Answer:
It's neither:
x =√ 9.000 = 3.00000 or :
x =√ 9.000 = -3.00000 or :
x =√ 8.000 = 2.82843 or :
x =√ 8.000 = -2.82843
Four solutions
Answer:
x^4 - 17x^2 + 72 = (x^2 - 9)(x^2 - 8)
Step-by-step explanation:
First, we need to find two numbers that multiply to give us 72 and whose sum is -17. We can see that 8 and 9 multiply to give us 72, and their sum is 8 + 9 = 17. Since we want the sum to be negative, we need to change one of the signs. So we write -(8 + 9) = -17.
Next, we write the expression as the product of two binomials. We factor out the common factor x^2 from the first two terms: x^4 - 17x^2 + 72 = x^2(x^2 - 17) + 72
Now, we complete the square in the first binomial. To do this, we need to add and subtract (17/2)^2 = (8.5)^2 = 72.25 inside the bracket:
x^2(x^2 - 17) + 72 = x^2(x^2 - 17 + 72.25 - 72.25) + 72 = x^2(x^2 - 17 + 72.25) - 72.25 + 72
Now we can rewrite the square of a binomial :
x^2(x^2 - 17 + 72.25) = x^2((x-8.5)^2)
Finally, we can combine the two binomials
x^2((x-8.5)^2) + 72 = (x^2(x-8.5)^2) + 8(9)
So the expression x^4 - 17x^2 + 72 factors completely as (x^2 - 9)(x^2 - 8)
Hope this helps!
Selena has 9 homemade bracelets for $12 each then 14 bracelets for $8 each. How much did she make in sales?
Answer:
$220
Step-by-step explanation:
first let's make the $12 bracelets as Type1 and the $8 bracelets as Type2,
then we calculate the amount she made by selling each type.
Eq.1 : No. of Type1 bracelets Selena made = 9
Amount she sold them for = $12
Amount she made by selling them = 9*12
= $108
Eq.2 : No. of Type2 bracelets Selena made = 14
Amount she sold them for = $8
Amount she made by selling them = 14*8
= $112
Now we calculate the Total Amount she made
we add both of the amounts
$108 + $112
= $220
Hope this helps :)
A triangle has side lengths of 3x, 24, and 5x. The side with 5x is the longest side. What value of x would make a right triangle?
Answer:
To form a right triangle, one of the sides of the triangle must be the hypotenuse and the other two sides must be the legs. The hypotenuse is the longest side of a right triangle and the side opposite the right angle. In this case, the side with length 5x is the hypotenuse. Therefore, the sides with lengths 3x and 24 must be the legs.
We can use the Pythagorean Theorem to determine the value of x that will make this a right triangle. The Pythagorean Theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have:
5x^2 = 3x^2 + 24^2
Solving for x, we get:
x = sqrt(24^2/(5^2 - 3^2)) = sqrt(576/16) = 6
Therefore, a value of x = 6 will make this a right triangle.
Step-by-step explanation:
Morgan bought 95 roses from the florist for her wedding. The roses cost $1.75 each, including sales tax. If Morgan gives the florist $200, how much change should she get back?
Answer:
33.75
Step-by-step explanation:
1.75*95 = 16 6.25
200 - 166.25 = 33.75
How to determine if a triangle is right acute or obtuse based on side lengths calculator?
A triangle is said to be acute if the sum of the squares of its two shorter sides is greater than the square of its longest side.
How do you know if its right obtuse or acute?Less than 90 degree angles are considered acute. Right angles have a 90 degree angle. Angles that are obtuse exceed 90 degrees.
See samples of various angles and learn about them. If and only if side lengths a, b, and c satisfy a2 + b = c2, a right triangle will be formed. These numbers are referred to as a Pythagorean triple. When the square of a triangle's longest side equals the sum of the squares of its other two sides, the triangle is said to be a right triangle. So, in the ABC equation, if c2=a2+b2, then C is a right triangle, with PQR serving as the right angle.
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PLEASE HELP ME I DONT UNDERSTAND :(( GIVIN 100 POINTS
Question 1: The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average of 3/4 foot per year
) Some students misunderstood question #1 and wrote the following equations in point-slope form:
a) y − 3 = 3/4(x-0)
b) y - 6 = 3/4(x-4)
c) y - 4.5 = 3/4(x-2)
d) y - 12 = 3/4(x-12)
(e) y - 15= 3/4(x-15)
Is this equation okay to use for the height of the trees in this problem?
There is one equation that is incorrect.... determine which one? why is it incorrectly?
Creat two new equations written in point slope form
The equation in option e) is not correct because it would not give correct height of the trees in this problem
How to write equation in slope-point form?Since the Magnolia trees are 3 feet tall and grow at an average of 3/4 foot per year.
If x is the number of years and y is the height. we can write:
y = 3/4(x) + 3
The slope-point equation of a line is given as:
y-y1 = m(x−x1)
y = 3/4(x) + 3 in slope-point form is:
y = 3/4(x) + 3
y-3 = 3/4(x-0)
This means option a) is correct
Yes, this equation is okay to use for the height of the trees in this problem
b) y - 6 = 3/4(x-4)
y - 6 = 3/4(x-4)
y - 6 = 3/4(x)- 3
y - 6 + 3 = 3/4(x)
y - 3 = 3/4(x)
This is correct
c) y - 4.5 = 3/4(x-2)
y - 4.5 = 3/4(x-2)
y - 4.5 = 3/4(x)- 1.5
y - 4.5 + 1.5 = 3/4(x)
y - 3 = 3/4(x)
This is correct
d) y - 12 = 3/4(x-12)
y - 12 = 3/4(x-12)
y - 12 = 3/4(x) - 9
y - 12 + 9 = 3/4(x)
y - 3 = 3/4(x)
This is correct
(e) y - 15= 3/4(x-15)
y - 15= 3/4(x-15)
y - 15= 3/4(x)-11.25
y - 15 + 11.25= 3/4(x)
y - 3.75 = 3/4(x)
This is not correct because it does not reflect the given information
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×/48 = 4
solve for x
Answer:
Step-by-step explanation:
x ÷ 48 = 4
Multiplying both sides by 48 we get:
x ÷ 48 x 48 = 4 x 48
x = 192
After a long morning of sledding, Mrs. Fieldhouse made a batch of hot cocoa for her daughter and nighborhood friends. She divided it among 8 mugs. Each mug had more than 9 fluid ounces of hot cocoa. Write an inequality to describe the situation.
x>9 perfectly describes the situation.
In mathematics, inequalities characterise the connection between two non-equal numbers. Inequality implies being unequal. If two values are not equal, we use the "not equal symbol ()". However, various inequalities are employed to compare the numbers, whether they are less than or higher than.
Let x be the amount of hot cocoa in fluid ounces that each mug contains.
Since each mug has more than 9 fluid ounces of hot cocoa, we can write the inequality as:
x > 9
We also know that the total amount of hot cocoa made is 8 mugs * the amount of hot cocoa in each mug = 8x.
So the inequality can be written as:
8x > 9*8 = 72
or
x>9
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How do you find the 3rd side of a triangle?
Answer:
a2 = b2 + c2 2bc cos(0)
Step-by-step explanation:
You just bought a new tablet computer for $500, including tax. There are no required payments for six months, but the company does charge 30% annual interest, compounded monthly, on any unpaid balance.
what is the effective annual rate of interest if you do not make any payments for a year?
The effective annual rate of interest if you do not make any payments for a year is 35%.
What is compound interest?Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -
[tex]$A = P(1 + \frac{r}{n})^{nt}[/tex]
where -
[A] = final amount
[P] = initial principal balance
[r] = interest rate
[n] = number of times interest applied per time period
[t] = number of time periods elapse
Given is that You just bought a new tablet computer for $500, including tax. There are no required payments for six months, but the company does charge 30% annual interest, compounded monthly, on any unpaid balance.
We can write -
A = 500(1 + 0.3/12)¹²⁽¹⁾
A = 500(1 + 0.025)¹²
A = 500 x (1.025)¹²
A = 675
Effective annual interest rate for a year is as follows -
A = 500(1 + r/1)⁽¹⁾⁽¹⁾
675 = 500(1 + r)
1 + r = 675/500
1 + r = 1.35
r = 0.35
r = 35%
Therefore, the effective annual rate of interest if you do not make any payments for a year is 35%.
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In the triangle below, the measure of angle G is 45 degrees, and the length of
HI = b cm. What is an expression for the length of HG?
Der b
G
I
H
45
The length of HG can be expressed as HG = b√2.
What is triangle?Triangle is a three-sided polygon with three straight sides that intersect at three vertices. It is one of the most basic shapes in geometry and is found in nature in the form of mountains, icebergs and even the human face. It has a variety of applications in mathematics, engineering, and other fields. Triangles are also used to define angles and even the area of a plane.
This is because the triangle is a right triangle, and the Pythagorean Theorem states that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Therefore,
HG2 = b2 + b2 = 2b2,
which reduces to HG = b√2.
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In the figure where 3x20 and 4x-36, which value of x will make aob, a traight line
The value of x that will make aob a straight line equation is x = -6.
To make aob a straight line, we need to make the gradients of both lines equal.
The gradient of the first line is 3x20 = 60.
The gradient of the second line is 4x-36 = 4x-36.
To make the gradients equal, we need to solve the equation 4x - 36 = 60.
Subtracting 36 from both sides gives us: 4x = 96.
Dividing both sides by 4 gives us x = -6.
Therefore, the value of x that will make aob a straight line is x = -6
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Select the interval where the graph h is decreasing.
Answer: A
Step-by-step explanation:
Based on the graph, we know that it is decreasing if it is going down from left to right.
A: correct
Looking at choice A, it says the interval is from -4<x<-3. This means we have to find x=-4 and x=-3. On the graph, that interval is going down from left to right, so it is decreasing.
B: incorrect
Looking at choice B, it says the interval is from -2<x<0. This means we have to find x=-2 and x=0. On the graph, that interval is going up from left to right, so it is increasing.
C: incorrect
Looking at choice C, it says the interval is from 0<x<2. This means we have to find x=0 and x=2. On the graph, that interval is going up from left to right, so it is increasing.
D: incorrect
Since we have identified A as decreasing, then none of the above can't be the answer.
Therefore, A is the correct answer.
Big Ideas:
Explain your reasoning.
Answer:
Stretch the graph of f(x) = x + 3 vertically by a factor of 2.
The "same" transformations result in f(x) = 2x + 5
The "different" transformation results in f(x) = 2x + 6
Step-by-step explanation:
Transformation Rules
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]a\:f(x) \implies f(x) \: \textsf{stretched parallel to the $y$-axis (vertically) by a factor of $a$}[/tex]
[tex]f(ax) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $\dfrac{1}{a}$}[/tex]
Carry out the given transformations.
Given function:
[tex]f(x) = 2x + 3[/tex]
Translation of 2 units up:
[tex]\begin{aligned}\implies f(x) + 2&= 2x + 3 + 2\\&=2x+5\end{aligned}[/tex]
Given function:
[tex]f(x) =x + 3[/tex]
Vertical stretch by a factor of 2:
[tex]\begin{aligned}\implies 2f(x)&=2(x+3)\\&=2x+6\end{aligned}[/tex]
Given function:
[tex]f(x) = x + 5[/tex]
Horizontal shrink by a factor of 1/2:
[tex]\implies f\left(\dfrac{1}{\frac{1}{2}}x\right)=f(2x)=2x+5[/tex]
Given function:
[tex]f(x) = 2x + 3[/tex]
Translation of 1 unit left:
[tex]\begin{aligned}\implies f(x+1) &= 2(x+1) + 3\\&=2x+5\end{aligned}[/tex]
Three of the transformations result in the same function f(x) = 2 + 5.
Therefore, the transformation that does not belong with the other three is:
Stretch the graph of f(x) = x + 3 vertically by a factor of 2.How do you graph 3 variable lines?
Three variable lines are drawn in the three dimensional coordinate system.
What is 3 dimensional coordinate plane?
Three-dimensional coordinate system is also called rectangular coordinate system. The system has three reference axes named X, Y and Z axis which are perpendicular to each other.
The above three axes intersect at the origin.
In the analytical geometry, location of each point is represented by three coordinate system. They give mathematical statement by using three-dimensional space.
How do we graph 3 variable lines?In order to plot in the three-dimensional plane, we need to determine the value of x, y and z. At first, we start from the origin and approach to the positive x direction if our x value is positive, otherwise we need to go to the negative x direction. After identifying the x coordinate, we need to move parallel to y direction and locate the y coordinate and finally we identify the z coordinate in the same way. In the last, we will join the points.
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Find the percent decrease from 133 to 120. Round your answer to the nearest tenth
Answer:
Approximately - 9.7%
Step-by-step explanation:
By using the percent change formula, you will be able to calculate the percent decrease.
(b-a)/a times 100 <-- (percent change formula)
(120-133)/133 times 100
-13/133 times 100
-9.7744%
Answer:
9.8% decrease
Step-by-step explanation:
You want the percent decrease from 133 to 120.
Percent changeThe amount of change as a percent can be found using the formula ...
percent change = ((new value)/(old value) -1) × 100%
Here, the new value is 120, and the old value was 133. The change is ...
percent change = (120/133 -1) × 100% ≈ (0.90226 -1) × 100%
= -0.09774 × 100% ≈ -9.8%
The change from 133 to 120 is a 9.8% decrease.
__
Additional comment
When the sign of the change is negative, as here, the change is a decrease. If the sign is positive, the change is an increase. That is, a change of -9.8% is a 9.8% decrease. (You can use either the minus sign or the word "decrease" to indicate the direction of the change. The acceptable form of the answer will depend on your grader.)
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150 people went to see "Ode to Algebra" performed in the school auditorium. If the number of children that attended the performance was c, how many adults attended?
Answer:
150-c
Step-by-step explanation:
150= total
c= children
adults=x
x=150-c
Please help I will give Brainiest answer
Answer: b
Step-by-step explanation:
4-3
——-
13.40- 10.05
= 1/3.35
=b
What is the measure of ∠A if it is complementary to ∠B that has a measure of 55?
For the given complementary angles, the measure of angle A is found to be 45°.
Define the term complementary angles?When two angles' measurements add up to 90 degrees, they are said to be complimentary. When two angles' measures sum up to 180 degrees, they are referred to as supplementary angles.When two angles sum up to 90 degrees, they are complementary (a Right Angle). They don't even have to be close to one another for the total to be 90 degrees. Examples: The complimentary angles of 40° and 50°.For the stated question-
Angle A is complementary to Angles B.
So,
Angle A + Angles B = 90°
Angle A + 55° = 90°
Angle A = 90° - 55°
Angle A = 45°
Thus, the measure of angle A is found to be 45°.
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A triangle has sides with lengths that are
consecutive even integers. The perimeter of the
triangle is 72 centimeters. Sketch the triangle
and label the lengths of the sides, using the
variable. Find the length of the largest side.
Show work
The largest side of the length is 26cm.
Now, According to the question:
Three consecutive even numbers can be expressed in terms of n. If n is an even number then,
(n -2), (n), (n + 2)
are three consecutive even numbers.
Therefore,
(n -2)+ (n)+ (n + 2) = 72cm.
We can simplify so...
3n + 2 - 2 = 72 cm.
3n + 0 = 72 cm.
3n = 72cm.
Divide both sides by 3 to solve for n
n = 24 cm.
24 is an even integer. Input 24 into the original equation.
(n -2)+ (n)+ (n + 2) = 72cm.
(24 - 2) + 24 + (24 + 2) = 72cm
22 + 24 + 26 = 72
72 = 72
Hence, The largest side of the length is 26cm.
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Can someone tell me what this is?
Answer:
there's one solution bc the lines have one point in common
.You have an "equality sign" that connects 1kg of NaCl to 27 ml of a solvent, how many ml are associated with 9100 grams?
Two tiny parallel horizontal lines serve as the "equality sign" connecting 1 kilogramme of NaCl to 27 ml of a solvent.
What does ≡ mean in math?is a synonym for exactly. This is comparable to equals but not quite the same. To avoid confusion, always use the symbol =, which stands for about equal to or virtually equal to. This symbol indicates two sides of a connection that are not precise enough to be mathematically manipulated.≅ (mathematics) equivalent to around. quotes (geometry) similar to. The computer science term "it is defined as" is denoted by the meta symbol::=, which is not a mathematical expression , everywhere.x ≔ y or x ≡ y indicates that x is understood to be another name for y (however it should be noted that can also denote other things, such as congruence). P :⇔ Q denotes the logical equivalence of P to Q. Congruent or, more generally, an arbitrary equivalence relation is denoted in some circumstances by the triple bar or equal sign with three lines.To learn more about equality sign refer to :
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The temperature in Paris, France is -7°C and the temperature in Malé, Maldives is -3°C
(a) write down how many degrees colder it is in Paris than Malé
(b) Rome is 23 degrees warmer than Paris
Write down the temperature in Rome.
Answer:
a) 3
b) 16 Celsius
Answer:
A. -4°C
B. 16°C
Step-by-step explanation:
A. (-7°C)-(-3°C)= -4°C
Therefore Paris is -4°C colder than Malé.
B. 23+(-7°C)=16°C
Therefore the temperature in Rome is 16°C
Hope it helps you
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Pop is on sale at Save-U-Lots. Which pack has the lowest cost per unit?
A. 6- pack for $2. 49
B. 12-pack for $3. 99
C. 24-pack for $5. 49
In the case of a 24-pack for $5. 49, the cost of the unit is the lowest.
The cost per item is nothing to the amount of money invested in buying one item.
As we have 3 different scenarios:
Case A. 6- pack for $2. 49
As here. cost of 6 packs is $2.49, so for determining the cost of one pack we will divide $2.49 by 6.
So, the cost of 1 pack will be = 2.49/6 = 0.415 $/pack
B. 12-pack for $3. 99
As here. cost of 12 packs is $3.99, so for determining the cost of one pack we will divide $3.99 by 12.
So, the cost of 1 pack will be = 3.99/12 = 0.3325 $/pack
C. 24-pack for $5. 49
As here. cost of 24 packs is $4.49, so for determining the cost of one pack we will divide $5.49 by 24.
So, the cost of 1 pack will be = 5.49/6 = 0.22875 $/pack
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make a the subject 11a = 7b
Answer:
a=7b/11
Step-by-step explanation:
11a=7b
11a/11=7b/11
a=7b/11
Answer: 11a=7b
-divide 11 from both sides
you'll end up with this result:
a=7b/11
The area of a sector of a circle is
18 pie cm². The radius of the circle is
6 cm. The angle in the sector is
Answer:
The angle in the sector is 180°.
Because the area of circle is 36 pie cm². So the angle is the half of 360°.
[tex]\boxed{\begin{array}{l} \\ \sf\huge{ \quad \underline{Answer} } \\ \\ \underline{ \underline\textsf{ Area of sector is given by : }} \\ \\ \dashrightarrow \sf{ A = \dfrac{ \theta}{360 \degree} \times \pi {r}^{2} } \\ \\ \dashrightarrow\sf{18 \pi = \dfrac{ \theta}{360 \degree} \times \pi {(6)}^{2} } \\ \\ \dashrightarrow \dfrac{ \theta}{360 \degree} = \dfrac{18 \pi}{ \pi(36)} \\ \\ \dashrightarrow \theta = 360 \degree \times \dfrac{1}{2} \\ \\ \dashrightarrow\theta = 180 \degree \\ \\ \end{array} } [/tex]
How Do You Solve 3 linear equations with 3 variables?
The standard way to solve 3 linear equations with 3 variables is to use elimination or substitution.
-Elimination: To solve the 3 equations using elimination, add or subtract equations together to eliminate one of the variables. Keep repeating this process until you are left with one equation with one variable. Solve the equation and then use the value of the variable to substitute back into the other equations to find the values of the other variables.
-Substitution: To solve the 3 equations using substitution, pick one of the equations and solve it for one of the variables. Then substitute the value of the variable into the other equations. Keep repeating this process with the other equations and variables until you have a system of equations with one variable that you can solve. Once you have the value of the variable, substitute it back into the other equations to find the value of the other variables.
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This probability distribution shows the
typical grade distribution for a Geometry
course with 35 students.
Grade
A
BCDF
Frequency
5
10
15
3
2
Find the probability that a student earns a
grade of A, B, or C.
p=[?]
Enter a decimal rounded to the nearest hundredth.
Answer:
85.71% probability
Step-by-step explanation:
30 of 35 of the students are in abc range so take 35/100% or 0.35 and go 30/0.35 and you get 85.71%
Write down the value of angle x, y and z and give a reason for your answers: Angles
The missing angles and their reasons are as follows;
a) x = 65°; Opposite angles
b) y = 71°; Alternate angles
c) z = 44°; sum of angles in a triangle
What are the missing angles of the triangle?a) In triangles or line geometry, we know that the angles that are directly opposite to each other are known as opposite angles. They are also referred to as as vertical angles or even vertically opposite angles in some cases and are always congruent to each other.
We see that x is an opposite angle to 65 and so;
x = 65°
b) Alternate angles are gotten on the opposite sides of a transversal line they always have the same size. In this problem, we see that y is an alternate angle to 71° and as such;
y = 71°
c) The sum of angles in a triangle is 180° and as such;
x + y + z = 180°
Thus;
65 + 71 + z = 180
z = 180 - 136
z = 44°
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From nose to tail your first dog is 5 feet long. Your first dog is the length of your second dog. How many feet long f is your second dog
According to fraction and ratio, second dog is 3/2 feet long.
In math, what is a fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
First dog is 5 feet long.
then,
5 feet is equal to 4/5 of the second dog's length.
multiply both sides by 5/4.
5/4 x 5 feet is the second dog's length.
The second dog is 25/4 feet long.
The second dog is 6(1/4) feet long.
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What are 2 examples of a solution?
The two examples of the solution are sugar water, and soda water.
The term solution is defined as a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
Here according to the definition of solution, here we know that Common examples of solutions are sugar in water and salt in water solutions, soda water, etc.
As we all know that the solutions have two components, one is solvent and the other is solute.
Here the components, that is the component that dissolves the other component is called the solvent where as the component(s) that is/are dissolved in the solvent is/are called solute(s).
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