Answer: (9 CDs)
If she has $45 and the CDs cost $5. The most she can buy is 9 CDs
The number of maximum CDs that Jennifer can buy is 9.
What is the arithmetic operator?Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,
Division = divide any two numbers or variables called division.
As per the given,
Cost of one CD = $5
Jennifer budget = $45
Number of CDs can buy = Jennifer's budget/cost of one CD
Number of CDs can buy = 45/5 = 9
Hence "The number of maximum CDs that Jennifer can buy is 9".
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Two problems here I need solved! I need every step, so please have that with your answers!!
1. Solve this rational equation:
[tex]\frac{1}{(x-4)}+\frac{x}{(x-2)}=\frac{2}{x^{2}-6x+8}[/tex]
1. Solve this radical equation:
[tex]\sqrt{x+11} -x=-1[/tex]
A guitar string is plucked at a distance of 0.6 centimeters above its resting position and then released, causing vibration. The damping constant of the guitar string is 1.8, and the note produced has a frequency of 105 cycles per second.
a.) Write a trigonometric function that models the motion of the string.
b.) Using a graphing calculator, determine the amount of time t that it takes the string to be damped so that -0.24 y 0.24. Please be sure to show a screenshot of your graph.
Answer:
The equation that represents the motion of the string is given by:
[tex]y =Ae^{-kt}\cos(2\pi ft)[/tex] .....[1] where t represents the time in second.
Given that: A = 0.6 cm (distance above its resting position) , k = 1.8(damping constant) and frequency(f) = 105 cycles per second.
Substitute the given values in [1] we get;
[tex]y =0.6e^{-1.8t}\cos(2\pi 105t)[/tex]
or
[tex]y =0.6e^{-1.8t}\cos(210\pi t)[/tex]
(a)
The trigonometric function that models the motion of the string is given by:
[tex]y =0.6e^{-1.8t}\cos(210\pi t)[/tex]
(b)
Determine the amount of time t that it takes the string to be damped so that [tex]-0.24\leq y \leq0.24[/tex]
Using graphing calculator for the equation
[tex]y =0.6e^{-1.8x}\cos(210\pi x)[/tex]
let x = t (time in sec)
Graph as shown below in the attachment:
we get:
the amount of time t that it takes the string to be damped so that [tex]-0.24\leq y \leq0.24[/tex] is, 0.5 sec
The trigonometric function that models the motion of the guitar string is y(t) = Asin(ωt)e^(-kt). Using a graphing calculator, the time it takes for the string to be damped within the given range can be determined.
Explanation:a) The trigonometric function that models the motion of the guitar string can be represented by the equation y(t) = Asin(ωt)e^(-kt), where A is the amplitude, ω is the angular frequency, t is the time, and k is the damping constant.
b) To determine the amount of time it takes for the string to be damped so that -0.24 ≤ y ≤ 0.24, you can use a graphing calculator to plot the trigonometric function and find the values of time at which the function crosses these y-values. You should set up the equation as follows: -0.24 ≤ Asin(ωt)e^(-kt) ≤ 0.24 and solve for t.
Please see the attached screenshot for an example of the graph.
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AD=6y+40
BC=9y+10
AB= 0.5y+50
Answer:
DC = 55
Step-by-step explanation:
Since this is a parallelogram, opposite sides are congruent. WE need to find the value of y from AD = BC
AD = BC
6y+40 = 9y+10
Subtract 6y from each side
6y-6y+40 = 9y-6y+10
40 = 3y+10
Subtract 10 from each side
40-10 = 3y+10-10
30 = 3y
Divide each side by 3y
30/3 = 3y/3
10 =y
Since opposite sides are congruent
DC = AB
DC = .5y + 50
= .5 (10) +50
=5 + 50
= 55
DC =55
Pls help I'm bad at math v.v
Lines m and n are parallel.
Answer:
The measure of angle 1 is 55.
Step-by-step explanation:
The top angle= 75 because of the vertical angle theorem
The right angle= 50 because of the alternate exterior angle theorem
75+50=125
There are 180 degrees in a triangle so the angle has to equal 55
Given a right triangle ACT, indicate the opposite side and the adjacent side for < c
Reference angle is angle C
AT is the opposite side as this leg is not adjacent to angle C (or put another way, point C is nowhere to be found in AT)
AC is the adjacent leg because angle C is part of this segment. It is next to or touching the segment, hence the name "adjacent"
side note: CT is the hypotenuse and always the longest side of the right triangle. It is opposite the largest angle (90 degrees) of this triangle.
Think about the function f(x) = 10 - x3. What is the input, or independent variable? f(x) x y What is the output, or dependent variable or quantity? x f(x) y What does the notation f(2) mean? multiply f by 2 the output (y-value) when x = 2 the value of x when the output is 2 Evaluate f(2) =
Answer:
x is the input, or independent variable and f(x) is the output, or dependent variable or quantity. f(2) represents the output (y-value) when x = 2. The value of f(2) is 2.
Step-by-step explanation:
If the values of a variable depends on the other variable, then it called dependent variable.
If the value of a variable does not depend on the other, then it is called independent variable.
If a function is f(x)=x, then x is an independent variable and f(x) is a dependent variable.
The given function is
[tex]f(x)=10-x^3[/tex]
Here, x is the input, or independent variable and f(x) is the output, or dependent variable or quantity.
The notation f(a) represents the output (y-value) when x = a. So, f(2) represents the output (y-value) when x = 2.
Substitute x=2 in the given function.
[tex]f(2)=10-(2)^3[/tex]
[tex]f(2)=10-8[/tex]
[tex]f(2)=2[/tex]
The value of f(2) is 2.
For a function y = f(x) we define x as the independent variable and y as the dependent variable. y = f(x) means that "y depends on x in a given way, defined by f(x)".
Here we know that:
f(x) = 10 - x^3
1) What is the input, or independent variable?
The independent variable is the one inside the function, in this case, is x.
2) What is the output, or dependent variable or quantity?
in this case, the output is f(x), the value of the whole function evaluated in x.
(note that we do not have y = f(x), so y can't be the output, as we can't invent a variable and add it there.)
3) What does f(2) mean?
This means that we need to replace all the "x's" in the function by 2, we get:
f(2) = 10 - 2^3 = 2
so f(2) is the output when x = 2.
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A baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold. How many muffins were sold by noon?
Answer:
27 muffins.
Step-by-step explanation:
We have been given that a baker made 60 muffins for a cafe. By noon, 45% of the muffins were sold.
To find the number of muffins sold by noon let us find 45% of 60.
[tex]\text{The number of muffins sold by noon}=\frac{45}{100}\times 60[/tex]
[tex]\text{The number of muffins sold by noon}=0.45\times 60[/tex]
[tex]\text{The number of muffins sold by noon}=27[/tex]
Therefore, 27 muffins were sold by noon.
which is the definition of a square?
A quadrilateral with four congruent sides and four congruent angles
A quadrilateral with four congruent sides
A quadrilateral with interior angles that sum to 360°
A quadrilateral with four right angles
Answer:
the first option
Step-by-step explanation:
SOMEONE PLEASE HELP EQUATION AND ANSWERS ARE ATTACHED IMAGES.
The stemplot below shows the heights (in inches) of students in a class.
5 | 0 1 1 3 6
6 | 2 9
7 | 1 1 3 5 7
Which of the following is a height of a student in the class?
A. 50 inches
B. 72 inches
C. 29 in ches
D. 57 inches
Answer:
Choice A) 50 inches
Step-by-step explanation:
The stem is the value on the left side of the vertical bar (5, 6, and 7 in that first column). The leaf is a single digit on the right side that pairs up with the stem to form the whole value. In the first row, the stem of 5 pairs up with the 0 to get 50. The next value is 51 because the stem 5 pairs up with the 1 after the 0. Then the value after that is 51 again. Repeated values are allowed.
The entire first row of values is: 50, 51, 51, 53, 56
The second row is: 62, 69
The third row is: 71, 71, 73, 75, 77
We see that only 50 is listed in the four answer choices and no other value.
Graphs of Polynomial Functions Gizmo
5 Answer Review
1. What are the degree and leading coefficient of the function y=4x2-3x+7?
A. degree=4 leading coefficient=2
B. degree=2 leading coefficient=4
C. degree=2 leading coefficient=7
D. degree=3 leading coefficient=4
2. What is the lowest degree of the function graphed here? (image is attached to this)
A. 1
B. 2
C. 3
D. 4
3. what is the maximum of x-intercepts that can be found on a graph with equation y=ax5+cx2+f? (the values a, c, and f are real numbers)
A. 2
B. 3
C. 4
D. 5
4. Which polynomial function has a y-intercept of 3?
A. y=2x4+x2-3
B. y=3x2+4
C. y=-4x7-5x+3
D. y=9x3+3x2
5. What is the end behavior of y=-2x13+25x8-3 as x approaches infinity?
a. y=-3
b. y=13
c. y approaches infinity
d. y approaches negative infinity
QUESTION 1
The given polynomial function is [tex]y=4x^2-3x+7[/tex]
The degree of the polynomial is the exponent on the leading term of the polynomial after the polynomial has been written in descending powers of [tex]x[/tex].
The leading term is [tex]4x^2[/tex] the exponent of [tex]x[/tex] in this term is [tex]2[/tex], hence the degree is 2.
The coefficient of this term is the leading coefficient which is [tex]4[/tex].
The correct answer is B.
QUESTION 2
The function graphed has two x intercepts.
The first x intercept has a multiplicity that is even. The least positive even integer is 2.
The second x intercept has a multiplicity that is odd.
The least positive odd integer is 1.
Therefore the lowest degree is the sum of the two least values which is
[tex]2+1=3[/tex]
The correct answer is C
QUESTION 3
The given polynomial function is [tex]y=ax^5+cx^2+f[/tex], where [tex]a,c[/tex] and [tex]f[/tex] are real numbers.
The x intercepts are the roots of the polynomial and we know the maximum number of real roots a polynomial of degree 5 can have is 5.
The maximum number of the x-intercepts of the polynomial is therefore 5.
The correct answer is D
QUESTION 4
To find the y-intercept, we substitute [tex]x=0[/tex] into each polynomial function.
The first function is [tex]y=2x^4+x^2-3[/tex]
When [tex]x=0[/tex], [tex]y=2(0)^4+(0)^2-3=-3[/tex]
The y-intercept is -3
The second function is [tex]y=3x^2+4[/tex].
When [tex]x=0[/tex], [tex]y=3(0)^2+4=4[/tex].
The y-intercept is 4
The third function is [tex]y=-4x^7-5x+3[/tex], when [tex]x=0[/tex],
[tex]y=-4(0)^7-5(0)+3=3[/tex]
The y-intercept is 3
The fourth function is [tex]y=9x^3+3x^2[/tex]
When [tex]x=0[/tex], [tex]y=9(0)^3+3(0)^2=0[/tex]
The y-intercept is 0
The correct answer is C.
QUESTION 5
The given polynomial function is [tex]y=-2x^{13}+25x^8-3[/tex].
This is already in standard form.
The degree of the polynomial is 13, which is odd.
The graph of the polynomial will rise at one end and fall at the other end.
The leading coefficient is negative, so the graph rises on the left and falls on the right.
Therefore as x approaches infinity, y will be approaching negative infinity.
The correct answer is D
The answers to the questions are as follows:
1. The correct option is B. degree=2 leading coefficient=4.
2. The correct option is c. 3. The lowest degree of the function graphed here is 3.
3.The correct option is D. 5.
4. The correct option is C. [tex]\( y = -4x^7 - 5x + 3 \).[/tex]
5.The correct option is d. [tex]\( y \)[/tex] approaches negative infinity.
1. The degree and leading coefficient of the function [tex]\( y = 4x^2 - 3x + 7 \)[/tex]are:
- Degree = 2
- Leading coefficient = 4
Therefore, the correct option is B. degree=2 leading coefficient=4.
The degree of a polynomial is the highest power of the variable [tex]\( x \)[/tex] that appears in the polynomial with a non-zero coefficient. In the given function, the highest power of [tex]\( x \)[/tex] is 2 (in the term [tex]\( 4x^2 \))[/tex], so the degree is 2. The leading coefficient is the coefficient of the term with the highest power, which is 4 in this case.
2. The function graphed has two x intercepts.
The first x intercept has a multiplicity that is even. The least positive even integer is 2.The second x intercept has a multiplicity that is odd.The least positive odd integer is 1.Therefore the lowest degree is the sum of the two least values which is 2+1=3The correct answer is C
3. The maximum number of x-intercepts that can be found on a graph with the equation [tex]\( y = ax^5 + cx^2 + f \)[/tex] is:
- A. 2
- B. 3
- C. 4
- D. 5
The correct option is D. 5.
The degree of the polynomial [tex]\( y = ax^5 + cx^2 + f \)[/tex] is 5, which means it is a fifth-degree polynomial. The maximum number of x-intercepts (real roots) for a polynomial is equal to its degree, provided that the roots are counted with multiplicity and include complex roots. Since we are looking for the maximum number of x-intercepts, we consider the degree of the polynomial, which is 5.
4. The polynomial function that has a y-intercept of 3 is:
- A. [tex]\( y = 2x^4 + x^2 - 3 \)[/tex]
- B. [tex]\( y = 3x^2 + 4 \)[/tex]
- C. [tex]\( y = -4x^7 - 5x + 3 \)[/tex]
- D. [tex]\( y = 9x^3 + 3x^2 \)[/tex]
The correct option is C. [tex]\( y = -4x^7 - 5x + 3 \).[/tex]
5. The end behavior of the function [tex]\( y = -2x^{13} + 25x^8 - 3 \) as \( x \)[/tex] approaches infinity is:
- a. [tex]\( y = -3 \)[/tex]
- b. [tex]\( y = 13 \)[/tex]
- c. [tex]\( y \)[/tex] approaches infinity
- d. [tex]\( y \)[/tex] approaches negative infinity
The correct option is d. [tex]\( y \)[/tex] approaches negative infinity.
If x = 5 and y = -4, evaluate this expression:
(-2x + 10) - (-6x + 5y + 12) + (x + 8y - 16)
A) -5
B) 0
C) 5
D) 10 what the answer
Answer: (A) -5
Step-by-step explanation:
(-2x + 10) - (-6x + 5y + 12) + (x + 8y - 16) ; x = 5, y = -4
= [-2(5) + 10] - [-6(5) + 5(-4) + 12] + [(5) + 8(-4) - 16]
= [-10 + 10] - [-30 - 20 + 12] + [5 - 32 - 16]
= (0) - (-38) + (-43)
= 0 + 38 - 43
= -5
What is the volume of a sphere which a diameter of 12 inches? Use 3.14 for pi. Round your answer to the nearest hundredth
Answer:
V≈ 904.78in³
Step-by-step explanation:
V= 4/3 π r cubed
diameter= 12 cm
radius= 1/2 diameter= 6 cm
3.14= pi
V= 4/3 * 3.14 * 6 cubed
V= 4/3 * 3.14 * 216
V= 1.33 * 3.14 * 216
V= 902.06
Look at the parallelogram ABCD shown below: The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:
Statement Reasons 1 AB is parallel to DC and AD is parallel to BC Definition of parallelogram 2
angle 1 = angle 2, angle 3 = angle 4 If two parallel lines are cut by a transversal then the _______________ are congruent 3
BD = BD Reflexive Property 4
triangles ADB and CBD are congruent If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate 5
AB = DC, AD = BC Corresponding parts of congruent triangles are congruent
Which choice completes the missing information for reason 2 in the chart?
alternate interior angles
corresponding angles
same-side interior angles
vertical angles
Answer:
The correct option is 1.
Step-by-step explanation:
Statement Reasons
1. AB is parallel to DC and Definition of parallelogram
AD is parallel to BC
2. angle 1 = angle 2, If two parallel lines are cut by a
angle 3 = angle 4 transversal then the alternate
interior angles are congruent
3. BD = BD Reflexive Property
4. [tex]\triangle ADB\cong \triangle CBD[/tex] ASA postulate
5. AB = DC, AD = BC (CPCTC)
If two angles and the included side of a triangle are congruent to the corresponding angles and side of another triangle then the triangles are congruent by ASA postulate.
According to alternate interior angles theorem, two parallel lines are cut by a transversal then the alternate interior angles are congruent.
Therefore option 1 is correct.
98 POINTS HELP PLEASE
f(x) = 2/3x − 8
The function in the graph is g(x). Which has the greatest value?
A.f(6)
B.g(2)
C.f(0)
Dg(-4)
Answer:
[tex]\displaystyle B.g(2)[/tex]
Step-by-step explanation:
we are given f(x) and the graph of g(x)
to figure out which function has the greatest value we need to figure out g(x) function first
the given graph is a parabola so g(x) has to be quadratic function
both vertex and y-intercept of the function is (0,-1)
remember,[tex]\sf \displaystyle Q_{\text{vertex}}=g(x)=a(x-h)^2+k[/tex]
vertex:(h,k)
we got from the graph (h,k)=(0,-1)
substitute the value of h and k to the vertex form:
[tex]\displaystyle g(x)=a(x-0)^2+( - 1)[/tex]
simplify:
[tex]\displaystyle g(x)=ax^2- 1[/tex]
now we need to know figure out a
to do so take (-4,-5) coordinate pair which means if x=-4 then g(x)=-5
it is helpful to figure out a
substitute the value -4 for x and -5 for g(x):
[tex]\displaystyle - 5=a( - 4)^2- 1[/tex]
simplify square:
[tex]\displaystyle - 5=16a- 1[/tex]
add 1 to both sides:
[tex]\displaystyle - 4=16a[/tex]
divide both sides by 16:
[tex]\displaystyle a = - \frac{1}{4} [/tex]
our quadratic function is
[tex]\displaystyle g(x)= - \frac{1}{4} x^2- 1[/tex]
for f(x) and g(x) substitute the values 6,0 and 2,-4 to determine which function has the greatest value
let's work with f(x)
when x is 6 then f(x)
[tex] \displaystyle \: f(6) = \frac{2}{3} \times 6 - 8[/tex]
simplify multiplication:
[tex] \displaystyle \: f(6) = 2\times 2- 8[/tex]
simplify:
[tex] \displaystyle \: f(6) = 4- 8[/tex]
simplify substraction:
[tex] \displaystyle \: f(6) = - 4[/tex]
when x is 0 then f(x)
[tex] \displaystyle \: f(0) = \frac{2}{3} \times 0 - 8[/tex]
simplify multiplication:
[tex] \displaystyle \: f(0) = - 8[/tex]
let's work with g(x) now
when x is 2 then g(x)
[tex]\displaystyle g(2)= - \frac{1}{4} \times 2^2- 1[/tex]
simplify square:
[tex]\displaystyle g(2)= - \frac{1}{4} \times 4- 1[/tex]
simplify:
[tex]\displaystyle g(2)= - 1- 1[/tex]
simplify substraction:
[tex]\displaystyle g(2)= -2[/tex]
when x is -4 then g(x)
[tex]\displaystyle g( - 4)= - \frac{1}{4} (- 4)^2- 1[/tex]
simplify square:
[tex]\displaystyle g( - 4)= - \frac{1}{4} \times 16- 1[/tex]
simplify;
[tex]\displaystyle g( - 4)= - 1 \times 4- 1[/tex]
simplify multiplication:
[tex]\displaystyle g( - 4)= - 4- 1[/tex]
simplify subtraction:
[tex]\displaystyle g( - 4)= - 5[/tex]
so
[tex] \begin{array}{c c c} g(2) > f( 6) > g( - 4) > f(0)\\ - 2 > - 4 > - 5> - 8 \end{array}[/tex]
hence,
our answer choice is [tex]\displaystyle B.g(2)[/tex]
To determine which function has the greatest value, value of f(x) was calculated at given points. Without knowing the form of g(x), we can't calculate values g(2) and g(-4). Comparing calculated values of f(6) and f(0), f(6) has the greater value.
Explanation:In order to answer this question, you should first calculate the value of the function f(x) at the given points. The function f(x) is given as f(x) = 2/3x − 8.
For f(6), substitute x = 6 into your function: f(6) = 2/3 * 6 - 8 = 4. For f(0), substitute x = 0: f(0) = 2/3 * 0 - 8 = -8.
Since we don't know the explicit form of function g(x), we can't calculate g(2) and g(-4). They could be any value depending on the form and graph of g(x), which is not provided. Therefore, we can only compare f(6) and f(0). Between these two, f(6) has the greater value.
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Please answer this question! 15 points and brainliest!
Answer:
x=5
Step-by-step explanation:
5x=7x-10
First get the variables on one side, and numbers on the other
-2x=10
Therefore,
x=5
A recipe calls for 2/3 of a cup of milk for 11 cookies. How many cups of milk are needed to make 99 cookies?
Answer:
6 cup of milk
Step-by-step explanation:
From question
for 11 cookies → [tex]\frac{2}{3}[/tex] of a cup of milk required
Now,
for 99 cookies
we multiply both sides by 9.
11 × 9 = [tex]\frac{2}{3}[/tex] × 9
for 99 cookies = 6 cup of milk
Bobby hopes that he will someday be more than 70 inches tall he is currently 61 inches tall how many more inches, x,does Bobby need to grow to reach his desired height
As given, the current height of Bobby is = 61 inches
Bobby hopes to be taller than 70 inches.
Let the number of inches Bobby needs to grow to reach 70 be = x
So, he needs to grow
[tex]x+61=70[/tex]
Hence, x=9 inches
So, Bobby needs to grow 9 inches to reach a height of 70 inches and more than 9 if he wants to be taller than 70 inches.
In a certain? chemical, the ratio of zinc to copper is 3 to 17. A jar of the chemical contains 544 grams of copper. How many grams of zinc does it? contain?
3/17 = x/544
If x=96 then there are 96 grams of zinc.
The amount of zinc that contains in the jar will be 96 grams based on the given ratio.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
Proportion is the relation of a variable with another. It could be direct or inverse.
Suppose the amount of zinc is Z while the copper is C.
The ratio Z/C = 3/17
And, C = 544
Z/544 = 3/17
Z = (3/17)544 = 96 grams.
Hence "The amount of zinc that contains in the jar will be 96 grams based on the given ratio".
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There are 10 students in a class: 5 boys and 5 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a boy?
There are 10 students in a class: 5 boys and 5 girls then the probability that everyone in the group is a boy is 1/12.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
P(E) = Number of favorable outcomes / total number of outcomes
It is given that the Total number of students = 10
Number of boys = 5
Number of girls= 5
The number of ways to choose 5 students from 10 is ₁₀C₅.
= 9! / 5! 5!
= 252
The number of ways to choose 5 students from 10 is ₁₀C₅.
The number of ways to choose 5 students from 7 girls is ₇C₅.
= 6! / 5! 2!
= 21
Then the probability that everyone in the group is a boy
P(E) = Number of favorable outcomes / total number of outcomes
= 21/252
= 1/12.
Thus, the probability that everyone in the group is a boy is 1/12.
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nearest millimeter, a cell phone is 76mm long and 42 mm wide. What is the ratio of the width to the length? The ratio of the width to the length
Answer:
21:38
Step-by-step explanation:
The answer you get is 42:76, but if you simplify it, it's 21:38 by dividing the ratio by 2.
The longest side of a triangle is six more inches than the shortest side. The third side is twice the length of the shortest side of the perimeter of the triangle is 26 units, what's all three lengths of the triangle?
Answer:
a=5, b=10, c=11
Step-by-step explanation:
a= shortest side
b= "third" side
c= longest side
Equations:
c=6+a
b=2a
a+b+c=26
so we can see there is a in all of the equations, so we can plug all of them into the equation for the perimeter
a+(2a)+(6+a)=26-->4a=20-->a=5
with a, we can plug that into the equations to get b and c
c=6+a-->6+(5)-->c=11
b=2a-->b=2(5)--> b=10
Find the value of x in the triangle below.
Answer:
[tex]x=\frac{-9}{2}[/tex]
Step-by-step explanation:
We have to find the value of x from the given triangle.
By mid segment theroem which says the midpoint in a triangle of any two sides is parallel to the third side and half of the third side's length
Therefore, [tex]3x+4=\frac{1}{2}\cdot (4x-1)[/tex]
On multiplying the left hand side of the above equation by 2 from right hand side of the equation we will get:
[tex]2(3x+4)=4x-1[/tex]
[tex]\Rightarrow 6x+8=4x-1[/tex]
On simplification
[tex]\Rightarrow 2x=-9[/tex]
[tex]\Rightarrow x=\frac{-9}{2}[/tex]
Combine like terms.
- 2/3p + 1/5 - 1 + 5/6p
Answer:
1/6 p -4/5
Step-by-step explanation:
- 2/3p + 1/5 - 1 + 5/6p
When I combine like terms, I put them next to each other.
- 2/3p + 5/6p+ 1/5 - 1
We need to get a common denominator of 6 for the p terms
-2/3 *2/2 p + 5/6 p
-4/6p + 5/6 p
1/6 p
We need to get a common denominator of 5 for the contant terms
1/5 - 1*5/5
1/5-5/5
-4/5
Substituting these in
2/3p + 5/6p+ 1/5 - 1
1/6 p -4/5
A store is having a sale where school supplies are 30% off their orignal price. A backpack is on sale for 11.20. What was the original price of the backpack
Answer:
16
Step-by-step explanation:
11.2/0.7=16
Which equation is in point-slope form for the given point and slope?
point-slope form: y-y1 = m(x-x1)
given m, (x1, y1)
m = 5
x1 = 1
y1 = 9
y - 9 = 5(x - 1)
aka: choice C
Answer:
your answer is C or number three (3)
-9=5(x-1)
i hope this helps ya out
Vince loads 10 boxes into his truck.Some of the boxes weigh 20 pounds, and some weigh 30 pounds.The total weight of the boxes is 280 pounds. If x= the number of 20-pound boxes and y= the number of 30-pound boxes, which pair of equations will give the number of 20-pound and 30-pound boxes Vince has?
Answer:
Here, x represents the number of 20-pound boxes and y represents the number of 30 pound boxes.
As per the given condition: Vince loads 10 boxes into his truck.Some of the boxes weigh 20 pounds, and some weigh 30 pounds and the total weight of the boxes is 280 pounds.
⇒ x+ y =10 .....[1]
and
20x+30y = 280 .....[2]
Multiply equation [1] by 20 we get;
[tex]20(x+y) = 20\cdot 10[/tex]
Using distributive property: [tex]a\cdot(b+c) = a\cdot b + a\cdot c[/tex]
20x + 20y = 200 ....[3]
Subtract equation [3] from [2] we get;
[tex]20x+30y-20x-20y = 280-200[/tex]
Combine like terms;
10y = 80
Divide both sides by 10 we get;
y = 8
Substitute this y value in equation [1] we get;
x + 8 = 10
Subtract 8 from both sides we get;
x + 8 -8 =10-8
Simplify:
x = 2
Therefore, the pairs of equation are: x+ y =10 and 20x+30y = 280
Vince has the number of 20-pound boxes is, 2 and the number of 30 pound boxes is, 8
Answer:
No, Jude’s graph is incorrect. The inequality symbol is “less than,” so -9 is not included. He should have used an open circle on -9.Step-by-step explanation:
2020 on eng
The width of Florida is 4/5 of its length if the length of Florida is about 450 miles what is the approximate width
If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?
Answer:
[tex]5\sqrt{3}[/tex] inches long is the other leg
Step-by-step explanation:
Given the statement: If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long.
Hypotenuse side = 10 inches
Let length of other leg be x.
Pythagoras theorem states that in a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Then; by definition of Pythagoras theorem;
[tex]{\text}(Hypotenuse)^2 = (5)^2 + x^2[/tex]
[tex](10)^2 = 5^2 + x^2[/tex]
[tex]100 = 25 + x^2[/tex]
Subtract 25 on both sides we get;
[tex]100-25= 25 + x^2-25[/tex]
Simplify:
[tex]75 = x^2[/tex]
Simplify:
[tex]x = \sqrt{75} = 5\sqrt{3}[/tex] inches
Therefore, the sides of other leg is [tex]5\sqrt{3}[/tex] inches
Final answer:
Using the Pythagorean theorem, and knowing the length of the hypotenuse (10 inches) and one leg (5 inches), we calculate the other leg to be approximately 8.66 inches in length.
Explanation:
The question involves finding the length of the other leg of a right triangle when the lengths of the hypotenuse and one leg are known. By applying the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). The theorem is usually written as a² + b² = c².
In this case, the hypotenuse (c) is given as 10 inches, and one leg (a) is 5 inches. To find the length of the other leg (b), rearrange the Pythagorean theorem as b² = c² - a². Substituting the known values gives us b² = 10² - 5² leading to b² = 100 - 25. Therefore, b² = 75. Taking the square root of both sides to solve for b gives us b = √75 which simplifies to approximately 8.66 inches when rounded to two decimal places.
Thus, the length of the other leg in the right triangle is approximately 8.66 inches.
Check my answers please
A = bh is the area of a rectangle, and also the area of a parallelogram. Any rhombus is also a parallelogram, so you can also use this formula for any rhombus. This helps explain why A = bh shows up three times to account for the three different types of shapes: rectangle, parallelogram, rhombus
A = (1/2)*bh is the area of a triangle which can be written as A = 0.5*b*h
The last formula, which is A = [ (b1+b2)/2 ] *h is the area of a trapezoid. The sides b1 and b2 are the parallel bases
note: the height is always perpendicular to the base