Answer:
C. T is not one-to-one because the standard matrix A has a free variable.
Step-by-step explanation:
Given
[tex]T(x_1,x_2,x_3) = (x_1-5x_2+4x_3,x_2 - 6x_3)[/tex]
Required
Determine if it is linear or onto
Represent the above as a matrix.
[tex]T(x_1,x_2,x_3) = \left[\begin{array}{ccc}1&-5&4\\0&1&-6\\0&0&0\end{array}\right] \left[\begin{array}{c}x_1&x_2&x_3\end{array}\right][/tex]
From the above matrix, we observe that the matrix does not have a pivot in every column.
This means that the column are not linearly independent, & it has a free variable and as such T is not one-on-one
What is the answer to
24 + y = 41
Answer:
y=17
Step-by-step explanation:
move the constant to the right hand side and change it's sign
y=41-24
then subtract the numbers y= 41-24
which = 17
Answer: i believe it is 24 + 17 = 41 ^^ can you give me brainly when you get the chance
Step-by-step explanation:
What is the value of “a” in the function equation?
Answer: the value of A is 2
Step-by-step explanation:
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.
Ms. Nellies has 2 1/2 pints of vinegar for her students to use in a science experiment.Each group of students needs 3/8 pint of vinegar.Trey draws the number line model and writes the equation below to help Ms. Nellies figure out how many 3/8-pint serving of vinegar she has.Are Trey's number line model and equation correct?
Trey's number line is _______ because it represents the expression _________.The correct equation is _______.Ms. Nellies has enough vinegar for _________ groups of students.
1st blank box: correct or incorrect
2nd blank box: 2 1/2 x 3/4,2 1/2 ÷ 3/4,2 1/2 x 3/8,or 2 1/2 ÷ 3/8.
3rd blank box: 2 1/2 ÷ 3/8= 6 2/3,2 1/2 ÷ 3/8 = 3 1/3,2 1/2 x 3/8 = 2 3/16, or 2 1/2 ÷ 3/8 = 15/16
4th blank box: 2,6,3,or 0
Answers:
Trey's number line is incorrect because it represents the expression 2 1/2 ÷ 3/4.
The correct equation is 2 1/2 ÷ 3/8 = 6 2/3.
Ms. Nellies has enough vinegar for 6 groups of students.
===========================================================
Explanation:
Trey has the right idea, but made a mistake on how the tickmarks are set up. Focus on the interval from 0 to 1. This section is cut into 4 equal pieces. So each tickmark represents 1/4 of a unit.
Going 3 tickmarks across means 3/4 of a unit is represented. Since each larger arc represents 3/4 of a unit, this means we're dividing the 2 & 1/2 over 3/4 instead of 3/8
That's why Trey's model represents 2 1/2 ÷ 3/4
The value 3 & 1/3 at the end is correct. Visually we see 3 whole jumps plus an extra 1/3 of a jump to arrive at 2 & 1/2. But again, Trey didn't cut the number line up in the right way, so it doesn't matter that he arrived at the correct result of 3 & 1/3 since his initial setup is faulty.
------------------------------
See the diagram below to see what Trey should have drawn. Notice each tickmark represents 1/8 instead of 1/4. Each large blue arc jump represents 3/8 of a unit. We have exactly 6 of these blue arcs plus 2 additional smaller arcs that are 1/3 of the blue arc. So that accounts for the 1/3+1/3 = 2/3 portion.
Overall, we would say that the equation is 2 1/2 ÷ 3/8 = 6 2/3
If you're curious why that equation works, check out the steps below
[tex]2 \frac{1}{2} \div \frac{3}{8} = \frac{5}{2} \div \frac{3}{8}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{5}{2} \times \frac{8}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{5*8}{2*3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{40}{6}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{20}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{18+2}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = \frac{18}{3}+\frac{2}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = 6+\frac{2}{3}\\\\2 \frac{1}{2} \div \frac{3}{8} = 6\frac{2}{3}\\\\[/tex]
So again, the equation is 2 1/2 ÷ 3/8 = 6 2/3
------------------------------
What does this all mean? Well it means the teacher can break up the vinegar into 6 whole parts plus an additional 2/3 of a part.
In other words, 6 groups will get 3/8 of a pint each. The leftover part 2/3 isn't enough to form that 7th group. Notice in the diagram below, we have 2/8 = 1/4 of a pint which is smaller than 3/8 of a pint.
1/4 = 0.25
3/8 = 0.375
So this is another way to see that the leftovers isn't enough to form a 7th group.
Therefore, she has enough vinegar for 6 groups
Matthew collected data on what types of pets sixth grade students owned.
He asked 200 students and then created this graph.
Based on the circle graph, how many students own a dog?
A ordinary fair dice is thrown once. What is the probability the dice lands on a even number
Determinar a posição da reta r, de equação 2x-3y+5=0, em relação à reta s, de equação 4x-6y-1=0
Answer:
[tex]2x - 3y = - 5 - - - (a) \\ 4x - 6y = 1 - - - (b) \\ no \: answers[/tex]
A certain group of test subjects had pulse rates with a mean of 75.2 beats per minute and a standard deviation of 11.2 beats per minute. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is a pulse rate of 147.6 beats per minute significantly low or significantly high?
Answer:
The z-score for a pulse rate of 147.6 beats per minute is 6.46 > 2, which means that this pulse rate is significantly high.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
By the Range Rule of Thumb, if Z < -2, the measure X is significantly low, and if Z > 2, the measure X is significantly high.
Mean of 75.2 beats per minute and a standard deviation of 11.2 beats per minute.
This means that [tex]\mu = 75.2, \sigma = 11.2[/tex]
Is a pulse rate of 147.6 beats per minute significantly low or significantly high?
We have to find Z when X = 147.6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{147.6 - 75.2}{11.2}[/tex]
[tex]Z = 6.46[/tex]
The z-score for a pulse rate of 147.6 beats per minute is 6.46 > 2, which means that this pulse rate is significantly high.
The diameter of a circle is equal to twice it's radius
TRUE OR FALSE
Answer:
true
Step-by-step explanation:
The diameter of a circle is a single line segment that stretches the entire width of the circle, intersecting with the center point and two points around the circumference. The diameter measures how wide the circle is, and is always equal to twice the radius (2r).
Which expression is equivalent to 1/2 (6x + 1/2)
Answer:
3x + 1/4
Step-by-step explanation:
1/2 (6x + 1/2)
Distribute
1/2 * 6x + 1/2 * 1/2
3x + 1/4
f(x) = x + 2 when x = 10
Answer:
f(10) = 12
Step-by-step explanation:
f(x) = x + 2
Substitute x for 10.
f(10) = 10 + 2
f(10) = 12
Answer:
12
Step-by-step explanation:
Substitute 10 into x -> 10+2=12
What is an inscribed polygon is being constructed
A square
Step-by-step explanation:
because there're only 2 circles being create whereas with an equilateral
Answer:
A square
Step-by-step explanation:
I need help please :)
At a sale this week, a suit is being sold for $235.60. This is a 62% discount from the original price.
What is the original price?
Answer:
$620
Step-by-step explanation:
（1-62%）X=235.6
X=235.6/38%
X=620
The original price is $620
Make x the subject of the formula p = x + a b
Answer:
Step-by-step explanation:
x + ab = p
x = p - ab
Simplify each expression by writing the expression without absolute value bars
Answer:
-1
Step-by-step explanation:
When b<4
|b-4| is negative
|b-4| = - ( b-4)
- (b-4) / ( b-4) =
Factoring out (b-4)
-1
helpppppppppppppppppppppppppp
Find the surface area of a square pyramid with side length 4 and slant height 5.
Answer:
56
Step-by-step explanation:
the surface area = (4×4) + (4×½×4×5)
= 16 + 40
= 56
this................................................................................................
Answer:
5
Step-by-step explanation:
3-(-2)
the two negative signs cancel out and it turns into
3 + 2
3 + 2 = 5
Answer:
5
Step-by-step explanation:
minus * minus = plus
3-(-2) = 3 + 2 = 5
40 oz < 3lb
Is it true or false ?
Answer:
True
Step-by-step explanation:
40oz = 2.5 lb
10 = 0.625
Tyler thinks that this figure has enough information to figure out the values of A and B.
Do you agree? Explain your reasoning.
Answer: No
Step-by-step explanation:
We know that A+B = 90, but without further information we cannot determine the specific values of A and B.
Suppose we want to choose for letters without replacement from 18 distant lovers how many ways can this be done if the order of the choices does not matter
Answer:
This can be done in 3,060 ways.
Step-by-step explanation:
Letters are chosen without replacement, and the order does not matter, which means that the combinations formula is used.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
Four letters from a set of 18. So
[tex]C_{18,4} = \frac{18!}{4!14!} = 3060[/tex]
This can be done in 3,060 ways.
how do i solve this ?
Answer:
[tex]2\sqrt{2}[/tex]
Step-by-step explanation:
The given triangle is an isosceles triangle. However, one can see that it has a right angle (indicated by the box around the angle). Thus the triangle is a (45 - 45 - 90) triangle. A (45- 45 - 90) triangle is the only right isosceles triangle. One of the properties of a right isosceles triangle is that its sides follow the following ratio,
[tex]a;a;a\sqrt{2}[/tex]
Where (a) represents the legs of the right triangle, the sides that are adjacent to the right angle, in this case, the congruent sides. ([tex]a\sqrt{2}[/tex]) is the hypotenuse, the side opposite the right angle.
It is given that the hypotenuse is equal to (4), one is asked to find the length of the legs. To do so, divide the hypotenuse by ([tex]\sqrt{2}[/tex]) to find the legs. One can do this because the triangle is a (45 - 45 - 90) triangle, thus it must follow the ratio of the sides.
[tex]=\frac{4}{\sqrt{2}}[/tex]
Rationalize the denominator,
[tex]\frac{4}{\sqrt{2}}\\\\=\frac{4\sqrt{2}}{2}\\\\=2\sqrt{2}[/tex]
need an answer quick, will give the first right answer brainliest, i need a step by step explanation please
Answer: Imma say C
Step-by-step explanation:
Find the area of the triangle, WILL GIVE BRAINLIEST
Answer:
10 cm^2
Step-by-step explanation:
area= 1/2 b*h
1/2 (5) (4)
= 1/2 (20)
=10
area= 10cm^2
Answer:
a = 10cm²
Step-by-step explanation:
a = (1/2)bh
a = (1/2)(5)(4)
a = 10cm²
Question: An expression is shown below: f(x) = x^2 – 6x + 5
Part A: What are the x-intercepts of the graph of f(x)? Show your work.
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the coordinates of the vertex? Justify your answers and show your work.
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part A and Part B to draw the graph.
given a parabola in standard form
y
=
a
x
2
+
b
x
+
c
then the x-coordinate of the vertex can be found using
∙
x
x
vertex
=
−
b
2
a
y
=
x
2
−
6
x
+
5
is in standard form
with
a
=
1
,
b
=
−
6
,
c
=
5
⇒
x
vertex
=
−
−
6
2
=
3
substitute this value into equation for y-coordinate
y
vertex
=
3
2
−
6
(
3
)
+
5
=
−
4
⇒
vertex
=
(
3
,
−
4
)
the axis of symmetry is vertical and passes through the
vertex with equation
x
=
3
to find x-intercepts let y = 0
⇒
x
2
−
6
x
+
5
=
0
the factors of + 5 which sum to - 6 are - 1 and - 5
⇒
(
x
−
1
)
(
x
−
5
)
=
0
equate each factor to zero and solve for x
x
−
1
=
0
⇒
x
=
1
x
−
5
=
0
⇒
x
=
5
⇒
x
=
1
and
x
=
5
←
x-intercepts
graph{(y-x^2+6x-5)(y-1000x+3000)=0 [-10, 10, -5, 5]}
4(x + 3) + 2x in the simplest form
Answer:
6x + 12
Step-by-step explanation:
Distribute the 4 first. Now you have 4x + 12 + 2x. 4x + 2x are like terms and therefore they can be added. Your final simplified answer is therefore 6x + 12.
If the original quantity is 14 and new quantity is 35 what is the percent change
Answer:
150%
Step-by-step explanation:
given:
original quantity = 14
new quantity = 35
increased quantity = 35 - 14
=21
percent change = increased quantity /original quentity * 100%
=21/14 *100%
=21100/14 %
=150 %
From the observation deck of a skyscraper,
Taylor measures a 67° angle of depression
to a ship in the harbor below. If the
observation deck is 1014 feet high, what is
the horizontal distance from the base of the
skyscraper out to the ship? Round your
answer to the nearest tenth of a foot if
necessary.
Given:
Angle of depression from observation deck to a ship = 67°
Height of observation deck = 1014 feet.
To find:
The horizontal distance from the base of the skyscraper out to the ship.
Solution:
Let x be the horizontal distance from the base of the skyscraper out to the ship.
Using the given information draw a diagram as shown below.
In a right angle triangle,
[tex]\tan\theta=\dfrac{Perpendicular}{Base}[/tex]
For triangle ABC,
[tex]\tan A=\dfrac{BC}{AB}[/tex]
[tex]\tan (67^\circ)=\dfrac{1014}{x}[/tex]
[tex]x=\dfrac{1014}{\tan (67^\circ)}[/tex]
On further simplification, we get
[tex]x=\dfrac{1014}{2.35585}[/tex]
[tex]x=430.41789[/tex]
[tex]x\approx 430.4[/tex]
Therefore, the horizontal distance from the base of the skyscraper out to the ship is 430.4 feet.
Applying the Trigonometry ratio, TOA, the horizontal distance from the base of the skyscraper out to the ship is: 430.4 ft.
Recall:
To solve a right triangle, apply any of the Trigonometry ratios, SOH CAH TOA, where necessary.The situation described is shown in an image attached below, where:
BA = horizontal distance from the base of the skyscraper out to the ship (adjacent side length)BC = 1014 ft (Opposite side length)∠A = 67° = reference angle (∅)To find BA, apply TOA, which is:
tan ∅ = Opp/Adjacent
Substitutetan 67 = 1014/BA
[tex]BA = \frac{1014}{tan(67)} \\\\\mathbf{BA = 430.4 $ ft}[/tex]
Therefore, applying the Trigonometry ratio, TOA, the horizontal distance from the base of the skyscraper out to the ship is: 430.4 ft.
Learn more about Trigonometry ratio on:
https://brainly.com/question/10417664
PLS HELP
Which is a solution for the inequality -6x – 5 <-23 ?
(1) O
(2) 2
(3) -2
(4) 5
If a rectangle has a length of 8 centimeters and a width of 5 centimeters, then what is the area of the rectangle in square centimeters?
Answer:
40 centimeters square.
Step-by-step explanation:
Area= length × width
8×5=40
Have a nice day
