Answer:
x = 15
∠AOB = 15°
∠BOC = 165°
Step-by-step explanation:
Angles on a straight line add up to 180°
[tex]\sf \implies \angle AOB + \angle BOC=180[/tex]
Substitute the given expressions for the angles:
[tex]\sf \implies (2x - 15) + 11x = 180[/tex]
Collect and combine like terms:
[tex]\sf \implies 2x +11x- 15=180[/tex]
[tex]\sf \implies 13x- 15=180[/tex]
Add 15 to both sides:
[tex]\sf \implies 13x- 15+15=180+15[/tex]
[tex]\sf \implies 13x=195[/tex]
Divide both sides by 13:
[tex]\sf \implies \dfrac{13x}{13}=\dfrac{195}{13}[/tex]
[tex]\sf \implies x=15[/tex]
Now substitute the found value of x into the expressions for each angle:
[tex]\sf \implies \angle AOB =2(15)-15=15^{\circ}[/tex]
[tex]\sf \implies \angle BOC =11(15)=165^{\circ}[/tex]
A line that passes through the points (x, 4) and (6, -1) has a slope of 56. what value of x will yield the given slope?
The value of x that yields a slope of 56 is 6.09
How to determine the value of x?The given parameters are:
Slope = 56Points: (x,4) and (6,-1)The slope of two points is:
[tex]m = \frac{y_2 -y_1}{x_2 -x_1}[/tex]
This gives
[tex]\frac{-1 -4}{6 -x} = 56[/tex]
Evaluate the difference
[tex]\frac{-5}{6 -x} = 56[/tex]
Cross multiply
56(6 - x) = -5
Divide both sides by 56
6 - x = -0.09
Make x the subject
x = 6 + 0.09
Evaluate
x = 6.09
Hence, the value of x that yields a slope of 56 is 6.09
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HELP NOW PLEASE
k(x)=x^(2)+3x+8
find k(-1)
find k(0)
find k(5)
Answer:
6, 8, 48
Step-by-step explanation:
substitute x = - 1, 0, 5 into k(x)
k(- 1) = (- 1)² + 3(- 1) + 8 = 1 - 3 + 8 = 6
k(0) = 0² + 3(0) + 8 = 0 + 0 + 8 = 8
k(5) = 5² + 3(5) + 8 = 25 + 15 + 8 = 48
can someone help me with this
angles in a triangle always equal to 180° so:
1. all the angles are equal to each other
180°÷3=60°
2.
•we know 1 angle, 68°
• straight lines are 180°-> 180°-126°= 54°
180°-68°-54°= 58°
Freida deposited money into a savings account. After a year the account had $4,200. If the interest rate is 5%, how much money did Frieda originally deposit?
Answer:
There is a total of 200 dollars profit
Angles 1 and 2 are supplementary
Angle 1 = 30°
Answer:
Angle 2 = 150°
Step-by-step explanation:
▪︎ Measures of supplementary angles add up to 180°.
Therefore,
Angle 1 + Angle 2 = 180°
Angle 1 = 30°
30° + Angle 2 = 180°
Angle 2 = 180° - 30° = 150°
A broken scale shows a false weight that is always higher than the actual weight by
the same number of grams. When a mobile phone is put on the scale, it shows 202
grams. When an headphone is put on the scale, it shows 221 grams. When the mobile
phone and the headphone are put on the scale together, it shows 415 grams. What is
the actual weight of the mobile phone in grams?
The actual weight of the mobile in grams is 194 grams.
What is Equation?In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
As broken scale shows a false weight that is always higher than the actual weight by the same number of grams.
When a mobile phone is put on the scale, the real weight will be 'x'
but it shows,
x+a= 202
When an headphone is put on the scale, the real weight will be 'y'
but it shows,
y+a=221
When the mobile phone and the headphone are put on the scale together, the weight is
x+y+a= 415
So,
x+221=415 [Since y+a= 221 grams]
x= 194 grams
The actual weight of the mobile phone in grams is 194 grams.
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A box of donuts has 12
total. One-fourth of
the donuts have sprinkles.
Of the remaining donuts,
one-third have cherry filling.
The rest are plain. How
many plain donuts are in
the box?
Answer:
6 donuts are left in the box
Step-by-step explanation:
12 divided by 4 is 3. take those three out of the 12. you are left with nine. 9 divided by 3 is 3. subtract three from the nine. you are left with 6.
The circle below is centred at O.
AB is a tangent to this circle.
Work out the size of angle y.
Justify your answer.
O
42°
y
A
B
Not drawn accurately
Answer:
y = 48°
Step-by-step explanation:
angle A = 90°
interior angles of a triangle = 180°
therefore
y = 180 - 42 - 90
y = 48°
[tex] \huge \tt \color{pink}{A}\color{blue}{n}\color{red}{s}\color{green}{w}\color{grey}{e}\color{purple}{r }[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Given ❒➣ Mid point of a circle➣ Tangent AB➣ Angle "o" of 42⁰➣ Angle "A" of 90⁰ (cuz it is the perpendicular of traingle given in circle)﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Note ❒➣here tangent AB with point O (mid point of circle) forming a traingle➣we have to find "y" in the given figure (angle B)﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Concept used ❒➣The sum of interior angles of traingle is of 180⁰➣to find the missing angle ( y ) we will use this theorem➣this Concept is also know as Sum theorem﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Assumption ❒➣angle B = y﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
❒ Let's solve ❒[tex] \large \pmb{➪ \: } \rm \pink{ \angle \: OAB+\angle \:ABO+\angle \:BOA = 180 \degree}[/tex]
➣let's substitute value now .....[tex] \pmb{➪ \: 90 + y +42 = 180 } \\ \pmb{➪ \:132 + y = 180 \: \: \: \: \: \: \: \: }\\ \pmb{➪ \:y = 180 - 132 \: \: \: \: \: \: \: \: }\\ \pmb{➪ \:y = 48 \degree \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }[/tex]
﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌﹌
Hence the size of angle is
[tex] \large \boxed{✥\underline{ \boxed{ \sf{y = 48 \degree \: \pmb{\green{✓}} }}}✥}[/tex]
▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂
Hope it helps !
Pam earns x dollars, Ryan earns (x+60) dollars and Rufus earns (x - 10) dollars. Together they earn a total of 530 dollars.
a) Calculate the value of x
b) the amount Ryan earns.
Answer:
A) 160 B) 220
Step-by-step explanation:
Combine like terms.
3x + 50 = 530.
Subtract 50 from both sides.
3x = 480.
Divide both sides by 3.
x = 160.
Since Ryan earns x + 60, add 60.
160 + 60 = 220.
A boat can travel 28 miles up a river in the same amount of time it takes to travel 36 miles down the same river. If the current is traveling at 2 miles per hour, what is the speed of the boat in still water?
Answer:
6
Step-by-step explanation:
What is muscular endurance
Muscular Endurance - The ability of a skeletal muscle or group of muscles to continue contracting over a long period.
Step-by-step explanation:
I hope it'll help you...
Answer:
Muscular endurance is the ability of a muscle or group of muscles to sustain repeated contractions against a resistance for an extended period of time.
Step-by-step explanation:
:)
I NEED HELP ASAP
A triangle with sides 3, 4 and 6 is ___________
Select one:
a. obtuse
b. acute
c. right
Answer:
obtuse
Step-by-step explanation:
A triangle with sides of 3,4and6 is NOT a Right triangle.
Simplify (sinx + cosx) ^2/ sin2x
[tex]\csc 2x+1[/tex]
Step-by-step explanation:
[tex]\frac{(\sin x+\cos x)^2}{\sin2x}[/tex]We expand [tex](\sin x+\cos x)^2[/tex] using algebraic identity [tex](a+b)^2=a^2+b^2+2ab[/tex][tex]=\frac{\sin^2x+\cos^2x+2\sin x.\cos x}{\sin2x}[/tex][tex]= \frac{1+\sin2x}{\sin2x}[/tex][tex]=\frac{1}{\sin2x}+\frac{\sin2x}{\sin2x}[/tex][tex]=\csc 2x+1[/tex]Pls help snaehdusjshdgydudjdjdhd
Answer:
17 games
Step-by-step explanation:
There are 68 games in total. Assuming that the number of games watched are equally divided between 4 people, then each person watches 68/4 = 17 games.
Solve the system of equations by the substitution method.
10x + 2y = 2
- 5x = y + 10
Select the correct choice below and, if necessary, fill in the answ
** PLS HELP BRAINLIEST!! ** THIS WILL AFFECT MY GRADE
Here are three lines that intersect at
one point.
Write a true equation based on this
diagram.
Answer:
64+18+z=180
Step-by-step explanation:
z=98, input 98 and it is true
HELP PLS PLS! WILL GIVE POINTS aND BRAINLYEST
Answer:
See below ~
Step-by-step explanation:
Blue inequality
y ≤ -x + 4Red Inequality
y > 1/4xAnswer:
See below
Step-by-step explanation:
Find the equation of the blue line....the blue shaded area is LESS than or EQUAL to this SOLID line
Blue line = y = -x+4 so y <= -x+4
Red line = y = 1/4 x y > 1/4x (dotted line says line is not included so the inequality is > NOT ≥ )
x^2=6x+1
1) rewrite the equation by completing the square
2) what are the solutions to the equation?
Answer:
x=+-√10+3
Step-by-step explanation:
x^2=6x+1
x^2-6x=1
To create a trinomial square on the left side of the equation, find a value that is
equal to the square of half of b
a is the number next to x^2
b is the number next to x
c is the last number
b is -6
half of b is -3
square of half of b is 9
put 9 on both sides of the = sign
x^2-6x+9=1+9
x^2-6x+9=10
(x-3)^2=10
take the square root of both sides of the = sign
√(x-3)^2=√10
x-3=√10
x=+-√10+3
1. As shown in the diagram below, the radius of a cone is 2.5 cm and its
slant height is 6.5 cm. How many cubic centimeters are in the volume of
the cone?
6.5
The number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³
Calculating the volume of a coneFrom the question, we are to determine the volume of the cone
The volume of a cone can be calculated by using the formula,
[tex]V = \frac{1}{3} \pi r^{2} h[/tex]
Where V is the volume
r is the radius
and h is the height
From the given information,
radius, r = 2.5 cm
slant height, l = 6.5 cm
First, we will determine the height of the cone
By Pythagoras' theorem
[tex]l^{2} = r^{2} + h^{2}[/tex]
Where [tex]l[/tex] is the slant height
r is the radius
and h is the height of the cone
Then, we can write that
[tex]6.5^{2} = 2.5^{2} + h^{2}[/tex]
[tex]42.25 = 6.25 + h^{2}[/tex]
[tex]h^{2}=42.25 - 6.25[/tex]
[tex]h^{2} =36[/tex]
[tex]h = \sqrt{36}[/tex]
∴ h = 6 cm
Now, putting the parameters into the equation for the determining the volume of a cone, we get
[tex]V = \frac{1}{3}\times \pi \times 2.5^{2} \times 6[/tex]
[tex]V = \pi \times 6.25\times 2[/tex]
[tex]V = 12.5 \pi[/tex] cm³ OR 39.27 cm³
Hence, the number of cubic centimeters that are in the volume of the cone is 12.5π cm³ OR 39.27 cm³
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Pls help :/
Find the expected value of the winnings from a game that has the following payout probability distribution.
I will give brainlies t
The expected value of the winnings from a game that has the following payout probability distribution is 2.3
What is expected value?In statistics and probability analysis, the expected value is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values.
To calculate the expected value ,
we have to multiply each of the given probability by the individual payout value and then add the following answers
So, expected value
=0(0.45) + 2(0.3) + 4(0.1) + 8(0.1) + 10(0.05)
=0+0.6+0.4+0.8+0.5
= $2.3
Hence, the expected value is 2.3
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ACTUAL ANSWER:
3.1
Step-by-step explanation:
0.45(0) + 0.3(4) + 0.1(6) + 0.1(8) + 0.05(10)
= 3.1
Also I checked on on Acellus and it was correct.
6 tractors take 10 days to collect the harvest. How long would it take 10 tractors to do the same work?
Answer:
6 days
Step-by-step explanation:
Relation :
Number of tractors ∝ 1/Number of days6 tractors took 10 days. Now, we have 10 tractors. This means the number of tractors has increased by 10/6 = 5/3. Therefore, the number of days will become 3/5 of the original time.
Solving :
10 × 3/52 × 36 dayswhat is a foot plus 9 feet plus 20 feet equal too
Answer:
30 ft.
Step-by-step explanation:
1 + 9 + 20
= 30.
Answer: 30
Step-by-step explanation:
1. Simplify 1+9 to 10
10+20
2. Simplify
30
Done! Hope this helps.
The radius of a semicircle is 9.1 centimeters. What is the semicircle's perimeter?
Answer:
28.6 cm
Step-by-step explanation:
Given radius of semicircle (r) = 9.1 cm
perimeter of a semicircle = πr
= 22/7 × 9
= 22 × 1.3
= 28.6
Help me on this question
Answer:
F.2:30 a.m.
8 revolutions= 8×90=720mn= 12h
So the sign starts from 2.30p.m.
Then the sign after 8 revolutions is 2.30 a.m.
Please give Brainliest
1. Amelia's annual salary increases by the same quantity every year. In her 1st
year at her job, she earned $24,000.In her 2nd year, she earned $36,000. In
her 3rd year, she earned $48,000. How much will she earn in her 20th year?
Then sketch a graph that represents the above information.
SALARY
Solution:
Answer:
Amelias salary increase by $12,000 every year so 12*20 = $240,000 salary in 20th year.
6) What will be the new position of the given
point (0, 6) after translation of 6 units down
and 3 units right?
a) (6, 3)
b) (3, 0)
c) (-6, 3)
d) (-3,0)
Please help omg
Which expression is equivalent to (startfraction (3 x y superscript negative 5 baseline) cubed over (x superscript negative 2 baseline y squared) superscript negative 4 baseline) endfraction) superscript negative 2? assume startfraction x superscript 10 baseline y superscript 14 baseline over 729 endfraction.
The equivalent expression of [tex](\frac{(3xy^{-5})^3}{(x^{-2} y^2) ^{-4}})^{-2}[/tex] is [tex]\frac{x^{10} y^{14}}{729}[/tex]
How to determine the equivalent expression?The expression is given as:
[tex](\frac{(3xy^{-5})^3}{(x^{-2} y^2) ^{-4}})^{-2[/tex]
Expand the expression
[tex](\frac{(3xy^{-5})^3}{(x^{-2} y^2) ^{-4}})^{-2} = (\frac{27x^3y^{-15}}{(x^{8} y^{-8}})^{-2[/tex]
Apply the law of indices
[tex](\frac{(3xy^{-5})^3}{(x^{-2} y^2) ^{-4}})^{-2} = (\frac{27}{(x^{5} y^{7}})^{-2[/tex]
Take the inverse of the expression
[tex](\frac{(3xy^{-5})^3}{(x^{-2} y^2) ^{-4}})^{-2} = (\frac{x^{5} y^{7}}{27})^2[/tex]
Apply the square exponent to the expression
[tex](\frac{(3xy^{-5})^3}{(x^{-2} y^2) ^{-4}})^{-2} = \frac{x^{10} y^{14}}{729}[/tex]
Hence, the equivalent expression of [tex](\frac{(3xy^{-5})^3}{(x^{-2} y^2) ^{-4}})^{-2}[/tex] is [tex]\frac{x^{10} y^{14}}{729}[/tex]
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Answer:A edge 2023
Step-by-step explanation:
Just did it and got it right
what’s the circumference, to this problem ?
Answer:
= 20.7345115137
or
≈ 21
Step-by-step explanation:
Circumference = 2 x π x radius
Circumference = 2 x π x 3.3
hope this helps
have a good day
Answer:
The formula to get the circumference of a circle is [tex]C=2*\pi * r[/tex]. We can then input the value and we get that [tex]C=2*\pi*3.3[/tex] and as we solve it more the final answer that we get is [tex]C=20.735[/tex].
Hope this helps! Let me know if you have any questions
Find the surface area of a right cone with a radius of 3 meters and a slant height of 5 meters.
The surface area of the right cone with a radius of 3 meters and a slant height of 5 meters is 47.1 m².
What is surface area?
To calculate the surface area of the cone, we use the formula below.
Formula:
A = πrl.............. Equation 1Where:
A = Surface area of the coneπ = Piel = Slight HeightFrom the question,
Given:
l = 5 metersr = 3 metersπ = 3.14Substitute these values into equation 1
A = 3.14×5×3A = 47.1 m²Hence, The surface area of the right cone is 47.1 m².
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I need help(!) I appreciate a good explanation so I can understand it too (!)
The ranges values of the function f(x) are: {-89,-9,7} - Option D.
Domain and RangeThe domain of a function is the set of input values for which the function is real and defined. In the other words, when you define the domain, you are indicating for which values x the function is real and defined.
While the domain is related to the values of x, the range is related to the possible values of y that the function can have.
Here, you need to replace the domain values in the given equation.
f(x)=-2x²+9
For x=-3f(x)=-2*(-3)²+9
f(x)=-2*9+9
f(x)=-18+9=-9
For x=1f(x)=-2*(1)²+9f(x)=-2*1+9f(x)=-2+9=7For x=7f(x)=-2*(7)²+9f(x)=-2*49+9f(x)=-98+9=-89Learn more about the range here:
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