Answers
[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:find}}{\blue{:}}}}}[/tex]
The value of [tex]x[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Solution}}{\orange{:}}}}}[/tex]
[tex]\longrightarrow{\green{x=12° }}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:of\:a\:triangle\:=\:180°}[/tex]
➪ 95° + (3[tex]x[/tex] +4)° + (4[tex]x[/tex] - 3)° = 180°
➪ 3[tex]x[/tex] + 4[tex]x[/tex] + 95° + 4° -3° = 180°
➪ 7[tex]x[/tex] + 96° = 180°
➪ 7[tex]x[/tex] = 180° - 96°
➪ 7[tex]x[/tex] = 84°
➪ [tex]x[/tex] = [tex]\frac{84°}{7}[/tex]
➪ [tex]x[/tex] = 12°
Therefore, the value of [tex]x[/tex] is 12°.
Now, the three angles of the triangle are 95°, 40° and 45° respectively.
[tex]\large\mathfrak{{\pmb{\underline{\purple{To\:verify}}{\purple{:}}}}}[/tex]
✒ 95° + 40° + 45° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\boxed{Hence\:verified.}[/tex]
Related Questions
simplify
(−5abc − 6ac + 7cb) − (10abc + 6ac − 8bc)
Answers
Answer:
-15abc - 12ac + 15bc
General Formulas and Concepts:
Pre-Algebra
Distributive PropertyAlgebra I
Terms/CoefficientsStep-by-step explanation:
Step 1: Define
Identify
(-5abc - 6ac + 7cb) - (10abc + 6ac - 8bc)
Step 2: Simplify
[Distributive Property] Distribute negative: -5abc - 6ac + 7cb - 10abc - 6ac + 8bcCombine like terms: -15abc - 12ac + 15bcCan anyone help with this question? The population of a small industrial town was 12 910 in 2000. Each year, the population decreases by an average of 5%. Estimate the population in the year 2020. Round to the nearest whole number.
Answers
Answer:
Population of town in 2020 = 4626 (Approx.)
Step-by-step explanation:
Given:
Population of town in 2000 = 12,910
Decrease rate = 5% = 0.05 yearly
Find:
Population of town in 2020
Computation:
Number of year = 20 years
Population of town in 2020 = Population of town in 2000[1-r]ⁿ
Population of town in 2020 = 12,910[1-0.05]²⁰
Population of town in 2020 = 12,910[0.95]²⁰
Population of town in 2020 = 12,910[0.3584]
Population of town in 2020 = 4625.944
Population of town in 2020 = 4626 (Approx.)
Answer:
The population is 4628.
Step-by-step explanation:
Population in 2000 = 12910
Rate of decrease = 5 %
Time, t = 2020 - 2000 = 20 years
Let the population is P.
Use the formula
[tex]P = Po\left ( 1-\frac{r}{100} \right )^t\\\\P = 12910\left ( 1-0.05 \right )^2\\\\P = 4628[/tex]
There are nine different marbles in a bag. Supposed you reach in and draw one at a time. And do this three times. How many ways can you draw the three marbles if you do not replace the marble each time
Answers
Answer: 504 ways
Step-by-step explanation:
Given
There are nine different marbles in a bag
For the first time, there are 9 possible ways to draw a marble
After removal of first marble, there are 8 possible ways to draw a marble
for the third time, there are 7 possible ways
so, total ways to draw three marble are
[tex]\Rightarrow 9\times 8\times 7=504\ \text{ways}[/tex]
for what is values of x does 4(3x-2) = 12x - 5? select all that apply.
A.12
B.-8
C.3
D.-3
E.none of these
Answers
Answer:
‼️A) 12‼️
Step-by-step explanation:
Key skills needed: Interior Angle Measure Theorem, Equation Creation
Step 1) First, we need to classify this shape. It has 7 sides, which means that we can use the Interior angle Theorem to find out the sum of all the interior angle measures
The theorem is: S = (n - 2)180S=(n−2)180
S is the sum of all interior angle measures
n is the number of sides of the polygon
Step 2) With this, we can plug in 7 for "n" (Since the figure has 7 sides) and get:
---> S = (7-2)180S=(7−2)180
---> (7-2) is 5 since 7 - 2 = 5 so --> S = 5(180)S=5(180)
---> 5(180) is the same as 5 x 180 which is 900 so --> S = 900S=900
This means that the sum of all interior angles is 900 degrees.
Step 3) Now, we have to find out the sum of all the angles that they gave us so:
---> 10x + 10x + 9 + 133 + 9x + 14 + 12x - 9 + 10x + 5 + 136 = 90010x+10x+9+133+9x+14+12x−9+10x+5+136=900
The left side is the sum of all interior angles in the shape, and the right side is what the sum should be when expressed as a number.
Step 4) We have to combine all like terms on the left side:
---> 10x + 10x + 9x + 12x + 10x = 51x10x+10x+9x+12x+10x=51x
---> 9 + 133 + 14 -9+5+136 = 2889+133+14−9+5+136=288
Step 5) This means that ---> 51x + 288 = 90051x+288=900
Subtract 288 from both sides and get:
---> 51x = 61251x=612 (900-288 = 612)
Then divide by 51 from both sides and get:
---> x = 12x=12 (612 ÷ 51 = 12)
Therefore A) 12 is your answer.
I think it should be none of these.
The term on the left has to be even no matter what value of x and the right has to be odd no matter what value of x. Therefore, there shouldn't be an integer value of x that satisfies the equation, let alone the answer choices A-D.
Please help me solve this!
Please help quickly!
Answers
==========================================================
Explanation:
Focus on triangle TUS. The inner angles here are:
T = yU = xS = 180-2xNote how the angle measure for S is the supplement of 2x, which is adjacent to the angle S we have.
Add up those three angles and set the sum equal to 180
T+U+S = 180
y+x+180-2x = 180
y-x = 180-180
y-x = 0
y = x
We'll use this later.
-----------------
The diagram shows that angle VTU = y+y = 2y.
Focus your attention on triangle TUV.
Since TU = UV, this means the base angles T and V (which are opposite the congruent sides) are congruent angles. We found that angle T was 2y earlier. This means angle V is also 2y.
-----------------
Now shift your focus to triangle TSV.
This triangle has the inner angles
S = 2xT = yV = 2yRecall earlier that we found y = x at the conclusion of the first section. Using that and the fact that the angles of triangle TSV add to 180, we get...
T+S+V = 180
2x+y+2y = 180
2x+3y = 180
2x+3x = 180 .... replace y with x, since y = x
5x = 180
x = 180/5
x = 36
This is the value of y as well.
A salesman sold twice as much pears in the afternoon than in the morning. If he sold 360 kilograms of pears that day, how many kilograms did he sell in the morning and how many in the afternoon?
Answers
Answer:
120 kg in morning and 240 kg in afternoon
Step-by-step explanation:
x+2x=360 kg
Work:
x + 2x = 360 kg
3x = 360 kg
3x/3 = 360 kg/3
x = 120
2x=2(120 kg) =240 kg
Final Answer:
So, 120 kg in morning and 240 kg in the afternoon.
Hope this helps!
Write the equivalent fraction, the reduced fraction, and the decimal equivalent for 45%. Jenny solved this problem and her work is shown below. What mistake did she make? 45% = StartFraction 45 Over 100 EndFraction = StartFraction 9 Over 20 EndFraction = 4.5
Answers
Answer: See explanation
Step-by-step explanation:
The equivalent fraction of 45% is solved as follows:
First, we'll change the percentage to fraction which will be:
45% = 45/100
Then, we'll reduce to lowest term which will be:
45/100 = 9/20
Now, we'll convert the fraction to decimal which will be:
9/20 = 0.45
The mistake that Jenny made was that she divided 90 by 20. This will give 4.5.
Answer: The decimal equivalent is not correct. The decimal point is in the wrong position. The decimal point should be to the left of the 4, so the correct answer is 0.45.y-step explanation:
write 2^60 as an exponent with a base of 16
Answers
Recall that 2⁴ = 16. So you have
2⁶⁰ = 2⁴ˣ¹⁵ = (2⁴)¹⁵ = 16¹⁵
Anyone knows the answer?
Answers
Answer:
a) yes
b) y = -x
c) yes it goes thru the origin (0,0)
Step-by-step explanation:
a) x**2 + y**2 = 17
(-4)**2 + (-1)**2 = 17
16 + 1 = 17 YES
b) the slope of DE is
(y1 - y2)/(x1 - x2)
(-1 -4)/(-4 -1) = -5/-5 = 1, so a perpendicular segment will have a
slope of - 1/current slope or -1.
The midpoint of DE is
x = (x1 + x2)/2 = (-4 +1)/2 = -3/2
y = (y1 + y2)/2 = (-1 +4)/2 = 3/2 so
y = mx + b
y = -x + b plug in the point (-3/2,3/2)
3/2 = -(-3/2) + b
b = 0 SO y = -x
c) The circle equation dictates that it has no offset so centers around the origin (0,0) and the equation of the bisector y = -x indeed fits (0,0).
Which equation can be used to find the number of students needed to make 1,500 in profit ?
Answers
Answer:
we can use simple equation
I need help and fast I was supposed to turn this in last week
Answers
Answer:
The answer is below
Step-by-step explanation:
If two lines intersected by a transversal form congruent corresponding angles, then the lines are parallel.
If two angles are supplementary to the same angle, then the two angles are congruent.
Statement Reason
1) line p is parallel to line q Given
2) angle 1 and angle 4 are Given
supplementary i.e. ∠1 + ∠4
= 180° (definition of supplementary)
3) angle 3 and angle 4 are consecutive interior angles
supplementary
4) angle 1 congruent to angle 3 congruent supplements theorem
supplementary
5) line r parallel to line s corresponding angle converse
Combine and simplify the following radical expression
Answers
Answer:
[tex]2 \sqrt[3]{3} [/tex]Step-by-step explanation:
[tex] \sqrt[3]{6} . \sqrt[3]{4} [/tex]
[tex] = \sqrt[3]{6 \times 4} [/tex]
[tex] = \sqrt[3]{3 \times 2 \times 2 \times 2} [/tex]
[tex] = 2 \sqrt[3]{3} (ans)[/tex]
Which is the graph of the linear inequality {x-2y> -6?
Answers
Answer:
7
Step-by-step explanation:
Answer:
I think it is d
Step-by-step explanation:
If the base of a triangle is 3 and its height is 4, then its area is 6. This triangle has an area of 6, so its base is 3 and its height is 4
Valid or invalid
Answers
9514 1404 393
Answer:
invalid
Step-by-step explanation:
There is more than one set of dimensions that will give a triangle with an area of 6. The fact that the area is 6 implies nothing about the dimensions (except that their product is 12).
The converse is invalid.
Answer:
The first sentence is valid but the second one is invalid.
Step-by-step explanation:
You can't say just because the area of the triangle is 6, its base is 3 and its height is 4, it might have a base of 1 and a hight of 12 so there are more than one answers for the second one.
Feel free to message me if you still have questions :)
Dividing with powers of 10
Answers
A square pyramid has a base with an area of 20 square meters, and its lateral faces have a slant height of x meters. Sydney is constructing a second square pyramid with the same size base, but the lateral faces of her pyramid have a slant height twice as long, 2x. Which statement best describes how the surface area of Sydney’s pyramid compares to the surface area of the original pyramid?
Sydney’s pyramid will have the same surface area because the One-half in the expression for the area of the triangular faces will make up for the slant height being doubled.
Sydney’s pyramid will have the same surface area because the slant height is not used when finding surface area.
Sydney’s pyramid will have a surface area that is exactly double the original pyramid’s because the slant height is used when finding the area of every lateral face.
Sydney’s pyramid will have a surface area that is greater than the original pyramid’s but not double the area because the slant height is not used when finding the area of the base.
Answers
1. Consider the pyramid ABCDE in the figure 1 attached:
Each side of the square base equals (units)
Area of 1 lateral side of pyramid ABCDE is
so the total lateral area is (units squared)
and the total surface area is (units squared)
2. Now consider the second figure KLMNP, Sydney's pyramid:
The lateral area is
so the total area of the second pyramid is
So 2 things can be said about the areas:
i) the lateral area of Sydney's pyramid is times larger than the lateral area of the original pyramid.
ii) The total area of Sydney's pyramid is units squared larger than the total area of the original pyramid.
Please help:)))))))))))
Answers
Answer:
good evening good evening good evening good evening
find the inverse of the following function
Answers
f-¹(x)=[tex]\frac{2-7x}{x+2}[/tex]
Answer:
Solution given:
f(x)=[tex]\frac{-2x+2}{x+7}[/tex]
Let f(x)=y
y=[tex]\frac{-2x+2}{x+7}[/tex]
Interchanging role of x and y
x=[tex]\frac{-2y+2}{y+7}[/tex]
doing crisscrossed multiplication
x(y+7)=-2y+2
now solve it:
xy+7x=-2y+2
keep like terms in one side
xy+2y=2-7x
take common
y(x+2)=2-7x
make a value of y
y=[tex]\frac{2-7x}{x+2}[/tex]
So,
f-¹(x)=[tex]\frac{2-7x}{x+2}[/tex]
Answer:
ƒ^-1 (x) = [tex]\frac{2-7x}{2+x}[/tex]
Step-by-step explanation:
Substitute y for f (x)
[tex]y = \frac{-2x+2}{x+7}[/tex]
Interchange x and y
[tex]x=\frac{-2y+2}{y+7}[/tex]
Swap the sides of the equation
[tex]\frac{-2y+2}{y+7} = x[/tex]
Multiply both sides of the equation by y + 7
-2y + 2 = (y + 7)x
Distribute x through the parentheses
-2y + 2 = xy + 7x
Move the expression/constant to the left-hand side and change its sign
-2y - xy + 7x - 2
Factor out from the expression
(-2 - x)y = 7x - 2
Divide both sides of the equation by -2 - x
[tex]y = \frac{7x-2}{-2-x}[/tex]
Simplify the expression
[tex]y = \frac{2-7x}{2+x}[/tex]
Substitute ƒ ^-1 (x) for y
[tex]f^{-1} (x) = \frac{2-7x}{2+x}[/tex]
hich math expression means "the product of 16 and 26"?
O 16 - 26
26-16
16 - 26
0 16 +26
Answers
Answer:
infjfkflflfmdbfufifldndndhfififkfnf
HELPPPP MEEEE OUTTTT!!!
Answers
Answer:
Solution given:
Relationship between base and hypotenuse is given by Cos angle
Cos Angle(?)=base/hypotenuse
Angle{?}=Cos-¹(40/58)
Angle{?}=46°
The indicated angle is 46°
David's goldfish ate 20 grams of food in 4 weeks. At this rate, how long would it take the fish to eat the food
in a 100-gram container?
Answers
jack takes a job after school to earn money to buy a sport car.He knows that the more hours he works .the more money he will make
Answers
Answer: What's the question? I'll edit my answer to the question if you would give me the actual problem
Step-by-step explanation:
6. Which of the following equations has a slope of -2 and passes
through the point (3,-4).
O) y=-2x - 4
O) y=-2x + 2
O) y = -2x+3
O) y = -2x - 1
Answers
Answer:
y=-2x+2
Step-by-step explanation:
substitute either the x or y value into the equations, if you substitute x=3 and get back y=-4, the equation is correct
please help
yuffytdgtutidrysryrdf
Answers
Answer:
19 + 1 + 9 + 1
put any of those in the slots
Answer:
19 + 1 + 9 + 1
peace
Write the words that represent s + 21.
Answers
Answer:
A number s plus 21
Step-by-step explanation:
s+21
A number s plus 21
Now that you know the vertex, find the y-values that pair with a few x-values that are less than 2 and a few that are greater than 2.
Plsssss help!!!!!!!
Answers
y when x=1: 2
y when x=3: 2
y when x=4: 3
Joyce paid $39.00 for an item at the store that was 70 percent off the original price. What was the original price?
Answers
Answer:the answer is 10 because if u subctract it will work
Step-by-step explanation:
please help with this too
Answers
Answer:
The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is approximately 125.66 square units
Step-by-step explanation:
The given parameters are;
The radius of the circle with center G, r = 15
The measure of the given angle, m∠AGB = 64°
The area of a sector is given as follows;
Area of a sector of a circle = (θ/360°) × π × r²
Therefore;
The area of the sector in circle G formed by segments [tex]\overline{AG}[/tex], and [tex]\overline {GB}[/tex] is given as follows;
The area of the sector in circle G = (64°/360°) × π × 15² ≈ 125.66 square units
25 x square - 4y Square = 36 equation 1
5 x - 2 y=2equation 2
Answers
It is hard to find out question cn u pls take a pic and upload so it will more easier to find out the question
congruent figure help please :)
Answers
Answer:
x = 29
Step-by-step explanation:
ΔABC ≅ ΔDEC,
So, ∠BAC ≅∠CDE {Corresponding parts of congruent triangles}
∠BAC = 74°
InΔABC,
∠ABC + ∠BAC + ∠BCA = 180
2x + 74 + 48 = 180
2x + 122 = 180
Subtract 122 from both sides
2x = 180 - 122
2x = 58
Divide both sides by 2
x = 58/2
x = 29
