Which equation would represent this problem?
Five added to 3 times a number is equal to 8 less than 5 times the number
Which equation can be used to solve for b?
A) tan(30°) = 5/b
B) tan(30°) = b/5
C) tan(30°) = 10/b
D) tan(30°) = b/10
In this exercise we want to calculate the value of angle B, so we have to:
Letter A
So knowing the tangent formula as:
[tex]tan(x) = opposite / adjacent[/tex]
Knowing some information given in the exercise such as:
the hypotenuse is the longest side of 10Side b is adjacent to the 30° angleSide 5 is opposite of the 30° angleSo we have:
[tex]tan(30)=5/b[/tex]
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If p||q, solve for x.
PLEASE HELP 30 POINTS!!!!!!
Turner has 6 pounds of pasta.Each Time he makes dinner he uses 3/4 pound of pasta.How many dinners can he make?
Kim was walking down a rocky path for 4 minutes the election dropped steadily altogether it dropped 8 feet what was the chance in elevation per minute for the 4 minutes?
in 4 minutes it changed 8 feet
so 8/4 =2 feet per minute change
and since it dropped it would be a negative change so -2 feet per minute
Suppose you have 48 feet of fencing to enclose a rectangular dog pen. The function : A = 24x-x^2 , where x = width , gives you the area of the dog pen in square feet. What width gives you the maximum area? What is the maximum area ?
PLEASE HELP ASAP!! *if you can give explanation/work it would be great* if not that is okay ..
The width that gives the maximum area of the rectangular pen is 12 feet, and the maximum area is 144 square feet.
Explanation:To maximize the area of a rectangle with a fixed perimeter, you want to make the rectangle as close to a square as possible. This maximizes the area because it distributes the available fencing evenly among the sides, optimizing the area enclosed. The given function, A = 24x - x^2, represents the area of a rectangle with width 'x' and length 'L' where L = (48-2x) / 2.
Maximization or minimization of a function occurs at its turning point. For a quadratic function like ours, the maximum or minimum happens at the vertex. The x-coordinate of the vertex is given by -b/2a. So, in our function A = -x^2 + 24x (which is the same as 24x - x^2), a = -1, b = 24.
Substitution gives: x = -(24) / 2*(-1) = 12 feet. Therefore, the width that gives you the maximum area is 12 feet.
Substitute x = 12 into the function to find the maximum area: A = 24*12 - 12^2 = 288 - 144 = 144 square feet.
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A number is a multiple of 3 if and only if the number is odd
True or false
Find the length of the hypotenuse of a right triangle with legs of lengths 12 ft and 16 ft answer
Answer:
Step-by-step explanation:
but what ab this one: Find the length of the hypotenuse of a right triangle with legs of 5 ft and 12 ft.
A right triangle in which one angle is the right angle and the two sides are perpendicular to each other. Hence, the length of the hypotenuse is [tex]20ft[/tex].
What s the right triangle?
A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangle triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular.
Here, the lengths of the triangle are [tex]12ft[/tex] and [tex]16ft[/tex] .
As we know,
[tex]H^{2}=P^{2}+B^{2}[/tex] ..........[tex](1)[/tex]
Now, substituting the values in the equation [tex](1)[/tex], we get
[tex]H^{2}=(12)^{2}+(16)^{2}\\H^{2}=144+256\\H^{2}=400\\H=\sqrt(400)\\H=20ft[/tex]
Hence, the length of the hypotenuse is [tex]20ft[/tex].
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If 5 ounces is equal to 140 grams, then 2 pounds of pizza dough is equal to how many grams?
Andrea is shopping for items for her pet sitting business because the store is having a sale where everything in the store is 5% off. Andrea buys a cat carrier for $39.99 and a cat tower for $19.99. She has a coupon for an additional 15% off on the cat tower. Before tax, Andrea estimates that her total, after discounts, will be about $54. Determine if Andrea has estimated correctly.
a. Yes. Andrea has estimated correctly.
b. No. Andrea has taken 20% of the total, which is not correct..
c. No. Andrea has taken successive discounts on the total, but the coupon is just on the cat tower.
d. No. Andrea has only taken the 5% discount on the cat tower and not on the carrier
What’s the answer pleaseeeeeeeee
y^2 +6^2 = 12^2
y^2 +36 = 144
y^2 = 108
sqrt(108) = 10.392 = 6sqrt(3)
Answer is B 6sqrt(3)
Expand and simplify (x-7)(x+3)
So the question says...
Suppose you have ∠SMB and m ∠SMB =125.35 °.
Part A: Determine the angle measure that is complement to ∠SMB, if possible. If ∠SMB does not have a complementary angle, then explain why it does not.
Part B: Determine the angle measure of the supplement of ∠SMB.
Part C: Determine the angle measure of the angle complement to ∠SMB’s supplement.
I’m stuck on this question so if anyone can help me with it that would be greatly appreciated. Thanks!
Part A: ∠SMB does not have a complementary angle
Part B: The angle measure of the supplement of ∠SMB is 54.65°
Part C: The angle measure of the angle complement to ∠SMB's supplement is 35.35°
The given angle is ∠SMB and m ∠SMB =125.35 °
For Part AComplementary angles are angles that sum up to 90°.
To determine the angle measure that is complement to ∠SMB, we will find the angles that adds up to ∠SMB to give 90°. Since ∠SMB is already greater than 90°, therefore, ∠SMB does not have a complementary angle.
For Part B.Supplementary angles are angles that sum up to 180°.
To determine the angle measure of the supplement of ∠SMB, we will find the angle that adds up to ∠SMB to give 180°. Let the measure of the angle be x, that is
x + 125.35° = 180°
∴ x = 180° - 125.35°
x = 54.65°
∴ The angle measure of the supplement of ∠SMB is 54.65°
For Part C
To determine the angle measure of the angle complement to ∠SMB's supplement, we will determine the measure of the angle that adds up to ∠SMB's supplement to give 90°. Let the angle be y
Then,
y + 54.65° = 90°
(NOTE: ∠SMB's supplement is 54.65°)
∴ y = 90° - 54.65°
y = 35.35°
∴ The angle measure of the angle complement to ∠SMB's supplement is 35.35°
Hence,
Part A: ∠SMB does not have a complementary angle
Part B: The angle measure of the supplement of ∠SMB is 54.65°
Part C: The angle measure of the angle complement to ∠SMB's supplement is 35.35°
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Can someone explain to me how to solve these ?
Find the approximate value of the circumference of a circle with the given radius. Use = 3.14. Round your results to one more decimal than in the given radius. 4 inches C = 12.5 inches 12.6 inches 25.1 inches 25.2 inches
Answer:
[tex]25.1\ inches[/tex]
Step-by-step explanation:
we know that
The circumference of a circle is equal to
[tex]C=2\pi r[/tex]
we have
[tex]r=4\ in[/tex]
substitute
[tex]C=2(3.14)(4)=25.1\ in[/tex] -----> one more decimal than the given radius (nearest tenth)
Prove the Converse of the Pythagorean Theorem using similar triangles. The Converse of the Pythagorean Theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures.
Answer:
To prove the Converse of Pythagorean Theorem:
Step-by-step explanation:
1. Draw a right triangle (Triangle ABC)
2. Draw an altitude from and A to the hypotenuse creating 2 new triangles
3. The part that intersects the hypotenuse will be point D, this makes a right angle
Triangle DBA and triangle ABC both have right angles and share angle B, this means that triangle ABC and triangle DBA are congruent by the AA postulate. Since triangle DAC and triangle ABC both have right angles(angle D and angle A) and they share angle C, triangle DAC and ABC are congruent by the AA postulate as well.
The ratios can be set up as:
AC/BC = DC/AC & AB/BC = DB/BA
Once cross multiplied, the result should be:
(AC)² = (BC)(DC) & (AB)² = (BC)(DB)
Now add both sides together to get:
(AC)² + (AB)² = BC(DC) + (BC)(DB)
To make things easier, factor out the like terms:
(AC)² + (AB)² = BC(DC + DB)
When looking at the triangle(must draw to see), it shows that (DC + DB) is actually side BC. This leaves:
(AC)² + (AB)² = BC(BC) → (AC)² + (AB)² = (BC)²
The Pythagorean theorem says that a² + b² = c². Knowing this, on the original triangle, side AB = a, side AC = b, and side BC = c. Knowing this:
(AC)² + (AB)² = (BC)² → a² + b² = c²
This proves the Converse of the Pythagorean Theorem.
The diagram shows triangle MNP. Which term describes point Q?
Answer:
(B) Incenter
Step-by-step explanation:
From the given figure, it can be seen that PMN is a triangle where MQ is the angle bisector of ∠NMP, PQ is the angle bisector of∠NPM and NQ is the angle bisector of ∠MNP.
Also, It is equally distant from the three line segments forming the sides of the triangle. Thus, By the definition of incenter, Q can be named as the incedntre of the given triangle PMN.
Since, the centroid, circumcenter and orthocenter does not satisfy the conditions given in the figure, thus Q can not be considered as centroid, circumcenter and orthocenter.
Hence, option B is correct.
Answer:
the answer is incenter
Step-by-step explanation:
took the apex quiz got it correct !
Abigail drives at an average speed of 60 miles per hour for 3 hours. The graph shows her distance versus time. Which statements are true? Check all that apply. As Abigail’s time increases, her distance increases. As Abigail’s time increases, her distance decreases. At 2 hours, Abigail has traveled 120 miles. At 1.5 hours, Abigail has traveled 100 miles. At 3 hours, Abigail has traveled 180 mile
The statements are to be checked whether they are true or not.
The true statements are:
As Abigail’s time increases, her distance increases.
At 2 hours, Abigail has traveled 120 miles.
At 3 hours, Abigail has traveled 180 mile
Abigail is driving at a speed of 60 miles per hour for 3 hours.
The function representing the situation will be
[tex]y=60x[/tex]
where,
[tex]y[/tex] is the distance in miles
[tex]x[/tex] is the time in hours
If time increases this means [tex]x[/tex] increases so, distance [tex]y[/tex] will also increase.
At 2 hours [tex]x=2[/tex]
[tex]y=60\times 2=120[/tex]
The distance traveled is 120 miles.
At 1.5 hours [tex]x=1.5[/tex]
[tex]y=60\times 1.5=90[/tex]
The distance traveled is 90 miles.
At 3 hours [tex]x=3[/tex]
[tex]y=60\times 3=180[/tex]
The distance traveled is 180 miles.
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Jared wants to purchase his favorite barbeque sauce. The barbeque sauce comes in two different size bottles. The 32 ounce bottle is on sale for $4.59. The 18 ounce bottle is priced at $3.06. Jared has a coupon for 60 cents off if you buy two 18 ounce bottles. Determine if Jared gets the better buy when he buys one 32 ounce bottle or when he buys two 18 ounce bottles. a. Jared will get the same deal on either purchase. b. Jared will get the better deal buying one 32 ounce bottle. c. Jared will get the better deal buying two 18 ounce bottles. d. Jared doesn’t need the coupon, he will get the best deal on one 18 ounce bottle.
Answer:
b. Jared will get the better deal buying one 32 ounce bottle.
Step-by-step explanation:
according to the rational root theorem, which is a factor of the polynomial f(x) = 3x^3 - 5x^2 - 12x + 20?
Without solving the equation, determine the nature of the roots of x2 - 2 x - 8 = 0.
The equation x² - 2x - 8 = 0 has two real and distinct roots.
Explanation:A quadratic equation is an equation of the form ax² + bx + c = 0. In this equation, the coefficient of the x² term is 1, so a = 1, b = -2, and c = -8. We can determine the nature of the roots without solving the equation by looking at the discriminant, which is the term inside the square root of the quadratic formula. The discriminant is given by b² - 4ac. If the discriminant is positive, the equation has two real and distinct roots. If the discriminant is zero, the equation has two real and identical roots. If the discriminant is negative, the equation has two complex roots.
In this case, we have b = -2 and a = 1, so the discriminant is (-2)² - 4(1)(-8) = 4 + 32 = 36. Since the discriminant is positive, the equation has two real and distinct roots.
What are the characteristics of a gas?
A. a definite shape but no definite volume
B. no definite shape but a definite volume
C. a definite volume and definite shape
D. no definite shape or definite volume
Answer:
D
Step-by-step explanation:
You want to embroider a square design. You have an embroidery hoop with a 6 inch diameter. Find the largest value of x so that the entire square will fit in the hoop. Round to the nearest tenth
The largest size of the square that can be embroidered within the 6 inch hoop is 4.2 inches per side (rounded to the nearest tenth). This is found using geometry principles involving squares and circles.
Explanation:This question is asking for the side length of a square that will fit within a circle, or in this case, an embroidery hoop, with a certain diameter. This is a concept from geometry that involves the relationship between squares and circles. Essentially, the diameter of the circle becomes the diagonal of the square.
To calculate the side length (x) of the square, we'll use the formula for the diagonal (d) of a square divided by the square root of 2 (d = √2 * x). Since the diameter of the hoop is 6 inches, rearranging the equation gives us x = d / √2 which results in x = 6 / √2 = 4.2 inches (rounded to the nearest tenth)
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1. simplify
9 x 5 + 2 / 8 - 3
by the way " / " means division.
What is the common difference of the arithmetic sequence 1/5, 6/5 , 11/5 ,16/5 , ...?
Crystal estimated that repairs to her car would cost about $100. The cost of repairs was actually $175. Fill in the box with Crystal's percent error
percent error=100 times error/predicted
error=175-100=75
predicted=100
percent error=100 times 75/100=75
the answer si 75% error
Find an equation of the line containing the point (3,3) and parallel to y = 2 x − 1 y=2x-1.
Tony started a blanket business. He purchased a sewing machine and some fabric to get started, and then sold each blanket for the same price. The expression −450+12x−450+12x represents the profit that Tony has earned based on the number of blankets sold.
Which expression represents the total amount Tony earns from selling blankets?
x
12x
-450+12x
12
If I set a goal of signing up 30% of customers to receive emails. that means that if I speak to 130 customers today I need to collect email addresses from ?
Answer:39
Step-by-step explanation:
130+30%=39