The shortest straight path they must run back to the starting line is the square root of 34 miles.
What is the shortest straight path?The distance run by the runners forms a right triangle. A right triangle is a polygon that has three sides. The length, base and the hypotenuse. The hypotenuse is the longest side of the right triangle.
The miles run north is the length, the miles run west is the base and the shortest straight path to the starting line is the hypotenuse.
In order to determine the hypotenuse, the Pythagoras theorem would be used.
The Pythagoras theorem: a² + b² = c²
where a = length
b = base
c = hypotenuse
3² + 5²
= 9 + 25
= 34
c = √34
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Check all the angles that are congruent to angle 5.
The angles congruent to ∠5 are as follows:
∠8∠1∠4∠9∠12How to find angles in parallel lines?According to the diagram, line l, m and n are parallel lines.
Therefore, when parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate angles, vertical opposite angle etc.
Hence, the angles that are congruent to ∠5 can be solved as follows:
∠5 ≅ ∠8 (vertically opposite angles)
Vertically opposite angles are congruent.
∠5 ≅ ∠1 (corresponding angles)
Corresponding angles are congruent.
∠5 ≅ ∠4 (alternate angles)
Alternate angles are congruent.
∠5 ≅ ∠9 (corresponding angles)
∠5 ≅ ∠12 (alternate exterior angles)
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pls help i dont get it
Answer:
Step-by-step explanation:
Answer: You can add 5. The question is asking you what can you do to make both sides equal 8. I am not a professional but I hope that helped.
Phillip added 15 pencils to his collection. He then gave 30 pencils to a friend. Write and evaluate an expression
Answer:
x + 15 - 30
x -15
Step-by-step explanation:
i need help with question 17
Answer:
[tex]42[/tex]Step-by-step explanation:
To find the median of a stem and leaf plot, use the equation:
[tex]\begin{gathered} median=\frac{n+1}{2} \\ where, \\ n=\text{ number of data} \end{gathered}[/tex]Therefore, for the given plot, there are 16 elements.
[tex]\begin{gathered} \text{ median=}\frac{16+1}{2} \\ \text{ median=8.5} \end{gathered}[/tex]When there are two middle values, the median is the mean of these two values:
[tex]\begin{gathered} \frac{3+1}{2}=2 \\ \text{ Hence, the median is 42.} \end{gathered}[/tex]g(x) = 5x – 3g(-2) =?
For
f(x) = 3x and g(x) = x4 + 2, find the following.
(b)(g ∘ f)(x)
Find a with the given information.
m=-6/7 (-10,0) and (a,-6)
Based on the slope formula for a line, the value of a is: a = -3.
How to Calculate the Slope of a Line?If two points on a line have the following coordinates, (x1, y1) and (x2, y2), to find the slope (m) of the line, the formula that is applied is given as:
Slope (m) = change in y /change in x = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex] = rise/run.
The given line has the following:
(-10, 0) = (x1, y1)
(a, -6) = (x2, y2)
Slope (m) of the line = -6/7.
Plug in the values into the slope formula for a line:
(-6 - 0) / (a - (-10)) = -6/7
-6/(a + 10) = -6/7
Cross multiply and solve to find the value of a in the equation:
-6(a + 10) = -6(7)
Apply the distributive property
-6a - 60 = -42
Add 60 to both sides
-6a - 60 + 60 = -42 + 60 [addition property of equality]
-6a = 18
Divide both sides by -6
-6a/-6 = 18/-6 [division property of equality]
a = -3
Therefore, the value of a is -3.
The line that has a slope of -6/7 will have the following points, (-10, 0) and (-3, -6).
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Can someone please help with this
Answer:
x = 8
y = 8
Step-by-step explanation:
The two equations are:
x + y = 16 (1)
x = y (2)
Since x = y substitute for y in terms of x in (1):
x + x = 16
2x = 16
2x/2 = 16/2
x = 8
y = 8
Jackie deposited $500 in an account for 10 years at 6% interest.How much money did she earn?
After 10 years, the money dis she earn is $800 with the interest of 6%.
Interest:
Interest is the amount for a particular principal amount of money at some rate of interest.
Given,
Jackie deposited $500 in an account for 10 years at 6% interest.
Here we need to find the money did she earned.
We know that, the interest for the amount is 6%.
So, the amount after 10 years is,
=> 500 x (6/100) x 10
=> 30 x 10
=> 300
Therefore, the interest amount is 300.
So, the total amount she will receive after 10 years is,
=> 500 + 300
=> 800
Therefore, she will earn $800 after 10 years.
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if f(x)=-5, what is x?
Answer:
x is any real number from -infinity to infinity.
Simplify: (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
7r³ + 11r²s -9rs² - 8s³ is the simplification of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
How to simplify equation?The process of writing an expression in the most effective and compact way possible without affecting the original expression's value is known as simplification of an algebraic expression.
Collecting similar terms is the process, which entails expanding or contracting the terms in an expression.
Let's review some of the crucial words used during expression simplification:
In an algebraic expression, a variable is a letter with an undetermined value.
A coefficient is a number that is used with a variable.A term with a fixed value is called a constant.Variables with the same letter and power are known as like terms. Sometimes, similar terms will have different coefficients.We have been asked to simplify the expression
(7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)
Let's simplify
⇒ (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²)
⇒ 7r³ + 10r²s −3rs² − 8s + r²s -6rs²
⇒ 7r³ + 11r²s -9rs² - 8s³
Thus, 7r³ + 11r²s -9rs² - 8s³ is the simplified form of the expression (7r³ + 10r²s) + (−3rs² − 8s³) − (−r²s + 6rs²).
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highest common factor of 106 and 104
The Greatest Common Factor (GCF) for 104 and 106, notation GCF(104,106), is 2.
Given that,
The numbers 106 and 104.
We have to find the greatest common factor of 106 and 104.
The greatest commo factor is nothing but the greatest common factor, which is the product of two or more numbers, is the largest number (GCF). By dividing them by the largest number, a natural number is produced (factor).There are a few factors that both share once all the number's factors have been identified. The common factor with the highest number among the others is said to be the greatest common factor. The GCF is often referred to as the highest common factor (HCF)
The factors of 104 are 1,2,4,8,13,26,52,104;
The factors of 106 are 1,2,53,106.
Therefore, as we can see, the Greatest Common Factor or Divisor is 2, because it is the greatest number that divides evenly into all of them.
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f(x) = x + 3g(x) = 2x2 - 4Find (f ·g)(x)
SOLUTION
f(x) = x + 3
[tex]undefined[/tex]f(x) = c f(-x) = c
Does f(x) = f(-x)?
Does f(-x) = f(x)?
+c does not equal -c
The equation of the functions given as f(x) =f(-x) and f(-x) = f(x) are true
How to determine the true statements?The functions are given as
f(x) = c
Also, we have
f(-x) = c
In the above function definitions, we can see that
The functions f(x) and f(-x) have the same value
i.e. f(x) = f(-x) = c
This means that f(x) =f(-x)
By the symmetric property of an equation, the above can also be rewritten as
f(-x) = f(x)
Hence, the functions f(x) =f(-x) and f(-x) = f(x) are true
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Write an equation for the quadratic graphed below:
x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2)
The equation for the quadratic graphed as x-intercepts: (-3,0) and (-1,0); y-intercept: (0,-2) can be written as y = -1/2 (x+3)(x+1)
Which of these equations is quadratic?An equation of the second degree, or one with at least one squared term, is a quadratic equation. The equation in standard form is written as ax2 + bx + c = 0, where a, b, and c are numerical coefficients that are constants, and x is an unknown variable.
The initial constant, “a,” cannot be 0, and this is an unbreakable rule.
How do you translate a graph into some equation?In order to put the equation in y-intercept (y=mx+b) form and determine the equation of a graphed line, first determine the slope and y-intercept. The slope is the ratio of the y-to-x change.
Thereafter draw a sloping triangle connecting the two spots you find on the line.
If the x intercepts are -3 and -1, then the factored form is y = a(x + 3)(x + 1). In order to find "a", we plug in the data point (x, y) of (0, -2) so:
-2 = a(0+3)(0+1)
-2 = 4a
a = -1/2
So the equation can be written as y = -1/2 (x+3)(x+1)
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Determine the distance between A(-3, 4) and B(2, -4).
5 units
Explanation
Step 1
the distance between 2 points P1 and P2 is given by:
[tex]\begin{gathered} \text{distance}=\sqrt[]{(x_2-x_1_{})^2+(y_2-y_1)^2} \\ \text{where} \\ P1(x_1,y_1)andP2(x_2,y_2) \end{gathered}[/tex]Let
P1=A(-3,4)
P2=B(2,-4)
Step 2
put the values into the equation
[tex]\begin{gathered} \text{distance}=\sqrt[]{(-4-4)^2+(2-(-3))^2} \\ \text{distance}=\sqrt[]{(0)^2+(2+3)^2} \\ \text{distance}=\sqrt[]{(0)^2+(5)^2} \\ \text{distance}=\sqrt[]{(25} \\ \text{distance}=5 \end{gathered}[/tex]Donna bought a desk on sale for $343. This price was 35% of the original price.
The original price for the desk is $980.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred.
Given:
Sale price = 343
price was 35% of the original price.
let the original price be x
35% of x = 343
35 / 100 * x = 343
x= 343 * 100/ 35
x=980
Hence, the original price of the desk was $980.
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please help me out i’ll give you brainlist !
Answer:
In order, the answers are d, b, c, a
Step-by-step explanation:
[tex] \frac{ {x}^{7} }{ {x}^{4} } = {x}^{3} [/tex]
[tex] {x}^{ - 3} = \frac{1}{ {x}^{3} } [/tex]
[tex] {x}^{0} = 1[/tex]
[tex] \frac{ {x}^{4} }{ {x}^{3} } = x[/tex]
A retailer owes a wholesaler $300,000 due in 45 days. If the payment is 15 days late, there is a 1% penalty charge. Since the bill isn't due immediately, the retailer can invest the $300,000 in a certificate of deposit and make money on the interest. The retailer has two options: a 45-day certificate of deposit (CD) earning 6% per year simple interest or a 60-day certificate earning 7% per year simple interest.
A 45-day certificate of deposit (CD) earning 6% per year simple interest. Simple interest and precise simple interest are the two types of simple interest. $2250 is simple interest for the 6% interest.
What is simple interest ?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest.
Simple Interest is the amount repaid for using borrowed funds over a predetermined amount of time.
Simple interest=p*n*r
=300000*6/100*45/365
=2250
Ordinary simple interest and precise simple interest are the two types of simple interest. In order to calculate interest, a year is divided into 360 days for ordinary simple interest and 365 days (or 366 days for leap years) for exact simple interest.
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Use the following information to prepare a classified balance sheet for Alpha Co. at the end of Year 1. Accounts receivable $ 26,500 Accounts payable 12,200 Cash 20,500 Common stock 30,000 Land 10,000 Long-term notes payable 17,500 Merchandise inventory 26,300 Retained earnings 23,600
The classified balance sheet for Alpha Co. at the end of Year 1 is illustrated below.
What is a classified balance sheet?A financial statement incorporating classifications as current assets and liabilities, long-term liabilities, and other things is called a classified balance sheet. It may be simpler to read and extract the information you need by categorizing the information than if it were just listed in a lot of line items.
It is a financial report that includes totals for all of the different revenue and expense classifications and displays revenues, expenses, and profits.
The balance sheet is illustrated below:
Current Assets
Accounts Receivable 26500
Cash 20500
Merchandise Inventory 26300
Total Current Assets 73300
Property, Plant and Equipment
Land 10000
Total Property, Plant and Equipment 10000
Total Assets 83300
Current Liabilities
Accounts Payable 12200
Long Term Liabilities
Long-Term Notes Payable 17500
Stockholders' Equity
Common Stock 30000
Retained Earnings 23600
Total 53600
Total Liabilties 83300
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Let f(x) = 5x²-2 and let g(x) = 3x + 1. Find (f + g)(2).
(f+g)(2)= (Simplify your answer.)
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:(f+g)(x) = 5x² + 3x - 1 [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: f(x) = 5 {x}^{2} - 2[/tex]
and
[tex]\qquad \tt \rightarrow \: g(x) = 3x + 1[/tex]
We need to find : (f + g) (x) = ?
[tex]\qquad \tt \rightarrow \: (f + g)(x) = f(x) + g(x)[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} - 2 + 3x + 1[/tex]
[tex]\qquad \tt \rightarrow \: (f + g)(x) = 5 {x}^{2} + 3x - 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.Lauren had brochures printed for her new business venture. She originally ordered 4 boxes of black-and-white brochures and 4 boxes of color brochures, which cost a total of $148. After those ran out, she spent $125 on 4 boxes of black-and-white brochures and 3 boxes of color brochures. Given that the prices didn't change, what was the price of each type of brochure?
Let the price of black and white brouchers be x
The price of color brochures be y.
A/q,
4x+4y=148.....(1)
4x+3y=125 .....(2)
The equation (1) becomes,
x+y=37
y=37-x.......(3)
Putting (3) in (2) we have,
4x+3(37-x)=125
4x+111-3x=125
x=14
Putting the value of x in (3) we have,
y=37-14=23
The price of black and white brouches is $14
The price of color brouchers is $23.
thank u plssssssss do it
Answer:
63
Step-by-step explanation:
23 + 94 = 117
180 degrees ( sum of all angles in a triangle)
180 - 117 = 63
For the triangle shown, find the length AD. (Assume u = 17, v = 17, ∠x = 25°, and ∠y = 25°
Using the law of Sines, the length of side AD, |AD|, is 7.44
Calculating lengthFrom the question, we are to determine the length of side AD
From the given information, we have that
u = 17 and v = 17
Then,
ΔBCD is an isosceles triangle
∴ m ∠DBC = m ∠ BCD
m ∠DBC = x = 25°
∴ m ∠BCD = 25°
Also,
m ∠BCA = ∠y + m ∠BCD
m ∠BCA = 25° + 25°
m ∠BCA = 50°
Now, we will determine the measure of ∠CAD.
m ∠CAD + m ∠DBC + m ∠BCA = 180° (Sum of angles in a triangle)
m ∠CAD + 25° + 50° = 180°
m ∠CAD = 180° - 25° - 50°
m ∠CAD = 105°
Now,
From law of Sines, we can write that
|AD| / sin DCA = |DC| / sin CAD
|AD| / sin y = u / sin CAD
|AD| / sin 25° = 17 / sin 105°
|AD| = (17 × sin 25°) / sin 105°
|AD| = 7.43795
|AD| ≈ 7.44
Thus,
Length AD is 7.44
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What is the equation of the following graph
Answer:
y = 1
The graph has no gradient and only intersects at the y-axis.
Please help I’ll mark you as brainliest if correct!
The value of a in the magic square is 25
The value of b in the magic square is 3
The value of c in the magic square is 14
The value of d in the magic square is 7
What are the missing values?The mathematical operations that would be used to determine the missing numbers are addition and subtraction. Addition is the process of determining the sum of two or more numbers. Subtraction is the process of determining the difference of two or more numbers.
According to the information provided in the question, all rows, diagonals and columns add to the same number. Thus, the first step is to determine the sum of all the squares.
The three squares of the diagonal from left to right has all the complete numbers.
Sum of the the squares = 5 + 16 + 27 = 48
a = 48 - 18 - 5 = 25
b = 48 - 18 - 27 = 3
c = 48 - 29 - 5 = 14
d = 48 - 27 - 14 = 7
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please its due tomorrow
1 Answer:
Evaluate the following expression when q = 13.
q-10
2 Answer:
Evaluate the following expression when x = 4.2.
34.5x
3 Answer:
You deposit $70 in a savings account that pays an annual interest rate
of 3%. How much simple interest would you earn in 2.5 years?
1. The value of the expression when q = 13 in q - 10 is 3.
2. The value of the expression when x = 4.2.
34.5x is 144.9
3. The interest will be $5.25.
How to illustrate the information?It should be noted that an expression is simply used to show the relationship between the variables.
1. The expression when q = 13 in q - 10 will be:
= q - 10
= 13 - 10
= 3
2. The value in the expression when x = 4.2 will be:
= 34.5x
= 34.5 × 4.2
= 144.9
3. Principal = $70
Rate = 3%
Time = 2.5 years
Interest = PRT / 100
= (70 × 3 × 2.5) / 100
= $5.25
The simple interest would you earn in 2.5 years is $5.25.
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the graph of g(x) = (x + 2)2 is a translation of the graph of f(x) ___ by ___ units
The provided translated function, f(x), shifts left by two units on the horizontal axis.
Describe translation.One type of transformation is translation. Both the scaling calculation and the compression calculation are performed using it. This approach wouldn't change the object's form or shape.
The given graph equation for the translation, as per the query, is g(x) = (x + 2)²
The translation of the given quadratic function is: y = g(x) = (x + 2)²
Consequently, the parent function is written as y = g(x) = x2.
Additionally, the vertex should be known when graphing the translated function:
a(x - h)2 + k = y = g(x);
where the parent function is (0, 0) and the vertex values are (h, k).
(h, k) = is the vertex for the function that is provided (-2, 0)
This information causes the translation function to move the graph two units to the left.
Horizontal translation is the name given to the translation.
As a result, the given function, f(x), shifts horizontally, or left, by 2 units.
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Karen the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday therewere 3 clients who did Plan A and 5 who did Plan B. On Tuesday there were 6 clients who did Plan A and 2 who did Plan B. Karen trained her Monday clients fora total of 10 hours and her Tuesday clients for a total of 10 hours. How long does each of the workout plans last?
ive n
lan A
Plan B
Monday: 3 clients - Plan A
5 clients - Plan B
Total 10 hours
Tuesday
6 clients - Plan A
2 clients - Plan B
Total 10 hours
rocedure
Let's define a system of linear equations that represents the above problem.
A: Number of hours of workout in plan A
B: Number of hours of workout in plan B
[tex]\begin{gathered} 3A+5B=10 \\ 6A+2B=10 \end{gathered}[/tex]The goal here is to solve
3A+5B=10 and
6A+2B=10 for the variables A and B.
The solutions to your equations are:
A = 5/4 hour
B = 5/4 hour
Match the following.
Matching the given mathematical operation equations to the specified choices, gives;
A•B = B•A ; Commutative Property of Multiplication
A + B = B + A ; Commutative Property of Addition
(A•B)•C = A•(B•C); Associative Property of Multiplication
A•0 = 0; Multiplicative Property of 0
(A + B) + C = A + (B + C); Associative Property of Addition
A•1 = A; Multiplicative Identity
A + 0 = A; Additive Identity
What are the properties of mathematical operations?The properties of mathematical operations includes; inverse, associative, distributive, associative and commutative properties
Commutative propertyCommutative property in mathematics is one in which for a binary operation, the result of an operation remains unchanged when the order in which the operands appears in the expression is changed.
Therefore;
Commutative property of multiplication is therefore; A•B = B•A
Commutative property of addition is; A+B = B+A
Associative propertyAssociative property relates with operations that have results which remains the same when the parentheses in the expressions are rearranged.
Therefore;
(A•B)•C = A•(B•C) represents the associative property of multiplication
The associative property of addition is represented by (A+B)+C = A+(B+C)
Multiplicative property of 0The multiplicative property of 0, which can be understood as the zero product property, states that the product of any number and 0 is 0
Therefore, the equation, A•0 = 0, represents the multiplicative property of 0
Multiplicative and additive identityThe multiplicative and additive identity states that an expression remains the same following the product of the expression with an identity element such as 1, or following the addition of the expression with an identity element such as 0
The multiplicative and additive identity are therefore represented by A•1 = A and A + 0 = A respectively
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