Final answer:
The domain for the base price of a car that Leonard can initially afford is [24,000, 30,000]. After buying car insurance worth $2,200, the domain changes to [24,000, 28,000], reflecting the reduced budget available for the car purchase.
Explanation:
Initially, Leonard can afford a car with a base price up to his budget of $33,000. Since car accessories cost one-tenth of the base price, we calculate the maximum base price he can afford as follows: Let x be the base price of the car. The total cost of the car, including accessories, would be x + (1/10)x = (1 + 1/10)x = (11/10)x. So, to stay within budget, (11/10)x ≤ $33,000. Solving for x gives us x ≤ $33,000 / (11/10) = $30,000.
Therefore, the domain representing the base price Leonard can afford is [24,000, 30,000].
After buying car insurance for $2,200, Leonard's budget for the car decreases. The new budget for the car including accessories is $33,000 - $2,200 = $30,800. Solving (11/10)x ≤ $30,800, we get x ≤ $30,800 / (11/10) = $28,000.
Now, the domain for the base price that Leonard can afford after the insurance payment is [24,000, 28,000].
What are the zeros of f(x)=(x-5)(x-4)(x-2)?
A 5, -4, 2
B 5, -4, -2
C 5,4,2
D 5,4,-2
f(x)=(x-5)(x-4)(x-2)
x-5=0
x-5+5=0+5
x=5
x-4=0
x-4+4=0+4
x=4
x-2=0
x-2+2=0+2
x=2
Answer: 5,4,2 -C
The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2
Option C is correct
Note that:
The zeros of a function f(x) are the values of x that makes f(x) to be equal to zero
If f(x) = (x - a)(x - b)(x - c), then the zeros of the function f(x) are:
x = a, x = b, x = c
Therefore, the zeros of f(x)=(x-5)(x-4)(x-2) are found by equating f(x) to zero
(x - 5)(x - 4)(x - 2) = 0
Equate each of the terms to zero
x - 5 = 0
x = 5
x - 4 = 0
x = 4
x - 2 = 0
x = 2
The zeros of the function f(x) = (x-5)(x-4)(x-2) are 5, 4, 2
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If a tire moves 0.88 feet from 1 rotation, what is the tires circumference?
Answer:
0.88 feet
Step-by-step explanation:
The tire covers 0.88 feet in 1 rotation.
1 rotation means the whole tire moves, which is basically its circumference. So, the distance it covers in moving 1 rotation IS ITS CIRCUMFERENCE.
Hence, 0.88 feet is the circle's circumference.
Which is a zero of the quadratic function f(x) = 9x2 – 54x – 19?
x =
x = 3
x = 6
x = 9
Answer: x=-3
Step-by-step explanation:
F(x)=9x^2-54x-19
F(x)=(x-57)(x+3)
X=57 X=-3
In the figure, polygon ABCD is transformed to create polygon A'B'CD
This transformation is a
by a factor of
Answer:
This transformation is a horizonta dilation by a factor of 2.Step-by-step explanation:
If you observe the image, you deduct that the polygon ABCD was increased in size, that means the scale factor applied dilated the figure. In other words, there was applied a factor of dilation.
To find the exact factor of dilation, we just have to divide each prime coordinate by the original ones.
For example, you can observe that coordinates [tex]A(3,0)[/tex] was changed to [tex]A'(6,0)[/tex], [tex]B(1,0)[/tex] was changed to [tex]B'(2,0)[/tex], [tex]C(1,2)[/tex] was changed to [tex]C'(2,2)[/tex] and [tex]D(3,2)[/tex] was changed to [tex]D'(6.2)[/tex].
Now, observe that the dilation was horizontal, that is, the scale factor was only applied to x-coordinates, and this factor is 2, beacuse each x-coordinate was increase by a factor of 2.
Therefore, this transformation is a horizonta dilation by a factor of 2.
Drag the tiles to the correct boxes to complete the pairs :
Q: In the figure, line a and line b are parallel. Based on the figure, match each given angle with its congruent angles.
Answer:
Angles congruent to angle 2 is first. Angles congruent to angle 6 is second. Angles congruent to angle 1 is third. Angles congruent to angle 7 is last.
Step-by-step explanation:
Opposite angles are always equal. Alterbate interior/exterior angles are always equal.
Properties of shape. Need help on this question!!
Answer:
The right answer us "is always" as its all angles are 60 degree.
The matrix equation below can be used to solve a system of linear equations. What is the solution to the system? [6 4 9 6] [x y] =[1 3]
A. x=1/2, y= 1
B. x= 1/10, y= 1/5
C. The system has no solution
D. The system has infinite solutions
Answer:
C. The system has no solution.
C. The system has no solution.
When a system has no solution?
A system of linear equations has no answer whilst the graphs are parallel. A coordinate plane. The x- and y-axes both scale by way of one-1/2. A graph of a line is going through the factors 0, one and a half of and three, two.
No solution would suggest that there's no answer to the equation. it's miles not possible for the equation to be proper regardless of what price we assign to the variable. infinite answers would suggest that any value for the variable would make the equation authentic.
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What is the area of this triangle?
Enter your answer in the box.
Answer:
A = 14 units ^2
Step-by-step explanation:
The area of a triangle is
A = 1/2 b h where b is the base and h is the height
b = the length of EF which is 7 units
h = D to the line EF which is 4 units
A = 1/2 (7*4)
A = 14 units ^2
What are the x- and y-intercepts of y=-3x -9?
Answer:
x-intercept (-3,0)
y-intercept (0,-9)
Step-by-step explanation:
The x-intercepts can be found by setting y to 0 and solving for x.
y=-3x-9
0=-3x-9
Add 9 on both sides:
9=-3x
Divide both sides by -3:
9/-3=x
-3=x
The x-intercept is (-3,0).
The y-intercepts can be found by setting x to 0 and solving for y.
y=-3x-9
y=-3(0)-9
y=0-9
y=-9
The y-intercept is (0,-9).
Answer:
x-intercept: x = -3 → (-3, 0)y-intercept: y = -9 → (0, -9)Step-by-step explanation:
x-intercept is for y = 0.
y-intercept is for x = 0.
y = -3x - 9
x-intercept (put y = 0):
0 = -3x - 9 add 9 to both sides
9 = -3x divide both sides by (-3)
-3 = x → x = -3
y-intercept (put x = 0):
y = -3(0) - 9
y = 0 - 9
y = -9
Which shows the graph of the solution set of 2x + y < 4?
Answer:
Shaded to the left
Step-by-step explanation:
I cannot see the illustration, but I know for a fact that after using the zero-interval test [plug 0 in for BOTH y and x], you get 0 < 4, which is a genuine statement, so it gets shaded on the left hand side, otherwise shaded on the right of it were false statement.
I am joyous to assist you anytime.
At what points on the given curve x = 4t3, y = 3 + 8t − 10t2 does the tangent line have slope 1?
Answer:
(4/3, 4 5/9) and (-32, -53)
Step-by-step explanation:
When a curve is given as a set of parametric equations, as this one is, then the slope of the tangent line to the curve is
dy/dt
dy/dx = ------------
dx/dt
which here is
dy/dt 8 - 20t
dy/dx = ----------- = --------------
dx/dt 12t^2
If the slope at a certain point on this curve is 1, then we conclude that:
8 - 20t = 12t^2, or
12t^2 + 20t - 8 = 0, or
3t^2 + 5t - 2 = 0
We have to solve this equation for the parameter, t:
Here a = 3, b = 5 and c = -2, and so the discriminant is
b^2 - 4ac = 25 - 4(3)(-2), or 49, and the square root of that is 7.
Thus, the roots are:
-5 ± 7
t = --------- = 1/3 and t = -2
2(3)
Evaluate x and y twice, once each for each t value.
Case 1: t = 1/3
x = 4(1/3) and y = 3 + 8(1/3) - 10(1/3)^2, or
x = 4/3 and y = 3 + 8/3 - 10/9: (4/3, 4 5/9)
Case 2: t = -2
x = 4(-2)^3 and y = 3 + 8(-2) - 10(-2)^2, or y = 3 - 16 - 40, or y = -53.
This gives us the point (-32, -53)
To find the points where the tangent line has a slope of 1 on the given curve, we derive expressions for dx/dt and dy/dt, set dy/dx equal to 1, and solve for t.
Explanation:The given equation defines a parametric curve with x = 4t3 and y = 3 + 8t − 10t2. To find the points on this curve where the tangent line has a slope of 1, we'll first need to find expressions for dx/dt and dy/dt, which represent the rates of change of x and y with respect to the parameter t.
By differentiating x = 4t3 with respect to t, we find dx/dt = 12t2. Similarly, by differentiating y = 3 + 8t − 10t2 with respect to t, we find dy/dt = 8 - 20t.
The slope of the tangent line at a particular point on the curve corresponds to dy/dx, which we can find by dividing dy/dt by dx/dt, yielding (8 - 20t) / (12t2). We can set this equal to 1 (since we want a slope of 1) and solve for t to find the points on the curve where the tangent line has slope 1.
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It took the race car 22 minutes to travel 114.4 kilometers. At what rate did the car travel? Use the formula r=d/t where r is the rate, d is the distance, and t is the time. Round your answer to the nearest tenth.
Answer:
5.2 Km/Min
Step-by-step explanation:
Speed/Rate= Distance/Time
Speed/Rate = 114.4/22
Speed/Rate = 5.2 KM/min
Answer:
5.3 km/min
Step-by-step explanation:
Distance = 114.4 kilometers
Time = 22 minutes
Rate = 114.4 km /22 min
Rate = 5.2 km/min
A catering service offers
6
appetizers,
7
main courses, and
10
desserts. A customer is to select
5
appetizers,
4
main courses, and
5
desserts for a banquet. In how many ways can this be done?
There are 52,920 ways to select 5 appetizers, 4 main courses, and 5 desserts for the banquet.
To solve this problem, we can use the concept of combinations, as we're selecting items without considering the order.
For appetizers:
We need to choose 5 appetizers out of 6 available. This can be calculated using the combination formula: nCr = n! / [r! * (n-r)!], where n is the total number of items, and r is the number of items to be chosen.
So, for appetizers, it's [tex]6C_5 = 6! / [5! * (6-5)!] = 6 ways[/tex].
For main courses:
Similarly, we need to choose 4 main courses out of 7 available. So, it's
[tex]7C_4 = 7! / [4! * (7-4)!] = 35 ways[/tex].
For desserts:
We need to choose 5 desserts out of 10 available. So, it's
[tex]10C_5 = 10! / [5! * (10-5)!] = 252 ways[/tex].
To find the total number of ways:
We multiply the number of ways for each category since these choices are independent.
Total ways = (6 ways for appetizers) * (35 ways for main courses) * (252 ways for desserts) = 52920 ways.
Thus, there are 52,920 ways to select 5 appetizers, 4 main courses, and 5 desserts for the banquet.
Complete Question:
A catering service offers 6 appetizers, 7 main courses, and 10 desserts. A customer is to select 5 appetizers, 4 main courses, and 5 desserts for a banquet. In how many ways can this be done?
PLEASEE HELP!!
The equation of a hyperbola is .
The equations of the asymptotes of the hyperbola are and .
Answer:
y = 3(x + 2) + 2 and y = -3(x + 2) + 2
Step-by-step explanation:
* Lets revise the equation of the hyperbola with center (h , k) and
transverse axis parallel to the y-axis is (y - k)²/a² - (x - h)²/b² = 1
- The coordinates of the vertices are (h , k ± a)
- The coordinates of the co-vertices are (h ± b , k)
- The coordinates of the foci are (h , k ± c) where c² = a² + b²
- The equations of the asymptotes are ± a/b (x - h) + k
* Lets solve the problem
∵ The equation of the hyperbola is (y - 2)²/9 - (x + 2)² = 1
∵ The form of the equation is (y - k)²/a² - (x - h)²/b² = 1
∴ h = -2 , k = 2
∴ a² = 9
∴ a = √9 = 3
∴ b² = 1
∴ b = √1 = 1
∵ The equations of the asymptotes are y = ± a/b (x - h) + k
∴ The equations of the asymptotes are y = ± 3/1 (x - -2) + 2
∴ The equations of the asymptotes are y = ± 3 (x + 2) + 2
* The equations of the asymptotes of the hyperbola are
y = 3(x + 2) + 2 and y = -3(x + 2) + 2
Answer: I just did this quiz in Plato the correct answer is in the pic I did this question 3 times because I listened to the other people and finally got the answer which is the correct one, Hope this helps :)
Step-by-step explanation:
Find the missing lengths in right triangle mno. Estimate your answer your answer to two decimal places..
Answer:
x = 11.79
? = 6.25
Step-by-step explanation:
Using the law of sines
[tex]\frac{10}{sin58}[/tex] = [tex]\frac{x}{sin90}[/tex]
x = sin 90° x [tex]\frac{10}{sin58}[/tex] = 11.79
by Pythagorean theorem,
?² + 10² = x²
? = √ (x²- 10²)
? = √ (11.79²- 10²) = 6.25
What is the difference of the polynomials?
(–2x3y2 + 4x2y3 – 3xy4) – (6x4y – 5x2y3 – y5)
Answer:
[tex]\large\boxed{-2x^3y^2+9x^2y^3-3xy^4-6x^4y+y^5}[/tex]
Step-by-step explanation:
[tex](-2x^3y^2+4x^2y^3-3xy^4)-(6x^4y-5x^2y^3-y^5)\\\\=-2x^3y^2+4x^2y^3-3xy^4-6x^4y+5x^2y^3+y^5\qquad\text{combine like terms}\\\\=-2x^3y^2+\underline{4x^2y^3}-3xy^4-6x^4y+\underline{5x^2y^3}+y^5\\\\=-2x^3y^2+9x^2y^3-3xy^4-6x^4y+y^5[/tex]
The magnitude of the resultant vector shown is _____.
Answer:
2√3
Step-by-step explanation:
You recognize this as a 30°-60°-90° triangle, so you know the hypotenuse (R) is twice the length of the shortest side (√3).
The magnitude of R is 2√3.
_____
In case you haven't memorized the ratios for a 30°-60°-90° triangle, you can use trigonometry and the fact that ...
Sin = Opposite/Hypotenuse
sin(30°) = √3/R
R = √3/sin(30°) = √3/(1/2) = 2√3
Of course, doing this on your calculator will give a numerical answer, which you may not want.
Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4.2 in. Each of the triangular faces has a base of 4.2 in and a height of 3.6 in. How much paper would it take to cover the entire pyramid?
Answer:
47.88 in^2 of paper.
Step-by-step explanation:
The amount of paper needed for the base = 4.2^2 = 17.64 in^2.
There are 4 triangular faces.
The area of each triangular face = 1/2* base * height
= 1/2 * 4.2 * 3.6
= 7.56 in^2
That is a total of 4 * 7.56 = 30.24 in^2.
So the total amount of paper need to cover the entire pyramid
= 17,64 + 30.24
= 47.88 in^2.
Find the value of b.
Answer:
b ≈ 17
Step-by-step explanation:
Using trigonometric ratio, sine we can find side b.
sine x = opposite/hypotenuse
sin 45 = 12/b
b ≈ 17
Answer:
b = 12[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the sine ratio in the right triangle and the exact value
sin45° = [tex]\frac{1}{\sqrt{2} }[/tex]
From the triangle
sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{12}{b}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex]
Cross- multiply
b = 12[tex]\sqrt{2}[/tex]
How to factor a trinomial with a degree of 3
Answer:
Step-by-step explanation:
It all depends upon what the terms are. If each term of the 3 all have a variable you can factor out, then you'd do that first. For example, if your trinomial looks like this:
[tex]x^3+3x^2+4x[/tex]
you would begin by factoring out the common x, reducing the third degree polynomial to a quadratic which can then be factored many ways.
[tex]x^3+3x^2+4x=x(x^2+3x+4)[/tex]
If that is not the case, then you are factoring higher degree polynomials, and the way I always recommend to my students is the Rational Root Theorem and then synthetic division.
A line has a slope of -3/5.which order pairs could be points on a Parnell line
Answer:
yes
Step-by-step explanation:
this is right i think
The correct answer is line HJ .
1. **Line AB**: The slope of line AB is not the negative reciprocal of 1/2, so it is not perpendicular.
2. **Line CD**: The slope of line CD is not the negative reciprocal of 1/2, so it is not perpendicular.
3. **Line FG**: The slope of line FG is not the negative reciprocal of 1/2, so it is not perpendicular.
4. **Line HJ**: The slope of line HJ is the negative reciprocal of 1/2, which makes it perpendicular.
A line with a slope of **-3/5** can be represented by the equation:
[tex]\[ y = -\frac{3}{5}x + b \][/tex]
where \(b\) is the y-intercept. To find points on this line, we need to consider different values of \(x\) and calculate the corresponding \(y\).
Let's explore some potential points:
1. **Point A (x, y)**:
- Assume \(x = 0\):
[tex]\[ y = -\frac{3}{5} \cdot 0 + b = b \] - So, point A is \((0, b)\).[/tex]
2. **Point B (x, y)**:
- Assume \(x = 5\):
[tex]\[ y = -\frac{3}{5} \cdot 5 + b = -3 + b \] - So, point B is \((5, -3 + b)\).[/tex]
3. **Point C (x, y)**:
- Assume \(x = 10\):
[tex]\[ y = -\frac{3}{5} \cdot 10 + b = -6 + b \] - So, point C is \((10, -6 + b)\).[/tex]
These are just a few examples. You can find more points by choosing different values of \(x\). Remember that any point on the line will satisfy the equation [tex]\(y = -\frac{3}{5}x + b\).[/tex]
Now, let's explore the concept of parallel lines. Two lines are parallel if they have the **same slope**. If we have another line with a slope of 1/2, we can find points on that line as well.
You have $60.00. You wish to buy a jacket costing $25.50. You would also like to buy a pair of shorts. There is 7% sales tax on clothing. What is the top tag price (excludes sales tax) you could pay for the shorts?
Answer:
The top tag price you could pay for the shorts = $32.71....
Step-by-step explanation:
Total amount = $ 60.00
Cost of jacket = $25.50
Sales tax = 7% = .07
First of all find the total price of the jacket including sales tax.
25.50* .07 = 1.79( this is the sales tax)
Now add this sales tax into the original price.
25.5 + 1.79 = 27.29
Total price of a jacket = $27.29
Now subtract the total amount by the amount of the jacket.
$60.00 - $27.29 = $32.71
Thus the top tag price you could pay for the shorts = $32.71....
Is her assertion correct ?
Check the picture below.
so, the vertex at N, is noticeably not a right angle is an acute angle, so is less than 90°, so we don't need to check that one.
now, is the angle at L 90°?
well, if that's true LM and LN are perpendicular, and if they're indeed perpendicular, their slopes are negative reciprocal, meaning the slope of one is the same as the other but negative and upside down, well, let's check.
[tex]\bf L(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad M(\stackrel{x_2}{2}~,~\stackrel{y_2}{2}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{2-0}{2-0}\implies \cfrac{2}{2}\implies 1 \\\\[-0.35em] ~\dotfill\\\\ L(\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad N(\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-0}{2-0}\implies \cfrac{-1}{2}\implies -\cfrac{1}{2}[/tex]
[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope~of~LM}{1\implies \cfrac{1}{\underline{1}}}\qquad \qquad \qquad \stackrel{reciprocal}{\cfrac{\underline{1}}{1}}\qquad \stackrel{negative~reciprocal}{-\cfrac{\underline{1}}{1}\implies -1}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{slope of LM}}{1}\qquad \stackrel{\textit{negative reciprocal of LM}}{-1}\qquad \stackrel{\textit{slope of LN}}{-\cfrac{1}{2}}~\hfill -1\ne -\cfrac{1}{2}[/tex]
so that means Lydia put too much espresso on her last cup.
A photo originally measuring 11 inches by 9 inches needs to be enlarged to a size of 55 by 45 inches. Find the scale factor.
Answer:
5
Step-by-step explanation:
Given
Original Measurement = 11*9 inches
Measurement after enlargement = 55 * 45 inches
In order to find the scale factor, we can choose one side of the figure or the whole area and find the ratio between the measurement before enlargement and after enlargement.
In case of a side the answer will be the scale factor while in case of finding scale factor using areas the answer will be the square of scale factor.
So,
[tex]Scale\ factor =s^2= \frac{55*45}{11*9} \\s^2 = \frac{2475}{99} \\s^2=25[/tex]
As we know that this is the square of scale factor.
Hence the scale factor will be:
[tex]\sqrt{s^2}=\sqrt{25} \\s=5[/tex]
So, the scale factor is 5 ..
Answer if you can :)
If f(x) = -7x – 3 and g(x) = radical over x+6,
what is (fºg)(-2)
Answer:
-17
Step-by-step explanation:
Plug in -2 as your x value for the g(x) equation and simplify.
[tex]g(-2)=\sqrt{-2+6} \\g(-2)=\sqrt{4} \\g(-2)=2[/tex]
Next, plug in your g(x) value (2) to the f(x) equation for x and simplify.
[tex]f(2)=-7(2)-3\\f(2)=-14-3\\f(2)=-17[/tex]
Brianna went to a carnival. She played five games and rode six rides. Justin went to the same carnival and played seven games and rode eight rides. If Brianna paid $11.75 and Justin paid $16.15, how much did one game cost to play?
$0.50
$1.45
$1.25
$1.50
Urgent!
Answer:
$1.45
Step-by-step explanation:
To answer the question, we would like to have an equation that has the cost of a game as its only variable. That is, we would like to eliminate the cost of a ride from the system of equations we must write.
Let g and r represents the costs of a game and a ride, respectively. Then the expenses of the two carnival-goers can be described by ...
5g +6r = 11.75
7g +8r = 16.15
We note that the ratio of coefficients in the variable (r) that we want to eliminate is 3:4. So we can subtract 4 times the first equation from 3 times the second to eliminate that variable.
3(7g +8r) -4(5g +6r) = 3(16.15) -4(11.75)
g = 1.45 . . . . . . simplify
The cost to play one game was $1.45.
Answer:
$1.45
Step-by-step explanation:
Examine the system of equations. 2x + y = 34 -3x + 1 2 y = 25 If you multiply the first equation by 2, what must you multiply the second equation by to eliminate the y-variable.
answer: -4
-2
1
4
Answer:
Lol you answered your own question but yes it is -4 thanks!
Step-by-step explanation:
Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15, end of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways.Write an inequality to determine the number of days, Darcie can skip crocheting and still meet her goal.
Answer:
x≤ 60 - (3÷1/15)
Step-by-step explanation:
Number of blankets to be made = 3
Darcie crochets 1/15 blanket per day
To crochet one carpet she needs = 15 days
To crochet three carpets she needs = 15*3 = 45 days
Number of days she had = 60 days
She can skip days = 60-45 = 15 days
Let x be the number of days to complete her work.
Thus the equation becomes x≤ 60 - (3÷1/15)
You can solve for x to determine the number of days, Darcie can skip crocheting, you will get the answer 15....
The answer explains how to set up and solve an inequality to determine the number of days Darcie can skip crocheting while still meeting her goal of donating blankets.
To determine the number of days Darcie can skip crocheting and still meet her goal, we need to set up an inequality based on the information given.
First, calculate the total number of blankets Darcie needs to crochet: 3 blankets.
Set up the inequality: 1/15 * (60 - x) ≥ 3, where x represents the number of days she can skip crocheting.
Solve the inequality: 60 - x ≥ 45, x ≤ 15.
Therefore, Darcie can skip crocheting for up to 15 days and still meet her goal of donating 3 blankets.
Find the value of x in the triangle shown below.
Answer:
37°
Step-by-step explanation:
By definition all internal angles of a triangle add up to 180°
Hence,
98° + 45° + x = 180°
x = 180° - 98° - 45° = 37°
Can somebody please help me with this problem please
Answer:
m = 3, n = 4
Step-by-step explanation:
Solve using the substitution process. First, start with the second equation:
2m + 2n = 14
Simplify. Divide 2 from all terms within the equation. What you do to one side, you do to the other:
(2m + 2n)/2 = (14)/2
m + n = 7
Isolate the variable m. Subtract n from both sides:
m + n (-n) = 7 (-n)
m = 7 - n
Plug in 7 - n for m in the first equation:
-5m + 9n = 21
-5(7 - n) + 9n = 21
Solve. First, distribute -5 to all terms within the parenthesis:
(-35 + 5n) + 9n = 21
Simplify. Combine like terms:
-35 + (5n + 9n) = 21
-35 + 14n = 21
Isolate the variable, n. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 35 to both sides:
14n - 35 (+35) = 21 (+35)
14n = 21 + 35
14n = 56
Isolate the variable n. Divide 14 from both sides:
(14n)/14 = (56)/14
n = 56/14
n = 4
Plug in 4 to n in one of the equations, and solve for m.
2m + 2n = 14
2m + 2(4) = 14
2m + 8 = 14
Isolate the variable, m. Do the opposite of PEMDAS. First, subtract 8 from both sides:
2m + 8 (-8) = 14 (-8)
2m = 14 - 8
2m = 6
Divide 2 from both sides:
(2m)/2 = (6)/2
m = 6/2
m = 3
Your answers: m = 3, n = 4
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Answer:
(3, 4)
Step-by-step explanation:
Please include the instructions. I'm assuming that you want to solve this system of linear equations.
If that's the case, let's use elimination by addition and subtraction.
Multiply the first equation, -5m + 9n = 21, by 2: -10m + 18n = 42, and
multiply the second equation, 2m + 2n = 14, by 5: 10m + 10n = 70
Next, combine these two "new" equations:
-10m + 18n = 42
10m + 10n = 70
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28n = 112. Dividing both sides by 28, we get n = 4.
Subbing 4 for n in the second equation, we get 2m + 2(4) = 14, or
2m = 6. Then m = 3, and the solution is thus
(3, 4).