Answer:
a = 1
b = 5
⇒ f(x) = x + 5
Step-by-step explanation:
Given
f(x) = ax + bf(1) = 6f(-2) = 3Therefore,
f(1) = 6 ⇒ a + b = 6
f(-2) = 3 ⇒ -2a + b = 3
Rewrite a + b = 6 to make a the subject, substitute into -2a + b = 3 and solve for b:
a = 6 - b
⇒ -2(6 - b) + b = 3
⇒ -12 + 2b + b = 3
⇒ -12 + 3b = 3
⇒ 3b = 15
⇒ b = 5
Substitute found value for b into a + b = 6 and solve for a:
⇒ a + 5 = 6
⇒ a = 1
Therefore, f(x) = x + 5
I need help please :)
Answer:
[ [tex]10000(2)^{-n}[/tex] ] where n is the number of hours.
Because the beginning will 10000/2 = 50000, then it keeps double the dividing the time.
In Chelsea's group, there are three boys and six girls. Write a fraction, in simplest form, to represent the amount of boys in the group.
Answer: 3/9 should be the answer :)
Step-by-step explanation:
Find the area of the shaded region.
Step-by-step explanation:
total area
20 × 17 = 340cm²
unshaded region
9 × 6 = 54cm²
area of shaded region
340 - 54 = 286cm²
Find the quadratic equation
[tex]9y {}^{2} - 12y - 14 = 0[/tex]
[tex]9y^2-12y-14=0\\D=(-12)^2-4\times9\times(-14)=144+504=648=(\pm18\sqrt{2})^2 \\\\y_1=\dfrac{12+18\sqrt{2} }{18} =\dfrac{2+3\sqrt{2} }{3} \\\\y_2=\dfrac{12-18\sqrt{2} }{18} =\dfrac{2-3\sqrt{2} }{3}[/tex]
Answer:
Solve the equation for y by finding a,b, and c of the quadratic then applying the quadratic formula.
Desimal Form: 2.08088022…,−0.74754689…
the guy on top of me is right I just gave you the desimal form he/she give you the rest
Step-by-step explanation:
PLS ANSWER AS SOON AS POSSIBLE
Answer:
-(x+8) (x-2) I think this is the answer
On a piece of paper, sketch or use a protractor to construct right triangle ABC with AB=3 in., m∠A=90°, and m∠B=45°.
What statement is true about the triangle?
A. BC=3 in
B. AC=3 in.
C. AC=6 in.
D. BC=6 in
A parachutist’s speed during a free fall reaches 165 feet per second. What is this speed in meters per second? At this speed, how many meters will the parachutist fall during 10 seconds of free fall? In your computations, assume that 1 meter is equal to 3.3 feet. Do not round your answer.
Answer:
[tex]x=750m[/tex]
Step-by-step explanation:
[tex]Assuming[/tex] [tex]That[/tex]:
[tex]1m=3.3ft[/tex]
We can make the conversion from feet per second to meters per second with this procedure:
[tex](165 \frac{ft}{s} ) (\frac{1m}{3.3ft} )=50\frac{m}{s}[/tex]
Let [tex]x[/tex] be the amount of meters the parachutist will fall during 15 seconds of free fall
Having that in 1 second the parachutist falls 50 meters, we can calculate [tex]x[/tex] :
[tex]x=(50\frac{m}{s} )(15s)[/tex]
[tex]x = 750 m[/tex]
Brainliest?!
The flight from Perth to London is 16 hours and 35 minutes. The time in Perth is 7 hours ahead of London. A flight leaves Perth at 8am on Wednesday. What is the time in London when the flight arrives?
Answer:
Flight arrived in london on 5 : 35 pm Wednesday
Step-by-step explanation:
Time = 16 h 35 min
Time difference = 7 h
Flight time = 8am
So
According to perth time flight reached in london is
8 am + 16 h 35 m = 8 am + ( 12 h + 4h + 35 m) =
8pm + 4h +35 = 12am + 35m = 12 : 35 am
The time difference is 7 h ,so minus this from perth time
12 : 35 am - 7h = 5 : 35 pm
Mark brainliest if you understand
PLEASE HELP ASAP I WILL GIVE BRAINSLET TO THE CORRECT ANSWER!!!!!!!!!!
Answer:
Therefore has one solution.
explanation:
Given equations:
6x + y = -7
-24x -7y = 25
Make y the subject:
6x + y = -7
y = -7 - 6x ..............equation 1
-24x -7y = 25
-7y = 25 + 24x
y = (25 + 24x)/-7 ..........equation 2
Solve them simultaneously:
(25 + 24x)/-7 = -7 - 6x
25 + 24x = -7 (-7 - 6x)
25 + 24x = 49 + 42x
42x - 24x = 25- 42
18x = -24
x = [tex]-\frac{4}{3}[/tex]
Then y is:
y = -7 - 6x
y = -7 - 6( [tex]-\frac{4}{3}[/tex])
y = 1
Has one separate value of x and y: ( [tex]-\frac{4}{3}[/tex] , 1 ); so it has one solution.
Help with this geometry problem
Answer:
∠DCA ≅ 56°
Reason: vertical angles theorem
∠DCF ≅ 144°
Reason: Angles on a straight line (DE) add up to 180°
∠ECB ≅ = 37°
Reason: Angles on a straight line (FA) add up to 180°
∠CAB ≅ ∠DCA ≅ 56°
Reason: Alternate interior angles theorem
∠CBA ≅ ∠ECB ≅ 37°
Reason: Alternate interior angles theorem
Step-by-step explanation:
∠DCA ≅ ∠ECF ≅ 56°
Reason: vertical angles theorem
∠DCF ≅ 180 - 56 = 144°
Reason: Angles on a straight line (DE) add up to 180°
∠ECB ≅ 180 - 56 - 87 = 37°
Reason: Angles on a straight line (FA) add up to 180°
∠CAB ≅ ∠DCA ≅ 56°
Reason: Alternate interior angles theorem
∠CBA ≅ ∠ECB ≅ 37°
Reason: Alternate interior angles theorem
the hypotonuse of a right triangle measures 15cm and one of its legs meauseres 8cm find the measure of the other leg
Answer:
7cm
Step-by-step explanation:
15 - 8
Hypotenuse is the longest side
Hello everyone, I'm just having trouble on two questions for my Calculus work. I need to solve them using trig substitution to eliminate the root. Does anyone know where to start with this problem? Any help would be greatly appreciated!
The main idea is to exploit the trigonometric identity,
sin²(θ) + cos²(θ) = 1
2. For an integral containing 16 - 81x², you might substitute x = 4/9 sin(θ) (with differential dx = 4/9 cos(θ) dθ, but without an actual integral to work with this isn't really important). Then
16 - 81x² = 16 - 81 (4/9 sin(θ))²
… = 16 - 81 (16/81 sin²(θ))
… = 16 - 16 sin²(θ)
… = 16 (1 - sin²(θ))
… = 16 cos²(θ)
so that in the root expression, we would end up with
[tex]\left(16 - 81x^2\right)^{7/2} = \left(16\cos^2(\theta)\right)^{7/2} = 2^{14} |\cos(\theta)|^7[/tex]
since [tex](ab)^c=a^cb^c[/tex] for all real a, b, and c; [tex]16^{7/2}=\left(2^4\right)^{7/2}=2^{14}[/tex]; and [tex]\sqrt{x^2}=|x|[/tex] for all real x.
The goal is to replace x with some multiple of sin(θ) that makes the coefficients factor out like they did here, which then lets you reduce 1 - sin²(θ) to cos²(θ).
And don't be discouraged by the absolute values; in the context of a definite integral, there are things that can be done to remove them or otherwise simplify absolute value expressions.
3. Substitute z = 1/√8 sin(θ) (so that dz = 1/√8 cos(θ) dθ). Then
1 - 8z² = 1 - 8 (1/√8 sin(θ))²
… = 1 - 8 (1/8 sin²(θ))
… = 1 - sin²(θ)
… = cos²(θ)
so that
[tex]\left(1-8z^2\right)^{3/2} = \left(\cos^2(\theta)\right)^{3/2} = |\cos(\theta)|^3[/tex]
Note: Figure is not drawn to scale.
If h = 7 units and r = 3 units, then what is the volume of the cone shown above?
We know:-
[tex] \bigstar \boxed{ \rm Volume \: of \: Cone = \frac{1}{3} \pi {r}^{2} h}[/tex]
[tex] \\ \\ [/tex]
So:-
[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{3} \pi {r}^{2} h[/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{3} \times \pi \times {3}^{2} \times 7 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{3} \times \pi \times 3 \times 3 \times 7 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto\sf Volume \: of \: Cone = \dfrac{1}{\cancel3} \times \pi \times \cancel3 \times 3 \times 7 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto\sf Volume \: of \: Cone =\pi \times 3 \times 7 \\ [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto\sf Volume \: of \: Cone =\pi \times 21\\ [/tex]
[tex] \\ \\ [/tex]
[tex] \leadsto\bf Volume \: of \: Cone = 21\pi[/tex]
[tex] \\ \\ [/tex]
Therefore option C is correct.
The Volume of the cone is 21π cubic units
The volume of a coneThe formula for calculating the volume of a cone is expressed as:
V = 1/3πr²h
where:
r is the radius = 3 units
h is the height = 7units
The volume of the cone = 1/3π(3)²*7
Volume of the cone = 3π * 7
Volume of the cone = 21π cubic units
Hence the Volume of the cone is 21π cubic units
Learn more on volume of a cone here: https://brainly.com/question/1082469
Which of the following is not directly related to the sample size calculations in the case of one sample z testing?
Answer:
here's your answer hope it helps you
Step-by-step explanation:
the upper bound of an interval uses the number of samples to get its value. same is said for the population standard deviation.
Find The Value Of x ?
[tex]1) \sf \large \: log_{3}( \frac{1}{3} ) = x[/tex]
[tex]2) \large\sf log_{3}(x - 1) = 2[/tex]
Thankuhh☃️
Answer:
1) [tex]x = -1[/tex] || 2) [tex]x = 10[/tex]
Explanation:
1)
→ [tex]\log _3\left(\frac{1}{3}\right)=x[/tex]
→ [tex]\frac{1}{3} = 3^x[/tex]
→ [tex]3^{-1} = 3^x[/tex]
→ [tex]x = -1[/tex]
2)
→ [tex]\log _3\left(x-1\right)=2[/tex]
→ [tex]x - 1 = 3^2[/tex]
→ [tex]x -1 = 9[/tex]
→ [tex]x = 9 +1[/tex]
→ [tex]x = 10[/tex]
[tex]\qquad \qquad\huge \underline{\boxed{\sf Answer}}[/tex]
Here's the solution ~
Question 1 :[tex]\qquad \sf \dashrightarrow \: log_{ {3} }( \frac{1}{3} ) = x[/tex]
[tex]\qquad \sf \dashrightarrow \: log_{ {3} }( {3}^{ - 1} ) = x[/tex]
[tex]\qquad \sf \dashrightarrow \: log_{ {3} }( {3})^{ - 1 } = x[/tex]
[tex]\qquad \sf \dashrightarrow \: - 1 \times log_{3}(3) = x[/tex]
[tex]\qquad \sf \dashrightarrow \: - 1 \times 1 = x[/tex]
[tex]\qquad \sf \dashrightarrow \: x = - 1[/tex]
Question 2 :[tex]\qquad \sf \dashrightarrow \: log_{3}(x - 1) = 2[/tex]
[tex]\qquad \sf \dashrightarrow \: x - 1 = {3}^{2} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 9 + 1[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 10[/tex]
Find the value of x.
to
890
121°
Answer:
32°
Step-by-step explanation:
Let the angle next to 121° be a,
a+121°=180°
a=180-121=59°
Now we have a=59°,
89° (given) and x, these threes form a triangle, therefore,
x+a+89°=180°
×+59°+89°=180°
x+148°=180°
x=180°-148°
x=32°
A line which passes through the point (0,4) has gradient 5.
Write down the equation of the line.
A(0;4); x=0, y=4; m=5
General equation of linear function is [tex]y=mx+b[/tex] ⇒
[tex]4=0\times x+b\\b=4[/tex]
Answer: [tex]y=5x+4[/tex]
Let (f)=^2−3 and (g)=5−x^2
(f+g)(7)=
(f−g)(7)=
(fg)(7)=
(f/g)(7)=
Answer:the answer is d
Step-by-step explanation: it a d bc i know
Identify fraction 40/40
Answer:
it's a unit fraction by cancelling it
Answer:
Whole fraction
Step-by-step explanation:
40/40
= 1
☆ Since we get 1 as the answer, the fraction is a whole fraction.
Hope it helps ⚜
Absolute minimum and maximum values of [tex]f(x)=2x^{3}-3x^{2} -12x+1[/tex] on the interval [-2,3]
Step-by-step explanation:
[tex]f'(x)=6x^{2}-6x-12[/tex]
So f'(x)=0:
x^2 - x - 2 = 0
(x-2)(x+1)=0
x=-1, 2
So we need to find the value of f at those critical points and also at the endpoints of the interval
f(-1)=-2-3+12+1=8
f(2)=16-12-24+1=-19
f(-2)=-16-12+24+1=-3
f(3)=54-27-36+1=-8
so the max is 8 and the min is -19
Express the following sentence in mathematic sentence, dividing 120 by 40 is equal to 3
Answer:
120/40=3
Step-by-step explanation: Hope this helps
If you have a distribution of 100 scores, and you want 20 intervals, what should be the size of your class interval
Answer:
5
Step-by-step explanation:
You simply just divide 100 by 20 and get your answer which is 5.
When you distribute something, you are dividing it into parts. In math, the distributive property helps simplify difficult problems because it breaks down expressions into the sum or difference of two numbers
If a vehicle is going 72 mph, how many feet does the vehicle travel
in one second?
Answer:
simple math convert mph to fps and multiply by 72: 105.6
Step-by-step explanation:
Paper clips and sand is a Mixture or Solution?
Answer:
solution
Step-by-step explanation:
you can separate it back into its original forms
(Reminder: mixtures cannot be separated and cannot return to its original forms. solutions can be separated and can return to its original forms)
Name the property shown 4 (x+6) = 4(x) + 4(6)
Answer:
Distributive property
Step-by-step explanation:
Shows the breakdown of distributing the 4
4(x+6)
4x + 4(6)
I’m so lost, please help!
Answer:
a = 156°
b = 132°
c = 108°
Step-by-step explanation:
The sum of the exterior angles of a polygon equals 360°. The sum of an interior and exterior angle equals 180°. There are two missing exterior angles that you need to find the measure of so we can find the value of x.
First exterior angle is with the 82° interior angle. Subtract from 180 to find the exterior angle.
180 - 82 = 98°
The second exterior angle is with the 134° interior angle. Subtract from 180 to find the exterior angle.
180 - 134 = 46°
Now add all the exterior angles together and set them equal to 360.
x + 2x + 3x +72 + 98 + 46 = 360
6x + 216 = 360
6x + 216 -216 = 360 -216
6x = 144
6x/6 = 144/6
x = 24
No find the exterior angles then subtract each one from 180°.
To find a.
a + x = 180
a + 24 = 180
a + 24 - 24 = 180 - 24
a = 156°
To find b.
b + 2x = 180
b + 2(24) = 180
b + 48 = 180
b + 48 - 48 = 180 - 48
b = 132°
To find c.
c + 3x = 180
c + 3(24) = 180
c + 72 = 180
c + 72 - 72 = 180 -72
c = 108°
Subtract (8b^2+7b+5)-(b+4)
finle answers
Answer:
[tex] {7}^{2} [/tex]
[tex]7[/tex]
equations
Solve for p.
-5 = p + 5
p=
Answer:
[tex]p=-10[/tex]
Step-by-step explanation:
Given the following question:
[tex]-5=p+5[/tex]
In order to find the answer, we subtract 5 on both sides:
[tex]-5=p+5[/tex]
[tex]5-5=0[/tex]
[tex]-5-5=-10[/tex]
[tex]-10=p[/tex]
[tex]p=-10[/tex]
Hope this helps.
I need the answer in the next 6 hours
Answer:
180m
Step-by-step explanation:
The figure shown in the picture is a right triangle.
We have two of it's sides and need to find the hypotenuse (the side in front of the right angle).
To find that we must use the Pythagorean theorem:
[tex]c^{2} = {a}^{2} + {b}^{2} [/tex]
Side a is 400m and side b is 300m.
Therefore:
[tex]c^{2} = {300}^{2} + {400}^{2} [/tex]
[tex]c = \sqrt{300 \times 300 + 400 \times 400} = 500[/tex]
Now that we know that side c is 500m we must just substract the distance between Marla and the dock with the lenght of the side to find the answer
500 - 320 = 180m
Answer:
She is 180m from the information Center
She walked 240m from the parking lot to the lake.
Step-by-step explanation:
I searched your question and found the key answers. below is my backup explanation, hope this helps! brainliest, please!
I don't understand this please help
Answer:
350
Step-by-step explanation:
The solution to the equation can be found by multiplying by the denominator, then dividing by its coefficient.
[tex]0.22 = \dfrac{77}{x}\qquad\text{given}\\\\0.22x = 77\qquad\text{multiply by $x$}\\\\x=\dfrac{77}{0.22}=350\qquad\text{divide by the coefficient of x}[/tex]
The missing value in the fraction is 350.
__
Additional comment
Here, we have rewritten the percentage as a decimal fraction. You could also rewrite it as a ratio of two integer: 22% = 22/100. Sometimes there is confusion about percentages. It can help to think of the % symbol as meaning /100:
22% = 22/100
Of course, that is "twenty-two hundredths" or 0.22.
If you just write the problem using 22/100 for 22%, then you get the proportion ...
22/100 = 77/x
22x = 7700 . . . . . "cross multiply" (multiply by 100x)
x = 7700/22 = 350 . . . . divide by the coefficient of x
__
If you're paying attention, you see that the solution of this kind of equation has the appearance that the denominator variable and the left-side value are simply swapped:
[tex]0.22 = \dfrac{77}{x}\ \leftrightarrow\ x=\dfrac{77}{0.22}[/tex]
Effectively, we have multiplied both sides of the equation on the left by x/0.22. There is a property of equality that lets us do that. There is no such thing as a property of equality that says "swap with denominator." You must always pay attention to what is allowed by the properties of equality.