10(1 + 3b) = -20
Isolate b.
Apply the distributive property: a(b + c) = ab + ac.
10(1 + 3b) = -20
10 + 30b = -20
Subtract 10 from both sides.
10 + 30b - 10 = -20 - 10
30b = -30
Divide both sides by the coefficient, 30.
b = -1
Answer:-1
The length of a rectangle is 6 inches longer than it is wide. If the area is 40 square inches, what are the dimensions of the rectangle?
Answer:
The length is 10 inches, and the width is 4 inches.
By creating a quadratic equation using the known facts and algebra, we can determine that the dimensions of the rectangle with an area of 40 square inches are length= 10 inches and width= 4 inches.
Explanation:This problem is a classic example of using algebra to solve for unknown dimensions. Given that the area (A) of a rectangle equals its length (L) times its width (W), written as A = L x W, you can substitute the given values into this formula. You're told the length is 6 inches longer than the width, which you can denote in algebra as L = W + 6. Secondly, you're given that the area is 40 square inches. Substituting these values gives us the following equation: 40 = W(W + 6).
Solving this equation will give us the width, and substituting the width into the formula L = W + 6, gives us the length.
Solving the Equation:
First, distribute the width on the right side of the equation to get 40 = W^2 + 6W. Re-arranging terms gives W^2 + 6W - 40 = 0. Factoring this quadratic equation yields (W - 4)(W + 10) = 0. Setting each factor equal to zero and solving for W gives W = 4 and W = -10. Because a width cannot be negative, the width of the rectangle is 4 inches. Substituting W = 4 into the length equation results in L = 4 + 6 = 10 inches. Hence, the dimensions of the rectangle are Length = 10 inches and Width = 4 inches.
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Step by step answer for
1/2n +3/4n=1/2
let's keep in mind that we have denominators of 2, 4 and 2, and thus we can use their LCD of 4, and multiply both sides by that LCD to do away with the denominators, let's proceed,
[tex]\bf \cfrac{1}{2}n+\cfrac{3}{4}n=\cfrac{1}{2}\implies \stackrel{\textit{multipying both sides by }\stackrel{LCD}{4}}{4\left( \cfrac{1}{2}n+\cfrac{3}{4}n \right)=4\left( \cfrac{1}{2} \right)}\implies 2n+3n=2 \\\\\\ 5n=2\implies n=\cfrac{2}{5}[/tex]
Six less than a number is greater than 54
Answer:
6<x>54 ASK YOUR TEACHER
Step-by-step explanation:
Solve by elimination
-5x+8y=-27
-8x+7y=-20
Answer:
x = -1 , y = -4
Step-by-step explanation by elimination:
Solve the following system:
{8 y - 5 x = -27 | (equation 1)
7 y - 8 x = -20 | (equation 2)
Swap equation 1 with equation 2:
{-(8 x) + 7 y = -20 | (equation 1)
-(5 x) + 8 y = -27 | (equation 2)
Subtract 5/8 × (equation 1) from equation 2:
{-(8 x) + 7 y = -20 | (equation 1)
0 x+(29 y)/8 = (-29)/2 | (equation 2)
Multiply equation 2 by 8/29:
{-(8 x) + 7 y = -20 | (equation 1)
0 x+y = -4 | (equation 2)
Subtract 7 × (equation 2) from equation 1:
{-(8 x)+0 y = 8 | (equation 1)
0 x+y = -4 | (equation 2)
Divide equation 1 by -8:
{x+0 y = -1 | (equation 1)
0 x+y = -4 | (equation 2)
Collect results:
Answer: {x = -1 , y = -4
The angles X degree and (90-x degree) are
Answer:
Complementary angles
Step-by-step explanation:
Complementary angles sum to 90°, that is
x + 90 - x = 90°
Thus x and (90 - x) are complementary angles
what is the total amount?
Total amount of what?
$8.75 * 7.5
about $65.63
Forgive me if I'm wrong
Hope this helps!
50pts!! Which expression is equivalent to the polynomial given below? 54x+30
A.) 9(5x+5)
B.) 6(9x+30)
C.) 6(9x+5)
D.) 6(9x+4)
Answer:
6(9x+5)
Step-by-step explanation:
6*9x = 54x
6*5 = 30
The expression should be 6(9x+5)
Given information;The equation is 54x + 30
Calculation of an expression:A polynomial represents an expression that comprises of indeterminates and coefficients, which includes only the operations of addition, subtraction, multiplication, and a non-negative integer.
So,
= 54x + 30
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Help it’s due by the end of class
Answer:
A
Step-by-step explanation:
Let's see...
It's a cube, so the total volume will be one length cubed or 10^3 which is 1000.
(2500 g)/(1000 cm^3) = [tex]2.5 g/cm^3[/tex]
I'm pretty sure the answer is A because it's the only one with correct scientific notation.
CAN SOMEONE HELP ME WITH THIS????????????????
[tex]\text{Hello there!}\\\\\text{We're trying to find the area of the shape}\\\text{We can do this by finding the area for the different shapes, then adding}\\\text{them together}\\\\\text{We can find the area of the rectangle,} \,\,84\cdot66=5,544\\\\\text{To find the area of the half circle, we would use the equation:}\,\,A=\frac{3.14r^2}{2}\\\\\text{The radius is half of the diameter, therefore it is 33. Plug 33 in r}\\\\A=\frac{3.14(33)^2}{2}\\\\\text{Solve:}\\\\A=\frac{3.14(33)^2}{2}\\[/tex]
[tex]A=\frac{3.14(1089)}{2}\\\\A=\frac{3419.46}{2}\\\\\text{Divide by 2}\\\\A=1709.73\\\\\text{Since there's two half circles, we would add 1709.73 twice}\\\\\text{Add all the areas together}\\\\1709.73+1709.73+5,544=8963.46\\\\\large\boxed{\text{Area:}\,\,8963.46\,\,\text{m}^2}}[/tex]
How to write 12,430,000 in expanded form?
find the possible values of a if the points with the given coordinates are the indicated distance apart.
1. (1, a), (3, -2); d=5
Answer:
Possible values of a = 2.58 and -6.58.
Step-by-step explanation:
Using the distance formula
√(3- 1)^2 + (-2-a)^2) = 5
(3- 1)^2 + (-2-a)^2 = 25
4 + 4a + a^2 + 4 = 25
a^2 + 4a - 17 = 0
a = [-4 +/- √(4^2 - 4*1*-17) ] / 2
a = -2 +/- √84 / 2
a = 2.58, -6.58.
ILL MARK BRAINLIEST ASAP IF CORRECT Write the equation of the quadratic function with roots -9 and and -3 and a vertex at (-6, -1).
Answer:
see explanation
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h. k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (- 6, - 1), thus
y = a(x + 6)² - 1
To find a substitute one of the roots into the equation
Using (- 3, 0), then
0 = a(- 3 +6)² - 1
0 = 9a - 1 ( add 1 to both sides )
1 = 9a ( divide both sides by 9 )
a = [tex]\frac{1}{9}[/tex], thus
y = [tex]\frac{1}{9}[/tex](x + 6)² - 1 ← in vertex form
Expand factor and simplify
y = [tex]\frac{1}{9}[/tex] (x² + 12x + 36) - 1 ← distribute
y = [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 4 - 1
= [tex]\frac{1}{9}[/tex] x² + [tex]\frac{4}{3}[/tex] x + 3 ← in standard form
Which property of real numbers is shown below?
-6+6=0
associative property of addition
commutative property of addition
identity property of addition
inverse property of addition
O
Answer:
The inverse property of addition.
Step-by-step explanation:
The number 6 is added to its inverse -6.
The property of real numbers (-6) + 6 = 0 will be Inverse property of addition. Then the correct option is D.
What are the properties of the Addition?Any of the many numerical laws governing how values are added.
Some Addition properties are as follows:
Associative property of addition – The total is unchanged when the order of the sub-blocks is changed.
For example, (2 + 3) + 4 = 2 + (3 + 4)
Commutative property of addition – No matter how the addends are arranged, the result remains constant.
For example, 4 + 2 = 2 + 4
Identity property of addition – The integer is that summation of 0 and that value.
For example, 0 + 4 = 4
Inverse property of addition – Zero is the result of adding any integer to its inverse.
For example, a + (-a) = 4
The property of real numbers -6+6=0 will be Inverse property of addition.
Then the correct option is D.
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If Bob paid $41.44 for 14 gallons what is the price of gas per gallon
Please need help on this
Answer:
there is an 88% chance it will land on teal, because if you do 16/18, you get 0.8 repeating. then, you multiply by 100 and get 88%
What is the simplified expression for 3 power 3 multiplied by 3 power 3 over 3 power 4? 30 31 32 34
Answer:
The simplest form of the expression is 3² ⇒ 3rd answer
Step-by-step explanation:
- The expression is 3 power 3 multiplied by 3 power 3 over 3 power 4
∵ 3 power 3 = 3³
∵ multiplied by 3 power 3 = × 3³
∵ over 3 power 4 = ÷ [tex]3^{4}[/tex]
- Lets write all of them in one expression
∴ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]
- All the numbers in the expression is 3 to the power
∴ The expression have the same base 3
- Remember: if we have numbers of same base multiplied then we
add their powers and if divided then we subtract their powers
[tex]\frac{a^{m}*a^{n}}{a^{q}}=a^{m+n-q}[/tex]
- Lets use this rule to simplify the expression
∵ The expression = [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex]
- Use the rule of the same base above
∴ [tex]\frac{3^{3}*3^{3}}{3^{4}}[/tex] = [tex]3^{3+3-4}=3^{6-4}=3^{2}[/tex]
∴ The simplest form of the expression is 3²
Answer:
3 to the 2nd power.
Step-by-step explanation:
Karina has determined that the weight of a newborn elephant increases at a rate of 6% per week for the first 14 weeks. She
needs to determine how much weight a baby elephant will gain on the 14th week if it weighs 92 lbs. at birth. Write the explicit
formula of the geometric sequence that could be used to model this scenario.
This is an exponential growth problem.
The formula is y = a(1+r)^x
Y would be the final answer
a is the starting value
r is the percent of growth
x is the amount of time ( number of weeks)
The equation is:
y(x) = 92(1.06)^x
For 14 weeks replace x with 14:
y(14) = 92(1.06)^14 = 208 pounds.
Answer: W(n) = 92lb*1.06^n
and W(14) = 92lb*1.06^14 = 208lb
Step-by-step explanation:
We know that at the beginning the baby elephant weighs 92Lbs, and for each week it augments by a 6% (or 0.06 in decimals)
Then, at the end of the first week, the weight is:
92lb*1.06 = 97.52lb
at the end of the second week:
(92lb*1.06)*1.06 = 103.37lb
and so on, so you can see that the pattern is:
W(n) = 92lb*1.06^n
where n is the number of weeks after the birth
W(0) = 92lb
W(1) = 97.52lb
...
And we want to know the weight at the end of the 14th week, so we must find:
W(14) = 92lb*1.06^14 = 208lb
please help 21 points!!!!!
Step-by-step explanation:
The measure of angle y is 62°.
I solve this by
We know: Measures of interior angles in a triangle add up to 180°.
Therefore we have the equation:
60° + 58° + y = 180°
118° + y = 180° subtract 118° from both sides
118° - 118° + y = 180° - 118°
y = 62°
The measure of angle x is 122°.
I solve this by
Angles 58° and x are supplementary angles.
Supplementary angles add up to 180°.
Therefore we have the equation:
x + 58° = 180° subtract 58° from both sides
x + 58° - 58° = 180° - 58°
x = 122°
X over 4 greater than or equal to negative 8
x/4 >= -8
Multiply both sides by 4.
x >= (-8)(4)
x >= -32
The value of X is greater than or equal to -32.
Explanation:To solve the inequality X/4 ≥ -8, we need to isolate the variable X. Firstly, we can multiply both sides of the inequality by 4 to get rid of the denominator: X ≥ -32. This means that the value of X is greater than or equal to -32. In interval notation, we can represent this as (-32, ∞).
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Depending on the cycle, washing a load of
clothes takes from 22 to 28 minutes. Diying
takes an additional 20 to 30 minutes. What
are the woun and maximum total times
to complete a load of laundry?
Final answer:
The time to complete a load of laundry ranges from a minimum of 42 minutes to a maximum of 58 minutes, combining the shortest and longest durations for both washing and drying cycles respectively.
Explanation:
The question asks about calculating the minimum and maximum total times for completing a load of laundry, including washing and drying cycles. The minimum time for washing is 22 minutes, and the minimum time for drying is 20 minutes. Therefore, the minimum total time to complete a load of laundry is 22 + 20 = 42 minutes.
On the other end, the maximum time for washing is 28 minutes, and the maximum time for drying is 30 minutes. The maximum total time to complete a load of laundry is 28 + 30 = 58 minutes.
In conclusion, the entire process of doing laundry, including both washing and drying, takes between 42 and 58 minutes in total.
Find the values of x and y.
(10x – 61)°
(18y + 5)°
(x + 10)°
Answer:
Part 1) The value of x is 21
Part 2 The value of y is 8
Step-by-step explanation:
step 1
Find the value of x
we know that
[tex](10x-61)\°+(x+10)\°=180\°[/tex] ------> by supplementary angles (linear pair)
[tex]11x-51=180[/tex]
[tex]11x=180+51[/tex]
[tex]11x=231[/tex]
[tex]x=21[/tex]
step 2
Find the value of y
we know that
[tex](10x-61)\°=(18y+5)\°[/tex] ----> by vertical angles
substitute the value of x and solve for y
[tex](10(21)-61)\°=(18y+5)\°[/tex]
[tex](149)\°=(18y+5)\°[/tex]
[tex]18y=149-5[/tex]
[tex]18y=144[/tex]
[tex]y=8[/tex]
Answer:
x=21 y=8
Step-by-step explanation:
Factorise fully 5x-15
To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms. The expression 5x - 15 can be factorised fully by finding the greatest common factor, which is 5. So the expression factorised fully is 5(x - 3).
Explanation:To factorise fully the expression 5x-15, we must search for the greatest common factor (GCF) that can be taken out of both terms.
The GCF of 5x and 15 is 5. Thus, we can pull 5 outside of the equation and divide each term by 5.
The equation becomes: 5(x - 3).
So, the expression 5x - 15 factorised fully is 5(x - 3).
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1 MP Reason There are 12,600 insects on display at the new
Science Center exhibit. Explain how you can use base-ten
blocks to show the value of the digit 2 in 12,600.
Answer:
The value of the digit 2 in the number 12,600 is 2,000
Step-by-step explanation:
we have the number 12,600
Rewrite the number in expanded form (write the number in its digits value)
[tex]12,600=10,000+2,000+600[/tex]
so
The value of the digit 1 in the number is 10,000
The value of the digit 2 in the number is 2,000
The value of the digit 6 in the number is 600
Factor the expression: (9x)(9x)+12x+4
Answer:
81x^2 + 12x + 4
Step-by-step explanation:
This expression doesn't factor
What does 70 times 500
Answer:
35000
Step-by-step explanation:
Multiply 7 by 5 and you would get 35, then add the zeros
Answer:
70*500= 35000
Step-by-step explanation:
What is -c - d
c = -3 and d = -6
Answer:
-3
Step-by-step explanation:
-(-3) = 3
-(-6) = 6
-3 - (-6) = 3
-c - d
c = -3
-3 - d
d = -6
-3 - (-6)
=-3+6
=3
Answer:
Step-by-step explanation:
-3 - (-6) = x (u would use Keep Change Flip [KCF] to solve)
-3 + 6 = x
3=x
so the answer is 3
Hope this helps!!
Consider the expression (x 6) – 3x
What is the value of the expression evaluated for x = 12?
Answer:
-26
Step-by-step explanation:
Please help me I help with this.
Answer:4(y+6)
Step-by-step explanation: y from -9 to 9
go to wolfram math to see the graph because i cant draw it
I hope this helps you.
Calcular el volumen en m3 de la esfera en el que el área de uno de sus círculos maximos es 36pim2
Answer:
The volume of the sphere is [tex]V=288\pi\ m^3[/tex]
Step-by-step explanation:
The question in English is
Calculate the volume in m^3 of the sphere in which the area of one of its maximum circles is 36pi m^2
we know that
The radius of the maximum circle in the sphere is equal to the radius of the sphere
Step 1
Find the radius of the maximum circle
The area of the circle is
[tex]A=\pi r^{2}[/tex]
we have
[tex]A=36\pi\ m^2[/tex]
substitute and solve for r
[tex]36\pi=\pi r^{2}[/tex]
Simplify
[tex]36=r^{2}[/tex]
take the square root both sides
[tex]r=6\ m[/tex]
Step 2
Find the volume of the sphere
The volume of the sphere is
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
substitute the value of r
[tex]V=\frac{4}{3}\pi (6)^{3}[/tex]
[tex]V=288\pi\ m^3[/tex]
In segment AC, the midpoint is B. If segments AC = 5x-9 and AB = 2x, what is the measure of segment AC.
Answer:
The measure of segment AC is 36 units
Step-by-step explanation:
- The mid-point divides the segment into two equal parts in length
- B is the mid point of segment AC
- That means B divides segment AC into two equal parts in length
∴ AB = BC
∵ AC = 5x - 9
∵ AB = 2x
- The two parts AB and BC are equal in length
∴ BC = 2x
∵ AC = AB + BC
- Substitute the values of AB and BC in the expression of AC
∴ AC = 2x + 2x
∴ AC = 4x
∵ AC = 5x - 9
- Equate the two values of AC
∴ 5x - 9 = 4x
- Add 9 to both sides
∴ 5x = 4x + 9
- Subtract 4x from both sides
∴ x = 9
- Substitute the value of x in any expression of AC
∵ AC = 4x
∵ x = 9
∴ AC = 4(9) = 36
* The measure of segment AC is 36 units