Answer:
(-3, 0) and (1, 0)
(0, 4)
Step-by-step explanation:
x-intercept is the point where y = 0.
y-intercept is the point where x = 0.
or points ...
f(x) = y = -4×|x + 1| + 8
let's start with the y-intercept (x = 0)
y = -4×1 + 8 = -4 + 8 = 4
the y-intercept point (only 1 point) is (0, 4).
for x = 0 the absolute value function contains 0+1. and that is always +1.
the x-intercept(s) :
0 = -4×|x + 1| + 8 (dividing by -4)
0 = |x + 1| - 2
|x + 1| = 2
because of the absolute value we have 2 possibilities :
+(x + 1) = 2
x + 1 = 2
x = 1
and
-(x + 1) = 2
-x - 1 = 2
-x = 3
x = -3
so the points of x-intercept are (-3, 0) and (1, 0)
What is the value of x?
Enter your answer in the box.
X
8 2
X=
30°
452
The length οf the perpendicular is 2√2.
What is Trigοnοmetry?Trigοnοmetry is a branch οf mathematics that deals with the study οf relatiοnships between the sides and angles οf triangles. It includes the study οf trigοnοmetric functiοns such as sine, cοsine, and tangent, which are used tο sοlve prοblems in fields such as engineering, physics, and navigatiοn.
Step 1:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 8√2 and the angle at the base is 30 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(30°) = p/8√2
We can simplify this expressiοn by nοting that sin(30°) = 1/2 and 8√2 = 8√(2/2) = 8√(1/√2) = 8/√2. Substituting these values, we get:
1/2 = p/(8/√2)
Simplifying further, we can multiply bοth sides by 8/√2:
4/√2 = p
Tο express the result in simplest radical fοrm, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by √2:
p = 4/√2 * √2/√2 = 4√2
Therefοre, the length οf the perpendicular is 4√2.
Step 2:
Let's call the length οf the perpendicular "p".
Frοm the given infοrmatiοn, we knοw that the hypοtenuse is 4√2 and the angle at the base is 45 degrees. We can use trigοnοmetry tο find the length οf the perpendicular.
In a right triangle, the sine οf an angle is defined as the length οf the side οppοsite the angle divided by the length οf the hypοtenuse. Sο we have:
sin(45°) = p/4√2
We can simplify this expressiοn by nοting that sin(45°) = √2/2 and 4√2 = 4√(2/2) = 4√(1/√2) = 4/√2. Substituting these values, we get:
√2/2 = p/(4/√2)
Simplifying further, we can multiply bοth sides by 4/√2:
2√2 = p
Therefοre, the length οf the perpendicular is 2√2.
To learn more about Trigonometry from the given link
https://brainly.com/question/24349828
#SPJ1
The length of the base of an isosceles triangle is x. The length of a leg is 2x - 2. The perimeter of the triangle is 71. Find
Answer:
x = 15
Step-by-step explanation:
x + 2x - 2 + 2x - 2 = 71
Solve for x, you get 15.
A rock is dropped from the top of a building and hits the ground at a velocity of −72ft/sec. If the acceleration due to gravity is −32ft/sec^2, what is the height of the building?
A high-altitude spherical weather balloon expands as it rises due to the drop in atmospheric pressure. Suppose that the radius r increases at the rate of 0.03 inches per second and that r=48 inches at time t=0. Determine a function that models the volume V of the balloon at time t and find the volume at t=300 seconds.
Considering a linear function for the radius, we have that:
The volume of the sphere is modeled by [tex]V(t) = \frac{4\pi(0.03t + 48)^3}{3}[/tex].After 300 seconds, it is of 775,735 in³.What is a linear function?A linear function is modeled by:
[tex]y = mx + b[/tex]
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value.What is the volume of a sphere?The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this problem, radius r increases at the rate of 0.03 inches per second and that r=48, hence it is represented by the following linear function:
[tex]r(t) = 0.03t + 48[/tex]
Thus, the volume of the sphere is given by:
[tex]V = \frac{4\pi r(t)^3}{3}[/tex]
[tex]V(t) = \frac{4\pi(0.03t + 48)^3}{3}[/tex]
After 300 seconds, the volume in cubic inches is given by:
[tex]V(300) = \frac{4\pi(0.03(300) + 48)^3}{3} = 775735[/tex]
More can be learned about linear functions at https://brainly.com/question/24808124
Kim is 15 years old. Her father is 4 times as old as her now. In how many years time their total age be 115 years.
Answer:
20 years time
Step-by-step explanation:
Taylor buys necklaces at wholesale for her store for $6, then she adds a mark up of
120% to the wholesale cost she paid for the necklaces. What is the sale price of
necklaces at Taylor's store?
Cost is 6 USD
Selling price is 6 + markup
Markup = 6 * 120 /100 put this expression and check again selling price
Selling price = 6 + (6 * 120) / 100
= 13,2 usd
How do you solve this problem?
Answer:
16 triangles I am pretty sure.
Step-by-step explanation:
. Find the angle between the given vectors to the nearest tenth of a degree. u = <2, -4>, v = <3, -8> (2 points)
Answer:
6.0
Step-by-step explanation:
practice many times
How do I do this this folks?
for the answer most likey it would be from the range of 88 to 66 that would make a little sence corecct me if im wrong
Step-by-step explanation:
y by the power of 2 + 4=20
Answer:
y is equal to 4 if that's what ur asking for
Answer:
16 if ur asking for y^2+4=20
Step-by-step explanation:
Match each word with the correct part of the expression.
5x + 12
coefficient
5x + 12
variable
5x + 12
term
5x + 12
constant
Expression: 5x + 12
Coefficients (The number directly next to the variable): 5
Variable (A letter that stands for a unknown number): x
Term (A single mathematical expression): 5x , 12
Constant (A term that has no attached variables): 12
Answer:
Step-by-step explanation:
There are two numbers. The smaller number is 32 less than the larger number. If the larger number is increased by 10, it will be 4 times that of the smaller number. Find the larger number.
Step-by-step explanation:
Let the larger no be = a
Difference of the numbers = a - 32
As per the question;
(a + 32) = 5(a - 32)
⇒ a + 32 = 5a - 160
⇒ 128 = 4a
⇒ a = 32
∴ The larger no is 32.
3. The object has the shape of a rectangular prism, but part of a face is missing.
Find the surface area of the object and show your work.
a)
Find the surface area of the complete prism.
5 cm
30 cm
20 cm
10 cm
15 cm
I need an answer
Solve each of the following equations. Show its solution set on a number line. Check your answers. 3(x-2)=12
PLS HELP WILL GIVE BRAINLIEST
x = 6
Step-by-step explanation:
[tex]\sf3(x - 2) = 12 \\ \sf3x - 6 = 12 \\\sf3x = 12 + 6 \\ \sf3x = 18 \\ \sf \: x = \frac{18}{3} \\ \sf \: x = 6[/tex]
Answer: (negative solution): x=-2, (positive solution): x=6
please help: perimeter of polygon ABCDEF
Answer:
Step-by-step explanation:
Add:
Help help help help
1350 + 238
Ron has a co-op in the Astor Cooperative development. There are 40,000 shares in the cooperative ownership. If Ron owns 500 shares, what percentage of the cooperative corporation does he own?
Answer:
Ron owns 1.25% of shares.
Step-by-step explanation:
400/50000 comes out to 0.0125 which can be converted into a decimal by moving the decimal two places to the right.
4 3/5 - 4/5 = ?
please explain it
ixl
Answer:
[tex] \frac{19}{3 } \: or \: 3 \frac{4}{5} [/tex]
Step-by-step explanation:
Change the mixed number into a regular fraction.
[tex] \frac{23}{5} - \frac{4}{5} [/tex]
Subtract the numerator.
[tex] \frac{19}{5} [/tex]
As a mixed number:
[tex]3 \frac{4}{5} [/tex]
A card is drawn at random from a standard deck of playing cards (no jokers). If the card is a spade, the player wins $7; if it is not a spade, the player loses $1.
What is the expected value of this game? $________________
The expected value of the game is the mean value of the game
The expected value of the game is $1
How to determine the expected value?There are 13 spades in a deck of card of 52
So, the probability of selecting a spade is:
P(Spade) = 13/52
Simplify
P(Spade) = 1/4
Winning = $7
The probability of not selecting a spade is:
P(Not spade) = 1 - 1/4
Simplify
P(Not spade) = 3/4
Lose = $1
The expected value of the game is:
[tex]E(x) = \sum x * P(x)[/tex]
This gives
[tex]E(x) = \frac 14 * 7 - 1 * \frac34[/tex]
Simplify
[tex]E(x) = \frac 74 - \frac34[/tex]
Evaluate
[tex]E(x) = 1[/tex]
Hence, the expected value of the game is $1
Read more about expected values at:
https://brainly.com/question/15858152
Rewrite the fraction in the sentence below as a percentage. At a certain wedding, 1/10 of the guests were over 60 years old.
Answer:
10%
Step-by-step explanation:
1/10 = 10%
Richard and Teo have a combined
age of 23. Richard is 2 years older than twice Teo's age. How old are Richard and
Teo?
Answer:
Richard= 16 years old
Teo= 7 years old
Step-by-step explanation:
Let Richard's and Teo's age be R and T years old respectively.
[tex]\textcolor{steelblue}{\text{Form 2 equations based on given information:}}[/tex]
R +T= 23 -----(1)
R= 2T +2 -----(2)
[tex]\textcolor{steelblue}{\text{Solving by substitution:}}[/tex]
Substitute (2) into (1):
(2T +2) +T= 23
3T +2= 23
3T= 23 -2
3T= 21
T= 21 ÷3
T= 7
Substitute T= 7 into (2):
R= 2(7) +2
R= 14 +2
R= 16
Thus, Richard is 16 years old and Teo is 7 years old.
find the e measure of the missing angle. round to 2 decimal places
Answer:
theta= 1.085
Step-by-step explanation:
please help i'm asking to help the second time hope someone sees this I'll give 10 points and brainliest I promise
2. i) 1/2 × x
x/2
ii) 1/5 × x
x/5
iii)1-(1/2+1/5)
1- (5/10+2/10)
10/10- 7/10
3/10
3/10×x
3x/10
3. i)15× $p
15p
ii) cost for 4 bananas= $g
cost for 1 banana = $g÷4
cost for 16 bananas = $g/4 ×16
=$g×4
=4g
iii)
Cost for an orange= $p
Cost for 5 oranges = 5×$p
Cost for 1 banana= $g÷4
Cost for 2 bananas = 2× ($g÷4)
Add both of the expressions to get the total cost for 2 bananas and 5 oranges.
(2×$g÷4)+(5×$p)
($g×2/4)+(5×$p)
2/4 can be simplified as 1/2
g×1/2+5p
(g/2)+5p
Hope this helps!
f(x) = 2 + 3x – 2x²
Determine a, b and c
Answer:
a = -2
b =3
c =2
Step-by-step explanation:
f(x) = 2 + 3x – 2x²
Rewrite in descending powers of x
-2x^2 +3x+2
The form is ax^2 +bx +c
a = -2
b =3
c =2
can someone help me with this math problem please
Answer: A (-7,-4)
Step-by-step explanation:
Took the same test
170 What is the mZBAC?
Answer:
m<BAC = 85°
Step-by-step explanation:
The measure of an inscribed angle is half the measure of its intercepted arc.
m<BAC = 170°/2
m<BAC = 85°
Find the roots of p(x)=x^3-10x^2+25
Answer:
{−1.47596288535, 1.73968983949, 9.73627304586}
Step-by-step explanation:
The roots of this cubic are real and irrational, as indicated by a graph of it. (Rational roots would be divisors of 25.) The same graphing calculator can provide an iterative solution to 12 significant figures. Here, we have used Newton's method iteration. The iteration function is ...
g(x) = x -p(x)/p'(x) . . . where p'(x) is the derivative: 3x^2-20x
We started each iteration using the value shown on the graph.
x ∈ {−1.47596288535, 1.73968983949, 9.73627304586}
__
The second attachment shows another calculator's solution. The values of x that are roots are the opposite of the constant in each binomial factor. You will notice this solution has a couple more significant figures than the one shown above.
__
Additional comment
There are several formulas for finding the "exact" roots of the cubic. Here's a trig approach that works reasonably well for cubics with 2 or 3 real roots.
We can define, for p(x) = x³ +ax² +bx +c, ...
s = -a/3 = 10/3
t = b -a²/3 = -100/3
r = a(2a² -9b)/27 +c = -10(200)/27 +25 = -1325/27
d = √(-4t/3) = √(400/9) = 20/3
h = 4r/d³ = -53/80
Now, the roots are ...
x = s +d·sin(arcsin(h)/3 +2nπ/3) . . . . for n=-1, 0, 1
= 10/3 +20/3·sin(arcsin(-53/80)/3 + n(2π/3)) . . . . . "exact solution"
= (10/3)(1 +2·sin(-13.8303° +n(120°))
= -1.47596..., or 1.73969..., or 9.73627...
please answer and use statement reason
Answer:
x = 15
Step-by-step explanation:
FD and AC are parallel because both are perpendicular to EB. Angle EDF and Angle DCA are congruent because they are corresponding angles. The measure of Angle DCA is also 3x because congruent angles have the same measure.
Now consider Triangle ACD. Because the sum of all three measures of the angles in a triangle add up to 180°.
x + 8x + 3x = 180°
12x = 180°
12x/12 = 180/12
x = 15
Cool scoops ice cream shop offers 60 different one topping sundaes. If there are different flavors of ice cream toppings and containers to hold the ice cream which of the following would not be the possible number of each category?
Answer:
I'm so confused. I don't get the question. I know the options are:
A) 3,4, 5
B) 2, 10, 4
C) 2, 10, 3
D) 2, 15, 2
but I don't understand the question. Could you maybe be a bit more specific?
What is the quotient of 2x3 + 3x2 + 53 - 4 divided by 22 +1 +1?
2x +1+
2- - 5
2 +2+1
22 +1+
2.1 - 1
2 +2+1
2x +1+
4z - 4
++1
21 +5+ 12 +1
2+2+1
Answer:
42
Step-by-step explanation: