Answer:
x = 6 + 3 sqrt(21/5) or x = 6 - 3 sqrt(21/5)
Step-by-step explanation:
Solve for x over the real numbers:
(x - 12) (x + 4 x) = 9
(x - 12) (x + 4 x) = 5 x (x - 12):
5 x (x - 12) = 9
Divide both sides by 5:
x (x - 12) = 9/5
Expand out terms of the left hand side:
x^2 - 12 x = 9/5
Add 36 to both sides:
x^2 - 12 x + 36 = 189/5
Write the left hand side as a square:
(x - 6)^2 = 189/5
Take the square root of both sides:
x - 6 = 3 sqrt(21/5) or x - 6 = -3 sqrt(21/5)
Add 6 to both sides:
x = 6 + 3 sqrt(21/5) or x - 6 = -3 sqrt(21/5)
Add 6 to both sides:
Answer: x = 6 + 3 sqrt(21/5) or x = 6 - 3 sqrt(21/5)
Help with this plz! Please❤️
Answer:
1) Qs= 24.4 cm
2) Perimeter= 72.8 m
Step-by-step explanation:
1).let qs= qos
Op is the height of the the triangle
Op= ,6.8cm
Angle ops = 180-(90+50)
Angle ops = 180-140
Angle ops = 40
Os/sin ops= op/sin pso
Os/sin 40= 6.8/sin 50
Os = sin 40(6.8)/sin50
Os= 0.6428(6.8)/0.7660
Os= 5.71
Angle oqp = 180-(90+70)
Angle oqp = 180-160.
Angle oqp = 20
Oq/sin qpo = op/sin oqp
Oq/sin 70=6.8/sin 20
Oq= sin70(6.8)/sin20
Oq= 0.9397(6.8)/0.3420
Oq= 18.68
Qs= os +oq
Qs= 5.71+18.68
Qs= 24.39
Qs= 24.4 cm
2). The other angle of the triangle
=180-90-53
= 37
Sin90 = 1
Let the length and breadth be x and y
X /sin 53 = 26
X= 26(sin53)
X= 26(0.7986)
X= 20.7636
Y/sin 37 = 26
Y= 26(0.6018)
Y= 15.6468
Perimeter= 2(x+y).
Perimeter= 2( 20.7636+15.6468)
Perimeter= 2(36.4104)
Perimeter= 72.8208 m
Perimeter= 72.8 m
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Find the following expression by multiplying.
(a + b)3
Answer:
[tex]a^3+3a^2b+3ab^2+b^3[/tex]
Step-by-step explanation:
If have [tex](a+b)^3[/tex], we can solve this as:
[tex](a+b)(a+b)(a+b)[/tex]
So, applying distribution with the first two factors and simplifying, we get:
[tex](a^2+ba+ab+b^2)(a+b)\\(a^2+2ab+b^2)(a+b)[/tex]
Then, multiplying both expressions and simplifying again, we get:
[tex]a^3+a^2b+2a^2b+2ab^2+b^2a+b^3\\a^3+3a^2b+3ab^2+b^3[/tex]
What does C represent in this equation (-9c)-4=-25
Answer:
[tex]c=2\frac{1}{3}[/tex]
Step-by-step explanation:
[tex](-9c)-4=-25\\(-9c)=-21\\9c=21\\c=21/9=2\frac{1}{3}[/tex]
5 meters.
The rectangle below has an area of x2 – 112 + 30 square meters and a length of x
What expression represents the width of the rectangle?
2 - 5
Width
22 – 110 + 30
Width
meters
Answer: The width is x-6
Step-by-step explanation:
To find the with factor out the area x^2 - 11x + 30
[tex]x^{2}[/tex] - 11x +30 to factor it find two numbers that multiply to get 30 and add up to get -11 . And that two numbers are -6 and -5 .
[tex]x^{2}[/tex] - 5x - 6x + 30 now group them
([tex]x^{2}[/tex] - 5x) (-6x+ 30) factor them out.
x(x - 5) - 6(x -5) Factor x-5 out
(x-5)(x-6) since the length is x-5 then the width is x-6.
I NEED HELP ASAP!!! LIKE RIGHT NOW RIGHT NOW ILL GIVE THE MOST BRAINLIEST
Answer:
see below
Step-by-step explanation:
We know that the center is (0,0) and the radius is |3 - 0| = 3.
Standard form of a circle: (x - h)² + (y - k)² = r² where (h, k) is the center and r is the radius. Plugging in h = 0, k = 0 and r = 3 gives us x² + y² = 9.
Answer:
See below.
Step-by-step explanation:
The equation for a circle is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
From the graph, we can see that (0,0) is the center.
Thus, h=0 and k=0:
[tex]x^2+y^2=r^2[/tex]
From the graph, we can also see that the radius is 3 as (-3,0) and (3,0) are points on the circle.
Thus, r=3, and r^2=9.
The equation is:
[tex]x^2+y^2=9[/tex]
PLVHGCHVBJGUYFTDCGVHJGYUJH
Answer:
The correct option is (B).
Step-by-step explanation:
The conditional probability of an event, say A is the probability of that events (A) when it is known that another event, say X has already occurred.
For example, consider the experiment of drawing two marbles from jar consisting of 8 white and 2 red, without replacement. The probability of selecting a red marble after a white marble is known as conditional probability.
In this case it is provided that:
40% of the students are licensed drivers55% students are female.The statement:
"the probability that a student who is a licensed driver is a male"
Is a statement of conditional probability.
This is because it is known from previous information that the student is a licensed driver and we need to determine the probability of this student being a male.
Thus, the correct option is (B).
Brian is solving the equation x squared minus three-fourths x = 5. What value must be added to both sides of the equation to make the left side a perfect-square trinomial?
Answer:
Term to add is (3/8)^2 = 9/64
Step-by-step explanation:
Here, we want to know the value that must be added to make the equation a perfect square.
x^2 - 3/4x = 5
x^2 -3/4x -(3/8)^2+ (3/8)^2 = 5
x^2 -3/4x + (3/8)^2 = 5 + (3/8)^2
= (x-3/8)^2 = 5 + (3/8)^2
So the term to add is (3/8)^2 = 9/64
Answer:
[tex]\dfrac{9}{64}[/tex]
Step-by-step explanation:
Given the equation: [tex]x^2-\frac{3}{4}x=5[/tex]
To make the left hand side of the equation a perfect trinomial, we follow these steps.
Step 1: Divide the coefficient of x by 2.
Coefficient of x [tex]=-\frac{3}{4}[/tex]
[tex]-\frac{3}{4} \div 2 =-\frac{3}{8}[/tex]
Step 2: Square your result from step 1
[tex]\implies (-\frac{3}{8})^2 \\=\dfrac{9}{64}[/tex]
Therefore, to make the Left-Hand side a perfect-square trinomial, we add 9/64.
The HCP prescribes methotrexate 7.5 mg PO weekly, in 3 divides doses for a child with rheumatoid arthritis whose body surface area (BSA) is 0.6 m2. The therapeutic dosage of methotrexate PO is 5 to 15 mg/m2/week. How many mg should the nurse administer in each of the three doses given weekly? (Enter the numeric value only. If round is required, round to the nearest tenth.)
Answer:
1.5mg
Step-by-step explanation:
From the question, we are told that the HCP prescribed 7.5 mg of PO weekly
The therapeutic dosage is given in the question as 5 - 15 mg/m² weekly.
The child's body surface area is given = 0.6m²
The mg of PO that the nurse should administer in each of the three doses given weekly is calculated as
7.5mg/ 5mg/m²
= 1.5 mg of PO
prove the following identity: sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x please provide a proof in some shape form or fashion :/
Answer:
Step-by-step explanation:
Hello,
Is this equality true ?
sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x
1. let 's estimate the left part of the equation
[tex]sec(x)csc(x)(tan(x) + cot(x)) =\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin(x)}{cos(x)}+\dfrac{cos(x)}{sin(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{sin^2(x)+cos^2(x)}{sin(x)cos(x)})\\\\=\dfrac{1}{cos(x)sin(x)}*(\dfrac{1}{sin(x)cos(x)})\\\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]
1. let 's estimate the right part of the equation
[tex]2+tan^2(x) + cot^2(x)=2+\dfrac{sin^2(x)}{cos^2(x)}+\dfrac{cos^2(x)}{sin^2(x)}\\\\=\dfrac{2cos^2(x)sin^2(x)+cos^4(x)+sin^4(x)}{cos^2(x)sin^2(x)}\\\\=\dfrac{(cos^2(x)+sin^2(x))^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1^2}{cos^2(x)sin^2(x)}\\\\=\dfrac{1}{cos^2(x)sin^2(x)}[/tex]
This is the same expression
So
sec x csc x(tan x + cot x) = 2+tan^2 x + cot^2 x
hope this helps
Here is a circle, centre O, and the tangent to the circle at the
point (8, 15) on the circle.
x
P (8, 15)
-17
O
17
Find an equation of the tangent at the point P.
Give your answer in the form y = ax + b where a and b are both
fractions with denominator 15.
Answer:
The equation of the tangent is [tex]y=-\frac{8}{15}x+\frac{289}{15}[/tex].
Step-by-step explanation:
Center = (0, 0). Point on the circle = (8, 15).
OP is a radius. The slope of the radius = [tex]\frac{15-0}{8-0}=\frac{15}{8}[/tex].
The tangent is perpendicular to the radius.
So, its slope is = [tex]-\frac{8}{15}[/tex].
The tangent passes through (8, 15).
So, the equation is:
[tex]y-15=-\frac{8}{15}\left(x-8\right)\\y-15=-\frac{8}{15}x+\frac{64}{15}\\y=-\frac{8}{15}x+\frac{289}{15}[/tex]
Learn more: https://brainly.com/question/1594198
A True/False quiz has three questions. When guessing, the probability of getting a question correct is the same as the probability of getting a question wrong. What is the probability that a student that guesses gets at least 2 questions correct
Answer:
1/4 or 25% chance
Step-by-step explanation:
the probability of getting each question right is 1/2, so for getting 2 questions right its 1/2 × 1/2, which is 1/4
The probability that a student that guesses gets at least 2 questions correct is 1/4.
GivenThe probability of getting a question correct is the same as the probability of getting a question wrong.
The probability of getting the question is correct is;
[tex]= \dfrac{1}{2}[/tex]
The probability of getting the question is wrong is;
[tex]= \dfrac{1}{2}[/tex]
Therefore,
The probability that a student that guesses gets at least 2 questions correct is;
[tex]= \dfrac{1}{2} \times \dfrac{1}{2}\\\\= \dfrac{1}{4}[/tex]
Hence, the probability that a student that guesses gets at least 2 questions correct is 1/4.
To know more about Probability click the link given below.
https://brainly.com/question/795909
While watching a football game, Jeevan decided to list yardage gained as positive integers and yardage lost as negative integers. After these plays, Jeevan recorded 14, –7, and 9. What was the net gain or loss?
Answer:
It was a gain, specifically 16
Step-by-step explanation:
14 + (-7) = 7
7 + 9 = 16
Please tell me if I'm wrong.
What is the solution to the equation? 98 + g = 150 98 + g = 150. 98 + 98 + g = 150 minus 98. t = 52. 98 + g = 150. 98 minus 98 + g = 150 minus 98. t = 52. 98 + g = 150. 98 + 98 + g = 150 + 98. t = 52. 98 + g = 150. 98 minus 98 + g = 150 + 98. t = 148.
Answer:
The solution to the question is g = 52
Step-by-step explanation:
Here, we want to find the solution to the equation ;
98 + g = 150
Apparently, we want to find the value of g.
To get the value of g, what we simply need is to bring 98 over the equal sign and this gives
g = 150-98
g = 52
Answer: B or how some people say it the second question. EDGE-MATHMATICS 2022
THE ANSWER IS B
step-by-step explanation: it is the second option because when you find out what number g is (52) you can take 98-98= 0 + g/52 and get 52.
and then the second part of it says 150-98 which is 52! so your answer is B hope this helps! have a wonderful day!
(ii) The scale 1 cm represents 50m can be written in the form 1:k.
Find the value of k.
k=
[1]
Answer:
k = 50
Step-by-step explanation:
The scale 1 cm represents 50m
It means that 1 cm length of pictorial representation of any obejct is equivalent to 50m in reality.
In scale terms it can be represented in ratio form of a:b
where
a is the length of picture and b is actual length
here length of pictorial representation is 1 cm
and 50m is actual length
thus scale will be 1:50
But is given that The scale 1 cm represents 50m can be written in the form 1:k.
1:50 is same as 1:k
thus
1:50 = 1:k
we know that in ratio
if a:b = c:d
then
a= c and b = d
Thus,
k = 50 Answer
The graph of the function f(x)=-(x+3)(x-1) is shown below. What is true about the domain and range of the function?
Answer:
The 3rd one is correct.
Step-by-step explanation:
This table values that represent a quadratic function.
Answer:
A
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
Here [ a, b ] = [ 3, 5 ] , thus
f(b) = f(5) = - 26 ← value of y for x = 5 from table
f(a) = f(3) = - 10 ← value of y for x = 3 from table
average rate of change = [tex]\frac{-26-(-10)}{5-3}[/tex] = [tex]\frac{-16}{2}[/tex] = - 8 → A
A box had twice as many grapes as a basket. Once 2 kg of grapes were added to the basket, it contained 0.5 kg more than the box. How many kilograms of grapes are in the basket now?
Answer:
there are now 3.5 kilograms of grapes in the basket (the mystery number is 1.5)
Let us suppose that the number of grapes in the box is x and the number of grapes in the basket is y.
It means that the weight of the grapes in the box is x kg and that of basket is y kg.
It has been given that the box had twice as many grapes as a basket. Therefore, we have
Now when we add 2 kg to the basket then the weight of the basket is y+2 and the weight of box will remain same.
Now, we have been given that after 2 kilograms were added to the basket it contained 0.5 kilograms more than the box. Hence, we have
Substituting the value x=2y in the equation, we get
Therefore, the basket contains 1.5 kilograms of grapes.
Help pls I will give BRAINLY
Answer: The missing length is 16/3
Step-by-step explanation:
First, you have to find the proportional value between the two lengths on the first figure and the two lengths on the second figure.
The first figure’s lengths are 8 and 9, so the shorter length is 8/9 of the longer length.
Now apply the same proportional value to the second figure.
6 * 8/9 = 48/9
48/9 = 16/3
Hi please help meeee
An experiment consists of tossing 3 coins at the same time.
1. Identify the sample space.
2. What is the probability of tossing 2 tails and 1 head?
3. Which is more likely to occur: tossing exactly 1 tail or tossing at least 2 heads? Explain.
Answer:
Step-by-step explanation:
The attachment will help you with your question:
The graph of y=h(x)y=h(x)y, equals, h, left parenthesis, x, right parenthesis is a line segment joining the points (1,9)(1,9)left parenthesis, 1, comma, 9, right parenthesis and (3,2)(3,2)left parenthesis, 3, comma, 2, right parenthesis. Drag the endpoints of the segment below to graph y=h^{-1}(x)y=h −1 (x)y, equals, h, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis.
Answer:
End points of the this segment are (9,1) and (2,3).
Step-by-step explanation:
The given function is
[tex]y=h(x)[/tex]
End points of the this segment are (1,9) and (3,2).
If a function is defined as
[tex]f=\{(a,b),a\in R,b\in R\}[/tex] then
[tex]f^{-1}=\{(b,a),a\in R,b\in R\}[/tex]
It means, we have to interchange x and y-coordinates of the end points.
So, end points of the this segment are (9,1) and (2,3).
Plot these point and join them by a line segment.
The inverse of the function will be a line segment joining the points (9,1) and (2,3). See the graph.
Given information:
The function y=h(x) is a line segment joining the points (1,9) and (3,2).
So, the endpoints of the function y=h(x) can be written as,
[tex]y=h(x)=\{(1,9),(3,2)\}[/tex]
The inverse of a function is simply the opposite relation. In the inverse, the range and domain interchange themselves.
So, the inverse of the given function can be written as,
[tex]y=h^{-1}(x)=\{(9,1),(2,3)\}[/tex]
Refer to the graph of the function for more details.
For more details, refer to the link:
https://brainly.com/question/10300045
What is the range of the linear parent function?
O A. All real numbers
B. Negative real numbers (y< 0)
C. Nonnegative real numbers (y=0)
D. Positive real numbers (y> 0)
Answer:
A. All real numbers
Step-by-step explanation:
We assume that the "linear parent function" is ...
y = x.
Its range is "all real numbers."
Answer:
all real numbers
Step-by-step explanation:
AP-EX
Simplify expression 1/4 •3(8a-5b-4)-(4a+1)+4b
Answer:
(8a+b-16)/4
Step-by-step explanation:
1/4×3(8a-5b-4)-(4a+1)+4b
Simplify:
-4a-1+4b+1/4×3×8a-1/4×3×5b-1/4×3×4
=1/4xax24-4a-1/4bx15+4b-1/4×12-1
=1ax24/4 -4a - 1bx15/4 +4b -1×12/4 -1
=ax24/4 -4a -bx15/4 + 4b -12/4 -1
= -4a + 24a/4 + 4b - 15b/4 -1 -3
= -4a + 6a + 4b - 15b/4 - 4
= 2a + 4b - 15b/4 - 4
= 8a + 16b - 15b - 16 / 4
= (8a + b - 16) / 4
= 8a + b - 16 / 4
The legs of a right triangle are 3 units and 5 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. 4.00 units 2.83 units 5.83 units 8.00 units
Answer:
5.83units
Step-by-step explanation:
from Pythagoras theorem;
a^2=b^2+c^2
where a is the hypotenuse,b is the opposite and c is the adjacent
b=3 and c=5
a^2=3^2+5^2
a^2=9+25
a^2=34
find the square root of both sides,
√a^2=√34
a=5.83units
Answer:5.83
Step-by-step explanation:
solve for x 42=7(x+5)
Answer:
42=7(x+5)
42=7x+35
42-35=7x
7=7x
X=7/7=1
Solve (x+3)^2=8 using the quadratic formula.
Answer:
Step-by-step explanation:
= x^2+6x+9-8=0
=x^2+6x+1=0
D=b^2-4ac
D= 36-4
D=32
x=-b±root D/2a
x=-6+4root2/2 , x = -6-4root2/2
simplify you get the least form...
hope it helps
What is the range of the function y= 3 startroot x+8 endroot?
Answer:
First Option
Step-by-step explanation:
When we graph the expression, we should see that an infinite amount of y-values work. Since the domain comprises of all working x-values, we have (negative infinity, positive infinity) or all real numbers as our range, since we have an infinite amount of y-value outputs.
two angles of a triangle measure 41 degrees and 44 degrees what is the measure of the third angle? A) 75 degrees B) 85 degrees C) 95 degrees D) 105 degrees
Answer:
95 degrees
Step-by-step explanation:
All triangles have an interior measure of 180 degrees
180-41-44=95
Answer:
95 degrees
Step-by-step explanation:
Classify the following triangle. Check all that apply.
Answer:
B and C
Step-by-step explanation:
Since all of it's sides are unequal, it is a scalene triangle.
It has 1 obtuse angle, so it is an obtuse angled triangle.
Hiiii someone please help me I'm confused please helppp
If the length of the bases of right triangle GHI are 9 units and 15 units respectively, what is the length of the hypotenuse of GHI?
Answer:
17.5 units
Step-by-step explanation:
a² + b²= c²
9² + 15² = c²
81 + 225 = c²
c² = 306
c = √306
c = 17.5
How many sides does a regular polygon have if the measure of each exterior angle is 24°?
Answer: 15 sides
Step-by-step explanation: Because the sum of the outer angles is always 360 degrees, if you divide 360 degrees by 24 degrees you get 15 which is the number of equivalent outer angles and therefore 15 vertices and sides to the polygon
Answer: angle is 24 degrees meaning that a regular polygon has more than 6 sides hope this is helpful
Step-by-step explanation: