-6x + 5 - (x² – 2x – 6) = -6x+5-x²+2x+6 = -x²-4x+11
One number is 20 greater than another. If the lesser number is subtracted from three times the greater number, the difference is 84. Find the numbers.
Answer:
The numbers are 12 and 32.
Step-by-step explanation:
x = One number
x - 20 = Another number
3x - (x - 20) = 84 (If the lesser number is subtracted from three times the greater number, the difference is 84)
Let's solve for x, this way:
3x - (x - 20) = 84
3x - x + 20 = 84
2x = 84 - 20 (Subtracting 20 at both sides)
2x = 64
x = 64/2
x = 32 ⇒ x - 20 = 12
For the given problem, by denoting the lesser number as 'x', we can form and solve an algebraic equation to find 'x=12' and 'x+20=32', which are the lesser and the greater numbers respectively.
Explanation:This problem involves the concepts of algebraic equations. Let's denote the lesser number as 'x'. Therefore, the greater number becomes 'x+20' because it is 20 more than the lesser number. The problem states that three times the greater number subtracted by the lesser number is 84. So, we can translate that into the equation: 3*(x+20) - x = 84.
Solving this equation we get: 3x + 60 - x = 84, which simplifies further to 2x + 60 = 84. Deducting 60 from both sides gives 2x = 24. Finally, dividing by 2 gives x = 12 which is the lesser number. So the greater number becomes x + 20 = 12 + 20 = 32.
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Which equation has the same solutions as x^2+6x−7=0?
Question options:
(x+3)^2=2
(x−3)^2=2
(x+3)^2=16
(x−3)^2=16
Answer:
[tex] {(x + 3)}^{2} = 16[/tex]
Step-by-step explanation:
The given equation is
[tex] {x}^{2} + 6x - 7 = 0[/tex]
To find the equation that has the same solution, we complete the square.
Add the square of half the coefficient of x to both sides
[tex] {x}^{2} + 6x + {3}^{2} = {3}^{2} + 7 [/tex]
This becomes:
[tex] {x}^{2} + 6x + 9 = 9 + 7 [/tex]
Factor the first three terms to get a perfect square;
[tex]{(x + 3)}^{2} = 16[/tex]
The correct answer is C
The equation c. (x+3)^2=16 has the same solutions as the given equation x^2+6x−7=0.
Explanation:The equation that has the same solutions as the given equation x^2+6x−7=0 is c. (x+3)^2=16.
Step 1: Set the given equation equal to zero: x^2+6x−7=0.Step 2: Factor the equation. In this case, the equation does not factor easily, so we move on to step 3.Step 3: Use the quadratic formula: x = (-b ± √(b^2-4ac)) / (2a).Step 4: Substitute the values for a, b, and c from the given equation, we get x= 1 and x= -7.Step 5: Simplify the equation (x+3)^2=16. We get x = -3 + 4 = 1 and x = -3 - 4 = -7.Therefore, the equation (x+3)^2=16 has the same solutions as the given equation x^2+6x−7=0.
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What is the probability of picking a p
Answer:
1/26
Step-by-step explanation:
the probably is 1/26 becasue there is 26 letter in the alphabet
Solve the equation for x, x-3= -x+5
Answer:
x=4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Hope this helps!!! Brainliest is appreciated.
x−3=−x+5
Add x to both sides.
x−3+x=−x+5+x
2x−3=5
Add 3 to both sides.
2x−3+3=5+3
2x=8
Divide both sides by 2.
2x /2 = 8 /2
x= 4
Hong Kong’s tallest building international is 88 stories tall.
the former Sears Tower is eight stories taller than the Empire State Building. if all the buildings were stacked on top of each other the combine Heights would have 300 stories. how many stories does the Sears Tower have?
Final answer:
The Sears Tower has 110 stories. We found this by setting up an equation with the given information and solving for the number of stories in the Sears Tower.
Explanation:
To find out how many stories the Sears Tower has, we need to set up an equation using the information provided.
We know that Hong Kong's tallest building (International) is 88 stories tall, and the combined height of all the buildings stacked on top of each other is 300 stories. Let's assign the variable S to represent the number of stories in the Sears Tower and E to represent the number of stories in the Empire State Building. According to the question, the Sears Tower is eight stories taller than the Empire State Building, so we can express this relationship as S = E + 8.
Now, let's add up the stories of all three buildings: Hong Kong's International + Sears Tower + Empire State Building = 300. Substituting the given information and our variable S, we get the equation 88 + S + (S - 8) = 300.
Let's solve this equation:
Combine like terms: 88 + 2S - 8 = 300.Simplify: 2S + 80 = 300.Subtract 80 from both sides: 2S = 220.Divide both sides by 2: S = 110.Therefore, the Sears Tower has 110 stories.
Camille has a collection of 61 nickels and quarters worth $6.85. How many of each coin does she have?
Answer: 42 nickles 19 quarters
hope this was helpful
Camille has 42nickels and 19 quarters.
What is the relation between product and price?
The price depends on how much amount of product one has/consumes.
How to calculate the number of nickels and quarters?Let, Camille has 'y' no. of nickels.
Therefore, she has (61-y) no. of quarters.
We know that,
1 nickel = 5cents
1 quarter =25 cents
$6.85 = 685cents (as 1 dollar = 100cents)
now,
5*y+25*(61-y)=685
or,5y-25y=685-1525
or, 20y = 840
or, y= 42
Therefore, Camille has 42 nickels and (62-41)=19 quarters.
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Algebra 1, Section 7.10
Answer:
Option D, 7xy^5 + 2y^2 - 10
Step-by-step explanation:
Step 1: Pull out 3xy from all of the top
[tex]\frac{3xy(7xy^5+2y^2-10)}{3xy}[/tex]
The 3xy on top and the 3xy cancel to make: 7xy^5 + 2y^2 - 10
Answer: Option D, 7xy^5 + 2y^2 - 10
One baseball team won 15 games throughout their entire season. Of all their games, this
team won 75% of them. Given this, how many games in total did this baseball team play?
Round your answer to the nearest whole number if necessary.
Answer:
20
Step-by-step explanation:
To get the answer, you have to find what number 15 is 75 percent of.
you receive 20% off on a pair of pants that cost $25, how much would you pay?
PLEASE ANSWERRRRRRRRRR
True or False: In Electromagnetic waves the frequency of the wave determines how much energy that wave carries.
Answer:
True
Step-by-step explanation:
Answer: True
Step-by-step explanation:
In electromagnetic waves, the more the work, the greater the energy expended.
What is the length of the rectangle?
Step-by-step explanation:
[tex]area \: of \: rectangle \: = 60 \: {yards}^{2} \\ \therefore \: (w + 4) \times \: w = 60\\ \\ \therefore \: {w}^{2} + 4w -60 = 0 \\ \\ \therefore \: {w}^{2} + 10w - 6w -60 = 0 \\ \\ \therefore \: w({w} + 10) - 6(w + 10)= 0 \\ \\ \therefore \: ({w} + 10) (w- 6)= 0 \\ \therefore \: {w} + 10 = 0 \: or \: w- 6 = 0 \\ \therefore \: {w} = - 10 \: or \: w = 6 \\ \because \: sides \: of \: rectangle \: cant \: be \: negative \\ \therefore \: w \neq \: - 10 \\ \\ \therefore \: w = 6 \\ \\ \therefore \: w + 4 = 6 + 4 = 10 \\ \\ length \: of \: rectangle \: = 10 \: yards.[/tex]
The length of a rectangle is 10 yards, and its width is 6 yards. The rectangle's area is 60 square yards. The length is 4 yards more than the width.
Let's call the width of the rectangle "W" in yards. According to the information given, the length of the rectangle is 4 more than the width, so the length can be represented as "W + 4" yards.
The formula for the area (A) of a rectangle is:
A = Length × Width
In this case, we know that the area is 60 square yards, so we can set up the equation:
60 = (W + 4) × W
Now, we can solve for the width (W). First, expand the equation:
60 = W^2 + 4W
Next, rearrange the equation to set it equal to zero:
W^2 + 4W - 60 = 0
Now, we can solve this quadratic equation for W. You can do this by factoring, completing the square, or using the quadratic formula. In this case, I'll use the quadratic formula:
W = (-b ± √(b^2 - 4ac)) / (2a)
In this equation, a = 1, b = 4, and c = -60. Plug these values into the formula:
W = (-4 ± √(4^2 - 4 * 1 * (-60))) / (2 * 1)
W = (-4 ± √(16 + 240)) / 2
W = (-4 ± √256) / 2
W = (-4 ± 16) / 2
Now, you have two potential solutions for W:
1. W = (-4 + 16) / 2 = 12/2 = 6
2. W = (-4 - 16) / 2 = -20/2 = -10
Since the width of the rectangle cannot be negative, we take the positive value, which is W = 6 yards.
Now that we know the width, we can find the length, which is W + 4:
Length = 6 + 4 = 10 yards
So, the length of the rectangle is 10 yards.
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evaluate expression 1/2a-5b when a= -12 and b= -3
Answer: 9
Step-by-step explanation:
1/2 * -12= -6
5*-3= -15
-15- (-6)= -9
The recipe for a dozen muffins calls for 4 teaspoons of vanilla. Tyler is making 6 dozen muffins for a bake sale.
How many tablespoons of vanilla does he need? Remember: 1 tablespoon = 3 teaspoons.
Answer:
12
Step-by-step explanation:
3X4=12
Answer:
8 tablespoons
Step-by-step explanation:
its is 8 because 4 teaspoons per dozen and there are 6 dozens so 4 times 6 is 24, then 24 divided by 3 because thats how many teaspoons are in 1 tablespoon so its 8 tablespoons
Sam says the longest ski trail is more than three times the length of the shortest ski trail. Eli says it is less than three times the length. Who is correct? Explain.
Answer:
Sam
Step-by-step explanation:
Sam: Longest ski trail >3x x = shortest ski trail
Eli: Longest ski train< 3x
Sam is correct because the longest ski trail has to be greater than the shortest and it can't be less than.
if the 3rd and 6th terms of an h.p are 5/16 and 1/5 then ,
the 10th term is
Answer:
The tenth term is
[tex] \frac{1}{20} [/tex]
Step-by-step explanation:
The 3rd term of an AP is 1/16.
This implies that:
[tex]a + 2d = \frac{5}{16} - - - (1)[/tex]
The 6th term of an AP is 1/5.
This means that:
[tex]a + 5d = \frac{1}{5} - - - (2)[/tex]
Subtract equation 1 from equation 2.
[tex]5d - 2d = \frac{1}{5} - \frac{5}{16} [/tex]
[tex]3d = - \frac{9}{80} \\ \implies \: d = - \frac{3}{80} [/tex]
From equation (1)
[tex]a + 2( - \frac{3}{80} )= \frac{5}{16} \\ a - \frac{3}{40} = \frac{5}{16} \\ a = \frac{5}{16} + \frac{3}{40} \\ a = \frac{31}{80} [/tex]
The tenth term is:
[tex]a + 9d = \frac{31}{80} + 9( - \frac{3}{80} ) \\ = \frac{31}{80} - \frac{27}{80} = \frac{4}{80} = \frac{1}{20} [/tex]
A rectangle has an area of 56 square inches and a perimeter of 36 inches.
Complete the table and write a system of equations to represent the length and width of the rectangle.
Answer:
Table #1:
Length (L) | Width (W) | Area (56)
Table #2:
Length (2L) | Width (2W) | Perimeter (36)
Equation #1: L · W = 56
Equation #2: 2L + 2W = 36
Step-by-step explanation:
The following are the formulas used to find the area and the perimeter of a rectangle:
Area = L · W
Perimeter = L + L + W + W
If you group common variables, you can simplify the formula used to find the perimeter down to:
Perimeter = L + L + W + W
Perimeter = 2L + 2W (Since you're adding 2 of each)
Using these formulas, we can insert our values into them. We know that the rectangle has an area of 56 square inches meaning:
L · W = 56
We know that the rectangle has a perimeter of 36 inches meaning:
2L + 2W = 36
Answer:
Table #1:
Length (L) | Width (W) | Area (56)
Table #2:
Length (2L) | Width (2W) | Perimeter (36)
Equation #1: L · W = 56
Equation #2: 2L + 2W = 36
Step-by-step explanation:
What is the x and y intercept of this equation 12x+4y=24
Answer:
y = 6,x = 2
Step-by-step explanation:
Answer:y = 6,x = 2
Step-by-step explanation:Geometric figure: Straight Line
Slope = -6.000/2.000 = -3.000
x-intercept = 6/3 = 2
y-intercept = 6/1 = 6.00000
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
12*x+4*y-(24)=0
Step by step solution :
Step 1 :
Pulling out like terms :
1.1 Pull out like factors :
12x + 4y - 24 = 4 • (3x + y - 6)
Equation at the end of step 1 :
Step 2 :
Equations which are never true :
2.1 Solve : 4 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve 3x+y-6 = 0
Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).
"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.
In this formula :
y tells us how far up the line goes
x tells us how far along
m is the Slope or Gradient i.e. how steep the line is
b is the Y-intercept i.e. where the line crosses the Y axis
The X and Y intercepts and the Slope are called the line properties. We shall now graph the line 3x+y-6 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 6/1 so this line "cuts" the y axis at y= 6.00000
y-intercept = 6/1 = 6.00000
Calculate the X-Intercept :
When y = 0 the value of x is 2/1 Our line therefore "cuts" the x axis at x= 2.00000
x-intercept = 6/3 = 2
Calculate the Slope :
Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 6.000 and for x=2.000, the value of y is -0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.000 - 6.000 = -6.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -6.000/2.000 = -3.000
Geometric figure: Straight Line
Slope = -6.000/2.000 = -3.000
x-intercept = 6/3 = 2
y-intercept = 6/1 = 6.00000
Subtract
5 + 5q - (3q - y)
Answer:
2q+y+5
Step-by-step explanation:
Simplify the expression
The circumference C of a circle with radius r can be calculated using the formula
C=2πr. Which formula represents r in terms of C ?
A) r=2πC
B)r=C-2π
C)r=Cπ/2
D)r=C/2π
Answer:
D
Step-by-step explanation:
Given
C = 2πr ( isolate r by dividing both sides by 2π )
[tex]\frac{C}{2\pi }[/tex] = r → D
The circumference of a circle is defined as the distance around the circle.
The formula that represents r in terms of C is r = C/ 2π. The correct option is Option D
From the question, we are given the formula for the circumference of the circle C as :
C = 2πr
To represent in terms of C,
2πr = C
Divide both sides by 2π
2πr/2π = C/ 2π
r = C/ 2π
Therefore, the formula that represents r in terms of C is r = C/ 2π. The correct option is Option D
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A table is cut and placed along a wall. After its cut, the edge along the wall is 6 feet. What is the area of the table after it's cut in half?
Please help! I'm confused
Answer:
18 square feet
Step-by-step explanation:
the table was most likely 6 by 6 before getting cut. that is an area of 36 you could half that making 18 or make one of the 6s a 3 so it is 3 by 6 after the table is cut.
Brent took out a 48-month loan
for $16,000 to buy a car. If the
compound interest rate was 8%,
how much will he pay for the car
including interest?
Step-by-step explanation:
8/100(8 over 100)×16000=1280
1280+16000=17280
Answer:
$21,767.82
Step-by-step explanation:
48 months = 48/12 = 4 years
16000 × (1 + 8%)⁴
16000 × 1.08⁴
= 21,767.82336
Angle KJL measures (7x-8)° Angle KML measures (3x +
What is the measure of are KL?
8)º
JM
20
40
48
96°
Answer:
40°
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
1 Each tire on Bruno's delivery truck weighs 48.25
pounds. If his truck has 6 tires, what is the total
weight of the tires?
A 289.5 pounds C 282.5 pounds
B 283.5 pounds D 288.5 pounds
Joe has 30 vegetables. He wants to increase the amount vegetables by 60%. How many vegetables would he have?
Answer: 48 vegetables
Step-by-step explanation:
30 vegetables
Increase is by 60% = 0.6 x 30= 18
30+18= 48 vegetables
Answer:
48
Step-by-step explanation:
30 x 60% (.60) = 18.
30 + 18 = 48
What is the height of an object thrown when time is 6 seconds? Also explain how u got your answer
Answer:
[tex]946.4\ m[/tex]
Step-by-step explanation:
Let
h(t) ---> the height of an object in meters
t ----> the time in seconds
we have
[tex]h(t)=-2.6t^2+40t+800[/tex]
For t=6 sec
substitute in the quadratic equation the value of t and solve for h
[tex]h(6)=-2.6(6)^2+40(6)+800[/tex]
[tex]h(6)=946.4\ m[/tex]
A ______ is e ratio of a number to 100
Write the equation of a line in y = mx + b form that has a slope
of 7/3 and a y-intercept of 2.
Answer:
y = 7/3 x + 2
Step-by-step explanation:
y = mx+b is the slope intercept form of a line
where m is the slope and b is the y intercept
Substituting in what we know
y = 7/3 x + 2
Tori went to see a monster truck show at the local arena before the show Tori got to see the truck up close he noticed that each tire monster truck tire has a radius of about 6 feet Based on that radius what would be the distance around each tire
Answer:
37.70 feet
Step-by-step explanation:
-The radius of each tire is given as 6 feet.
-Distance around each tire is equivalent to the circumference of each tire.
#Circumference is calculated as:
[tex]C=\pi D=2\pi r\\\\=2\pi \times 6 \\\\=12\pi\\\\=37.70\ feet[/tex]
Hence, the distance around each tire is 37.70 feet
i need help with this question please
arc ABC = 4π[tex]\frac{134}{180}[/tex]
Step-by-step explanation:
Given,
∠BOA = 51° and ∠AOC=83°
We take O as the center
So, ∠BOC = 51°+83° = 134°
To find the arc ABC
Formula,
The relation between arc and radius is, s = rθ where s be the arc and θ be the angle measured in radian]
θ degree = θΠ×[tex]\frac{1}{180}[/tex] in radian
Hence,
arc ABC = 4π[tex]\frac{134}{180}[/tex]
a rectangle is 5 cm and other side is 3cm what is the perimeter of the rectangle? also what is the are of the same rectangle?
Answer:
Perimeter: 16 centimeters
Area: 15 square centimeters
I hope this helps! :)
Answer:
Step-by-step explanation:
so, the perimeter is 5+5+3+3 which is 16
and the area is 5 x 3 so it is 15