Answer:
The missing side is 22.98, or rounded to the nearest tenth, 23
The angles are 90, 40.37, and 49.63
Step-by-step explanation:
We can use the Pythagorean theorem to solve this problem;
[tex]a^2 + b^2 = c^2[/tex]
Since a = 14.9 and b= 17.5, we need to find the missing side, or c
[tex]14.9^2 + 17.5 ^2 = c^2[/tex]
Using a calculator this gives us;
528.26 = [tex]c^2[/tex]
Now to undo [tex]c^2[/tex], we have to square root both sides
[tex]\sqrt{528.26} = \sqrt{c^2}[/tex]
22.98 = c
Now to round to the nearest tenth, we know that .9 is greater than 5, so we can round 22.98 to 23
Now to find the angles.
We know that the triangle has a hypotenuse of 23, a short side of 14.9 and a long side of 17.5.
I labeled the side opposite of 14.9, x, and I will use sin to solve for the angle.
We know that sin= opposite/hypotenuse
So, sin(x)=14.9/23
Since we want to find the angle we must use the inverse of the trig function.
[tex]sin^-^1[/tex](14.9/23) = x
By using a calculator we get
x=40.37
Now since we know that this is a right triangle, we have a 90 degree angle.
So, we can subtract from 180 to find the third angle.
180-90-40.37=49.63
The angles of the triangle are 90, 40.37 and 49.63.
Hope this helped let me know if this can be explained further or if anything is wrong! : )
Solve the following equation using any method of your choosing: 6x² +24x = 0
Answer:
x = 0 or x = -4
Step-by-step explanation:
Solve: 6x² +24x = 0
First you can factor this binomial.
6x² +24x = 6x (x + 4) = 0
so x = 0 or x + 4 = 0
x = 0 or x = -4
6x2+40=31x factorise the quadratic equation
Answer:
Step-by-step explanation:
6x² + 40 = 31x
6x² - 31x + 40 = 0
6x² - 16x - 15x + (-5)*(-8) = 0
2x(3x - 8) - 5(3x -8) = 0
(3x - 8) (2x - 5) = 0
Please help me I’m about to cry
Answer:
LKH and JKM
Step-by-step explanation:
Aye, if you're gonna cry bro, take a break. This stuff means nothing in like 2 or 3 years. Trust me :)
Answer: it is angle LKH and angle JKM
Step-by-step explanation:
Verticals angles are angles that are opposite to each other and have the same degree measure. Since line JL is parallel to line GI, then MF is the transversal, creating some vertical angles. I’m not sure how else to explain it but you can connect the letters (in order) of the different angles to figure out what angles they are, and then find ones that are opposite angles. I hope this helped!
Graph the function.
h(x) = -1/5x^2+2x
Answer:
Hello there I would love to assist but could you give me a little more info I think I know the answer but I want to make sure I got it 100% correct unless you cant give me more info ill just tell you what I think it is but if u can give me more info before I give u the answer to make sure its correct would be appreciated
Step-by-step explanation:
Jessie installed 12 more axles than the number of engine blocks her friend Gus installed yesterday. Write an equation for g, the number of engine blocks Gus installed yesterday.
Answer:
g = j - 12
Step-by-step explanation:
We know that if g is Gus' number of engine quantity, then j is Jessie's number of engine quantity, from this statement we have that Jessie made 12 more than Gus, therefore:
j = g + 12
if we solve for g:
g = j - 12
which is the same as saying that Gus made 12 number of engine less than Jessie
Answer:
g = x - 12
where x is the number of axles installed by Jessie
Step-by-step explanation:
Using a simple analogy. If a man has 7 cars while his friend has 3 cars, The statement may be written as the man has 4 cars more than his friend. The 4 cars being the difference between the number of cars he has and the number his friend has.
As such, if the number of engine blocks installed by Gus is g and Jessie installed 12 more axles than the number of engine blocks Gus installed yesterday, where Jessie must have installed x axles,
x = g + 12
Such that
g = x - 12
The area of a square is 16 square units. What is the length of a side?
Answer:
4 is the length of a side.
Step-by-step explanation:
16 divided by 4 equals 4
Answer:
4 units
Step-by-step explanation:
The area of a square is denoted by: A = s², where s is the side length.
Here, we know that the area is 16, so plug this in for A:
A = s²
16 = s²
s = √16 = 4
Thus, the side length is 4 units.
~ an aesthetics lover
Write the equation of the circle graphed below.
Answer:
The equation of the circle is [tex]{ \left(x - 1 \right)^2 + \left( y - 2 \right)^2 = \frac{ 25 }{ 4 } }[/tex].
Step-by-step explanation:
This is the general standard equation for the circle centered at (h, k) with radius r.
[tex](x-h)^2+(y-k)^2=r^2[/tex]
From the graph we know that the center, the red point, is (1, 2) and the circle pass through the point (2.5, 4) the blue point.
To find the standard equation of the circle you must:
Step 1: Find circle radius.
To find a radius of a circle we will compute the distance between points [tex]C=(1, 2)[/tex] and [tex]P=(2.5, 4)={ \left( \frac{ 5 }{ 2 } , 4 \right) }[/tex]. The distance can be computed by using formula:
[tex]r = \sqrt{ \left(C_x - P_x\right)^2 + \left(C_y - P_y\right)^2 }\\\\r = \sqrt{ \left(1 - \frac{5}{2} )^2 + \left(2 - 4)^2 }[/tex]
[tex]r=\sqrt{\frac{3^2}{2^2}+2^2}=\sqrt{\frac{9}{4}+4}=\sqrt{\frac{25}{4}}=\frac{5}{2}[/tex]
Step 2: Substitute the values of the radius and the center into the general standard equation for the circle.
[tex]\begin{aligned} \left(x - 1 \right)^2 + \left(y - 2 \right)^2 &= \left(\frac{ 5 }{ 2 }\right)^2 \\ \left(x - 1 \right)^2 + \left( y - 2 \right)^2 &= \frac{ 25 }{ 4 } \end{aligned}[/tex]
which of the following statements correctlydescribes the points
The first statement is correct
To calculate the distance we have to substrate the values of the Y axis only since X values are constant so the distance IS 4 - - 7=4+7=11
Answer:
The first answer. The distance is 11.
HELPPP I NEED IT I DONT KNOW WHAT TO DO
Answer:
3/2
Step-by-step explanation:
Its because its saying the largest box to the smallest.
since the largest box has a side of 3 it should be on top and the smallest is 2, should be on the bottom.
Ignore all negetive fraction because they are useless.
Una caja grande cuesta lo mismo que tres pequeñas. Si 7 cajas grandes y 4 pequeñas cuestan $12 más que 4 grandes y 7 pequeñas ¿Cuál es el sistema de ecuaciones que modela el sistema?
Answer:
[tex] x = 3y [/tex]
[tex]7x+4y= 12 + 4x+7y[/tex]
Step-by-step explanation:
Para resolver la pregunta, basta con definir variables adecuadas y traducir cada relación. Sea x el costo de una caja grande e y el costo de una caja pequeña. Tenemos que el costo de una caja grande es igual a 3 cajas pequeñas. Es decir, x = 3y. Luego, tenemos que
[tex]7x+4y= 12 + 4x+7y[/tex]
pues al sumarle 12 al costo de 4grande y 7 pequeñas obtenemos el costo de 7 grande y cuatro pequeñas. De aquí, el sistema de ecuaciones que modela el sistema es
[tex] x = 3y [/tex]
[tex]7x+4y= 12 + 4x+7y[/tex]
if suresh made a deposit of AED 2700 on the first day of the tear and same amount again after every 4 months at the end of the year how much money will he get if the interest is compounded quarterly and the rate of interest is 7.5% per annum
Answer:
48.048
Step-by-step explanation:
multiply 77 time 0.60 since 60%in decimal form is 0.60. you then get the answer of that(46.2) and mutiply 0.04 since that the decimal form for 4%. you get 1.848 and add it to 46.2 and get the final answer 48.048. Hope this helped you
Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the east coast, to $3 in the mid-US, to $5 on the west coast. B On their way back they had more baggage in the car and spend $601 for 174 gallons of gas. Based on the same ratio as in Part (a), how many gallons of gas did they buy at each price?
Answer:
A) The amount of gas they bought on each coast;
East Coast = 35 gallons
Mid-US = 100 gallons
West Coast = 15 gallons
B) The amount of gas they bought on each coast on the return journey;
East Coast = 37 gallons
Mid-US = 116 gallons
West Coast = 21 gallons
Step-by-step explanation:
Complete Question
Maxis taking a cross-country road trip. Gas prices vary as the friends travel across the US from $4 dollars per gallon on the east coast to $3 in the mid-US, to $5 on the west coast.
(a) If they used twice as much gas in the mid-US than on either coast combined, and they spend $515 on gas to purchased 150 gallons of gas, how many gallons of gas did they buy at each price?
The answer to this question is East Coast - 35 gal, Mid-US - 100 gal, West Coast - 15 gal.
(b) On their way back they had more baggage in the car and spend $601 for 174 gallons of gas. Based on the same ratio as in Part (a), how many gallons of gas did they buy at each price? I don't know the answer to this one
Solution
Let the amount of fuel bought on the east coast = x gallons
Let the amount of fuel bought on the mid-coast = y gallons
Let the amount of fuel bought on the west coast = z gallons
a) - They used twice as much gas in the mid-US than on either coast combined
y = 2(x + z) = 2x + 2z (eqn 1)
- They spend $515 on gas to purchase 150 gallons of gas.
Total gallons purchased = x + y + z = 150
Total amount spent = 4x + 3y + 5z = 515
From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations
x + y + z = x + 2x + 2z + z = 150
3x + 3z = 150
Divide through by 3
x + z = 50 (eqn *)
4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 515
4x + 6x + 6z + 5z = 515
10x + 11z = 515 (eqn **)
x + z = 50
10x + 11z = 515
Solving the simultaneous equation,
x = 35 gallons
z = 15 gallons
y = 2x + 2z = 2(35 + 15) = 100 gallons
B) On the return journey, the ratio between x, y and z is still the same, but the total gallons and total amount spent is now different.
They used twice as much gas in the mid-US than on either coast combined
y = 2(x + z) = 2x + 2z (eqn 1)
- They spend $601 on gas to purchase 174 gallons of gas.
Total gallons purchased = x + y + z = 174
Total amount spent = 4x + 3y + 5z = 601
From eqn 1, y = 2x + 2z, inserting this value for y in the 2 other equations
x + y + z = x + 2x + 2z + z = 174
3x + 3z = 174
Divide through by 3
x + z = 58 (eqn *)
4x + 3y + 5z = 4x + 3(2x + 2z) + 5z = 601
4x + 6x + 6z + 5z = 601
10x + 11z = 601 (eqn **)
x + z = 58
10x + 11z = 601
Solving the simultaneous equation,
x = 37 gallons
z = 21 gallons
y = 2x + 2z = 2(37 + 21) = 116 gallons
Hope this Helps!!!
Miguel stated that any monomial can be a cube root. Sylvia disagreed and said that a monomial cube root must have exponents divisible by 3. Who is correct, and why?
Sylvia is correct. Any variable term, when it is cubed, always has an exponent divisible by 3.
Miguel is correct. Any monomial can be a perfect cube root because, when it is cubed, the variables will have exponents divisible by 3.
Sylvia is correct. In order for the cube to have exponents that are divisible by 3, the cube root has to be divisible by 3.
Miguel is correct. Sylvia confused the perfect square root with the perfect cube root.
Option B. is correct
Polynomial equation are equation of number independent variables having relationship with dependent variable.
Since,
A monomial can have higher exponents so its exponents has probability to get divisible by 3 so when cube root for monomial performed.
for example [tex]\sqrt[3]{x^3}[/tex] = x
Thus, Miguel is correct. Any monomial can be a perfect cube root because, when it is cubed, the variables will have exponents divisible by 3.
Learn more about polynomial here:
brainly.com/question/11536910
#SPJ2
Answer:
option B
Step-by-step explanation:
edge 2023
Which is the simplified form of m Superscript negative 8 p Superscript 0?
StartFraction 1 Over m Superscript 8 Baseline p EndFraction
StartFraction 1 Over m Superscript 8 EndFraction
StartFraction p over m Superscript 8 EndFraction
m Superscript 8
i think it is C
Step-by-step explanation:
Answer:
1 or D
Step-by-step explanation:
The growth of a population of bacteria can be modeled by an exponential function. The graph models the population of the bacteria colony P(t) as a function of the time t, in weeks, that has passed. The initial population of the bacteria colony was 500. What is the domain of the function? What does the domain represent in this context?
Answer:
t ≥0
Step-by-step explanation:
Given the information:
The initial population: 500
The graph models the population of the bacteria colony P(t) as a function of the time t, in weeks,
=> our function is: P(t) =500*[tex]b^{t}[/tex] where b is the base number and it is ≥0
What is the domain of the function?The domain of exponential functions is all real numbers greater than zero
<=> t ≥0 (because t present for the time and time can not have negative value)
What does the domain represent in this context?t is the independent variable is this exponential function and the population of bacteria depends on the change of t.
Because it is the growth function so the range (the population of bacteria) increase over its domain (the time)
Hope it will find you well.
Need help plssssss fast hurry plsss
Answer:
50 ft2
Step-by-step explanation:
im not sure if this is right but this is what i got when i worked it out
Answer: [tex]150ft^2[/tex]
Step-by-step explanation:
length: [tex]7\frac{1}{2}in[/tex] Convert to an improper fraction. [tex]\frac{7*2+1}{2}=\frac{15}{2}[/tex]
width: [tex]5 in[/tex]
[tex]Formula: A=w*l[/tex]
[tex]A=(5in)(\frac{15}{2}in)\\A=\frac{75}{2}in^2[/tex]
Convert to ft. I assume your conversion factor is [tex]\frac{1}{2}in. : 1ft[/tex]. However, the unit we need is squared. Square both sides.
[tex](\frac{1}{2}in.)^2 : (1ft)^2[/tex]
[tex]\frac{1}{4}in^2 : 1ft^2[/tex]
Convert.
[tex]\frac{75}{2}in^2(\frac{1ft^2}{\frac{1}{4}in^2 } )=[/tex]
Invert the fraction in the denominator and multiply it by the numerator.
[tex]\frac{75}{2}in^2*1ft^2*4in^-^2=75*2ft^2=150ft^2[/tex]
Jimmy pumps 288,000 cubic centimeters of air into a spherical balloon. What is the radius of the balloon?
There are no options to choose from
Answer:
r: radius of balloon
V = (4/3)*pi*r^3 = 288000
=> r^3 = 288000*(3/4)/pi
=> r^3 = 68754.94
=> r = [tex]\sqrt[3]{68754.94}[/tex] = ~40.97 cm
What is the equation of a line passing through 1,2 and -2,5
Answer:
y=-1x+3
Step-by-step explanation:
2-5/1+2
-3/3
-1
y=-1x+b
2=-1+b
b=3
y=-1x+3
The circular ring of the fountain has a radius of 9 feet. What is the area of the ring?
Answer:
about 254.47
Step-by-step explanation
Circle are equation: pi(r)^2
pi(9)^2 = 254.47
Karina bought 8 bagels and used a gift certificate for $4. Her total cost is represented by the expression 8b - 4, where b is the cost of a bagel. What is an equivalent expression?
Answer:
An equivalent expression = 8b + (-4)
Step-by-step explanation:
In Mathematics, numbers exhibit or are guided by certain properties that they can show.
Some of those of properties are :
a) Commutative property where:
a + b = b + a
b) Associative property
a+( b + c) = (a + b) + c
c) Additive inverse property
a - b = a + ( - b)
For the question above, we are told that the total cost of what Karen bough is represented by the expression 8b - 4. We are asked find the equivalent expression.
An equivalent expression is defined as an expression that has the exact value for all the values obtained from the variable.
Hence, using the Additive inverse property
a - b = a + ( - b)
The equivalent expression for 8b - 4 = 8b + ( -4)
What is the negative square root of 4,900?
Answer: -70
Step-by-step explanation: hope I helped
Consider the system of equations. 5x + 2y = 6, 10x + 4y = 12 Which equation is equivalent to the first equation of the system and can be used to solve the system using the linear combination method
Step-by-step explanation:
(5x+2y=6)2
10x+4y=12
10x+4y=12 then substract
10x+4y=12
0=0 true so, it have infinite s/n
0.7(1.5+ y) = 3.5y - 1.47
Solve
Answer:
y = .9
Step-by-step explanation:
0.7(1.5+ y) = 3.5y - 1.47
Distribute
1.05 +.7y = 3.5y -1.47
Subtract .7y from each side
1.05 +.7y.-.7y = 3.5y-.7y -1.47
1.05 =2.8y -1.47
Add 1.47 to each side
1.05+1.47 = 2.8y
2.52 = 2.8y
Divide by 2.8
2.52/2.8 = y
.9 = y
Answer:
y = 0.9
C, the third one
Step-by-step explanation:
Examine this multistep equation with variables on both sides.
0.7(1.5 + y) = 3.5y - 1.47
Which of the following is the solution to this equation?
y = 0.09
y = 0.17
y = 0.9
y = 1.7
can someone tell me how to do this
Answer:
must not be
Step-by-step explanation:
The whole thing equals 360 degrees
Angle B and Angle D are equal; which equals 190 degrees.
Add Angle A to 190 degrees; which is 86 + 190 = 276.
Subtract 360, which is what the whole thing equals, and 276, which is the known angle added together, and you get 56.
In order for this to be a parallelogram, the opposite angles need to be equal.
Since they are not, the answer is must not be.
The sum of the two shorter sides of a triangle must be equal to the longest side to be classified as a triangle
Answer:
False
Step-by-step explanation:
For example if you follow the pythagoras theorem a triangle has sides of 3,4 and 5
but when you add 3 and 4 they do not give you 5
so that is false
Please answer as soon as you see this it’s urgent
Answer:
m∠DEH= 128.6°
Step-by-step explanation:
∠GHJ and ∠DEH are both congruent to each other because lines DF and GI are both parallel to each other.
This means, if m∠GHJ is 128.6°, m∠DEH is also 128.6°.
Answer:
128.6
Step-by-step explanation:
GHJ= DEH
adjasent angle
A jar contains 666 red jelly beans, 444 green jelly beans, and 444 blue jelly beans.
If we choose a jelly bean, then another jelly bean without putting the first one back in the jar, what is the probability that the first jelly bean will be blue and the second will be blue as well?
Answer:
Step-by-step explanation:
P(first blue) = 444/ 1554
P(second blue) = 443/1553
P(first blue + second blue) = 444/ 1554 * 443/1553 = 0.08
what is the answer to 22% of 49.6?
Answer:
10.912
Step-by-step explanation:
0.22*49.6=10.912
Answer:
the answer is 225.45
Step-by-step explanation:
49.6 ÷ 22% =
49.6 ÷ (22 ÷ 100) =
(100 × 49.6) ÷ 22 =
4,960 ÷ 22 ≈
225.454545454545 ≈
225.45
3
Find the volume of the prism. *
1.5 m
2 m
4 m
Answer choices are:
A) 8m^3
B) 12m^3
C)10m^3
6m^3
Answer:
[tex]12m^{3}[/tex]
Step-by-step explanation:
Multiply all the variables together to get the answer (only for rectangular prism).
So I basically did 4 x 2 x 1.5 = 12 Then I applied the unit of measurement and cubic meters as it is volume.The formula is length x width x heightIdentify the outlier of the data set.
3,4,4,5,5,6,6,7,7,7,8,20
a
20
b
8
oooo
C
6.8
d
3
Answer:
a.20
Step-by-step explanation:
20 is standing out from the rest of the numbers
