Answer:
6 ft and 8 ft
Step-by-step explanation:
let x be the length of one leg then (x + 2) is the other leg.
Using Pythagoras' identity in the right triangle, that is
x² + (x + 2)² = 10² ← expand left side and simplify
x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )
2x² + 4x - 96 = 0 ( divide all terms by 2 )
x² + 2x - 48 = 0 ← in standard form
(x + 8)(x - 6) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 8 = 0 ⇒ x = - 8
x - 6 = 0 ⇒ x = 6
But x > 0 ⇒ x = 6
Thus the 2 sides are 6 ft and x + 2 = 6 + 2 = 8 ft
a sinusoid always function has an amplitude of 3, a frequency of 1/8pi, and a midline at 2. Which of the following equations satisfies these conditions? a. f(x)=3sin x/8pi +2 b. f(x)=3sin(4x) +2 c. f(x)=3sin(8pi x) +2 d. f(x)=3sin x/4 +2
Answer:
The correct option is;
f(x) = 3·sin x/8·π + 2
Step-by-step explanation:
The given parameters for the sinusoidal function are;
Amplitude of oscillation = 3
Frequency of oscillation = 1/8·π
Midline of oscillation= 2
The general form of sinusoidal equation is y = A·sin(B(x - C)) + D
Where;
A = The amplitude
B = The frequency
C = The horizontal shift
D = The midline or vertical shift
Substituting the given values into the general form of sinusoidal equation, we have;
f(x) = y = 3·sin(1/8·π(x - 0)) + 2 = 3·sin(x/8·π) + 2
Which gives;
f(x) = 3·sin(x/8·π) + 2.
(३) एक शब्द में उत्तर लिखो:
१. कवि की जिह्वा पर इसके गीत हों -
२. मातृभूमि के चरण धोने वाला
३. मातृभूमि के सपूत -
४. प्रतिदिन सुनने/सुनाने योग्य नाम -
५. मातृभूमि के चरणों में इसे नवाना है
करना चाहिए। वे तुम्हें नष्ट कर देंगे।
आप कोई मौका नहीं खड़े हैं। तुम
उसके हाथ पर मर जाओगे। पछताना
Solve for x: |x| − 8 = −5 (2 points) A. x = −13 and x = −3 B. x = 3 and x = −3 C. x = 3 and x = 13 D. No solution
Answer:
x = 3 and x = -3
Step-by-step explanation:
/x/ - 8 = -5
Add 8 to both sides
/x/ -8 + 8 = -5 +8
/x/ = 3
/ x / will be always positive as it is absolute value of x. So, x = 3 & x= -3
Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
One fifth of the square of a number
Answer:
The statement, one fifth of the square of a number is written as
[tex] \frac{1}{5} {x}^{2} [/tex]
Hope this helps you
Scarlett bought an ant farm with 80 ants. Frond the following week forward, the ant population tripled every week. Let g(n) be the number on ants in scarletts farm in the nth week since she got it. G is a sequence. What kind is it? Write an explicit formula for the sequence starting with g(n)=? Need help really bad I’m stuck and can’t figure out what it is
Answer:
g(n)=80×3^(n-1)
Step-by-step explanation:
First term (a)=80
The ant population tripled every week.
So, the population of ant after 1st week will be (80 × 3) = 240
After 2 weeks, the population triples again.
We have, (240 × 3) = 720
Common ratio (r)=720/240
=3
r=3
The ants population is increasing in a geometric progression
A geometric progression is given by
g(n)=a × r^(n-1)
Substitute values of a and r to get the explicit formula
g(n)=a × r^(n-1)
g(n)=80×3^(n-1)
PLEASE 40 POINTS AND I WILL GIVE BRAINLIESTHow many solutions does this system have? 2 x minus 3 y = 10. Negative 4 x + 6 y = negative 20. one two an infinite number no solution
Answer:
Infinite solutions
Step-by-step explanation:
2x-3y=10
-4x+6y=-20
Turn them into point-slope form.
y = 2/3x - 10/3
y = 2/3x - 10/3
They are the same equation, so they will have infinite solutions.
Answer:
infinite solutions i did the quiz and got a 100 pls give brainliest
Step-by-step explanation:
Pleaseeee helppppp❤️
Answer:
The expression will be simplified into [tex]26x^4y^3+35xy^6-42xy^5\\[/tex]
Step-by-step explanation:
It's like addition, when you multiply exponents that are on the same bases as each other.
Which set of points does NOT represent a function?
OA) (8,5), (7,5), (6,5), (5,5)
O B) (3,-5), (3, -1), (3, 2), (3, 4)
OC) (-2,3), (-3,2), (2, -3), (3, -2)
OD) (4, -1), (5, 1), (-1,4), (1,5)
Answer:
Answer A does not represent a function(I think)
Step-by-step explanation:
Because the Y-coordinates are the same.
Can someone help me with this
Answer:
D. [tex] \frac{{7}^{11} }{ {4}^{11} } [/tex]
Step-by-step explanation:
[tex]( \frac{7}{4}) {}^{11} = \frac{7 {}^{11} }{4 {}^{11} }[/tex]
Since we are multiplying an exponential number to a fraction the answer is going to be
[tex] \frac{7 {}^{11} }{4 {}^{11} } [/tex]
Hope this helps ❤❤❤ ;)
Answer:
[tex]D. \frac{7^{11} }{4^{11} } \\[/tex]
Step-by-step explanation:
Hello, I can help you with this
Let's remmber some propiertis of the fraction numbers and the potenciation
Let
[tex]a^{m} * a^{n}=a^{m+n}\\(a^{m})^{n}=a^{m*n}\\(\frac{a}{b})^{m}=\frac{a^{m} }{b^{m}}[/tex]
Step 1
All you have to do is identify and use the formula
let
[tex](\frac{7}{4})^{11}\\ a=7\\b=4\\m=11\\so\\(\frac{7}{4})^{11}=\frac{7^{11} }{4^{11} } \\[/tex]
so, the answer is D.
I hope it helps, have a nice day
Write a pair of negative integers whose difference is 8.
Answer:
(-5,-13) has a difference of 8
Answer:
-2 and -10
Step-by-step explanation:
negative integers are whole numbers below 0
difference is the same as (-)subtraction
x-y=8
if x= -2
-2-y=8
-y=8+2
-y=10
y= -10.
confirmation-2 - (-10)=8
-2+10=8
8=8
a map has a scale of 1cm:11.5km.two cities are 5.5cm apart on the map.to the nearest tenth of a kilometer,what is the actual distance corresponding to the map distance?
Answer:
63.3 km
Step-by-step explanation:
All that you need to do here is to multiply 5.5 by 11.5 which equates to...
=5.5x11.5
=63.25
because the second decimal is five you have to round up so that means that the answer is 63.3km.
Hope it helped.. Tysm... Plz.. Mark me BRAINLIEST..
Answer:
[tex]\boxed{63.3 \ km}[/tex]
Step-by-step explanation:
1 cm : 11.5 km
We need the distance for 5.5 cm So,
Multiplying both sides by 5.5
1 cm : 11.5 cm
× 5.5 ×5.5
5.5 cm : 63.25 km
For every 5.5 cm, the actual distance is 63.25 km but to the nearest tenth, it is 63.3 km
What is the measurement of angle 1?
What is the measurement of angle 2?
What is the measurement of angle 3?
What is the measurement of angle 4?
What is the measurement of angle 5?
What is the measurement of angle 67
What is the measurement of angle 7?
Answer:
Angle 1= 180 - 110 = 70 (straight angle)
Angle 2 = 180 - 115 =65 (straight angle)
Angle 3= angle 2 =65 (corresponding alternating angles)
Angle 4 =180 - angle3 = 180 - 65 = 115 (straight angle)
Angle 5 = 180 - angle 1 - angle 3= 180 - 70 - 65 = 45 (sum of triangle angles is equal to 180)
Angle 6 = angle 5= 45 ( interior alternating angles)
Angle 7 = angle 6= 45 (vertical opposite angles)
[tex]hope \: this \: helps[/tex]Angle 1= 180 - 110 = 70
Angle 2 = 180 - 115 =65
Angle 3= angle 2 =65
Angle 4 =180 - angle3 = 180 - 65 = 115 (straight angle)
Angle 5 = 180 - angle 1 - angle 3= 180 - 70 - 65 = 45
Angle 6 = angle 5= 45
Angle 7 = angle 6= 45
Not to sound like the other person but yeah,these are the answers.
steven wants to buy a 495 steven has no money saved,but will be able to deposit 40 into a savings account when he receives his paycheck each Friday however before steven can buy the bike he must give his sister 65 that he owes her
Answer:
14 paychecks
Step-by-step explanation:
$495 + $65 = $560
$560 / 40 = 14
Therefore , he must save for 14 paychecks
Hope this helps and pls mark as brainliest :)
Answer:
14
Step-by-step explanation:
$495 + $65 = $560
$560 / 40 = 14
He must save for 14 paychecks.
Hope this help
Mark me BRAINLIEST
Tysm
when 5 more than 2 lots of a number is tripled the result is 10
Answer:
-5/6
Step-by-step explanation:
a number is x
then two lots will be 2 x
five more will be 2x+5
then tripled so 3(2x+5)
will equal 10
Answer: [tex]-\frac{5}{6}[/tex]
Step-by-step explanation:
3(2x+5)=10
Distribute
6x+15=10
Subtract 15
6x=-5
x = -5/6
Hope it helps <3
Please answer it now in two minutes
Answer:
m∠F = 20.6°
Step-by-step explanation:
In the given right triangle ΔHGF,
∠G = 90°
By applying tangent rule in the triangle,
tan(∠F) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{\text{HG}}{\text{GF}}[/tex]
= [tex]\frac{3}{8}[/tex]
= 0.375
m∠F = [tex]\text{tan}^{-1}(0.375)[/tex]
= 20.556°
= 20.6°
Therefore, measure of angle F is 20.6°
which of the following is the Pythagorean theorem
Answer:
[tex]a^2+b^2=c^2[/tex]
Step-by-step explanation:
The Pythagorean Theorem is used to find a missing side length in a right triangle, and the formula [tex]a^2+b^2=c^2[/tex] is used to find the missing side, assuming a and b are legs, while c is the hypotenuse.
Answer:
in a right triangle, the sum of the squares of the leg lengths is equal to the square of the hypotenuse length
The equation of the graphed line in point-slope form and it’s equation in slope-intercept form is (-2,3)(3,0)
Answer:
y = -9/5x + 9/5
Step-by-step explanation:
From this points, we can determine the slope and the y-intercept.
First, we do: y/x - y1/x1
=> 0/3 - (3 - 2)
=> 0-3/ 3 + 2
=> -3/5
So the slope of the equation is -3/5.
The equation is: y = mx + b
In this equation "m" = slope.
=> b = constant
Now we take the x and y points from the above numbers.
=> Let's take 3 as x and 0 as y.
=> 0 = -3/5 *3 + b
=> 0 = -9/5 + b
=> Take the -9/5 to the other side
=> 9/5 = b
So, the constant number which is not multiplied by the x is 9/5
Now, our equation looks like:
y = -9/5x + 9/5
If you have any doubts about this question, ask me the comments and I will answer it as soon as possible.
The equation of a line that is parallel to y = -3x + 6 and passes through the point (0, -4) please help this is an emergency I need this ASAP please!!!!
Answer:
y = - 3x - 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 6 ← is in slope- intercept form
with slope m = - 3
Parallel lines have equal slopes.
The line crosses the y- axis at (0, - 4 ) ⇒ c = - 4, thus
y = - 3x - 4 ← equation of parallel line
Find the product.
(6a + 3b)(a - b)
Enter the correct answer.
Answer:
See below.
Step-by-step explanation:
[tex](6a+3b)(a-b)\\[/tex]
Distribute:
[tex]=(6a+3b)(a)-(6a+3b)(b)\\=6a^2+3ab-(6ab+3b^2)\\=6a^2+3ab-6ab-3b^2\\=6a^2-3b^2-3ab[/tex]
Answer:
6a^2-3b^2-6ba+3ba
Step-by-step explanation:
(6a+3b)(a+b)....expand the term
6axa - 6axb + 3bxa - 3b×b ....simplify
6a^2 - 6ba + 3ba - 3b^2, then reorder so highest order terms come first
6a^2 - 3b^2 - 6ba + 3ba
Which data set has the largest standard deviation?
O A. 12, 14, 13, 14, 12, 13, 12
O B. 1,6,3, 15, 4, 12,8
O C. 20, 21, 23, 19, 19, 20, 20
D. 3,4,3, 4, 3, 4,3
SU
Answer:
I thinks it's B.not sure...
The deviation of the mean between the sample is less in option B.
What is a standard deviation?It is the measure of the dispersion of statistical data. Dispersion is the extent to which the value is in variation.
The mean is the numerical normal of a bunch of at least two numbers. The number juggling means and the mathematical mean are two sorts of implications that can be determined.
If the deviation of the mean between the sample is more, then the deviation will be more.
Let's check all the options.
A. 12, 14, 13, 14, 12, 13, 12
The mean is calculated as,
Mean = (12 + 14 + 13 + 14 + 12 + 13 + 12) / 7
Mean = 12.86
B. 1,6,3, 15, 4, 12,8
The mean is calculated as,
Mean = (1 + 6 + 3 + 15 + 4 + 12 + 8) / 7
Mean = 7
C. 20, 21, 23, 19, 19, 20, 20
The mean is calculated as,
Mean = (20 + 21 + 23 + 19 + 19 + 20 + 20) / 7
Mean = 20.28
D. 3,4,3, 4, 3, 4, 3
The mean is calculated as,
Mean = (3 + 4 + 3 + 4 + 3 + 4 + 3) / 7
Mean = 3.43
The deviation of the mean between the sample is less in option B.
More about the standard deviation link is given below.
https://brainly.com/question/12402189
#SPJ2
MATH PLEASE HELP ME. WILL GIVE BRAINLIEST
Answer:
The answer is - 17Step-by-step explanation:
g(x) = 2x³ - 3x + 5
To find g(- 2) substitute the value of - 2 into g(x)
That's
g(- 2) = 2(-2)³ - 3(-2) + 5
= 2(-8) - 3(2) + 5
= - 16 - 6 + 5
= - 17Hope this helps you
Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2ab-6a+5b+__
Answer:
37
Step-by-step explanation:
Please help me with this problem! If anybody answers first in this, i will give brainliest to you! Be the first one to answer this then i will give out a brainliest award to you!
Are you sure your that person?
Answer:
32 remainder 2
Step-by-step explanation:
To divide 162 by 5, we simply do the following:
5 goes into 16 => 3
Multiply 5 by 3 => 3 × 5 = 15
Subtract 15 from 16 => 16 – 15 = 1
Put the 1 before 2 => 12
5 goes into 12 => 2
Multiply 5 by 2 => 5 × 2 = 10
Subtract 10 from 12 => 12 – 10 => 2
In summary,
162 divided by 5 => 32 remainder 2
Please see attached photo for further details.
Sketch the graph of y=-3(x-3)2+4 and identify the axis of symmetry.
Answer:
The axis of symmetry of parabola is the equation where it cuts the middle of the graph.
So the axis of symmetry is x = 2 .
1. an alloy contains zinc and copper in the ratio of 7:9 find weight of copper of it had 31.5 kgs of zinc.
2. compare the following ratios
i) 2:3 and 4:5
ii) 11:19 and 19:21
iii) ½ : ⅓ and ⅓ : ¼
iv ) 1⅕ : 1⅓ and ⅖ : 3/2
v) if a : b = 6:5 and b:c = 10:9, find a:c
vi) if x : y = ⅙:⅛ and y : z = ⅛: ⅒, find X : z
sorry many questions
Answer:
Step-by-step explanation:
Question (1). An alloy contains zinc and copper in the ratio of 7 : 9.
If the weight of an alloy = x kgs
Then weight of copper = [tex]\frac{9}{7+9}\times (x)[/tex]
= [tex]\frac{9}{16}\times (x)[/tex]
And the weight of zinc = [tex]\frac{7}{7+9}\times (x)[/tex]
= [tex]\frac{7}{16}\times (x)[/tex]
If the weight of zinc = 31.5 kg
31.5 = [tex]\frac{7}{16}\times (x)[/tex]
x = [tex]\frac{16\times 31.5}{7}[/tex]
x = 72 kgs
Therefore, weight of copper = [tex]\frac{9}{16}\times (72)[/tex]
= 40.5 kgs
2). i). 2 : 3 = [tex]\frac{2}{3}[/tex]
4 : 5 = [tex]\frac{4}{5}[/tex]
Now we will equalize the denominators of each fraction to compare the ratios.
[tex]\frac{2}{3}\times \frac{5}{5}[/tex] = [tex]\frac{10}{15}[/tex]
[tex]\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}[/tex]
Since, [tex]\frac{12}{15}>\frac{10}{15}[/tex]
Therefore, 4 : 5 > 2 : 3
ii). 11 : 19 = [tex]\frac{11}{19}[/tex]
19 : 21 = [tex]\frac{19}{21}[/tex]
By equalizing denominators of the given fractions,
[tex]\frac{11}{19}\times \frac{21}{21}=\frac{231}{399}[/tex]
And [tex]\frac{19}{21}\times \frac{19}{19}=\frac{361}{399}[/tex]
Since, [tex]\frac{361}{399}>\frac{231}{399}[/tex]
Therefore, 19 : 21 > 11 : 19
iii). [tex]\frac{1}{2}:\frac{1}{3}=\frac{1}{2}\times \frac{3}{1}[/tex]
[tex]=\frac{3}{2}[/tex]
[tex]\frac{1}{3}:\frac{1}{4}=\frac{1}{3}\times \frac{4}{1}[/tex]
= [tex]\frac{4}{3}[/tex]
Now we equalize the denominators of the fractions,
[tex]\frac{3}{2}\times \frac{3}{3}=\frac{9}{6}[/tex]
And [tex]\frac{4}{3}\times \frac{2}{2}=\frac{8}{6}[/tex]
Since [tex]\frac{9}{6}>\frac{8}{6}[/tex]
Therefore, [tex]\frac{1}{2}:\frac{1}{3}>\frac{1}{3}:\frac{1}{4}[/tex] will be the answer.
IV). [tex]1\frac{1}{5}:1\frac{1}{3}=\frac{6}{5}:\frac{4}{3}[/tex]
[tex]=\frac{6}{5}\times \frac{3}{4}[/tex]
[tex]=\frac{18}{20}[/tex]
[tex]=\frac{9}{10}[/tex]
Similarly, [tex]\frac{2}{5}:\frac{3}{2}=\frac{2}{5}\times \frac{2}{3}[/tex]
[tex]=\frac{4}{15}[/tex]
By equalizing the denominators,
[tex]\frac{9}{10}\times \frac{30}{30}=\frac{270}{300}[/tex]
Similarly, [tex]\frac{4}{15}\times \frac{20}{20}=\frac{80}{300}[/tex]
Since [tex]\frac{270}{300}>\frac{80}{300}[/tex]
Therefore, [tex]1\frac{1}{5}:1\frac{1}{3}>\frac{2}{5}:\frac{3}{2}[/tex]
V). If a : b = 6 : 5
[tex]\frac{a}{b}=\frac{6}{5}[/tex]
[tex]=\frac{6}{5}\times \frac{2}{2}[/tex]
[tex]=\frac{12}{10}[/tex]
And b : c = 10 : 9
[tex]\frac{b}{c}=\frac{10}{9}[/tex]
Since a : b = 12 : 10
And b : c = 10 : 9
Since b = 10 is common in both the ratios,
Therefore, combined form of the ratios will be,
a : b : c = 12 : 10 : 9
A research agency asks a random sample of respondents, ‘Would you vote for a female candidate for President if she were qualified in every other way?” The design of this study is flawed. How?
A. More information should have been provided about this potential female candidate for president, such as age, race, and religious affiliation.
B. Only carefully screened subjects should have been allowed to answer this survey question because not everyone is likely to vote in the next presidential election.
C. Research agencies should not ask survey questions about differences in age, race, gender, or religious affiliation as there is an increased risk in offending some sample respondents.
D. Wording the question in this manner implies that being female by itself makes you less qualified than a male…it says “if she were qualified in every other way.”
The correct answer is D. Wording the question in this manner implies that being female by itself makes you less qualified than a male…it says “if she were qualified in every other way.”
Explanation:
One of the factors that can make a study flaw is bias, this means the study includes questions or content influenced by personal judgements or that tries to influence the answers of the respondents. This occurs in the question "‘Would you vote for a female candidate for President if she were qualified in every other way?” because the phrase "if she were qualified in every other way" indirectly tells respondents women are less qualify or might not be qualified to be in the role of a president, which shows a personal judgment. Also, this wording might influence respondents to answer they would not vote for a woman.
1. Arjun puts £750 into his savings account. The account earns 5% simple interest per annum. After 4 years, how much money will Arjun have in his savings account? £ 1. Connor invests £1500 of his money for 2 years at a simple interest rate of 10%. How much money will he get back in interest?
Answer:
1. 900
2. 350
Step-by-step explanation:
the formula,
A= P(1+rt)
A= final amount
P= starting amount
r= intrest rate
t= time
1. A=750(1+.05*4)
A=750(1.2)
A=900
2. A=1500(1+.1*2)
A=1500(1.1)
A=1650
But theyre
asking for how much intrest will they get back, so you subtract the new amount by the starting amount to find how much intrest was earned
1650-1500=350
Find the area a. 530 b. 779 c. 390 d. 1060
Answer:
a. 530 ..I think.. i'm pretty sure
Step-by-step explanation:
40*26.5 is 1060
1060/2=530
area=530
WHAT IS THE ANSWER PLS HELPPPPP!!!!!
Answer:
5^x - 5^-x
Step-by-step explanation:
g(x) = 5^-x
h(x) = 5^x
We want h(x) - g(x)
h(x) - g(x) = 5^x - 5^-x
This cannot be simplified
Find the standard deviation for the given data. Round your answer to one more decimal place than the original data. To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below: $124 $256 $118 $441 $122 $335 $340 $191
Answer:
$122.1
Step-by-step explanation:
We are given the following data in the question
$124, $256 , $118, $441, $122, $335, $340, $191
Step 1
Find the mean
Mean = Sum of Terms / Number of Terms
Number of Terms = 8
Mean = ($124 + $256 + $118 + $441 + $122 + $335 + $340 + $191 )/ 8
Mean = $1927/8
= $240.875
Approximately to 1 decimal place
$240.9
Step 2
Standard deviation formula
S = √( x - μ)²/ N - 1),
N = Number of terms
μ = Mean
S = √[($124 - $240.9)² + ($256 - $240.9)² + ($118 - $240.9)² + ($441 - $240.9)² + ($122 - $240.9)² + ($335 - $240.9)² + ($340 - $240.9)²+ ($191 -$240.9)²/ 8 - 1]
S = $122.0895
Approximately to 1 decimal place
S = $122.1
Therefore, the standard deviation for the given data is $122.1