Answer:
slope=5/4 y intercept=-3/4
Step-by-step explanation:
put it into slope intercept form y=5/4x-3/4
pull out 5/4 as slope and -3/4 as y intercept
By the triangle sum theorem, the sum of the angles in a triangle is equal to Response area. Therefore, m∠A+m∠B+m∠C=180°. Using the Substitution Property, (4x)°+90°+(x+10)°=180°. To solve for x, first combine like terms to get 5x + 100 = 180. Using the Response area, 5x = 80. Then, using the division property of equality, x = 16. To find the measure of angle A, use the Response area to get m∠A=4(16)°. Finally, simplifying the expression gets m∠A=64°.
The required measure of the angle is m∠A=64°.
orientation of one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
,
Here,
Angles are represented by an algebraic expression, and the sum of the angle is 180°.
According to the question,
m∠A+m∠B+m∠C=180°
Substitute the value in the equation,
4x+90°+x+10=180°
5x = 180 - 100
5x = 80
x = 16°
Thus, the required measure of the angle is m∠A=64°.
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An ocicat eats $\frac 35$ of a pound of food daily. How many whole ocicats can a $19\frac 12$-pound bag of food feed for one week?
Number of ocicats that [tex]19\frac{1}{2}[/tex] food will last for one week is 4 .
In the question ,
it is given that
the amount of food that the ocicat eats in 1 day = 3/5 pound
So , the amount of food that the ocicat eats in 1 week = (3/5) × 7 = 21/5
we have to find the number of ocicat that can eat [tex]19\frac{1}{2}[/tex] pound of food feed .
So ,
the number of ocicat that can eat [tex]19\frac{1}{2}[/tex] pound of food feed = [tex]19\frac{1}{2}[/tex] ÷ 21/5
= (19*2+1)/2 ÷ 21/5
= 39/2 × 5/21
= (39 × 5)/(2 × 21)
= 195/42
= 65/14
= [tex]4\frac{9}{14}[/tex] ocicats
since the number of ocicats cannot be in fraction ,
so number of ocicats = 4
Therefore , Number of ocicats that [tex]19\frac{1}{2}[/tex] food will last for one week is 4 .
The given question is incomplete , the complete question is
An ocicat eats 3/5 of a pound of food daily. How many whole ocicats can a [tex]19\frac{1}{2}[/tex] -pound bag of food feed for one week?
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The value of function is positive so the function have maximum value 30 at x=3.
In the given question we have to find the maximum or the minimum value of a function.
The given function is
f(x) = -3x^2+18x+3
To find the maximum or minimum value we firstly find the value of f'(x).
f'(x) = -6x+18
Now put f'(x)=0
-6x+18=0
Subtract 18 on both side we get
-6x=-18
Divide by -6 on both side we get
x = 3
Now finding the value of function at x=3
f(3)= -3*(3)^2+18*3+3
f(3)= -3*9+54+3
f(3)= -27+54+3
f(3)= 30
Since the value of function is positive so the function have maximum value 30 at x=3.
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Change the standard form equation y=x^2-4x+9 to vertex form by completing the square.
Find x if AC= 17, BD = 2x - 6, AD= x + 16, and BC = 6
Answer:
Hey, hope it helps my friend
Step-by-step explanation:
In the image
What is the inequality of the graph below?
Answer:
it should be the first one, if not it’s the third
Step-by-step explanation:
use the following to answer the next 2 questions. solar-heat installations successfully reduce the utility bill 60% of the time. suppose 10 houses with solar-heat installations are selected at random and the outcome between houses is independent. suppose x is the number of houses that successfully reduced the utility bill out of the 10. 14. which discrete distribution will appropriately model x? explain. binomial 15. what is the probability that at least 9 out of 10 solar-heat installations are successful and will reduce the utility bill? a. 0.0464 b. 0.9432 c. 0.0403 d. 0.8429
The probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.
What is a binomial distribution?
The probability distribution known as the binomial distribution, which is used in statistics, quantifies the chances that a value will take one of two independent values given a particular set of conditions or hypotheses.
Formula to calculate the binomial distribution
P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ
Here, we know that
Solar-heat installations successfully reduce the utility bill 60% of the time.
We have to calculate the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill.
We have 60% = 0.6 = p and n = 10.
We have a binomial distribution: X : (10, 0.6).
We use the binomial distribution formula to calculate the probability
P(X = x) =ⁿCₓ× pˣ×(1-p)ⁿ⁻ˣ, we get
P(x ≥ 9) = 1 - P(x < 9)
P(x ≥ 9) = 1 - P(x ≤ 8)
P(x ≥ 9) = 1 - ∑⁸₀ P(x = x)
P(X ≥ 9) = 1 - ∑⁸₀¹⁰Cₓ × (0.6)ˣ × (1-0.6)¹⁰⁻ˣ
P(X ≥ 9) = 1 -( 0.00011 + 0.00157 + 0.01062 + 0.04247 + 0.11148 + 0.20066 + 0.25082 + 0.21499 + 0.12093)
P(X ≥ 9) = 1 -0.95365
P(X ≥ 9) = 0.04635
Hence, the probability that at least 9 out of 10 solar-heat installations will succeed and reduce the utility bill is 0.0464.
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1. Which is an example of an experiment? (1 point)
OA company asks its website users to rate its new features to navigate the site.
O Researchers working for a company test their new sneaker design to see if it helps athletes run faster.
OA scientist watches a group of local birds to see what type of tree they prefer to make their nests in.
An ice cream company asks people to identify their top three ice cream flavors.
An example of experiment is B. Researchers working for a company test their new sneaker design to see if it helps athletes run faster.
What is an experiment?An experiment simply means a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. It should be noted that experiments provide insight into cause-and-effect as they demonstrate what outcome occurs when a particular factor is manipulated
Experiments have a vital place in the development of science because experiments are used to test the reality of a thought, an axiom, or a phenomenon with a theoretical basis and to turn it into a law or a theorem.
In this case, testing the new sneakers is an experiment.
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On Friday night, Clara ate a pizza for dinner and had 1/5 of the pizza left over. On Saturday, she ate 2/3 of what was left. How much of the pizza did Clara eat on Saturday? Write your answer as a fraction or as a whole or mixed number.
Answer:
Clara ate 2/15
Step-by-step explanation:
1/5 equals 3/15
A cell phone provider offers a plan that costs 40$ per month plus 0.10$ per text message sent or received. A comparable plan costs 50$ per month but offers unlimited text messaging. Complete parts a. and b. below.
a. How many text messages would have to be sent or received in order for the plans to cost the same each month?
In order for the plans to cost the same,
enter your response here text messages would have to be sent or received.
(Simplify your answer. Type an integer or a decimal.)
answer:
100 text messages.
$50-$40 = $10
$10/$0.1 = 100
100 text messages
Tank B is 60% full of water. It requires an additional 2800 litres of water to be full. How many litres of water fills tank B?
jake's on 49 tickets to the school are, and jeans sold 12 tickets. what is the ratio, in simplest form, of the number of tickets jeans sold to the number of tickets jake sold?
The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.
Given that,
Jake sold 49 tickets while jeans sold 12 for the school.
In simplest form the ratio of the given case will be;
Simplest form:
A fraction is a number that falls between the whole numbers but is not a whole number. It belongs to the entire. A fraction also consists of a denominator and a numerator. We obtain the fraction in its simplest form when both the numerator and denominator can no longer be independently reduced to any smaller integer.
The ratio we get;
→ 12/49
The ratio in simplest form, of the number of tickets jeans sold to the number of tickets jake sold is 12/49.
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the p-value is 0.026, so we reject the null hypothesis and accept the alternative hypothesis. we conclude that this year the proportion of americans who support federal spending cuts to medicaid is less than 0.12 what type of error is possible here?
The proportion of Americans who support federal spending cuts to Medicaid is less than 0.12 leads to Type 1 error.
What is Type 1 error and Type 2 error?When we reject a true H₀ it is known as type 1 error. The probability of type 1 errors is inversely proportional to the amount of confidence you choose. There is a 5% possibility of receiving a type 1 error on a test with a 95% confidence level.
When we feel to reject a false H₀ it is known as type 2 error.
H₀:P= 0.12
Hₐ:P= 0.12
The question implies that we actually rejected the null hypothesis, while there is a chance that it is true and we are rejecting a true null hypothesis.
Therefore, it only suggests that there is a possibility that we will make a type 1 error.
Consequently, Type 1 error is the response to our query.
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which are the solutions of x2= -5x +8
subtract 2w+4 from 2w-6 show your work
Answer:
10
Step-by-step explanation:
(2w + 4) - (2w - 6)
2w + 4 - 2w + 6
2w - 2w + 4 + 6
10
I hope this helps!
8 + (-3) +15 - (-40)
For a ride on a rental scooter, Eric paid an $8 fee to start the scooter plus 6 cents per minute of the ride. The total bill for Eric's ride was $17.84. For how many
minutes did Eric ride the scooter?
minutes
Answer:
164 minutes
Step-by-step explanation:
$8 + $0.06m = $17.84
To isolate the m, first bring the eight to the other side
0.06m = 9.84
then divide both sides by 0.06
m = 164
The average mass of a man is 84 kg and of a woman is 70 kg
a lift can safely carry 620 kg
work out the maximum number of people the lift can safely carry
The maximum number of people the lift can safely carry is 8 people.
Given that, the average mass of a man is 84 kg and of a woman is 70 kg.
What is the average?In maths, the average value in a set of numbers is the middle value, calculated by dividing the total of all the values by the number of values. When we need to find the average of a set of data, we add up all the values and then divide this total by the number of values.
Now, average = (84+72)/2
= 156/2
= 78
Let the number of people in the left be n.
So, 78n≤620
Divide 78 to both the sides of the inequality
78n/78≤620/78
⇒ n≤7.9
⇒ n≤8
Therefore, the maximum number of people the lift can safely carry is 8 people.
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(a) Annie and Dermot share $600 in the ratio 11:9.
(i) Show that Annie receives $330.
Ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount received by Annie is $330 and Dermot is $270.
As given in the question,
Total amount share by Annie and Dermot is $600.
Ratio of amount share by Annie and Dermot is 11 : 9
Let x be the amount of money.
11x + 9x = $600
⇒ 20x = $600
⇒20x/20 = $600/20
⇒x= $30
Amount received by Annie is equal to
= 11 × 30
= $330
Amount received by Dermot is equal to
= 9 × 30
= $270
Therefore, ratio of amount $600 share by Annie and Dermot is 11 : 9, then amount received by Annie is $330 and Dermot is $270.
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I need help to solve this please!!
Answer:
Adult is 10$ and Child is 7$.
Unfortunately for the family, they do not have enough to go to the theater. They do not have that extra dollar.
Hope this helps!
Step-by-step explanation:
2x + 4y = 48
5x + 2y = 64
2x + 4y = 48
10x + 4y = 128
( 10x - 2x ) + ( 4y - 4y ) = ( 128 - 48 )
8x = 80
x = 10
2 ( 10 ) + 4y = 48
20 + 4y = 48
4y = 48 - 20
4y = 28
y = 7
NEED HELP WRITING THE EQUATION!!!
The equation of line with undefined slope and passes through the point
(1/2, 5) will be;
⇒ x = 1/2
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point = (1/2 , 5)
And, The slope = undefined
Now,
Since, We know that;
The equation of line with undefined slope and passes through the point will be;
⇒ x = a
Where, 'a' is the x - intercept.
Here, The point = (1/2 , 5)
The slope = undefined
And, The x - intercept = 1/2
So, The equation of line with undefined slope and passes through the point (1/2, 5) will be;
⇒ x = 1/2
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Noah went into a movie theater and bought 9 drinks and 4 candies, costing a total of $60. Nachelle went into the same movie theater and bought 10 drinks and 2 candies, costing a total of $57.50. Determine the price of each drink and the price of each candy.
Answer:
See below.
Step-by-step explanation:
Let the price of drinks be x and the price of candies be y.
Condition # 1:9x + 4y = 60 --------------------(1)
Condition # 2:10x + 2y = 57.50 --------------(2)
Multiply Eq. (2) by 22(10x + 2y) = 57.50*2
20x + 4y = 115 --------------(3)
Subtract Eq. (3) from (1)9x + 4y - 20x - 4y = 60 - 115
9x - 20x = -55
-11x = -55
11x = 55
Divide both sides by 11x = 55/11
x = $5Put x = 5 in Eq. (1)
9(5) + 4y = 60
45 + 4y = 60
Subtract 45 to both sides4y = 60 - 45
4y = 15
Divide both sides by 4y = 15/4
y = $3.75So, the cost of one drink is $5 and the cost of one candy is $3.75.
[tex]\rule[225]{225}{2}[/tex]
Use the method of adding y-coordinates to graph the function.
f(x) = 3x - sin 4x
Graph of f(x) = 3x - sin 4x is using method of adding y-coordinates is attached below.
What is graphing method by adding ordinates?
The function y = 3x - sin 4x is actually the sum of two functions, y = 3x and y = - sin 4x.
For every value in the domain, there is a corresponding value in the range so that the point (x, 3x - sin 4x) is on the graph of y = 3x - sin 4x.
According to the given question:
Follow these steps to graphing the function:
1. Open an Excel file. Label the first column "x-coordinates," the second column "y = 3x," the third column "y = -sin 4x," and the fourth column "y = 3x - sin 4x." Set each column to round to four decimal places.
2. Set up the first column to range from -2pi to 2pi by intervals of pi/4.
3. Fill in the second and third columns by utilizing the equations y = 3x and y = - sin 4x, respectively.
4. Fill in the fourth column by simply adding the second and third columns.
5. Graph y = 3x - sin 4x by using the x-coordinates from column A and the y-coordinates from column D.
Check the attachment below for the required graph obtained after plotting the points.
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what is 5/2x + 1/2x = 9 + 7/2
Answer: x = 25/6
Step-by-step explanation: yes
Answer: x=25/6
Step-by-step explanation:
combine multiplied terms into 1 fraction
5/2*+1/2x=9+7/2
5x/2+1/2x=9+7/2
combine
5x/2+1/2x=9+7/2
5x/2+1x/2=9+7/2
multiply by 1
5x/2+1x/2=9+7/2
5x/2+x/2=9+7/2
Use the diagram and the given angle measure to find the other three angle measures
By using the diagram and the given angle measure we get that:
if, m∠1 = 143°
then, m∠2 = 37°
m∠3 = 143°
m∠4 = 37°
What is angles?
An angle is formed when two straight lines or rays meet at a common endpoint.
What is Properties of Congruence?
Reflexive Property:For all angles A ,
∠A≅∠A .
An angle is congruent to itself.
Symmetric Property:For any angles A and B ,
if ∠A≅∠B , then ∠B≅∠A .
Order of congruence does not matter.
Transitive Property:For any angles A,B, and C ,
if ∠A≅∠B and ∠B≅∠C , then ∠A≅∠C .
If two angles are both congruent to a third angle, then the first two angles are also congruent.
I assume that, this refers to two intersecting lines which form four angles.
∠1 and ∠2 are supplementary angles whose sum is 180°.∠1 + ∠2 = 180°
143° + ∠2 = 180°
∠2 = 180° - 143°
∠2 = 37°.
∠1 and ∠3 are vertical angles so do with ∠2 and ∠4.Therefore, it is easy to find their measures because vertical angles are congruent in measure.It means that, ∠1 = ∠3 =143° (properties of congruency)
and ∠2 = ∠4 =37° (properties of congruency).
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a rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth side. two kinds of fencing will be used with heavy duty fencing selling for $4 a foot on the side opposite the wall. the two remaining sides will use standard fencing selling for $3 a foot. what are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $6600?
An area 825 by 550 ft gives max area for $6600.
What is the area of rectangle?Any shape's area can be calculated by counting how many unit squares will fit inside of it.A square with a side of 1 unit is referred to as a unit square in this context. Therefore, the quantity of unit squares that make up a rectangle's perimeter is its area. Alternately, the area of the rectangle is the area contained within the boundary of this shape. The unit-length tiles in your home are a good illustration of a rectangle form. By counting the number of tiles, you can quickly determine how much space the floor takes up. This will also enable you to calculate the rectangle floor's area.acc to our question-
he perimeterP = L + 2WThe cost4L + 3(2W) = $66004L + 6W = $66004L = (6600-6W)divide both sides by 4L = 1650 - 1.5WReplace L with (1650-1.5w)A = W(1650-1.5W)A quadratic equationA = -1.5w^2 + 1650wFind the axis of symmetry: x = -b/(2a); In this equation: a=-1.5; b=1650w = %28-1650%29%2F%282%2A-1.5%29w = +550 ft is the widthfind the lengthL = 1650 - 1.5(550)L = 825 ft is the lengthhence, 3300 + 3300 = $6600
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3x - 2 when x=4
please be quickkkkkkkk
Answer:
10
Step-by-step explanation:
substitute x = 4 into the expression
3x - 2 = 3(4) - 2 = 12 - 2 = 10
Answer: 10
Step-by-step explanation:
4 × 3 = 12
12 - 2= 19
Hope it helps
The total weekly profit p, in dollars, from producing and selling x units of a certain product is given by the
function p(x) = 225x-(165x+c), where c is a constant. If 75 units were produced and sold last week for a profit
of $3,365, what is the value of c?
-1,135
Step-by-step explanation:
The total weekly profit p, in dollars, from producing and selling x units of a certain product is given by the function p(x) = 225x-(165x+c), where c is a constant. If 75 units were produced and sold last week for a profit of $3,365, what is the value of c?
$3,365 = 225(75) - (165(75) + c)
$3,365 = 16,875 - 165(75) - c
$3,365 = 16,875 - 12,375 - c
$3,365 = 4,500 - c
=1,135 = - c
c = 1,135
5. (x+3)(x-3)+(x-3)²
Simplify the expression above in standard form.
Answer: 2x^2 -6x
Step-by-step explanation:
First you should distribute the x's as shown:
(x)(x)+(x)(−3)+(3)(x)+(3)(−3)+x2+−6x+9=x2+−3x+3x+−9+x2+−6x+9
Then combine Like terms:
↓x2+−3x+3x+−9+x2+−6x+9=↓
↓(x2+x2)+(−3x+3x+−6x)+(−9+9)↓
2x2+−6x
Hope this helped... :)
Scott will purchase a new computer on an installment plan. The computer costs $2,300 and requires a 15% down payment.
a.) How much is the down payment?
The value of the down payment for the car is $345.
How to calculate the.dow payment?From the information, Scott will purchase a new computer on an installment plan and the computer costs $2,300 and requires a 15% down payment.
The value of the down payment will be:
= Down payment percentage × Total cost
= 15% × $2300
= 0.15 × $2300
= $345
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