Answer:
x = - 7
Step-by-step explanation:
Given
3x + 5 = - 16 ( subtract 5 from both sides )
3x = - 21 ( divide both sides by 3 )
x = - 7
Two-step equations can get more difficult the higher the numbers get, but they're not too hard! ;)
To solve 3x+5=-16:
First subtract 5 from each side
Now its 3x=-21
Next divide 3 from each side
You get x=-7!
Always check your work! To check your work plug your answer "-7" into x.
So it looks like this: 3(-7)+5=-16 then distribute and solve!
You'll get -16=-16, that means its correct/true!
Tony has $727.29 in his checking account. He must maintain a $500 balance to avoid a fee. He wrote a check for $248.50 today. Write and solve an inequality to solve for the least amount of money he needs to deposit to avoid a fee.
727.29 + 248.50 − x ≥ 500; x ≥ $475.79
727.29 + 248.50 − x ≤ 500; x ≤ $475.79
727.29 − 248.50 + x ≥ 500; x ≥ $21.21
727.29 – 248.50 − x ≤ 500; x ≤ $21.21
Answer:
727.29 − 248.50 + x ≥ 500; x ≥ $21.21
Step-by-step explanation:
Write down all the data given :
Beginning amount : $727.29
Balance to be maintained : $ 500
Check : $248.5
Current balance = 727.29 - 248.5 = $478.79
Tony must maintain a balance of $500 so he should have at least $21.21 more (500-478.79)
727.29 - 248.5 + 21.21 = 500
500=500
x can be 21.21 or greater than that which would maintain the balance of $500 or more.
Therefore the third statement is correct.
727.29 − 248.50 + x ≥ 500; x ≥ $21.21
!!
why can 0.825 be written as a fraction explain
Answer:
It can be written as 825/1000. You can simplify this to get the simplest form which would be 33/40. All decimals are out of one, they are a part. When you first get a decimal, put the numbers such as 825 on top. The last number is in the thousandths place, so it is out of 1000. 1000 is your denominator. Your fraction is then 825/1000. From here you can simplify if possible.
Hope this helps ^-^
please please please help and try to explain
Answer:
-3 , 21
Step-by-step explanation:
RS = R + S = 12
S lies on 9
There are 12 spaces in between R & S, so you can add and subtract 12 from S:
9 - 12 = -3
9 + 12 = 21
R can be located on either -3 or 21.
~
solve using the quadratic formula x2+3x-3=0
Answer:
x=(-3+-sqrt15)/2
Step-by-step explanation:
Without using calculatorsoup,
we can use the quadratic formula for x^2+3x-3=0
using it we find:
x=(-b+-sqrtb^2-4ac)/2a
x=(-3+-sqrt3-4*1*-3)/2
x=(-3+-sqrt15)/2
For this case we must resolve the following expression:
[tex]x ^ 2 + 3x-3 = 0[/tex]
The roots will be given by:
[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}[/tex]
We have to:
[tex]a = 1\\\b = 3\\c = -3[/tex]
So:
[tex]x = \frac {-3 \pm \sqrt {3 ^ 2-4 (1) (- 3)}} {2 (1)}\\x = \frac {-3 \pm \sqrt {9 + 12}} {2}\\x = \frac {-3 \pm \sqrt {21}} {2}[/tex]
We have two roots:
[tex]x_ {1} = \frac {-3+ \sqrt {21}} {2} = 0.7913\\x_ {2} = \frac {-3- \sqrt {21}} {2} = - 3.7913[/tex]
Answer:
[tex]x_ {1} = \frac {-3+ \sqrt {21}} {2} = 0.7913\\x_ {2} = \frac {-3- \sqrt {21}} {2} = - 3.7913[/tex]
We just found that a = -0.1 in this system of equations: 3 = 10a + b 2= 20a + b. Find the value of b.
Answer:
b = 4Step-by-step explanation:
Put a = -0.1 to the first an second equation and find velue of b:
3 = 10a + b
3 = 10(-0.1) + b
3 = -1 + b add 1 to both sides
4 = b → b = 4
2 = 20a + b
2 = 20(-0.1) + b
2 = -2 + b add 2 to both sides
4 = b → b = 4
CORRECT
What are the solutions to the equation (x – 2)(x + 5) = 0?
Answer:
x = 2 or x = -5
Step-by-step explanation:
It s given that, (x – 2)(x + 5) = 0
To find the solution of given equation
Let (x – 2)(x + 5) = 0
From this we get
either (x – 2) = 0 or (x + 5) = 0
If (x - 2) = 0 then x = 2
If (x + 5) = 0 then x = -5
Therefore the solutions of given equation (x – 2)(x + 5) = 0 are,
x = 2 or x = -5
Answer: X = 2 or X = -5
Step-by-step explanation:
(X - 2) x ( X - 5) = 0
X - 2 = 0 or X - 5 = 0
Therefore X=2 or X=5
Find the second, fifth, and ninth terms of the sequence.
an = -7 + (n - 1) 4
Answer:
- 3, 9, 25
Step-by-step explanation:
To find the required terms of the sequence substitute n = 2, 5, 9 into the given rule, that is
[tex]a_{2}[/tex] = - 7 + (2 - 1)4 = - 7 + (1 × 4) = - 7 + 4 = - 3
[tex]a_{5}[/tex] = - 7 + (5 - 1)4 = - 7 + (4 × 4) = - 7 + 16 = 9
[tex]a_{9}[/tex] = - 7 + (9 - 1)4 = - 7 + (8 × 4) = - 7 + 32 = 25
The second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.
The second, fifth, and ninth terms of the sequence defined by the formula an = -7 + (n - 1) * 4 are -3, 9, and 25, respectively.
To find the second, fifth, and ninth terms of the sequence given by the formula an = -7 + (n - 1) * 4, we can simply plug the corresponding values of n into the formula.
For the second term (a2), where n=2:
a2 = -7 + (2 - 1) * 4
a2 = -7 + 1 * 4
a2 = -7 + 4
a2 = -3
For the fifth term (a5), where n=5:
a5 = -7 + (5 - 1) * 4
a5 = -7 + 4 * 4
a5 = -7 + 16
a5 = 9
For the ninth term (a9), where n=9:
a9 = -7 + (9 - 1) * 4
a9 = -7 + 8 * 4
a9 = -7 + 32
a9 = 25
Therefore, the second, fifth, and ninth terms of the sequence are -3, 9, and 25, respectively.
a house increased in value by 36% since it was purchased. The current value is $306,000. What was the value when purchased?
Answer:
$225,000
Step-by-step explanation:
To calculate the percentage change we will apply the formula:
p= N-O/O *100
p is the increased percentage
N is the current value
O is the old value.
Substitute the values in the formula:
36 = 306,000 - O/O *100
Divide both the sides by 100
36/100 = 306,000 - O/O *100/100
36/100 = 306,000 - O/O
Now multiply O at both sides
36/100 * O = 306,000-O/O * O
At R.H.S O will be cancelled by O
At L.H.S 36/ 100 = 0.36
0.36 O= 306,000-O
Combine the like terms:
0.36 O+O =306,000
1.36 O = 306,000
Divide both the terms by 1.36
1.36 O/ 1.36 = 306,000/1.36
O= $225,000
Therefore when the house was purchased its value was $225,000....
Georgia filled her kitchen sink up with water so that she could do the dishes. When she was done with the dishes, she pulled out the drain stopper so the water could begin to drain out of the sink.
A linear model of this situation contains the values (2, 8.4) and (4, 7.8), where x represents the number of seconds, and y represents the water level in the sink, in inches.
What is the rate of change in this linear model?
A.
-0.3 of an inch per second
B.
0.3 of an inch per second
C.
-9 inches per second
D.
-0.6 of an inch per second
Answer:
A) -0.3 of an inch per second
Step-by-step explanation:
You'll have to put (2, 8.4) and (4, 7.8) into the slope formula.
It's represented as (∆y)/(∆x) = m
(y1 + y2)/(x1 + x2) = m
You subtract both y's in the numerator and subtract both x's in the denominator.
Like this:
(8.4-7.8)/(2-4) = m
(0.6)/(-2) = m
-0.3 = m
Answer:
y = (-0.3 in/sec)x + 9.0 in
Step-by-step explanation:
(2, 8.4) and (4, 7.8) are points on a linear graph.
As we go from (2, 8.4) to (4, 7.8), x increases by 2 and y decreases by 0.6.
Thus, the slope of the line is m = rise / run = -0.6 / 2, or m = -0.3 inches/sec
Let's use the slope-intercept form of the equation of a straight line, with m = -0.3 in/sec and one point being (2, 8.4).
Then y = mx + b becomes 8.4 = (-0.3 in/sec)(2) + b, or
8.4 = -0.6 + b. Thus, b = 9.0, and the desired equation is thus:
y = (-0.3 in/sec)x + 9.0 in
In △ABC, m∠A=72°, c=61, and m∠B=16°. Find the perimeter of the triangle.
Answer:
136
Step-by-step explanation:
The perimeter of the triangle is about 136
Further explanationFirstly , let us learn about trigonometry in mathematics.
Suppose the ΔABC is a right triangle and ∠A is 90°.
sin ∠A = opposite / hypotenusecos ∠A = adjacent / hypotenusetan ∠A = opposite / adjacentThere are several trigonometric identities that need to be recalled, i.e.
[tex]cosec ~ A = \frac{1}{sin ~ A}[/tex]
[tex]sec ~ A = \frac{1}{cos ~ A}[/tex]
[tex]cot ~ A = \frac{1}{tan ~ A}[/tex]
[tex]tan ~ A = \frac{sin ~ A}{cos ~ A}[/tex]
Let us now tackle the problem!
This problem is about Sine Rule.
First of all, we will calculate the ∠C :
∠A + ∠B + ∠C = 180°
72° + 16° + ∠C = 180°
∠C = 180° - 72° - 16°
∠C = 92°
Next, we will use the Sine Rule to find the length of the other side of the triangle.
[tex]\frac{c}{\sin \angle C} = \frac{b}{\sin \angle B}[/tex]
[tex]\frac{61}{\sin 92^o} = \frac{b}{\sin 16^o}[/tex]
[tex]b \approx \boxed {16.82}[/tex]
[tex]\frac{c}{\sin \angle C} = \frac{a}{\sin \angle A}[/tex]
[tex]\frac{61}{\sin 92^o} = \frac{a}{\sin 72^o}[/tex]
[tex]a \approx \boxed {58.05}[/tex]
Finally, we can find the perimeter of a triangle with the following formula
[tex]\text{Perimeter of the triangle} = a + b + c[/tex]
[tex]\text{Perimeter of the triangle} = 58.05 + 16.82 + 61[/tex]
[tex]\text{Perimeter of the triangle} \approx \boxed {136}[/tex]
Learn moreCalculate Angle in Triangle : https://brainly.com/question/12438587Periodic Functions and Trigonometry : https://brainly.com/question/9718382Trigonometry Formula : https://brainly.com/question/12668178Answer detailsGrade: College
Subject: Mathematics
Chapter: Trigonometry
Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse
For f (x) = 3x+1 and g(x) = x2 - 6, find (f.g)(x).
Answer:
So we have
[tex](fg)(x)=3x^3+x^2-18x-6[/tex]
[tex](f \circ g)(x)=3x^2-17[/tex]
Step-by-step explanation:
I'm going to do two problems just in case.
We are given [tex]f(x)=3x+1[/tex] and [tex]g(x)=x^2-6[/tex].
[tex](fg)(x)=f(x)g(x)=(3x+1)(x^2-6)[/tex]
Multiply out using foil!
First: 3x(x^2)=3x^3
Outer: 3x(-6)=-18x
Inner: 1(x^2)=x^2
Last: 1(-6)=-6
-------------------Add together:
[tex]3x^3+x^2-18x-6[/tex]
[tex](f \circ g)(x)=f(g(x))=f(x^2-6)=3(x^2-6)+1=3x^2-18+1=3x^2-17[/tex]
Find the exact value of tan ^-1 (-root of 3)
Write your answer in radians in terms of n.
To find the exact value of tan^-1(-sqrt(3)), we first rewrite the equation using the definition of the arctangent function. Next, we use the trigonometric identity sin^2(x) + cos^2(x) = 1 to simplify the equation and solve for sin(x). We find that sin(x) = sqrt(3)/2. By looking at the unit circle, we determine that the angle whose sine is sqrt(3)/2 is pi/3 radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.
To find the exact value of tan^-1(-sqrt(3)), we need to recall the definition of the arctangent function. The arctangent function returns an angle whose tangent is equal to a given number. In this case, we are looking for an angle whose tangent is -sqrt(3). Since tan(x) = sin(x)/cos(x), we can rewrite the equation as -sqrt(3) = sin(x)/cos(x).
Next, we can use the fact that sin^2(x) + cos^2(x) = 1 to rewrite the equation as -sqrt(3) = sin(x)/sqrt(1 - sin^2(x)). Cross-multiplying and rearranging, we get -sqrt(3)*sqrt(1 - sin^2(x)) = sin(x).
Now, we can square both sides and simplify the equation to get -3*(1 - sin^2(x)) = sin^2(x). Expanding and rearranging, we have -3 + 3sin^2(x) = sin^2(x). Combining like terms and isolating sin^2(x), we get sin^2(x) = 3/4. Taking the square root of both sides, we find sin(x) = sqrt(3)/2.
Finally, we can find the angle whose sine is sqrt(3)/2 by looking at the unit circle. The angle is pi/3 in radians. Therefore, the exact value of tan^-1(-sqrt(3)) in radians is -pi/3 + 2*pi*n, where n is an integer.
Learn more about Finding exact value of arctangent function here:https://brainly.com/question/33989272
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Tiles spelling the word “Restaurant” are placed on a sign above a building. If one of the letters falls down at random, what is the probability that the letter is not a vowel? JUSTIFY
Answer:
3/5
Step-by-step explanation:
The word "Restaurant" contains a total of 10 letters, out of which 4 of the letters are vowels and 6 of the letters are consonants. The probability of selecting a vowel out of this word is:
P(selected letter is a vowel) = number of vowels/number of letters.
P(selected letter is a vowel) = 4/10 = 2/5.
Similarly, probability of selecting a non-vowel out of this word is:
P(selected letter is not a vowel) = number of non-vowels/number of letters.
P(selected letter is not a vowel) = 6/10 = 3/5.
Given that one of the letters randomly falls down, and assuming that the probabilities of each letter falling down is uniform and independent from each other, then:
P(a non-vowel falls down) = non-vowels/total = 6/10 = 3/5.
So the correct answer is 3/5!!!
t + 3/4t - 7/2 how do I simplify the 3/4t fraction with t?
Answer:
1 3/4 t -7/2
Step-by-step explanation:
t + 3/4t - 7/2
Get a common denominator for the t terms, which is 4
4/4t + 3/4t - 7/2
7/4 t -7/2
This is an improper fraction so change it to a mixed number
1 3/4 t -7/2
Kite ABCD has an area of 48 ft2. Calculate the length of AC.
A. 6 ft
B. 12 ft
C. 18 ft
Answer:
B. 12ft
Step-by-step explanation:
Area of kite is 2 times the area of triangle
= 2[(1/2)(4)AC] = 48, ie., AC = 12 ft
Simplify (-3c^-3w^5)^3
A -9w^8
B. -27cw^8
C. w^15/27c^9
D.-27w^15/c^9
Answer:
[tex]\large\boxed{D.\ \dfrac{-27w^{15}}{c^9}}[/tex]
Step-by-step explanation:
[tex](-3c^{-3}w^5)^3\qquad\text{use}\ (ab)^n=a^nb^n\\\\=(-3)^3(c^{-3})^3(w^5)^3\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=-27c^{-3\cdot3}w^{5\cdot3}=-27c^{-9}w^{15}\qquad\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=-27\left(\dfrac{1}{c^9}\right)w^{15}=\dfrac{-27w^{15}}{c^9}[/tex]
Final answer:
To simplify (-3c⁻³w⁵)³, you must distribute the power of 3 to each factor inside the parenthesis and apply the rule for negative exponents to end up with -27w¹⁵/c⁹, which is answer choice D.
Explanation:
The expression to simplify is (-3c⁻³w⁵)³. We will apply the rule for exponents to simplify the expression. When applying this rule and the negative exponent rule which states that a⁻ⁿ = 1/aⁿ, we get:
Step 1: Apply the power to each term inside the parenthesis: (-3)3 * c⁻⁹ * w¹⁵.Step 2: Simplify each term: -27 * c⁻⁹* w¹⁵.Step 3: Apply the negative exponent rule to c⁻⁹: -27 * (1/c⁹) * w¹⁵.Step 4: Write the final simplified expression as a single fraction: -27w¹⁵/c⁹.The correct answer is D. -27w¹⁵/c⁹.
Find the distance between these points.
R(-1,0), S(8,6)
V(26)
V(85)
3V(13)
Answer:
The distance is equal to [tex]3\sqrt{13}\ units[/tex]
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]R(-1,0)\\S(8,6)[/tex]
substitute the values
[tex]d=\sqrt{(6-0)^{2}+(8+1)^{2}}[/tex]
[tex]d=\sqrt{(6)^{2}+(9)^{2}}[/tex]
[tex]d=\sqrt{36+81}[/tex]
[tex]d=\sqrt{117}\ units[/tex]
Simplify
[tex]d=3\sqrt{13}\ units[/tex]
There are 3,280.84 feet in a kilometer. There are 5,280 feet in a mile. To the nearest hundredth, how many kilometers are in a mile?
Answer:
1.609344 kilometers
Step-by-step explanation:
Cal is trying to raise his average weekly income to be at least $131. His first
two weekly paychecks were $128 and $135. What is the lowest amount on his next
paycheck that Cal must earn so that he can reach his goal?
a) $132
b) $131
c) $135
d) $130
Answer:
d) $130
Step-by-step explanation:
Average means you add up the numbers and divide by the number of numbers.
We want our average to be 131.
We have 128,135, and the next pay check amount.
So let's average the three numbers together.
[tex]\frac{128+135+x}{3}[/tex]
[tex]x[/tex] represent the amount on the next pay check.
We want this average to equal 131 so we have this equation to solve:
[tex]\frac{128+135+x}{3}=131[/tex]
First step: Add 128 and 135:
[tex]\frac{263+x}{3}=131[/tex]
Second step: Multiply both sides by 3:
[tex]263+x=3(131)[/tex]
Third step: Multiply 3 and 131:
[tex]263+x=393[/tex]
Fourth step: Subtract 263 on both sides:
[tex]x=393-263[/tex]
Fifth step: Subtract 393 and 263:
[tex]x=130[/tex]
d. 130
D). $130
Step-by-step explanation:In this question, we're trying to figure out what would be the lowest amount of money he earned on his next paycheck in order for his income to be an average of $131.
To do this, we would need to use some important information in the question.
Important information:
$128 paycheck$135 paycheckWith the information above, we can use that to get the answer to the question.
We know that he made $128 and $135 on his recent paychecks, but we need to find on how much he needs to make on his next paycheck in order to reach his goal average.
We would be solving for x:
128, 135, x
131, 131, 131
We would add the numbers:
128, 135, x = 263 + x
131, 131, 131 = 393
We will now solve.
[tex]393 = 263+x\\\\\text{Subtract 263 on both sides}\\\\130=x[/tex]
When you're don solving, you should get 130. This means that Cal needs to make $130 on his next paycheck in order to have an average of $131.
Checking to see if it's right:We can check to see if it's right by adding up all of the numbers and divide by how many there are (3).
[tex]128+130+135=393\\\\393\div3=131[/tex]
Now, we can confirm that D). $130 would be the correct answer.
I hope this helps you out.Good luck on your academics.Have a fantastic day!Does anyone understand this?? Please help me, will mark brainlest!! Since it’s a lot I will give 30 points, please don’t answer just for the points
Answer:
f(x)=a(x-h)^2+k =f(x)=5(3-2)^(2)-4 and f(x)=1
Step-by-step explanation:
i really hope this helps im sorry if it doesnt
Which graph represents a linear function that has a slope of 0.5 and a y-intercept of 2?
Step-by-step explanation:
[tex]slope=\dfrac{rise}{run}=\dfrac{\Delta y}{\Delta x}\\\\\text{We have}\ m=0.5=\dfrac{1}{2}\to\Delta y=1,\ \Delta x=2\\\\\text{From given point (y-intercept: (0, 2), run 1 unit up and 2 units to the right.}\\(x+2,\ y+1)\to(0+2,\ 2+1)=(2,\ 3)\\\text{Mark new point.}\\\text{Plot the line passes throught given points.}\\\\======================\\\\\Delta x > 0-\text{run to the right}\\\Delta x<0-\text{run to the left}\\\Delta y>0-\text{run up}\\\Delta y<0-\text{run down}[/tex]
Answer:
D the last one
Fiona is serving iced tea and lemonade at a picnic. She has only 44 glasses in which to serve the drinks. If x represents the number of glasses of iced tea and y represents the number of glasses of lemonade, which equation represents the number of glasses of ice tea she can serve?
Answer:
x = 44 − y
Step-by-step explanation:
x is the number of glasses of iced tea, and y is the number of glasses of lemonade. The sum is 44, so:
x + y = 44
Solving for x:
x = 44 − y
Answer: 44-y represents the number of glasses of ice tea she can serve.
Step-by-step explanation:
Since we have given that
Let x be the number of glasses of iced tea.
Let y be the number of glasses of lemonade.
Total number of glasses = 44
According to question,
[tex]x+y=44[/tex]
So, the number of glasses of ice tea she can serve is given by
[tex]x=44-y[/tex]
Hence, 44-y represents the number of glasses of ice tea she can serve.
I need help I keep getting confuse
Answer:
Step-by-step explanation:
2(9+4)
According to the BODMAS rule:
B = BRACKET
O = OPEN
D= DIVISION
M = MULTIPLICATION
A = ADDITION
S= SUBTRACTION
First we will solve the bracket:
=2(9+4)
=2(13)
=26....
Answer:
A, B, and C
Step-by-step explanation:
= 2 (9 +4)
= 2 (13)
= 26
A
= 2(9) + 2 (4)
= 18 + 8
= 26
B
= 2(13)
= 26
C
= 18 + 8
= 26
D
= 22
D does not apply because it does not equal 26
-7 + m = 8 please answer the question
Answer:
m=15
Step-by-step explanation:
-7 + m = 8
=>m=8+7
=>m=15
Write the parametric equation of the line 10x-4y=20
Answer:
x = 1 - t and y = -2.5 - 2.5t.
Step-by-step explanation:
Parametric equations are the equations in which the all the variables of the equation are written in terms of a single variable. For example in 2-D plane, the equation of the line is given by y=mx+c, there x is the independent variable, y is the dependent variable, m is the slope, and c is the y-intercept. The equation of the given line is 10x - 4y = 20. The goal is to convert the variables x and y in terms of a single variable t. First of all, take two points which lie on the line. By taking x=1, y comes out to be -2.5 and by taking x=0, y comes out to be -5. The general form of the straight line is given by:
(x, y) = (x0, y0) + t(x1-x0, y1-y0), where (x, y) is the general point, (x0, y0) is the fixed point, t is the parametric variable, and (x1-x0, y1-y0) is the slope.
Let (x0, y0) = (1, -2.5) and (x1, y1) = (0, -5). Substituting in the general equation gives:
(x, y) = (1, -2.5) + t(-1, -2.5). This implies that x = 1 - t and y = -2.5 - 2.5t!!!
Answer:
C. x=2t, y=5t-5
Step-by-step explanation:
In parallelogram EFGH, the measure of angle F is (3x − 10)° and the measure of angle G is (5x + 22)°. What is the measure of angle G?
Answer:
So angle G has measurement 127 degrees.
Step-by-step explanation:
E F
H G
I had to write it out the parallelogram so I could have a better visual.
F and G are consecutive angles in a parallelogram (not on opposite sides).
This means they add to be 180 degrees.
F+G=180
(3x-10)+(5x+22)=180
(3x+5x)+(-10+22)=180
8x +12=180
Subtract 12 on both sides:
8x =180-12
Simplify:
8x =168
Divide both sides by 8:
x =168/8
x =21
If x=21 and want the measurement of angle G, then
(5x+22)=(5*21+22)=127.
So angle G has measurement 127 degrees.
Answer: [tex]127^{\circ}[/tex]
Step-by-step explanation:
Given : In parallelogram EFGH, the measure of angle F is (3x − 10)° and the measure of angle G is (5x + 22)°.
We known that in a parallelogram , the sum of two adjacent angles is 180° .
Therefore , we have
[tex]3x -10+5x + 22=180\\\\\Rightarrow\ 8x+12=180\\\\\Rightarrow\ 8x=180-12\\\\\Rightarrow\8x=168\\\\\Rightarrow\ x=21[/tex]
Now, the measure of angle G =[tex](5x + 22)^{\circ}=(5(21)+22)^{\circ}=127^{\circ}[/tex]
Hence, the measure of angle G = [tex]127^{\circ}[/tex]
Ben sold his small online business for $100,000. The purchaser will pay him $20,000 today, then $20,000 every year for the next four years. Assume
that Ben could invest a lump-sum payment today in an account yielding an interest rate of 4% annually. Find the total present value of all five
payments
A.
$87,096
B
$88,384
c. $92,598
D. $93,964
The answer is c $92,598
Answer:
$92,598
Step-by-step explanation:
The purchaser pays Ben $20,000 today and then $20,000 every year for the next 4 years.
The interest rate is 4% per annum.
So the net present value of all the payments is :
20000 + 20000/1.04 + 20000/(1.04^2) + 20000/(1.04^3) + 20000/(1.04^4)
= 20000 + 19230.77 + 18491.12 + 17779.73 + 17096.08
= 92597.7
= 92,598 (approx)
So the net present value of all the payments made to Ben is $92,598.
Which set of ordered pairs could be generated by an exponential function?
(0,0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0,0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)
ANSWER
(0, 1), (1, 3), (2, 9), (3, 27)
EXPLANATION
The first and third options are completely out because the y-value of an exponential function is never zero.
For the second option the y-values has no geometric pattern or common ratio.
For the last option, we can observe the following pattern
[tex]1 = {3}^{0} [/tex]
[tex] {3}^{1} = 3[/tex]
[tex] {3}^{2} = 9[/tex]
[tex] {3}^{3} = 27[/tex]
:
:
[tex] {3}^{x} = y [/tex]
The correct choice is the last option
Answer:
D
Step-by-step explanation:
If a triangle has sides of lengths 5, 8 and 12, it is a right triangle. true or false
Answer:
False.
Step-by-step explanation:
To see if these sides can form a right triangle, all we need to do is see if the following equation holds [tex]a^2+b^2=c^2[/tex] where [tex]c[/tex] is the larger measurement. [tex]a \text{ and } b[/tex] it doesn't really matter which you assign as 5 or 8.
So I'm choosing the following [tex]a=5,b=8,c=12[/tex].
[tex]c[/tex] has to be 12 because 12 is the largest.
Now we got to see if [tex]a^2+b^2=c^2[/tex] holds.
That is, we need to see if [tex]5^2+8^2=12^2[/tex] holds.
[tex]5^2+8^2=12^2[/tex]
[tex]25+64=144[/tex]
[tex]89=144[/tex]
That's totally false. 89 is definitely not 144 so 5,8, and 12 cannot be put together to form a right triangle.
Berto has $12 to put gas in his car. If gas costs $3.75 per gallon, which ordered pair relating number of gallons of
gas, x, to the total cost of the gas, y, includes the greatest amount of gas Berto can buy?
Answer:
(12, 3.2) would be the max amount of gas he could buy. (11.25, 3) for an even gallon amount.
Step-by-step explanation:
Answer:
(3.2, 12)
Step-by-step explanation:
Total cost for gas = $12
Cost per gallon = $3.75
Letting total cost of gas be y and number of gallons be x, maximum number of gallons of gas he can buy would be ;
Total cost of gas/ cost per gallon = 12 / 3.75 = 3.2 gallons
Therefore , the coordinate pair (x, y) = (3.2, 12)