Answer
[tex] \boxed{10p}[/tex]
Step by step explanation
[tex] \mathsf{ - 4p + (- 6p)}[/tex]
When there is a ( + ) in front of an expression in parentheses, the expression remains the same
[tex] \mathsf{ - 4p - 6p}[/tex]
Collect like terms
[tex] \mathsf{ - 10p}[/tex]
Hope I helped!
Best regards!
Oliver completed his project in no more than twice the amount of time it took Karissa to complete her project. Oliver spent 4 and one-fourth hours on his project. If k represents the amount of time that it took Karissa to complete her project, which inequality can be used to represent the situation?
Answer:
4 1/4 <_ 2K
Step-by-step explanation:
The inequality that represents the situation is k ≥ 2.125 hours.
What is Inequality ?Inequality is the statement where two algebraic expressions are equated using an inequality operator, <, >, <> etc.
Karissa takes k time to complete the project.
Oliver takes ≤ 2k
The time spent by Oliver is 4 1/4 = 17/4 = 4.25 hours
2k ≥ 4.25
k ≥ 2.125 hours
Therefore, the inequality that represents the situation is k ≥ 2.125 hours.
To know more about Inequality
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20 points! Thank you :)
Answer:
[tex]\Large \boxed{x=-2 \ \mathrm{and} \ x=3}[/tex]
Step-by-step explanation:
The quadratic expression is given.
[tex]2x^2-2x-12=0[/tex]
Factor the left side of the equation.
[tex]2(x+2)(x-3)=0[/tex]
Set the factors equal to 0.
[tex]x+2=0[/tex]
[tex]x=-2[/tex]
[tex]x-3=0[/tex]
[tex]x=3[/tex]
The two solutions work in the original equation. The solutions make the equation true.
The quadratic expression:
[tex]2 {x}^{2} - 2x - 12[/tex]
★ By split middle term,we get
[tex]2 {x}^{2} - 6x + 4x - 12[/tex]
[tex]2x(x - 3) + 4( x - 3)[/tex]
[tex](2x + 4) (x - 3)[/tex]
[tex]2x + 4 = 0 \: \: and \: \: x - 3 = 0[/tex]
[tex]2 x = - 4 \: \: and \: \: x = 3[/tex]
[tex]x = - 2 \: \: and \: \: x = 3[/tex]
Therefore , the two solution of given quadratic equations is -2 and 3.
20 POINTS! Please help.! 1) Given the following three points, find by hand the quadratic function they represent. (0,6), (2,16), (3, 33) A. f(x)=4x2−3x+6 B. f(x)=4x2+3x+6 C. f(x)=−4x2−3x+6 D. f(x)=−4x2+21x+6 2) Given the following three points, find by hand the quadratic function they represent. (−1,−8), (0,−1),(1,2) A. f(x)=−3x2+10x−1 B. f(x)=−3x2+4x−1 C. f(x)=−2x2+5x−1 D. f(x)=−5x2+8x−1 3) Find the equation of a parabola that has a vertex (3,5) and passes through the point (1,13). A. y=−3(x−3)2+5 B. y=2(x−3)2+5 C. y=−2(x−3)2+5 D. y=2(x+3)2−5
Answer:
1) f(x) = 4·x² - 3·x + 6
2) f(x) = -2·x² + 5·x - 1
3) y = 2·(x - 3)² + 5
Step-by-step explanation:
1) The quadratic function that is represented by the points (0, 6), (2, 16), (3, 33) is found as follows
The general form of a quadratic function is f(x) = a·x² + b·x + c
Where, in (x, y), f(x) = y, and x = x
Therefore for the point (0, 6), we have;
6 = 0·x² + 0·x + c
c = 6
We have c = 6
For the point (2, 16), we have;
16 = a·2² + b·2 + 6
10 = 4·a + 2·b.............................(1)
For the point (3, 33), we have;
33 = a·3² + b·3 + 6
27 = 9·a + 3·b............................(2)
Multiply equation (1) by 1.5 and subtract it from equation (2), we have;
1.5 × (10 = 4·a + 2·b)
15 = 6·a + 3·b
27 = 9·a + 3·b - (15 = 6·a + 3·b) gives;
27 - 15 = 9·a - 6·a+ 3·b - 3·b
12 = 3·a
a = 12/3 = 4
a = 4
From equation (1), we have;
10 = 4·a + 2·b = 4×4 + 2·b
10 - 4×4 = 2·b
10 - 16 = 2·b
-6 = 2·b
b = -3
The function, f(x) = 4·x² - 3·x + 6
2) Where the points are (-1, -8), (0, -1), (1, 2), we have;
For point (-1, -8), we have -8 = a·(-1)² - b·(-1) + c = a - b + c......(1)
For point (0, 1), we have -1 = a×0² + b×0 + c = c.........................(2)
For point (1, 2), we have 2 = a×1²+ b×1 + c = a + b + c..............(3)
Adding equation (1) to equation (3) gives
-8 + 2 = a - b + c + a + b + c = 2·a + 2·c where, c = -1, we have
-8 + 2 = -6 = 2·a + 2
2·a = -6 + 2 = - 4
a = -8/2 = -2
From equation (3), we have;
2 = a + b + c
b = 2 - a - c = 2 - (-2) - (-1) = 2 + 2 + 1 = 5
f(x) = -2·x² + 5·x - 1
3) The equation of a parabola that has vertex (3, 5) and passing through the point (1, 13) is given by the vertex equation of a parabola
The vertex equation of a parabola is y = a(x - h)² + k
Where;
(h, k) = Vertex (3, 5)
(x, y) = (1, 13)
We have
13 = a·(1 - 3)² + 5
13 = a·(-2)² + 5
13 - 5 = a·(-2)² = 4·a
4·a = 8
a = 8/4 = 2
The equation is y = 2·(x - 3)² + 5.
Janice deposited $750 in a savings account that earns 3.5% simple interest. How much interest has Janice earned by the end of the first year? (1 point)
Answer:
$26.25
Step-by-step explanation:
We know that I = Prt where I = Interest, P = Principal, r = rate (as a decimal) and t = time (in years). Therefore:
I = 750 * 0.035 * 1 = $26.25
What would -4|5+-3| be
Answer:
-8
Step-by-step explanation:
15 over r when r = 5
Answer:
15 over r when r. so 15-5 : 10
how to solve 1168 divided by 8
85 POINTS! PLEASE HELP! Explain how to write an equation parallel to the equation y = 2x + 3 and the new line also includes the ordered pair (1,-2).
Answer:
[tex]\huge\boxed{\sf y = 2x -4}[/tex]
Step-by-step explanation:
The given equation is:
y = 2x + 3
Where Slope = m = 2 , Y-intercept = b = 3
Parallel lines have equal slopes
So, Slope of new line = m = 2
Now, Finding y-intercept:
Given Point = (x,y) = (1,-2)
So, x = 1 , y = -2
Putting m, x and y in standard form of equation to get b:
[tex]\sf y = mx+b[/tex]
[tex]\sf -2 = (2)(1) + b\\-2 = 2 + b\\[/tex]
Subtracting 2 to both sides
[tex]\sf b = -2-2\\[/tex]
b = -4
So, the standard form og equation for the new line is :
[tex]\sf y = mx+b[/tex]
[tex]\sf y = 2x -4[/tex]
Answer:
y = 2x - 4
Step-by-step explanation:
the problem is called (slope-intercept form)
the equation of the line is y = mx + b
the equation of a line is given as y = 2x + 3
slope = 2
b = y-intercept is where the line crosses the y-axis = 3
so point (x1, y1) = (1, -2)
by using the equation.
y = mx + b
-2 = 2 (1) + b
-2 -2 = b
therefore b = -4
writing the new equation using the slope intercept form
y = mx + b would be y = 2x + 4
so the equation parallel to the equation y = 2x + 3 is y = 2x - 4
Evaluate. (-2 1/4)^2
Answer:
[tex]5 \frac{1}{16}[/tex]
Step-by-step explanation:
I did this before. Also sometimes once I look at the question I just find out the answer without steps.
The Tama, Japan, monorail carries 92,700 riders
each day. If the monorail usually carries
5,150 riders per hour, how many hours does
the monorail run each day?
Answer:
The monorail runs 18 hours runs every day.
Step-by-step explanation:
You know that the total number of riders the monorail carry each day is 92700 and the number of riders the monorail carry per hour is 5150.
The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
A direct proportionality relationship is established between two quantities if:
The greater the quantity in one quantity, the greater the quantity in the other quantity, in the same proportion. The less quantity in the magnitude corresponds to the less quantity in the other magnitude, in the same proportion.If the relationship between the magnitudes is direct the direct rule of three must be applied and to solve a direct rule of three, the following formula must be followed:
a ⇒ b
c ⇒ x
Being
[tex]x=\frac{c*b}{a}[/tex]
In this case the rule of three can be applied in the following way: if the monorail carries 5,150 passengers in 1 hour, the monorail will transport 92,700 passengers in how many hours?
[tex]amount of hours=\frac{92,700 passengers*1hour}{5,150 passengers}[/tex]
amount of hours= 18 hours
So the monorail runs 18 hours runs every day.
G is a transformation of f. The graph below shows f as a solid blue line and g as a dotted red line. What is the formula of g in terms of f?
Answer: f(x-2) which is choice A.
The blue f(x) curve is shifted 2 units to the right to get the red g(x) dashed curve.
============================================================
Explanation:
For now, ignore the red dashed curve g(x). Imagine that the blue curve f(x) is fixed in place. If we shifted the xy axis to the left 2 units, then this gives the illusion the blue curve is moving even though the curve is fixed in place.
The operation "shift xy axis 2 units to the left" means each x input is 2 units smaller. So each x input is now x-2.
Therefore, going from f(x) to f(x-2) will shift the blue curve 2 units to the right to land perfectly on the red dashed g(x) curve.
Duncan took a math quiz last week. There were 55 problems on the quiz and Duncan
answered 40% of them correctly. How many problems did Duncan get correct?
Answer: Duncan got 22 questions correct
Step-by-step explanation:
Total questions in quiz = 55
Total answered correctly by Duncan = 40% of 55
Total answers he got correct = 40% of 55
= 40/100×55
= 22
Therefore Duncan got 22 questions correct
please click thanks and mark brainliest if you like :)
Please help!! Two birds sit at the top of two different trees. The distance between the first bird and a birdwatcher on the ground is 32 feet. The distance between the birdwatcher and the second bird is 45 feet. What is the angle measure, or angle of depression, between this bird and the birdwatcher? Round your answer to the nearest tenth. 35.4° 44.7° 45.3° 54.6°
Answer:
45.3°
Step-by-step explanation:
A right triangle is formed given the information above.
Angle of depression = x°
Distance between first bird and birdwatcher = opposite to angle x° = 32 ft
Distance between second bird and birdwatcher = hypotenuse of the right triangle formed = 45 ft
The trigonometric ratio formula to use is:
[tex] sin(x) = \frac{opp}{hypo} [/tex]
[tex] sin(x) = \frac{32}{45} [/tex]
[tex] sin(x) = 0.7111 [/tex]
[tex] x = sin^{-1}(0.7111) [/tex]
[tex] x = 45.3 [/tex] (nearest tenth)
Angle of depression = 45.3°
Answer:
45.3°
Step-by-step explanation:
Hope this helps :)
In an examination ,80%examines passed in english,70%In mathematics and 60% in both subjects.if 45 examines failed in both subject.
1.draw a venn-diagram to represent the above information .
2.find the number of examines who passed only one subject.
3.find the number of student who failed in mathematics.
Answer:
1. Please refer to attached diagram.
2. 135
3. 135
Step-by-step explanation:
Given that
80%examines passed in English, n(E) = 80%
70%In mathematics, n(M) = 70%
and 60% in both subjects, n(E [tex]\cap[/tex] M) = 60%
45 examines failed in both subject.
1. Venn Diagram is attached in the answer area.
One circle represents the pass examines in Maths and
Other circle represents the pass examines in English.
Rectangle represents the total number of examines that appeared for the exam.
Rectangle minus the area of union of circles represent the number of students who failed in both subjects.
2. To find the number of examines who passed in only one subject.
i.e. n(E) - n(E [tex]\cap[/tex] M) + n(M) - n(E [tex]\cap[/tex] M) = (80 - 60 + 70 - 60)% = 30%
Let us find the number of students who passed in atleast one subject:
[tex]n(E\cup M) = n(E) +n(M)-n(E \cap M)\\\Rightarrow n(E\cup M) = (80 +70-60)\% = \bold{90\%}[/tex]
So, number of students who failed in both subjects = 100 - 90% = 10% of total students = 45
So, total number of students appeared = 450
So, number of examines who passed in only one subject = 450 [tex]\times[/tex] 30% = 135
3. Number of students who failed in mathematics.
100% - Passed in Mathematics = 100% - 70% = 30% of 450 = 135
what is .7 of a mile
Answer:
1232 yards or 3696 feet or 44352 inches or 0.7 of a mile
Step-by-step explanation:
Please help.. I'm really stuck
Answer:
C. C only
Step-by-step explanation:
Well to determine if the given graphs are functions we need to do the vertical line test to all the graphs,
A. This fails the vertical line test because the vertical line could pass through 2 points on the lines.
B. this also fails because a vertical line could pass through 2 points.
C. This passes because the vertical line doesn’t touch 2 points.
Helppp please!! Thank you
Answer:
The answer is 4
Find the area of the triangle
Answer:
73.64 ft²
Step-by-step explanation:
bad at explaining but hope this helped <3
Can someone please help!! ****This problem is multiple choice!
Answer:
I believe it's A) 302.94
Step-by-step explanation:
There are 360 degrees in a circle. So I enetered 360/112 in a calculator and got 3.214.
Then I multiplied 3.214 by 30pi and got 302.939 AKA 302.94. I did this because I looked at it like a ratio problem but idk if thats correct.
Which question can be answered using the expression 1/3 ÷ 3/4 ?
Answer:
0.4444444
Step-by-step explanation:
yes
Combine like terms to create an equivalent expression. -3.6-1.9t+1.2+5.1t
Answer:
3.2t-2.4Step-by-step explanation:
[tex]\\-3.6-1.9t+1.2+5.1t\\\mathrm{Group\:like\:terms}\\\\=-1.9t+5.1t-3.6+1.2\\\\\mathrm{Add\:similar\:elements:}\:-1.9t+5.1t=3.2t\\\\=3.2t-3.6+1.2\\\\=3.2t-2.4[/tex]
Answer:
3.2t -2.4
Step-by-step explanation:
-3.6-1.9t+1.2+5.1t
Like by terms = -1.9t+5.1t - 3.6 +1.2
Solve left to right step 1 = 3.2t - 3.6 +1.2
Solve step 2 = 3.2t - 2.4
ABCD is a rectangle. Its diagonals meet at O. Find the value of x if
OA = 2x + 4 and OD = 3x + 1.
step by step explanation
Answer:
x = 3
Step-by-step explanation:
The diagonals bisect each other and are congruent , then
OD = OA , that is
3x + 1 = 2x + 4 ( subtract 2x from both sides )
x + 1 = 4 ( subtract 1 from both sides )
x = 3
What is the product of complex conjugates? (1 point)
the product of complex conjugates is a difference of two squares and is always a real number
the product of complex conjugates may be written in standard form as a+bi where neither a nor b is zero
the product of complex conjugates is the same as the product of opposites
the product of complex conjugates is a sum of two squares and is always a real number
Answer:
A. the product of complex conjugates is a difference of two squares and is always a real number
Step-by-step explanation:
Given a complex number z1 = x+iy where x is the real part and y is the imaginary part.
The conjugate of a complex number is the negative form of the complex number z1 above i.e z2= x-iy (The conjugate is gotten by mere changing of the plus sign in between the terms to a minus sign.
Taking the product of the complex number and its conjugate will give;
z1z2 = (x+iy)(x-iy)
z1z2 = x(x) - ixy + ixy - i²y²
z1z2 = x² - i²y²
.since i² = -1
z1z2 = x²-(-1)y²
z1z2 = x²+y²
The product gave a real function x²+y² since there is no presence of complex number 'i'
It can also be seen that the product of the complex numbers z1z2 is like taking the difference of two square. An example of difference of two square is that of two values a and b which is (a+b)(a-b).
From the above solution, it can be concluded that the product of complex conjugates is a difference of two squares and is always a real number.
How do -11.5 and -9.5 compare? Choose the correct symbol.
-11.5 _ -9.5
A.<
B.=
C.>
Answer:
A. <
Step-by-step explanation:
-9.5 is greater than -11.5
Answer:
A) <
less than
Step-by-step explanation:
-11.5 < -9.5
2 Mayra is a caterer and charges $75 per plate plus a
set up fee of $30. The cost per person is represented
by C = 30+75p. If she is catering a wedding for 150
people, how much does the bride and groom spend
on food?
Answer:
$11,280
Step-by-step explanation:
Plug in 150 as p into the equation to solve for the cost, C:
C = 30 + 75p
C = 30 + 75(150)
C = 30 + 11,250
C = 11,280
= $11,280
Point A(8,4) is reflected over point (6,−2) and its image is point B. What are the coordinates of point BB?
Answer:
If Point A (8,4) is reflected over point (6,−2), then that point becomes (4, -8).
Let me know if this helps!
What is 164.362 rounded to 4, 3 and 1 significant figures
Answer:
4 sigfig is 164.4
3 sigfig is 164.
1 sigfig is 200
hope that answers your question
comment for more explanation
write the mixed numbers as fractions
1/1/2
Answer:
3/2
Step-by-step explanation:
16+6-6x-4=-7x+3+7
how to solve for x
Answer:
x = -8
Step-by-step explanation:
16+6-6x-4=-7x+3+7
Combine like terms
18 -6x = -7x+10
Add 7x to each side
18-6x+7x = -7x+7x+10
18+x = 10
Subtract 18 from each side
18+x-18 = 10-18
x = -8
Answer:
x = -8
Step-by-step explanation:
16+6-6x-4 = -7x+3+7
18 - 6x = -7x + 10
-6x + 7x = 10 - 18
x = -8
Check:
18 - 6*-8 = -7*-8 + 10
18 + 48 = 56 + 10 = 66
show that (2x+3)^3 = 8x^3+36x^2+54x+27 for all values of x
Answer:
see explanation
Step-by-step explanation:
Given
(2x + 3)³
= (2x + 3)(2x + 3)(2x + 3) ← expand the last 2 factors using FOIL
= (2x + 3)( 4x² + 12x + 9)
= 2x(4x² + 12x + 9) + 3(4x² + 12x + 9) ← distribute parenthesis
= 8x³ + 24x² + 18x + 12x² + 36x + 27 ← collect like terms
= 8x³ + 36x² + 54x + 27