Step-by-step explanation:
[tex]\bullet\hookrightarrow\sf 7 (x+4)=21 [/tex]
[tex]\bullet\Rrightarrow\sf 7x+28=21 [/tex]
[tex]\bullet\rightarrowtail\sf 7x=21-28 [/tex]
[tex]\bullet\twoheadrightarrow\sf 7x=-7 [/tex]
[tex]\bullet\looparrowright\sf x=\dfrac{-7}{7}[/tex]
[tex]\bullet\rightharpoonup\sf x=-1 [/tex]
Find the missing side ?
Answer:
37
Step-by-step explanation:
What is the partial fraction decomposition of 11x-38/(2x-5)(x-4)
Answer:
D
Step-by-step explanation:
7/2x-5+2/x-4 is the partial fraction decomposition of 11x-38/(2x-5)(x-4)
What is Fraction?A fraction represents a part of a whole.
We need to write the partial fraction decomposition of 11x-38/(2x-5)(x-4)
(11x-38)/(2x-5)(x-4)=A/2x-5+B/x-4
11x-38=A(x-4)+B(2x-5)
11x-38=Ax-4A+2Bx-5B
We need to find the values of A and B
Compare the coefficients of x
11=A+2B
A=11-2B
Compare the constants
-38=-4A-5B
-38=-4(11-2B)-5B
-38=-44+8B-5B
-38=-44+3B
-38+44=3B
6=3B
Divide both sides by 3
B=2
Now A=11-2(2)=7
Hence, 7/2x-5+2/x-4 is the partial fraction decomposition of 11x-38/(2x-5)(x-4)
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centra
Jonah drives his car to and from work. The total length of the trip to and from work is 19.8 miles. In
August, Jonah worked 26 days.
How many miles in all did Jonah drive to and from work that month? Complete the explanation.
19.8
26
Jonah drove
miles in August
Plz
514.8 your welcome
All you have to do is multiply 19.8 x 26
Using the triangles shown below, explain how the ASA congruence criteria follows from the definition of congruence in terms of rigid motions.
Answer:
I have this question too
Step-by-step explanation:
All i know is that the ASA shows that even when they are rotated or translated due to rigid motions, they are still congruent because it shows that the angles and sides are equal.
What is the area of triangle ABC if a = 10 (degrees), B = 22 (degrees), and C = 70 (degrees) please help me.
A. 454.32 Sq Units
B. 103.37 Sq Units
C. 1.76 Sq Units
D. 17.61 Sq Units
Answer:
D. 17.61 square units
Step-by-step explanation:
To find the area of the ∆ABC, we can apply the formula below:
Area of ∆ABC = ½×a×c×sin(B)
a = 10
c = ??
B = 22°
Let's find c using Sine Rule:
Thus:
[tex] \frac{a}{sin(A)} = \frac{c}{sin(C)} [/tex]
Where,
a = 10
c = ??
A = 180 - (22 + 70) = 88°
C = 70°
Plug in the values
[tex] \frac{10}{sin(88)} = \frac{c}{sin(70)} [/tex]
Multiply both sides by sin(70)
[tex] \frac{10}{sin(88)} \times sin(70) = \frac{c}{sin(70)} \times sin(70) [/tex]
[tex] \frac{10 \times sin(70)}{sin(88)} = c [/tex]
[tex] 9.4 = c [/tex] (nearest tenth)
✔️Area of ∆ABC = ½×a×c×sin(B)
Plug in the values
Area of ∆ABC = ½ × 10 × 9.4 × sin(22)
Area = 17.61 square units (nearest tenth)
Joe marked up all the shoes in his store by 15%. If a pair of shoes originally cost $45, what was the price after the markup?
Answer:
The price would be $51.75.
Step-by-step explanation:
Since Joe is marking up by 15%, the price will increase for the pair of shoes. Multiply 45 by 1.15 since you are increasing the price by 15% to get your final answer which is $51.75.
Use the following function rule to find f(-7).
f(x) = 9x - 7
O 70
O-56
0 -70
56
In equilateral triangle ABC above, y =
(A) 40
(B) 60
(C) 70
(D) 75
(E) 80
Answer:
60°
Step-by-step explanation:
In an equilateral triangle all sides are equal so as all angles are same,
3 sided fig. 180÷3= 60°
What is the factorization of the trinomial below?
x^2- 5x+4
Answer:A
Step-by-step explanation:
FOIL
The factors of the quadratic equation x²- 5x + 4 are (x - 4)(x - 1) option (A) is correct.
What is a quadratic equation ?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] Where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
We have a quadratic equation:
= x²- 5x + 4
= x² -x - 4x + 4
= x(x - 1) - 4(x - 1)
= (x - 4)(x - 1)
Thus, the factors of the quadratic equation x²- 5x + 4 are (x - 4)(x - 1) option (A) is correct.
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Plz help with question
Answer:
x=25 and c=75
Step-by-step explanation:
(x+5)+(3x)+c=180
x+5+3x+c=180
x+3x+c=175
4x+c=175
c=-4x+175
c=3x
-4x+175=3x
175=7x
x=25
c=3x
c=3(25)
c=75
A school janitor has mopped
1/3 of a classroom in 5 minutes. At what rate is he mopping?
Answer:
1/3 of the school in 5 minutes or in 15 minutes he will mop the whole entire school.
Step-by-step explanation:
=================================================
Work Shown:
1/3 of a classroom = 5 minutes
3*(1/3 of a classroom) = 3*5 minutes
1 classroom = 15 minutes
It takes the janitor 15 minutes to mop a full classroom.
The rate is expressed in units of classrooms per minute. This means we'll need to divide both sides by 15 to get
1 classroom = 15 minutes
1/15 classroom = 15/15 minutes
1/15 of a classroom = 1 minute
The janitor's rate is 1/15 of a classroom per minute.
what is 5 and 9 tenths times 1 and 9 tenths
Answer:
11.21
Step-by-step explanation:
5.9*1.9
What is the solution set for 2x – (x + 5) < 3x – 9 ?
Answer:
x > 2
Step-by-step explanation:
x - 5 < 3x - 9
x - 5 + 5 < 3x - 9 + 5
x < 3x - 4
x - 3x < 3x - 4 - 3x
-2x < -4
(-2x)(-1) > (-4)(-1)
2x > 4
2x/2 > 4/2
x > 2
Answer:
x > 2.
The solution in interval notation is (2, ∞).
Step-by-step explanation:
2x - (x + 5) < 3x - 9
2x - x - 5 < 3x - 9
2x - x - 3x < -9 + 5
-2x < -4
Divide both sides by -2
x > 2 (Note that the sign flips because we are dividing by a negative)
Which equation describes the function whose y-intercept is 6 and whose
graph has slope 2?
HELPP
Answer:
y=2x+6
slope intercept form: y=mx+y-intercept
m=slope
Simplify 8 - (14) please help
Answer:
The answer is - 6 hope this helped
A block of ice has a square top and bottom and rectangular sides. At a certain point in
time, the square top and bottom each have a length of 30 cm, which are decreasing at a
rate of 2 cm/h. At the same time, the height of the ice block is 20 cm and decreasing at
3 cm/h. How fast is the ice melting?
Answer:
[tex]\frac{dV}{dt} = 360 \ cm^3/h[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Geometry
Volume of a Rectangular Prism: V = lwhCalculus
Derivatives
Derivative Notation
Differentiating with respect to time
Basic Power Rule:
f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
[tex]l = 30 \ cm\\w = l\\\frac{dl}{dt} = 2 \ cm/h\\h = 20 \ cm\\\frac{dh}{dt} = 3 \ cm/h[/tex]
Step 2: Differentiate
Rewrite [VRP]: [tex]V = l^2h[/tex]Differentiate [Basic Power Rule]: [tex]\frac{dV}{dt} = 2l\frac{dl}{dt} \frac{dh}{dt}[/tex]Step 3: Solve for Rate
Substitute: [tex]\frac{dV}{dt} = 2(30 \ cm)(2 \ cm/h)(3 \ cm/h)[/tex]Multiply: [tex]\frac{dV}{dt} = 360 \ cm^3/h[/tex]Here this tells us that our volume is decreasing (ice melting) at a rate of 360 cm³ per hour.
Show distributive property steps to evaluate 9 · 67 ?
603
Step-by-step explanation:We are given the expression:
9*67
Evaluating the expression:
We can write 67 as (60+7). So, we can rewrite the given expression as:
9*(60+7)
Using the distributive property:
(9*60) + (9*7)
540 + 63
603
if f = 3, g = -4 and h = -5
[3-h]+13
Write a number that when rounded to the nearest TENTHS is 382.9
Answer:
380
Step-by-step explanation:
If its a number 4-1 than it stays in the same tenths place if it a number 5- and up than it goes to a new number.
Since the Boston marathon began in 1897, the finish time has been incrementally decreasing. The mean finish time to date is 231 minutes with a standard deviation of 40 minutes. Based on this information, what would allow us to use a Z-score in order to construct a confidence interval to estimate the mean finishing time of the most recent Boston Marathon with a sample size of 40 participants. Choose all that apply.
Answer:
hello your question lacks the required options but i will provide a general answer to your question
answer : The mean value and the standard deviation would allow us use a Z-score
Step-by-step explanation:
mean value = 231 minutes
standard deviation ( std ) = 40 minutes
sample size = 40
The parameters that would be applicable while use Z-score are : The given mean value and the standard deviation
This is because the value of a z-score gives us an information on how far we are from the mean score i.e. number of standard deviations
+Zscore means that the score is above the average value
-Zscore means that the score is below the average value
Corinna is taking a test in which short-answer questions are worth 10 points each and essay questions are worth 15 points each. She estimates that it takes 3 min to answer each short- answer question and 6 min to answer each essay question. The total time allowed is 60 min, and no more than 16 questions can be answered. Assuming that all her answers are correct, how many questions of each type should Corinna answer in order to get the best score?
Solve the following problems:
Find x , y PLEASE HELP
Answer:
x=5/4, y=7/4
Step-by-step explanation:
This is a similar triangles problem.
The first triangle (the smaller one) has the lengths 5, 8 and 7.
The second triangle (the lager one) has the lengths 5+x, 10, and 7+y
Let's first solve for x
In any similar triangles problem, you can make two ratios (all the ratios of the sides are the same)
since we don't know the measures for x and y first, we can use the ratio of the parallel lines (the bases) as the first ratio (8/10)
For the second ratio, it's smaller/bigger, so it'll be 5/(x+5)
here's the proportion
5/(x+5)=8/10
But before we multiply, we can simplify 8/10 to 4/5
so
5/(x+5)=4/5
Cross multiply
25=4x+20
5=4x
5/4=x
For y, we can do a similar process
We can use 8/10 or 4/5 again
and the ratio of the sides for y will be 7/(y+7)
7/(y+7)=4/5
35=4y+28
7=4y
7/4=y
Hope this helps!
Determine whether the relationship is a function. Complete the explanation.
(0, 4), (8, 8), (3, 2), (9, 1), (8, 7)
Answer:
the relationship is not a function
Step-by-step explanation:
it's not a function because two of the domains are the same.
The relationship represented by these ordered pairs is not a function.
We have,
To determine whether the relationship is a function, we need to check if each input (x-value) is associated with exactly one output (y-value).
If there is any x-value that is associated with multiple y-values, then the relationship is not a function.
Let's analyze the given set of ordered pairs:
(0, 4), (8, 8), (3, 2), (9, 1), (8, 7)
Here, we can see that the x-value 8 is associated with both y-values 8 and 7.
Therefore, the relationship is not a function because one input (x-value) is mapped to multiple outputs (y-values).
In a function, each input must have a unique output, but in this case, the x-value 8 is associated with both 8 and 7 as the corresponding y-values.
Thus,
The relationship represented by these ordered pairs is not a function.
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Which of the numbers shown in the box below is the largest? 19/3, 31/5, 13/2, 25/4 pls help urgent
Answer: i think they are all the exact same 6 with a remainder of 1
Step-by-step explanation:
a store buys shirts for $12 each and marks up the price by %25. what is the price for a shirt at this store??
Answer:
Step-by-step explanation:
The price of the shirt at the store is $16
12 x .25 = 4
4 + 12 = 16
Write the data from greatest to least: 0.8, 0.79, 0.08, 0.81, 0.09, 0.9, 0.89
Answer:
0.9, 0.89, 0.81, 0.8, 0.79, 0.09, 0.08
Step-by-step explanation:
Answer: 0.09 , 0.89 , 0.81, 0.08, 0.79 , 0.9, 0.8
Step-by-step explanation:
First find the greatest
0.09, 0.89,0.81, 0.08, 0,79
Then the least
0.9 .0.8
Now put it all together
0.09, 0.89. 0.81 , 0.08, 0.79 , 0.9, and lastly 0.8
How do you write 22over5 in this
Answer:
00004.40 if you need to fill in every box. If not, 4 in front of the decimal, and a 4 after.
11) It takes you 15 minutes to frost a 2 layer cake. You and a friend have 100 1 point
cakes to frost for the church bake sale. How many hours will it take the two
of you to frost all of the cakes if you work at the same time rate? Hint: It
takes you 15 minutes to frost one cake, you can frost 4 cakes in 1 hr. *
B. 8 hours
O c. 12.5 hours
Answer:
12.5 hours
Step-by-step explanation:
100/4=25
25/2=12.5
What is the rule for the function shown in the table?
Input x -2 -1 0 1/2
Output y -8-5-2 1 4
O y=2x-2
Oy= x-6
O y= 4x
O y = 3x - 2
PLS HELP LOL
Answer:
2nd
Step-by-step explanation:
Please help me I really need to turn this in !!!! Please
Answer:
Please check the explanation.
Step-by-step explanation:
Part a)
Given the table
Year Value ($)
1 18,000
2 15,300
3 13,005
Let us check the sequence
18000, 15300, 13005,...
Let us find the common ratio 'r' of all the adjacent terms to check whether the sequence represents the geometric sequence or not, using the formula such as:
[tex]\:r=\frac{a_{n+1}}{a_n}[/tex]
[tex]\frac{15300}{18000}=\frac{17}{20},\:\quad \frac{13005}{15300}=\frac{17}{20}[/tex]
As the ratio of all the adjacent terms is the same, so
[tex]r=\frac{17}{20}[/tex]
Therefore, the given sequence is a geometric sequence
Part b)
Given the sequence
18000, 15300, 13005,...
The nth term of the geometric sequence is
[tex]a_n=a_1\cdot r^{n-1}[/tex]
here
[tex]a_1=18000[/tex]
[tex]r=\frac{17}{20}[/tex]
so
[tex]a_n=18000\left(\frac{17}{20}\right)^{n-1}[/tex]
In order to determine the car worth in the 15th year, substitute n = 15
[tex]a_{15}=18000\left(\frac{17}{20}\right)^{15-1}[/tex]
[tex]a_{15}=18000\frac{17^{14}}{20^{14}}[/tex]
[tex]a_{15}=18000\times \:\:0.10276[/tex]
[tex]a_{15}=1850[/tex] $
Therefore, the worth of a car in the 15th year will be: $1850