Answer:
x = 2.1
Step-by-step explanation:
We have:
[tex]\frac{x}{sin90}[/tex] = [tex]\frac{1.3}{sin38}[/tex]
=> sin38 × x = sin90 × 1.3
=> x = 1.3 ÷ sin38
=> x = 2.11155001... = 2.1
<3 Have a nice day!!
The value of x for the given triangle will be, x = 2.1.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is used to solve problems involving angles and distances and is applied in a wide range of fields such as engineering, physics, architecture, and navigation, among others.
The value of x will be calculated as,
x / sin(90) = 1.3/ sin(38)
sin38 × x = sin90 × 1.3
x = 1.3 ÷ sin38
x = 2.11155001...
x = 2.1
The value of x will bed x =2.1.
To know more about trigonometry follow
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plz help me with this math and also explain
Step-by-step explanation:
[1]SI = $250Rate (R) = 12[tex] \sf \dfrac{1}{2}[/tex] %Time (t) = 4 years[tex]\longrightarrow \tt { SI = \dfrac{PRT}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 12\cfrac{1}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times \cfrac{25}{2} \times 4}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 25 \times 2}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 = \dfrac{P \times 50}{100} } \\ [/tex]
[tex]\longrightarrow \tt { 250 \times 100 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { 25000 = P \times 50} \\ [/tex]
[tex]\longrightarrow \tt { \dfrac{25000}{50} = P } \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green{ \tt { \$ \; 500 = P }}}} \\ [/tex]
Therefore principal is $500.
__________________[2]2/7 of the balls are red.3/5 of the balls are blue.Rest are yellow.Number of yellow balls = 36Let the total number of balls be x.
→ Red balls + Blue balls + Yellow balls = Total number of balls
[tex]\longrightarrow \tt{ \dfrac{2}{7}x + \dfrac{3}{5}x + 36 = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{10x + 21x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{31x + 1260}{35} = x} \\ [/tex]
[tex]\longrightarrow \tt{ 31x + 1260= 35x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 35x-31x} \\ [/tex]
[tex]\longrightarrow \tt{ 1260= 4x} \\ [/tex]
[tex]\longrightarrow \tt{ \dfrac{1260 }{4}= x} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \tt { 315 = x }}} \\ [/tex]
Total number of balls is 315.
A/Q,
3/5 of the balls are blue.
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}x} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} =\dfrac{3 }{5}(315)} \\ [/tex]
[tex]\longrightarrow \tt{ Balls_{(Blue)} = 3(63)} \\ [/tex]
[tex]\longrightarrow \underline{\boxed{ \green {\tt { Balls_{(Blue)} = 189 }}}} \\ [/tex]
a 10 foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle betwween the top of the ladder and the wall changing when that angle is
Answer:
d∅/dt = √2/5 Rad/sec
Step-by-step explanation:
According to the Question,
Given That, a 10-foot ladder rests against a vertical wall if the bottom of the ladder slides away from the wall at a speed of 2 ft/s how fast is the angle between the top of the ladder and the wall changing when that angle is π/4.Solution,
Let x be the Distance between the base of the wall and the bottom of the ladder.
and let ∅ be the angle between the top of the ladder and the wall.
Then, Sin∅ =x/10 so, x=sin∅ *10
Differentiating with respect to time t we get,
dx/dt = 10 * cos∅ * d∅ /dt
We have given that dx/dt = 2 ft/s and ∅ =π/4Now, Put these value we get
2 = 10 *(cos(π/4))* d∅/dt
2 = 10/√2 * d∅/dt
d∅/dt = √2/5 Rad/sec
The sum of three consecutive odd numbers is 63. What are the numbers?
Answer:
19, 21 and 23
Step-by-step explanation:
→ Make an algebraic expression for the 3 consecutive numbers
2x + 1, 2x + 3 and 2x + 5
→ Add the expressions together and make it equal to 63
2x + 1 + 2x + 3 + 2x + 5 = 63
→ Simplify
6x + 9 = 63
→ Minus 9 from both sides
6x = 54
→ Divide both sides by 6
x = 9
→ Resubstitute x = 9 into the 3 expressions
x = 9 into 2x + 1 is 19
x = 9 into 2x + 3 is 21
x = 9 into 2x + 5 is 23
What is 6.273 rounded to the nearest thousandths?
Answer:
6.270
Step-by-step explanation:
3 is below 5 so you just turn it into a 0. If it was 5 or above you would just add a number to the 7.
In In 5x + In In (x - 1) = 2
Answer:
exact form: x=-1/2
decimal form: x=-0.5
In which section of the number line is 32−−√?
where's the number line?
maybe u can attach it at the comments:)
Answer:
Section B
Step-by-step explanation:
if f(x) = 2x/7 +4, which of the following is the inverse of f(x)?
Answer:
The answer is C
Step-by-step explanation:
Switch x and y
[tex]x = \frac{2y}{7} + 4[/tex]
Solve for y
[tex]y = \frac{7(x - 4)}{2} [/tex]
Find the value of y
Help please
Answer:
6
Step-by-step explanation:
Set your formula up as
15 = 2y+3
15 - 3 = 2y
12 = 2y
12 / 2 = y
6 = y
Identify a horizontal or vertical stretch or compression of the function by observing the equation of the function .
Find the measure of the missing angle using the exterior angle sum theorm.
Answer:
85°
Step-by-step explanation:
The exterior angle of a triangle is=sum of the opposite interior angles
So
? °=45°+40°
log8-log4 ÷ log4-log2=
For the function G defined by G(x)=5x+3, find G(r+5)
Given function:
g(x) = 5x + 3Find
g(r+5)Substitute x with r = 5:
g(r + 5) = 5(r + 5) + 3 = 5r + 25 + 3 = 5r + 28
Answer:
G ( r + 5 ) = 5r + 28
Step-by-step explanation:
Given ;
G ( x ) = 5x + 3
To Find :-
G ( r + 5 )
Solution :-
plug r + 5 as x in the function.
G ( r + 5 ) = 5 ( r + 5 ) + 3distribute 5
G ( r + 5 ) = 5r + 25 + 3combine like terms
G ( r + 5 ) = 5r + 28One leg of a right triangle is 7 inches longer than the other leg, and the hypotenuse is 35 inches. Find the lengths of the legs of the triangle.
Answer: 21, 28
Step-by-step explanation:
Side #1 = xSide #2 = x + 7Hypotenuse = 35Use the Pythagorean Theorem [tex]a^{2}+b^{2}=c^{2}[/tex]:
a = xb = x + 7c = 35Substitute in the values & solve:
[tex]x^{2}+(x+7)^{2}=35^{2}\\x^{2}+x^{2}+14x+49=1225\\2x^{2}+14x+49-1225=0\\2x^{2}+14x-1176=0\\2(x^{2}+7x-588)=0\\2(x + 28)(x - 21)=0\\x_{1}=-28, x_{2}=21[/tex]
-28 is not a possible solution since you can't have negative inches...
a = x = 21b = x + 7 = 21 + 7 = 28c = 35Someone please help me ASAP
Step-by-step explanation:
a vector multiplied by a scalar is equal to it's image. The expression above gives an equation and after solving, it gives you the image
help help help pls :)
Answer:
[tex]opposite\approx 70.02[/tex]
Step-by-step explanation:
The triangle in the given problem is a right triangle, as the tower forms a right angle with the ground. This means that one can use the right angle trigonometric ratios to solve this problem. The right angle trigonometric ratios are as follows;
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Please note that the names ([tex]opposite[/tex]) and ([tex]adjacent[/tex]) are subjective and change depending on the angle one uses in the ratio. However the name ([tex]hypotenuse[/tex]) refers to the side opposite the right angle, and thus it doesn't change depending on the reference angle.
In this problem, one is given an angle with the measure of (35) degrees, and the length of the side adjacent to this angle. One is asked to find the length of the side opposite the (35) degree angle. To achieve this, one can use the tangent ([tex]tan[/tex]) ratio.
[tex]tan(\theta)=\frac{opposite}{adjacent}[/tex]
Substitute,
[tex]tan(35)=\frac{opposite}{100}[/tex]
Inverse operations,
[tex]tan(35)=\frac{opposite}{100}[/tex]
[tex]100(tan(35))=opposite[/tex]
Simplify,
[tex]100(tan(35))=opposite[/tex]
[tex]70.02\approx opposite[/tex]
find the volume of the rectangular prism. plz answer this lol
Answer:
.....how when the dimensions are not even clear lol
Answer:
48 cm³
Step-by-step explanation:
the volume of a rectangular prism= length × breadth × height
= 8× 3 × 2
= 48 cm³
On a coordinate plane, a line goes through (negative 3, negative 4) and (3, 0).
What are the necessary criteria for a line to be perpendicular to the given line and have the same y-intercept?
The slope is Negative three-halves and contains the point (0, 2).
The slope is Negative two-thirds and contains the point (0, −2).
The slope is Three-halves and contains the point (0, 2).
The slope is Negative three-halves and contains the point (0, −2
Answer:
The slope is Negative three-halves and contains the point (0, 2).
Step-by-step explanation:
(-3,-4)(3,0)
M= -4/-6 = 2/3
⊥M = -3/2
0 = 2/3(3) + B
B=2
P(x) is a polynomial. here are a few values of p(x).
P(-5) = - 2
P(-3) = 6
P(3) = 7
P(5) = -1
What is the remainder when P(x) is divided by (x+5)?
What is the remainder when P(x) is divided by (x-3)?
Given:
Values of a polynomial P(x).
[tex]P(-5)=-2[/tex]
[tex]P(-3)=6[/tex]
[tex]P(3)=7[/tex]
[tex]P(5)=-1[/tex]
To find:
The remainder when P(x) is divided by (x+5).
The remainder when P(x) is divided by (x-3).
Solution:
If a polynomial P(x) is divided by (x-a), then the remainder is P(a).
If the polynomial P(x) is divided by (x+5), then the remainder is P(-5).
[tex]P(-5)=-2[/tex]
Therefore, the remainder is -2 when P(x) is divided by (x+5).
If the polynomial P(x) is divided by (x-3), then the remainder is P(3).
[tex]P(3)=7[/tex]
Therefore, the remainder is 7 when P(x) is divided by (x-3).
solve the simultaneous equation: x-y=2
xy=36
Answer:
Y= –7.08, 5.08
Step-by-step explanation:
hope ya ready bro.
X=36/Y
replace 36/y instead of X
36/Y–Y=2===> 36–Y²=2Y===> Y²+2Y–36=0
Y1= –1+√37≈ –7.08
Y2= –1–√37≈ 5.08
The equation d = m/v can be used to calculate the density,d, of an object with mass,m, and volume,V. Which is an equivalent equation solver for V?
Answer:
v = m/d
Step-by-step explanation:
since
[tex]d = \frac{m}{v} \: \\ \\ v = \frac{m}{d} [/tex]
Which point is in the solution set of this system inequalities?
A. (0,0)
B. None of these
C. (5,1)
D. (3,7)
Answer:
B
Step-by-step explanation:
To find which ordered pairs are solutions to the inequalities we can simply plug in the x and y values of the ordered pairs into the inequalities and if the equation is true for both inequalities then the ordered pair is a solution to the inequalities.
For (0,0)
x = 0
y = 0
y > x + 5
Substitute 0 for y and x
0 > 0 + 5
Simplify right side
0 > 5
The inequality is not true as 5 is greater than 0, not less than. So immediately we can eliminate answer choice A.
For (5,1).
x = 5
y = 1
y > x + 5
Substitute 5 for x and 1 for y
1 > 5 + 5
Simplify right side
1 > 10
Again, the equation is not true as 1 is not greater than 10. This means that c cannot be the answer
For (3,7)
x = 3
y = 7
y > x + 5
Substitute 3 for x and y for 7
7 > 3 + 5
Simplify right side
7 > 8
7 is not greater than 8 meaning that (3,7) cannot be a solution to the inequalities
None of the ordered pairs created true equations hence the answer is B
A number ending in ___ is never a perfect square.
Answer:
2, 3, 7 or 8
Step-by-step explanation:
If
5
3 cosα = in the first quadrant, what does cot α
equal?
Answer:
5/4
Step-by-step explanation:
To Find :-
cot a .Solution :-
By question ,
=> cos a = 5/3 = b/h
=> p = √ 5² - 3² = √ 25 -9 = 4
Therefore ,
=> cot a = b/p = 5/4
Arvin has $10000 to invest. He invests part in a term deposit paying 5%/year, and the remainder in Canada savings bonds paying 3.4%/year. At the end of the year, he earned simpler interest of $413. How much did he invest at 5%/year?
Answer:
$4,562.5
Step-by-step explanation:
The amount Arvin has to invest, P = $10,000
The interest paid on the investment in the term deposit = 5%/year
The interest paid om the investment in Canada savings bonds = 3.4%/year
The amount Arvin earned at the of the year as simple interest, A = $413
Let, x, represent the amount Arvin invested in the term deposit and let, y, represent the amount he invested in Canada savings bonds, we can get the following system of equations
x + y = 10,000...(1)
0.05·x + 0.034·y = 413...(2)
Making y the subject of equation (1) and substituting the value in equation (2), we get;
From equation (1), we get, y = 10,000 - x
Plugging the above value of y in equation (2) gives;
0.05·x + 0.034 × (10,000 - x) = 413
∴ 0.05·x - 0.034·x + 340 = 413
x = (413 - 340)/(0.05 - 0.034) = 4,562.5
Therefore, the amount Arvin invested in the term deposit at 5%, x = $4,562.5
(y = 10,000 - x
∴ y = 10,000 - 4,562.5 = 5,437.5
The amount Arvin invested in Canada savings bonds, y = $5,437.5.)
one more question
(-8)+___=-17
Answer:
-9
Step-by-step explanation:
Answer:
-9
Step-by-step explanation:
-8 +___= - 17
___=-17 +8
___=-9
=-9
sue has 18 pieces of candy
tony has 18 pieces of candy
sue then gives some to tony
sue then eats five of hers
tony eats half of his
write the expressions for the number of pieces candy sue and tony now have?
Answer:
Sue candy = 13 - x
Tony candy = 9 + 1/2x
Step-by-step explanation:
Sue candy = 18
Tony candy = 18
Let x = some candy gives to tony
Sue candy = 18 - x
Tony candy = 18 + x
sue then eats five of hers
Sue candy = 18 - x - 5
= 13 - x
tony eats half of his
Tony candy = 1/2(18 + x)
= 18/2 + x/2
= 9 + 1/2x
Expressions for the number of pieces candy sue and tony now have:
Sue candy = 13 - x
Tony candy = 9 + 1/2x
someone help me for this algebra task please
Answer:
200
Step-by-step explanation:
Substitute 15 for y
[tex] \frac{1}{5} x - \frac{2}{3} (15) = 30[/tex]
[tex] \frac{1}{5} x - 10 = 30[/tex]
[tex] \frac{1}{5} x = 40[/tex]
[tex]x = 200[/tex]
a^2×c^2/c^2×d^2+bc/ad reduce the algebraic
Answer:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
Step-by-step explanation:
Given
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Required
Simplify
We have:
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}[/tex]
Cancel out [tex]c^2[/tex]
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^2}{d^2}+\frac{bc}{ad}[/tex]
Take LCM
[tex]\frac{a^2*c^2}{c^2*d^2}+\frac{bc}{ad}= \frac{a^3 + bcd}{ad^2}[/tex]
Please help. I don’t understand I rlly appreciate it if you help!
Hi there!
We know that the angles ∠B and ∠A are supplementary because they are both interior angles. Therefore:
180 = ∠A + ∠B
Rewrite:
180 = (6x - 48) + (4x + 38)
Combine like terms:
180 = 10x - 10
Solve for x:
190 = 10x
x = 19
Solve for ∠B by plugging in this value of x:
∠B = 4(19) + 38
∠B = 76 + 38
∠B = 114
What is the slope of the line? What is the y-intercept of the line? y = -3x + 4
Answer:
slope= -3/1
y-intercept= 4
Answer:
m = -3
y intercept = 4
Step-by-step explanation:
The given equation of the line is ,
[tex]\implies y = -3x+4[/tex]
We know that the Standard equation of Slope Intercept Form of the line is,
[tex]\implies y = mx + c[/tex]
Where ,
m is slope c is y interceptOn comparing to the Standard form of the line we get ,
[tex]\implies Slope = -3 [/tex]
[tex]\implies y - intercept= 4 [/tex]