Answer:
The quadratic equation [tex]2\, x^{2} - 3\, x + 8 = 0[/tex] has no real solution.
Step-by-step explanation:
Rewrite the quadratic equation [tex]2\, x^{2} - 3\, x + 8 = 0[/tex] in the standard form [tex]a\, x^{2} + b\, x + c = 0[/tex]:
[tex]2\, x^{2} + (-3)\, x + 8 = 0[/tex], for which:
[tex]a = 2[/tex].[tex]b = (-3)[/tex].[tex]c = 8[/tex].The quadratic discriminant of [tex]a\, x^{2} + b\, x + c = 0[/tex] is [tex](b^{2} - 4\, a\, c)[/tex]. The quadratic discriminant of [tex]2\, x^{2} + (-3)\, x + 8 = 0[/tex] would be:
[tex]\begin{aligned}& b^{2} - 4\, a\, c \\ =\; & (-3)^{2} - 4 \times 2 \times 8 \\ =\; & (-55)\end{aligned}[/tex].
Since the quadratic discriminant of this equation is negative, this quadratic equation has no real solution.
If the volume of this rectangular prism is 385 cubic inches, what is the value of x?
(x - 2) in.
xin.
W + 4) in
X
inches
Answer:
x=7
Step-by-step explanation:
x(x-2) (x+4) =385
distribute the x and solve
The value of x is 8 in.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
Length = x + 4
Width = x
Height = x - 2
The volume of the rectangular prism = 385 in³
The volume of the rectangular prism = length x width x height
Now,
length x width x height = 385
(x + 4) x (x - 2) = 385
(x + 4) (x² - 2x) = 385
x³ - 2x² + 4x² - 8x = 385
x³ + 2x² - 8x = 385
This is a cubic polynomial.
f(x) = x³ + 2x² - 8x - 385
f(x) = a³ + bx² + cx + d = 0
Using the calculator we get,
Roots:
x = -3.20181 + 5.96339 i (rejected)
x = -3.20181 - 5.96339 i (rejected)
x = 8.40362 = 8
Thus,
The value of x is 8 in.
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3 + 4ab - 5b + m
Number of terms:
Coefficients:
Constant terms:
Answer:
Number of terms = 4 (there are four terms)
coefficients = the coefficient of ab = 4
✓✓✓ ✓✓✓ ✓ b = -5
✓✓✓ ✓✓✓ ✓ m = 1
constant terms = 3
Hope it helped!!
Number of terms, Coefficients, Constant terms are 4,2 and 1
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given;
3 + 4ab - 5b + m
Number of terms here are
=4
Coefficients we have
=2
Constant terms
=1
Therefore, the answer to this algebra will be 4,2 and 1
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help plsls I’ll brainlist i promise this one’s abit confusing tho.
Answer:
25
Step-by-step explanation:
Please refer to the picture;
Determine the missing value, x. Then, classify the triangle by side and by angle measure.
Question in below;
The value of x in the right angle triangle is approximately 45 degrees.
How to find an angle in a right angle triangle?The angle of the right angle triangle can be found as follows:
Therefore, let's find the hypotenuse side using Pythagoras theorem,
6² + 6² = c²
c² = 72
c = √72
c = 8.48528137424
c = 8.5 cm
Hence,
sin x = opposite / hypotenuse
sin x = 6 / 8.5
sin x = 0.70588235294
x = sin⁻¹ 0.70588235294
x = 44.9006818301
x = 45°
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Does the graph show a linear function?
DOES THE GRAPH SHOW A LINEAR FUNCTION?
[tex] \sf \large \color{grey}{YES IT SHOWS A GRAPHIC LINEAR}[/tex]
Answer:
yeah, cuz it's a line that's straight
In a class of students, the following data table summarizes how many students play an instrument or a sport. What is the probability that a student who plays a sport does not play an instrument?
Plays an instrument Does not play an instrument
Plays a sport 12 13
Does not play a sport 3 2
The probability that a student who plays a sport does not play an instrument is 13 / 30.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that a student who plays a sport does not play an instrument = 13 / total number of students
13 / (12 + 13 + 2 + 3) = 13 / 30
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What is the length of the diagonal of the rectangle?
a) 2.5 units
b) 4.5 units
c) 5 units
d) 7 units
Answer:
I do believe its 5 units, if I am incorrect I apologize
Step-by-step explanation:
a tv studio has brought in 4 boy kittens and 5 girl kittens for a cat food commercial. the director is going to choose 5 of these kittens at random to be in the commercial.
what is the probability that the director chooses 3 boy kittens and 2 girl kittens? round your answer to three decimal places.
The probability that the director chooses 3 boy kittens and 2 girl kittens is 0.32.
What is probability?It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have total number of kitten = 4+5 = 9
Total number of outcomes if the director is going to choose 5 of these kittens at random to be in the commercial:
= C(9, 5) = 126
The director chooses 3 boy kittens number of ways:
= C(4, 3) = 4
The director chooses 2 girl kittens number of ways:
=C(5, 2) = 10
Total favourable outcomes = 10×4 = 40
The probability = 40/126
= 0.317 ≈ 0.32
Thus, the probability that the director chooses 3 boy kittens and 2 girl kittens is 0.32.
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multiply 7 by the fourth power of the square root of forty-nine.
Answer:
16807
Step-by-step explanation:
7 * ((sqrt49)^4 = 7 * 7^4 = 7^5 = 16807
The ratio of number of student wearing sneakers in a class to the number of students wearing sandals in the class is 3:4 How many were are waring sneakers if there are 28 student in the class
12 students are wearing sneakers.
Answer:
12
Step-by-step explanation:
So, the ratio is 3:4. That means this is for every 7 students. We have 28 students, so we need to know how many times 7 was multiplied to get to 28. 28 divided by 7 gives you 4. Now, we have to multiply both numbers in the ratio by 4. 3 times 4 is 12, and 4 times 4 is 16. The new ratio is 12:16. The students wearing sneakers were originally the 3 that got multiplied into 12, so the answer is 12.
Hope this helps!
Y=5+x how do we solve for x?
pls answer asap!!! much appreciated
Answer:
e. 0.308.
Step-by-step explanation:
I can't draw the tree diagram but the answer is
P(red first) = 7/14 = 1/2
P( then black) = 4/13
P(red then black) = 1/2 * 4/13 = 2/13
P(black first) = 4/14 = 2/7
P( then red) = 7/13
P(black then red) =2/7 * 7/13 = 2/13
So Probability of red and black in any order
= 2/13 + 2/13 = 4/13
= 0.308.
Draw and label a point, a line, a line segment, a ray, and an angle in a triangle
Answer:
a point
a line
a line segment
a ray
and an angle in a triangle
Step-by-step explanation:
Help with these 10th grade geometry angle problems? I'm desperate and my teacher won't help me. Please also explain how you got your answer. Thank you.
Answer: 60
Step-by-step explanation:
See
m<COB and m<EOD are opposite anglesHence they are equal in measure.Hence
m<COB=60°
I need help with this problem
A cube has a side length of 6 cm. The cube is reduced by a scale factor of 1/3. Find the volume of the reduced cube. 2 cm3 4 cm3 6 cm3 8 cm3
Answer:
8 cm
Step-by-step explanation:
because when it's reduced we multiply the side length by 1/3 * 6 = 2cm and the volume will equal v = a^3 = 2^3 = 8cm
Answer:
8cm
Step-by-step explanation:
step1: 6/3=2
volume of a cube =x*x*
v
:=8cm
v=2×2×2
vvv v
Michael has a room in his house that is shaped like a parallelogram the length of the room measures 16 feet and the width measures 26 what is the perimeter of the
Answer:
84 ft
Step-by-step explanation:
16 + 16 + 26 +26 = 84
39 ft.². The length should be 10 feet more than its width. What should the dimensions of
the deck be?
Answer:
13 x 3 ft
Step-by-step explanation:
RECTANGULAR deck
L x W = 39 ft^2
(w+10) x w = 39
w^2 + 10w - 39 = 0
(w-3)(w+13) = 0 w = 3 or -13 (throw out)
w = 3 then l = 10 +3 = 13
Help me please! so jarring
Answer:
y = -5x + 4.
Step-by-step explanation:
y = mx + c is the general form
- where m = the slope of the line and c is the y-value where the graph cuts the y-axis.
The graph passes through the points (0, 4) and (1, -1) so the slope
= (Y2 - y1) / (x2 - x1)
= (-1-4) / (1-0)
= -5 = m.
and c = 4.
I need help with this ASAP
Answer:
hope this will help you........
You have a standard deck of 52 cards. Find the probability of drawing one card, then drawing another without replacement.
A) You draw an even-numbered card and then a face card.
B) Both cards you drew are "4" or higher (if aces are considered low cards and face cards are nonnumerical)
C) You drew a black face card and then a black "5".
Assuming that the all the cards have the same probability of being drawn we get:
A) P = 0.07B) P = 0.21C) P = 0.001How to find the probabilities?
We have a deck of 52 cards.
A) The probability of drawing an even-numbered card is given by the quotient between the number of even-numbered cards and the total number of cards.
On the 52 card deck, there are 16 even cards (2, 4, 6, 8 for each type), so the probability is:
p = 16/52
Then the probability of drawing a face card is given in the same way, notice that now there are 51 cards in the deck and 12 face cards, so we get:
q = 12/51
The joint probability is the product of these two:
P = (16/52)*(12/51) = 0.07
b) Both cards are 4 or larger.
There are 6 cards equal or larger than 4 for each type, so the probability for the first card is:
p = 24/52
For the second card, there is one card less in the deck (and one card less that is equal or larger than 4) so the probability is:
q = 23/51
The joint probability is:
P = (24/52)*(23/51) = 0.21
C) There are 6 black face cards, so the probability first is:
p = 6/52
Then there are 2 black cards with the number 5, so the probability is:
q = 2/51
The joint probability is:
P = (6/52)*(2/51) = 0.001
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In the figure below, what is the value of x?
Answer:
x = 31.
Step-by-step explanation:
93 = x + 62 (External Angle Theorem).
x = 93 - 62
= 31
Which describes the association between the number of DVDs sold and the number of DVDs rented?
The integer representing the change in the number of DVDs sold is -10000.
What is a change in number?Given, The number of DVDs shipped to an online retailer was 10,000 less than the previous year.
We have to Use an integer to describe the change in the number of DVDs sold.
Now, let the number of DVDs shipped to an online retailer in the previous year be x.
Then, according to the given information, DVDs shipped to the online retailer this year will become x – 10000
So, now, the change in the number of DVDs sold = DVDs sold this year – DVDs sold last year
= x – 10000 – x
= 0 – 10000
= - 10000
Hence, the integer representing the change in the number of DVDs sold is -10000.
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Solve the question within the screenshot please
Answer:
See below in bold.
Step-by-step explanation:
Let t be the number of tulips you buy and r be the number of rose bushes.
a.
The system is:
t + r = 13
4t + 10r = 100
b.
Solving:
4t + 10r = 100
t + r = 13 Multiply this by 4:
4t + 4r = 52 Subtract this from the first equation:
0 + 6r = 48
r = 8.
Now substitute for r in t + r = 13:
t + 8 = 13
t = 5.
c.
To buy 13 plants and spend $100 you need to buy 5 tulips and 6 rose bushes.
Which of the following could be calculated using the Pythagorean theorem? Select all that apply.
area of a circle
length of an arch
height of a building
distance to an airport
size of a window pane
Answer: height of a building
Step-by-step explanation:
a^2 + b^2 = c^2
used for finding missing side angle of a triangle
5. A wheel makes 726 revolutions per minute. How many
revolutions does it make per second?
Solve for [x]. The pair of polygons are similar.
5x+2
B
16
The scale factor from A to B is 2:9
the graph of y=x^3+x^2-6x is shown estimate the x coordinates of the turning point of the graph,
(a). From the graph the x estimates of the turning points are
-1.8 and 1.1.
(b). The solutions are where the graph crosses the x axis .. They are:
x = -3, 0 and 2.
What is polynomial?A polynomial is defined as the sum of the same variables having different powers.
Here we have the two third-degree polynomials
x³+x²-6x=0
For this the value of the variable at the turning point of the graph will be
at x=-1.8 and 1.1.
The another equation is :-
x³+x²-6x=0
The solution of the equation will be x = -3, 0 and 2. where the graph crosses the x-axis.
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Find the area that the curve encloses and then sketch it.
r = 3 + 8 sin(6)
Answer:
[tex]A=41\pi\: \text{units}^2\approxA\approx128.8053\:\text{units}^2[/tex]
Step-by-step explanation:
I assume you mean [tex]r=3+8\sin\theta[/tex]:
Use the formula [tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta[/tex] where [tex]a[/tex] and [tex]b[/tex] are the lower and upper bounds and [tex]r(\theta)[/tex] is the equation of the polar curve.
Since the graph is symmetrical about the line [tex]\displaystyle \theta=\frac{\pi}{2}[/tex], let the bounds of integration be [tex]\displaystyle \biggr(-\frac{\pi}{2},\frac{\pi}{2}\biggr)[/tex] to find half the area of the curve, and then find twice of that area:
[tex]\displaystyle A=\int\limits^a_b \frac{1}{2} {r(\theta)^2} \, d\theta\\\\A=2\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} \frac{1}{2} {(3+8\sin\theta)^2} \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\sin^2\theta \, d\theta\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} 9+48\sin\theta+64\biggr(\frac{1-\cos2\theta}{2} \biggr) \, d\theta\\\\\\A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (9+48\sin\theta+32-32\cos2\theta) \, d\theta[/tex]
[tex]\displaystyle A=\int\limits^{\frac{\pi}{2}}_{-\frac{\pi}{2}} (41+48\sin\theta-32\cos2\theta) \, d\theta\\\\A=41\theta-48\cos\theta-16\sin2\theta\biggr|^{\frac{\pi}{2}}_{-\frac{\pi}{2}}\\\\[/tex]
[tex]A=\biggr[41\biggr(\frac{\pi}{2}\biggr)-48\cos\biggr(\frac{\pi}{2}\biggr)-16\sin2\biggr(\frac{\pi}{2}\biggr)\biggr]-\biggr[41\biggr(-\frac{\pi}{2}\biggr)-48\cos\biggr(-\frac{\pi}{2}\biggr)-16\sin2\biggr(-\frac{\pi}{2}\biggr)\biggr]\\\\A=\biggr[\frac{41\pi}{2}-24\sqrt{2}\biggr]-\biggr[-\frac{41\pi}{2}+24\sqrt{2}\biggr]\\ \\A=41\pi\\\\A\approx128.8053[/tex]
Thus, the area of the curve is 41π square units. See below for a graph of the curve and its shaded area.
Reflect the figure over the line x = 0.
The coordinate of J’ is ?
The coordinate of K’ is ?
After the reflection over the line x = 0, the coordinates will be:
J' = (2, 1)
K' = (0, 4) = K
How to find the coordinates after the reflection?For any point (x, y), if we apply a reflection across the line x = 0, the image after the reflection will be (-x, y).
So it only changes the sign of the x-component.
In the graph, we can see that J = (-2, 1). So after the reflection, we will have:
J' = (2, 1).
And we also can see that K = (0, 4), then after the reflection, we have:
K' = (-0, 4) = (0, 4) = K
So point K does not change under that reflection.
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