Answer:
1. 13 2. 10
Step-by-step explanation:
In the isosceles triangle ABC, we have AB=AC=4. The altitude from B meets AC at H. If AH=3(HC) then determine BC.
In isosceles triangle ABC with AB=AC=4, and AH=3HC, the length of BC is [tex]\( \frac{4\sqrt{5}}{5} \)[/tex] units, determined using the Pythagorean Theorem and the given relationship between AH and HC.
In isosceles triangle ABC, let BH be the altitude from B to side AC. Given AB = AC = 4 and AH = [tex]3 \cdot[/tex] HC, we can use the Pythagorean Theorem in right triangle ABH:
[tex]\[ BH^2 + AH^2 = AB^2 \][/tex]
Substitute the given values:
[tex]\[ BH^2 + (3HC)^2 = 4^2 \][/tex]
Simplify:
[tex]\[ BH^2 + 9HC^2 = 16 \][/tex]
Since BH = HC in an isosceles triangle, substitute BH with HC:
[tex]\[ HC^2 + 9HC^2 = 16 \][/tex]
Combine like terms:
[tex]\[ 10HC^2 = 16 \][/tex]
Solve for HC :
[tex]\[ HC^2 = \frac{8}{5} \][/tex]
Now, use the Pythagorean Theorem in right triangle BHC:
[tex]\[ BC^2 = BH^2 + HC^2 \][/tex]
Substitute the known values:
[tex]\[ BC^2 = HC^2 + HC^2 \]\[ BC^2 = 2HC^2 \]\[ BC^2 = 2 \cdot \frac{8}{5} \]\[ BC^2 = \frac{16}{5} \][/tex]
Therefore, BC is the square root of [tex]\( \frac{16}{5} \)[/tex], which simplifies to [tex]\( \frac{4}{\sqrt{5}} \)[/tex] or [tex]\( \frac{4\sqrt{5}}{5} \)[/tex].
The length of BC in an isosceles triangle with sides AB=AC=4 and altitude BH, where AH=3(HC), is 2√2 units.
Explanation:To determine the length of BC in an isosceles triangle ABC with sides AB=AC=4 and altitude BH, where AH=3(HC), we can use the properties of similar triangles and the Pythagorean theorem.
Since the triangle is isosceles, the altitude BH will bisect the base AC at H, creating two right triangles ABH and CBH. We know that AH=3(HC), which can be expressed as AH=3x and HC=x for some value x. Therefore, AC = AH + HC = 3x + x = 4x.
Using the Pythagorean theorem (a² + b² = c²), in triangle ABH, we get:
AH² + BH² = AB²(3x)² + BH² = 4²9x² + BH² = 16And in triangle HBC, we have:
HC² + BH² = BC²x² + BH² = BC²Since we want to find BC, we first solve for BH from the first right triangle:
BH² = 16 - 9x²Substitute BH² into the second equation:
x² + (16 - 9x²) = BC²-8x² + 16 = BC²To find x, we use AC = 4x = 4, thus x = 1. Substituting x into the equation for BC, we get:
-8(1)² + 16 = BC²-8 + 16 = BC²BC² = 8BC = √8BC = 2√2 unitsFlavor of Crisps Probability of Buying
Cheese Crisps 7/25
Bacon Crisps 1/4
Ranch Crisps 3/25
Salsa Crisps 7/20
A grocery chain conducted a random survey to determine the favorite flavor of a new potato crisp. The results are shown on the table. Which flavor is MOST LIKELY to sell BEST if stocked by the grocery chain?
A) Ranch Crisps
B) Salsa Crisps
C) Cheese Crisps
D) Barbecue Crisps
Answer:
b
Step-by-step explanation:
The flavor most likely to sell best if stocked by the grocery chain is B. Salsa Crisps, as it has the highest probability of purchase at 0.35.
To determine which flavor of potato crisps is most likely to sell best if stocked by the grocery chain, we need to compare the given probabilities.
Cheese Crisps: [tex]\frac{7}{25}[/tex] = 0.28Bacon Crisps: [tex]\frac{1}{4}[/tex] = 0.25Ranch Crisps: [tex]\frac{3}{25}[/tex] = 0.12Salsa Crisps: [tex]\frac{7}{20}[/tex] = 0.35From these calculations, we can see that Salsa Crisps have the highest probability (0.35) of being bought. Therefore, Salsa Crisps are the most likely to sell best if stocked by the grocery chain.
The correct answer is Salsa Crisps.
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue , 1 red , and 1 orange section is?
Hey there!
[tex]\large\boxed{25\%}[/tex]
Assuming that all the sections are the same size, there are four sections of equal size.
Blue would be one out of those four sections, so the probability is 1/4. In decimal form this is .25, and as a percent this is 25%.
Hope this helps!
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue , 1 red , and 1 orange section is 1/4.
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue, 1 red, and 1 orange section is 1/4 or 25%.
Total = 1+1+1+1 = 4
Number of blue =1
Therefore, probability =1/4
Why do you think George Washington wanted the us to avoid entangling alliances
A new car is Purchased for 16200 dollars. The value of the car depreciates at 14.25% per year. What will the value of the car be, to the nearest cent,after 6 years?
Answer:
6,440.5
Step-by-step explanation:
So the car starts at 16,200. For the first part of the equation it's 16,200 × x raised to the y. X in this equation would be 1-.1425 = 0.8575. 16,200×(.8575)^y. Y is the number of years after you purchased the car. So, 16,200×(.8575)^6 and that equals 6,440.5
Answer:
$6440.5
Step-by-step explanation:
I hope this helps!
In circle A. MRH = 45° and mÞH =
80°. What is m&PAR?
Answer:
D
Step-by-step explanation:
∠ PAR is an angle at the centre of the circle subtended by the arc PR
The central angle is equal to the arc that subtends it, thus
∠ PAR = arc PH + arc HR = 80° + 45° = 125° → D
Create a chart to show how to use the distributive property to simplify the expression: 7 (5x +
10) – 10x.
Answer:
25x + 70
Step-by-step explanation:
Step 1: Distribute
7 (5x + 10) - 10x
7*5x + 7*10 - 10x
35x + 70 - 10x
25x + 70
Answer: 25x + 70
What is the value of x, given that PQ parallel to BC
Answer:
since PQ ||BC,
Angle A is common for both triangles angle P = angle B
triangles ABC, APQ are similar,then their corresponding sides are in proportion
AP/PB =AQ/QC
4/8=x/16
x=8
Do you know basic proportionality theorem ? You can solve the problem easily by this.
In short: BPT is if a line is parallel to a side of the triangle which intersects the other sides imto two distinct points, then the line divides those sides in proportion.
In your problem, it's given that the mutual lines are parallel (PQ || BC), so it makes it divide |AP| with |AB| and |AQ| with |AC| proportionally.
|AP| / |AB| = |AQ| / |QC|
4/12 = x/16+x
4(16+x) = 12x
x=8
Hope it helps!
#MissionExam001
find the recursive formula.
-28, -35, -42, -49, ...
Answer:
[tex]a_{n+1}[/tex] = [tex]a_{n}[/tex] - 7
Step-by-step explanation:
Note the common difference d between consecutive terms in the sequence, that is
d = - 35 - (- 28) = - 42 - (- 35) = - 49 - (- 42) = - 7
Thus to obtain a term in the sequence subtract 7 from the previous term
[tex]a_{n+1[/tex] = [tex]a_{n}[/tex] - 7 with a₁ = - 28
The width of a rectangle is 2m less than the length. The area is 48m squared. Find the dimensions.
Length of the rectangle is 8m and width is 6m
Step-by-step explanation:
Step 1: Given area of the rectangle = 48m². Let the length be x, then the width is x - 2. Find the dimensions using the area of the rectangle = length × breadth48 = x (x - 2)
48 = x² - 2x
x² - 2x - 48 = 0
x² - 8x + 6x - 48 = 0
x(x - 8) + 6(x - 8) = 0
(x + 6)(x - 8) = 0
x = -6, 8 (neglecting the negative value)
∴ Length of the rectangle = 8m
∴ Width of the rectangle = 8 - 2 = 6m
What is the value of x in the figure?
Enter your answer in the box.
x =
Answer:
X = 29
fyfufubivih8g8hih
Answer: X = 29
X + 61 = 90
x+61−61=90−61
x=29
True or false the triangle was rotated 90 degrees counterclockwise?
Answer:
False
Step-by-step explanation:
if it was counter clockwise it be in the 2 and 3 quadrants
Select from the drop-down menu to correctly complete the statement about the given figures.
Triangles ABC and DEF are (similar or not similar)
ΔABC and ΔDEF are similar by AAA similarity.
Solution:
Sum of the interior angles = 180°
In triangle ABC,
60° + 60° + m∠C = 180°
120° +m∠C = 180°
Subtract 120° from both sides, we get
m∠C = 60°
In triangle DEF,
60° + 60° + m∠F = 180°
120° +m∠F = 180°
Subtract 120° from both sides, we get
m∠F = 60°
Consider ΔABC and ΔDEF,
∠A ≅ ∠D
∠B ≅ ∠E
∠C ≅ ∠F
Therefore by AAA similarity ΔABC ≅ ΔDEF.
ΔABC and ΔDEF are similar triangles.
Answer: The answer above is correct.
Solve 3x + k = cfor x.
What is (-7a^4bc^3)(5ab^4c^2)
Answer:=-35a^5b^5c^5
Step-by-step explanation:
Answer:
-35a^5b^5c^7
Step-by-step explanation:
Step 1: Distribute
(-7a^4bc^3)(5ab^4c^4)
(-7 * 5) * (a^4 * a) * (b * b^4) * (c^3 * c^4)
(-35) * (a^5) * (b^5) * (c^7)
-35a^5b^5c^7
Answer: -35a^5b^5c^7
How do you solve 21÷1/3
Answer:
63
Step-by-step explanation:
When dividing by a fraction, it is the same a multiplying that fraction but the reciprocal of it.
21 / 1/3 is same as 21 * 3/1
63
Answer: 63
$800 is deposited in an account
that pays 9% annual interest,
compounded annually. Find the
balance after four years.
Answer:
The balance after four years is $1129.27
Step-by-step explanation:
The formula for compound interest, including principal sum, is [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A = the future value of the investment/loan, including interestP = the principal investment amount (the initial deposit or loan amount)r = the annual interest rate (decimal)n = the number of times that interest is compounded per unit tt = the time the money is invested or borrowed for∵ $800 is deposited in an account
∴ P = 800
∵ The account pays 9% annual interest
∴ r = 9% = 9 ÷ 100 = 0.09
∵ The interest is compounded annually
∴ n = 1
∵ The time is 4 years
∴ t = 4
- Substitute the values of P, r, n, and t in the formula above
∵ [tex]A=800(1+\frac{0.09}{1})^{(1)(4)}[/tex]
∴ [tex]A=800(1.09)^{4}[/tex]
∴ A = 1129.265
∴ The balance after four years is $1129.27
Brainliest Giveaway!! Also gives all of my points.!!
Answer:
wf
axStep-by-step explanation:
Answer:
Her ride is about 15.1 miles long.
Step-by-step explanation:
40.03 = 6.75 + 3.20m
33.28 = 3.20m
ISOLATE M
m = 15.1272
m = 15.1
Explain how to write the equations of vertical lines, and why they are written this way
1. Recall the vertical line equation.
2. Plug in the x that we know.
3. Write down the final equation
Pls mark me brainiest :)
What is 3 to the power of 2 plus 4 to the power of 2
Answer: 25
Step-by-step explanation:
3² + 4 ² = ?
(3x3) + (4x4) = ?
9 + 16 = 25
Answer:
25
Step-by-step explanation:
3² +4² = 9 +16 = 25
_____
Your calculator can help you figure this.
_____
25 = 5², which means that the lengths 3, 4, and 5 could be the sides of a right triangle. They are the smallest integer solution to the equation ...
a² +b² = c²
help! need asap! brainiest if right
Step-by-step explanation:
After the translation, rotation and reflection position of the image may differ but the side lengths, angle, orientation remains the same, so that the congruence is maintained, but in dilation the size of the image may get enlarged or reduced, so that congruence is not there.
Parallelograms are congruent when
Reflect across the y- axis and then translate 1 unit left.
Reflect across the y- axis then rotate 45° counterclockwise.
Translate 4 units up then rotate 180° counterclockwise
Parallelograms are non-congruent when
Translate 5 units right then dilate by a factor of 2
Rotate 90° clockwise then dilate by a factor of 6
Dilate by a factor of 3 then reflect across the x- axis
I WILL GIVE BRAINLIEST
Answer must be simplified
4x ≤ 12
Answer: x ≤ 3
Step-by-step explanation:
4x ≤ 12
divide each side by 4
x≤3
Two linear equations are shown.
What is the solution to the system of equations?
(7,4)
• (31)
• (s. *)
(9,7)
y=
1/3x + 2
4
5
6
x
y = 4/3x - 5
The solution to the system of equations is (7, 13/3).
We have Equations,
y= 1/3x + 2,
y= 4/3 x - 5
Solving above two equations we get
1/3 x + 2 = 4/ 3 x - 5
1/3 x - 4/3 x = -5 - 2
-3/3 x = -7
-x = -7
x = 7
and, y = 4/3(7) - 5 = 28/3-5 = 13/3
Thus, the solution of equation is (7, 13/3).
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Find the value of x.
m∠FGH = 148°
m∠FGL = (x + 12)°
m∠LGH = (16x)°
A) 3
B) 5
C) 6
D) 8
Option D:
x = 8
Solution:
Given data:
m∠FGH = 148° , m∠FGL = (x + 12)° and m∠LGH = (16x)°
To find the value of x:
m∠FGL + m∠LGH = m∠FGH
⇒ (x + 12)° + (16x)° = 148°
⇒ x° + 12° + 16x° = 148°
⇒ 17x° + 12° = 148°
Subtract 12° from both sides of the equation.
⇒ 17x° = 136°
Divide by 17 on both sides, we get
⇒ x° = 8°
⇒ x = 8
Option D is the correct answer.
Answer:D
Step-by-step explanation:I did it on usatestprep trust me.
Norma has 9 pies to divide among 4 friends. How many pies will each friend receive if all of the pies must be used and can be divided into smaller parts?
Answer:
2 1/4
Step-by-step explanation:
Elle earned $45 last month babysitting. This month she earned $35. What is the percent decrease?
Answer:
10percent
Step-by-step explanation:
I think
Elle experienced a 22.22% decrease in earnings from babysitting, from $45 to $35. This is calculated by finding the difference between the two amounts, dividing by the original amount, and then multiplying by 100 to convert to a percentage.
Explanation:Elle's decrease in earnings can be calculated using the formula for calculating the percentage decrease, which is [(Original value - New value)/(Original value)] * 100.
In Elle's case, the original value is $45 (the amount she earned last month), and the new value is $35 (the amount she earned this month). So, follow the formula:
Subtract the new value from the original value: $45 - $35 = $10Divide the decrease by the original value: $10/$45 = 0.2222Multiply the result by 100 to convert it to a percentage: 0.2222 * 100 = 22.22%So, Elle experienced a 22.22% decrease in her earnings from babysitting.
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Write an inequality to describe the relationship between -1 2/3 and -1/4.
Answer:
-14>-1 2/3
Step-by-step explanation:
Answer:
-14>-1 2/3
Step-by-step explanation:
Find the value of X. Please answer.
Answer:
x= 12
Step-by-step explanation:
Please see attached picture for full solution.
I NEED HELP ASAP WITH THE QUESTION
Equivalent expression for x + x + x + x + x is 5x and that of 18y - 12 are 6·3y - 6·2 and 6(3y - 2)
Step-by-step explanation:
Step 1: Find equivalent expression for x + x + x + x + x. It is 5x. Step 2: Find equivalent expressions for 18y - 12Equivalent expressions are 6·3y - 6·2 and 6(3y - 2)
Honeycrisp apples are on sale if you buy a crate, 15 pounds for $30. What is the unit price per pound
Answer:
$2
Step-by-step explanation:
$30 ÷ 15 pounds
30 ÷ 15 = 2
Answer: $2 per pound
The unit price of apple per pound is $2.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.
Given, Honeycrisp apples are on sale if you buy a crate, 15 pounds for $30.
To find the unit price,
we divide the total cost to total pound of a crate.
unit price of an apple
= $30 / 15
= $2
Therefore, the unit price of an apple per pound is $2.
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