Answer:
Step-by-step explanation:
Here the coefficients of the x terms in this quadratic are a = 15, b = 13 and c = 0. The discriminant is b^2 - 4ac, or 13^2 - 4(15)(0) = 169 - 60, or 109.
The solutions are:
-13 ± √109
x = -----------------
30
Hence, the roots of the quadratic equation is
[tex]x=0,x=-\frac{13}{15}[/tex]
What is the quadratic equation?
A quadratic equation is any equation that can be rearranged in standard form as + or offer insight into other areas of mathematics.
Here given equation is [tex]15x^2+13x=0[/tex].
As the general formula is
[tex]x=\frac{-b+-\sqrt{b^2-4ac}}{2a}\\\\[/tex]
Here, [tex]a=15,b=13[/tex]
Substituting these values in general formula
[tex]x=\frac{-13+-\sqrt{(13)^2-4(15)(0)}}{2(15)}\\\\x=\frac{-13+-\sqrt{169-0}}{30}\\\\x=\frac{-13+-\sqrt{169}}{30}\\\\x=\frac{-13+-13}{30}\\\\\\x=\frac{-13-13}{30},x=\frac{-13+13}{30}\\\\x=\frac{-26}{30},x=0\\\\x=\frac{-13}{15},x=0[/tex]
Hence, the roots of the quadratic equation is
[tex]x=0,x=-\frac{13}{15}[/tex]
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The circumference of a circle is 60π cm. What is the radius of the circle
Answer:
15 cm
Step-by-step explanation:
Circumference of circle= 2πr, where r us the radius of the circle.
Given that the circumference of circle is 60πcm,
60π= 2πr
Divide by 2 on both sides,
15π= πr
Divide by π on both sides,
15= r
Thus, radius of circle= 15cm.
25. On a farm, there are c cows and 15
sheep. There are 4 more sheep than
cows. Which equation represents the
situation?
A C= 15 +4
B C= 15-4
CC=4 - 15
D C = 4 x 15
Answer:b because if there is 4 more sheep than cows just subtract 4 and you get the number of cows
Step-by-step explanation:
A car is known to be 88% likely to pass inspection at a certain Motor Vehicle Agency inspection office. What is the probability that at least 90 cars pass inspection if a random sample of 100 cars is taken at this Motor Vehicle Agency inspection office? A. 0.4032 B. 0.6663 C. 0.3337 D. 0.88
Answer:
The correct option is;
C. 0.3337
Step-by-step explanation:
We note that for a binomial probability distribution, we have;
[tex]p(r\geq \gamma)=\sum_{\gamma = r}^{ n}\dbinom{n}{r}\cdot \left (p\right )^{\gamma }\cdot \left (1-p\right )^{n - \gamma}[/tex]
Which gives;
[tex]p(x \geq 90)=\sum_{r = 90}^{ 100}\dbinom{100}{90}\cdot \left (0.88\right )^{\gamma }\cdot \left (1-0.88\right )^{100 - \gamma}[/tex]
[tex]\dbinom{100}{90}\cdot \left (0.88\right )^{90 }\cdot \left (1-0.88\right )^{10} = 0.108033[/tex]
[tex]\dbinom{100}{91}\cdot \left (0.88\right )^{91 }\cdot \left (1-0.88\right )^{9} = 0.08706[/tex]
[tex]\dbinom{100}{92}\cdot \left (0.88\right )^{92 }\cdot \left (1-0.88\right )^{8} = 0.062456[/tex]
[tex]\dbinom{100}{93}\cdot \left (0.88\right )^{93 }\cdot \left (1-0.88\right )^{7} = 0.039399[/tex]
[tex]\dbinom{100}{94}\cdot \left (0.88\right )^{94 }\cdot \left (1-0.88\right )^{6} = 0.021516[/tex]
[tex]\dbinom{100}{95}\cdot \left (0.88\right )^{95 }\cdot \left (1-0.88\right )^{5} = 0.09965[/tex]
[tex]\dbinom{100}{96}\cdot \left (0.88\right )^{96 }\cdot \left (1-0.88\right )^{4} = 0.003806[/tex]
[tex]\dbinom{100}{97}\cdot \left (0.88\right )^{97 }\cdot \left (1-0.88\right )^{3} = 0.001151[/tex]
[tex]\dbinom{100}{98}\cdot \left (0.88\right )^{98 }\cdot \left (1-0.88\right )^{2} = 0.000258[/tex]
[tex]\dbinom{100}{99}\cdot \left (0.88\right )^{99 }\cdot \left (1-0.88\right ) = 0.0000383[/tex]
[tex]\dbinom{100}{100}\cdot \left (0.88\right )^{100 }\cdot \left (1-0.88\right )^{0} = 0.00000281[/tex]
P(r≥90) is therefore 0.1083 + 0.08706 + 0.062456 + 0.039399 + 0.021516 + 0.09965 + 0.003806 + 0.001151 + 0.000258 + 0.0000383 + 0.00000281 = 0.333685 ≈ 0.3337.
Which theorem proves that MNO = QPO?
A. SAA
B. SSS
C. ASA
D. AAA
Answer:
ASA
Step-by-step explanation:
<M is congruent to <Q
MO is congruent to QO
<MON is congruent to <QPO by vertical angles
That gives you ASA (angle-side-angle).
What does it mean to make connections when comparing and contrasting? (10 points)
Answer:
When making connections using compare and contrast, you should look for hidden similarities and differences. Compare/contrast aims to show all the necessary information or details that makes a topic or an object similar of different. Therefore, you should not only state the obvious, but also cite.
If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (f circle g) (x)? (3x + 2)(x 2 + 1) 3x 2 + 1 + 2 (3x + 2)2 + 1 3(x 2 + 1) + 2
Answer:
(f circle g) (x) = 3x^2 + 5
Step-by-step explanation:
To find (f circle g)(x), we substitute function g(x) for x in f(x) = 3x + 2:
(f circle g) (x) = 3(x^2 + 1) + 2, or
3x^2 + 3 + 2, or
(f circle g) (x) = 3x^2 + 5
Answer:
(f circle g) (x) = 3x^2 + 5
Step-by-step explanation:
*ANSWER PLS TY!* The radius of a salad bowl is 11.4 inches. What is the surface area of the bowl? (Assume the bowl is half a sphere). a.) 1633.13 in2 b.) 408.28 in2 c.) 204.14 in2 d.) 816.56 in2
Answer:
The answer is A: 1633.13 is the surface area
Hope this help :)
The surface area of the bowl is 816.56 square inches if the radius of a salad bowl is 11.4 inches option (d) is correct.
What is a sphere?It is defined as three-dimensional geometry when half-circle two-dimensional geometry is revolved around the diameter of the sphere that will form.
[tex]\rm V = \dfrac{4}{3} \pi r^3[/tex]
The surface area of the hemisphere = 2πr²
The radius r = 11.4 inches
The surface area of the hemisphere = 2π(11.4)²
The surface area of the hemisphere = 259.92π square inches
or
= 816.56 square inches
Thus, the surface area of the bowl is 816.56 square inches if the radius of a salad bowl is 11.4 inches option (d) is correct.
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What is the 1st term in the sequence of cube numbers?
Answer:
1
Step-by-step explanation:
The n th term of cube numbers is calculated as
[tex]a_{n}[/tex] = n³
To find the first term let n = 1, that is
a₁ = 1³ = 1
Answer:
1.
Step-by-step explanation:
1 is the first term in the square numbers, as it is in the sequence of cube numbers.
1^3 = 1 * 1 * 1 = 1.
Hope this helps!
ABCD is a parallelogram.
Given that,
DC = CE
prove that,
area of the ADE triangle is equal to the area of the parallelogram.
need explanation
plzz help!!
will give the brainliest!!
Answer:
Step-by-step explanation:
We khow that ABCD is a parallelogram so its area is the product of the base (DC) and the the height
Let H be the height of the paralellogram and A its area So A= DC*HADE is a triangle . Its area is the product of the height and the base(DE) over 2
We notice that the paralellogram and the triangle have both the same height Let S be the area of the triangle S= (DE*H)/2= DE/2 *H = DC *HSo the triangle and the parallelogram have the same area
Question Progress
Homework Progress
3/ 18
Express the recurring decimal 0.004 as a fraction.
Answer: 1/250
Step-by-step explanation:
Given the recurring decimal : 0.004
Firstly:
Let x = 0.004 - - - (1)
Due to the number of decimals places and value of x;
We multiply (1) by 1000 to obtain an integer
Multiply (1) by 1000
1000x = 4 - - - (2)
From (2) we can solve for x and leave our answer as a fraction.
Divide (2) by 1000 to obtain the value of x
1000x / 1000 = 4 / 1000
x = 1 / 250
Recall x = 0.004
Therefore, x = 0.004 = 1/250
* ANSWER ASAP PLS !!! * Suppose angle P is 110°. What would be the measure of arc LF? (Figure may not be drawn to scale)
Answer:
220 degrees
Step-by-step explanation:
An inscribed angle is always one-half the measure of either the central angle or the intercepted arc sharing endpoints of the inscribed angle's sides.
10 points and giving out brainiest!! Please help, this is pretty easy, I forgot how to do it though
Answer:
Equation of the line; y=x+3
Step-by-step explanation:
Graph the line that passes through the points (5,8) and (3,6) and determine the equation of the line.
Equation of a line: y=mx +b
Let's find the slope: [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
8-6/ 5-3= 2/2 = 1
y=x+b
Substitute the points in.
y= 8
x = 5
8 = 5+b
b= 3
The y-intercept is 3.
y=x+3
Points on the line: (-2,1) (-1,2) (0,3) (1,4) (2,5)
Which of the following is a zero of the quadratic function shown?
Answer:
(6,0)
Step-by-step explanation:
A zero of an equation is the x-intercept of the graph, meaning whenever the graph hits the x-axis. You can see that (2,0) and (6,0) are the x-intercepts, as I can see from the picture of the graph. There are other ways to solve this as well, but there is no need since the graph is provided. I hope this helps you!! Have a great rest of your day.
Graph the line: a through the point (3,2) with a slope of −2. PLEASE HELP ONLY 20 MINS LEFT
Answer:
y = -2x + 8
Step-by-step explanation:
The slope is given, and if we plug in 2 and 3 for y and x respectively, we can solve to get b=8. When graphed, it looks like the picture below.
(-1)\times (-(-2)) \times (-(-(-3))) \times (-(-(-(-4)))
Answer: the answer that I got was 24
Step-by-step explanation:
I hope it’s right and it helps!
Answer:
[tex]24[/tex]
Step-by-step explanation:
[tex](-1)\times (-(-2)) \times (-(-(-3))) \times (-(-(-(-4)))[/tex]
Negative times negative is positive.
Negative times negative times negative is negative.
Negative times negative times negative times negative is positive.
[tex](-1)\times (+2) \times (-3) \times (+4)[/tex]
Multiply.
[tex]-1 \times 2 \times -3 \times 4[/tex]
[tex]= 24[/tex]
In triangle ABC , m angle A=(3x)^ , m angle B=(3x+10)^ , and m angle C=(4x-30)^ Find m m angle C
Answer:
B
Step-by-step explanation:
Interior angles of a triangle = 180°
3x°+3x+10°+4x-30°=180°
10x°-20°=180°
10x°=180°+20°
10x°= 200°
10x°/10=200°/10
x°=20°
Hence, the angle is [tex]x=20[/tex] degree.
What is the angle?
An angle can be defined as the figure formed by two rays meeting at a common end point.
Here given that,
As we know that the sum of interior angles of a triangle is [tex]180[/tex] degree.
[tex]3x+3x+10+4x-30=180\\\\10x-20=180\\\\10x=180+20\\\\10x= 200\\\\\frac{10x}{10}=\frac{200}{10}\\\\x=20[/tex]
Hence, the angle is [tex]x=20[/tex] degree.
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Please answer the question!
Answer:
[tex]30[/tex]
Step-by-step explanation:
Here, we will have to use [tex]LCD[/tex] or, least common denominator.
The least common [tex]LCD[/tex] here that we will be using is going to be 30. We can always make sure by multiplying.
[tex]\frac{3}{10}[/tex]*[tex]\frac{3}{3}[/tex][tex]=\frac{9}{30}[/tex]
Our final answer for the first fraction is [tex]\frac{9}{30}[/tex] which could be simplified back to [tex]\frac{3}{10}[/tex].
For the second fraction, we will be multiplying with [tex]\frac{2}{2}[/tex].
[tex]\frac{2}{15}[/tex]*[tex]\frac{2}{2}[/tex][tex]=\frac{4}{30}[/tex].
Again, it simplifies back to [tex]\frac{2}{15}[/tex].
Hence, the [tex]LCD[/tex] is [tex]30[/tex].
Hope that helps:D
-Jazz
write the inequality shown by the shaded area
Answer: y≤ [tex]\frac{7}{3}x+2[/tex]
Step-by-step explanation:
Since we are given the equation, all we have to do is to fix the inequality. We have four options: <, >, ≤, and ≥. The line in the graph is a solid line. This means the line reaches and is equal to the points on the line. We can automatically eliminate ≤ and ≥. Now, we know the answer is ≤. The shading shows that the answer is less than 7/3x+2. In other words, y≤ [tex]\frac{7}{3} x+2[/tex].
Find the perimeter of the shaded region. Round your answer to the nearest hundredth.
Answer:
20.56 units.
Step-by-step explanation:
Perimeter of the shaded region is the sum of all straight sides and all 4 arcs.
Perimeter of 4 straight sides [tex]=4\times 2=8\text{ units}[/tex]
Perimeter of a arc [tex]=\dfrac{1}{4}\times 2\pi r[/tex]
Perimeter of 4 arcs [tex]=4\times \dfrac{1}{4}(2\pi r)=2\pi r[/tex]
Here, r is the radius. So,
[tex]r=\dfrac{6-2}{2}=\dfrac{4}{2}=2[/tex]
Perimeter of 4 arcs [tex]=2(3.14)(2)=12.56[/tex]
Perimeter of the shaded region = Perimeter of all straight sides + Perimeter of all 4 arcs
[tex]=8+12.56[/tex]
[tex]=20.56\text{ units}[/tex]
Therefore, the perimeter of the shaded region is 20.56 units.
Which number has a repeating decimal form?
Answer:
Option D
Step-by-step explanation:
A. [tex]\sqrt{15}[/tex] = 3.87298
B. 11/25 = 0.44
C. 3/20 = 1.25
D. 2/6 = 0.333........
So, D had a repeating decimal form because it repeats the number 3.
Answer:
Step-by-step explanation:
D: 2/6. Note that 2/6 = 1/3 = 0.3333333.... (repeating decimal form)
Drag the tiles to the correct boxes to complete the pairs.
Match the subtraction expressions with their answers,
1
2
1
a203 ad
1
ad2438
2.
2383a203
adora
aaga
a2b
a282
gბებ
2 - ab
a288
his is confusing
explanation:
Cecil is replacing lightbulbs in the office where he works. When he started, he had x boxes of lightbulbs with 2 bulbs in each box. After replacing 16 lightbulbs, he has at least 12 bulbs left. Which inequality represents the number of boxes of lightbulbs Cecil started with? How many boxes of lightbulbs is that?
The inequality represents the number of boxes of lightbulbs that Cecil started with.
Cecil had boxes of lightbulbs when he started.
Answer:
If we add the Replaced, the Left, that would be 28 LB, 14 boxes.
Answer:
at most or at least
Step-by-step explanation:
Find the area of the triangle with vertices (3, 4), (8, 4), and (-6,-6).
Answer:
The area is 25 :)
Step-by-step explanation:
This Is An Obtuse scalene triangle.
Sides: a = 17.205 b = 13.454 c = 5
Area: T = 25
Perimeter: p = 35.658
Angle ∠ A = α = 131.987° = 131°59'14″ = 2.304 rad
Angle ∠ B = β = 35.538° = 35°32'16″ = 0.62 rad
Angle ∠ C = γ = 12.475° = 12°28'30″ = 0.218 rad
Height: ha = 2.906
Height: hb = 3.716
Height: hc = 10
Median: ma = 5.385
Median: mb = 10.735
Median: mc = 15.24
Inradius: r = 1.402
Circumradius: R = 11.573
Vertex coordinates: A[3; 4] B[8; 4] C[-6; -6]
Centroid: CG[1.667; 0.667]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[1.963; 1.402]
Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 48.013° = 48°46″ = 2.304 rad
∠ B' = β' = 144.462° = 144°27'44″ = 0.62 rad
∠ C' = γ' = 167.525° = 167°31'30″ = 0.218 rad
Solve and graph |-8x|<8 help me lol
Step-by-step explanation:
|-x|<1 --> -1<-x<1 --> -1<x<1
so the graph is the striped part
PM is the median of trapezoid KLNO. If ON= 30 centimeters and KL= 20 centimeters, which is the length of PM?
A. 22cm
B. 25cm
C. 26cm
D. 28cm
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 85 miles per hour. The westbound train
travels at 75 miles per hour. How long will it take for the two trains to be 192 miles apart?
Do not do any rounding.
Answer:
It will take 1 hour and 12 minutes for the two trains to be 192 miles apart
Step-by-step explanation:
The total distance between the two trains is the distance traveled by both trains. The distance traveled by the eastbound train is 85 mph * elapsed time and the distance traveled by the westbound train is 75 * elapsed time.
The combined formula is distance traveled = speed of first train * elapsed time + speed of second train * elapsed time.
Since the elapsed time is equal for both trains then the formula is modified as distance traveled = (speed of first train + speed of second train) * elapsed time.
Solving for the elapsed time
distance traveled = (speed of first train + speed of second train) * elapsed time
192 miles = (85mph + 75 mph) * elapsed time
192 miles = 160 mph * elapsed time
elapsed time = 192 miles / 160 mph
elapsed time = 1.2 hours
elapsed time = 1 hour and 12 minutes
It will take 1 hour and 12 minutes for the two trains to be 192 miles apart.
A box with a volume of 16 $\text{cm}^3$ can hold 50 paperclips. How many paperclips could a box with a volume of 48 $\text{cm}^3$ hold?
Answer:
150 paperclips
Step-by-step explanation:
set up the equation as a fraction equaling a fraction i.e. volume 16/ 50 paperclips = volume 48/ x paperclips
cross multiply so you get 16x = 2400
solve for x by dividing 2400 by 16
you should get x = 150
Which of the following represents a rotation of △LMN, which has vertices L(−7,7), M(9,9), and N(5,−5), about the origin by 90°?
Answer:
L'(-7, -7), M'(-9, 9), and N'(5, 5)
Step-by-step explanation:
Assuming you mean 90° counterclockwise, you would use the formula: A(x,y) becomes A'(-y,x)
so L'(-7, -7), M'(-9, 9), and N'(5, 5)
The question was incomplete. Please check below the full content.
Which of the following represents a rotation of ΔLMN. which has vertices L (-7,7), M (9,9), and N(5, -5) about the origin by 90°?
a) L(-7, -7) M(-9. -9) N(5, 5)
b) L(-7. -7) M(-9. 9) N(5, 5)
c) L(-7, -7) M(-9, 9) N(5, -5)
d) L (7, -7) M(9, 9) N(-5, 5)
The rotation of the vertices L (-7,7), M (9,9), and N(5, -5) are
L'(-7,-7), M'(-9,9) and N'(5,-5) respectively.
Rotation of a point :
The rotation of a point (x,y) about the origin by 90° is (-y,x).Given vertices of ΔLMN are L(-7,7), M(9,9), and N(5, -5)Let the rotations of L, M, and N are L', M', and N' respectively.
The rotation of a point L(-7,7) about the origin by 90° is (-7,-7).The rotation of a point L(9,9) about the origin by 90° is (-9,9).The rotation of a point L(5,-5) about the origin by 90° is (5,-5).Hence L'(-7,-7), M'(-9,9), and N'(5,-5) are the rotation of vertices
L, M, and N of ΔLMN about the origin by 90°.
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*DIFFICULT QUESTION, PLS ANSWER* Wrapping paper costs $0.045 per square inch. If a moving box that is an 5.5 inch cube is being wrapped, how much would the wrapping paper for this box cost (rounded to the nearest dollars and cents)?
Answer:
$8.17
Step-by-step explanation:
I got it correcty on the test.
The costs $0.045 per square inch will be $8.17. Then the correct option is B.
What is the surface area of the cube?Let the length of the cube be a.
Then the surface area of the cube will be
SA = 6a²
If a moving box that is an 5.5 inch cube is being wrapped.
Then the surface area of the cube will be
SA = 6 x (5.5)²
SA = 181.5 square inches
Then the costs $0.045 per square inch will be
Total cost = 181.5 x 0.045
Total cost = $8.1675 ≈ $8.17
Then the correct option is B.
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In a city, taxicab fare is .80 cents for the first 1/4 mile and .20 for additional 1/4 mile. How far can you travel for $5.00?
Answer:
5 1/2 MILES
Step-by-step explanation:
$5.00-$.80=$4.20
4.20/.20=21/4= 5 1/4+1/4= 5 2/4 OR 5 1/2 MILES
Hope this help!