Answer:
212
Step-by-step explanation:
3m² + 2p² - 15
= 3 * 3² + 2 * 10² - 15
= 27 + 200 - 15
= 212
If the point (a, 7) lies on the graph of the equation 5x - y = 8, then a= -3 3 1/5 plz help
Answer:
a = 3
Substitute the value of point (a,7) in the equation and solve for a
5(a)-7=8
5(a)=8+7
5(a)=15
a = 15/5 = 3
God Bless and stay safe!
- Eli <3
(2x + 3)(5x2 - 2x - 1) = Ax3 + Bx2 + Cx + D. What are the values of B and C?
Answer:
B = 11; C = -8
Step-by-step explanation:
When simplified I get 10x^3 + 11x^2 - 8x - 3
Factor (x^2-1x)(-4x+4), with work shown
Answer:
4 ( -x^3 + 2x - x)
Step-by-step explanation:
refer the attachment
Find angle x, giving your answer to 1 decimal place.
Answer:
57.8 degrees and 122.2 degrees (to one decimal place)
Step-by-step explanation:
Since there are two pairs of angle/side involved, we can use the sine rule.
sin(A)/a = sin(B)/b
where
A = angle x
a = 11cm
B = 38 degrees
b = 8 cm
substitute in the sine rule equation,
sin(A) = sin(x) = sin(38)/8 * 11 = 0.61566 * 11/8 = 0.84653
Now there are two solutions for x where sin(x) = 0.84653, they are supplement angles, namely 57.8367 degrees and 122.1633 degrees.
The reason for the two solutions is because the 8cm side can swing in two positions, one that makes x acute, and the other one obtuse.
13 points, please answer!
Which shows the dilation with a possible scale factor of 1/2?
Answer:
Option B
Step-by-step explanation:
With a scale factor of 1/2, the dilated shape should be smaller because of the scale factor, So in Option B the dilated shape is smaller than the real one.
1) Option A is an enlargement
2) Option B is reduction
3) Option C is equality
The snail moved 6 inches in 120 minutes. What was the average speed of the snail in inches per minute?
Answer:
0.05 in per min.
Step-by-step explanation:
We simply divide 6 by 120 to find our unit rate:
6 in/120 min = 1/20 = 0.05 in/1 min
Answer:
1/20 Inch per. Minute
Step-by-step explanation:
6/120 -->
6/1 x 1/120 --> cancel out 6 and 120 for 1 and 20 respectively
1/1 x 1/20 --> 1 x 1/20 => 1/20
Hope this helps!
Point S is located on RT so that RS/ST = 1/4. What are the coordinates of Point S? (4 , 4 ) (2.4, 2.4) (8 , 8 ) (4.4, 4.4)
Answer:
(4.4, 4.4)
Step-by-step explanation:
The point S can be found as the weighted average of the end points. The relative weights are the reverse of the distances to the end points:
RS : ST = 1 : 4
S = (4R +1T)/5
S = (4(2, 2) +(14, 14))/5 = (22, 22)/5
S = (4.4, 4.4)
[tex](7^{x})=\frac{7^{2}*7^{3} }{7^{3x} }[/tex] PLEASE SHOW ME HOW TO DO THIS STEP BY STEP I ALREADY KNOW THE ANSWER. IT IS 1.25 I AM GIVING BRAINLIEST
Answer:
I hope it will help you....
Need help again ?!???
Answer:
11.47
Step-by-step explanation:
Use SohCahToa. In this problem, you are given the hypotenuse and you are trying to solve for the adjacent side so it will be cosine. (cosine = [tex]\frac{adjacent}{hypotenuse}[/tex])
1. set up the equation
cos55 = [tex]\frac{x}{20}[/tex]
2. Multiply both sides by 20 to solve for x
20 · cos55 = 11.47
Answer:
11.47Solution,
From the figure,
[tex]cos \: 55 = \frac{PQ}{PR} [/tex]
[tex]cos \: 55 = \frac{PQ}{20} [/tex]
[tex]PQ = 20 \: cos \: 55[/tex]
[tex]PQ= 11.472[/tex]
[tex]PQ= 11 .47[/tex]
Hope this helps...
Good luck on your assignment...
what is teh surface area of a rectangular prism, if its length is 17 meters, its width is 2 meters and its height is 3 meters
Answer:
102m^2
Step-by-step explanation:
2x3x17=102m^2
can u pls mark brainliest :)
Answer:
182 m²
Step-by-step explanation:
The formula for surface area of a rectangular prism is;
Surface Area = 2(wl) + 2(lh) + 2(hw) where w is the width, l is the length and h is the height.
SA = 2(2 * 17)m² + 2(17 * 3)m² + 2(3 * 2)m²
= 2(34)m² + 2(51)m² + 2(6)m²
= 68 m² + 102 m² + 12 m²
= 182 m²
quadrilateral ghjk is a rectangle. find measure <2 and <7 if m<3 = 37. image attached
Answer:
[tex]m\angle 2=53^{\circ}[/tex]
[tex]m\angle 7=74^{\circ}[/tex]
Step-by-step explanation:
It is given that quadrilateral GHJK is a rectangle and [tex]n\angle 3=37^{\circ}[/tex].
All interior angles of a rectangle are right angles. Diagonals are equal and bisect each other.
Now,
[tex]m\angle HKJ+m\angle HKG=90^{\circ}[/tex] (Interior angles of a rectangle are right angles)
[tex]m\angle 3+m\angle HKG=90^{\circ}[/tex]
[tex]37^{\circ}+m\angle HKG=90^{\circ}[/tex]
[tex]m\angle HKG=90^{\circ}-37^{\circ}[/tex]
[tex]m\angle HKG=53^{\circ}[/tex]
In an isosceles triangle, angle with equal sides are equal.
[tex]m\angle JGK=m\angle HKG[/tex]
[tex]m\angle 2=53^{\circ}[/tex]
Therefore, measure of angle 2 is 53 degrees.
Let the diagonals intersect each other at point O.
In triangle OGK,
[tex]m\angle OGK+m\angle OKG+m\angle GOK=180^{\circ}[/tex] (Angle su property)
[tex]53^{\circ}+53^{\circ}+m\angle GOK=180^{\circ}[/tex]
[tex]106^{\circ}+m\angle GOK=180^{\circ}[/tex]
[tex]m\angle GOK=180^{\circ}-106^{\circ}=74^{\circ}[/tex]
Vertical opposite angles are equal. So,
[tex]m\angle 7=74^{\circ}[/tex]
Therefore, measure of angle 7 is 74 degrees.
Find the slope of the line
Answer:
3/2
Step-by-step explanation:
Using two points we can find the slope of a line
(0,1) and (2,4)
The slope is given by
m= (y2-y1)/( x2-x1)
= (4-1)/(2-0)
= 3/2
Plot the zeros of this function:
f(x) = (x – 1)(x – 7).
Answer:
[tex]\boxed{\mathrm{view \: attachment}}[/tex]
Step-by-step explanation:
The zeros of a function is where the function crosses the x-axis. The x-intercepts are the zeros of a function.
[tex]f(x) = (x - 1)(x - 7)[/tex]
Let output equal to 0.
[tex]0 = (x - 1)(x - 7)[/tex]
Set factors equal to 0.
[tex]x-1=0\\x=1[/tex]
[tex]x-7=0\\x=7[/tex]
The zeros of the function are [tex]x=1[/tex] and [tex]x=7[/tex].
Answer:
Step-by-step explanation:
Hope this Helps ;)
9.
((x - 2)2
The function f(x) = ax2 + bx
3x – 6
if x < -1
if - 1
if x 2
is continuous for all real values of x.
Find a and b.
Answer:
a = 0.3 and b = - 1.1
Step-by-step explanation:
(x - 2)² = x² -4x + 4
Hence, x² - 4x + 4 = 3x - 6
x² - 7x + 10 = 0
(x - 5)(x - 2) = 0
∴ x = 5 or 2
f(5) = 25a + 5b = 2 ----- (i)
f(2) = 4a + 2b = -1 ------ (ii)
(i) X 2: 50a + 10b = 4 ----- (iii)
(ii) X 5: 20a + 10a = -5 ---- (iv)
Subtract (iv) from (iii): 30a = 9
a = 0.3
Substitute a into (ii) to obtain b
4(0.3) + 2b = -1
2b = -1 - 1.2 = -2.2
∴ b = -1.1
Solve for x. Write both solution, separated by a comma. 4x^2-x-3=0.
Answer:
x = -3/4, 1
Step-by-step explanation:
Factor left side of the equation.
(4x + 3)(x - 1) = 0
Set factors equal to 0.
4x + 3 = 0
4x = -3
x = -3/4
x - 1 = 0
x = 1
Answer:
x₁ = -3/4
x₂ = 1
Step-by-step explanation:
4x² - x - 3 = 0
4x² + 3x - 4x - 3 = 0
xx(4x + 3) - 4x - 3 = 0
xx(4x + 3) - (4x + 3) = 0
(4x + 3) × (x - 1) = 0
4x + 3 = 0 → x = -3/4
x - 1 = 0 → x = 1
Hope this helps! :)
Plz, help if you have the time too
Answer:
Hey there!
You can use the ASA postulate, when two angles are congruent, and one side is congruent.
Hope this helps :)
Melissa of Melissa’s Landscaping Service mows many of the lawns in her neighborhood for $100 per lawn, per month. She also offers full landscape maintenance services for $130 per yard, per month. If Melissa provides full landscaping service for two times the number of yards for which she provides lawn mowing only, and her earnings are $8,280 for a month, for how many yards does Melissa provide the full landscape maintenance service? (25 points)
Answer:
46 yards
Step-by-step explanation:
let x = number of lawns mowed per month
let y = number of full landscape maintenance service
y = 2x
100x + 130y = 8,280
100x + 260x = 8,280
360x = 8,280
x = 8,280 / 360 = 23
Melissa provides only lawn service to 23 yards and full landscape maintenance service to 46 yards.
Answer:
The answer of the question is 46 Yards.On a very cold morning, it was -8°F. As the day went on, the temperature rose 2 degrees each hour. Which equation shows the temperature over time? CLEAR CHECK y = -2x + 8 y = -2x – 8 y = 2x + 8 y = 2x – 8
Answer:
y=2x-8
Step-by-step explanation:
Every hour, temperatures INCREASE by two degrees, so 2x.
At the beginning (x=0), the temperature was -8 degrees, so -8.
So temperature as a function of time is y=2x-8
Answer:
y = 2x-8
Step-by-step explanation:
At the beginning = -8 F
Let y be the temperature and x be the no. of hours
So, the equation becomes
=> y = -8 + 2x
Writing it in proper form
=> y = 2x-8
In an isosceles right triangle, the length of the hypotenuse is 8 units. Which measurement is NOT associated with the triangle? * A. 4√2 units B. 8√2 units C. 45° D. 90°
Answer:
B. 8sqrt(2)
Step-by-step explanation:
The legs of an isosceles right triangle are congruent and measure 45 deg. The right angle measures 90 deg. The ratio of the lengths of the sides of a 45-45-90 deg triangle is 1 : 1 : sqrt(2).
Since the hypotenuse measures 8, then the legs measure 8/sqrt(2)
8/sqrt(2) * sqrt(2)/sqrt(2) = 8sqrt(2)/2 = 4sqrt(2)
Answer: B. 8sqrt(2)
If (x+3) varies directly as y and x=3 when y=12, what is the value of x when y=8?
Answer:
x = 1.
Step-by-step explanation:
y = k(x + 3)
When x = 3 y = 12 so
12 = k(3 + 3)
6k = 12
k = 2.
So the relation is y = 2(x + 3)
When y is 8:
8 = 2(x + 3)
2x = 8 - 2*3 = 2
x = 1.
exact value of :7 1/2 - 1 5/8 +(1 3/8 × 2 7/11 )
Answer:
261/44
Step-by-step explanation:
hope this helps. :)
Answer:
9 1/2
Step-by-step explanation:
7 1/2 - 1 5/8 + (1 3/8 × 2 7/11) =
= 7 4/8 - 1 5/8 + 11/8 * 29/11
= 6 12/8 - 1 5/8 + 29/8
= 5 7/8 + 3 5/8
= 8 12/8
= 8 + 8/8 + 4/8
= 9 1/2
PLEASE. NEED HELP. Find the sum.
Distribute the sum:
[tex]\displaystyle\sum_{i=1}^{24}(3i-2)=3\sum_{i=1}^{24}i-2\sum_{i=1}^{24}1[/tex]
Use the following formulas:
[tex]\displaystyle\sum_{i=1}^n1=n[/tex]
[tex]\displaystyle\sum_{i=1}^ni=\dfrac{n(n+1)}2[/tex]
[tex]\implies\displaystyle\sum_{i=1}^{24}(3i-2)=3\cdot\frac{24\cdot25}2-2\cdot24=\boxed{852}[/tex]
In case you don't know where those formulas came from:
The first one is obvious; you're just adding n copies of 1, so 1 + 1 + ... + 1 = n.
The second can be proved in this way: let S be the sum 1 + 2 + 3 + ... + n. Rearrange it as S = n + (n - 1) + (n - 2) + ... + 1. Then 2S = (n + 1) + (n + 1) + (n + 1) + ... + (n + 1), or n copies of n + 1. So 2S = n(n + 1). Divide both sides by 2 and we're done.
A student answered 12 out of 15 questions on an exam correctly.
a) What fraction of the 15 questions did the student answer correctly? Write your answer in
simplest terms.
b) What percent of the 15 questions did the student answer correctly?
Answer:
1. 4/5
2. 80%
Step-by-step explanation:
What decimal represents the shaded part in the picture?
Answer:
40/100 = 0.4
your welcome
HELP IF YOU KNOW THIS PLEASEEEE
Answer:
63m
Step-by-step explanation:
If 12^x = ^11√12, what value of x makes this equation true?
The root of a number is equivalent of being raised to its inverT
11 cubic root is = 1/11
X = 1/11
Rachel rides her bicycle due east at 12 kilometers per hour. Amos rides his
bicycle due north at 16 kilometers per hour. If they left from the same point at
the same time, how far apart will they be after 2 hours?
Answer:
40 km away.
Step-by-step explanation:
a^2 + b^2 = c^2
In this case, a = 16 * 2 = 32 km, since he travels 16 km per hour for 2 hours.
b = 12 * 2 = 24 km, since she travels 12 km per hour for 2 hours.
32^2 + 24^2 = c^2
1,024 + 576 = c^2
1600 = c^2
c^2 = 1600
c = plus or minus 40
Since distance cannot be negative, they will be 40 km away.
Hope this helps!
The required, after 2 hours, Rachel and Amos will be 40 kilometers apart.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
We can use the Pythagorean theorem to solve this problem. After 2 hours, Rachel will have traveled 24 kilometers (12 km/hour x 2 hours) due east, and Amos will have traveled 32 kilometers (16 km/hour x 2 hours) due north. Let's call the distance between them after 2 hours "d".
Using the Pythagorean theorem, we can write:
d² = (24 km)²+ (32 km)²
Simplifying this expression:
d² = 576 km² + 1024 km²
d² = 1600 km²
Taking the square root of both sides,
d = 40 km
Therefore, after 2 hours, Rachel and Amos will be 40 kilometers apart.
Learn more about Pythagorean triplets here:
brainly.com/question/22160915
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HELP ASAP!!!
Identify the volume and surface area of a sphere with great circle area 9 pi m^2 in terms of pi. Give your answer in terms of pi.
Step-by-step explanation:
great circle = 9[tex]\pi[/tex] = r^2.[tex]\pi[/tex] --> r = 3 m
Surface area S = 4[tex]\pi[/tex].r^2 = 36[tex]\pi[/tex] m^2
Volume V = 4/3[tex]\pi[/tex].r^3 = 36[tex]\pi[/tex] m^3
The volume of a sphere is 36π m³ and the Surface area of sphere 36π m². Therefore, option A is the correct answer.
What is the volume of a sphere?The volume of sphere is the measure of space that can be occupied by a sphere. If the radius of the sphere formed is r and the volume of the sphere is V. Then, the volume of the sphere is given by: Volume of Sphere, V = (4/3)πr³
Given that, sphere with great circle area 9π m².
We know that, area of a circle = πr²
Now, πr²=9π m²
r=3 m
Here, volume of a sphere = 4/3 ×π×3³
= 36π m³
Surface area of sphere = A = 4πr²
= 4×π×3²
= 36π m²
Therefore, option A is the correct answer.
To learn more about the volume of a sphere visit:
https://brainly.com/question/9994313.
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Write an equation (a) in slope intercept form and (b) in standard form for the line passing through (2,7) and perpendicular to 3x + 5y = 1
Answer:
Step-by-step explanation:
Solve 3x + 5y = 1 for y to obtain the slope of the given line:
5y = -3x + 1, or y = (-3/5)x + 1.
Any line perpendicular to this one has the slope which is the negative reciprocal of (-3/5): That would be 5/3.
The desired line has slope 5/3 and passes through (2, 7);
Adapt y = mx + b by substituting the known values, to find b:
7 = (5/3)(2) + b. The LCD is 3, so multiply each term by 3 to eliminate the fractional coefficient:
21 = 10 + 3b, or 11 = 3b. Then b = 11/3, and the desired equation in slope intercept form is
y = (5/3)x + 11/3
To obtain the standard form, multiply all three terms by 3 again:
3y = 5x + 11, or
5x + 11 - 3y = 0, or
5x - 3y + 11 = 0
Use the given degree of confidence and sample data to construct interval for the population proportion. Of 369 randomly selected medical students, 23 said that they planned to work in a rural community. Construct a 95% confidence interval for the percentage of all medical students who plan to work in a rural community. (4.16%, 8.30%) (3.77%, 9.47%) (3.30%, 9.17%) (2.99%, 9.47%) (3.77%, 8.70%) In a poll of registered voters nationwide, 43% of those polled blamed of companies the most for the recent increase in gasoline prices. The margin of error at the 96% confidence level for this point estimate is 2.4%. Construct a 95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices. (0.382, 0.478) (0.368, 0.492) (0.406, 0.477) (0.383, 0.477) Cannot be determined from the information given.
Answer:
e) (3.77%, 8.70%)
95% confidence interval for the percentage of all medical students who plan to work in a rural community
(3.83% , 8.69%)
95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices
(0.406 , 0.454)
Step-by-step explanation:
Step(i):-
Given random sample size 'n' = 369
Sample proportion
[tex]p = \frac{x}{n} = \frac{23}{369} = 0.0623[/tex]
95% confidence intervals are determined by
[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.0623 - 1.96 \sqrt{\frac{0.0623(1-0.0623)}{369} } , 0.0623 + 1.96\sqrt{\frac{0.0623(1-0.0623)}{369} })[/tex]
(0.0623 - 0.0246 , 0.0623 + 0.0246)
(0.0383 , 0.0869)
(3.83% , 8.69%)
95% confidence interval for the percentage of all medical students who plan to work in a rural community
(3.83% , 8.69%)
Step(ii):-
Given 43% of those polled blamed of companies the most for the recent increase in gasoline prices
sample proportion 'p' = 0.43
Given Margin of error (M.E) = 0.024
95% confidence intervals are determined by
[tex](p^{-} - Z_{0.05} \sqrt{\frac{p(1-p)}{n} } , p^{-} + Z_{0.05} \sqrt{\frac{p(1-p)}{n} })[/tex]
[tex](0.43 - 0.024 } , 0.43 +0.024 )[/tex]
(0.406 , 0.454)
Final answer:-
95% confidence level for the population proportion who blame oil companies for the recent increase in gasoline prices
(0.406 , 0.454)