The rate of change of the size of the diagonal is; 25.2 ft/s
By Pythagoras theorem;
The length, l of a diagonal of a rectangle whose sides have lengths x and y is;
l² = x² + y².In essence; the length of the diagonal is dependent on the length, x and y of the sides.
Therefore;
(dl/dt)² = (dx/dt)² + (dy/dt)²
where;
(dx/dt) = 19 ft/s(dy/dt) = -15 ft/sTherefore,
(dl/dt)² = 19² + (-15)²
(dl/dt)² = 361 + 225
dl/dt = √586
dl/dt = 25.2
Therefore, the size of the diagonal is changing at a rate of; 25.2 ft/s.
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Select the correct answer from each drop-down menu.
1. Congruent, not congruent or supplementary
2 adjacent, corresponding or vertical
1. Congruent
2. verticle (across from each others)
The height of a ball in feet is modeled by f(x) = -16x² +96x, where x is the time in seconds after it is hit. How long is the ball in the air?
Answer:
The answer is 144 feet and it will be in the air for 6 sec
Step-by-step explanation:
Answer:
92
Step-by-step explanation:
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help ! which of the following are the roots of the given quadratic equation ?
[tex]2 {x}^{2} + 18x + 36 = 0[/tex]
a. 6
b. -6
c. 3
d. -3..
Answer:
The roots are {-6, -3}
Step-by-step explanation:
We are given four possible roots. To determine whether or not a particular possible root is actually a root, we use synthetic division. If the remainder is zero, we may conclude that this is actually a root.
Determine whether or not -3 is a root. Setting up synthetic division, we get
-3 / 2 18 36
-6 -36
---------------------
2 12 0
Since the remainder is zero, -3 is a root.
Try -6: Is this a root of 2x + 12? Setting up synthetic division, we get
-6 / 2 12
-12
----------------
2 0
The remainder is again zero, so -6 is also a root of the original equation.
The roots are {-6, -3}
[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]
The Correct choices are ~
b and d
[tex] \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}[/tex]
Let's solve ~
[tex]2 {x}^{2} + 18 {x}^{} + 36 = 0[/tex][tex]2 {x}^{2} + 12x + 6x + 36 = 0[/tex][tex]2x(x + 6) + 6(x + 6) = 0[/tex][tex](2x + 6)(x + 6) = 0[/tex]There's two cases here,
Case # 1 - when 2x + 6 = 0
[tex]2x + 6 = 0[/tex][tex]2x = - 6[/tex][tex]x = - 6 \div 2[/tex][tex]x = - 3[/tex]Case # 2 - when x + 6 = 0
[tex]x + 6 = 0[/tex][tex]x = - 6[/tex]Hence, the roots are -3 and -6 ~
The points (5, -5) and (7,r) lie on a line with slope - 1. Find the missing coordinate r.
Answer:
r = -7
Step-by-step explanation:
Slope = Change in y/Change in x
-1 = r - (-5) / 7 - 5
-1 = r + 5/ 2
-2 = r + 5
r = -7
-Chetan K
Who Is Nathan Drake?
Answer:
he's the guy from uncharted
Answer: Nathan Drake is a fictional character and the protagonist of the Uncharted video game series, developed by Naughty Dog.
leslie weighs her marbles in a jar and the scale reads 474 grams. The empty jat weighs 439 grams. each marble weighs 5. How many marbles are in the jar
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x
1
,
y
1
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=
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3
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4
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If the simple interest on 4,000 for 10 years is 2,400 then what is the interest rate
Answer:
6%
Step-by-step explanation:
I =Prt I being interest paid, P is Principal, r is rate, t is term
2400=4000x r x 10
2400=40000r
2400/40000=.06 convert to percentage by multiplying by 100 x. 06=6
HELP
One chocolate bar and two coconut bars contain 780 calories. Two chocolate bars
and one coconut bar contains 786 calories. Find the number of calories in each kind
of bar.
Answer:
Choc Bar: 258 cals
Coco Bar: 264 cals
Step-by-step explanation:
What we can do here is something called making a system of equations.
Let us name the choc. bars x and the coco. bars y.
Then, we can get:
x+2y=780
2x+y=786
Next, we solve for x in the first equation
x=780-2y
Now, we can substitute:
2(780-2y)+y=786
1560-3y=786
-3y=-774
y=258
x=780-516
x=264
The range of F(x) = logo x is the set of all real numbers.
A. True
O B. False
Answer:
The range of F(x) = logo x is the set of all real numbers is True.
Step-by-step explanation:
Yes, Because range of the logarithmic function is the set of ''all real numbers.'
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
We have to given that;
The function is,
⇒ f (x) = log x
Now,
The given function is a logarithmic function.
And, The range of the logarithmic function is the set of all real numbers.
Hence, The range of function F(x) = log x is the set of all real numbers.
Thus, The range of F(x) = log x is the set of ''all real numbers''.
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find the area of each of the following polygons. aj 1 cm b) 1 cm c 1 cm 1 cm
Answer:
1 cm
Step-by-step explanation:
Eli is following this recipe to bake bread rolls.
He uses 500 g of flour.
How much of the other ingredients does he use?
Recipe: Makes 12 bread rolls
400 g flour
6 g salt
8 g yeast
40 mL oil
360 mL water
Answer:
7.5 g salt
10g yeast
50 ML oil
450 ML water
Step-by-step explanation:
You would do 1/4 of the amount of (insert ingredient amout) added to the total (insert ingredient amount)
Which choice models this situation? Marcus needs to sell 25 tickets to a fundraiser by Friday. So far, he has sold 9 tickets. How many tickets does he still need to sell?
Answer:
16
Step-by-step explanation:
Because 25 - 9 = 16
Somebody please help
Answer:
c/ y=20x
Step-by-step explanation:
According to the glossary, what are large meteors that enter the Earth's atmosphere?
A) Active galaxy
B) Blueshift
С) Coma
D) Bolide
Write each phrase as a numerical or algebraic expression. 189 subtracted from t
Answer:
t-189
Step-by-step explanation:
Ritta purchased a package of stickers. She noticed 4 out of every 5 stickers where purple. Which table shows the relationship between the number of purple stickers, p, and the total number of stickers, t?
Answer:
4:5
Step-by-step explanation:
I don't see the table but since it is 4 out of every 5 stickers are purple, the ratio would be 4:5, 4/5, or 4 to 5. It doesn't really matter, because all of these mean the same thing.
Tell me if I'm wrong :)
which of the following lines has a negative slope?
Red or Black,Blue
Answer:
black <3
Step-by-step explanation:
The difference between two times a number and eight is twenty two. What is twice the number?
Answer: 30
Step-by-step explanation:
2x -8 = 22
2x = 22 + 8
2x = 30
Divide both sides by 2
X = 15
Twice of x
2 x X = 2 x 15 = 30
the point (-2,6) is on a line with a slope of 3/4. If the point -8,k) is also on the same line what is the value of k
For a point with a slope 3/4 and which passes through the points (-2, 6) and (-8, k), the value of k is 1.5
The line passes through the points (-2, 6) and (-8, k)
That is, [tex]x_1=-2, y_1=6, x_2=-8, y_2=k[/tex]
The slope of the line, m = 3/4
The formula for calculating the slope of a line is given as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Substitute [tex]x_1=-2, y_1=6, x_2=-8, y_2=k, m = \frac{3}{4}[/tex] into the formula above
[tex]\frac{3}{4} = \frac{k-6}{-8-(-2)} \\\\\frac{3}{4} = \frac{k-6}{-8+2}\\\\\frac{3}{4} = \frac{k-6}{-6}\\\\-6(3)=4(k-6)\\\\-18=4k-24\\\\4k=-18+24\\\\4k=6\\\\k=\frac{6}{4} \\\\k=1.5[/tex]
Therefore, the value of k is 1.5
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Two lines are
perpendicular if the
of their
А
and
Lline are also perpendicular.
If a line is perpendicular to one of the
two given parallel lines then it is also perpendicular to the other line.
As we know that by the theorem of perpendicular transversal theorem that in the plane, if a transverse is perpendicular to one or two parallel lines, then it is perpendicular to the third line. ... Since, they do not touch or interact with each other they are said to be parallel to each other.
Thnx for marking me as brainlistYou’re loading bags of cement into a truck. You load bags weighting 175lbs, 154lbs, and 118lbs. What is the total weight you have loaded onto the truck?
Answer:
447 lbs
Step-by-step explanation:
175+154+118=447
Write the equation of the line in fully simplified slope-intercept form.
solve pls brainliest
Answer:
1/4
Step-by-step explanation:
The constant of proportionality is 1/4.
Answer:
b
Step-by-step explanation:
The form of an equation representing proportion is
y = kx ← k is the constant of proportionality
y = [tex]\frac{1}{4}[/tex] x ← is in standard form
with k = [tex]\frac{1}{4}[/tex]
I will give brainliest who ever answers fastest what is 1+1=?
Answer:
2
Step-by-step explanation:
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It takes 39 pounds of seed to completely plant a 4-acre field.
How many acres can be planted per pound of seed?
Answer:
0.1
Step-by-step explanation:
the first term of an AP is 2,and the last term is 59.if the sum of the first terms is 610,Find the common difference
Answer:
d = 3
Step-by-step explanation:
The sum to n terms of an AP is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] ( a + l)
where a is the first term and l the last term
Here a = 2, l = 59 and sum = 610 , then
[tex]\frac{n}{2}[/tex] (2 + 59) = 610
[tex]\frac{n}{2}[/tex] × 61 = 610 ( divide both sides by 61 )
[tex]\frac{n}{2}[/tex] = 10 ( multiply both sides by 2 to clear the fraction )
n = 20
Then the sequence has 20 terms with a₂₀ = 59
The nth term of an AP is
[tex]a_{n}[/tex] = a + (n - 1)d
where d is the common difference , then
2 + 19d = 59 ( subtract 2 from both sides )
19d = 57 ( divide both sides by 19 )
d = 3
Pls helpp
1: Find the slope:
m = (3 - 1) / (0 - (-4)) = 2 / 4 = 2
Find the area of a circle with a radius of 6 feet. Use 3.14 for pi
Answer:
Replace the value of r in the formula :
A = π • r²
A = π • 6²
A = 113,097
Since you need to round off your answer to one decimal, your final answer is :
A = 113.1 square ft
Step-by-step explanation:
I don’t know how i’m supposed to do this it’s basically dividing a fraction with a fraction or something
It is 1.3 in decimal form
Answer:
84/63
Step-by-step explanation:
when you are dividing two fractions that is the equal of multiplying the upper one with the opposite of the one below