Answer:
x = 4 , y = -1
Step-by-step explanation:
x - 3y = 7 -- (1)
3x - 3y = 15 -- (2)
Rewriting (1), x = 3y + 7 -- (1)'
Substituting (1)' into (2),
3 ( 3y + 7 ) - 3y = 15
9y + 21 - 3y = 15
6y = -6
y = -1 -- (3)
Substituting (3) into (1),
x - 3 ( - 1 ) = 7
x + 3 = 7
x = 4 -- (4)
According to (3) and (4),
x = 4 , y = -1
Combine like terms. What is a simpler form of each expression?
-3(4y - 8) – 4y
Answer:
A) -16y+24
Step-by-step explanation:
Distribute -3 with 4y and -8
-12y+24-4y
Add -12y and -4y
-16y+24
Answer is -16y+24
Hope this helps!
After completing the square, what are the solutions to the quadratic equation
below?
x^2 + 2x = 25
A. x = 1+-√26
B. x = -1+-√26
C. x = -2+-√26
D. x = 4,-6
Answer: I think the answer is B
Hope this helps :)
The solutions to the quadratic equation [tex]\rm x^2 + 2x = 25[/tex] is [tex]-1\pm \sqrt{26 }[/tex].
What is quadratic equation?Quadratics can be defined as a polynomial equation of a second degree, which implies that it comprises a minimum of one term that is squared. It is also called quadratic equations.
The given equation is;
[tex]\rm x^2 + 2x = 25\\\\x^2+2x-25=0[/tex]
The solutions to the quadratic equation is determined by the following formula;
[tex]\rm x =\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}[/tex]
Where the value of a = 1, b = 2, and c = -25.
Substitute all the values in the formula;
[tex]\rm x =\dfrac{-b\pm \sqrt{b^2-4ac} }{2a}\\\\\rm x =\dfrac{-2\pm \sqrt{2^2-4\times 1\times (-25)} }{2\times 1}\\\\ x =\dfrac{-2\pm \sqrt{4+100} }{2}\\\\x =\dfrac{-2\pm \sqrt{104} }{2}\\\\x =\dfrac{-2\pm \sqrt{26 \times 2\times 2} }{2}\\\\x =\dfrac{-2\pm 2\sqrt{26 }}{2}\\\\x = 2 \times \dfrac{-1\pm \sqrt{26 }}{2}\\\\x=-1\pm \sqrt{26 }[/tex]
Hence, the solutions to the quadratic equation [tex]\rm x^2 + 2x = 25[/tex] is [tex]-1\pm \sqrt{26 }[/tex].
Learn more about quadratic equation here;
https://brainly.com/question/14336752
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The question is.. "The expression 5(3r - 10) means the product of 5 and the difference of three times r minus 10. If r = 4, the value of the expression is [?] This is 6th grade math and im kinda stuck here
Answer:
10
Step-by-step explanation:
5(3r - 10)
Let r = 4
5(3*4 - 10)
5( 12 - 10)
5 (2)
10
Answer:
10
Step-by-step explanation:
5(3r-10)
5(3(4)-10)
so forget the 5 and solve inside first
3*4= 12
12-10= 2
now bring the 5 back and multiply
5*2= 10
PLEASE HELP I DONT KNOW HOW TO DO THIS
Answer:
step by step
Step-by-step explanation:
where
r = radius
h= height
Area of a cylinder = 2πrh+2πr^2
Area of a cylinder = 2π8(3)+2π8^2
Area of a cylinder = 176π = 552.92
Area of a hemisphere= 3r2π
Area of a hemisphere= 3(2)2π
Area of a hemisphere= 12π = 37.699111843
Area of the cylinder in this problem
176π - 12π = 164π
3y + 6 + 4y - 7 = -8
please help
Answer:
Step-by-step explanation:
3y+6+4y-7=-8
7y-1=-8
7y=-8+1
y=-7/7
y=-1
Step-by-step explanation:
[tex]3y + 4y = - 8 + 7 - 6 [/tex]
[tex]7y = - 7[/tex]
[tex]y = \frac{ - 7}{7} [/tex]
[tex]y = - 1[/tex]
A shirt is on sale for 30% off. The original price is $26.98. What is the sale price?
100% - 30% = 70%
The shirt is selling for 70% of the original price.
Multiply the original price by 70%
26.98 x 0.70 = 18.89
The sale price is $18.89
Answer:
$18.89
Step-by-step explanation:
26.98x0.3= 8.094
26.98-8.094= 18.886
Please help with this question from Khan Academy!!!!!!!!!!!!!!!!!!!!!!
Answer:
B = 42
Step-by-step explanation:
B × 2/7 = A
A ÷ 2/7 = B
12 ÷ 2/7 = B
B = 42
What is the least common multiple of these two denominators? 3/6 , 2/12
A: 18
B:12
C:6
D:15
Step-by-step explanation:
simple
multiples of 6= 1, 2, 3, 6
multiples of 12= 1, 2, 3, 4, 6, 12
.L.C.M of 12 and 6= 12
which term best describes a relationship in which is a multiple of the other quantity?
*pls help* *10 brainly points*
Answer: (c)
Step-by-step explanation: Direct Variation describes a relationship in which one quantity is a multiple of the other quantity
What are the values of x and y
Answer:
??
Step-by-step explanation:
Can't see that clear
Help a bab out please?
Answer: 5
Step-by-step explanation:
Which of the following phases translate to the expression y+7
Answer:
what are the phrases to choose from?
Step-by-step explanation:
An item is regularly priced at $85. It is on sale for 40% off the regular price. How much in dollars) is discounted from the regular price?
Answer:
34 dollars were discounted
Step-by-step explanation
40 percent of 85 is 34
maeve has 2 cubic meters of soil does she have enough to fill a garden bed with the dimmension 4m by 2 m by 30 cm
Answer:
no
Step-by-step explanation:
cause she will need (4 x 2) X 30
The first five terms of an arithmetic sequence are shown below: 20, 17, 14, 11, 8, . . . Let n represent the term number and f(n) the term in the sequence. The function represents the sequence.
ANSWER IS: f(n)= -3n +23
Step-by-step explanation:
everything can be found in the picture
Answer:
f(n) = -3n + 23
Step-by-step explanation:
Just got it right on EDG.
Find the scale factor from Triangle ABC to Triangle DEF.
Answer:
The ratio of any two corresponding lengths in two similar geometric figures.
Step-by-step explanation:
You can see immediately that the length of each of the sides in triangle DEF is equal to the length of the corresponding side in ABC multiplied by “a”.
If you divide the length of DE by the length of AB:
a^2/a =a.
You get a scale factor of “a”
Write the fve-number summary for each set of data
Answer:
Step-by-step explanation:
first arrange the data from ascending to decending order
1,5,8,10,11,14,17,19,20,23
Q1=(N+1)/4
=(10+1)/4
=11/4
=2.75
=2 nd item+(3 rd -2 nd)term
=5+(8-5)
=5+3
=8
Q2=(N+1)/2
=(10+1)/2
=11/2
=5.5 term
=(5 th term+6 th term)
=(11+14)/2
=25/2
=12.5
Q3=3(N+1)/4
=3(10+1)/4
=3*11/4
=33/4
=8.25
=8 th term +(9 th -8 th )term
=19+(20-19)
=19+1
=20
A truck is traveling at a constant speed. The diagram represents the truck's distance and time. What is the speed of the truck?
Answer:
distance divided by time
Step-by-step explanation:
distance is the speed of the moving object multiplied by the time taken to complete a certain distance therefore the speed is the distance covered divided by the time taken.
this is the question
Answer:
Step-by-step explanation:
From her eye, which stands 1.69 meters above the ground, Penelope measures the angle of elevation to the top of a prominent skyscraper to be 16∘. If she is standing at a horizontal distance of 200 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest hundredth of a meter if necessary.
Answer: 59.04
Step-by-step explanation:
tan 16= x/200
tan16/1=x/200
200 tan 16=x
x=57.349077...
x=57.349077...
Add 1.69, the distance from the ground to her eye:
57.349077...+1.69= 59.039077...
≈ The skyscraper is 59.04 meters tall.
You can use right triangles to get the height of the skyscraper.
The height of the skyscraper is 59.04 meters approximately.
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation. See the figure where angle DCE is the angle when Penelope saw the skyscraper. It is measured from the horizontal line DC.
How to use right triangles to find the height of the specified sky scrapper?Remember that we assume that building is vertical to the ground. This means, there is 90° formation.
Since the distance from the base of the building is given and the angle of elevation is given, we have enough data to construct a specific right triangle where the vertical line opposite to the angle of elevation is of the measure of the height of the building.
And then we can use tangent ratio which relates perpendicular and base to the considered angle.
Remember that trigonometric ratios are defined for right triangles only(those triangles who have one of the angle as of 90 degrees).
See the diagram attached below, where the length AE is the building's height. AD is same as CB which is height of Penelope(a person who is watching the top of that given skyscraper).
For the right angle triangle EDC, and for the angle considered ∠ECD, we have the perpendicular as side opposite to the angle ∠ECD which is ED and the base is DC. Thus, the tangent ratio of ∠ECD is given by
[tex]tan(\angle ECD) = \dfrac{Perpendicular \: to \: \angle ECD}{Base \: to \: \angle ECD } = \dfrac{ED}{DC} = \dfrac{h - 1.69}{200}\\tan(16^\circ) = \dfrac{h - 1.69}{200}\\[/tex]
DC = AB and DA = CB because of ABCD being a rectangle because of building and person both standing vertical to the ground and the line DC being parallel to the ground, thus all angles being right angle(of 90 degrees).
From the calculator, the value of tan(16°) is approx 0.2867
Thus, putting this value in the obtained equation, we get:
[tex]tan(16^\circ) = \dfrac{h - 1.69}{200}\\0.2867 = \dfrac{h-1.69}{200}\\\\0.2867 \times 200 = h - 1.69 \\57.35 + 1.69 = h\\h = 59.04 \: \rm meters[/tex]
Thus, the height of the specified skyscraper is approx 59.04 meters.
Learn more about trigonometric ratios here:
https://brainly.com/question/22599614
Do the ratios 4:18 and 2:9 form a proportion?
yes
no
Answer:
Yes. A propotion is to check if two things are equivelent. The ratios 4:18 and 2:9 are equivelent.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
take 69 degree as reference angle
using sin rule
sin 69=opposite/hypotenuse
0.93=7.2/x
x=7.2/0.93
x=7.74
x=7.7
Which equation is correct?
please help me :((
Answer:
sin x° = opposite ÷ hypotenuse
Step-by-step explanation:
Cosine is represented by the expression adjacent ÷ opposite and sine is represented by opposite ÷ hypotenuse. Only the fourth option lines up with the functions defined above.
If you are having trouble remembering the ratios for each trig function, you can use the acronym SohCahToa. This stands for:
S - sine
o - opposite
h- hypotenuse
C - cosine
a - adjacent
h - hypotenuse
T - tangent
o - opposite
a - adjacent
Alright, I am getting annoying at this point but who can help me with this one?
Answer:
A
Step-by-step explanation:
F(x) = 4x^2 + 1
G(x) = x^2 - 5
(F-G)(x) = (4x^2+1 - x^2-5)
collect like terms
(F-G)(x) = (4x^2-x^2 + 1-5)
= (3x^2 - 4)
Help with these two questions
Answer:
11. = D) x is greater than or equal to -1
12. = A) x is less than -2
Step-by-step explanation:
Answer:
11. -1 ≤ x
or
x ≥ -1, D
Because it is starting at -1, and the arrow is pointing up showing that x is greater than. BUT the circle is not hallow and is filled meaning that is is greater than, OR EQUAL TOO.
12. X < -2, A
Because it is starting at -2 and is going down showing that -2 is greater, and since the circle is hallow it just means X is less than NOT OR EQUAL TOO.
How many yards are in 18 feet?
Answer:
it is 6 yards
Step-by-step explanation:
since 1 yard is equal to 3 feet, 18 feet divided by 3 is 6
hope this helped :D
solve y= -2^(-x-3)= -4
HELP!!! ME!!!! PLEZ!!!
Answer:
option 2, because g-h and j -k is congruent
The results of a national survey showed that on average, adults sleep hours per night. Suppose that the standard deviation is hours. Round your answers to the nearest whole number. a. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least b. Use Chebyshev's theorem to calculate the percentage of individuals who sleep between and hours. At least c. Assume that the number of hours of sleep follows a bell-shaped distribution. Use the empirical rule to calculate the percentage of individuals who sleep between and hours per day. At least
Answer:
Following are the solution to the given question:
Step-by-step explanation:
For point a:
[tex]6.5 - 4.9 = 2.4 \\\\\frac{2.4}{1.2} = 2 \\\\\sigma \ \ so \ k = 2[/tex]
For point b:
[tex]\frac{3}{1.2}\ \ \sigma\ \ so \ k =\frac{3}{1.2} \ \ so\ \ 1- \frac{1}{k ^2} = 0.84[/tex]
For point c:
Once again, we have k = 2 though with Chebyshev discrepancy of witness numbers in the same number of standard deviations off mean = at least 75 percent.
what is the surface area?
Answer:
30.
3×4=12
12×5=60
60÷2=30
