ANSWER
[tex]h = - 4,k = - 6[/tex]
Minimum value: y=-6
Occurs at: x=-4
EXPLANATION
Given
[tex]f(x) = {x}^{2} + 8x + 10[/tex]
We need to write the equivalent of this function in vertex form:
[tex]f(x) = ({x - h)}^{2} + k[/tex]
where (h,k) is the vertex.
We must complete the square to get the function to this form.
We add and subtract the square of half the coefficient of x.
[tex]f(x) = {x}^{2} + 8x +( \frac{8}{2}) ^{2} - ( \frac{8}{2}) ^{2} + 10[/tex]
This gives us;
[tex]f(x) = {x}^{2} + 8x +16- 16 + 10[/tex]
The first three terms form a perfect square quadratic trinomial.
[tex]f(x) =( x + 4) ^{2} - 6[/tex]
or
[tex]f(x) =( x - - 4) ^{2} - 6[/tex]
Therefore we compare to
[tex]f(x) = ({x - h)}^{2} + k[/tex]
h=-4 and k=-6
The minimum value of the function is
[tex]y = - 6[/tex]
and this occurs at;
[tex]x = - 4[/tex]
please find the unknown with all steps
Answer:
see explanation
Step-by-step explanation:
Since AC = BC then ΔABC is isosceles with base angles
∠BAC =∠ABC, thus
3x + x = 70
4x = 70 ( divide both sides by 4 )
x = 17.5
----------------------------------------------------
∠ADC is an external angle of ΔABD and the external angle is equal to the 2 opposite interior angles, hence
y = 70 + x = 70 + 17.5 = 87.5
114.4 is 65% of what amount
65% × 114.4 =
(65 ÷ 100) × 114.4 =
(65 × 114.4) ÷ 100 =
7,436 ÷ 100 =
74.36
and how you can check yourself kinda do the opposite of what you did to get the answer
74.36 ÷ 114.4 =
0.65 =
0.65 × 100/100 =
0.65 × 100% =
(0.65 × 100)% =
65%
In a class of 32 students, 25% of the students wear glasses. How many students wear glasses?
32×.25=8
so 8 students wear glasses
(i really need help with this , and you can get branliest
If s = unit and A = 12s2, what is the value of A, in square units? square unit(s). (Input whole number only.)
The equation below shows the total volume (V), in cubic units, of 5 identical boxes with each side equal to s units:
V = 5s3
If s = 1.4 units, what is the value of V?
13.72 cubic units
19.21 cubic units
21 cubic units
25 cubic units
Answer:
13.72 cubic units
Step-by-step explanation:
The equation below shows the total volume (V), in cubic units, of 5 identical boxes with each side equal to s units: V = 5s3
If s = 1.4 units, what is the value of V?
Substitute s = 1.4 into V = 5s³ = 5(1.4)³ = 13.72 cubic units.
What is the distance between the points (-7, 3) and (4, -5) in the coordinate plane?
A. Square root of 125
B. Square root of 57
C. Square root of 13
D. Square root of 185
the correct answer is d
Please help me and please don't answer if you're not 100% sure!
The answer choices are
A. 1120 people
B. 280 people
C. 100 people
D. 112 people
Answer:a
Step-by-step explanation:
it just looks like it
An equation is shown below. 12 - 9 + c = 12 What value of c makes the equation true?
The correct answer is C = 9.
Step by step:
Subtract 12 - 9 = 3
3 + 9 = 12.
It’s that simple. Hold this helps!
The value of c is 9 makes the equation true.
It is given that the equation 12 - 9 + c =12.
It is required to find the value of c that makes the equation true.
What is a linear equation?It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.
If in the linear equation one variable is present then the equation is known as the linear equation in one variable.
We have a linear equation in one variable:
12 - 9 + c = 12
-9 + c =0 (subtract 12 on both sides)
c = 9 ( add 9 on both sides)
Thus, the value of c is 9 makes the equation true.
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HELP FAST PLEASE 3 QUESTIONS (30 POINTS)
Answer:
[tex]d\geq 5\\\\w<7\\\\a\leq 4[/tex]
Step-by-step explanation:
For each you have to look at three things - the direction of the arrow, if the circle is filled in, and the number the point is located on.
If the arrow is pointed right and the numbers are increasing, you use the greater than sign (>).
If the arrow is pointed left and the numbers are decreasing, you use the less than sign (<).
If the circle is filled in, it means you use the greater than or equal to (≥) less than or equal to signs (≤).
For the first inequality, the arrow is pointing right, the circle is filled in, and the point is on five so the inequality is [tex]d\geq 5[/tex].
For the second inequality, the arrow is pointing left, the circle is not filled in, and the point is on seven so the inequality is [tex]w<7[/tex].
For the third inequality, the arrow is pointing left, the circle is filled in, and the point is on four so the inequality is [tex]a\leq 4[/tex].
25 points for answer!! Consider the circle graph below of the type of flowers planted in a garden. If 57 carnations are in the garden, how many roses are in the garden?
The ratio of carnations to roses in the garden is 19:31.
Since there are 57 carnations in the garden, there are 57 * 31/19 = 93 roses in the garden.
Answer:
The answer is 93
Step-by-step explanation:
Please help me out on this question I been stuck on it
Answer:
B, C
Step-by-step explanation:
[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{3^2 - 4(1)(-5)}}{2(1)} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{9 + 20}}{2} [/tex]
[tex] x = \dfrac{-3 \pm \sqrt{29}}{2} [/tex]
Answer: B, C
Find the distance d. (2,4) and (7,2)
Answer:
The answer is d = [tex]\sqrt{29}[/tex]
Step-by-step explanation:
To find the distance, use the distance formula.
d = [tex]\sqrt{(x1 - x1)^{2} + (y1 - y2)^{2} }[/tex]
d = [tex]\sqrt{(7 - 2)^{2} + (2 - 4)^{2} }[/tex]
d = [tex]\sqrt{(5)^{2} + (-2)^{2} }[/tex]
d = [tex]\sqrt{25 + 4 }[/tex]
d = [tex]\sqrt{29}[/tex]
what is equivalent to the expression below?
(-6) to the -5 power
a. 6 to the 5 power
b. (1/6) to the 5 power
c. (-1/6) to the 5 power
d. 30
Solve H^2-2h- 2=0 and round answer to the nearest hundredth
Answer:
h1=2.75 and h2=-0,75
Step-by-step explanation:
You need to use the cuadratic formula for this case (see apex)
Best regards
Which expression shows the total price including tax?
Answer:
1.04p
Step-by-step explanation:
You will pay the whole price of the item which is p or 1p. Then you will add 4% tax or 0.04p. So the total will be 1p + 0.04p = 1.04p.
Two values of x that are roots of xsquared+2x-6=0
The two values of x are
1.65 , -3.65
Answer:
Two values of x that are :
[tex]x=-\sqrt{7}-1[/tex]
[tex]x=\sqrt{7}-1[/tex]
Step-by-step explanation:
Given= [tex]x^2+2x-6=0[/tex]
To find = Two values of x
Solution :
[tex]x^2+2x-6=0[/tex]
Adding and subtracting 1 in the equation :
[tex]x^2+2x+1-1-6=0[/tex]
[tex](x^2+2\times x\times 1+1^2)-1-6=0[/tex]
[tex](x+1)^2-7=0[/tex]
[tex](x+1)^2=7[/tex]
[tex](x+1)=\pm \sqrt{7}[/tex]
Two values of x that are :
[tex]x=-\sqrt{7}-1[/tex]
[tex]x=\sqrt{7}-1[/tex]
Evaluate (–1)8 + (–1)7 + –16 + –14 – (–1)2. A. 5 B. –3 C. –4 D. –23
Answer:
= -43
Step-by-step explanation:
Evaluating the expression;
(–1)8 + (–1)7 + –16 + –14 – (–1)2
We can use Bodmas
We remove the brackets first
(–1)8 + (–1)7 + –16 + –14 – (–1)2
We get
-8 + - 7 + -16 + -14 - -2
but; - × + = - and - × - = +
Thus;
-8 - 7 - 16 - 14 + 2
= -8 -7 - 16 - 12
= -43
WILL GIVE BRAINLIEST
What is the period of a wave if the wavelength is 100m and the speed of 200m/s
A. 100s
B. 200,000s
C. 0.5s
D. 2s
Answer:
C. O.5s
Step-by-step explanation:
If the wave length is 100m and it goes at a speed of 200m/s then it will only take 0.5 seconds because 100 is half of the speed of 200
Answer:
C
Step-by-step explanation:
The formula we use to solve this would be: [tex]T=\frac{\lambda}{v}[/tex]
Where
T is the period in seconds
[tex]\lambda[/tex] is the wavelength in m, and
v is the speed of the wave in m/s
We have [tex]\lambda[/tex] equal to 100, and v = 200 m/s. Plugging these into the equation, we get the period:
[tex]T=\frac{\lambda}{v}\\T=\frac{100}{200}\\T=0.5[/tex]
C is the right answer.
Please help lol ............
Answer:
1 X 16 and 8 X2
Step-by-step explanation:
1 X 16 = 16
2 X 8 = 16
3 X nothing = 16
4 X 4 = 16
5 X nothing = 16
6 X nothing = 16
7 X nothing = 16
8 X 2 = 16
etc.
[tex]\bold{Hey\ there!} \\ \\ \bold{Choose\ all\ of\ the\ correct\ factors\ of\ 16}[/tex]
[tex]\bold{It \underline{CAN'T} \ be\downarrow} \\ \bullet\ \bold{3\times5\ because\ it\ equals\ to\ 15} \\\bullet\ \bold{4\times3\ because\ it \ equals\ to\ 12} \\ \\ \\ \\ \bold{It\ \underline{CAN} \ be\downarrow} \\ \bullet \ \bold{1\times16\ because\ it\ equals\ to \ 16} \\ \bullet \ \bold{8\times2\ because\ it\ equals\ to\ 16} \\ \\ \\ \boxed{\boxed{\bold{Answer(s):1\times16\ \& \ 8\times2}}}\checkmark[/tex]
[tex]\bold{Good\ luck\ on\ your\ assignment\ \& \ enjoy\ your \ day!} \\ \\ \frak{LoveYourselfFirst:)}[/tex]
Simplify. Rewrite the expression in the form 10^n
10^5 x 10 = ?
10 to the power of 6
10^5 × 10 = 10^6
--------------------------
What is the end point of a ray?
Answer:
A ray is a part of a line that has one endpoint and goes on infinitely in only one direction you can't measure the length of a ray ..hope this helps
Step-by-step explanation:
The endpoint of a ray is the starting point from which the ray extends indefinitely in one direction. It's different from a line, which has no endpoint as it extends indefinitely in both directions.
Explanation:In mathematics, specifically in geometry, a ray is a part of a line that starts at a particular point, known as the initial point, origin, or endpoint, and extends indefinitely in one direction. This is different from a line, which extends in both directions. When you draw a ray, you put an arrow on one end to show that it continues without end in that direction. The
end point of a ray is essentially the starting point from which the ray extends. For example, if you have a ray AB, point A is the endpoint and the ray extends towards point B but beyond it indefinitely. Thus, a ray has only one endpoint, not two.
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Gina is the chairperson of a group. Last week, she set up 22 folding chairs for the group meeting. This week, some of the members could not attend the meeting, so she set up only 15 chairs. How many chairs did Gina set up in the past two weeks?
Answer:
37 Chairs
Step-by-step explanation:
Last week she set up 22 chairs.
This week, that amount was 15
Add those together, and you have 37.
Gina set up a total of 37 chairs in the past two weeks.
Explanation:To find the total number of chairs Gina set up in the past two weeks, we need to add the number of chairs she set up last week to the number of chairs she set up this week.
Last week, Gina set up 22 chairs for the group meeting.This week, she set up 15 chairs for the meeting.To find the total number of chairs she set up in the past two weeks, we add the number of chairs from last week and this week: 22 + 15 = 37.if f(x) = (1/7), what is F(3)
A.343
B.1/49
C.49
D.1/343
Answer:
Step-by-step explanation:
None of them
Perhaps the original question was f(x) = (1/7)^x or f(x)=(1/7)^-x
The first one would give A as an answer
The second one would give D as an answer.
A similar answer could be worked out for B and C
In any event correct your question, please
Answer:
49
Step-by-step explanation:
The zeros of a quadratic function are -8 and 5. Write the quadratic function in Standard Form.
Answer:
y = x² + 3x - 40
Step-by-step explanation:
Given the zeros are x = - 8 and x = 5, then the factors are
(x + 8) and (x - 5) and
y = (x + 8)(x - 5) ← expand factors
y = x² - 5x + 8x - 40, hence
y = x² + 3x - 40 ← in standard form
Timothy drove his race car 10% farther using the gasoline from Smith's Station compared to gasoline from Jack's Station. After Timothy filled his gas tank at Jack's Station, he traveled 480 miles. How far did he travel on a tank of gas from Smith's Station?
Answer:
528
Step-by-step explanation:
x = 480
1.1 x = 480 * 1.1
480 + 48 = 528
Timothy traveled 528 miles using the gasoline from Smith's Station, which is 10% farther than the 480 miles he traveled with gasoline from Jack's Station.
Explanation:To calculate how far Timothy traveled using the gasoline from Smith's Station, we need to determine what 10% more than the 480 miles he traveled using gasoline from Jack's Station is. First, let's find 10% of 480 miles:
10% of 480 miles = 0.10 × 480 miles = 48 miles.Now, let's add this additional distance to the original 480 miles to find the total distance traveled with gas from Smith's Station:
480 miles + 48 miles = 528 miles.Therefore, Timothy traveled 528 miles on a tank of gas from Smith's Station.
I need help please and thank you.
Answer:
0
Step-by-step explanation:
The formula gives you a relation between S and n. For every n, you can perform the calculation and obtain an S.
So, for n=0 we get 0/2 (0+1) which equals 0. So (0,0) is an (n,S) pair.
The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. What are the restrictions on the domain of ? u(x) 0 and v(x) 2 x 0 and x cannot be any value for which u(x) 2 x 2 and x cannot be any value for which v(x) 0 u(x) 2 and v(x) 0
Answer:
Third option
x ≠2 and x cannot be any value for which v(x) = 0
Step-by-step explanation:
In this problem we are asked to find the domain of the function
[tex](UoV)(x)[/tex]
We know that [tex](UoV)(x) = U(V(x))[/tex].
We know that:
Domain of U(x) is all real numbers except x = 0
Domain of V(x) is all real numbers except x = 2.
Then the domain of the composite function U(V (x)) is:
all real numbers except x = 2. (since x = 2 does not belong to the domain of V(x) and all values of x for which V(x) = 0 (since x = 0 does not belong to the domain of U(x))
Finally the domain of [tex](UoV)(x)[/tex]) is:
[tex]x \neq 2[/tex] and [tex]V(x) \neq 0[/tex]
Answer:
The answer is C on edge.
Your food bill was $80 at a restaurant.
You left a tip of $16.
What percentage of the food bill did you leave for the tip?
Answer:
20 percent tip
Step-by-step explanation:
Answer: 20% tip (i got the answer for that one right :)! )
to the right of the garden draw a different shape that has the same perimeter as part A of elton's garden what is the area of your shape?
Answer:
wats part A?
Step-by-step explanation:
Give me the data:)
perform the indicated operation (3x^3-2x^2+4x-3)(x+2)
Answer:
3x^{4} + 4x³ + 5x - 6
Step-by-step explanation:
Given in the question is an expression
(3x³ - 2x² + 4x - 3)(x + 2)
Apply distributive law
(3x³ - 2x² + 4x - 3)(x) + (2)(3x³ - 2x² + 4x - 3)
3[tex]x^{4}[/tex] - 2x³ + 4x² -3x + 6x³ - 4x² + 8x - 6
Rearrange the like terms
3[tex]x^{4}[/tex] + x³(-2+6) +x²(4-4) +x(-3+8) - 6
3[tex]x^{4}[/tex] + 4x³ + 5x - 6
After performing indicated operation the result is
[tex]3x^{4}+4x^{3}+5x-6[/tex]
An architect built a scale model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sports stadium is 180 feet.
What is the height of the scale model in inches?
A] 3in
B} 105 in
C[ 12in
D{ 60in
PLEASE HELP‼️ AND SHOW WORK‼️
A. 12 in
We know that the sports stadium is 180 ft tall and that in the scale model there is 2 in for every 30 ft. If we divide 180 by 30 we get 6. There is 2 in for every 30 ft, so the answer would be 6 x 2 or 12 in.
Unit rate is the quantity of an amount of something at a rate of one of another quantity.
If 2 inches = 30 feet and the height of the sports stadium is 180 feet.
The height of the sports stadium in scale model in inches is 12 inches.
Option C is the correct answer.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
In 5 minutes a machine can cut 10 potato
In 1 minute a machine can cut 2 potato.
We have,
30 feet = 2 inches
Divide both sides by 30.
1 feet = 2/30 inches
Now,
1 feet = 2/30 inches
Multiply 180 on both sides.
180 feet = 180 x 2/30 inches
180 feet = 6 x 2 inches
180 feet = 12 inches
Thus,
If 2 inches = 30 feet and the height of the sports stadium is 180 feet.
The height of the sports stadium in scale model in inches is 12 inches.
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