Answer:
5(5x + 3)
Step-by-step explanation:
Given
25x + 15 ← factor out the common factor 5 from each term
= 5(5x + 3) ← in factored form
five more than a half number is 6. find the number.
Zara ate 75 almonds this week, or 150% as many as she ate last week. How many almonds did Zara eat last week?
Zara ate 50 almonds last week which is 150% as many as she ate last week.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We have been given that Zara ate 75 almonds this week, or 150% as many as she ate last week.
Let's assume that she eat x almonds last week
As per the given question, we can write the percentage would be as
⇒ 150% of x = 75
⇒ (150/100) x = 75
Apply the cross-multiplication operation,
⇒ 150x = 7500
Divided by 150 into both sides of the above equation,
⇒ x = 7500/150
⇒ x = 50
Therefore, she eat 50 almonds last week.
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Suppose f(x)=x^2 Find the graph of f(x-2) *Will make Brainliest If answered asap*
Answer:
the root is 2 . thus, the correct graph is graph 2
Part 3
1. Be sure your work is shown and steps are in order.
2. List all the possible rational roots.
3. Use synthetic division to test the possible rational roots and factor possible.
4. Identify complex roots if possible.
5. Sketch a graph of the function, please show:
a. the end behavior correctly
b. the shape of the near x-intercepts
c. (if possible) anything you can learn by considering symmetry and transformations.
3a. p(x)= 2x^5 - 9x^4 + 6x^3 + 22x^2 - 20x - 25
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
p(x) = (x +1)^2(2x -5)(x^2 -4x +5)
complex roots: 2±i
see the last attachment for a graph
Step-by-step explanation:
2. The leading coefficient of p(x) is 2, and the constant term is 25. The Rational Root Theorem tells you possible rational roots will be of the form ...
±(divisor of 25)/(divisor of 2)
That is, they are ...
±1/2, ±1, ±5/2, ±5, ±25/2, ±25
__
3. Before we get into synthetic division, we choose to see if we can reduce this list any. We note that p(0) = -25. The value of p(1) is the sum of the coefficients:
p(1) = 2 -9 +6 +22 -20 -25 = 30 -54 = -24
Similarly, the value of p(-1) is the same sum with odd-degree coefficients negated:
p(-1) = -2 -9 -6 +22 +20 -25 = 42 -42 = 0
So, we found our first root: -1. Using synthetic division, we can reduce the polynomial and start over. See the first attachment for this division.
__
The reduced polynomial is ...
p1(x) = 2x^4 -11x^3 +17x^2 +5x -25
We already know that +1 is not a of it. Checking -1, we have ...
p1(-1) = 2 +11 +17 -5 -25 = 0
So, we found our second root: -1. Using synthetic division, we can reduce the polynomial and start over. See the second attachment for this division.
__
The reduced polynomial is ...
p2(x) = 2x^3 -13x^2 +30x -25
The alternating signs tell us there are no more negative real roots. They also tell us there are 1 or 3 positive real roots. We know p2(0) = -25. Then ...
p2(1) = 2 -13 +30 -25 = 32 -38 = -6
The average rate of change between these points is (-6 -(-25))/(1 -0) = 19. At this rate, we expect a root between x=1 and x=2. Testing x=2 using synthetic division, we get a remainder of -1. (See the 3rd attachment.) Then the rate of change between x=1 and x=2 is (-1 -(-6))/(2-1) = 5, suggesting x=5/2 might be a worthwhile test value.
The synthetic division is shown in the 4th attachment. You will note that we divide the polynomial p2(x) by its leading coefficient, so the coefficients used for p2(x) in the synthetic division are 1, -13/2, 15, -25/2. The remainder of 0 tells us that (x -5/2) is a factor of p2(x)/2, or (2x -5) is a factor of p2(x).
__
The reduced polynomial is ...
p3(x) = x^2 -4x +5
This can be written in vertex form as ...
p3(x) = (x -2)^2 +1
The positive leading coefficient means the graph opens upward, and the vertex at (2, 1) means there are no real solutions.
The real solutions to p(x) are x = -1, -1, and 5/2.
__
4. The complex solutions will be the solutions to ...
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i . . . . complex roots of p(x)
__
5. The graph is shown in the last attachment. The odd degree and positive leading coefficient of p(x) means the overall shape will be from lower left to upper right (/). That is, the sign of the end value of p(x) will match the sign of x.
The graph will touch the x-axis from below at x = -1, and will cross at x = 2.5. There is no particular symmetry.
The final quadratic factor is graphed and its vertex shown. The vertex matches that of the vertex-form equation for p3(x), above.
Answer:
possible rational roots: ±1/2, ±1, ±5/2, ±5, ±25/2, ±25
real solutions to p(x) are x = -1, -1, and 5/2.
(x -2)^2 +1 = 0
(x -2)^2 = -1
x -2 = ±√(-1) = ±i
x = 2 ±i complex roots
I will mark you brainliest!!! Identify the type of function.
Answer:
quadratic
Step-by-step explanation:
hlp me hlp me hlp me hlp me
The unit rate would be points per game.
To find the points per game, divide both numbers by 6:
288/6 = 48
the unit rate would be 48 points / 1 game.
The answer is the first choice.
Answer:
[tex]\frac{288 points}{6 games}[/tex] ÷ [tex]\frac{6}{6} =\frac{48 points}{1 game}[/tex] or the 1st option
Step-by-step explanation:
[tex]\frac{288 points}{6 games}[/tex] ÷ [tex]\frac{6}{6} =\frac{48 points}{1 game}[/tex]
We get this answer because to find the unit rate, we need to get however many points over one game.
Which point represents the vertex of the marked angle?
Hey school system is reducing the amount of dumpster loads of trash removed each week in week five there are 45 dumpster load the waste removal in Wheaton there were 30 dumpster load removed assume that the reduction in the amount of waste each week is Linnea write an equation in function form to show the amount of trash removed each wwHey school system is reducing the amount of dumpster loads of trash removed each week in week five there a 45 dumpster load the waste removal in Wheaton there were 30 dumpster loads removed assume that the reduction in the amount of waste each week is linear write an equation in function form to show the amount of trash removed each week
Answer:
y = -3x + 60
Step-by-step explanation:
For the answer to the question above,
let x = number of weeks let y = amount of waste.
The linear equation may be expressed as,y = mx + b
m and b are the slope and y - intercept, respectively. Substituting the corresponding values,
(Week 5) 45 = 5m + b
(Week 10) 30 = 10m + b
Solving for m and b gives the values as m = -3 and b = 60. Thus, the equation is
y = -3x + 60
Answer: C
Step-by-step explanation: the other dude is right, he just didnt change y to f(x) (f of x).
DEFG is an isosceles trapezoid. Find the measure of 2 G.
Answer:
B
Step-by-step explanation:
In an isosceles trapezoid the upper base angles are congruent, thus
∠ G = ∠ D = 121° → B
Answer:
121
Step-by-step explanation:
i took the quiz
Is number one congruent? If it is how?
Answer:
Yes, Triangles in (1) are congruent
Step-by-step explanation:
Two conditions must be satisfied before two triangles can be deemed or declared as being congruent.
1.) They must posses similar shape
2.) They must posses similar size ( that is the corresponding sides and angles of both triangles must be the same)
Triangles in (1) meet both criterias by possessing similar shape with the size and length of the corresponding angles also being the same.
Therefore, the two triangles are congruent.
While making oatmeal cookies, Angela needs to add cup of milk to her dough. However, she has only a -cup measuring cup. How many times does she need to fill the measuring cup to pour cup of milk? The number of times Angela needs to fill the -cup measuring cup to pour cup of milk is .
Answer:
the number of times Angela needs to fill the 1/4-cup measuring cup to pour 1/2 cup of milk is 2.
Complete question:
While making oatmeal cookies, Angela needs to add 1/2 cup of milk to her dough. However, she has only a 1/4-cup measuring cup. How many times does she need to fill the measuring cup to pour 1/2 cup of milk? The number of times Angela needs to fill the 1/4-cup measuring cup to pour 1/2 cup of milk is?
Step-by-step explanation:
Number of cups Angela needs to add to her dough = 1/2 cup of milk
The only measuring cup she has = 1/4-cup measuring cup.
To determine the number of times she needs to fill the measuring cup to pour 1/2 cup of milk, we would divide the 1/2 cup of milk by 1/4-cup measuring cup
= ½ ÷ ¼
= ½ × 4/1
= 4/2
= 2
Angela would need to fill 2 times
Therefore, the number of times Angela needs to fill the 1/4-cup measuring cup to pour 1/2 cup of milk is 2
Answer:
The answer is 2 (:
Step-by-step explanation:
I got it right on the test in Edmentum
Hope this helps
Help
Two distinct number cubes are rolled together. Each number cube has sides numbered 1 through 6.
What is the probability that the outcome of the roll is an even sum or a sum that is a multiple of 3?
Enter your answer, in simplest fraction form, in the box.
Answer:
The probability is 2/3
Step-by-step explanation:
The first thing to write here is the sample space.
I have shown this in the attachment.
Kindly note that the number of expected outcome is 36
The outcome we are looking at is either an even sum or a multiple of 3
These are what i have circled in the addition results
The number of circles is 24
The probability is thus 24/36 = 2/3
Can someone please explain what I did wrong here? Thank you!
Answer:
[tex]P(Tamika)=\frac{1}{3} \times\frac{1}{3} =\frac{1}{9} \\P(Jayden)=\frac{1}{3} ;\\P=P(Tamika)\timesP(Jayden)=\frac{1}{9}\times\frac{1}{3}=\frac{1}{27}[/tex]
Suppose p and q are inversely proportional. If p=25 when q=6, find the value of p when q=15 Please help me!!!
Answer:
p=10 when q=15
Step-by-step explanation:
p and q are inversely proportional
It means
p=k/q
p=25 when q=6
p=k/q
25=k/6
k=25÷1/6
k=25×6/1
=150
k=150
Find p when q=15
p=k/q
p=150/15
=10
p=10
Q.4 a) If a= x+y and b= x-y , show that I) (a+b)²= 4x² ii) ( a-b)²= 4y²
Answer:
Below.
Step-by-step explanation:
i) (a + b)^2 = a^2 + 2ab + b^2
= (x + y)^2 + 2(x + y)(x - y) + (x - y)^2
= x^2 + 2xy + y^2 + 2(x^2 - y^2) + x^2 - 2xy + y^2
= x^2 + 2x^2 + x^2 + y^2 - 2y^2 + y^2 + 2xy - 2xy
= 4x^2.
ii) (a - b)^2 = a^2 + b^2 - 2ab
= (x + y)^2 + (x - y)^2 - 2 - 2(x^2 - y^2)
= x^2 + 2xy + y^2 + x^2 - 2xy + y^2 - 2x^2 + 2y^2
= x^2 + x^2 - 2x^2 + y^2 + y^2 + 2y^2 + 2xy - 2xy
= 4y^2.
I have 2 questions, What is 1/4 x 9 =? then 2/5 x 12 ( Multiplying fractions by whole numbers using tape diagrams)
Answer:
What is 1/4*9=2.25 then 2/5*12=4.8
Step-by-step explanation:
solve the equation
7h-5(3h-8) = 72
Answer:
h = -4
Step-by-step explanation:
7h-5(3h-8) = 72
Distribute
7h - 15h +40 = 72
Combine like terms
-8h +40 = 72
Subtract 40 from each side
-8h+40-40 = 72-40
-8h = 32
Divide each side by -8
-8h/-8 = -32/-8
h = -4
Steps:
Step 1: Simplify both sides of the equation.
7h−5(3h−8)=72
7h+(−5)(3h)+(−5)(−8)=72(Distribute)
7h+−15h+40=72
(7h+−15h)+(40)=72(Combine Like Terms)
−8h+40=72 −8h+40=72
Step 2: Subtract 40 from both sides.
−8h+40−40=72−40
−8h=32
Step 3: Divide both sides by -8
Answer: h=−4
The answer for this question is h=-4
Please mark me brainliest
Hope this helps.
The congruency theorem Side-Angle-Side (SAS) proves two triangles are congruent because both triangles have an included angle in between two congruent sides.
True
False
which of the following is the solution to the inequality below?
Answer:
14≤x
Step-by-step explanation:
-6(x-4) ≤-4(x+1)
Distribute
-6x+24 ≤-4x-4
Add 6x to each side
24 ≤-4x-4+6x
24 ≤ 2x-4
Add 4 to each side
24+4≤2x
28≤2x
Divide by 2
28/2≤2x/2
14≤x
Ok so this question is about scientific notation. Which isn’t hard. But the numbers given are too much for a calculator. I don’t get how to do it. Please help and please provide an explanation
Answer:
1.1 x 10^24
Step-by-step explanation:
Mass of earth: 5.97 x 10^24
Mass of venus: 4.87 x 10^24
There are 24 numbers in the mass of venus before the 4, in 4.87. So, that is why we use 10^24.
5.97-4.87=1.1
does anyone know the bottom answer please
Answer:
6000000 divided by 10 = 600000
Step-by-step explanation:
Your answer should make sense
Which of the following linear equations corresponds to the table above?
The linear equation of the corresponding table is y = 4x+3 which is correct option(D).
What is the slope of a linear function?The slope of a linear function is defined as the angle of the line. It is denoted by m.
Slope m = (y₂ - y₁)/(x₂ -x₁ )
Consider two points on a linear function —Point 1 and Point 2. Point 1 has coordinates (x₁, y₁) and Point 2 has coordinates (x₂, y₂)
We need two of those points to come up with the equation of the corresponding line.
Solution in y-intercept form y = mx+b
We can calculate the slope of the line using any 2 of the given points: I pick (0,3) and (3,15).
The formula for determining the slope of the line through 2 points (x₁,y₁) and (x₂,y₂) as m=(y₂-y₁)/(x₂-x₁)
By plugging in the corresponding values,
m = (15-3)/(3-0) = 12/3 = 4
Since the value of y when x is zero, i.e. the point (0,3) of the table, then the value of b is 3.
Now, Substitute the values in y = mx+b,
y = 4x+3
Hence, the linear equation of the corresponding table is y = 4x+3.
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Write an equation to represent the following statement. 33 is 15 less than k. Solve for k. k= ___
Answer:
k = 48
Step-by-step explanation:
k - 15 = 33
Add 15 to both sides
k - 15 +15 = 33 +15
k = 48
What is the equation of the following line? Be sure to scroll down first to see all answer options.
Answer:
y = 9x
Step-by-step explanation:
The y intercept is zero since it goes through the point (0,0)
We need to find the slope
m = (y2-y1)/(x2-x1)
= (9-0)/(1-0)
= 9/1
Putting this into slope intercept form y = mx+b
y = 9x +0
y = 9x
Presenting a graph with a skewed scale would be a: A measurement error. B sampling error. C interpretation error. D data collection error. PLEASEEE HELPPP!!!!!!!!!!!
Answer:
C. interpretation error
Step-by-step explanation:
Interpretation error is how data is interpreted (i.e. wrong meaning). For instance, when data results are presented in a wrong or misleading way.
Answer:
The answer is C.
Step-by-step explanation:
it just is.
Find the difference of the complex numbers (7+3i)-(3-7i)
Answer:
4 + 10i
Step-by-step explanation:
Expanding the bracket we have;
(7+3i)-(3-7i) = 7+3i-3+7i
(7+3i)-(3-7i) = 7+3i-3+7i = 7-3 + 3i + 7i= 4 + 10i
Answer Option C
=7+3i-3+7i
=7-3+3i+7i=
=4+10i
A movie theater is giving away a souvenir poster to any customer with a concession stand receipt that exceeds 560. The theater
sells a bag of popcorn for $6 and bottle of soda for $3.50. Let x represent the number of bags of popcorn, and let y represent the
number of bottles of soda. Which Inear inequality can be used to find the quantities of popcorn and soda that should be purchased
to receive a poster?
What is the first step in simplifying the expression 11x-2-3(1-7x)^2\(x+1)
Answer:
3(1-7x) is first step
Step-by-step explanation:
Answer:
BIDMAS
Step-by-step explanation:
brackets
indices
division
multiplication
addition
subtraction
so.. do everything inside the brackets and then use the square
hope this helps! :)
The volume of a cuboid is 360cm3. The length is 3cm and the width is 80mm. Work out the height of the cuboid in cm.
Answer:
[tex]15\:cm[/tex]
Step-by-step explanation:
Use the formula for the volume of a cuboid.
[tex]V=lwh[/tex]
[tex]80\:mm=8\:cm[/tex]
[tex]360=3 \times 8 \times h[/tex]
[tex]360=24 \times h[/tex]
[tex]360 \div 24 = h[/tex]
[tex]15=h[/tex]
The height of the cuboid 15 cm.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
Here, we have,
The volume of a cuboid is 360cm3.
The length is 3cm and the width is 80mm.
now,
80mm=8cm
volume= l*w* h
i.e. 360 = 3* 8*h
so, h= 15
Hence, The height of the cuboid 15 cm.
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need help with soh cah toa will award most brainliest
Answer:
46.07
Step-by-step explanation:
CAH (cosine=adjacent/hypotenuse)
cos (71)=15 (adjacent)/x (hypotenuse)
x=15/cos(71)
x=46.07
Answer
so what you do is
Step-by-step explanation:
do Cos71= 15/x
becomes x times cos71 = 15
becomes x = 15/cos71
then if u put in calculater and type 15 divided by the cos of 71 and make sure oyur calculater is on degrees an you will get answer
