If the angle bisector also bisects the opposite side, then it's also a median *and* an altitude. The triangle is isosceles.
Draw the diagram: you have that altitude forming a pair of mirror-image right triangles. In each, the short side is 1 and the hypotenuse is 2. What does this tell you about the large triangle?
Then the rest you have to think... cuz it wasn't that hard.( If you still don't understand comment it, and then I will explain to you!)
HOPE IT HELP!
20 POINTS! An 85-foot wire is tied from the top of a utility pole to the top of the building as shown. Find d, the distance from the pole to the building.
Answer:
d = 78.810 feetStep-by-step explanation:
To find the distance d we use sine
sin∅ = opposite / hypotenuse
d is the opposite
the hypotenuse is 85ft
∅ = 68°
sin 68 = d / 85
d = 85 sin 68
d = 78.810 feet
Hope this helps you
In the diagram, OP = 2 and OP’ = 8. Find the scale factor of the dilation. a) 1/4 b) 1/2 c) 4 d) 6
Answer:
c
Step-by-step explanation:
Consider the ratio of image to original, that is
scale factor = [tex]\frac{OP'}{OP}[/tex] = [tex]\frac{8}{2}[/tex] = 4 → C
The scale factor of the dilation will be option C; 4.
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
Since the scaling is done by multiplication of some constant, that constant is called scale factor.
Dilation of a figure will leave its sides get scaled (multiplied) by same number.
Let suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.
Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]
Consider the ratio of image to original, that is;
Scale factor = OP'/OP
OP'/OP = 8/2 = 4
Hence, the scale factor of the dilation will be option C; 4.
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If a(x) = 3x + 1 and b(x) = sqrt x-4 what is the domain of (b•a)(x)
Answer:
[4, infinity)
Step-by-step explanation:
(b·a)(x) = (sqrt(x - 4)·(3x + 1). The domain of 3x + 1 is "all real numbers," but the presence of the sqrt function limits the input to (b·a)(x) to [4, infinity); recall that the argument of the sqrt function must be zero or greater.
Find the value of the trigonometric ratio, tan C.
Answer:
4/3
Step-by-step explanation:
TanC = opposite/adjacent
TanC = 40/30 ➡ 4/3
Find the measure of the remote exterior angle.
Answer:
m∠x = 128°
Step-by-step explanation:
Step 1: Find n
We use Supplementary Angles and Sum of Triangle Interior Angles to find n.
180 - (198 - 5n) = 5n - 18
m∠z + m∠y + m∠x₁ = 180°
(5n + 37) + (n + 7) + (5n - 18) = 180
Step 2: Solve for n
Solve by combining like terms and properties.
11n + 26 = 180
11n = 154
n = 14
Step 3: Plug in n into m∠x equation
198 - 5(14)
198 - 70
m∠x = 128°
The answer is D) 128
The remote exterior angle here is x. The remote exterior and is always equivalent to the remote interior angles. Thus, x = y + z.
198 - 5n = 5n + 37 + n + 7
198 = 11n + 44
154 = 11n
n = 14
x = 198 - 5n
x = 198 - 70
x = 128 degrees
Hope it helps, and would greatly appreciate it if you could mark this brainliest if it does <3
A rectangular field is twelve times as long as it is wide. If the perimeter of the field is 1690 feet, what are the dimensions of the field?
The width of the field is __ feet.
The length of the field is __ feet.
Answer:
The width of the field is 65 feet.
The length of the field is 780 feet.
You would like to have $4000 in 3 years for a special vacation following graduation by making deposits at the end of every six months in an annuity that pays 4.5% compounded semiannually. a. Use one of the formulas below to determine how much you should deposit at the end of every six months.
Answer:
666.70 at the end of every six months.
Step-by-step explanation:
At the end of every six months deposit amount is 666.70
What is compound interest ?Compound interest is the interest paid on both principal and interest, compounded at regular intervals.
Formula of compound interest :
[tex]A = P(1+\frac{r}{100} )^{n}[/tex]
where,
A = final amount
P = initial principal
n = time in years
r = rate per annum
According to the question
Final Amount needed for a special vacation (A) = $4000
Time in years needed to collect Amount (n) = 3 years
Rate per compounded semiannually (r) = 4.5%
Substituting values in formula for six months
Now time (n) = 3 * 6 = 18 years
using formula of compound interest
[tex]A = P(1+\frac{r}{100} )^{n}[/tex]
[tex]4000 = P(1+\frac{4.5}{100} )^{18}[/tex]
[tex]4000 = P(1.045 )^{18}[/tex]
now,
P = 666.70
Hence, at the end of every six months deposit amount is 666.70
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Rewrite the equation by completing the square
y
5
One of the solutions of the system of equations shown in
the graph has an x-value of -4. What is its corresponding
integer y-value?
4+
UCAT
ETEN
2
1
3
5 4 3 2
1
2
3
4
5
X
HERE
-2 +
-3
3
-4
-5
Answer:
-3
Step-by-step explanation:
Identify the volume of the composite figure, rounded to the nearest tenth. PLEASE HELP!!!
Answer:
The volume of the composite figure is:
312 ft^3Step-by-step explanation:
To identify the volume of the composite figure, you can divide it in the known figures there, in this case, you can divide the figure in a cube and a pyramid with a square base. Now, we find the volume of each figure and finally add the two volumes.
VOLUME OF THE CUBE.
Finding the volume of a cube is actually simple, you only must follow the next formula:
Volume of a cube = base * height * widthSo:
Volume of a cube = 6 ft * 6 ft * 6 ft Volume of a cube = 216 ft^3VOLUME OF THE PYRAMID.
The volume of a pyramid with a square base is:
Volume of a pyramid = 1/3 B * hWhere:
B = area of the base.
h = height.
How you can remember, the area of a square is base * height, so B = 6 ft * 6 ft = 36 ft^2, now we can replace in the formula:
Volume of a pyramid = 1/3 36 ft^2 * 8 ft Volume of a pyramid = 96 ft^3Finally, we add the volumes found:
Volume of the composite figure = 216 ft^3 + 96 ft^3 Volume of the composite figure = 312 ft^3PLATO: Type the correct answer in each box. The vector is first dilated by a factor of 2.5 and then rotated by pi/2 radians. If the resulting vector is [a / b], then a = __ and b = __
Answer:
a = -1, b = -2.5
Step-by-step explanation:
Rule for the dilation of a vector [tex]\binom{x}{y}[/tex] by a scale factor of k is,
(x, y) → (kx, ky)
BY using this rule for a vector [tex]\binom{-1}{4}[/tex] by a scale factor of 2.5
[tex]\binom{-1}{4}[/tex] → [tex]\binom{-2.5}{1}[/tex]
Followed by the rotation by 90° Or [tex]\frac{\pi }{2}[/tex] radians,
Rule for rotation of a vector by 90° is,
(x, y) → (-y, x)
By this rule vector [tex]\binom{-2.5}{1}[/tex] will become,
[tex]\binom{-2.5}{1}[/tex] → [tex]\binom{-1}{-2.5}[/tex]
If we represent this vector by [tex]\binom{a}{b}[/tex],
Then a = -1 and b = -2.5 will be the answer.
Answer:
a= -10 b= -2.5
Step-by-step explanation:
GPAs at CCSU are normally distributed with a mean of 2.38 and a standard deviation of 0.45. Find the z-score for a GPA of 3.06. and discuss the significance of the z-score.
Step-by-step explanation:
Z-score = (score-mean)/standard deviation
= (3.06-2.38)/0.45
= +1.51
The significance of z-score will be "1.5111".
Given values are:
Mean,
[tex]\mu = 2.38[/tex]
Standard deviation,
[tex]\sigma = 0.45[/tex]
GPA,
[tex]\bar x = 3.06[/tex]
Now,
→ The z-score will be:
= [tex]\frac{\bar x - \mu}{\sigma}[/tex]
By putting the given values, we get
= [tex]\frac{3.06-2.38}{0.45}[/tex]
= [tex]\frac{0.68}{0.45}[/tex]
= [tex]1.5111[/tex]
Learn more about standard deviation here:
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If a cow has a mass of 9×102 kilograms, and a blue whale has a mass of 1.8×105 kilograms, which of these statements is true?
Answer:
The mass of the Blue whale is 200 times the mass of the cow
Step-by-step explanation:
Given
Mass of Cow = 9 * 10² kg
Mass of Blue Whale = 1.8 * 10⁵ kg
Required
Determine the relationship between both weights
Represent the mass of the cow with C and the mass of the whale with B
[tex]C = 9 * 10^2kg[/tex]
[tex]C = 9 *100kg[/tex]
[tex]C = 900kg[/tex]
[tex]B = 1.8 * 10^5kg[/tex]
[tex]B = 1.8 * 100000kg[/tex]
[tex]B = 180000kg[/tex]
Divide the bigger weight by the smaller weight
[tex]\frac{B}{C} = \frac{180000kg}{900kg}[/tex]
[tex]\frac{B}{C} = \frac{180000}{900}[/tex]
[tex]\frac{B}{C} = {200}{}[/tex]
Multiply both sides by C
[tex]C * \frac{B}{C} = {200}{} * C[/tex]
[tex]B = {200}{} * C[/tex]
[tex]B = 200}C[/tex]
From the expression above, it can be concluded that the mass of the Blue whale is 200 times the mass of the cow
{5,9,13,17,21,25,...}
How to write condition?
Answer:
Step-by-step explanation:
is an arithmetic progression with ratio=4
a1=5
a2=a1+4=5+4=9
a3=a2+4=9+4=13
...............
a n+1 = a n+4
the condition can be written as the set of sequence of numbers from 5 to infinite which are written from nth term 4n + 1.
the volumes of two similar solids are 729m^3 and 125m^3. the surface area of the larger solid is 324m^2. what is the surface area of the smaller solid? A. 56m^2 B. 100m^2 C. 500m^2 D. 200m^2
Answer:
B. Is the Answer 100 m²
Step-by-step explanation:
The ratio of the two solid is 729/125
The ratio of the surface area = (729/125)^(2/3)=81/25
Surface area = 25 * 324 / 81 = 100 m²
David bought a bag of candy that contains 300 pieces. He wants to split the bag among his 21 students. How many pieces of candy will each student receive? How many extra pieces of candy will David have for himself?
Answer:
each student will receive 14 pieces of candy and that leaves 6 pieces for himself.
14*21=294
294+6=300
Points A,B,C and D are midpoints of the sides of the larger square. If the smaller square has area 60, what is the area of the bigger square? HELP ASAP!!! Will give brainiest if u get it right!
Answer:
120
Step-by-step explanation:
The area of the smaller square is half of the area of the larger square because it's formed by joining the midpoints. Therefore, the area of the big square is 60 * 2 = 120.
Answer:
120
Step-by-step explanation:
SOMEONE PLEASE HELP ME ASAP PLEASE!!!
Answer:
Step-by-step explanation:
eq. of any line parallel to y=1/2 x-4 is
y=1/2 x+a,where a is constant.
∵ it passes through (4,5)
5=1/2(4)+a
5=2+a
a=5-2=3
so reqd. eq. is y=1/2 x+3
Answer:
Equation of the line is
y = 1/2x + 3Step-by-step explanation:
Equation of a line is y = mx + c
where
m is the slope
c is the y intercept
[tex]y = \frac{1}{2} x - 4[/tex]
comparing this equation with the above formula
Slope or m is 1/2
Since the lines are parallel their slope are also the same
That's
m = 1/2
Equation of the line using point (4,5) is
[tex]y - 5 = \frac{1}{2} (x - 4) \\ y - 5 = \frac{1}{2} x - 2 \\ y = \frac{1}{2} x - 2 + 5 \\ y = \frac{1}{2} x + 3[/tex]
Hope this helps you.
Hey guys! I need help ASAPPPP thanks, if u do :)
pls i need it aaaaaaaahg
Answer:
5.1
Step-by-step explanation:
Answer:
1.7√9.18
= 5.4
Hope it helps
PLEASEEEE HELPP !!In each figure, a//b . Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain your answer.
Answer:
No it’s not a translation
Step-by-step explanation:
No it’s not a translation because a translation is when you are just moving a shape not resizing or rotating the shape.
Identify the domain of the function shown in the graph.
A. x is all real numbers.
B. X>0
O c. -1 ≤ x ≤ 0
D. -1 ≤ x ≤ 1
Answer:
A. x is all real numbers.
Step-by-step explanation:
The domain is the input values for the function, in this case the x values
As we can see in the graph, x can be any real value
Answer:
A) x is all real numbers
Step-by-step explanation:
Domain = x
In the graph, x seems to continue infinitely in both directions. This means that x is all real numbers.
The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line. On a coordinate plane, a line goes through (0, negative 2) and (2, 4). What is the solution to the system of equations? (–2, –8) (–1, –5) (0, –2) (2, 4)
Answer:
(–1, –5)
Step-by-step explanation:
Two linear equations are represented by using the tables below. A 2-column table with 4 rows titled Equation A. Column 1 is labeled x with entries negative 2, 0, 3, 4. Column 2 is labeled y with entries negative 8, negative 2, 7, 10. A 2-column table with 4 rows titled Equation B. Column 1 is labeled x with entries negative 3, negative 1, 1, 5. Column 2 is labeled y with entries negative 9, negative 5, negative 1, 7. The data points for equation A are graphed on the coordinate plane below and are connected by using a straight line. On a coordinate plane, a line goes through (0, negative 2) and (2, 4). What is the solution to the system of equations? (–2, –8) (–1, –5) (0, –2) (2, 4)
Answer: To find the equation of line A, we can use any two points. Let us use points (-2, -8) and (0, -2). Therefore, the equation of line A can be gotten using the equation:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ Substituting:\\y-(-8)=\frac{-2-(-8)}{0-(-2)}(x-(-2))\\y+8=3(x+2)\\y+8=3x+6\\y=3x+6-8\\y=3x-2[/tex]
To find the equation of line B, we can use any two points. Let us use points (-3, -9) and (-1, -5). Therefore, the equation of line B can be gotten using the equation:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\\ Substituting:\\y-(-9)=\frac{-5-(-9)}{-1-(-3)}(x-(-3))\\y+9=2(x+3)\\y+9=2x+6\\y=2x+6-9\\y=2x-3[/tex]
To find the solution to the system of equations, we solve them simultaneously
y = 3x - 2 . . . 1)
y = 2x - 3 . . . 2)
Subtracting equation 2 from 1:
x + 1 = 0
x = -1
Put x = -1 in equation 1)
y = 3(-1) - 2
y = -3 - 2
y = -5
Therefore the solution to the equation is (-1, -5)
the correct answer is B (–1, –5)
convert 2 quarts/minute to gallons per hour (15 points)
Answer:
30 us liquid gallons / hour
Step-by-step explanation:
Multiply the volume / time value by 15
Answer:
30 gallons per hourStep-by-step explanation:
2 quarts per minute is:
2/4 gallons per minute is:
0.5 gallons per minute is:
0.5*60 gallons per hour is:
30 gallons per hourThe average rate of change for an exponential function grows by equal [blank1] per unit interval. FILL IN THE BLANK...
Answer:
Factors
Step-by-step explanation:
For example, consider the exponential function
y =2(4)ˣ
Let's make a table of a few values.
[tex]\begin{array}{rcc}\mathbf{x} & \mathbf{y} & \textbf{Factor}\\-2 & \frac{1}{8}& \\& &\mathbf{4} \\-1 & \frac{1}{2} & \\& &\mathbf{4} \\0 & 2 & \\& & \mathbf{4}\\1 & 8 & \\& &\mathbf{4} \\2 & 32 & \\\end{array}[/tex]
The average rate of change for the exponential function grows by equal factors of 4 per unit interval.
A gambler loses $100 Saturday night and wins $65 on Sunday. What is the gambler’s total loss or gain? Express your answer as an integer.
Answer:
-35 dollar net loss
Step-by-step explanation:
Since the gambler won $65 but still lost $100, we can see that we would still have a negative net loss.
-
Given the graph of y = f(x), shown as a red dashed curve, drag the movable blue point to obtain the graph of
y = f(x - 4) + 3.
Answer:
The blue point will be at (4, 3)
Step-by-step explanation:
Numbers inside the parenthases only affect x, but are revered. If it is -4, move right 4. lf it is 4, move left 4.
Numbers after the patentheses affect the movement of y. When the point is at (4, 0), move up 3.
2. Points A, B and C are all on the
circumference of the circle.o
represents the centre.
DA and DB are tangents to the
circle. Angle BDO = 31
Work out the size of angle.
Question
Points A, B and C are all on the
circumference of the circle. O represents the centre. DA and DB are tangents to the circle. Angle BDO = 31°
Work out the size of angle x
Answer:
62°
Step-by-step explanation:
To solve for the above question, we would be using circle theorems.
Step 1
Angle OBD = 90° This is because a radius and a tangent meet at 90°
Step 2
The sum of Angles in a triangle = 180°
180° = Angle OBD + Angle BDO + Angle BOD
180° = 90° + 31° + Angle BOD
Angle BOD = 180° - (90° + 31°)
= 180° - 121°
Angle BOD = 59°
Step 3
Angle BOD = Angle AOD because they are congruent ,therefore, Angle AOD = 59°
Step 4
The sum of angles of a straight line = 180°
Angle BOD, Angle AOD and Angle x are angles on a straight line
Hence,
180° = Angle BOD + Angle AOD + Angle x
180° = 59° + 59° + x
x = 180° - ( 59 + 59)°
x = 180° - 118°
x = 62°
Therefore Angle x = 62°
pppppplzzz HELPS ME!!!!
The answer is B)
Explanation:
In the equation 7(2B + J), the 7 indicates the seven days in a week, and the J indicates the money spent on juice. Thus, the B must represent the money spent on granola bars.
2(x+3)=x-4 i really need help on this plss
Answer:
X = -10Step-by-step explanation:
[tex]2(x + 3) = x - 4[/tex]
Multiply each term in the parenthesis by 2
[tex]2 x + 6 = x - 4[/tex]
Move variable to L.H.S and change its sign
[tex]2x - x + 6 = - 4[/tex]
Move constant to R.H.S and change its sign
[tex]2x - x = - 4 - 6[/tex]
Calculate
[tex]x = - 10[/tex]
Hope this helps...
Good luck on your assignment...