Answer:
A
The leading coefficient is negative.
Step-by-step explanation:
Quadratic equation:
A quadratic equation has the following format:
[tex]y = ax^2 + bx + c[/tex]
The leading coefficient is a.
a negative:
The graph of the function is concave down, that is, it displays values that approach negative infinity.
a positive:
The graph of the function is concave up, that is, it displays values that approach up infinity.
In this question:
Displays values that approach negative infinity, so the leading coefficient is negative, and the correct answer is given by option A.
Answer:
B it's positive.. I went with negative because that's what it said, but it was wrong!
Step-by-step explanation:
factorize: x² + 6x + 5-4y - y²
Answer:
below
Step-by-step explanation:
that is the procedure above
The factorized form of x² + 6x + 5 - 4y - y² is:(x + 1)(x + 5) - (4y + y²)
To factorize the expression x² + 6x + 5 - 4y - y², group the terms and factor them separately.
Rearranging the terms
(x² + 6x + 5) - (4y + y²)
Now let's factor each group separately:
1. Factoring x² + 6x + 5:
The quadratic expression x² + 6x + 5 can be factored into two binomial factors. We look for two numbers that multiply to give 5 and add up to 6 .
These numbers are 1 and 5:
(x + 1)(x + 5)
2. Factoring -4y - y²:
The terms -4y - y² have a common factor of -1.
Factoring out -1 gives
-1(4y + y²)
Combining the factorization of both groups
(x + 1)(x + 5) - 1(4y + y²)
Therefore, the factorized form is (x + 1)(x + 5) - (4y + y²).
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An angle measures 73.6° less than the measure of its supplementary angle. What is the measure of each angle?
Answer:
Smaller angle = 53.2
Larger angle = 126.8
Step-by-step explanation:
Lets say x is the measure of the supplement. Since we know they're supplementary, we know their angle measure sum will equal 180. We can set up our equation like this [tex]x + (x-73.6) = 180[/tex]. Note: (x - 73.6) is the measure of the smaller angle. By solving, we get 126.8 degrees for the measure of the supplement. If we plug in the value of x into (x-73.6), we get 53.2 degrees as the angle measure of the smaller angle.
The difference between 15 and 9 is subtracted from 5 times the sum of 7 and 3
Answer:
44
Step-by-step explanation:
The difference between 15 and 9 is 6. 5 times the sum of 7 and 3 is 50 because 7+3=10 and 10 times 5 is 50. So if you subtract the difference between 15 and 9 from 50 you get 44.
use a double angle or half angle identity to find the exact value of each expression
Answer:
Step-by-step explanation:
There are 2 very distinct and important things that we need to know before completing the problem. First is that we are given that the cos of an angle is 1/3 (adjacent/hypotenuse) and it is in the first quadrant. We also need to know that the identity for sin2θ = 2sinθcosθ.
We already know cos θ = 1/3, so we need now find the sin θ. The sin ratio is the side opposite the angle over the hypotenuse, and the side we are missing is the side opposite the angle (we do not need to know the angle; it's irrelevant). Set up a right triangle in the first quadrant and label the base with a 1 (because the base is the side adjacent to the angle), and the hypotenuse with a 3. Find the third side using Pythagorean's Theorem:
[tex]3^2=1^2+y^2[/tex] which simplifies to
[tex]9=1+y^2[/tex] and
[tex]y^2=8[/tex] so
[tex]y=\sqrt{8}=2\sqrt{2}[/tex] so that's the missing side. Now we can easily determine that
[tex]sin\theta=\frac{2\sqrt{2} }{3}[/tex]
Now we have everything we need to fill in the identity for sin2θ:
[tex]2sin\theta cos\theta=2(\frac{2\sqrt{2} }{3})(\frac{1}{3})[/tex] and multiply all of that together to get
[tex]2sin\theta cos\theta=\frac{4\sqrt{2} }{9}[/tex]
If the speed of an object in motion is doubled, its kinetic energy becomes how many times the original kinetic energy
Answer: Becomes four times
Step-by-step explanation:
Given
Speed is doubled for a moving object
Suppose initial speed is u
Increased speed is 2u
Kinetic Energy is given by
[tex]\Rightarrow K=0.5mu^2[/tex]
When speed is doubled
[tex]\Rightarrow K'=0.5m(2u)^2\\\Rightarrow K'=(0.5mu^2)\times 4\\\Rightarrow K'=4K[/tex]
Kinetic energy becomes four times
SOMEONEEEE HELPPP MEEEE OUTTTTTTT!!!!!
Answer:
4/3
Step-by-step explanation:
Since this is a right triangle,
tan C = opp side / adjacent side
tan C = 36/ 27
tan C = 4/3
the tens digit of a two digit number is 5 greater the units digit. If you subtract double the reversed number from it, the result is a fourth of the original number. Find the original number.
Given:
The tens digit of a two digit number is 5 greater the units digit.
If you subtract double the reversed number from it, the result is a fourth of the original number.
To find:
The original number.
Solution:
Let n be the two digit number and x be the unit digit. Then tens digit is (x+5) and the original number is:
[tex]n=(x+5)\times 10+x\times 1[/tex]
[tex]n=10x+50+x[/tex]
[tex]n=11x+50[/tex]
Reversed number is:
[tex]x\times 10+(x+5)\times 1=10x+x+5[/tex]
[tex]x\times 10+(x+5)\times 1=11x+5[/tex]
If you subtract double the reversed number from it, the result is a fourth of the original number.
[tex]11x+50-2(11x+5)=\dfrac{1}{4}(11x+50)[/tex]
[tex]11x+50-22x-10=\dfrac{1}{4}(11x+50)[/tex]
[tex]40-11x=\dfrac{1}{4}(11x+50)[/tex]
Multiply both sides by 4.
[tex]160-44x=11x+50[/tex]
[tex]160-50=11x+44x[/tex]
[tex]110=55x[/tex]
Divide both sides by 55.
[tex]\dfrac{110}{55}=x[/tex]
[tex]2=x[/tex]
The unit digit is 2. So, the tens digit is [tex]2+5=7[/tex].
Therefore, the original number is 72.
Three red balls, 5 green balls and a number of blue balls are put together in a sac. One ball is picked at random from the sac. If the probability of picking a red ball is 1|6, find the a) The number of blue balls in sac. B) the probability of picking a green ball
Answer:
total balls = 18 .... 3/x = 1/6
blue = 10 ... 18-(5+3) = 10
p of green = 5/18 = .277
Step-by-step explanation:
Find cos 0
A. 15/8
B. 15/17
C. 8/15
D. 8/17
Answer:
A.15/8
Step-by-step explanation:
the answer is 15/8
Answer:
D.
[tex]{ \tt{ \cos( \theta) = \frac{adjacent}{hypotenuse} }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{ \sqrt{ {15}^{2} + {8}^{2} } } }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{ \sqrt{289} } }} \\ \\ { \tt{ \cos( \theta) = \frac{8}{17} }}[/tex]
Easton is deciding between two landscaping companies for his place of business. Company A charges $25 per hour and a $150 equipment fee. Company B charges $35 per hour and a $100 equipment fee. Let AA represent the amount Company A would charge for tt hours of landscaping, and let BB represent the amount Company B would charge for tt hours of landscaping. Write an equation for each situation, in terms of t,t, and determine the number hours, t,t, that would make the cost of each company the same.
Answer:
5 hours
Step-by-step explanation:
Company A:
Charge for an hour =$ 25
Charge for 't' hours = 25 *t = 25t
Total cost = Equipment fee + charge for t hours
AA = 150 + 25t
Company B:
Charge for an hour =$ 35
Charge for 't' hours = 35 *t = 35t
Total cost = Equipment fee + charge for t hours
BB = 100 + 35t
BB = AA
100 + 35t = 150 + 25t
Subtract 25t from both sides
100 + 35t - 25t = 150
100 + 10t = 150
Subtract 100 from both sides
10t = 150 - 100
10t = 50
Divide both sides by 10
t = 50/10
t = 5
A square has a side length of 36 feet. This square is dilated by a scale factor of 2/3 to create a new square. What is the side length of the new square?
Answer:
24
Step-by-step explanation:
Multiply the side length by the dilation
36 x 2/3
72/3
Simplify
72/3 = 24
Your answer is correct
Find the measure of the missing angle using the exterior angle sum theorm.
Answer:
95 degrees
Step-by-step explanation:
First find the angles within the triangle. 180 - 43 - 52 = 85, so the missing angle within the triangle is 85. The exterior angle would be supplementary to that, so 180 - 85 = 95.
Find cosθ+cos3θ+cos5θ+cos7θ by using the Sum-to-Product Formula.
Please also show your work as well. Thanks!
Answer:
[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]
Step-by-step explanation:
I assume the question want us to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula and note that it's not an equation therefore θ can never be specified
===========================
so we want to rewrite cosθ+cos3θ+cos5θ+cos7θ by using Sum-to-Product Formula the good news is that the number of the function of the given expression is even so there's a way to do so, rewrite the expression in parentheses notation:
[tex] \rm\displaystyle \left( \cos( \theta) + \cos(3 \theta) \right) + \left(\cos(5 \theta) + \cos(7 \theta) \right)[/tex]
recall that,Sum-to-Product Formula of cos function:
[tex] \rm \boxed{\displaystyle \cos( \alpha ) + \cos( \beta ) = 2 \cos \left( \frac{ \alpha + \beta }{2} \right) \cos \left( \frac{ \alpha - \beta }{2} \right) }[/tex]
notice that we have two pair of function with which we can apply the formula thus do so,
[tex] \rm\displaystyle \left( 2\cos \left( \frac{ \theta + 3 \theta}{2} \right)\cos \left( \frac{ \theta - 3 \theta}{2} \right) \right) + \left(2\cos \left( \frac{5 \theta + 7 \theta}{2} \right) \cos \left( \frac{5 \theta - 7 \theta}{2} \right) \right)[/tex]
simplify addition:
[tex] \rm\displaystyle \left( 2\cos \left( \frac{4 \theta}{2} \right)\cos \left( \frac{ - 2\theta }{2} \right) \right) + \left(2\cos \left( \frac{12 \theta }{2} \right) \cos \left( \frac{ - 2 \theta}{2} \right) \right)[/tex]
simplify division:
[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { - \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { - \theta} \right) \right)[/tex]
By Opposite Angle Identities we acquire:
[tex] \rm\displaystyle \left( 2\cos \left( {2 \theta} \right)\cos \left( { \theta } \right) \right) + \left(2\cos \left( {6 \theta } \right) \cos \left( { \theta} \right) \right)[/tex]
factor out 2cosθ:
[tex] \rm\displaystyle 2 \cos( \theta) (\cos \left( {2 \theta} \right) + \cos \left( {6 \theta } \right) )[/tex]
once again apply Sum-to-Product Formula which yields:
[tex] \rm\displaystyle 2 \cos( \theta) (2\cos \left( {4\theta} \right) \cos \left( {2 \theta } \right) )[/tex]
distribute:
[tex] \rm\displaystyle 4\cos( \theta) \cos \left( {2\theta} \right) \cos \left( {4 \theta } \right) [/tex]
and we're done!
Find the length of the segment indicated. Round your answer to the nearest 10th if necessary.
Answer:
x=13.6
Step-by-step explanation:
By Pythagoras theorem, 5.5^2+x^2=14.7^2. x^2=14.7^2-5.5^2. x=13.6
can someone please help
Answer:
see image
Step-by-step explanation:
State what additional information is required in order to know that the triangle in the image below are congruent for the reason given…
Reason: HL Postulate
Answer:
FG ≈ FL (Both are hypotenuse, supposed to be equal in order to the congruency to become HL)
Answered by GAUTHMATH
Given: x - 7 > -2.
Choose the solution set.
A. {x | x R, x > 14}
B. {x | x R, x > -5}
C. {x | x R, x > 5}
D. {x | x R, x > -9}
Given set:- x - 7 > - 2
Solving It:-
x - 7 > - 2
x > -2 + 7 [Here '7' is greater than '-2' So Sign Changes To Positive]
x > 5
So Correct Solution Set Will Be
Option C= {x | x R, x > 5}
Hope This Helps YouIf f is continuous for all x, which of the following integrals necessarily have the same value?
Answer:
B
Step-by-step explanation:
Given the three integrals, we want to determine which integrals necessarily have the same value.
We can let the first integral be itself.
For the second integral, we can perform a u-substitution. Let u = x + a. Then:
[tex]\displaystyle du = dx[/tex]
Changing our limits of integration:
[tex]u_1=(0)+a=a \text{ and } u_2 = (b+a)+a = b+2a[/tex]
Thus, the second integral becomes:
[tex]\displaystyle \int_{0}^{b+a}f(x+a)\, dx = \int_a^{b+2a} f(u)\, du[/tex]
For the third integral, we can also perform a u-substitution. Let u = x + c. Then:
[tex]\displaystyle du = dx[/tex]
And changing our limits of integration:
[tex]\displaystyle u_1=(a-c)+c=a \text{ and } u_2=(b-c)+c=b[/tex]
Thus, our third integral becomes:
[tex]\displaystyle \int_{a-c}^{b-c}f(x+c)\, dx = \int_{a}^{b} f(u)\, du[/tex]
Since the only difference between f(x) and f(u) is the variable and both the first and third integral have the same limits of integration, our answer is B.
A house on the market was valued at $472,000. After several years, the value increased by 19%. By how much did the house's value increase in dollars? What is the current value of the house?
Step-by-step explanation:
Increase in dollars
19/100 x 472.000 = $89,670
and the current value house is $472,000 + $89,670 = $561,680
Aisha wants to paint the four walls of her living room.
Each wall is 2.2 m high and 5.5 m long.
One wall has a door of 1.8 m by 0.9 m.
Tins of paint cost £13 per 2 L tin.
Each litre of paint can cover 8 m2 of wall.
There is an offer of: Buy 2 tins get the 3rd at half price.
How much will Aisha pay to paint her living room?
Answer:
£32.50
Step-by-step explanation:
my first question to the teacher : so, no windows in the living room ?
so, it is a square living room with 5.5 m side length.
but each wall is a rectangle of 2.2 × 5.5 m.
for one wall we have to deduct a door area of 1.8×0.9 m.
so, one wall
2.2 × 5.5 = 12.1 m²
4 walls
4 × 12.1 = 48.4 m²
minus one door area
1.8 × 0.9 = 1.62 m²
48.4 - 1.62 = 46.78 m² total paint area
1 L paint covers 8 m².
so, we need 46.78/8 = 5.85 liters.
she gets the paint in 2 L tins. so, she needs 3 tins (6 L).
each tin costs £13.
and because she buys 3 tins, she gets the third one for half the price (13/2 = £6.50).
so, she has to pay
2×13 + 6.50 = 26 + 6.50 = £32.50
please help me its urgent
Answer:
number of students who like only iphone is 36...
Step-by-step explanation:
100 is the total number..
from that 40 like both so we subtract..
100-40=60..
60 = 2x + 3x..
60 / 5 = 12..
so numbet who like iphone is 3x which is 3 * 12=36..
cos theta / sec theta -1 - sin theta / 1+cos theta = 2 cot theta
Step-by-step explanation:
Explanation is in the attachmentHope it is helpful to you
Please help! Identify an equation in point-slope form for the line parallel to y=3/4x-4 that passes through (-1,7).
Grandma is making a quilt. She has 540 cm of fabric to border the quilt. What is the greatest possible area for the quilt?
Question 1 options:
11 664 cm^2
18225 cm^2
72900 cm^2
291600 cm^2
Show your work:
Answer:
18225 cm²
Step-by-step explanation:
Divide 540 by 4 to get the length of all sides
540/4 = 135
Square 135 to get the max possible size
135² = 18225
18225 cm² is the greatest possible area for the quilt.
What is area?The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.
Given
Divide 540 by 4 to obtain the length of all sides
540/4 = 135
Square 135 to acquire the max possible size
135² = 18225
18225 cm² is the greatest possible area for the quilt.
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When AG = 16 ft, find the area of the region that is NOT shaded. Round to the nearest tenth.
Answer:
730.88
Step-by-step explanation:
Area of the entire circle = pi * r^2
r = 16
Area = 3.14 * 16^2
Area = 803.84
1/4 of the circle contains the shaded area. It's area = 1/4 * 803.84
Area of 1/4 circle =
200.96
the area of the triangle
Area = 1/2 AG * G?
AG and G? are equal
Area = 1/2 * 16^2
Area = 128
Area of 1/4 circle - area of the triangle = area of the shaded portion
shaded portion = 200.95 - 128
Shaded Portion = 72.96
So the area of the unshaded part
unshaded = 803.84 - 72.96
Unshaded = 730.88
Tre and Hector want to calculate the maximum possible throw at this field.
They calculate that the farthest point on the field would be the center fielder standing back at the dead center wall at point (322, 322). Suppose the center fielder threw the ball from here to home base.
How far is the throw?
Answer:
[tex]d=455.38~units[/tex]
Step-by-step explanation:
The coordinates of the dead center of the field, [tex]D\equiv (322,322)[/tex]
Home base in a coordinate system is always the origin, [tex]O\equiv(0,0)[/tex]
The center fielder threw the ball form the dead center to the home base, hence the distance of throw:
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
[tex]d=\sqrt{(322-0)^2+(322-0)^2}[/tex]
[tex]d=455.38~units[/tex]
Answer:Hector threw the ball 65 feet while Tre threw the ball 63 feet far
Step-by-step explanation:
The farthest throw would probably be around 450 feet
The function f(t) = 3 - t shows the cost of an ice cream sundae ($) with a different number of toppings (t). What is the slope of the function?
Answer:
-1
Step-by-step explanation:
are you sure this is the right equation ? it would mean that the more toppings the cheaper the ice cream.
but as it is written, the slope is -1.
the slope of a line is always the factor of the variable in the equation.
it is the ratio of y/x indicating how many units y is changing for a given change of x.
in our example here, if x changes 1 unit to the right (+1), then y changes 1 unit down (-1).
so, -1/+1 = -1
The slope of the function f(t) = 3 - t is -1
What is function?"It defines a relation between input and output values."
What is the slope of the function?"It is the rate of change of the dependent variable of the function with respect to that of the independent variable."
For given question,
We have been given a function f(t) = 3 - t
We need to find the slope of the function.
[tex]m=\frac{d}{dt}f(t)\\\\ m=\frac{d}{dt}( 3 - t)\\\\m=-1[/tex]
Therefore, the slope of the function f(t) = 3 - t is -1
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Convert to decimal degrees.
-(167° 31”)
[?]°
Enter your answer with three decimal places.
Answer:
The angle in decimal form is 167.009°.
Step-by-step explanation:
We know an angle in terms of integer angles, minutes and seconds, whose conversion into decimal degrees is expressed by the following formula:
[tex]\theta = n + \frac{m}{60}+\frac{s}{3600}[/tex] (1)
Donde:
[tex]n[/tex] - Integer angle, in sexagesimal degrees.
[tex]m[/tex] - Minutes.
[tex]s[/tex] - Seconds.
If we know that [tex]n = 167[/tex], [tex]m = 0[/tex] and [tex]s = 31''[/tex], then the angle in decimal form is:
[tex]\theta = 167^{\circ}+\frac{0}{60}^{\circ} + \frac{31}{3600}^{\circ}[/tex]
[tex]\theta = 167.009^{\circ}[/tex]
The angle in decimal form is 167.009°.
Correct and fastest answer gets brainest! 12 divided 2/5
30
Answer:
12÷2/5=12*5/2=30 is a required answer
Answer:
30
Step-by-step explanation:
6. Solve the triangle by finding the length of DF and the measures of all the angles. For side lengths, round to the
nearest tenth. For angles, round to the nearest degree. (2 points)
D
5 ft
E
DF =
D
LE=
5.83 ft
ZF =
F
Answer:
∠F = 59°
∠E = 31°
DF = ≅ 3 (2.98)
Step-by-step explanation:
