Answer:
the answer is 8 because when you set the equation equal to 12 and solve it you get 12
Step-by-step explanation:
Final answer:
To find the input for f(x) = 2x + 4 when the output is 12, solve the equation 12 = 2x + 4 for x, resulting in the input-value x being 4, with the ordered pair being (4, 12).
Explanation:
The question concerns finding the input for a given function when the output is known. The function provided is f(x) = 2x + 4, and we want to find the input value, or x, that produces an output, or f(x), of 12. To do this, we set up an equation where 12 = 2x + 4 and solve for x.
We first subtract 4 from both sides of the equation to get 8 = 2x. Then, we divide both sides by 2 to isolate x, resulting in x = 4.
The ordered pair representing the input-output relationship for the function when the output is 12 is (4, 12).
What is the lateral area of the prism?
A triangular prism has bases with three congruent sides,
each measuring 4 feet. The height of each triangle is
approximately 3.5 feet. The distance between the triangular
bases is 7 feet.
73.5 feet
73.5 square feet
84 feet
84 square feet
4 ft
Answer:
84 square feet as law of prism = perimeter of traingle ×length
Answer:
84 square feet
Step-by-step explanation:
thats the answer i got on edg
Complete the following equation, then distribute 9 multiply 27=9(_+7)
Answer:
9(x + 7)= 27
9x + 63 = 27
9x = -36
x = -4
Step-by-step explanation:
Find the missing endpoint if S is the midpoint of RT
R(-9,4) and S(2,-1) ; Find T
Answer:x-coordinate of T: from -9 to 2, there's 11 units, so you add 11 to 2 to find the x-coordinate of T, which is 13.
y-coordinate of T: from 4 to -1 there's -5 units, so you subtract 5 from -1 to find the y-coordinate of T, which is -6.
Step-by-step explanation:
Find the equation of a line that is perpendicular to the line y=(1/3)x+4 and contains the point (-9,0)?
Answer:
y = -3x - 27
Step-by-step explanation:
0 = -3[-9] + b
-27 = b
y = -3x - 27
* Perpendicular Lines have OPPOSITE MULTIPLICATIVE INVERSE RATE OF CHANGES [SLOPES]:
⅓ → -3
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(a) A dog owner records the weight of her dog. She finds that from the age of 20 weeks to the age of 48 weeks, the dog’s weight can be modelled by the equation w = 0.92t−0.15 (20 ≤ t ≤ 48), where w is the weight of the dog in kilograms, and t is the age in weeks.
(i) Find the weight of the dog at age 26 weeks according to this model.
(ii) Explain the inequality (20 ≤ t ≤ 48) that follows the equation.
(iii) Using algebra, calculate the age at which the dog’s weight is 40kg
(iv) Write down the gradient of the straight line represented by the equation w = 0.92t−0.15. What does this measure in the practical situation being modelled? (v) Either using Graphplotter or by hand, sketch the graph of w = 0.92t−0.15, putting w on the vertical axis and covering the time interval 20 ≤ t ≤ 48.
(vi) Explain why the model cannot be extended to model accurately the dog’s weight at birth
Answer:
(i)23.77kg
(ii)(ii) the inequality 20≤t≤48 means the weight of the dogs determined is for dogs that have the age of 20 weeks or less to the age of 48 weeks not more.
(iii)44 weeks
(iv)0.92
(v)Attached
(vi)The value of weight will be negative,which is unrealistic.
Step-by-step explanation:
(i)Given that the weight is modeled by the equation;
w = 0.92t−0.15 (20 ≤ t ≤ 48)
then substitute the value of t in the equation given that t=26 weeks
w=0.92*26-0.15=23.77kg
(ii) the inequality 20≤t≤48 means the weight of the dogs determined is for dogs that have the age of 20 weeks or less to the age of 48 weeks not more.
(iii)Apply the equation for weight
w=0.92t-0.15
40=0.92t-0.15
40+0.15=0.92t
40.15=0.92t
40.15/0.92=t
43.6⇒⇒44 weeks
(iv) Here , write the equation in slope intercept form of y=mx+c where m is the slope and c is the y-intercept
w=0.92t-0.15
y=mx+c
m=0.92
(v)sketch attached
(vi)
At birth, t=0 hence to find weight
w=0.92t-0.15
w=0.92*0-0.15
w=0-0.15
w=-0.15
The model cannot be extended to model accurately the dog's weight at birth because you will get a negative value for weight which is not realistic.
What is the area of rectangle ABCD
given the information in the diagram?
AD=16
FE =23
FD=DE
DE = To DC
F DE
Answer:
1,840 units squared
Step-by-step explanation:
Suppose that y is directly proportional to x, and y = 150 when x = 15. What is the constant of proportionality?
Answer: The required constant of proportionality is 10.
Step-by-step explanation: Given that y is directly proportional to x, and y = 150 when x = 15.
We are to find the constant of proportionality.
According to the given information, we can write
[tex]y\propto x\\\\\Rightarrow y=kx~~~~~~~~~~~~~~~~[\textup{where k is the constsnt of propotionality}].[/tex]
When y = 150 and x = 15, we get from the above equation that
[tex]y=kx\\\\\Rightarrow 150=k\times15\\\\\Rightarrow k=\dfrac{150}{15}\\\\\Rightarrow k=10.[/tex]
Thus, the required constant of proportionality is 10.
Answer:
10 gugvtbfvghmfjgncgfhfdg
Find each of the following square roots. (Hint: All examples are perfect squares.)
a. √16
b. √169
c. √64
d. √400
Step-by-step explanation:
[tex]\sqrt{a}=b\iff b^2=a,\ \text{for}\ a\geq0\ \text{and}\ b\geq0.\\\\a.\ \sqrt{16}=4\ \text{because}\ 4^2=16\\\\b.\ \sqrt{169}=13\ \text{because}\ 13^2=169\\\\c.\ \sqrt{64}=8\ \text{because}\ 8^2=64\\\\d.\ \sqrt{400}=20\ \text{because}\ 20^2=400[/tex]
Answer:
Step-by-step explanation:
√16 = √4² = 4
√169=√13² = 13
√64 = √8² = 8
√400 = √20² = 20
What is the mass of a liquid having a density of 1.40g/ml and volume of 30ml
Answer:
42mL
Step-by-step explanation:
Density equals Mass divided by Volume. In that way, you are missing the Mass, so it would be Density multiplied by Volume.
Write each expression in exponential form 2 x 2 x 2 x 2 =
Step-by-step explanation: Exponential form contains a base and an exponent. The base is the number that is multiplied so in this case, 2 is the base. Next we write the exponent which is the number of times that the base is multiplied. Since 2 is multiplied 4 times, the exponent is 4.
So in exponential form, 2 x 2 x 2 x 2 can be written as [tex]2^{4}[/tex].
The expression 2 x 2 x 2 x 2 can be written in exponential form as [tex]2^{4}[/tex]
What is Exponential form?In a variety of mathematical applications, such as scientific notation, computations using powers, and illustrating development or decay processes, exponential form is frequently used. A base and an exponent are both present in exponential form. The multiplied number, in this example 2, is known as the base. The exponent, which represents the number of times the base has been multiplied, is then written. The exponent is 4 since 2 has been multiplied 4 times.
Then we can see that there are four 2s then we can write in exponential as 2 x 2 x 2 x 2 =[tex]2^{4}[/tex]
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Write the equation of the line perpendicular to y= 2x +1 that passes through the point (6,2)
Answer:
Step-by-step explanation:
Hello:
the equation is : y = ax+b
the slope is a : a×(2) = -1......( perpendicular to a line with a slope of 2 for : y=2x+1)
a =-1/2 y=(-1/2)x+b
the line that passes through (6, 2) : 2 = (-1/2)(6)+b
b = 5
the equation is : y = (-1/2)x+5
You can use the fact that perpendicular lines have slopes such that their multiplication ends up as -1.
The equation of the line perpendicular to line y = 2x + 1 and passing through (6,2) point coordinate is given as
[tex]y = -\dfrac{1}{2}x + 5[/tex]
What is the slope of perpendicular lines?Suppose that first straight line has slope 's'
Let another straight line be perpendicular to this first line.
Let its slope be 'a'
Then due to them being perpendicular, they have their slopes' multiplication as -1
or
[tex]s \times a = -1\\\\a = -\dfrac{1}{s}[/tex]
How to get the slope intercept form of a straight line equation?If the slope of a line is m and the y-intercept is c, then the equation of that straight line is given as:
[tex]y = mx + c[/tex]
The first line y = 2x + 1 is in slope intercept form and its slope is s = 2
Now, let the second line which is perpendicular to this line and passing through (6,2) coordinate be
y = [tex]ax + b[/tex]
Then as both lines are perpendicular, thus
[tex]a = -\dfrac{1}{s} = -\dfrac{1}{2}[/tex]
Thus, equation of second line is
[tex]y = -\dfrac{1}{2}x + c[/tex]
Since this line passes through coordinate (6,2), thus, this point coordinate should satisfy the equation of line as an equation is true for all points the graph represented by it passes through.
Thus,
[tex]y = -\dfrac{1}{2}x + c[/tex]
[tex]2 = -\dfrac{1}{2} \times 6 + c\\\\2 = -3 +c\\\\c=2+3 = 5[/tex]
Thus, equation of the second line is
[tex]y = -\dfrac{1}{2}x + 5[/tex]
Thus,
The equation of the line perpendicular to line y = 2x + 1 and passing through (6,2) point coordinate is given as
[tex]y = -\dfrac{1}{2}x + 5[/tex]
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36×41 help me pls pls pls pls pls pslsp sp
Answer: 36x41=1476
I hope I helped.
Answer:
36×41=1476
Step-by-step explanation:
Mental math :D
A free floating bubble has a diameter between 5 and 6 feet. Calculate the exact volume of a sphere with a diameter of 6 feet
Answer:
Find the volume of the sphere where its diameter is 15 inches. Take π=3.14.
Step-by-step explanation:
Alright, since we are finding the volume of a sphere, we will be using the following volume formula:
the formula for the volume of a sphere
where π is a number that is approximately equals to 3.14 (or use the number given to you) and r is the radius of the sphere.
Note that, to use the formula, we need the value of the radius. Since the radius is half of the diameter, we can find the value of the radius by dividing 15 with 2. This is shown below:
Answer:
I think the answer would be 30
sorry if it is wrong
Step-by-step explanation:
The formula for the area of a rectangle is A = lw. What
is the area of rectangle WXYZ?
16 square units
18 square units
20 square units
22 square units
Answer:
20 square units
Step-by-step explanation:
we know that
The area of rectangle is equal to
[tex]A=LW[/tex]
In this problem
[tex]L=WX=ZY\\W=WZ=XY[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance WX
we have
W(-3,1), X(3,3)
substitute the values in the formula
[tex]d=\sqrt{(3-1)^{2}+(3+3)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(6)^{2}}[/tex]
[tex]d_W_X=\sqrt{40}\ units[/tex]
Find the distance XY
we have
X(3,3),Y(4,0)
substitute the values in the formula
[tex]d=\sqrt{(0-3)^{2}+(4-3)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(1)^{2}}[/tex]
[tex]d_X_Y=\sqrt{10}\ units[/tex]
Find the area of rectangle
[tex]A=(WX)(XY)[/tex]
substitute the values
[tex]A=(\sqrt{40})(\sqrt{10})=20\ units^2[/tex]
Answer:
c
Step-by-step explanation:
A snack package has 4 cheese sticks. How many cheese sticks are in 4 packages?
Answer:There is 16
Step-by-step explanation:
There is 16 because 4 × 4 is 16
there are 78 tourists going on a sightseeing trip.the tour company's buses hold 12 people each how many buses will they need?
Answer:
6.5
Step-by-step explanation:
Answer:
7 buses
Step-by-step explanation:
when doing a problem like this you have to divide the larger group of people by the smaller group
78 divided by 12 = 6.5
if u answered this multiplication problem correctly you would get 6.5 but u cannot put .5 people on a bus lol. so therefore u are not done yet... so u need to round up
here's a poem to help with ur rounding...
Find a place look next door
4 or less let it rest
5 or more raise the score!!!
so in conclusion your answer would be 7!
Using the graph as your guide, complete the following statement.
The discriminant of the function is
Answer:
Using the graph as your guide, complete the following statement.
The discriminant of the function is
Step-by-step explanation: Remember a parable of the form f(x) = a[tex]a x^{2} + bx + c[/tex], satisfy:
(1) has only one root if and only if [tex] b^2 - 4ac = 0[\tex]
(2) has two real roots if and only if [tex] b^2 - 4ac > 0[\tex]
(3) has two complex roots if and only if [tex] b^2 - 4ac < 0[\tex].
The number b^2 - 4ac is called the discriminant of the parable f(x).
From the graph we can see that the parable has only one root approx in x =1. Thus from point (1) we can conclude that the discriminant should be zero.
PD: a root of a polynomial f(x) is a number a such thast f(a) =0.
The answer is A.
Answer: The answer is A because the vertex lies on the x axis which makes it zero.
Answer= A
Which problem can be represented by the equation 49y−8=89 ?
A. A water filter filters 89 ounces of water per day. The first 8 ounces of water cannot be consumed and must be dumped out. How many days will it take the water filter to produce 49 ounces of consumable water?
B. A water filter filters 49 ounces of water per day. The first 8 ounces of water cannot be consumed and must be dumped out. How many days will it take the water filter to produce 89 ounces of consumable water?
C. A water filter filters 89 ounces of water per day. The first 49 ounces of water cannot be consumed and must be dumped out. How many days will it take the water filter to produce 8 ounces of consumable water?
D. A water filter filters 8 ounces of water per day. The first 49 ounces of water cannot be consumed and must be dumped out. How many days will it take the water filter to produce 89 ounces of consumable water?
Answer: B
Step-by-step explanation:
How do you write
three and two thirds times a number equals two ninths
as an equation?
Answer:
(11/3)x=(2/9)
Step-by-step explanation:
1) Three and two thirds can be simplified to 11/3
2) A number can be rewritten as "x"
(11/3)x=(2/9)
What is the value of the expression given below? (5+3i)-(5+3i)(5-5i)
Answer:
-35 + 13iStep-by-step explanation:
[tex]i=\sqrt{-1}\to i^2=-1\\\\(5+3i)-(5+3i)(5-5i)\qquad\text{distribute}\\\\=(5+3i)(1-(5-5i))=(5+3i)(1-5-(-5i))=(5+3i)(-4+5i)\\\\\text{use}\ FOIL:\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(5)(-4)+(5)(5i)+(3i)(-4)+(3i)(5i)\\\\=-20+25i-12i+15i^2=-20+13i+15(-1)\\\\=-20+13i-15=-35+13i[/tex]
Classify the following angles.
13°
180°
Answer: The acute angle is the small angle which is less than 90°. If you choose the larger angle you. will have a Reflex Angle instead: The smaller angle is an Acute Angle, but the larger angle is a Reflex Angle.
Step-by-step explanation: An angle that is exactly 90 degrees is called a right angle. Angles greater than 90 degrees and less than 180 degrees are called obtuse angles. An angle that is exactly 180 degrees is called a straight angle. butt
What is 0.888 as a fraction, in simplest form?
Answer:
111÷125
Step-by-step explanation:
0.888 as fraction is 888÷1000
Divide by 2 u get
444÷500 furher divide by 2
222÷250
and last divide
111÷125 and u cant change into more lower fraction so the answer is 111÷125
The required fraction of the number 0.888 is 111 / 125.
Given that,
To determine the 0.888 as a fraction, in simplest form.
What is a number system?
A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing the numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
Here,
Given number = 0.888
Fraction = 0.888 = 888 / 1000
Faction = 111 / 125
Thus, the required fraction of the number 0.888 is 111 / 125.
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Solve the problem using
READ, DRAW, WRITE.
Andy had $38. He spent $5 on
a toy and gave $3 to his
brother. How much money.
does he have left?
Answer: Andy has 30 dollars left
Step-by-step explanation: 38 - 5 - 3 = 30
Answer:
$30
Step-by-step explanation:
I’m having trouble on that one in the picture
Answer:
c.) 4 2/3
Step-by-step explanation:
look at the screenshot below it'll explain the answer
Solve for x.
3 - |8x-6I = 3
x= or x=
Answer:
¾ = x
Step-by-step explanation:
Since 3 - 0 gives us the 3, we do this:
[tex]0 = -|8x - 6|[/tex]
0 = -8x + 6 >> Distributive Property
-6 - 6
___________
-6 = -8x
__ ___
-8 -8
¾ = x
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What is the simplified form of i ^32?
A. -i
B. 1
C. i
D. -1
divide exponent by 4
since the remainder is zero, the equation can be rewritten as i^0 and any number to the 0 power is 1
Answer:
1
Step-by-step explanation:
The pattern of imaginary numbers taken to exponents goes as thus:
i^1= i
i^2= -1
i^3= -i
i^4= 1
To solve this problem, divide the exponent by 4:
32/4= 8
Now rewrite i^32 as (i^4)^8
(When exponents are raised by an exponent you multiply them together)
i^4=1, this is your answer
Please answer this question?
Solve the inequality 3 ≥ t + 1 Question 12 options: a) {t | t ≤ 4} b) {t | t ≤ 2} c) {t | t ≥ 2} d) {t | t ≥ 4}
Answer: b
Step-by-step explanation:
ok, lets see the answers one for one.
a) in this case, t can be 4, if t= 4 then t + 1 = 5 and the inequality is false.
b) in this case, the maximum vale of t is 2, then 2 + 1 = 3, the inequality is true here, and all the other numbers in the set is smaller than 2, then all this set keeps the inequality true.
c and d) both sets allow to take, for example, t= 10, wich makes the inequality false.
now in this type of exercises, you should se the biggest and lowest number that keeps the inequality true, in this case the biggest is 2, because 2 + 1 = 3, and there is no lowest limit because any negative number + 1 will be less than 3. With those limits then you can figure the set of valid solutions with all the numbers in between.
Final answer:
The solution to the inequality 3 ">=" t + 1 is option b) {t | t ">=" 2}, which means that t is any number less than or equal to 2.
Explanation:
Before solving the inequality 3 ">=" t + 1, first, let's isolate the variable t. To do that, we subtract 1 from both sides of the inequality:
3 - 1 ">=" t + 1 - 1
2 ">=" t
This can be read as 't is less than or equal to 2' or 't must be any number that is 2 or smaller.' Therefore, the correct answer is:
{t | t ">=" 2}
When comparing with the question options, it is clear that option b) matches our solution.
Thus, option b) {t | t ">=" 2} is the correct answer to the inequality given in the question.
If a triangle has sides of lengths 3, 4, and 5 units, then it is
a right triangle. All right triangles have an area equal to one
half the product of the two smaller side lengths.
Which statement is valid, based on deductive reasoning?
OA)
A polygon has an area of 6 square units if it is a
triangle
OB)
A triangle has a perimeter of 12 units if its sides are consecutive
integers.
If a triangle has side lengths 3, 4, and 5 units, then its area is 6
square units.
If a triangle has side lengths 4, 5, and 6 units, then its
area is 10 square units.
OC)
Answer:
If a triangle has side lengths 3, 4, and 5 units, then its area is 6
Step-by-step explanation:
Deductive reasoning represents an important form of logical reasoning in which a conclusion is based on the concordance of multiple premises that are generally assumed to be true
we have
If a triangle has side lengths 3, 4, and 5 units, then its area is 6
we know that
1) If triangle has side lengths 3, 4 and 5, then is a right triangle because satisfy the Pythagoras Theorem
2) All right triangles have an area equal to one half the product of the two smaller side lengths
[tex]A=\frac{1}{2}(a)(b)[/tex]
substitute the values
[tex]A=\frac{1}{2}(3)(4)[/tex]
[tex]A=6\ units^2[/tex]
therefore
The statement is valid based on deductive reasoning
Final answer:
A valid statement derived from deductive reasoning is that a right triangle with side lengths of 3, 4, and 5 units has an area of 6 square units. This is consistent with the properties of right triangles and the formula for the area of a triangle.
Explanation:
Based on deductive reasoning and the properties of right triangles, we can make a valid statement regarding the triangle with side lengths of 3, 4, and 5 units. Since the sum of the squares of the two smaller sides (3² + 4²) equals the square of the longest side (5²), by the Pythagorean theorem, this is a right triangle. Additionally, the area of a right triangle is given by A = (base × height) / 2, therefore, if we take the two shorter sides as the base and height, the area of this triangle would be (3 × 4) / 2 = 6 square units.
The valid statement based on the given information is that if a triangle has side lengths 3, 4, and 5 units, then its area is 6 square units. The other statements about polygons, perimeters, and other triangles' side lengths are not necessarily valid based on the given information alone.
PLEASE help... how would i even go about solving these? i’m so confused
Answer:
Step-by-step explanation:
Ok so supplementary angles add up to 180°. If A and B add up to 180, then they can be added together to be solved. x+2x-30=180 would be your equation. From here you must balance the variable values on one side and numerical values on the other side. This can simply be done by adding 30 to both sides. Not the -30 is gone but 180 increased by 30 degrees to 210. next, combine like terms on the x side to get 3x. (2x+x=3x). set 3x equal to 210 and divide both sides to lose the 3 in front of the x value. 210/3 is equal to 70, making x=70! This may be hard to follow, so comment below if you need a broader explanation. Have good day!