Answer:
AB = 7
AC = 21
Step-by-step explanation:
Because AD is an angle bisector it divides the triangle into proportional parts. That is ...
AC/DC = AB/BD
(28 -AB)/9 = AB/3 . . . . use AC = 28 -AB
28 -AB = 3AB . . . . . . . . multiply by 9
28 = 4AB . . . . . . . . add AB
AB = 28/4 = 7 . . . . divide by 4
AC = 28 -7 = 21
The lengths AB and AC are 7 and 21, respectively.
_____
Additional comment
The triangle ABC cannot exist. The reason is that its side measures are 7, 12, and 21. The sum of 7 and 12 is not greater than 21, so the side measures do not satisfy the triangle inequality.
For the triangle to exist, the sum of AB and AC cannot exceed 24 for the given values of BD and DC.
HELPPP PLS
What is the vertex form of the equation?
y = x² – 2x+8
Determine if this is a valid statistical question: What proportion of New Jersey residents would choose vanilla as their favorite ice cream flavor? *
Given f(x)=2x²+2x-4, which is correct?
A) f(0)=0
B) f(-1)=4
C) f(b+1)=2b²+6b-4
D) f(a)=2a²+2a-4
Answer:
Option D: f(a) = 2a²+2a-4 is the correct answer.
Step-by-step explanation:
Given that:
f(x)=2x²+2x-4
We will check the function at the given value;
A. f(0)
Putting x=0 in given function
f(0) = 2(0)²+2(0) - 4
f(0) = 0+0-4
f(0) = -4
B. f(-1)
Putting x=-1
f(-1) = 2(-1)²+2(-1)-4
f(-1) = 2(1) -2-4
f(-1) = 2-6
f(-1) = -4
C. f(b+1) = 2b²+6b-4
Putting x=b+1
f(b+1) = 2(b+1)²+2(b+1)-4
f(b+1) = 2(b²+2b+1)+2b+2-4
f(b+1) = 2b²+4b+2+2b+2-4
f(b+1) = 2b²+6b
D. f(a) = 2a²+2a-4
Putting x=a
f(a) = 2(a)²+2(a)-4
f(a) = 2a²+2a-4
Hence,
Option D: f(a) = 2a²+2a-4 is the correct answer.
Ellen writes 2 pages in a hour. Determine the equation that represents the function and state it graphically.
Answer:
1 page every 0.5hours, or 1 page every 30 minutes. The equation is
2x = y
Am I doing this right? The question is... At the first store Arlene visited, she spent 40% of her money plus $4. At the second store she spent 50% of her remaining money plus $5. At the third store Arlene spent 60% of her remaining money plus $6. When Arlene finished shopping at the three stores, she had $2 left over. How many dollars did she have when she started shopping?
My equation was x - 2 = ((0.4x+4)0.5+5)0.6+6. Both sides of the equation were to find how much she spent. I got 13.86363...
9514 1404 393
Answer:
$90
Step-by-step explanation:
Let's consider the remaining money. If x represents the amount Arlene started with, then the remaining amounts are ...
after first store: x -(0.4x +4) = 0.60x -4
After spending 50% of her money, the amount remaining will be 1-50% = 50%. Then spending 5 more dollars reduces the amount remaining by another 5.
after second store: (0.60x -4)(0.50) -5 = 0.30x -2 -7 = 0.30x -7
After spending 60% of her money, the amount remaining will be 1-60% = 40%. Then spending 6 more dollars reduces the amount remaining by another 6.
after third store: (0.30x -7)(0.40) -6 = 0.12x -2.80 -6 = 0.12x -8.80
This is reported to be $2, so we have ...
0.12x -8.80 = 2
0.12x = 10.80
x = 90
Arlene started shopping with $90.
_____
Check
At the first store, Arlene spent 0.40×$90 +$4 = $40, so she had $90-40=$50 remaining.
At the second store, Arlene spent 0.50×$50 +$5 = $30, so she had $50-30=$20 remaining.
At the third store, Arlene spent 0.60×$20+$6 = $18, so she had $20-18 =$2 remaining.
A person standing close to the edge on top of a 32-foot building throws a ball vertically upward. The quadratic function h(t)=−16t^2+124t+32 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown. a) What is the maximum height of the ball? __feet b) How many seconds does it take until the ball hits the ground? ____ seconds
Answer:
a) The maximum height of the ball is 272.25 feet
b) The balls take 8 seconds to hit the ground.
Step-by-step explanation:
a) You know that the quadratic function h(t)=−16*t²+124*t+32 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown.
Being a quadratic function of the form:
f (x) = a*x² + b*x + c
The vertex of a quadratic or parabola equation is the highest or lowest point on the graph corresponding to that function. When a> 0, the vertex of the parabola is at the bottom of it and indicates the minimum of the function. When a <0 the vertex is at the top and indicates the maximum of the function.
The value of x at the vertex is calculated by the expression:
[tex]x=\frac{-b}{2*a}[/tex]
The value of y at the vertex is calculated by substituting the value of x at the vertex into the quadratic function.
In this case, being a=-16, b=124 and c=32 you get that the maximum time is:
[tex]x=\frac{-124}{2*(-16)}=3.875[/tex]
Then a maximum height of:
h(3.875)=−16*(3.875)²+124*3.875+32
h(3.875)= 272.25
The maximum height of the ball is 272.25 feet
b) When the ball hits the ground the height is zero. So h (t) = 0:
0=−16*t²+124*t+32
Applying the resolvent:
[tex]\frac{-b+-\sqrt{b^{2} -4*a*c} }{2*a} =\frac{-124+-\sqrt{124^{2} -4*(-16)*32} }{2*(-16)}[/tex]
you get:
[tex]\frac{-124+\sqrt{124^{2} -4*(-16)*32} }{2*(-16)} =-0.25[/tex]
[tex]\frac{-124-\sqrt{124^{2} -4*(-16)*32} }{2*(-16)} =8[/tex]
Since the time cannot be negative, the balls take 8 seconds to hit the ground.
I need help doing this equation
Answer:
Candy = $ 0.5
Soda = $ 4.0
Step-by-step explanation:
x + 2y = 5
x + 4y = 6
2y = 1
y = 1/2
= two candies were added and the price increased by 1 dollar, meaning that the a single candy is 0.5 dollar
1 candy = 0.5
x + 2(0.5) = 5
x + 1 = 5
x = 4
I got this question on a math homework and I don't understand it, 5 5/8 cups of water fill 4 1/2 identical water bottles. How many cups fill each bottle?
Answer:
1-1/4 cups (1 and 1/4 cups) or 1.25 cups
Step-by-step explanation:
To find the answer you need to take the total volume (5-5/8 cups) and divide it by the number of bottles you have:
5-5/8 divided by 4-1/2
There are two easy ways to do this: you can convert the mixed fractions into decimal form (A) or into improper fractions (B).
A)
First, convert to decimal form:
5-5/8 = 5.625 and 4-1/2 = 4.5
Then, you divide them:
5.625 / 4.5 = 1.25 (converted back to fraction form, if thats what you need, is 1-1/4)
B)
First, convert to mixed numbers:
5-5/8 = 45/8 and 4-1/2 =9/2
Then, you divide them:
45/8 / 9/2
When you divide fractions, you multiply by the inverse of the number you're dividing by (that means swapping the numerator and denominator):
45/8 * 2/9 = 90/72 (converted back to a mixed fraction, this equals 1-1/4)
not prime number in 12n- 5
Answer:
55
Step-by-step explanation:
12 x 5 = 60
60-5 = 55
55 is not prime
Solve the system by elimination. {2x+y=13x−y=−4 A. (3, 7) B. (2, 6) C. (4, 8) D. no solution
Answer:
A
Step-by-step explanation:
Given the 2 equations
2x + y = 13 → (1)
x - y = - 4 → (2)
Add the 2 equations term by term to eliminate the y- term, that is
3x = 9 ( divide both sides by 3 )
x = 3
Substitute x = 3 into either of the 2 equations and solve for y
Substituting into (1)
2(3) + y = 13
6 + y = 13 ( subtract 6 from both sides )
y = 7
solution is (3, 7 ) → A
Answer:
Step-by-step explanation:
2x+y=13
x - y =-4 lets add both equations
3x=13-4
x=9/3 , x=3
3-y=-4, y=7
choice A
Find the least whole number that can replace blank 80 to make the statement true. ÷ 18 > 86
Answer:
649
Step-by-step explanation:
Given the expression :
__ ÷ 18 > 86
Let blank = y
y ÷ 18 > 36
y / 18 > 36
Multiply both sides by 18
(y / 18) * 18 > 36 * 18
y > 648
Hence, the least whole number which can make the statement true is (648 + 1) = 649
90% of the workers are men. If 590 people work for the company who aren't men, how many workers are there in all?
Step-by-step explanation:
do 590 divided by 90 if that doesn't work multiply it
I PROMISE I WILL MARK AS BRAINLIEST please i want an answer
in the unit circle whose center is (o)if the length of the arc BC =1/3π , then sec (∠BOC) =
Answer:
Answer is = 1
Step-by-step explanation:
Hope it's answered you
Answer:
nice
Step-by-step explanation:
In 1 hour the employee dropped 635 chocolates. If this represents 25% of the days chocolate molds, how many chocolates were planned to be
produced
Answer:
2540
Step-by-step explanation:
25% is a quarter of 100% so if 635 is 25% you multiple 635 x 4 to get your final answer concluding in 2540. if i'm wrong let someone else correct me :b
1.3181818...... as fraction units lowest term
Answer:
29/22
Step-by-step explanation:
Let x = 1.31818181818....
Then, 10x = 13.18181818..., and 1000x = 1318.18181818..... Subtracting the first equation from the second, we get that 990x = 1305. This means that x = 1305/990. In lowest terms, this is 29/22.
You decide to make lasagna for dinner. The baking dish in the shape of a rectangular prism measures 13 inches by 9 inches by 2 inches. What is the volume of the container?
Volume = 13in * 9in * 2in = 234in³.
Answer:
234 inches³
Step-by-step explanation:
Formula for volume of a prism = [tex]L \times W \times H[/tex] (L = length, W = width, H = height)
[tex]\therefore[/tex] volume for baking dish = 13 × 9 × 2
= 234 inches³
Hope this helps :)
Use the formula a^2-b^2= (a+b)(a-b) to factor completely. What are the factors of 36x^8-49 ?
Answer:
(6x^4-7)(6x^4+7)
Step-by-step explanation:
36x^8-49
1. look for a gcf. since there isn't one, you move on to the next step.
2. what multiplies to what you need. you can do box method or diamond method.
3. (6x^4-7)(6x^4+7)
Answer:
C
Step-by-step explanation:
Hey guys help me with this question plzzzzzz
Answer:
625 cm³ and 64000 cm³
Step-by-step explanation:
Given
x = [tex]\sqrt[3]{V}[/tex] ( cube both sides )
x³ = V
(a)
x = 25 cm , then
V = 25³ = 625 cm³
(b)
x = 40 cm , then
V = 40³ = 64 000 cm³
Which situation could be represented by 5x > 15? Jakiera makes $5 per hour working at her father's repair shop. She needs to make more than $15 to buy the calendar that she wants for next year. How many hours can she work to achieve this goal? Thomas brought 5 cans for the campus food drive. How many more cans does he need to have at least 15 cans for the food drive? Clarice collects comic books. Her brother, Samuel, has 15 comic books. How many comic books does Clarice need to have more comics than Samuel? Elizabeth is five times older than her grandchild, who is 15. How old is Elizabeth?
Answer:
First situation
More than 3 hours
At least 10
15
75
Step-by-step explanation:
Let x be the number of hours
The equation will be
[tex]5x>15\\\Rightarrow x>\dfrac{15}{5}\\\Rightarrow x>3[/tex]
So, she needs to work more than 3 hours in order to make more than $15.
The situation that represents [tex]5x>15[/tex] is the first one.
Let x be the additional number of cans
The inequality will be
[tex]x+5\geq15\\\Rightarrow x\geq 15-5\\\Rightarrow x\geq 10[/tex]
So, the additional number of cans to be bought is at least 10.
Let x be the number of comic books Clarice has.
[tex]x>15[/tex]
So, Clarice needs to have more than 15 comic books.
Let x be age of Elizabeth
The equation will be
[tex]x=5\times 15\\\Rightarrow x=75[/tex]
So, Elizabeth is 75 years old.
Madelyn has a total of 15 dimes and quartets in her piggy bank. The total amount of money in her piggie bank is $2.85. Write and solve a system of equations to determine the number of dimes and the number of quarters in madelyn’s piggie bank.
The system of equations is x + y = 15 and 0.10x + 0.25y = 2.85. Then the number of dimes and quarters will be 6 and 9, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Madelyn has a total of 15 dimes and quartets in her piggy bank. The total amount of money in her piggy bank is $2.85.
Let 'x' be the number of dimes and 'y' be the number of quarters. Then the equations are given as,
0.10x + 0.25y = 2.85 ....1
x + y = 15 ....2
From equations 1 and 2, then we have
0.10(15 - y) + 0.25y = 2.85
1.5 - 0.10y + 0.25y = 2.85
0.15y = 1.35
y = 9
Then the value of the variable 'x' is given as,
x + 9 = 15
x = 6
The system of equations is x + y = 15 and 0.10x + 0.25y = 2.85. Then the number of dimes and quarters will be 6 and 9, respectively.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ5
can someone please help me im struggling on this one
Answer:
Equation: 32° + 30° + x° = 180°Solved: x = 118°Step-by-step explanation:
3 angles = 180°32° + 30° + x° = 180°62° + x = 180°Subtract 62 from each side, so it now looks like this: x = 118°So, x is 118°I hope this helps!
jasmine deals 2 cards. whats the probability of dealing 2 hearts in a row if she didn't replace the card after it was dealt?
WILL GIVE BRAINLIEST FOR CORRECT ANSWER
Yorkeuri has a cake that weighs 80 ounces. How many pounds does the cake weigh? *
Answer: 5 pounds
Step-by-step explanation:
80 / 16 = 5
Answer:
5 pounds
Step-by-step explanation:
Hope this helps!
Mike bulit a sand casitle that mersured 54 inches by 77 inches and dug a moat aorund it afterward, he decided to change the size, making it 112 inches by 38 inches how much longer wil the new moat be than the old one?
Step-by-step explanation:
Initial dimension of a sand castle is 54 inches by 77 inches. Mike decided to change the size, making it 112 inches by 38 inches.
He wanted to dug a moat around it.
The perimeter of moat with initial dimensions,
P = 2(54+77)
= 262 inches
The perimeter of moat with new dimensions,
P = 2(112+38)
= 300 inches
Difference in perimeter = 300 - 262
= 38 inches
Hence, the new dimension is 38 inches longer than the initial dimensions.
i need help i dont understand
Answer:
D. 1/3^3
Step-by-step explanation:
Divide 3/3 as usual and get 1.
When dividing exponents, you are actually subtracting them. 5-8 = -3.
D is the answer because positive exponents in the denominator of the fraction is the same as a negative exponent in the numerator.
The rule with exponents is that when dividing similar bases with different exponents (or power), you subtract the exponents respectively.
3⁵ / 3⁸ = 3⁽⁵ ⁻ ⁸⁾ = 3⁻ ³ = 1 / 3³
So the answer is
D) 1/3³
a small pool can hold 42.8 gallons of water it is currently 5/8 full how many gallons are in the pool
Answer:
There are 26.75 gallons in the pool.
Step-by-step explanation:
Divide 42.8 by 8, multiply the quotient by 5.
Answer:
26.75
Step-by-step explanation:
42.8 * 5/8 = 26.75
A home cleaning service takes more time to clean larger spaces. The table shows the number of minutes it takes for
the service to clean a certain number of square feet within a home.
Square Feet and Cleaning Time
80
Nurnber of Square
50
100
150
Feet, x
Time in Minutes,
32
40
60
Based on the table, how many minutes would it take for the service to clean 200 square feet?
O 20 minutes
O 80 minutes
O 125 minutes
O 400 minutes
y^3-8y^2+19y=12
Solve
Answer:
Step-by-step explanation:
steps are below
step 1
y^3-8y^2+19y=12 equation
step 2
y^3-8y2+19y(-12)=12(-12) minus 12 from both sides
y^3-8y^2+19y-12=0
step 3
(y-1)(y-3)(y-4)=0 add brackets
step 4
(y-1)(y-3)(y-4)=0 factor
step 5
y-1=0 or y−3=0 or y-4=0 set them equal
Answer:
y=1 or y=3 or y=4
OH MY GOSH PLEASE IM ABOUT TO CRY HELP ASAPP
Answer:
All systems have 2 real solutions.
Explanation: there are X and Y unknowns.
0.5 is equivalent to what rational number?
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation: