[tex] \large{f(x) = g(x)} \\ \large{ {x}^{2} + 3x = x + 3}[/tex]
Since we are solving the quadratic equation because the highest degree in the equation is second. We arrange in the form of ax²+bx+c = 0.
[tex] \large{ {x}^{2} + 3x - x - 3 = 0}[/tex]
Combine like terms.
[tex] \large{ {x}^{2} + 2x - 3 = 0}[/tex]
Solve the equation by factoring.
[tex] \large{(x + 3)(x - 1) = 0} \\ \large{x = - 3,1}[/tex]
Hence the values of x that make f(x) = g(x) are -3 and 1.
Answer
x = -3,1Let me know if you have any doubts!
Pleasee help with this question asap I’m begging y’all
==================================================
Work Shown:
[tex]y = \frac{4x+30}{x+5}\\\\y = \frac{4x+20+10}{x+5}\\\\y = \frac{(4x+20)+10}{x+5}\\\\y = \frac{4(x+5)+10}{x+5}\\\\y = \frac{4(x+5)}{x+5}+\frac{10}{x+5}\\\\y = 4+\frac{10}{x+5}\\\\[/tex]
Therefore, a = 10
--------------
As an alternative approach, we could work in reverse like this:
[tex]y = 4+\frac{a}{x+5}\\\\y = 4*\frac{x+5}{x+5}+\frac{a}{x+5}\\\\y = \frac{4(x+5)}{x+5}+\frac{a}{x+5}\\\\y = \frac{4(x+5)+a}{x+5}\\\\y = \frac{4x+20+a}{x+5}\\\\[/tex]
Then notice that the 20+a must be 30, so solving 20+a = 30 leads to a = 10
--------------
As yet another alternative approach (well I suppose it's actually 2 extra approaches) we could use either polynomial long division or synthetic division. Either way, you should end up with a remainder of 10, which corresponds directly to a = 10
Factor the expression x^2+6x+8
100 divided by 2
please show work
thank you
Answer:
100÷2= 50
Step-by-step explanation:
Because if we divide a 100 equally by 2 it will be 50
please help me answer this
9514 1404 393
Answer:
B, C, D
Step-by-step explanation:
You can solve for x, or you can try x=3.5 to see if that makes the equation true. Here, we decided to solve for x.
A. x =(8×3 -3)/7 = 3
B. x = 15 -11.5 = 3.5
C. x = (34 -6)/8 = 3.5
D. x = 15.5 -12 = 3.5
E. x = 20 -15.5 = 4.5
The graph of f(x) = |x – h| + k contains the points (–6, –2) and (0, –2). The graph has a vertex at (h, –5). Describe how to find the value of h. Then, explain how this value translates the graph of the parent function.
Answer:
ty
Step-by-step explanation:
mtj
A rectangle is removed from a right triangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.
Answer:
See below.
Step-by-step explanation:
Length * width
4 * 3 = 12 ft[tex]^2[/tex]
Answer:
24 square feet
Step-by-step explanation:
Area = area of triangle - area of rectangle
[tex]Area \ of \ triangle = \frac{1}{2} \times base \times height =\frac{1}{2} \times(4 +5) \times (5+3) = 9 \times 4 = 36 \ ft^2\\\\Area \ of \ rectangle = Length \times Breadth = 3 \times 4 = 12 \ ft^2\\\\\\Area \ of \ the\ shaded \ region = 36 - 12 = 24 \ ft^2[/tex]
A power company calculates a person's monthly bill from the number of
kilowatt-hours (kWh), x, used.
The function b(x) = {
0.15x,
x < 200
0.10 (x - 200) + 30, 2 > 200
determines
the bill.
How much is the bill for a person who uses 700 kWh in a month?
A. $100
оо
B. $80
O C. $105
O D. $95
PREVIOUS
Answer: (b)
Step-by-step explanation:
Given
Function for bill calculation is
[tex]\Rightarrow b(x)=\left \{ {{0.15x\quad \quad \quad \, \ \ \ \ x<200} \atop {0.1(x-200)+30\quad x>200}} \right.[/tex]
The consumption is 700 kWh i.e. more than 200
Therefore, bill is given by the second function i.e. [tex]0.10(x-200)+30[/tex]
Substitute 700 for x to get the bill
[tex]\Rightarrow 0.1(700-200)+30\\\Rightarrow 50+30=\$80[/tex]
Hence, option (b) is correct.
whats the anserw plz (8x+10y)+(-4x-3y) i need help!!!
Answer:
me :- mighty assassin-,-
xd
Two sides of a triangle are perpendicular. If the two sides are 8cm and 6cm, calculate correct to the next degree, the smallest angle of the triangle. (A)35° (B)36° (C)37° (D)38° (E)53°
[tex]\boxed{Given:}[/tex]
Length of the perpendicular ( opposite ) = 6 cm.
Length of the base ( adjacent ) = 8 cm.
[tex]\boxed{To\:find:}[/tex]
The smallest angle of the triangle.
[tex]\boxed{Solution:}[/tex]
[tex]\sf\purple{C.\:37°}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
In a right-angled triangle, if two sides are given, the measure of the unknown angle can be known.
Since the value of opposite and adjacent sides are given, we use the tangent formula.
tan θ = [tex]\frac{opposite}{adjacent}[/tex]
✒ tan θ = [tex]\frac{6 \: cm}{8 \: cm}[/tex]
✒ θ = [tex]{tan}^{ - 1}[/tex] (0.75)
✒ θ = 36.9°
✒ θ = 37°
Now let us find the other unknown angle 'x'.
We know that,
Sum of angles of a triangle = 180°
✒ 37° + x + 90° = 180° (90° since it is a right-angled triangle)
✒ x + 127° = 180°
✒ x = 180° - 127°
✒ x = 53°
Therefore, the three angles of the triangle are 37°, 53° and 90°.
Hence, the smallest angle is 37°.
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{♡}}}}}[/tex]
Does this app actually work for ya'll????
Answer:
Yessssss!
Step-by-step explanation:
Answer:
yess!! look up your question before you ask it :))))
thx for the points too hehe
Which is the correct answer!!!
Answer:
the answer is the alphabet a
Use the tree diagram below to answer the question how many outcomes are there that contain blue shirts
Answer:
3
Step-by-step explanation:
i got it right on my test
PLS HELP ASAPPPPPPPPPPPPPP
Answer:
G
Step-by-step explanation:
36+36=72
180-72=108
360-(108×2)
144
144÷2
72
84784+24849+748429+123456
Answer:
981,518
Step-by-step explanation:
Have a nice day :)
Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°.
Answer:
you first find the radius which is given by r=√(5^2)+(-5^2)=5√2,and then you find the angle which is given by tan^-1(y÷x),that is tan^-1(-5÷5)=-45°.This angle lies between (5,-5)
so 360-45=315°.
The ordered pair will be (5√2,315°)
To obtain the second ordered pair 315°-180°=135°
(5√2,135°)
the two pairs of polar coordinates are (5√2,135°,
5√2,315°)
Which transformation is a translation?
Answer:
i don't know but o o o o right e o right e auto park
Answer:
4234324tgfgdfgdgd
Step-by-step explanation:
Find the surface area of the rectangular prism
Answer:
22mi
Step-by-step explanation:
Formula: A=2(wl+hl+hw)
h=1mi
l=5mi
w=1mi
Using the formula,
2·(1·5+1·5+1·1)=22mi
Therefore, the surface area of the rectangular prism is 22mi
Solve for xxx in the diagram below.
Which step in the construction of copying a line segment ensures that the new line segment has the same length as the original lie segment?
Answer:
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
Step-by-step explanation:
Here are the steps I think you probably will go through.
1. Draw a line that is longer than the segment but shorter than the width of the page.
1a. Make sure this line is at least 1/2 inch from the left hand side.
2. Use a compass to measure the length of the original segment. Never use a ruler. Rulers do not exist in pure geometry.
3. Measure out the distance on the line you just drew with the compass. One end is on the left hand edge and the other end (the pencil end) is marking the segment so it is the same length as the compass. You are done.
The key step either two or three.The steps to copy a line segment are given below:
1. Lets start with a line segment AB that we have to copy.
2. Now mark a point C. below or above AB, that will be one endpoint of the new line segment.
3. Now, put the compass tip on point A of the line segment AB.
4. Spread the compass up to point B, so as the compass width is equal to length of AB.
5. Without changing the compass width, now place the compass tip on the point C that you made in step 2.
6. Now, draw an arc roughly without changing the compass settings. Mark that point D. This will form the new line segment.
7. Draw a line from C to D.
Now out of these points, i guess steps 5 and 6 are the main steps that ensure that the copied line segment is exactly the same as the original segment.
Please help me! That would be great if you can.
Answer the question.
Answer:
[tex] \frac{8 {x}^{2} y}{6 {x}^{2} {y}^{2} } \\ = \frac{8×3}{6 {y}^{2} } \\ = \frac{24}{6 \times {3}^{2} } \\ = \frac{4}{9} [/tex]
2 + (-17) i need the correct answer and show your work
Answer:
-15
Step-by-step explanation:
2 + (-17) = (-15)
If two integers have different sign, subtract and the result will have the bigger number sign.
17 - 2 = 15 and the bigger number is 17 & sign of 17 is negative. So answer is (-15)
2 + (-17) = (-15)
If two integers have different sign, subtract and the result will have the bigger number sign.
17 - 2 = 15 and the bigger number is 17 & sign of 17 is negative. So answer is (-15)
[tex] \tt{ \verified} \: \: \: \: \red{ \checkmark}[/tex]
If carpet costs $11 a square yard including padding and installation, what would it
cost to carpet a room measuring 14ft. by 20ft? (Note: 3 feet = 1 yard)
Round to the nearest dollar.
$1386
o $374
$342
o $1027
o$3080
Answer:$342
Step-by-step explanation: First we convert to yards: which gives us 14/3 yards and 20/3 yards. We multiply these to find a combined area of 280/9 yards, which we then multiply to get 280*11/3. Simplify to get 342.22 repeating, which rounds to 342.
If p and q vary inversely and p is 9 when q is 16, determine q when pis equal to 18.
Answer:
[tex]p \: \alpha \: \frac{1}{q} \\ p = \frac{k}{q} \\ k \: is \: a \: constant \: of \: proportionality \\ when \: p \: is \: 9.. \: \: q = 16 \\ 9 = \frac{k}{16} \\ k = 144 \\ when \: p \: is \: 18 : \\ 18 = \frac{144}{q} \\ q = \frac{144}{18} \\ q = 8[/tex]
You roll a number cube. Find the probability and write your answer in the simplest form. P(4)= ------------------------------------------- P(not a 2) = ------------------------------------ P(3 or 5) = ------------------------------------
Answer:
[tex]P(4) = \frac{1}{6}[/tex]
[tex]P(\text{not a 2}) = \frac{5}{6}[/tex]
[tex]P(\text{3 or 5}) = \frac{1}{3}[/tex]
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
Number cube:
A number cube is a dice, which has six sides, numbered 1 to 6.
P(4)
One the sides is a 4, thus:
[tex]P(4) = \frac{1}{6}[/tex]
P(not a 2)
Of the 6 sides, one is a 2, and the other 5 are not 2. So
[tex]P(\text{not a 2}) = \frac{5}{6}[/tex]
P(3 or 5)
One sides is 3, other is 5, 1 + 1 = 2. So
[tex]P(\text{3 or 5}) = \frac{2}{6} = \frac{1}{3}[/tex]
if f(x)=3x+2 what is f(5)?
Answer:
17
Step-by-step explanation:
f(x)=3x+2
Let x = 5
f(5)=3*5+2
Multiply first
f(5) = 15+2
Then add
= 17
the function f is given by f(x) = (x - 6)(x - 2). Multiply out the factors using the area model or distributive property. What expression do you get
What is the total Jeff has a painted
A. 180 square inches
B.40 square inches
C.100 square inches
D.90 square inches
Answer:
180 square inches
Step-by-step explanation:
let separate the figure and form two rectangles
first rectangle
length = 10 in
breadth = 9 in
let's find its area
area =l*b
=10*9
=90 in.^2
second rectangle
length = 15 in.
breadth = 6 in.
area =l*b
=15 *6
=90 in.^2
area of a whole he painted =area of first rectangle + area of second rectangle
=90 + 90 in.^2
=180 in .^2
identify the precision unit for the measuring tool below
Let a=2 and b=1, find the value of 2a + 3b
Answer:
7 is a answer
Step-by-step explanation:
2a+3b
2×2+3×1
4+3
7
hope it helps....
[tex] \sf a = 2,\: b = 1[/tex]
[tex] \sf Q) \:2a + 3b = {?}[/tex]
[tex] \sf \implies 2a + 3b[/tex]
[tex] \sf \implies 2(2) + 3(1)[/tex]
[tex] \sf \implies 4 + 3[/tex]
[tex] \sf \implies 7[/tex] is the required answer.
