We find the slope(m) by replacing the values in the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]That is:
[tex]m=\frac{7-14}{8-5}\Rightarrow m=-\frac{7}{3}[/tex]So, the slope equals -7/3.
find the slope of the line through each pair of points (2, -11), (7, -20)
Reggie carves and sells wooden sculptures online. He uses the function f(x) = 15x + 60 to determine the selling price, f(x), for a sculptures that took him x hours to make. Which statement explains the meaning of the value of f(75)
Given data:
The given selling price funnction is f(x)=15x+60.
SUbstitute 75 for x in the given expression.
ff(75)=15(75)+60
=1125+60
=1185
So, the selling price obtained after 75 hours is 1,185.
The price of fuel changed from $3.50 per gallon to $3.20 per gallon.
The percentage change though = 25%.
What is Percentage?
A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a measurement system.
Bob's price dropped by $0.30, or BLANK, between April 1 and May 1.
Considering that the initial price was $3.20, the percentage change was 0.3/3.2, or 9.37%.
Bob's cost grew by $0.30 between May 1 and June 1 (or BLANK).
Price change was -0.3/3.5 = -8.57% since the initial price was $3.50.
Consider that the prices at the gas station across the street are consistently 20% more than those at Bob's. When gas costs $3.50 instead of $3.20, the price difference between Bob's and the prices across the street is BLANK in absolute terms.
Since 20% of $3.50 is greater than 20% of $3.20, the absolute difference will be greater when gas costs $3.50.
Let's say the Federal Reserve increases the federal funds rate objective from 2% to 2.5%. The Fed increased its target by almost BLANK percentage points as a result of this change.
It is 1% for each percentage point. Half a percentage point is the difference between 2% and 2.5%. However, the percentage change was 25% (0.5/2).
Hence, The percentage change is 25%
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8 wholes and one eighth divided by five sixths
The expression is:
[tex]8\frac{1}{8}/\frac{5}{6}[/tex]To divide this quantities, first we need to convert 8 and 1/8 to a fraction.
We do this as follows:
[tex]8\frac{1}{8}=\frac{8\times8+1}{8}=\frac{64+1}{8}=\frac{65}{8}[/tex]As you can see, to make the conversion we multiply the whole number by the denomitar and add the numerator (8x8+1) and divide by the same denominator.
So the division to make is:
[tex]\frac{65}{8}/\frac{5}{6}[/tex]A division between two fractions is made as follows:
So applying this to our division we get:
[tex]\frac{65}{8}/\frac{5}{6}=\frac{65\times6}{8\times5}=\frac{390}{40}=\frac{39}{4}[/tex]The answer is: 39/4, which represented as a mixed fraction is:
[tex]\frac{39}{4}=9\frac{3}{4}[/tex]I need help creating an equation to match the table
Let x be "the number of hours worked"
And y be "Amount of money earned"
If both variables vary proportionality, you can say that the constat of proportionality is
[tex]k=\frac{y}{x}[/tex]Choosing one pair of values of the table:
For example x=2 and y=125
Assuming the flat fee the painter changes is 25 (I choose it to be 25 because the variation turns proportional if you subtract 25 fromm all values of y)
Then subtract it from the value of y
125-25=100
And use it to calculate the the constant k
[tex]k=\frac{100}{2}=50[/tex]So the painter earns $50 per hour worked
The function is then y=25+50x
The correct option is the first one.
Henry bought a car for $14, 000. After two years, the value of the car was $8, 400 What was the percent decrease in the value of the car after two years? Enter the correct number in the box.
Answer:
I think it would be 60%
Step-by-step explanation:
Rashad chose C as the correct answer. How did he get that answer?
Answer:
He multiplies the denominator by 7.
Step-by-step explanation:
4) Which is the best deal?OA) $56 for 25 gallonsB) $32.05 for 15 gallonsO C) $51.29 for 23 gallonsOD) $22.50 for 10 gallons
To know the best deal, we have to know which one gives us the least cost per gallon.
To do that we divide the price by the quantity or volume.
A) $56 for 25 gallons
[tex]\frac{56\text{ \$}}{25\text{ gal}}=2.24\text{ \$/gal}[/tex]B) $32.05 for 15 gallons
[tex]\frac{32.05\text{ \$}}{15\text{ gal}}\approx2.14\text{ \$/gal}[/tex]C) $51.29 for 23 gallons
[tex]\frac{51.29\text{ \$}}{23\text{ gal}}=2.23\text{ \$/gal}[/tex]D) $22.50 for 10 gallons
[tex]\frac{22.50\text{ \$}}{10\text{ gal}}=2.25\text{ \$/gal}[/tex]The best deal is B: $32.05 for 15 gallons, because it offers a price per gallon that is lower than the others.
1 What is the value of x? 45° m (2x - 5)° n
45, and
2x - 5
make up a straight angle pair.
So, they add up to 180 degrees.
Thus, we can write:
45 + 2x - 5 = 180
Now, we simply solve for x. Shown below:
[tex]\begin{gathered} 45+2x-5=180 \\ 2x+40=180 \\ 2x=180-40 \\ 2x=140 \\ x=\frac{140}{2} \\ x=70 \end{gathered}[/tex]There is a raffle with 200 tickets. One ticket will win a $240 prize, three tickets will win a $90 prize, eight tickets will win a $50 prize, and the other tickets will win nothing. If you have a ticket, what is th expected payoff?
Teshawn, this is the solution:
As we had this same question before, the expected payoff is:
1/200 * 240 + 3/200 * 90 + 8/200 * 50 + 188/200 * 0
1.2 + 1.35 + 2 + 0
Therefore, the expected payoff for a raffle ticket is $ 4.55
Can someone help me Im confused
lenght=177
width= 46
Step-by-step explanation:
l= lenght w=widht
l= 4*w -7
perimeter= 2l+2w = 446
so:
2(4*w -7)+2w=446
8w-14+2w=446
10w=460
w=46
and
l=4*46-7
l= 177
Answer:
Explanation:
To find the dimensions of the playing field, let's assign variables. Let's say the width of the field is "w" yards.
According to the problem, the length of the field is 7 yards less than quadruple the width. This can be written as:
Length = 4w - 7
The perimeter of a rectangle is the sum of all its sides. In this case, the perimeter is given as 446 yards.
The formula for the perimeter of a rectangle is:
Perimeter = 2(Length + Width)
Substituting the given values, we get:
446 = 2(4w - 7 + w)
Now, let's solve the equation step-by-step to find the value of "w" and then find the dimensions of the field.
1. Distribute 2 to the terms inside the parentheses:
446 = 2(5w - 7)
2. Simplify the expression inside the parentheses:
446 = 10w - 14
3. Move -14 to the other side of the equation:
446 + 14 = 10w
4. Combine like terms:
460 = 10w
5. Divide both sides of the equation by 10:
46 = w
Now that we have the value of "w", we can find the length of the field by substituting it into the equation for the length:
Length = 4w - 7
Length = 4(46) - 7
Length = 184 - 7
Length = 177 yards
Therefore, the dimensions of the playing field are:
Width = 46 yards.
Length = 177 yards.
Which ordered pairs are in the solution set of 8x + 16y > 32? (select two ordered pairs).
The ordered pair which is solution of 8x+16y > 32 is (-3,5) , the correct option is (b) .
In the question ,
it is given that ,
the linear inequality is 8x+16y > 32 .
to find the solution set ,
we substitute the options that are given
Option(a)
Substituting (0,2) in 8x+16y > 32 ,
we get ,
8(0) + 16(2) > 32
32 > 32 ,
false , hence it is not a solution .
Option(b)
Substituting (-3,5) in 8x+16y > 32 ,
we get ,
8(-3) + 16(5) > 32
-24 + 80 > 32
56 > 32
true , yes it is the solution .
Option(c)
Substituting (-1,1) in 8x+16y > 32 ,
we get ,
8(-1) + 16(1) > 32
-8 + 16 > 32
8 > 32
False , hence it is not a solution .
Option(d)
Substituting (4,0) in 8x+16y > 32 ,
we get ,
8(4) + 16(0) > 32
32 + 0 > 32
32 > 32
False , hence it is not a solution .
The only solution that satisfy the inequality is (-3,5) .
Therefore , The ordered pair which is solution of 8x+16y > 32 is (-3,5) .
The given question is incomplete , the complete question is
Which ordered pair is in the solution set of 8x+16y > 32 ?
(a) (0,2)
(b) (-3,5)
(c) (-1,1)
(d) (4,0)
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can yall help me with this
The resultant answer after solving the given expression is (C) 2/3.
What are expressions?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.You must substitute a number for each variable and carry out the arithmetic operations in order to evaluate an algebraic expression. Since 6 + 6 equals 12, the variable x in the example above is equal to 6. If we are aware of the values of our variables, we can substitute those values for the original variables before evaluating the expression.So, solve for ⁴√16/81:
Apply radical rule as follows:
⁴√16/81⁴√16/⁴√81We know, ⁴√16 = 2.
Then,
2/⁴√81 ⁴√81 = 3Then,
2/3Therefore, the resultant answer after solving the given expression is (C) 2/3.
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Triangle A B C is shown. Side A C has a length of 27. Side C B has a length of 54.
Based on the diagram, which expresses all possible lengths of segment AB?
AB = 25
27 < AB < 81
AB = 85
AB< 27 or AB > 81
The possible length of segment AB is 27 < AB < 81
From the question, we have
In triangle ABC
AC = 27
CB = 54
Using Pythagoras theorem,
AC² = AB² + CB²
54² = AB² + 27²
AB = 47
The possible length of segment AB is 27 < AB < 81
Multiplication:
To determine the sum of two or more numbers, mathematicians multiply the numbers. It is a basic mathematical procedure that is widely used in daily life. Multiplication is used when we need to mix groups of like sizes. Multiplication is a representation of the underlying idea of adding the same number repeatedly. The outcome of multiplying two or more numbers is referred to as the product of those numbers, and the factors are the quantities that are multiplied. Multiplying the numbers makes it simpler to add the same number repeatedly.
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If f(1) = 9 and f(n) = 5f(n − 1) then find the value of f(4).
The value of f(4) is 1125.
Here,
we have given the value of f(1)=9 and f(n)=5f(n-1) and we have to find out the value of f(4).
From the above equation of f(n), it is clear that for finding value of f(4) we have to find value of f(3).
And for f(3) we have to find out the value of f(2)
So,
first, we will find out value of f(2) and then eventually value of f(3) and f(4) by using the given formula of f(n)
The given formula for f(n) is
f(n)=5f(n-1)
So,
f(2)=5f(2-1)
f(2)=5f(1)
f(2)=5×9
f(2)=45
Now,
f(3)=5f(3-1)
f(3)=5f(2)
f(3)=5×45
f(3)=225
And,
f(4)=5f(4-1)
f(4)=5f(3)
f(4)=5×225
f(4)=1125
Hence, we got
The value of f(4) is 1125.
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what is (2x−6)+4(x−3)
Answer:
Step-by-step explanation:
6*(x-3) yeah that is it.
Answer:
[tex]6x-18[/tex]
Step-by-step explanation:
Step 1: Distribute
[tex]2x-6+4x-12[/tex]
Step 2: Add like terms
[tex]2x+4x[/tex]
[tex]-6-12[/tex]
Step 3: Consolidate
[tex]6x-18[/tex]
Tell weather the ratios form proportion 3/11 and 17/6True or False
Answer:
False
They are not proportional
Kendall puts 1,000.00 into an account to use for school expenses the account earns 9% interest compounded monthly how much will be in the account after 9 years
To calculate the total amount accrued when you deposit the money in an account that earns compound interest you have to use the following formula
[tex]A=P(1+\frac{r}{n})^{tn}[/tex]A: amount accrued
P: principal amount
t: time, years
r: interest rate, expresed as a decimal value
n: number of coumpound periods
For this exericse
The principal amount is P=$1000
The time is t= 9 years
The interest rate is 9%/100=0.09
The compounding periods are 12/year (the interest is compounded monthly) so for the 9 year time period is 9*12=108
[tex]\begin{gathered} A=1000(1+\frac{0.09}{108})^{9\cdot108} \\ A=2247.15 \end{gathered}[/tex]Solve for the unknown 8k-2k=42
ANSWER
k = 7
EXPLANATION
The unknown variable in this equation is k,
[tex]8k-2k=42[/tex]To find its value, first, we have to combine like terms. This means that on the left side of the equation, we have to combine the coefficients of k,
[tex]\begin{gathered} (8-2)k=42 \\ \\ 6k=42 \end{gathered}[/tex]And then, divide both sides by 6,
[tex]\begin{gathered} \frac{6k}{6}=\frac{42}{6} \\ \\ k=7 \end{gathered}[/tex]Hence, the value of k is 7.
I have taken a picture of the question I am needing help with. Thank you.
Answer:
Width: 20 in
Length: 25 in
Explanation:
We can represent the situation with the following figure
Where x is the width of the rectangular piece of metal, (x + 5) is the length of the rectangular because it is 5 in longer than its wide, and the corners have squares of side 1 in.
Therefore, the volume of the box will be equal to
Volume = Length · Width · Height
Volume = (x + 5 - 1 - 1) · (x - 1 - 1) · (1)
Volume = (x + 3)(x - 2)(1)
Volume = (x + 3)(x - 2)
Because the length of the box will be the length of the rectangle less the length of the squares and the width of the box will be the length of the rectangle less the width of the squares.
The volume is 414 in³, so we need to solve the following equation:
414 = (x + 3)(x - 2)
414 = x² + 3x - 2x + 3(-2)
414 = x² + x - 6
414 - 414 = x² + x - 6 - 414
0 = x² + x - 420
Factorizing x² + x - 420, we get:
(x + 21)(x - 20) = 0
Then
x + 21 = 0
x + 21 - 21 = 0 - 21
x = -21
or
x - 20 = 0
x - 20 + 20 = 0 + 20
x = 20
Since x = -21 doesn't have sense, the width is x = 20 and the length is:
x + 5 = 20 + 5 = 25 in.
So, the original width is 20 in and the original length is 25 in
Divide. Reduce the answer to lowest terms. 5 2/3÷ 3 1/9 28/51 1 23/28 1 3/476 17 17/27 PWEASE HELP
The correct mixed fraction is 2) 1 [tex]\frac{23}{28}[/tex]
What is mixed fraction and improper function ?
A mixed fraction is one that has both a whole number portion and a proper fraction, and whose value is always larger than 1. A mixed number is, for instance, 3[tex]\frac{2}{5}[/tex]. A fraction is deemed inappropriate if the numerator is consistently greater than or equal to the denominator. 4/3, 7/3, 11/5, etc. are a few instances of incorrect fractions.
Here the given division is,
=> 5 [tex]\frac{2}{3}[/tex] ÷ 3 [tex]\frac{1}{9}[/tex]
=> [tex]\frac{15+2}{3}[/tex] ÷ [tex]\frac{27+1}{9}[/tex]
=> [tex]\frac{17}{3}[/tex] ÷ [tex]\frac{28}{9}[/tex]
=> [tex]\frac{17}{3}[/tex] * [tex]\frac{9}{28}[/tex]
=> [tex]\frac{51}{28}[/tex]
=> 1 [tex]\frac{23}{28}[/tex]
Hence the correct option is 2) 1 [tex]\frac{23}{28}[/tex]
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The length of a rectangle is 3 meters greater than 2 times the width. The perimeter of rectangle is 30 meters. What is the length of the rectangle?
The length of a rectangle of the rectangle is 11m.
What is a rectangle?A rectangle is a polygon with four sides and four angles. Each angle is 90° and it has two lines of symmetry.
let the length of the rectangle be L and the width be w, so that
L = 3 + 2w
Also perimeter = 2 ( L + w)
2( L + W) = 30
substitute L = 3 + 2W into the above equation
2( 3 + 2W + W) = 30
2(3 +3W) = 30
multiply the bracket by 2
6 + 6W = 30
6W = 24
W = 24/6
W = 4m
but L = 3 + 2W, when W = 4m
L = 3 + (2 x 4)
L = 3 + 8
L = 11m
In conclusion the length of the rectangle is 11m
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what value is equivalent to the expression 5-2(3+9)+4?a= -15b= -23c= 33d= 40
5- 2(3+9) +4
Apply PEMDAS
First solve parentheses: (3+9) = 12
5- 2 (12) + 4
Then, the multiplication:
5- 24 + 4
Add and subtract
-15
a=-15
18. Find m∠VSW if ∠WSR and ∠VSW are complementary and m∠WSR is four times m∠VSW. A 72 C 22.5 B 36 D 18
We will have the following:
First, we have that:
[tex]m<\text{VSW}+m<\text{WSR}=90[/tex]And we have that:
m[tex]m<\text{VSW}+4m<\text{VSW}=90\Rightarrow5m<\text{VSW}=90[/tex][tex]\Rightarrow m<\text{VSW}=18[/tex]So, the measurement of angle VSW is 18°.
What is the value of 13(a • b + a2) + 4 if a = 5 and b = −3?
308
134
−74
−126
please helpppppp
i need you if you get correct ill give brainlyest
need now
The value of the expression 13(a • b + a²) + 4 if a = 5 and b = −3 is B 134.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.
The expression is illustrated thus:
13(a • b + a²) + 4
= 13(5 • (-3) + 5²) + 4
= 13(-15 + 25) + 4
= (13 × 10) + 4
= 130 + 4
= 134
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Math COLL, help me plis
Using trigonometric functions, the value of cos O in simplest terms is 5/17.
What are trigonometric functions?The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (CSC).So, we know that: cos α = Adjacent Side/Hypotenuse
We have,
adjacent side = 5hypotenuse = 17OM = 17 and ON =5As we know,
cos O = Adjacent Side/HypotenuseWe obtain:
cos O = ON/OMcos O = 5/17Therefore, using trigonometric functions, the value of cos O in simplest terms is 5/17.
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Angles. Solve for Vaule of D
Tim is a wildlife biologist studying deer parasites. During a study, he finds that 12 out of 32 deer were affected by parasites. How many of the 1200 deer in the local population would he expect to be affected by parasites?
It is expected that 450 out of the total 1,200 are to be affected by parasites
Here, using a study of sample, we want to infer the number of casualty in a larger sample
To do this, we need to get the percentage of the Deers that are affected by parasites
We can have this as;
[tex]\frac{12}{32}\text{ }\times\text{ 100 = 37.5\%}[/tex]From the above, we can see that 37.5% is affected
So, to get the number affected on the larger scale, we have that;
[tex]\frac{37.5}{100}\text{ }\times\text{ 1200 = 450}[/tex]help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 2.5, 5.4
Step-by-step explanation:
[tex]-16t^2 +126t=213\\\\16t^2 -126t+213=0\\\\t =\frac{-(-126) \pm \sqrt{(-126)^2 -4(16)(213)}}{2(16)}\\\\t \approx 2.5, 5.4[/tex]
i need help understand exponential functions
Given:
Exponential function
Required:
To define the exponential function.
Explanation:
The exponential function is represented in the form of
[tex]y=a^x[/tex]Where a>1 and x represent the variable.
Here x is an independent variable and y is dependent, a is called the base. The value of the base is always constant.
The most important exponential function is
[tex]y=e^x[/tex]Where the value of e is 2.7182818.
Final Answer:
Explain in the explanation part.