Answer:
[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Double Angle Identities}\\\\$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$\\\\$\cos (A \pm B)=\cos A \cos B \mp \sin A \sin B$\\\\$\tan (A \pm B)=\dfrac{\tan A \pm \tan B}{1 \mp \tan A \tan B}$\\\end{minipage}}[/tex]
Given equation:
[tex]\tan (x + \pi) + \sin(x + \pi) + \sin(x - \pi)=0[/tex]
Simplify using the double angle identities:
[tex]\implies \dfrac{\tan x + \tan \pi}{1 -\tan x \tan \pi} + \sin x \cos \pi+\cos x \sin \pi + \sin x \cos \pi -\cos x \sin \pi=0[/tex]
[tex]\implies \dfrac{\tan x + 0}{1 -\tan x(0)} + \sin x (-1)+\cos x (0) + \sin x(-1) -\cos x (0)=0[/tex]
[tex]\implies \dfrac{\tan x}{1} -\sin x - \sin x=0[/tex]
[tex]\implies \tan x-2\sin x =0[/tex]
Use the tan identity to rewrite tan(x) in terms of sin(x) and cos(x):
[tex]\implies \dfrac{\sin x}{ \cos x}-2\sin x=0[/tex]
Multiply both sides by cos(x):
[tex]\implies \dfrac{\sin x\cos x}{ \cos x}-2\sin x\cos x=0(\cos x)[/tex]
[tex]\implies \sin x-2\sin x \cos x=0[/tex]
Factor out sin(x) from the left side of the equation:
[tex]\implies \sin x(1-2 \cos x)=0[/tex]
Apply the zero-product property.
Case 1
[tex]\implies \sin x=0[/tex]
[tex]\implies x=\sin^{-1}(0)[/tex]
[tex]\implies x=2\pi n, \; \pi+2\pi n[/tex]
Case 2
[tex]\implies 1-2 \cos x=0[/tex]
[tex]\implies 1=2 \cos x[/tex]
[tex]\implies \cos x=\dfrac{1}{2}[/tex]
[tex]\implies x= \cos ^{-1} \left(\dfrac{1}{2}\right)[/tex]
[tex]\implies x=\dfrac{\pi }{3}+2\pi n, \;\dfrac{5\pi }{3}+2\pi n[/tex]
Solution
[tex]x=\dfrac{\pi }{3}+2\pi n, \quad x=\dfrac{5\pi }{3}+2\pi n,\quad x=2\pi n,\quad x=\pi+2\pi n[/tex]
Can anyone write the equation of the graph?
The absolute equation in the graph is f(x) = |x - 3| + 5
How to find the equation of the graph line?From the question, we can see that the lines on the graph has a sharp v-shape
Graphs that have this form are absolute value graphs
The general form of an absolute value equation is expressed as
y = |x - h| + k
From the above form, we have
Vertex = (h, k)
By definition, the vertex of a function is either the maximum point or the minimum point
On the given graph, the minimum point is (3, 5)
So, we have the following representation
(h, k) = (3, 5)
Substitute (h, k) = (3, 5) in the above equation
So, we have:
y = |x - 3| + 5
Hence, the function represented by the graph has an equation of f(x) = |x - 3| + 5
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F(x)=-2x-3 find f(-1)
Answer:
x = -1
Step-by-step explanation:
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Answer:
-1
Step-by-step explanation:
Replace the variable x with 1 in the expression .
f(1)= 2(1) - 3
Remove the parenthasis
2(1) - 3
Multiply 2 by 1
2 - 3
subtract 2 from 3
-1
a school has 400 grade 9's, 375 grade 10's, 300 grade 11's and 325 grade 12's. twenty students from each grade are surveyed
The type of bias that can be present in stratified sampling is that the students cannot be selected to accurately reflect the population.
How are samples classified?Samples may be classified according to the five options as follows:
A convenient sample is drawn from a conveniently available pool of options.A random sample is equivalent to placing all options into a hat and taking some of them.In a systematic sample, every kth element of the sample is taken.Cluster sampling divides population into groups, called clusters, and each element of the group is surveyed.Stratified sampling also divides the population into groups. However, an equal proportion of each group is surveyed.In this problem, an equal amount of students from each class was surveyed, hence a stratified sample was used.
The type of bias present in stratified sampling is that the students cannot be selected to accurately reflect the population.
Missing InformationThe problem asks for which type of bias is present in this sample.
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y= 3cos 4 0(theta) -1
The graph of the cosine function y = 3cos(4θ) - 1 is given by the image presented at the end of the answer.
What is a cosine function?The cosine function is defined by the rule presented as follows:
g(x) = acos(bx+c)+d.
The coefficients have the roles listed as follows:
a is the amplitude of the cosine function.b: The period of the cosine function is of 2π/b.c is the phase shift of the cosine function.d is the vertical shift of the cosine function.In this problem, the definition of the function is:
y = 3cos(4θ) - 1
Considering the amplitude of 3 and the vertical shift of -1 the function will oscillate between:
-4 and 2.
(Without the vertical shift it would be between -3 and 3).
The period of the function will be as follows:
2π/b = 4
b = 2π/4
b = π/2.
Considering these features, the graph is given at the end of the answer.
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Find the equation of the line that is parallel to another line whose equation is x+2y+8=0 and passes though the point(-2,-3)
There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.
How to determine the equation of a line parallel to another line and that passes through a given point.
In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:
x + 2 · y + 8 = 0
2 · y = - x - 8
y = - (1 / 2) · x - 4
Then, the resulting line has a slope of - 1 / 2.
Second, determine the intercept of the resulting line:
y = m · x + b
b = y - m · x
b = - 3 - (- 1 / 2) · (- 2)
b = - 3 - 1
b = - 4
The intercept of the resulting line is - 4.
Third, transform the equation of the resulting line into standard form:
y = - (1 / 2) · x - 4
- 2 · y = x + 8
x + 2 · y + 8 = 0
There is no parallel line for the point (x, y) = (- 2, 3).
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There are five people competing in the track meet this weekend. They are competing for 1st, 2nd, and 3rd place ribbons. How many different ways can the winners be chosen? A. 30 B. 60 C. 120 D. 150
If they are competing for 1st, 2nd, and 3rd place ribbons. The number of different ways can the winners be chosen is: B. 60.
How to find the total possibilities?Given data:
Number of people =5
Number of places = 1st, 2nd, and 3rd
Hence,
Different combinations =5 ×4×3
Different combinations = 60 ways
Therefore the winners will be chosen by 60 different possible ways ,
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T
4) a) On the grid, draw
the line y = 3
b) On the grid, draw
the line x = -2
6
5
4
-3-
2
1-
-3 -2 -1 0
-1-
-2
1
2
3
4
5
Fe
Be
1.
2.
3
4
Answer:
Step-by-step explanation:
The triangles shown below must be congruent.
A. True
• B. False
Answer:
true
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
solve the question math
Which of the following functions does not have
zeros at - 1 and 47.
A.f(x)=x²-3x-4
B. f(x) = 2x² + 6x - 8
C. f(x) = -x² + 3x +4
D.f(x) = 2x² - 6x-8
Answer:
B
Step-by-step explanation:
f(-1)=(-1)²-3(-1)-4
f(-1)=1-3(-1)-4
f(-1)=1+3-4
f(-1)=0
Do this same process with all the equations until you find one that doesn't equal 0.
last year at a certain high school, 10 students sought the nomination for president of the student body. in how many ways could the voters (student body) rank their first 5 choices? a) 5 b) 50 c) 30,240 d) 3,628,800 e) 252 f) none of the above.
The number of ways voters could rank their first 5 choices out of 10 is 30240.
Given,
Number of students sought the nomination for president of the student body = 10 students
We have to find the number of ways voters could rank their first 5 choices.
Permutation;
An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.
Here we have to use permutation formula;-
ⁿPr = n! / (n - r)!
Here,
n is the number of students = 10
r is the choices = 5
Then,
ⁿPr = n! / (n - r)!
¹⁰P₅ = 10! / (10 - 5)!
¹⁰P₅ = 10! / 5!
¹⁰P₅ = 10 x 9 x 8 x 7 x 6
¹⁰P₅ = 30240
That is,
The number of ways voters could rank their first 5 choices out of 10 is 30240.
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Write the equation of the line in fully simplified slope-intercept form.
ANSWER ASAP
WILL GIVE BRAINLIEST
The equation of the line in fully simplified slope - intercept form is 5x + 4y = 12 .
In the question ,
a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .
to find the equation , we need minimum two points ,
So , from the given graph ,
we can find that
when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 3 ,
the first point is (0 [tex],[/tex] 3) .
when x [tex]=[/tex] 4 , the value of y [tex]=[/tex] -2 ,
the second point is (4 [tex],[/tex] -2) .
the slope can be calculated by
slope = (-2-3)/(4-0)
= -5/4
So , the equation of the line passing through point (4,-2) with slope -5/4 , in the slope intercept form is
(y -(-2)) = (-5/4)(x-4)
y + 2 = (-5/4)x + 5
y = (-5/4)x + 5 - 2
y = (-5/4)x + 3
Simplifying further , we get
4y = -5x + 12
5x + 4y = 12
Therefore , The equation line in fully simplified slope - intercept form is 5x + 4y = 12 .
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26% of all college students major in stem (science, technology, engineering, and math). if 36 college students are randomly selected, find the probability that a. exactly 7 of them major in stem. b. at most 10 of them major in stem. c. at least 7 of them major in stem. d. between 9 and 15 (including 9 and 15) of them major in stem.
The probabilities will be 0.1081 , 0.676, 0.863, 0.605 respectively.
let us consider, the chances of getting stem be a success(S) and not getting it be a failure(F) , and the total probability be 1 .
as per the statement 26% students are major in stem
total students selected randomly are 36.
∴ P(S) = 0.26
P( F) = 1 - 0.26 = 0.74
Now the binomial probability of success is given by
[tex]P(x) = C^{n} _{x} S^{x} F^{n-x}[/tex]
where C is for the combination formula
S is changes of success
F is chances of failure
x = no. of times success
n = total times the experiment done
From the provided information we can solve each case as follows :
A) exactly 7 of them major in stem
P(7) = [tex]C^{36} _{7} (0.26)^{7} (0.74)^{29}[/tex]
= 0.1081
B)at most 10 of them major in stem
it means P(0,1,2...10)
∴ P = P(0) + P(1) +......+P(10)
P = 0.676
C) at least 7 of them major in stem.
it means P(7,8,9...36)
∴ P = P(7) + P(8) + ...+ P(36)
P = 0.863
D) between 9 and 15 (including 9 and 15) of them major in stem.
In this case we subtract P(0,1,2...8) from P(0,1,2,...15)
and get P(9,10,11,...15)
∴ P(9,10,11,...15) = P(0,1,2,...15) - P(0,1,2...8)
= 0.987 - 0.382
= 0.605
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Jacob distributed a survey to his fellow students asking them how many hours they spent on the Internet in the past day. He also asked them to rate their mood on a scale from 0,10, with ten being the happiest. A line was fit to the data to model the relationship.
Answer:
The answer is B. y = -x + 7.5.
Step-by-step explanation:
The slope is -1 and the y-intercept is 7.5.
PLEASE MARK AS BRAINLIEST!!!Determine which of the lines, if any, are parallel or perpendicular. explain. line a passes through (2, 10) and (4, 13). line b passes through (4, 9) and (6, 12) . line c passes through (2, 10) and (4, 9) .
Line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
Line a passes through (2, 10) and (4, 13).
Line b passes through (4, 9) and (6, 12).
Line c passes through (2, 10) and (4, 9).
If a line passes through two points, then the slope of the line is
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Line a passes through (2, 10) and (4, 13). So, the slope of this line is
[tex]m_{a}=\frac{13-10}{4-2}=\frac{3}{2}[/tex]
Line b passes through (4, 9) and (6, 12). So, the slope of this line is
[tex]m_{b}=\frac{12-9}{6-4}=\frac{3}{2}[/tex]
Line c passes through (2, 10) and (4,9). So, the slope of this line is
[tex]m_{c}=\frac{9-10}{4-2}=\frac{1}{2}[/tex]
The product of slopes of perpendicular lines is -1.
and if the slope of 2 lines is equal then those lines are parallel
so, line a and line b are parallel to each other, and c is neither parallel nor perpendicular.
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A box of volume 216 m3 with a square bottom and no top is made of two different materials. the cost of the bottom is $40/m2 and the cost of the sides is $30/m2. find the dimensions of the box that minimize the total cost. (use symbolic notation and fractions where needed. write the objective function with respect to the length of the square bottom.)
The dimensions of the box that minimize total cost are height h =3.17m, width, w and length, l=9.52m are equal to .
How to find the height of the box ?Let h is the height of the box.
Given Volume of the box is 216 m³ with no top.
And the cost of the bottom is 40USD/m².
For the sides, it is 30USD/m².
The bottom of the box is square, so l = w.
So Volume
[tex]V=hl^{2}[/tex]
[tex]216=hl^{2}[/tex]
[tex]h=\frac{216}{l^{2} }[/tex]
Now Surface Area of the box without a top is
S = 4hl + l²
So,
cost = 4 × 30hl +40l²
cost = 120 hl + 40 l²
Putting h ,
cost = 120 × [tex](\frac{216}{l^{2} })l + 40l^{2}[/tex]
cost = [tex]\frac{25960}{l^{2} }+40l^{2}[/tex]
To find minimum cost, derivate the by using the calculator at
[tex]l=3\sqrt[3]{4}[/tex]
l=4.762203 m
[tex]h=\frac{216}{4.762203^{2} }[/tex]
h = 9.5244069354 m
Hence the dimensions of the box are
l=w
=9.52 m
and height ,h=3.17 m
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help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
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The value of function is positive so the function have maximum value 30 at x=3.
In the given question we have to find the maximum or the minimum value of a function.
The given function is
f(x) = -3x^2+18x+3
To find the maximum or minimum value we firstly find the value of f'(x).
f'(x) = -6x+18
Now put f'(x)=0
-6x+18=0
Subtract 18 on both side we get
-6x=-18
Divide by -6 on both side we get
x = 3
Now finding the value of function at x=3
f(3)= -3*(3)^2+18*3+3
f(3)= -3*9+54+3
f(3)= -27+54+3
f(3)= 30
Since the value of function is positive so the function have maximum value 30 at x=3.
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Which expression is equivalent to -51 - (-60)−51−(−60)minus, 51, minus, left parenthesis, minus, 60, right parenthesis?
The required expression which is equivalent to -51 -(-60) is -51 + 60.
Given that,
Which expression is equivalent to -51 - (-60) is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression = -51 - (-60)
Simplify by applying the property of distribution under the parenthesis,
= -51 + 60
Thus, The required expression which is equivalent to -51 -(-60) is -51 + 60.
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street light is at the top of a 19-ft-tall pole. a 6-ft tall woman walks away from the pole with a speed of 6 ft/sec along a straight path (see figure). how fast is the tip of her shadow moving, in ft/sec, when she is 50 ft from the base of the pole?
8.77 ft/sec is the tip of her shadow moving with a speed of 6 ft/sec .
What is speed, for instance?
Speed is the rate of change in location of an item, expressed in meters per second. If something starts at the origin and moves three meters in three seconds, for instance, its speed is one meter per second. The formula for speed is as straightforward as dividing a distance by a time.Let H = the height of the pole.
h = the height of the woman.
x = the length of the woman's shadow.
s = the distance from the pole to the woman.
By similar triangles, H/h = (s + x)/x or Hx = h(s + x).
Differentiating, H dx/dt = h(ds/dt + dx/dt)
19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt
13 dx/dt = 36
dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.
The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.
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Part A Write a paragraph proof to prove ABC ≌ ABD. Explain in complete sentences each statement and reason. Be sure to give the reason the two triangles are congruent.
Part B Now that you have proven the two triangles are congruent, can you show that ∠CBA ≌ ∠DBA? Explain your reasoning in a complete sentence.
A. Both triangles have two pairs of corresponding sides and a pair of included angles, therefore, ΔABC ≌ ΔABD by SAS.
B. ∠CBA ≌ ∠DBA by CPCTC.
What is the SAS Congruence Theorem?The SAS congruence theorem state that if we have two triangles that we can show that they posses two pairs of corresponding sides that are equal and a pair of included angles that are also equal, then we can state that the two triangles are congruent to each other
When two triangles are proven to be congruent to each other, every corresponding parts of both triangles will be equal to each other based on CPCTC.
Part A:
We are given that AC ≌ AD, and ∠CAB ≌ ∠DAB.
Also, AB ≌ AB based on the reflexive property.
Therefore, both triangles are congruent to each other based on SAS.
ΔABC ≌ ΔABD
Part B:
Since both triangles are congruent, therefore ∠CBA ≌ ∠DBA by CPCTC.
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Which of these strategies would eliminate a variable in the system of equations?
2x + 8y = -3
3x + 6y = -4
A: Multiply the top equation by 333, multiply the bottom equation by -2−2minus, 2, then add the equations.
B: Multiply the top equation by 333, multiply the bottom equation by 444, then subtract the bottom equation from the top equation.
C: Multiply the top equation by -4−4minus, 4, multiply the bottom equation by 333, then add the equations
Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.
Rewriting the equation -
2x + 8y = -3 : Equation 1
3x + 6y = -4 : Equation 2
Multiplying equation 1 with and equation 2 with -2.
6x + 24y = -9 : Equation 3
-6x - 12y = 24 : Equation 4
Adding the equation 3 and equation 4. This will eliminate the variable x.
12y = 15
y = 5/4
So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.
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when a certain unfair die is rolled, an even number is times as likely to appear as an odd number. the die is rolled twice. what is the probability that the sum of the numbers rolled is even?
The probability that the sum of the numbers rolled on the dice is even =1/2.
What is referred as probability?A probability is a measure of the magnitude of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages including several from 0% to 100% can be used to describe probabilities.For the given question,
A fair dice is rolled twice.
Six different results are available with a single roll of the dice (1,2,3,4,5,6)
Therefore, if two dice are rolled, there are a total of 36 possible results, or 6².
Sample space for the sum of even = [(1,1), (1,3), (1,5), (2,2), (2, 4),(2,6), (3, 1), (3,3),(3,5),(4,2),(4,4),(4,6), (5, 1), (5,3),(5,5),(6,2),(6,4),(6,6)]
Total sample space for sum of even = 18
For the probability that the sum of the numbers rolled is even is -
probability (sum is even) = 18 / 36 = 1/2
Thus, the probability that the sum of the numbers rolled is even is 1/2.
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15 POINTS HELP!
A liquid used to unclog sinks has a pH value of 14. This liquid is _____.
neutral
an acid
a base
Answer:
A base
Step-by-step explanation:
its not an acid bc a ph level of 14 means is has a strong base.
Suppose m<4 =108 find m<5 and m<7
m ∠5 and m ∠7 is 72 ° . All straight angles are 180 degrees, according to the straight angle theorem. A straight angle is formed when the angle's legs point precisely in the opposite directions. The symbol for a straight angle is 180 degrees, or π (in radians).
How to find angle ?An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.
The names of basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle and full rotation. An angle is geometrical shape formed by joining two rays at their end-points. An angle is usually measured in degrees.
m ∠4 = 108°
m ∠5 = m ∠1
m ∠1 is in same line of m ∠4
So
m ∠1 = 180 - m ∠4
m ∠1 = 180 - 108
m ∠1 = 72 °
So m ∠5 = 72 °
m ∠7 is opposite to m ∠5 , opposite angles will be equal
Therefor m ∠7 = 72 °
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A number is raised to the third power, then subtracted from 15 to get 7. What is the number squared?
Answer:
x=22
Step-by-step explanation:
Let the unknown number be x
:- the power of x = x³
From the question
x³-15=7 and x²
x³=7+15
x³ * x²= 22
x= 22
A polygon has vertices A (5, -1), B (21, 11), C (26, -1), and D (2, -8).
Part A. What is the perimeter of ABCD to the nearest tenth of a unit?
Part B. What is the area of ABCD to the nearest tenth of a square unit?
Enter the correct answers in the boxes.
A. Perimeter: units
B. Area: square units
The graph of the coordinate points of the vertices of ABCD indicates;
Part A The perimeter of ABCD ia approximately 61.2 units
Part B. The area of ABCD is 199.5 square units
What is the perimeter of a figure in geometry?The perimeter of a figure is length of the line that goes round the figure.
A. The perimeter of the polygon is the sum of the length of the sides of the polygon, which is found as follows;
AB = √((21-11)²+(11-(-1))²) ≈ 15.6
BC = √((21-26)²+(11-(-1))²) = 13
CD = √((26-2)²+(-1-(-8))²) = 25
AD = √((2-5)²+(-8-(-1))²) ≈ 7.6
The perimeter of the polygon = 15.6 + 13 + 25 + 7.6 = 61.2
The polygon has a perimeter of approximately 61.2 unitsB. Plotting the figure indicates that the figure consists of two triangles, ΔABC and ΔACD
The base length of triangle ΔABC = 26 - 5 = 21
The height of triangle ΔABC = 11 - (-1) = 12
The area of triangle ΔABC = 0.5 × 21 × 12 = 126
Base length of triangle ΔADC = 21
Height of triangle ΔADC = -1 - (-8) = 7
Area of triangle ΔADC = 0.5 × 21 × 7 = 73.5
Area of the composite figure is therefore;
A = 126 + 73.5 = 199.5
The area of the figure is therefore; 199.5 square units
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Please help
The equation y = -8/3x + 40 represents an alternative speed slide the city of Geocove is thinking of constructing in their waterpark. The graph of this equation is shown. Suppose that a rider travels downward 8 feet on this slide. What is the value of their horizontal change?
6 feet
2.7 feet
8 feet
3 feet
The value of their horizontal change is 2.7 feet
How to determine the value of their horizontal change?The equation of the function is given as
y = -8/3x + 40
From the question, the distance travelled by the rider is given as
Distance = 8 feet downward
This means that
Horizontal change = slope
A linear equation is represented as
y = mx + c
Where
Slope = m
By comparing y = mx + c and y = -8/3x + 40, we have
Slope = m = 8/3
This gives
Horizontal change = 8/3
Evaluate
Horizontal change = 2.7
Hence, the horizontal change is 2.7 feet
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please help me with this math problem
Ms. Kirkland is baking muffins. Each batch of muffins uses 1 ½ pounds of flour. How many batches of muffins can she bake with 7 ½ pounds of flour? ______________ batches.
The number of batches of muffins Ms. Kirkland can bake with 7 ½ pounds of flour is 5 batches.
Given that, Ms. Kirkland is baking muffins. Each batch of muffins uses 1 ½ pounds of flour.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, [tex]1\frac{1}{2} = \frac{3}{2}[/tex] and [tex]7\frac{1}{2} = \frac{15}{2}[/tex]
The number of batches of muffins can she bake
= 15/2 ÷ 3/2
= 15/2 × 2/3
= 5 batches
Hence, the number of batches of muffins Ms. Kirkland can bake with 7 ½ pounds of flour is 5 batches.
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Answer: The answer is 5
Step-by-step explanation: I have my ways ;>
Pls help/ The y-intercept of f(x)=(1.6)x is ______________________ the y-intercept of the function in the graph:
The y-intercept of f(x) = (1.6)x is (a) less than the y-intercept of the function in the graph
How to complete the blank?The equation of the function is given as
f(x) = (1.6)x
To determine the y-intercept, we set x = 0
So, we have
f(0) = 1.6 * 0
Evaluate
f(0) = 0
For the graph, we have
When x = 0, the function has a value of 1
This means that
y-intercept is 1
0 is less than 1
Hence, the y-intercept of f(x) = (1.6)x is (a) less
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