Final answer:
Using the properties of isosceles triangles, the acute base angle of the isosceles trapezoid, which is part of an isosceles triangle with a 46° vertex angle, is found to be 67°.
Explanation:
To find the measure of an acute base angle of the isosceles trapezoid that is part of an isosceles triangle with a 46° vertex angle, we can apply the properties of isosceles triangles. By the Isosceles Triangle Theorem, we know that the angles opposite the equal sides are equal.
Since the given triangle is isosceles, the two base angles must also be equal. Additionally, we know that the sum of all angles in any triangle is 180°.
Let's call each of the base angles B. Then, the sum of all angles in the triangle is:
46° + B + B = 180°
Now we solve for B:
2B = 180° - 46° = 134°
B = 134° / 2 = 67°
Thus, each base angle of the isosceles triangle is 67°. Next, considering the isosceles trapezoid, we know the adjacent angles must be supplementary because they are on the same line. This means that one base angle of the isosceles trapezoid equals:
180° - 67° = 113°
However, since the student is looking for the measure of an acute base angle of the trapezoid and 113° is an obtuse angle, the acute base angle is the original 67° angle that we found. This is because the acute and obtuse angles in the trapezoid are adjacent angles around the same vertex, and the acute angle is the angle that's interior to the triangle.
Therefore, the measure of an acute base angle of the trapezoid is 67°.
Create an equation where the solutions are 1/3 and 4 plus or minus i sqrt 7
Answer:
[tex] 3 {x}^{3} - 25 {x}^{2} + 35x - 23 = 0[/tex]
Step-by-step explanation:
We want to create an equation that will have the solution
[tex]x = \frac{1}{3},x = 4 + \sqrt{7}i,x = 4 - \sqrt{7}i[/tex]
This implies that:
[tex]3x -1= 0,x -( 4 + \sqrt{7}i) = 0,x - ( 4 - \sqrt{7}i) = 0[/tex]
We put the roots in factored form by reversing the zero product principle to get:
[tex](3x -1)(x -( 4 + \sqrt{7}i))(x - ( 4 - \sqrt{7}i)) = 0[/tex]
We expand the last two parenthesis to get:
[tex](3x - 1)( {x}^{2} - 4x + \sqrt{7}ix - 4x - \sqrt{7}ix + 16 - 7 {i}^{2}) = 0 [/tex]
We simplify to get:
[tex](3x - 1)( {x}^{2} - 8x + 23) = 0[/tex]
We expand further to obtain:
[tex]3 {x}^{3} - 25 {x}^{2} +35x - 23 = 0[/tex]
Jenni wrote a rational number that is positive. Which of the following is not a possible number that she wrote?
51/4
0
7/8
1
Answer:
There is no answer.
0 is rational since it can be written as a fraction (0/5, 0/69)
1 is obviously rational. 7/8 is .875 and 5 1/4 is 5.25
The equation d = d equals StartFraction m Over V EndFraction. can be used to calculate the density, d, of an object with mass, m, and volume, V. Which is an equivalent equation solved for V?
Answer:
m/d = V
Step-by-step explanation:
Answer:
m/d=V
Step-by-step explanation:
I did the quiz
B is the midpoint of AC. If: AB = 9x+1 and BC= 6x+25 Find AC
Answer:
AC = 146
Step-by-step explanation:
Given that B is the midpoint of AC, then
AB = BC, that is
9x + 1 = 6x + 25 ( subtract 6x from both sides )
3x + 1 = 25 ( subtract 1 from both sides )
3x = 24 ( divide both sides by 3 )
x = 8
Hence
AC = AB + BC = 9x + 1 + 6x + 25 = 15x + 26, thus
AC = (15 × 8) + 26 = 120 + 26 = 146
Answer:
146
Step-by-step explanation:
AB = BC (Definition of midpoint) so:
9x+1=6x+25.
Solve it as you would any other algebraic equation >>> 9x+1=6x+25 >>> 9x+1-1=6x+25-1 >>> 9x=6x+24 >>> -6x+9x=6x-6x+24 >>> 3x=24 >>> 3x/3=24/3 >>> x=8
AB=9x+1 >>> AB=9*8+1 >>> AB=73
BC=6x+25 >>> BC=6*8+25 >>> BC=73
AC=AB+BC >>> AC=73+73 >>> AC=146
Calculate a6 for the geometric sequence in which a1=1500 and the common ratio is 3/5.
Answer:
The sum would be a₅ = 506.25!
Step-by-step explanation:
Given that,
first term a₁ = 1600
common ratio (r) =
We need to find the fifth term of the geometric progression
We know that the nth term formula
aₙ = a₁rⁿ-¹
where a₁ is first term and r is the common ratio
n is the number of terms
So, n = 5
a₅ = 1600
a₅ = 1600*
a₅ = 1600*81/256
a₅ =
a₅ = 506.25
Answer:
116.64
Step-by-step explanation:
116.64 is the correct answer
when a1 = 1500 the a6 = 116,64
What is the definition of a real number?
Answer:
A real number encompasses all numbers, whether it be irrational (irrational numbers go on forever) like pi or the square root of 5, an integer like a negative, a decimal, a fraction, 0, a whole number, a natural number etc.
Step-by-step explanation:
A real number encompasses all numbers, whether it be irrational (irrational numbers go on forever) like pi or the square root of 5, an integer like a negative, a decimal, a fraction, 0, a whole number, a natural number etc. (This doesn't include imaginary numbers however, like the square root of -1.)
Answer:
Step-by-step explanation:
A real number is a number that can be found on a number line. Numbers we use everyday. Real numbers include : natural numbers, whole numbers, integers, fractions, rational numbers, and irrational numbers. They do not include imaginary numbers, numbers that cannot be quantified, such as square root of -1.
I am three years younger than my brother, and I am 2 years older than my sister. My mom age is one less than three times my brothers age . When you add all our you get 87. What are our pages ?
Answer:
The "I" figure is 13 years old. Her brother is 16. Her Sister is 11. Her mother is 47.
Step-by-step explanation:
13+16=29
29+11=40
40+47=87
Find the median. Round to the nearest tenth if necessary.
49, 13.9, 5.9, 16.6, 43.1, 11.2, 36.8, 43.7, 22.9, 45.1, 44.2
Answer:
The median refer to the middle
value or number when arranged ascendingly or descendingly therefore the MEDIAN IS 36.8
Step-by-step explanation:
By arranging the numbers ascendingly we have
5.9, 11.2, 13.9, 16.6, 22.9, 36.8, 43.1, 43.7, 44.2, 45.1, 49
Therefore the median which is the number at the centre is 36.8
A recipe uses 1 1/4 cups of oil to make 20 servings. If the same amount of oil is used for each serving, how many servings can be Made with one gallon of oil ?
Answer:
12.8
Step-by-step explanation:
Solve for x.
Enter your answer in the box.
Answer:
x = 3
Step-by-step explanation:
Since all 3 sides of the triangle are congruent then the triangle is equilateral
The 3 angles are congruent and equal to 60°, thus
25x - 15 = 60 ( add 15 to both sides )
25x = 75 ( divide both sides by 25 )
x = 3
6 Elizabeth bought 2 large bags of Doritos. She then spent $14 on soda. She spent a total
of $22. How much was each bag of Doritos?
Answer Statement:
Doritas Doritos
Answer: $4
Step-by-step explanation:
2d + 14 = 22
subtract 14
2d = 8
divide by 2
d = $4
each bag of Doritos costs $4
Elizabeth spent a total of $8 on 2 large bags of Doritos after spending $14 on soda, which means each bag costs $4.
Explanation:To determine the price of each bag of Doritos, we need to subtract the amount spent on soda from the total amount spent. Elizabeth spent $14 on soda and had a total of $22 in expenses. So, the money spent on Doritos is the difference between the total amount and the soda amount.
Amount spent on Doritos = Total amount - Amount spent on soda
Amount spent on Doritos = $22 - $14
Amount spent on Doritos = $8
Since Elizabeth bought 2 large bags of Doritos, we can find the price per bag by dividing the total amount spent on Doritos by 2.
Price per bag of Doritos = Total spent on Doritos / Number of bags
Price per bag of Doritos = $8 / 2
Price per bag of Doritos = $4 per bag
Therefore, each large bag of Doritos costs $4.
An online retailer charges $6.99 plus $0.55 per pound to ship electronics purchases. How many pounds is a DVD player for which the shipping charge is $11.94?
Answer:
[tex]9\ pounds[/tex]
Step-by-step explanation:
Let
x ----> the number of pounds of a DVD player
we know that
The number of pounds of a DVD player multiplied by the cost per pound ($0.55) plus the charge of $6.99 must be equal to $11.94
so
The linear equation that represent this situation is
[tex]0.55x+6.99=11.94[/tex]
solve for x
subtract 6.99 both sides
[tex]0.55x=11.94-6.99[/tex]
[tex]0.55x=4.95[/tex]
divide by 0.55 both sides
[tex]x=9\ pounds[/tex]
in trapezium abcd, as shown in the figure, ab is parallel to dc, ad=dc=bc=20cm and ‹a=60°. find: (i) length of ab (ii) distance between ab and dc
Answer:
AB = 40 cm
Distance = [tex]10\sqrt{3}[/tex] cm
Step-by-step explanation:
Draw two heights DE and CF. These heights together with bases of trapezoid form rectangle DEFC. In this rectangle, DC=EF=20 cm.
Consider right triangle ADE. In this triangle, angle ADE has the measure of 30° (the sum of the measures of all interior angles is always 180°, so m∠ADE=180°-60°-90°=30°)
Leg opposite to 30° angle is equal to half of the hypotenuse, so
[tex]AE=\dfrac{1}{2}AD=\dfrac{1}{2}\cdot 20=10\ cm[/tex]
Similarly, in triangle CBF, BF=10 cm.
Hence,
[tex]AB=AE+EF+FB=10+20+10=40\ cm[/tex]
The height of the trapezoid (the second leg of triangle ADE) is the distance between DC and AB. By the Pythagorean theorem,
[tex]AD^2=AE^2+DE^2\\ \\DE^2=20^2-10^2=400-100=300\\ \\DE=\sqrt{300}=10\sqrt{3}\ cm[/tex]
which expression is equivalent to 2m+m+m
3m
4m
2m^3
4m^3
Answer:
4m
Step-by-step explanation:
since it is not multiplication, there would be no power.
think of it as 2m + 1m + 1m
The answer is 4m
I hope this helped! If so, please mark brainliest!
if sec thita . sin thita =0,then find the value of thita
Answer:
[tex]\large\boxed{\theta=k\pi,\ k\in\mathbb{Z}}[/tex]
Step-by-step explanation:
[tex]\sec\thets\cdot\sin\theta=0\iff \sec\theta=0\ \vee\ \sin\theta=0\\\\\sec\theta\neq0\ \text{for any value of}\ \theta\\\\\sin\theta=0\Rightarrow\theta=k\pi\ \text{where}\ k\in\mathbb{Z}[/tex]
Find the indicated probability. Round to three decimal places. The participants in a television quiz show are picked from a large pool of applicants with approximately equal numbers of men and women. Among the last 11 participants there have been only 2 women. If participants are picked randomly, what is the probability of getting 2 or fewer women when 11 people are picked? 0.006 0.033 0.027 0.032
Answer:
0.033
Step-by-step explanation:
Use binomial probability:
P = nCr pʳ (1−p)ⁿ⁻ʳ
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
Here, p = 0.5, q = 0.5, and n = 11.
We need to find P when r is 0, 1, and 2, then add up the results to get the total probability.
r = 0:
P = ₁₁C₀ (0.5)⁰ (0.5)¹¹⁻⁰
P ≈ 0.0005
r = 1:
P = ₁₁C₁ (0.5)¹ (0.5)¹¹⁻¹
P ≈ 0.0054
r = 2:
P = ₁₁C₂ (0.5)² (0.5)¹¹⁻²
P ≈ 0.0269
Therefore, the total probability is:
P = 0.0005 + 0.0054 + 0.0269
P = 0.0328
Round to the thousandths place, the probability is 0.033.
What is the y-intercept of f(x)=8x^5-3x^3+12
The y intercept is (0, 12)
Solution:
Given function is:
[tex]f(x) = 8x^5 - 3x^3 + 12[/tex]
To find: y intercept
y-intercept or vertical intercept is a point where the graph of a function or relation intersects the y-axis of the coordinate system.
To find the y intercept using the equation of the line, plug in 0 for the x variable and solve for y
Substitute x = 0 in given function
[tex]f(0) = 8(0) -3(0) + 12[/tex]
y = 0 - 0 + 12
y = 12
Thus y - intercept is (0, 12)
what is the formula for the nth term of the given sequence?
3, 5, 7...
Paul and Cindy own different pizza shops. Paul makes 12 pizzas the first day and 6 pizzas each day after that. Cindy makes 16 pizzas the first day and 4 pizzas each day after that. Who will have made more pizzas after 9 days? How many pizzas will that person have made?
A . Paul. He has made 80 pizzas after 9 days.
B . Cindy. She has made 132 pizzas after 9 days.
C. Paul. He has made 60 pizzas after 9 days.
D . Cindy. She has made 48 pizzas after 9 days.
Answer:
Paul. He has made 60 pizzas after 9 days.
Step-by-step explanation:
Paul makes 12 pizzas the first day and 6 pizzas each day after that.
So, after 9 days Paul will make total [12 + (9 - 1)6] = 60 pizzas.
Now, Cindy makes 16 pizzas the first day and 4 pizzas each day after that.
So, after 9 days Cindy will make total [16 + (9 - 1)4] = 48 pizzas.
Therefore, after 9 days Paul will make more pizzas and the number is 60 pizzas. (Answer)
Answer:
B
Step-by-step explanation:
given: <1 and <2 and supplements, <3 and <4 are supplements, and <1 ≅ <4
prove: <2 ≅ <3
By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3
Step-by-step explanation:
The supplementary angles are:
Two angles their sum is 180°The supplement of an acute angle is an obtuse angle and vice versaThe supplement of a right angle is a right angleIf one angle is supplement to two other angles, then the two angles are equal in measure (if 50° is supplement to angles X and Y, then X and y must be 130°)Supplement angles of congruent angles are congruent (If angles X and Y are supplement to angles A , B and angles A , B are congruent, then angles X and Y are congruent∵ ∠1 and ∠2 are supplementary
∴ m∠1 + m∠2 = 180° ⇒ (1)
∵ ∠3 and ∠4 are supplementary
∴ m∠3 + m∠4 = 180° ⇒ (2)
We can equate the left hand sides of (1) and (2) because the right hand sides are equal
∴ m∠1 + m∠2 = m∠3 + m∠4 ⇒ (3)
∵ ∠1 ≅ ∠4
∴ m∠1 = m∠4
- Substitute m∠4 by m∠1 in (3)
∴ m∠1 + m∠2 = m∠3 + m∠1
- Subtract m∠1 from both sides
∴ m∠2 = m∠3
∴ ∠2 ≅ ∠3
By using the fact of supplement angles of congruent angles are congruent, we proved that ∠2 ≅ ∠3
Learn more:
You can learn more about supplementary angles in brainly.com/question/10483199
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Find the volume of the prism. Round to the nearest tenth if necessary.
Answer:
The volume of the prism will be given by 204.7 cubic cm.
Step-by-step explanation:
The area of a triangle whose three side lengths are given is equal to
Δ = [tex]\sqrt{s(s - a)(s - b)(s - c))}[/tex] .......... (1)
Where, a, b, and c are the three side lengths and s is the half perimeter i.e.
[tex]s = \frac{a + b + c}{2}[/tex] ......... (2)
Now, in our case, [tex]s = \frac{6 + 7 + 6}{2} = 9.5[/tex] {From equation (2)}
So, Δ = [tex]\sqrt{9.5(9.5 - 6)(9.5 - 7)(9.5 - 6)} = 17.05[/tex] sq. cm.
{From equation (1)}
Hence, the volume of the prism will be given by (17.05 × 12) = 204.7 cubic cm. (Answer)
Mary says 1/8 is
greater than 1/4 because 8 is greater than 4.
Is Mary's reasoning correct? Explain.
Answer:
No, Mary is incorrect. If you turn the fractions into decimals, 1/4 would be 0.25 and 1/8 would be 0.12½. Since 0.25 is greater than 0.12½, Mary is incorrect.
Mary's reasoning is incorrect because in fractions, the larger the denominator, the smaller the fraction's value, making 1/4 greater than 1/8.
Mary's reasoning that 1/8 is greater than 1/4 because 8 is greater than 4 is not correct. In the context of fractions, the larger the denominator (the bottom number), the smaller each part of the whole it represents. Thus, 1/4 is actually greater than 1/8 because dividing something into 4 parts results in larger parts than dividing it into 8 parts. This can be further understood by transforming both fractions into equivalent fractions with a common denominator or by converting them into decimal form (0.25 for 1/4 and 0.125 for 1/8) to directly compare their sizes.
An employee at a party store is assembling balloon bouquets. For a graduation party, he assembled 2 small balloon bouquets and 3 large balloon bouquets, which used a total of 75 balloons. Then, for a Father's Day celebration, he used 33 balloons to assemble 2 small balloon bouquets and 1 large balloon bouquet. How many balloons are in each bouquet?
There are 6 balloons in small bouquet and 21 balloons in large bouquet.
Step-by-step explanation:
Let,
Number of balloons in small balloon bouquet = x
Number of balloons in large balloon bouquet = y
According to given statement;
2x+3y=75 Eqn 1
2x+y=33 Eqn 2
Subtracting Eqn 2 from Eqn 1
[tex](2x+3y)-(2x+y)=75-33\\2x+3y-2x-y=42\\2y=42[/tex]
Dividing both sides by 2
[tex]\frac{2y}{2}=\frac{42}{2}\\y=21[/tex]
Putting y=21 in Eqn 2
[tex]2x+21=33\\2x=33-21\\2x=12[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{12}{2}\\x=6[/tex]
There are 6 balloons in small bouquet and 21 balloons in large bouquet.
Keywords: linear equation, subtraction
Learn more about subtraction at:
brainly.com/question/7932185brainly.com/question/8054589#LearnwithBrainly
Final answer:
In solving the system of linear equations, we determined that a small balloon bouquet contains 6 balloons and a large balloon bouquet contains 21 balloons.
Explanation:
Solving a System of Equations
Let's denote the number of balloons in a small bouquet as s and in a large bouquet as l. The given problem provides us with two equations based on the information about the graduation party and Father's Day celebration:
For the graduation party: 2s + 3l = 75
For the Father's Day celebration: 2s + l = 33
Now we solve this system of linear equations to find the values of s and l. Subtracting the second equation from the first gives us:
2s + 3l - (2s + l) = 75 - 33
Which simplifies to:
2l = 42
Dividing by 2 gives us:
l = 21
Now we can plug in the value of l into any of the original equations to find the value of s. Let's use the Father's Day equation:
2s + 21 = 33
Subtracting 21 from both sides gives us:
2s = 12
Finally, dividing by 2 gives us:
s = 6
Therefore, a small balloon bouquet contains 6 balloons and a large balloon bouquet contains 21 balloons.
What is (1+2x3) squared
Answer:
[tex]\large\boxed{(1+2x^3)^2=4x^6+4x^3+1}[/tex]
Step-by-step explanation:
[tex](1+2x^3)^2\\\\\bold{METHOD\ 1:}\\\\(1+2x^3)^2=(1+2x^3)(1+2x^3)\qquad\text{use FOIL}\ (a+b)(c+d)=ac+ad+bc+bd\\\\=(1)(1)+(1)(2x^3)+(2x^3)(1)+(2x^3)(2x^3)\\\\=1+2x^3+2x^3+4x^6\qquad\text{combine like terms}\\\\=1+4x^3+4x^6[/tex]
[tex]\bold{METHOD\ 2:}\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(1+2x^3)^2=1^2+2(1)(2x^3)+(2x^3)^2\\\\=1+4x^3+2^2(x^3)^2\\\\=1+4x^3+4x^6[/tex]
Write a numerical expression that represents the number of increments it will take to reach -60 feet.
Answer:
Step-by-step explanation:
Write a numerical expression that represents the number of increments it will take to reach -60 feet
Answer:
(-60) ÷ (-10)
Step-by-step explanation:
Lin is saving $300 per year in an account that pays 4.5% interest per year, compounded annually. How do I find the value after 20 years?
To find the value after 20 years, use the future value of a series formula with the given parameters, resulting in an approximate amount of $9,321.
Explanation:To find the value of $300 saved annually at 4.5% interest compounded annually after 20 years, we use the future value of a series formula:
FV = [tex]P * ((1 + r)^n - 1) / r[/tex]
Where:
FV = Future value of the seriesP = Yearly deposit ($300)r = Annual interest rate (4.5% or 0.045)n = Number of years (20)Substituting the given values:
FV = $300 * ((1 + 0.045)^20 - 1) / 0.045
= $300 * ((1.045)^20 - 1) / 0.045
= $300 * (2.398 - 1) / 0.045
= $300 * 1.398 / 0.045
= $300 * 31.07
= $9,321
Therefore, after 20 years, the value will be approximately $9,321.
Mrs. Kelly creates a garden. She buys 15 flowers and 3 bushes for a total cost of $160.32. Each bush costs $11.50 more than each flower. How much does each bush cost?
The cost of each bush is $ 18.49
Solution:Let "f" be the cost of each flower
Let "b" be the cost of each bush
Given that Mrs. Kelly buys 15 flowers and 3 bushes for a total cost of $160.32
15 flowers x cost of each flower + 3 bushes x cost of each bush = 160.32
[tex]15 \times f + 3 \times b = 160.32[/tex]
15f + 3b = 160.32 ----- eqn 1
Each bush costs $11.50 more than each flower
Cost of each bush = 11.50 + cost of each flower
b = 11.50 + f ------ eqn 2
Let us solve eqn 1 and eqn 2 to find values of "b" and "f"
Substitute eqn 2 in eqn 1
15f + 3(11.50 + f) = 160.32
15f + 34.5 + 3f = 160.32
18f = 160.32 - 34.5
18f = 125.82
f = 6.99Substitute f = 6.99 in eqn 2
b = 11.50 + 6.99 = 18.49
b = 18.49Thus the cost of each bush is $ 18.49
Please help! I really need help!
Answer:
Equation: y = 15x.
:)
Answer:
y = 15x
Step-by-step explanation:
The question asked, what equation shows the line through the data points. And it stated the equation needed to be in the form y = kx
Where
y represents the vertical axis
x represents the horizontal axis
k = constant
K is the constant interval and can be use to get the next points
y = kx
viewing the most visible points from the graph , let use the point where total saved is 90(y axis) and the time in weeks (x axis) is 6, the constant K can be gotten.
y = 90
x = 6
y = kx
90 = 6k
divide both sides by 6
k = 90/6
k = 15
Therefore,
y = 15x
4. Solve this equation: Y/g + 5 = 0.
O A. y = 5
O B.y=-5
O C.y=-45
O D. y = 45
Answer:
C) Y = -45
Step-by-step explanation:
Y/9 + 5 = 0
Y/9 = -5
y = -5 * 9
Y= -45
What is the scale factor and length of side x
Answer:
The scale factor is 2
x=11 units
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
The ratio of its corresponding sides is called the scale factor
In this problem
Triangles RST and MNO are similar
so
[tex]\frac{NO}{ST}=\frac{MN}{RS}[/tex]
substitute the given values
[tex]\frac{x}{5.5}=\frac{6}{3}[/tex]
solve for x
[tex]\frac{x}{5.5}=2[/tex]
[tex]x=2(5.5)\\x=11\ units[/tex]
The scale factor of triangle RST to triangle MNO (enlargement) is equal to 2