Answer:
The solution point is (4,2).
Step-by-step explanation:
Equation of straight line passing through the points (0,0) and (4,2) is given by
[tex]\frac{y - 2}{2 - 0} = \frac{x - 4}{4 - 0}[/tex]
⇒ 2y = x ............ (1)
And the other straight line is y = - x + 6 .............. (2)
Now, solving equations (1) and (2) we get, y = - 2y + 6
⇒ 3y = 6
⇒ y = 2
And from equation (1) we get, x = 2y = 4
Therefore, the solution point is (4,2). (Answer)
Answer:
C: (4,2)
Step-by-step explanation:
What is -1/4 times 5/3
Answer:
_
-0.416 or for rounded 0.417
Step-by-step explanation:
when you multiply -1/4 and 5/3 you will get a repeating decimal so what you will do is ether round it or put a line on top of the 6 showing that the number six never ends so when you round it you should round the thousandths plae making it -0.417
Write equivalent fractions to 2.5
Answer:
5/2 or 2 1/2
Step-by-step explanation:
if I work 2 days a week and get 8 dollars a day. How much will I make in 3 months
The data depicted in a histogram show approximately a normal distribution if the distribution
bunches up on either end and tapers off toward the center
bunches up in the middle and tapers off symmetrically at either end
is relatively even from one end to the other
bunches up on one end and tapers off toward the other end
Answer:
bunches up in the middle and tapers off symmetrically at either end
Step-by-step explanation:
By definition a normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.
Because the data towards the mean is more frequent in occurrence, the graph peaks at the center. The data occurs less frequently at the tail ends of the distribution, thus the shape of the distribution is a bell shape that peaks at the center and tapers off towards the tails. The key characteristic is that the distribution of data is perfectly symmetrical.
This is why the answer is:
The data depicted in a histogram show approximately a normal distribution if the distribution bunches up in the middle and tapers off symmetrically at either end.
plz hurry 19 points will mark brainliest
which is a measurment of an angle that is supplementary to an angle that measures 80?
10
90
100
260
Good evening,
Answer:
100°
Step-by-step explanation:
Two angles are supplementary if the sum of their measures is equal to 180°
then the measurement of an angle that is supplementary to an angle that measures 80° is :
180 - 80 = 100°
Steve gets $100 a week, plus 15% of sales. Which equation best represents his salary?
A.) y = 100x + 0.15
B.) y = 0.15x + 100
C.) y = -0.15 x + 100
D.) y = -100x +0.15
Answer y = 0.15x + 100
Step-by-step explanation:
Drag the tiles to the correct boxes to complete the pairs.
Match each transformation or sequence of transformations to an equivalent transformation or sequence of transformations.
a 90° counterclockwise rotation about the origin
a 180° rotation about the origin
a 90° clockwise rotation about the origin
Answer:
a 90° clockwise rotation about the origin
a 180° rotation about the origin
a 90° counterclockwise rotation about the origin
Step-by-step explanation:
Transformations are done on a Cartesian Plane, which is the grid with four quadrants. (See picture) Each quadrant is 90°, so two quadrants is 180°.
When you rotate counterclockwise it is like in the picture. When you want to rotate clockwise, it's the other way.
When we rotate 180°, it does not matter if it is counterclockwise or clockwise because the result is the same (both move two quadrants).
We can imagine an example to help us solve the problem. Let's say we are rotating an object starting in first quadrant. (Upper right quadrant).
Find out which quadrant the object ends up with each instruction:
FROM THE PICTURE:
"a 90° counterclockwise rotation about the origin (Q2) and then a 180° rotation about the origin"
End: Quadrant 4
"a reflection across the x-axis (Q4) and then a reflection across the y-axis"
End: Quadrant 3
"a 90° clockwise rotation about the origin (Q4) and then a rotation 180° about the origin"
End: Quadrant 2
FROM YOUR LIST:
"a 90° counterclockwise rotation about the origin " Quadrant 2
"a 180° rotation about the origin " Quadrant 3
"a 90° clockwise rotation about the origin" Quadrant 4
Match each ending quadrant from your list with the same ending quadrant from the picture.
The order that you should put your list into the boxes is:
a 90° clockwise rotation about the origin
a 180° rotation about the origin
a 90° counterclockwise rotation about the origin
If f(x)=4x 2 +5x+2, then what is the remainder when f ( x ) is divided by x + 7?
Answer:
Step-by-step explanation:
Final answer:
The remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7 is found using the remainder theorem, which gives us a result of 163.
Explanation:
To find the remainder when the function f(x) = 4x² + 5x + 2 is divided by x + 7, we can use the remainder theorem. The remainder theorem states that if a polynomial f(x) is divided by a linear divisor of the form x - r, the remainder is f(r). Here, our linear divisor is x + 7, which we can rewrite as x - (-7). So, we substitute x = -7 into the polynomial to get the remainder.
Substituting x = -7 into the function gives us:
f(-7) = 4(-7)² + 5(-7) + 2 = 4(49) - 35 + 2 = 196 - 35 + 2 = 163.
Therefore, the remainder when f(x) is divided by x + 7 is 163.
please help asap will give brainliest
Answer:
1) a = 3189 b = 5
2) a = 53 b = -5
Step-by-step explanation:
The following data represent the number of people aged 25 to 64 years covered by health insurance (private or government) in 2018. Approximate the mean and standard deviation for age.
Age: 25-34. 35-44. 45-54. 55-64
Number 22.1. 31.5. 37.7. 25.3
(Millions)
The approximate mean age is [tex]\(45.15\)[/tex] years, and the approximate standard deviation for age is [tex]\(9.22\)[/tex] years, both rounded to two decimal places.
To approximate the mean and standard deviation for the age groups provided, we can calculate the weighted average based on the midpoint of each age group and use the formula for the standard deviation of a weighted dataset.
First, calculate the midpoints of the age groups:
- For 25-34 years: midpoint = (25 + 34) / 2 = 29.5
- For 35-44 years: midpoint = (35 + 44) / 2 = 39.5
- For 45-54 years: midpoint = (45 + 54) / 2 = 49.5
- For 55-64 years: midpoint = (55 + 64) / 2 = 59.5
Next, calculate the weighted mean using the formula:
[tex]\[ \text{Weighted Mean} = \frac{\sum (\text{Midpoint} \times \text{Number of People})}{\sum \text{Number of People}} \][/tex]
[tex]\[ \text{Weighted Mean} = \frac{(29.5 \times 22.1) + (39.5 \times 31.5) + (49.5 \times 37.7) + (59.5 \times 25.3)}{22.1 + 31.5 + 37.7 + 25.3} \][/tex]
[tex]\[ \text{Weighted Mean} \approx \frac{651.45 + 1244.25 + 1867.35 + 1503.35}{116.6} \][/tex]
[tex]\[ \text{Weighted Mean} \approx \frac{5266.4}{116.6} \][/tex]
[tex]\[ \text{Weighted Mean} \approx 45.15 \text{ years (approx)} \][/tex]
Now, calculate the standard deviation using the formula:
[tex]\[ \text{Weighted SD} = \sqrt{\frac{\sum (\text{Number of People} \times (\text{Midpoint} - \text{Weighted Mean})^2)}{\sum \text{Number of People}}} \][/tex]
[tex]\[ \text{Weighted SD} = \sqrt{\frac{(22.1 \times (29.5 - 45.15)^2) + (31.5 \times (39.5 - 45.15)^2) + (37.7 \times (49.5 - 45.15)^2) + (25.3 \times (59.5 - 45.15)^2)}{116.6}} \][/tex]
[tex]\[ \text{Weighted SD} \approx \sqrt{\frac{9919.575}{116.6}} \][/tex]
[tex]\[ \text{Weighted SD} \approx \sqrt{85.004} \][/tex]
[tex]\[ \text{Weighted SD} \approx 9.22 \text{ years (approx)} \][/tex]
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How do I solve this question
The solution set is x = 3, y = 4 (or) x = 3, y = –4.
Solution:
Given system of algebraic equations are
[tex]y^{2}+(x-8)^{2}=41[/tex] – – – – – (1)
[tex]y^{2}-25=-x^{2}[/tex] – – – – – (2)
Expand equation (1) using algebraic identity: [tex](a-b)^2=a^2-2ab+b^2[/tex]
[tex]y^{2}+x^2-16x+64=41[/tex]
subtract 64 from both sides of the equation
[tex]y^{2}+x^2-16x+64-64=41-64[/tex]
[tex]y^{2}+x^2-16x=-23[/tex] – – – – – (3)
Now, to arrange equation (2) in order, add [tex]x^2[/tex] on both sides.
[tex]y^{2}-25+x^2=-x^{2}+x^2[/tex]
[tex]y^{2}-25+x^2=0[/tex]
Add 25 on both sides of the equation,
[tex]y^{2}+x^2=25[/tex] – – – – – (4)
To solve this subtract equation (4) from equation (3)
[tex]\Rightarrow y^{2}+x^2-16x-(y^{2}+x^2)=-23-25[/tex]
[tex]\Rightarrow y^{2}+x^2-16x-y^{2}-x^2=-23-25[/tex]
[tex]\Rightarrow -16x=-48[/tex]
Divide both sides of the equation by –16,
⇒ x = 3
Substitute x = 3 in equation (4), we get
[tex]\Rightarrow y^{2}+3^2=25[/tex]
[tex]\Rightarrow y^{2}=25-9[/tex]
[tex]\Rightarrow y^{2}=16[/tex]
[tex]\Rightarrow y=\pm 4[/tex]
i. e. y = 4 (or) y = –4
The solution set is x = 3, y = 4 (or) x = 3, y = –4.
What is the answer 5(9 + p) = 125
Answer:
p=17
The drawing will help
Answer: p = 16
Step-by-step explanation: To solve for p in this equation, our first step is to simplify the left by distributing the 5 through both terms inside the parentheses.
When we do that,
we get 5 times 9 which is 45 and 5 times p which is 5p.
So we have 45 + 5p = 125.
Our next step is to isolate the p term by subtracting 45 from both sides of the equation. On the left side of the equation, 45 - 45 cancels and we're left with 5p.
On the right side of the equation, 125 - 45 simplifies to 80.
So we have 5p = 80.
We want to solve our equation for p so we want to get p by itself on the left side of the equation. Since p is being multiplied by 5, we need to divide both sides of the equation by 5. On the left side of the equation.notice that the 5 and 5 cancel each other out so we're just left with p and on the right side, 80 divided by 5 is 16 so we have p = 16.
In trapezoid PQRS, PQ is parallel to RS. Let X be the intersection of diagonals PR and QS. The area of triangle PQX is 20 and the area of triangle RSX is 45. Find the area of trapezoid PQRS.
Answer:
The area of trapezoid PQRS is 125 square units
Step-by-step explanation:
The picture of the question in the attached figure
we know that
If trapezoid PQRS with parallel sides PQ and RS is divided into four triangles by its diagonals PR and QS , intersecting at X, then the area of triangle PSX is equal to that of triangle QRX, and the product of the areas of triangle PSX and triangle QRX is equal to that of triangle PQX and triangle RSX
Let
A_1 ----> the area of triangle PSX
A_2----> the area of triangle QRX
A_3 ---> the area of triangle PQX
A_4 ---> the area of triangle RSX
[tex]A_1*A_2=A_3*A_4[/tex]
[tex]A_1=A_2[/tex]
so
[tex]A_1^2=A_3*A_4[/tex]
we have
[tex]A_3=20\ units^2\\A_4=45\ units^2[/tex]
substitute
[tex]A_1^2=(20)(45)\\A_1^2=900\\A_1=30\ units^2[/tex]
The area of trapezoid is equal to
[tex]A=A_1+A_2+A_3+A_4[/tex]
substitute
[tex]A=30+30+20+45=125\ units^2[/tex]
Final answer:
The area of trapezoid PQRS is found by adding the areas of triangle PQX (20 square units) and triangle RSX (45 square units) together, which equals 65 square units.
Explanation:
The area of trapezoid PQRS can be found by summing up the areas of triangle PQX and triangle RSX. Since diagonals PR and QS intersect at point X, both triangles share the same height, which is the perpendicular distance from point X to the bases PQ and RS. Thus, the area of trapezoid PQRS is simply the sum of the areas of the two triangles.
To calculate the area of trapezoid PQRS, we add the area of triangle PQX, which is given as 20, to the area of triangle RSX, which is given as 45. Therefore, the area of trapezoid PQRS is:
Area of trapezoid PQRS = Area of triangle PQX + Area of triangle RSX = 20 + 45 = 65
So, the area of trapezoid PQRS is 65 square units.
what is the distance between -2/3 and 4/3 on a number line?
A number line can be defined as a horizontal line that can be extended and have numbers on it. The distance between -2/3 and 4/3 on a number line is 3 units.
What is a number line?A number line can be defined as a horizontal line that can be extended in any direction indefinitely and has all the integers over it. As one walks from left to right on the number line, the numbers grow, and as one proceeds from right to left, the numbers decrease.
The distance between the two can be found by deducting -2/3 from 4/3. Therefore, the distance between the two can be written as,
[tex]\rm Distance = \dfrac{4}{3}-(- \dfrac{2}{3}) = \dfrac{4}{3}+\dfrac{2}{3} = \dfrac{4+2}{3} = \dfrac{6}{3} = 2[/tex]
Thus, the distance between -2/3 and 4/3 on a number line is 3 units.
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Mrs.Rome has 2/3 of a pan of lasagna left after dinner she wants to divide the leftover lasagna into 4 equal servings what fraction of the original pan does each serving represent
[tex]\frac{1}{6}[/tex] of the original pan represents each serving
Solution:
Given that,
Mrs.Rome has 2/3 of a pan of lasagna left after dinner
She wants to divide the leftover lasagna into 4 equal servings
2/3 is divided into 4 equal servings
Therefore,
[tex]1\ equal\ serving = \frac{\frac{2}{3}}{4}\\\\1\ equal\ serving = \frac{2}{12} = \frac{1}{6}[/tex]
Thus [tex]\frac{1}{6}[/tex] of the original pan represents each serving
3. A bicycle is pedaled at a constant speed of 2 m/s. Find the time taken to cover a distance of
300m.
Answer:
2.5 minutes or 150 seconds
Step-by-step explanation:
Time = Distance / speed
300/2 = 150.
150 seconds, or 2 and a half minutes
Write the equation of a line that passes through the point (-2, 1) and has a slope of 4.
2. All
OA. y=4x - 7
OB. y= 4x+1
OC. y= 4x+3
OD. y= 4x + 9
Question serial: 1154203447-dhwm78.2
Answer:
look at picture shown please
I will give you brainliest if you get it right!!!!!!!
Answer:
The answer you have is Correct!
Which of the following values are in the range of the function graphed below? Check all that apply.
A. 2
B. 1
C. 3
D. 5
E. -2
Answer:
1, 2, 3
Step-by-step explanation:
The range includes only the y-axis. On this graph, the line only passes by the 1,2, and 3 on the y-axis.
The figure on the left represents a scale drawing of the figure on the right. What is the scale?
Answer:
[tex]\frac{1}{90}[/tex]
Step-by-step explanation:
Before calculating the scale we require the dimensions to be in the same units.
Using the conversion
1 yard = 3 ft and
1 foot = 12 inches, then
5 yards = 5 × 3 × 12 = 180 inches
The scale is then
2 in : 180 in ← divide both quantities by 2
= 1 : 90
= [tex]\frac{1}{90}[/tex]
The scale of the drawing given is 1/90
Using the following conversion :
1 yard = 3 feets 1 feet = 12 inchesThis means that ;
1 yard = 12 * 3 = 36 inchesThen ;
5 yards = 36 * 5 = 180 inchesRelating the expression :
2 inches = 180 inches
divide both sides by 2
1 inch : 90 inches
Hence, the scale is 1 /90
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Which function has a domain of (-∞, ∞) and a range of (-3, ∞)?
Answer:
Step-by-step explanation:
The function that will have the domain [tex](\infty, \infty)[/tex] and a range of [tex](-3, \infty)[/tex] is the
function in option d.) [tex]f(x) = e^x - 3[/tex]
Solve for x: the quantity of x plus 16 all over 3 = 3x (1 point) x = −7 x = −13 x = 8 x = 2
Step-by-step explanation:
We have,
[tex]\dfrac{x+16}{3}=3x[/tex]
To find, the value of x in the given equation = ?
∴ [tex]\dfrac{x+16}{3}=3x[/tex]
By crossmultiplication, we get
3(3x) = x + 16
⇒ 9x = x + 16
⇒ 9x - x = 16
⇒ 8x = 16
⇒ x = [tex]\dfrac{16}{8}[/tex]
⇒ x = 2
∴ The value of x = 2
Thus, the required value of x is equal to 2.
she wants the base length of this triangle to be 8 inches. the area of the pennant must be less than 36 square inches
Answer: The height/width has to be less than 9 for the area to be less than 36
Step-by-step explanation:
Pennant's are triangle.
Triangle area = bh(1/2)
the base is 8in
(8 * h)/2 = 36
*2
8 * h = 72
/8
h = 9
The height/width has to be less than 9
Can somebody please help me answer this and please also explain where I can understand . Thank you .
Answer:
a. 1/10
b. 4/10
c. 20
Step-by-step explanation:
There are 10 equal sections.
a. 1 section is labeled "Large Prize", so the probability of winning a large prize is 1/10.
b. 1 section is labeled "Large Prize" and 3 sections are labeled "Small Prize", so there's 4 prize section. Therefore, the probability of winning a prize is 4/10.
c. Each person has a 4/10 chance of winning a prize. So if there are 50 people, we would expect 4/10 × 50 = 20 people to win a prize.
It takes 22 pounds of seed to completely plant a 4-acre field. How many pounds of seed are needed per acre?
Answer:
5.5 pounds of seeds
Step-by-step explanation:
22 pounds seeds = 4-acre field
(x) pounds seeds = 1-acre(per acre)
x= 22/4
= 5.5 pounds of seeds
There are 25 students in the class. Ten students have sports practice after school. What is the ratio of students that do have practice, to those that do not?
Answer:
10/25 or 2/5
Step-by-step explanation:
since only 10 have sport as all the other students don't
A small bottle of Dr.Pepper holds 31.2 cm^3 of the delicious drink. For a New Years Eve party, you need enough juice to fill 6 cone- shaped glasses that have a 4cm diameter and a 3 cm height. How many full bottles of Dr. Pepper do you need to buy to completely fill the 6 glasses you need?
Approximately 3 bottles are needed to buy to completely fill the 6 glasses you need
Solution:
Given that,
A small bottle of Dr.Pepper holds 31.2 cm^3 of the delicious drink
Therefore,
[tex]Volume\ of\ small\ bottle\ of\ Dr.pepper = 31.2\ cm^3[/tex]
For a New Years Eve party, you need enough juice to fill 6 cone- shaped glasses that have a 4 cm diameter and a 3 cm height
Find the volume of cone
[tex]V = \frac{\pi r^2h}{3}[/tex]
Where, r is the radius and h is the height
Diameter = 4 cm
Radius = 4/2 = 2 cm
Height = 3 cm
Therefore,
[tex]V = \frac{3.14 \times 2^2 \times 3}{3}\\\\V = \frac{3.14 \times 12}{3}\\\\V = \frac{37.68}{3}\\\\V = 12.56[/tex]
Thus, for 6 cone shaped glasses:
Volume of 6 cone shaped galsses = 12.56 x 6 = 75.36 [tex]cm^3[/tex]
How many full bottles of Dr. Pepper do you need to buy to completely fill the 6 glasses you need?
[tex]\text{Number of Dr.pepper bottles } = \frac{\text{Volume of 6 cone shaped galsses}}{\text{Volume of small bottle of dr pepper}}\\\\\text{Number of Dr.pepper bottles } = \frac{75.36}{31.2}\\\\\text{Number of Dr.pepper bottles } = 2.4153[/tex]
Thus approximately 3 bottles are needed to buy to completely fill the 6 glasses you need
Final answer:
To fill 6 cone-shaped glasses for a New Year's Eve party, you would need to buy 3 full bottles of Dr. Pepper. The volume of each glass is calculated using the formula for the volume of a cone, and then this volume is multiplied by 6 to find the total volume required for all glasses. The number of bottles needed is found by dividing this total volume by the volume of one bottle of Dr. Pepper.
Explanation:
To determine how many full bottles of Dr. Pepper you need to buy to fill 6 cone-shaped glasses with a 4cm diameter and a 3cm height, we need to calculate the volume of one glass and then multiply it by 6 to get the total volume required. The formula to calculate the volume of a cone is V = (1/3)πr^2h, where V is the volume, r is the radius of the base, and h is the height of the cone.
First, we find the radius of the glass by dividing the diameter by two, which yields 2cm. Plugging the values into the formula, we get:
V = (1/3)π(2^2)(3) = (1/3)π(4)(3) = 4π cm^3
Since π is approximately 3.14, we can simplify this to:
V = 4(3.14) cm^3 = 12.56 cm^3 per glass.
Now, multiplying the volume of one glass by 6 gives us the total volume needed:
Total volume = 12.56 cm^3/glass × 6 glasses = 75.36 cm^3.
To find out how many bottles of Dr. Pepper are needed, we divide the total volume by the volume of one bottle:
Number of bottles = 75.36 cm^3 / 31.2 cm^3/bottle ≈ 2.415 bottles.
Since you cannot buy a fraction of a bottle, you would need to purchase 3 full bottles of Dr. Pepper to ensure you have enough to fill all 6 glasses.
1. In right triangle ABC, C is the right angle. Given m2. In right triangle ABC, C is the right angle. Which of the following is cos B if sin A=0.4?
Answer:
[tex]\cos B=0.4[/tex]
Step-by-step explanation:
Given
[tex]\Sin A=0.4=\frac{4}{10}=\frac{2}{5}\\\\In\ right\ triangle\\\\\sin A=\frac{Perpendicular}{Hypotenuse}=\frac{BC}{AB}=\frac{2}{5}\\\\Then\ \ \cos B=\frac{Base}{Hypotenuse}=\frac{BC}{AB}=\frac{2}{5}=0.4[/tex]
Answer:
Part a)
[tex]c=9.3\ units\\b=7.2\ units[/tex]
Part b) [tex]cos(B)=0.4[/tex] see the explanation
Step-by-step explanation:
The correct question is
In right triangle ABC, C is the right angle. Given measure of angle A = 40 degrees and a =6
Part a) which of the following are the lengths of the remaining two side, rounded to the nearest tenth?
Part b) Which of the following is cos B if sin A=0.4?
see the attached figure to better understand the problem
Part a)
step 1
Find the length of side c
Applying the law of sines
[tex]\frac{a}{sin(A)}=\frac{c}{sin(C)}[/tex]
we have
[tex]a=6\ units\\A=40^o\\C=90^o[/tex]
substitute
[tex]\frac{6}{sin(40^o)}=\frac{c}{sin(90^o)}[/tex]
solve for c
[tex]c=\frac{6}{sin(40^o)}=9.3\ units[/tex]
step 2
Find the length of side b
In the right triangle ABC
[tex]tan(40^o)=\frac{BC}{AC}[/tex] ----> by TOA (opposite side divided by the adjacent side)
substitute the values
[tex]tan(40^o)=\frac{6}{AC}[/tex]
[tex]AC=\frac{6}{tan(40^o)}=7.2\ units[/tex]
therefore
[tex]b=7.2\ units[/tex]
Part b) we know that
If two angles are complementary, the cofunction identities state that the sine of one equals the cosine of the other and vice versa
In this problem
Angle A and angle B are complementary
therefore
the sine of angle A equals the cosine of angle B
we have
sin(A)=0.4
so
cos(B)=0.4
Complete this statement 0.743 mL = ?L
A 743
B 74.3
C 0.000743
D 0.0743
Answer:
0.743ml=0.000743
Step-by-step explanation:
You can buy school uniforms though an online catalog.Boys can order either navy blue or khaki pants with a red,white,or blue shirt.How many uniform combinations are there online for boys
Answer:
6 combinations
Step-by-step explanation:
Pants options: Navy Blue, Khaki
Shirt options: Red, white, blue
Possible combinations:
Navy Blue with: Khaki with:
Red Red
White White
Blue Blue
There are 6 outfit possibilities
Hope this helps and let me know if you have any questions about my answer :)