Answer:
a = 3
Step-by-step explanation:
Simply substitute 2 for x and y for 1 and solve.
This will get you 2a + 2 = 8
Then simplifying, 2a = 6.
a = 3.
The value of a and the coefficient of x is 3.
What is substitution?
Substitution means putting numbers in place of letters to calculate the value of an expression .
According to the given question.
We have a equation.
ax + 2y = 8.
Also, the solution to the equation is (2, 1).
So, substitute x = 2 and y = 1 in the equation ax + 2y = 8.
⇒ [tex]a(2) + 2(1) = 8[/tex]
⇒ [tex]2a + 2 = 8[/tex]
⇒ [tex]2a = 8-2[/tex] ( subtracting 2 from both the sides)
⇒ [tex]2a = 6[/tex]
⇒ [tex]a = \frac{6}{2}[/tex] (dividing both the sides by 2)
⇒ [tex]a = 3[/tex]
Hence, the value of a and the coefficient of x is 3.
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2. A book with a green sticker costs $2 less than half the price of a
book with a yellow sticker
I need help with this one
For this case we can propose an equation that will allow us to find the price of one of the books knowing the price of the other.
x: Let the variable that represents the price of the book with a green sticker
y: Let the variable that represents the price of the book with a yellow sticker
According to the statement we have:
[tex]x = \frac {y} {2} -2\\[/tex]
[tex]y=2(x+2)[/tex]
Finally, we can substitute the price of one of the books and clear the value of the other as the case may be.
Answer:
[tex]x = \frac {y} {2} -2[/tex]
What is the product of (3x-9) and 6x↑2-2x+5 Write your answer in standard form.
(a) Show your work.
(b) Is the product of (3x-9) and 6x↑2-2x+5 equal to the product of (9x-3) and 6x↑2-2x+5
Explain your answer.
Answer:
a. [tex]18x^3 -60x^2 + 33x - 45[/tex]
b. No
Step-by-step explanation:
Given:
(3x-9) and [tex]6x^2-2x+5[/tex]
=> the production of them is:
[tex](3x-9)(6x^2-2x+5)[/tex] , we will use distributive law to solve this To do that. we first multiply [tex]6x^2-2x+5[/tex] by 3x then by -9. This is done as follows
= [tex]3x (6x^2-2x+5) - 9(6x^2-2x+5)[/tex] [tex]= (3x * 6x^2-3x * 2x+3x *5) - (9* 6x^2-9* 2x+9* 5)\\\\= (18x^3 -6x^2+ 15x) - (54x^2 - 18x +45)[/tex]
Then Open both brackets
= [tex]18x^3 -6x^2+ 15x -54x^2 + 18x -45[/tex]
After that, we group the same terms
= [tex]18x^3 -(6x^2 +54x^2)+ (15x + 18x) -45[/tex]
= [tex]18x^3 -60x^2 + 33x - 45[/tex]
(b) Is the product of (3x-9) and [tex]6x^2-2x+5[/tex] equal to the product of (9x-3) and [tex]6x^2-2x+5[/tex]
No, let find the product of (9x-3) and [tex]6x^2-2x+5[/tex] , we will use distributive law to solve this as the above example.
= (9x-3)[tex](6x^2-2x+5)[/tex]
= [tex]9x (6x^2-2x+5) - 3(6x^2-2x+5)[/tex]
=[tex](9x * 6x^2 - 9x * 2x + 9x *5) - (3* 6x^2 - 3 * 2x + 3* 5)[/tex]
= [tex](54x^3 - 18x^2+ 45x) - (18x^2 - 6x +15)[/tex]
After that, we open the bracket to find the same terms
= [tex]54x^3 - 18x^2+ 45x -18x^2 + 6x -15[/tex]
= [tex]54x^3 - 18x^2 -18x^2 + 45x + 6x -15[/tex]
= [tex]54x^3 - 36x^2 + 51x -15[/tex]
As you can see [tex]54x^3 - 36x^2 + 51x -15[/tex] ≠[tex]18x^3 -60x^2 + 33x - 45[/tex]
Hope it will find you well.
Tools: calculator
1. Which of the following are statistical
questions? Circle all answers.
M
a) Do you have any pets?
b) What dáy does school get out?
c) How many home runs were hit in
MLB last year?
d) How many goals did each soccer
team score in each game last
season?
e) What was the average number of
home runs hit over the last 10
seasons?
Answer:
c d e?
Step-by-step explanation:
btw I'm not sure :")
Answer:
A,d,e
Step-by-step explanation:
Tina rides the bus to school, Theo bikes to school, and Tony walks to school. Their probabilities of being the first one to school are as follows:
\text{P(Tina is first}) = 0.05P(Tina is first)=0.05start text, P, left parenthesis, T, i, n, a, space, i, s, space, f, i, r, s, t, end text, right parenthesis, equals, 0, point, 05
\text{P(Theo is first}) = 85\%P(Theo is first)=85%start text, P, left parenthesis, T, h, e, o, space, i, s, space, f, i, r, s, t, end text, right parenthesis, equals, 85, percent
\text{P(Tony is first}) = \dfrac{1}{10}P(Tony is first)=
10
1
Answer:
Tina is first
Tony is first
Theo is first
Step-by-step explanation:
Events with greater probability are more likely.
Let's put the probabilities in decimal form.
P(Tina is first) = 0.05
P(Theo is first) = %85 = 0.85
P(Tony is first) = 1/10 = 0.1
0.05 < 0.1 < 0.85
The events are listed below from least to most likely.
Tina is first, Tony is first, Theo is first
hope it helps
Answer:
Tina is first
Tony is first
Theo is first
Step-by-step explanation:
Oliver hits a baseball at 3 feet above the ground with an initial speed of 135ft/sec at an angle of 20 degrees with the horizontal.
The outfield wall is 380 feet away and is 15 feet high.
At approximately what height will the ball hit the wall?
A) 3 ft
B) the ball lands in front of the wall
C) the ballet goes over the wall
D) 8 ft
Answer:
Option B) the ball lands in front of the wallExplanation:
1. Find the vertical and horizontal components of the initial velocity
a) Horizontal component:
[tex]v_{0,x}=v_0\times cos(20\º)=135ft/s\times cos(20\º)=126.86ft/s[/tex]
b) Vertical component:
[tex]v_{0,y}=v_0\times sin(20\º)=135ft/s\times sin(20\º)=46.17ft/s[/tex]
2. Find the time when the ball runs 380 feet horizontally:
[tex]x=v_{0,x}\times t\\\\380ft=126.86ft/s\times t[/tex]
[tex]t= (380ft)/(126.86ft/s)=2.995s\approx 3.0s[/tex]
3. Find the height of the ball when the time is 3.0s
[tex]y=y_0+v_{0,y}\times t-gt^2/2[/tex]
y₀ = 3 ftg ≈ 32.174 ft/s²[tex]y=3ft+46.17ft/s\times 3.0s-32.174ft/s^2\times (3.0s)^2/2[/tex]
[tex]y=-3.3ft[/tex]
This result means that the ball does not reach the wall because it has fallen to the ground (when y = 0) before 3.0s.
For a club gathering you were having, you bought a total of 50 burgers, and spent $90. You paid $2 per turkey burger, and $1.50 for each veggie burger. Next year, you want to spend the same amount of money on burgers, $90. If the number of turkey burgers is doubled, would you have to cut the number of veggie burgers in half? Explain your reasoning.
Answer:
No. You would have to cut the number of veggie burgers in more than half.
Explanation:
1. Model the situation with a system of equations
a) Name the variables:
number of turkey burgers: tnumber of veggie burgers: vb) Number of burgers:
50 = t + vc) Cost of the 50 burgers:
$90 = 2t + 1.50v2. Solve that system of equations:
a) System
50 = t + v90 = 2t + 1.50vb) Mutliply the first equation by 2 and subtract the second equation
100 = 2t + 2v 90 = 2t + 1.50v10 = 0.5vv = 20 ⇒ t = 50 - 20 = 30c) How much would you spend if the next year you buy the double of 20 turkey burgers (40) and the half of 30 veggie burgers (15)
$2(40) + $1.50(15) = $80 + $22.50 = $102.50Then, you if you double the number of turkey burgers, and cut the number burgers in half, you would spend more than $90 ($102.50).
A company manufactures two different sizes of boat lifts. The smaller lift requires 1 hour in the welding department and 2 hours in the packaging department. The larger lift requires 3 hours in the welding department and 1 in the packaging department. The company has 150 hours/day available in welding and 120 hours/day available in packaging. If the profit is $25 for each small lift and $90 for each large lift, how many of each type should be produced to maximize profits? (1) List your variables (2) List your constraints
Answer:
The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.Below are all the steps explained in detail.The graph is attached.
Explanation:
1. Name the variables:
x: number of smaller liftsy: number of larger lifts2. Build a table to determine the number of hours each lift requires from each department:
Number of hours
small lift large lift total per department
Welding department 1x 3y x + 3y
Packaging department 2x 1y 2x + y
3. Constraints
150 hours available in welding: x + 3y ≤ 150120 hours available in packaging: 2x + y ≤ 120The variables cannot be negative: x ≥ 0, and y ≥ 0Then you must:
draw the lines and regions defined by each constraintdetermine the region of solution that satisfies all the constraintsdetermine the vertices of the solution regiontest the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)4. Graph
See the graph attached.
Here is how you draw it.
x + 3y ≤ 150draw the line x + 3y = 150 (a solid line because it is included in the solution set)shade the region below and to the left of the line2x + y ≤ 120draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)shade the region below and to the left of the linex ≥ 0 and y ≥ 0: means that only the first quadrant is consideredthe solution region is the intersection of the regions described above.take the points that are vertices inside the solutoin region.5. Test the profit function for each vertex
The profit function is P(x,y) = 25x + 90y
The vertices shown in the graph are:
(0,0)(0,50)(42,36)(60,0)The profits with the vertices are:
P(0,0) = 0P(0,50) = 25(0) + 90(50) = 4,500P(42,36) = 25(42) + 90(36) = 4,290P(60,0) = 25(60) + 90(0) = 1,500Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.
Final answer:
To maximize profits from manufacturing boat lifts, define variables as x for small lifts and y for large lifts, and list the constraints from the welding and packaging departments' available hours alongside non-negative production quantities.
Explanation:
To find how many of each type of boat lifts should be produced to maximize profits, first, we need to define our variables and list our constraints.
List your variables
Let x be the number of small lifts.Let y be the number of large lifts.List your constraints
For the welding department: 1x + 3y ≤ 150 (hours/day available).For the packaging department: 2x + 1y ≤ 120 (hours/day available).Non-negative constraint: x ≥ 0, y ≥ 0.These constraints represent the limits on production based on the available hours in each department, whilst also considering that the production of both types of lifts must be a non-negative quantity.
does 5x+20=4(x+6) have one solution
Answer:
One solution x=4
Step-by-step explanation:
5x+20=4(x+6)
Distribute
5x+20 =4x+24
Subtract 4x from each side
5x -4x +20 = 4x-4x+24
x+20 = 24
Subtract 20 from each side
x+20-20 =24-20
x =4
Rewrite the expression using only positive integer exponents.
Answer:
the answer is D) m4/n2
Step-by-step explanation:
(m 2/3 n -1/3) 6
2/3 x 6= 4
-1/3 x 6 =-2
you cannot have a negative exponent in this situation so you would put n -2 on the bottom which makes it positive.
Answer:
Other guy is correct it's D
Step-by-step explanation:
The table and graph show that there are 32 ounces in a quart.
Conversion between Quarts and Ounces
Ounces
(x)
Quarts
(y)
8
0.25
16
0.5
32
1
40
1.25
On a coordinate plane, the x-axis is labeled Ounces and the y-axis is labeled quarts. The line goes through points (8, 0.25) and (16, 0.5).
Which statement about the graph is true?
The number of quarts is the independent variable, and the number of ounces is the dependent variable.
The point (56, 1.75) is on the line.
The number of ounces is graphed on the y-axis, and the number of quarts is graphed on the x-axis.
The two variables are the number of quarts and the number of ounces in a quart.
Answer:
The point (56, 1.75) is on the line.
Step-by-step explanation:
Given two points, we can get the slope (m) as follows:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) and (x2, y2) are the points. Replacing with (8, 0.25) and (16, 0.5):
m = (0.5 - 0.25)/(16 - 8) = 0.03125
The point-slope form of a line is:
y - y1 = m(x - x1)
Replacing with data:
y - 0.25 = 0.03125(x - 8)
To know if point (56, 1.75) is on the line, we have to replace x = 56 in the obtained equation and check y-value, as follows:
y - 0.25 = 0.03125(56 - 8)
y - 0.25 = 1.5
y = 1.5 + 0.25 = 1.75
Then, the point is on the line. This means that there are 56 ounces in 1.75 quarts.
Answer:
b
Step-by-step explanation:
hope it helps
At 4:00p.m the temperature was 90F after this point the temperature dropped 1.5F per hour until sunrise the next morning write an equation to represent the temperature,t,after h hours
Answer:
90t-21t=69t
Step-by-step explanation:
4:00pm to 6:00 am is 14 hours. 14 x 1.5 is in fact 21 which means the temperature dropped 21 degrees in those 14 hours.
The equation to represent the temperature after a certain number of hours is t = 90 - 1.5h.
Explanation:The equation to represent the temperature, t, after h hours can be written as: t = 90 - 1.5h.
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Michael is planting a garden in the shape of a right triangle. He wants 4 tickseed plants for each square meter of area. How many tickseed plants does Michael want in his garden?
Please Help Me!
Answer:
336 plants
Step-by-step explanation:
To find the number of tickseed plants that Michael needs to plant in his garden, we have to find the area of the garden first.
We notice that the garden has the shape of a right triangle: so, we have to find the area of the right triangle.
The area of a triangle is given by the formula
[tex]A=\frac{1}{2}bh[/tex]
where
A is the area
b is the length of the base
h is the height of the triangle
From the figure, we see that:
b = 7 m is the length of the base
h = 24 m is the height of the triangle
Therefore, applying the formula, we find the area of the garden:
[tex]A=\frac{1}{2}7\cdot 24 =84 m^2[/tex]
We also know that Michael wants to plant 4 tickseed plants for each square meter of area; therefore, the total number of plants that Michael will plant is 4 times the area of the garden, so:
[tex]N=4A=4\cdot 84=336[/tex]
Answer:
336 tickseed plants
Step-by-step explanation:
Can someone please help me
The values StartRoot 8 EndRoot and StartRoot 14 EndRoot are plotted on the number line.
A number line going from 0 to 4. StartRoot 8 EndRoot is between 2 and 3, StartRoot 14 EndRoot is between 3 and 4.
What is the approximate difference in tenths between the two values?
0.5
0.9
1.1
2.4
Answer:
The answer is 0.9
Step-by-step explanation:
I got it right
Step-by-step explanation: ANSWER is B 0.9
Angles J X M, M X N, and N X P form a straight line. Angle M X N is a right angle.
Which statement is true about ∠JXM and ∠NXP?
Answer:
∠JXM and ∠NXP are complementary
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
[tex]m\angle JXM+m\angle MXN+m\angle NXP=180^o[/tex] ----> form a straight line
we have
[tex]m\angle MXN=90^o[/tex]
substitute
[tex]m\angle JXM+90^o+m\angle NXP=180^o[/tex]
[tex]m\angle JXM+m\angle NXP=180^o-90^o[/tex]
[tex]m\angle JXM+m\angle NXP=90^o[/tex]
Remember that
Two angles are complementary, if their sum is equal to 90 degrees
therefore
∠JXM and ∠NXP are complementary
Answer:The answer is A, I got it right
Step-by-step explanation:
Because the length cannot be negative the height of the plane is ___ miles.
????????????????
????????????????
????????????????
????????????????
????????????????
????????????????
????????????????
Look at all the steps above. They lead to a double solution. The symbol
[tex]x=\pm 5[/tex]
means that [tex]x[/tex] can be either positive or negative 5. You can't accept negative values for lengths, so you're left with one option only.
Need help dumb and bad at this but good and smart at other things !!!
Answer:
The answer is A my dude
Step-by-step explanation:
Answer:
He loses 12 limbs over 4 days (need one more branliest to level up)
Step-by-step explanation:
loses 3 on monday (-3)
loses 3 on tuesday (-3)
see the pattern
Luetta is out shopping and finds a $190 video game that
was marked down by 5%.
How much was the item originally?
Answer:
i think the answer is 38
Step-by-step explanation:
$190 divided by 5% = 38
There are 500 coffins and 500 men who need them. The undertaker asks the first man to go to every coffin and open them. Then he tells the second man to go to every one and close it. The third one goes to every third coffin and so on. How many are open?
Answer:
166
Step-by-step explanation:
Answer:
Step-by-step explanation:
I mean I'm not sure if I'm right but if the third one just went to every third coffin and so on then he technically didn't open any which makes them all closed. I'm not sure if I'm right tho.
I need help figuring out which two grids have the same % please
Answer:
a and c
Step-by-step explanation:
The first one is 3/6 = 50%
The second one is 3/8 = 37.5%
The third one is 2/4 = 50%
The fourth one is 5/8 = 62.5%
The ones with the same percent shaded are the first and third
Answer:
a and c
Step-by-step explanation:
A has 3 out of a total of 6 shaded, and that would be 3/6. 3/6 simplifies into 1/2 which is also 50%. Same with c. 2 out of four pieces are shaded, 2/4. 2/4 becomes 1/2 which is also 50%.
If 5 lessened by 1/2 of a number, the result is equivalent to subtracting 3/4 of the number from 11
Answer:
no lose yo ablo español
The cost of a car rental is $35 per day plus 19cents per mile. You are on a daily budget of $73. Write and solve an inequality to find the greatest distance you can drive each day while staying within your budget.
Answer:
73 ≥ 35+.19 m
Answer:
the answer is 200 miles per day
Evan was randomly creating a one topping pizza at a "Bake Your Own Pie" restaurant. Each
one topping pizza has one crust type, one cheese type, and one topping
Thin
Mozzarella
Pepperoni
Thick
White Cheddar
Sausage
Parmesan
Pepper
Onion
Mushroom
If the choice of each choice was equally likely, what is the probability that Evan made a
Thick Crust Pizza with White Cheddar and Sausage?
A: 1/8
B: 1/10
C:1/15
D. 1/30
Answer:
D, 1/30
Step-by-step explanation:
There are 2 crust types, 3 cheeses, and 5 toppings.
That means there are 2*3*5 total pizzas, which is 30.
You are asking for the probability of choosing one of those pizzas, meaning the answer is D, 1/30
b over 7 plus 1 equals 6
Answer:
b=35
Step-by-step explanation:
Let's start by interpreting the question first
b/7 +1=6
Lcm is 7
b+7/7=6
Cross multiply
b+7=7×6
b+7=42
Substrate 7 from both sides
b=42-7
b=35
Therefore the final answer is 35
find angles j and k wishing the triangle
Answer: Angle J= 75 degrees and angle K=40 degrees.
how to factor 3x^2-x-30
Answer:
(x + 3)(3x - 10)
Step-by-step explanation:
[tex]3 {x}^{2} - x - 30 \\ = 3 {x}^{2} + 9x - 10x - 30 \\ = 3x(x + 3) - 10(x + 3) \\ = (x + 3)(3x - 10) \: are \: the \: required \: factors.[/tex]
To factor the expression [tex]3x^2-x-30[/tex], use factoring by grouping. The factored form is (3x + 3)(x - 10).
To factor the expression [tex]3x^2-x-30[/tex], we can use factoring by grouping or the quadratic formula. Let's use factoring by grouping:
Step 1: Multiply the leading coefficient (3) by the constant term (-30) to get -90.
Step 2: Find two numbers whose product is -90 and whose sum is the coefficient of the linear term (-1). In this case, the numbers are -10 and 9.
Step 3: Rewrite the middle term (-x) as the sum of the numbers found in step 2 (-10x + 9x).
Step 4: Group the terms and factor out the greatest common factor from each group (3x(x - 10) + 3(x - 10)).
Step 5: Factor out the common binomial (x - 10) from each group to get the final factored form: (3x + 3)(x - 10).
Helpppppppppppp meeeeeeee please
Answer:
Point M
Step-by-step explanation:
4/5=8/10
Point M was on 8/10.
Which equation can be used to determine the distance between the origin and (-2,-4)?
So the right answer is of option B..
3. Matt bought a pack containing 12 of his favorite Spring cookies. He wants to make the cookies last longer, so he
decides to eat only 1/2 of each cookie a day. How long will this pack of cookies last him
if he follows through with his plan to only eat V2 of a cookie each day?
Answer:
Step-by-step explanation:
if he eats half a cookie each day then they cookies will last 24 days.
A bag contains 40 marble 12 red and 16 yellow what is the probability that a blue is randomly seclected
Answer:
Fraction=3/10
Decimal=0.3
Percent=30%
Step-by-step explanation:
First we have to add 12+16 so we can find how many marbles are left
12+16=38
Then, we subtract it from the total number of marbles.the outcome of this operation would be equivalent to the number of blue marbles
40-38=12
There are 12 blue marbles.
Now, the we have to use experimental probability if you are familiar with the term is that the number of outcomes(the blue marbles) must be over the total sample space(total marbles) in a fraction.
Probability=
12/40
Simplify
12/40
6/20
3/10
Probability
Fraction=3/10
Decimal=0.3
Percent=30%
The line of symmetry of the parabola whose equation is y = ax^2 -4x + 3 is
x = -2. What is the value of "a"?
A. -2
B. -1
C. -1/2
Answer:
B. -1
Step-by-step explanation:
If we have a parabola whose equation is:
[tex]y=ax^{2} +bx+c[/tex]
The line of symmetry is calculated as:
[tex]x=\frac{-b}{2a}[/tex]
Now, we have the equation [tex]y=ax^{2}-4x+3[/tex] and the line of symmetry is [tex]x=-2[/tex]
Where:
[tex]b=-4\\c=3[/tex]
So, we can replace [tex]b[/tex] by -4 and [tex]x[/tex] by -2 and solve for [tex]a[/tex] using the following equation as:
[tex]x=\frac{-b}{2a}\\-2=\frac{-(-4)}{2a}\\-2(2)a=4\\-4a=4\\a=-1[/tex]
It means that the equation of the parabola is equal to:
[tex]y=-1x^{2}-4x+3[/tex]