In ΔABC, m∠B = m∠C. The angle bisector of ∠B meets
AC at point H and the angle bisector of ∠C meets AB at point K. Prove that BH = CK.
To prove that BH = CK in triangle ABC, we can use the angle bisector theorem. The theorem states that the angle bisector of an angle in a triangle divides the opposite side into two segments proportional to the other two sides. By applying this theorem and representing BH as x and CK as y, we can show that x = y, thus proving that BH = CK.
Explanation:In triangle ABC, to prove that BH = CK, we can use the angle bisector theorem. Since m∠B = m∠C, the angle bisector of ∠B will divide the side AC into two segments proportional to the other two sides. Let's denote BH as x and CK as y. According to the angle bisector theorem, we have:
AB / BC = AH / HCAC / BC = AK / BKSince AB = AC (isosceles triangle), we can rewrite the first equation as:
x / BC = AH / HC
And the second equation as:
AC / BC = AK / y
Since AB = AC, we can substitute AC with AB:
x / BC = AK / y
Now, we can cross-multiply and solve for x and y:
x * BC = AK * HC
y * BC = x * HK
Simplifying, we get:
x = AK * HC / BC
y = x * HK / BC
Since HK = HC, we have:
x = AK
y = x
Therefore, BH = x = CK = y.
Type an equation of the line that passes through the origin with the slope 3
The required equation of the line is y = 3x which passes through the origin with the slope 3.
What is the slope of the line?The slope of the line is defined as the gradient of the line. It is denoted by m
Slope m = (y₂ - y₁)/(x₂ -x₁ )
We have to determine the equation of the line that passes through the origin with slope 3.
Let's assume slope-intercept form:
So required line in the slope-intercept form is:
y = mx + b
where m is the slope and b is the y-intercept.
In this case, the slope of line m = 3, and the line passes through the origin
So, therefore equation will be:
y = 3x + 0 or
y = 3x
Thus, the required equation of the line is y = 3x which passes through the origin with the slope 3.
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The equation d = m/v 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:
The equivalent equation of [tex]d=\frac{m}{V}[/tex] is [tex]V=\frac{m}{d}[/tex].
Step-by-step explanation:
The given equation is
[tex]d=\frac{m}{V}[/tex]
Where d is density, m is mass and V is volume.
We have to solve this equation for V. To separate the variable V on one side multiply both sides by V.
[tex]d\times V=\frac{m}{V}\times V[/tex]
[tex]dV=m[/tex]
Diven both sides by d.
[tex]\frac{dV}{d}=\frac{m}{d}[/tex]
[tex]V=\frac{m}{d}[/tex]
Therefore the equivalent equation of the given equation is [tex]V=\frac{m}{d}[/tex].
f(x)=24x+7 What is the domain of f
David and his family went out to eat in the bill was $80 and he gave the waiter 30% how much was did he give the waiter
Perpendicular bisector of MU. Find the values of m.
Which of the following statements is true?
The interquartile range of weights of both apples is the same.
The upper quartiles of each group are within 2 grams of each other.
There were more Red Delicious apples weighed than Granny Smith apples.
The median weight of Granny Smith apples is less than the median weight of Red Delicious apples.
True or false the product of a complex number and its conjugate is a real number
It is true that the product of a complex number and its conjugate is a real number and this can be determined by using arithmetic operations.
Let the complex number be (a + bi). Therefore, its conjugate is given by (a - bi).
The following calculation can be used to determine the product of a complex number and its conjugate:
= (a + bi).(a - bi)
Multiply (a) by (a - bi) and then multiply (bi) by (a - bi) in the above expression.
[tex]\rm =a^2-abi+abi-b^2i^2[/tex]
Simplify the above expression.
[tex]\rm =a^2-b^2i^2[/tex]
Remember the value of ([tex]\rm i^2 = -1[/tex]). So substitute the value of [tex]\rm i^2[/tex] in the above expression.
[tex]\rm = a^2+b^2[/tex]
From the above calculation, it can be concluded that it is true that the product of a complex number and its conjugate is a real number.
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A lamp manufacturer uses 714 meters of electrical cord each week. The cord comes on spools that hold 12 meters each. How many spools of electrical cord does the manufacturer use each week?
divide 714 by 12
714 / 12 = 59.5 spools per week
Which is equivalent to 243 2/5 ? 3 6 9 12
Answer:
The answer is [tex]9[/tex]
Step-by-step explanation:
we have
[tex](243)^{\frac{2}{5}}[/tex]
we know that
[tex]a^{\frac{n}{m}}=\sqrt[m]{a^{n}}[/tex]
so
[tex](243)^{\frac{2}{5}}=\sqrt[5]{243^{2}}[/tex]
Remember that
[tex]243=3^{5}[/tex]
Substitute
[tex]\sqrt[5]{243^{2}}=\sqrt[5]{(3^{5})^{2}}\\ \\= \sqrt[5]{(3^{10})}\\ \\=3^{\frac{10}{5}}\\ \\= 3^{2} \\ \\=9[/tex]
He ages of mark and adam add up to 28 years total. mark is 20 years older than adam. how many years old is adam
Write an expression for the quantity 506 000 cm in which it is clear that all zeros are significant
What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x/4+5 ?
How many distinct triangles can be formed for which m∠X = 51°, x = 5, and y = 2? zero one two
Answer: B: One
Step-by-step explanation:
Alan bowls one game, which consists of 10 frames. The number of pins he knocked down in each frame is 5, 6, 7, 5, 7, 9, 2, 4, 8, and 7. Which measure should Alan use to learn the difference of the greatest and the least number of pins he knocked down?
Answer:
Range.
Step-by-step explanation:
Alan must use the measure called Range, which indicates the dispersion between the extreme values of a variable. It is calculated as the difference between the highest and the lowest value of the variable. It is denoted as R. First the data is sorted, then it is calculated as:
R = x (n) - x (1) where,
x (n): It is the largest value of the variable.
x (1): It is the smallest value of the variable.
In the given case (5, 6, 7, 5, 7, 9, 2, 4, 8, and 7), we sort the data, and get,
2, 4, 5, 5, 6, 7, 7, 7, 8, 9
x (n) = 9
X (1) = 2
R = 9 - 2 = 7
Hope this helps!
Sawyer has triple the number of Hot Wheels cars as Fisher. If Fisher has x number of cars, how many does Sawyer have?
A) x + 3
B) 3x
C) 3/x
D) 2x
The graphs of the equations 2x+5y=3 and 2x+5y=7 are parallel lines. Find the equation of the line that is parallel to both lines and lies midway between them.
Write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 .
an equation of the line passing through point P(0, 0) that is perpendicular to the given line is
[tex]y=\frac{1}{9} x[/tex]
Given :
the line passing through point P(0, 0) that is perpendicular to the line
y = −9x−1
The given equation is in the form of y=mx+b
where m is the slope and b is the y intercept
Find out slope from the given equation y=-9x-1
Slope of the given equation is -9
Slope of perpendicular lines are negative reciprocal of one another
slope of perpendicular line is negative reciprocal of -9 is [tex]\frac{1}{9}[/tex]
slope of perpendicular line m=[tex]\frac{1}{9}[/tex]
The line passes through the point (0,0) that means y intercept is 0
the value of b=0
[tex]m=\frac{1}{9} , b=0\\y=mx+b\\y=\frac{1}{9} x+b\\y=\frac{1}{9} x[/tex]
an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1 is
[tex]y=\frac{1}{9} x[/tex]
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The equation of the line passing through point P(0, 0) and perpendicular to the line y = -9x-1 is y = (1/9)x, with the slope of the line being the negative reciprocal of -9.
Explanation:To write an equation of the line passing through point P(0, 0) that is perpendicular to the line y = −9x−1, we first identify the slope of the given line. The slope of the line y = −9x−1 is −9, so the slope of a line perpendicular to it will be the negative reciprocal. Therefore, the perpendicular slope is 1/9.
Since the point P(0, 0) is also the y-intercept, we can directly write the equation of the perpendicular line in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Thus, the equation of the line we are looking for is y = (1/9)x.
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In two days, 48,000 gallons of oil gushed out of a well. At what rate did the oil flow from the well?
gallons per hour
The sides of a square are 5 2/5 inches long. what is the area of the square?
a. 5 4/5 square inches
b. 5 4/25 square inches
c. 25 4/5 square inches
d. 25 4/25 square inches
Answer:
29 4/25 square inches (not given in the options)
Step-by-step explanation:
A square is a plain 4 sided shape with equal sides. As such, all sides of a square are equal. If the length o a side of a square is s, the area of the square will be s² while the perimeter will be 4s.
Area of square = (5 2/5 inches)²
= (27/5 inches)²
= 729/25 square inches
= 29 4/25 square inches
Need the calculations please
Simplify. Express your answer as a single term, without a denominator. t0u/tu
True or false if a function y = f(x) satisfies dy/dx = y, then y = e^x
△ABC△ABC is similar to △XYZ△XYZ. Also, angle A measures 45° and angle C measures 60°.
What is the measure of angle Y?
Answer: The value of angle Y is 75 ° .
Step-by-step explanation:
Given Δ ABC ≈ Δ XYZ
∠ A = 45°
∠ C = 60°
To find =
∠Y =? in ΔXYZ
Solution:
In Δ ABC
∠ A = 45 °
∠ C = 60 °
∠ B = ?
∠ A + ∠ C +∠ B = 180 ° (angle sum property of triangle)
∠ B = 75 °
Since, given that Δ ABC ≈ Δ XYZ and in similar triangles ,angles of respective vertices are equal. As shown in the image attached
∠ A = 45 ° = ∠ X
∠ B = 75 ° = ∠ Y
∠ C = 60 ° = ∠ Z
So, the value of angle Y is 75 ° .
If the typical balance on Lucy's credit card is $750 and the interest rate (APR) on her credit card is 16%, how much in interest would you expect Lucy to be charged in a typical month?
The measures of two complementary angles are 3x+1 and 5x-y. Find x
A: 8
B: 12
C: 14
D: 23
You are paid $8.25/hour. You work 35 hours/week for 3 weeks. Your involuntary deductions are FICA (7.65%), federal withholding (13%), and state withholding (9%). How much is your realized income?
The answer is:
$609.39
in the graph below, point D is reflected across the y axis. what are the coordinates of its image ?
Generally, whenever a point (x,y) is reflected across the y axis, the y coordinate stays the same and the sign of x coordinate changes.
So [tex](x,y)[/tex] changes to [tex](-x,y)[/tex].
Point D in the diagram shown has coordinates [tex](3,-1)[/tex]. According to the rule, the x-coordinate, 3, will change to -3 and the y-coordinate, -1, would stay the same.
Hence, our image of D after the reflection about y-axis would have coordinates [tex](-3,-1)[/tex].
ANSWER: [tex](-3,-1)[/tex]
Answer:
(-3, -1)
Step-by-step explanation:
A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $504. What was the simple interest rate of the bonds? Do NOT round off a decimal answer.
What is the simplified form of each expression? (1 point)
1.) -(10)^-1
-1/10
-1/1^10
1/10
10
2.) 1/c^-5 (1 point)
c^5
5c
-c^5
-5/c
3.) What is the value of y^-5/x^-3 for x = 2 and y = -4? (1 point)
10/3
128
-1/128
-128
4.) Is the number written in scientific notation if not, explain. 5.1 x 10^8 (1 point)
Yes; the number is written in scientific notation.
No; the first factor is not a number between 1 and 10.
No; it is not written as a number times a power of 10.
5.) What is the number written in a standard notation? (1 point)
5.71 x 10^-3
-171.3
0.0571
0.000571
0.00571
6.) Suppose that the diameters of different types of hairs are 1.7 x 10^-4 cm, 1.4 x 10^-3 cm, 1.2 x 10^-5 cm, and 1.9 x 10^-4 cm? what is the order of the hairs from least to greatest diameter? (1 point)
Who ever is good at math please ''Try'' to help me out here?! :D And Thank you so much if ya do! :P
Answer:
a
b
a
d
a
a
Step-by-step explanation: