Answer:
A: (2, 11).
Step-by-step explanation:
For an ordered pair to be a solution of an equation, the ordered pair must "fit".
A: (2, 11).
11 = 3(2) + 5
11 = 6 + 5
11 = 11
So, (2, 11) is a solution.
B: (3, 13).
13 = 3(3) + 5
13 = 9 + 5
13 = 14
Since 13 is not the same thing as 14, (3, 13) is not a solution.
Since A works but B doesn't, choices C and D are both eliminated. A is your answer.
Hope this helps!
A regular polygon is drawn in a circle so that each vertex is on the circle and is connected to the center by a radius,
Each of the central angles has a measure of 40' How many sides does the polygon have?
8
9
010
O 12
Answer:
9 sides
Step-by-step explanation:
The formula for number of sides of a polygon with a given central angle
Number of sides = 360°/ central angle
In the above question, we were told that each of the central angles in the polygon ha a measure of 40°
Hence,
Number of sides = 360°/40°
9 sides.
Therefore, the number of sides that polygon in the above question has is 9 sides.
WHY CAN'T ANYONE HELP ME: ( Two computer disks and three notebooks cost $29. However, five computer disks and four notebooks cost $48. Find the price of each.
Answer:
Disks = $4 each and Notebooks = $7 each
Step-by-step explanation:
-4(2D + 3N = 29)
3(5D + 4N = 48)
-8D - 12N = -116
15D + 12N = 144
7D = 28
D = $4
2(4) + 3N = 29
8 + 3N = 29
3N = 21
N = $7
The Coffee Counter charges $8 per pound for Kenyan French Roast coffee and $7 per pound for Sumatran coffee.
How much of each type should be used to make a 20 pound blend that sells for $7.30 per pound?
Answer:
Kenyan French Roast coffee x=6
Sumatran coffee y=14
Step-by-step explanation:
x+y=20 blend coffee
8x+7y=7.3(20) selling price
x+y=20 ⇒ x=20-y
substitute in the equation:
8x+7y=7.3(20)
8(20-y)+7y=7.3(20) for 20 pound blend
160-8y+7y=146
-y=146-160
y=14 pond
x+y=20
x=20-14=6
check : 14*7+6(8)=146/7.3=20 pound
The price of the Kenyan French Roast coffee is $6 and the price of Sumatran coffee is $14.
Two equations can be derived from the question:
8x + 7y = 20(7.3)
8x + 7y = 146 equation 1
x + y = 20 equation 2
Where: x
x = Kenyan French Roast coffee
y = Sumatran coffee.
To determine the value of y, multiply equation 2 by 8
8x + 8y = 160 equation 3
Subtract equation 1 from 3
y = 14
Substitute for y in equation 2
x + 14 = 20
x = 20 - 14
x = 6
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Amy have 398.5 L of apple juice . Avery have 40098 ml of apple juice how many do they have all together
Answer: 438.5L = 438000ml
Step-by-step explanation:
Which algebraic description maps the point (x, y) 8 units to the left and 12 units up? Question 14 options: A) (x, y) → (x – 8, y + 12) B) (x, y) → (x – 12, y + 8) C) (x, y) → (x + 12, y – 8) D) (x, y) → (x + 8, y – 12)
The algebraic description maps the point (x, y) 8 units to the left and 12 units up is (x, y) -> (x - 8, y +12)
Translation of coordinatesTranslation is the way of changing the position of an object on an xy plane.
If the coordinate points (x, y) is translated 8 units to the left and 12 units up, the resulting coordinate will be:
(x, y) -> (x - 8, y +12)
Hence the algebraic description maps the point (x, y) 8 units to the left and 12 units up is (x, y) -> (x - 8, y +12)
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6(a+2b+3c) USE THE DISTRIBUTIVE PROPERTY TO CREATE AN EQUIVALENT EXPRESSION!!!!!!!!
Answer:
6a + 12b + 18c
Step-by-step explanation:
To solve, we distribute the 6 to all of the terms inside the parentheses.
[tex]6*a\\6*2b\\6*3c\\6a+12b+18c[/tex]
Our answer is 6a + 12b + 18c. Hope this helps!
Vocabulary:
Distribute: Give shares of something. In math: Divide / give to each term (in this case)
Answer:
6a+12b+18c
Step-by-step explanation:
To create an equivalent expression, we must distribute the 6. Multiply each term inside of the parentheses by 6.
6(a+2b+3c)
(6*a)+(6*2b)+(6*3c)
6*a=6a
6a+(6*2b)+(6*3c)
6*2b=(6*2)b=12b
6a+12b+(6*3c)
6*3c=(6*3)c=18c
6a+12b+18c
The equivalent expression using the distributive property is 6a+12b+18c
A line has a slope of $-\frac{3}{7},$ and its $y$-intercept is $(0,18)$. What is its $x$-intercept?
Answer:
(42, 0)
Step-by-step explanation:
Since we know the slope and y-intercept we can write the equation of the line in slope-intercept form which is y = mx + b; therefore, the equation is y = -3/7x + 18. To find the x-intercept, we just plug in y = 0 which becomes:
0 = -3/7x + 18
-18 = -3/7x
x = 42
[tex]\text{In order to find your x intercept, plug in 0 to y and solve:}\\\\0=-\frac{3}{7}x+18\\\\\text{Subtract 18 from both sides}\\\\-18=-\frac{3}{7}x\\\\\text{Multiply both sides by 7}\\\\-126=-3x\\\\\text{Divide both sides by 3}\\\\42 = x\\\\\text{This means that the x-intercept is (42,0)}\\\\\boxed{\text{x-intercept: (42,0)}}[/tex]
A researcher predicts that the proportion of people over 65 years of age in a certain city is 11%. To test this, a sample of 1000 people is taken. Of this sample population, 126 people are over 65 years of age.
The following is the setup for this hypothesis test:
H0:p=0.11
Ha:p≠0.11
The p-value was determined to be 0.106.
Come to a conclusion and interpret the results for this hypothesis test for a proportion (use a significance level of 5%) Select all that apply:
a. Reject the H0.
b. Fail to reject the H0.
c. There is NOT sufficient evidence to conclude the proportion of people over 65 years of age in a certain city is 11%.
d. There is sufficient evidence to conclude the proportion of people over 65 years of age in a certain city is 11%.
Answer:
Option b and d
Step-by-step explanation:
With the following data,
H0:p=0.11
Ha:p≠0.11
The p-value was determined to be 0.106 and significance level of 0.05.
Since the p value (0.106) is great than 0.05, then we will fail to reject the null hypothesis and conclude that There is sufficient evidence to conclude the proportion of people over 65 years of age in a certain city is 11%
helpppp with this will give bralienst but need hurry
Answer:
20.25is how much each friend gets.Step-by-step explanation:
40.50/2 = 20.25
You have to divide by 2. This way both of the people will get the same amount of money.
Answer:
each friend will get
Step-by-step explanation:
20 .25
as 40 .50 ÷ 2 = 20 .25
hope this helps
pls can u heart and like and give my answer brainliest pls i beg u thx !!! : )
The manager of a grocery store took a random sample of 100 customers. The avg. length of time it took the customers in the sample to check out was 3.1 minutes with a std. deviation of 0.5 minutes. We want to test to determine whether or not the mean waiting time of all customers is significantly > 3 min. At 95% confidence, it can be concluded that the mean of the population is
Answer:
Step-by-step explanation:
The data given are;
sample size n = 100
sample mean x = 3.1
standard deviation σ = 0.5
mean = 3
The value for Z can be determined by using the formula:
[tex]Z = \dfrac{x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]Z = \dfrac{3.1 - 3.00}{\dfrac{0.5}{\sqrt{100}}}[/tex]
[tex]Z = \dfrac{0.1}{\dfrac{0.5}{10}}}[/tex]
Z = 0.2
At 95% Confidence interval, level of significance ∝ = 0.05
From the z table ;P- value for the test statistics at ∝ = 0.05
P = 0.0228
We can see that the P-value is < ∝
Decision Rule:
Reject the null hypothesis [tex]H_o[/tex] if P-value is less than ∝
Conclusion:
At 0.05 level of significance; we conclude that the mean of the population is significantly > 3 min
Multiply (x2 + 3x + 4)(3x2 - 2x + 1).
Answer:
The answer is
3x⁴ + 7x³ + 7x² - 5x + 4Step-by-step explanation:
(x² + 3x + 4)(3x² - 2x + 1)
Expand the terms
We have
3x⁴ - 2x³ + x² + 9x³ - 6x² + 3x + 12x² - 8x + 4
Group like terms
That's
3x⁴ - 2x³ + 9x³ + x² - 6x² + 12x² + 3x - 8x + 4
Simplify
We have the final answer as
3x⁴ + 7x³ + 7x² - 5x + 4Hope this helps you
Points A,B,C and D are midpoints of the sides of the larger square. If the smaller square has area 60, what is the area of the bigger square?
Answer:
80
Step-by-step explanation:
Find the y-intercept and x-intercept of the line.
– 3x+9y= 14
Answer:
[tex]\huge\boxed{x-intercept=-\dfrac{14}{3}=-4\dfrac{2}{3}}\\\boxed{y-intercept=\dfrac{14}{9}=1\dfrac{5}{9}}[/tex]
Step-by-step explanation:
[tex]-3x+9y=14\\\\x-intercept\ \text{for}\ y=0:\\\\-3x+9(0)=14\\-3x+0=14\\-3x=14\qquad\text{divide both sides by (-3)}\\\boxed{x=-\dfrac{14}{3}=-4\dfrac{2}{3}}}[/tex]
[tex]y-intercept\ \text{for}\ x=0:\\\\-3(0)+9y=14\\0+9y=14\\9y=14\qquad\text{divide both sides by 9}\\\boxed{y=\dfrac{14}{9}=1\dfrac{5}{9}}[/tex]
What is the length of JM in the given figure?
Answer: B. 30
Step-by-step explanation:
When given a secant and a tangent, the formula is:
exterior of secant × secant = tangent²
KM × JK = LK²
10 × (JM + 10) = 20²
10JM + 100 = 400
10JM = 300
JM = 30
A private jet can fly 1,095 miles in 3 hours with a tailwind but only 987 miles in 3 hours into a headwind find the speed of the jet in still air
Answer:
The speed of the jet is 347 mph and the speed of the wind is 18 mph.
Step-by-step explanation:
We have the following:
x = the speed of the jet in still air.
y = the speed of the wind
we know that the speed is equal to:
v = d / t
therefore the distance would be:
d = v * t
if we replace with the information of the exercise we have:
3 * (x + y) = 1095
3 * (x - y) = 987
we must solve this system of equations, add both equations and we are left:
3 * x + 3 * y = 1095
3 * x - 3 * y = 987
3 * x + 3 * y + 3 * x - 3 * y = 1095 + 987
6 * x = 2082
x = 2082/6 = 347
now to calculate y, we replace:
3 * (347 + y) = 1095
1041 + 3 * y = 1095
3 * y = 1095 - 1041
y = 54/3 = 18
The speed of the jet is 347 mph and the speed of the wind is 18 mph.
Write as an algebraic expression and simplify if possible:
A number that is 20% greater than b
Answer:
1.2b
Step-by-step explanation:
When we say, "a number that is 20% greater than b," we're talking about a number that is ...
b + 20%×b
= b + 0.20b
= b(1 + 0.20)
= 1.2b
One positive integer is 6 less than twice another. The sum of their squares is 801. Find the integers
Answer:
[tex]\large \boxed{\sf 15 \ \ and \ \ 24 \ \ }[/tex]
Step-by-step explanation:
Hello,
We can write the following, x being the second number.
[tex](2x-6)^2+x^2=801\\\\6^2-2\cdot 6 \cdot 2x + (2x)^2+x^2=801\\\\36-24x+4x^2+x^2=801\\\\5x^2-24x+36-801=0\\\\5x^2-24x-765=0\\\\[/tex]
Let's use the discriminant.
[tex]\Delta=b^4-4ac=24^2+4*5*765=15876=126^2[/tex]
There are two solutions and the positive one is
[tex]\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{24+126}{10}=\dfrac{150}{10}=15[/tex]
So the solutions are 15 and 15*2-6 = 30-6 = 24
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Explain what a directed line segment is and describe how you would find the coordinates of point P along a directed line segment AB that partitions AB so that the ratio of AP to PB is 3:1.
Answer: see below
Step-by-step explanation:
In order to partition line segment AB so that AP and PB have a ratio of 3 : 1
1) Find the x- and y-lengths of the segment AB.
2) Divide the x- and y-lengths by (3 + 1) to find the length of one section.
3) Add 3 times those lengths to point A to find point P ...or...
Subtract 1 times those lengths from point B to find point P.
For example: Consider A = (0, 0) and B = (4, 8)
1) The length from A to B is
x = 4-0 = 4
y = 8-0 = 8
2) Divide those by (3 + 1):
x = 4/4 = 1
y = 8/4 = 2
3) Add 3 times those values to A to find point P:
x = 0 + 3(1) = 3
y = 0+3(2) = 6
--> P = (3, 6)
Note: We could have also subtracted 1 from the x-value of B and 2 from the y-value of B to find that point P = (4-1, 8-2) = (3, 6)
Now we know that the distance from point A to point P is 3 times the distance from point P to point B.
The radius of a nitrogen atom is 5.6 × 10-11 meters, and the radius of a beryllium atom is 1.12 × 10-10 meters. Which atom has a larger radius, and by how many times is it larger than the other?
Answer:
Beryllium, 2 times
Step-by-step explanation:
1.12×10⁻¹⁰ has a higher exponent than 5.6×10⁻¹¹.
-10 > -11
The ratio between them is:
(1.12×10⁻¹⁰) / (5.6×10⁻¹¹)
(1.12 / 5.6) (10⁻¹⁰ / 10⁻¹¹)
0.2 × 10¹
2
What is x? The angle x
Answer:
x=60
Step-by-step explanation:
This is an equilateral triangle which means all the sides are equal.
If all the sides are equal then all the angles are equal
180/3 = 60
x=60
Answer:
x= 60°
Step-by-step explanation:
We can tell that both of these triangles are equilateral. We can tell because all of their sides have little tick marks, meaning that they are all equal, meaning that the triangle is equilateral. In an equilateral triangle, we know that through definitions all of the angles are equal to 60°. Since y is an angle inside of an equilateral triangle, it is equal to 60°
hi if anyone is good with extraneous solutions pleaseeeeeee help meeee tessa solves the equation below by first squaring both sides of the equation√x^2-3x-6=x-1 what extraneous solution does tessa obtain x=
Answer:
x = -7/5
Step-by-step explanation:
If we square both sides of the equation, we get:
[tex]\sqrt{x^2-3x-6}=x-1\\ (\sqrt{x^2-3x-6})^2=(x-1)^2\\x^2-3x-6=x^2-2x+1\\[/tex]
Then, solving for x, we get:
[tex]x^2-3x-6=x^2-2x+1\\-3x-6=2x+1\\-6-1=2x+3x\\-7=5x\\\frac{-7}{5}=x[/tex]
So, x is equal to -7/5
Answer:
its -7
Step-by-step explanation:
gots it right!
Solve the proportion below.
X =
A. 24
B. 49
c. 27
D. 6
Answer:
A. 24
Step-by-step explanation:
4/9 = x/54
x= 54*4/9 ===== multiplying both sides by 54
x= 24
Answer is 24, choice A is correct one
which is bigger 4 or
[tex] \frac{12}{7} [/tex]
obviously 4 is bigger coz 12/7 will yeild you 1.71
The area of a circle is found using the formula A=\pi r^(2) , where r is the radius. If the area of a circle is 36π square feet, what is the radius, in feet? A. 6 B. 6π C. 18 D. 9π
Answer:
A. 6 feetStep-by-step explanation:
[tex]A=\pi r^2\\Area = 36\pi\\r = ?\\36\pi = \pi r^2\\Divide \:both \:sides \:of\: the \:equation\: by\: \pi\\\frac{36\pi}{\pi} = \frac{\pi r^2}{\pi} \\r^2 = 36\\Find\: the\: square\: root\: of\: both\: sides\: \\\sqrt{r^2} =\sqrt{36} \\\\r = 6\: feet\\[/tex]
Need help with trig questions
Answer:
-8 i + 19 j , 105.07°
Step-by-step explanation:
Solution:
- Define two unit vectors ( i and j ) along x-axis and y-axis respectively.
- To draw vectors ( v and w ). We will move along x and y axes corresponding to the magnitudes of unit vectors ( i and j ) relative to the origin.
Vector: v = 2i + 5j
Mark a dot or cross at the originMove along x-axis by 2 units to the right ( 2i )Move along y-axis by 5 units up ( 5j )Mark the point.Connect the origin with the marked point determined aboveMake an arrow-head at the determined pointLies in first quadrant
Vector: w = 4i - 3j
Mark a dot or cross at the originMove along x-axis by 4 units to the right ( 4i )Move along y-axis by 3 units down ( -3j )Mark the point.Connect the origin with the marked point determined aboveMake an arrow-head at the determined pointLies in 4th quadrant- The algebraic manipulation of complex numbers is done by performing operations on the like unit vectors.
[tex]2*v - 3*w = 2* ( 2i + 5j ) - 3*(4i - 3j )\\\\2*v - 3*w = ( 4i + 10j ) + ( -12i + 9j )\\\\2*v - 3*w = ( 4 - 12 ) i + ( 10 + 9 ) j\\\\2*v - 3*w = ( -8 ) i + ( 19 ) j\\[/tex]
- To determine the angle ( θ ) between two vectors ( v and w ). We will use the " dot product" formulation as follows:
v . w = | v | * | w | * cos ( θ )
v . w = < 2 , 5 > . < 4 , -3 > = 8 - 15 = -7
[tex]| v | = \sqrt{2^2 + 5^2} = \sqrt{29} \\\\| w | = \sqrt{4^2 + 3^2} = 5\\\\[/tex]
- Plug the respective values into the dot-product formulation:
cos ( θ ) = [tex]\frac{-7}{5\sqrt{29} }[/tex]
θ = 105.07°
Simplify the expression.
Write your answer without negative exponents. NEED AN ANSWER ASAP
Answer:
[tex]\boxed{\frac{-3b^4 }{a^6 }}[/tex]
Step-by-step explanation:
[tex]\frac{-18a^{-8}b^{-3}}{6a^{-2}b^{-7}}[/tex]
[tex]\frac{-18}{6} \times \frac{a^{-8}}{a^{-2}} \times \frac{b^{-3}}{b^{-7}}[/tex]
[tex]-3 \times \frac{a^{-8}}{a^{-2}} \times \frac{b^{-3}}{b^{-7}}[/tex]
Apply the law of exponents, when dividing exponents with same base, we subtract the exponents.
[tex]-3 \times a^{-8-(-2)} \times b^{-3- (-7)}[/tex]
[tex]-3 \times a^{-8+2} \times b^{-3+7}[/tex]
[tex]-3 \times a^{-6} \times b^{4}[/tex]
[tex]{-3a^{-6}b^{4}}[/tex]
The answer should be without negative exponents.
[tex]a^{-6}=\frac{1}{a^6 }[/tex]
[tex]\frac{-3b^4 }{a^6 }[/tex]
Answer:
[tex] - \frac{3 {b}^{4} }{ {a}^{6} } [/tex]Step-by-step explanation:
[tex] \frac{ - 18 {a}^{ - 8} {b}^{ - 3} }{6 {a}^{ - 2} {b}^{ - 7} } [/tex]
Reduce the fraction with 6
[tex] \frac{ - 3 {a}^{ - 8} {b}^{ - 3} }{ {a}^{ - 2} {b}^{ - 7} } [/tex]
Simplify the expression
[tex] \frac{ - 3 {b}^{4} }{ {a}^{6} } [/tex]
Use [tex] \frac{ - a}{b} = \frac{a}{ - b} = - \frac{a}{b \: } [/tex] to rewrite the fraction
[tex] - \frac{3 {b}^{4} }{ {a}^{6} } [/tex]
Hope this helps...
Best regards!!
use what you know about zeros of a function and end behavior of a graph that matches the function f(x) = (x+3)(x+2)(x-1)
Answer:
The zeros are x=-3,-2,1
end behavior is one up one down
Step-by-step explanation:
The zeros are x=-3,-2,1
The end behaviors are one up one down because the function is of degree 3 meaning it is odd function and has opposite end directions.
What is the output of the function f(x) = x + 21 if the input is 4?
When the input is 4, the output of f(x) = x + 21.
Work Shown:
Replace every x with 4. Use the order of operations PEMDAS to simplify
f(x) = x + 21
f(4) = 4 + 21
f(4) = 25
The input 4 leads to the output 25.
Enter a range of vaules for x
A range for the values of x:
-2, -1, 0, 1, 2,
Happy to help! You can certainly extend this range
A cylinder with a base diameter of x units has a volume
of sex cubic units.
Which statements about the cylinder are true? Select
two options.
The radius of the cylinder is 2x units.
The area of the cylinder's base is 2-ox? square units.
The area of the cylinder's base is nexsquare units.
The height of the cylinder is 2x units.
The height of the cylinder is 4x units.
Answer:
(C) The area of the cylinder's base is [tex]\dfrac{1}{4} \pi x^2[/tex] square units.
(E)The height of the cylinder is 4x units.
Step-by-step explanation:
If the Base Diameter = x
Therefore: Base radius = x/2
Area of the Base
[tex]=\pi (x/2)^2\\=\dfrac{ \pi x^2}{4} $ square units[/tex]
Next, we know that:
The volume of a cylinder = Base Area X Height
[tex]\pi x^3=\dfrac{ \pi x^2}{4} \times Height\\Height =\pi x^3 \div \dfrac{ \pi x^2}{4}\\=\pi x^3 \times \dfrac{ 4}{\pi x^2}\\\\Height=4x$ units[/tex]
Therefore, the correct options are: C and E.
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