maya to the lighthouse, y?From the figure, we have
y + 8 = x
Recall that
x = 64
So, we have
y + 8 = 64
Evaluate
y = 56
Hence, the distance is 56 ft
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What is the slope of a line that is parallel to the line represented by the equation x - y = 8?
Answer:
Below
Step-by-step explanation:
x - y = 8 find slope of this line , parallel slope is the same
re-arrange the given line equation to y = mx + b form (m= slope)
y = (1) x-8 has slope = 1
A patient is receiving an infusion of 750mL with a rate of 250mL/h. How long will it take
to complete the infusion?
Answer:
3 hr
Step-by-step explanation:
750 ml / (250 ml/hr) = 3 hr
How do I turn this limit into a definite integral? Could you go step by step please
(The xi's are "x sub i" not "x times i")
To turn the specified limit, which is a Riemann sum, within the known interval, [2, 6], and variable, [tex]x_i[/tex], to a definite integral, the value, Δx is dx as n approaches infinity, to get;
[tex]\displaystyle \lim\limits_{n\to \infty}\sum\limits^n_{i=1}x_i\cdot \ln \left(1+x_i^2 \right) \Delta x, [2, \,6] = \int\limits^6_2 {x\cdot \ln \left(1+x_i^2 \right)} \, dx[/tex]
What is a Riemann sum?A Riemann sum is an approximation of an integral, which is the area of a region, by making use of the sum of simplified slices that make up the region.
A definite integral is a calculation used to find the area under a graph of a function by making use of very small or infinitesimal stripes of the region under the graph of the function.
The expression in the question is a Riemann sum
[tex]\lim\limits_{n \to \infty} \sum\limits_{i=1}^n x_i\cdot ln \left(1 + x_i^2 \right) \Delta x, [2, 6][/tex]
The Riemann sum can be converted into a definite integral, using the equation, [tex]\displaystyle{\lim\limits_{n \to \infty} \sum\limits_{i=1}^n f(x_i)\Delta x = \int\limits^b_a {f(x)} \, dx }[/tex]as follows;
The value of Δx is the value which values in the parenthesis are multiplying on the left, therefore; Δx is replaced with dx, as n → ∞
The limits of the Riemann sum in the question = [2, 6]
[tex]f(x_i) = x_i \cdot \ln\left(1 + x_i^2 \right)[/tex], therefore, [tex]f(x) = x \cdot \ln\left(1 + x^2 \right)[/tex]
Plugging in the the above values into the expression for the Riemann sum, we get the following definite integral;
[tex]\displaystyle{\lim\limits_{n \to \infty} \sum\limits_{i=1}^n x_i\cdot \ln \left(1 + x_i^2 \right) \Delta x, [2, 6] = \int\limits^6_2 {x\cdot \ln\left(1 + x^2\right)} \, dx[/tex]
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12. After 2 hours, Morgan had earned $12.75 at her lemonade stand. After 5
hours, she had earned $44.25. Assuming a linear function, write an
equation in the form y=mx+b that shows the profit earned from selling
lemonade for x hours.
Answer:
y = 10.5x - 8.25
Step-by-step explanation:
m = (44.25 - 12.75)/(5 - 2) = 10.5
y = mx + b
y = 10.5x + b
12.75 = 10.5 × 2 + b
b = -8.25
y = 10.5x - 8.25
what is the slope of the line on the graph?
Answer:
1/6
Step-by-step explanation:
A (6,1)
B (12,2)
slope = (2-1)/(12-6)
1/6
7. Find the value of x . First decide which trig function to use!
12.3
7.9
10.1
25.4
Using the trigonometric function of sine, the value of x is 10.1 units
From the given right triangle
The length of the hypotenuse = 16 units
The given angle = 39 degrees
The opposite side of the angle = x units
Here we have to use the trigonometric functions
sin θ = Opposite side / Hypotenuse
cos θ = Adjacent side / Hypotenuse
tan θ = Opposite side / Adjacent side
Use the equation of sin θ
Substitute the values in the equation
Sin 39 = x / 16
x = 16 × sin 39
x = 10.1 units
Therefore, the value of x is 10.1 units
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Match the equations of perpendicular lines. (You will not use all answer choices on the right.)
The following equation are perpendicular to each other .
y = 1 / 3 x + 4 → y = -3x - 4.y = 2 / 5 x - 7 → y = - 5 / 2 x + 7.y = - 5 / 2 x + 8 → y = 2 / 5 x - 6.y = -2x + 6 → y = 1 / 2 x + 3.y = 7 / 5 x - 9 → y = - 5 / 7 x - 11.How to represent the equation of a line?The equation of a line in slope intercept form can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, perpendicular lines have slopes that are the opposite of the reciprocal of each other.
Hence,
The equation perpendicular to y = 1 / 3 x + 4 is y = -3x - 4.
The equation perpendicular to y = 2 / 5 x - 7 is y = - 5 / 2 x + 7.
The equation perpendicular to y = - 5 / 2 x + 8 is y = 2 / 5 x - 6.
The equation perpendicular to y = -2x + 6 is y = 1 / 2 x + 3.
The equation perpendicular to y = 7 / 5 x - 9 is y = - 5 / 7 x - 11.
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what is the slope of the line parallel to the line whose slope is m=3/4
Answer:
The slope of a line parallel to the line with slope m=3/4 is also m=3/4. Parallel lines have the same slope.
0.20 is what fraction?
Answer: 20/100 or 1/5 (reduced)
Step-by-step explanation: To find the fraction, it is helpful to write a proportion. So. if we know every # will be out of 100, we can infer that it will be our whole (can also be represented by being written as 1 ) So now, if we move the decimal 2 places, we now have our fraction 20 out of 100. You can reduce this by dividing the 20 by 20 and the 100 by 20, to get 1/5. I hoped this helped.
Write an equation of the line passing through the point (4, 2) that is perpendicular to the line 4x+3y=7.
Answer:
y = 3/4x - 1
Step-by-step explanation:
4x + 3y = 7
3y = -4x + 7
y = -4/3x + 7/3
The slope of the given line is -4/3 so the slope of a line perpendicular to it is 3/4 (negative reciprocal).
y = 3/4x + b
Substitute x = 4 and y = 2:
2 = 3/4(4) + b
2 = 3 + b
b = -1
Thus the final equation is y = 3/4x - 1
figure a is a right triangle, and two of its sides have a length of 1 foot. therefore, its third side is greater than 1 foot in length.
According to the Pythagorean theorem, The Answer is Yes the third side is greater than 1 foot.
What do you mean by right angle triangle?A right triangle is one that has an interior angle of 90 degrees. The hypotenuse, which is also the side of the right triangle that faces the right angle, is its longest side. The height and base make up the two arms of the right angle.
What is the Pythagorean Theorem?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
p=1 foot
b=1 foot
[tex]h^{2} = p ^{2} + b ^{2}[/tex]
[tex]h=\sqrt {1^{2}+1^{2}}\\=\sqrt 2\\=1.41\\[/tex]
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Are the triangles similar, if so write how you know.
Answer:
no
Step-by-step explanation:
If the triangles are similar, then the ratios of the lengths of corresponding sides must be equal.
3/4 must equal 5/6 which must equal 6/7
3/4 = 0.75
5/6 = 0.8333...
6/7 = 0.857142...
None of the ratios are equal, so the triangles are not similar.
Anna went to the ice cream shop and found that ice cream was $0.20 per scoop (s). Write an equation that shows how many scoops of ice cream that Anna can purchase with $5.00.
The equation that calculates the number of scoops of ice cream that can be purchased is 0.20x = 5, and the number of scoops that can be purchased is 25.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
The definition of an equation is algebra is a mathematical assertion that shows the equality of two mathematical equations.
For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.
So, we know that 1 scoop of ice cream is $0.20.
Anna wants to purchase scoops for $5.00.
Let, the number of scoops is x.
Now, form the equation as follows:
0.20x = 5
x = 5/0.20
x = 25
Therefore, the equation that calculates the number of scoops of ice cream that can be purchased is 0.20x = 5, and the number of scoops that can be purchased is 25.
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5 x 4.5 - 12.6 ÷ 2 + 0.3 x 2.6
Answer:
5.73
Step-by-step explanation:
I solved it by just multiplying and adding. I didn't use pemdas so it might be wrong and if it is I'm sorry..
Pls help it urgent sove it
Answer:
x = 4
Step-by-step explanation:
2x + 1 ≥ 0
2x ≥ -1
2/2 x ≥ -1/2
x ≥ -1/2
√(2x+1)² = (4-1)²
2x + 1 = 3²
2x = 9 - 1
2x = 8
2/2 x = 8/2
x = 4
a study was made on the amount of converted sugar in a certain process at various temperatures. the data were coded and recorded in the accompanying table. use this information to answer parts a through c.
a. Correlation coefficient, r. =0.76751
b. Linear regression line y=6.5071+1.3929x
c. mean amount of sugar when temp. is 1.7
then y=8.87503
What a correlation coefficient means?A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.
What is linear regression with example?According to linear regression, sales are predicted to equal 168 + 23 advertising when using advertising as the predictor variable. This means that if spending on advertising is increased by one million euros, sales should grow by 23 million euros, and if no advertising was done, sales should be 168 million euros.
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If LM = x + 1, MN = 2x, and LN = 7, what is MN?
x + 1
Simplify your answer and write it as a proper fraction, mixed number, or integer.
The value of the MN is 4 according to the assumption on the number line.
According to the statement
We have to find that the value of the MN with the help of the value of the x.
So, For this purpose, we know that the
A number line is a horizontal line that has equally spread number increments.
Now,
Assuming that L, M, and N are points on a number line with L < M < N,
According to the assumption, the equation become
2x + x+1 = 7
3x +1 =7
3x =6
x = 2.
Now, the value of the MN become:
MN = 2x
MN = 2*2
MN = 4.
So, The value of the MN is 4 according to the assumption on the number line.
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In order for this ratio of volumes to be true, what measurements would have to be equal in all 3 solids?
O
a
Ob
0
C
d
The volume and the height
The radius and the surface area
The radius and the height
The surface area and the base
The measurements of the figures that should be equal in order for the ratio of volumes between the volumes of the cone, sphere, and cylinder of 1:2:3 to be true is; The radius and the height
What is a ratio?A ratio is a comparison between the magnitudes or measurements of items, expressing the number of times one item in the ratio is contained within another item in the ratio.
The formula for the volume of a cone, [tex]V_p[/tex] is, [tex]V_p[/tex] = (1/3)·π·r₁²·h₁
The formula for the volume of a sphere, [tex]V_s[/tex], is [tex]V_s[/tex] = (4/3)·π·r₂³
The formula for the volume of a cylinder, [tex]V_c[/tex], is [tex]V_c[/tex] = π·r₃²·h₃
The ratio of the volumes in the question is 1:2:3
Therefore; The volume of the sphere is twice the volume of the cone, and the volume of the cylinder is three times the volume of the cone, which indicates;
(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁...(1)
π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁...(2)
Equation (1) indicates that we have;
(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·h₁
Where, h₁ = 2·r₂, we get;
(4/3)·π·r₂³ = 2 × (1/3)·π·r₁²·(2·r₂) = (4/3)·π·r₁²·r₂
Therefore; r₁ = r₂, and the diameter of the sphere is equal to the height of the cone
The radius of the cone is equal to the radius of the sphere
Equation (2) indicates;
π·r₃²·h₃ = 3 × (1/3)·π·r₁²·h₁ = π·r₁²·h₁
Therefore;
r₃²·h₃ = r₁²·h₁
r₃ = r₁
h₃ = h₁
The radius of the cone = The radius of the cylinder
The height of the cone = The height of the cylinder
The ratio of the volumes, 1 : 2 : 3 is true when the measurements of the radius and the height are equal for all three solids.Learn more about the volume of regular solids here:
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Solve the equation. 3 2/3x = 2 2/5
The value of the given equation 3 2/3x = 2 2/5 is 36/55.
What is a mixed number?A mixed number is one that combines a whole number and a legal fraction. A number that contains both an integer (whole number) and a correct fraction is known as a mixed number or mixed fraction.
Pretzels, peanuts, Cheerios, and of course, rice and corn Chex are all included in this mix, which is why it is called a mix. Mixed numbers are those that contain both an integer and a fraction.
A mixed fraction is a fraction that is represented by both its quotient and remainder. For instance, 2 1/3 is a mixed fraction, where 2 is the quotient and 1 is the remainder. Therefore, a mixed fraction is a combination of a whole number and a proper fraction.
3 2/3x= 2 2/5
11/3 x=12/5
55x=36
x=36/55
Therefore, the value of the given equation 3 2/3x = 2 2/5 is 36/55.
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A cave explorer is at an elevation of −38 feet. The explorer starts moving at a rate of −12 feet per minute. The relationship between the explorer's elevation y, and her rate of decrease x, can be represented be the inequality 7 = -12x -38.
Solve the inequality to determine how many minutes it will take the explorer to reach an elevation deeper than -200 feet.
-200 [tex]\geq \\[/tex] -12x - 38
Answer:
To solve this inequality, we need to isolate the x-variable on one side of the equation. To do this, we can add 38 to both sides of the equation to get the following:
-200 - 12x - 38 = 38
-200 - 12x = 76
Next, we can divide both sides of the equation by -12 to get the following:
-200 - 12x = 76
x = -17
Finally, we can use the value of x to determine how long it will take the explorer to reach an elevation deeper than -200 feet. Since the explorer moves at a rate of -12 feet per minute, it will take her 17 minutes to reach this depth.
if a t-value is 1.67 in an upper-tailed test and degrees of freedom are 21, locate the correct interval below that contains the p-value. group of answer choices .90 < p-value.Group of answer choicesNot enough information is given to answer this question.a.01 < p-value < .02b.98 < p-value < .99c.99 < p-value < .995d.005 < p-value < .01
For a given t-value is 1.67 in an upper-tailed test , the interval below that contains the p-value is 0.05487.. So, the correct option is option (d) .
Values are given as,
test- statistic , t-value = 1.67
degree of freedom = 21
Using upper tailed test,
Using EXCEL function to find the p-value:
Function : =T.DIST.RT (t-value , deg -freedom)
Settings : =T.DIST.RT (1.67 , 21) = 0.05487
We used only positive value to find the upper tailed p-value .
lower tailed p-value ,
Settings : =T.DIST.RT ( - 1.67 , 21) = 0.94516
So, 0.05 < p-value < 0.95.. The interval value of p-value for upper tailed test is 0.005..
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Compare√150and 114/9 using <,>, or }=
√150>114/9
√150=114/9
114/9<√150
114/9>√150
114/9 > √150 that is, 114/9 is greater than √150
Given,
We have to compare √150 and 114/9 using <, >, or =
Comparison between two numbers;
Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than."
Here,
First we have to find the value of √150 and 114/9
That is,
The value of √150 = 12.25
The value of 114/9 = 12.66
Therefore,
We came to know that 114/9 is greater than √150 that is, 114/9 > √150
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Picture of coordinates (5,4) (3,4)
On a Cartesian plan
Both the coordinate points are plotted on the graph. The cartesian graph is attached with the answer.
What are coordinates?Coordinates are numbers which determine the position of a point or a shape in a particular space (a map or a graph). In the cartesian coordinate system, the coordinates are of the form (x, y).Other coordinate systems are : cylindrical and spherical coordinate systemGiven are the two coordinates to be plotted on a Cartesian plan -
(5, 4) , (3, 4).
The two given coordinate points are (5, 4) , (3, 4).
Refer to the graph attached. It shows both the points plotted.
Therefore, both the coordinate points are plotted on the cartesian graph.
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Question 4 of 10
Which number below is a prime number?
A. 12
B. 13
C. 24
D. 6
Answer:13 is a prime number
Step-by-step explanation:
Answer:
b) 13
Step-by-step explanation:
Now we have to,
→ find prime number from the options.
Generally we know that,
→ 2 is the only even prime number.
→ Other all prime numbers are odd.
Then the prime number is,
→ 13
(Because, it is the only odd number given)
Hence, the option (b) is correct.
why does dividing 5 by a number less than 1 give a qouient greater than 5?
Answer: It takes more five to reach that answer
Step-by-step explanation: