Answer:
value of t is greater than equal to -9 / 28.
Step-by-step explanation:
Given Quadratic Polynomial : tx² + 3x - 7 = 0
Also, It has real solutions.
Standard Quadratic equation, is ax² + bx + c = 0
here, Determinant, D = b² - 4ac
decides nature of the roots.
if D < 0 , roots / solutions are complex
if D = 0 , roots are real and equal.
if D > 0 , roots are real and different.
As given roots are real solutions.
Means Dis either equal to 0 or greater than 0
when D = 0
we have, 3² - 4 × t × (-7) = 0
9 + 28t = 0
t = -9 / 28
when D > 0
we have, 3² - 4 × t × (-7) > 0
9 + 28t > 0
t > -9 / 28
Therefore, value of t is greater than equal to -9 / 28.
What is the measure of ∠A, to the nearest degree? 15 POINTS
a) 17°
b) 33°
c) 57°
d) 73°
Answer:
33 degrees
Step-by-step explanation
I used arcos, ∠A = arccos((a2 + b2 - c2)/2ab)
= 0.5795 rad = 33.203° = 33°12'11"
b, 33 degrees is correct
7.5 cm=__ m
A.0.0075
B.0.075
C.0.75
D.750
Your answer is B. 0.075 m
The answer is B I think
which is the equation of the line that is parallel to y=-4x+3 and has a y intercept of -1/3
Answer:
y= -4x-1/3
Step-by-step explanation:
i think. but dont quote me on that. and Stan BTS!!!!!!
Sarah randomly selected 80 shoppers at a grocery store to taste two different type of greek yogurt. Yogurt brand B was chosen as the favorite by 35 of them. To the nearest percent what is the 95% confidence interval (z*-score 1.96) for the proposition of shoppers who tasted the two types of yogurt and preferred brand B? PLEASE HELP!!!!!
Answer:
D: 56 and 77
Step-by-step explanation:
help me asap.........
Answer:
F. 4h ≥ 18
Step-by-step explanation:
Liang wants ...
distance ≥ goal
We know that ...
distance = speed · time . . . . . . where speed = 4 mph, and time = h hours
Then the appropriate inequality for Liang's goal of 18 miles or more is ...
4h ≥ 18
A man bought a refrigerator at a discount of 12 percent. It's usual price was $900.How much did he pay for the refrigerator
Multiply by .88, he paid $792
Answer:
$792
Step-by-step explanation:
What is the measure of ∠ D?
101°
112°
122°
111°
Answer:
101
Step-by-step explanation:
360 - (78+91+90)
360- 259 = 101
HOPE THIS HELPS!!
What is the value of X?
Answer: x=8
Step-by-step explanation: Since we know that segment AB and BC are the same measure indicated by the black lines running perpendicular to the lines in triangle themselves, we know that angle A and angle C are the same measure. This means we know this equation... Solve this to complete step 1...
69°=(9y-3)°
If you solve for y, you should get 8. This means that y=8. In knowing that a triangle's interior angles add up to 180°, we know that Angle B must be... Solve this equation for step 2...
∠B=180°-(∠A+∠C)
If you solve to find angle B, you should get that ∠B=42°. Knowing this, we can set up another equation similar to that in step 1 (when we found y knowing the angle) to find x... Solve this equation for your third and final step...
42°=(5x+2)°
If done step 1 through 3 correctly, you should get x to be equal to... and the final answer... x=8
What are the zeros of the polynomial function f(x)=x^3-x^2-12x
Answer:
{0, 4 and -3}
Step-by-step explanation:
f(x)=x^3-x^2-12x can be factored, starting by taking out the 'x' factor:
f(x)=x^3-x^2-12x = x(x^2 - x - 12), and then by factoring the quadratic:
f(x) = x(x - 4)(x + 3) = 0
Then the zeros are {0, 4 and -3}.
Answer:
The zeros are;
x=-3,x=0, and x=4
Step-by-step explanation:
The given polynomial is
[tex]f(x)=x^3-x^2-12x[/tex]
We equate the function to zero to obtain;
[tex]fx^3-x^2-12x=0[/tex]
We factor the GCF to get;
[tex]x(x^2-x-12)=0[/tex]
We split the quadratic trinomial to get;
[tex]x(x^2-4x+3x-12)=0[/tex]
Factor by grouping
[tex]x(x(x-4)+3(x-4))=0[/tex]
[tex]x(x-4)(x+3)=0[/tex]
The zeros are;
x=-3,x=0, and x=4
use the elimination method to solve the system of equations.choose the correct ordered pair. -3y=x-5 x+5y=7.
Answer:
B. (2, 1)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}-3y=x-5&\text{subtract x from both sides}\\x+5y=7\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x-3y=-5\\x+5y=7\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad2y=2\qquad\text{divide both sides by 2}\\.\qquad\qquad y=1\\\\\text{Put the value of y to the second equation:}\\x+5(1)=7\\x+5=7\qquad\text{subtract 5 from both sides}\\x=2[/tex]
The solution of the system of equations is (2, 1).
What is the elimination method?The elimination method is a process that uses elimination to reduce the simultaneous equations into one equation with a single variable.
The given system of equations are;
[tex]\rm -3y=x-5\\\\x+5y=7[/tex]
From equation 1
[tex]\rm -3y=x-5\\\\x = -3y+5[/tex]
Substitute the value of x in the equation 2
[tex]\rm x+5y=7\\\\-3y+5+5y=7\\\\2y =7-5\\\\2y=2\\\\y=\dfrac{2}{2}\\\\y=1[/tex]
Substitute the value of y in the equation 1
[tex]\rm -3y=x-5\\\\-3(1)=x-5\\\\-3=x-5\\\\x=5-3\\\\x=2[/tex]
Hence, the solution of the system of equations is (2, 1).
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Identify which of the following represents a function. Select all that apply
Answer:
A and E
Step-by-step explanation:
whats the y-intercept of 5x-3y=4
Answer:
y = - [tex]\frac{4}{3}[/tex]
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange 5x - 3y = 4 into this form
Subtract 5x from both sides
- 3y = - 5x + 4 ( divide all terms by - 3 )
y = [tex]\frac{5}{3}[/tex] x - [tex]\frac{4}{3}[/tex] ← in slope- intercept form
with y- intercept c = - [tex]\frac{4}{3}[/tex]
Method 1: Plunging in 0 for x in the equation and solve for y
5(0) - 3y = 4
0 - 3y = 4
-3y= 4
y = [tex]\frac{-4}{3}[/tex] <<< y - intercept
Method 2: Converting the equation to slope-intercept form ( y = mx + b) and see what b is (that is the y-intercept). Do do this isolate y
-3y = 4 - 5x
y = [tex]\frac{-4}{3} +\frac{5}{3} x[/tex]
[tex]y = \frac{5}{3} x- \frac{4}{3}[/tex]
b = [tex]\frac{-4}{3}[/tex] <<< y - intercept
Y- intercept : (0, [tex]\frac{-4}{3}[/tex])
Hope this helped!
Cassie bought 300 shares of CAB Inc. stock and later sold them for a $500 profit. What type of income did she have?
Select the best answer from the choices provided.
A.
dividend income
B.
stock options
C.
capital gains
D.
equity income
Answer:
Hi,
The correct answer option is C. capital gain.
Step-by-step explanation:
Divided is the money a company pays to its shareholders every year after calculating the profits. A company can decided to distribute its earnings to the shareholders from the stock owned by the members.This income is called the divided income.When this income is specifically from stock divided, its called equity income.When Cassie sold the shares for a higher profit, she obtained a capital gain.The two main ways investors can get returns from stock are through divided and capital gains.
Best of Luck!
Find the area of the polygon XYZ that has its vertices at X(–3, 6), Y(–3, 1), and Z(5, 1).
Hope you can understand
Using the distributive property, which number sentence represents the total area of the rectangle?
A) 4 x 5 = 20 square units
B) (4 x 3) + (4 x 2) = 20 square units
C) (4 x 3) + (3 x 2) = 18 square units
D) (4 x 3) + (4 x 3) = 24 square units
The correct option that represents the total area of the rectangle using the distributive property is B) (4 x 3) + (4 x 2) = 20 square units.
Explanation:The correct option that represents the total area of the rectangle using the distributive property is B) (4 x 3) + (4 x 2) = 20 square units.
The distributive property states that when you multiply a number by a sum or difference of numbers, you can multiply each number individually and then add or subtract the products.
In this case, the rectangle has a length of 4 units and a width of 3 units.
So, the area of the rectangle can be found by multiplying the length by the width, which is 4 multiplied by 3. Then, you add the product of the length multiplied by the width, which is 4 multiplied by 2. This gives us a total area of 20 square units.
Alan earned 23$ 26$ 25$ 24$ 23$ 24$ 6$ 24$ and 23$ gardening. What is the amount he earned?
Answer:
151
Step-by-step explanation:
23+26=$49
49+25=74
74+24=98
98+6=104
104+24=128
128+23=151
Alan earned a total of $198 from gardening by adding all individual earnings together.
The student is asking about the total amount earned by Alan from gardening. To find the total, we simply add all the amounts mentioned: 23 + 26 + 25 + 24 + 23 + 24 + 6 + 24 + 23. Adding these up, Alan earned a total of $198 from gardening.
Darren is painting a wooden block as part of his art project. The block is a rectangular prism that is 12 cm long by 9 cm wide by 5 cm high. Describe the rectangles that make up the net for a prism
Answer:
The answer in the procedure
Step-by-step explanation:
we know that
The rectangles that make up the net for a prism are six rectangles
two rectangles are L by W ----> 12 cm by 9 cm
two rectangles are L by H ----> 12 cm by 5 cm
two rectangles are W by H ---> 9 cm by 5 cm
Final answer:
The rectangular prism net Darren is painting consists of two 12x5 cm rectangles for the top and bottom, two 9x5 cm rectangles for the front and back, and two 12x9 cm rectangles for the sides.
Explanation:
Darren is working on an art project involving painting a wooden block that is in the shape of a rectangular prism. To understand the net for this prism, we need to describe the rectangles that would make it up when the prism is unfolded into a flat shape.
The net of a rectangular prism is made up of six rectangles, each corresponding to a face of the prism. For Darren's block, which has dimensions of 12 cm in length, 9 cm in width, and 5 cm in height, we can determine the rectangles as follows:
When painting, Darren would treat each of these rectangles as separate sections to ensure complete coverage.
Six out of the 114 elements are noble gases. You write the names of all the elements on cards and select a card at random. What is the probability of not picking a noble gas?
Answer:
18/19 = About 95%
Step-by-step:
If only six are noble gases, 108 are not noble gases.
114-6= 108
So, the probability of not picking a noble gas is 108 out of 114. This simplifies to 18/19 which is about 95%.
Plz help me with this
Answer: Observational study
observational studies
Find the probability that a randomly selected dog is Male given it is a boxer. Enter your answer in decimal form rounded to two decimal places.
Answer:
0.63
Step-by-step explanation:
M: The selected dog is a male. P(M) = 24/40 = 0.6
B: The selected dog is a boxer. P(B) = 22/40 = 0.55
M and B: 14/40 = 0.35
P(M/B) = 0.35 / 0.55 = 0.63
Tom is clearing brush from a large piece of land. The table shows how many acres he cleared over time
Tom takes 1 day to clear 1 acre.
To find out how many days it takes Tom to clear 1 acre, we can calculate the rate at which he clears brush in acres per day.
Let's use the given information:
[tex]\frac{2}{3}[/tex] acre cleared in 2 days,
[tex]1\frac{2}{3}[/tex] acres cleared in 5 days,
[tex]2 \frac{1}{3}[/tex] acres cleared in 7 days.
First, let's find the rate in acres per day for each interval:
For the first interval:
[tex]\frac{\frac{2}{3} }{2} = \frac{1}{3}[/tex] acre per day.
For the second interval:
[tex]\frac{1\frac{2}{3} }{5} = \frac{5}{3} \times \frac{1}{5} = \frac{1}{3}[/tex] acre per day.
For the third interval:
[tex]\frac{2\frac{1}{3} }{7} = \frac{7}{3} \times \frac{1}{7} = \frac{1}{3}[/tex] acre per day.
It appears that the rate at which Tom is clearing brush is consistent at
[tex]\frac{1}{3}[/tex] acre per day.
Therefore, Tom takes 1 day to clear 1 acre.
Need help ASAP
1) A new truck that sells for $42,000 depreciates 11% each year. write a function that models the value of the truck. Find the value of the truck after 8 years. Round to the nearest dollar.
2) Earl mows lawns one weekend. He earns $15 for each lawn that he mows. He spends $50 on gas and other supplies. What function equation represents Earl's profit from mowing x lawns?
A)f(x)=50x-15
B)f(x)=50x+15
C)f(x)=15x-50
D)f(x)=15+50
3) find the common geometric series.
-2,-4,-8,-16.....
Answer:
[tex]\boxed{1) V = 40 000(0.89)^{n}, \text{\$15 746; }\text{2) C) f(x) = 15x - 50 ; 3) }a_{n} = -2^{n}}[/tex]
Step-by-step explanation:
1) Depreciation
The formula for the value V of an asset after depreciation by an annual percentage rate is
V = P(1 - r)ⁿ
where
P = present value
r = annual percentage rate
n = number of years
Data:
V = 40 000
r = 11 % = 0.11
n = 8 yr
Calculations:
(a) Function model
V= 40 000(1 - 0.11)ⁿ = 40 000(0.89)ⁿ
The function model is [tex]\boxed{ V= 40 000(0.89)^{n} }[/tex]
(b) Future value
V = 40 000(0.89)ⁿ = 40 000 × 0.393 659 = $15 746
In eight years, the truck will be worth [tex]\boxed{ \text{\$15 476}}.[/tex]
2) Profit function
Income from 1 lawn = $15
Income from x lawns = 15x
Less gas and supplies = -50
Net income = 15x – 50
The function is [tex]\boxed{f(x) = 15x - 50}[/tex].
3) Geometric series
(a) Calculate the common ratio
a₁ = -2
a₂ = -4
a₃ = -8
a₄ = =16
The ratios of consecutive pairs are
a₄/a₃ = -16/(-8) = 2
a₃/a₂ = -8/(-4) = 2
a₂/a₁ = -4/(-2) = 2
All adjacent pairs have the same common ratio r = 2.
(b) Write the formula for the series
The formula for the nth term of a geometric series is
aₙ = a₁rⁿ⁻¹
If a₁ = -2, the formula for the series is
aₙ = -2(2)ⁿ⁻¹ = -2ⁿ
The formula for the series is [tex]\boxed{a_{n} = -2^{n}}[/tex].
How do you solve by graphing
Answer:
See Explanation Below :)
Step-by-step explanation:
To solve a pair linear equations by graphing, you would first need to find the slope and y-intercept of each of the equation and then graph it in a coordinate plane. Then, you would see where the two lines intersect, and the coressponding coordinates for that point will be your solution.
Example:
y = 2x +2
y = x -1
For the first equation we know the slope (m) is 2 becuase y = mx + b, and m is 2. We know that the y intercept (b) is also 2 becuase y = mx + b, and b is 2.
Similarly, for the second equation the slope (m) is 1 and the y-intercept (b) is -1.
When you use this data and plot the two lines, we can see that they intersect on the 3rd quadrant at (-3,-4) which will be your solution. See the attached graph for this example.
Which statement about the dilation of these triangles is true?
Answer:
answer is b
Step-by-step explanation:
The Scale factor is 2.
What is dilation?A dilation in mathematics is a function f from a metric space M into itself that, for any locations x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is some positive real number. Such a dilatation is a resemblance to the space in Euclidean space.
Given
in pre -- image sides are 4, 5, 3
in the image, the sides are 4(2), 5(2), 3(2)
The scale factor is 2.
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What is the smallest solution to this equation?
Answer:
x = - 6
Step-by-step explanation:
Given
[tex]\frac{2}{3}[/tex] x² = 24 ( multiply both sides by 3 )
2x² = 72 ( divide both sides by 2 )
x² = 36 ( take the square root of both sides )
x = ± [tex]\sqrt{36}[/tex] ← note plus or minus
x = ± 6
solutions are x = - 6, x = + 6
The smallest solution is x = - 6
In Hillcrest School, 36% of middle school students are in Grade 6, 31% are in grade 7, and 33% are in grade 8.
If a middle school student is selected randomly, what is the probability that the student is either in grade 6 or in grade 7?
Answer:
0.67
Step-by-step explanation:
A 3cm x 2cm rectangle sits inside a circle with radius of 4 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth.
Answer:
The area of the shaded region is [tex]44.24\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the circle minus the area of rectangle
step 1
Find the area of circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=4\ cm[/tex]
substitute
[tex]A=\pi (4)^{2}[/tex]
[tex]A=16\pi\ cm^{2}[/tex]
step 2
Find the area of rectangle
The area of rectangle is equal to
[tex]A=(3)(2)=6\ cm^{2}[/tex]
step 3
Find the difference
[tex]16\pi\ cm^{2}-6\ cm^{2}[/tex]
assume
[tex]\pi=3.14[/tex]
[tex]16(3.14)\ cm^{2}-6\ cm^{2}=44.24\ cm^{2}[/tex]
In the total number of People attending the Game was 64,000, how many people were supporters of the home team
Answer:
51200 people
Step-by-step explanation:
Multiply the total number by the corresponding decimal to the percentage desired.
64000*.8=51200
PLZ HURRY IT'S URGENT!!
A square tray has an area of 196 square inches. What is the length of one side of the tray? A. 12 inches B. 13 inches C. 14 inches D. 16 inches
Answer:
C. 14 inches
Step-by-step explanation:
The area of a square is given by
A = s^2
We know the area is 196 in ^2
196 in^2 = s^2
Take the square root of each side
sqrt(196) = sqt (s^2)
14 =s
Each side is 14 inc
Answer:
C.14
Step-by-step explanation:
a=length time width so 14*14=196
Given: p: 3x + 7 = –5 q: 4x + 12 = –4 Which is the contrapositive of p → q?
Answer:
D :If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.
If 4x + 12 ≠ –4, then 3x + 7 ≠ −5. Then the correct option is D.
What is a contrapositive?If the statement is: p ⇒ q
Then the Contrapositive statement will be: ~q ⇒ ~p
p: 3x + 7 = –5 q: 4x + 12 = –4
The value of x in both cases is the same. Then the p and q are converses with each other.
If 4x + 12 ≠ –4, then 3x + 7 ≠ −5.
Then the correct option is D.
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