Answer:
0Step-by-step explanation:
Given,
[tex] - \frac{2}{3} [/tex]
Now, let's find the value of 9x + 6
[tex]9x + 6[/tex]
plug the value of X
[tex] = 9 \times (- \frac{2}{3} ) + 6[/tex]
Multiplying a positive and negative equals a negative
[tex]( + ) \times ( - ) = ( - )[/tex]
[tex] = - 9 \times \frac{2}{3} + 6[/tex]
Reduce the number with Greatest Common Factor 3
[tex] = - 3 \times 2 + 6[/tex]
Multiply the numbers
[tex] = - 6 + 6[/tex]
The sum of two opposites equals 0
[tex] = 0[/tex]
Hope this helps..
best regards!!
Find the width of a rectangle if the diagonal is 19 and the length is 16
Answer:
≈10.25
Step-by-step explanation:
use the Pythagorean Theorem: a² + b² = c²
c is the hypotenuse, the diagonal, or the longest side of the triangle
a = 16
b = ?
c = 19
(16)² + b² = (19)²
256 + b² = 361
b² = 105
b = √105 ≈ 10.25
PLEASEEEEEEEEEEEEE HELPPPPPPPPPPP!
Dylan uses the expressions (x2 – 2x + 8) and (2x2 + 5x – 7) to represent the length and width of his bedroom. Which expression represents the area (lw) of Dylan's room?
Answer:
2x⁴+x³-x²+54x+56
Step-by-step explanation:
Given the expression length of dylan room = (x² – 2x + 8) and width = (2x² + 5x – 7), assuming the shap of the room is rectangular in nature, the formula for calculating area of a triangle is given as;
Area of rectangle = Length *Width
Area of the rectangle = (x² – 2x + 8)(2x² + 5x – 7)
Area of the rectangle = x²(2x² + 5x – 7) - 2x (2x² + 5x – 7) + 8(2x² + 5x – 7)
= (2x⁴+5x³-7x²)-(4x³+10x²-14x)+(16x²+40x-56)
expanding the bracket
= 2x⁴+5x³-7x²-4x³-10x²+14x+16x²+40x-56
Collecting the like terms;
= 2x⁴+5x³-4x³-7x²-10x²+16x²+40x+14x+56
= 2x⁴+x³-x²+54x+56
Hence, the expression that represents the area (lw) of Dylan's room is 2x⁴+x³-x²+54x+56
Answer:
2x^4+ x^3 - x^2 + 54x - 56 expression represents the area of Dylan’s room
Step-by-step explanation:
C on edge :)
The roots of x^2 + 5x + 3 = 0 are p and q, and the roots of x^2 + bx + c = 0are p^2 and q^2. Find b + c.
Answer:
[tex]\large \boxed{\sf \ \ \ b=-19, \ \ c=9, \ \ \ b+c=-10 }[/tex]
Step-by-step explanation:
Hello,
we can write
[tex]x^2+5x+3=(x-p)(x-q)=x^2-(p+q)x+pq[/tex]
it means that p+q = -5 and pq=3
And then we are looking for b and c so that
[tex]x^2+bx+c=(x-p^2)(x-q^2)=x^2-(p^2+q^2)x+p^2q^2[/tex]
So
[tex]b=-(p^2+q^2)=-[(p+q)^2-2pq]=-[(-5)^2-2*3]=-(25-6)=-19\\\\c=p^2q^2=3^2=9[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Answer:
b + c = -10
Step-by-step explanation:
Notice that according to he quadratic formula, the solutions to a quadratic equation of the form:
[tex]x^2+bx+c=0[/tex]
are:
[tex]x=\frac{-b+/-\sqrt{b^2-4\,c} }{2}[/tex]
and such solutions verify the following conditions:
a) the product of the solutions is:
[tex](\frac{-b+\sqrt{b^2-4c} }{2} )\,(\frac{-b-\sqrt{b^2-4c} }{2} )=\frac{b^2-(b^2-4c)}{4} =\frac{4\,c}{4} =c[/tex]
b) the addition of the solutions is:
[tex](\frac{-b+\sqrt{b^2-4c} }{2} )+(\frac{-b-\sqrt{b^2-4c} }{2} )=\frac{-b-b}{2} =\frac{-2\,b}{2} =-b[/tex]
Therefore, applying these to the first equation, we get that the solutions p and q must verify:
[tex]p\,*\,q=3\,\,\,\,and\,\,\,\,p\,+\,q=-\,5[/tex]
On the other hand, we know that the solutions of the equation
[tex]x^2+bx+c=0[/tex]
are [tex]p^2\,\,\, and \,\,\,q^2[/tex]
Then considering what we found in step a), the product of these two solutions should equal the constant term"c":
[tex]p^2\,*\,q^2= c\\(p\,*\,q)\,(p\,*\,q)=c\\3\,*\,3 = c\\9=c[/tex]
so we know the value of "c" in the second quadratic expression: c = 9
Now, according to what we found in step b), the addition of the two solutions for the second quadratic expression should equal the opposite of the coefficient in the linear term. That is:
[tex]p^2+q^2=-b[/tex]
So, we need to find what the addition of these two squares is in order to find "b". We consider then what the expression [tex](p+q)^2[/tex] renders, since we know that [tex](p+q)=-5[/tex]:
[tex](p+q)^2=p^2+2\,p\,q+q^2\\(-5)^2=p^2+q^2+2\,(p\,*\,q)\\25=p^2+q^2+2\,(3)\\p^2+q^2=25-6\\p^2+q^2=19[/tex]
This means that
[tex]-b=19\\\\b=-19[/tex]
Now, knowing b and c, we can find what b+c is:
[tex]b+c=-19+9=-10[/tex]
Find the other endpoint of the line segment with the given endpoint
and midpoint
Endpoint 1: (9,1)
Midpoint: (1,6)
Endpoint 2= (
Step-by-step explanation:
Let the other endpoint be (x,y)
Since, (1,6) is the midpoint between (9,1) and (x,y)
Therefore,
1=(9+x)/2
=> 2=9+x
=> x= -7
and,
6=(1+y)/2
=>12= 1+y
=> y=11
So, the other endpoint is ( -7, 11)
Answer:
( - 7 , 11)Step-by-step explanation:
Let the coordinates of Endpoint 2 be
(x ,y)
The midpoint of the endpoints is given by
[tex](1,6) = ( \frac{9 + x}{2} , \frac{1 + y}{2} )[/tex]
Where x and y are coordinates of Endpoint 2
Comparing with the midpoint we have
[tex]1 = \frac{9 + x}{2} \\ 2 = 9 + x \\ \\ x = 2 - 9 \\ \\ x = - 7[/tex]
[tex]6 = \frac{1 + y}{2} \\ 12 = 1 + y \\ \\ y = 12 - 1 \\ \\ y = 11[/tex]
Therefore x = - 7 and y = 11
The coordinates of Endpoint 2 are
( - 7 , 11)Hope this helps you
2. Hessa was playing a computer game. She scored 43 points in Round 1 and 26 points in Round 2. Which sum could she use to add the points together? a. 40 + 20 + 3 + 6 b. 4 + 3 + 2 + 6 c. 40 + 30 + 20 + 60 d. 30 + 4 + 60 + 2
Answer:
a. 40 + 20 + 3 + 6Step-by-step explanation:
Points scored by Hessa is as shown below;
Round 1 = 43 points
Round 2 = 26 points
Total points for both rounds = 43 + 26 = 69 points
To determine the sum she could use to add the points together, we must select the sum that will give us the same total of points for both rounds i.e 69 points.
The Round 1 score (43 pt)can also be expressed as (40+3) points
The Round 2 score (26 pt)can also be expressed as (20+6) points
The sum she could use to add the points together will be (40+3)+(20+6)
which is also equal to 40 + 20 + 3 + 6 = 69points
Hence, option a is correct
Given a normal population which has a mean of 110 and a standard deviation of 5, find the probability that a random sample of 49 has a mean between 109 and 112. Report your answer to four decimal places.
Answer:
0.9168
Step-by-step explanation:
From the data given:
Mean = 110
standard deviation = 5
Let consider a random sample n =49 which have a mean between 109 and 112.
The test statistics can be computed as:
[tex]Z_1 = \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z_1 = \dfrac{109- 110}{\dfrac{5}{\sqrt{49}}}[/tex]
[tex]Z_1= \dfrac{-1}{\dfrac{5}{7}}[/tex]
[tex]Z_1[/tex] = -1.4
[tex]Z_2= \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z_2 = \dfrac{112- 110}{\dfrac{5}{\sqrt{49}}}[/tex]
[tex]Z_2 = \dfrac{2}{\dfrac{5}{7}}[/tex]
[tex]Z_2 =2.8[/tex]
Thus; P(109 < [tex]\overline x[/tex] < 112) = P( - 1.4 < Z < 2.8)
= P(Z < 2.8) - P( Z < -1.4)
= 0.9974 - 0.0806
= 0.9168
how do you know if the solutions to a quadratic equations are inside, outside, on, inside and on, or outside and on the parabola? with the different equality signs?
Answer:
Option (1)
Step-by-step explanation:
Given quadratic equation in this question is,
y < -x²+ 4x + 5
Now we will convert this standard quadratic equation into vertex form,
y < -(x² - 4x) + 5
y < -[x² - 2(2)x + 2²] + 5
y < -(x - 2)²+ 5
This equation is in the form of y < a(x - h)² + k
where (h, k) is the vertex of the parabola.
Therefore, y < -(x - 2)²+ 5 will show the parabola with properties as,
1). Parabola having vertex at (2, 5).
2). Coefficient 'a' is negative, so parabola will open downwards.
3). In the inequality notation of less than, (sign < ) will show the solution area inside the parabola.
[If an inequality has a sign of greater than, solution area will be outside the parabola.]
Therefore, Option (1) will be the answer.
The length of 7 (the minor arc) is 15 cm. What is the circumference of Z?
Answer:450 cm
Step-by-step explanation:
A middle school took all of its 6th grade students on a field trip to see a play at a theatre that has 2000 seats. The students filled 65% of the seats in the theatre. How many 6th graders went on the trip?
Answer: 1,300 students went on the trip
Step-by-step explanation: So we know that 65% filled the seats so let's turn that into a fraction. [tex]\frac{65}{100}[/tex] . Now we know that there are 2,000 seats in total so let's put that into a fraction. [tex]\frac{x}{2,000}[/tex] The x represents the students that went on the trip.
[tex]\frac{65}{100} = \frac{x}{2,000}[/tex] we have to cross multiply
65(2,000) = 100 (x)
130,000 = 100 (x)
130,000 ÷ 100
1,300 = x So now we know that 1,300 went to the trip students
The step function g(x) is defined as shown. g(x) = StartLayout Enlarged left-brace 1st row 1st column negative 3, 2nd column x less-than-or-equal-to 0 2nd row 1st column 2, 2nd column 0 less-than x less-than-or-equal-to 4 3rd row 1st column 5, 2nd column 4 less-than x less-than-or-equal-to 10 EndLayout
Answer:
{–3, 2, 5}
Step-by-step explanation:
The range refers to the values for the axis i.e to be dependent when there is a defined function
And the range is the combination of the integer i.e to be compounded by these three values
Data provided in the question
-3 , x ≤ 0
2, 0 < x ≤ 4
5, 4 < x ≤ 10
Based on the above information, the range of g(x) is {-3,2,5}
Hence, the correct option is c.
Answer:
C
Step-by-step explanation:
Pls answer the image given
Answer:
[tex]4 \frac{1}{4} [/tex] hours
Step-by-step explanation:
Given,
Time spent in studies : [tex]1 \frac{3}{4} [/tex] hours
Time spent in playing cricket : [tex]2 \frac{1}{2} [/tex] hours
Now, let's find the time that he spent in all:
[tex]1 \frac{3}{4} + 2 \frac{1}{2} [/tex]
Add the whole number and fractional parts of the mixed numbers separately
[tex](1 + 2)( \frac{3}{4} + \frac{1}{2} )[/tex]
Add the numbers
[tex]3 +( \frac{3}{4} + \frac{1}{2} )[/tex]
Add the fractions
[tex]3 + ( \frac{3 + 1 \times 2}{4} )[/tex]
[tex]3 + ( \frac{3 + 2}{4} )[/tex]
[tex]3 + \frac{5}{4} [/tex]
Convert the improper fraction into mixed number
[tex] 3 + 1\frac{1}{4} [/tex]
Write the mixed number as a sum of the whole number and the fractional part
[tex]3 + 1 + \frac{1}{4} [/tex]
Add the numbers
[tex]4 + \frac{1}{4} [/tex]
Write the sum of whole number and the fraction as a mixed number
[tex]4 \frac{1}{4} [/tex] hours
Hope this helps..
Best regards!!
Answer:
4 1/4 hours.
Step-by-step explanation:
1 3/4 + 2 1/2
= 1 + 2 + 3/4 + 1/2
= 3 + 3/4 + 1/2 The LCM of 2 and 4 is 4 so 1/2 = 2/4. and so we have:
3 + 3/4 + 2/4
= 3 + 5/4
= 3 + 1 1/4
= 4 1/4 hours.
PLEASE HELP ME with this question! I really need help...
Answer:
One of the other perpendicular bisectors must pass through point B
Step-by-step explanation:
Let's look at the choices:
— incenter equidistant from B and C.
The incenter is on the perpendicular bisector of BC. Every point on that line is equidistant from B and C. This statement is True.
__
— angles B and C are congruent.
As we said above, A (on the perpendicular bisector of BC) is equidistant from B and C. That makes the triangle isosceles. The congruent angles are B and C, opposite congruent sides AC and AB. This statement is True.
__
— the perpendicular bisector of BC passes through the incenter.
The incenter is the point of concurrence of the angle bisectors. Since the perpendicular bisector of BC goes through the a.pex of triangle ABC at A, it is the angle bisector there. Hence the incenter lies on that line. The statement is True.
__
— B lies on one of the other perpendicular bisectors.
This will be true if the triangle is equilateral. Nothing in the problem statement indicates this is the case. The statement is False.
Helpppppppppp pleasessssss
Answer:
A.
Step-by-step explanation:
When it says (x + 7), that means the graph will be shifting to the right (so parallel to the x-axis.
Factor 1
Which expression is the factored form of
x2 - 7x + 10?
+x
-X
42
-
+
0 (x+3)(x + 4)
o (x - 3)(x - 4)
(x-2)(x - 5)
(x + 2)(x + 5)
ON
-
+
+
-X
Factor
+
+
-
+
+
LY
+
+
-
+
+
Reset
Intro
ODNO
Answer:
(x - 2)(x - 5)Step-by-step explanation:
[tex]x^2 - 7x + 10=\\\\=x^2 - 5x -2x + 10=\\\\=x(x-5)-2(x-5)=\\\\=(x-5)(x-2)[/tex]
Answer:
[tex]\boxed{(x-2)(x-5)}[/tex]
Step-by-step explanation:
=> [tex]x^2-7x+10[/tex]
Using mid-term break formula
=> [tex]x^2-5x-2x+10[/tex]
=> x(x-5)-2(x-5)
Taking (x-5) as common
=> (x-2)(x-5)
what is 3x^3 - 11x^2 - 26x + 30 divided by x-5?
Answer:
Most likely the answer is
3x^2+4x-6
Answer:
3x^2+4x-6 is correct
Am I the only person that is having problems with seeing answers?
Answer:
Been having issues all night
Answer:
Step-by-step explanation: no
Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the segment lengths that equal the following functions (in the correct order):
sin(theta),
cos(theta),
tan(theta),
csc(theta),
sec(theta),
cot(theta).
So, for example, you would answer a,k,h,c,b,d if you thought
sin(theta) = a,
cos(theta) = k,
tan(theta) = h,
csc(theta) = c,
sec(theta) = b,
cot(theta) = d.
I was able to come up with:
sin(theta) = d,
cos(theta) = a,
tan(theta) = h,
csc(theta) = f,
sec(theta) = g,
cot(theta) = h.
Answer:
32
Step-by-step explanation:
Simplify. Rewrite the expression in the form 4^n. 4^11/4^-8
Answer:
S6tep-by-step explanation:
4^(11+8) = 4^19 is the solution
Latesha’s mother puts $85 in Latesha’s lunch account at school. Each day Latesha uses $3 from her account for lunch. The table below represents this situation. Latesha’s Lunch Account Day Amount Left in Account ($) 0 $85 1 2 3 4 5 How much is left in Latesha’s lunch account after she has had lunch for 5 days? $15 $67 $70 $82
Answer: it 70
Step-by-step explanation:
Latesha’s mother puts $85 in Latesha’s lunch account at school. Each day Latesha uses $3 from her account for lunch. The table below represents this situation.
How much is left in Latesha’s lunch account after she has had lunch for 5 days?
$15
$67
$70 is correct$82
you tube guests are for hire
Find the missing side. Round your answer to the nearest tenth.
Answer:
44.8
Step-by-step explanation:
cos α = adjacent leg/hypotenuse
cos 48° = 30/x
x = 30/(cos 48°) = 44.8
One angle of an isosceles triangle is 80º. What are the other two angles?
Answer:
80 and 20
Step-by-step explanation:
80+80+20=180
Please answer this in two minutes
Answer:
k = 4Step-by-step explanation:
It is half of equilateral triangle where 2√3 is its hight so:
[tex]2\sqrt3=\frac{k\sqrt3}2\\\\4\sqrt3=k\sqrt3\\\\k=4[/tex]
Which ordered pair is a solution of the equation? y = 7 x − 3 y=7x−3
Answer:
(1,4)
Step-by-step explanation:
Which ordered pair is a solution of the equation? y = 7 x − 3
a. (1,4) b. (-1,-4) c. both d. neither
Solution
y=7x-3
Solve by trying each ordered pair
a. (1,4)
x=1, y=4
Substituting the value of x and y into the equation
y=7x-3
4=7(1)-3
4=7-3
4=4
This is a true statement
b. (-1,-4)
x=-1, y=-4
Substitute the value into the equation
y=7x-3
-4=7(-1)-3
-4= -7-3
-4= -11
This is not a true statement
This true statement is when x=1 and y=4
So, the ordered pair (1, 4) is the solution
PLEASE HELP ME I DONT UNDERSTAND AND NOW IM WRITING STUFF TO GET AT LEAST 20 WORDS SO I CAN ASK THE QUESTION
Answer:
The answer is 75 degrees
Step-by-step explanation:
Supplementary angles add to 180 and 105 + Y= 180.
So, you subtract 105 from 180 and Y is 75
ANSWER FAST A 10 ft long ladder has one end that leans against a wall and another that rests on the ground 6 feet from the wall. How high on the wall does the ladder rest?
Answer:
8 feet
Step-by-step explanation:
[tex]h = \sqrt{10^{2} - 6^{2} } = \sqrt{100 - 36} = \sqrt{64} = 8[/tex]
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answer:
4x-2
Step-by-step explanation:
4x(3x+5)-2(3x+5)
(4x-2)(3x+5)
you can see that 4x-2 is a factor
15 points are placed on a circle. How many triangles is it possible to form, such that their vertices will be the given points?
Answer: 445 triangles can be form with 15 dots of a circle (I hope good luck)
Step-by-step explanation:
Answer:
455
Step-by-step explanation:
There are 15 points on a circle.
We need three points to form a triangle
Therefore the number of triangles = 15 choose 3 = 15!/(3!x12!) = (15x14x13)/(3x2x1) = 5x7x13 = 455
Hence the number of triangles formed is 455
How much will Bob need to save each month if he wants to buy a $30,000 car with cash in 5 years? He can earn a nominal interest rate of 10% compounded monthly.
a) $2.50
b) $250.00
c) $25.00
d) $1,862.76
Answer:
B
Step-by-step explanation:
C is too little and D is too much
A: Top 6% of scores B: Scores below the top 6% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 7% F: Bottom 7% of scores Scores on the test are normally distributed with a mean of 79 and a standard deviation of 8.4. Find the numerical limits for a B grade. Round your answers to the nearest whole number, if necessary.
Answer:
The numerical limits for a B-grade is between 81 and 92
Step-by-step explanation:
Here in this question, our task is to find the numerical limits for B grade. This means the range between a test taker would be scored a B grade
Please check attachment for complete solution and explanation
