The two numbers that sum to -6 and have a product of 12 are -3 ± √3i and -3 ± √3i respectively.
What is a numerical data?A numerical data is also referred to as a quantitative data and it can be defined as a data set that is primarily expressed in numbers (numerals) only. This ultimately implies that, a numerical data simply refers to a type of data set consisting of numbers (numerals) rather than words.
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In order to solve this word problem, we would assign variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
Let the two unknown numbers be x and y.
Translating the word problem into an algebraic equation, we have;
Sum: x + y = -6 .....equation 1.
Product: xy = 12 ....equation 2.
From equation 1, we have:
x = -6 - y
Substituting equation 3 into equation 2, we have:
(-6 - y)y = 12
-6y - y² = 12
y² + 6y + 12 = 0
Solving the quadratic equation, we have:
y = -3 ± √3i
For the value of x, we have:
x = -6 - y
x = -6 - (-3 ± √3i)
x = -6 + 3 ± √3i
x = -3 ± √3i
Read more on an algebraic equation here: brainly.com/question/2190003
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Solve the following quadratics equation for all values of x in simplest form
9(3x - 7) ^2= 16
Answer:
x= 17 /9 or x= 25 /9
Step-by-step explanation:
9(3x - 7) ^2= 16
9(3x - 7) ^2-16= 0
as we know that (a-b)^2=a^2-2ab+b^2
9((3x)^2-2(3x)(7)+(7)^2=0
solving this we got the below equation
81x2−378x+425=0
By Factorizing the equation
(9x−17)(9x−25)=0
9x−17=0 or 9x−25=0
x= 17 /9 or x= 25 /9
Find the value of x in the triangle shown below.
a. x=4
b.x=5
c.x=2
d.x=32
Answer:
4√2
Step-by-step explanation:
Using Pythagoras Theorem ,
[tex]\implies h^2 = p^2 + b^2\\\\\implies 9^2 = x^2 + 7^2 \\\\\implies 81 = x^2 + 49 \\\\\implies x^2 = 81 - 49 \\\\\implies x^2 = 32 \\\\\implies \boxed{x = 4\sqrt2} [/tex]
Answer:
Answer:[tex] \huge\mathfrak\pink{S} \huge\mathfrak\purple{o} \huge\mathfrak\blue{l} \huge\mathfrak\red{u} \huge\mathfrak\green{t} \huge\mathfrak\pink{i}\huge\mathfrak\purple{o}\huge\mathfrak\red{n}\huge\mathfrak\orange{➔}\ [/tex] Pythagoras law:h²=p²+b²
9²=x²+7²
x²=81-49
x=√32 units
A model rocket is launched directly upward at a speed of 15 meters per second from a height of 10 meters. The function f(t)=-4.9t^ 2 +15t+10. models the relationship between the height of the rocket and the time after launch, t, in seconds. When, in seconds after launch, will the rocket reach its highest pointRound to two decimal places.
Answer:1.53
Step-by-step explanation:
A net and the prism it will form when it is folded are shown below.
A prism is made up of 4 rectangles with a base of 12 centimeters and height of 11 centimeters and 2 rectangles with a base of 12 centimeters and height of 10 centimeters.
What is the surface area of the prism in square centimeters?
724 square centimeters
972 square centimeters
1,089 square centimeters
1,320 square centimeters
Answer:
724
Step-by-step explanation:
PLEASE MARK BRAINLIEST!!!!!!!!!Answer: 724
Step-by-step explanation: I multiplied and then got this i also did the quiz for this :) have a good day!
Solve these equations.
Answer:
x=0, -28.
Step-by-step explanation:
abs(x+14)=14
x+14=14
x=14-14=0
----------------
x+14=-14
x=-14-14
x=-28
During a baskethall game, you want to pass the ball to either Player A or Player B. You estimate that Player B is about 15 feet from you, as shown. How far away from you is Player A?
Answer: 19.2 ft
Step-by-step explanation:
The distance between you, Player A and Player B are in the form of a right angled triangle so using the Pythagorean Rule, we can find the distance between you and Player A.
c² = a² + b²
c = hypotenuse = Distance between you and player A
a = Length of triangle
b = Height of triangle
c² = 12² + 15²
c² = 144 + 225
c = √369
c = 19.2 ft
An item on sale cost 80% of the original price. If the original was$75.00 what is the sale price
Answer:
sale prive would be 15$ but 60$ off
Step-by-step explanation:
Answer:
$60
Step-by-step explanation:
To solve this problem you can multiply 75 by .8, 80%, or 8/10. Multiplying by these numbers is equal 80%
Triangle ABC is formed by connecting the points A (2,6), B (6,6) and C (6,1). What is the exact length of the hypotenuse of triangle ABC? Express your answer as an entire radical.
Step-by-step explanation:
ndnndndndjdjdjdfjfjfgnn
I WILL GIVE BRAINLIEST!!
Just need help for questions 88 and 90.
find the surface area of this prism. geometry hw
Answer:
395.2 cm²
Step-by-step explanation:
2x12.7x6.72=170.688
2x6.72x5.78=77.6832
2x5.78x12.7=146.812
170.688+77.6832+146.812=395.1832
Answer: A=395.2
Step-by-step explanation:
A=2(wl+hl+hw)
A=2[(12.7x5.78)+(6.72x5.78)+(6.72x12.7)]
A=2(73.406+38.8416+85.344)
A=2(197.5916)
A=395.1832
Rounded to nearest tenth..
A=395.2
A sewing instructor asked his students how many spools of knitting yarn they carried in their sewing kits. The table shows the data he recorded.
Item $80 yesterday. Today it's $36. What's the % difference
Answer:
$36 is 45% of $80. The percent difference is 55%.
Step-by-step explanation:
what is 8 (x/4 - 6) < 4
Answer:
x<26
Step-by-step explanation:
8(x/4 - 6) < 4
Divide both sides by 8;
8(x/4 - 6)/8 < 4/8
Simplify;
x/4-6<1/2
Add 6 to both sides;
x/4-6+6<1/2+6
Simplify;
x/4-6+6<1/2+6
Simplify
x/4-6+6
=x/4
Simplify;
1/2+6
Convert it into a fraction;
6*2/2+1/2
Since the denominators are equal combine the fractions;
6*2+1/2
6*2+1=13
=13/2
x/4<13/2
Multiply both sides by 4;
4x/4<13*4/2
Simplify 4x/4
4x/4
4/4=1
=x
Simplify 13*4/2
Multiply the numbers:13*4=52
=52/2
Divide the numbers:52/2=26
=26
x<26
HOPE THIS HELPED!!!
Bill buys a large can of paint. The size of the can measured in which units
Answer:
Paint is measured in gallons
Step-by-step explanation:
Will name brainliest
Congruence proofs and reasons
Reasons must be from this list:
Reflexive property, segment bisector, angle bisector, linear pair, transitive property, perpendicular, SAS, ASA, CPCTC, AAS, HL, and SSS
Every word may not be used, but each may not be used more than once.
Answers must be structured as:
17,
2:
3(1):
3(2):
18,
2:
3:
4(1):
4(2):
19,
2:
3:
4:
5:
6:
7(1):
7(2):
20,
2:
3:
4:
Answer:
huh? Can you put it in a pdf
Step-by-step explanation:
I need help SHOW YOUR WORK
Answer:
[tex] F)\displaystyle \: 100\pi{ x}^{8} {y}^{2} {z}^{ 6} [/tex]
Step-by-step explanation:
we are given r and the formula
we want to find the surface area of the shpare with the given r
to do so
we need our algebra skills
substitute the value of r:
[tex] \displaystyle \: S = 4\pi( {5x}^{4} y {z}^{ 3} {)}^{2} [/tex]
recall law of exponent
[tex] \displaystyle \: ({x}^{m} {)}^{n} \iff \: {x}^{mn} [/tex]
to simplify:
[tex] \displaystyle \: S = 4\pi({ {5}^{2} x}^{4 \times 2} {y}^{1 \times 2} {z}^{ 3 \times 2} )[/tex]
simplify multiplication:
[tex] \displaystyle \: S = 4\pi({ 25x}^{8} {y}^{2} {z}^{ 6} )[/tex]
distribute:
[tex] \displaystyle \: S = 100\pi{ x}^{8} {y}^{2} {z}^{ 6} [/tex]
hence our answer is F
A triangular prism is 37 millimeters long and has a triangular face with a base of 20
millimeters and a height of 24 millimeters. The other two sides of the triangle are each 26
millimeters. What is the surface area of the triangular prism?
formula- tsa of prism- 2*area of trangular base + lateral surface area
to make easy
area of trangular base = 1/2(breathe×height)
lateral surface area =
area of trangluar bases+ perimeter of trangular base
The amount of time required to reach a customer service representative has a huge impact on customer satisfaction. Below is the Excel output from a study to see whether there is evidence of a difference in the mean amounts of time required to reach a customer service representative between two hotels. Assume that the population variances in the amount of time for the two hotels are not equal.
t-Test: Two-Sample Assuming Unequal Variances
Hotel 1 Hotel 2
Mean 2.214 2.0115
Variance 2.951657 3.57855
Observations 20 20
Hypothesized Mean Difference 0
df 38
t Stat 0.354386
P(T<=t) one-tail 0.362504
t Critical one-tail 1.685953
P(T<=t) two-tail 0.725009
t Critical two-tail 2.024394
A) State the null and alternative hypotheses for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.
B) What is the value of the test statistic for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels? Explain how you obtain.
C) What is the critical value for testing if there is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels at the 5% level of significance? Explain how you obtain.
D) Suppose α = 0.05. Which of the following represents the correct conclusion for a test on a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels?
1) There is no evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.
2) There is evidence of a difference in the variabilities of the amount of time required to reach a customer service representative between the two hotels.
3) There is no evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same.
4) There is evidence that the variabilities of the amount of time required to reach a customer service representative between the two hotels are the same.
Answer:
A) H0: σ₁²-σ₂²= 0 against the claim Ha: σ₁²-σ₂²≠0
B) t= 0.3543860
C) t≥ t∝/2 ( d.f)=2.024394
D)1) There is no evidence of a difference in the variability of the amount of time required to reach a customer service representative between the two hotels.
Step-by-step explanation:
The claim is that there is evidence of a difference in the variability of the amount of time required to reach a customer service representative between the two hotels which is the
alternate hypothesis
The null hypothesis is the reverse of the alternate hypothesis
The null hypothesis is that there is not enough evidence of a difference in the variability of the amount of time required to reach a customer service representative between the two hotels.
Part A) H0: σ₁²-σ₂²= 0 against the claim Ha: σ₁²-σ₂²≠0
Part B) t= x1`-x2`/ sqrt ( s₁²/n₁ + s₂²/n₂)
t= 2.214- 2.0115/ sqrt ( 2.951657/20+ 3.57855/20)
t= 0.2025/ sqrt(0.14758285 + 0.1789275)
t= 0.2025/0.5714108
t= 0.3543860
Part C) for 2 tailed test the critical value of t is obtained by
t≥ t∝/2 ( d.f)= ± 2.024394
We look at the table with values 0.025 as ∝/2= 0.05/2= 0.025
in the degrees of freedom 38
The d.f = n1+n2-2= 20+20-2= 40-2= 38
Part D) Since the calculated value of t= 0.3543860 does not fall in the critical region t≥ t∝/2 ( d.f)= ± 2.024394 we conclude that H0 is true and accept the null hypothesis.
So option 1 is correct
1) There is no evidence of a difference in the variability of the amount of time required to reach a customer service representative between the two hotels.
Juliette is a waitrees at Applebee's. The total for one of the tables she served was $51.87. The table wants to leave her an 18% tip. How much should Juliette make for her tip?
Answer:
They should leave Juliette about a $9.34 tip because 18% of 51.87 is 9.3366 which rounds up to 9.34
Answer:
18% of $51.87=9.3366tip is a required tip.
Circle all of the sums which
are odd.
11 + 22
42 + 96
55 + 86
Answer:
11+22, and 55+86
Step-by-step explanation:
11+22 = 33 which is odd
55+86 = 141 which is also odd
42+96 = 138 which is EVEN
Even is the opposite
of odd
Michael deposited $1,500 into a savings account with a simple interest rate of 2%. How much money will he have in his account after 4 years if no additional deposits or withdrawals are made?
Answer:
$1,620
Step-by-step explanation:
2% per year:
2% of 1,500 = 30
30 x 4 = 120
1500 + 120 = 1620
Use the equation and type the ordered-pairs.
Y = 2^x
Answer:
(0,1)
Step-by-step explanation:
A right triangle has side lengths d, e, and f as shown below.
Use these lengths to find tanx, sinx, and cosx.
Answer:
tanx=d/f, sinx=d/e, cosx=f/e
Step-by-step explanation:
Find the opposite, Adjacent and hypotenuse of the right triangle.
Opposite= d , Adjacent= f, Hypotenuse= e
Tanx = opposite/adjacent
Sinx= opposite/hypotenuse
Cosx= adcajent/hypotenuse
Help please! :) I don’t know how to solve this!
Answer:
261
Step-by-step explanation:
→ Substitute 2 into g( x )
( 3 × 2 ) + 10 = 16
→ Substitute that answer into f( x )
16² + 5 = 261
Anh randomly surveyed 36 students
Anh randomly surveyed 36 students to see if there was interest in starting the 7th grade science club he found 4 students said they would be interested if 180 students are in the 7th grade how many can be expected to join?
4/36 = x/180
180/36 = 5
20/180
20 students would be intrested
The table shows the results of drawing 44 cards from a deck of 104 game cards. After each draw, the card is replaced.Based on the results, what is the chance that a draw results in a wild card?
Cards :Wild|Number|Penalty|
Freq: 10 | 32 | 2 |
10/44, =
5/22
ZABD and ZDBC are supplementary angles.
What is the measure of x?
x = [?]
7D
AK
100%
B
>C
Angles are not drawn to scale
Answer:
Solution given:
x+100=180°{linear pair}
x=180-100
x=80
Answer:
x = 80
Step-by-step explanation:
<ABD and <DBC
If AB has endpoints A(-15,9) and B(0,3) what is the slope of AB. Please show all your work
Answer:
-2/5
Step-by-step explanation:
slope = (y2-y1)/(x2-x1)
= ( 3-9)/(0+15)
= -6/15
= -2/5
A right rectangular prism is shown what is the volume in cubic inches of the prism
Answer:
Step-by-step explanation:
Exact value is (130 )
Answer:
130
Step-by-step explanation:
Find the value of x?
Answer:
x = 12
Step-by-step explanation:
An inscribed angle has half the measure of the arc it intercepts.
arc SU +arc UT = 180°
2(43°) +(9x -14)° = 180°
9x = 108 . . . . . . . divide by °, subtract 72, simplify
x = 12 . . . . . divide by 9
Challenge You have two spinners with colors on them. The probability of spinning green on both spinners is 5/22 the probability of spinning green on the first one alone is 1/3. What is the probability of spinning green on the second spinner alone?
Answer:
hi i know this not the answer but hope it help:)))
Step-by-step explanation:
Multiply the probabilities just calculated for each individual spinner together to find the probability of getting any specific combination of outcomes from spinning the arrows on both spinners. In the example, you would multiply 1/4 by 1/3 to obtain 1/12.