Answer:
a. -13
b. 14
c. -6
Step-by-step explanation:
a.
Substitute x = -3 into the equation.
f(-3) = 2(-3) - 7
= - 6 - 7
= -13
b.
Substitute f(x) = 21 into the equation.
2x - 7 = 21
2x = 28
x = 14
c.
Substitute x = 1/2 into the equation.
f(1/2) = 2(1/2) - 7
= 1 - 7
= -6
I Need help wit this one
The area of the shaded region is 422.16 cm sq.
Given,
In the question:
Radius of the circle is 12 cm.
The length of rectangle is 10cm
and, Breadth of the rectangle is 3cm.
A rectangle sits inside a circle.
To find the Area of the shaded region.
Now, According to the question;
we know that:
Area of a circle is = [tex]\pi r^2[/tex]
Radius = 12cm
Area of a circle is = 144[tex]\pi[/tex]
Using [tex]\pi[/tex] = 3.14
Area of a circle is = 144 x 3.14 = 452.16 cm sq.
The area of rectangle = 3 x 10 = 30cm sq.
So, The area of the shaded region:
452.16 - 30 = 422.16cm sq.
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help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!help meeeeeeeeeeee pleaseee rnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
A. 7.8
B. 9.8
Step-by-step explanation:
A. 2006 = 3 years
y = 7.1(1.03)ˣ
y = 7.1(1.03)⁽³⁾
y = 7.1(1.092727)
y = 7.7511907
y = 7.8
----------------------------------------------------------------------------------------------------------
B. 2014 = 11 years
y = 7.1(1.03)ˣ
y = 7.1(1.03)⁽¹¹⁾
y = 7.1(1.38423387)
y = 9.82806047
y = 9.8
If it says, "Round to the nearest tenth," the answer is 9.8. If the answer says, "Round to the nearest whole number," the answer is 10
I hope this helps!
Whiskers the cat weights 2 2/3 kg piglio weighs 4 kg how many times as heavyas whiskers is piglio
The weight of Piglio is 3/2 times of weight of Whishkers.
Fraction is comparison between two mathematical numbers or quantities.
Given that, Whisker weights 2 2/3 kg
Piglio weights 4 kg
Weight of Piglio is fraction of weight of Whisker = 4/(2 2/3) = 4/(8/3) = (4*3)/8 = 3/2 times
The weight of Piglio is 3/2 times of weight of Whishkers.
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PLEASE HELP !!!! brainliest will be given to first answer
John is in charge of feeding the pigs and cows on the farm. The cow's food costs twice as much as the pig's food. There are 46 cows and 22 pigs on the farm. John has a $860 budget for food a month. How much can John spend on food for each cow per month?
Answer:
Approximately $15 per cow
Step-by-step explanation:
2 is a factor of 81. Show how you know
6 people carry the weight 216kg at a time. How many people are needed to carry the weight of 360kg
The number of people needed to carry the weight of 360 kg is 10 people.
The number of people are needed to carry the weight of 360kg can be calculated as follows ?
The first step is to put the demanded weight and the known weight of the required number of people into a formula which demanded weight is placed on numerator side and the known weight of the required number of people is placed on denominator side.
Formula
= [tex]\frac{360}{216}[/tex]
The next step is to multiply the number that has been entered into the fractional formula by the number of people who are known to be able to carry 216 kg
= [tex]\frac{360}{216}[/tex] × 6
= 10
Hence, the number of people needed to carry the weight of 360 kg is 10 people.
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You would need 10 people to carry a weight of 360 kg.
To find out how many people are needed to carry a weight of 360 kg, we can set up a proportion based on the information provided.
Let's assume that x represents the number of people needed to carry the weight of 360 kg.
The proportion can be set up as follows:
6 people / 216 kg = x people / 360 kg
We can solve this proportion by cross-multiplying:
216 kg · x people = 6 people · 360 kg
216x = 2,160
Dividing both sides of the equation by 216:
x = 2,160 / 216
x = 10
Therefore, you would need 10 people to carry a weight of 360 kg.
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Write the following expressions in correct algebraic notation:
a) 7 x p
b) p x p
The Algebraic Notation of the expression is :
a) 7 x p
7 is multiplied to the p
b) p x p
p is multiplied itself.
Given,
In the question:
a) ) 7 x p
b) p x p
To write the above expressions in correct algebraic notation.
What are the algebraic notations and operations?
The algebraic expressions are used to solve mathematical equations. There are 3 types of algebraic expressions namely, monomial, binomial, and polynomial expressions. The basic algebraic operations are addition, subtraction, multiplication, and division.
Come to the question:
a) 7 x p
7 is multiplied to the p
b) p x p
p is multiplied itself.
Hence, The Algebraic Notation of the expression is :
a) 7 x p
7 is multiplied to the p
b) p x p
p is multiplied itself.
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Factorise the following 2x + 10
Answer:
2(x+5) I believe
Step-by-step explanation:
Barabas received a mark of 50% on a recent test. Barabas answered 13 of the first 20 questions correctly. Barabas also answered 25% of the remaining questions on the test correctly. If each question on the test was worth one mark, how many questions in total were on the test?
Answer:
32
Step-by-step explanation:
You want the total number of questions on the test if the final score was 50%, and there were 13 correct out of the first 20, and 25% correct among the remainder.
SetupLet q represent the number of questions on the test. Then (q-20) is the number of remaining questions, and the number correct is ...
13 +0.25(q -20) = 0.5(q)
Solution8 +0.25q = 0.5q . . . . . . . simplify
8 = 0.25q . . . . . . . . . . . . subtract 0.25q
32 = q . . . . . . . . . . . . . . multiply by 4
There were 32 questions in total on the test.
In a direct variation, y=80 when x=5. Write a direct variation equation that shows the relationship between x and y.
As per the concept of direct variation, y = 80 when x = 5, then the direct variation equation shows the relationship between x and y will be y = 16x
Equation
Basically, the equation is a statement that two expressions, which include variables and/or numbers, are equal. And in essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Given,
In a direct variation, y=80 when x=5.
Here we have to write a direct variation equation that shows the relationship between x and y.
Here we have given that,
The value of y = 80 when x = 5
Therefore, there are often two different sorts of variables in analytics.
And we have obtained that independent variables will have an impact on dependent variables.
Now, what occurs as a result of the independent variable is referred to as a dependent variable.
Here we have given equation x is the independent variable while y is the dependent variable.
So, it can be written as,
=> 80 = 16(5)
Therefore, the resulting equation is y = 16x
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Challenge Andy and Emily each go to a hardware store to buy wire. The table shows the cost y in dollars for x inches of the
wire they need. Andy needs 25 feet of the wire. Emily needs 15 yards of the wire. How much will each of them spend for wire?
Cost of Wire
Length in
Inches (x)
110
125
160
185
Cost in
Dollars (y)
5.50
6.25
8.00
9.25
Andy will spend $15 for her wire. Emily will spend $27.25 for her wire.
1 = 12 ℎ
1 = 3 = 36 ℎ
=5.50/110 (⁄ℎ)
=6.25/125 (⁄ℎ)
=8.00/160 (⁄ℎ)
=9.25/185 (⁄ℎ)
Andy needs 25 feet of the wire
25(12 inches) = 300 inches
300(5.50 / 110) = 15(Dollars)
Andy will spend $15 for her wire.
Emily needs 15 yards of the wire
15(36 ℎ) = 540 ℎs
110a + 125b + 160c + 185d ≥ 540
6(110) = 660
4(110) + 125 = 565
3(110) + 2(125) = 580
110 + 3(125) = 485
2(125) + 2(160) = 570
110(5.50/110) + 3(145)6.25/125 = 27.25
540 (5.50/110) = 27
Emily will spend $27.25 for her wire.
If she can cut the wire, then Emily will spend $27 for her wire.
∴ Andy will spend $15 for her wire. Emily will spend $27.25 for her wire.
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also confused about this
Graph (B) represents the base function f (x)=√x and the stretched function [tex]g (x) = \frac{-3}{2} \sqrt{x}[/tex].
What is graph?Graphs are used to map functions of two variables on a Cartesian coordinate system, which is composed of a horizontal x-axis, vertical y-axis.
The graph of this function can be obtained by putting different values of x.
x = 0 gives f (x) = 0
x = 1 gives f (x) = 1
x = 2 gives f (x) = 1.414
x = 3 gives f (x) = 1.732
Drawing these points in the graph and connecting we get a curve(black) which can be seen in all given diagram (A), (B), (C), (D).
Now, we have stretched function [tex]g (x) = \frac{-3}{2} \sqrt{x}[/tex]
The graph of this function can be obtained by putting different values of x.
x = 0 gives g (x) = 0
x = 1 gives g (x) = -1.5
x = 2 gives g (x) = -2.121
x = 3 gives g (x) = -2.598
Drawing these points in the graph and connecting we get a curve(red) which can be seen in diagram (D).
By combining these two graphs we get the graph of diagram (D).
Therefore, the base function f (x) and the stretched function g (x) together represents the diagram (D).
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Determine the y-intercept of the line
11x - 8y = 22
Answer:
- 2.75 or - 2 [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Put in zero for x to solve for y
11x -8y = 22
11(0) -8y = 22
-8y = 22 Divide both sides by -8
y = -2.75
(0, -2.75)
Answer:
[tex]-\frac{22}{8}[/tex] or [tex]- \frac{11}{4}[/tex] in mixed number form, [tex]-2\frac{3}{4}[/tex] simplified
Step-by-step explanation:
Minus 11x from 11x and 22.
You will then get -8y=11x+22.
Divide all the numbers by -8y.
You will get y=-11/8x-22/8
So the y-intercept is -22/8 or -11/4
I hope I got this right
What value of x is in the solution set of the inequality 9 2x 1 9x 18?.
The value of x in the solution set of the inequality 9(2x+1) < 9x-18 is
x <-3.
Given inequality:
9(2x+1) < 9x-18
simplifying
9*2x + 9*1 < 9x - 18
18*x + 9 < 9x - 18
18x + 9 < 9x - 18
combining the like terms
18x - 9x + 9 < -18
9x + 9 < -18
combining the constants
9x < -18-9
9x < -27
divide by 9 on both sides
9x/9 < -27/9
x < -27/9
x < -3
Therefore the value of x in the solution set of the inequality 9(2x+1) < 9x-18 is x <-3.
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Ben and Katy throw darts at a target.
Ben's ratio of hits to misses is
5:1
Katy's ratio of hits to misses is 3:1
Ben says,
"5 is bigger than 3, so I must have more hits than Katy."
Give an example to show that this might not be true
In the given ratio, the statement "5 is bigger than 3, so I must have more hits than Katy." is false. Because this one refer the missing rate.
Ratio:
The relationship between two things when it is expressed in numbers or amounts is known as ratio.
Given,
Ben and Katy throw darts at a target. Ben's ratio of hits to misses is
5:1 Katy's ratio of hits to misses is 3:1
Ben says, "5 is bigger than 3, so I must have more hits than Katy."
Here we need to show that this might not be true.
Here we have the following missing ratios,
Ben's missing ratio = 5 : 1
Katy's missing Ratio = 3 : 1
Here Ben says "5 is bigger than 3, so I must have more hits than Katy."
While we carefully, looking into the given question, we have identified that the given ratios are represents the loosed dart.
So, the given statement is wrong.
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Hynix is comparing two numbers.He knows the larger number is twice the value of 4 more than the smaller number X. He also knows their difference is 11. Which equation can he use to find the value of the smaller number X
The equation that he can use to find the value of the smaller is 8+2x = y and y-x = 11 where y is the larger number.
According to the question,
We have the following information:
Hynix is comparing two numbers. He knows the larger number is twice the value of 4 more than the smaller number X. He also knows their difference is 11.
Now, let's take the larger number to be y.
So, we have:
y = 2(4+x)
y = 8+2x
y-x = 11 ....(2)
Putting the value of y from above equation:
8+2x-x = 11
8+x = 11
x = 11-8
x = 3
Now, putting the value of x in equation 2:
y-3 = 11
y = 11+3
y = 14
Hence, the equation that he can use to find the value of the smaller is 8+2x = y and y-x = 11 where y is the larger number and the value of x is 3 and that of y is 14.
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Given that x is a nonnegative number, a student conjectured that x+4
The value of x is a counter example to the student's conjecture (x = 2).
What is an expression?
The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that x is a non-negative number, a student conjectured that x + 4 < x².
Since x is a non-negative number, A and B are eliminated.
This leaves C and D at the value of x = 2,
2 + 4 < 2²
6 < 4 is false.
Therefore, the value of x is a counterexample to the student's conjecture (x = 2).
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What is 2+2 - 5 + 42 - 64 (5 x 5) - 32 x 1/2 + 6/5 * 2^5
Answer:
-1536.6 if not the answer den sorry
Step-by-step explanation:
Answer:
its -39363/25, -1574.32, and -1574 13/25 (hopefully this helps, sorry if its wrong)
can you please answer this? its timed so dont take too long!
2g³-5g²+6 is the equivalent expression of (5g⁴+5g³-17g²+6g)-(3g⁴+6g³-7g²-12)/g+2
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is (5g⁴+5g³-17g²+6g)-(3g⁴+6g³-7g²-12)/g+2
5g⁴+5g³-17g²+6g-3g⁴-6g³+7g²+12/g+2
2g⁴-g³-10g²+6g+12/g+2
Factorize the numerator
(g+2)(2g³-5g²+6)/g+2
g+2 in numerator and denominator will be cancelled.
2g³-5g²+6
Hence, 2g³-5g²+6 is the equivalent expression of (5g⁴+5g³-17g²+6g)-(3g⁴+6g³-7g²-12)/g+2
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Bella manages a cafe.She bought 15.625 pounds of oranges . She mutiplies the weigh of the oranges by 0.4 to find the weight of the oranges she will use in fruit salads
The weight of an object is the amount of gravitational force applied on the object by the earth. The weight of the oranges to be used is 6.25 pounds.
The level of influence of the earth's gravitational pull on an object determines its weight. This depends also on the size of the mass of the object.
Given that Bella bought 15.625 pounds of oranges.
Let the weight of the oranges required to prepare fruit salad be represented by W. Then the weight of the oranges required is 0.4 of the weight of oranges bought, so that;
W = 0.4 * 15.625
= 6.25
W = 6.25
Thus, the weight of the oranges required to be used for fruit salad is 6.25 pounds.
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Find the equation of the straight line passing through each of the following pairs of points.
( 11, 13) and ( 14, 19)
The equation of the line is, y = 2x - 9.
What is the point slope form of the equation of line?
The general form of a linear equation is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
Consider, the given two points, (11, 13) and (14, 19).
First to find the slope of the line, using the given two points,
[tex]m = \frac{y_2-y_1}{x_2 -x_1}[/tex]
[tex]m = \frac{19-13}{14-11} = \frac{6}{2} =2[/tex]
Therefore, the slope of the line is, 2.
Now to find the equation of line.
Consider, the point - slope form of the line,
[tex]y-y_1=m(x-x_1)[/tex] ..(1)
where, [tex](x_1, y_1)[/tex] is one of the given point and m is the slope of the line.
Here, [tex](x_1, y_1) = (11, 13), m = 2[/tex]
Substitute the values in the equation (1).
[tex]y-13=2(x-11)\\y-13=2x-22\\y=2x-22+13\\y=2x-9[/tex]
Therefore, the equation of line is, [tex]y=2x-9[/tex].
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Look at this set of ordered pairs:
(0, 0)
(0, -19)
(-8, 0)
Is this relation a function?
yes
no
The equation of line s is y=1/3x-3. The equation of line t is y=-x+5. The equations of line s and t form a system of equations. The solution to the system of equations is located at point P. Which graph correctly shows line s, line t, and point P?
The graph A is correctly shows for the line s, line t, and point P.
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 equation of line for s,
⇒ y = 1/3x - 3
And, The equation of line for t,
⇒ y = - x + 5
Now,
Solve the both equation of line for the solution as;
Since, The equation of line for s,
⇒ y = 1/3x - 3
And, The equation of line for t,
⇒ y = - x + 5
Equate both equation, we get;
⇒ 1/3x - 3 = - x + 5
⇒ 1/3x + x = 5 + 3
⇒ 4/3x = 8
⇒ x = 8 × 3 / 4
⇒ x = 2 × 3
⇒ x = 6
And, ⇒ y = - x + 5
⇒ y = - 6 + 5
⇒ y = - 1
Thus, The solution of the lines is;
Point P = (6, - 1)
Clearly, The graph A is correctly shows for the line s, line t, and point P.
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help
If f(1) = 3 and f(n) = f(n − 1) – 3 then find the value of f(4).
If f(1) = 3 and f(n) = f(n − 1) – 3 then the value of f(4) is -6.
Define function.A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). A function is a type of rule that produces one output for a single input. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.
Given,
Function:
f(1) = 3
f(n) = f(n - 1) -3
Let n = 2
f(2) = f(2-1) - 3
f(2) = 3 - 3
Relation:
f(2) = 0
Let n = 3
f(3) = f(3 -1) - 3
f(3) = 0 -3
f(3) = -3
Let n = 4
f(4) = f( 4 -1) - 3
f(4) = -3 -3
Value:
f(4) = -6
If f(1) = 3 and f(n) = f(n − 1) – 3 then the value of f(4) is -6.
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Suppose T: ℝ3→ℝ2 is a linear transformation. Let U, V and W be the vectors given below, and suppose that T(U) and T(V) are as given. Find T(W).
U = 1, -3, 3 V = −1,3,−2 W = −3,9,−7 T(U) = 2,2 T(V) = 0,1
T(W) = ???
By using the concept of Linear Transformation, the value of T(W) obtained is T(W) = (2, 6)
What is Linear Transformation?
A function through one vector space to the next that respects this same underlying (linear) structure of the each vector space is called a linear transformation. A linear operator, or map, is another name for a linear transformation. The transformation is known as just an endomorphism as well as, if invertible, an automorphism when the range of a transformation matches the domain. The underlying field of the two vector spaces must be identical.
Let u, v be two element of a vector space V and let c be a scalar
T is said to be a Linear Transformation if
i) T(u + v) = T(u) + T(v)
ii) T(cu) = cT(u)
T: [tex]\mathbb{R}^{3} \rightarrow \mathbb{R}^2[/tex] is a linear transformation
U = (1, -3, 3), V = (−1,3,−2)
W = [tex]c_1[/tex] U + [tex]c_2[/tex] V
(-3, 9, -7) = [tex]c_1[/tex](1, -3, 3) + [tex]c_2[/tex](-1, 3, -2)
[tex]c_1 - c_2 = -3[/tex] ...... (1)
[tex]3c_1 - 2c_2 = -7[/tex] ..... (2)
Multiplying (1) by 2
[tex]2c_1 - 2c_2 = -6[/tex] .... (3)
Subtracting (2) from (3),
[tex]c_1 = 1[/tex]
Putting the value of [tex]c_1[/tex] in (1)
1 - [tex]c_2[/tex] = -3
[tex]c_2 = 3 + 1\\c_2 = 4[/tex]
T(W) = T(U) + 4T(V)
T(W) = (2, 2) + 4(0, 1)
T(W) = (2, 6)
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When collecting data, what is a sample?
Thank you for helping.
Answer:
Step-by-step explanation:
Artista , it's the 3rd answer, a random set from the group being studied
2B math need help with this problem have a math test tomorrow
Answer:
∴ x = 113
Step-by-step explanation:
5-sided polygon: pentagon
total interior angles of a pentagon
= (5-2) × 180°
= 540°
x + x + x + 14 = 540° - 90° - (180 - 83)°
3x + 14 = 540 - 90 - 97
3x = 353 - 14
3x = 339
∴ x = 113
how to solve peggy is preparing a colored frosting for a cure. for the right shade of purple, she needs 25 milliliters of a 44% concentration food coloring. the store has a 25% red and a 50% blue concentration of food coloring. how many milliliters each of blue food coloring and red food coloring should be mixed to make the necessary amount of purple food coloring?
Answer:
25% red and 28% blue.
Step-by-step explanation:
If someone uses 400 liters of orange juice, how much strawberry juice would they need?
Answer:
you need to post the rest of the problem for us to figure it out. if someone walked up to you and asked you this you'd think they're out of their mind
Which equation is the standard form of -8x + 3x² = -19?
8r 32² 19 0
The standard form of the equation -8x + 3x² = -19 is 3x² - 8x + 19 = 0.
How to write equation in standard form?The standard form of quadratic equation is ax² + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number.
The standard form of quadratic equation with a variable x is of the form ax² + bx + c = 0, where a ≠ 0, and a, b, and c are real numbers.
Therefore, a, b and c are constant and x are the variables.
Let's represent the quadratic equation in standard form.
-8x + 3x² = -19
using the format ax² + bx + c = 0,
3x² - 8x + 19 = 0
where
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