Answer:
To prove: The equation x2+px−1=0 has real and distinct roots for all real values of p.
Consider x2+px−1=0
Discriminant D=p2−4(1)(−1)=p2+4
We know p2≥0 for all values of p
⇒p2+4≥0 (since 4>0)
Therefore D≥0
Hence the equation x2+px−1=0 has real and distinct roots for all real values of p
Phan fills the tank of her car with gasoline before starting her road trip. The table below shows the amount of gas left in her tank as she drives. Number of Hours vs. Amount Left in Tank Number of Hours Spent Driving (h) 3 5 7 9 Amount of Gas Left in Tank, in gallons (g) 12 8 4 0 Which equation models the amount of gas left in the car as Phan drives, and how many gallons of gasoline does it take to fill her tank? g = 18 â€" 2h; 18 gallons g = 18 â€" 2h; 16 gallons g = 3h 3; 30 gallons g = 3h 3; 12 gallons.
The equation that models the amount of gas left in the car as Phan drives is [tex](g = 18 - 2h)[/tex] and the total amount of gasoline does it take to fill her tank is 18 gallons.
Given :
The table below shows the amount of gas left in her tank as she drives.Number of Hours Spent Driving (h) 3 5 7 9 Amount of Gas Left in Tank, in gallons (g) 12 8 4 0The following steps can be used in order to determine the equation that models the amount of gas left in the car as Phan drives and the total amount of gasoline:
Step 1 - The two-point form of the line can be used in order to determine the equation that models the amount of gas left in the car as Phan drives.
[tex]\dfrac{y-y_1}{x-x_1}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Step 2 - Now, substitute the value of [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] in the above expression.
[tex]\dfrac{g-12}{h-3}=\dfrac{8-12}{5-3}[/tex]
Step 3 - Simplify the above equation.
[tex]\begin{aligned}\\(g - 12)&=-2(h-3)\\g - 12&=-2h+6\\g &= 18-2h\\\end{aligned}[/tex]
Step 4 - Now, substitute the value of (h = 0) in the above equation.
[tex]g = 18-2(0)\\g = 18 \; {\rm gallons}[/tex]
Therefore, the correct option is A).
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Answer:
g = 18 – 2h; 18 gallons
Step-by-step explanation:
The answer above is correct.
Find the value of x that makes △DEF∼△XYZ.
Answer:
x = 5
Step-by-step explanation:
5×2 = 10
8×2 = 16
so
2(3x-5) = 20
3x-5 = 10
3x = 15
x = 5
what label would not be appropriate for volume
A football team had 55 players at the start of the season
Please help I don't understand i'm in the lowest class!
Answer:
Step-by-step explanation:
I WILL GIVE 30 POINTS TO THOSE WHO FILL IN THE BLANK CORRECTLY
Answer:
25
Step-by-step explanation:
20^2 + 15^ = c^2
400 + 225 = c^2
625 = c^2
25 = c
Answer: The length of the ladder is 25 feet.
The diagram shows the floor of a living room. What area of carpet will be needed to cover the floor? Remember to include your units of measure.
By using the given diagram, we want to find the area of carpet needed to cover the floor. We will see that we need 188 ft^2 of carpet to cover the floor.
First, remember that for a rectangle of length L and width W, the area is given as:
[tex]A = W*L[/tex]
Now, if we look at the diagram we can see that the area of the carpet is equivalent to the area of a rectangle of 18ft by 14ft minus the area of two rectangles of 8ft by 4ft.
The area of the first rectangle is:
[tex]A = 18ft*14ft = 252 ft^2[/tex]
The area of each one of the smaller ones is:
[tex]A' = 8ft*4ft = 32 ft^2[/tex]
Then the area that we need for the carpet is:
[tex]A - 2*A' = 252 ft^2 - 2*32 ft^2 = 188 ft^2[/tex]
We need 188ft^2 of carpet to cover the floor.
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math #lollololollollol
Answer:
the answer is 2
Step-by-step explanation:
find x .....merry Christmas :)))
The value of x in the triangle is 70°
What is a scalene triangle?A scalene triangle is a plane figure that has 3 different length sides and 3 different angles. The sum of all the angles in a scalene triangle is equal to 180°
i.e
[tex]\mathbf{\hat x + \hat y + \hat z = 180 ^0}[/tex]
Let's assume that angle y = 60° and angle z = 50°Then;
[tex]\mathbf{\hat x + 60^0 + 50^0 =180^0}[/tex]
x + 110° =180°
x = 180° - 110°
x = 70°
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QUESTION
[tex] {45}^{4} + {72}^{3} [/tex]
note: bye, i'm go back to Indonesian server. my rank in Indonesian server is ace. si hebat=ace
Step by step explanation:
4100625+373248
so the answer is;
4473873
answer in Alternative Form
4.473873x10⁶
trust my answer and liked and make it brainliest please
In which direction must the graph of Rx) = 7% be shifted to produce the graph of g(x) = 7% + 7?
O A right
OB. Up
OC. left
OD. down
Answer:
B. Up
Step-by-step explanation:
If you alter a function by adding or subtracting a constant to the end of the expression, then the graph will slide up (down if subtracting) If you alter the x value by altering the expression in close to the x with addition or subtraction the graph will slide left or right.
Vertical translations (sliding up or down) go up when adding and down when subtracting as you would expect it to.
Horizontal translations are the oppoof what you might expect. A (x-h) will shift the graph right, while a (x+k) will shift the graph left.
The answer to your question is UP.
help please I'm stuck on this question
Answer:
120 yd²
Step-by-step explanation:
The floor consists of a square and a triangle
area of square = 10² = 100 yd²
area of triangle = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 4 and h = 10 , then
area = [tex]\frac{1}{2}[/tex] × 4 × 10 = 2 × 10 = 20 yd²
company needs 100 + 20 = 120 yd²
brainliset
Solve.
p217=−5.3
Enter your answer as a mixed number in simplest form in the box.
p =
Answer: - 11 5/14 or -159/14
Step-by-step explanation:
Multiply both sides by 2 1/7.
Correct me if I am incorrect.
The value of p for the given expression is equal to 11(⁵/₁₄).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
The given expression is P / 2(¹/₇) =-5.3. the value of p will be calculated as,
P / 2(¹/₇) =-5.3
P = -5.3 x 2(¹/₇)
Solve the equation by changing the mixed fraction to a simple fraction.
P = -5.3 x 15 / 7
P = 159 / 14
P = 11(⁵/₁₄).
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A tortoise moves at a speed of 22 inches in 7 seconds. What is its average speed in feet per hour?
The average speed in feet per hour will be;
⇒ 942.85 feet per hour
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Distance = 22 inches
Time = 7 seconds
Now,
Since, A tortoise moves at a speed of 22 inches in 7 seconds.
Hence, Distance = 22/12 feet
And, Time = 7 / 3600
Thus, The average speed = (22/12) / (7/3600)
= 22 × 3600 / 12 × 7
= 942.85 feet per hour
Therefore, The average speed in feet per hour will be;
⇒ 942.85 feet per hour
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How many 1/6's are in 45/2
Please find the equation for this ASAP
Answer:
y=-2x-3
Step-by-step explanation:
the slope is 2/1 going down and the y intercept is -3
What is mAngleMHJ? 35 50 72.5 92.5
Answer:
Do you have any picture?
Answer:
50
Step-by-step explanation:
B.
45/100 in its simplest form
Answer:
9/20
Step-by-step explanation:
5×9=45
5×20=100
we need to convert it in lowest term by dividing it..
how do i solve use the GCF and the distributive property to express a sum as a product 52 +20+36
Answer: just add them all up add 50+20+36 then you get 106
Step-by-step explan
help pls, i will give brainliest :)
Find the value of a and b in parallelogram QRST
Answer:
a=7
b=11
Step-by-step explanation:
4a=3a+7
-3a -3a
a=7
2b=b+11
-b -b
b=11
sides parallel from eachother in a parallelogram are equal to eachother.
what is the set of all the output values in a function called?
Answer:
Set Y I’m pretty sure
Step-by-step explanation:
Which situation results in a zero balance?
A Jenny uses her credit card to buy a $1,400 refrigerator and then makes a payment of
$1,400 to her credit card company.
B Pedro deposits $2,346 into a new checking account and then writes a check for $346.
C Eliza spends $150 on supplies for her business and then spends $150 in rent.
D Juanita earns $75 from her job and receives $75 from her sister.
Answer:
A
Step-by-step explanation:
0 - 1400 = -1400 + 1400 = 0
A biologist wonders if the life span of bats will be affected by two new food sources from invasive species moving into an area. To conduct the experiment, the biologist needs three treatment groups: a group where the diet will not include invasive species (control), a group where the diet will include one invasive species (treatment group 1), and another group where the diet will include the other invasive species (treatment group 2). The biologist chooses the first cloud-free night and catches the first 18 bats that fly out of a cave, placing them into three equal groups of six bats. To decide the treatment for each group, the biologist places three slips of paper labeled control, treatment group 1, and treatment group 2 in a hat and randomly selects 2 slips of paper. The first piece of paper gives the treatment for the first group, the second piece of paper gives the treatment for the second group, and the remaining treatment is given to the third group.
Which component is missing from the biologist’s process?
The biologist did not use proper labeling on the pieces of paper.
The biologist did not use the appropriate number of treatment groups.
The biologist did not randomly assign the individual bats to the treatment groups.
The biologist did not randomly choose the weather on the night for bat capture.
Answer:
The biologist did not use proper labeling on the pieces of paper.
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Write an equation of the line passes through (4,1) and is parallel to y=-2x+7 .
Neika is saving her money to buy a DVD that costs $45. If she has a job that pays $8 per hour, write and solve an inequality that shows the minimum number of hours that Neika will need to work in order to pay for the DVD.
Answer:
8x6=48 so in 6 hours she will have enough money to buy it
Step-by-step explanation:
6 hours will give her 48 dollars if the dvd costs 45 so she will have to work 6 hours
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x = ____
m
m
m
Answer:
x = 8
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Sum the 3 given angles and equate to 180
13x - 8 + 7x + 4 + 3x = 180 , simplify left side
23x - 4 = 180 ( add 4 to both sides )
23x = 184 ( divide both sides by 23 )
x = 8
juliana wrote the terms below. –8, –4, 0, 4, 8, 12 what do these terms represent? an arithmetic series an arithmetic sequence a geometric series a geometric sequence
Answer:
B. an arithmetic sequence
Step-by-step explanation:
hope this helps :)
Which pairs of angles are alternate interior angles? Select all that apply.
There are two vertical parallel lines and a transversal. The angle formed by the transversal on the left of the first vertical line are labeled as 1, and 2, and the angle formed by the transversal on the right of the first vertical line are labeled as 3 and 4. The angle formed by the transversal on the left of the second vertical line are labeled as 5 and 6, and the angle formed by the transversal on the right of the second vertical line are labeled as 7 and 8.
Answer:
9 and 10 i dont know why they have us doing this confusing stuff
Step-by-step explanation:
PLS SOMEONE HELP I WILL GIVE U 28 POINT
Answer:
z=37
x=105
y=68?
Step-by-step explanation:
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