Answer: The solutions are x = 3+sqrt(2), and x = 3-sqrt(2). The quadratic equation has two solutions because it has a positive discriminant.
Step-by-step explanation:
Using the quadratic formula, we have: 6+-sqrt(8)/2, which become 3+-sqrt(2).
Souvenir hats, T-shirts, and jackets are sold at a rock concert. Three hats, two T-shirts, and one jacket cost $40. Two hats, two T-shirts, and two jackets cost $60. One hat and three T-shirts cost $10. Find the prices of the individual items. (you have to use substitution and/or elimination method, NO matrix or Graph.)
Answer:
j = 24
t = 2
h = 4
Step-by-step explanation:
Three hats, two T-shirts, and one jacket cost $40.
3h + 2t + j = 40
Two hats, two T-shirts, and two jackets cost $60.
2h + 2t + 2j = 60
One hat and three T-shirts cost $10.
h + 3t = 10
3h + 2t + j = 40 (1)
2h + 2t + 2j = 60 (2)
h + 3t = 10. (3)
From (3)
h = 10 - 3t
Substitute into (1) and (2)
3(10 - 3t) + 2t + j = 40 (1)
2(10 - 3t) + 2t + 2j = 60 (2)
30 - 9t + 2t + j = 40
20 - 6t + 2t + 2j = 60
- 7t + j = 40 - 30
-4t + 2j = 60 - 20
-7t + j = 10 (1a)
-4t + 2j = 40 (1b)
Multiply (1a) by 2
-14t + 2j = 20
-4t + 2j = 40
Subtract to eliminate j
-4t - (-14t) = 40 - 20
-4t + 14t = 20
10t = 20
t = 20/10
t = 2
Substitute t = 2 into
h = 10 - 3t
h = 10 - 3(2)
= 10 - 6
= 4
h = 4
Substitute t = 2 and h = 4 into
3h + 2t + j = 40
3(4) + 2(2) + j = 40
12 + 4 + j = 40
16 + j = 40
j = 40 - 16
= 24
j = 24
PLEASE HELP!!!
Tony has 6 dollars in change in his car. Every time he drives to visit his grandma, he pays $1.25 in tolls. Which graph represents the change Tony has in his car?
Answer:
I'd assume the last one but I don't know exactly what the graph is measuring
Shelley's pet food store sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20. Write a proportion that compares the sales of these two items, and find the cross products. The cross products are both equal to
Given that,
Shelley's pet food store sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20.
For peanut, the cost is ratio is
[tex]\dfrac{5}{3}[/tex]
For beef, the ratio is
[tex]\dfrac{7}{4.2}[/tex]
If we take cross product of these items,
[tex]\dfrac{5}{3}=\dfrac{7}{4.2}\\\\5\times 4.2=3\times 7\\\\21=21[/tex]
It implies, that the sale is in true proportion. From the cross product, we find that it is equal.
Answer:
21
Step-by-step explanation:
Janet hiked 3/8 mile in 1/4 hour. How fast did she hike, per hour?
Answer: answer is A
A:3/32
B:2/3
C: 1 1/2
D:4
She hike 1.5 miles per hour.A common unit of measurement is the mile (mi).
How to fast she hike per hour?1.609344 kilometers are exactly one unit of length. mile, any of several different measures of distance, such as the statute mile, which has a length of 5,280 feet, is also equivalent to 1,760 yards (1.609 km). It derives from the mile passus, or "thousand paces," of the Romans, which was equivalent to 5,000 Roman feet.
A common unit of measurement is the mile (mi). It is typically used to express the distance between cities, the length of rivers, and the distance between roadways. The letter "mi" stands for the unit mile in writing. Therefore, a marathon race would be roughly 26.3 miles or 26.3 mi in length.
Given ,
1/4hrs=15mins
15mins=3/8miles
60mins=more
60/15 × 3/8
=4/1 × 3/8
=12/8
=1.5miles
Therefore 1.5 miles fast she hike per hour.
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A truck can be rented from company A for $120 a day plus $0.50 per mile. Company b chargers $80 a day plus $0.70 per mile to rent the same truck. Part A write a equation. To find the number of miles in a day at which the rental costs for company A and company B are the same Part b solve the equation
Answer:
Part A: [tex].50x+120 = .70x+80[/tex]
Part B: [tex]200[/tex] miles
Step-by-step explanation:
So to start, we need to put this information into slope-intercept form. Slope intercept form is [tex]y=mx+b[/tex] where [tex]m[/tex] represents the slope of a line and [tex]b[/tex] represents the y-intercept. In this question [tex]y[/tex] represents the total cost of the rental, [tex]x[/tex] represents the number of miles driven, [tex]m[/tex] represents the price per mile, and [tex]b[/tex] represents the base price of the rental. Now that we know the variables, we need to plug in the information we have.
Since we know that company A charges $125 a day and $0.50 per mile we would have [tex]y=.50x+120[/tex]
Since we know that company B charges $80 a day and $0.70 per mile we would have [tex]y=.70x+80[/tex]
Now that we have two equations we can move onto the next step. We're looking to know the number of miles ([tex]x[/tex]) that would make the total cost ([tex]y[/tex]) equal. To do this we can make the equations equal each other since we know that [tex]y[/tex] will be the same.
Written out, the equation will look like this: [tex].50x+120 = .70x+80[/tex]
Now, we are trying to find [tex]x[/tex] so we need to isolate the variable.
To start we need to put [tex]x[/tex] on the same side so we'll subtract [tex].70x[/tex] from both sides to get [tex]-.20x+120=80[/tex]
Next, we'll subtract [tex]120[/tex] from both sides of the equation to get [tex]-.20x=-40[/tex]
Finally, we'll divide both sides by [tex]-.20[/tex] to get [tex]x=200[/tex]
This means that at [tex]200[/tex] miles, both companies will cost the same amount.
Who wants to smash some COD in the morning
Answer:
Sorry Ion play COD
Step-by-step explanation:
daniel kicks a soccer ball and the trajectory is modeled by f(t) = -16t^ +32t. what would be the value of f(1)
Answer:
f(1)=16
Step-by-step explanation:
f(t)=-16t+32t
f(1)=-16(1)+32(1)
f(1)=-16+32
f(1)=16
Answer:
f(1)=16
Step-by-step explanation:
You measure a tree's shadow and find that it is x = 13 meters long. Then you measure the shadow of a nearby two-meter lamppost and find that it is 75 centimeters long. (See figure.) How tall is the tree? (Round your answer to one decimal place.)
Answer:34.7
Step-by-step explanation:
h/ 13 = 2/0.75
h= 2 • 13 / 0.75
34.7 m (rounded)
Tree is 34.7m tall.
What is similar triangle?In similar triangle, shape is same but size is varing. So the ratio of corresponding sides are also equal.
So according to asked question,
Let height of the tree =h
The triangle formed by the tree and its shadow is similar with the triangle formd by the the trangle formed by the lamppost and its shadow.
So, according to the propoties of the similar triangle
a₁/a₂=b₁/b₂
h/x=2m/75cm
⇒h/13=2/(3/4)
⇒h/13=2*4/3=8/3
⇒h=8*13/3=34.666≅34.7m
Therefore tree is 34.7m tall.
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find the missing side lengths!! pls help!!!!!!!!! marking brainliest
Answer:
y = 5.19615 or 3√3
x = 10.3923 or 6√3
also missing angle is 60°.
hope this helps!
Step-by-step explanation:
use the graph to answer the following question. For what values of x does f(x)=4
0,4
is where it would land and you can
Find the x- and y-intercepts :
Y= 3x + 9
Answers:
y = -3 and x = 9
y = 9 and x= -3
Which one should I choose?
Answer:
(y= -3 and x = 9)
Step-by-step explanation:
For the y intercept, make x = 0 and solve. For the x intercept, make f(x) = 0 and solve.
· Jim put a fence around a rectangular area. A scale drawing of the area
has a length of 3.5 inches and width of 2.5 inches. If the scale of the
drawing is 1 inch = 5 feet, what is the actual perimeter of the fenced
area?
Answer: 73 feet
Step-by-step explanation:
1inch =5feet
L=3.5 inches W=2.5 inches
P= L1+L2+W1+W2
L=3.5(5) =17.5
W= 2.5(5) = 12.5
17.5+ 17.5 +12.5+ 12.5= 73 feet
How would -9-(-5) look like as an addition problem?
Answer:
-9+5=-4
Step-by-step explanation:
a negative times a negative is always a positive.
Answer:
-9 + 5
Step-by-step explanation:
If there is a negative sign in front of a negative number in parenthesis, then that makes the negative number a positive number which is -9 + 5
solve 2x-4y=10 and x+5y=40
Answer:
y = 1/2x + 2.5 and y = -1/5x + 8
Step-by-step explanation:
2x - 4y = 10 (subtract 2x on each side)
-4y = -2x + 10 ( divide by - 4 on both sides)
y = 1/2x + 2.5
x + 5y = 40 (subtract x on both sides)
5y = -x + 40 (divide by 5 on both sides)
y = -1/5x + 8
Hope this helped!!
Two numbers that are the same distance from zero on a number line are called ___ numbers
Answer:
They are called opposites.
Step-by-step explanation:
"Zero is called the origin, and it's neither negative nor positive. For every positive integer, there's a negative integer an equal distance from the origin. Two integers that lie the same distance from the origin in opposite directions are called opposites. For example, negative 5 is the opposite of positive 5."
Hope this helps :)
I need help #17 please!
Answer:
Step-by-step explanation: it would be B= 3/20
hope this helps!!!!
Answer: B) m=3/20
Step-by-step explanation: X is increasing by 3 each time, while Y is increasing by 20. Therefore, it is 3/20.
help i need an answer asap
Answer:
The answer is 3.7
✨
use the zero product property to find the solutions to the equation (x+2)(x+3)=12
Answer:
x=-6, x=1
Step-by-step explanation:
The zero product property
It states that if a.b=0, then it must be satisfied that a=0 or b=0. It's commonly used to solve equations where one of the sides is 0.
The given equation is:
(x+2)(x+3)=12
Since neither side is 0, we operate the expression:
x^2+3x+2x+6=12
Moving 12 to the left side and simplifying:
x^2+3x+2x+6-12=0
x^2+5x-6=0
Factoring:
(x+6)(x-1)=0
Now, since there is zero on the right side, we apply the property to solve:
x+6=0, or x-1=0
The two solutions come directly:
x=-6, x=1
6+4=210
9+2=711
8+5=313
3+2=15
8+3=??
Answer:
11
Step-by-step explanation:
Paco grew 12 plants with 4 seeds packets. How many seeds packets does Paco need to have a total of 18 plants in his backyard? Solve using unit rates.
Answer: 72
Step-by-step explanation: i multiplied 18 and 4 and that gave me 72
hopefully im not wrong let me know if i am
Answer:
5 and half packet of seeds or 5.5 which is 6 packets
Step-by-step explanation:
12 / 4 = 3
he can plant 3 plants with 1 seed packet
which means he needs 5 packets and half
the answer is 6
Solve for r:
6r-12=-30
Answer:
r=-3
Step-by-step explanation:
the first step in this equation is to isolate 6r,to do this you got to add 12 to -30 which you get -18 which gives the equation 6r=-18 which now you got to divide both sides by 6 which you should get r=-3
Answer:
r=-3
Step-by-step explanation:
add 12 to -30 you get -18 divide -18 by 6 and you get -3
Find the measure of each angle.
Answer:
I mite be rong but I think 8x and 3x
What is the image of (9,-6) after a reflection over the y-axis?
Answer:
(- 9, - 6 )
Step-by-step explanation:
Under a reflection in the y- axis
a point (x, y ) → (- x, y ) , thus
(9, - 6 ) → (- 9, - 6 )
Find the slope
please help!
Answer: the slope is 1/1
Step-by-step explanation:
it rises up 1 and goes over 1
Answer:
4/5
Step-by-step explanation:
(4, 2)
(-1, -2)
Slope = (y2 - y1)/(x2 - x1)
2 - (-2)/4 -(-1)
Slope = 4/5
Hope this helps!
Let me know if I'm incorrect :)
b) Write 36 as a product of its prime factors.
Write the factors in order, from smallest to largest
Answer:
1, 2, 3, 4, 6, 9, 12, 18
hey help quick...please
Answer:
A
Step-by-step explanation:
2Red 6 Blue Balls
+4Yellow
= 6 balls
represent in number line
1/5 and 2/5
See picture for math work and answer.
Pls help meeeeeeee Solve 10 + 6p = 22
Answer:
p=2
Step-by-step explanation:
22-10=12
12/6p=2
Can someone please tell me the answers!?!?! It’s due today! (I’ll give brainliest to the one who is right)
-3 -24
-120 9
-21 -9
8 -48
Answer:
(-27) / 9 = -3 4 * (-6 )= -24
12 * (-10) = -120 (-45) / (-5) = 9
7 * (-3) = -21 72 / (-8) = -9
64 / 8 = 8 (-8) * 6 = -48
Which value is a solution of the equation 3 - 2x=-5?
02
04
0-2
01/5
Answer:
4
Step-by-step explanation:
answer is four don't worry it's correct
The value is a solution of the equation is x= 4.
The correct option is B.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
We have an Equation as 3- 2x = -5.
Now, solving the above equation for x
Subtract 3 from both side
3- 2x - 3 = -5 -3
-2x = -8
Now, divide both by (-2) we get
-2x/(-2) = -8/(-2)
x = 4
Thus, the value of x is 4.
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