Answer:
Vertex: (-4, -1)
Y-intercept: (0, 15)
Step-by-step explanation:
Given the quaratic function, h(x) = x² + 8x + 15:
In order to determine the vertex of the given function, we can use the formula, [tex][x = \frac{-b}{2a}, h(\frac{-b}{2a})][/tex].
Use the equation: [tex][x = \frac{-b}{2a}, h(\frac{-b}{2a})][/tex]In the quadratic function, h(x) = x² + 8x + 15, where:
a = 1, b = 8, and c = 15:
Substitute the given values for a and b into the equation to solve for the x-coordinate of the vertex.
[tex]x = \frac{-b}{2a}[/tex]
[tex]x = \frac{-8}{2(1)}[/tex]
x = -4
Subsitute the value of the x-coordinate into the given function to solve for the y-coordinate of the vertex:
h(x) = x² + 8x + 15
h(-4) = (-4)² + 8(-4) + 15
h(-4) = 16 - 32 + 15
h(-4) = -1
Therefore, the vertex of the given function is (-4, -1).
Solve for the Y-intercept:The y-intercept is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:
h(x) = x² + 8x + 15
h(0) = (0)² + 8(0) + 15
h(0) = 0 + 0 + 15
h(0) = 15
Therefore, the y-intercept of the quadratic function is (0, 15).
Solve please
May God bless you
Answer:
We will use a Pythagorean identity and alegbra to prove this.
sin^2 + cos^2 = 1, dividing by cos^2 gives
tan^2 + 1 = sec^2.
Now, breaking down the fraction into parts and simplifying gives:
(1-sin^4)/cos^4 = 1/cos^4 - sin^4/cos^4 = sec^4 - tan^4
Now use difference of squares factoring from alegbra.
= (sec^2 + tan^2)*(sec^2 - tan^2)
By rewriting our Pythagorean identity to
sec^2 - tan^2 = 1 and tan^2 = sec^2 - 1,
we can finish the problem.
= (sec^2 + tan^2) * 1 = sec^2 + tan^2
= sec^2 + (sec^2 - 1) = 2*sec^2 - 1.
solve for x someone pls help
Answer:
50+90+3x+1=180.....................
Can anyone help me if you get it right i'll give 30!
[tex]LHS \\ = 8 + 7 - {2}^{2} \\ = 8 + 7 - 4 \\ = 15 - 4 \\ = 11[/tex]
[tex]RHS \\ = {3}^{2} + 2 \\ = 9 + 2 \\ 11[/tex]
So, LHS = RHS
Answer:=
Hope it helps.
Do comment if you have any query.
Answer:
Below!
Step-by-step explanation:
Let's try the 'equal' sign for this equation.
8 + 7 - 2² = 3² + 2Remember, when it comes to simplifying, exponents come first. This means that we need to simplify the exponents first.
=> 8 + 7 - (2 x 2) = 9 + 2=> 15 - 4 = 9 + 2=> 11 = 11Since the LHS and the RHS are equal, the 'equal' sign will fit into the equation. Hence, this is proven as true. Let's try the 'not equal' sign.
=> 8 + 7 - 2² ≠ 3² + 2=> 15 - 4 ≠ 9 + 2=> 11 ≠ 11Now, this is a definite false. The 'not equal' sign is used when two values are not equal to each other, however, in this situation, 11 does equal 11. In between them is a 'not equal' sign. Hence, this is proven false.
We can conclude that the sign you are looking for is an 'equal' sign.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
Please help! Asap.
I suck at this.
I need to find y
Answer:
y° = 25°
Step-by-step explanation:
Given the diagram of a triangle, where it shows an exterior angle with a measure of ∠115°, and that an angle bisector bisects the triangle into two right triangles.
According to the Exterior Angle Theorem, the measure of the exterior angle is equal to the sum of the measures of two non-adjacent interior angles. In other words, the given exterior angle, m∠115° is equal to m∠y° + m∠90°.
Solve for y:Hence, we could simply solve for the value of y algebraically:
m∠y° + m∠90° = m∠115°
y° + 90° = 115°
Subtract 90° from both sides:
y° + 90° - 90° = 115° - 90°
y° = 25°
Double-check:Verify whether we have the correct value for y by solving for x:
Since the exterior angle, ∠115°, and ∠x° are supplements, then it means that:
m∠115° + m∠x° = 180°
115° + x° = 180°
Subtract 115° from both sides:
115°- 115° + x° = 180° - 115°
x = 65°
According to the Triangle Sum Theorem, the sum of the measures of the interior angles of a triangle is 180°.
Hence:
m∠x° + m∠y° + m∠90° = 180°
65° + 25° + 90° = 180°
180° = 180° (True statement).
Therefore, the correct answer is: y = 25°. This measure represents either one of the ∠y.
A woman can invest some money at 10% simple interest or at 8% compound interest. If
she invests $8000 for 3 years, find which is the more profitable investment and by how much.
Answer:
3/12 percent
Step-by-step explanation:
At a concert the ratio of adults to children is 4:5. There are 720 children in a concert how many adults are there?
BRAINLIEST QUEATION !!
Answer:
576 adults
Step-by-step explanation:
The 5 part of the ratio relates to 720 children, then
720 ÷ 5 = 144 ← value of 1 part of the ratio , then
4 parts = 4 × 144 = 576 ← number of adults
Answer:
576
Step-by-step explanation:
Adults : Children
4 : 5
x : 720
Let the number of adults be x.
Use cross multiplication.
[tex]4 : 5\\ x : 720\\[/tex]
[tex]4 *720=5*x[/tex]
[tex]\frac{4*720}{5} =\frac{5x}{5}[/tex]
4 × 144 = x
576 = x
Hope this helps you.
Let me know if you have any other questions :-)
a Rose Garden is formed by joining a rectangle and a semicircle the rectangle is 33 ft long and 26 ft wide. If the gardener wants to build a fence around the garden how many feet of fence are required?
Heyyyyyyyyyyyyyyyyyyyyyyyyyy!
Please help answer this! I will give you 10 pts! :DD ( please don't say non-sense I really need the answer! )
Answer:
angle a = angle bac = 90 degrees
angle b = angle abc
angle c = angle acb
Please any math experts help thanks you
Answer:
[tex]\frac{p^2-25}{p^2-10p+25}[/tex]
We can factorise the numerator with the difference of squares formula:[tex]x^2-y^2=(x+y)(x-y)[/tex]
-----------------------------
[tex]\frac{p^2-5^2}{p^2-10p+25} =\frac{(p+5)(p-5)}{p^2-10p+25}[/tex]
Now we can factorise the denominator:
[tex]\frac{(p+5)(p-5)}{p^2-10p+25} =\frac{(p+5)(p-5)}{(p-5)^2}[/tex]
[tex]\frac{(p+5)(p-5)}{(p-5)^2} =\frac{(p+5)(p-5)}{(p-5)(p-5)}[/tex]
Cancel out the common factor of (p-5):
[tex]\frac{(p+5)(p-5)}{(p-5)(p-5)} =\frac{(p+5)}{(p-5)}[/tex]
C is wrong help me please
Answer:
A
Step-by-step explanation:
x from 0 < x < 2 is wrong because < means goes to but does not equal that value, and [tex]\leq[/tex] means it INCLUDES that value. Because the function includes it (not an open hole), you should choose A.
Matthew poured 28 quart of lemonade from a pitcher into a smaller container. There was 58 quart left in the pitcher. What amount of lemonade did Matthew originally have in the pitcher?
Answer:
86 quarts
Step-by-step explanation:
If you took away 28 quarts and were left with 58 quarts then you add the two numbers to get 86 quarts which is what you started with.
Write the equation of the line that passes through the points (-9,9) and (8, -2).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answer:
y + 2 = (11/17)(x - 8)
Step-by-step explanation:
Working with the x- and y-components of the given points, we see that the x component increases by 17 and the y-component decreases by 11. Thus, the slope of this line is m = rise / run, or 11/17.
Start with the general point-slope form: y - k = m(x - h) and use the coordinates of the 2nd point for h and k in this equation:
y + 2 = (11/17)(x - 8)
This is based on the point (-2, 8)
and the slope 11/17.
This result is the desired equation in point-slope form. If we wish to reduce this, proceed as follows:
17(y + 2) = 11x - 88, or 17y + 34 = 11x - 88
This last result simplifies to 17y = 11x - 54, or y = (11/17)x -54/17 (which is in slope-intercept form).
If AD = 12 and BD = 14, what is CD?
Write your answer as a whole number or as a decimal rounded to the nearest hundredth.
a. 7
b. 10.29
C. 12.54
d. 16.33
Answer: D. 16.33
Step-by-step explanation:
whats the answer can someone answer please
Answer:
21. 2x + 28
22. 18a - 17b
23. He flipped the numerator and denominator, 6.4 with 7.2 and he added the exponents instead of subtracting.
24. 8.8888888888889 × 10^{0}
Step-by-step explanation:
100 POINT QUESTION!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Solve 2x2 – 6x + 10 = 0 by completing the square.
Question 10 options:
A)
x = 3∕2 + 1∕2 i, x = 3∕2 – 1∕2i
B)
x = 3 + i, x = 3 – i
C)
x = 3∕2 + i , x = 3∕2 – i
D)
x = 3 + i, x = 3 – i
Answer:
Ok I don't know waht you mean but the answer is
Step-by-step explanation:
Answer:
x=3/2±(√11)2
x=1.5+1.65831i
x=1.5−1.65831i
Find the Solution for
2x^22−6x+10=0
using the Quadratic Formula where
a = 2, b = -6, and c = 10
x=(−b±√(b^2−4ac))/2a
x=(−(−6)±√((−6)2−4(2)(10)))2(2)
x=(6±√(36−80))/4
x=(6±√−44)/4
The discriminant b^2−4ac<0
so, there are two complex roots.
Simplify the Radical:
x=(6±2√11 i)/4
x=6/4±(2√11 i)4
Simplify fractions and/or signs:
x=3/2±(√11)2
which becomes
x=1.5+1.65831i
x=1.5−1.65831i
increase R700 in the ratio 3:2
Answer:
3 over5 multiplied by 320 equals 192
Solve for x. Round to the nearest tenth.
Answer:
24.8
Step-by-step explanation:
An employee worked 36 hours last week. This week, she worked 48 hours. Find the percent increase. Round to the nearest percent. O 25% increase 0 33% increase O 12% increase O 75% increase
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today!
We can solve this problem in two steps, one is Comprehending and another is Solving. I'll start off with Comprehending.
Comprehending
We can start off by looking at the problem, it wants us to find the percentage increase from 36 to 48. We can then find difference between 48 and 36; that would be 12.
Now that we know the increase from 36 to 48 is 12. We need to find how much percent 12 is of 36.
Now that we know what we have to do, we can start solving.
Solving
We can solve the problem by setting up and equation, but we can also just use our logic in finding it out.
Since we know that we need to find how much 12 is of 36, we can just solve for that and we will get our answer.
We can do that with one step.
[tex]\frac{12}{36}=0.33[/tex]
Since it is a percent, we can multiply 0.33 by 100 and we get our answer of 33%
. At a certain airport, 75% of the flights arrive on time. A sample of 10 flights is studied. a. Find the probability that all 10 of the flights were on time.
Answer:
0.5256
Step-by-step explanation:
X ~ B(10,0.75)
q = 1 - 0.75 = 0.25
use the given circle. Find the length s to the nearest tenth A. 33.5 cm B. 8.4 cm C. 16.8 cm D. 5.3 cm
Answer:
16.8
Step-by-step explanation:
s = ∅ × r
= 2π/3 × 8
= 16/3 * π
= 16.75516
= 16.8
Answer:
C.) 16.8 is your answer
Step-by-step explanation:
Find the volume of this cylinder.
Give your answer to 1 decimal place.
11 cm
io
14 cm
Answer:
1330.5 cm³
Step-by-step explanation:
The formula for the volume of a cylinder is ...
V = πr²h . . . . . for radius r and height h
The radius of the given cylinder is 1/2(11 cm) = 5.5 cm. Filling in the formula values, we have ...
V = π(5.5 cm)²(14 cm) = 423.5π cm³ ≈ 1330.5 cm³
The volume of the cylinder is about 1330.5 cm³.
Answer:
1330.5
Step-by-step explanation:
Radius is half of diameter (11), so 5.5 was the other number I plugged in.
toby used 4 inches of tape to wrap a gift how much tape will he need to wrap 5 more of the same gift?
Answer:
20
Step-by-step explanation:
4*5 = 20%
4. If the paint costs $30 per gallon and you need to spend $60 on supplies, and you can
save $45 per month, in how many months will you have enough money for the project?
Step-by-step explanation:
if I understand this right, then you need paint and additional supplies.
but I don't see any information indicating how many gallons of paint I will need.
so, I can go only with the 1 gallon specified.
so,
1×30 + 60 = $90
we can save $45 per month.
then we need
90 / 45 = 2
months to have enough money.
please update the numbers to how many gallons you really need, and then take that result and divide it by the 45 savings per month.
Please Help, This is Due in 4 Hours.
At the deli counter, Dalton bought 0.38 of a pound of roast beef and 0.7 of a pound of ham. Compare the amounts of roast beef and ham that Dalton bought.
Record the comparison using the <, >, or = symbol and explain how you know.
Answer:
0.38 < 0.70
Step-by-step explanation:
What is the solution to -4(8- 3x) >6x - 8?
A)x>-4/3
B)x<-4/3
C)x>4
D)x<4
I think you got your answer
The initial amount of money that is deposited into an account or that is borrowed is called what
Answer:
Step-by-step explanation:
Answer: In the context of borrowing, principal is the initial size of a loan or a bond (the amount the bond issuer must repay). In the context of investing, principal is the original sum committed to the purchase of assets—independent of any earnings or interest.
The equation of two functions f(x) And g(x) are typed into a graphing calculator to see both graphs on the same coordinate plane. The graphs shown below represents the two functions.
Which are approximate solutions of the equation f(x)=g(x) Select all that apply.
A. 6
B. 0.7
C. 0
D. 4.6
Answer:
The solution of the equation f(x) = g(x) is the set of all x for which the graphs of f and g intersect. The solution of the inequality f(x) < g(x) is the set of all x for which the graph of f lies below the graph of g
8 m good wire how long is the wire in millimeters
Answer:
Converting m to mm
=> 1 m = 1000 mm
=> 8 m = 8000 mm
Therefore,
The wire will be 8000 mm long.
Hope it helps you...
Please mark as brainlliest!!!
Evaluate.
(1/5) −1 ⋅ 4^0
0
1
5
20
Answer:
-1519 4/5
-1519.8
-7599/5
Step-by-step explanation: