Answer: The graph crosses the x-axis at x = 2.
Step-by-step explanation:
The root has a multiplicity of 3, meaning that it crosses the x axis at x=2.
solve for x -
[tex]\bold{x {}^{2} + 5x + 6 = 0}\\\\[/tex]
ty! ~
The solution of the given quadratic equation is x=-2 or x=-3.
The given quadratic equation is x²+5x+6=0.
What are different methods to solve a quadratic equation?The different methods of solving quadratic equations are factoring, completing the square or using the quadratic formula.
By using the splitting middle term method we can solve x²+5x+6=0.
That is, x²+2x+3x+6=0
⇒x(x+2)+3(x+2)=0
⇒(x+2)(x+3)=0
⇒(x+2)=0, (x+3)=0
⇒x=-2 or x=-3.
Therefore, the solution of the given quadratic equation is x=-2 or x=-3.
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The triangular prism below has a base area of 28.7 units² and a height of 11 units.
Find its volume.
The volume of the triangular prism is 315.70 units³.
What is the volume?A triangular prism is a three-dimensional shape that has a triangular base.
Volume =base area x height
28.7 x 11 = 315.70 units³
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If the line segment AB is on a number line, and point A is at 6 and Point B is at 13, then the length of AB is ____.
Answer:
7
Step-by-step explanation:
The length of AB is the distance between A and B which is B-A -> 13-6= 7
If the cost, C, for manufacturing x units of a certain product is given by C= x² + 10x + 65, find the number of units manufactured at a cost of $7265
Answer:
80
Step-by-step explanation:
when you do the math you get two answers, -90 and 80
we dont use -90 because -90 units cannot be manufactured
Find the measure of the indicated angle to the nearest degree.
?
58
30
Find the number of distinguishable ways the letters of the following word can be arranged. KNICKKNACK
The number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.
When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.
The number of different permutations of n objects with m₁ repeated items, m₂ repeated items,...,mₙ repeated items can be computed as
m!/(m₁!)(m₂!)...(mₙ!)
Here, the letter 'KNICKKNACK' is a total of 10 letters with 4 K's, 2 N's, 1 I, 2 C's, and 1 A.
So, the number of possible arrangements is
(10!)/(4!*2!*1!*2!*1!) = (10*9*8*7*6*5*4!)/(4!*2*2) = 10*9*7*6*5*2 = 37800
Therefore the number of distinguishable ways the letters of the following word can be arranged 'KNICKKNACK' is 37800.
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square root of 0.98 simplified
Answer:
0.98994949366117
√0.98 = 0.98994949366117
Step 1:
Divide the number (0.98) by 2 to get the first guess for the square root.
First guess = 0.98/2 = 0.49.
Step 2:
Divide 0.98 by the previous result. d = 0.98/0.49 = 2.
Average this value (d) with that of step 1: (2 + 0.49)/2 = 1.245 (new guess).
Error = new guess - previous value = 0.49 - 1.245 = 0.755.
0.755 > 0.01. As error > accuracy, we repeat this step again.
Step 3:
Divide 0.98 by the previous result. d = 0.98/1.245 = 0.7871485944.
Average this value (d) with that of step 2: (0.7871485944 + 1.245)/2 = 1.0160742972 (new guess).
Error = new guess - previous value = 1.245 - 1.0160742972 = 0.2289257028.
0.2289257028 > 0.01. As error > accuracy, we repeat this step again.
Step 4:
Divide 0.98 by the previous result. d = 0.98/1.0160742972 = 0.9644963982.
Average this value (d) with that of step 3: (0.9644963982 + 1.0160742972)/2 = 0.9902853477 (new guess).
Error = new guess - previous value = 1.0160742972 - 0.9902853477 = 0.0257889495.
0.0257889495 > 0.01. As error > accuracy, we repeat this step again.
Step 5:
Divide 0.98 by the previous result. d = 0.98/0.9902853477 = 0.9896137535.
Average this value (d) with that of step 4: (0.9896137535 + 0.9902853477)/2 = 0.9899495506 (new guess).
Error = new guess - previous value = 0.9902853477 - 0.9899495506 = 0.0003357971.
0.0003357971 <= 0.01. As error <= accuracy, we stop the iterations and use 0.9899495506 as the square root.
So, we can say that the square root of 0.98 is 0.989 with an error smaller than 0.01 (in fact the error is 0.0003357971). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(0.98)' is 0.9899494936611666.
Note: There are other ways to calculate square roots. This is only one of them.
To round it to the tenths, it's 1
To round to the hundredths, it's.99
Thousandth is.990
I need the answer for number 4 please!!
Answer:
-3 - false
0 - true
1 - true
2 - false
4 - true
Step-by-step explanation:
the "zeros" of a function are its x-intercepts
(because that is when the function = zero [0])
So, we can look at the x-intercepts of the graph to find the zeros:
at 0, 1, and 4 the function = 0, meaning that those are zeros of the function
hope this helps!! have a lovely day :)
How many gallons of a 60% antifreeze solution must be mixed with 70 gallons of 15% antifreeze to get a mixture that is 50% antifreeze?
There are 245 gallons of antifreeze solution required.
What is Percentage?Percentage can be calculated by dividing the value by the total value, and then multiplying the result by 100.
Here, Let 60% antifreeze solution volume = x
15% antifreeze solution volume = 15%
Final concentration 50%
Process
0.6x + 0.15(70) = 0.5(70 + x)
Simplification
0.6x + 10.5 = 35 + 0.5x
0.6x - 0.5x = 35 - 10.5
0.1x = 24.5
x = 24.5/0.1
x = 245 gallons
Thus, There are 245 gallons of antifreeze solution required.
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The area of a rectangle is 44m2 , and the length of the rectangle is 3m
less than double the width. Find the dimensions of the rectangle.
Answer:
width=11/2
length=8
Step-by-step explanation:
44=(2w-3) x w area for a rectangle (44) = the length (2w-3) times the width (w)
44=2w^2 - 3w distribute
2w^2-3w-44 = 0 subtract 44 from both sides
(w+4)(2w-11) factor
width=11/2
(11/2 x 2) - 3
length = 8
i needs help with it
Answer:
a) initial height = 0 m
b) 8 s
c) vertex = (4, 32)
maximum height = 32 m
Step-by-step explanation:
Given equation:
[tex]h=-2t^2+16t[/tex]
where:
h is the height of the arrow about the ground (in metres)t is the time (in seconds)Part (a)The initial height of the arrow will be at the beginning of its journey, so when t = 0
Substitute t = 0 into the equation and solve for h:
[tex]\implies h=-2(0)^2+16(0)[/tex]
[tex]\implies h=0[/tex]
Therefore, the initial height of the arrow is 0 m.
Part (b)The arrow will hit the ground when the height is 0 m.
Substitute h = 0 into the given equation:
[tex]\implies -2t^2+16t=0[/tex]
Factor out -2t:
[tex]\implies -2t(t-8)=0[/tex]
Therefore:
[tex]\implies -2t=0 \implies t=0[/tex]
And:
[tex]\implies t-8=0 \implies t=8[/tex]
Therefore, the arrow will hit the ground at 8 seconds.
Part (c)The vertex is the turning point of a parabola - it's minimum or maximum point.
As the leading coefficient for the given equation is negative, the parabola opens downwards and so its vertex is its maximum point.
There are different ways to find the vertex of a parabola. The easiest way to find the x-coordinate is by calculating the midpoint of the x-intercepts.
We have determined that the arrow has a height of 0 m at 0 seconds and 8 seconds. Therefore, t = 0 and t = 8 are the x-intercepts. The midpoint is halfway between zero and 8, so the midpoint is t = 4
To find the y-coordinate, substitute t = 4 into the equation and solve for h:
[tex]\implies h=-2(4)^2+16(4)[/tex]
[tex]\implies h=-32+64[/tex]
[tex]\implies h=32[/tex]
Therefore, the coordinates of the vertex are (4, 32)
The maximum height is the y-coordinate of the vertex.
Therefore, the maximum height is 32 m
You have loaned a friend $100 and will charge him 5% annua simple interest when he pays it back.
The annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount of borrowed amount.
We have:
You have loaned a friend $100 and will charge him 5% annually.
As we know:
A = P(1 + rt)
P = $100
r = 5% = 0.05
t = 1 years
A = 100(1 + 0.05×1)
A = $105
I = A - P = 105 - 100 = $5
Thus, the annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.
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. In 1 hour, a car can cover 70 km. How much distance will it cover in 2 hours?
I need it fast
Answer:
140km
Step-by-step explanation:
Distance = Speed x Time
= 70km/h x 2 hours
= 140km
Find f(x) and g(x) so that the
function given can be described
as y = f(g(x)).
y = e^sin x
Answer:
g(x) = sin(x)
f(x) = e^x
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]f(x)=e^x\\g(x)=sin~x\\y=f(g(x))=f(sin~x)=e^{sin~x}[/tex]
3
O Find the perimeter of the following shape, given its curves are made from parts of circles.
Give your answers in terms of π.
4cm
4cm
4cm
The diagram is not drawn to scale.
Answer:
12pi cm
Step-by-step explanation:
The Perimeter of the full shape is the sum of the lengths of the edges of the parts. For convenience in referencing them, we'll call the large curve "[tex]curve_{big}[/tex]" and the three smaller curves "[tex]curve_1[/tex]" "[tex]curve_2[/tex]" "[tex]curve_3[/tex]" in order from left to right.
Thus, the Perimeter of the full shape can be written as an equation:
[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex]Since all of those edge lengths are curves, and the question states that all of the curves are made from parts of circles, then we need to know how to find the length of the edge of a circle.
Parts of a circle
Since values in the diagram are diameters, use the formula for the Perimeter of a circle [tex]P=\pi d[/tex] (where d is the diameter).
Let's call the diameters of each of our curves "[tex]d_{big}[/tex]" "[tex]d_1[/tex]" "[tex]d_2[/tex]" "[tex]d_3[/tex]", with the subscripts denoting which curve we're referring to.
Note that for each curve, the curve only represents half of a circle. So, to find the length of each curve, we'll need half of the full perimeter of each circle.
So for instance: [tex]Length(curve_{big})=\frac{1}{2} \pi d_{big}[/tex]
Substituting back into the main equation above:
[tex]P_{overall} = Length(curve_{big})+Length(curve_1)+Length(curve_2)+Length(curve_3)[/tex][tex]P_{overall}=\frac{1}{2} \pi d_{big} + \frac{1}{2} \pi d_{1} + \frac{1}{2} \pi d_{2} + \frac{1}{2} \pi d_{3}[/tex]
Note that all terms have common factors of "one-half" and "pi" in them. These can be factored out:
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]
The diameter for the large Curve, is the sum of the three small diameters, so [tex]d_{big}=12cm[/tex], and [tex]d_{1}=d_{2}=d_{3}=4cm[/tex]
Substituting and simplifying (in terms of pi):
[tex]P_{overall}=\frac{1}{2} \pi ( (12cm) + (4cm) + (4cm) + (4cm) )\\P_{overall}=\frac{1}{2} \pi ( 24cm)\\P_{overall}=12 \pi cm[/tex]
Additional Understanding
Interesting for this problem, since the diameters of the 3 small curves formed the diameter of the large curve [tex]d_{1} + d_{2} + d_{3} =d_{big}[/tex], one could make a different substitution into one of our formulas above:
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + d_{1} + d_{2} +d_{3})[/tex]
[tex]P_{overall}=\frac{1}{2} \pi (d_{big} + (d_{big}))[/tex]
[tex]P_{overall}=\frac{1}{2} \pi (2d_{big})[/tex]
[tex]P_{overall}=\pi d_{big}[/tex]
Notice that [tex]\pi d_{big}[/tex] is just the full perimeter of a circle with the big diameter.
So, if one imagined starting with a full circle with the big diameter, even though the bottom half of the circle was turned into a bunch of smaller half circles, since they were in a line along the diameter of the large circle, the full perimeter of the new shape didn't change.
The number of smaller circles doesn't need to be 3 either... as long as it goes the full distance across, right along the diameter.
Select the correct answer from each drop-down menu.
The function f is given by the table of values as shown below.
x 1 2 3 4 5
f(x) 13 19 37 91 253
Use the given table to complete the statements.
If function f was translated down 4 units, the _
values would be _
A point in the table for the transformed function would be _
Using translation concepts, the correct statement is given by:
If function f was translated down 4 units, the f(x) values would be subtracted by 4. A point in the table for the transformed function would be (1,9).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
A translation down 4 units means that the output values are subtracted by 4, hence the table would be given by:
x 1 2 3 4 5
f(x) 9 15 33 87 249
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Answer:
The CORRECT answer is:
1. f(x)
2. decreased by 4
3. (4, 87)
Step-by-step explanation:
Took the test
hi can you please help me with this question.
I need explanation too.
I'll like and rate your answer if your answer is right.
0 like and 1 rate for nonsense answer.
0 like and 2 rate if it's incorrect.
0 like and 3 rate if it is un-answer
1 like and 4 rate if it's correct a bit
1 like and 5 rate if it's very good answer.
Answer:
It appears to already be solved. What do you need help with?
Step-by-step explanation:
What is:
[tex]5x + 5 = 5 \times (10 \div 5)[/tex]
Solve this equation.
Answer:
x = 1
Step-by-step explanation:
To solve an equation for a variable, we need to isolate (get the variable alone on one side)
(the order of the following was determined by PEMDAS)
5x + 5 = 5 (10 ÷ 5) [simplify inside parentheses]
5x + 5 = 5 (2)
5x + 5 = 10
- 5 -5 [subtract 5 from both sides to isolate x]
5x = 5
÷5 ÷5 [divide both sides to get x]
x = 1
hope this helps!!
A 3-gallon bucket of paint costs $108.60. What is the price per quart?
Answer:
9.05
Step-by-step explanation:
make gallons into quarts
quar prefix in many languages means 4
1 gallon is 4 quarts
3 gallons is 4 times 3 -> 12 quarts
just by seeing 108 and 12 the answer will be around 9
108.90 ÷ 12 = 9.05
Help me with this I’m stuck!!!
The intersection between the complement of set A and the complement of set B is 7.
What is a Venn diagram?A Venn diagram is a visual representation that shows mathematical sets as circular curves inside of a rectangle (known as the universal set).
From the Venn diagram, we are to find the intersection between the complement of set A and the complement of set B.
[tex]\mathbf{A^c = \{ 7,6,11 \}} \\ \\ \\ \mathbf{B^c = \{7,9,13 \}}[/tex]
Therefore, the intersection between the two sets is the set of elements that exists in both of them. Therefore, we have:
[tex]\mathbf{n(A^c \cap B^c) = \{7\}}[/tex]
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How do you write 189% as a fraction, mixed number, or whole number?
ind two negative and three positive angles, expressed in radians, for which the point on the unit circle that corresponds to each angle is (√2/2,√2/2)
.
Remember that for a given angle θ, any point on the unit circle is written as:
(cos(θ), sin(θ)).
And remember that:
cos(45°) = sin(45°) = √2/2
Then the angle θ = 45° is a solution.
To find another positive solution, we just add the period of the circle, which is 360°.
θ = 45° + 360° = 405°
Adding the period again:
θ = 405° + 360° = 765°
So the 3 positive solutions can be:
{45°, 405°, 765°}
To get the negative angles we just subtract the period:
45° - 360° = -315°
We can do that again:
-315° - 360° = -675°
So the two negative angles are:
{-315°, -675°}
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A family originally bought a home for $654,030. Now, a few years later, the home is worth
$457,821. What was the percent of decrease in its value?
Answer:
30%
Step-by-step explanation:
First we find out the difference between them:
$654,030 - $457,821 = $196,209
Then we compare it with the original price:
196,209/654,030 = 0.3
Since 0.3 is 30%, that is 30% decrease in value.
Give the slope and the y-intercept of the line y=10x+9
Answer:
Slope: 10
Y-intercept: +9
Step-by-step explanation:
An equation written in slope-intercept form is y=mx+b. "m" is your slope and b is your y-intercept.
Origami is the Japanese art of paper folding. The diagram below represents an unfolded paper kabuto, a samurai warrior's helmet. Which of the following are pairs of congruent segments? Check all that apply. A. PO and ON B. FR and NR C. NO and NM D. RC and RO E. DV and EW
Option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.
What is congruence in geometry?The measurements of the sides and angles of two or more geometrical figures determine their congruence. For example triangle's size is determined by its three sides, and its shape is determined by its three angles.
We have:
The diagram represents an unfolded paper kabuto, a samurai warrior's helmet.
Unfolded paper can be seen in the provided figure. The sheet is square.
The diagonals, in this case, are FN and AK, and the midline is CM and OI. At point R, all of these lines converge.
FR ≅ NR
AO ≅ ON
RC ≅ RO
NO ≅ NM
DV ≅ HV
Thus, option (B) FR and NR, option (C) NO and NM, and option (D) RC and RO are correct.
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Find sin
A. 12/13
B. 1
C. 13/12
D. 13/5
Answer: A. [tex]\frac{12}{13}[/tex]
Step-by-step explanation:
The best way to remember this is SOH-CAH-TOA. For sin, it would be the opposite angle over the hypotenuse. The opposite angle of ∠C is 24 and the hypotenuse is 26. But that isn't in the answer choices, so you'll simplify the fraction.
[tex]\frac{24}{26} =\frac{12}{13}[/tex], therefore, the answer is A.
I hope this helps! Pls mark brainliest!! :)
curved surface area of a cone = Trl, where r is the
radius and is the slant height.
The ice cream cone below is made from a piece of wafer.
Work out the area of wafer required to make the ice
cream cone.
Give your answer to 1 d.p.
2 cm
9 cm
The area of wafer required to make the ice cream cone 68.75 cm²
What is Area?The area is the amount of space within the perimeter of a 2D shape. It is measured in square units, such as cm², m², etc.
Given:
r= 2cm, l=9 cm
Surface area,
=πr(l +r)
=3.14*2(9 + 2)
= 6.25*11
=68.75 cm²
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Warm Shelters.org received a donation of $32,000 to buy beds and dressers for its new dormitories. Each bed will cost $320.00 and each dresser will be $75.00 each. A total of 132 pieces of beds and dressers are needed. What is the percentage of dressers with respect to the number of beds?
Please HELP
Answer:
you can buy 98 beds and buy dresses by rest of the money
...............
................
Let the numbers be x and x/7
Now
sum=824x+x/7=8248x/7=8248x=824(7)8x=5768x=721The numbers are
721 and 721/7=103Answer:
7x+X=824
8X/8=834/8
x=108
Step-by-step explanation:
hope I helped
Which of the numbers below are whole numbers?
A. 546
B. 7317
C. 1/3
D. 47
E. 93.3.
F. 907.68