Express your answer as a polynomial in standard form.
f(x) = 2x + 7
g(x) = 2x2 - 6x +5
Find: g(f(x))
Answer:
[tex]16x^{2}+44x+61[/tex]
Step-by-step explanation:
g(f(x)) means that you substitute f(x) as x in g(x)
[tex]2(2x+7)^{2}-(6)(2x+7)+5[/tex]
expand
(2x+7)(2x+7)=
4x^2+28x+49
(2)(2x+7)(2x+7)=16x^2+56x+98
16x^2+56x+98-12x-42+5
16x^2+44x+61
Please help I’ll give brainliest
Answer:
1000 cubic metre
Step-by-step explanation:
hopes it help
Answer:
solution,
length=10 cm
volume=?
now,
volume of cube=l×l×l
=10×10×10
therefore,the answer is 1000 cubic centimeter
Please explain the answer and show your work
Answer:
6
Step-by-step explanation:
Arc length ACB = 6 pi
The arc length = fraction of a circle times the circumference
6 pi = 180/360 * 2 * pi *r
6 pi = 1/2 * 2 * pi*r
6 pi = pi r
The radius is 6
Write "five thousand six hundred eighty-five and twelve hundredths" in expanded form
Answer:
56851200
Step-by-step explanation:
The expanded form of the number is 5000 + 600+ 80 + 5 + 0.1 + 0.02 and the number is 5685.12
What is number?A number is a mathematical entity that can be used to count, measure, or name things. For an example, 1, 2, 56 etc. are the numbers.
It is given that:
The word expression:
"five thousand six hundred eighty-five and twelve hundredths"
The number would be:
= 5685.12
In the expanded form the number can be written as:
The expanding form can be used to indicate the value of each digit in a number in arithmetic.
Numbers that are expressed as the sum of each digit multiplied by its place value are known as expanded numbers.
Expanded Form:
5685.12 = 5000 + 600+ 80 + 5 + 0.1 + 0.02
Thus, the expanded form of the number is 5000 + 600+ 80 + 5 + 0.1 + 0.02 and the number is 5685.12
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Classify the following triangle. Check all that apply.
Answer:
Option(B) & Option(C)
Step-by-step explanation:
Right angled triangle (One angle is 90 degree)
Isosceles(Two sides of triangle are equal)
Kharter goes to a gas station near his house where it costs $2.95 per gallon. Kharter’s car hold’s 13.2 gallons. The gas station near Devin’s house sells gas for $3.03 per gallon and his car holds 11.8 gallons
A John and Kate share £180 in the ratio
2:3. Work out how much money each person
receives.
Answer:
John's share = £72
Kate's share = £108
Step-by-step explanation:
Given:-
Share amount of John and Kate = £180
Share amount given in ratio = 2:3
Find:-
Work out how much money each person
receives.
Solution:-
Ratio:
John Kate
2 : 3
Add the ratio:
2 + 3 = 5
Divide the total amount from the added ratio:
180 / 5 = 36
Each part of the ratio is 36.
John's amount:
{multiply 36 with 2}
36 × 2 = £72
Kate's amount:
{multiply 36 with 3}
36 × 3 = £108
(CHECK:- £108 + £72 = £180 )
Given two similar cylinders with a height ratio of 2:3 what is the ratio of their volumes?
Answer:
8 : 27
Step-by-step explanation:
The ratio of the volumes is the ratio of the scale factor cubed
2^3 : 3^3
8 : 27
Answer:
8 : 27
Step-by-step explanation:
Given 2 similar cylinders with height ratio = a : b , then
ratio of volumes = a³ : b³
Here height ratio = 2 : 3
ratio of volumes = 2³ : 3³ = 8 : 27
Chef Antonio works at a Latin restaurant and doing a great job. During his yearly evaluation, the owner increased his salary from $42,500 to $46,000. What is the percent of increase, to the nearest whole percent, in Chef Antonio's salary?
Answer:
8%
Step-by-step explanation:
To find the percent change, we first have to find the amount changed, which is (46000-42500) = 3500. Then, we find what percentage that is of the original amount. Remember that when calculating percentage change, it's important to calculate change with respect to the initial value.
To find the percentage, we can divide 3500 by 42500, and multiply that by 100, resulting in 8 being our nearest whole percent
I need help but they are getting confused with the z as a 2 please don’t get confused the z is a z
Step-by-step explanation:
everything can be found in the picture
Answer:
w = - (7/2) z
Step-by-step explanation:
5w + 9z = 2z + 3w
Subtract 3w from both sides
2w + 9z = 2z
Subtract 9z from both sides
2w = -7z
Divide both sides by 2
w = - (7/2) z
In the afternoon, the person (who is 1.8 m tall) casts a shadow that is 10 m. The distance along the ground from the person (H) to the tree (G) is 24 m, and the distance from the tree (G) to the building (F) is 150 m. Calculate the height of the tree and the building. Round answers to the nearest tenth of a meter and show all your work.
Answer:
The height of the tree is 6.12 meters and the height of the building is 33.12 meters.
Step-by-step explanation:
Since the person is 1.8 meters tall, HC = 1.8
And since their shadow is 10 meters long, HD = 10.
We are also given that GH is 24 meters and that FG is 150 meters.
Height of the Tree:
The height of the tree is given by GB.
Again, since m∠BGD = m∠CHD = 90°, ∠BGD ≅ ∠CHD.
Likewise, ∠D ≅ ∠D. So, by AA-Similarity:
[tex]\displaystyle \Delta BGD\sim \Delta CHD[/tex]
Corresponding parts of similar triangles are in proportion. Therefore:
[tex]\displaystyle \frac{GB}{GD}=\frac{HC}{HD}[/tex]
Note that:
[tex]GD=GH+HD[/tex]
Find GD:
[tex]GD=(24)+(10)=34[/tex]
Substitute the known values into the proportion:
[tex]\displaystyle \frac{GB}{34}=\frac{1.8}{10}[/tex]
Cross-multiply:
[tex]10GB=61.2[/tex]
Therefore:
[tex]GB=6.12\text{ meters}[/tex]
The height of the tree is 6.12 meters.
Height of the Building:
The height of the building is given by FA.
Since m∠AFD = m∠CHD = 90°, ∠AFD ≅ ∠CHD.
∠D ≅ ∠D. So, by AA-Similarity:
[tex]\Delta AFD\sim \Delta CHD[/tex]
Corresponding parts of similar triangles are in proportion. Therefore:
[tex]\displaystyle \frac{FA}{FD}=\frac{HC}{HD}[/tex]
Note that:
[tex]FD=FG+GH+HD[/tex]
Find FD:
[tex]FD=(150)+(24)+(10)=184[/tex]
Substitute the known values into the proportion:
[tex]\displaystyle \frac{FA}{184}=\frac{1.8}{10}[/tex]
Cross-multiply:
[tex]10FA=331.2[/tex]
Therefore:
[tex]FA=33.12\text{ meters}[/tex]
The height of the building is 33.12 meters.
2. Solve by finding square roots. 9x^2 = 25
A. 5/3
B. (-5/-3),(5/3)
C. 2/3
D. (-2/-3),(2/3)
John has 50 missing assignments in his history and science class. He only has 15 days to turn everything in. How many assignments will John have to do everyday?
Answer:
3.3333 (repeating)
Step-by-step explanation:
He has 50 missing assignments and 15 days to do them.
So you do 50 missing assignments divided by 15 days, to see how many assignments a day he would have to do.
50 / 15 = 3.33 (repeating)
Answer:
3.333333333333333
Step-by-step explanation:
You will have to divide 15 by 50 to get the answer. That will give you 3.333333333333333 which is your answer.
How to sketch the graph?
Step-by-step explanation:
sketch the mother function of |x| then go 3 steps to the right horizontally and that's it
Charlie has $775 saved up.
He plans on spending about
$50 a week on food. Write
an equation to represent y.
the amount of money he has
left after x weeks?
Answer:
y = -50x +775
Step-by-step explanation:
The second one: Find the nearest 10th.
Answer:
∅ = 44.9º
Step-by-step explanation:
sin = opp/hyp
Assuming ∅ is the top angle
∅ = arcsin(353/500)
use calculator
∅ = 44.910389254710144
∅ = 44.9º
Add [25+(-13)+(-17) using associative property
Answer:
[25+(-13)+(-17)
25-13-17
-5
3g - 4 = 17
show ur work
Answer:
g = 7
Step-by-step explanation:
3g - 4 = 17
+ 4 + 4
3g = 21
÷3 ÷3
g = 7
Answer:
g=7
Step-by-step explanation:
First add 17+4=21 to find out how much 3g needs to equal. 3g needs to get to 21. Next, do 21/3=7. g=7
Hope this helps!
NEED AN ANSWER ASAP
a linear piecewise function is represented by the graph. use the graph to evaluate the function.
when x = -5, y = ___
a) -5
b) 3
c) 5
when x = –1, y = ___
a) -2
b) 1
c) 3
When x = 3, y = ___
a) -4
b) 1
c) 3
Step-by-step explanation:
When X is - 5 then y is 3
When X is-1 then y is - 2
When X is 3 then y is -4
From the graph we get, when x is - 5 then y is 3, when x is -1 then y is - 2, and when x is 3 then y is -4.
What is a point?A point is a dot in space used to indicate an exact location in space.
Consider the first line, which has constant y values. its x value ranges from -1 to negative infinity.
The second line is starts from (-1,-2) point and tend towards positive infinity but its y values and x values are varying.
Hence, when x = -5 y is 3 and at x = -1 the y values is -2. Similarly, when x = 3 then y = -4.
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If f(x) = 5x, what is rx)?
Answer:
18x
Step-by-step explanation:
If f(x) is 5x which can also be expressed 5(x)
Then r(x) is a number then x
f is the fifth digit in the alphabet
So fx is 5x
r is the 18 th letter so
18x
A circular garden is surrounded by a rectangular grassy area. The garden takes up nearly half the grassy area. The base of the grassy area is 6 yards by 3 yards.
A rectangle with a length of 6 yards and width of 3 yards. A circle inside of the rectangle has a diameter of 3 yards.
Use the base of the grassy area to find the approximate area of the circular garden. Use Pi = 3.14. If necessary, round to the nearest tenth.?
Answer:
The area of the circular garden is approximately 7.1 square yards
Step-by-step explanation:
The given parameters are;
The area surrounding the circular garden = A rectangular grassy area
The area of the circular garden ≈ (1/2) × The base of the grassy rectangular area
The dimensions of the base of the rectangular grassy area = 6 yards by 3 yards
The diameter of the circle, D = 3 yards
The area of the rectangular grassy area = 6 yards × 3 yards = 18 yards²
∴ The approximate area of the circular garden = (1/2) × 18 yards² = 9 yards²
The area of the circular garden, A = π·D²/4
∴ A = 3.14 × (3 yards)²/4 = 7.065
The area of the circular garden, A ≈ 7.1 yd².
Help me please I need help .
Answer:
cos A =1.0
sin B=0.02
tan C=9.1
I need help here please
Answer:
Simultaneous equations
Step-by-step explanation:
4a + 7m = 17.75
2a + 5m = 10.75
Double the 2nd equation and then subtract the two equations to cancel the 4a out
Work with the 'm' terms and find the value of m
After finding the value of 'm', substitute it into one of the original equations (the ones given in the question) and solve to find the value of 'a'
Hope this helped
Write a quadratic equation that has the solutions: 4 and -7
Answer:
y = ( x-4)(x+7)
Step-by-step explanation:
When we know the zeros of the equation, we can write the equation in the form
y= a(x-z1) (x-z2) where a is a constant and z1 and z2 are the zeros (solutions)
y = a( x-4)(x--7)
y =a( x-4)(x+7)
Since its says write an equation, we can pick a and I will let a=1
y = ( x-4)(x+7)
The density of a certain material is such that it weighs 4 kilograms per cubic foot of
volume. Express this density in ounces per cubic meter. Round your answer to the
nearest whole number.
Answer:
Step-by-step explanation:
4986 ounces/m³
Step-by-step explanation:
1 kilogram = 35.274 ounces
1 cubic foot = 0.0283 cubic metre
We are converting kg/ft³ to ounces/m³
Hence:
4kg/ft³ × 35.274 ounces/ 1 kg × 1 ft³/0.0283m³
= 4985.7243816 ounces/m³
Approximately to the nearest whole number = 4986 ounces/m³
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The density of the material is approximately 123 ounces per cubic meter.
Density [tex](\(D\))[/tex] is defined as mass [tex](\(m\))[/tex] per unit volume [tex](\(V\))[/tex], and it is calculated using the formula:
[tex]\[ D = \frac{m}{V} \][/tex]
In this case, the density is given in kilograms per cubic foot. To convert this to ounces per cubic meter, we need to perform the following steps:
Step 1: Convert kilograms to ounces:
1 kilogram = 35.27396 ounces
Step 2: Convert cubic feet to cubic meters:
1 cubic foot = 0.0283168 cubic meters
Now, let's substitute the given values and perform the conversion:[tex]\[ \text{Density in ounces per cubic meter} = \frac{4 \, \text{kg} \times 35.27396 \, \text{ounces/kg}}{1 \, \text{cubic foot} \times 0.0283168 \, \text{cubic meters/cubic foot}} \][/tex]
Solving this equation gives us the density in ounces per cubic meter:
[tex]\[ \text{Density} \approx 123 \, \text{ounces/m}^3 \][/tex]
Rounded to the nearest whole number, the density of the material is approximately 123 ounces per cubic meter.
In summary, we converted the given density from kilograms per cubic foot to ounces per cubic meter using unit conversions.
This involved converting the mass units and volume units before performing the calculation to obtain the final density value in the desired units.
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Alice, Bernice, and Carol have £600 altogether. The ratio of Alice’s money to Bernice’s money is 3:7. Carol has £60 more than Alice. What is the amount of money each girl got?
Answer:
Alice - £124.62
Bernice - £290.77
Carol - £184.62
Step-by-step explanation:
Let the amount of money Alice has be a. This way, the sentence "The ratio of Alice’s money to Bernice’s money is 3:7." can be translated into a proportion:
Alice's money / Bernice's money = 3 / 7
We can substitute Alice's money with a, and cross multiply and solve for Bernice's money:
a / Bernice's money = 3 / 7
7a = 3(Bernice's money)
Bernice's money = 7/3 a
Now, we can represent Carol's money in terms of Alice's money, she has 60 more, or a + 60. We can create can equation to represent the total:
Alice's money + Bernice's money + Carol's money = total
We can plug in what we have and solve for a:
a + 7/3 a + a + 60 = 600
13/3 a = 540
a = 124.62
This means Alice has £124.62
Bernice has 7/3 a amount of money, so we can substitute the value of a to get Bernice has 7/3 (124.62), or £290.77
We can do the same for Carol who has 60 more, 124.62 + 60 is £184.62
Which fraction is represented by point A on the number line?
Answer:
-1/3
(the second choice)
Which expression has a value of 3
A. (12 + 6) ÷ (3 + 3)
B. 12 + (6 ÷ 3 + 3)
C. (12 + 6) ÷ 3 + 3
D. 12 + 6 ÷ (3 + 3)
Answer:
(12 + 6) / (3 + 3) = 18 / 6 = 3
your answer is : (12 + 6) / (3 + 3)
Answer:
A
Step-by-step explanation:
A) 18/6 = 3
B) 12+5 = 17
C) (18 / 3) + 3 = 9
D) 12 +(6/6) = 13
(2x2 + 4x + 1) + (3x2 + 6x + 5)
Answer:
5x^2+10x+6
Step-by-step explanation:
If f(x) = 5x + 3, what is the value of f(-2)?
Step-by-step explanation:
it's called answer is minus 7
Answer:
[tex]{ \tt{f(x) = 5x + 3}} \\ { \tt{f( - 2) = 5( - 2) + 3 }}\\ { \bf{f( - 2) = - 7}}[/tex]