Answer:
[tex] \boxed{x = 3}[/tex]
Step-by-step explanation:
[tex] {5}^{2} = {4}^{2} + {x}^{2} \\ {x}^{2} = {5}^{2} - {4}^{2} \\ {x}^{2} = 9 \\ x = \sqrt{9} \\ x = 3[/tex]
One of the roots of the quadratic equation dx^2+cx+p=0 is twice the other, find the relationship between d, c and p
Answer:
[tex]c^2 = 9dp[/tex]
Step-by-step explanation:
Given
[tex]dx^2 + cx + p = 0[/tex]
Let the roots be [tex]\alpha[/tex] and [tex]\beta[/tex]
So:
[tex]\alpha = 2\beta[/tex]
Required
Determine the relationship between d, c and p
[tex]dx^2 + cx + p = 0[/tex]
Divide through by d
[tex]\frac{dx^2}{d} + \frac{cx}{d} + \frac{p}{d} = 0[/tex]
[tex]x^2 + \frac{c}{d}x + \frac{p}{d} = 0[/tex]
A quadratic equation has the form:
[tex]x^2 - (\alpha + \beta)x + \alpha \beta = 0[/tex]
So:
[tex]x^2 - (2\beta+ \beta)x + \beta*\beta = 0[/tex]
[tex]x^2 - (3\beta)x + \beta^2 = 0[/tex]
So, we have:
[tex]\frac{c}{d} = -3\beta[/tex] -- (1)
and
[tex]\frac{p}{d} = \beta^2[/tex] -- (2)
Make [tex]\beta[/tex] the subject in (1)
[tex]\frac{c}{d} = -3\beta[/tex]
[tex]\beta = -\frac{c}{3d}[/tex]
Substitute [tex]\beta = -\frac{c}{3d}[/tex] in (2)
[tex]\frac{p}{d} = (-\frac{c}{3d})^2[/tex]
[tex]\frac{p}{d} = \frac{c^2}{9d^2}[/tex]
Multiply both sides by d
[tex]d * \frac{p}{d} = \frac{c^2}{9d^2}*d[/tex]
[tex]p = \frac{c^2}{9d}[/tex]
Cross Multiply
[tex]9dp = c^2[/tex]
or
[tex]c^2 = 9dp[/tex]
Hence, the relationship between d, c and p is: [tex]c^2 = 9dp[/tex]
What is the slope the line?
Answer:
the slope is 3/4x
Step-by-step explanation:
if you need it in slope intercept form too its y=3/4x-1
HELP!! please, quick!
Answer:
The answer is B
Step-by-step explanation:
To rotate a figure 90 degrees clockwise the figure needs to be moved from (x,y) to (y,-x)
The original figure lies at A (5,5) B (5,1) C (2,1) D (1,5)
Rotating the figure 90 degrees clockwise would be A' (5-,5), B' (1,-5), C' (1,-2), D' (5-1)
Please answer, I’ve been stuck on this the whole day, so basically I only need the four digit code. You can read the instructions on the paper. Thank you so much if you decide to answer ❤️.
The formula for converting degrees Fahrenheit (F) to degrees Celsius (C) is c= 5/9 (f-32) Find C for F = 59
Answer:
(59°F − 32) × 5/9 = 15°C
Step-by-step explanation:
Simply follow the equation and you will get your answer.
plz, help I will give you the brainiest How likely is it to get a red card? A heart? A red or black card? A 2 of Hearts? Use the Probability Scale
Answer:
[tex]\frac{26}{52}[/tex], [tex]\frac{13}{52}[/tex], [tex]\frac{52}{52}[/tex], [tex]\frac{1}{52}[/tex]
Step-by-step explanation:
In a deck of playing cards there are 52 cards total.
13 clubs
13 hearts
13 spades
13 diamonds
half are red and half are black
all of the cards are red or black
plz mark me brainliest ;)
***PLEASE HELP ME WITH THIS I AM BEHIND*** I WOULD BE HAPPy
Which of the following values make the inequality x≤16.3 true?
Select all that apply. pick that all work more than one answer 17 points
. 18.5
. 8
. 16.3
. 14
. −3
. 32
Answer:
16.3, 14, 8, -3
Step-by-step explanation:
Any number less than 16.3 and 16.3 are acceptable answers
greatest integer of x < -3
Answer:
-4
Step-by-step explanation:
Here, we want to get the greatest integer less than -3
The integer less than -3 that is the greatest is -4
It is the internet directly after it to the left of the number line
A project manager has ordered 252 pallets of concrete blocks for a construction project. Casone's trucks can each carry 14 pallets of blocks at a time. The project manager used partial quotients to find the number of delivery trucks to expect. His work is shown at the right. Is his solution correct? Explain
Answer:
18 trucks of delivery
Step-by-step explanation:
Total pallets of concrete blocks ordered = 252 pallets
If each truck can carry 14pallets, then;
1 truck = 14pallets
To determine the number of delivery truck 252pallets can carry, we can express this as:
x truck = 252pallets
Divide both expressions
1/x = 14/252
Cross multiply
14x = 1×252
14x = 252
x = 252/14
x = 18
Hence the manger should expect 1 18 trucks of delivery
Simplify this radical expression → 3√24
Answer:
[tex]\\\sqrt[1]{8}[/tex][tex]\sqrt[1]{8}[/tex]
Step-by-step explanation:
A sub shop sold sandwiches that were one-half of a foot long. If you were to cut the sandwich into 9 equal pieces, what fraction of a foot would each piece be?
Answer:
[tex]\frac{1}{18}[/tex]
Step-by-step explanation:
[tex]\frac{1}{2} / \frac{9}{1} = \frac{1}{2} (\frac{1}{9} ) = \frac{1}{18}[/tex]
which point on this number line best represents square route of 10
(tap the whole photo the see the equation)
Answer:
the answer is B
Step-by-step explanation:
since 10 isn't a perfect square
9 strings of lights for $52.65 .how much does one string of lights cost ?
Answer:$5.85
Step-by-step explanation: you divide 52.65 divided by 9 and it will equal $5.85
Answer:
$5.85. Hope this helped! :')
Step-by-step explanation:
1. Use the algorithm method.
5 . 8 5
9 | 5 2 . 6 5
4 5 .
7 . 6
7 . 2
4 5
4 5
2. Therefore, 52.62 divided by 9=5.85
5.85
There were 54 runners to start a race. In the first half of the race, 1/3 of them dropped out. In the second half of the race, 5/6 of the remaining runners dropped out. How many runners finished the race?
Answer:
6 runners finished the race
Step-by-step explanation:
Total number of runners = 54
In the first half of the race, 1/3 of them dropped out
= 1/3 of 54
= 1/3 * 54
= 54/3
= 18 runners
Runners remaining after first half = total runners - dropped out runners at first half
= 54 - 18
= 36 runners
In the second half of the race, 5/6 of the remaining runners dropped out
= 5/6 * 36
= (5*36)/6
= 180/6
= 30 runners
Runners remaining after second half = runners remaining after first half - dropped out runners at second half
=36 - 30
= 6 runners
Therefore, 6 runners finished the race
whats the line in fully simplified slope form pls help me.
Answer:
y = -5/6x - 7
Step-by-step explanation:
Use quadrilateral ABCD with A(1, 5), B(2, 6), C(3, 3) and D(1, 3) and its transformation A'B'C'D' with A'(-3, 1), B'(0, 4), C'(3, -5) and D'(-3, -5). What is the scale factor of the transformation
Answer:
The scale factor that transforms quadrilateral ABCD to quadrilateral A'B'C'D' is 3
Step-by-step explanation:
Quadrilateral ABCD has the following coordinates
A(1, 5), B(2, 6), C(3, 3) and D(1, 3)
The image A'B'C'D' has the following coordinates;
A'(-3, 1), B'(0, 4), C'(3, -5), D'(-3, -5)
The length of segment [tex]\overline {AB}[/tex] = √((2 - 1)² + (6 - 5)²) = √2
The length of segment [tex]\overline {BC}[/tex] = √((3 - 6)² + (3 - 2)²) = √10
The length of segment [tex]\overline {CD}[/tex] = √((1 - 3)² + (3 - 3)²) = 2
The length of segment [tex]\overline {DA}[/tex] = √((1 - 1)² + (3 - 5)²) = 2
For quadrilateral, we have;
A'(-3, 1), B'(0, 4), C'(3, -5), D'(-3, -5)
The length of segment [tex]\overline {A'B'}[/tex] = √(0 - (-3))² + (4 - 1)²) = 3·√2
The length of segment [tex]\overline {B'C'}[/tex] = √((3 - 0)² + (-5 - 4)²) = 3·√10
The length of segment [tex]\overline {C'D'}[/tex] = √((-3) - 3)² + (-5 - (-5))²) = 6
The length of segment [tex]\overline {D'A'}[/tex] = √((-3) - (-3))² + ((-5) - 1)²) = 6
The scale factor that transforms quadrilateral ABCD to A'B'C'D' is given as follows;
[tex]The \, scale \, factor \, of \, transformation = \dfrac{\overline {A'B'}}{\overline {AB}} = \dfrac{\overline {B'C'}}{\overline {BC}} = \dfrac{\overline {C'D'}}{\overline {CD}} = \dfrac{\overline {D'A'}}{\overline {DA}} = 3[/tex]
Therefore, the scale factor that transforms quadrilateral ABCD to A'B'C'D' = 3
Plz help I will give brainliest
Answer:
the last one
Step-by-step explanation:
a square's sides should be the same angle
Answer:
i believe its the last one but im not 100% sure
Step-by-step explanation:
cubic feet= 1 cubic yard
Answer:
(1 yard) 3 = 1 3 yard*yard*yard = 1 yard*yard*yard = 1 cubic yard. Since 1 yard = 3 feet, we have.
1 cubic yard = (1 yard) 3 = (3 feet) 3 = 33 feet*feet*feet = 27 cubic feet.
Step-by-step explanation:
Surface area of a cushion
Answer:
need measurments
Step-by-step explanation:
Which of the division expressions below has a quotient that is greater than 15? Select all
that apply.
A) 345 : 15
B) 196 : 14
C) 212 : 16
D) 455 = 25
E) 221 : 13
Answer:
The answer is D
Step-by-step explanation:
because if you do the methoes method you know that it rules out 1 and 2 and 3 after you do that its just between C and D, for the caunususicon it has to be D, that is why i think its D. hope this helps
please help me with this i need is rn thank you so much
Answer:
18
Step-by-step explanation:
C = 2πr
r = 3
2π(3) = 18.85
9.) Water covers about 361,736,000, or about 70.8% of Earth's surface. What is the approximate surface area of Earth?
Answer: 511,000,000 km^2
Step-by-step explanation: divide 361,736,000 by .708 looks like
361,736,000///.708 Then you get your answer!
You are selling concessions at a local swim meet. Hot dogs are being sold for
$1.00 and soda is being sold for $0.50. At the end of the day you made $150.
Let x represent the number of hotdogs sold and y represent the number of
sodas sold. Write an equation that can be used to find the number of hotdogs
and sodas sold at the swim meet.
Answer:
150 = 0.50y + 1.00x
Step-by-step explanation:
$1500 = $25x + $50
What is the x in this question?
Answer:
x= 58
Step-by-step explanation:
$1500 = $25x + $50
minus 50
1450 = 25x
divide by 25
58 = x
hope this helps!
Answer:
$58
Step-by-step explanation:
1,500-50=1450
1450/25=58
According to the property a/b = a/b which choice is equivalent to the quotient below? 30/5
Answer:
Answer is
Step-by-step explanation:
D
Lala!smzl!smzkaka
Bills family is driving across the country on vacation . They plan to stop at historical sites in each state they drive through. The total mileage of the trip is 3,000 miles. They have driven 900 miles so far what percent of driving do they still have left?
Answer: Blll's family has 70% of driving left.
Step-by-step explanation:
The total mileage of the trip = 3,000 miles.
miles driven so far = 900miles
Miles of diatance left = 3000- 900=2100
Percentage of driving left = Miles of diatance left / Total miles to cover x 100
=2100/3000 x 100
= 7/10 x100
70%
Solve this and whoever is right I'll mark if I can remeber
Answer:
14
Step-by-step explanation:
Answer:
14m squared
Step-by-step explanation:
2.5×2=5
5÷2=2.5
2.5 is the area for each triangle and there are four triangles altogether so
2.5×4=10
to find the square do 2×2=4
so 4m+10m=14m
2.A filled provides grazing for sheep for 8 days. How many days grazing would it provide for 24 sheep
Given:
Consider the complete question is "A field provides grazing for 18 sheep for 8 days. How many days grazing would it provide for 24 sheep?".
To find:
The number of days the field provides grazing for 24 sheep.
Solution:
We have,
If number of sheep = 18, then, number of days = 8.
If number of sheep = 24, then, number of days = x.
Now, the products of number of sheep and number of days are equal because they represent the total work done.
[tex]18\times 8=24\times x[/tex]
[tex]\dfrac{18\times 8}{24}=x[/tex]
[tex]\dfrac{144}{24}=x[/tex]
[tex]6=x[/tex]
Therefore, the field provides grazing for 24 sheep for 6 days.
A square has side length represented by X +4 inches write an expression to represent the area. Express your answer as a trinomial.
Answer:
[tex]A=(x^2+16+8x)\ \text{inches}^2[/tex]
Step-by-step explanation:
Given that,
The side length of a square, l = (x+4) inches
We need to find an expression to represent the area of the square.
The area of a square is given by :
[tex]A=\text{side}^2[/tex]
So,
[tex]A=(x+4)^2\\\\A=(x^2+16+8x)\ \text{inches}^2[/tex]
So, the area of the square is [tex](x^2+16+8x)\ \text{inches}^2[/tex].
Solve.
952448 / 112 =
Answer:
10
Step-by-step explanation:
yup that's all have sorry