4.9.21
Solve the system of equations.
y=x² + 6x-2
y= - x2 + 4x + 22
Select the correct choice below and, if necessary, fill in box
- the solution(s) are:
- there is no solution
Answer:
x = -4 or 3
Step-by-step explanation:
[tex]x^{2}[/tex] + 6x - 2 = -[tex]x^{2}[/tex] + 4x + 22
2[tex]x^{2}[/tex] + 2x - 24 = 0
[tex]x^{2}[/tex] + x - 12 = 0
(x + 4)(x - 3)=0
x = -4 or 3
TeeVee Electronics, Inc., makes console and wide-
screen televisions. The equipment in the factory allows +
for making at most 450 console televisions and 200
wide-screen televisions in one month. It costs $600 per
unit to make a console television and $900 per unit to
make a wide screen television. The profit on each
console television is $125 per unit, while the profit for
each wide screen television is $200 per unit. During the -
month of November, the company can spend $360,000 to make these televisions. To
maximize profits, how many of each type should they make?
LET
Answer:
First we need to put all the given information in a table, that way we'll express it better into inequalities.
Cost Production Max.
Console screen (x) $600 450
Wide-screen (y) $900 200
$360,000
We have:
[tex]600x+900y \leq 360,000[/tex]
Because they can't spend more than $360,000 in production.
[tex]x\leq 450\\y\leq 200[/tex]
Because the number of television is restricted.
The profit function is
[tex]P(x,y)=125x+200y[/tex] (this is the function we need to maximize).
First, we need to draw each inequality. The image attached shows the region of solution, which has vertices (0,200), (300,200), (450, 100) and (450,0).
Now, we test each point in the profit function to see which one gives the highest profit.
For (300,200):
[tex]P(300,200)=125(300)+200(200)=37,500+40,000=77,500[/tex]
300 console screen and 200 wide screen give a profit of $77,500.
For (450,100):
[tex]P(450,100)=125(450)+200(100)=56,250+20,000=76,250[/tex]
450 console screen and 100 wide screen give a profit of $76,250.
Therefore, to reach the maximum profits, TeeVee Electronic, Inc., must produce 300 console screen televisions and 200 wide-screen televisions to profit $77,500,What is the least common multiple of 8, 12 and 16?
Answer:
b
Step-by-step explanation:
A movie theater has a seating capacity of 195. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1404, How many children, students, and adults attended?
Answer:
78 Children, 78 students, and 39 adults
Step-by-step explanation:
TOok me so long but if u add all that u get 195, correct.
78 times 5 is 390
78 times 7 is 546
39 times 12 is 468
which all added together is 1404.
A triangle has sides with lengths of 6 yards, 8 yards, and 10 yards. Is it a right triangle?
Answer:
Step-by-step explanation:
so, by the Pythagorean theorem
If it is a right triangle:
a^2 + b^2 = c^2
so,
6^2 = 36
8^2 = 64
10^2 = 100
okay, now we plug these into the equation
36 + 64 = 100
so yes, it is a right triangle.
Hope this helped!
Answer:
No, it's not a right triangle.
Explanation:
If you think about it a right triangle has 2 equal sides. So no this isn't a right traingle.
B
The measure of ZDAB equals 110° The
measure of ZACB equals 20°.
What is mZ ABC?
D
A
Enter your answer in the box
Answer:
Given
¯¯¯¯¯¯¯¯¯
D
A
C
is a straight line, we can say its full measurement is 180°. If we know a segment of this angle,
∠
D
A
B
, is 105°, we can know that the other segment
∠
B
A
C
must equal 75, since
105
+
75
=
180
.
Once we've found the measure of
∠
B
A
C
to be 75°, and given the measure of
∠
A
C
B
to be 35, we can then find the measurement of
∠
A
B
C
.
Since we know that the sum of any triangle's angles is 180°, we can then use these known measurements as I said above.
75
+
35
+
m
∠
A
B
C
=
180
110
+
m
∠
A
B
C
=
180
m
∠
A
B
C
=
70
Question 1
2 pts
P is between Jand K. The distance between Jand Pis 7 more than 3 times the distance
between P and K. If JK = 55, what is PK?
Answer:
29
Step-by-step explanation:
Consider the triangle shown. Triangle R P Q is shown. Angle Q R P is 40 degrees. Angle R P Q is 105 degrees. Angle P Q R is 35 degrees. Which shows the sides in order from longest to shortest? Line segment P Q, line segment R Q, line segment R P Line segment R Q, Line segment P Q, line segment P Q Line segment R Q, line segment R P, line segment P Q Line segment R P, line segment P Q, line segment R Q
Answer:
RQ, PQ and RP.
Step-by-step explanation:
Note: Options are not correct.
From the given information, in triangle RPQ
[tex]\angle QRP=40^\circ[/tex]
[tex]\angle RPQ=105^\circ[/tex]
[tex]\angle PQR=35^\circ[/tex]
In a triangle, greatest angle has longest opposite side and smallest angle has shortest opposite side
Now,
[tex]\angle RPQ>\angle QRP>\angle PQR[/tex]
[tex]RQ>QP>PR[/tex]
[tex]RQ>PQ>RP[/tex]
Therefore, the order from longest to shortest is RQ, PQ and RP.
Answer:
RQ, PQ and RP.
Step-by-step explanation:
What is the height of the pole?
top
O 12 ft
O 125 ft
O 18 ft
O 182 ft
Which of the following number lines represents the solution to m/-2 - 7 = -9?
Answer:
Step-by-step explanation:
Answer: m=1
Step-by-step explanation:
What is the mean absolute deviation of her math scores?
5.4
6.4
7.8.
o
8.8
Answer:
The mean absolute deviation (MAD) of her Math scores would be 1.2.
Step-by-step explanation:
Mean: 5.4 + 6.4 + 7.8 + 8.8 = 28.4/4 = 7.1
7.1 - 5.4 = 1.7
7.1 - 6.4 = 0.7
7.1 - 7.8 = 0.7
7.1 - 8.8 = 1.7
Mean Absolute Deviation: 1.7 + 0.7 + 0.7 + 1.7 = 4.8/4 = 1.2
hope this helps :)
Answer: I'm guessing but the answer should beD. 8.8.Tell me if I'm wrong. But at least I tried.
Step-by-step explanation:
. A kite is in the shape of a parallelogram
with a 4.5 cm base and a height of
7.9 cm. What is the area of the kite?
Answer:
I believe the answer is 35.55 cm
Step-by-step explanation:
Answer:
35.55 cm
Step-by-step explanation:
To find the answer of this question is to use the method bxh.
4.5 cm
x 7.9 cm
----------------
35.55 cm
math question down below
Answer:
type the question picture isnt showing up
Step-by-step explanation:
Sarah claims that when you divide, the number you are dividing always gets smaller. John says this is not true. Who is correct? If John is correct, give a counterexample.
A) Sarah is correct.
B) John is correct. A counterexample is 4 ÷ 5.
C) John is correct. A counterexample is 4 ÷ 1.25.
D) John is correct. A counterexample is 4 ÷ 1/2
Answer:
D
Step-by-step explanation:
John is correct as Dividing does not always gets the quantity smaller for example if we divide 4 by 0.5
We get
4/0.5= 8
The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students. General High rented and filled 14 vans and 12 buses with 738 students. How many students would fill 2 buses and 3 vans?
Answer:
133 students would fill 2 buses and 3 vans
Step-by-step explanation:
Let x be the no. of students in each van
No. of students in 12 vans = 12x
No. of students in 14 vans = 14x
Let y be the no. of students in each bus
No. of students in 14 buses = 14y
No. of students in 12 buses = 12y
We are given that The senior class at Snellville rented and filled 12 vans and 14 buses with 796 students.
12x+14y=796 ---1
We are also given that General High rented and filled 14 vans and 12 buses with 738 students.
14x+12y=738 ---2
Plot 1 and 2 on graph
12x+14y=796 --- Green line
14x+12y=738 --- Purple line
Intersection point gives the solution
Intersection point=(x,y)=(15,44)
No. of students in 1 van = 15
No. of students in 3 vans = [tex]15 \times 3 = 45[/tex]
No. of students in 1 bus = 44
No. of students in 2 buses =[tex]44 \times 2 = 88[/tex]
So,Total no. of students in 3 vans and 2 buses = 45+88=133
Hence 133 students would fill 2 buses and 3 vans
Please help with this
Answer:
[tex]\frac{\sqrt{8} }{\sqrt{10} }[/tex]
Step-by-step explanation:
A perfect square is a number that has two identical factors, meaning it can be square rooted. The numbers 64 and 100 are an example:
8 · 8 = 64
10 · 10 = 100
So when you take the square root of [tex]\frac{64}{100}[/tex], you get:
[tex]\frac{\sqrt{8} }{\sqrt{10} }[/tex]
It doesn't say to simplify, so we can just leave it at that.
A student is ordering a flower arrangement. She can choose any combination of tulip and carnations for her flower arrangement , and she does not want to spend more than $45. If tulip cost $5 each and carnations cost $3 each, which inequality represents all possible combinations of x tulips and y carnations ? A. 5x + 3y < 45 B. 5x + 3y <= 45 C. 3x + 5y > 45 3x + 5y <= 45
Helppp!
Answer:
[tex]5x+3x \leq 45[/tex] represents all possible combinations of x tulips and y carnations
Step-by-step explanation:
We are supposed to find inequality represents all possible combinations of x tulips and y carnations
Cost of 1 tulip = $5
Cost of x tulips = 5x
Cost of 1 carnation =$3
Cost of y carnations = 3y
We are given that she does not want to spend more than $45.
So, She can spend less than or equal to 45
So, required inequality :[tex]5x+3x \leq 45[/tex]
So, Option B is true
[tex]5x+3x \leq 45[/tex] represents all possible combinations of x tulips and y carnations
Answer:
it would be 5x + 3y <= 45
Step-by-step explanation:
I literally just did this question on my math homework and I got it right .
Sara solved the equation -6(x-2) + 3x = -3(x+3) + 21 What is the solution?
pls help :)
To solve you can use inverse operations.
Here are the steps to find the answer:
1. Write out the equation: -6(x-2)+3x= -3(x+3) +21
2. Distribute both sides: -6x+12+3x= -3x-9+21
3. Simplify both sides: -3x+12=-3x+12
4. This equation is true for all values, or infinity, because the equation is the same on both sides
Let me know if you need further explanation. I hope this helps.
Need Help ASAP it's due today. Angelica uses the point (4,3) to represent the location of her house and uses the point (10,8) to represent the location of a gas station. Each unit on the graph represents 1 mi. How far is the gas station from Angelica's house? SHOW YOUR WORK. ( The teacher said to Plot a third point, connect the third point to make a right triangle, find the lengths of the legs of the triangle and then use the pythagorean theorem to find the distance between the gas station and Angelica's house). Only answer if you truly know how to solve this please. Will Mark Brainliest
Answer:
About 7.8 miles.
Step-by-step explanation:
We can use the distance formula to find the distance from the gas station to the house.
However, your teacher said to use the Pythagorean Theorem to find the distance.
Going by your teacher's preferred method:(4,3), (10,8), and (10,3) would make a right triangle.
[See Picture]
Angelica's house is at point (4,3). It is 6 units from our new third point.
The gas station is at point (10,8). It is 5 units form out new third point.
The legs are 5 and 6 units. The distance from the house to the gas station would be our hypotenuse.
Use the Pythagorean Theorem to find the length of the hypotenuse.
[tex]a^2 + b^2 = c^2\\\\\text {Replace a and b with the appropriate values: }\\6^2 + 5^2 = c^2\\\text {Solve: }\\6^2 + 5^2 = c^2\\6^2 = 36\\5^2 = 25\\\rightarrow 36 + 25 =c^2\\36 + 25 = 61\\\rightarrow 61=c^2\\\sqrt{61}=\sqrt{c} \\\boxed {7.81024967591=c}[/tex]
7.81024967591 ≈ 7.8
The hypotenuse is about 7.8.
Therefore, the distance between the gas station and Angelica's house should be about 7.8 miles.
Brainilest Appreciated!
Answer:
AG = 7,8
Step-by-step explanation:
Plot the third point at (10,3) and let's call it point B.
Now construct the right sided triangle A B G
With A = (4,3) , B = (10,3) and G = (10,8).
AB is horizontal so subtract the x coordinates of point A and point B. So AB has length 10 - 4 = 6
BG is vertical so subtract the y coordinates of point B and point G. So BG has length 8 - 3 = 5
Now use pythagorean theorem to calculate AG
In any right sided triangle you can use a² + b² = c²
In our case AB² + BG² = AG²
Substitute AB = 6 and BG = 5
6² + 5² = AG²
AG² = 6*6 + 5*5
AG² = 36 + 25
AG = + - SQRT(61)
{Only the + variant of the SQRT has a meaning here.}
AG = 7,81 rounded on one decimal AG = 7,8
Problem PageQuestion
Pamela's age is two times Jiri's age. The sum of their ages is 66. What is Jiri's age?
Answer:
Jiri is 22
Pamela is 44
Step-by-step explanation:
Look at the attachment
Answer:
Jiri is 22 years old.
Step-by-step explanation:
P=2J
P+J=66
2J+J=66
3J=66
J=22
What are the solution(s) of the quadratic equation 98 - x2 = 0?
x = +27
x= 163
x = 17/2
no real solution
Answer: it’s c
Step-by-step explanation:
What is 1/2 of 7/8? In fraction firm
1/2*7/8=7/16
Answer:
7/16
The required fraction of 1/2 of 7/8 is given as 7/16.
What is the fraction?Fraction is defined as the number of compositions that constitutes the Whole.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
1/2 of 7/8 = 1/2 × 7/8
= 7 / 16
Thus, the required fraction of 1/2 of 7/8 is given as 7/16.
Learn more about fractions here:
https://brainly.com/question/10708469
#SPJ2
Please help with question off algebra nation
Answer:I’m on that same question and I need help to
Step-by-step explanation:
Answer:
Table C is a linear function. Table A is an exponential function. And lastly table B is a quadratic function.
Step-by-step explanation:
I know that table C is linear because it has a constant rate of change the whole entire time.
I know table A is exponential because of the way it drastically increases at the end.
And lastly I know that table B is quadratic because if I were to graph it and keep on placing points, it would make a parabola.
I hope I helped.
Hunter decides to invest $840,000 in a period annuity that earns a 4.2% APR,
compounded monthly, for a period of 30 years. How much money will Hunter
be paid each month?
Answer: $4107.74
Step-by-step explanation:
can someone plz help me with i don't understand it at allll
Calculating Vacation Costs
Situation:
Imagine that you’ve just won the coveted “Most Likely to Succeed in Math” award! Your prize is $4,500.00, which must be applied to a vacation. You will be provided a list of choices. You, a parent/guardian, and two others will be traveling by car, and you must plan all the expenses for your trip without exceeding $4,500.00.
Special Considerations:
• Do not include costs for souvenirs or extras. These items do not get deducted from the prize money.
• Travel and lodging must be calculated for a round trip.
• You may need two hotel rooms, such as one for girls and one for boys, so make sure to consider who is in the group. All boys or all girls can stay in one room.
• You have various choices and options. Choose what will give you an outstanding vacation.
• You may remain on vacation as long as the prize money is available.
• You must pay all expenses of the group of 4.
• Calculate costs on this sheet.
• Be sure to total costs.
Answer:
i don't understand
Step-by-step explanation:
What is the vertex of the quadratic function with a positive a value?
Answer:
If the coefficient of the squared term is positive, the parabola opens up. The vertex of this parabola is called the minimum point. If the coefficient of the squared term is negative, the parabola opens down. The vertex of this parabola is called the maximum point.
The graph opens upward, if the vertex of the quadratic function with a positive a value.
Given that, the quadratic function with a positive a value.
What is the vertex of the quadratic function?The vertex of the graph of a quadratic function is the highest or lowest possible output for that function. If you're looking at a graph, the vertex would be the highest or lowest point on the parabola. The easiest way to find the vertex is to use the vertex formula.
If a is positive, the graph opens upward, and if a is negative, then it opens downward. The line of symmetry is the vertical line x = h, and the vertex is the point (h, k). Any quadratic function can be rewritten in standard form by completing the square.
Therefore, the graph opens upward, if the vertex of the quadratic function with a positive a value.
To learn more about the vertex of the quadratic function visit:
https://brainly.com/question/22526994.
#SPJ2
Jack divided his fortune of $92,000 into 8 equal parts. He gave 4 parts to his wife, 1 part to his son and divided the remaining 3 parts equally among 5 charities.
How much more money did his son get than each charity?
Answer:
4,600
Step-by-step explanation:
92,000/8= 11500
11500 x 4= 46000 to his wife
11500 for the son
92000-57500= 34500
34500/5= 6,900 each charity
11500-6900= 4600 is how more he is getting than each charity
Answer:
4600 more money
Step-by-step explanation:
92000 ÷ 8 = 11500
1 part to his son
3(11500)= 34500
34500 ÷ 5 = 6900
11500-6900= 4600
What creatures terrify Aeneas as he enters the realm of the dead?
Answer:
The sibyl tells Aeneas that he must find and pluck a golden bough from a tree in an ... First, however, he must find and bury the body of a dead comrade. ... spirits and monsters and eventually reach Acheron, one of the underworld's rivers. Here ... Also punished in Tartarus's realm are mortals who have sinned abhorrently
Step-by-step explanation:
help quick!!!!?????
Omg I’m so sorry to interrupt but I really need help on my homework :( it’s two questions for 20 points||| can someone please help
Answer:
none
Step-by-step explanation:
57+75+95= 227
24+70+75= 169
48+64+80= 192
19+27+80=73
A right triangle equals 180 degrees.
okay who knows there stuff good ? i failed geometry last year and were back at it plz helppp
