Answer:
D. x = 3+i√5 or 3-i√5
Step-by-step explanation:
Given the equation x² - 6x = -14, on rewriting the equation in the firm if a quadratic equation ax²+bx+c = 0 will give x² - 6x + 14= 0.
Required
Use the quadratic formula to solve the equation.
The quadratic formula is expressed as x = (-b±√b²-4ac)/2a
From the equation given, a = 1, b = -6 and c = 145.
x = (-(-6)±√(-6)²-4(1)(14))/2(1)
x = = (6±√36-56)/2
x = = (6±√-20)/2
x = (6±√20*√-1)/2
Since √-1= i
x = (6±√20 i)/2
x = (6±√5*4 i)/2
x = (6±2√5 i)/2
x = 6/2 ± 2√5 i/2
x = 3±√5 i
x = 3+i√5 and 3-i√5
Hence the solution to the quadratic equation is x = 3+i√5 and 3-i√5
What is the total surface area of the square pyramid below? A square pyramid. The square base has side lengths of 10 centimeters. The triangular sides have a height of 14 centimeters. 100 cm2 200 cm2 280 cm2 380 cm2
Answer:
380 cm^2
Step-by-step explanation:
10*10=100(base square)
Each triangle= (14*10) /2=70
4 sides, so therefore: 70*4=280
280+100=380
Since the square base has side 10 cm and triangular side has height 14 cm, the total surface area of square pyramid is 380 cm²
To answer the question, we need to find the total surface area of the square pyramid
Total surface area of a square pyramid.Since a square pyramid has a square base and four triangular sides, its surface area, A = area of square base + 4 × Area of triangular side.
Area of square base
Area of square with side, L is A = L²
Area of triangular base
Area of triangle with height, h and base, L which is the length of the square base is A' = 1/2Lh
So, total surface area of square pyramid is A" = L² + 4 × 1/2Lh
= L² + 2Lh
Given that the length of the square base is 10 cm and the height of the triangular side is 14 cm.
We have that
L = 10 cm and h = 14 cmSo, substituting the values of the variables intot he equation, we have
A" = L² + 2Lh
A" = (10 cm)² + 2 × 10 cm × 14 cm
A" = 100 cm² + 280 cm²
A" = 380 cm²
So, the total surface area of square pyramid is 380 cm²
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Match each number with its place in order from smallest (1st) to largest (6th). 1. 6th -56 2. 4th 90 3. 3rd -84 4. 1st 59 5. 2nd -80 6. 5th 48 HELP ASAP IM GETTING GRADED ON THIS
Answer:
1st -842nd -803rd -564th 485th 59 6th 90Step-by-step explanation:
To match each number with its place in order from smallest (1st) to largest (6th).
1. 6th -56 2. 4th 90 3. 3rd -84 4. 1st 59 5. 2nd -80 6. 5th 48
First we write all numbers: -56, 90, -84, 59, -80, 48
In Ascending order ( from smallest to largest): -84, -80,-56, 48, 59, 90
Here, the required arrangement:
1st -842nd -803rd -564th 485th 59 6th 90
Please Help me!! An 8 foot high camel is loping away from a streetlight. The camel is loping at 12 feet/second. The streetlight is 20 feet high. How fast is the camel’s shadow growing?
Answer:
Camel's shadow is growing at a rate of 8 ft/sec.
Step-by-step explanation:
Given:
Height of camel = 8 ft
Height of streetlight = 20 ft
Speed of camel = 12 ft / sec
To find:
How fast is the camel's shadow growing = ?
Solution:
First of all, have a look at the image attached for the situation as given in the question statement.
PQ be the streetlight.
AB be the camel.
Camel is loping away from the streetlight.
BT will be the shadow of the camel.
We are given that speed of camel = 12 ft / sec
And we know that Speed is the Rate of change of distance w.r. to time.
i.e. as per the image, we are given:
[tex]\dfrac{dx}{dt} = 12 ft /sec[/tex]
And we have to find the value of:
[tex]\dfrac{ds}{dt} = ?[/tex]
(Because s is the shadow length and we have to find the rate of change of shadow's length w.r.to time.)
Here, let us consider the two similar triangles [tex]\triangle TAB\ and\ \triangle TPQ[/tex]as per the image attached:
Ratio of corresponding sides will be same.
[tex]\dfrac{AB}{PQ}=\dfrac{TB}{TQ}\\\Rightarrow \dfrac{8}{20}=\dfrac{s}{s+x}\\\Rightarrow 8s+8x=20s\\\Rightarrow 12s = 8x\\\Rightarrow s = \dfrac{2}{3}x[/tex]
Now, differentiating w.r.to t:
[tex]\dfrac{ds}{dt}=\dfrac{2}{3}\dfrac{dx}{dt}\\\Rightarrow \dfrac{ds}{dt}=\dfrac{2}{3}\times 12\\\Rightarrow \dfrac{ds}{dt}=\bold{8\ ft/sec}[/tex]
Camel's shadow is growing at a rate of 8 ft/sec.
Which expression would be easier to simplify if you used the commutative property to change the order of the numbers?
Answer:
the 3rd one
Step-by-step explanation:
20+17=37
-1/2+(-5/2)= -3
so 37 + ( -3 ) = -3 + 37 have the same value which is 34
asap please x÷7=11÷15help
Answer:
x = 77/15 or 5 2/15
Step-by-step explanation:
x/7 = 11/15
Multiply each side by 7
x/7 *7 = 11/15 *7
x = 77/15
We can leave as an improper fraction or change to a mixed number
15 goes into 77 5 times with 2 left over
5 2/15
━━━━━━━☆☆━━━━━━━
▹ Answer
x = 77/15, 5 2/15, or 5.13
▹ Step-by-Step Explanation
x ÷ 7 = 11 ÷ 15
15x = 77
Divide both sides by 15:
x = 77/15, 5 2/15, or 5.13
Hope this helps!
CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
what are the four different ways to solve a quadratic equation? When would you prefer to use each method?
Answer:
4
Step-by-step explanation:
factoring , using square roots , completing the square and the quadratic formular
Answer:
See below.
Step-by-step explanation:
The four main ways to solve a quadratic equation are:
1) Factoring, 2) Completing the Square, 3) Graphing, and 4) Quadratic Formula.
Each method has it's own pros and cons.
1) Factoring. You should factor when the given equation is easily factor-able or already factored. For instance:
[tex]0=x^2-4x-12\\0=(x+7)(x-1)[/tex]
These problems are easily factored so factoring is preferred here. However, factoring will not always work.
2) Completing the Square. You complete the square if you are able to complete the perfect square trinomial with only integers. For instance:
[tex]x^2-2x-7=0\\(x^2-2x+1)-7-1=0\\(x-2)^2-8=0[/tex]
However, you wound't use completing the square if:
[tex]x^2-3x+2=0\\(x^2-3x+9/4)+2-9/4=0[/tex]
The perfect square trinomial includes fractions so you would use alternative methods here (and factoring works here!).
Despite the complexity of completing the square, if done correctly, it works every time. However, sometimes, it can be time-consuming.
3) Graphing. Graphing (if on paper) is time-consuming. You would only use graphing when you only need an approximation. Unless directed to, you probably won't need to use graphing.
However, if you have a graphing calculator, graphing the equation can allow you to check your answer. So, graphing won't get you precise answer, but it will allow you to check your answer is necessary.
4) Quadratic Formula. Use the quadratic formula if the equation isn't factor-able and completing the square is too tedious. For instance:
[tex]4.1x^2-3x-7=0\\[/tex]
This doesn't seem factor-able and completing the square will take a while. Graphing won't get the exact answer, so the quadratic formula is the only avenue left.
The quadratic method, like completing the square, will always work.
Only con is that you need to memorize the formula.
One-quarter of the top of a round wedding cake is covered in yellow roses. The top of the wedding cake has a diameter of 12 inches. Each yellow rose covers an area of 0.75 square inch. About how many roses were used to cover this section of the cake?
PLZ ANSWER QUICKLY AND ACCURATLY WILL MARK BRAINLIEST
Answer:
I believe the answer to your question is 38.
Step-by-step explanation:
Here is what I did: First, I found the radius, and to do that, I did 12 divided by 2, which gave me 6. then I did 6 divided by 2, to find the radius, of the radius I just found. which gave me 3, then I did 3 times 12, which gave me 36, so the answer should be 38 :)
Answer:
8
Step-by-step explanation:
I need help ASAP!! I have no idea how to do this and what side does it mean when it says other side??!
Answer:
1 point should be located before 4 points below C.
1 point should be located before 4 points above B.
1 point should be located at point A.
Lance can paint the room in 5 hours, while Kim can paint the same room in 4 hours.
How many hours would it take for them to paint the room together?
Answer:
1.5 hours
Step-by-step explanation:
What effect will replacing x with (x−3) have on the graph of the equation y=x2 y = x 2 ? A. slides the graph 3 units down B. slides the graph 3 units right C. shrinks the graph by a factor of 3 D. slides the graph 3 units left
Answer:
B. slides the graph 3 units right
Step-by-step explanation:
Replacing x with x-h moves the graph 'h' units to the right. In this case, the graph is moved 3 units right by replacing x with x-3.
Solve for x: x - 15 = -30
Answer:
x = -15
Step-by-step explanation:
x - 15 = -30
add 15 to both sides
x = -15
Find the value of a. A. 52 B. 26 C. 104 D. 93.5
Answer:
Option (A)
Step-by-step explanation:
To find the value of 'a' we will use the tangent-chord theorem,
"Angle formed by the chord and a tangent to the circle measure the half of the intercepted minor arc"
Angle 'a' is formed between the chord and the tangent.
Measure of the intercepted arc = (2 × 52)°
Therefore, measure of the angle 'a' = [tex]\frac{104}{2}[/tex]
a = 52°
Therefore, Option (A) will be the correct option.
Two joggers start from different locations and simultaneously begin heading toward each other. One of the joggers jogs 19mph, while the other jogs 17mph. If the two joggers are 324 miles apart how many hours will it take before they meet?
Answer:
It would take 9 hours for them to meet.
Step-by-step explanation:
Total distance covered by both per hour: 19+17=36
The total time to go 324 miles for them: 324/36=9
what comparison does the ratio 6 to 21 represent
Answer:
3:7
Step-by-step explanation:
hope it help you....
Answer:
2:7
Step-by-step explanation:
You have to find the common denominator and divide both numbers by that for example: 6 and 21 they can both be equally divided by 3 without becoming a fraction or a decimal.(Pls do correct me if i'm wrong don't be scared to)
Which ordered pair is a solution of the equation? 2x+4y=6x−y
Answer:
Step-by-step explanation:
"Which ordered pair" implies that there were several answer choices for this problem. It's important that you share such answer choices.
2x+4y=6x−y reduces to 5y = 8x, and so y = (8/5)x
If we choose x = 2, then y = (8/5)(2) = 16/5 is a solution of the given equation. There are an infinite number of such solutions. All lie on the line y = (8/5)x.
Give three equivalent rates that describe the top speed of a tuna.
Given that F( x ) = x 2 + 2, evaluate F(1) + F(5).
Hi there! :)
Answer:
[tex]\huge\boxed{f(1) + f(5) = 30}[/tex]
Given:
[tex]f(x) = x^{2} + 2[/tex]
Evaluate [tex]f(1) + f(5)[/tex]
Solve for each:
[tex]f(1) = (1)^{2} + 2 = 3[/tex]
[tex]f(5) = (5)^{2} + 2 = 27[/tex]
[tex]27 + 3 = 30[/tex]
Answer:
30
Step-by-step explanation:
Please help me! I will give brainly!
Example: To do the answer draw on my screenshot. So then you can make the dots.
David is making rice for his guests based on a recipe that requires rice, water, and a special blend of spice,
where the rice-to-spice ratio is 15 : 1. He currently has 40 grams of the spice blend, and he can go buy
more if necessary. He wants to make 10 servings, where each serving has 75 grams of rice. Overall, David
spends 4.50 dollars on rice.
How many servings can David make with the current amount of spice he has?
Answer:
8 servings of rice
Step-by-step explanation:
Use the model below to find the area of the shaded region.
Answer:4/12
Step1- 3 times 4 is 12
Step2- count how many twelvths are shaded
Step3- 4 twelvths are shaded
Answer: 4/12
Answer:
C. 1/3 square yard
Step-by-step explanation:
Given:
The length of shaded area = 2/3 yardThe width of shaded area = 2/4 yardTo find:
The area of shaded regionSolution:
The shaded region is a rectangle. Area of a rectangle is the product of the length and width:
Area = 2/3 yard * 2/4 yard = 1/3 square yardAnswer choice: C. 1/3 square yard
Math Question (10 Points):
Answer:
0
Step-by-step explanation:
Like terms are terms that have the same variable part.
The variable part of all three terms is u, so all terms are like terms.
5u + u - 6u =
= 5u + 1u 6u
= 6u - 6u
= 0
12(43)
5 (88)
8 (63)
7 (28)
Please help me i tried to do this but I really don't get this can somebody help? plsssssssssssssssssssssssssssssss(sorry for spam)
Find the measure of the remote exterior angle. m∠x=(197−5n)°m∠y=(6n+22)°m∠z=(n+7)°
Answer:
x=127°
Step-by-step explanation:First you have to solve for n and to do so you have to add the interior angles together and equal them to the remote exterior angle.
n+7+6n+22=197-5n
12n+29=197
12n=168
n-14
once you get n you have to plug it into 197-5n
197-5(14)
197-70
127
The required value of exterior angle m∠x is 127.
From figure x is remote exterior angle m∠x=(197−5n)°. and y and z are interior angles m∠y=(6n+22)° and m∠z=(n+7)° respectively. value of x to be determine.
Angle made at outer side of the corner is called exterior angles.
Here, by properties, sum of the interior angle = remoter exterior angle
So,
m∠x = m∠y + m∠z
197−5n = 6n+22+n+7
168 = 12n
n = 14
put n in m∠x
m∠x=(197−5n)°
m∠x=(197−5*14)°
m∠x=(197−70)°
m∠x=127°
Thus, the required value of exterior angle m∠x is 127.
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HELPPPPPP PLEASE AND THANK YOU D:
Answer:
2.
Step-by-step explanation:
2 . is the correct pair.
Find X. Round your answer to the nearest tenth of a degree.
Answer:
48.6 degrees
Step-by-step explanation:
The sine function is appropriate here:
9
sin x = ------------- = 0.75
12
The inverse sine function arcsin x provides with the angle measurement:
arcsin 0.75 = 0.848 radian, or 48.6 degrees
You are planning to use a tile design in your new room. The tiles are equilateral triangles. You decide to arrange the tiles in a hexagonal shape as shown. If the side of each tile measures 11 cm, what will be the exact area of each hexagonal shape? A. 3,993 cm^2 B. 181.5 root 3 cm^2 C. 132 root 3 cm^2 D. 33 cm^2
Answer:
B. 181.5√3 cm^2
Step-by-step explanation:
The area of a regular hexagon with side length s is given by ...
A = (3√3/2)s²
For side length s = 11 cm, the area is ...
A = (3√3/2)(11 cm)² = 363√3/2 cm²
A = 181.5√3 cm²
165°
145
x =
Please Help!!!!
Answer:
15°
Step-by-step explanation:
The 165° and x forms a straight line or a supplementary angle. Supplementary angles add up to 180°. Therefore:
[tex]165+x=180[/tex]
Solve for x:
[tex]165+x=180\\x=15\textdegree[/tex]
Answer:
15 degress
165 and x lie on a 180 degress.
and 180 - 165 is 15.
Bye!
Step-by-step explanation:
Both of these question please help me!!!!!!
Answer:
1. A=3x^4y^4 2.B= 2^6=64
Step-by-step explanation:
hope this helps pls mark brainliest
Help me pls Will mark best
Answer:
i think the answer is 5 i am not sure if wrong i am sorrry
Step-by-step explanation:
solve for W
14/W=26/39
Answer:
I think the answer is 21
Step-by-step explanation:
The answer is 21 because we can simple reduce 26/39 = 2/3. And now that you have done that all we need to do is find what 14/w = 2/3 this is quite simple as we just have to mutiply the 3*7 to get 21 as your answer. I don't know if this is correct or not but this is my best answer.
Answer:
21
Step-by-step explanation:
14 : w = 26 : 39
w = 14 * 39 : 26
w = 21