Which of the following are solutions to the equation below?Check all that apply.x2 – 6x + 40 = 6x + 5
a. -5 b. -6 c. 7 d. 5 e. 6
Answer:
c.7 and d.5
Step-by-step explanation:
Given the following equation :
[tex]x^{2}-6x+40=6x+5[/tex]
This equation is equivalent to the following equation :
[tex]x^{2}-6x+40=6x+5[/tex]
[tex]x^{2}-6x+40-6x-5=0[/tex]
[tex]x^{2}-12x+35=0[/tex]
Given an equation [tex]ax^{2}+bx+c=0[/tex] we can find the solutions using the quadratic equation (x1 and x2 are the solutions) :
[tex]x1=\frac{-b+\sqrt{b^{2}-4ac}}{2a}[/tex]
[tex]x2=\frac{-b-\sqrt{b^{2}-4ac}}{2a}[/tex]
Using this equations :
[tex]x^{2}-12x+35=0[/tex]
[tex]a=1\\b=-12\\c=35[/tex] ⇒
[tex]x1=\frac{-(-12)+\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=7[/tex]
[tex]x2=\frac{-(-12)-\sqrt{(-12)^{2}-4.(1).(35)}}{2.(1)}=5[/tex]
Given the two solutions x1 and x2 we can write the equation :
[tex]ax^{2}+bx+c=0[/tex] ⇒ [tex]a.(x-x1).(x-x2)=0[/tex] ⇒
[tex]x^{2}-12x+35=0[/tex] is equivalent to
[tex](x-7).(x-5)=0[/tex]
The solutions for this equation are 7 and 5.
Therefore, c.7 and d.5 are the solutions for this exercise.
The graph shows the altitude of a helicopter over time. A graph measuring altitude and time. A line runs through coordinates (0, 10,000) and (15, 4000) and shows a decrease in altitude as time increases What is the slope of the line and what does it mean in this situation? The slope is –2000 . This means that the helicopter descends 2000 ft each minute. The slope is –400 . This means that the helicopter descends 400 ft each minute. The slope is 400. This means that the helicopter ascends 400 ft each minute. The slope is 2000. This means that the helicopter ascends 2000 ft each minute. 1 2 3 4 5
We can calculate for the slope of the line using the formula:
m = (y2 – y1) / (x2 – x1)
From the given values:
m = (4,000 – 10,000) ft / (15 – 0) min
m = -400 ft/min
This means that the altitude is decreasing by 400 ft per minute.
> The slope is –400 . This means that the helicopter descends 400 ft each minute.
What is the range of f(x) = (3/4)^x – 4
Answer:
{y | y > –4}
Step-by-step explanation:
The range of f(x) = (3/4)^x - 4 is (-∞, -4].
Explanation:The range of the function f(x) = (3/4)^x - 4 can be determined by finding the minimum and maximum values that the function can reach.
First, let's determine the minimum value of f(x). The base of the exponent, 3/4, is less than 1, which means that as x approaches positive or negative infinity, the function approaches negative infinity. Therefore, the minimum value of f(x) is negative infinity.Next, let's determine the maximum value of f(x). Since the base is less than 1, as x approaches positive or negative infinity, the function approaches 0. However, f(x) can never actually reach 0 because of the constant -4 subtracted from it. Therefore, the maximum value of f(x) is -4.Putting it all together, the range of f(x) is (-∞, -4].
Write as a decimal: 203% 0.203 2.03 20.3 203
The decimal form of the given percent 203% is 2.03
What is percent?A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction. The word "percent" means "per hundred." So, whenever you see a number with a percent sign (%), you can imagine it as a fraction,
Percent is from the Latin adverbial phrase per centum meaning “by the hundred.” The Latin phrase entered English in the 16th century.
Example: 10% means 10 out of every 100. So if 10% of 500 people have ice cream, then 50 people have ice cream.
Given that, what is decimal form for the 203 percent,
Since, the percent is any number in its 100th part,
Therefore, 203% = 203/100
Since, it is 100 in the denominator,
The decimal will be put after two digits in the numerator,
Therefore,
203% = 203/100 = 2.03
Hence, the decimal form of the given percent 203% is 2.03
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15 POINTS
Is it possible for a system of equations to be both independent and inconsistent? Explain
When a system has one answer or in other words, the graphs of the equations intersect one time, the system is called a consistent system of linear equations and therefore the equations are independent.
When a system has no solution meaning, the graphs of the equations don’t interconnect at all, the system is known to be an inconsistent system of linear equations and the equations are independent.
So therefore, the answer is yes.
Kite WXYZ is graphed on a coordinate plane.
What is the area of the kite?
a.7 square units
b.8 square units
c.14 square units
d.16 square units
Answer-
Area of the kite is 14.0 sq.units
Solution-
[tex]\text{Area}_{WXYZ}=\text{Area}_{WXY}+\text{Area}_{WZY}[/tex]
From the graph, in the triangle WXY
Base = WY=4 units,
Height = 3 units
[tex]\text{Area}_{WXY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 3=6\ sq.unit[/tex]
From the graph, in the triangle WZY
Base = WY=4 units,
Height = 4 units
[tex]\text{Area}_{WZY}=\dfrac{1}{2} \cdot base\cdot height=\dfrac{1}{2} \cdot 4\cdot 4=8\ sq.unit[/tex]
[tex]\therefore \text{Area}_{WXYZ}=6+8=14\ sq.units[/tex]
describe two methods for adding and subtracting linear expressions
LM = JK then JK = LM
What property is this?
The principle being demonstrated is known as the Symmetric Property, which holds that if an equation or statement is valid, then its switched or flipped version will also be true.
Explanation:The question refers to a fundamental property in mathematics called the Symmetric Property. The Symmetric Property states that if an equation or statement is true, then its mirror or flipped version will also hold true. In this case, if LM = JK, then under Symmetric Property, it must be true that JK = LM.
For instance: If 5 = 2 + 3, then 2 + 3 = 5.
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Which of the following options represents the graph of the function shown below?
ƒ(x) = (x - 3)^3 1 1
ƒ(x) = (x - 3)^3 + 1
ƒ(x) = (x + 3)^3 - 1
ƒ(x) = (x + 3)^3 + 1
The function that best represents the graph of the function which is given is:
[tex]f(x)=(x-3)^2+1[/tex]
Step-by-step explanation:From the graph that is provided to us we observe that the graph passes through the point (3,1).
Hence, we will check which of the following function satisfies this point.
a)
[tex]f(x)=(x-3)^3-1[/tex]
when x=3 we see that:
[tex]f(x)=(3-3)^3-1\\\\i.e.\\\\f(x)=-1\neq 1[/tex]
Hence, option: a is incorrect.
c)
[tex]f(x)=(x+3)^3-1[/tex]
when x=3 we have:
[tex]f(3)=(3+3)^3-1\\\\i.e.\\\\f(3)=9^3-1\\\\i.e.\\\\f(3)=729-1\\\\f(3)=728\neq 1[/tex]
Hence, option: c is incorrect.
d)
[tex]f(x)=(x+3)^3+1[/tex]
when x=3 we have:
[tex]f(3)=(3+3)^3+1\\\\i.e.\\\\f(3)=9^3+1\\\\i.e.\\\\f(3)=729+1\\\\f(3)=730\neq 1[/tex]
Hence, option: d is incorrect.
Now we are left with option: b)
i.e.
b)
[tex]f(x)=(x-3)^2+1[/tex]
Also, when x=3 we have:
[tex]f(3)=(3-3)^2+1\\\\f(3)=0+1\\\\f(3)=1[/tex]
Hence, it passes through the point (3,1)
Also, when we will plot this function we observe that it matches the given graph.
Which of the following equations has the solution x= all real numbers?
a. 4(3−x)+6x=x+12−3x
b. 4(3−x)+6x=3x+12+2x
c. 4(3−x)+6x=3x+12−x
d. 4(3−x)+6x=3x+10−x
Option (b) 4(3-x)+6x=3x+12+2x is the equation that has the solution x = all real numbers because it simplifies to an identity, which is true for any value of x.
Among the given equations, the one that has the solution x = all real numbers is essentially an identity, meaning that for any value of x you plug into the equation, the equation will hold true. To determine which equation is an identity, each equation must be simplified.
Let's take option (b) as an example:
4(3−x)+6x=3x+12+2x
4∙3 - 4∙x + 6∙x = 3∙x + 12 + 2∙x
12 - 4∙x + 6∙x = 3∙x + 12 + 2∙x
12 + 2∙x = 5∙x + 12
12 - 12 + 2∙x - 2∙x = 5∙x - 2∙x + 12 - 12
0 = 3∙x - 3∙x
After simplifying, we end up with 0 = 0, which is an identity and is true for all values of x, hence this is the equation where x is all real numbers.
15x+14y+3x+7y simplified is
a.39xy
b.29x+10y
c.29xy+10xy
d.18x+21y
The simplification form of the expression 15x+14y+3x+7y is 18x + 21y option (D) 18x + 21y is correct.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
It is given that:
15x+14y+3x+7y
After simplification,
Adding like terms:
= 18x + 21y
Thus, the simplification form of the expression 15x+14y+3x+7y is 18x + 21y option (D) 18x + 21y is correct.
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The Yoga class you wish to take is offering two price quotes: $108 for 5 weeks as (15 classes) or $125 for 8 weeks (24 classes). How much per class would you save by taking the 8 week class?
A $2.10
B $2.05
C $1.99
D $1.89
Answer: Option 'C' is correct.
Step-by-step explanation:
Since we have given that
Cost for 5 weeks i.e. 15 classes = $108
Cost of per class is given by
[tex]\frac{108}{15}=7.2[/tex]
Cost for 8 weeks i.e. 24 classes = $125
Cost of per class is given by
[tex]\frac{125}{24}=5.21[/tex]
Amount of saving of per class by taking the 8 week class is given by
[tex]7.2-5.21=\$1.99[/tex]
Hence, Option 'C' is correct.
Mike collects toy cars. he decides to put all of his toy cars in a line so that he can count them. the 9th car in line ends up being exactly at the middle of the line. how many toy cars does mike have?
Answer:
17 cars
Step-by-step explanation:
Mike collects toy cars. He decides to put all of his toy cars in a line so that he can count them.
It is given that 9th car in the line ends up being exactly at the middle of the line.
This statement shows that before and after the middle car there were 8 cars.
So the cars in the line is 8 + 1(middle) + 8 = 17 cars
Mike have total 17 cars.
An Olympic sprinter runs 200 meters in 20.1 seconds. Calculate the runner's speed in miles per hour.
Write the point-slope form of the line that passes through (-8, 2) and is parallel to a line with a slope of -8. Include all of your work in your final answer. Type your answer in the box provided or use the upload option to submit your solution.
there are 8 boxes, which contain a total of 56 sweaters, in a store warehouse. If the store needs 35 sweaters, how many boxes should they take. can you explain please thank you
I NEED THIS ANSWERED ASAP! PLEASE!!
The height h (in feet) of an object t seconds after it is dropped can be modeled by the quadratic equation h = -16t^2 + h0, where h0 is the initial height of the object. Suppose a small rock dislodges from a ledge that is 255 ft above a canyon floor. Solve the equation h = -16t^2 + 255 for t, using the quadratic formula to determine the time it takes the rock to reach the canyon floor.
The time it takes the rock to reach the canyon floor is after 3.99seconds
Application of intercept to a functionThe intercept is the point where the axis is equal to zero. Give the quadratic equation that represents the height h (in feet) of an object t seconds after it is dropped expressed as:
h = -16t² + 255
The rock reaches the ground when h(t) = 0. Substitute
h = -16t² + 255
h = -16t² + 255 = 0
16t² = 255
t² = 255/16
t² = 15.9375
t = 3.99seconds
Hence the time it takes the rock to reach the canyon floor is after 3.99seconds
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A van travels 150 miles on 5 gallons of gas. how many gallons will it need to travel 630 miles?
What is the converse of the statement? "If you wash the dishes today, then I will wash the dishes tomorrow." Question 5 options: If I wash the dishes tomorrow, then you will wash the dishes today. If I will not wash the dishes tomorrow, then you will not wash the dishes today. If you wash the dishes today, I will dry the dishes today. If you do not wash the dishes today, then I will not wash the dishes tomorrow.
Answer:
Step-by-step explanation:dhdjdbfbd
What is the average speed of a person that travels 40 miles to their grandmothers house and then 40 miles back home in 6 hours?
The number of sides of a polygon that has n vertices is what?
The total number of sides in a polygon with n vertices is = n sides.
We have a Polygon with n vertices.
We have to determine the number of sides of this polygon.
What is Polygon?In geometry, a polygon can be defined as a plane, two-dimensional closed shape bounded with straight sides.
According to the question, we have -
A polygon with n vertices.
The total number of sides in a polygon with n vertices is = n sides.
The sides of the polygon are connected end to end in a cyclic order. The side with endpoints as nth and (n - 1)th vertices is connected to the side with endpoints as (n - 1)th and (n - 2)th vertices and so on.
Hence, the total number of sides in a polygon with n vertices is = n sides.
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Which of the following was a primary reason France sought to colonize North America?
A To reduce overpopulation in Europe
B To create communities founded on religious tolerance
C To profit from trading in furs and other goods
D To create joint ventures with other European powers
Answer: The answer is C on Quizizz.
Step-by-step explanation:
Factor a 2 bc + ab 2 c + abc 2
A. a2b2c2(a + b + c)
B. a2bc(a + b + c)
C..abc(a + b + c)
Answer:
abc(a + b + c)
That's your answer!!!
What is the first step of adding 12.65 + 30.75?
two parallel lines cut by a transversal. What is the value of x?
1. At the grocery store checkout, you watch at the register as it rings up your purchases and coupons. The prices were as follows:
$2.95
$1.19
$4.61
$1.74
$3.04
$8.83
$1.16
– $0.75 (coupon)
– $1.00 (coupon)
The register gives your total bill as $21.77. Estimate the total amount of the bill and use your answer to determine whether the total on the register is reasonable.
Answer:
estimate by rounded to the nearest dollars
2 +1 +5 +2 +3 +9 +1 = $23
-2
23-2 = 21
yes the amount is reasonable
Answer: 3+1+5+2+3+9+1-1-1=22
The total on the register is reasonable because if you estimate $21.77 to the nearest dollar you would get $22.00.
Step-by-step explanation:
REALLY NEED HELP I HAVE NO IDEA WHAT THE ANSWER IS
Isosceles triangle ABC has a perimeter of 96 centimeters. The base of the triangle is and measures 24 centimeters.
What is the measure of ?
12 cm
36 cm
48 cm
72 cm
Answer:
The measure of length of equal side is 36 cm each.
B is correct.
Step-by-step explanation:
Isosceles triangle ABC has a perimeter of 96 centimeters.
The base of the triangle is BC and measures 24 cm
We need to find the length of equal side of triangle.
AB=AC
The perimeter of triangle is 96 cm
AB + AC + BC = 96
AB + AB + 24 = 96 ( ∵ AB=AC)
2AB = 96-24
2AB = 72
AB = 36
Hence, The measure of length of equal side is 36 cm each.
What is 1.2+d+0.4=9.7?
Use the graph of the function to find its average rate of change from
=x−3
to
=x3
.
PLEASE HELP NO ONE EVER ANSWERS!
The average rate of change of the function over the interval is 2
Finding the average rate of change
From the question, we have the following parameters that can be used in our computation:
The graph
The interval is given as
From x = -3 to x = 3
The function is a quadratic function
This means that it does not have a constant average rate of change
From the graph
y = -8, when x = -3
y = 4, when x = 3
This means that
f(-3) = -8
f(3) = 4
The average rate is calculated using
Rate = (Change in y values)/(Change in corresponding x values)
So, we have
Rate = (4 + 8)/(3 + 3)
Evaluate
Rate = 2
Hence, the average rate of change is 2