Answer:
y = 8
Step-by-step explanation:
remove the constant, 6:
3y=24
divide both by 3. leave x by itself
3y/3=24/3
y = 8
do these steps and you can do these easily
The solution to the equation 3y + 6 = 30 is y = 8.
To solve the equation 3y + 6 = 30 and find the value of y, we need to isolate the variable y on one side of the equation by performing various operations. Here are the steps to solve the equation:
Step 1: Begin with the given equation:
3y + 6 = 30
Step 2: Subtract 6 from both sides of the equation to move the constant term to the other side:
3y + 6 - 6 = 30 - 6
3y = 24
Step 3: Divide both sides of the equation by 3 to isolate the variable y:
(3y)/3 = 24/3
y = 8
Step 4: Verify the solution by substituting the value of y back into the original equation:
3(8) + 6 = 30
24 + 6 = 30
30 = 30
Since the equation is true, we can conclude that the solution to the equation 3y + 6 = 30 is y = 8. By performing the necessary operations, we successfully isolated the variable y and found its value that satisfies the original equation.
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The sum of two consecutive integers is one less than three times the smaller integer. Find the two integers.
The small number is 2.
The large number is 3.
Step-by-step explanation:
Let the two consecutive numbers be x and x+1.
x be the small integer.x+1 be the large integer.The sum of these two consecutive integers = small integer + large integer
The sum of these two consecutive integers is x+x+1 = (2x+1)
It is given that,
The sum of two consecutive integers is one less than three times the smaller integer.This means that, (2x+1) is one less than three times the smaller integer.Here, the small integer is represented as x.Therefore, it can determined that :
(2x+1) = 3x-1
Keeping x term on one side and constants on other side,
3x-2x = 1+1
x = 2
Therefore, the small number is 2 and the large number is x+1 = 3.
What is the range of the given function
table A
x y
4 1
8 2
12 3
16 4
Compare the table of Object A and the equation y = 5x of Object B. Which of the two moving objects has greater speed and by what factor? (round to nearest hundredth)
A) Object A by a factor of 1.05
B) Object B by a factor of 1.05
C) Object A by a factor of 1.25
D) Object B by a factor of 1.25
Answer:
D
Step-by-step explanation:
1. Find the rate of change of the graph. Which is 4.
2. Because 5 is greater of 4, Object B has the greater speed.
3. To find the factor you must divide 4 from 5. 5 ÷ 4
4. 5 ÷ 4 = 1.25
5. The correct answer is D
Answer:C)Object A by a factor of 1.25
Step-by-step explanation:this is the answer for USA test prep.
9 yd
12 yd
What is the length of the hypotenuse?
Answer:
Hi there!
The correct answer will be 15 yd
Step-by-step explanation:
There are two ways you can go about solving this problem
Method One: Pythagorean Theorem
a^2 + b^2 = c^2 then all you have to do is plug in the values
(12)^2 + (9)^2 = c^2 you should get c^2 = 225 then you square root both sides and you get c = 15
Method Two: Pythagorean Identities
This triangle represents a 3,4,5 triangle
All the sides just tripled so that means the hypotenuse is 5*3 which equals 15
The polynomial is a difference of perfect squares. Use the formula a2 – b2 = (a + b)(a – b) to factor completely.
81x2 – 49
The value of a is .
The value of b is .
The product of the prime factors is
Answer:
a=9x
b=7
(9x-7)(9x+7)
Step-by-step explanation:
81x^2-49=(9x)^2 - 7^2=(9x-7)(9x+7)
Answer:
1: 9x
2: 7
3: (9x-7)(9x+7)
OR
1: 3rd option
2: 2nd option
3: 4th option
Step-by-step explanation:
got it right on Edge
have a great day!!!
PLZ MARK BRAINLIEST
An arithmetic sequence is given below.
14, 21, 28, 35, ...
Write an explicit formula for the nth term an.
(a) How far does a car travel if it moves at 52 miles per hour for 3.5 hours?
Answer:
182 miles
Step-by-step explanation:
52 times 3.5=182
The Answer is 182 miles
When multiplying 52 by 3.5 you'll get 182 as the product
The circle has an angle of 40° and an area of 8 cm2. Calculate the area of the entire circle.
Step-by-step explanation:
answer it yourself
The sum of two numbers is 141. One number is 37 more than the other. Find the numbers
Answer:
104
Step-by-step explanation:
x+37=141
subtract 37 from both sides
-37=141-37
x= 104
Step-by-step explanation:
x = First number
x + x + 37 = 141 (Because we know that the 2nd number is 37 more than the first, we can just say x + 37.)
2x + 37 = 141 (Combine like terms.)
2x = 104 (Subtract 37 from both sides.)
x = 52 (Divide 2 from both sides.)
Now we know that the first number is 52. Now we just add the 37 to 52 to find the second number.
37 + 52 = 89 = Second number
Proof: 52 + 89 = 141
4-2y+3=-9
What is y?
y = 8
hope this helps :)
What ratio is equivalent to 20/10
Hello There!
The answer to your problem is 10:5 or 2:1
How to get 10:5
To get 10:5 you divide a number that can go into 20 and 10 which is 2. You divide 20/2 and 10/2 and get 10:5.
How to get 2:1
To get 2:1 you divide a number that can go into 10 and 5 which is 5. You divide 10/5 and 5/5 and get 2:1.
Hope This Helps!
The equivalent ratio of 20 : 10 will be 40/20 or 40 : 20.
What are ratios and proportion?
Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other. A statement expressing the equality of two ratios A:B and C:D is called a proportion. We can express proportion as -
A : B ∷ C : D
AND
A x D = B x C
Product of extremes equal to product of means.
Given is the ratio 20 : 10
The equivalent ratio of 20 : 10 will be -
20 : 10 = 20/10 = (20 x 2)/(10 x 2) = 40/20 = 40 : 20
Therefore, the equivalent ratio of 20 : 10 will be 40/20 or 40 : 20.
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Please help me I’m terrible at algebra.
Answer:
72 lbs
Step-by-step explanation:
t=tail h=head b=body
t = 9
h = t + .5b
b = h + t
Substitute
b = h + 9
h = 9 + .5b
h = 9 + .5h + 4.5
.5h = 13.5
h = 27
b = 36
TOTAL = t + h + b = 27 + 36 + 9 = 72
When plotting point on the coordinate plane below, which point would lie on the y-axis?
Answer:
The attached picture shows the location of each of the coordinates on the Cartesian plane. Hence, (0, 1) is the coordinate that lies on the y- axis.
Step-by-step explanation:
The solution to the question above is answered thus:
Note that the first value in each bracket is for x while the other is for y. Hence; 0, 7, 6 and 8 are value of x while 1, 0, 8 and 2 are values of y.
Thus:
Coordinate (0, 1) lies on the y - axis.
Coordinate (7, 0) lies on the x - axis.
Coordinates (6, 8) and (8, 2) lie on the 1st quadrant of the Cartesian plane
Coordinates.
Therefore, coordinate (0, 1) is the answer because it lies on the y- axis.
The answer is (0,1)
What is the co-ordinate system?In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
Given here: The points (0,1), (7,0), (6,8), (8,2)
For the point to lie on the y-axis its x-coordinate or abscissa must be zero
Only (0,1) satisfies this.
Hence, The answer is (0,1)
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construct a polynomial function with the stated properties. third degree with zeros of -2,-1, and 3 and passes through the point (2,12)
Answer:
[tex]f(x) = - (x + 2)(x + 1)(x - 3)[/tex]
Step-by-step explanation:
Let f(x) be the 3rd degree polynomial function.
The roots of this function are:
x=-2, x=-1 and x=3.
The factored form is:
[tex]f(x) = a(x + 2)(x + 1)(x - 3)[/tex]
This equation passes through (2,12)
This implies that;
[tex]a(2 + 2)(2+ 1)(2 - 3) = 12 \\ - 12a = 12 \\ a = - 1[/tex]
The polynomial function is
[tex]f(x) = - (x + 2)(x + 1)(x - 3)[/tex]
pLeAsE hElP! HuRrY!
Solve for A:
14a < 112
A.) a < -8
B.) a > 8
C.) a > -8
D.) a < 8
2x - 4(x + 2) = -2X-8
Answer:
x= 0
Step-by-step explanation:
in order to find the value of x in the 2x - 4(x + 2) = -2X-8
we are going to apply bodmas rule by first opening the bracket
we have,
2x-4x-8 = 2x -8
we proceed to collect the like terms
2x -4x-2x = -8 +8
-4x = 0
divide both sides by -4
-4x/-4 = 0/-4
x= 0
-4x + 26 = -2 whats x?
Answer:
The value of x is equal to 7
Step-by-step explanation:
if -4x + 26 = -2
-4x = -2 - 26
-4x = - 28
Divide both sides by -4, then we will have
x = -28/-4
x = 7
Steps to solve:
-4x + 26 = -2
~Subtract 26 to both sides
-4x + 26 - 26 = -2 - 26
~Simplify
-4x = -28
~Divide -4 to both sides
-4x/-4 = -28/-4
~Simplify
x = 7
Best of Luck!
Alyssa and Gabriel play the following game. Alyssa rolls a die. If she rolls a 1, 2, or 3, Gabriel gives Alyssa $4. If Alyssa rolls a 4 or 5, Gabriel gives Alyssa $1. However, if Alyssa rolls a 6, she gives Gabriel $12.
a) Determine Alyssa's expectation.
b) Determine Gabriel's expectation.
11.3 #12
Answer:
Part a) Alyssa's expectation is equal to $0.33
Part b) Gabriel's expectation is equal to -$0.33
Step-by-step explanation:
we know that
The expected value is the probability of winning multiplied by the value you get when you win, plus the probability of losing multiplied by the value you get when you lose (which is negative as it is a loss).
Part a) Determine Alyssa's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
The probability is 3/6
so
we have
[tex]\frac{3}{6}(4)=\$2[/tex]
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
The probability is 2/6
so
we have
[tex]\frac{2}{6}(1)=\$0.33[/tex]
3) if Alyssa rolls a 6, she gives Gabriel $12
The probability is 1/6
so
we have
[tex]-\frac{1}{6}(12)=-\$2[/tex] ---> is negative because is a loss
therefore
Alyssa's expectation is equal to
[tex]\$2+\$0.33-\$2=\$0.33[/tex]
Part b) Determine Gabriel's expectation
we know that
1) If Alyssa rolls a 1, 2, or 3, Gabriel gives Alyssa $4
Is a loss for Gabriel
The probability is 3/6
so
we have
[tex]-\frac{3}{6}(4)=-\$2[/tex] ---> is negative because is a loss
2) If Alyssa rolls a 4, or 5, Gabriel gives Alyssa $1
Is a loss for Gabriel
The probability is 2/6
so
we have
[tex]-\frac{2}{6}(1)=-\$0.33[/tex] ---> is negative because is a loss
3) if Alyssa rolls a 6, she gives Gabriel $12
Is a win for Gabriel
The probability is 1/6
so
we have
[tex]\frac{1}{6}(12)=\$2[/tex]
therefore
Gabriel's expectation is equal to
[tex]-\$2-\$0.33+\$2=-\$0.33[/tex]
The expected outcomes for both Alyssa and Gabriel from the game are $0. This is calculated using the probabilities of each outcome and their respective gains or losses.
Explanation:In the game between Alyssa and Gabriel, we are to calculate the expected outcomes for both players. To calculate the expectation, we will weigh the possible outcomes ($4, $1, -$12 for Alyssa and -$4, -$1, $12 for Gabriel) by their probabilities.
The dice has six faces, so the probability for each outcome is determined by the number of corresponding faces divided by six. Let's calculate the expectation for both:
Alyssa's expectation: (1/2 * $4) + (1/3 * $1) - (1/6 * $12) = $2 - $2 = $0. Gabriel's expectation: -(1/2 * $4) - (1/3 * $1) + (1/6 * $12) = -$2 + $2 = $0.
So, both Alyssa and Gabriel have an expected gain of $0 from this game.
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Which number is a factor of 22 , but not a multiple of 2?
Answer:
11
Step-by-step explanation:
i think.............
4,139 divided by 14 equals what?
Answer:
that would be 57,946
Answer: 295.642 (Work is shown below in the image)
Step-by-step explanation:
−4 5/9+8/9+ 0+0+0+0+0+0+0+0=
Answer:
-3.66666666668
Step-by-step explanation:
The zero's you do not have to add because they have to content or value.
-4 5/9 into improper = 31/9 = -4.55555555556
8/9 = 0.88888888888
ADD
[tex]\left\begin{array}{ccc}-4.55555555556\\+\\0.88888888888\end{array}\right\\---------[/tex]
-3.66666666668
Hope this helps you!
Have a good night! :)
Answer:
-3.66666666668
Step-by-step explanation:
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, -13, and 5 + 4i
f(x) = x4 - 8x3 - 12x2 + 400x - 1599
f(x) = x4 - 200x2 + 800x - 1599
f(x) = x4 - 98x2 + 800x - 1599
f(x) = x4 - 8x3 + 12x2 - 400x + 1599
Answer:
third option
Step-by-step explanation:
Given f(x) has zeros x = a, x = b, then
the factors are (x - a), (x - b) and the polynomial is the product of the factors.
Complex zeros occur as conjugate pairs, thus
5 + 4i is a zero then 5 - 4i is a zero
The zeros are x = 3, x = - 13, x = 5 + 4i, x = 5 - 4i, thus the factors are
(x - 3), (x - (- 13)), (x - (5 + 4i)), (x - (5 - 4i)), that is
(x - 3), (x + 13), (x - 5 - 4i), (x - 5 + 4i)
= (x - 3), (x + 13), ((x - 5) - 4i), ((x - 5) + 4i)
The polynomial is the product of the factors
f(x) = (x - 3)(x + 13)((x - 5) - 4i)((x - 5) + 4i) ← expand factors in pairs
= (x² + 10x - 39)((x - 5)² - 16i²) → i² = - 1
= (x² + 10x - 39)(x² - 10x + 25 + 16)
= (x² + 10x - 39)(x² - 10x + 41) ← distribute
= [tex]x^{4}[/tex] - 10x³ + 41x² + 10x³ - 100x² + 410x - 39x² + 390x - 1599 ← collect terms
= [tex]x^{4}[/tex] - 98x² + 800x - 1599
Answer:
The third option
Step-by-step explanation:
Write an equivalent expression for x + x + x + 2x + x
Answer:
6x
Step-by-step explanation:
x + x + x + 2x + x
Simplify the equation
4x + 2x
6x
Hope this was useful to you!
How many tens are in 50,000
If one factor of x2 + 2x - 24 is (x+6), what is the other factor?
(x+8)
(x-8)
(x+4)
(x-4)
Answer:
( x - 4)
Step-by-step explanation:
x² + 2x - 24
From here, you must find the two factors of -24 (the first and third terms' coefficients multiplied together) that add up to 2 (the middle terms coefficient)
( x - 4) ( x + 6)
Other factor of x² + 2x - 24 is (x - 4).
What is factor?Factors and multiples are two related concepts in math. A factor is a number that divides the given number exactly with 0 as the remainder.
Given expression
x² + 2x - 24 has factor (x + 6)
So, the expression should be divisible by (x + 6)
(x² + 2x - 24)/(x + 6)
It can be written as
(x² + 6x - 4x -24)/(x + 6)
Factoring out common factor
(x (x + 6) - 4 (x + 6))/(x + 6)
factoring out common factor
(x + 6)(x - 4)/(x + 6)
Simplifying
= (x - 4).
Hence, (x - 4) is other factor of x² + 2x - 24.
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Somebody please help me I only have 46 min ! Please ASAP !
7/-21=7/4.58=350/229=1whole number 121/224
Ariyonne claims that (6,3) is the point of intersection of the lines y=4x-2 and y=1/2x+5. Is she correct? How do you know ?
In order to solve the following system of equations by subtraction, which of
the following could you do before subtracting the equations so that one
variable will be eliminated when you subtract them?
4x – 2y = 7
3x – 3y=15
A. Multiply the top equation by 1/3
B. Multiply the top equation by 3 and the bottom equation by 4.
C. Multiply the top equation by-3 and the bottom equation by 2.
D. Multiply the top equation by 15 and the bottom equation by 7.
Answer:
B
Step-by-step explanation:
B produces the term 12x that cancels out after subtraction.
In order to eliminate one variable by subtracting, you should multiply the top equation by -3 and the bottom equation by 2. In doing so, this will make the coefficients of y equal and opposite, allowing this variable to be eliminated when the two equations are added together.
Explanation:The question relates to the method of solving a system of linear equations by subtraction. In order to eliminate one variable when subtracting these equations, we would need to manipulate the equations such that the coefficients of one variable are exact opposites. Hence, the objective is to make the coefficients of y, -2 and -3, opposite each other.
To achieve this, the correct answer is C. Multiply the top equation by -3 and the bottom equation by 2.
By performing these multiplications we'll have:
-12x + 6y = -21.
6x - 6y = 30.
Now, if we add these two equations, we'll be able to eliminate the y variable and can proceed to solve for x.
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U. AD-3
3. One of the acute angles in a right triangle has a measure of 34.6°. What is the measure of the other acute
angle?
a. 145.40
c. 55.4°
b. 34.6°
d. 90°
Solution:
Given that,
One of the acute angles in a right triangle has a measure of 34.6°
The sum of the three angles of a triangle is always 180 degrees.
Also, that the measure of a right angle is always 90 degrees
Let "x" be the other acute angle
Therefore,
x + 90 + 34.6 = 180
x + 124.6 = 180
x = 180 - 124.6
x = 55.4
Thus the measure of other acute angle is 55.4 degrees
Answer:
Yes, what the other person said
Step-by-step explanation: basically you subtract 90.0 - 34.6
A swimming pool is shown below.
Two maintenance workers correctly found the total area of the pool by adding the areas of 3 rectangles. But each worker wrote a different expression for the area.
Which could be the expressions the two workers wrote?
Answer:
the answer is c
Step-by-step explanation
Answer:
c
Step-by-step explanation: