Answer:
y = 2x
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 0.8 when x = 0.4
k = [tex]\frac{y}{x}[/tex] = [tex]\frac{0.8}{0.4}[/tex] = 2
y = 2x ← equation of variation
To find an equation of direct variation given that y = 0.8 when x = 0.4, we use the form y = kx to determine the constant k, which is 2. Thus, the equation of variation is y = 2x.
To find an equation of direct variation where y varies directly as x, we use the form y = kx, where k is the constant of variation.
Given that y = 0.8 when x = 0.4, we can substitute these values into the equation to find k.
Solving for k, we get k = y / x = 0.8 / 0.4 = 2. Therefore, our equation of variation is y = 2x.
Use the functions a(x) = 3x + 10 and b(x) = 5x − 6 to complete the function operations listed below.
Part A: Find (a + b). Show your work.
Part B: Find (a - b). Show your work.
Part C: Find (a * b). Show your work.
Answer:
(a + b) = 8x +4
(a - b) = -2x +16
(a * b) = [tex]15x^{2}+32x-60[/tex]
Step-by-step explanation:
We have been given the functions;
a(x) = 3x + 10 and b(x) = 5x − 6
Part A:
(a + b) = a(x) + b(x) # we simply add the two given functions
(a + b) = 3x + 10 + 5x − 6
(a + b) = 8x + 4
Part B:
(a - b) = a(x) - b(x) # we simply subtract the two given functions
(a - b) = (3x + 10 ) - (5x − 6)
(a - b) = 3x + 10 -5x +6
(a - b) = -2x + 16
Part C:
(a * b) = a(x)*b(x)
# we simply find the product of the two given functions
(a * b) = (3x + 10)*(5x − 6)
(a * b) = [tex]15x^{2}-18x+50x-60=15x^{2}+32x-60[/tex]
Part A
The functions a(x) = 3x + 10 and b(x) = 5x − 6 to complete the function operations listed below.
(a+b)(x)=a(x)+b(x)
(a+b)(x)=(3x+10)+(5x-6)
(a+b)(x)=3x+5x+10-6
(a+b)(x)=8x+4
Part B.
(a-b)(x)=a(x)-b(x)
(a-b)(x)=(3x+10)-(5x-6)
Expand the parenthesis to get:
(a-b)(x)=3x+10-5x+6
(a-b)(x)=3x-5x+10+6
(a-b)(x)=-2x+16
Part C
(a*b)(x)=a(x)*b(x)
(a*b)(x)=(3x+10)*(5x-6)
We expand to get:
[tex]a \times b = 15 {x}^{2} - 18x + 50x - 60[/tex]
[tex]a \times b = 15 {x}^{2} + 32x - 60[/tex]
In the following diagram, a circle is inscribed in a square. How can you find the area of the shaded region?
Notice that the shaded region of the figure is composed of four identical pieces. However, each piece has a curved side, which makes it very difficult to find its area using a direct method. In this type of diagram, the easiest way to find the area uses an indirect method. Look at the diagram using a different perspective. The shaded region is composed of four identical pieces. OR, the shaded region is the area of the square minus the area of the circle. Since you know how to find the area of both a square and a circle, this is a much easier method for solving!
Area of square: s2 = (6 cm)2 = 36 cm2
Area of circle: r2 ≈ (3.14)(3 cm)2 ≈(3.14)(9 cm2) ≈ 28.26 cm2
Area of shaded region: 36 cm2 - 28.26 cm2 = 7.74 cm2
The area of the shaded region is approximately 7.74 square centimeters.
Answer the questions based on the following diagram. Note: The two triangles meet at the center of the circle.
What is the approximate area of the circle? Use 3.14 in your calculation.
What is the area of one of the triangles?
What is the approximate area of the shaded region of the diagram?
Answer:
approx area of circ.=254.34
area of triangl=40.5
shaed region=173.34
just add sq. units
Step-by-step explanation:
areas of the triangle are 9*9=81
r=9
a=pi*r^2
=3.14*81
=254.34
254.34-81=173.34
A Medical company tested a new drug on 100 people for possible side effects. This table shows the results...
Compare the probability that an adult has side effects with the probability that a child has side effects. Draw a conclusion based on your results.
Answer:
p(side effects|child) = 0.44
p(side effects|adult) = 0.14
Conclusion: children have a much greater chance of having side effects than adults.
Step-by-step explanation:
i just did it on apex. good luck!
Answer:
p(side effects/child) = 0.44
p(side effects/adult) = 0.14
Conclusion: Children have a much greater chance of having side effects than adults
~apex
Find the exact value of tan 195 degrees
Answer:
0.267949192 8s the value of tan 195°
i need help asap ! 6th grade math surface area .
Answer:
136 un²
Step-by-step explanation:
Rectangles/linear faces: 7 * (5 + 6 + 5) = 7 * 16 = 112
Triangles/bases: 2 * 1/2(6 * 4) = 24
Total: 24 + 112 = 136 un²
The surface area-to-volume ratio is used in Biology to predict cell efficiency in eliminating wastes or procuring nutrients by diffusion.
Explanation:In Biology, the surface area-to-volume ratio is used to predict which cells might eliminate waste or procure nutrients faster by diffusion. This ratio is calculated by dividing the surface area of a cell by its volume. Cells with a larger surface area-to-volume ratio are more efficient at exchanging materials with their surroundings.
For example, consider a small cell with a high surface area-to-volume ratio. This cell has a relatively larger surface area compared to its volume, which allows for faster diffusion of nutrients into the cell and waste products out of the cell. In contrast, a larger cell with a lower surface area-to-volume ratio has a relatively smaller surface area compared to its volume, resulting in slower diffusion.
By analyzing the surface area-to-volume ratio, we can predict which cells have a greater capacity for diffusion and therefore can eliminate wastes or procure nutrients at a faster rate.
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A grocery store needed eight hundred ninety five cans of peas.If the peas came in boxes with thirty two cans in each box,how many boxes would they need to order?
Answer:
28 boxes
Step-by-step explanation:
We need to take the total number of cans needed and divide by the number of cans per box to determine the number of boxes
895 / 32 =27 with 31 left over
Making this a fraction
27 31/32 boxes
We cannot normally order part of a box
Rounding up to the next whole box
28 boxes
Please help me I need all right
Answer:
Jimmy and Jane
Step-by-step explanation:
They have used Pythagoras to find the length of BC. Moe is wrong because she wrote ( 1 - 4 ) ² but it's meant to be ( 4 - 1 ) ² and Alice is wrong because she forget to square 3,4 and x
PLEASE HELP BRAINIEST ANSWER IS WORTH 20 POINTS
The table below shows data for a class's mid-term and final exams:
Mid-Term Final
100 98
100 95
100 93
95 91
95 88
92 82
92 78
88 78
85 65
75 60
Which data set has the largest IQR?
A.Mid- term exams
B.Final exams
C.They have the same IQR
D.There is not enough information
Answer:
B. Final Exams.
Step-by-step explanation:
The IQR is the difference between the lower and upper quartiles of the data and is a measure of the spread of the data.
Mid Term Exam:
First find the Median
This is (95+92)/2 = 93.5.
The Lower quartile is the median of the bottom 5 values = 88.
The upper quartile is the median of the top 5 values = 100
So the IQR = 100 - 88 = 12.
Final Exam.
We find the IQR of the Final exam data in a similar way:
It comes to 93 - 78 = 15.
A stadium has a seating capacity of 8,000. Suppose it is divided into 20 equal sections. How many seats are in each section?
Answer:
400 seats would be in each section.
Step-by-step explanation:
8,000/20 is equal to 400.
Hope this helps!
Please give brainliest :)
Apples sell for $1.90 per pound, and bananas sell for $0.75 per pound. Troy bought some apples and some bananas. Together they weighed 3.8 pounds, and cost $5.84.
How many pounds of apples and how many pounds of bananas did Troy buy?
2.6 pounds of apples; 1.2 pounds of bananas
1.9 pounds of apples; 1.9 pounds of bananas
1.5 pounds of apples; 2.3 pounds of bananas
1.2 pounds of apples; 2.6 pounds of bananas
Answer:
2.6 pounds of apples; 1.2 pounds of bananas
Step-by-step explanation:
A = pounds of apples and B = pounds of bananas
The total weight is 3.8 pounds, so:
A + B = 3.8
Apples are $1.90 per pound and bananas are $0.75 per pound, and the total cost is $5.84, so:
1.90A + 0.75B = 5.84
We can solve the system of equations using either elimination or substitution.
Using substitution:
1.90A + 0.75(3.8 - A) = 5.84
1.90A + 2.85 - 0.75A = 5.84
1.15A = 2.99
A = 2.6
B = 3.8 - A
B = 1.2
At a college production of A Streetcar Named Desire, 400 tickets were sold. The ticket prices were $8, $10, and $12, and the total income from ticket sales was $3700. How many tickets of each type were sold if the combined number of $8 and $10 tickets sold was 7 times the number of $12 tickets sold?
Answer:
There are 200 $8 tickets
There are 150 $10 tickets
There are 50 $12 tickets
Step-by-step explanation:
Let a = number of $8 tickets
Let b = number of $10 tickets
Let +c = number of $12 tickets
given:
(1) a+b+c = 400
(1) 8a+10b+12c = 3700
(1) a+b = 7c
--------------
This is 3 equations and 3 unknowns, so
it should be solvable
Substitute (3) into (1)
(1) 7c+c = 400
(1) 8c= 400
(1) c = 50
Plug this value into (2)
(2) 8a+10b+12*50= 3700
(2) 8a+10b+600= 3700
(2) 8a+10b= 3100
(2) 4a+5b= 1550
and
(1) a+b+c= 400
(1) a+b+50= 400
(1) a+b= 350
Multiply both sides of (1) by +4+
(1) 4a+4b= 1400
Subtract (1) from (2)
(2) 4a+5b+=+1550+
(1) -4a-4b= -1400
b= 150
and, since
(3) a+b= 7c
(3) a+150= 7*50
(3) a= 350-150
(3) a= 200
_________________
There are 200 $8 tickets
There are 150 $10 tickets
There are 50 $12 tickets
____________________________
check:
(2) 8*200+10*150+12*50= 3700
(2) 1600+1500+600= 3700
(2) 3700= 3700
Each type was sold are 200 for $8, 150 for $10, and 50 for $12 if the ticket prices were $8, $10, and $12, and the total income from ticket sales was $3700.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
At a college production of A Streetcar Named Desire, 400 tickets were sold. The ticket prices were $8, $10, and $12, and the total income from ticket sales was $3700.
Let x be the number of $8 tickets
Let y be the number of $10 tickets
Let z be the number of $12 tickets
From the data given in the question, we can frame three linear equation in three variables:
x + y + z = 400
8x + 10y + 12z = 3700
x + y = 7z
After solving the above equations by elimination method:
We get:
x = 200
y = 150
z = 50
Thus, each type was sold are 200 for $8, 150 for $10, and 50 for $12 if the ticket prices were $8, $10, and $12, and the total income from ticket sales was $3700.
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A mouse is trapped in a maze. To find his way out he walks 10 m, makes a 90° right turn, walks 5 m, makes another 90°, and walks 7 m. What is the magnitude of the resultant vector? Round to the nearest tenth
The mouse's overall displacement or the magnitude of the resultant vector after moving through the maze is 17.7 m, calculated based on principles of vectors in physics and using the Pythagorean theorem.
Explanation:To find the magnitude of the resultant vector, indicating the mouse's displacement after traversing through the maze, we can use the principles of vectors in physics. The mouse goes through three separate displacement vectors, one of 10 m (right), another of 5 m (downward), and the last one of 7 m (right) again.
We can consider these displacements as components of two dimensions: X (horizontal) and Y (vertical). We sum the horizontal (rightward) displacements and vertical (downward) displacements separately. The horizontal displacement is 10 m + 7 m = 17 m (rightward). The vertical displacement is 5 m (downward).
To find the magnitude of the resultant displacement, we apply the Pythagorean theorem. The magnitude is the square root of the sum of the squares of the horizontal and the vertical displacement, so sqrt((17 m)^2 + (5 m)^2) = 17.7 m (rounded to the nearest tenth).
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In the diagram a || b, if m∠6 = 21°, what is m∠4?
A) 21°
B) 10.5°
C) 159°
D) 339°
Answer:D
Step-by-step explanation:
In corresponding angles formed by parallel lines intersected by a transversal line, the angles are equal. So, if the measure of angle 6 is 21°, the measure of corresponding angle 4 will also be 21°.
Explanation:The subject of this question is geometry, specifically dealing with parallel lines and the angles formed when a line intersects them. In the given diagram, we are told that lines a and b are parallel (represented as a || b). Therefore, we can use the properties of parallel lines to find the measure of angle 4. When a line intersects two parallel lines, it forms corresponding angles which are equal. Since we know the measure of angle 6, which is 21°, and angle 4 and 6 are corresponding angles, therefore the measure of angle 4 is also 21°. So, the answer is A) 21°.
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Floras flowers sells 3 rose for 13.50 $. The Green Thumb sells 4 roses for 15 $. Discount Flowers sells 6 roses for 23 $. Who sells roses at the lowest price?
Green thumbs sells lowest price. If you divide the$amount by the amount of roses, you'll get
Flora's : $13.50/3= $4.50 each rose
Green: $15/4= $3.75 each rose
Discount F: $23/6= $3.83 each rose
How do I solve this question? It says determine the next 3 terms in each arithmetic sequence. -24, -14, -4,6
Answer:
16, 26, 36Step-by-step explanation:
[tex]a_1=-24\\a_2=-24+10=-14\\a_3=-14+10=-4\\a_4=-4+10=6\\\\\text{Add the common difference d = 10 to the previous term.}\\\\a_5=a_4+10\to a_5=6+10=16\\a_6=a_5+10\to a_6=16+10=26\\a_7=a_6+10\to a_7=26+10=36\\\vdots[/tex]
Find the measure of CD.
Round to the nearest tenth.
Please Help Me I Need It.
you need to find the median angle so you take the triangle (A) and solve for the angle using the inverse of sin.(B) take this angle and multiply it by 2 and you should have you arc length I think.
Answer:
89.0
Step-by-step explanation:
Please help I’m really slow.
Write an equation to solve each problem and then solve it. The sum of three consecutive integers is 54. Find the integers. if the smallest integer is x, what will the equation be?
Answer:
It is 17,18 and 19
Step-by-step explanation:
Consecutive numbers are
x, x+1, x+2
x+x+1+x+2=54
3x+3=54
-3 -3
3x=51
x=17
17
17+1=18
17+2=19
17, 18 and 19
what is b in 12-b=12.5
Answer:
b=-.5
Step-by-step explanation:
The value of b in the equation 12 - b = 12.5 is determined by subtracting 12 from both sides and then multiplying by -1, resulting in b = -0.5.
Explanation:The student is asking to solve for b in the equation 12 - b = 12.5. To find the value of b, you need to isolate the variable on one side of the equation. This is done by subtracting 12 from both sides, resulting in -b = 12.5 - 12, which simplifies to -b = 0.5. To get b by itself and not -b, you multiply both sides of the equation by -1, giving b = -0.5.
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which of the following expressions cannot be factored?
A. 15x-10
B. 4x+8
C. 3x+8
D. 2x-2
Answer:
C. 3x + 8
Step-by-step explanation:
A. can be factored; Factor 5 from all terms:
(15x - 10)/5 = 3x - 2
B. can be factored; Factor 4 from all terms:
(4x + 8)/4 = x + 2
D. can be factored; Factor 2 from all terms:
(2x - 2)/2 = x - 1
~
The number of beads on 500 necklaces follow normal distribution whose mean is 24 beads and standard deviation os 4 beads. How many necklaces have more than 28 beads?
Answer:
The numbers of beads on 500 handcrafted bead necklaces follow a normal distribution whose mean is 24 beads and standard deviation is 4 beads.
so....
About 24 necklaces have more than 28 beads.
About 48 necklaces have more than 28 beads.
About 80 necklaces have more than 28 beads.
About 96 necklaces have more than 28 beads
About 80 necklaces have more than 28 beads.
Step-by-step explanation:
About 80 necklaces have more than 28 beads.
Solve 3(x-2) < 18.
Please help.
The answer is:
The correct option is the first option,
[tex]{x|x<8}[/tex]
Why?To solve the problem, we need to remember that the way to solve inequalities is almost the same that solving normal equations.
So, we are given the inequality, we have:
[tex]3(x-2)<18[/tex]
Now, solving we have:
[tex]3(x-2)<18\\\\(x-2)<\frac{18}{3} \\\\x-2<6\\\\x<6+2\\\\x<8[/tex]
Hence, we have that solution to the inequality is:
[tex]x<8[/tex]
So, the correct option is the first option,
[tex]{x|x<8}[/tex]
Have a nice day!
Answer:
[tex]\large\boxed{\{x\ |\ x<8\}}[/tex]
Step-by-step explanation:
[tex]3(x-2)<18\qquad\text{use the distributive porperty}\ a(b+c)=ab+ac\\\\(3)(x)+(3)(-2)<18\\\\3x-6<18\qquad\text{add 6 to both sides}\\\\3x-6+6<18+6\\\\3x<24\qquad\text{divide both sides by 3}\\\\\dfrac{3x}{3}<\dfrac{24}{3}\\\\x<8}[/tex]
Divide 21a^3-14a by -7
A.-3a^3+2a
B.-3a^3-2a
C.-3a^2+2
D.3a^3+2a
Answer:
The correct answer is A:-3a^3+2a
For this case we must find the quotient of [tex]21a^3-14a[/tex] between -7:
That is to say:
[tex]\frac {21a ^ 3-14a} {- 7} =\\\frac {21a ^ 3} {- 7} + \frac {-14a} {- 7}[/tex]
We know that:
[tex]\frac {21} {7} = 3\\\frac {14} {7} = 2\\\frac {+} {-} = -[/tex]
Finally:
[tex]-3a ^ 3 + (2a) =\\-3a ^ 3 + 2a[/tex]
Answer:
[tex]-3a ^ 3 + 2a[/tex]
Option A
Step by step???????????
Answer:
The measure of angle x is 12°
Step-by-step explanation:
we know that
(4x+4)°+(5x-22)°=90° ----> by complementary angles
Solve for x
(9x-18)°=90°
9x=90°+18°
9x=108°
x=12°
how many ounces are equal to 7pounds
7 Pounds Equals 112.0000oz.
Have A Great Day!
Find the solutions(s) to 9x^2-54x=0
Answer:
Two solutions were found :
x = 6
x = 0
Step-by-step explanation:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Step by step solution :
Step 1 :
Equation at the end of step 1 :
32x2 - 54x = 0
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
9x2 - 54x = 9x • (x - 6)
Equation at the end of step 3 :
9x • (x - 6) = 0
Step 4 :
Theory - Roots of a product :
4.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
4.2 Solve : 9x = 0
Divide both sides of the equation by 9:
x = 0
Solving a Single Variable Equation :
4.3 Solve : x-6 = 0
Add 6 to both sides of the equation :
x = 6
Answer:
x = 6...... x = 0
Step-by-step explanation:
a p e x.
Step-by-step explanation:
I need help please and thank you . I am try to pass this.
Answer:
11 ≤ n
Explanation:
[tex] \frac{66}{6} = 11[/tex]
More than indicates the minimum value, so you use the greater than or equal to.
The above answer is written in reverse, which the exact same result.
I am joyous to assist you anytime.
How many terms does the polynomial have? a 2 + b - cd 3 2 3 4
ANSWER
3
EXPLANATION
The given polynomial is
[tex] {a}^{2} + b - cd[/tex]
The terms of the polynomial are:
First term:
[tex] {a}^{2} [/tex]
Second term:
[tex]b[/tex]
Third term:
[tex] - cd[/tex]
Therefore the given polynomial has 3 terms.
a circle has a radius of 2 cm. find the length s of the arc intercepted by a central angle of 1.9 radians.
Answer:
3.8 cm
Step-by-step explanation:
The arc length formula is s = r·Ф, where Ф is the central angle in radians.
Here, s = (2 cm)(1.9 rad) = 3.8 cm
The length of the arc intercepted by a central angle of 1.9 radians in a circle with a radius of 2 cm is 3.8 cm, calculated by multiplying the radius (2 cm) by the angle in radians (1.9).
Explanation:A circle has a radius of 2 cm and we need to find the length (s) of the arc intercepted by a central angle of 1.9 radians. The formula to find the arc length 's' for a circle is s = r * Θ, where 'r' is the radius and 'Θ' is the central angle in radians. We have 'r' = 2 cm and 'Θ' = 1.9 radians.
To find the arc length 's', we simply multiply the radius by the angle:
s = 2 cm * 1.9 radians = 3.8 cm.
Therefore, the length of the arc intercepted by a central angle of 1.9 radians in a circle with a radius of 2 cm is 3.8 cm.
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Solve for an angle in right triangles.
C is 90°fare and height
Answer:
[tex] \sin(x) = \frac{4}{6 } \\ x = arcsin( \frac{2}{3} ) \\ x = 41.81 \: degrees [/tex]
Step-by-step explanation:
Google search inverse trigonometry geometry for an explanation
answer technically should say
measure of angle A equals 41.81 degrees
there should be the letter m in front of the angle symbol.