Step-by-step explanation:
2x + x + 57 = 90
3x = 33
x = 11
m1 = 2 × 11 = 22°
m2 = 11 + 57 = 68°
check: 22 + 68 = 90
Alvin is 5 years older than Elga. The sum of their ages is 53. What is Elga's age?
Answer:
24
Step-by-step explanation:
53-5=48
48/2=24 Elgas age
24+5=29 Alvin's age
Consider the first quadrant of the unit circle. How does the covenant ratio change as the sine ratio increases?
Answer:
For acute angles, remember what sine means: opposite over hypotenuse. If we increase the angle, then the opposite side gets larger. That means "opposite/hypotenuse" gets larger or increases.
Step by Step:
Keep this in mind >>
Consider the unit circle > The sine and cosine ratios are the only ratios that have 1 (the radius or hypotenuse) as the denominator. The numerators (sides) vary between 0 and 1, thus determining that the sine and cosine do the same.
All of the other ratios (tangent, cotangent, secant, cosecant) have a side as the denominator, varying between 0 and 1. As any denominator approaches 0, the value of the ratio approaches infinity.
b) The completed construction of a regular hexagon is shown below. Explain why AACF is a 30°-
60°-90° triangle. (10 points)
ACF is a 30º-60º-90º triangle because of the following:
1) Based on a theorem, in a 30°-60°-90° triangle the sides are in the ratio 1 : 2 : \(\sqrt{3}\)
1 → short leg
2 → hypotenuse
\(\sqrt{3}\) → long leg
Side length of the hexagon is the short leg of the triangle. It is 1.
r1 is the radius of the incircle in a regular hexagon. 2(r1) is the diameter of the incircle. It is also the hypotenuse of the right triangle. It is 2.
Using Pythagorean theorem.
\(a^2 + b^2 = c^2\)
\(1^2 + b^2 = 2^2\)
\(b^2 = 2^2 - 1^2\)
\(b^2 = 4 - 1\)
\(b^2 = 3\)
\(\sqrt{b^2} = \sqrt{3}\)
\(b = \sqrt{3}\)
Which sequences are geometric? Select three options.
Answer:
there are no sequences pls edit or repost so i can help : )
In solving the following system of equations, what would you multiply by in order to eliminate the y?
Equation 1: x + y = 7 Equation 2: 5x + 2y = 8
A. 0
B. -5
C. -2
D. 2
E. 5
Give the solution to the system above
A. (7, 0)
B. (1, 6)
C. ( 8, - 1)
D. ( 3, 4)
E. ( -2, 9)
Answer:
D
E
Step-by-step explanation:
we need to multiply x+y=7 by 2
2x+2y=14
5x+2y=8
subtract
-3x=6
x=6/(-3)=-2
-2+y=7
y=7+2=9
solution is (-2,9)
A. 180
B. 108
C. 54
D. 90
Answer:
The answer is D
Step-by-step explanation:
Answer:
B. 108
Step-by-step explanation:
good luck!! sorry if this isnt right lol
volume of sphere
give your answer to one decimal point
Answer:
Step-by-step explanation:
surface area: 4pir^2
4*pi*(5)^2
25*4*pi
100pi
volume:
4/3pir^3
4/3pi(5)^5
4/3(pi)(125)
(500/3)pi
A state gets it money from a state lottery, a property tax, a sales tax of 5%, and an excise tax. This year it projects that it will receive $24 million from the state lottery, $32 million from the property tax, and 14 million from the excise tax. If the state needs $100 million to cover it's expenses, how many dollars worth of taxable items must be purchased in the state this year for the state to break even?
A. $600,000,000
B. $150,000,000
C. $1,500,000
D. $ 30,000,000
Answer:A
Step-by-step explanation:
The items of worth $600,000,000 should be purchased in the state to meet the requirement, the correct option is A.
What is an Equation?An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.
The state has predicted to get $24 million from the state lottery,
The amount from property tax is $32 million
The amount form excise tax is $14 million
The state needs $100 million to cover its expenses
A sales tax of 5% is charged by the state
Let the total sales is $x in million dollars then the equation that can be formed is
24 + 32 +14 +(5/100 ) * x = 100
70+ (5/100 ) * x = 100
(5/100 ) * x = 100 -70
(5/100 ) * x = 30
x = 30 * 100 / 5
x = $600,000,000
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The measure of ∠1 is 150°. What are the measures of ∠4, ∠3 and ∠2?
Answer:
∠1 is 150°
∠2 is 30°
∠3 is 150°
∠4 is 30°
Step-by-step explanation:
∠1 is vertically opposite to ∠3 so they are equal
360° - (150° + 150°) = 360° - 300° = 60°
∠2 and ∠4 must sum to 60°
Step-by-step explanation:
From the question
∠1 is opposite to ∠ 3 and vertically opposite angles are equal
So
∠1 = ∠ 3
That's
∠ 3 = 150°∠ 3 and ∠ 4 are on a straight line and angles on a straight line add up to 180°
So to find ∠4, subtract ∠3 from 180°
That's
∠ 4 = 180 - ∠ 3
∠ 4 = 180 - 150
∠ 4 = 30°Since ∠ 4 and ∠ 2 are opposite they are also equal
That's
∠ 4 = ∠ 2
Therefore
∠ 2 = 30°Hope this helps you
There are 15 floors of an office building each floor is 10 2/5 feet tall 24 9/10 feet of the building are completed 1 1/4 feet of the building can be finished each day how many days are needed to complete the building
The days it would take to complete the building is 104 22/25 days.
How many days would it take to complete the building?A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/4.
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a non-integer in which the numerator is less than the denominator. An example of a mixed number is 3 1/2.
The first step is to determine the total height of the office bulding = height of each floor x total number of floors
15 x 10 2/5
15 x 52/5 = 780 /5 = 156
The next step is to determine the floors left to complete the office building :
156 - 24 9/10 = 131 1/10 feet
The last step is to divide the feet that can be built each day by the number of floors needed to complete the builfing :
1311/10 ÷ 1 1/4
1311 / 110 ÷ 5/4
1311 / 10 x 4/5 = 104 days 44/50
104 22/25 days
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4) Daniella and Brayan have a joint checking account. They have a balance of $3,839.25 in the check register. The balance on the bank statement is $3,450.10. Not reported on the statement are deposits of $2,000, $135.67, $254.77, and $188.76 and four checks for $567.89, $23.83, $598.33, and $1.000. Reconcile the bank statement.
End Balance: $3,839.25 + $2,579.20 - $2,190.05 = $5,735.15, so the reconciled balance of $5,735.15.
What is bank reconciliation theory?This theory is used to compare the bank statements to the check register in order to properly reconcile the two balances.
The theory used in this question is the bank reconciliation theory.
Step 1: Begin by looking at the two balances - the check register balance and the bank statement balance.
In this case, the check register balance is $3,839.25 and the bank statement balance is $3,450.10.
Step 2: Add up all of the deposits that are not reported on the bank statement. In this case, the deposits are $2,000, $135.67, $254.77, and $188.76.
Step 3: Subtract all of the checks that are not reported on the bank statement. In this case, the checks are $567.89, $23.83, $598.33, and $1,000.
Step 4: Add the deposits and subtract the checks from the check register balance.
In this case, the check register balance ($3,839.25) plus the deposits ($2,579.20) minus the checks ($2,190.05) gives a reconciled balance of $5,735.15.
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Which graph represents a line with a slope of and a y-intercept equal to that of the line y = x – 2? A coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2) and (2, 1). A coordinate plane with a line passing through (negative 3, 0) and (0, 2). A coordinate plane with a line passing through (0, 2) and (2, negative 1). A coordinate plane with a line passing through (negative 3, 0) and (0, negative 2). Mark this and return
The first option is the correct one for the line y = x - 2:
" coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2)"
Which is the graph of the line?Here we want to identify the graph of the linear equation:
y = x - 2
First, notice that when we evaluate this in x = 0 we get the y-intercept:
y = 0 - 2
y = -2
Then the y-intercept there is (0, -2)
Also, evaluating the linear equation in x = -2, then we will get:
y = -2 - 2
y = -4
So we have the point (-2, -4)
Then the correct option is the first one:
" coordinate plane with a line starting at (negative 2, negative 4), passing through (0, negative 2)"
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Factor -9y - 3 with a negative GCF
Answer:
-3(3y-1)
Step-by-step explanation:
−9y−3
Factor out 3.
3(−3y−1)
Rearrange Terms.
-3(3y-1)
match the volume formula to the description
Answer:
145236 4236. b. fjdjfjfjfjfjdjfjfjfjfjfnfjfjfjfnfjgjfjfnfjf
What is the meaning of "the universal class V is a proper class"?
The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.
We have,
In set theory, a proper class is a class that is not a set.
A class is a collection of objects, and a set is a class that can be a member of other classes.
On the other hand, a proper class cannot be a member of another class.
The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.
This means that V cannot be an element of any other class or set within the context of the set theory being considered.
The concept of proper classes is used to prevent paradoxes and contradictions that can arise when unrestricted comprehension is allowed in set theory.
Thus,
The statement "the universal class V is a proper class" means that class V, which represents the universal set that contains all sets, is not itself a set but rather a proper class.
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What is the surface area of an ice cube that has 4 cm sides?
TA
4 cm
4 cm
The surface area of an ice cube with 4 cm sides is 96 square centimeters.
What is surface area?It is a measurement of the sum of all the areas of the faces, sides, and any other surfaces of an object. For example, a cube has six square faces, each with the same area.
According to question:To find the surface area of an ice cube with 4 cm sides, we need to add up the areas of all six faces. Each face is a square with side length 4 cm, so the area of each face is:
Area of one face = (side length)² = 4 cm × 4 cm = 16 cm²
Since there are six faces on a cube, the total surface area of the ice cube is:
Total surface area = 6 × (area of one face) = 6 × 16 cm² = 96 cm²
Therefore, the surface area of an ice cube with 4 cm sides is 96 square centimeters.
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What number is 25% of 0.875?
Answer:
≈ 0.22
Step-by-step explanation:
To get the solution, we are looking for, we need to point out what we know.
1. We assume, that the number 0.875 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 0.875 is 100%, so we can write it down as 0.875=100%.
4. We know, that x is 25% of the output value, so we can write it down as x=25%.
5. Now we have two simple equations:
1) 0.875=100%
2) x=25%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
0.875/x=100%/25%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 25% of 0.875
0.875/x=100/25
(0.875/x)*x=(100/25)*x - we multiply both sides of the equation by x
0.875=4*x - we divide both sides of the equation by (4) to get x
0.875/4=x
0.21875=x
x=0.21875
now we have:
25% of 0.875=0.21875
≈ 22%
The graph compares the weights in pounds of 100 dogs and cats that are brought in
to a veterinarian's office. Using the medians, how much more does a typical dog weigh than a typical cat?
Answer:20
Step-by-step explanation:this is wrong
Answer:
40
Step-by-step explanation:
subtract median of dogs and median of cats
Triangle XYZ, X equals 27 cm, Y equals 79 cm and angle C equals 142Degrees. Find the length of Z, to the nearest centimeter.
Given:
In triangle XYZ, x = 27 cm, y = 79 cm and \(\angle C=142^\circ\).
To find:
The length of z.
Solution:
In triangle XYZ, using the Law of cosine, we get
\(z^2=x^2+y^2-2xy\cos Z\)
Putting the given values in the above formula, we get
\(z^2=(27)^2+(79)^2-2(27)(79)\cos (142^\circ)\)
\(z^2=729+6241-4266(-0.788)\)
\(z^2=6970+3361.608\)
\(z^2=10331.608\)
Taking square root on both sides.
\(z=\pm \sqrt{10331.608}\)
\(z=\pm 101.6445178\)
Approx the above value to the nearest number and side length cannot be negative. So,
\(z\approx \pm 102\text{ cm}\)
Therefore, the length of z is about 102 cm.
Answer:102
Step-by-step explanation:
Plot four lines. Each line should pass through the point
on the y-axis and one of the other four points. One is done for you.
The necessary equations for the lines are y = 5/3x, y = -3/4x, and y = -4x, respectively, which cross the y axis at the point (-3, -5), (-4, 3), and (1, -4).
How do lines work?The shortest path between two places is what is referred to as a line. The equation for the line is typically written as y = mx + c, where c stands for intercept and m, for slope.
Three lines are to be plotted on the curve that passes through (-3, -5), (-4, 3), and (1, -4) in this case. At any point on the y-axis, any of the three lines should intersect.
In other words, the y=5/3x equation runs between (-3, -5) and 0 on the y-axis.
On the y axis, y = -3/4x goes between (-4, 3) and 0.
On the y axis, y = -4x goes between (1, -4) and 0.
As a result, the necessary equations for the lines are y = 5/3x, y = -3/4x, and y = -4x, respectively, which pass through the y axis and the locations (-3, -5) (-4, 3), and (1, -4)
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The correct question is:
I just need help man
The error in finding the perimeter of the rectangle is that the length was not calculated correctly, as it is of 5 units.
What is the perimeter of a rectangle?The perimeter of a rectangle of dimensions l and w is given by:
P = 2l + 2w.
From the graph, the dimensions are given as follows:
l = 4 - (-1) = 4 + 1 = 5.w = 3 - 0 = 3.Hence the perimeter is:
P = 2l + 2w = 2(5) + 2(3) = 16 units.
The calculated length was of 4, hence the error in finding the perimeter of the rectangle is that the length was not calculated correctly, as it is of 5 units.
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Vijay is celebrating his birthday at Pizza Ranch. The all-you-can-eat meal costs $12 per adult
and $5 per child. He wants to stay under a budget of $180 for the party.
Select the inequality in standard form that describes this situation. Use the given numbers and the
following variables
• X = the number of adults attending
· y = the number of children attending
12x + 5y < 180
B
12x + 5y < 180
52 + 12y < 180
5x + 12y < 180
Answer:
12x+5y < 180
Step-by-step explanation:
12 (adults) + 5 (kids) < needs to be less than 180 dollars
write and equation for the nth term of the geometric sequence for 2,8,32,128
then find a6 round to the nearest tenth if necessary.
The sixth term of the geometric sequence is 2048.
The given geometric sequence is 2, 8, 32, 128. We can observe that each term is obtained by multiplying the previous term by 4. Therefore, the common ratio (r) of the sequence is 4.
The formula for the nth term (an) of a geometric sequence is given by:
an = a1 * r^(n-1)
where a1 is the first term and r is the common ratio.
For this sequence, a1 = 2 and r = 4. Plugging in these values into the formula, we get:
an = 2 * 4^(n-1)
To find a6, we substitute n = 6 into the formula:
a6 = 2 * 4^(6-1)
= 2 * 4^5
= 2 * 1024
= 2048
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The Probable question may be:
Write an equation for the nth term of the geometric sequence 2, 8, 32, 128,
Then find a6. Round to the nearest tenth if necessary.
a = 5×4 X
a1 = n-1 X
The formula for any arithmetic sequence is an = a1 + d(n - 1), where an represents the value of the nth term, a1 represents the value of the first term, d represents the common difference, and n represents the term number. What is the formula for the sequence -1, -5, -9, ...?
an = -1 + 4( n - 1)
an = -1 + (-4)( n - 1)
an = 4 + (-1)( n - 1)
an = -4 + (-1)( n - 1)
Answer: The correct formula for the sequence -1, -5, -9, ... is an = -4 + (-1) n - 1). This formula uses the common difference of -4 and the first term of -1 to calculate the value of the nth term in the sequence.
What is the correct algebraic expression of the following statement? The product of two consecutive odd integers.
1. n + (n + 2)
2. x(x + 2)
3. y + (y + 3)
4. z(z + 1)
Answer: Let X = the smaller of the two consecutive odd integers. Therefore (X + 2) = the larger of the two consecutive odd integers.
SOMEONE PLEASE HELP
help
Answer:
K1. 25 K2. 25 K3. 22.5 K4. 22
Step-by-step explanation:
im kinda confused what its asking
Draw the image of quadrilateral ABCD after each translation. The translation that takes B to D
Marc drives his car 500 miles using 20 gallons of gas. How many miles per gallon does his car get
Answer:
25 miles per gallon
Step-by-step explanation:
We want to find miles per gallon so take the miles and divide by the gallons
500 miles / 20 gallons
25 miles per gallon
Answer:
\(= 25 \: \: \: miles \: \: \: per \: \: \: gallon \\ \)
Step-by-step explanation:
You have to find miles per gallon.
So to solve that you have to divide miles by gallon.
\( \frac{500}{20} \\ = 25 \: \: \: miles \: \: \: per \: \: \: gallon\)
hope this helps
brainliest appreciated
good luck! have a nice day!
find the equation of the lines passing through the points (2,1) and (5,10)
Answer: y = 3x - 5
Step-by-step explanation:
Answer: y=3x-5
Step-by-step explanation:
using the data on this scatter plot
Answer:
\( - 8(45) + 482 = - 360 + 482 = 122\)