We start by substituting the value of 3x for y in the first equation
We have this as;
[tex]\begin{gathered} 4x-2(3x)\text{ = -4} \\ 4x\text{ - 6x = -4} \\ -2x=\text{ -4} \\ x\text{ = }\frac{-4}{-2} \\ x\text{ =2} \\ \text{From i}i\colon\text{ y = 3x ; y = 3(2) ; y = 6} \end{gathered}[/tex].1.2_Updated_FY21 Question: 1-3 The elevation of the Vander's home is -108 feet. The elevation of the Gail's home is exactly of that depth below sea level. What is the elevation of the Gail's home in feet? -36 -72 -162 -180
Given:
Elevation of Vander's home = -108 feet
Elevation of Gali's home is ⅔ of that depth below sea level.
Thus, the elevation of Gali's home is:
⅔ of -108 feet =
[tex]\frac{2}{3}(-108)\text{ = }\frac{2(-108)}{3}=\frac{-216}{3}=\text{ -72 f}eet[/tex]We know that the elevation of Vander's home is already below sea level since it's a negative value.
Therefore, since the elevation of Gali's home is ⅔ of the depth of Vander's home below sea level, the elevation of Gali's home is:
-72 feet
ANSWER:
-72 feet
In the rectangle below, B D = 4x – 2, AC = 5x-11, and m ZAED = 82º.Find AE and m ZECB.BEAE =m ZECB =DС
Given :
[tex]\begin{gathered} BD\text{ = 4x + 2} \\ AC\text{ = 5x - 11} \\ \angle AED=82^0 \end{gathered}[/tex]Required :
[tex]AE\text{ , }\angle\text{ ECB}[/tex]Recall from the properties of a rectangle that
[tex]\text{The diagonals have the same length}[/tex]Hence :
[tex]\begin{gathered} AC\text{ = BD} \\ 5x\text{ - 11 = 4x -2 } \\ \text{collect like terms} \\ 5x\text{ - 4x = 11 - 2} \\ x\text{ = 9} \end{gathered}[/tex]if you are paid $4.50 per hour, how many hours will you have to work to earn $1000.00
Answer:
222.22 hours
Explanation:
To know how many hours you will have to work, we need to use the given rate of $4.50 per hour as follows:
[tex]\text{ \$1000}\times\frac{1\text{ hour}}{\text{ \$4.50}}=\frac{1000\times1}{4.5}=\frac{1000}{4.5}=222.22\text{ hours}[/tex]Because 1 hour is equivalent to $4.50.
Therefore, you will have to work 222.22 hours to earn $1000
I have this practice question from my ACT prep guide, THE SUBJECT IS PRE CALC!! MEANING ITS HARD AND COMPLEX. Below will be the questions to this problem ( includes 5 questions )1. What is the balance of Albert’s $2000 after 10 years? 2. What is the balance of Marie’s $2000 after 10 years? 3. What is the balance of Han’s $2000 after 10 years?4. What is the balance of Max’s $2000 after 10 years? And lastly, 5. Who is $10,000 richer at the end of the competition?
Albert
Compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where:
A: final amount
P: principal
r: annual interest rate, as a decimal
t: time in years
n: number of times interest applied per year
Substituting with P = $1000, r = 0.012 (= 1.2/100), n = 12 (interest is compounded monthly), t = 10 years, we get:
[tex]\begin{gathered} A=1000(1+\frac{0.012}{12})^{12\cdot10} \\ A=1000(1.001)^{120} \\ A=1127.43\text{ \$} \end{gathered}[/tex]If $500 lost 2%, then it keeps 98% of its original value, that is,
$500x98% = $490
Continuous compound formula:
[tex]A=Pe^{rt}[/tex]where the variables have the same meaning as before.
Substituting with P = $500, r = 0.008 ( = 0.8/100), and t = 10 years, we get:
[tex]\begin{gathered} A=500\cdot e^{0.008\cdot10} \\ A=541.64\text{ \$} \end{gathered}[/tex]The balance of Albert’s $2000 after 10 years is:
$1127.43 + $490 + $541.64 = $2159.07
Marie
Substituting in the compound interest formula with P = $1500, r = 0.014 (= 1.4/100), n = 4 (interest is compounded quartely), t = 10 years, we get:
Question 8: What is the measure of Angle C?*c525°47°43°1330
SOLUTION
Angle C is 133 degrees
From the image , angle c is the same as angle a, reason been that they are vertically opposite angles and they are always equal.. let us call angle c and a = x
Angle b = 47 degrees, because they are both vertically opposite angles, and they are always equal.
Angle c + angle a + angle b + 47 = 360 ( sum of angles at a point)
x + x + 47 + 47 = 360
2x + 94 =360
2x = 360-94
2x =266
x= 266/2
x=133 degrees
So angle C is 133 degrees
Option D
17. Show your work-Factor the expression: 35x+63 * Your answer
35x + 63
7 can go into the two
7 (5x + 9)
Solve the equation for x, and enter your answer below.3x-3 + 5x = 37
The given equation is-
[tex]3x-3+5x=37[/tex]First, we reduce like terms
[tex]8x-3=37[/tex]Now, we sum 3 on each side
[tex]\begin{gathered} 8x-3+3=37+3 \\ 8x=40 \end{gathered}[/tex]At last, we divide the equation by 8
[tex]\begin{gathered} \frac{8x}{8}=\frac{40}{8} \\ x=5 \end{gathered}[/tex]Therefore, the solution is 5.A company purchased 10,000 pairs of men's slacks for $19.16 per pair and marked them up $22.43. What was the selling price of each pair of slacks? Use the formula S=C+M
Given that each slack is purchased at $19.16, so the cost price is $19.16
Also given that each slack is marked at $22.43, so the marked price is $22.43
It is asked to use the formula,
[tex]S=C+M[/tex]Substitute the values and simplify,
[tex]S=19.16+22.43=41.59[/tex]Thus, the selling price of each pair os slacks is $41.59
which of the following is the correct factorization of the polynomial below?27x^3+1000
The polynomial is given to be:
[tex]27x^3+1000[/tex]We can rewrite this expression by applying the knowledge of exponents:
[tex]\Rightarrow(3x)^3+10^3[/tex]Apply the sum of cubes formula:
[tex]x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)[/tex]Therefore, we have:
[tex]\left(3x\right)^3+10^3=\left(3x+10\right)\left(3^2x^2-10\cdot \:3x+10^2\right)[/tex]Hence, we can simplify the expression to give the answer:
[tex]27x^3+1000=\left(3x+10\right)\left(9x^2-30x+100\right)[/tex]The correct option is OPTION B.
When 3.5 is added to 7 times a number the result is 65.1 find the number
Let x be the number we are looking for; therefore, 7 times a number is '7x'.
Then, 3.5 added to 7 times a number is
[tex]3.5+7x[/tex]Thus, the whole equation is
[tex]\begin{gathered} 3.5+7x=65.1 \\ \Rightarrow7x=65.1-3.5=61.6 \\ \Rightarrow x=\frac{61.6}{7}=8.8 \end{gathered}[/tex]Hence, the number is 8.8
Image courtesy of NASAWhich of New Zealand's physical features is circled by number 2 on the map above?A. the Northern PeninsulaB. the Southern AlpsC. the Canterbury PlainsD. the Eastern HillsPlease select the best answer from the choices providedABOeCD
C) Canterbury Plains
A python (p) is 3.9 feet longer than a boa constrictor (6).Select an expression from each box to create an equation that compares the lengths of the snakes
Since the python is 3.9 feet longer than the boa.
Therefore,
p=b+3.9
This implies that,
b=p - 3.9
In the first box you pick b
In the second box pick p-3.9
I answered a few of these already. Am I right? What are the others? Thank you.
Answer:
Step-by-step explanation:
1. Number 1 is correct.
2. Number 2 is base angles.
3. Number 3 is correct.
4. Number 4 is vertical angles.
5. Number 5 is alternate interior angles.
6. Number 6 is corresponding parts.
7. Number 7 is correct.
8. Number 8 is vertex angles.
9. Number 9 is reflexive property.
10. Number 10 is correct.
Good luck! I hope you give me brainliest!
Find the 8th term of the sequence using the explicit formula: 2 × (7)(n - 1).1647086164706816478061647860
Given:
The explicit formula is
[tex]2\times7^{(n-1)}[/tex]Required:
To find the 8th term of the sequence.
Explanation:
For n=8,
[tex]\begin{gathered} =2\times7^{(8-1)} \\ \\ =2\times7^7 \\ \\ =2\times7\times7\times7\times7\times7\times7\times7 \\ \\ =1647086 \end{gathered}[/tex]Final Answer:
The first option is correct.
[tex]1647086[/tex]The pilot in a plane is cruising at 4 miles sees a tree. The angle of elevation from the base of the tree to the plane is 40°.
We have to find x.
We can use the trigonometric relations to find the value of x.
We know that, for a right triangle, the sine of an angle is equal to the quotient between the opposite side and the hypotenuse.
In this case, the opposite side of the angle is the height of the plane (4 mi) and the hypotenuse is x, so we can write:
[tex]\begin{gathered} \cos (40\degree)=\frac{\text{Opposite}}{\text{Hypotenuse}}=\frac{4}{x} \\ x=\frac{4}{\cos (40\degree)}\approx\frac{4}{0.766}\approx5.22 \end{gathered}[/tex]Answer: the value of x is approximately 5.22 miles.
Write an equation of the line that passes through a pair of points: 5 4 37 2 1+ 4 -3 -2 -1 1 -3 a. y = x + 3 b. y = x - 3 C. y = -x + 2 d. y = -x-2 Please select the best answer from the choicon
From the given, it shows two points that pass through the given graph. These points are:
Point A : x1, y1 = 4, 1
Point B : x2, y2 = 5, 2
We will be using these points in generating the equation of the line.
Step 1: Let's determine the slope m of the line.
[tex]\text{ m = }\frac{y_2-y_1}{x_2-x_1}\text{ = }\frac{\text{ 2 - 1}}{\text{ 5 - 4}}\text{ = }\frac{1}{1}\text{ = 1}[/tex]Step 2: Let's determine the y-intercept b. Substitute x,y = 4, 1 and m = 1 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ 1 = (1)(4) + b}[/tex][tex]\text{ 1 = 4 + b}[/tex][tex]\text{ 1 - 4 = b}[/tex][tex]\text{ -3 = b}[/tex]Step 3: Let's complete the equation. Substitute m = 1 and b = -3 in y = mx + b.
[tex]\text{ y = mx + b}[/tex][tex]\text{ y = (1)x + (-3)}[/tex][tex]\text{ y = x - 3}[/tex]Therefore, the equation of the line is y = x - 3.
The answer is letter B.
a line has a slope of 3 and a y-i yet dot of 5. what is it’s equation in slope-intercept form? write you answer using integers, proper fractions, and improper fractions in simplest form.
y = 3x + 5
Explanation:slope = 3
y - intercept = 5
To get the equation in slope intercept form, we'll use:
[tex]\begin{gathered} y\text{ = mx + b} \\ m\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex][tex]\begin{gathered} \text{The equation becomes:} \\ y\text{ = 3x + 5} \\ \end{gathered}[/tex]What is the least common multiple of 3,4,and 8
Answer:the least common multiple of 3, 4, 8 is 48
Step-by-step explanation:
Answer:
24
Step-by-step explanation:
The diagram shows how 6-foot boards and 8-foot boards are joined to form rectangular frames in a wall. Which is closest to the length of the diagonal brace for the wall? 6 ft 8 ft A. 10 ft B. 12 ft C. 13 ft D. 11 ft
A right triangle is formed, where 6 ft and 8 ft are the legs, and the hypotenuse is unknown. Using the Pythagorean theorem:
c² = a² + b²
c² = 6² + 8²
c² = 36 + 64
c² = 100
c = √100
c = 10 ft
Consider the following linear equation.2y = -1-ainStep 2 of 2: Graph the line.
As given by the question
There are given that the equation
[tex]y=-1-\frac{2}{5}x[/tex]Now,
The graph of the line is given below:
(Right angle) Trigonometry Help me find the X value please!
To solve for x, we will simply use the trigonometric ratio
[tex]\sin \theta=\frac{\text{opposite}}{\text{hypotenuse}}[/tex]From the figure given;
θ=24.3 opposite=2.06 and hypotenuse =x
substitute the values and evaluate
[tex]\sin 24.3=\frac{2.06}{x}[/tex]cross-multiply
x sin24.3 = 2.06
Divide both-side by sin24.3
[tex]x=\frac{2.06}{\sin 24.3}[/tex][tex]x\approx5.0[/tex]Use a system of equations to solve the following problem.The sum of three integers is 244. The sum of the first and second integers exceeds the third by 48. The third integer is 36 less than the first Findthe three integersAnswer How to enter your answer topens in new windon 5 PointsKeypadKeyboard Shartofirst integer =second integer =third integer =
Given:
The sum of three integers is 244. The sum of the first and second integers exceeds the third by 48. The third integer is 36 less than the first.
Aim:
We need to find the values of all three integers.
Explanation:
Let x be the first integer.
Let y be the second integer.
Let z be the third interger.
The sum of three integers is 244.
[tex]x+y+z=244[/tex]The sum of the first and second integers exceeds the third by 48.
[tex]x+y=z+48[/tex]The third integer is 36 less than the first.
[tex]z=x-36[/tex]Substitute z=x-36 in the equation x+y=z-48 .
[tex]x+y=x-36+48[/tex][tex]x+y=x+12[/tex]Subtract x from both sides of the equation.
[tex]x+y-x=x+12-x[/tex][tex]y=12[/tex]Substitute z=x-36 and y=12 in the equation x+y+z=244.
[tex]x+12+x-36=244[/tex]Add 24 to both sides of the equation.
[tex]2x-24+24=244+24[/tex][tex]2x=268[/tex]Divide both sides by 2.
[tex]\frac{2x}{2}=\frac{268}{2}[/tex][tex]x=134[/tex]Substitute x=134 in the equation z=x-36
[tex]z=134-36[/tex][tex]z=98[/tex]We get x=128, y=12 and z =98.
Final answer:
first integer = 128
second integer =`12
third integer = 98.
what is the answer
1-m=6-6m
Answer:
m = 1
Explanaton:
Given the expression;
1 - m = 6 - 6m
Collect the like terms
-m + 6m = 6 - 1
5m = 5
Divide both sides by 5
5m/5 = 5/5
m = 1
Hence the value of m is 1
dividing 5 by 10 + 1
I'm having trouble finding the length of NP and MN, thinking it has something to do with tan, cos, and sin, but not completely sure.
Bisects: to divide into two equal parts.
In this case, DB is bisecting the ∠ABC, then the ∠ABD
As OP is bisecting ∠MON, that means that ∠NOP and ∠POM have the same measure.
Then:
[tex]m\angle MON=m\angle NOP+m\angle POM[/tex]As ∠NOP = ∠POM, we get:
[tex]m\angle MON=m\angle NOP+m\angle NOP=2\cdot m\angle NOP[/tex]Replacing the value we get:
[tex]m\angle MON=2\cdot20=40[/tex]Based on this, we can use the trigonometric functions, as we have an angle and one side. Specifically, the tangent function:
[tex]\tan \alpha=\frac{opposite}{\text{adyacent}}[/tex]First, to calculate NP, we get the following:
[tex]\tan 20=\frac{NP}{6}[/tex]Isolating for NP:
[tex]NP=6\cdot\tan 20[/tex][tex]NP=2.18[/tex]Then, calculating for MN we get the following:
[tex]\tan 40=\frac{MN}{6}[/tex]Isolating for MN:
[tex]MN=6\cdot\tan 40[/tex][tex]MN=5.03[/tex]Answer:
• NP = 2.18
,• MN = 5.03
Find the LCD of the list of fractions. 11/20, 1/18, 13/90
LCD state for Least Common Denominator
The given fraction are :
[tex]\frac{11}{20},\text{ }\frac{1}{18},\text{ }\frac{13}{90}[/tex]For the least common denominator, first find the LCM of all the denominator of the given values:
Denominator are : ( 20, 18, 90)
LCM of (20,18, 90) = 180
So, the fraction will value can be written as :
[tex]\begin{gathered} \frac{11}{20}\text{ to make denominator equal to 180,} \\ \text{ Multiply up \& down by 9} \\ \frac{11\times9}{20\times9}=\frac{99}{180} \\ \text{ } \\ \frac{1}{18}\text{ to make denominator equal to 180} \\ \text{ Multiply up and down by 10} \\ \frac{1\times10}{18\times10}=\frac{10}{180} \\ \\ \frac{13}{90},\text{ to make denominator equal to 180} \\ \text{Multiply up and down by 2} \\ \frac{13\times2}{90\times2}=\frac{26}{180} \end{gathered}[/tex]Thus, the fraction will convert as :
[tex]\begin{gathered} \frac{11}{20}=\frac{99}{180} \\ \frac{1}{18}=\frac{10}{180} \\ \frac{13}{90}=\frac{26}{180} \end{gathered}[/tex]The least common denominator is 180
Answer : LCD of 11/20, 1/18, 13/90 is 180
What is the solution to the equation k - 4 3/4 = 8 1/4?k = 4 1\2k = 12k = 13k = 4
Answer:
Explanation:
The given equation is
k - 4 3/4 = 8 1/4
The fist step is to convert the mixed number to improper fractions.
4 3/4 = 19/4
8 1/4 = 33/4
Thus, the expression becomes
k - 19/4 = 33/4
Adding 19/4 to both sides, we have
k - 19/4 + 19/4= 33/4 + 19/4
k = 52/4
k = 13
Which is NOT true?a) 9+4=17-4b)8+7=14+3c)11=19-8d)5+8=20-7
To determine which expression is true, we have to do the operations and check that on both sides of the equation is the same number.
Then, in this case we have:
[tex]\begin{gathered} a)9+4=13 \\ 17-4=13 \\ b)8+7=15 \\ 14+3=17 \\ c)19-8=11 \\ d)5+8=13 \\ 20-7=13 \end{gathered}[/tex]notice that the only option that don't match is b, therefore, the option b is not true
What is the term-to-term rule for the following sequences? Solve (A)A) 1,2,3,4,5,6,7,8,…B) 4,9,14,19,24,29,…C) 32,30,28,26,24,22,…D) 6,13,20,27,34,41,…E) 3,6,12,24,48,96,…F) 36,30,24,18,12,6,…G) -13,-11,-9,-7,-5,…H) 48,45,42,39,36,…I) 1,7,49,343,2401,…
A) Given:
The sequence is,
[tex]1,2,3,4,5,6,7,8,…[/tex]To find: The term-to-term rule
Since the given sequence has the common differnce 1.
So, it is of the arithmetic sequence.
Therefore, let us take
[tex]a_1=1[/tex]Then the second term will be,
[tex]\begin{gathered} a_2=a_1+1 \\ =1+1 \\ =2 \end{gathered}[/tex]The third term will be,
[tex]\begin{gathered} a_3=a_2+1 \\ =2+1 \\ =3 \end{gathered}[/tex]And so on.
So, the term to term rule must be,
[tex]a_n=a_{n-1}+1[/tex]Final answer: The term to term rule is,
[tex]a_{n}=a_{n-1}+1[/tex]Five companies have each sent one representative to a competition to pitch their newest business idea to a group of angel investors. The conference has 5 time slots designated for one representative to present their company's idea.How many different ways can the representatives be ordered to present their ideas?
Let's use the counting principle:
[tex]\begin{gathered} Let: \\ n=number_{\text{ }}slots=5 \\ T=Total_{\text{ }}number_{\text{ }}of_{\text{ }}ways \end{gathered}[/tex]so:
[tex]T=n\cdot(n-1)\cdot(n-2)...1=n![/tex]So:
[tex]\begin{gathered} T=5! \\ T=120 \end{gathered}[/tex]Answer:
120
The number of different ways can the representatives be ordered to present their ideas is 120 ways.
Given that, 5 companies have each sent one representative to a competition to pitch their newest business idea to a group of angel investors.
What are Permutations?Permutations are different ways of arranging objects in a definite order. It can also be expressed as the rearrangement of items in a linear order of an already ordered set. The symbol nPr is used to denote the number of permutations of n distinct objects, taken r at a time.
Using nPr =n!(n-r)! we get
Here, n=5 and r=5
So, P(n, r) = P(5, 5) = 5!(5-5)!
= 5!/1
= 5×4×3×2×1
= 120 ways
Therefore, the number of different ways can the representatives be ordered to present their ideas is 120 ways.
To learn more about the permutation visit:
https://brainly.com/question/3867157.
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