Answer:
[tex]\sqrt{85}[/tex] (about 9.2195) units
Step-by-step explanation:
The formula for the distance between two points is: [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
Substitute the values. [tex]\sqrt{(-5 - 4)^2 + (8 - 6)^2}[/tex]
Subtract. [tex]\sqrt{(-9)^2 + 2^2}[/tex]
Solve the exponents. [tex]\sqrt{81 + 4}[/tex]
Add. [tex]\sqrt{85}[/tex]
This is as simple as the solution can get without estimating, but we can use a calculator to estimate that the distance is about 9.2195 units.
Hey there! :)
Find the distance between (-5, 8) (4, 6)
The formula to find the distance is : d = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2[/tex]
Where : -5 = x1 , 4 = x2 , 8 = y1 , 6 = y2
Now, simply plug everything into our equation.
[tex]d = \sqrt{(4 + 5)^2 + (6 - 8)^2}[/tex]
Let's simplify this now.
[tex]d = \sqrt{9^2 - 2^2}[/tex]
Simplify again.
[tex]d = \sqrt{81 + 4} = \sqrt{85}[/tex]
Therefore, our distance is [tex]\sqrt{85}[/tex] OR 9.22
Hope this helped! :)
Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the corresponding face of the other prism.
How are the surface areas of the figures related?
Answer:
The surface area of the larger triangular prism is 4 times the surface area of the smaller triangular prism
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its perimeters is equal to the scale factor and the ratio of its surface areas is equal to the scale factor squared
Let
z ----> the scale factor
In this problem
z=2
therefore
z²=2²=4
The surface area of the larger triangular prism is 4 times the surface area of the smaller triangular prism
Answer:
The surface area of the larger prism is 4 times the surface area of the smaller prism.
Step-by-step explanation:
Was right on edge
Please help me .....
Answer:
150 feet of flowers would be planted along side C
[tex]a=5400[/tex]
Step-by-step explanation:
Use the pythagorean theorem to find the length of side C
[tex]a^2+b^2=c^2[/tex]
Input the corresponding numbers into the formula
[tex]90^2+120^2=c^2[/tex]
[tex]c^2=22500[/tex]
[tex]c = \sqrt{22500} \\ c=150[/tex]
150 feet of flowers would be planted along side C
To find the area multiply the base and height together, and divide the total by two
[tex]a = \frac{bh}{2}[/tex]
[tex]a = \frac{90 * 120}{2} \\ a=5400[/tex]
Answer:
a) c = 150 ftb) A = 5400 ft²Step-by-step explanation:
[tex]a)\ \text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have:}\ leg=90\ ft,\ leg=120\ ft,\ hypotenuse=c.\\\\\text{Substitute:}\\\\c^2=90^2+120^2\\\\c^2=8100+14400\\\\c^2=22500\to c=\sqrt{22500}\\\\c=150\ ft[/tex]
[tex]b)\ \text{The formula of an area of a right triangle:}\\\\A=\dfrac{ab}{2}\\\\a,\ b-legs\\\\\text{We have}\ a=90\ ft\ \text{and}\ b=120\ ft.\ \text{Substitute:}\\\\A=\dfrac{(90)(120)}{2}=(90)(60)=5400\ ft^2[/tex]
if π/2 π and sin A = 4/5 , then tan A/2 =??
Answer: 2
Step-by-step explanation:
[tex]\text{If the angle is in Quadrant II and sin A }=\dfrac{4}{5}, \text{then cos A }=-\dfrac{3}{5}.\\use\ Pythagorean\ Theorem: x^2+4^2=5^2\implies x=3,\quad cos =\dfrac{x}{h}\\\\\\tan\bigg(\dfrac{A}{2}\bigg)=\dfrac{1-cosA}{sinA}\\\\\\.\qquad \qquad =\dfrac{1-(-\dfrac{3}{5})}{\dfrac{4}{5}}\\\\\\.\qquad \qquad =\dfrac{\dfrac{8}{5}}{\dfrac{4}{5}}\implies \dfrac{8}{5}\div\dfrac{4}{5}\implies \dfrac{8}{5}\times\dfrac{5}{4}=\dfrac{8}{4}=\large\boxed{2}[/tex]
The reflection of a Quadrant II point is located in Quadrant I. Assuming no error was made, what kind of reflection occurred?
Answer:
Reflection against the y-axis
Step-by-step explanation:
A motorist travels at 35 mi/h for 4 h and then at 55 mi/h for t h. Express the distance d traveled as a function of t.
Answer:
d = 35(4) + 55(t)
Step-by-step explanation:
35 * 4 then added to 55 * the hours that "t" equals will then equal the total distance traveled, d
The distance traveled by a motorist travelling at 35 miles/hour for 4 hours and then at 55 miles/hour for t hours can be expressed as a function of time t, d(t) = 140 + 55t.
Explanation:The subject of this question is functions, which is a topic in Mathematics. To express the total distance traveled as a function of t, we need to use the formula distance = speed x time. The motorist travels at 35 miles per hour for 4 hours, and then at 55 miles per hour for t hours. Therefore, the total distance d can be calculated as follows:
d = (35 mi/h x 4 h) + (55 mi/h x t h).
So, d = 140 mi + 55t mi.
Thus, the total distance traversed by the motorist, expressed as a function of time t in hours, is d(t) = 140 + 55t.
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Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model a sample of 2700 bacteria selected from this population reach the size of 2976 bacteria in 2 hours find hourly growth rate parameter
The point-slope form of the equation of the line that passes through (-5, -1) and (10,-7) is
y+7=-(x-10). What is the
standard form of the equation for this line?
2x-5y = -15
2-5y=-17
2x+6y=-15
2x+5v=-17
Answer:
That should be 2x + 5y = 20.
Step-by-step explanation:
First, you have to correct this: y + 7 = -⅖(x - 10). Now, first convert to Slope-Intercept Form by moving -7 to the other side of the equivalence symbol to get y = -⅖x + 4, then finally convert to Standard Form by moving ⅖x to the other side of the equivalence symbol to end up with ⅖x + y = 4.. Now, there is an extended step when it comes to fractional coefficients, and that is multiplying the whole equation by the denominator to get rid of the denominator being there in the first place, REALLY ending with 2x + 5y = 20.
BUT, if your assignment says otherwise, then the first looks correct. I hope this helps.
One method of indirect measurement involves setting up a right triangle and measuring one of the
obligue angles
depression angles
elevation angles
acute angles
Answer:
Acute angles.Step-by-step explanation:
This is called the shadow method to make an indirect measurement of an specific highness. For example, indirect measurement to calculate a building highness.
20points!
kyndal wants to buy a lamp that originally cost $82, but the lamp when on sale for 20% off. the store is having an additional sale that is 40% off the sale price. what is the price of the lamp!?
Answer:
$39.36
Step-by-step explanation:
The first sale we saw, which was 20% off, needs to be applied first as the second discount is additional. With that being said, we need to multiply 82 times 80%. This is because we removed 20% of the standard 100% amount and we are left with 80%. To convert this, keep in mind 100% is equal to 1. So 80% is equal to .80 with this logic. So 82x0.8=65.6. Now we need to take 40% off of the modified price 65.6. By converting 40% off is equal to 0.60(keyword off). Now 65.6x0.60=39.36. The final price is 39.36
Plz mark me brainliest cuz then I'll answer evertything
Kyndal can buy the lamp for $39.36 after a 20% and an additional 40% discount on the original price of $82.
Explanation:To solve this problem, we need to calculate 20% of $82, then subtract that from $82 to find the sale price. Then, we need to calculate 40% of that sale price and subtract it to find the final price. Let's break it down:
Calculate 20% of $82: 0.20 * 82 = $16.40.Subtract that from the original price to find the sale price: 82 - 16.40 = $65.60.Calculate 40% of the sale price: 0.40 * 65.60 = $26.24.Subtract that from the sale price to find the final price: 65.60 - 26.24 = $39.36. So the price of the lamp after all discounts is $39.36.Learn more about Percentage here:https://brainly.com/question/30697911
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Linda had $15 in her coin bank. On her birthday, 5 relatives sent her
money as a birthday gift. Each relative sent the same amount. She
then had $115. How much money did Linda receive from each relative?
Final answer:
Linda received $20 from each of her 5 relatives, as found by subtracting her original amount from the final amount and then dividing by the number of relatives.
Explanation:
The student has asked how much money Linda received from each relative. Linda started with $15 in her coin bank and ended up with $115 after receiving equal amounts from 5 relatives. To find out how much money Linda received from each relative, you need to perform a simple subtraction to find the total amount of birthday money received, and then divide that number by 5.
Subtract the starting amount of $15 from the ending amount of $115 to find the total amount received.
Total received = $115 - $15 = $100
Divide the total received by the number of relatives to find out how much each relative gave.
Amount per relative = $100 / 5 = $20
Therefore, Linda received $20 from each of her 5 relatives.
Abbey is stacking boxes of candles for a store display. The volume of each cube-shaped box is 125 cubic inches. If the display has six layers of boxes, how high is the display?
Answer: 30 inches
Step-by-step explanation:
We know that the formula for calculate the volume of a cube is:
[tex]V=s^3[/tex]
Where "s" is the length of each side.
Since the volume of each cube-shaped box is 125 cubic inches, we can find "s":
[tex]125\ in^3=s^3\\\\\sqrt[3]{125\ in^3}=s\\\\s=5\ in[/tex]
We know that the display has six layers of boxes, then , to calculate the height of the display, we can multiply the value of "s" obtained before by 6. Then:
[tex]height=(5\ in)(6)=30\ in[/tex]
Answer:
Step-by-step explanation:
V=8^3
30 inches answer
Please help!
Use kite DEFG and the given information to solve #25 - 26.
25) If mZ1 = 42° , find m22.
26) If DE = 4x – 2 and DG = 22.5, find the value of x.
Use kite ABCD and the given information to solve #27.
27) Find the value of x.
Answer:
see explanation
Step-by-step explanation:
25
The diagonals of a kite are perpendicular to each other, hence
∠EHF = 90°
The sum of the 3 angles in a triangle = 180°
In ΔEHF
∠1 + ∠2 + 90 = 180, that is
42 + ∠2 + 90 = 180
132 + ∠2 = 180 ( subtract 132 from both sides )
∠2 = 48°
26
DE and DG are congruent sides, hence
4x - 2 = 22.5 ( add 2 to both sides )
4x = 24.5 ( divide both sides by 4 )
x = 6.125
27
∠A and ∠C are congruent, hence
∠A = ∠C = 82°
The sum of the interior angles of a kite = 360°, hence
x = 360 - (82 + 82 + 140) = 360 - 304 = 56
25). Measure of angle 2 will be 48°.
26). Value of x = 6.125
27). Value of x = 56°
Properties of a kite,Two pairs of the adjacent sides of kite are equal.Diagonals of a kite intersect each other at 90°.One pair of opposite angles are equal.25). Given in the picture,
DEFG is a kite having diagonals EG and DF perpendicular. m∠1 = 42°Apply triangle sum theorem in ΔEHF,
m∠EHF + m∠2 + m∠1 = 180°
90° + m∠2 + 42° = 180° [Since, m∠EHF = 90°]
m∠2 = 180° - 132°
m∠2 = 48°
Therefore, measure of angle 2 will be 48°.
26). Given in the question,
DE = 4x - 2 and DG = 22.5By the property of a kite,
DE = DG
(4x - 2) = 22.5
4x = 24.5
x = 6.125
Therefore, value of x will be 6.125
27). Given in the question,
Kite ABCD with m∠B = 140°, m∠C = 82°, m∠D = x°Sum of the interior angles of a kite = 360°
Therefore, m∠A + m∠B + m∠C + m∠D = 360°
By the property of a kite,
m∠A = m∠C = 82°
m∠A + m∠B + m∠A + m∠D = 360°
2(m∠A) + m∠B + m∠D = 360°
2(82°) + 140° + x° = 360°
x = 360° - 304°
x = 56°
Therefore, value of 'x' will be 56°.
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what is the factored form of 2x^2-7x+6?
a) 2
b) y-8
c) x-4
d) x+6
[tex]
2x^2-7x+6=(2x-6)(x-1)=\boxed{2(x-3)(x-1)}
[/tex]
Hope this helps.
r3t40
What is the order of steps to calculate the volume of a prism
Image result for What is the order of steps to calculate the volume of a prism
Method 3 Calculating the Volume of a Rectangular Prism
Write down the formula for finding the volume of a rectangular prism. The formula is simply V = length * width * height. ...
Find the length. ...
Find the width. ...
Find the height. ...
Multiply the length, the width, and the height. ...
State your answer in cubic units.
The order of steps to calculate the volume of a prism is given below:
What is the Volume of Prism?The volume of a prism is defined as the amount of space a prism occupies.
Step 1: Write the given dimensions of the prism.
Step 2: Determine the volume of the prism using the formula V = B × H where V, B, and H are the volume, base area, and height of the prism.
Step 3: The value of the volume of the prism is once obtained then add the unit of volume of prism in the end (in terms of cubic units).
Example: Find the volume of a prism whose base area is 3 square inches and height is 7 inches.
Given that: B = 3 square inches, H = 7 inches
Thus, the Volume of the prism, V = B × H ⇒ V = 3 × 7 = 21 in³
Therefore, the volume of the prism is 21 cubic inches.
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Joey is buying plants for his garden. He wants to have at least twice as many flowering plants as nonflowering plants and a minimum of 36 plants in his garden. Flowering plants sell for $8, and nonflowering plants sell for $5. Joey wants to purchase a combination of plants that minimizes cost. Let x represent the number of flowering plants and y represent the number of nonflowering plants.
Answer:
Step-by-step explanation:
Set up two equations:
2y >/=x
X+y=36
Solve by substituting x for 2y.
This is using the method of substitution.
The measure of b is ___ ?
Answer:
21
Step-by-step explanation:
Use Pythagorean Theorem
If you are looking for leg given the other sides of the right triangle: just do bigger square minus small square
and take square root
so 29^2 - 20^2
And then sqrt it!
sqrt(29^2-20^2)
21
Answer:
b=21
Step-by-step explanation:
a^2 + b^2 = c^2
20^2 +b^2 = 29^2
b^2+400=841
b^2=441
b=21 or b= - 21
Since we are using the values for a triangle we take the positive value.
Multiply.
(x-6)(4x + 3)
Answer:
Fully simplified it equals 4x^2 -21x -18
Explanation:
-You need to distribute the x to all of the terms in the second binomial and you also need to distribute -6 to all the terms in the second binommial giving you 4x^2 +3x - 24 -18
-You combine like terms to simplify and your answer is 4x^2 -21x -18
Answer: 4x² -21x -18
Step-by-step explanation: a p e x
What is the value of the rational expression x^2-2x-3/4x^2-12 when x = 3?
a) -1/4
b) 0
c) 1/4
d) Undefined
Answer:
b
Step-by-step explanation:
Given
[tex]\frac{x^2-2x-3}{4x^2-12}[/tex]
Substitute x = 3 into the expression
= [tex]\frac{3^2-2(3)-3}{4(3)^2-12}[/tex]
= [tex]\frac{9-6-3}{36-12}[/tex]
= [tex]\frac{0}{24}[/tex] = 0 → b
Answer:
b
Step-by-step explanation:
the answer is b:0
How do I solve this ?
Answer:
J 36
Step-by-step explanation:
AB = 9, BC = 12, and m∠B = 90°. Since this is a right triangle, we can use Pythagorean theorem to find AC.
c² = a² + b²
c² = 9² + 12²
c = 15
So the perimeter is:
P = 9 + 12 + 15
P = 36
Evaluate each expression if a=2, b=3 and c=4
A.) 2a+4b-c
B.) 6(a+c)-b
Answer:
Step-by-step explanation:
A.) 2a+4b-c: Replacing a with 2, b with 3 and c with 4, we get:
2(2) + 4(3) - (4) = 4 + 12 - 4 = 12
B.) 6(a+c)-b: Replacing a with 2 and c with 4, we get 6(2 + 4) - 3.
The work inside parentheses should be done first, resulting in 6(6) - 3.
This comes out to 33.
Sally can complete a sales route by herself in 7 hours. James can do the same job in 9 hours. How long will it take them to do it working together?
Answer:
(4 days) is the homogeneous mixture
Which property is shown?
Answer:where is the question for the property
Step-by-step explanation:
Which table of values represents the equation
y = 7x - 3?
The table of values that represents the equation y = 7x - 3 is:
x y
-2 -17
-1 -10
0 -3
1 4
2 11
Option D is the correct answer.
We have,
Equation:
y = 7x - 3
Now,
Substitute x = -2, -1, 0, 1, 2 on the equation.
So,
y = 7 x (-2) - 3 = -14 - 3 = -17
y = 7 x (-1) - 3 = -7 - 3 = - 10
y = 7 x 0 - 3 = -3
y = 7 x 1 - 3 = 7 - 3 = 4
y = 7 x 2 - 3 = 14 - 3 = 11
Thus,
The table of values that represents the equation y = 7x - 3 is:
x y
-2 -17
-1 -10
0 -3
1 4
2 11
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How many solutions are in 7( x+2)=7x-10
7(x + 2) = 7x - 10
7x + 14 = 7x - 10
let's recall the slope-intercept form, now, both equations on each side of the equals sign have the same slope, of 7, that is a flag that both equations are parallel.
their y-intercept is 14 and -10 respectively, however that just means that one is above the other, but since they're parallel they will never touch each other and any solutions is where the graphs intersect, and for parallel lines that never happens, thus no solutions.
The inside walls of a closed cooler form a right rectangular prism with dimensions 1.5 feet by 3 feet by 1 feet which Of These is the volume of the cooler
A) 6 cubic feet
B)4.5 cubic feet
C) 5.5 cubic feet
D) 18 cubic feet
Answer:
B)4.5 cubic feet
Step-by-step explanation:
To find the volume of a rectangular prism, we use the formula
V = l*w*h
V = 1.5*3*1
V = 4.5 ft^3
Find AB using the given matrices.
The entry in row 1, column 1 of [tex]\mathbf{AB}[/tex] is
[tex]\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}5\\6\end{bmatrix}=2\cdot5+4\cdot6=34[/tex]
(i.e. the dot product of row 1 of [tex]\mathbf A[/tex] and column 1 of [tex]\mathbf B[/tex])
The entry in row 1, column 2 of [tex]\mathbf{AB}[/tex] is
[tex]\begin{bmatrix}2&4\end{bmatrix}\begin{bmatrix}-9\\-4\end{bmatrix}=2\cdot(-9)+4\cdot(-4)=-34[/tex]
The second option is the correct answer.
Subtract. (4x2+8x−2)−(2x2−4x+3) Enter your answer, in standard form, in the box.
the answer is 2x2+12z-5 (its also in the picture)
Which ratios are equivalent to 10:16? Check all that apply.
30 to 48
25:35
8:32
5 to 15
Answer:
30:48
Step-by-step explanation:
because 30 divides into 10 and 48 divides into 16
Answer:
Option A is correct
30 to 48
Step-by-step explanation:
Given the ratio:
10 : 16
We have to find the ratios are equivalent to 10:16.
Option A.
30 to 48
⇒[tex]\frac{30}{48}[/tex]
Divide numerator and denominator by 3 we have;
⇒[tex]\frac{10}{16}[/tex]
Option B.
25:35
⇒[tex]\frac{25}{35}[/tex]
Divide numerator and denominator by 5 we have;
⇒[tex]\frac{5}{7}[/tex]
or
5 : 7
Option C:
8 : 32
⇒1 : 4
Option D:
5 to 15
⇒[tex]\frac{5}{15}[/tex]
Divide numerator and denominator by 5 we have;
⇒[tex]\frac{1}{3}[/tex]
or
1 : 3
Therefore, the ratio equivalent to 10:16 is, 30 to 48.
Which of the following are geometric sequences
(check all that apply)
A.) 1, 1, 2, 3, 5, 8, 13
B.) 10,5, 2.5, 1.25, 0.625, 0.3125
C.) -9, -3, -1, -1/3, -1/9, -1/27
D.) 5, 10, 15, 20, 25
Answer:
B and C are geometric sequences.
Step-by-step explanation:
A geometric sequence is a sequence of numbers in which the ratio between consecutive terms is constant.
A is not a geometric sequence because the number 1 is repeated twice in the sequence.
B is a sequence because the sequence is being multiplied by 0.5 each time.
C is a geometric sequence because it is being multiplied by 1/3 each time.
D is not a geometric sequence because it is not being multiplied each time - it is increasing by +5 (arithmetic progression - not geometric).
Hope this helps!
The following are geometric sequences
1. 10,5, 2.5, 1.25, 0.625, 0.3125
2. -9, -3, -1, -1/3, -1/9, -1/27
The correct option is (B) & (C)
What is Geometric sequence?A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r.
1. A is not a geometric sequence because the '1' is repeated two times in the sequence.
2. B is a geometric sequence because the sequence is being multiplied by 0.5 each time.
5/10=0.5
2.5/5=0.5
1.25/2.5=0.5
0.625/1.25=0.5
3. C is a geometric sequence because it is being multiplied by 1/3 each time.
-3/-9=1/3
-1/-3=1/3
-1/3/-1= 1/3
-1/9/-1/3= 1/3
4. D is not a geometric sequence because the multiplicative factor is not same.
Hence, 10,5, 2.5, 1.25, 0.625, 0.3125 and -9, -3, -1, -1/3, -1/9, -1/27 is geometric sequence.
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Find the measure of z
Answer:
z = 70
Step-by-step explanation:
The angles 110 and z form a straight angle and are supplementary, thus
110 + z = 180 ( subtract 110 from both sides )
z = 70