Answer:
B.) The only solution is (4, - 1/2)
Step-by-step explanation:
To solve this system of equations using the substitution method, we need to use one equation to find an expression for one of the terms or variables that can be substituted for that term or variable in the other equation.
__
expression for xHere, it is convenient to use the second equation to write an expression for x:
x -2 = -4y
x = 2 -4y . . . . add 2 to both sides
substituteUsing this expression for x, we can write the second equation as ...
3x +2y = 11
3(2 -4y) +2y = 11 . . . . . substitute for x
6 -10y = 11 . . . . . . . . eliminate parenthses
solveThis 2-step equation can be solved in the usual way:
-10y = 5 . . . . . . . subtract the constant to isolate the variable term
y = -5/10 = -1/2 . . . . . divide by the coefficient of the variable
x = 2 -4(-1/2) = 2 +2 = 4 . . . . . find the corresponding x-value
The only solution is (x, y) = (4, -1/2).
The only solution is (x, y) = (4, -1/2). so, the correct option is B.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
we have the system of equations;
3x+2y=11
x−2=−4y
By the substitution method;
use the second equation to write an expression for x:
x -2 = -4y
x = 2 -4y
substitute
3x +2y = 11
3(2 -4y) +2y = 11
6 -10y = 11
solve
-10y = 5
y = -5/10 = -1/2
x = 2 -4(-1/2)
x = 2 +2 = 4
Thus, The only solution is (x, y) = (4, -1/2). so, the correct option is B.
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help please
what is
Answer:
sure how can I help you? please tell me
Prove Triangle ABC is congruent to Triangle CDA.
The triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
What is the similarity?If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.
In the given triangles we can see that:-
Angle BAC is congruent to Angle DCA Angle B and Angle D are congruent.The two triangles are sharing common side which is AC.Therefore we can see that the triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.
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given the following pyramid identify the L, P, and B then find the surface area
Answer:
slant length (l) = 7.5 m
perimeter of base P = 40 m
area of base B = 100 m^2
Surface Area = 250 m^2
Step-by-step explanation:
Surface area of a pyramid formula
1/2Pl + B
1/2 (40)(7.5) + 100
150 + 100 = 250 square meters
What is the vertex of the parabola defined by the equation
(x-2)² =-12(y-2)?
A (-12, 2)
B.
(2, 2)
C. (6,2)
D. (2,-2)
Answer: B. (2,2)
Step-by-step explanation:
The vertex of the parabola in the form [tex](x-h)^2 = 4p(y-k)[/tex] is (h, k).
1 x 1 x 99 x 100 hat is the awnser
Jaira is completing construction of a regular hexagon inscribed in a circle, as shown below: What should be the next step in her construction?
Jaira is completing the construction of a regular hexagon inscribed in a circle, as shown below: The next step in her construction should be:
construct another pont E by placing her compass at the locus DRepeat the process to get 6 more points on the given circle then join all of them together.A closed polygon with six equal sides and six equal angles is called a regular hexagon.
Thus, the steps highlighted above will help Jaira complete her construction.
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The probability that the number of students who will take the mathematics exam is 40 out of 50. What is the expressed as a percentage
Answer:
I think it's 80%
Step-by-step explanation:
Method 1: (40/50)*100 = 80%
Method 2: [tex]\frac{40*2}{50*2} = \frac{80}{100}[/tex] = 80%
The points (0, -8) and (10, 2) represent the endpoints of a diameter of a circle. Which of the following represents the equation of this circle?
Answer:
(x-5)²+(y+2)²=200.
Step-by-step explanation:
1) using the given coordinates it is possible to calculate
- the centre of the given circle:
[tex]x_0=\frac{10+0}{2}=5; \ y_0=\frac{2-8}{2}=-2;[/tex]
- the radius of the given circle:
[tex]r=\sqrt{(10-0)^2+(2+8)^2} =\sqrt{200} ;[/tex]
2) finally, the required equation (common form is (x-x₀)²+(y-y₀)²=r²):
(x-5)²+(y+2)²=200.
What is another way to write the equation 7/8x3/4=-6
Another way to write the equation is 7x + 54 = 0
How to rewrite the equationGiven the equation;
[tex]\frac{7}{8}x + \frac{3}{4} = -6[/tex]
Find the LCM on the left side, which is 8
[tex]\frac{7x + 6}{8} = -6[/tex]
Cross multiply
[tex]7x + 6 = -6[/tex] × [tex]8[/tex]
[tex]7x + 6 = -48[/tex]
Collect like terms
[tex]7x = -48 - 6[/tex]
[tex]7x = -54[/tex]
Take all to one side
[tex]7x + 54 = 0[/tex]
Thus, another way to write the equation is 7x + 54 = 0
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if 3t -7 = 5t, then 6t =
Answer:
21
Step-by-step explanation:
[tex]3t-7=5t[/tex]
subtract 3t from both sides
[tex]-7 = 2t[/tex]
multiply both sides by 3
[tex]-21 = 6t[/tex]
so 6t = -21
An auto mechanic charges (C) an initial fee of $50 and then $40 per hour. If (h) represents hours, how much will the mechanic charge if they worked 10 hours in one day?
$450
$400
$550
None of these choices are correct.
Answer:
$800
Step-by-step explanation:
per hour $40×10hours=$400
$400÷$50=8 times initial fee
8×$50=$400 total initial fee
$400hours fee+$400 initial fee=$800 total payment
Solve for u. -5/6u = 15
Answer:
u = -18
Step-by-step explanation:
[tex]\frac{-5u}{6} =15[/tex]
Multiply both sides by 6.
-5u = 15 × 6
-5u = 90
Divide both sides by -5.
u = -18
need help with this please
The values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
Given the equation of x as the function of t is
x= 5 cos t
similarly, the equation of y as the function of t is
y= 3 sin t
At t=3 the value of x will be
x (at t=3) = 5 cos 3= 5(-0.989)= -4.95
At t=3 the value of y will be
y (at t=3) = 3 sin 3= 3(0.141)= 0.423
The derivative of the function of x with respect to t will be
dx/dt= d(5 cos t)/dt= 5d(cos t)/dt= -5 sin t
at t=3 the value of dx/dt will be
dx/dt (at t=3) = -5 sin 3= -5(0.141)= 0.71
The derivative of the function of y with respect to t will be
dy/dt= d(3 sin t)/dt= 3d(sin t)/dt= 3 cos t
at t=3 the value of dy/dt will be
dy/dt (at t=3) = 3 cos t= 3(-0.989)= -2.97
The tangent slope is dy/dx which can be calculated by
dy/dx= (dy/dt)(dt/dx)= (dy/dt)/(dx/dt)= 3 cos t/ -5 sin t= (-3/5) cot t
at t=3 the value of tangent slope will be
dy/dx (at t=3) = (-3/5) cot 3= 4.21
The speed at t=3 will be
speed v= [tex]\sqrt{v_{x} ^{2} + v_{y} ^{2} }[/tex]
= √(dx/dt)²+(dy/dt)²
at t=3
= √(0.71)²+(-2.97)²
= √9.325
= 3.05 unit/sec
Therefore the values of x and y at t=3 are -4.95 and 0.423 respectively.
The value of dx/dt and dy/dt are 0.71 and -2.97 respectively.
The value of the tangent slope at t=3 is 4.21.
The speed at t=3 is 3.05 units/sec.
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Use the point-slope formula to write an equation of the line that passes through (4,10) and has a slope of m= 3. Write the
answer in slope-intercept form (if possible).
The equation of the line is
What is the solution to the equation 7(a-10)=13-2(2a+3)?
26
O a=11
O a=7
89
O a = 11
O a=621
Answer:
[tex]a = 7[/tex]
Step-by-step explanation:
[tex]1. \: 7a - 70 = 13 - 4a - 6 \\ 2. \: 7a - 70 = - 4a + 7 \\ 3. \: 7a = - 4a + 7 + 70 \\ 4. \: 7a = - 4a + 77 \\ 5. \: 7a + 4a = 77 \\ 6. \: 11a = 77 \\ 7. \: a = \frac{77}{11} \\ 8. \: a = 7[/tex]
identify the percentage in 15 is 25% of 60
Answer:
25%
Step-by-step explanation:
In the sentence "15 is 25% of 60.", 25% is the percentage.
15 is the partial amount and 60 is the total amount.
15/60 = .25
convert a decimal to a percentage by multiplying by 100
.25 × 100 = 25
Some people use a shortcut of moving the decimal two places to the right. This is the same as multiplying by 100.
15/60 is 25%
If 13 metres of a uniform iron rod weights 23.4 kg then what will be the weight of 6 metres of the same rod?
Answer:
Solution:
Here,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline 13 \rm{m}& \rm{23.4kg} \\ \hline \rm{6m}&?\\ \hline\end{array}[/tex]
Weight of 13 m of rod=23.4 kg
Weight of 1 m of rod=23.4/13 kg
[less length,less weight]
Weight of 6 m of rod=23.4/13 ×6 kg=10.8 kg
[more length,more weight]
Thus,the weight of 6 m of rod is 10.8 kg.
Alternative method:
Let,the required weight be x kg.
Then,
[tex]\begin{array}{ | c| c c | } \hline\ \ \text{length \: of \: iron \: rod}& \text{weight} \\ \hline \rm{13m}& \rm{23.4 \: kg }\\ \hline \rm{6m}& \rm{x =? } \\ \hline\end{array}[/tex]
We know that,
More length of iron rod([tex]\red{\uparrow}[/tex]) will have the more weight([tex]\red{\uparrow}[/tex]).
So,using the rule of direct proportion;
i.e. Ratio of length=Ratio of weight
[tex] \displaystyle{ \frac{13}{6} = \rm\frac{23.4}{x} }[/tex]
[tex] \rm{13x = 6 \times 23.4}[/tex]
[tex] \rm{x = \displaystyle{ \frac{6 \times 23.4}{13} }}[/tex]
[tex] \therefore{x = 10.8}[/tex]
Thus,the weight of 6 m long iron rod is 10.8 kg.
Factorize: 1+4a+4a^2
Answer: (1+2a)^2 or (1+2a)(1+2a)
Step-by-step explanation:
Answer:
[tex](2a +1)( 2a + 1)[/tex]
Step-by-step explanation:
[tex]1+4a+4a^2[/tex][tex]=4a^2 +4a +1[/tex][tex]=4a^2 +2a + 2a + 1[/tex][tex]=2a(2a +1) +1( 2a + 1)[/tex][tex]=(2a +1)( 2a + 1)[/tex]❗️URGENT❗️
Chase has won 80% of the 30 football video games he has played with his brother, Jacob. If Chase and Jacob continue to play the video game, how many more games in a row goes Chase have to win to achieve an 85% win percentage?
Answer:
10
Step-by-step explanation:
24/30 = 0.8
24+x/30+x =0.85
10=x
If you want more clarification just ask
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
We can write the total number game won by Chase as -
w = 80% of 30
w = 80/100 x 30
w = 4/5 x 30
w = 24
Assume that he wins {x} games after winning 24 games to achieve 85% win percentage. Now, we can write that out of (30 + x) number of games played, Chase won (24 + x) games to achieve 85% win percentage. So, we can write that -
(24 + x)/(30 + x) = 85/100
(24 + x)/(30 + x) = 0.85
(24 + x) = 0.85(30 + x)
24 + x = 25.5 + 0.85x
0.15x = 1.5
x = 10
Total games Chase has to win in a row to achieve an 85% win percentage would be 10.
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there are 1,500 pupils in school , 0.6 are boys how many pupils are girls
Answer:
1491 girls (99.4 percent)
Step-by-step explanation:
explanation is in the attached picture
Juan is learning about like terms in his math class. He must check all the combinations below that are like terms which ones should he check
Step-by-step explanation:
please attach a picture for us to see the choices
What are the measures of ∠1 and ∠2? Show your work or explain your answers.
Answer:
angle 1 is 105degrees and angle 2 is 75degrees
Step-by-step explanation:
The angle below angle 2, presumably angle 6, is also 75 degrees since line c and line d are parallel. If angle 2 is 75 degrees then we know that angle 1 is 105 degrees since both angles equal a straight line and a straight line has 180 degrees.
Question Content Area
Strait Co. manufactures office furniture. During the most productive month of the year, 3,500 desks were manufactured at a total cost of $83,800. In the month of lowest production, the company made 1,240 desks at a cost of $61,900. Using the high-low method of cost estimation, total fixed costs are
a.$21,900
b.$49,885
c.$61,900
d.$83,800
b. Total fixed cost are $49885
What is fixed cost of product ?Sometimes production of a product may increase or decrease, but the cost which do not change with the change of output is called fixed cost of the product.
What is the total fixed cost ?
Highest monthly total cost = $83800
Highest monthly production units = 3500 desks
Lowest monthly total cost = $61900
Lowset monthly production units = 1240 desks
So, variable cost per unit = (Highest cost-lower cost)/(highest production units-lowest production units)
= ($83800-$61900)/(3500-1240)
= $21900/2260
= $9.7
∴ Total fixed costs=Highest monthly total cost-(highest production units×variable cost per unit)
= $83800-(3500×$9.7)
= $83800-$33950
= $49850
Nearest value is $49885, whch is the correct one.
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Given: A = { -1,5,6} B = {-1,2,3,4,6,8} Find the union of sets A and B.
Step-by-step explanation:
{-1,2,3,4,5,6,8} is the answer
For the function y= -2+5 sim {pi/12(x-2)}, what is the minimum value
The function has a local minima at ( 20 , -7 )
What is a Function ?Function is a mathematical statement formed when two algebraic expression are equated by an equal sign.
The expression given is
y = -2 +5sin ( (π/12) (x-2))
the minima of the given expression will be when
the sine term = -1
as the lowest value sin can have is -1
y = -2 +5 * (-1)
y = -7
The sin ( (π/12) (x-2)) = -1
(π/12) (x-2) = 3π /2
On solving this
x = 20
Therefore the function has a local minima at ( 20 , -7 )
It can also be confirmed form the graph attached with the answer.
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Which of the following rational functions is graphed below?
Answer:
ANSWER IS B
Step-by-step explanation:
NEXT TIME USE any graph website online
In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°. Find m∠G. Round your answer to the nearest tenth.
The value of m∠G = 48.6° .
What is a Triangle ?A triangle is a polygon with three sides , angles and vertices.
It is given that
In ΔFGH, FH = 9 ft, FG = 11 ft, and m∠F = 65°
m∠G = ?
well, using the law of cosines,
GH ² = 9² + 11² - 2(9)(11) cos65°
f = 10.88 ft
now, using the law of sines,
sinG/9 = sin65°/10.88
m∠G = 48.6°
Therefore the value of m∠G = 48.6° .
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There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does this situation represent a linear or non-linear function, and why?
Answer:
Step-by-step explanation:
It represents a linear function because there is a constant rate of change.
Step-by-step explanation:
Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.
Here, number of hours represents input value and minutes represents the output value,
Now, By the given table,
The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),
Also,
⇒ The rate of change output value with respect to input value remains constant,
Hence, It represents a linear function because there is a constant rate of change.
What is the quotient of -27.375 divided by 7.5
A)–3.65
B)–0.365
C)0.365
D)3.65
Answer: A. -3.65
Step-by-step explanation: The best way to figure this out is by using a calculator. One specific rule to remember is the positive/negative rule. When it applies to multiplication, it also applies to division.
[tex](+)*(+)=+\\(+)*(-)=-\\(-)*(+)=-\\(-)*(-)=+\\[/tex]
Knowing this, we can input it into the calculator and find the answer's sign.
[tex]-27.375/7.5=-3.65[/tex]
Therefore, the answer is A. -3.65.
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How can the logarithmic expression be rewritten?
Select True or False for each statement.
Answer:
True, True, False
Step-by-step explanation:
