The required value of x for the given figure is 2√7 units.
What is right angled triangle?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular edges. The foundation of geometry is the relationship between the sides and other angles of the right triangle.
According to question:In the given figure we have two triangle big and small triangle.
To find the value of x;
first we use Pythagoras theorem in big triangle.
So; let base of big triangle is b
9² = 7² + b²
b² = 81 - 49
b = √32
Now in small triangle;
(√32)² = x² + 2²
32 = x² + 4
x² = 28
x = √28
x = 2√7 units.
Thus, required value of x is 2√7 units.
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QUESTION 9
Consider the following argument: If Benji's parents buy him a puppy for Christmas, he learns important care-giving skills.
Benji learns important care-giving skills. So, Benji's parents buy him a puppy for Christmas. What is the logical form of
this argument?
O a. Modus Ponens
O b. Hypothetical Syllogism
O c. Disjunctive Syllogism
O d. Denying the antecedent
O e. Affirming the consequent
e. Affirming the Consequent. The argument takes the form of "If P then Q. Q, therefore P."
What is Consequent?Consequent is an outcome or result of an event, action, or decision. It is the result of a cause or premise. Consequents are usually expected and predictable, and can be measured or observed. Consequents are important in the study of cause and effect relationships and can be used to determine the success or failure of certain actions. Consequents can also be used to measure the degree of success or failure of certain objectives. Consequents are often used in decision-making, as well as in research and problem-solving, to help determine the best course of action and the best solution.
In other words, the conclusion (Benji's parents buy him a puppy for Christmas) is based on the premise that Benji learns important care-giving skills.
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Part B
Interest can be calculated on money invested and money borrowed. Based on her four options, in which account should
Brianna choose to invest her summer earnings?
Use your answers from Part A to justify your response. Explain your reasoning using complete sentences.
Based on the four options, Brianna should choose to invest her summer earnings in the Account 4 (compounded continuously) because interest is at highest in the account after like 3 years.
Why is interest higher when compounded continuously is used?Interest is higher in compounded continuously because it is calculated more frequently than in other compounding methods, such as annually or semi-annually. In continuous compounding, interest is calculated and added to the principal an infinite number of times over a given period, which results in a higher effective interest rate than other compounding methods.
This means that the amount of interest earned on an investment or loan increases more rapidly, which can result in greater returns for investors or higher costs for borrowers. Continuous compounding is often used in financial markets where small changes in interest rates can have significant impacts on returns, such as in the case of short-term bonds or options trading.
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In a classroom 1/6 of the students are wearing blue shirts and 2/3 are wearing white shirts. There are 12 students in the classroom. How many students are wearing shirts other than blue shirts or white shirts.
Answer:
Step-by-step explanation:
Blue shirts: [tex]\frac{1}{6}[/tex]×[tex]12=2[/tex]
White shirts: [tex]\frac{2}{3}[/tex]×[tex]12=8[/tex]
∴ there are 2 students(12-2-8=2) wearing a different shirt.
How many more saplings with a height of 27 1/4 inches or less were there than saplings with a height greater than 27 1/4 inches?
(Total saplings- Saplings with a height greater than 27 1/4 inches) = Number of saplings with a height of 27 1/4 inches or less.
How to find height of an object?To find the height of an object in mathematics, you must first identify the shape of the object. Then, use the relevant formula for the shape to calculate the height. For example, if the object is a right triangle, the height can be found by using the Pythagorean Theorem. Additionally, if the object is a rectangle, you can use the formula for the area of a rectangle to calculate the height. Finally, if the object is a circle, you can use the formula for the circumference of a circle to find the height.
To solve this question, we will use the numerical approach. First, we need to subtract the number of saplings with a height greater than 27 1/4 inches from the total number of saplings. Then, we subtract the result from the total number of saplings. The result will be the number of saplings with a height of 27 1/4 inches or less.
Therefore, the equation is (Total saplings- Saplings with a height greater than 27 1/4 inches) = Number of saplings with a height of 27 1/4 inches or less.
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the sum is -7 and the difference is 14
Answer:
please give more information like what to find
3.5, -10.5
Step-by-step explanation:
5.An inequality is shown below.
x < 20
Which equation has a solution that satisfies the inequality?
A. ³/4x=12
B. x = 37
C. 21.2=x-12/1/2
D. x = 2.2 6+2³
Answer:
the answer is d because 2.2 6+2 with a exponent of 3 = 14 and 14 is less than 20
Step-by-step explanation:
Question In the coordinate plane, what is the length of the line segment that connects points at (5, 4) and (−3, −1)? Enter your answer in the box. Round to the nearest hundredth. units?
The length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.
Explain about the distance formula?The distance formula is still a formula used to determine how far apart two places are from one another. The dimensions of these points are unlimited. For instance, you could need to determine the separation between two points in space, a plane, or a line (1, 2, or 3 dimensions) .Using the formula obtained from Pythagoras' theorem, distance can be computed.
The distance formula in coordinate geometry is:
(P, Q) = √ (x2 – x1)² + (y2 – y1)².
Given points: (5, 4) and (−3, −1)
d = √ (-3 - 5)² + (4 + 1)²
d = √ 64 + 25
d = √ 89
d = 9.43
Thus, the length of the line segment that connects points at (5, 4) and (−3, −1) is found to be 9.43 units.
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Write an integer for each situation. 1. a profit of php 100.00
The integer to represent the profit of php 100.00 is +100.
What is an Integer?Integers include all whole numbers and negative numbers. This means if we include negative numbers along with whole numbers, we form a set of integers.
Given that, a profit of php is 100.00.
The profit or gain is equal to the selling price minus the cost price. Loss is equal to the cost price minus the selling price.
So, here the integer is +100
Therefore, the integer to represent the profit of php 100.00 is +100.
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The question is in the photo
The value of y, given that Triangle FEG is similar to Triangle IHJ is 10.
How to find the value of y ?Seeing as Triangle FEG is similar to Triangle IHJ, we can assume that angle EGF is the same as angle HJ1.
This means that 5 y + 8 is equal to 58 degrees.
The value of y is therefore :
5 y + 8 = 58
5 y = 50 - 8
y = ( 50 - 8 ) / 5
y = 50 / 5
y = 10
In conclusion, given the two similar triangles and the angles EGF and HJI, the value of y can be found to be 10.
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On a recent fishing trip , Marty hooked a fish 12 feet directly under his boat . At the same time, he saw and eagle flying 50 feet above the boat. Which number sentence accurately compares these distances above and below the boat ?
Answer:
-12 +50
Step-by-step explanation:
Helping in the name of Jesus.
Please help me answer this
Answer:
x = 229
Step-by-step explanation:
x = 467 - 238
x = 229
Please anyone help me with this ?!!! Thank you:))!!
The solution is, he had 68 marvels.
What is addition?
Addition is a way of combining things and counting them together as one large group. ... Addition in math is a process of combining two or more numbers.
here, we have,
given that,
he added 36 marvels, now, he has 104 in total,
we have to find that, how many he had.
let, he had = x
so, we know, added = 36
i.e. now total is = x+36
ATQ, we get,
x+36 = 104
or, x = 104 - 36
or, x = 68
Hence, The solution is, he had 68 marvels.
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Plssssss help--- Jordan bought 3 books and Felicia bought 5 books. They spent a total of $60. How much did each book cost if they were all the same price.
Step-by-step explanation:
$60÷8=$7.50
divide by 8 because 5+3=8
each book should of cost $7.50
Select the correct answer. What are the solutions to the equation x2 − 1 = 399? A. B. C. D.
Answer:
x = 20
Step-by-step explanation:
x² − 1 = 399
x² = 400
x = 20
p+20°
What is the value of p?
p=
3p
O
бр
Appreciate it a lot
Answer:
16°
Step-by-step explanation:
10p+20=180
10p=120
p=16
What is the solution of
3+
x <3
O x≤3
O x > 3
O x≥3
X-2
x-3542
Answer:25
Step-by-step explanation: easy
Two families purchased lunch at a hotdog cart. The first family paid $18.00 for 4 hot dogs and 4 drinks. The second famliy paid $20.00 for 5 hot dogs and 3 drinks.
What is the price, in dollars, of a hot dog? Enter your answer as $0.00
one answer only
Answer:
The price of a hot dog is $2.00
Let h = height. Write an
inequality to show that a child must be at least 48 inches tall to ride the rollercoaster.
Answer:
h [tex]\ge[/tex] 48
Step-by-step explanation:
This inequality states that the height h, must be either equal to 48 to greater than 48.
Find the area of the figure.
b) Work out the size of angle x. Give your
answer in degrees (º).
56°
X
59°
77°
Answer:
Step-by-step explanation how do I use this appp :
5,10,15,20,25 is this an arithmetic or geometric sequence
Because of the common difference of 5, this series is math because it has a common difference of 5.
What in mathematics is an arithmetic sequence?An arithmetic series is one in which each term grows by adding or removing a certain number, k. In a geometric series, each term grows by dividing by or increasing by a certain constant k. For instance, a1 = 25 and a(n) Equals a(n-1) Plus 5.
This is a list of numbers.
Each term in an arithmetic series is created by adding a fixed difference to the term before it. The distance between successive words in this order is 5:
10 - 5 = 5
15 - 10 = 5
20 - 15 = 5
25 - 20 = 5
Therefore, this sequence has a common difference of 5, which means it is an arithmetic sequence.
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Can someone please help me with this math problem?
Determine if the relation is a function. If it is not, What are the two ordered pairs as proof?
Using the vertical line test we can see that this is not a function.
Is the relation a function?When we have a graph of a relation, one thing we can do to check if this is a function is do the vertical line test.
If you can draw a vertical line that intercepts the graph more than once, then it is not a function.
Here we can see a circle, multiple lines intercept the graph twice,so this is not a function.
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Answer the following payroll calculations
1. If you make $14 an hour and you work 32 hours a week, what is your gross pay for the week?
2. What is your net pay, if you have Federal taxes taken out at 10%, State taxes at 4.5% and FICA at 6%?
3. If you make $17 an hour and you work 40 hours a week, what is your gross pay for the week?
What is your net pay, if you have Federal taxes taken out at 10%, State taxes at
4.5% and FICA at 6%?
4. If you make $20 an hour and you work 40 hours a week, You also worked 5 hours of overtime, at time and a half, what is your gross pay for the week?
5. What is your net pay, if you have Federal taxes taken out at 14%, State taxes at 4.5% and FICA at 6%?
Answer:
1. Gross pay = hourly rate x hours worked
Gross pay = $14 x 32 = $448
2. Net pay = gross pay - deductions
Federal taxes = 10% of gross pay = 0.1 x $448 = $44.80
State taxes = 4.5% of gross pay = 0.045 x $448 = $20.16
FICA = 6% of gross pay = 0.06 x $448 = $26.88
Total deductions = $44.80 + $20.16 + $26.88 = $91.84
Net pay = $448 - $91.84 = $356.16
3. Gross pay = hourly rate x hours worked
Gross pay = $17 x 40 = $680
4. Regular pay = hourly rate x hours worked
Regular pay = $20 x 40 = $800
Overtime pay = (hourly rate x 1.5) x overtime hours
Overtime pay = ($20 x 1.5) x 5 = $150
Gross pay = regular pay + overtime pay
Gross pay = $800 + $150 = $950
5. Net pay = gross pay - deductions
Federal taxes = 14% of gross pay = 0.14 x $950 = $133
State taxes = 4.5% of gross pay = 0.045 x $950 = $42.75
FICA = 6% of gross pay = 0.06 x $950 = $57
Total deductions = $133 + $42.75 + $57 = $232.75
Net pay = $950 - $232.75 = $717.25
Step-by-step explanation:
find the axis of symmetry for f(x)=x^{2}+12x+31
so since the squared variable is the "x", we're looking at a vertical parabola, and its axis of symmetry will be at the x-coordinate for its vertex, let's find its vertex then
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ f(x)=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+31} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 12}{2(1)}~~~~ ,~~~~ 31-\cfrac{ (12)^2}{4(1)}\right) \implies \left( - \cfrac{ 12 }{ 2 }~~,~~31 - \cfrac{ 144 }{ 4 } \right) \\\\\\ \left( -6 ~~~~ ,~~~~ 31 -36 \right)\implies (\stackrel{ x }{-6}~~,~-5)\hspace{5em}\stackrel{ \textit{axis of symmetry} }{x=-6}[/tex]
EASY MATH POINTS! Answer from the screenshot :)
Answer: Y = X2
Step-by-step explanation:
A and C aren't proportional and D is increasng
Find the value of x.
Leg= 8
Leg=x-4
Hypotenuse=8
The value of x is 10 if Leg= 8 and Leg=x-4.
What is Pythagoras theorem?This states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“.
In this scenario we were given
Leg= 8
Leg=x-4
Hypotenuse=x
Therefore : x² = 8² + (x-4)²
x² = 64 + x² - 8x + 16
x² - x² = 80 - 8x
8x = 80
x = 80/8 = 10
Therefore hypotenuse is 10 and the length of the other side is (10-4) = 6.
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PLEASE HELP,what is the answer to (b) the median.ITS NOT 2,5 or 7.
The mode of the data set is 7
The median is 6
the mean is 5.2
The range is 7
How to solve for modeThis is the number with the highest frequency or occurrence. This is 7
How to solve the medianarrange based on ascending order
1, 2, 3, 4, 5, 7, 7, 7, 8, 8
median = 5 + 7 / 2
= 6
How to solve for the meanadd all the numbers / total number
52 /10
= 5.2
The range = highest - lowest
= 8 - 1
= 7
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100 POINTS PLEASE HELP
Consider the surface
Find the following partial derivatives
The value of dz/ dt using Chain Rule is (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex].
What is Chain Rule?The chain rule states that the derivative D of a composite function is given by a product, as D(f(g(x))) = Df(g(x)) ∙ Dg(x).
In other words, the first factor on the right, Df(g(x)), indicates that the derivative of f(x) is first found as usual, and then x, wherever it occurs, is replaced by the function g(x).
Given:
By chain rule we can write z= f(x, y) = f( x(t), y(t))
dz/ dt = df/ dx . dx/ dt + df/ dy. dy/dt
So, df/ dx = [tex]e^y[/tex]
df/dy = [tex]e^y[/tex] + (x+ y) [tex]e^y[/tex]
x(t)=5t, while y(t)=1-t², So,
So, dx/dt = 5
and, dy/dt = -2t
Now, dz/ dt = 5 . [tex]e^y[/tex] + -2t ( [tex]e^y[/tex] + (x+ y) [tex]e^y[/tex])
= (2t³ -10t² -4t + 5) [tex]e^ {1- t^2[/tex]
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Keisha can ride her skateboard two and one half miles an hour how far can you ride in 3/4 of an hour
Answer:
1 and 7/8.
Step-by-step explanation:
Two and a half= 5/2
5/2 x 3/4 = 15/8 = 1 7/8
GIVING 100 POINTS PLEASE HELP I NEED IT DUE OR ELSE SHOW WORK AND ANSWER
Answer:1
Step-by-step explanation: