Graph the functions on the same coordinate plane.
f(x)=−x+4
g(x)=x2−2
What are the solutions to the equation f(x)=g(x) ?
Select each correct answer.
3
−3
−2
2
0
Answer:
[tex]x = 2~\text{and} ~x = -3[/tex]
Step-by-step explanation:
[tex]~~~~~~f(x) = g(x)\\\\\implies -x +4 =x^2 -2\\\\\implies x^2 -2+x -4=0\\\\\implies x^2 +x -6 = 0\\\\\implies x^2 +3x -2x -6 =0\\\\\implies x(x+3) - 2(x+3) = 0\\\\\implies (x-2)(x+3) = 0\\\\\implies x = 2,~ x = -3[/tex]
Answer:
x = -3 and x = 2
Step-by-step explanation:
Plotting the graphs :
f(x)
⇒ Find two points (preferably the x and y intercepts)
⇒ 0 = -x + 4
⇒ x = 4
⇒ Point 1 : (4, 0)
⇒ f(x) = 0 + 4
⇒ f(x) = 4
⇒ Point 2 : (0, 4)
g(x)
⇒ g(x) = 0 - 2
⇒ g(x) = -2
⇒ Point 1 : (0, -2)
⇒ g(x) = 2² - 2
⇒ g(x) = 2
⇒ Point 2 : (2, 2)
* Graph with both functions is attached below *
=============================================================
Finding the solutions :
⇒ Equate f(x) and g(x)
⇒ -x + 4 = x² - 2
⇒ x² + x - 6 = 0
⇒ x² + 3x - 2x - 6 = 0
⇒ (x + 3)(x - 2) = 0
⇒ x = -3 and x = 2
the roof of this garden shed has a gradient of 0.35. find the height of the shed
The height of the shed is 2.325 m
The complete question is
The roof of a lean-to-garden shed has a gradient of 0.35.find the height....they have given the base as 1.5m and a shorter height 1.8m its like a house
What is a right Triangle ?In a Triangle when one angle is 90 degree , the triangle is called Right Triangle .
Structure of the house is a right triangle with base = 1.5m
(height of that triangle)/1.5 = 35/100
height of that triangle = 1.5*0.35 = 0.5250
Ans: greater height of the lean-to = 1.8 + 0.5250 = 2.325 meters.
The height of the shed is 2.325 m.
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20.
30a³-26a² - 36a + 8
(10a - 2)
i have to divide
Answer:
112.8
Step-by-step explanation:
Hope this help!!
which graph shows that Cindy reads about 3/4 of the time while riding in the car?
The graph that shows a unit rate of 3/4, which is the time Cindy reads while riding in the car is the graph attached below.
What is Unit Rate?Unit rate can be described as a constant or exactly how much of one quantity is per 1 unit of another quantity.
Unite rate (k) = x/y.
In the graph attached below, when x (hours driving) = 3, y (hours reading) = 4.
Therefore, unit rate = 3/4. We can then conclude that the graph that shows that Cindy reads 3/4 of the time she rides in a car is the graph attached below.
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rewrite √32/8 into simplified radical form
How to remember nagative exponents how to solve nagative exponents
To solve the negative exponents , we have to apply the negative exponent rule or the fractional exponent rule.
How are negative exponent calculated?To calculate the negative exponent we need to remember about the negative exponent that the base is on the opposite side of the fraction. Here , We need to flip the fraction so that the base will be on the other side.
Negative exponent Rule :-
[tex]a^{-n} = \frac{1}{a^{n} }[/tex]
Now , we will solve a fraction with negative exponent
For example ; Simplify the fraction [tex]\frac{3^{-2} }{9^{-2} }[/tex]
Solution : [tex]\frac{3^{-2} }{9^{-2} } = \frac{9^{2} }{3^{2} }= \frac{81}{9}[/tex]
= 9
Here, 9 is the answer of the above example.
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Can anyone help solve this inequality (ps, also make sure to read the bottom)
Which statements are true?
Select each correct answer.
All rhombuses are rectangles.
All parallelograms are quadrilaterals.
All rectangles are squares.
All squares are rhombuses.
Answer:
OTHER ANSWER IS WRONG
Step-by-step explanation:
B. All parallelograms are quadrilaterals.
D. All squares are rhombuses.
A 5-course banquet has 3 options for each course.
The number of possible 5-course meals is m.
Find the value of m.
Total courses =5
Each course has 3 options
5 courses has
5(3)15choicesHence
m=15Answer: m = 15
Explanation:
Each (1 course) has 3 options
By multiplication,
5 courses shall have: (5 × 3) = 15 choices
By addition,
Sum of choices for 5 courses: (5 + 5 + 5) = 15 choices
What is 2 over 7 is greater than 4 over 12
The value 2 / 7 is greater than 4 / 12 is - 1 / 21
How to perform subtraction in algebra?To know the value 2/7 is greater by 4 / 12, we have to subtract 4 / 12 from 2 / 7 .
Therefore,
2 / 7 - 4 / 12 = 24 - 28/84
Therefore,
24 - 28/84 = - 4/ 84 = - 1 / 21
Therefore, it is greater by - 1 / 21
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find the solution to x^2 = 24
please answer asap!!!
Answer:
[tex]C) ~x = \pm 2\sqrt 6[/tex]
Step-by-step explanation:
[tex]~~~~~~x^2 = 24\\\\\implies x = \pm\sqrt{24}\\\\\implies x = \pm\sqrt{4 \times 6}\\ \\\implies x = \pm 2\sqrt 6[/tex]
Answer:
C
Step-by-step explanation:
x² = 24 ( take square root of both sides )
x = ± [tex]\sqrt{24}[/tex] = ± [tex]\sqrt{4(6)}[/tex] = ± ( [tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] ) = ± 2[tex]\sqrt{6}[/tex]
can someone please give ,e a good explanation of associative property and examples please
Answer:
See below
Step-by-step explanation:
Basically, the associative property states that when an expression has three terms, they can be grouped in any way to solve that expression.
For example, [tex](8*4)*5=8*(4*5)[/tex] if you're doing multiplication, or [tex](8+4)+5=8+(4+5)[/tex], if you're doing addition.
The equation y= -3x7 describes a parabola. Which way does the parabola
open?
Answer:
See below
Step-by-step explanation:
y = -3 x^7 is NOT a parabola.... y = -3x^2 IS a parabola that opens downward due to the negative coefficient (-3)
rewrite each expression using the distributive property 5x2+35x
Answer:
Common factor
5x^{2}+35x
5(x^{2}+7x)
2
Rewrite in factored form
5(x^{2}+7x)
5x(x+7)
Solution
5x(x+7)
Step-by-step explanation:
mark me brainlist
A macaroni and cheese recipe calls for 2/3 of a 2 1/2 pound block of cheese. How many pounds are needed?
Answer:
4/6
Step-by-step explanation:
if the pas is a dozen brownies
1/2 of a pan is 6 2/3 of 6 would be 4/6
Write the equation in slope-intercept form for the line with the given slope that contains the given point.
slope = 1; (3,5)
A) y=2x+1
B) y=3x+5
C) y=5x+3
D) y=1x+2
Answer:
D) y = 1x + 2
Step-by-step explanation:
The general structure of an equation in slope-intercept form is:
y = mx + b
In this equation, "m" stands for the slope and "b" stands for the y-intercept. You can substitute the given value of the slope into the equation. Since you are not given "b", you can plug the value of the points into the half-completed equation (with the slope) and isolate "b".
slope = m = 1
y = (1)x + b
(3,5) ------> y = 5 and x = 3
5 = 1(3) + b
5 = 3 + b
2 = b
Final Equation:
y = 1x + 2
please help... Find the volume of pyramid that has a square base.
Answer:
V = 324 cm³
Step-by-step explanation:
the volume (V) of the pyramid is calculated as
V = [tex]\frac{1}{3}[/tex] Ah ( A is the area of the base and h the height )
here A = 9² = 81 cm² and h = 12 , then
V = [tex]\frac{1}{3}[/tex] × 81 × 12 = 27 × 12 = 324 cm³
You have an account with a principal of $200. it pays 8% at the end of every year. calculate the principal at the end of 3 years.
Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. The principal at the end of 3 years is $248.
What is simple interest?Simple interest is a method of calculating interest on an amount for n period of time with a rate of interest of r. It is calculated with the help of the formula,
SI = (P × R × T)/100
where SI is the simple interest, P is the principal amount, R is the rate of interest, and T is the time period.
The principal at the end of 3 years is,
Principal after 3 years = P + (P × R × T)
= $200 + ($200 × 0.08 × 3)
= $200 + $48
= $248
Hence, the principal at the end of 3 years is $248.
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There is a bag filled with 6 blue and 5 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting at least 1 blue?
Answer:
What you need to remember for answering this question is that the probability of any event is the number of sample points in the event divided by the number of sample points in the sample space.
If you have multiple trials and if the sampling is with replacement then, no matter how many samples are drawn, the probabilities remain the same for each trial.
MATH!!! 15 points;)) find the surface area of the pyramid
please answer correctly & check your work...
Answer:
20ft²
Step-by-step explanation:
In triangle ABC, points D and E are on sides AB and BC, respectively,
such that DE | AC, and AD:DB = 3:5.
If DB = 6.3 and AC = 9.4, what is the length of DE, to the nearest
tenth?
The length of DE in the triangles is 5.9
How to determine the length of DE?The given parameters are:
DB = 6.3
AC = 9.4
AD : DB = 3 : 5
Substitute DB = 6.3 in AD : DB = 3 : 5
AD : 6.3 = 3 : 5
Express as fraction
AD / 6.3 = 3 / 5
Multiply both sides by 6.3
AD = 3.78
The length DE is then calculated using the following ratio:
BD : DE = BA : AC
Where:
BA = BD + AD
This gives
BD : DE = BD + AD : AC
Substitute known values
6.3 : DE = 6.3 + 3.78 : 9.4
Simplify
6.3 : DE = 10.08 : 9.4
Express as fraction
DE/6.3 = 9.4/10.08
Multiply both sides by 6.3
DE = 5.9
Hence, the length of DE is 5.9
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3. What is the surface area of the triangular prism shown below?
Answer:
1233cm^2
Step-by-step explanation:
a of triangle = 1/2 bh
1/2 x 12 x 9 = 54
108 x 2 = 108
a of regtangle = l x w
25 x 15 = 375
375 x 3 = 1125
total surface area = 1125 + 108 = 1233cm^2
Angle C and angle D are vertical angles. Angle C is 36 degrees. What is the measure of angle D?
Answer:
Angle D is 36 Degree!
Step-by-step explanation:
In vertical angle theorem, it stated that if two angles are vertical, then they are congruent to each other.
Answer:
d=144°
Step-by-step explanation:
Vertical angles add up to 180
c+d=180
36+d=180
d=180-36
d=144°
What is the circumference of a circle with a diameter of 7 feet? Use 3.14 for
TT.
d=7 ft
Answer:
21.99
Step-by-step explanation:
Simplify: -4x542x5
Enter the original expression if it cannot be
simplified.
Enter the correct answer.
000
008
Clear all
+?
DONE
multiply left to right:
-4 x 542 = -2,168
-2,168 x 5 = -10,840
answer: -10,840
The simplified expression is -4x^(547).
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
To simplify -4x^(542)x^5.
You can use the property of exponents that states that when you multiply two terms with the same base, you add their exponents.
So,
-4x^(542)x^5
= -4x^(542+5)
= -4x^(547)
Thus,
The simplified expression is -4x^(547).
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A money market account is a collection of stock and bonds true or false
Answer:
A money market fund is a type of mutual fund that invests in high-quality, short-term debt instruments and cash equivalents.
If α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2, then the value of
1. α²+β²
2. 1/α+1/β
Can Someone Answer This Quick Thank You<3
Answer:
1. α²+β² = 25/36
2. 1/α+1/β = 1/2
Step-by-step explanation:
Formula :
Consider the quadratic equation ax² + bx + c = 0
Where x₁ and x₂ are the zeros of the equation.
Then
[tex]x_{1}+x_{2}=-\frac{b}{a} \\x_{1}\times x_{2}=\frac{c}{a}[/tex]
……………………………………
α and β are the zeros of the quadratic polynomial f(x) = 6x²+x-2
Then
[tex]\alpha +\beta =-\frac{1}{6}[/tex]
[tex]\alpha \times \beta =-\frac{1}{3}[/tex]
……………………
[tex]\alpha^{2} +\beta^{2} =\left( \alpha +\beta \right)^{2} -2\alpha \beta[/tex]
[tex]=\alpha^{2} +\beta^{2} =\left( -\frac{1}{6} \right)^{2} -2\times(-\frac{1}{3} )[/tex]
[tex]=\frac{25}{36}[/tex]
………………………………
[tex]\frac{1}{\alpha } +\frac{1}{\beta } =\frac{\alpha +\beta }{\alpha \beta }[/tex]
[tex]=\frac{-\frac{1}{6} }{-\frac{1}{3} } =\frac{1}{2}[/tex]
I need help asap please? and this is for the math question? what is 77x+93=360? put in a fraction and decimal and you can round to nearest tenths, plus I will give out brainlists to whom ever answers first
[tex]\\ \rm\Rrightarrow 77x+93=360[/tex]
[tex]\\ \rm\Rrightarrow 77x=360-93[/tex]
[tex]\\ \rm\Rrightarrow 77x=367[/tex]
[tex]\\ \rm\Rrightarrow x=4.77[/tex]
[tex]\\ \rm\Rrightarrow x=4.8[/tex]
Aswer with Nina ^-^
Don't report my answer ✅
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Answer:
20cm²
Step-by-step explanation:
We can solve this by dividing the volume of the cuboid by the height of the cuboid. The formula for the volume of a cuboid is Length * Width * Height, so dividing the volume will leave us with the Length * Width, which is also the area of the shaded face.
100cm³/5cm = 20cm²
The area of the shaded face is 20cm².
Step-by-step explanation:
We can solve this by dividing the volume of the cuboid by the height of the cuboid. The formula for the volume of a cuboid is Length * Width * Height, so dividing the volume will leave us with the Length * Width, which is also the area of the shaded face.
100cm³/5cm = 20cm²
The area of the shaded face is 20cm².
Bryannasalaz
Im Not Understanding!
Answer:
3/2 + 3/2 + 3/2 = 3/1
so 3 over 1 times 1 over 2